Review
E?cacy,tolerability and management of raltitrexed (Tomudex TM )monotherapy in patients with advanced colorectal cancer:a review
of phase II/III trials
D.Cunningham a,*,J.Zalcberg b ,J.Maroun c ,R.James d ,S.Clarke e ,T.S.Maughan f ,
M.Vincent g ,J.Schulz h ,M.Gonza
lez Baro n i ,T.Facchini j a
GI Unit,The Royal Marsden Hospital,Sutton,Surrey,UK
b
Division of Haematology and Medical Oncology,Peter MacCallum Cancer Institute,Victoria 3000,Australia
c
Ottawa Regional Cancer Centre,Department of Medical Oncology,Ottawa,Ontario,Canada
d
The Kent Cancer Centre,Maidstone District General,Kent,UK
e
Department of Medical Oncology,Sydney Cancer Centre,Royal Prince Alfred Hospital,Camperdown,New South Wales,Australia
f
Department of Clinical Oncology,Velindre Hospital,Cardi?,UK
g
London Regional Cancer Centre,Ontario,Canada h
Virginia Oncology Associates,Virginia,USA
i
Hospital la Paz,Servicio Oncolog?′a Me
′dica,Madrid,Spain j
Polyclinique Courlancy,Reims,France
Received 6April 2001;received in revised form 25September 2001;accepted 22November 2001
Abstract
Raltitrexed (Tomudex TM ),a thymidylate synthase inhibitor,is an alternative to 5-?uorouracil (5-FU)/leucovorin (LV)for the ?rst-line treatment of advanced colorectal cancer.Following the completion of four phase III studies with raltitrexed at the recommended dose of 3.0mg/m 2,it is opportune to review the e?cacy and tolerability data of raltitrexed and suggest guidelines for appropriate patient management.Data are analysed from four phase III and ?ve phase II studies including over 1300patients with advanced colorectal cancer,some of whom were elderly or received higher doses of raltitrexed.Median survival with raltitrexed was comparable to that of bolus or infusional 5-FU/LV in three of the four randomised studies and objective response rates in the four trials were similar for the two agents.Response rates were at least comparable in elderly patients in phase II studies.For the majority of patients,treatment with raltitrexed was well tolerated even at doses higher than that recommended or in the elderly.As with other cytotoxic agents,serious and potentially life-threatening side-e?ects can occur;nevertheless,adherence to simple patient guidelines should minimise the incidence of serious side-e?ects with raltitrexed;these include the assessment of renal function before each and every treatment,dosage adjustment in the presence of renal impairment and close monitoring with prompt treatment of toxicities,particularly diarrhoea and neutropenia.#2002Elsevier Science Ltd.All rights reserved.
Keywords:Raltitrexed;Tolerability;Creatinine clearance;Toxicity
1.Introduction
Raltitrexed (Tomudex TM )is approved as mono-therapy,at a dose of 3.0mg/m 2every 3weeks,for the ?rst-line treatment of advanced colorectal cancer (CRC)in over 40countries worldwide.Like 5-?uorouracil (5-FU),
raltitrexed is an inhibitor of thymidylate synthase (TS).However,5-FU and raltitrexed inhibit TS via di?erent mechanisms and with di?erent speci?cities and binding sites on the enzyme.The di?erent pharmacokinetic and pharmacodynamic properties of raltitrexed and 5-FU lead to distinct tolerability pro?les.
Raltitrexed gives prolonged TS inhibition due to the rapid formation of polyglutamates and its subsequent retention within cells,enabling it to be administered in a convenient 3-week dosing schedule [1].Accordingly,the mean terminal half-life of raltitrexed in patients with
0959-8049/02/$-see front matter #2002Elsevier Science Ltd.All rights reserved.P I I:S 0959-8049(01)00413-
European Journal of Cancer 38(2002)478–486
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*Corresponding author.Tel.:+44-20-8661-3156;fax:+44-20-8643-9414.
E-mail address:david.cunningham@https://www.doczj.com/doc/149505401.html, (D.Cunningham).
advanced solid tumours is168h(approximately7days) [2,3].Raltitrexed is excreted essentially unchanged by the kidneys(40–50%)[3];hence,its elimination has been investigated in patients with renal impairment.A study of16cancer patients showed that the terminal half-life of raltitrexed was statistically signi?cantly longer in patients with mild-to-moderate renal impair-ment(0.42–1.08ml/s)compared with those with normal renal function(>108ml/s)(11.4days versus5.8days, respectively,P=0.03)[2].In comparison,5-FU is rapidly eliminated,predominantly via catabolism in the liver[4].During the?rst24h following intravenous (i.v.)administration,90%of the5-FU dose is excreted; it is,therefore,administered more regularly,generally on successive days or as a continuous infusion for max-imum e?ect.
Raltitrexed has now been extensively evaluated in clinical trials involving patients with advanced CRC. The aim of this paper was to review the e?cacy and tolerability data from nine phase II/III studies,involv-ing over1300patients with advanced CRC who were treated with raltitrexed,and discuss implications for e?ective patient management.
2.Phase II/III trials of raltitrexed monotherapy in patients with advanced colorectal cancer
The recommended dose of raltitrexed(3.0mg/m2)was initially identi?ed in a European phase Istudy[5]. Subsequently,a multinational phase II study(study2) was conducted during1992–1993in patients with advanced CRC[6](Table1).Three randomised,open phase III studies,conducted between1993and1996, compared raltitrexed(3.0mg/m2)with two regimens of bolus5-FU plus leucovorin(LV):the Mayo regimen (5-FU425mg/m2i.v.bolus+LV20mg/m2)in study3 [7]and study10[8]and the Machover regimen(5-FU 400mg/m2i.v.bolus+LV200mg/m2)in study12[9]. As a phase Itrial conducted in the USA had reported a maximum tolerated dose of4.5mg/m2,suggesting a phase II dose of4.0mg/m2[10],study10also included a third arm,with raltitrexed at a dose of4.0mg/m2.A further,recently completed phase III study(the Molec-ular Research Council(MRC)CR06study),conducted in the United Kingdom,has compared raltitrexed(3.0 mg/m2)with two infusional5-FU regimens(de Gra-mont(5-FU400mg/m2iv bolus,5-FU600mg/m222-h infusion,LV200mg/m2)and Lokich(5-FU300mg/m2/ day prolonged venous infusion(PVI))in patients with advanced CRC[11].The baseline characteristics of patients in the phase II and III studies were comparable with the exception of performance status;in studies2,3, 10and12between5and12%of patients had a perfor-mance status of2at entry compared with22%in the MRC study.
Other clinical studies have investigated the use of ral-titrexed at doses higher than the recommended dose of 3.0mg/m2.The4.0mg/m2arm of study10was closed early,because three treatment-related deaths were reported;however,two phase II studies have since been conducted in Canada and the USA with doses of ralti-trexed>3.0mg/m2.The Canadian study used ralti-trexed 3.5mg/m2as?rst-or second-line therapy in patients who had not received prior treatment for metastatic disease[12]and the US study used raltitrexed 4.0mg/m2as second-or third-line therapy for meta-static CRC[13].Two further phase II studies,one in France[14]and one in Spain[15]have assessed the e?-cacy and tolerability of raltitrexed(3.0mg/m2)in elderly patients(570years).
3.E?cacy of raltitrexed monotherapy in patients with advanced colorectal cancer
In three of the four large,randomised phase III stud-ies,median survival with raltitrexed(range9.7–10.9 months),was comparable to that of the5-FU/LV regi-mens(bolus or infusion)(Table2).This range is also consistent with the values for median survival reported in the literature for standard5-FU/LV regimens[16]. Median time to progression in studies3,10and12ran-ged between3.1and4.8months for patients treated with raltitrexed and between3.6and5.3months for those treated with bolus5-FU/LV;the di?erence between the treatment groups was not signi?cant for study3,but was signi?cantly shorter for the raltitrexed-treated patients in studies10and12.In the MRC CR06 study,progression-free survival(which includes patients who died without tumour progression)was reported rather than time to progression,although this was not a protocol-directed endpoint.Furthermore,the response rate was only a subsidiary endpoint of the MRC CR06 study and the measurement of responses did not use a standardised radiological technique or undergo external review.Nevertheless,there was no statistically sig-ni?cant di?erence between the median progression-free survival for the de Gramont and raltitrexed-treated patients(5.8versus4.8months,P=0.057).Objective response rates with raltitrexed were similar to those of the5-FU/LV regimens(bolus or infusion)in all four studies(Table3).
