Geodesic

Sommaire du Fascicule no. 1

The Problem of Apollonius1
p. 1-17
A New Construction of the Injective Hull
p. 19-21
A Note on Lower Radical Constructions for Associative Rings
p. 23-30
On the Conversion of the Determinant into the Permanent
p. 31-34
Near-Ring Homomorphisms
p. 35-41
Group Theory and the Principle of Duality
p. 43-50
A Class of Positive Linear Operators
p. 51-59
On Operators and Distributions
p. 61-64
The Nucleus of a Set
p. 65-72
On a Discrete Analogue of Inequalities of Opial and Yang
p. 73-77
Note on Pairs of Consecutive Residues of Polynomials
p. 79-83
A Note on Homogeneous Dendrites
p. 85-93
Matrix Characterizations of Topological Properties
p. 95-105
On the Evaluation of Some Expressions Concerning the PBIB Designs
p. 107-114
On Real Almost Hermitian Structures Subordinate to Almost Tangent Structures
p. 115-133
Non-Existence of Estimates of Prescribed Accuracy in Fixed Sample Size
p. 135-139
On the Minimal Lipschitz Constant
p. 141-143
Éléments de mathématique, fascicule 17; Théorie des ensembles Chapitres 1 et 2. by Nicolas Bourbaki. Hermann, Paris, 1966. Troisième édition, 137 pages. 36 francs.
p. 156-157
News From the Departments
p. 173-174
The selected papers of E. S. Pearson, issued by the Biometrika Trustees to celebrate his 30 years as editor. University of California Press, Berkely and Los Angeles, 1966. $6.75.
p. 167
536 Puzzles and curious problems, by Henry E. Dudenay Saunders of Toronto Ltd., 1967. 428 pages. $9.75.
p. 158
A course in tensors with applications to Riemannian geometry, by R. S. Mishra. Pothishala Private Ld, Allahabad 1965. iii + 199.
p. 164-165
Emile Borel, philosophe et homme d'action. Pages choisies présentées par Maurice Fréchet. Paris, Gauthier-Villars, 1967. 406 pages.
p. 153-154
Les fondements de la géométrie. Tome II: Géométrie projective par Bêla Kerékjarto. Gauthier-Villars, Paris, et Académie des Sciences hongroise, 1966. 528 pages. $14.50.
p. 167-169
Ordinary differential equations, by I. G. Petrovskii. Translated from the Russian by R. A. Silverman, Prentice-Hall, Inc., Englewood Cliffs, N. J. x + 232 pages. $7.95.
p. 166
Sur les algebras de Hilbert, by A. Diego. Gauthier-Villars, Paris, 1966, Collection de logique mathématique, série A. No. 2 1 . 56 pages. 20 francs.
p. 159
The four-color problem, by Oystein Ore. Academic Press, New York, 1967. xv + 259 pages. $12.00.
p. 161-163
Elements of Nonparametric Statistics, by G. E. Noether. John Wiley and Sons, New York, 1967. ix + 104 pages. $7.95.
p. 152-153
Ontario Mathematical Meetings
p. 146-150
Lecons sur les fonctions calculables, par V.A. Ouspenski, Traduit du russe par André Chauvin. Hermann, Paris, 1966. 412 pages. 48F.
p. 163-164
De proportionibus proportionum and Ad pauca respicientes, by Nicole Oresme. Edited with introductions, English translations, and critical notes by Edward Grant. The University of Wisconsin Press: Madison, Milwaukee, and London, 1966. xxii + 466 pages, 11 plates. $10.75.
p. 163
Recursive functions, by Rozsa Peter. Academic Press Inc., New York, 1967. 300 pages. $13.50.
p. 158
Characters of finite groups, by W. Feit. W. A. Benjamin Inc., New York, 1967. viii + 186 pages. $9.50 hardcover, $4.95 paperback.
p. 151-152
Elements of Mathematics - General Topology, by Nicolas Bourbaki. Hermann, Paris, and Addison-Wesley, Reading, 1967. Part 1, vii + 438 pages. $18.50. Part 2, iv + 368 pages. $18.50.
p. 160-161
Stationary and related stochastic processes : sample function properties and their applications, by Harald Cramer and M.R. Leadbetter. John Wiley and Sons, New York, 1967. 348 pages. $12.50.
p. 159-160
Abstracts of Theses
p. 170-172
An introduction to nonassociative algebras, by Richard D. Schafer. Academic Press, New York and London, 1966. x + 166 pages. $7.95.
