Clinical Science (2010)118,31–41(Printed in Great Britain)doi:10.1042/CS20090047
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R E V I E W
Inhibitor selectivity in the clinical application of
dipeptidyl peptidase-4inhibition
Mark KIRBY ?,Denise M.T.YU ?,Stephen P .O’CONNOR ?and Mark D.GORRELL ?1
?
Bristol-Myers Squibb,Princeton,NJ 08540,U.S.A.,and ?Centenary Institute,Faculty of Medicine,The University of Sydney,Newtown,NSW 2042,Australia
A B S T R A C T
DPP-4(dipeptidyl peptidase-4)degrades the incretin hormones GLP-1(glucagon-like peptide-1)and GIP (gastric inhibitory polypeptide),decreasing their stimulatory effects on β-cell insulin secretion.In patients with T ype 2diabetes,meal-related GLP-1secretion is reduced.DPP-4inhibitors (alogliptin,dutogliptin,linagliptin,saxagliptin,sitagliptin and vildagliptin)correct the GLP-1de?ciency by blocking this degradation,prolonging the incretin effect and enhancing glucose homoeostasis.DPP-4is a member of a family of ubiquitous atypical serine proteases with many physiological functions beyond incretin degradation,including effects on the endocrine and immune systems.The role of DPP-4on the immune system relates to its extra-enzymatic activities.The intracytosolic enzymes DPP-8and DPP-9are recently discovered DPP-4family members.Although speci?c functions of DPP-8and DPP-9are unclear,a potential for adverse effects associated with DPP-8and DPP-9inhibition by non-selective DPP inhibitors has been posed based on a single adverse preclinical study.However,the preponderance of data suggests that such DPP-8and DPP-9enzyme inhibition is probably without clinical consequence.This review examines the structure and function of the DPP-4family,associated DPP-4inhibitor selectivity and the implications of DPP-4inhibition in the treatment of T ype 2diabetes.
INTRODUCTION
DPP-4(dipeptidyl peptidase-4;E.C.3.4.14.5)inhibitors,a novel modality for the treatment of Type 2diabetes,augment glucose homoeostasis by preventing degrada-tion of the incretin hormones GIP (gastric inhibitory polypeptide)and GLP-1(glucagon-like peptide-1).The latter hormone accounts for the majority of the incretin effect and is essential for regulating both fasting and postprandial plasma glucose by stimulating insulin secretion,supporting pancreatic β-cell proliferation and inhibiting glucagon production by the pancreatic α-cells to decrease glucose production by the liver [1].
In patients with Type 2diabetes,meal-related GLP-1secretion is impaired,most probably as a consequence of the disease [2],and enhancement of endogenous incretin levels with DPP-4inhibitors should help preserve GLP-1function.Clinical trials of DPP-4inhibitors have demonstrated signi?cant glycaemic ef?cacy,including sustained HbA 1c (glycated haemoglobin A 1c )reductions for up to 2years in patients treated with monotherapy and combination therapy [1,3,4].Advantages over existing diabetes treatments include a low risk of hypoglycaemia,a neutral effect on body weight and the potential,based on animal and in vitro studies,for preservation or enhancement of β-cell function [1,3,5,6].The ?rst
Key words:diabetes,dipeptidyl peptidase-4,enzyme inhibition,immunity,selectivity.
Abbreviations:CI,con?dence interval;DPP ,dipeptidyl peptidase;DPL,DPP-like;FAP ,?broblast activation protein;FDA,Food and Drug Administration;GIP ,gastric inhibitory polypeptide;GLP ,glucagon-like peptide;IP-10,interferon-γ-induced protein-10;I-TAC,interferon-inducible T-cell αchemoattractant;MMP-9,matrix metalloproteinase-9;NEP ,neutral endopeptidase;NPY,neuropeptide Y;PYY,peptide YY;SDF-1,stromal cell-derived factor-1;3D,three-dimensional.
1Mark
D.Gorrell has been a consultant to and/or received honoraria or indirect bene?t from AstraZeneca,Bristol-Myers Squibb,
Merck (U.S.A.),Merck Sharp &Dohme (Australia),Boehringer Ingelheim (Germany)and IMTM (Germany).Correspondence:Dr Mark D.Gorrell (email m.gorrell@https://www.doczj.com/doc/367572578.html,.au).
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agent in the gliptin class,sitagliptin,received US FDA(Food and Drug Administration)approval in 2006,followed by saxagliptin in2009.Both sitagliptin and vildagliptin received approval from the EMEA (European Medicines Agency)in2007.A num-ber of additional DPP-4inhibitors are in various phases of clinical development.As the understanding of the mechanism of DPP-4function progresses and competing products become available,an important consideration is the degree of enzyme selectivity exhibited by different agents in this therapeutic class.
DPP-4is in a family of ubiquitous atypical serine proteases with numerous functions,including roles in nutrition,metabolism,the endocrine and immune systems,cancer growth,bone marrow mobilization and cell adhesion[7].Given that these many functions are associated with the DPP-4family,selective interactions might be necessary for optimal ef?cacy,safety and toler-ability.The present review covers the structure and function of the DPP-4family,mechanisms of DPP-4 inhibition,extra-enzymatic activities independent of catalysis,and the relationship between DPP-4enzyme inhibition and non-selective DPP inhibition as a means of examining the relevance of selectivity in the clinical application of DPP-4inhibitors.
DPP-4FAMILY
The DPP-4family,a subfamily of the prolyl oligopepti-dase superfamily,includes four enzymes,DPP-4,FAP (?broblast activation protein),DPP-8and DPP-9,and two non-enzymes,DPP-4-like protein-6(DPP-6,DPL-1 or DPP-X)and DPP-10(DPL-2).Members of the DPP-4family preferentially cleave Xaa-Pro-and Xaa-Ala-dipeptides(where Xaa is any amino acid except proline)from the N-terminus of proteins[8].The DPP-4 family differentiates itself from the prolyl oligopeptidase superfamily by the presence of two glutamate residues located within the catalytic pocket,which are essential for enzymatic activity[9].The absence of catalytic activity in DPL-1and DPL-2is attributed to a number of amino acid substitutions in the catalytic pocket[10].
DPP-4
DPP-4is widely distributed,existing both as a mem-brane-anchored cell-surface peptidase and as a smaller soluble form in blood plasma.In humans,DPP-4is expressed in epithelial cells,capillary endothelia and lymphocytes.This includes expression in the gastroin-testinal tract,biliary tract,exocrine pancreas acinar cells, kidney,thymus,lymph nodes,uterus,placenta,pros-tate,the adrenal,parotid,sweat and mammary glands, liver,spleen,lungs and brain[11].
A766-amino-acid protein,DPP-4is arranged in two domains:an N-terminalβ-propeller domain and a C-terminalα/β-hydrolase domain.The two domains form a large cavity that houses the active site(Figure1) [12].The tertiary structure of DPP-4reveals a dimer that may form a dimer of dimers,suggesting a potential for inter-cellular homotypic binding(Figure2)[13].Theα/β-hydrolase domain is involved in dimerization,and the β-propeller domain is involved in both the dimeric and tetrameric interactions[12].
Both the cell-surface and soluble forms of DPP-4are catalytically active as dimers.Access to the cavity,and thus to the active site,is via an opening in the centre of theβ-propeller or through the larger opening between the propeller and hydrolase domains(Figure1)[12,13]. Essential to the catalytic activity of DPP-4are residues Ser630,Asp708and His740of the catalytic triad,Tyr547 in the hydrolase domain,and Glu205and Glu206in the β-propeller domain[12,14].The two glutamate residues align the substrate peptide such that only two amino acids with smaller side chains,such as proline and alanine,reach the active serine residue.These features help explain the preferential Xaa-Pro-and Xaa-Ala-cleaving activity and substrate speci?city of DPP-4(Figure3)[14].
Substrates of DPP-4include numerous neuropeptides, hormones and chemokines(Table1).However,although the majority of the substrates identi?ed serve as pharma-cological substrates in vitro,relatively few have been determined to be endogenous physiological substrates (de?ned as peptides whose endogenous circulating levels of intact compared with N-terminally cleaved forms are altered following reduction or elimination of DPP-4activity in vivo).Both GIP and GLP-1are endogenous physiological substrates for DPP-4;in rats and mice with targeted genetic inactivation or inhibition of DPP-4,there are increased circulating levels of intact GIP and GLP-1, and levels of intact GIP and GLP-1are increased relative to their N-terminally truncated forms[15].
Similarly,substance P,a neurotransmitter/neuromod-ulator associated with many physiological functions, including nociception,pain transmission,smooth muscle contraction,anxiety and stress-related responses,and the chemokines SDF-1α(stromal cell-derived factor-1α) and SDF-1β,chemoattractants for lymphocytes and monocytes that regulate the development of T-and B-lymphocytes,and the survival of mature lymphocytes,are cleaved by DPP-4at the N-terminus,and plasma levels of active forms of these substrates are increased in Dpp-4-knockout mice[16].Whether partial or full reduction of DPP-4activity due to selective DPP-4inhibitors results in biologically signi?cant increases in the levels of active SDF-1α/βor substance P at their sites of action in humans,as it does for the incretin hormones,is unknown.
FAP
The enzyme FAP,also known as seprase,is the most similar family member to DPP-4,as it shares a52%amino acid identity(human enzymes)and
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Figure 1Schematic representation of the catalytic pocket of DPP-4
DPP-4combines two distinct structural domains,the α/β-hydrolase domain and the β-propeller domain,that form a central cavity (shaded)which contains the catalytic pocket (outlined by dotted line).Reprinted with permission from Macmillan Publishers Ltd:Nature Structural Biology [12],copyright (2003)(https://www.doczj.com/doc/367572578.html,/nsmb/index.html).
similar substrate speci?city.Despite these similarities,DPP-4and FAP differ markedly in their expression patterns.FAP expression is con?ned predominantly to activated ?broblasts in diseased tissue,such as ?brotic and epithelial tumours,and invasive cancers,and may be important in wound healing [17].FAP immunostaining intensity correlates with the histological severity of ?brosis in chronic liver disease,which involves chronic wound healing [18].FAP has narrow prolyl endopeptidase activity,con?ned to Z -Gly-Pro-derived substrates,and a dipeptidyl peptidase activity that more effectively hydrolyses H -Ala-Pro-than H -Gly-Pro-derived substrates [19,20].
