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1.

図書

図書
Wolfgang Lück
出版情報: Berlin ; Tokyo : Springer, c2002  xv, 595 p. ; 25 cm
シリーズ名: Ergebnisse der Mathematik und ihrer Grenzgebiete ; 3. Folge, v. 44
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2.

図書

図書
Derek Richards
出版情報: Cambridge ; New York : Cambridge University Press, c2002  xv, 862 p. ; 26 cm
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3.

図書

図書
George Greaves
出版情報: Berlin ; Tokyo : Springer, c2001  xii, 304 p. ; 24 cm
シリーズ名: Ergebnisse der Mathematik und ihrer Grenzgebiete ; 3. Folge, v. 43
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目次情報: 続きを見る
Introduction
The Structure of Sifting Arguments / 1:
The Sieves of Eratosthenes and Legendre / 1.1:
The Contribution of Eratosthenes / 1.1.1:
Legendre's Sieve / 1.1.2:
An Estimate for n(X) / 1.1.3:
The Distribution of Primes / 1.1.4:
Examples of Sifting Situations / 1.2:
Notations / 1.2.1:
The Integers in an Interval (Y - X, Y ) / 1.2.2:
Numbers Given by Polynomial Expressions / 1.2.3:
Arithmetic Progressions / 1.2.4:
Sums of Two Squares / 1.2.5:
Polynomials with Prime Arguments / 1.2.6:
A General Formulation of a Sifting Situation / 1.3:
The Basic Formulation / 1.3.1:
Legendre's Sieve in a General Setting / 1.3.2:
A Generalised Formulation / 1.3.3:
A Further Generalisation / 1.3.4:
Sifting Density / 1.3.5:
The Sifting Limit Β(k) / 1.3.6:
Composition of Sieves / 1.3.7:
Notes on Chapter 1 / 1.4:
Selberg's Upper Bound Method / 2:
The Sifting Apparatus / 2.1:
Selberg's Theorem / 2.1.1:
The Numbers (lambda)(d) / 2.1.2:
A Simple Application / 2.1.3:
General Estimates of G(x) and E(D, P) / 2.2:
An Estimate by Rankin's Device / 2.2.1:
Asymptotic Formulas / 2.2.2:
The Error Term / 2.2.3:
Applications / 2.3:
Prime Twins and Goldbach's Problem / 2.3.1:
Polynomial Sequences / 2.3.3:
Notes on Chapter 2 / 2.4:
Combinatorial Methods / 3:
The Construction of Combinatorial Sieves / 3.1:
Preliminary Discussion of Brun's Ideas / 3.1.1:
Fundamental Inequalities and Identities / 3.1.2:
Buchstab's Identity / 3.1.3:
The Combinatorial Sieve Lemma / 3.1.4:
Brun's Pure Sieve / 3.2:
Inequalities and Identities / 3.2.1:
The "Pure Sieve" Theorem / 3.2.2:
A Corollary / 3.2.3:
Prime Twins / 3.2.4:
A Modern Edition of Brun's Sieve / 3.3:
Rosser's Choice of X / 3.3.1:
A Technical Estimate / 3.3.2:
A Simplifying Approximation / 3.3.3:
A Combinatorial Sieve Theorem / 3.3.4:
Brun's Version of his Method / 3.3.5:
Brun's Choice of x / 3.4.1:
The Estimations / 3.4.2:
The Result / 3.4.3:
Notes on Chapter 3 / 3.5:
Rosser's Sieve / 4:
Approximations by Continuous Functions / 4.1:
The Recurrence Relations / 4.1.1:
Partial Summation / 4.1.2:
The Leading Terms / 4.1.3:
The Functions F and f / 4.2:
The Difference-Differential Equations / 4.2.1:
The Adjoint Equation and the Inner Product / 4.2.2:
Solutions of the Adjoint Equation / 4.2.3:
Particular Values of F(s) and f(s) / 4.2.4:
Asymptotic Analysis as k -> $(infinity$) / 4.2.5:
The Convergence Problem / 4.3:
The Auxiliary Functions / 4.3.1:
Adjoints and Inner Products / 4.3.2:
The Case k
A Sieve Theorem Following Rosser / 4.4:
The Case k >/= 1/2: a First Result / 4.4.1:
Theorem 1 when k
An Improved Version of Proposition 1 / 4.4.3:
A Two-Sided Estimate / 4.4.4:
Extremal Examples / 4.5:
The Linear Case / 4.5.1:
The Case k=1/2 / 4.5.2:
Notes on Chapter 4 / 4.6:
The Sieve with Weights / 5:
Simpler Weighting Devices / 5.1:
Logarithmic Weights / 5.1.1:
Modified Logarithmic Weights / 5.1.2:
Some Applications / 5.1.3:
More Elaborate Weighted Sieves / 5.2:
An Improved Weighting Device / 5.2.1:
Buchstab's Weights / 5.2.2:
A Weighted Sieve Following Rosser / 5.3:
Combining Sieving and Weighting / 5.3.1:
The Reduction Identities / 5.3.2:
An Identity for the Main Term / 5.3.3:
The Estimate for the Main Term / 5.3.4:
Notes on Chapter 5 / 5.4:
The Remainder Term in the Linear Sieve / 6:
The Bilinear Nature of Rosser's Construction / 6.1:
The Factorisation of x.d / 6.1.1:
Discretisations of Rosser's Sieve / 6.1.2:
Specification of Details / 6.1.3:
The Leading Contributions to the Main Term / 6.1.4:
The Remainder Term / 6.1.5:
Sifting Short Intervals / 6.2:
The Smoothed Formulation / 6.2.1:
The Remainder Sums / 6.2.2:
Trigonometrical Sums / 6.2.3:
Notes on Chapter 6 / 6.3:
Lower Bound Sieves when k > 1 / 7:
An Extension of Selberg's Upper Bound / 7.1:
The Integral Equation and the Function $(sigma$) (s) / 7.1.1:
The Estimation of G(s) / 7.1.2:
A Lower Bound Sieve via Buchstab's Identity / 7.2:
Buchstab's Iterations / 7.2.1:
The Buchstab Transform of the $(lambda$)2 Method / 7.2.2:
The Sifting Limit as k -> $(infinity$) / 7.2.3:
Selberg's a2 a" Method / 7.3:
The Improved Sifting Limit for Large k / 7.3.1:
Notes on Chapter 7 / 7.4:
References
Index
Introduction
The Structure of Sifting Arguments / 1:
The Sieves of Eratosthenes and Legendre / 1.1:
4.