p. 165
Topological groups, by L. S. Pontryagin. Second edition. Translated by Arlen Brown. Gordon and Breach, New York 1966. xiv + 543 pages. Ref. ed. $32.50, Prof. ed. $17.50.
p. 154-155
An introduction to the theory of numbers, by Ivan Niven and Herbert S. Zuckerman. John Wiley and Sons, New York, 1966. 2nd edition. 280 pages. $7.95.
p. 157-158
Éléments de mathématique, fascicule 22; Théorie des ensembles, Chapitre 4: Structures, by Nicolas Bourbaki. Hermann, Paris, 1966. Deuxième édition, 108 pages, broché. 36 francs.
p. 155-156

Sommaire du Fascicule no. 2

On a Theorem of Niven
p. 145
The Circle Problem in an Arithmetic Progression
p. 175-184
A Note on Henselian Valuation Rings
p. 185-189
A Room Design of Order 14
p. 191-194
On Detours in Graphs1
p. 195-201
On Partitioning Planar Graphs
p. 203-211
On the Non-Cutpoint Existence Theorem
p. 213-216
On a Modification of Romberg Quadrature
p. 217-224
Moment Problems and Quasi-Hausdorff Transformations
p. 225-236
On Polynomials with Real Zeros
p. 237-240
A Transformation Connecting Products of Generalised Basic Hypergeometric Functions
p. 241-248
Gap Formulae for the Weierstrass Transforms
p. 249-254
On Banach Limit of Fourier Series and Conjugate Series I
p. 255-262
Some Distribution Problems of Order Statistics From Exponential and Power Function Distributions1
p. 263-274
A Theorem on Henselian Rings
p. 275-277
On Exceptional Polynomials
p. 279-282
Note on a Theorem on Singular Matrices
p. 283-284
Diameter of a (0, 1)-Matrix*
p. 285-288
Representation of m as
p. 289-293
On the Cube of a Graph
p. 295-296
A Genuine Topology for the Field of Mikusiński Operators
p. 297-299
Lectures on rings and modules, by J. Lambek. Blaisdell Publishing Co., Waltham, Massachusetts, 1966. viii + 184 pages. $8.50.
p. 319-320
A graduate course in probability, by Howard G. Tucker. Academic Press, New York and London, 1967. xiii + 273 pages. $14.00.
p. 326-327
Geometrische ordnungen, by O. Haupt and H. Kunneth. Springer-Verlag, Berlin, Heidelberg, New York, 1967. viii +429 pages. $17.00.
p. 328-329
Polish logic, 1920-1939, edited by Storrs McCall. Oxford University Press, 1967. viii + 406 pages. $15.00.
p. 346
Foundations of the calculus, by H. F. DeBaggis and K.S. Miller. Saunders, 1966. $5.00.
p. 330-331
A first course in Stochastic Processes, by Samuel Karlin. Academic Press N.Y. and London 502 pages. $11.95.
p. 317
Probability: a survey of the mathematical theory, by John Lamperti. W. A. Benjamin, Inc. N.Y., Amsterdam, 1966. 150 pages. $3.95
p. 317
Introduction to modem abstract algebra, by D.M. Burton. Addison-Wesley, Reading, Massachusetts, 1967. vii +310 pages. $3.95.
p. 330
A selection of early statistical papers of J. Neyman. University of California Press, 1967. ix + 429 pages. $14.95.
p. 340-341
Définition des fonctions eulériennes par des équations fonctionelles, by Jean Anastassiadis. Mémor. Sci. Math., Fasc. CLVI. Gauthier-Villar s et Cie, Éditeur-Imprimeur, Paris, 1964. v + 77 pages. 16 F.
p. 356-357
Modular lie algebras, by G.B. Seligman. Ergebnisse der Mathematik und ihrer Grenzgebiete, Vol. 40, 1968. x + 166 pages. $9.75.
p. 349-350
Ring and radicals, by N. J. Divinsky. University of Toronto. $7.50.
p. 320-323
Proceedings of Symposia in Pure Mathematics. Vol. IX: Algebraic groups and discontinuous subgroups, edited by Armand Borel and George D. Mostow. (Proceedings of the Symposium in Pure Mathematics of the American Mathematical Society held at the University of Colorado, Boulder, Colorado, July 5 - August 5, 1965). American Mathematical Society, Providence, R. I., 1966. vii +426 pages. $110.20.
p. 355
Abstract Algebra, by CrH. Sah. Academic Press, New York and London, 1967. xiii + 352 pages. $9.75.