Surprisingly,the response rate of8%(95%Con-?dence Interval(CI):0.9–15.1%)in the Canadian high-dose study(3.5mg/m2)was lower than response rates observed with standard raltitrexed treatment(3.0mg/ m2)in the initial multinational phase II and subsequent phase III trials(14–19%).The e?cacy results of the US high-dose study are under evaluation.Nevertheless, high response rates(complete or partial responses)were determined in elderly patients;29%in the French study
D.Cunningham et al./European Journal of Cancer38(2002)478–486479
and24%in the Spanish study.The median overall sur-vival in the Spanish study of elderly patients was41 weeks(9.5months).
4.Tolerability of raltitrexed monotherapy in patients with advanced colorectal cancer
4.1.Adverse events
The underlying features of raltitrexed toxicity are now well understood from these trials and the major dose-limiting toxicities are asthenia,gastrointestinal or hae-matological(myelosuppression)in nature[5–10,17]. 4.2.Gastrointestinal toxicity
During phase II and phase III trials,using the recommended dose(3.0mg/m2),the incidence of grade 3/4diarrhoea and grade3/4nausea/vomiting ranged from10to14%and9to13%,respectively(nausea and vomiting were reported separately in the MRC CR06 study)(Table4).Similar incidences of grade3/4diar-rhoea(13to19%)and grade3/4nausea/vomiting
Table2
Phase II/III studies—median survival
Study Treatment
(regimen)Median survival
(months)
Deaths during
follow-up(%)
Hazard ratio
(95%CI)
P value
2Raltitrexed11.247––
3Raltitrexed10.189 1.09(0.89–1.33)0.42 (Mayo)10.285
10Raltitrexed9.775 1.35(1.07–1.71)0.01 (Mayo)12.765
12Raltitrexed10.975 1.15(0.93–1.42)0.20 (Machover)12.369
CRO6a Raltitrexed
8.7500.99(0.79–1.25)a0.94a
(de Gramont)9.739
(Lokich)9.932
Canadian Raltitrexed na na––US Raltitrexed na na––French Raltitrexed na na––Spanish Raltitrexed9.5na––95%CI,95%Con?dence Interval;na,not available.
a Raltitrexed versus de Gramont.
Table3
Phase II/III studies—objective responses d
Study Treatment
(regimen)Minimum follow-up
(months)
CR+PR
(%)
Odds ratio
(95%CI)
P value
2Raltitrexed11a26––
3Raltitrexed2619 1.20(0.73–1.97)0.48 (Mayo)17
10Raltitrexed12140.86(0.50–1.49)0.60 (Mayo)15
12Raltitrexed919 1.03(0.65–1.63)0.90 (Machover)18
CRO6b Raltitrexed12weeks18na0.20c (de Gramont)23
(Lokich)25
Canadian Raltitrexed na8––
US Raltitrexed na na––French Raltitrexed na29––Spanish Raltitrexed na24––
95%CI,95%Con?dence Interval;CR,Complete Response;PR,Partial Response;na,not available.
a Median.
b No external review.
c Raltitrexe
d versus d
e Gramont.
d E?cacy results under evaluation.
D.Cunningham et al./European Journal of Cancer38(2002)478–486481
(8–9%)occurred in patients receiving bolus5-FU/LV in studies3,10and12.The incidences of nausea and diarrhoea were statistically signi?cantly higher follow-ing raltitrexed treatment compared with the de Gra-mont infusional5-FU/LV regimen in the MRC CR06 study(10%versus3%and12%versus3%,respec-tively,P<0.01for both).Grade3/4mucositis was observed in43%of patients receiving raltitrexed in comparison with10–22%of patients receiving bolus 5-FU regimens;this di?erence was statistically sig-ni?cant(P<0.001)in studies3and12.
Neither raltitrexed doses of 3.5or 4.0mg/m2nor increased patient age appear to be associated with an elevated risk of grade3/4diarrhoea or nausea/vomiting in the phase II studies.Similarly,in study3there were no statistically signi?cant di?erences in the incidence of grade3/4diarrhoea and nausea/vomiting between patients aged<60years,60–69years or those570 years[18].
4.3.Haematological toxicity
Grade3/4leucopenia was reported by14–18%of patients in studies2,3and10,although lower inci-dences were reported in the MRC CR06and study12(5 and6%,respectively).Similarly,varying incidences of leucopenia were reported in the studies using higher doses of raltitrexed,5and20%,in the Canadian and US studies,respectively.The incidence of leucopenia was not reported for the Spanish study in elderly patients and did not appear to be a?ected by age in the French study,as it was only reported for4%of the elderly patients in this trial.The incidence of severe leucopenia was lower with raltitrexed treatment than with bolus5-FU/LV in studies3,10and12,with sta-tistical signi?cance in studies3and10(P<0.001). Although the incidence of severe neutropenia was sta-tistically signi?cantly lower following de Gramont infu-sional5-FU/LV compared with raltitrexed in the MRC CR06study(8%versus3%,P<0.01),as expected for infusional5-FU regimens.
Grade3/4thrombocytopenia and grade3/4anaemia were reported by1–6%and2–9%of patients,respec-tively,in the phase II/III studies,with no obvious dif-ferences for elderly patients or those receiving a higher dose of raltitrexed.Although the incidence of thrombo-cytopenia reported with raltitrexed treatment was only 3%in the MRC CR06study,this was statistically signi?cantly higher than with the de Gramont infusional 5-FU/LV regimen(0%,P<0.01).The incidence of severe anaemia was statistically signi?cantly higher with raltitrexed treatment compared with bolus5-FU/LV in study3only.
Although the incidence of infection did not appear to be a?ected by age or increasing dose in the phase II studies reported herein,there was a statistically sig-ni?cant di?erence(P=0.0018on univariate analysis)in the incidence of infection between di?erent age groups in study3:the incidences of grade3/4infection were0,6 and14%in patients aged<60years,60–69years and 570years,respectively[18].
4.4.Other adverse events
The most frequently occurring adverse events,other than gastrointestinal or haematological toxicities,inclu-ded asthenia and transient elevation in hepatic transa-minases(typically peaking at the third cycle of
Table4
Incidence of Grade3/4events that occurred in55%of patients treated with raltitrexed in large phase II/III trials
Patients with adverse event(%)
High dose Elderly Study:231012CR06a Canadian(3.5mg/m2)US(4.0mg/m2)French Spanish (n=177)(n=222)(n=217)(n=245)(n=301)b(n=56)(n=54)(n=51)(n=90) Leucopenia151418655204na Neutropenia na na na na8136722 Thrombocytopenia14533na62na Anaemia29953na11122 Infection0564na na710na Increase in transaminases1010713na na0246 Nausea/vomiting111313910(nausea)9(nausea)11147
8(vomiting)5(vomiting)
Severe asthenia/lethargy12618519132201 Diarrhoea1014101012na6103 Pain05145na na11na na na,not available.
a Anorexia was also reported by11%of patients treated with raltitrexed in the Molecular Research Council(MRC)CR06study,but was not reported in any of the other studies.
b Based on between267and275patients with data available,grade3/4toxicity at6or12weeks as reported by clinicians.
482 D.Cunningham et al./European Journal of Cancer38(2002)478–486
treatment and reversible on continuing treatment with raltitrexed).The reported incidence of severe asthenia/ lethargy with raltitrexed was relatively low(5–6%)in studies3and12[6,9]but higher in studies2and10,the Canadian high-dose study and the MRC CR06study (12–19%).The higher incidence of lethargy with ralti-trexed compared with5-FU/LV treatment was statisti-cally signi?cant in the MRC CR06study only(19% versus8%,P<0.01).
Grade3/4transient elevation of hepatic transami-nases were reported in6–13%of patients receiving raltitrexed treatment in studies2,3,10and12and in the Spanish study in elderly patients.A higher inci-dence of24%(12patients)was found,however,in elderly patients in the French study.No cases of ele-vated transaminase levels were reported in the US high-dose study.The occurrence of elevated transami-nase levels was not collected in the MRC CR06study. The incidence of grade3/4increases in hepatic transa-minases was statistically signi?cantly higher with raltitrexed than with5-FU/LV treatment in studies3 and12,but such changes were usually asymptomatic and self-limiting when not associated with disease progression.
4.5.Adverse events leading to death
Between2.3and6.0%of patients in the large phase II/III studies had treatment-related deaths with ralti-trexed(Table5).Of the26treatment-related deaths in studies3,10and12,17occurred in patients who had calculated creatinine clearance values at some stage during their treatment that should have led to dose reductions,according to prescribing recommendations. Similarly,in the MRC CR06study,11of the18treat-ment-related deaths occurred in patients who had a protocol violation(4patients)or who had a predispos-ing factor indicating that caution was necessary(7 patients),such as prior pelvic radiotherapy,hydrone-phrosis or deteriorating performance status.Although the protocol for the MRC CR06study speci?ed the routine assessment of creatinine clearance prior to each administration of raltitrexed,creatinine levels were not documented routinely.One patient(2.0%)in the French study had a treatment-related death,the cause of which was unknown and three patients(3.1%)had treatment-related deaths in the Spanish study of elderly patients due to infection and/or gastrointestinal adverse events.Overall,the incidence of treatment-related deaths in the four phase III studies in patients who were treated with raltitrexed according to the protocol and who did not have predisposing factors to increased toxicity ranged between0.6and2.0%.