DPP-8and DPP-9
The other two catalytically active DPP-4family members,DPP-8and DPP-9,share 61%amino acid identity with each other,and a 26and 21%amino acid identity with the protein sequences of DPP-4and FAP respectively (human enzymes)[21].In contrast with DPP-4and FAP ,which have an extracellular catalytic domain,both DPP-8and DPP-9proteins are localized to the cytoplasm (Figure 4)[21].DPP-8expression is up-regulated in activated T-cells.DPP-8and DPP-9enzyme activity has been detected in human blood lymphocytes and monocytes [22],and there is some evidence of
DPP-8and DPP-9expression in mouse pulmonary leuco-cytes [23].High levels of DPP-9are found in cancer cells,normal skeletal muscle,the heart and liver.DPP-8and DPP-9hydrolyse H -Ala-Pro-and H -Gly-Pro-derived substrates,although with less ef?ciency than DPP-4.In vitro peptide substrates of DPP-8or DPP-9identi?ed to date include GLP-1,GLP-2,NPY (neuropeptide Y),PYY (peptide YY),SDF-1,IP-10(interferon-γ-induced protein-10)and I-TAC (interferon-inducible T-cell αchemoattractant)(Table 1)[24,25].However,a physiological substrate or role for the DPP activity of either DPP-8or DPP-9remains to be demonstrated in vivo .
Other enzymes involved in DPP-4substrate degradation
Although DPP-4has been established as the primary inactivation enzyme of GLP-1,other enzymes degrade GLP-1,in particular NEP 24.11(neutral endopeptidase 24.11).NEP 24.11,expressed mainly in the kidney,is a widespread membrane-bound zinc metallopeptidase with broad-spectrum speci?city that is involved in the inactivation and renal clearance of peptide hormones [26].In vivo studies have shown that up to 50%of GLP-1degradation may be due to NEP 24.11[26].It has been demonstrated that when DPP-4and NEP
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Figure 2Schematic representation of the structure of DPP-4
DPP-4is shown as a dimer of a dimer.3D structure of DPP-4puri?ed from porcine kidney.Modi?ed with permission from Engel,M.,Hoffmann,T.,Wagner,L.,Wermann,M.,Heiser,U.,Kiefersauer,R.,Huber,R.,Bode,W.,Demuth,H.U.and Brandstetter,H.(2003),The crystal structure of dipeptidyl peptidase IV (CD26)reveals its functional regulation and enzymatic mechanism,Proc.Natl.Acad.Sci.U.S.A.,vol.100,pp.5063–5068.Copyright (2003)National Academy of Sciences,U.S.A.
24.11inhibitors are administered concomitantly,the combined effect is greater than the effect of either inhibitor alone,resulting in signi?cant improvements in the antihyperglycaemic and insulinotropic effects of exogenous GLP-1[26].Therefore the relevance of DPP-4in physiological cleavage of other substrates in vivo may similarly depend on the relative rates of substrate cleavage by DPP-4compared with other enzymes.This might explain why,even though DPP-4has nine chemokine substrates,no in vivo role for DPP-4cleavage of chemokines has been demonstrated.For example,SDF-1is proteolytically inactivated by NEP ,cathepsin G and MMP-9(matrix metalloproteinase-9)[27].Further studies utilizing Dpp-4-knockout mice and a DPP-4-selective inhibitor in an appropriate model of
cell migration may aid in demonstrating the importance
of DPP-4-mediated chemokine degradation.
ENZYMATIC INHIBITION OF THE DPP-4FAMILY
The leading DPP-4inhibitors in clinical use or late-phase clinical development are alogliptin,saxagliptin,sitagliptin and vildagliptin.Inhibition of the DPP-4enzyme based on IC 50(concentration at which there is 50%inhibition of measured activity in vitro ,dependent on substrate concentration)and K i (enzyme–inhibitor dissociation constant,independent of substrate concentration)values for these DPP-4inhibitors show values in the low
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Figure 3DPP-4active site with active-site residues
The catalytic pocket of DPP-4is shown containing the selective inhibitor saxagliptin (magenta)with polar contacts between the inhibitor and DPP-4(dashed lines).This Figure was taken from Protein Science ,Vol.17,No.2,2008,pp.240–250.Copyright (2008and The Protein Society).Reprinted with permission of John Wiley &Sons,Inc.
nanomolar range.In contrast,these inhibitors have a low af?nity for DPP-8and DPP-9(Table 2),and other proteases are not inhibited by DPP-4inhibitors.Whether DPP-8and DPP-9are inhibited in vivo during administration of therapeutic doses of these selective DPP-4inhibitors remains unknown.No in vivo effects have been reported that point to a pharmacological impact of the inhibition of other peptidases [1].
It is important to recognize that comparisons among the different inhibitors are different because a standardized DPP-4enzyme assay is not used.IC 50values depend on the substrate used and the ratio of substrate concentration to its K i for that enzyme;for rapidly dissociating DPP-4inhibitors,such as alogliptin and sitagliptin,substrate choice alters the K m and,therefore,results in different IC 50values for a single enzyme [28].Saxagliptin and vildagliptin have been reported to have slow binding.Therefore a suitable incubation period for the equilibration of enzyme and inhibitor needs to occur prior to substrate addition,otherwise inhibition by these compounds could be severely underestimated.Finally,K i increases with temperature;thus ambient and physiological assays’temperatures produce differing data [1].
Another important consideration is that assays measuring plasma DPP-4activity introduce a dilution step that produces a dilution artifact for rapidly dissociating DPP-4inhibitors.Methodology in most selectivity papers is incomplete and generally includes non-physiological conditions.Thus there is a major need to adopt a standardized DPP-4assay and focus upon K i .
As DPP-4preferentially cleaves substrates with a proline residue at the P1(1-position of the pyrrolidine ring)and accepts most residues at P2and in prime side positions,many inhibitors (including a whole class of cyano-and boronic-substituted pyrrolidine DPP inhibitors)incorporate a proline or proline mimetic at P1,with either a reversible or an irreversible electrophilic isostere to form an adduct with the active site Ser 630in the hydrolase domain.These are typi?ed by saxagliptin and vildagliptin [1].Saxagliptin and vildagliptin both contain cyanopyrrolidines that bind to DPP-4in the S1pocket.Saxagliptin has been shown by extensive nuclear magnetic resonance,isothermal titration calorimetry and X-ray diffraction-derived structural studies to form a reversible covalent bond between the catalytic hydroxy group of Ser 630in DPP-4with the nitrile carbon atom to hydroxy
oxygen bond length of <1.3A
?(where 1A ?=0.1nm)[14].This strong interaction of saxagliptin and vildagliptin with the enzyme may be a major determinant of their inhibitor potency.
Two glutamate residues (Glu 205and Glu 206)in the β-propeller domain are highly conserved across the DPP family and are essential for its enzymatic activity [9].The amino groups contained within the DPP-4inhibitors alogliptin,saxagliptin,sitagliptin and vildagliptin are all believed to interact with these two glutamate residues with different interaction strengths.This interaction has been demonstrated experimentally through single-crystal X-ray diffraction for the bound DPP-4complexes of sitagliptin [29],saxagliptin [14]and a close analogue of alogliptin [30].The interactions with Glu 205and Glu 206are thought to be crucial
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Table1DPP-4substrates
CCL,CC chemokine ligand,CXCL,CXC chemokine ligand;GCP-2,granulocyte chemotactic protein-2;GHRH,growth hormone-releasing hormone;GRO,growth-related protein;GRP,gastrin-releasing peptide;IGF-1,insulin-like growth factor1; LD78,macrophage in?ammatory protein1αisoform;MIG,interferon-γ-induced monokine;MDC,macrophage-derived chemokine;PACAP,pituitary adenylate cyclase-activating polypeptide;PHM,peptide histidine methionine;RANTES, regulated on activation normal T-cell expressed and secreted.
Pharmacological substrate Physiological substrate
Chemokines Glucagon family MIG/CXCL9GLP-1
IP-10/CXCL10GLP-2
I-TAC/CXCL11GIP
LD78β/CCL3L1Other RANTES/CCL5Substance P MDC/CCL22SDF-1α/β/CXCL12 Eotaxin/CCL11
GROβ/CXCL2
GCP-2/CXCL6
Pancreatic polypeptide family
NPY
PYY
PACAP27
PACAP38
Other
Vasostatin-1
GRP
GRP-(3–27)
GHRH
IGF-1
PHM
β-Casomorphin-2
Endomorphin-2
Morphiceptin
Enterostatin
Haemorphin-7
β-Type natriuretic peptide
interactions for alogliptin and sitagliptin.Although saxagliptin and vildagliptin both contain a hydroxy-substituted adamantane fragment,with each occupying the S2pocket of the DPP-4active site,the carbon-linked adamantane of saxagliptin,as well as its lipophilic cyano-containing methanopyrrolidine,provide it with a high level of binding ef?cacy.With regard to vildagliptin,the nitrogen-linked adamantane and smaller S1pocket-?lling cyanopyrrolidine may be factors that limit its potency. Therefore,because saxagliptin has strong interactions with both Ser630and Glu205/Glu206[14],the combination of these interactions results in its highly potent DPP-4 inhibition compared with alogliptin,sitagliptin and vildagliptin(Table2).