図書

図書
Jürgen Neukirch, Alexander Schmidt, Kay Wingberg
出版情報: Berlin : Springer, c2000  xv, 699 p. ; 25 cm
シリーズ名: Die Grundlehren der mathematischen Wissenschaften ; 323
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5.

図書

図書
John Oprea
出版情報: Providence, RI : American Mathematical Society, c2000  xiii, 266 p. ; 22 cm
シリーズ名: Student mathematical library ; v. 10
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6.

図書

図書
Alexander Mehlmann ; translated by David Kramer
出版情報: Providence, RI : American Mathematical Society, c2000  xx, 159 p. ; 22 cm
シリーズ名: Student mathematical library ; v. 5
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目次情報: 続きを見る
The glass bead game: Introduction
Games, form(ula)s, and scholars
Equilibrium and game as metaphor
In the forest of game trees
Games against time
The myths of game theory: Introduction
The prisoner's dilemma
Paradoxes of backward induction
Strategic accents of game-theoretic scholasticism
Odysseus goes to war
A postlude in rhyme
Games in the network of networks
References
Index
The glass bead game: Introduction
Games, form(ula)s, and scholars
Equilibrium and game as metaphor
7.

図書

図書
Arthur Cayley
出版情報: Cambridge : Cambridge University Press, 2009  14 v. ; 30 cm
シリーズ名: Cambridge library collection ; . Mathematical sciences
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目次情報:
Preface
Papers 888-967 (1889-1895)
Notes and references
Preface
Papers 888-967 (1889-1895)
Notes and references
8.