The incidence of treatment-related deaths with ralti-trexed is comparable with that following treatment with bolus5-FU/LV:6/212patients(2.8%),5/210patients (2.4%)and3/248patients(1.2%)in studies3,10and 12,respectively,had5-FU-related deaths.When patients were excluded who did not have appropriate dose reductions or delays,or who were not treated according to the protocol,the overall raltitrexed-related death rate in studies3,10and12were in line with those of bolus5-FU/LV(1.3%versus1.7%,respectively)[19]. There were three treatment-related deaths observed in the MRC CR06study following administration of 5-FU/LV,one with the de Gramont regimen and two with the Lokich regimen.
No deaths have occurred in either of the phase II studies that used higher doses of raltitrexed.However, in the raltitrexed 4.0mg/m2arm of study10,three treatment-related deaths occurred after31patients had received this therapy:two were attributed to haemato-logical adverse events and one to a combination of diarrhoea and thrombocytopenia.Consequently,the trial was temporarily closed,with permanent closure of the higher dose arm of the study,and further study entry and dose-reduction criteria were changed for patients with elevated creatinine concentrations. Patients with serum creatinine concentrations greater than the upper limit of normal were no longer con-sidered eligible for the trial and all patients were required to have a normal creatinine concentration in order to receive a subsequent full dose of raltitrexed. For patients with abnormal serum creatinine con-centrations,the creatinine clearance was calculated or performed and the subsequent dose of raltitrexed mod-
Table5
Raltitrexed-related deaths in large phase II/III studies
Study:231012CR06
(n=177)(n=222)(n=217)(n=245)(n=301) All raltitrexed-related deaths(%)4(2.3)9(4.1)9(4.1)8(3.3)18(6.0)a Deaths in patients with no appropriate dose
reduction/protocol violations/caution was requested(%)
3(1.7)7(3.2)5(2.3)5(2.0)11(3.7) Deaths in patients who were treated according to the protocol
and who did not have predisposing factors indicating that
special caution was necessary(%)
1(0.6)2(0.9)4(1.8)3(1.2)7(2.3) a An additional patient died>30days post-dosing.
D.Cunningham et al./European Journal of Cancer38(2002)478–486483
i?ed accordingly;these are now standard requirements for treatment with raltitrexed.
Across all the?rst three phase III studies,in both treatment groups,fatal adverse events that appeared to be causally related to study treatment were often due to a combination of diarrhoea complicated by neutro-penia,as expected with cytotoxic agents of this class [19].Similarly,11of the18patients with treatment-related deaths with raltitrexed in the MRC CR06study presented with a combination of severe gastrointestinal and haematological toxicity.
5.Implications for patient management
Although raltitrexed provides a convenient?rst-line treatment option for patients with advanced colorectal cancer,patients and oncologists need to be aware of possible side-e?ects.As with all cytotoxics,careful patient management is necessary to prevent or reduce unacceptable toxicity.Although raltitrexed is adminis-tered as a convenient3-weekly schedule,it is important for patients to be adequately monitored prior to and during treatment to ensure early detection and prompt management of toxicity.In addition,as approximately 50%of the dose of raltitrexed is excreted unchanged in the urine[2],it is essential that patients have evaluation of their renal function prior to and during their treat-ment with raltitrexed and that those with renal impair-ment have the dose of raltitrexed modi?ed as shown in Table6.5.1.Recommendations for optimal patient management
The following recommendations,which are in line with treatment guidelines and raltitrexed prescribing information[20],should be followed:
1.Serum creatinine measurements should be per-
formed prior to the initiation of treatment and before each subsequent treatment.For patients with abnormal serum creatinine before the?rst or any subsequent treatment,a creatinine clearance should be performed or calculated.Where serum creatinine may not correlate well with creatinine clearance due to factors such as age or weight loss, creatinine clearance should also be determined.
The creatinine clearance may be calculated using the Cockcroft–Gault formula[21],which takes the gender,age and weight of the individual patient into consideration:
Male patients:creatinine clearance
?
88:4?140àage
eT?weight
72?serum creatinine Female patients:creatinine clearance
?
75:23?140àage
eT?weight
72?serum creatinine
where the units are:creatinine clearance,ml/min;
age,years;weight(kg);serum creatinine,m mol/l.
2.In the presence of renal impairment,and particu-
larly with creatinine clearances41.08ml/s,dose reductions and increases in the schedule from3–4 weeks are necessary as shown in Table6.
3.Full blood counts and liver function tests also
need to be performed before each cycle of treat-ment.The use of raltitrexed in patients with pre-existing hepatic impairment is not recommended.
4.Based on the worst grade of gastrointestinal and/
or haematological toxicity in the previous cycle,all subsequent doses of raltitrexed should be reduced in accordance with Table7.
Table6
Dose modi?cation based on creatinine clearance[20]
Creatinine clearance Dose as%of3.0mg/m2Dosing interval
>1.08ml/s1003-weekly
0.92–1.08ml/s754-weekly
0.42–0.90ml/s504-weekly
<0.42ml/s No treatment or stop
treatment
Table7
Dose modi?cation based on the worst grade of gastrointestinal and haematological toxicity in the previous cycle[20]
Gastrointestinal toxicity a
WHO toxicity Grade0Grade1Grade2Grade3Grade4 Haematological toxicity b Grade010********Stop treatment Grade11001007550Stop treatment
Grade21001007550Stop treatment
Grade375757550Stop treatment
Grade4505050Stop treatment Stop treatment WHO,World Health Organization.
a Diarrhoea or mucositis.
b Leucopenia,neutropenia or thrombocytopenia.
484 D.Cunningham et al./European Journal of Cancer38(2002)478–486
5.Elderly patients should be monitored particularly
closely for the development of gastrointestinal toxi-city.Patients who develop signs of gastrointestinal toxicity should have their full blood counts mon-itored regularly for signs of haematological toxicity.
6.It has been suggested that LV could be used as a
rescue agent for patients who present with severe antiproliferative toxicities following treatment with raltitrexed.In vitro and in vivo studies have indicated that LV would compete with raltitrexed for uptake into tissues and for polyglutamation, thus reducing its tissue concentration[22].A simi-lar dose has been recommended to that used for high-dose methotrexate(i.e.25mg/m26-hourly, until symptoms resolve).Further use of raltitrexed in such patients is not recommended.
In addition,results reported at the American Society of Clinical Oncology(ASCO)meeting in2000,suggest that the prophylactic use of the5-HT3antagonist ondansetron reduces the severity of nausea and diar-rhoea,preventing dehydration and use of the steroid dexamethasone reduces the incidence of fever and fat-igue[23].Prophylactic hydration may also be considered for patients who may be more susceptible to the cyto-toxic e?ects of raltitrexed.O sterlund and colleagues[24] also reported the use of metoclopramide or5-HT3 antagonists as antiemetics.Further anecdotal informa-tion indicates that some physicians use loperamide to manage diarrhoea.