As theβ-propeller domain of DPP-4,DPP-8and DPP-9is not as conserved as theα/β-hydrolase domain and the active sites of DPP-4,DPP-8and
DPP-9Figure4Cellular localization of the six members of the DPP-4gene family
sDPP-4,soluble form of DPP-4.
differ[24,31,32],selective inhibition of DPP-4may be achieved.The precise origin of this selectivity must await the crystal structures of DPP-8and DPP-9.A number of indirect studies,however,have given insight into the differential binding in these peptidases.For instance,a3D(three-dimensional)quantitative structure–activity relationship study provided a highly predictive CoMFA(comparative molecular?eld analysis)model [33]and supported?ndings in other reports[34,35]that the S1pocket of DPP-4is smaller than in DPP-8/9, whereas the S1 site is larger in DPP-4and more capable of accommodating negatively charged groups.Further subtle analysis suggests that the positions between the S2 and S3sites are larger in DPP-4,while the S3-binding site itself is smaller in DPP-4than in DPP-8/9.The S3site in particular is believed to exhibit the greatest variance between the three enzymes,and the speci?c interactions around Phe357(DPP-4)have been proposed to play an important role in enhancing the selectivity against DPP-8 [33,34].More recently,Van der Veken et al.[36]reported on a series of compounds with a4S-azido substituent on the P12S-cyanopyrrolidine that were selective for DPP-8/9over DPP-4.In addition,these authors also de-scribe substituted isoindoline P1inhibitors that had signi-?cant selectivity for DPP-8/9over DPP-4[37].These results support further the conclusion above that the S1 pocket in DPP-4is smaller than that in DPP-8or DPP-9.
Linking proteases with their substrates is crucial for understanding protease function.Two key steps in identifying the role of DPP-4in glucose homoeostasis were the discoveries that GLP-1is a DPP-4substrate and that DPP-4is a major determinant of the half-life of GLP-1in vivo.Similarly,knowledge of DPP-8and DPP-9substrates is crucial for understanding their biological roles.Although the substrate speci?city of DPP-8and DPP-9is very similar to DPP-4,their cleavage rates are signi?cantly slower than DPP-4[25].
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Table2Alogliptin,saxagliptin,sitagliptin and vildagliptin inhibition of DPP-4/8/9
Data taken from[52]*,[53]?,[28]?,[54]§,[55] and[46]?.IC50,concentration at which there is50%inhibition of measured activity in vitro,dependent on substrate concentration;K i,enzyme–inhibitor dissociation constant,independent of substrate concentration.?,not applicable.
DPP-4(nmol/l)DPP-8(nmol/l)DPP-9(nmol/l)
Inhibitor Temperature IC50K i IC50K i IC50K i Alogliptin Room7??>100000??>100000??Saxagliptin Room?0.6?????37?C? 1.3??508??100?Sitagliptin Room18§?48000§?>100000§?Vildagliptin Room 3.5 3??810??95?
Table3DPP-4inhibitors approved and in clinical develop-ment
EU,European Union.
Inhibitor name Stage in development Company
SSR162369Phase1Sano?-Aventis
TS-021Phase1Taisho
ALS2-0426Phase2Amgen/Servier
GRC8200Phase2Glenmark
PF-00734200Phase2P?zer
SYR-472Phase2Takeda
TA-6666Phase2Mitsubishi/Tanabe Dutogliptin Phase3Phenomix Linagliptin Phase3Boehringer Ingelheim Alogliptin Filed to FDA Takeda Vildagliptin Filed to FDA;approved in EU Novartis Saxagliptin Approved by FDA;?led in EU Bristol-Myers Squibb/
AstraZeneca Sitagliptin Approved by FDA;approved
in EU
Merck
This difference suggests that these in vitro substrates will not prove to be the biologically relevant substrates of DPP-8and DPP-9,and that the most readily hydrolysed DPP-8and DPP-9substrates are yet to be discovered.Whereas DPP-4can access chemokines extracellularly,the intracellular location of DPP-8and DPP-9makes it unclear whether DPP-8or DPP-9makes physical contact with incretin hormones, chemokines or substance P in vivo[25].Thus the physiological relevance of most substrate cleavage in the DPP family is unclear.Such uncertainty concerning the biological importance of substrate discovery applies to most proteases because substrates have often been identi?ed only by in vitro assay and substrates are generally inactivated by two or more proteases.
Elucidating the effects of DPP-8or DPP-9inhibition is dif?cult because few useful reagents are available. There are no speci?c substrates,fully selective inhibitors or gene-knockout mice for either enzyme.Therefore comparisons between selective and less selective DPP-4inhibitors or DPP-8/DPP-9-selective inhibitors have not been made.The availability of compounds selective for DPP-8and DPP-9would be useful.Furthermore,in contrast with DPP-4,which is extracellular,DPP-8and DPP-9are cytosolic,so for each inhibitor compound the potential effects on DPP-8and DPP-9depend upon the intracellular concentration achieved.Moreover, unlike DPP-4and FAP,DPP-8and DPP-9activity diminishes in mildly oxidizing conditions[32]and so may be in?uenced by intracellular redox state.
The mechanism of toxicity observed in a preclinical study of DPP inhibitors is unclear[38].Evidence indicating that DPP-8and DPP-9are not involved in such toxicity is summarized below.Important to note is that small differences in compound chemistry can produce signi?cant differences in biological effects.
EXTRA-ENZYMATIC ACTIVITY IN THE DPP-4 FAMILY
Determining the functions of the DPP family is complicated further by the fact that DPP-4,FAP,DPP-8 and DPP-9possess extra-enzymatic activities,which are not in?uenced by enzyme inhibitors and are crucial for DPP-4action in immunity.Mutation of active-site residues has shown that enzyme activity is not required for the observed effects of DPP-4,DPP-8,DPP-9or FAP overexpression on cell adhesion,migration,proliferation and apoptosis in epithelial and hepatic stellate cell lines[39,40].Melanoma and lung cancer cells exhibit similar effects when DPP-4is overexpressed,including increased apoptosis and inhibition of cell migration and anchorage-independent growth,whether transfected with wild-type or enzyme-negative mutant DPP-4 [41,42].The DPP-4-mediated effect on cell adhesion involves p38MAPK(mitogen-activated protein kinase) dephosphorylation andβ1-integrin[43].Interestingly, DPP-9overexpression causes cells to produce less of the extracellular matrix-interacting molecule DDR1 (discoidin domain receptor family1),a receptor tyrosine kinase activated by collagen binding[40].DDR1is an integrin-independent cell adhesion molecule.In vivo
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evidence supporting the role of extra-enzymatic rather than enzymatic activity in these processes is primarily derived from experiments comparing nude mice injected with melanoma cells stably expressing wild-type DPP-4 or mutant DPP-4.No differences in tumour progression were observed[44].
Moreover,DPP-4has been shown to interact with other proteins,including adenosine deaminase, caveolin-1,plasminogen-3ε,glypican-3and?bronectin type III[17].These interactions do not interfere with the catalytic function of DPP-4as their sites of interaction are or very likely to be located on the lower outer surface of the DPP-4protein,distant from the catalytic pocket located on the inside surface of the enzyme[7,45].
Thus DPP-4extra-enzymatic functions,such as protein–protein interactions,are crucial in these biological roles of the DPP-4family enzymes.Directly studying extra-enzymatic functions by blocking protein–protein interactions of DPP-4and its relatives would be interesting,but such reagents are unavailable.
INTERPRETING ANIMAL TOXICITY DATA
A preclinical study[38]assessing toxicities in rodents and dogs treated with inhibitors of DPP-8and DPP-9(allo-isoleucyl thiazolidine and threo-isoleucyl thiazolidine),a selective DPP-4inhibitor and non-selective DPP inhibit-ors found that selective DPP-4inhibition has no adverse toxicity effects in rodents and dogs,but the non-selective DPP inhibition resulted in severe toxicities and,in some cases,mortality.Toxicity-related outcomes included death,alopecia,thrombocytopenia,reticulocytopenia and splenomegaly in rodents given100mg·kg?1of body weight·day?1for up to2weeks.Similar toxicities were observed when using a DPP-8and DPP-9inhibitor at similar doses in rodents and10mg/kg of body weight in dogs.The DPP-8/DPP-9inhibitors produced similar toxicities in Dpp-4-de?cient and wild-type mice,thus the observed toxicities were not due to DPP-4inhibition[38].
The suggestion that DPP-8and DPP-9inhibition produces toxicity in preclinical species is principally disputed by recent results showing that high doses of vildagliptin,producing nearly complete in vivo inhibition of DPP-8and DPP-9enzyme activity,yielded no toxicities in rodents[46].Vildagliptin is a selective DPP-4 inhibitor with modest DPP-8/DPP-9inhibitory activity, 200-fold selective against DPP-8and more than30-fold selective against DPP-9.In that study[46],the DPP-4inhibitor dose was up to1500mg·kg?1of body weight·day?1in mice and900mg·kg?1of body weight·day?1in rats for13weeks,resulting in plasma concentrations well above those that would produce24-h inhibition of both DPP-8and DPP-9.Although the initial observations were interpreted as indicating that inhibition of DPP-8and DPP-9is toxic in rodents and dogs[38],compounds associated with the toxicities were close structural peptidic analogues of each other,with shared stereochemistry of the unnatural(l-allo)form of isoleucine,and the observed toxicities could have been related to the common structural feature,completely independent of DPP-8/DPP-9inhibition[46].
Concordantly,an absence of gastrointestinal toxicity with DPP-8and DPP-9inhibition in dogs has been observed using a non-selective DPP inhibitor compound ‘G’[47].Compound‘G’was shown to be cell-permeant, thereby having access to DPP-8and DPP-9in the cytosol.The dose of600mg/kg of body weight in dogs caused compound‘G’to reach plasma levels1000-fold above the IC50for both DPP-8and DPP-9,and caused inhibition of DPP-8and DPP-9throughout the gastrointestinal tract and brain.In that study, the allo-isoleucyl isoindoline derivative that inhibits DPP-8and DPP-9again produced toxicities similar to those reported previously[38].However,compound ‘G’,despite inhibiting DPP-8/DPP-9in vivo far more than that allo-isoleucyl isoindoline derivative,was non-toxic[47].These?ndings strongly suggest that the report of toxicity associated with certain DPP inhibitor compounds relates to properties of those compounds rather than inhibition of DPP-4,DPP-8or DPP-9.
Additional preclinical assessment of potential clinical candidates is important to understand further the signi-?cance of DPP-4inhibitor selectivity,and the effects of DPP-8/DPP-9inhibition at pharmacologically relevant plasma concentrations.The serum concentrations of clinically available DPP-4inhibitors are unlikely to approach that of the DPP-8/DPP-9-selective inhibitors used in in vitro studies.
