Classification of equivariant real vector bundles over a circle

96 | 城市研究作者简介陈群元长沙市城市规划研究室主任，高级工程师，博士，****************蒋 伟湖南中规设计院有限公司副院长，高级工程师，硕士Research on the Residential Floor Area Ratio Assignment Method under the Constraint of Density Zoning: A Case Study of Changsha强度分区约束下的居住容积率赋值方法研究——以长沙市为例陈群元 蒋 伟 CHEN Qunyuan, JIANG Wei传统容积率赋值方法主观性较强，具有很大程度的片面性。

首先分析长沙市现行容积率确定与管理存在的问题，基于容积率强度分区，推算各强度分区的居住平均容积率。

进而选取交通、服务、环境等多方面影响因素，运用层次分析法从定性与定量相结合的方法确定容积率影响因子及其权重，构建居住用地容积率影响因子模型和计算方法，并运用GIS空间分析方法求得各地块综合得分。

最后以长沙滨江新城控制性详细规划为例，运用此方法为各居住地块容积率赋值，并与原控制容积率进行对比，评估其合理性。

The traditional FAR assignment method is highly subjective and has a large degree of one-sidedness. First, it analyzes theexisting problems in the determination and management of the current floor area ratio in Changsha City, and calculates the average residential floor area ratio of density zoning. By selecting traffic, service, environment and other influencing factors, this paper uses the analytic hierarchy process to determine the floor area ratio influencing factors and their weights from a combination of qualitative and quantitative methods, constructing an influencing factor model and calculation method and using GIS spatial analysis to obtain the comprehensive score of each block. Finally, taking the regulatory detailed planning of Changsha Binjiang New City as an example, this method is used to assign the floor area ratio of each residential plot and compare it with the original value to evaluate its rationality.容积率；控制性详细规划；赋值方法；长沙floor area ratio; regulatory detailed plan; assignment method; Changsha文章编号 1673-8985（2022）04-0096-06 中图分类号 TU984 文献标志码 A DOI 10.11982/j.supr.20220416摘 要Abstract 关 键 词Key words 控制性详细规划作为当前重要的法定规划之一，其法定地位由2008年颁布实施的《中华人民共和国城乡规划法》确定。

