01799nam--2200481---450-99000238044020331620090604154556.03-406-45683-9vol. 13-406-45751-7vol. 23-406-31421-Xvol. 3000238044USA01000238044(ALEPH)000238044USA0100023804420050126g19999999km-y0itay0103----bagerDE||||||||001yyVerwaltungsrechtein Studienbuchbegrundet von Hans J. Wolfffortgefuhrt von Otto Bachofneubearb. von Rolf StoberMunchenC.H. Beck1999-v.23 cmJuristische Kurz-Lehrbucher<Bd. 1>. - 1999. - 11., neubearb. Auflage. - LXXXIII, 710 p. ; <Bd. 2>. - 2000. - 6., neubearb. Auflage. - XC, 771 p. ; <Bd. 3>. - 2004. - 5., neubearb. Auflage. - L, 938 p.2001Juristische Kurz-LehrbucherDiritto amministrativoGermania342.4306WOLFF,Hans Julius459689BACHOF,OttoSTOBER,RolfITsalbcISBD990002380440203316XXIV.3.S 53/1 (IG XXI 703/1)42292 G.XXIV.3.S 53/1 (IG XXI)00135855XXIV.3.S 53/2 (IG XXI 703/2)42297 G.XXIV.3.S 53/2 (IG XXI)00135880XXIV.3.S 53/3 (IG XXI 703/3)42295 G.XXIV.3.S 53/3 (IG XXI)00135870BKGIUMARIASEN9020050126USA011631MARIASEN9020050126USA011636RSIAV59020090604USA011530RSIAV59020090604USA011531RSIAV59020090604USA011545Verwaltungsrecht1064348UNISA05887nam 2200673Ia 450 991046188790332120220126212021.00-88385-955-6(CKB)2670000000205163(EBL)3330416(OCoLC)923220108(SSID)ssj0000577632(PQKBManifestationID)11376743(PQKBTitleCode)TC0000577632(PQKBWorkID)10562363(PQKB)11199582(UkCbUP)CR9780883859551(MiAaPQ)EBC3330416(Au-PeEL)EBL3330416(CaPaEBR)ebr10729387(OCoLC)929120334(EXLCZ)99267000000020516320001102d2000 uy 0engur|n|---|||||txtccrThe geometry of numbers[electronic resource] /C.D. Olds, Anneli Lax, Giuliana P. DavidoffWashington, DC Mathematical Association of Americac20001 online resource (193 p.)The Anneli Lax new mathematical library ;v. 41Description based upon print version of record.0-88385-643-3 Includes bibliographical references and index.""Cover ""; ""Title Page""; ""Contents""; ""Preface""; ""Part I Lattice Points and Number Theory""; ""1 Lattice Points and Straight Lines""; ""1.1 The Fundamental Lattice""; ""1.2 Lines in Lattice Systems""; ""1.3 Lines with Rational Slope""; ""1.4 Lines with Irrational Slope""; ""1.5 Broadest Paths without Lattice Points""; ""1.6 Rectangles on Paths without Lattice Points""; ""Problem Set for Chapter 1""; ""References""; ""2 Counting Lattice Points""; ""2.1 The Greatest Integer Function, [x ]""; ""Problem Set for Section 2.1""; ""2.2 Positive Integral Solutions of ax + by = n""""Problem Set for Section 2.2""""2.3 Lattice Points inside a Triangle""; ""Problem Set for Section 2.3""; ""References""; ""3 Lattice Points and the Area of Polygons""; ""3.1 Points and Polygons""; ""3.2 Pick's Theorem""; ""Problem Set for Section 3.2""; ""3.3 A Lattice Point Covering Theorem for Rectangles""; ""Problem Set for Section 3.3""; ""References""; ""4 Lattice Points in Circles""; ""4.1 How Many Lattice Points Are There?""; ""4.2 Sums of Two Squares""; ""4.3 Numbers Representable as a Sum of Two Squares""; ""Problem Set for Section 4.3""""4.4 Representations of Prime Numbers as Sums of TwoSquares""""4.5 A Formula for R(n)""; ""Problem Set for Section 4.5""; ""References""; ""Part II An Introduction to the Geometry of Numbers""; ""5 Minkowski's Fundamental Theorem""; ""5.1 Minkowski's Geometric Approach""; ""Problem Set for Section 5.1""; ""5.2 Minkowski M-Sets""; ""Problem Set for Section 5.2""; ""5.3 Minkowski's Fundamental