6.Conclusions
Raltitrexed is an e?ective single agent for the?rst-line treatment of advanced CRC and may be used as an alternative to bolus or infusional5-FU-based regimens. Data from phase III studies indicate that raltitrexed produces similar median survival times to that which can be achieved with standard5-FU/LV regimens.In addition,its potential as combination therapy with a number of other agents is currently being evaluated.For the majority of patients,treatment with raltitrexed is manageable,but in a minority of cases it produces ser-ious and potentially life-threatening side-e?ects,in par-ticular diarrhoea and neutropenia.One of the most important indicators of this serious toxicity is renal function.For this reason,we recommend the routine measurement of serum creatinine levels prior to each and every study treatment and determination of creati-nine clearance in any patient with an abnormal serum creatinine.Increasing experience with raltitrexed,fur-ther clinician and patient education,and the adoption of clear and straightforward patient guidelines for the use of raltitrexed,should minimise the incidence of ser-ious side-e?ects.References
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1 建桥初四 9 月 11 日数学《二次函数对称性增减性练习》课堂学案 【典例】抛物线 y = ax 2 + bx + c 上部分点的横坐标 x ，纵坐标 y 的对应如下，从表可知： x … -2 -1 0 1 2 … y … 4 6 6 4 … 下列说法: ①抛物线与 x 轴的另一个交点为（3，0）， ②函数的最大值为 6 ③抛物线 1 的对称轴是直线 x= ，④在对称轴的左侧，y 随 x 的增大而增大，正确的有 2 【跟踪训练】、1、已知二次函数 y = ax 2 + bx + c 的 y 与 x 的部分对应值如下表： x … - 1 0 1 3 … y … -3 1 3 1 … 则下列判断:①抛物线开口向上， ②抛物线与 y 轴交于负半轴， ③当 x ＝4 时， y ＞ 0 ， ④方程 ax 2 + bx + c = 0 的正根在 3 与 4 之间. 其中正确的是 （只填写序号） 2、二次函数 y = ax 2 + bx + c （ a ≠ 0 ）中，自变量 x 与函数 y 的对应值如下表： 请你观察表中数据，并从不同角度描述该函数图象的特征是： 、 、 【巩固练习】 1、已知抛物线 y = a (x -1)2 + h (a ≠ 0) 与 x 轴交于 A (x ，0)，B (3，0) 两点，则线段 AB 的长 度为（ ） 2、抛物线 y = a (x + 1) 2 + 2 的一部分如图所示，该抛物线在 y 轴右侧部分与 x 轴交点的坐标 是( ) 第 2 题图 第 3 题图 第 4 题图 3、抛物线 y = -x 2 + bx + c 的部分图象如图所示，若 y > 0 ，则的取值范围是（ ） A . - 4 < x < 1 B . - 3 < x < 1 C . x < -4 或 x > 1 D . x < -3 或 x > 1 4、抛物线y=ax 2+2ax+a 2+2的一部分如图所示，那么该抛物线在y 轴右侧与x 轴交点的坐标是 x … 0 1 2 3 2 5 2 … y … 1 7 4 7 4 - 1 4 …
二次函数的对称轴 二次函数的图像是关于某条直线对称的抛物线，这条直线就叫做对称轴。我们用公式这样表示对称轴，直线x=-b/2a，有图像可知，当二次函数图像上两点的纵坐标相等时，那么这两点必然关于对称轴对称，且对称轴为这两点横坐标之和的一半。形如：点 A(x1，y1)、B(x2，y2)在二次函数的图像上，若y1=y2，那么图像的对称轴为 (x1+x2)/2。抛物线的顶点必然通过对称轴。所以可以根据顶点坐标直接求出对称轴。例如已知二次函数的顶点坐标为（x1，y1），那么二次函数的对称轴为直线x=x1。 在平面直角坐标坐标系中，已知两点坐标便可求其连线的中点坐标，例如：已知点 A(x1，y1)、B(x2，y2)，则两点连线的中点为 C((x1+x2)/2,(Y1+Y2)/2),一般情况，出题者会结合一次函数，中垂线，三角形，二次函数进行综合考查。
例题演练 1、已知抛物线y=ax2+bx+c（a＞0）过（﹣2，0），（2，3）两点，那么抛物线的对称轴（） A．只能是x=﹣1 B．可能是y轴 C．在y轴右侧且在直线x=2的左侧D．在y轴左侧且在直线x=﹣2的右侧 2、已知二次函数y=a（x﹣h）2+k（a＞0）的图象过点A（0，1）、B（8，2），则h的值可以是（） A． 3 B． 4 C． 5 D． 6 3、如图，已知二次函数y1=﹣x2+x+c的图象与x轴的一个交点为A（4，0），与y轴的交点为B，过A、B的直线为y2=kx+b． （1）求二次函数y1的解析式及点B的坐标； （2）由图象写出满足y1＜y2的自变量x的取值范围； （3）在两坐标轴上是否存在点P，使得△ABP是以AB为底边的等腰三角形？若存在，求出P的坐标；若不存在，说明理由．
浅谈纳米二氧化钛 纳米二氧化钛(Ti0 2 )是一种重要的无机功能材料，由于其粒子具有表面效应、量子尺寸效应、小尺寸效应、宏观量子隧道效应等性质；其晶体具有防紫外线、光吸收性好、随角异色效应和光催化等性能；而且它的耐候性、耐用化学腐蚀性和化学稳定性较好，因此纳米二氧化钛被广泛应用于光催化、太阳能电池、有机污染物降解、涂料等领域。但纳米二氧化钛也有一定的局限性，可在纳米二氧化钛中添加合适的物质（如树脂、聚苯胺、偶联剂、氟碳树脂等），对其进行改性。 1. 纳米TiO 2的制备（纳米TiO 2 溶胶） 纳米TiO 2的制备方法一般分为气相法和液相法。由于气相法制备纳米TiO 2 有诸多缺点如:能耗大、成本高、设备复杂等，且条件苛刻,大大限制了其发展。液相法主要包括水解法、沉淀法、溶胶-凝胶法、水热法、微乳液法、微波感应等离子体法等制备技术。而液相法能耗小、设备简单、成本低,是实验室和工业上广泛使用的制备方法。由于传统的方法不能或难以制备纳米级二氧化钛，而溶胶-凝胶法则可以在低温下制备高纯度、粒径分布均匀、化学活性大的单组分或多组分分子级纳米催化剂，在此仅介绍用溶胶-凝胶法制备纳米TiO 2 溶胶。 溶胶一凝胶法制备纳米TiO 2：是以钛的醇盐Ti(OR) 2 ，(R为-C 2 H 5 、-C 3 H 7 、-C 4 H 9 等烷基)为原料。其主要步骤为：钛醇盐溶于溶剂中形成均相溶液，以保证钛醇盐的水解反应在分子均匀的水平上进行，由于钛醇盐在水中的溶解度不大，一般选用醇(乙醇、丙醇、丁醇等)作为溶剂；钛醇盐与水发生水解反应，同时失去水和失醇缩聚反应，生成物聚集成1nm左右的粒子并形成溶胶；经陈化、溶胶形成三维网络而成凝胶；干燥凝胶以除去残余水分、有机基团和有机溶剂，得到干凝胶；干凝胶研磨后煅烧，除去化学吸附的羟基和烷基团，以及物理吸附的有机溶剂和水，得到纳米TiO 2 粉体。因为钛醇盐的水解活性很高，所以需添加抑制剂来减缓其水解速度，常用的抑制剂有盐酸、醋酸、氨水、硝酸等。但在制备过程中要注意加水方式、水量、pH值、溶剂量、反应温度、拌速度等因素对凝胶形成的影响。
工业工程专业《可靠性工程》第1章可靠性工程概述 讲授人:吴泽 E-mail: wuze@https://www.doczj.com/doc/149505401.html, 机械工程学院工业工程系
Chapter 1 Introduction to Reliability Engineering 2 ?可靠性基本概念 ?可靠性研究与应用的目的和意义 ?可靠性工程的发展 ?可靠性工程的内涵 ?可靠性工程面临的问题 ?可靠性工作要求 内容提要