李幼蒸《纯粹现象学通论》用语对照表（1995商务版）德、法、英、中abbilden depeindre,/copier depict 映像，描绘（动词）Abbildung copie depiction 映像，描绘（名词）Abgehobenheit relief saliency 突出abgeschlossen clos self-contained 封闭的，完结的Ablehnung refus refusal 拒绝Ableitung dérivation derivation 派生(项)，偏离abschatten s’esquisser adumbrate 侧显Abschattung esquisse adumbration 侧显（物）Abstraktum abstrait abstractum 抽象物Abstufung gradation different levels 层次组Abwandlung mutation variation 变异、变体、派生项Abweisen (sich) (se) démentir reject 中断achten observe heed 注意、注视achtung observation respect,attention 注意、注视Adäquatheit adéquation adequateness 充分（性）Affirmation affirmation affirmation 肯定Akt acte act 行为、作用Aktivität activitéactivity 活动性Aktualität actualitéactuality 实显性Aktualisierung actualisation actualization实显化Allgemeinheit géréralitéuniversality 普遍性、一般性Animalia être animés psychophysical being生命存在、有生命物Anknüpfung liason connexion联结anmuten supputer deem possible推测Anmutung supputation deeming possible推测Annahme supposition assumption假定annehmen admettre assume假定Ansatz supposition supposed statement, starting 假定、开端Anschaulichkeit intuitivite intuitiveness直观性Anschaung intuition intuition 直观ansetzen supposer suppose,start假定、开端Apodiktizität apodicitéapodicticity确真性Apophansistik apophansistique apophantics命题逻辑、命题学Apperzeption apperception apperception 统觉apriopri 先天的Art espèce,sorte,maniere/ sort,species,manner,character 种、方式、特性Artikulation articulation articulation （分节）连结Attention attention attention 注意Attribution attribution attribution属性归与、赋与Auffassung apprehension, conception apprehension, conception统握、理解Aufhebung suspension suspension, abolition中止Aufmerksamkeit attention attention注意Ausbreitung étendue spread 扩大Ausdehnung extension extension扩展、广袤Ausdruck expresion expresion词语、表达ausdrücklich expressive expressive表达的、明确的Ausfüllung remplissement filling充实（化）Aussagesatz énoncé,proposition enonciative/ statement, predicative sentence 陈述ausschalten mettre hors circuit suspend, exclude排除、中断Ausweisung légitimation showing, demostration证明、明示Bau structure structure 结构Beachten vermarquer heed 审视bedeuten signifier signify 意指、意谓Bedeutung signification significance, meaning意义、意谓Begehrung desir desire 欲望Begründung fondation grounding基础Behauptung assertion assertion断言、主张Bejahung affirmation affirmation 肯定bekraftigen confirmer confirm断言、证实、加强bekunden(sich) s’annoncer evince显示bemerken remarquer notice 注意、指出Beschaffenheit propriétéquality 性质Beschreibung description description描述beseelen animer animate使活跃、赋予活力Besonderung particularisation particularity, particularization特殊化、特殊性(das) besondere le particulier the particular特殊项、特殊物Bestand composition composition组成（成分）、性质Bestände composantes components组成成份Bestandstück composantes component组成成份bestätigen confirmer corroborate 证实Bestimmtheit détermination determination规定、规定性Bewährung vérification verification证实Bewusstsein conscience consciousness意识bewusst dont on a conscience conscious有意识的bewusstseinsmässig en rapport avecla conscience relative to consciousness 相关于意识的beziehen mettre en relation relate使相关Beziehung relation relation关系beziehend relationnel relating to （有）关系的Bezogenheit reference relatedness相关性Bezeichnung désignation designation, denotation标记、名称Bild portrait image, picture形象、图象bildlich en portrait pictorial 形象的bilden construire form形成Bildung construction formation形成Blick regard regard, glance目光Blickstrahl rayon du regard ray of regard目光射线bloss simple mere,bare 简单的、仅只、纯Bürgschaft garantie guarantee 保证Charakter caractere character特性Charakteisirung caracterisation characteristic（表明）特性Cogitatio(nes) 我思思维、我思行为．．．．．．．．．Cogitatum我思．．对象、被思者Cogito我思．．darstellen figurer present 呈现、描述Darstellung figuration presentation 呈现、描述Dasein existence factual existence 事实存在、定在decken(sich) coincider coincide 相符、一致Deckung coincidence coincidence相符、相互符合Denkstellungnahme position adoptee par la pensee cogitative position-taking 思想设定Description description description 描述Deutlichkeit distinction distinctness 清晰性Dies-da ceci-la this-there此处这个Diesheit eccéitéthisness此物性Differenz difference difference差异(niederste)Differenz difference ultime ultimate difference种差Ding chose thing物、事物Dinggegebenheit donne de chose physical thing data所与物、物所与性Dinglichkeit chose physical affairs, thingness物性、物质事物Dingwelt monde des choses world of physical things物质世界disjunkt disjonctif disjunctive,mutually exclusive相互排斥的、析取的Doxa 信念doxisch doxique doxi c信念的durchstreichen biffer cancel抹消echt authentique genunine真正的Echtheit authenticitégenuineness真正（性）Eidos 艾多斯、本质eidetisch eidétique eidetic 本质的Eidetik eidetique eidetics本质学eigen propre own特有的、自己的Eigenheit spécificitéownness特殊性Eigenschaft proprietéproperty特性Eigentumlichkeit trait caracteristique peculiarity特性Einbilden feindre imagine虚构，想象Einbildung fiction imagination 虚构，想象eindeutig univoque univocal单义的Einfühlung intropathie empathy 移情作用Einheit unitéunity统一（体）einheitlich unitaire unitary统一的Einklammerung mise entre parentheses parenthesizing置入括号einsehen voir avec evidence have insight into洞见，领会einseitig unilateral one-sidedly单面的Einsicht évidence intellectuelle insight洞见，领会Einstellung attitude attitude态度，观点Einstimmigkeit concordance accordance 一致（性）Einzelheit cas individuel single case, singleness单一（体）Empfindungsdata data de sensation data of sensation感觉材料Entkräftigung infirmation refutation使无效Entrechnung invalidation invalidation（使）无效Entschluss decision decision决定、决断Entstehung genèse origin产生Epoché悬置erblicken regarder regard 注视Erfahrung expérience experience经验erfassen saisir grasp把握Erfassung saisie grasping把握Erfüllung remplissement fulfilling,fulfillment 充实（化），履行，实现Erinnerung souvenir memory记忆Erkenntnis connaissance cognition认识，知识erkenntnismassig cognitif cognitional认识的erkenntnis-theoretisch epistemologique epistemological认识论的Erlebnis le vécu lived experience, mental process体验，心理经验Erlebnis-strom flux du vécu stream of experience体验流erscheinen apparaitre appear显现Erscheinung apparence appearance显现，显相erschauen voir see 看erzeugen produire produce产生Erzeugung production production产生Essenz essence essence本质Evidenz évidence evidence明证（性）Exakt exact exact精确的Extention extension extension广延faktisch de fait de facto事实性Faktizität facticitéfactualness事实性，事实因素Faktum fait fact事实fern remote distant离远的Fiktion fiction fiction 虚构，假想Fiktum fictum figment虚构fingieren feindre phantasy虚构，想象fingiert fictif phantasied虚构的fingierende Phantasie imagination creatrice inventive figment 虚构的想象Folge consequence consequence后果Folgerung consecution deduction推论Form forme form形式Formalisierung passage au formal formalization形式化Formung formation forming形成Formenlehre morphologie theory of forms形式理论fortdauern perdurer last持续fraglich problematique questionable成问题的Fülle le plein fullness充实（性）fundierend fondatrice founding根基性的fundierte Akt actes fondés founded act有根基的行为funktionellen Problemen problems fonctionnels functional problems 功能的问题Gattung genre genus属gebende Akt acte donateur giving(presentive) act给与的行为(originar) gebende Anschauung intuition donatrice originaire original giving intuition（原初）给与的直观Gebiet domaine province（领）域Gebilde formation formation,structure 形成、构成、构造Gefallen plaisir pleasure喜悦Gefühl sentiment feeling感情、情绪Gegebenheit donnée giveness,something given,data 给与性、给与物Gegennoema contre-noéme conter-noema对应意向对象Gegenstand object object对象Gegenstand schlechtin objet per se object pure and simple对象本身、纯对象gegenständlich objectif objective对象的Gegenstandlichkeit objectivitéobjectivity,something objective 对象（性）Gegenwärt présence present现在，现前gegenwärtig present present现在的Gegenwärtigung presentation presentation呈现Gegenwesen contre-essence conter-essence对应本质gegliedert articuléarticulated有分段的、分节的Gehalt contenu content内容，内包Geltung(Gultigkeit) validitélegitimacy有效（性），妥当Gemüt affectivitéemotion情绪Generalthese thèse general general thesis总设定Generalität généralisation generality 一般（性）Generalisierung généralisation generalization 一般化Gerichtetsein(auf) dirigé sur directedness to 指向Gestalt forme,figure formation,structure构形，形态Gestaltung configuration configuration构成（形成）物，构成gewahren s’apercevoir perceive attentively觉察gewährleisten garantir guarantee 保证Gewicht poids weight重（量）Gewissheit certitude certaity确定性Glaubensmodalität modalité de la croyance doxic modality 信念样态gleichsam quasi quasi准（的）Glied membre member组成项，肢Gliederung articulation articulation分节，分段Grenze limite limit界限Grenzepunkt point limite limit限制Grund fondement ground根基，基础gültig valable valid有效的Habitulität(Habitus) habitus habitus习性，习态handeln agir act行动Handelung action action行动Hintergrund arriere-plan background背景hinweisen renvoyer a point to 指示，指出Hof aire halo光晕，场地Horizont horizon horizon边缘域，视界（野），界域Hyle 质素Hyletik hyletique hyletic质素学Ich je(moi) I, ego我，自我Ichsubjekt sujet personnel Ego subject主体我Ideal 理想，观念Idee idee idea观念ideal ideal ideal观念的ideel ideel ideal观念的Ideation ideation ideation观念化，观念化作用Identifikationssynthesen syntheses d’identification identifying synthesis同一综合Immanenz immanence immanence内在（性），内在物Impression impression impression印象Inaktualität inactualiténon-actionality非实显性，非活动性individuel individuel individuel个体的Individuum individu individual个体Inhalt contenu content内容Intention intention intention意向intentional intentionnel intentional意向的Intentionalität intentionalitéintentionality意向性，意向关系Intersubjektivität intersubjectivitéintersubjectivity主体间性，主体间共同体Intuition intuition intuition直观，直觉Iteration redoublement reiteration 重复jetzt present present现在Kategorie catégorie category范畴Kern noyau core核（心）Klarheit clartéclarity明晰（性）Klärung clarification clarification阐明，澄清Kollektion collection collection集合，集聚Kolligation colligation collecting汇集kolligieren colliger collect汇集Komponent composante component组成成分Konkretum concret concretum具体项Konkretion concretion concretion具体化Konstitution constitution constitution构成Körper corps body身体，物体Körperlichkeit corporeitécorporeity身体性，物体性Korrelat correlat correlat相关项Korrelation correlation correlation相关（关系）lebendig vivant living活生生的，生动性的Leerform forme vide empty form 空形式Leervorstellung representation vide empty objectivation空表象leibhalf(ig) corporel in person机体的、身体的Mannigfaltigkeit/le divers,multiplicite/multiplicity,manifoldness多样性，复合体，集合，复多体Materie matiere material,matter质料meinen viser mean意指，意欲Meinung la visée meaning意指Menge groupe set集合Mengenlehre theorie des groupes theory of set集合论Modalität modalitémodality样态，模态Modifikation modification modification变样，改变Modus mode mode样式Möglichkeit possibilitépossibility可能性Moment moment moment因素，机因，要素monothetisch monothetique monothetic单设定的Morphe 形态Motivation motivation motivation动机Nähe proximiténearness靠近Neutralisation neutralisation neutralization中性化Neutralität neutraliténeutrality中性（体）Neutralitatsmodifikation modification de neutralite neutral modification 中性变样nichtig nul null无效的，极微的Noema noéme noema意向对象noematisch noematique noematic意向对象的Noesis noèse noesis意向作用，意向行为，意向过程Noetik noetique noetics意向行为学noetisch noetique noetics意向行为的Nominalisierung nominalisation nominalization 名词化Objekt objet object客体Objektivität objectivitéobjectivity客体（性）Objektivation objectivation objectivation客体化，对象化ontisch ontique ontic存在的Ontologie ontologie ontology本体论Operation operation operation实行，运作，程序Ordnung ordre order秩序，级次originär originaire original原初的originär gebende Erfahrung experience donatrice originaire original giving experience 原初给与的（呈现的）经验Parallelism parallelisme parallelism平行关系，类似性Passivität passivitépassivity被动性Phänomen phenomeno phenomenon现象Phantasie image phantasy想象phantasierend imageant phantasying想象着的phantasiert imaginaire phantasied想象的phantasma phantasme phantasma幻影Plural plural plural多数的polythetisch polythetique polythetic多设定的Position position position设定Positionalität positionalitépositionality设定性positionnal positionnel positional设定的potential potentiel potential潜在的Potentialität potentialitépotentiality 潜在性Prädikat prédicate predicate谓词Prädikation predication predication 述谓（作用）prädizieren prediquer predicate述谓化，论断prinzipiell de principe essential本质的、必然的、原则的Production production production产生、实行Protention protention protention预存Qualität qualitéquality性质Rationalisierung rationalisation rationalization 理性化、合理化Rationalität rationalitérationality 合理性real réel real实在的Realität realitéreality实在（性），现实Rechtsprechung juridiction legitimation判定Reduktion réduction reduction还原reell réel real,genuine 真实的Referent objet de reference referent所指者Reflexion rélexion reflection反思Regel régle rule规则Regellung regulation regulation调节Regung amorce stirring引动（者）Representation représentation representation表象，代表，再现Reproduktion reproduction reproduction再生，复现Retention rétention retention持存richten(sich) se diriger direct to指向Richtung direction direction方向Rückbeziechung rétro-reférence backward relation自反关涉Rückerinnerung rétro-souvenir reminiscence回忆Sache chose matter,matter in question事物，有关问题，真正问题sachhaltig ayant un contenu having material content 实质的Sachlage situation state of affairs状态，事况，所谈事项sachlich objective,concret material有关的，事物的，事实上的Sachlichkeit ensemble de choses materiality 全体事情，事物性Sachverhalt état de chose state of affairs事态Satz proposition proposition命题Schachtelung emboitement encasement套接Schatten ombre shadow影子Schauen voir see看、注视Schein simulacre illusion假象Schichte couche stratum层Schichtungen stratification stratification分层sehen voir see看Sein être being存在Seinscharakter caractere d’etre character of being存在特性Selbst soi-meme it itself自身selbständig independant independent独立的Selbstbeobachtung introspection self-observation 自省Setzung position position,positing设定Sichtighaben avoir un apercu sighting察看Singularität singularite singularity单个性、单个体Sinn sens sense意义Sinnesdaten data sensuels sense-data感觉材料Sinngebung donnation de sens sense-bestowing 意义给与Sinnlichkeit sensibilitésensuality感性Spezialität specification specificity 特殊性Spezies espéce species种Spontanetät spontanéitéspontaneite自发性Steigerung accroissement enhancement增加Stellungnahme prise de position position-taking采取设定Stoff matiére material质料，素材Strahl rayon ray射线Struktur structure structure结构Stück fragment piece片断，部分Stufe niveau level,degree 层阶，段，度Stufenbildung hierarchie hierarchical formation层阶系统Subjekt sujet subject主体Subjektivität subjectivitésubjectivity主体（性）Substrat substrat substrat基底Synkategorematika syncategorematique syncategorems互依词，非独立词Syntax syntaxe syntax句法Synthesis synthese synthesis综合（设定）Tatsache fait fact事实Teil partie component部分Thema thème theme主题，论题Thematisierung thematisation thematization主题化Thesis these thesis设定，论题thetisch thetique theti c设定的Transzendenz transcendance transcendence超验（者），超越transzendental transcendantal transcendental先验的treu fidel true忠实的Triebe impulsion impulse冲动triftig valide valid有效的Triftigkeit validite validity有效性tun agir do 做，行动Typik typologie set of types类型分化Umfang extension sphere,extention范围，外延Umformung transformation transformation变形，转换unselbständig dependant dependant从属的，非独立的Unterschicht intrastructure lower stratrum基层，基础结构Unverträglichkeit incompatibilitéincompatibility不相容性Ur-aktualität proto-actualitéproto-autuality原现实Urdoxa croyance-mere proto-doxa原信念Urform forme-mere primitive mode原形式Urmodus mode-primitif primitive mode原样式Ursprung origine origin起始，始源，根源Urteil jugement judgment判断V erallgemeinerung generalisation universalization普遍化V erdunkelung obscurcissement darkening暗化V ereinzelung individuation singularzation单一化V erflechtung entrelacement combination联结体，介入，交织V ergegenständlichung objectivation objectification再现，对象化V ergegenwärtigung presentification presentiation,re-presentation再现，现前化V erhalt état de chose state of affairs事态V erknüpfung liasion connexion联结（体）vermeinen viser mean意志，意念vermuteng conjecture deeming likely 推测V ernichtung aneantissement annihilation消除V ernunft raison reason理性V ernunftigkeit rationalitérationality理性，合理性V erworrenheit confusion confusion含混V orerinnerung pro-souvenir anticipation预期记忆V orfindlichkeit faits decouverts facts呈现物，事物V ollständig integral complete完全的vorschwebend flotte en suspens hover before us 浮动的V orstellung représentation objectivation,representation观念，表象，呈现vorzeichnen prescrire prescribe指示vollziehen opérer effect实行，运行V ollzug opération operation实行，运行waches Ich moi vigilant waking ego醒觉自我wahr vrai true真的wahrnehmbar perceptible perceivable可知觉的Wahrnehmung perception perception知觉Wandlung mutation change改变Weise mode manner方式Wert(sach)verhalt etat de valeur value-complex 价值事态Wertung evaluation evaluation评价Wesen essence essence本质Wesensbestand fonds eidetique essential composition本质构成因素Wesenserschauung intuition de l’essence seeing essence本质看Wesensverhalt relation essentielle eidetic relationship本质事态Widersinn absurditéabsurdity悖谬Wiedererinnerung resouvenir recollection重忆wirklich reel actual现实的，真实的，实在的Wirklichkeit realitéactuality现实，真实，实在wissen savoir know知道wollen vouloir will意愿Wortlaut mot prononcésound of words字音Wunsch souhait wish愿望Zeichen signe sign记号Zeit temts time时间Zeitbewusstsein conscience de temps consciousness of time时间意识zufällig contingent accidental偶然的Zusammengehörigkeit appartennance belongingness together关联性，相关Zusammenhang connexion connexion,interconnexion关联体，关联域zusammenhängend coherent coherent一致的Zusammenschliessen(sich) s’agréger join together聚合Zustand etat state状态Zustimmung assentiment assent同意zuwenden(sich) se tourner turn to 朝向Zuwendung conversion turning towards朝向Zweifel doute doubt 怀疑。