DPP-4-RELATED IMMUNE RESPONSES
DPP-4is also known as CD26,a cell-surface marker for T-cell activation that has a co-stimulatory role in T-cell activation.Several lines of evidence indicate that its DPP-4enzyme activity is not involved in CD26-mediated T-cell activation and proliferation[11].The most recent study has shown that T-cell-dependent antibody responses and cytotoxic T-cell responses are not affected when DPP-4is selectively inhibited in mice.Moreover, these immune responses are the same in Dpp-4-knockout and wild-type mice[51].Previous in vitro analyses concorded with that study.In transfected Jurkat cells,inactivating DPP-4by substitution of the catalytic serine with alanine residues has no effect on CD26-dependent T-cell activation[48].All of the DPP enzyme inhibitors that inhibit T-cell proliferation in vitro inhibit DPP-8and DPP-9in addition to,and often more than,DPP-4[38].The DPP-4-negative Fischer344rat strain has no defects in in vitro responses to mitogens or antigens[49].Moreover,suppression of in vitro responses
C The Authors Journal compilation C 2010Biochemical Society
Dipeptidyl peptidase-4inhibitor selectivity
39
to mitogens or Mycobacterium tuberculosis antigen by the non-selective DPP inhibitor Lys(Z[NO2])-thiazolidide, is equally effective in wild-type lymphocytes and cells from the DPP-4-negative Fischer344rat substrain[50], demonstrating that such effects do not relate to DPP-4. These results indicate that DPP-4proteolytic activity is not a prerequisite for the T-cell-activating or co-stimulating properties of DPP-4/CD26.
The suppression of in vitro T-cell proliferation by the non-selective DPP inhibitory pyrrolidides{e.g. Lys[Z(NO2)]-pyrrolidide}appears to be mediated by DPP-8and/or DPP-9,because these pyrrolidides are two to three logs more potent against DPP-8and DPP-9than DPP-4[38].In addition,the DPP-8/DPP-9-selective inhibitor compound(2S,3R)-2-(2-amino-3-methyl-1-oxopentan-1-yl)-1,3-dihydro-2H-isoindole hydrochloride,but not the DPP-4-selective inhibitor compound(2S)-2-[4-[[[[(2S)-1-[(3R)-3-amino-4-(2,5-di?uorophenyl)-1-oxobutyl]-2-pyrrolidinyl]carbonyl] amino]methyl]phenoxy]-3-methylbutanoic acid tri-?uoroacetate attenuates proliferation and IL-2(inter-leukin-2)release in in vitro human T-cell activation[38]. These are the central?ndings illustrating that DPP-4 catalytic activity is not required for T-cell activation. Immunological effects observed previously with several DPP inhibitors in preclinical models may indirectly indicate a role for DPP-8and DPP-9enzyme activity in immune responses,but this question requires further investigation,including separating the roles of DPP-8 from DPP-9.
DPP-4INHIBITORS IN CLINICAL DEVELOPMENT
Among the three DPP-4inhibitors currently in clinical use,saxagliptin,sitagliptin and vildagliptin,or those in late-stage clinical development(Table3),no indication of DPP-8/DPP-9-related adverse events has been observed in respective extensive clinical development programmes. Although adverse preclinical?ndings observed in one study of DPP inhibition have been reported[38],the aforementioned lack of clinical adverse events is the most relevant information when considering the use of selective DPP-4inhibitors in the treatment of Type2diabetes.
DPP-4inhibitors are generally well tolerated.In monotherapy trials,the overall incidence of adverse effects with vildagliptin and sitagliptin has been similar between DPP-4inhibitor and comparator groups.The most common side effects reported in DPP-4inhibitor clinical trials are nasopharyngitis and headache.A recent meta-analysis of sitagliptin and vildagliptin reported a small increased risk of nasopharyngitis{6.4%for DPP-4inhibitor compared with6.1%for comparator; risk ratio,1.2[95%CI(con?dence interval),1.0–1.4]} and headache[5.1%for DPP-4inhibitor compared with3.9%for comparator;risk ratio,1.4(95%CI, 1.1–1.7)][3].Although not considered a class effect, rare cases of mild hepatic dysfunction have been reported with vildagliptin leading to a request to moni-tor liver enzyme in patients treated with vildagliptin (see European Public Assessment Report at http://www. emea.europa.eu/humandocs/Humans/EPAR/galvus/ galvus.htm)and very rare serious hypersensitivity reactions,including Stevens–Johnson syndrome,have occurred with sitagliptin(see https://www.doczj.com/doc/367572578.html,/ sitagliptin/januvia/hcp/januvia/safety_profile/safety _pro?le.jsp?WT.svl=2).In a pooled?ve-study analysis up to week24,hypersensitivity-related events were recorded in1.5%of patients who received2.5-and 5-mg doses of saxagliptin(see http://packageinserts.bms. com/pi/pi_onglyza.pdf).These are not exceptional issues in a new drug class.
CONCLUSIONS