図書

図書
George Gabriel Stokes
出版情報: Cambridge : Cambridge University Press, 2009  5 v. ; 22 cm
シリーズ名: Cambridge library collection ; . Mathematical sciences
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目次情報: 続きを見る
On the effect of the internal friction of fluids on the motion of pendulums / 1:
An examination of the possible effect of the radiation of the heat on the propagation of sound / 2:
On the colours of thick plates / 3:
On a new elliptic analyser / 4:
On the conduction of heat in crystals / 5:
On the total intensity of interfering light / 6:
On the composition and resolution of streams of polarised light from different sources / 7:
Abstract of a paper 'On the change of refrangibility of light' / 8:
On the change of refrangibility of light / 9:
Index
On the optical properties of a recently discovered salt of quinine
On the change of refrangibility of light and the exhibition thereby of the chemical rays
On the cause of occurrence of abnormal figures in photographic impressions of polarised rings
On the metallic reflexion exhibited by certain non-metallic substances
Extracts from letter to Dr W. Haidinger: on the direction of the vibrations in polarised light: on shadow patterns and the chromatic aberration of the eye: on Haidinger's brushes
On the theory of electric telegraph
On the achromatism of a double object-glass
Remarks on Prof. Challis' paper, entitled 'A theory of the composition of Colours, etc.'
Supplement to the 'Account of pendulum experiments undertaken in the Harton Colliery...' / 10:
On the polarisation of diffracted light / 11:
On the discontinuity of arbitrary constants which appear in divergent developments / 12:
On the effect of wind on the intensity of sound / 13:
On the existence of a second crystallisable fluorescent substance (paviin) in the bark of the horse-chestnut / 14:
On the bearing of the phenomena of diffraction on the direction of the vibrations of polarised light / 15:
Note on paviin / 16:
On the colouring matters of madder / 17:
Extracts relating to the early history of spectrum analysis / 18:
Note on internal radiation / 19:
On the intensity of the light reflected from or transmitted through a pile of plates / 20:
Report on double refraction / 21:
On the long spectrum of electric light / 22:
On the change of form assumed by wrought iron and other metals when heated and then cooled by partial immersion in water / 23:
On the supposed identity of biliverdin with chlorophyll, with remarks on the constitution of chlorophyll / 24:
On the discrimination of organic bodies by their optical properties / 25:
On the application of the optical properties of bodies of detection and discrimination of organic substances / 26:
On the reduction and oxidation of the colouring matter of the blood / 27:
On a property of curves / 28:
On the internal distribution of matter which shall produce a given potential at the surface of a gravitating mass / 29:
Supplement to a paper on the discontinuity of arbitrary constants which appear in divergent developments / 30:
On the communication of vibration from a vibrating body to a surrounding gas / 31:
Account of observations of the total eclipse of the sun... / 32:
On a certain reaction of quinine / 33:
Explanation of a dynamical paradox / 34:
On the law of extraordinary refraction in Iceland Spar / 35:
Sur l'emploi du prisme dans la vérification de la loi de la double réfraction / 36:
Notice of the researches of the late Rev. W. Vernon Harcourt on the conditions of transparency in glass and the connexion between the chemical constitution and optical properties of different glasses / 37:
On the principles of the chemical correction of object-glasses / 38:
On the improvement of the spectroscope / 39:
On the construction of a perfectly achromatic telescope / 40:
On the optical properties of a titano-silicic glass / 41:
On a phenomenon of metallic reflection / 42:
Preliminary note on the compound nature of the line-spectra of elementary bodies / 43:
Appendix
Obituary notice by Lord Rayleigh
Note on certain formulæ in the calculus of operations
An experiment on electro-magnetic rotation
On the foci of lines seen through a crystalline plate
On certain movements of radiometers
On the question of a theoretical limit to the apertures of microscopic objectives
On an easy and at the same time accurate method of determining the ratio of the dispersions of glasses intended for objectives
On a method of detecting inequalities of unknown periods in a series of observations
Description of the card supported for sunshine recorders adopted at the meteorological office