I.J. Education and Management Engineering, 2020, 6, 27-33Published Online December 2020 in MECS (/)DOI: 10.5815/ijeme.2020.06.04Predicting Students' Academic Performance in Educational Data Mining Based on Deep Learning Using TensorFlowMussa S. Abubakari *, Fatchul ArifinDepartment of Electronics & Informatics Engineering Education, Postgraduate Program, Universitas Negeri Yogyakarta, Yogyakarta 55281, IndonesiaE-mail: abu.mussaside@*, fatchul@uny.ac.idGilbert G. HungiloDepartment of Informatics Engineering, Graduate Program, University Atma Jaya Yogyakarta, Yogyakarta 55281, IndonesiaE-mail: gutabagaonline@Received:07 May 2020; Accepted: 26 July 2020; Published: 08 December 2020Abstract: The study was aimed to create a predictive model for predicting students’ academic performance based on a neural network algorithm. This is because recently, educational data mining has become very helpful in decision making inan educational context and hence improving students’ academic outcomes. This study implemented a Neural Network algorithm as a data mining technique to extract knowledge patterns from student’s dataset consisting of 480 instances (students) with 16 attributes for each student. The classification metric used is accuracy as the model quality measurement. The accuracy result was below 60% when the Adam model optimizer was used. Although, after applying the Stochastic Gradient Descent optimizer and dropout technique, the accuracy increased to more than 75%. The final stable accuracy obtained was 76.8% which is a satisfactory result. This indicates that the suggested NN model can be reliable for prediction, especially in social science studies.Index Terms: Classification, Data Mining Techniques, Educational Data Mining, Neural Network Algorithm, Predictive Model.1.IntroductionCurrently, data mining has become an interesting topic for many researchers in various fields such as medicine, engineering, and even educational field. Especially in educational context, through mining of students’ information, it has become easier to make decisions concerning students in their academic performance [1, 2]. The prediction of students’ performance is a vital matter in educational context as predicting future performance of students after being admitted into a college, can determine who would attain poor marks and who would perform well. These results can help make efficient decisions during admission and hence improve the academic services quality [3–5].Analysis of educational data using data-mining techniques helps extract unique information of students from educational database and use that hidden information to solve various academic problems of students by understanding learners, improve teaching-learning methods and process [6, 7]. Moreover, these data mining techniques help educational stakeholders to make quality decisions to enhance students’ outcomes.Various methods like Decision tree and Naïve Bayesian were used by many researchers for predicting learners’ academic performance and make decisions to help those who need help immediately [7]. Other researchers used ensemble methods such as Random Forest (RF), AdaBoosting, and Bagging as classification methods [7, 8]. Different data mining methods can solve different educational problems such as classification and clustering. The famous known data mining method in prediction models is classification. Various deep learning algorithms like Neural Networks, are used under28 Predicting Students' Academic Performance in Educational Data Mining Based on Deep Learning Using TensorFlow classification matter [9].In the current study, neural network (NN) classification algorithm is implemented to create a predictive model in predicting academic performance of students in a particular academic institution by using students’ characteristics and their distinctive demographic data. A predictive model based on NN approach can be useful in decision making on academic success of students and therefore enhancing academic management and improving quality education.2. Related WorksVarious studies have been conducted concerning data mining in educational context for uncovering knowledge patterns from students’ information for improving academic performance of students. This current study will base its theoretical background on the previous research done on the educational data mining contexts as explained below.The study was conducted on engineering students based on different mining techniques for making academic decisions. Techniques involving classification rules and association rules for discovering knowledge patterns, were used to predict the engineering student’s performance. The study experiment also clustered the students based on k-means clustering algorithm [10]. In another study, students’ performance was evaluated based on association rule algorithm. The research was done by assessing the performance of students based on different features. The experiment was implemented based on real time dataset found in the school premises using Weka [11].Baradwaj and Pal explained in their study on student’s assessment by using a number of data mining methods. Their study facilitated teachers to identify students who need special attention to reduce the fail percentage and help to take valid measure for next semesters [3]. Also, another study was done to develop a classification model to predict student performance using Deep Learning which learns multiple levels of representation automatically. They used unsupervised learning algorithm to pre-train hidden layers of features layer-wisely based on a sparse auto-encoder from unlabeled data, and then supervised training was used for the parameters fine-tuning. The resulted model was trained on a relatively huge real-world students’ dataset, and the experimental findings indicate the effectiveness of the proposed method to be implemented into academic pre-warning mechanism [12].Other researchers developed models to predict students' university performance based on students' personal attributes, university performance and pre-university characteristics. The studies included the data of 10,330 students Bulgaria with every student having 20 attributes. Algorithms such as the K-nearest neighbour (KNN), decision tree, Naive Bayes, and rule learner's algorithms were applied to classify the students into 5 classes: Excellent, Very Good, Good, Bad or Average. Overall accuracy was below 69%. However, decision tree classifier showed best performance having the highest overall accuracy, followed by the rule learner [13, 14].Recently, the study was conducted to predict user’s intention to utilize peer-to-peer (P2P) mobile application for transactions. Logistic regression (LR) analysis technique together with neural network were used to predict the technology adoption. The results indicated that NN model has higher accuracy than LR model [15]. Another study proposed a student performance model with behavioral characteristics. These characteristics are associated with the student interactivity with an e-learning platform. Data mining techniques such as Naïve Bayesian and Decision Tree classifiers were used to evaluate the impact of such features on student’s academic performance. The results of that study revealed that there is a strong relationship between learner behaviors and its academic achievement [16].In this study, a predictive model is created based on neural network (NN) classification algorithm in predicting academic performance of students by using students’ behavioral characteristics and their distinctive demographic data as variables. A predictive model using NN data mining approach can help in making decisions and conclusions on academic success of students hence enhancing academic management and improve education quality.3. Methodology3.1 Data CollectionThe student data implemented in this project were obtained from educational dataset collected by [16] from learning management system (LMS) in The University of Jordan, Amman, Jordan during the study conducted in 2015. The dataset is available in the kaggle website (https:///aljarah/xAPI-Edu-Data). The dataset comprised of 480 (instances) of student records and their 16 respective attributes. These attributes were grouped into three classes, namely (i) Behavioral attributes include parents answering survey, school satisfaction, opening resources, and raised hand on class, (ii) Academic background attributes including grade Level, educational stage, and section, and (iii) Demographic features including nationality and gender. The dataset also includes 175 females and 305 males. The students have different nationalities including from Kuwait (179), USA (6), Jordan (172), Iraq (22), Lebanon (17), Tunis (12), Saudi Arabia (11), Egypt (9), from Iran, Syria, and Libya were 7 each, Morocco (4), 28 students from Palestine, and one from Venezuela.Another attribute is school attendance having two groups based on days of class absence: 191 students exceeded 7 days and 289 students were absent under 7 days. Moreover, the dataset includes also a new kind of attribute namely parent participation having two sub attributes: Parent School Satisfaction and Parent Answering Survey. 270 parents participated in a survey answering and 210 did not, 292 parents were satisfied from the school and 188 were not. The students arePredicting Students' Academic Performance in Educational Data Mining Based on Deep Learning Using TensorFlow 29 grouped into three classes based on their total grades, namely High-Level, Middle-Level, and Low-Level [8]. Appendix A summarizes the students’ attributes and their description.3.2 Methods and Data PreparationFor this study, authors used Anaconda software environment for python machine learning language together with keras machine learning library and specifically TensorFlow utility which is powerful to create and evaluate the proposed NN classification model [17–19]. Keras is a python library widely used in deep-learning that run on top of TensorFlow and Theano, providing an intuitive best API for Python in NNs [20, 21]. Since the dataset used in this study contains variables (attributes) with different categories, there was a need to transform them into a form the computer and NN model can understand. The dataset explained above consists of three main categories of variables. First are nominal variables with two categories such as gender (male or female), semester (first or second), and others. Second, are variables with numerical values such as visited resources, raised hand, and others. And third, are nominal variables with more than three categories such as grade levels (G-01 to G-12), topic (English, Math, Chemistry, and so on), and other variables as it can be seen in Appendix A.Nominal variables with two categories were transformed using label encoder mechanism. While, those with three or more categories were transformed using one-hot encoding (dummies method). Furthermore, continuous numerical variables were transformed by normalizing them using min-max scaler mechanism for normal distribution.4. Experiment Process and ResultsAfter data transformation as explained above, the inputs increased from 16 inputs to 39 inputs and the output (classification outputs) of 3 outputs making a total of 42 columns in the NN model. After that, the dataset was split into train data and test data with data for testing consisting of less than 26% of all dataset and the remaining percentage for training.The following step was to create a predictive model based on Artificial Neural Network (ANN) classification technique to evaluate the attributes which influence directly or indirectly student's academic success. ANN technique is an implementation of artificial neural network that involves training data inputs for the best accuracy achievement. A cross validation with 10-fold was used to divide the dataset for training and testing process. Then the process was followed by fitting the model by 200 iteration (epochs) with 10 batch-size of inputs and then followed by the results evaluation for generating knowledge representation. The evaluation measure used is accuracy for classification quality. Accuracy is the proportion or ratio of the total number of correct predictions to incorrectly predicted.Fig. 1. The NN Model Structure.Figure 1 above shows the NN model structure created by a python code as can be seen in the last code line in Appendix B. The NN predictive model used in this study consists of three layers: (1) input layer with 39 neurons, (2) hidden layer30 Predicting Students' Academic Performance in Educational Data Mining Based on Deep Learning Using TensorFlowwith 19 neurons and (3) an output layer with 3 outputs. The input layer receives input data from 16 attributes and the output layer send output of three grade categories, namely Low (L). Middle (M), and High (H). There is a hidden layer between the input layer and output layer. Appendix B illustrate the python code used to create, fit, and validate the NN model.In this study, we used accuracy as the metric for prediction quality of the developed NN model. Also, only NN algorithm was used for classification of the student dataset.The result of the experiment has two versions due to the implementation of two different model (function) optimizers namely, Adam and Stochastic gradient descent (SGD) as well as due to the introduction of dropout technique to the NN model development to drop (20% of neurons were dropped in this study) loosely connected neuron. The result indicates that when we applied Adam optimization technique the accuracy was below 60%. While, when we applied the SGD optimizer the accuracy improved to more than 76%.Moreover, the dropout technique helped to improve the accuracy value to more than 76.5%. The dropout technique is used to remove the loosely connected neurons as the NN technique performs better with fully connected neurons. The final stable result was 76.8% accuracy.5. Conclusion and Future WorkEducation is a vital element in any community for their social-economic development. Data mining techniques or business intelligence allows extracting knowledge patterns from students’ raw data offering interesting chances for the educational context. Particularly, various studies have implemented machine learning techniques like Decision Tree and Random Forest to enhance the management of college resources and hence improving education quality.In this study, the authors have presented a predictive model using NN technique to learn the patterns from students’ data and predict their academic performance. By applying data mining techniques on students’ database, academic stakeholders can find the important factors which have direct or indirect impacts on the student’s academic success. The knowledge patterns and results discovered in this study after applying NN classification method indicate that different attributes of students have impacts on their learning process as it can be seen in the classification accuracy results. The final classification accuracy obtained in this study is 76.9% which is more than satisfactory percentage for our predictive model developed using NN algorithm.Like other studies, this study is with some limitations too. One of which is the dataset can only be applied to the similar context as this study. Also, the results presented here involves the accuracy as the only predictive measure of model quality. Moreover, only one algorithm, NN algorithm was used for classification purpose.For future studies, authors intend to use the localized student data from a particular university in Yogyakarta, especially from Yogyakarta State University. Also, in the future we expect to apply other data mining methods such as RF, DT, and others in the localized dataset. Moreover, future experiments will add more measurement classification qualities such as Precision, sensitivity, and Recall.AcknowledgementsMuch appreciation to my close friends who inspired me to do this work.References[1]S. K. Mohamad and Z. Tasir, “Educational Data Mining: A Review,” Procedia - Soc. Behav. Sci., vol. 97, pp. 320–324, 2013.[2]M. Chalaris, S. Gritzalis, M. Maragoudakis, C. Sgouropoulou, and A. Tsolakidis, “Improving Quality of Educational ProcessesProviding New Knowledge Using Data Mining Techniques,” Procedia - Soc. Behav. Sci., vol. 147, pp. 390–397, 2014.[3] B. Brijesh Kumar and P. Saurabh, “Mining Educational Data to Analyze Students‟ Performance,” Int. J. Adv. Comput. Sci.Appl., vol. 2, no. No. 6, pp. 59–63, 2011.[4]W. F. W. Yaacob, S. A. M. Nasir, W. F. W. Yaacob, and N. M. Sobri, “Supervised data mining approach for predicting studentperformance,” Indones. J. Electr. Eng. Comput. Sci., vol. 16, no. 3, pp. 1584–1592, 2019.[5]H. Aldowah, H. Al-Samarraie, and W. M. Fauzy, “Educational data mining and learning analytics for 21st century highereducation: A review and synthesis,” Telemat. Informatics, vol. 37, pp. 13–49, 2019.[6]S. Hussain, N. A. Dahan, F. M. Ba-Alwib, and N. Ribata, “Educational data mining and analysis of students’ academicperformance using WEKA,” Indones. J. Electr. Eng. Comput. Sci., vol. 9, no. 2, pp. 447–459, 2018.[7]S. S. M. Ajibade, N. B. Ahmad, and S. M. Shamsuddin, “A data mining approach to predict academic performance of studentsusing ensemble techniques,” in Advances in Intelligent Systems and Computing, 2020, vol. 940, no. March, pp. 749–760.[8] E. A. Amrieh, T. Hamtini, and I. Aljarah, “Mining Educational Data to Predict Student’s academic Performance using EnsembleMethods,” Int. J. Database Theory Appl., vol. 9, no. 8, pp. 119–136, 2016.[9] A. M. Shahiri, W. Husain, and N. A. Rashid, “A Review on Predicting Student’s Performance Using Data Mining Techniques,”in Procedia Computer Science, 2015, vol. 72, pp. 414–422.[10]R. Singh, “An Empirical Study of Applications of Data Mining Techniques for Predicting Student Performance in HigherEducation,” Int. J. Comput. Sci. Mob. Comput., vol. 2, no. February, pp. 53–57, 2013.Predicting Students' Academic Performance in Educational Data Mining Based on Deep Learning Using TensorFlow 31 [11]S. Borkar and K. Rajeswari, “Predicting students academic performance using education data mining,” Int. J. Comput. Sci. Mob.Comput., vol. 2, no. 7, pp. 273–279, 2013.[12]B. Guo, R. Zhang, G. Xu, C. Shi, and L. Yang, “Predicting Students Performance in Educational Data Mining,” in Proceedings -2015 International Symposium on Educational Technology, ISET 2015, 2016, pp. 125–128.[13]D. Kabakchieva, “Predicting student performance by using data mining methods for classification,” Cybern. Inf. Technol., vol.13, no. 1, pp. 61–72, 2013.[14]D. Kabakchieva, K. Stefanova, and V. Kisimov, “Analyzing university data for determining student profiles and predictingperformance,” in EDM 2011 - Proceedings of the 4th International Conference on Educational Data Mining, 2011, pp. 347–348.[15]J. Lara-Rubio, A. F. Villarejo-Ramos, and F. Liébana-Cabanillas, “Explanatory and predictive model of the adoption of P2Ppayment systems,” Behav. Inf. Technol., vol. 0, no. 0, pp. 1–14, 2020.[16]E. A. Amrieh, T. Hamtini, and I. Aljarah, “Preprocessing and analyzing educational data set using X-API for improvingstudent’s performance,” in 2015 IEEE Jordan Conference on Applied Electrical Engineering and Computing Technologies, AEECT 2015, 2015.[17]P. S. Janardhanan, “Project repositories for machine learning with TensorFlow,” Procedia Comput. Sci., vol. 171, pp. 188–196,2020.[18]L. Hao, S. Liang, J. Ye, and Z. Xu, “TensorD: A tensor decomposition library in TensorFlow,” Neurocomputing, vol. 318, pp.196–200, 2018.[19]R. Orus Perez, “Using TensorFlow-based Neural Network to estimate GNSS single frequency ionospheric delay (IONONet),”Adv. Sp. Res., vol. 63, no. 5, pp. 1607–1618, 2019.[20]V.-H. Nhu et al., “Effectiveness assessment of Keras based deep learning with different robust optimization algorithms forshallow landslide susceptibility mapping at tropical area,” CATENA, vol. 188, p. 104458, 2020.[21]K. Akyol, “Comparing of deep neural networks and extreme learning machines based on growing and pruning approach,”Expert Syst. Appl., vol. 140, p. 112875, 2020.Authors’ ProfilesMussa S. Abubakari was born in Kondoa, Tanzania in 1990. He received the B.Sc. degree inTelecommunications Engineering from the University of Dodoma, Tanzania in 2016. Currently he is thepostgraduate candidate taking master degree in Electronics & Informatics Engineering Education atUniversitas Negeri Yogyakarta, Indonesia. His research interests include technology enhanced learning,human computer interaction, technology acceptance, Internet of Things, mobile technologies, intelligentsystems, and signal processing.Dr. Fatchul Arifin was born on 08 Mei 1972. He received a B.Sc. in Electric Engineering at UniversitasDiponegoro and PH.D. degree in Electric Engineering from Institut Teknologi Surabaya, in 1996 and 2014,respectively. Currently he is the lecturer at both undergraduate faculty of engineering and postgraduateprogram at Universitas Negeri Yogyakarta. His research interests include but not limited to intelligentcontrol systems, machine learning, expert systems, and neural-fuzzy system.Gilbert G. Hungilo is a master degree graduate from department of Informatics Engineering at theUniversity Atma Jaya Yogyakarta, Indonesia. He received Bachelor of Science in Computer Science fromthe University of Dar es salaam, Tanzania. His research interests include technology adoption, big dataanalytics, and machine learning.How to cite this paper: Mussa S. Abubakaria, Fatchul Arifin, Gilbert G. Hungilo. "Predicting Students' Academic Performance in Educational Data Mining Based on Deep Learning Using TensorFlow ", International Journal of Education and Management Engineering (IJEME), Vol.10, No.6, pp.27-33, 2020. DOI: 10.5815/ijeme.2020.06.0432 Predicting Students' Academic Performance in Educational Data Mining Based on Deep Learning Using TensorFlowAppendix A. Students’ Attributes [16]SN Attribute Description Variable Type1 Gender Gender of Student: Female or Male. Nominal(binary)2 Nationality Student's Origin: Kuwait, Iraq, Libya Lebanon, Egypt, USA,Morocco, Jordan, Iran, Tunis, Syria, Palestine, Saudi Arabia,Venezuela.Nominal(dummy)3 Birth Place Student's Birth Place: Kuwait, Iraq, Libya Lebanon, Egypt,USA, Morocco, Jordan, Iran, Tunis, Syria, Palestine, SaudiArabia, Venezuela.Nominal(dummy)4 Stage ID Student Educational Level: High School, Middle School,Lower level.Nominal(dummy)5 Grade ID Student Grade: G-01 up to G-12. Nominal(dummy)6 Section ID Classroom student belongs: A, B, C. Nominal(dummy)7 Topic Course Studied: Arabic, Biology, Chemistry, English,Geology, French, Spanish, IT, Math, Science, History, Quran.Nominal(dummy)8 Semester School year semester: First, Second. Nominal(binary)9 Relation Responsible Parent: Mom, Father. Nominal(binary)10 Raised hand Frequency of raising hand in classroom: 0-100. Numeric11 VisitedresourcesFrequency of visiting course online content: 0-100. Numeric12 AnnouncementsViewFrequency of checking the new online announcement: 0-100. Numeric13 Discussion Frequency of participating in online discussion forums: 0-100. Numeric14 Parent SurveyAnsweringWhether Parents answered or not the survey: Yes, No. Nominal(binary)15 Parent SchoolSatisfactionWhether a parent is satisfied or not: Yes, No. Nominal(binary)16 Student AbsenceDays The number of absence days a student was absent: Above orUnder 7 days.Nominal(binary)17 Class The grade class: High-Level (H): from 90-100; Middle-Level(M): from 70 to 89; Low-Level (L): from 0 to 69.Nominal(dummy)Predicting Students' Academic Performance in Educational Data Mining Based on Deep Learning Using TensorFlow 33 Appendix B. A Piece of Python Code Used to Create and Validate an NN Model。