The understanding that DPP-4is the major inactivator of GLP-1prompted the clinical development and application of DPP-4inhibitors for the treatment of Type2diabetes to improve glycaemic control by increasing GLP-1longevity.Clinical trials indicate that the selective DPP-4inhibitors alogliptin,saxagliptin, sitagliptin and vildagliptin are generally well tolerated, with the bene?ts of increases in active incretin hormones, less circulating glucagon and the possibility of preserved or enhancedβ-cell function.As the DPP-4family are ubiquitous serine proteases with numerous functions,the roles of DPP-4as well as its inhibitory effects continue to be studied extensively.Although DPP-4and the related enzymes DPP-8and DPP-9form a family of proline-targeted serine proteases and have a close structural similarity,they also have a number of dissimilarities. One notable dissimilarity is that DPP-4is extracellular, whereas DPP-8and DPP-9are present exclusively in the cytoplasm.In addition,in vitro and in vivo models have demonstrated that the roles of DPP-4in the immune system are independent of the protease activity of DPP-4(GLP-1and GIP inactivation/metabolism).A single adverse preclinical study led to controversy concerning non-selective inhibition of DPP-4and the potential for adverse effects associated with inhibition of DPP-8and DPP-9.However,recent studies reviewed here indicate that enzyme inhibition of DPP-8and DPP-9probably lacks an adverse clinical consequence and that these observed toxicities were probably due to the non-enzymatic actions of these compounds.
ACKNOWLEDGEMENTS
We thank Ms Lingsi Lu for illustrative services.Technical and editorial assistance for this manuscript prior to
C The Authors Journal compilation C 2010Biochemical Society
40M.Kirby and
others
submission was provided by Diane Kwiatkoski,Ph.D. (Innovex Medical Communications).
FUNDING
M.D.G.was supported by the National Health and Medical Research Council of Australia[grant number 518228].
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Received30January2009/27May2009;accepted1June2009
Published on the Internet28September2009,doi:10.1042/CS20090047
C The Authors Journal compilation C 2010Biochemical Society
五．容斥原理问题 1．有100种赤贫.其中含钙的有68种,含铁的有43种,那么,同时含钙和铁的食品种类的最大值和最小值分别是( ) A 43,25 B 32,25 C32,15 D 43,11 解：根据容斥原理最小值68+43-100＝11 最大值就是含铁的有43种 2．在多元智能大赛的决赛中只有三道题.已知:(1)某校25名学生参加竞赛,每个学生至少解出一道题;(2)在所有没有解出第一题的学生中,解出第二题的人数是 解出第三题的人数的2倍:(3)只解出第一题的学生比余下的学生中解出第一题的人数多1人;(4)只解出一道题的学生中,有一半没有解出第一题,那么只解出第二题的学生人数是( ) A，5 B，6 C，7 D，8 解：根据“每个人至少答出三题中的一道题”可知答题情况分为7类：只答第1题，只答第2题，只答第3题，只答第1、2题，只答第1、3题，只答2、3题，答1、2、3题。 分别设各类的人数为a1、a2、a3、a12、a13、a23、a123 由（1）知：a1+a2+a3+a12+a13+a23+a123＝25…① 由（2）知：a2+a23＝（a3+ a23）×2……② 由（3）知：a12+a13+a123＝a1－1……③ 由（4）知：a1＝a2+a3……④ 再由②得a23＝a2－a3×2……⑤ 再由③④得a12+a13+a123＝a2+a3－1⑥ 然后将④⑤⑥代入①中，整理得到 a2×4+a3＝26 由于a2、a3均表示人数，可以求出它们的整数解： 当a2＝6、5、4、3、2、1时，a3＝2、6、10、14、18、22 又根据a23＝a2－a3×2……⑤可知：a2>a3 因此，符合条件的只有a2＝6，a3＝2。 然后可以推出a1＝8，a12+a13+a123＝7，a23＝2，总人数＝8+6+2+7+2＝25，检验所有条件均符。 故只解出第二题的学生人数a2＝6人。 3．一次考试共有5道试题。做对第1、2、3、、4、5题的分别占参加考试人数的95%、80%、79%、74%、85%。如果做对三道或三道以上为合格，那么这次考试的合格率至少是多少？ 答案：及格率至少为71％。 假设一共有100人考试 100-95＝5 100-80＝20 100-79＝21 100-74＝26 100-85＝15 5+20+21+26+15＝87（表示5题中有1题做错的最多人数）
【导读】国家公务员考试网为您提供：2015国家公务员考试行测：数学运算-容斥原理和抽屉原理，欢迎加入国家公务员考试QQ群：242808680。更多信息请关注安徽人事考试网https://www.doczj.com/doc/367572578.html, 【推荐阅读】 2015国家公务员笔试辅导课程【面授+网校】 容斥原理和抽屉原理是国家公务员考试行测科目数学运算部分的“常客”，了解此两种原理不仅可以提高做题效率，还可以提高自己的运算能力，扫平所有此类计算题。中公教育专家在此进行详细解读。 一、容斥原理 在计数时，要保证无一重复，无一遗漏。为了使重叠部分不被重复计算，在不考虑重叠 的情况下，把包含于某内容中的所有对象的数目先计算出来，然后再把计数时重复计算的数 目排斥出去，使得计算的结果既无遗漏又无重复，这种计数的方法称为容斥原理。 1.容斥原理1——两个集合的容斥原理 如果被计数的事物有A、B两类，那么，先把A、B两个集合的元素个数相加，发现既是 A类又是B类的部分重复计算了一次，所以要减去。如图所示： 公式：A∪B=A+B-A∩B 总数=两个圆内的-重合部分的 【例1】一次期末考试，某班有15人数学得满分，有12人语文得满分，并且有4人语、 数都是满分，那么这个班至少有一门得满分的同学有多少人? 数学得满分人数→A，语文得满分人数→B，数学、语文都是满分人数→A∩B，至少有一 门得满分人数→A∪B。A∪B=15+12-4=23，共有23人至少有一门得满分。 2.容斥原理2——三个集合的容斥原理 如果被计数的事物有A、B、C三类，那么，将A、B、C三个集合的元素个数相加后发现 两两重叠的部分重复计算了1次，三个集合公共部分被重复计算了2次。 如图所示，灰色部分A∩B-A∩B∩C、B∩C-A∩B∩C、C∩A-A∩B∩C都被重复计算了1 次，黑色部分A∩B∩C被重复计算了2次，因此总数A∪B∪C=A+B+C-(A∩B-A∩B∩C)-(B∩ C-A∩B∩C)-(C∩A-A∩B∩C)-2A∩B∩C=A+B+C-A∩B-B∩C-C∩A+A∩B∩C。即得到： 公式：A∪B∪C=A+B+C-A∩B-B∩C-C∩A+A∩B∩C
第一章绪论 1、雷达的任务：测量目标的距离、方位、仰角、速度、形状、表面粗糙度、介电特性。 雷达是利用目标对电磁波的反射现象来发现目标并测定其位置。 当目标尺寸小于雷达分辨单元时，则可将其视为“点”目标，可对目标的距离和空间位置角度定位。目标不是一个点，可视为由多个散射点组成的，从而获得目标的尺寸和形状。采用不同的极化可以测定目标的对称性。 β任一目标P所在的位置在球坐标系中可用三个目标确定：目标斜距R，方位角α，仰角 在圆柱坐标系中表示为：水平距离D，方位角α，高度H 目标斜距的测量：测距的精度和分辨力力与发射信号的带宽有关，脉冲越窄，性能越好。目标角位置的测量：天线尺寸增加，波束变窄，测角精度和角分辨力会提高。 相对速度的测量:观测时间越长，速度测量精度越高。 目标尺寸和形状：比较目标对不同极化波的散射场，就可以提供目标形状不对称性的量度。 2、雷达的基本组成：发射机、天线、接收机、信号处理机、终端设备 3、雷达的工作频率：220MHZ-35GHZ。L波段代表以22cm为中心，1-2GHZ;S波段代表10cm，2-4GHZ；C波段代表5cm，4-8GHZ；X波段代表3cm，8-12GHZ；Ku代表2.2cm，12-18GHZ；Ka代表8mm，18-27GHZ。 第二章雷达发射机 1、雷达发射机的认为是为雷达系统提供一种满足特定要求的大功率发射信号，经过馈线和收发开关并由天线辐射到空间。 雷达发射机可分为脉冲调制发射机：单级振荡发射机、主振放大式发射机；连续波发射机。 2、单级振荡式发射机组成：大功率射频振荡器、脉冲调制器、电源 触发脉冲 脉冲调制器大功率射频振荡器收发开关 电源高压电源接收机 主要优点：结构简单，比较轻便，效率较高，成本低；缺点：频率稳定性差，难以产生复杂的波形，脉冲信号之间的相位不相等 3、主振放大式发射机：射频放大链、脉冲调制器、固态频率源、高压电源。射频放大链是发射机的核心，主要有前级放大器、中间射频功率放大器、输出射频功率放大器 射频输入前级放大器中间射频放大器输出射级放大器射频输出固态频率源脉冲调制器脉冲调制器 高压电源高压电源电源 脉冲调制器：软性开关调制器、刚性开关调制器、浮动板调制器 4、现代雷达对发射机的主要要求：发射全相参信号；具有很高的频域稳定度；能够产生复杂信号波形；适用于宽带的频率捷变雷达；全固态有源相控阵发射机 5、发射机的主要性能指标：