Chapter 1 Introduction to Reliability Engineering 3 ?可靠性：产品在规定条件下、规定时间内完成规定功能的能力 ?对象：元件、组件、零件、部件、机器、设备、系统?使用条件：环境、操作、使用方法、运行条件等?规定时间：时间或等价于时间的衡量指标 ?规定功能：在规定参数下正常运行 ?可靠度：可靠性的概率表达 1.1 可靠性基本概念 ?可靠性的分类 ?固有可靠性和使用可靠性 ?广义可靠性（包含可靠性和维修性）和狭义可靠性
Chapter 1 Introduction to Reliability Engineering 4 ?维修性：故障部件在规定条件下、规定时间内，按照规定程序和方法进行维修，修复到指定状态的概率?维修时间：固有维修时间、维修延误、供应延误?可用性：部件在规定时间点、规定条件下完成规定功能的概率 ?与可靠性区别：可用性表示部件处于非故障状态的概率，同时考虑部件的可靠性与维修性 ?可靠性与质量 ?质量：依赖于制造过程和制造精度 ?可靠性：同时受质量和工作条件影响 1.1 可靠性基本概念
Chapter 1 Introduction to Reliability Engineering 5 ?为什么要搞可靠性？ 1.2 可靠性研究与应用的目的和意义?世界上没有永恒的事物 ?产品故障会造成巨大的损失 ?经济损失 ?人员安全 ?武器装备丧失战斗力 ?政治、社会问题
纳米TiO2的制备及其改性和应用研究进展 摘要：简要介绍了TiO 纳米材料的制备、改性方法及其应用； 2 其制备方法包括气相法和液相法,液相法又包括溶胶-凝胶法、水热/溶剂热法、液相沉积法和微乳液法；其改性主要包括贵金属沉积、离子掺杂、染料敏化和半导体复合；其应用领域则主要包括光催化、光伏电池和光解水。 关键词：二氧化钛；纳米材料；制备；改性；应用 前言 俗称钛白粉,无毒、无味、无刺激性,热稳定性好,且原料TiO 2 来源广泛易得。它有三种晶型:板钛矿、锐钛矿和金红石型。TiO 2 电极光最早用来做涂料。自从1972年Fujishima 等[1]发现用TiO 2 催化分解水现象之后TiO 纳米材料的研究受到了极大的关注。包 2 纳米材料的性括纳米颗粒、纳米棒、纳米线和纳米管在内的TiO 2 质、制备和改性方法及其在光催化、光伏电池、光电化学电池等领域的应用得到了广泛的研究。 在二十世纪早期，二氧化钛就已经被广泛应用于颜料、防晒霜、涂料、药膏、牙膏等领域中，而自从1972年Fujishima发现二氧化钛电极在紫外光照射下可以光解水制氢以来，二氧化钛的光催化性能得到了广泛的研究，目前已经在光电性能和光催化净化环境方面开发了很多实际的应用。作为一种光催化材料，二氧化钛在净化污染和保护环境方面被认为是最有潜力的一种材料，众所周知二氧化钛的量子产率是由光致电子与空穴的产生与复合决定的，而二氧化钛的颗粒大小与几何结构则会直接影响光致电子与空穴的运动变化，具有较小的晶粒大小一般来说会提高二氧化钛的光学性能。因此，通过制备均匀细小的二氧化钛纳米颗粒以及对二氧化钛进行改性如：掺杂、半导体复合、表面贵金属修饰和有机染料敏化等方法，都可以提高二氧化钛的光催化性能，使其满足现代生活中各种不同的需求。本文将重点介绍通过掺杂的方法对二氧化钛纳米颗粒进行改性。 1 TiO2纳米材料的制备方法 TiO 纳米材料的制备方法很多,大体可以分为气相法和液相2 法。 1.1 气相法
二次函数图象的几何变换 内容基本要求略高要求较高要求 二次函数 1.能根据实际情境了解 二次函数的意义； 2.会利用描点法画出二 次函数的图像； 1.能通过对实际问题中 的情境分析确定二次函 数的表达式； 2.能从函数图像上认识 函数的性质； 3.会确定图像的顶点、 对称轴和开口方向； 4.会利用二次函数的图 像求出二次方程的近似 解； 1.能用二次 函数解决简 单的实际问 题； 2.能解决二 次函数与其 他知识结合 的有关问 题； 一、二次函数图象的平移变换 （1）具体步骤： 先利用配方法把二次函数化成2 () y a x h k =-+的形式，确定其顶点(,) h k，然后做出二次函数2 y ax =的图像，将抛物线2 y ax =平移，使其顶点平移到(,) h k.具体平移方法如图所示： （2）平移规律：在原有函数的基础上“左加右减”.
二、二次函数图象的对称变换 二次函数图象的对称一般有五种情况，可以用一般式或顶点式表达 1. 关于x 轴对称 2y ax bx c =++关于x 轴对称后，得到的解析式是2y ax bx c =---； ()2 y a x h k =-+关于x 轴对称后，得到的解析式是()2y a x h k =---； 2. 关于y 轴对称 2y ax bx c =++关于y 轴对称后，得到的解析式是2y ax bx c =-+； ()2 y a x h k =-+关于y 轴对称后，得到的解析式是()2y a x h k =++； 3. 关于原点对称 2y ax bx c =++关于原点对称后，得到的解析式是2y ax bx c =-+-； ()2y a x h k =-+关于原点对称后，得到的解析式是()2y a x h k =-+-； 4. 关于顶点对称 2 y ax bx c =++关于顶点对称后，得到的解析式是2 2 2b y ax bx c a =--+-； ()2 y a x h k =-+关于顶点对称后，得到的解析式是()2y a x h k =--+． 5. 关于点()m n ，对称 ()2 y a x h k =-+关于点()m n ，对称后，得到的解析式是()222y a x h m n k =-+-+- 根据对称的性质，显然无论作何种对称变换，抛物线的形状一定不会发生变
二次函数的对称变换 学习目标：1.掌握二次函数关于x轴、y轴、原点对称的解析式的确定。 2.会研究二次函数关于某条直线，某个点的对称变换。 一、课前练习 1.点（1，-4）关于x轴对称点坐标，关于y轴对称点，关于原点对称。 2.点（x,y）关于x轴对称点坐标，关于y轴对称点，关于原点对称。 二、新课探究 类型一：二次函数关于x轴、y轴、原点的对称变换 问题一：画出y=x2-2x-3的草图方法： 问题二：画出y=x2-2x-3关于x轴对称的图像 方法： 问题三：请确定新抛物线的解析式 方法一：一般式 方法二：顶点式 问题四：观察两个解析式的区别与联系 角度一：一般式 角度二：顶点式
问题五：请用同样的方法研究二次函数y=x2-2x-3关于y轴和原点的对称变换 总结：一般式y=ax2+bx+c (a≠0)关于x轴对称的解析式为： 关于y轴对称的解析式为： 关于原点对称的解析式为： 顶点式：y=a(x-h)2+k(a≠0) 关于x轴对称的解析式为： 关于y轴对称的解析式为： 关于原点对称的解析式为： 练习：1.y=2x2-3x关于y轴对称的解析式为, 2.y=-(x-3)2+3关于原点对称的解析式为, 3已知y=-2x2+x+1与y=ax2+bx+c关于x轴对称，则a= b= c= 类型二：二次函数关于某条直线或某个点的对称变换（给个开口向上的图像） 问题一：选取关于某条直线对称 问题二：选取关于某一点对称
总结：研究对称变换的方法 二次函数图象的对称 二次函数图象的对称一般有五种情况，可以用一般式或顶点式表达 1. 关于x 轴对称 2y a x b x c =++关于x 轴对称后，得到的解析式是2y ax bx c =---； ()2y a x h k =-+关于x 轴对称后，得到的解析式是()2 y a x h k =---； 2. 关于y 轴对称 2y a x b x c =++关于y 轴对称后，得到的解析式是2y ax bx c =-+； ()2y a x h k =-+关于y 轴对称后，得到的解析式是()2 y a x h k =++； 3. 关于原点对称 2y a x b x c =++关于原点对称后，得到的解析式是2y ax bx c =-+-； ()2y a x h k =-+关于原点对称后，得到的解析式是()2y a x h k =-+-； 4. 关于顶点对称（即：抛物线绕顶点旋转180°） 2y a x b x c =++关于顶点对称后，得到的解析式是2 2 2b y ax bx c a =--+-； ()2y a x h k =-+关于顶点对称后，得到的解析式是()2y a x h k =--+． 5. 关于点()m n ， 对称 ()2y a x h k =-+关于点()m n ，对称后，得到的解析式是()2 22y a x h m n k =-+-+- 根据对称的性质，显然无论作何种对称变换，抛物线的形状一定不会发生变化，因此a 永远不变．求抛物线的对称抛物线的表达式时，可以依据题意或方便运算的原则，选择合适的形式，习惯上是先确定原抛物线（或表达式已知的抛物线）的顶点坐标及开口方向，再确定其对称抛物线的顶点坐标及开口方向，然后再写出其对称抛物线的表达式．