(0,2) 插值||(0,2) interpolation0#||zero-sharp; 读作零井或零开。

0+||zero-dagger; 读作零正。

1-因子||1-factor3-流形||3-manifold; 又称“三维流形”。

AIC准则||AIC criterion, Akaike information criterionAp 权||Ap-weightA稳定性||A-stability, absolute stabilityA最优设计||A-optimal designBCH 码||BCH code, Bose-Chaudhuri-Hocquenghem codeBIC准则||BIC criterion, Bayesian modification of the AICBMOA函数||analytic function of bounded mean oscillation; 全称“有界平均振动解析函数”。

BMO鞅||BMO martingaleBSD猜想||Birch and Swinnerton-Dyer conjecture; 全称“伯奇与斯温纳顿－戴尔猜想”。

B样条||B-splineC*代数||C*-algebra; 读作“C星代数”。

C0 类函数||function of class C0; 又称“连续函数类”。

CA T准则||CAT criterion, criterion for autoregressiveCM域||CM fieldCN 群||CN-groupCW 复形的同调||homology of CW complexCW复形||CW complexCW复形的同伦群||homotopy group of CW complexesCW剖分||CW decompositionCn 类函数||function of class Cn; 又称“n次连续可微函数类”。

Cp统计量||Cp-statisticC。

现代电子技术Modern Electronics TechniqueJan. 2024Vol. 47 No. 22024年1月15日第47卷第2期0 引 言集料是一种重要的建筑用料，合理的集料级配（不同大小颗粒占比）对道路桥梁的安全起着至关重要的作用。

其中粗集料俗称石子，细集料俗称砂子。

集料的级配不均会使混凝土的和易性降低，或者粗集料中针、片状颗粒含量过多也会使和易性降低，还会增加水泥用量，并且导致混凝土强度下降[1]。

因此JTG F40—2004《公路沥青路面施工技术规范》对集料规格做了详细规定，同时其规格的检测以多个方孔筛的筛网筛分，然后称重为准[2]，但是筛分法过程繁琐、筛孔易堵塞，极大地影响了检测效率[3]，难以满足拌合站现场快速检测的需求。

随着机器视觉的发展，越来越多的科研人员通过视觉检测获取集料图像特征以此达到拌合站快速检测要求。

2014年，史源利用LabVIEW 研发了可以自动提取DOI ：10.16652/j.issn.1004‐373x.2024.02.026引用格式：巨鹏飞，陆艺，范伟军，等.基于贝叶斯统计推断的粗集料级配测试研究[J].现代电子技术，2024，47（2）：140‐146.基于贝叶斯统计推断的粗集料级配测试研究巨鹏飞1， 陆 艺1， 范伟军1， 赵 静2（1.中国计量大学， 浙江 杭州 310018； 2.杭州沃镭智能科技股份有限公司， 浙江 杭州 310018）摘 要： 拌合站现场粗集料来料的检测一般是通过筛网筛分的方式进行，检测效率低下。

因此，引入一种基于贝叶斯统计推断的机器视觉检测方法，实现对集料的快速筛分。

利用工业相机采集下落过程中的集料颗粒并进行图像预处理，选取每颗集料的图像序列中最大的Feret 短径作为图像特征。

此特征为集料颗粒的局部特征，无法代表颗粒的全局三维特征。

因此引入贝叶斯统计推断的方法，首先利用贝叶斯公式计算出每颗集料在不同实际粒径区间的后验概率，然后通过概率累加获得被测集料在不同集料规格的可能颗粒数量。

一类特殊粗糙核算子有界性马丽 谢显华 许绍元赣南师范学院数学与计算机科学学院 江西赣州 341000摘要：本文主要研究一类特殊粗糙核奇异积分算子dy y x f y y y b V P x f T n Rn b )(||)'(|)(|.)(,,-Ω=⎰--Ωαα当)2(≥∆∈γγb ，0≥α，且)()'(11-∈Ωn S L y 下的)(n pR L α有界性，该积分条件较[1]弱，从而推广了[1]中定理1的结论。

关键词：Littlewood-Paley 理论； 粗糙核； Fourier 变换估计； 算子插值理论 中图分类号：O177.6 文献标识码：A1 引言设)2(≥n R n 是n -维欧氏空间，1-n S 为nR 中赋予Lebesgue 测度)(⋅=σσd d 的单位球面对非零点nR x ∈，记.||'x xx =设)(11-∈Ωn S L 为n R 的零次齐次函数，且满足⎰-=Ω1.0)'()'(n S x d x σ （1.1）对1≥s ，令s ∆表示如下定义在),0[+∞上可测函数类：})|)(|1(sup :)({:10+∞<==∆⎰>∆s us u s dt t b u bt b s. 显然若+∞<≤≤211s s 时，则有.121∆≤∆≤∆<∆∞s s 如下定义奇异积分算子)(f SI b ： .)(||)'(|)(|.)).((dy y x f y y y b VP x f SI nRn b -Ω=⎰--α （1.2）明显地，当1≡b 时，)(f SI b 即为经典的Calderon-Zygmund ]1[算子，此时我们记)(f SI b =)(f SI . Calderon-Zygmund 证明了当)(log 1-+∈Ωn S L L 且满足消失性和（1.1）式时，bSI 是)1)((∞<<p R L np有界的。