2015国考行测暑期每日一练数学运算：容斥原理和抽屉原理精讲 容斥原理和抽屉原理是国家公务员测试行测科目数学运算部分的“常客”，了解此两种原理不仅可以提高做题效率，还可以提高自己的运算能力，扫平所有此类计算题。中公教育专家在此进行详细解读。 一、容斥原理 在计数时，要保证无一重复，无一遗漏。为了使重叠部分不被重复计算，在不考虑重叠的情况下，把包含于某内容中的所有对象的数目先计算出来，然后再把计数时重复计算的数目排斥出去，使得计算的结果既无遗漏又无重复，这种计数的方法称为容斥原理。 1.容斥原理1——两个集合的容斥原理 如果被计数的事物有A、B两类，那么，先把A、B两个集合的元素个数相加，发现既是A类又是B类的部分重复计算了一次，所以要减去。如图所示： 公式：A∪B=A+B-A∩B 总数=两个圆内的-重合部分的 【例1】一次期末测试，某班有15人数学得满分，有12人语文得满分，并且有4人语、数都是满分，那么这个班至少有一门得满分的同学有多少人? 数学得满分人数→A，语文得满分人数→B，数学、语文都是满分人数→A∩B，至少有一门得满分人数→A∪B。A∪B=15+12-4=23，共有23人至少有一门得满分。 2.容斥原理2——三个集合的容斥原理 如果被计数的事物有A、B、C三类，那么，将A、B、C三个集合的元素个数相加后发现两两重叠的部分重复计算了1次，三个集合公共部分被重复计算了2次。 如图所示，灰色部分A∩B-A∩B∩C、B∩C-A∩B∩C、C∩A-A∩B∩C都被重复计算了1次，黑色部分A∩B∩C被重复计算了2次，因此总数A∪B∪C=A+B+C-(A∩B-A∩B∩C)-(B∩C -A∩B∩C)-(C∩A-A∩B∩C)-2A∩B∩C=A+B+C-A∩B-B∩C-C∩A+A∩B∩C。即得到：公式：A∪B∪C=A+B+C-A∩B-B∩C-C∩A+A∩B∩C
第一讲集合与容斥原理 数学是一门非常迷人的学科，久远的历史，勃勃的生机使她发展成为一棵枝叶茂盛的参天大树，人们不禁要问：这根大树到底扎根于何处？为了回答这个问题，在19世纪末，德国数学家康托系统地描绘了一个能够为全部数学提供基础的通用数学框架，他创立的这个学科一直是我们数学发展的根植地，这个学科就叫做集合论。它的概念与方法已经有效地渗透到所有的现代数学。可以认为，数学的所有内容都是在“集合”中讨论、生长的。 集合是一种基本数学语言、一种基本数学工具。它不仅是高中数学的第一课，而且是整个数学的基础。对集合的理解和掌握不能仅仅停留在高中数学起始课的水平上，而要随着数学学习的进程而不断深化，自觉使用集合语言(术语与符号)来表示各种数学名词，主动使用集合工具来表示各种数量关系。如用集合表示空间的线面及其关系，表示平面轨迹及其关系、表示方程(组)或不等式(组)的解、表示充要条件，描述排列组合，用集合的性质进行组合计数等。集合的划分反映了集合与子集之间的关系，这既是一类数学问题，也是数学中的解题策略——分类思想的基础，在近几年来的数学竞赛中经常出现，日益受到重视，本讲主要介绍有关的概念、结论以及处理集合、子集与划分问题的方法。 1．集合的概念 集合是一个不定义的概念，集合中的元素有三个特征： （1）确定性设A是一个给定的集合，a是某一具体对象，则a或者是A的元素，或者不是A的元素，两者必居其一，即a∈A与a?A仅有一种情况成立。 （2）互异性一个给定的集合中的元素是指互不相同的对象,即同一个集合中不应出现同一个元素. （3）无序性 2．集合的表示方法 主要有列举法、描述法、区间法、语言叙述法。常用数集如：R , ,应熟记。 N, Z Q 3．实数的子集与数轴上的点集之间的互相转换，有序实数对的集合与平面上的点集可以互相转换。对于方程、不等式的解集，要注意它们的几何意义。 4．子集、真子集及相等集 （1）A?? B A?B或A＝B； （2）A?B?A?B且A≠B； （3）A＝B?A?B且A?B。 5．一个n阶集合（即由个元素组成的集合）有n2个不同的子集，其中有n2－1个非空子集，也有n2－1个真子集。 6．集合的交、并、补运算 x∈} A B={A |且B x∈ x x∈} A B={A |或B x x∈ x?} A∈ {且A =| I x x 要掌握有关集合的几个运算律： （1）交换律A B＝B A，A B＝B A； （2）结合律A （B C）＝（A B） C， A （ B C）＝(A B) C；
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简单 1.在一米长的线段上任意点六个点。试证明：这六个点中至少有两个点的距离不大于20厘米。 2.在今年入学的一年级新生中有370多人是在同一年出生的。请你证明：他们中至少有两个人是在同一天出生的。 3.夏令营有400个小朋友参加，问：在这些小朋友中， (1)至少有多少人在同一天过生日？ (2)至少有多少人单独过生日？ (3)至少有多少人不单独过生日？ 4.学校举行开学典礼，要沿操场的400米跑道插40面彩旗。试证明：不管怎样插，至少有两面彩旗之间的距离不大于10米。 5.在100米的路段上植树，问：至少要植多少棵树，才能保证至少有两棵之间的距离小于10米？ 6.在一付扑克牌中，最少要拿多少张，才能保证四种花色都有？ 7.在一个口袋中有10个黑球、6个白球、4个红球。问：至少从中取出多少个球，才能保证其中有白球？ 8.口袋中有三种颜色的筷子各10根，问： (1)至少取多少根才能保证三种颜色都取到？ (2)至少取多少根才能保证有两双颜色不同的筷子？ (3)至少取多少根才能保证有两双颜色相同的筷子？ 9.据科学家测算，人类的头发每人不超过20万根。试证明：在一个人口超过20万的城市中，至少有两人的头发根数相同。 10.第四次人口普查表明，我国50岁以下的人口已经超过8亿。试证明：在我国至少有两人的出生时间相差不超过2秒钟。 11.证明：在任意的37人中，至少有四人的属相相同。
问：有源相阵控雷达和无源相阵控雷达的区别是什么？ h t p:/b s.t i e x u e.n e t/] [ 转自铁 血社区 答：区别就是无源是只有单个或者几个发射机子阵原只能接收，而有源是每个阵原都有完整的发射和接收单元！ 机载雷达经历了从机械扫描形式到相控阵电子扫描，再到最新的保形"智能蒙皮"天线的发展过程，电子扫描雷达在作战使用中的优势在哪里？未来的综合式射频（RF）传感器系统的总体特点和关键技术是哪些？您将从本文中得到启发 近50多年来，机载雷达不断采用新的技术成果，性能不断提高，其中重要的有全向多脉冲射频（MPRF）模式和高分辨率多普勒波束锐化（DBS）技术在雷达中的实际应用。目前，由于在信号处理和砷化镓微波集成电路领域技术的进步，雷达作为战术飞机主传感器的地位仍然会继续保持下去。 电子扫描技术的发展 雷达波束天线电子扫描应用的第一步是无源电子扫描阵列（ESA），其主要优点是实现了波束的无惯性扫描，在作战中有助于对辐射能量的控制。现役的此种类型的雷达有美国空军的B1-B和俄罗斯的米格-31装备的雷达，在研的有法国装备其"阵风"战斗机的RBE-2雷达。 有源ESA的出现是技术上的又一进步。它的每一个阵元中都有一个RF发射机和灵敏的RF接收机，在各个发射/接收（T/R）模块内都有一个功率放大器、一个低噪声放大器和用砷化镓技术制造的相位振幅控制装置。有源ESA雷达技术放弃了传统的中心式高功率发射机，除了具有无源相控阵雷达的优点外，还提高了能量的使用效率并具有自适应波束控制、强抗干扰能力和高可靠性等优点。 h t p:/b s.t i e x u e.n e t/] 血社区 [ 转自铁 西方国家第一代有源相控阵雷达系统接近定型的有美国装备F-22和日本装备 FS-X的雷达。英、法和德国共同研制的AMSAR项目也确定使用先进的有源相控阵雷达技术，为其后续的欧洲战斗机雷达的升级改装做准备。从今天的角度来看，雷达技术未来的下一个发展方向是保形"智能蒙皮"阵列，它把有源ESA技术和多功能共用RF孔径结合了起来，在天线阵元的安排上，与飞机机身的结构巧妙地配合，实现宽波段和多功能。保形天线阵列有高性能的处理器并使用空-时自适应处理技术有效地抑制了外部的噪声、干扰和杂波并能以最优化的方式来探测所感兴趣的目标。虽然有许多相关的技术问题需要解决，但保形"智能蒙皮"技术并非是个不切实际的解决方案，预计在20～25年的时间内就可以达到实用阶段。 在10～15年内，对战术飞机射频传感器（包括雷达）未来所执行的任务来说，最迫切的需要是增加功能、提高性能，并且还要注重经济性和可维护性。美国的"宝石路"计划已经证明，航空电子系统通过采用通用模块、资源共享和传感器的空间重构（重构的设备包括雷达、电子战及通信-导航-识别等射频传感器）可以做到系统的造价和重量减小一半，而可靠性提高三倍。它所确立的综合模块化航空电子的设计原则已用于JSF战斗机的综合传感器系统（ISS）和多重综合式射频传感器工程的设计中，欧洲类似的用于未来战术飞机的综
I ．抽屉原则 10个苹果放入9个抽屉中，无论怎么放，一定有一个抽屉里放了2个或更多个苹果.这 个简单的事实就是抽屉原则.由德国数学家狄利克雷首先提出来的.因此，又称为狄利克雷原则. 将苹果换成信、鸽子或鞋，把抽屉换成信筒、鸽笼或鞋盒，这个原则又叫做信筒原则、 鸽笼原则或鞋盒原则.抽屉原则是离散数学中的一个重要原则，把它推广到一般情形就得到下面几种形式： 原则一：把m 个元素分成n 类（m >n ），不论怎么分，至少有一类中有两个元素. 原则二：把m 个元素分成n 类（m >n ） （1）当n |m 时，至少有一类中含有至少 n m 个元素； （2）当n |m 时，至少有一类中含有至少[n m ]+1个元素. 其中n m 表示n 是m 的约数，n m 表示n 不是m 的约数，[ n m ]表示不超过n m 的最大整数. 原则三：把1221+-+++n m m m 个元素分成n 类，则存在一个k ，使得第k 类至 少有k m 个元素. 原则四：把无穷多个元素分成有限类，则至少有一类包含无穷多个元素. 以上这些命题用反证法极易得到证明，这里从略. 一般来说，适合应用抽屉原则解决的数学问题具有如下特征：新给的元素具有任意性. 如10个苹果放入9个抽屉，可以随意地一个抽屉放几个，也可以让抽屉空着. 问题的结论是存在性命题，题目中常含有“至少有……”、“一定有……”、“不少于……”、“存在……”、“必然有……”等词语，其结论只要存在，不必确定，即不需要知道第几个抽屉放多少个苹果. 对一个具体的可以应用抽屉原则解决的数学问题还应搞清三个问题： （1）什么是“苹果”？ （2）什么是“抽屉”？ （3）苹果、抽屉各多少？ 用抽屉原则解题的本质是把所要讨论的问题利用抽屉原则缩小范围，使之在一个特定
包含与排除 例题1，(1)五年级一班参加体育兴趣小组的有30人，参加文艺兴趣小组的有25人，两项活动都参加的有13人，全班每人至少参加一项活动。问这个班有多少人？ (2)三年级一班参加合唱队的有40人，参加舞蹈队的有20人，既参加合唱队又参加舞蹈队的有14人。这两队都没有参加的有10人。请算一算，这个班共有多少人？ 1，学校文艺组每人至少会演奏一种乐器，已知会拉手风琴的有24人，会弹电子琴的有17人，其中两种乐器都会演奏的有8人。这个文艺组一共有多少人？ 2,某班在一次测验中有26人语文获优，有30人数学获优，其中语文、数学双优的有12人，另外还有8人语文、数学均未获优。这个班共有多少人？ 3，第一小组的同学们都在做两道数学思考题，做对第一题的有15人，做对第二题的有10人，两题都做对的有7人，两题都做错的有2人。第一小组共有多少人？ 例题2，(1)五年级一班有42人，参加体育兴趣小组的有30人，参加文艺兴趣小组的有25人，全班每人至少参加一项活动。问这个班两项活动都参加的有多少人？ (2)一个旅行社有36人，其中会英语的有24人，会法语的有18人，两样都不会的有4人。两样都会的有多少人？