云南化工Yunnan Chemical Technology Apr.2018 Vol.45，No.4 2018年4月第45卷第4期 半导体光催化材料能够直接利用太阳光将水中的有机污染物降解为无毒的二氧化碳和水，且不造成二次污染，受到人们广泛关注。TiO2半导体光催化材料因其具有良好的化学稳定性、高效的光催化效率以及无毒无害、环境友好和生产成本低等优点倍受人们的青睐。为充分利用太阳光降解各类污染物，提高TiO2光催化性能，使其能够在实际应用中充分发挥自身的优势，研究人员对TiO2光催化材料进行改进，结果表明掺杂对于TiO2光催化过程中存在的禁带宽度大、量子产率低、光催化活性低等缺点有显著的改善，但也各自存在着一些不足。文章就近年来TiO2掺杂改性方面的最新研究进展进行综述。 1 金属掺杂[1] 于晓彩等[2]在TiO2中掺杂Li+，研究发现，掺杂Li+能明显提高TiO2的结晶度，从而提高了样品的光催化性能。当Li+掺杂量为5%时，样品为锐钛矿型和金红石型的混合晶型，有效提高了可见光的利用率以及光催化活性。谭昌会等[3]采用溶胶-凝胶法制备了Al3+掺杂TiO2光催化剂，研究其对亚基蓝污染物的降解率，研究表明，当Al3+掺杂量为1%时，降解效率最佳。晁显玉等[4]制备了纳米Cu2+/TiO2光催化剂，研究其对头孢类污染物阿莫西林的降解效率。发现Cu2+掺杂，有效提高了对紫外线的吸收性能，提高了光能的利用率。Cu2+/TiO2光催化剂光吸收范围的扩展程度优于Fe3+/TiO2光催化剂[5]。 2 非金属掺杂 Sato等[6]率先开始了非金属掺杂TiO2光催化剂的研究，他们从氧化氮气体中分解出了氮气，并且把它导入了TiO2。王志宇[7]等采用水热法制备了S掺杂 TiO2光催化剂，研究了其在可见光下对甲基橙的降解率，结果表明，S的掺杂有效拓展了 TiO2的吸收光谱至可见光区，有效提高了其在可见光区的光催化性能。夏勇[8]等制备了N/TiO2光催化剂，研究发现氮掺杂使TiO2的吸收带发生明显红移，在自然光照下，120min时降解率为95.4%。 3 稀土离子掺杂 镧系稀土元素具备独特的电子结构、光学性质以及活泼的化学活性，在对TiO2的能带结构、晶体结构以及光吸收性能等方面进行改性时，稀土元素是一个理想的选择。刘丽静[8]利用溶胶-凝胶法制备了Dy3+掺杂TiO2复合光催化剂，发现掺杂少量稀土离子能细化晶粒，同时具有良好的热稳定性。徐晓虹等[9]制备了Y3+掺杂TiO2纳米粉体，研究表明，掺杂Y3+有效降低了禁带宽度，发生红移现象，且光催化记得平均粒径随着掺杂量的增加而减小。薛寒松等[10]合成了Ce3+掺杂TiO2纳米管，通过与未掺杂TiO2纳米管相比，光催化效果明显提高。光照150min后，甲基橙的降解率超过了80%。 4 共掺杂 近年来，多种与非金属共掺杂 TiO2引起人们的研究兴趣。刘元[11]等采用Fe3+-Ce4+复合掺杂改性 TiO2光催化剂处理真丝产品的印染废水，结果表明，Fe3+-Ce4+共掺杂TiO2光催化剂处理后废水去色率为 98.7%，COD去除率为70%，比单一元素的改性处理工艺更加有效。江鸿等[12]合成了Fe、N共掺杂的TiO2纳米粉体，其对可见光的响应范围明显大于纯TiO2，禁带宽度减少至2.74 eV，使其在可见光下的催化活性显著提高。双元素掺杂比单元素掺杂优越，是因为双元素掺杂克服了单一元素掺杂中总速率仍为较慢的界面反应所控制的弊端，使两个界面反应的速度同时加快保证了整个光催化反应的加快和完善，对污染物种类多，含有毒成分的废水有着良好的处理效果。 5 展望 随着人们对改性纳米 TiO2光催化材料研究的深入，制备出了不同离子掺杂的改性纳米 TiO2 光催化材料，改善了最初二氧化钛光催化材料催化效率低、太阳光光谱利用率低等问题。但是，改性纳米 TiO2 光催化材料在一定程度上仍然无法避免光催化剂制备工艺复杂、成本高、易于团聚等问题。因此，深入理论探讨、优化反应工艺，制备出低密度、光利用率高的催化剂成为当今研究的重点和热点。同时，降低粒子尺寸，提高重复利用率等也成为亟待解决的问题。 参考文献： [1] 王瑶,武志刚.银掺杂多孔氧化钛制备、表征及光催化性能探 究[J].山东化工,2016,45(7):17. [2] 于晓彩,徐晓,金晓杰,等.Li+-TiO2复合纳米光催化剂制备及 其光催化降解海产品深加工废水的研究[J].大连海洋大学学 doi：10.3969/j.issn.1004-275X.2018.04.004 改性二氧化钛纳米材料的研究进展 韩金轩，甘子萱，白美玲，毕 菲 （吉林建筑大学，吉林 长春 130118） 摘 要：TiO 2 半导体光催化材料因其具有良好的化学稳定性、高效的光催化效率以及无毒无害、环境友好和生产成本低等优点倍受人们的青睐。为在实际应用中充分发挥TiO2的优势，研究人员对TiO2光催化材料进行改进，金属，非金属，稀土元素等多种化学成分和物质都被用于TiO2的掺杂改性。文章就近年来TiO2掺杂改性方面的最新研究进展进行综述。 关键词：TiO 2 ；光催化材料；离子掺杂；改性 中图分类号：X703；TB33 文献标识码：B 文章编号：1004-275X（2018）04-006-02 ·6·
二次函数图象对称性的应用 一、几个重要结论： 1、抛物线的对称轴是直线__________。 2、对于抛物线上两个不同点P1（），P2（），若有，则P1，P2两点是关于_________对称的点，且这时抛物线的对称轴是直线_____________；反之亦然。 3、若抛物线与轴的两个交点是A（，0），B（，0），则抛物线的对称轴是__________（此结论是第2条性质的特例，但在实际解题中经常用到）。 4、若已知抛物线与轴相交的其中一个交点是A（，0），且其对称轴是，则另一个交点B 的坐标可以用＿＿＿＿表示出来（注：应由A、B两点处在对称轴的左右情况而定，在应用时要把图画出）。 5、若抛物线与轴的两个交点是B（，0），C（，0），其顶点是点A，则?ABC是＿＿＿＿三角形，且?ABC的外接圆与内切圆的圆心都在抛物线的＿＿＿＿＿＿＿上。 二、在解题中的应用： 例1已知二次函数的图象经过A（-1，0）、B（3，0），且函数有最小值-8，试求二次函数的解析式。 例2已知抛物线,设,是抛物线与轴两个交点的横坐标，且满足 . （1）求抛物线的解析式； （2）设点P（，），Q（，）是抛物线上两个不同的点，且关于此抛物线的对称轴对称，求的值。 例3已知抛物线经过点A（-2，7）、B（6，7）、C（3，-8），则该抛物线上纵坐标为-8的另一点的坐标是。 例4已知抛物线的顶点A在直线上。 （1）求抛物线顶点的坐标； （2）抛物线与轴交于B、C两点，求B、C两点的坐标； （3）求?ABC的外接圆的面积。
y O x -1 -2 1 2 - 3 3 -1 1 2 -2 二次函数专题训练——对称性与增减性 一、选择 1、若二次函数 ，当x 取 ， （ ≠ ）时，函数值相等，则 当x 取+时，函数值为（ ） （A ）a+c （B ）a-c （C ）-c （D ）c 2、抛物线2)1(2++=x a y 的一部分如图所示，该抛物线在y 轴右 侧部分与x 轴交点的坐标是 （A ）（ 2 1 ，0） （B ）（1，0） （C ）（2，0） （D ）（3，0） 3、已知抛物线2 (1)(0)y a x h a =-+≠与x 轴交于1(0)(30)A x B ，，，两点，则线段AB 的长度为（ ） Ａ．1 Ｂ．2 Ｃ．3 Ｄ．4 4、抛物线c bx x y ++-=2 的部分图象如图所示，若0>y ，则的取值范围是（ ） A.14<<-x B. 13<<-x C. 4- (一)、教学内容 1.二次函数得解析式六种形式 ①一般式y＝ax2 +bx+c(a≠0) ②顶点式（a≠０已知顶点) ③交点式(a≠0已知二次函数与X轴得交点） ④y=ax２(ａ≠0）（顶点在原点） ⑤y=ax２＋c(a≠0) (顶点在y轴上) ⑥ｙ=ax2 +ｂx (a≠０) (图象过原点) 2.二次函数图像与性质 对称轴: 顶点坐标: 与y轴交点坐标(0,c) 增减性:当a＞0时，对称轴左边,y随x增大而减小;对称轴右边,ｙ随x增大而增大 ?当a<０时,对称轴左边，y随x增大而增大;对称轴右边，y随x增大而减小 ☆二次函数得对称性 二次函数就是轴对称图形,有这样一个结论:当横坐标为x1, x2 其对应得纵坐标相等那么对称轴: 与抛物线y=ax2 ＋ｂx+c(a≠0）关于y轴对称得函数解析式:y=ａx２-bｘ+c(a≠0) 与抛物线y=ax2 +ｂx+c(a≠0）关于x轴对称得函数解析式:y=-ax2–bx-c(a≠0） 当a>0时，离对称轴越近函数值越小,离对称轴越远函数值越大； 当a＜０时,离对称轴越远函数值越小,离对称轴越近函数值越大; 【典型例题】 题型 1 求二次函数得对称轴 1、二次函数y＝－ｍx+3得对称轴为直线x=３,则m=_＿_____＿。 2、二次函数得图像上有两点(３，-８)与(－5，-8）,则此拋物线得对称轴就是( ) (A) (Ｂ） (C) (D) 3、y=２ｘ－４得顶点坐标为___ ___＿_，对称轴为___＿__＿___。 4、如图就是二次函数y＝ａx２+bx＋c图象得一部分,图象过点Ａ(－3,0)，对称轴为x=-１.求 它与x轴得另一个交点得坐标( , ) 5、抛物线得部分图象如图所示,若,则x得取值范围就是( ) A、 B、 C、或 D、或 6、如图,抛物线得对称轴就是直线,且经过点(3,0),则得值为 ( ） A、0 B、－1 C、 1 D、２ 题型2 比较二次函数得函数值大小 1、、若二次函数,当x取，(≠)时，函数值相等,则当x取＋时,函数值为 ( ) (A)a＋c （B）a-c （C)-ｃ (D)ｃ 2、若二次函数得图像开口向上,与x轴得交点为(4,0),(-2,0）知,此抛物 线得对称轴为直线x=1,此时时,对应得y 1 与ｙ ２ 得大小关系就是( ) Ａ．