离散数学中英⽂名词对照表离散数学中英⽂名词对照表外⽂中⽂AAbel category Abel 范畴Abel group (commutative group) Abel 群(交换群)Abel semigroup Abel 半群accessibility relation 可达关系action 作⽤addition principle 加法原理adequate set of connectives 联结词的功能完备（全）集adjacent 相邻（邻接）adjacent matrix 邻接矩阵adjugate 伴随adjunction 接合affine plane 仿射平⾯algebraic closed field 代数闭域algebraic element 代数元素algebraic extension 代数扩域（代数扩张）almost equivalent ⼏乎相等的alternating group 三次交代群annihilator 零化⼦antecedent 前件anti symmetry 反对称性anti-isomorphism 反同构arboricity 荫度arc set 弧集arity 元数arrangement problem 布置问题associate 相伴元associative algebra 结合代数associator 结合⼦asymmetric 不对称的(⾮对称的)atom 原⼦atomic formula 原⼦公式augmenting digeon hole principle 加强的鸽⼦笼原理augmenting path 可增路automorphism ⾃同构automorphism group of graph 图的⾃同构群auxiliary symbol 辅助符号axiom of choice 选择公理axiom of equality 相等公理axiom of extensionality 外延公式axiom of infinity ⽆穷公理axiom of pairs 配对公理axiom of regularity 正则公理axiom of replacement for the formula Ф关于公式Ф的替换公式axiom of the empty set 空集存在公理axiom of union 并集公理Bbalanced imcomplete block design 平衡不完全区组设计barber paradox 理发师悖论base 基Bell number Bell 数Bernoulli number Bernoulli 数Berry paradox Berry 悖论bijective 双射bi-mdule 双模binary relation ⼆元关系binary symmetric channel ⼆进制对称信道binomial coefficient ⼆项式系数binomial theorem ⼆项式定理binomial transform ⼆项式变换bipartite graph ⼆分图block 块block 块图（区组）block code 分组码block design 区组设计Bondy theorem Bondy 定理Boole algebra Boole 代数Boole function Boole 函数Boole homomorophism Boole 同态Boole lattice Boole 格bound occurrence 约束出现bound variable 约束变量bounded lattice 有界格bridge 桥Bruijn theorem Bruijn 定理Burali-Forti paradox Burali-Forti 悖论Burnside lemma Burnside 引理Ccage 笼canonical epimorphism 标准满态射Cantor conjecture Cantor 猜想Cantor diagonal method Cantor 对⾓线法Cantor paradox Cantor 悖论cardinal number 基数Cartesion product of graph 图的笛卡⼉积Catalan number Catalan 数category 范畴Cayley graph Cayley 图Cayley theorem Cayley 定理center 中⼼characteristic function 特征函数characteristic of ring 环的特征characteristic polynomial 特征多项式check digits 校验位Chinese postman problem 中国邮递员问题chromatic number ⾊数chromatic polynomial ⾊多项式circuit 回路circulant graph 循环图circumference 周长class 类classical completeness 古典完全的classical consistent 古典相容的clique 团clique number 团数closed term 闭项closure 闭包closure of graph 图的闭包code 码code element 码元code length 码长code rate 码率code word 码字coefficient 系数coimage 上象co-kernal 上核coloring 着⾊coloring problem 着⾊问题combination number 组合数combination with repetation 可重组合common factor 公因⼦commutative diagram 交换图commutative ring 交换环commutative seimgroup 交换半群complement 补图(⼦图的余) complement element 补元complemented lattice 有补格complete bipartite graph 完全⼆分图complete graph 完全图complete k-partite graph 完全k-分图complete lattice 完全格composite 复合composite operation 复合运算composition (molecular proposition) 复合（分⼦）命题composition of graph (lexicographic product)图的合成（字典积）concatenation (juxtaposition) 邻接运算concatenation graph 连通图congruence relation 同余关系conjunctive normal form 正则合取范式connected component 连通分⽀connective 连接的connectivity 连通度consequence 推论（后承）consistent (non-contradiction) 相容性（⽆⽭盾性）continuum 连续统contraction of graph 图的收缩contradiction ⽭盾式（永假式）contravariant functor 反变函⼦coproduct 上积corank 余秩correct error 纠正错误corresponding universal map 对应的通⽤映射countably infinite set 可列⽆限集（可列集）covariant functor (共变)函⼦covering 覆盖covering number 覆盖数Coxeter graph Coxeter 图crossing number of graph 图的叉数cuset 陪集cotree 余树cut edge 割边cut vertex 割点cycle 圈cycle basis 圈基cycle matrix 圈矩阵cycle rank 圈秩cycle space 圈空间cycle vector 圈向量cyclic group 循环群cyclic index 循环（轮转）指标cyclic monoid 循环单元半群cyclic permutation 圆圈排列cyclic semigroup 循环半群DDe Morgan law De Morgan 律decision procedure 判决过程decoding table 译码表deduction theorem 演绎定理degree 次数,次(度)degree sequence 次(度)序列derivation algebra 微分代数Descartes product Descartes 积designated truth value 特指真值detect errer 检验错误deterministic 确定的diagonal functor 对⾓线函⼦diameter 直径digraph 有向图dilemma ⼆难推理direct consequence 直接推论（直接后承）direct limit 正向极限direct sum 直和directed by inclution 被包含关系定向discrete Fourier transform 离散 Fourier 变换disjunctive normal form 正则析取范式disjunctive syllogism 选⾔三段论distance 距离distance transitive graph 距离传递图distinguished element 特异元distributive lattice 分配格divisibility 整除division subring ⼦除环divison ring 除环divisor (factor) 因⼦domain 定义域Driac condition Dirac 条件dual category 对偶范畴dual form 对偶式dual graph 对偶图dual principle 对偶原则(对偶原理) dual statement 对偶命题dummy variable 哑变量（哑变元）Eeccentricity 离⼼率edge chromatic number 边⾊数edge coloring 边着⾊edge connectivity 边连通度edge covering 边覆盖edge covering number 边覆盖数edge cut 边割集edge set 边集edge-independence number 边独⽴数eigenvalue of graph 图的特征值elementary divisor ideal 初等因⼦理想elementary product 初等积elementary sum 初等和empty graph 空图empty relation 空关系empty set 空集endomorphism ⾃同态endpoint 端点enumeration function 计数函数epimorphism 满态射equipotent 等势equivalent category 等价范畴equivalent class 等价类equivalent matrix 等价矩阵equivalent object 等价对象equivalent relation 等价关系error function 错误函数error pattern 错误模式Euclid algorithm 欧⼏⾥德算法Euclid domain 欧⽒整环Euler characteristic Euler 特征Euler function Euler 函数Euler graph Euler 图Euler number Euler 数Euler polyhedron formula Euler 多⾯体公式Euler tour Euler 闭迹Euler trail Euler 迹existential generalization 存在推⼴规则existential quantifier 存在量词existential specification 存在特指规则extended Fibonacci number ⼴义 Fibonacci 数extended Lucas number ⼴义Lucas 数extension 扩充（扩张）extension field 扩域extension graph 扩图exterior algebra 外代数Fface ⾯factor 因⼦factorable 可因⼦化的factorization 因⼦分解faithful (full) functor 忠实（完满）函⼦Ferrers graph Ferrers 图Fibonacci number Fibonacci 数field 域filter 滤⼦finite extension 有限扩域finite field (Galois field ) 有限域（Galois 域）finite dimensional associative division algebra有限维结合可除代数finite set 有限（穷）集finitely generated module 有限⽣成模first order theory with equality 带符号的⼀阶系统five-color theorem 五⾊定理five-time-repetition 五倍重复码fixed point 不动点forest 森林forgetful functor 忘却函⼦four-color theorem(conjecture) 四⾊定理（猜想）F-reduced product F-归纳积free element ⾃由元free monoid ⾃由单元半群free occurrence ⾃由出现free R-module ⾃由R-模free variable ⾃由变元free-?-algebra ⾃由?代数function scheme 映射格式GGalileo paradox Galileo 悖论Gauss coefficient Gauss 系数GBN (G?del-Bernays-von Neumann system)GBN系统generalized petersen graph ⼴义 petersen 图generating function ⽣成函数generating procedure ⽣成过程generator ⽣成⼦（⽣成元）generator matrix ⽣成矩阵genus 亏格girth （腰）围长G?del completeness theorem G?del 完全性定理golden section number 黄⾦分割数（黄⾦分割率）graceful graph 优美图graceful tree conjecture 优美树猜想graph 图graph of first class for edge coloring 第⼀类边⾊图graph of second class for edge coloring 第⼆类边⾊图graph rank 图秩graph sequence 图序列greatest common factor 最⼤公因⼦greatest element 最⼤元（素）Grelling paradox Grelling 悖论Gr?tzsch graph Gr?tzsch 图group 群group code 群码group of graph 图的群HHajós conjecture Hajós 猜想Hamilton cycle Hamilton 圈Hamilton graph Hamilton 图Hamilton path Hamilton 路Harary graph Harary 图Hasse graph Hasse 图Heawood graph Heawood 图Herschel graph Herschel 图hom functor hom 函⼦homemorphism 图的同胚homomorphism 同态（同态映射）homomorphism of graph 图的同态hyperoctahedron 超⼋⾯体图hypothelical syllogism 假⾔三段论hypothese (premise) 假设(前提)Iideal 理想identity 单位元identity natural transformation 恒等⾃然变换imbedding 嵌⼊immediate predcessor 直接先⾏immediate successor 直接后继incident 关联incident axiom 关联公理incident matrix 关联矩阵inclusion and exclusion principle 包含与排斥原理inclusion relation 包含关系indegree ⼊次（⼊度）independent 独⽴的independent number 独⽴数independent set 独⽴集independent transcendental element 独⽴超越元素index 指数individual variable 个体变元induced subgraph 导出⼦图infinite extension ⽆限扩域infinite group ⽆限群infinite set ⽆限（穷）集initial endpoint 始端initial object 初始对象injection 单射injection functor 单射函⼦injective (one to one mapping) 单射（内射）inner face 内⾯inner neighbour set 内（⼊）邻集integral domain 整环integral subdomain ⼦整环internal direct sum 内直和intersection 交集intersection of graph 图的交intersection operation 交运算interval 区间invariant factor 不变因⼦invariant factor ideal 不变因⼦理想inverse limit 逆向极限inverse morphism 逆态射inverse natural transformation 逆⾃然变换inverse operation 逆运算inverse relation 逆关系inversion 反演isomorphic category 同构范畴isomorphism 同构态射isomorphism of graph 图的同构join of graph 图的联JJordan algebra Jordan 代数Jordan product (anti-commutator) Jordan乘积（反交换⼦）Jordan sieve formula Jordan 筛法公式j-skew j-斜元juxtaposition 邻接乘法Kk-chromatic graph k-⾊图k-connected graph k-连通图k-critical graph k-⾊临界图k-edge chromatic graph k-边⾊图k-edge-connected graph k-边连通图k-edge-critical graph k-边临界图kernel 核Kirkman schoolgirl problem Kirkman ⼥⽣问题Kuratowski