On a simple mode of eliminating errors of adjustment in delicate observations of compared spectra
Discussion of the results of some experiments with whirled anemometers
On the determination of the constants of the cup anemometer by experiments with a whirling machine
Note on the reduction of Mr Crookes's experiments on the decrement of the arc of vibration of a mice plate oscillating within a bulb containing more or less rarefied gas
On the cause of the light border frequently noticed in photographs just outside the outline of a dark body seen against the sky
Extracts from reports of the Committee of Solar Physics
Memorandum for the use of observers with Professor Balfour Stewart's actinometer
On the highest wave of uniform propagation
On the maximum wave of uniform propagation
Note on the theory of the solitary wave
The outskirts of the solitary wave
On a remarkable phenomenon of crystalline reflection
The coefficient of viscosity of air
Note on the determination of arbitrary constants which appear as multipliers of semi-convergent series
On a graphical representation of the results of Dr Alder Wright's experiments on ternary alloys
On an optical proof of the existence of suspended matter in flames
On the reactions occurring in flames
The influence of surface-loading on the flexure of beams
On the best methods of recording the direct intensity of solar radiation
On the nature of the Röntgen rays
On the nature of the Röntgen rays (Wilde lecture)
Mathematical proof of the identity of the stream lines obtained by means of a viscous film with those of a perfect fluid moving in two dimensions
On the discontinuity of arbitrary constants that appear as multipliers of semi-convergent series
On the methods of chemical fractionation
The ultra-violet Spectrum of Radium
Notes on hydrodynamics, III
On the constitution of the luminiferous ether
On the theory of certain bands seen in the spectrum
Notes on hydrodynamics, IV
On a difficulty in the theory of sound
On the formation of the central spot of Newton's Rings beyond the critical angle
On some points in the received theory of sound
On the perfect blackness of the central spot of Newton's Rings, and on the verification of Fresnel's formulae for the intensities of reflected and refracted rays
On attractions, and on Clairaut's theorem
On the variation of gravity at the surface of the Earth
On a mode of measuring the astigmatism of a defective eye
On the determination of the wave length corresponding with any point of the spectrum
Discussion of a differential equation relating to the breaking of railway bridges
Notes on hydrodynamics, VI
On the dynamical theory of diffraction
On the numerical calculation of a class of definite integrals and infinite series
On the mode of disappearance of Newton's Rings in passing the angle of total internal reflection
On metallic reflection
On a fictitious displacement of fringes of interference
On Haidinger's Brushes
On the steady motion of incompressible fluids
On some cases of fluid motion
On the motion of a piston and of the air in a cylinder
On the theories of the internal friction of fluids in motion, and of the equilibrium and motion of elastic solids
On the proof of the proposition that (Mx + Ny)-1 is an integrating factor of the homogeneous differential equation M + N dy/dx = 0
On the aberration of light
On Fresnel's theory of the aberration of light
On a formula for determining the optical constants of doubly refracting crystals
On the constitution of the luminiferous ether, viewed with reference to the aberration of light
Report on recent researches on hydrodynamics
Supplement to a memoir on some cases of fluid motion
On the theory of oscillatory waves
On the resistance of a fluid to two oscillating spheres
On the critical values of the sums of period series
Supplement to a paper on the theory of oscillatory waves
On the effect of the internal friction of fluids on the motion of pendulums / 1:
An examination of the possible effect of the radiation of the heat on the propagation of sound / 2:
On the colours of thick plates / 3:
9.

図書

図書
Thomas Kappeler, Jürgen Pöschel
出版情報: Berlin ; Tokyo : Springer, c2003  xii, 279 p. ; 24 cm
シリーズ名: Ergebnisse der Mathematik und ihrer Grenzgebiete ; 3. Folge, v. 45 . A series of modern surveys in mathematics
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10.

図書

図書
Reinhard Siegmund-Schultze
出版情報: Basel ; Boston, Mass. : Birkhäuser, c2001  xiii, 341 p. ; 24 cm
シリーズ名: Science networks, historical studies ; v. 25
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