Theorem""; ""Problem Set for Section 5.3""; ""5.4 (Optional) Minkowski's Theorem in n Dimensions""; ""References""; ""6 Applications of Minkowski's Theorems""; ""6.1 Approximating Real Numbers""""6.2 Minkowski's First Theorem""""Problem Set for Section 6.2""; ""6.3 Minkowski's Second Theorem""; ""Problem for Section 6.3""; ""6.4 Approximating Irrational Numbers""; ""6.5 Minkowski's Third Theorem""; ""6.6 Simultaneous Diophantine Approximations""; ""Reading Assignment for Chapter 6""; ""References""; ""7 Linear Transformations and Integral Lattices""; ""7.1 Linear Transformations""; ""Problem Set for Section 7.1""; ""7.2 The General Lattice""; ""7.3 Properties of the Fundamental Lattice""; ""Problem Set for Section 7.3""; ""7.4 Visible Points""""8 Geometric Interpretations of Quadratic Forms""""8.1 Quadratic Representation""; ""8.2 An Upper Bound for the Minimum Positive Value""; ""8.3 An Improved Upper Bound""; ""8.4 (Optional) Bounds for the Minima of Quadratic Formsin More Than Two Variables""; ""8.5 Approximating by Rational Numbers""; ""8.6 Sums of Four Squares""; ""References""; ""9 A New Principle in the Geometry of Numbers""; ""9.1 Blichfeldt's Theorem""; ""9.2 Proof of Blichfeldt's Theorem""; ""9.3 A Generalization of Blichfeldt's Theorem""; ""9.4 A Return to Minkowski's Theorem""""9.5 Applications of Blichfeldt's Theorem""The Geometry of Numbers presents a self-contained introduction to the geometry of numbers, beginning with easily understood questions about lattice-points on lines, circles, and inside simple polygons in the plane. Little mathematical expertise is required beyond an acquaintance with those objects and with some basic results in geometry. The reader moves gradually to theorems of Minkowski and others who succeeded him. On the way, he or she will see how this powerful approach gives improved approximations to irrational numbers by rationals, simplifies arguments on ways of representing integers as sums of squares, and provides a natural tool for attacking problems involving dense packings of spheres. An appendix by Peter Lax gives a lovely geometric proof of the fact that the Gaussian integers form a Euclidean domain, characterizing the Gaussian primes, and proving that unique factorization holds there. In the process, he provides yet another glimpse into the power of a geometric approach to number theoretic problems.Anneli Lax new mathematical library ;v. 41.Geometry of numbersNumber theoryElectronic books.Geometry of numbers.Number theory.512/.75Olds C. D(Carl Douglas),1912-1979.1074126Lax Anneli42255Davidoff Giuliana P622037MiAaPQMiAaPQMiAaPQBOOK9910461887903321The geometry of numbers2572438UNINA01161nam0 22002773i 450 VAN0010935420240806100739.472978-88-939107-9-820170522d2017 |0itac50 baitaIT|||| |||||+nemici del popoloCarlo Lanza, Luciano Minieri NapoliEditoriale scientifica201760 p.21 cm.001VAN001093432001 Cinema diritto società210 NapoliEditoriale scientifica2017-2022.10NapoliVANL000005LanzaCarloVANV007000208118MinieriLucianoVANV054960313910Editoriale scientifica <editore>VANV107979650ITSOL20260130RICAVAN00109354BIBLIOTECA DEL DIPARTIMENTO DI GIURISPRUDENZA00CONS VIII.Eo.863 10 00UBG1517 20170522 BIBLIOTECA DEL DIPARTIMENTO DI GIURISPRUDENZA00CONS VIII.Eo.863 10 00VS 109354 bis 20180703 +nemici del popolo1465960UNICAMPANIA