y 1 <ｙ 2 Ｂ、 y １ =y ２ Ｃ、 y 1 ＞y ２ Ｄ、不确定 点拨:本题可用两种解法y x O –1 1 3 O –1 3 3 1 编号：SM-ZD-19351 可靠性工程基本理论Organize enterprise safety management planning, guidance, inspection and decision-making, ensure the safety status, and unify the overall plan objectives 编制：____________________ 审核：____________________ 时间：____________________ 本文档下载后可任意修改 可靠性工程基本理论 简介：该安全管理资料适用于安全管理工作中组织实施企业安全管理规划、指导、检查和决策等事项，保证生产中的人、物、环境因素处于最佳安全状态，从而使整体计划目标统一，行动协调，过程有条不紊。文档可直接下载或修改，使用时请详细阅读内容。 1 可靠性（Reliability） 可靠性理论是从电子技术领域发展起来，近年发展到机械技术及现代工程管理领域，成为一门新兴的边缘学科。可靠性与安全性有密切的关系，是系统的两大主要特性，它的很多理论已应用于安全管理。 可靠性的理论基础是概率论和数理统计，其任务是研究系统或产品的可靠程度，提高质量和经济效益，提高生产的安全性。 产品的可靠性是指产品在规定的条件下，在规定的时间内完成规定功能的能力。 产品可以是一个零件也可以是一个系统。规定的条件包 括使用条件、应力条件、环境条件和贮存条件。可靠性与时间也有密切联系，随时间的延续，产品的可靠程度就会下降。 可靠性技术及其概念与系统工程、安全工程、质量管理、价值工程学、工程心理学、环境工程等都有十分密切的关系。所以，可靠性工程学是一门综合性较强的工作技术。 2 可靠度（Reliablity） 是指产品在规定条件下，在规定时间内，完成规定功能的概率。 可靠度用字母R表示，它的取值范围为0≤R≤1。因此，常用百分数表示。 若将产品在规定的条件下，在规定时间内丧失规定功能的概率记为F，则R=1－F。其中F称为失效概率，亦称不可靠度。 求二次函数解析式之对称式 用“对称式”求抛物线解析式分为下面几种情况： 1.抛物线关于x 轴对称.抓住关于抛物线关于x 轴对称其对应点横坐标相同，而纵坐标互为 相反数.也就是图象()2y ax bx c a 0=++≠关于x 轴对称的图象为 ()'2y y ax bx c a 0=-=++≠ 整理为()'2y ax bx c a 0=---≠. 结论：抛物线关于x 轴对称各项系数及常数项均互为相反数. 2.抛物线关于y 轴对称.抓住关于抛物线关于y 轴对称其对应点横坐标互为相反数，而纵坐 标相同.也就是图象()2y ax bx c a 0=++≠关于y 轴对称的图象为 ()()()'2 y a x b x c a 0=-+-+≠ 整理为()'2y ax bx c a 0=-+≠. 结论：抛物线关于y 轴对称二次项系数及常数项相同，而一次项系数互为相反数. 3.抛物线关于原点对称.抓住关于抛物线关于原点对称其对应点横纵坐标均互为相反数，. 也就是图象()2y ax bx c a 0=++≠关于y 轴对称的图象为()()()'2 y y a x b x c a 0=-=-+-+≠ 整理为()'2y ax bx c a 0=-+-≠. 结论：抛物线关于原点对称二次项系数及常数项互为相反数，而一次项系数相同. 例.下面的图是在《几何画板》中制作的抛物线2y x 2x 3=--自动生成的对称抛物线（红 色）： 4.关于直线x k =（k 是常数）和关于直线y h =（h 是常数）对称. ①.关于直线x k =（k 是常数）对称.根据轴对称的性质，对称点的横坐标和的一半等于k ，即，对称点的横坐标之和 =2k .若原抛物线配方成()()2 y a x m n a 0=++≠，则其关于直线x k =（k 是常数）对称的抛物线应表示为()()'2 y a 2k x m n a 0=-++≠，即()()'2 y a x 2k m n a 0=--+≠ （注意k 和m 都要变号,n 不变号） ②. 关于直线y h =（h 是常数）对称.根据轴对称的性质，对称点的纵坐标和的一半等于h ， 第一章绪论 第一节医学美学的形成与发展 一、医学美学产生的必然性 （一）医学美学产生与现代医学模式相适应 1.医学模式的转变扩大了医学本身的内涵，更新了人们的健康观念。 2.现代医学模式促进了医学社会学、医学伦理学、医学美学、美容医学等一批新兴交叉性学科、综合性学科的产生。 （二）医学发展的艺术化趋势 1.临床医学既是一门科学，也是一门艺术 （三）美学发展的应用化趋势 （四）美学与医学的渗透 1.现代科学发展的一个突出特点，就是个传统学科已打破原来学科的界限、范围和束缚，多角度、多层次、全方位地交叉、渗透和综合，高度综合交替进行，从而导致了交叉学科的繁荣。 2.科学与艺术并行不悖。科学的理性向艺术的感性渗透，极大地提高了艺术创造能力；艺术向科学领域渗透，会科学注入新的创造力和活力。 二、美与健康的关系 （一）美与健康 1.健康的含义：健康是人躯体上、心理上和社会上的完满状态，而不是没有疾病和衰弱的现象。 2.健康是美的前提和基础：只有在健康基础上的美才是真正的美，失去了健康的人体不可能美。 3.人体的美丑对人的健康产生重要的影响 （二）美与心理健康 1.体验生命意识，促进自我意识的发展:从审美体验激发自我体验，从生命体验的肯定增强自我认识，到感情的自由和释放，最终推动自我功能的调节。 2.激励个性进取，塑造完善人格品质 3.丰富感情空间，协调人际关系 4.调整心理定势，消除心理疾病 （三）美容应坚持健康优先的原则 作为一个美容师应遵循的原则是： 1.要做到任何美容手术都无损健康，凡有损健康的手术都应拒绝。 2.所有美容手术，也应和其他医疗手术一样，认真实行知情同意原则。 3.对某些效果不明或，或没有远期效果观测依据的美容手术不应草率实行。 4.不片面追求经济利益，更不为了获取经济利益做有损健康的手术。 三、医学美学的发展历程 （一）中国古代朴素医学美学思想与医学技艺的萌发 （二）国外现代美容医学技术发展概述 （三）我国当代医学美学与美容医学的兴起与发展 （四）医学美学与美容医学整体学科是社会文明的产物 第二节医学美学的对象、任务和作用 一、医学美学的研究对象 西北工业大学航空学院 可靠性技术发展简介 01041201 摘要 可靠性理论是近30年来发展起来的一门新兴学科，它对现代军事、宇航、电子等工业的发展起了重要作用。从六十年代开始逐渐发展到研究结构、机械、机电系统及由上述系统组成的综合系统的可靠性问题。其应用范围也从比较尖端的工业部门扩展到一般工业部门。目前，可靠性设计和分析技术已成为许多工业部门中产品发展工作不可缺少的一环。但在现代科技飞速发展的时期，系统可靠性在理论和研究模式上还有欠缺，需要结合其他理论如模糊理论、人工智能等，是可靠性理论、试验和管理能够更成熟、更完美。 关键词：可靠性工程航空工业电子工业宇航工业核工业机械和非电子产品人可靠性现代化 可靠性技术发展简介 二十世纪以前 可靠性是伴随着兵器的发展而诞生和发展的，在人类文明经历了4000多年发展成长的漫长过程中，人类已经对当时所制作的石兵器进行了简单检验。在殷商时代已有的文字记载中，就有关于生产状况和产品质量的监督和检验，对质量和可靠性方面已有了朴素的认识。与可靠性工程学有关的数学理论早就发展起来了，可靠性工程最主要的理论基础——概率论早在十七世纪就由伽利略、巴斯卡、费米、惠更斯、伯努利、德·莫根、高斯、拉普拉斯、泊松等人逐步确立。布尼科夫斯基在十九世纪写了第一本概率论教程，他的学生切比雪夫发展了大数定律，他的另一个学生马尔科夫创立了随机过程论，这是可修系统最重要的理论基础。可靠性工程另一门主要的基础理论——数理统计学在本世纪三十年代初也得到了迅速发展。 二十世纪三十至四十年代，可靠性工程的准备和萌芽阶段 除了三、四十年代提出的机械维修概率、长途电话强度的概率分布、更新理论、试件疲劳与极限理论的关系外，1939 年瑞典人威布尔为了描述材料的疲劳强度而提出了威布尔分布，后来成为可靠性最常用的分布之一。 美国 最早的可靠性概念来源于航空。二战期间，因可靠性引起的飞机损失惨重，损失飞机2100架，是被击落飞机的1.5倍。1939年，美国航空委员会出版的《适航性统计学注释》中，提出了飞机由于各种失效造成的事故率不应超过0.00001/小时，相当于飞机在一小时飞行中的可靠度为0.99999，尽管这里并未明确提出“可靠度”的概念。现在所用的“可靠性”定义是在1952年美国的一次学术会议上提出来的。电子管的可选性太差是导致美国航空无线电设备可靠性问题的最大因素，美国当时的航空无线电设备有60%不能正常工作，其电子设备在规定的使用期限内仅有30%的时间能有效工作。为了解决这一问题，美国国防部组织人力，开始对电子管的可靠性进行研究，在1934年成立电子管开发委员会（VTD），1946年成立电子管专业小组（PET）和航空无线小组（ARINC）。这标志着可靠性的起步。 在美国，四十年代改进可靠性的努力集中于质量的提高方面。更好的设计、更强的材料、更坚硬更光滑的摩擦表面、先进的检验仪器等等——强调这一切都是为了延长零件或组合件的使用寿命。