(3)3,某班有36个同学在一项测试中，答对第一题的有25人，答对第二题的有23人，两题都答对的有15人。问多少个同学两题都答得不对？ 1，五年级有122名学生参加语文、数学考试，每人至少有一门功课取得优秀成绩。其中语文成绩优秀的有65人，数学优秀的有87人。语文、数学都优秀的有多少人？ 2，一个俱乐部有103人，其中会下中国象棋的有69人，会下国际象棋的有52人，这两种棋都不会下的有12人。问这两种棋都会下的有多少人？ 3，学校开展课外活动，共有250人参加。其中参加象棋组和乒乓球组的同学不同时活动，参加象棋组的有83人，参加乒乓球组的有86人，这两个小组都参加的有25人。问这250名同学中，象棋组、乒乓球组都不参加的有多少人？ 例题3，(1)四年级一班有54人，订阅《小学生优秀作文》和《数学大世界》两种读物的有13人，订《小学生优秀作文》的有45人，每人至少订一种读物，订《数学大世界》的有多少人？ (2)全班46名同学，仅会打乒乓球的有28人，会打乒乓球又会打羽毛球的有10人，不会打乒乓球又不会打羽毛球的有6人。仅会打羽毛球的有多少人？ 1，40人都在做加试的两道题，并且至少做对了其中的一题。已知做对第一题的有30人，做对第二题的有21人。只做对第一题的有多少人？
人教版初中《抽屉原理和容斥原理》竞赛专题复习含答案 抽屉原理和容斥原理 24.1 抽屉原理 24.1.1★在任意的61个人中，至少有6个人的属相相同． 解析 因为一共有12种属相，把它看作12个抽屉，61151612?? +=+=????，根据抽屉原理知， 至少有6个人的属相相同． 评注 抽屉原理又称鸽笼原理或狄里克雷原理．这一简单的思维方式在解题过程中却可以有很多颇具匠心的运用．抽屉原理常常结合几何、整除、数列和染色等问题出现．许多有关存在性的证明都可用它来解决． 抽屉原理1 如果把1n +件东西任意放入n 个抽屉，那么必定有一个抽屉里至少有两件东西． 抽屉原理2 如果把m 件东西任意放人n 个抽屉，那么必定有一个抽屉里至少有女件东西，这里 ,1,m m n n k m m n n ??? =? ??? +????? ?是的位不是的位当数时; 当数时. 其中[]x 表示不超过x 的最大整数 ，例如[]33=，[]4.94=，[]2.63-=-等等． 24.1.2★从2，4，6，…，30这15个偶数中任取9个数，证明：其中一定有两个数之和是34． 解析 把2，4，6，…，30这15个数分成如下8组（8个抽屉）； （2）（4，30），（6，28），（8，26），（10，24），（12，22），（14，20），（16，18）． 从2，4，6，…，30这15个数中任取9个数，即是从上面8组数中取出9个数．抽屉原理知，其中一定有两个数取自同一组，这两个数的和就是34． 24.1.3★★在1，2，3， …，100这100个正整数中任取11个数，证明其中一定有两个数的比值不超过 32 ； {}1，{2，3}，{4，5，6}，{7，8，9，10}， {11，12，…，16}，{17，18，…，25}， {26，27，…，39}，{40，41，…，60}． {61，62，…，91}，{92，93，…，100}． 从1，2，…，100中任取11个数，即是从上面10组中任取11个数，由抽屉原理知，其中 一定有两个数取自同一组，这两个数的比值不超过 32 ． 24.1.4★求证：任给五个整数，必能从中选出三个，使得它们的和能被3整除． 解析 任何数除以3所得余数只能是0、1、2，分别构造3个抽屉：{0}、{1}、{2}．（1）若这五个自然数除以3后所得余数分别分布在这3个抽屉中，从这三个抽屉中各取1个，其和必能被3整除．（2）若这5个余数分布在其中的两个抽屉中，根据抽屉原理，其中一个抽
高中数学抽屉原理容斥原理 在数学问题中有一类与“存在性”有关的问题，例如：“13个人中至少有两个人出生在相同月份”；“某校400名学生中，一定存在两名学生，他们在同一天过生日”；“2003个人任意分成200个小组，一定存在一组，其成员数不少于11”；“把[0，1]内的全部有理数放到100个集合中，一定存在一个集合，它里面有无限多个有理数”。这类存在性问题中，“存在”的含义是“至少有一个”。在解决这类问题时，只要求指明存在，一般并不需要指出哪一个，也不需要确定通过什么方式把这个存在的东西找出来。这类问题相对来说涉及到的运算较少，依据的理论也不复杂，我们把这些理论称之为“抽屉原理”。 “抽屉原理”最先是由19世纪的德国数学家迪里赫莱（Dirichlet）运用于解决数学问题的，所以又称“迪里赫莱原理”，也有称“鸽巢原理”的。这个原理可以简单地叙述为“把10个苹果，任意分放在9个抽屉里，则至少有一个抽屉里含有两个或两个以上的苹果”。这个道理是非常明显的，但应用它却可以解决许多有趣的问题，并且常常得到一些令人惊异的结果。抽屉原理是国际国内各级各类数学竞赛中的重要内容，本讲就来学习它的有关知识及其应用。 （一）抽屉原理的基本形式 定理1、如果把n+1个元素分成n个集合，那么不管怎么分，都存在一
个集合，其中至少有两个元素。 证明：（用反证法）若不存在至少有两个元素的集合，则每个集合至多1个元素，从而n个集合至多有n个元素，此与共有n+1个元素矛盾，故命题成立。 在定理1的叙述中，可以把“元素”改为“物件”，把“集合”改成“抽屉”，抽屉原理正是由此得名。 同样，可以把“元素”改成“鸽子”，把“分成n个集合”改成“飞进n个鸽笼中”。“鸽笼原理”由此得名。 例题讲解 1．已知在边长为1的等边三角形内（包括边界）有任意五个点（图1）。证明：至少有两个点之间的距离不大于 2．从1-100的自然数中，任意取出51个数，证明其中一定有两个数，它们中的一个是另一个的整数倍。 3．从前25个自然数中任意取出7个数，证明：取出的数中一定有两个数，这两个数中大数不超过小数的1.5倍。 4．已给一个由10个互不相等的两位十进制正整数组成的集合。求证：这个集合必有两个无公共元素的子集合，各子集合中各数之和相等。 5．在坐标平面上任取五个整点（该点的横纵坐标都取整数），证明：其中一定存在两个整点，它们的连线中点仍是整点。 6．在任意给出的100个整数中，都可以找出若干个数来（可以是一个数），它们的和可被100整除。 7．17名科学家中每两名科学家都和其他科学家通信，在他们通信时，只讨论三个题目，而且任意两名科学家通信时只讨论一个题目，证明：其中至少有三名科学家，他们相互通信时讨论的是同一个题目。
毕业论文（设计） 相控阵雷达的发射和接收机制分析 学生姓名：杨雨杭 指导教师：姜国兴（副教授） 合作指导教师： 专业名称：通信工程 所在学院：信息工程学院 2013年5月
目录 摘要 (4) Abstract (5) 第一章前言 (6) 1.1 研究目的和意义 (6) 1.2 国内外研究现状 (6) 1.3 研究内容和方法 (6) 第二章雷达原理 (8) 2.1 相控阵雷达的原理 (8) 2.2 相控阵雷达的特点 (9) 2.3 相控阵雷达的分类 (9) 第三章相控阵天线的分析 (11) 3.1 相控阵天线的简介及应用 (11) 3.2 相控阵天线的基本原理 (11) 3.3 相控阵基本特性 (17) 3.4 相控阵天线馈电 (21) 3.5 多波束阵列天线 (21) 第四章雷达发射和接收机制分析 (23) 4.1 雷达发射机制分析 (23) 4.2固态发射机 (25) 4.3 脉冲调制器 (26) 4.4 雷达发射机的主要质量指标 (26) 4.5雷达接收机制分析 (28) 4.6 接收机工作的考虑因素 (30) 4.7 接收机前端 (33) 4.8本振 (33) 4.9增益控制放大器 (37) 4.10 滤波 (38) 4.11 雷达接收机的主要质量指标 (39) 第五章结论 (41) 致谢 (42)
参考文献 (43)
摘要 在当代，雷达的应用越来越广泛，从事雷达研究和开发的人也越来越多。本论文对雷达的工作原理进行了分析，便于帮助大家了解掌握雷达的基本信息。 本论文第一章主要讲述了研究相控阵雷达的意义，目前国内外此领域的发展现状等。第二章介绍了相控阵雷达的原理、分类、和优缺点。第三章着重分析相控阵天线的特点，与其他天线的比较，以及相控阵天线的原理、算法等。第四章具体阐述了雷达的发射机和接收机，分别讨论他们的各个组成部分，技术指标，工作原理等。最后对于全篇进行了总结，对未来的发展进行了展望。 关键字：相控阵雷达，发射机，接收机
相参技术 相参雷达是指雷达系统的发射信号、本振电压、相参震荡电压和定时器的触发脉冲均由同一基准信号提供，使得这些信号之间可以保持确定的相位关系，同时接收的回波信号也可以提取信号的相位信息。 相参技术对主振源信号具有极高的频率稳定度要求和频谱纯度，对天线性能，信号处理器等都具有很高的要求。 相同频率，不同相位的信号叠加效果 移相器
移相器的作用是将信号的相位移动一个角度，相位和频率保持稳定的对应关系是移相器的一个重要特性。 铁氧体移相器 铁氧体移相器的基本原理是利用外加直流磁场改变波导内铁氧体的导磁系数，从而改变电磁波的相速，得到不同的相移量。铁氧体移相器的主要优点是承受功率较高，插入损耗较小，带宽较宽。其缺点是所需激励功率比PIN管移相器大，开关时间在微秒(us)量级。 半导体PIN二极管 PIN二极管开关从“开”到“关”或者相反动作的起始状态达到稳定状态的时间称为开关时间。以半导体PIN二极管作为开关器件的数字式移相器相位转换时间可以达到纳秒(ns)量级。
GaAs FET GaAs FET开关是数控移相器的主要构成元素，它作为一个三端器件，可以通过对栅偏置电压的控制来改变源漏间电阻，从而实现开关动作，转换时间也在纳秒(ns)量级。 相控阵雷达原理 有了信号叠加的原理和移相器，相控阵雷达原理就好理解了，其基本思想：通过移相器改变每个辐射元件发射信号的相位，以提供相长/相消干涉，从而实现波束的电子扫描，在期望的方向上形成窄波束，雷达天线不需要机械转动。 电子扫描阵列很好的解决了机械雷达的机械惯性和扫描需要时间长等问题，实现了波束指向的无惯性快速扫描，为任务的灵活敏捷性创造了很好的条件。
容斥原理和抽屉原理 第一课时 教学内容：容斥原理和抽屉原理 教学目标： 本节课是在学生已学过两个基本原理和排列组合基础知识后，对学生提出的较高要求。根据数学学科的特点、学生身心发展的合理需要，本节课从知识、方法、能力和发展性等层面确定了相应的教学目标。 教学重点：容斥原理作为解决计数问题的重要方法成为本节课教学重点； 教学难点：而容斥原理由一般到特殊的归纳和推广是本节课的教学难点。 教学方法的选择： 本节课运用“问题解决”课堂教学模式，采用探究、讨论的教学方法。通过问题激发学生求知欲，使学生主动参与数学实践活动，以独立思考和相互交流的形式，在教师的指导下发现、分析和解决问题，总结规律，培养积极探索的科学精神。 教学手段的利用： 采用多媒体技术，目的在于通过大容量信息的呈现和生动形象的演示，提高学生学习兴趣、激活学生思维、加深理解。 学法指导： 学法指导的目标：(1)指导学生对一系列问题进行化归，找到解决问题的方法。(2)通过对学生发言的点评，规范语言表达，指导学生进行交流和讨论。 教学过程： |一、脑筋急转弯激趣，导入新课 师：同学们，喜欢脑筋急转弯吗？老师出个脑筋急转弯考考你