theorem Kuratowski 定理Llabeled graph 有标号图Lah number Lah 数Latin rectangle Latin 矩形Latin square Latin ⽅lattice 格lattice homomorphism 格同态law 规律leader cuset 陪集头least element 最⼩元least upper bound 上确界（最⼩上界）left (right) identity 左（右）单位元left (right) invertible element 左（右）可逆元left (right) module 左（右）模left (right) zero 左（右）零元left (right) zero divisor 左（右）零因⼦left adjoint functor 左伴随函⼦left cancellable 左可消的left coset 左陪集length 长度Lie algebra Lie 代数line- group 图的线群logically equivanlent 逻辑等价logically implies 逻辑蕴涵logically valid 逻辑有效的（普效的）loop 环Lucas number Lucas 数Mmagic 幻⽅many valued proposition logic 多值命题逻辑matching 匹配mathematical structure 数学结构matrix representation 矩阵表⽰maximal element 极⼤元maximal ideal 极⼤理想maximal outerplanar graph 极⼤外平⾯图maximal planar graph 极⼤平⾯图maximum matching 最⼤匹配maxterm 极⼤项（基本析取式）maxterm normal form(conjunctive normal form) 极⼤项范式（合取范式）McGee graph McGee 图meet 交Menger theorem Menger 定理Meredith graph Meredith 图message word 信息字mini term 极⼩项minimal κ-connected graph 极⼩κ-连通图minimal polynomial 极⼩多项式Minimanoff paradox Minimanoff 悖论minimum distance 最⼩距离Minkowski sum Minkowski 和minterm (fundamental conjunctive form) 极⼩项（基本合取式）minterm normal form(disjunctive normal form)极⼩项范式（析取范式）M?bius function M?bius 函数M?bius ladder M?bius 梯M?bius transform (inversion) M?bius 变换（反演）modal logic 模态逻辑model 模型module homomorphism 模同态(R-同态)modus ponens 分离规则modus tollens 否定后件式module isomorphism 模同构monic morphism 单同态monoid 单元半群monomorphism 单态射morphism (arrow) 态射（箭）M?bius function M?bius 函数M?bius ladder M?bius 梯M?bius transform (inversion) M?bius 变换（反演）multigraph 多重图multinomial coefficient 多项式系数multinomial expansion theorem 多项式展开定理multiple-error-correcting code 纠多错码multiplication principle 乘法原理mutually orthogonal Latin square 相互正交拉丁⽅Nn-ary operation n-元运算n-ary product n-元积natural deduction system ⾃然推理系统natural isomorphism ⾃然同构natural transformation ⾃然变换neighbour set 邻集next state 下⼀个状态next state transition function 状态转移函数non-associative algebra ⾮结合代数non-standard logic ⾮标准逻辑Norlund formula Norlund 公式normal form 正规形normal model 标准模型normal subgroup (invariant subgroup) 正规⼦群（不变⼦群）n-relation n-元关系null object 零对象nullary operation 零元运算Oobject 对象orbit 轨道order 阶order ideal 阶理想Ore condition Ore 条件orientation 定向orthogonal Latin square 正交拉丁⽅orthogonal layout 正交表outarc 出弧outdegree 出次(出度)outer face 外⾯outer neighbour 外（出）邻集outerneighbour set 出(外)邻集outerplanar graph 外平⾯图Ppancycle graph 泛圈图parallelism 平⾏parallelism class 平⾏类parity-check code 奇偶校验码parity-check equation 奇偶校验⽅程parity-check machine 奇偶校验器parity-check matrix 奇偶校验矩阵partial function 偏函数partial ordering (partial relation) 偏序关系partial order relation 偏序关系partial order set (poset) 偏序集partition 划分,分划,分拆partition number of integer 整数的分拆数partition number of set 集合的划分数Pascal formula Pascal 公式path 路perfect code 完全码perfect t-error-correcting code 完全纠-错码perfect graph 完美图permutation 排列（置换）permutation group 置换群permutation with repetation 可重排列Petersen graph Petersen 图p-graph p-图Pierce arrow Pierce 箭pigeonhole principle 鸽⼦笼原理planar graph （可）平⾯图plane graph 平⾯图Pólya theorem Pólya 定理polynomail 多项式polynomial code 多项式码polynomial representation 多项式表⽰法polynomial ring 多项式环possible world 可能世界power functor 幂函⼦power of graph 图的幂power set 幂集predicate 谓词prenex normal form 前束范式pre-ordered set 拟序集primary cycle module 准素循环模prime field 素域prime to each other 互素primitive connective 初始联结词primitive element 本原元primitive polynomial 本原多项式principal ideal 主理想principal ideal domain 主理想整环principal of duality 对偶原理principal of redundancy 冗余性原则product 积product category 积范畴product-sum form 积和式proof (deduction) 证明（演绎）proper coloring 正常着⾊proper factor 真正因⼦proper filter 真滤⼦proper subgroup 真⼦群properly inclusive relation 真包含关系proposition 命题propositional constant 命题常量propositional formula(well-formed formula,wff)命题形式（合式公式）propositional function 命题函数propositional variable 命题变量pullback 拉回(回拖) pushout 推出Qquantification theory 量词理论quantifier 量词quasi order relation 拟序关系quaternion 四元数quotient (difference) algebra 商（差）代数quotient algebra 商代数quotient field (field of fraction) 商域（分式域）quotient group 商群quotient module 商模quotient ring (difference ring , residue ring) 商环（差环，同余类环）quotient set 商集RRamsey graph Ramsey 图Ramsey number Ramsey 数Ramsey theorem Ramsey 定理range 值域rank 秩reconstruction conjecture 重构猜想redundant digits 冗余位reflexive ⾃反的regular graph 正则图regular representation 正则表⽰relation matrix 关系矩阵replacement theorem 替换定理representation 表⽰representation functor 可表⽰函⼦restricted proposition form 受限命题形式restriction 限制retraction 收缩Richard paradox Richard 悖论right adjoint functor 右伴随函⼦right cancellable 右可消的right factor 右因⼦right zero divison 右零因⼦ring 环ring of endomorphism ⾃同态环ring with unity element 有单元的环R-linear independence R-线性⽆关root field 根域rule of inference 推理规则Russell paradox Russell 悖论Ssatisfiable 可满⾜的saturated 饱和的scope 辖域section 截⼝self-complement graph ⾃补图semantical completeness 语义完全的（弱完全的）semantical consistent 语义相容semigroup 半群separable element 可分元separable extension 可分扩域sequent ⽮列式sequential 序列的Sheffer stroke Sheffer 竖（谢弗竖）simple algebraic extension 单代数扩域simple extension 单扩域simple graph 简单图simple proposition (atomic proposition) 简单（原⼦）命题simple transcental extension 单超越扩域simplication 简化规则slope 斜率small category ⼩范畴smallest element 最⼩元（素）Socrates argument Socrates 论断（苏格拉底论断）soundness (validity) theorem 可靠性（有效性）定理spanning subgraph ⽣成⼦图spanning tree ⽣成树spectra of graph 图的谱spetral radius 谱半径splitting field 分裂域standard model 标准模型standard monomil 标准单项式Steiner triple Steiner 三元系⼤集Stirling number Stirling 数Stirling transform Stirling 变换subalgebra ⼦代数subcategory ⼦范畴subdirect product ⼦直积subdivison of graph 图的细分subfield ⼦域subformula ⼦公式subdivision of graph 图的细分subgraph ⼦图subgroup ⼦群sub-module ⼦模subrelation ⼦关系subring ⼦环sub-semigroup ⼦半群subset ⼦集substitution theorem 代⼊定理substraction 差集substraction operation 差运算succedent 后件surjection (surjective) 满射switching-network 开关⽹络Sylvester formula Sylvester公式symmetric 对称的symmetric difference 对称差symmetric graph 对称图symmetric group 对称群syndrome 校验⼦syntactical completeness 语法完全的（强完全的）Syntactical consistent 语法相容system ?3 , ?n , ??0 , ??系统?3 , ?n , ??0 , ??system L 公理系统 Lsystem ?公理系统?system L1 公理系统 L1system L2 公理系统 L2system L3 公理系统 L3system L4 公理系统 L4system L5 公理系统 L5system L6 公理系统 L6system ?n 公理系统?nsystem of modal prepositional logic 模态命题逻辑系统system Pm 系统 Pmsystem S1 公理系统 S1system T (system M) 公理系统 T(系统M)Ttautology 重⾔式（永真公式）technique of truth table 真值表技术term 项terminal endpoint 终端terminal object 终结对象t-error-correcing BCH code 纠 t -错BCH码theorem (provable formal) 定理（可证公式）thickess 厚度timed sequence 时间序列torsion 扭元torsion module 扭模total chromatic number 全⾊数total chromatic number conjecture 全⾊数猜想total coloring 全着⾊total graph 全图total matrix ring 全⽅阵环total order set 全序集total permutation 全排列total relation 全关系tournament 竞赛图trace (trail) 迹tranformation group 变换群transcendental element 超越元素transitive 传递的tranverse design 横截设计traveling saleman problem 旅⾏商问题tree 树triple system 三元系triple-repetition code 三倍重复码trivial graph 平凡图trivial subgroup 平凡⼦群true in an interpretation 解释真truth table 真值表truth value function 真值函数Turán graph Turán 图Turán theorem Turán 定理Tutte graph Tutte 图Tutte theorem Tutte 定理Tutte-coxeter graph Tutte-coxeter 图UUlam conjecture Ulam 猜想ultrafilter 超滤⼦ultrapower 超幂ultraproduct 超积unary operation ⼀元运算unary relation ⼀元关系underlying graph 基础图undesignated truth value ⾮特指值undirected graph ⽆向图union 并(并集)union of graph 图的并union operation 并运算unique factorization 唯⼀分解unique factorization domain (Gauss domain) 唯⼀分解整域unique k-colorable graph 唯⼀k着⾊unit ideal 单位理想unity element 单元universal 全集universal algebra 泛代数（Ω代数）universal closure 全称闭包universal construction 通⽤结构universal enveloping algebra 通⽤包络代数universal generalization 全称推⼴规则universal quantifier 全称量词universal specification 全称特指规则universal upper bound 泛上界unlabeled graph ⽆标号图untorsion ⽆扭模upper (lower) bound 上（下）界useful equivalent 常⽤等值式useless code 废码字Vvalence 价valuation 赋值Vandermonde formula Vandermonde 公式variery 簇Venn graph Venn 图vertex cover 点覆盖vertex set 点割集vertex transitive graph 点传递图Vizing theorem Vizing 定理Wwalk 通道weakly antisymmetric 弱反对称的weight 重（权）weighted form for Burnside lemma 带权形式的Burnside引理well-formed formula (wff) 合式公式(wff) word 字Zzero divison 零因⼦zero element (universal lower bound) 零元（泛下界）ZFC (Zermelo-Fraenkel-Cohen) system ZFC系统form)normal(Skolemformnormalprenex-存在正则前束范式(Skolem 正则范式)3-value proposition logic 三值命题逻辑。