例如，通用汽车公司的电动分布通过使用更好的绝缘，高温和试验，和改进了的锥-球形滚柱轴承等办法，把机车所使用的牵引马达的使用寿命从25万英里延长到100万英里。通过对曲轴和凸轮轴的轴承表面进行新式的TOCCO硬化处理大大延长了柴油发动机的寿命。可靠性工程在易维护型设计、以及为预防性的维护安排规划、设施、技术和进度等方面都取得了进展。四十年代展现的其他显著的进步还有管理部门对于检验抽样方案，高生产率机床的生产控制图，估算水平和促进购买优质产品 第31卷第2期 唐山师范学院学报 2009年3月 Vol.31 No.2 Journal of Tangshan Teachers College Mar. 2009 ────────── 基金项目：河北省科学研究与发展计划项目（07215107） 收稿日期：2008-04-19 作者简介：刘立华（1969-），女，河北唐山人，硕士，唐山师范学院化学系副教授，研究方向为纳米复合材料制备和应用。 -31- 纳米二氧化钛表面改性 刘立华，刘会媛，张相平 （唐山师范学院 化学系，河北 唐山 063000） 摘 要：对纳米二氧化钛进行表面改性处理是钛白粉工业生产中必不可少的关键步骤，处理的方法和包覆的程度直接影响产品的应用范围。阐述了纳米二氧化钛的表面改性原理和化学表面改性的两种方法──无机包膜改性和有机包膜改性。无机包膜改性包括铝包膜改性、硅包膜改性、铁包膜改性和硅铝复合包膜改性；有机包膜改性主要是醇类化合物和羧酸类化合物对纳米二氧化钛的包覆改性。 关键词：二氧化钛；表面改性；纳米 中图分类号： O 621.4 文献标识码：A 文章编号：1009-9115(2009)02-0031-03 Surface Modification of Nano-Sized Titania LIU Li-hua, LIU Hui-yuan, ZHANG Xiang-pin (Department of Chemistry, Tangshan Teachers College, Hebei Tangshan 063000, China) Abstract: Surface modification of nano-sized titania is one of the key steps in commercial production of titania and it can directly effecte the application fields of titania powder. The principles of modification of nanoscale titania were introduced in this article. Coating a film of organic or inorganic compound on its surface which is two means of surface modification is reviewd in the paper. Inorganic surface modification includes surface modification with Aluminium, surface modification with silicon surface modification with iron and composite surface modification with silicon and aluminium. Organic surface modifications were mainly interpreted by the alcohol compounds and carboxylic acid compounds coating on the surface of titania. Key words: titania; surface modification; nano 纳米二氧化钛因具有光催化活性好、毒性低、稳定、价廉、易于回收等优势而倍受人们的关注。特别是随着环境污染的日益严重，纳米二氧化钛以其高效的光催化降解污染物的能力而成为当前最为活跃的研究热点之一[1]。纳米二氧化钛这种独特的性能主要取决于其粒度的大小。一般来说，粒径越小，比表面积越大，其光催化活性也就越高。 由于纳米二氧化钛表面极强的活性，使得它们很容易团聚，这大大降低了纳米二氧化钛的实际应用效果，同时由于纳米二氧化钛表面亲水疏油，在有机高分子树脂中难以均匀分散，界面上会出现空隙，当空气中的水分进入空隙中就会引起界面处高聚物的降解、脆化、导致材料性能下降。为了充分利用二氧化钛的优良性能，在表面包覆一层无机物或有机物膜对其进行表面改性。 1 表面改性原理 由溶胶稳定性的DLVO 理论可知，纳米级的二氧化钛细粉，单位面积的超额吉布斯自由能升高，表面张力变大，促使二氧化钛发生团聚，此时ζ电位比较高。若要使团聚体重新分散，首先应使表面充分润湿。判断固体能否在液体中润湿以及润湿程度的标准一般有两种。一是根据润湿热的大小，可以用润湿热来比较二氧化钛粉末在不同溶剂中的润湿程度。二氧化钛在水中的润湿程度比较好。实际上，在把二氧化钛粉末中加入水以后，由于颗粒外表面附着的空气与水的置换作用，使细小颗粒的润湿速度较慢。为了加大润湿程度，可以加入少量表面活性剂以降低其表面张力，提高润湿性。通常使用的表面活性剂有三乙醇胺、硅酸盐、烷基萘磺酸等。二是根据接触角的大小判断。二 文 献 检 索 院系：生化学院 专业：10环境工程 姓名：林局 学号：201010903024 指导教师：田从学 日期：2012、5、2 纳米二氧化钛表面改性研究 姓名：林局学号：201010903024 摘要:纳米二氧化钛作为一种重要的无机功能材料,有着广泛的应用领域。它的应用使其表面改性技术也成为研究的一个热点。表面改性技术是提高性能、扩大应用领域的重要手段。对不同的纳米二氧化钛表面改性方法(无机改性和有机改性)和应用,特别是最常用的偶联剂法、表面活性剂法和聚合物包覆法进行了介绍,在此基础上提出了存在的问题,指出改善界面相容性,使纳米粒子在基材中均匀分散及稳定的必要性等,同时展望了今后的研究发展方向。关键词:二氧化钛;表面改性;包覆 Progress on surface modification of nano-titania Lin ju Abstract:Nano-sized titania (TiO2) is an important inorganic function material,l which has wide application in many fields. It′s widespread application causes its surface modification technology becoming a hot spot of research.Meanwhile, surface modification is an important method to improve titania′s performances and to expand its application domain. In this paper, the aim and mechanism of TiO2modification were introduced. The different modification methods ( inorganic modification and organic modification) and their application were summarized. Especially the most commonly used methods, such as coupling reagent, surfactant and polymer coating methods were introduced in detail On these basis, the problems existed were put forwarded and the necessity of interface compatibility improvement, the uniform dispersedness of nano-particles in base material and stability control were pointed out.At the same time, further research direction was also proposed. Key words:titania; surface modification; coating 1 引言 二氧化钛具有一些独特的性质，如表面效应、小尺寸效应、量子尺寸效应、宏观量子隧道效应等，这些效应导致了纳米二氧化钛在光催化氧化、光电转换、化学反应性、光学与电学性质、磁性、相变温度等许多方面都显示出独特的性能，因而被作为一种重要的无机功能材料。目前，纳米二氧化钛已在光催化与环境工程、清洁能源、太阳能电池、涂料、日用化妆品、功能陶瓷以及湿度传感器等众二次函数的对称性
可靠性工程基本理论
求二次函数解析式之对称式
美学与医学美学
可靠性技术发展简介概述
纳米二氧化钛表面改性
二氧化钛表面改性研究
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