们？ 脑筋急转弯：一张照片上有两对父子，数数却只有三个人,为什么？ 学：因为多数了一个人，爷爷和爸爸，爸爸和儿子，爸爸多数了，所以，是2+2-1=3（人） 二、讲授新课 师：同学们，你们知道什么容斥原理。 学：不知道。 师：在计数时，必须注意无一重复，无一遗漏。为了使重叠部分不被重复计算，人们研究出一种新的计数方法，这种方法的基本思想是：先不考虑重叠的情况，把包含于某内容中的所有对象的数目先计算出来，然后再把计数时重复计算的数目排斥出去，使得计算的结果既无遗漏又无重复，这种计数的方法称为容斥原理。 师：就像是我们看到的图片一样，把重复的数目排斥出去。你们知道了吗？ 学：知道了 师：下面让我们实际挑战吧 三：出示例1 例1:从1到20中2或3的倍数的个数共有（）个。 师：同学们，我们想知道从1到20中2或3的倍数的个数共有多少个？我们应该怎么来做这题？ 学：我们可以先把2的倍数数出来，在再把3 的倍数数出来 师：那我们现在来数2的倍数？ 学：2的倍数是：2，4，6，8，10，12，14，16，18，20。一共有10个。 师：那么3的倍数又有多少个？
相控阵天线的基本原理介绍 相控阵天线是目前卫星移动通信系统中最重要的一种天线形式，由三个部分组成：天线阵、馈电网络和波束控制器。基本原理是微处理器接收到包含通信方向的控制信息后，根据控制软件提供的算法计算出各个移相器的相移量，然后通过天线控制器来控制馈电网络完成移相过程。由于移相能够补偿同一信号到达各个不同阵元而产生的时间差，所以此时天线阵的输出同相叠加达到最大。一旦信号方向发生变化，只要通过调整移相器的相移量就可使天线阵波束的最大指向做相应的变化，从而实现波束扫描和跟踪。相控阵天线有相控扫描线天线阵和平面相控阵天线。图一 图一 N单元相阵 远区观察点P处的总场强可以是认为线阵中N个单元在P点产生的辐 射场强叠加：
图二线性相控阵天线 这一天线阵的方向图函数为： 图三平面相控阵天线 相控阵在快速跟踪雷达、测相等领域得到广泛的应用，它可以使主瓣指向随着通信的需要而不断地调整。相控阵为主瓣最大值方向或方向图形主要由单位激励电流的相对来控制天线阵。通过控制阵列天线中辐射单元的馈电相位改变方向图形状的天线。控制相位可以改变
天线方向图最大值的指向，以达到波速扫描的目的。在特殊情况下，也可以控制副瓣电平、最小值位置和整个方向图的形状。用机械方法旋转天线时，惯性大、速度慢，相控阵天线克服了这已缺点，波速的扫描高。它的馈电相一般用电子计算机控制，相位变化速度快，即天线方向图最大值指向或其他参数的变化迅速。这是相控阵天线的最大特点。 一般相控阵天线应对每一辐射单元的相位进行控制。为了节省移相器和简化控制线路，有时几个辐射单元共用一个移相器。相控阵天线的关键器件是移相器和天线辐射单元。移相器分连续式移相器和数字式移相器两种。连续式移相器的移相值可在0°～360°范围内连续变化，数字式移相器的移相值是离散的，只能是360×(1/2)^n的整数倍，移相器应保证在一定的频率范围内获得所需要的移相值。天线辐射单元的设计应使一定移相范围内和一定频率范围内的输入阻抗的变化尽可能小，以保证发射机正常工作，防止由于射频信号的多次反射而出现寄生副瓣和方向图中出现凹点的现象。相控阵天线的馈电方式分传输线馈电和空间馈电两种。在传输线馈电方式下，射频能量通过波导、同轴线和微带线等微波传输线馈给辐射单元。在空间馈电方式下，发射机产生的射频能量通过辐射装置辐射至自由空间，传输一段距离后由一个接收阵接收，接收阵的每个单元或一组单元所接收到的信号，经过移相器移相后再馈给发射阵的发射单元并辐射出去。 相控阵天线阵列本身的设计主要是幅度、相位分布设计和单元阻
相控阵雷达简介 第一部分：引言 论坛上朋友们对相控阵雷达很感兴趣，而且对美军的有源相控阵雷达表示出近乎崇拜的热情，总是哀叹我们为什么没有这么神气的雷达。但是在很多朋友的帖子中，都表现出我们对相控阵雷达的概念不是很清楚，甚至有的雷达专业的网友有时也有一些似是而非的说法。 其实要正确的了解雷达中的很多基本概念，并不是很容易的事情，要能给别人讲清楚，更需要实际的工作经验。碰巧我参加过相控阵雷达研制，虽然做的工作是边边角角的，但是想结合自己的体会和一些专业书上的概念，尽可能把我认为正确的概念介绍给各位朋友。 第二部分：相控阵技术综述 相控阵技术是一种通过控制阵列天线的各个单元的相位和幅度以便形成在空间满足一定分布特性的波束，并且能够改变其扫描角度（指向）的技术。这种技术目前一般都是用计算机控制波束的形成和扫描，因此最大和好处是可以实现一些传统天线没有的优势，即：形状、指向和波束的个数无惯性的改变。这里解释一下什么是波束，波束实际上是一个形象的说法，在天线和传播技术领域，我们经常讲某个天线发射的（或者接收的）波束是“笔型波束”、“扇行波束”等等之类的，并不是说在空间存在这样的一个笔形或者扇形的东西，而是说当这个天线发射信号时（或者接受信号时）它在不同的方向信号放大倍数是不同的（或者对接收在不同空间到达方向的信号放大倍数不同），有的方向倍数大（叫增益），有的方向小，就形成了一个增益和方向的关系曲线，形象的说，就是一个“笔形的波束”或者“扇形波束”。需要说明的是，所有的天线都有波束的概念，而且接收的时候和发射的时候可以是不同的。相控阵的天线通过电控的单元相位改变，使波束指向、形状、个数等可以很快的改变，这是它根本的优势。还有一个顺便可以提到的问题，就是雷达干扰和抗干扰问题。在雷达对抗领域，经常提到一个旁瓣干扰的概念，这个又是一个和波束概念有关系的。一般在天线增益最大的方向附近是天线的主波瓣，在这个方向附近之外，天线增益下降很快，但是
第一章 相控阵雷达系发射信号的设计与分析 1.1 雷达工作原理 雷达是Radar （RAdio Detection And Ranging ）的音译词，意为“无线电检测和测距”，即利用无线电波来检测目标并测定目标的位置，这也是雷达设备在最初阶段的功能。典型的雷达系统如图1.1，它主要由发射机，天线，接收机，数据处理，定时控制，显示等设备组成。利用雷达可以获知目标的有无，目标斜距，目标角位置，目标相对速度等。现代高分辨雷达扩展了原始雷达概念，使它具有对运动目标(飞机，导弹等)和区域目标(地面等)成像和识别的能力。雷达的应用越来越广泛。 图1.1：简单脉冲雷达系统框图 雷达发射机的任务是产生符合要求的雷达波形（Radar Waveform ），然后经馈线和收发开关由发射天线辐射出去，遇到目标后，电磁波一部分反射，经接收天线和收发开关由接收机接收，对雷达回波信号做适当的处理就可以获知目标的相关信息。 假设理想点目标与雷达的相对距离为R ，为了探测这个目标，雷达发射信号 ()s t ,电磁波以光速C 向四周传播，经过时间R C 后电磁波到达目标，照射到目标上的电磁波可写成：()R s t C - 。电磁波与目标相互作用，一部分电磁波被目标散射，被反射的电磁波为()R s t C σ?-，其中σ为目标的雷达散射截面（Radar Cross Section ,简称RCS ），反映目标对电磁波的散射能力。再经过时间R 后，被雷 达接收天线接收的信号为(2)R s t C σ?-。 如果将雷达天线和目标看作一个系统，便得到如图1.2的等效，而且这是一
个LTI （线性时不变）系统。 图1.2：雷达等效于LTI 系统 等效LTI 系统的冲击响应可写成: 1 ()()M i i i h t t σδτ==-∑ (1.1) M 表示目标的个数，i σ是目标散射特性，i τ是光速在雷达与目标之间往返一次的时间， 2i i R c τ= (1.2) 式中，i R 为第i 个目标与雷达的相对距离。 雷达发射信号()s t 经过该LTI 系统，得输出信号(即雷达的回波信号)()r s t ： 1 1 ()()*()()*()()M M r i i i i i i s t s t h t s t t s t σδτστ====-=-∑∑ (1.3) 那么，怎样从雷达回波信号()r s t 提取出表征目标特性的i τ(表征相对距离)和 i σ(表征目标反射特性)呢？常用的方法是让()r s t 通过雷达发射信号()s t 的匹配 滤波器，如图1.3。 图1.3：雷达回波信号处理 ()s t 的匹配滤波器()r h t 为： *()()r h t s t =- (1.4) 于是， *()()*()()*()*()o r r s t s t h t s t s t h t ==- （1.5） 对上式进行傅立叶变换：
初中数学抽屉原理与容斥原理 有人说：“13个人中至少有两个人出生在相同月份”；又说：“某校一个年级的400名学生中，一定存在两名学生，他们在同一天过生日”，你认为他的说法对吗？你能说明为什么对或为什么不对吗？ 1947年匈牙利全国数学竞赛有一道这样的试题：“证明：任何六个人中，一定可以找到三个互相认识的人，或者三个互不认识的人。”这道题看起来与数学没有多大关系，似乎无法用数学知识解决。但解决时并不要用到多少高深知识，立即引起了许多数学爱好者的关注和兴趣。以上问题就是数学中的一类与“存在性”有关的问题。 解决以上这几个问题，要用到数学中的抽屉原理。 我们很容易理解这样一个事实：把3只苹果放到两个抽屉中，肯定有一个抽屉中有2只或2只以上的苹果。用数学语言表达这一事实，就是：将n+1个元素放入n 个集合内，则一定有一个集合内有两个或两个以上的元素（n 为正整数）。这就是抽屉原理，也称为“鸽笼（巢）”原理。这一原理最先是由德国数学家狄里克雷明确提出来的，因此，称之为狄里克雷原理。 抽屉原理还有另外的常用形式： 抽屉原理2：把m 个元素任意放入n n m ()<个集合里，则一定有一个集合里至少有k 个元素，其中： k m n n m m n n m =????? ?+???????，（当能整除时）（当不能整除时）1. m n m n m n ???????????? 表示不大于的最大整数，亦即的整数部分。 抽屉原理3：把无穷多个元素放入有限个集合里，则一定有一个集合里含有无穷多个元素。 现在你能肯定前面的两种说法是正确的吗？你能说明这两种说法是正确的吗？ 利用抽屉原理，可以解决一些相当复杂甚至感到无从下手的问题，抽屉原理也是解决存在性问题的常用方法。 例1. 在1，4，7，10，…，100中任选20个数，其中至少有不同的两对数，其和等于104。 分析：解这道题，可以考虑先将4与100，7与97，49与55……，这些和等于104的两个数组成一组，构成16个抽屉，剩下1和52再构成2个抽屉，这样，即使20个数中取到了1和52，剩下的18个数还必须至少有两个数取自前面16个抽屉中的两个抽屉，从而有不同的两组数，其和等于104；如果取不到1和52，或1和52不全取到，那么和等于104的数组将多于两组。 解：1，4，7，10，……，100中共有34个数，将其分成{4，100}，{7，97}，……，{49，55}，{1}，{52}共18个抽屉，从这18个抽屉中任取20个数，若取到1和52，则剩下的18个数取自前16个抽屉，至少有4个数取自某两个抽屉中，结论成立；若不全取1和52，则有多于18个数取自前16个抽屉，结论亦成立。 试一试：从2，5，8，11，……，101中任取20个数，其中必有两对数，它们的和为106。