LOOKING BEYOND THE FIVE-FACTOR MODEL: COLLEGE SELF-EFFICACY AS A MODERATOR OF THE RELATIONSHIPBETWEEN TELLEGEN’S BIG THREE MODEL OF PERSONALITY AND HOLLAND’S MODEL OF VOCATIONAL INTEREST TYPESBy Elizabeth A BarrettThe Five-Factor Model (FFM) of personality and Tellegen’s Big Three Model of personality were compared to determine their ability to predict Holland’s RIASEC interest types. College self-efficacy was examined as a moderator of the relationship between Tellegen’s Big Three model and the RIASEC interest types. A sample of 194 college freshmen (i.e., less than 30 credits completed) was drawn from the psychology participant pool of a mid-sized Midwestern university. Instruments included the International Personality Item Pool (IPIP) to measure the FFM; the Multidimensional Personality Questionnaire Brief Form (MPQ-BF) to measure Tellegen’s Big Three model of personality; the College Self-Efficacy Inventory (CSEI) to measure college self-efficacy; and the Self Directed Search (SDS) to measure Holland’s RIASEC model of vocational interests. Findings from correlational analyses supported previous research regarding relationships among the FFM and the RIASEC interest types, and relationships among Tellegen’s Big Three and the RIASEC interest types. As hypothesized and tested via regressions for each of the six interest types, Tellegen’s Big Three model predicted all six vocational interests types (p < .001 for all), while the FFM only predicted two types at p < .05. College self-efficacy did not moderate the relationship between Tellegen’s Big Three and the RIASEC interest types. Implications and future research are discussed.ACKNOWLEDGEMENTSSeveral people have assisted me with the completion of this thesis, and I wish to thank the following people for their help and guidance:In acknowledgement of excellent guidance of this project, Dr. McFadden chairperson, whose knowledge and encouragement pushed the progress of this thesis and my development as a writer and researcher.Dr. Adams and Dr. Miron, committee members, who graciously gave their time and shared their expertise in the completion of this project, specifically, Dr. Adams who aided with the data analysis of this project and worked through multiple analysis problems with me.iiTABLE OF CONTENTSPage INTRODUCTION (1)THEORY AND LITERATURE REVIEW (4)Personality Traits and Vocational Interests Defined (4)The Five-Factor Model (FFM) of Personality (4)Holland’s Theory of Vocational Interest Types (5)Overlap between the FFM and RIASEC (7)Criticisms and Limitations of the FFM (9)Looking Beyond the FFM: Tellegen’s Big Three Model of Personality (11)Comparing Tellegen’s Big Three and the FFM (14)College Self-Efficacy: Moderating Role (16)Conclusion (20)METHOD (22)Participants (22)Procedure (23)Measures (23)Methods of Data Analysis and Missing Data (27)RESULTS (29)Descriptive Statistics (29)Relationship between the FFM and the RIASEC Interest Types:Hypothesis 1a-1e (29)Relationship between Tellegen’s Big Three and the RIASEC InterestTypes: Hypothesis 2a-2c (30)Comparing the FFM and Tellegen’s Big Three: Hypothesis 3 (31)College Self-Efficacy as Moderator: Hypothesis 4 (32)iiiTABLE OF CONTENTS (continued) DISCUSSION (34)The Relationship between the FFM and the RIASEC Interest Types (34)The Relationship between Tellegen’s Big Three and the RIASECInterest Types (35)Comparing Tellegen’s Big Three and the FFM (36)College Self-Efficacy as a Moderator (37)Limitations (38)Implications and Future Research (39)Conclusions (41)APPENDIXES (42)Appendix A: Tables (42)Table A-1. Holland’s Vocational Personality Types Described: RIASEC.. 43 Table A-2. Overlap Between the FFM and RIASEC (44)Table A-3. The Big Three of Tellegen measured by the MPQ: HigherOrder and Primary Trait Scales (45)Table A-4. Means, Standard Deviations, and Intercorrelations (47)Table A-5. Regression Analysis: Realistic Interest Type as DependentVariable (48)Table A-6. Regression Analysis: Investigative Interest Type as DependentVariable (48)Table A-7. Regression Analysis: Artistic Interest Type as DependentVariable (49)Table A-8. Regression Analysis: Social Interest Type as DependentVariable (49)Table A-9. Regression Analysis: Enterprising Interest Type as DependentVariable (50)Table A-10. Regression Analysis: Conventional Interest Type asDependent Variable (50)Table A-11. Hierarchical Multiple Moderated Regression Analysis:Realistic Interest Type as Dependent Variable (51)Table A-12. Hierarchical Multiple Moderated Regression Analysis:Investigative Interest Type as Dependent Variable (51)Table A-13. Hierarchical Multiple Moderated Regression Analysis:Artistic Interest Type as Dependent Variable (52)Table A-14. Hierarchical Multiple Moderated Regression Analysis: SocialInterest Type as Dependent Variable (52)Table A-15. Hierarchical Multiple Moderated Regression Analysis:Enterprising Interest Type as Dependent Variable (53)ivTABLE OF CONTENTS (continued)Table A-16. Hierarchical Multiple Moderated Regression Analysis:Conventional Interest Type as Dependent Variable (53)Appendix B: Figure (54)Figure B-1. Holland’s Hexagonal Model (55)Appendix C: Information Sheet and Surveys (56)REFERENCES (73)vINTRODUCTIONPersonality traits and vocational interests are two major individual difference domains that influence numerous outcomes associated with work and life success. For example, research has shown that congruence between personality traits and one’s vocation is related to greater job performance and job satisfaction (Barrick, Mount, & Judge, 2001; Hogan & Blake, 1999; Zak, Meir, & Kraemer, 1979). Additionally, specific personality traits are hypothesized to play a role in determining job success within related career domains (Sullivan & Hansen, 2004). Personality is a relatively enduring characteristic of an individual, and therefore could serve as a stable predictor of why people choose particular jobs and careers.Personality traits and vocational interests are linked by affecting behavior through motivational processes (Holland, 1973, 1985). Personality traits and vocational interests influence choices individuals make about which tasks and activities to engage in, how much effort to exert on those tasks, and how long to persist with those tasks (Holland, 1973, 1985; Mount, Barrick, Scullen, & Rounds, 2005). Research has shown that when individuals are in environments congruent with their interests, they are more likely to be happy because their beliefs, values, interests, and attitudes are supported and reinforced by people who are similar to them (Mount, Barrick, Scullen, & Rounds, 2005). Furthermore, research has demonstrated that personality and interests may shape career decision making and behavior; personality and interests guide the development ofknowledge and skills by providing the motivation to engage in particular types of activities (Sullivan & Hansen, 2004).As relatively stable dispositions, personality traits influence an individual’s behavior in a variety of life settings, including work (Dilchert, 2007). Individuals often prefer jobs requiring them to display behaviors that match their stable tendencies. Thus individuals will indicate a liking for occupations for which job duties and job environments correspond to their personality traits. Such a match between personal tendencies and job requirements can support adjustment and eventually occupational success, making the choice of a given job personally rewarding on multiple levels (Dilchert, 2007).People applying for jobs need to try to understand themselves more fully in order to determine if they will be satisfied with their career choices based on their personality traits. This process can be aided by vocational counselors who conduct vocational assessments. The purpose of vocational assessment is to enhance client self-understanding, promote self-exploration, and assist in realistic decision making (Carless, 1999). According to a model proposed by Carless (1999), career assessment is based on the assumption that comprehensive information about the self (e.g., knowledge of one’s personality) in relation to the world of work is a necessary prerequisite for wise career decision making.Self-efficacy beliefs--personal expectations about the ability to succeed at tasks (Bandura, 1986)--are often assessed by vocational counselors. This study examines college self-efficacy--belief in one’s ability to perform tasks necessary for success incollege (Wang & Castaneda-Sound, 2008). Self-efficacy determines the degree to which individuals initiate and persist with tasks (Bandura, 1986), and research has found that personality may influence exploration of vocational interests, through high levels of self-efficacy (Nauta, 2007).There is an abundance of literature supporting that the Five-Factor Model (FFM) (discussed in depth in following sections) of personality predicts Holland’s theory of vocational interest types; however, there is little literature that extends beyond use of the Five-Factor Model. This is due to the adoption of the FFM as an overriding model of personality over the past fifteen years. However, as will be demonstrated later, several criticisms of the model have surfaced. In light of these criticisms the purpose of this study is to extend the existing literature that has established links between the FFM and Holland’s vocational interest types, while examining the relationship between an alternate personality model, Tellegen’s Big Three (as measured by the Multidimensional Personality Questionnaire (MPQ)) and Holland’s types. Furthermore, this study will examine the moderating role that college self-efficacy plays on the relationship between Tellegen’s Big Three and Holland’s interest types.THEORY AND LITERATURE REVIEWPersonality Traits and Vocational Interests DefinedPersonality traits refer to characteristics that are stable over time and are psychological in nature; they reflect who we are and in aggregate determine our affective, behavioral, and cognitive styles (Mount, Barrick, Scullen, & Rounds, 2005). Vocational interests reflect long-term dispositional traits that influence vocational behavior primarily through one’s preferences for certain environments, activities, and types of people (Mount, Barrick, Scullen, & Rounds, 2005).The Five-Factor Model (FFM) of PersonalityThe FFM, often referred to as the Big Five personality dimensions, is a major model that claims personality consists of five dimensions: Openness to Experience (i.e., imaginative, intellectual, and artistically sensitive), Conscientiousness (i.e., dependable, organized, and persistent), Extraversion (i.e., sociable, active, and energetic), Agreeableness (i.e., cooperative, considerate, and trusting), and Neuroticism, sometimes referred to positively as emotional stability (i.e., calm, secure, and unemotional) (Harris, Vernon, Johnson, & Jang, 2006; McCrae & Costa, 1986; McCrae & Costa, 1987; Mount, Barrick, Scullen, & Rounds, 2005; Nauta, 2004; Sullivan & Hansen, 2004). The FFM provides the foundation for several personality measures (e.g., NEO-PI, NEO-PI-R, NEO-FFI) that have proved to be valid and reliable and are widely utilized in research today (Costa & McCrae, 1992). There appears to be a large degree of consensusregarding the FFM of personality and the instruments used to measure the model. For instance, the FFM has been shown to have a large degree of universality (McCrae, 2001), specifically in terms of stability across adulthood (McCrae & Costa, 2003) and cultures (DeFruyt & Mervielde, 1997; Hofstede & McCrae, 2004, McCrae, 2001).Holland’s Theory of Vocational Interest TypesHolland’s theory of vocational interests has played a key role in efforts to understand vocational interests, choice, and satisfaction.Holland was very clear that he believed personality and vocational interests are related:If vocational interests are construed as an expression of personality, then theyrepresent the expression of personality in work, school subjects, hobbies,recreational activities, and preferences. In short, what we have called ‘vocational interests’ are simply another aspect of personality…If vocational interests are anexpression of personality, then it follows that interest inventories are personalityinventories. (Holland, 1973, p.7)Vocational interest types, as classified by Holland, are six broad categories (discussed later in the section) that can be used to group occupations or the people who work in them. Holland’s theory of vocational interest types and work environments states that employees’ satisfaction with a job as well as propensity to leave that job depends on the degree to which their personalities match their occupational environments (Holland, 1973, 1985). Furthermore, people are assumed to be most satisfied, successful, and stable in a work environment that is congruent with their vocational interest type. Two ofHolland’s basic assumptions are: (a) individuals in a particular vocation have similar personalities, and (b) individuals tend to choose occupational environments consistent with their personality (Holland, 1997).A fundamental proposition of Holland’s theory is that, when differentiated by their vocational interests, people can be categorized according to a taxonomy of six types, hereinafter collectively referred to as RIASEC (Holland, 1973, 1985). Holland’s theory states that six vocational interest types--Realistic, Investigative, Artistic, Social, Enterprising, and Conventional (RIASEC)--influence people to seek environments which are congruent with their characteristics (Harris, Vernon, Johnson, & Jang, 2006; Holland, 1973, 1985; Nauta, 2004; Roberti, Fox, & Tunick, 2003; Sullivan & Hansen, 2004; Zak, Meir, & Kraemer, 1979). Holland used adjective descriptors to capture the distinctive characteristics of each interest type (Hogan & Blake, 1999). These are summarized in Table A-1. Holland’s approach to the assessment of vocational interest types was based on the assumption that members of an occupational group have similar work-related preferences and respond to problems and situations in similar ways (Carless, 1999).Realistic types like the systematic manipulation of machinery, tools, or animals. Investigative types have interests that involve analytical, curious, methodical, and precise activities. The interests of Artistic types are expressive, nonconforming, original, and introspective. Social types want to work with and help others. Enterprising types seek to influence others to attain organizational goals or economic gain. Finally, Conventional types are interested in systematic manipulation of data, filing records, or reproducing materials (Tokar, Vaux, & Swanson, 1995).According to Holland’s theory, these interest types differ in their relative similarity to one another, in ways that can be represented by a hexagonal figure with the types positioned at the six points (see Figure B-1). Adjacent types (e.g., Realistic and Investigative) are most similar; opposite types (e.g., Realistic and Social) are least similar, and alternating types (e.g., Realistic and Artistic) are assumed to have an intermediate level of relationship (Holland, 1973, 1985; Tokar, Vaux, & Swanson, 1995).Overlap between the FFM and RIASECMany studies provide evidence of the links between the FFM of personality and the RIASEC interest types. An extensive review of the research investigating the links between the FFM and the RIASEC types identified ten studies that found Extraversion predicts interest in jobs that focus on Social and Enterprising interests. Ten studies showed Openness to Experience predicts interest in jobs that focus on Investigative and Artistic interests. Six studies found Agreeableness predicts interest in jobs that focus on Social interest; six studies showed Conscientiousness predicts interests in jobs that focus on Conventional interests; and one study found Neuroticism predicts interests in jobs that focus on Investigative interests (see Table A-2 for the citations). One discrepancy in this research has been Costa and McCrae’s claims that the FFM applies uniformly to all adult ages, but Mroczek, Ozer, Spiro, and Kaiser (1998) found substantial differences between the structures emerging from older individuals as compared to undergraduate students, in that the five factor structure failed to emerge in the student sample (i.e., agreeableness failed to emerge) as it did with the older sample.All of the links discussed between the FFM of personality and the RIASEC interest types provide the foundation for hypotheses 1a – 1e. Hypotheses 1a – 1e will add to the literature, previously discussed, by assessing current college students early in their college careers. These are the people who have the potential to be most influenced by vocational and career counselors. Given that research has found a discrepancy in FFM profiles of younger and older individuals, it is important to test its efficacy in predicting vocational interests.Hypothesis 1a (H1a): Extraversion will significantly positively correlate withSocial and Enterprising types, but not Realistic, Investigative, Artistic, andConventional types.Hypothesis 1b (H1b): Openness to Experience will significantly positivelycorrelate with Investigative and Artistic types, but not Realistic, Conventional,Social, and Enterprising types.Hypothesis 1c (H1c): Agreeableness will significantly positively correlate withSocial types, but not Realistic, Conventional, Enterprising, Investigative, andArtistic types.Hypothesis 1d (H1d): Conscientiousness will significantly positively correlatewith Conventional types, but not Realistic, Enterprising, Investigative, Social, and Artistic types.Hypothesis 1e (H1e): Neuroticism will significantly negatively correlate withInvestigative types, but not Realistic, Enterprising, Conventional, Social, andArtistic types.Criticisms and Limitations of the FFMThe whole enterprise of science depends on challenging accepted views, and the FFM has become one of the most accepted models in personality research. Many critiques of the FFM ask “Why are there five and only five factors? Five factor protagonists say: it is an empirical fact…via the mathematical method of factor analysis, the basic dimensions of personality have been discovered.” (McCrae & Costa, 1989, p. 120). Has psychology as a science achieved a final and absolute way of looking at personality or is there a way to further our conceptualization of personality? In the article by Costa and McCrae (1997) explaining the anticipated changes to the NEO in the new millennium, they anticipate only minor wording modifications and simplifications. Thus it appears as if the FFM is viewed as a final or almost final achievement (Block, 2001). One claimed benefit of the FFM is evidence of heritability is strong for all 5 factors, but evidence is strong for all personality factors studied; it does not single out the Costa and McCrae factors (Eysenck, 1992). In other words, all the criteria suggested by Costa and McCrae are necessary but not sufficient to mark out one model from many which also conform to this criteria.The debate that has been most prominent over the past 15 years, and which has probably attracted the most attention, concerns the number and description of the basic, fundamental, highest-order factors of personality. Evidence from meta-analyses of factorial studies provide evidence that three, not five personality factors, emerge at the highest level of analysis (Royce & Powell, 1983; Tellegen & Waller, 1991; Zuckerman, Kuhlman, & Camac, 1988; Zuckerman, Kuhlman, Thornquist, & Kiers, 1991).Altogether, Eysenck (1992) has surveyed many different models, questionnaires and inventories, reporting in most cases a break-down into 2 or 3 major factors; but never 5. Additionally, Jackson, Furnham, Forde, and Cotter (2000) and Tellegen (1985) have contradicted Costa and McCrae’s (1995) assertions that a five-factor model seems most appropriate, with results showing that a three-factor solution is both more clear and parsimonious.Another critique of the FFM lies in its development. The initial factor-analytic derivations of the Big Five were not guided by explicit psychological theory, and therefore some have asked the question, “Why these five?” (e.g., Revelle, 1987; Waller & Ben-Porath, 1987). As Briggs (1989) points out, the original studies leading to the FFM “prompted no a priori predictions as to what factors should emerge, and a coherent and falsifiable explanation for the five factors has yet to be put forward” (p. 249).A further developmental critique of the FFM is the lack of lower order factors. Theoretically, factors exist at different hierarchical levels, and the FFM only measures five higher order factors (Block, 2001). The FFM operates at a broadband level to measure the main (i.e., higher order) categories of traits (McAdams, 1992). Within each of the five categories, therefore, may be many different and more specific traits, as traits are nested hierarchically within traits (McAdams, 1992).Another limitation of the FFM lies in researchers’ inability to consistently link the personality traits to the Holland interest types. Research has found that although there is a significant overlap between the FFM and RIASEC interest types, the RIASEC types do not appear to be entirely encompassed by the Big-Five personality dimensions (Carless,1999; Church, 1994; DeFruyt & Mervielde, 1999; Tokar, Vaux, & Swanson, 1995). Three personality dimensions in the FFM predict the RIASEC types, but there is less evidence to support that the other two predict the RIASEC types. Specifically, there appears to be significant overlap with Conscientiousness, Openness, and Extraversion in predicting the RIASEC interest types, but less research has been able to find links between Agreeableness and Neuroticism with the RIASEC interest types. This is a limitation of the FFM in relating to vocational interests (Costa, McCrae, & Holland, 1984; Gottfredson, Jones, & Holland, 1993; Tokar, Vaux, & Swanson, 1995).Looking Beyond the FFM: Tellegen’s Big Three Model of PersonalityIn light of these criticisms of the FFM, it seems attention could be paid to alternate models of personality to investigate the dimensions underlying Holland’s interest types. The literature base is sparse here, and alternative personality models warrant further study, particularly with regard to vocational interests (Blake & Sackett, 1999; Church, 1994; Larson & Borgen, 2002; Staggs, Larson, & Borgen, 2003). One such model is Tellegen’s Big Three which addresses many of the criticisms of the FFM.Many vocational psychology researchers use the Big Five model of personality, often measured by the NEO-PI or NEO-PI-R, but less often the Big Three model of personality measured by the Multidimensional Personality Questionnaire (MPQ) is used (Tellegen, 1985; Tellegen & Waller, 1991). This model of personality resulted from ten years of research on focal dimensions in the personality literature (Tellegen, 1985; Tellegen & Waller, 1991). Tellegen’s (1985; Tellegen & Waller, 1991) Big Three modeldefines three higher order factors. These represent the clusters of items from a factor analysis that composed the three higher order traits. The lower order factors consist of items clustered in each of the higher order factors. The higher order factors are: Positive Emotionality (PEM), Negative Emotionality (NEM), and Constraint (CT) (Tellegen, 1985; Tellegen & Waller, 1991). These higher order traits correlate minimally with one another and encompass 11 lower order traits. Refer to Table A-3 for a description of the three higher order traits and the 11 lower order traits.There are only three published studies that have examined the Big Three model as relating to vocational interests. Blake and Sackett (1999) reported that the Artistic type moderately related with the MPQ Absorption lower order trait (Larson & Borgen, 2002). The Social type negatively related to the MPQ Aggression lower order trait; the Enterprising type related moderately to the MPQ Social Potency lower order trait; and the Conventional type related moderately to the MPQ Control lower order trait.Staggs, Larson, and Borgen (2003) also analyzed the lower order traits, specifically, as opposed to the higher order factors of PEM, NEM, and CT. They identified seven personality dimensions that have a substantial relationship with vocational interests: Absorption predicted interest in Artistic occupations; Social Potency predicted interest in Enterprising occupations; Harm Avoidance predicted interest in science and mechanical activity occupations; Achievement predicted interest in science and mathematic occupations; Social Closeness predicted interest in mechanical activity occupations; Traditionalism predicted interest in religious activities; and Stress Reaction predicted interest in athletic careers. Staggs, Larson, and Borgen (2003) used a collegestudent sample, but were not studying the RIASEC types; they were using a different conceptualization of vocational interests as measured by the Strong Interest Inventory which measures General Occupational Themes.Larson and Borgen (2002) found that the PEM factor was more strongly correlated with Social interests than with Enterprising interests; however, PEM did strongly correlate with all six RIASEC types (p < .001). This finding shows strong evidence that the PEM higher order trait relates to the RIASEC types. Larson and Borgen (2002) also found that the CT factor was negatively related to Realistic and Artistic interest types, and that the NEM factor was negatively related to Artistic interest types. Larson and Borgen (2002) utilized a sample of “gifted” adolescent students, which is a very limited and non-generalizable sample. In contrast, the current study tests a freshman college student sample, which is more generalizable to the population of students who are seeking vocational guidance.The links between the MPQ and the RIASEC interest types are under-researched. Although some vocational research has utilized the MPQ, more needs to be done to determine the relationships between Tellegen’s Big Three and Holland’s RIASEC interest types. However, the research provides support for the idea that there are alternative personality dimensions (i.e., Tellegen’s Big Three), outside of the FFM, that can significantly predict vocational interests, in particular the RIASEC types. Hypotheses 2a – 2c will test relationships between the Tellegen’s Big Three (as measured by the MPQ-BF) and the RIASEC interest types.Hypothesis 2a (H2a): The PEM factor will significantly positively correlate with all six RIASEC types.Hypothesis 2b (H2b): The CT factor will significantly negatively correlate withRealistic and Artistic types, but not with Investigative, Social, Enterprising, andConventional types.Hypothesis 2c (H2c): The NEM factor will significantly negatively correlate with Artistic types, but not with Investigative, Social, Enterprising, Realistic, andConventional types.Comparing Tellegen’s Big Three and the FFMAn earlier discussion proposed criticisms of the FFM. In light of these criticisms an alternate personality model was considered: Tellegens’ Big Three, measured by the MPQ. This model of personality resolves all the previous criticisms of the FFM: five versus 3 factors, lack of lower order factors, and model development issues.Tellegen’s (1985) understanding of personality differs from the conception of the FFM. Tellegen believes personality can be summed by three overriding traits or factors versus the 5 factors of the FFM. This is an inherent difference in the two models of personality, which guided the development of instruments used to measure these models, in terms of a three versus a five factor structure. Furthermore, Tellegen (1985) utilized a bottom-up approach to development of the MPQ, in which constructs were based on iterative cycles of data collection and item analyses designed to better differentiate the primary scales. In contrast, Tupes and Chrtistal (1961) emphasized deductive, top-down。