p. 311-312
Theory of Rank Tests, by J. Hajek and Z. Sidak. Academic Press, 1967. 297 pages. $8.00.
p. 340
Books Received
p. 361-364
Solutions
p. 306-309
A Remark on the Gibbs Phenomenon and Lebesgue Constants for a Summability Method of Melikov
p. 301-303
An introduction to the foundations and fundamental concepts of mathematics, by H. Eves and C.V. Newsom. Holt, Rinehart and Winston, revised edition, 1965. xi + 398 pages. $9.95.
p. 324-325
Lectures on Boolean algebras, by P.R. Halmos. Van Nostrand. iv + 147 pages. $2.95.
p. 350-351
A theory of sets, by Anthony P. Morse. Academic Press, New York, 1965. xxxii + 130 pages. $7.95.
p. 354-355
Joint statistical papers, by J. Neyman and E. S. Pearson. University of California Press, 1966. 299 pages. Selected papers $6.75.
p. 341
On the syllogism, by Augustus de Morgan. Edited by Peter Heath. Yale University Press, 1966. Distributed by McGill University Press, xxxi + 355 pages. $10.00.
p. 348
Topics in algebra, by I. N. Herstein. Blaisdell, 1964/1965. 342 pages. $9.50.
p. 341-342
University Algebra, by Richard E. Johnson. Prentice-Hall, 1966. xii + 271 pages. $7.95.
p. 311
Multiple integrals in the calculus of variations by C.B. Morrey. Springer-Verlag, New York, 1966. ix + 506 pages.
p. 313-314
A first course in abstract algebra, by John B. Fraleigh. Addison-Wesley Publishing Co., Reading, Massachusetts, xvi +447 pages. $9.75.
p. 331-332
Problèmes de calcul des probabilités, D. Dacunha-Castelle, D. Revuz et M. Schreiber. Preface du Professeur A. Tortrat. Masson et Cie, Paris, 1965. vi + 196 pages. 36 F.
p. 353
The problem of the minimum of a quadratic functional, by S.G. Mikhlin, translated by A. Feinstein. Holden-Day, 1965. ix + 151 pages. $9. 50. (Original published in 1952 as Problema Minimuma Kvadratichnogo Funktsionala, State Publishing House, Moscow-Leningrad. )
p. 348-349
The basic laws of arithmetic, by Gottlob Frege. Translated and edited by Montgomery Furth. University of California Press, 1967. lxiii + 144 pages. Paperback $1.95.
p. 348
Topological spaces, by Eduard Cech (revised edition by Z. Frolic and M. Katetov). John Wiley and Sons Inter science publication, 1966, New York. 893 pages. $22.50.
p. 358-360
Mathematics of Choice : How to count without counting, by Ivan Niven. Random House, New Mathematical Library No. 15., 1965. xi + 202 pages. $1.95.
p. 319
The variational theory of geodesies by M. M. Postnikov. Translated from the Russian by Scripta Technica Inc. edited by Bernard R. Gelbaum. W.B. Saunders Company, Philadelphia and London, 1967. viii + 200 pages.
p. 312-313
Ordinary differential equations - a first course, by Fred Brauer and John A. Nohel. W.A. Benjamin, Inc., New York, 1967. $10.75.
p. 352-353
Estimation theory, by Ralph Deutsch. Prentice-Hall, Inc., Englewood Cliffs, N. J., 1965. xiv + 269 pages. $9.75.
p. 357
Iterative solution of elliptic systems and applications to the neutron diffusion equations of reactor physics, by Eugene L. Wachpress. Prentice-Hall Inc., Englewood Cliffs, N. J., 1966. xiv + 299 pages. $12.95.
p. 345-346
Mathematical theory of probability and statistics, by Richard von Mises, edited and complemented by H. Geiringer. Academic Press, New York, 1964. vii + 694 pages. $22.00.
p. 326
Introduction to finite mathematics, by J. G. Kemeny, J. L. Snell, G. L. Thompson. Prentice-Hall Inc., Englewood Cliffs, N. J., Second edition, 1966. xiv + 465 pages. $8.95.
p. 351-352
Introduction to elementary vector analysis, by J. C. Tallack. Cambridge University Press (The MacMillan Company of Canada Limited), 1966. i + 140 pages. $3.00.
p. 345
Modern university calculus, by Bell, Blum, Lewis and Rosenblatt. Holden-Day 1966. lxix + 905 pages. $12. 95.
p. 357-358
Introduction to measure and probability by J. F. C. Kingman and S.J. Taylor. Cambridge, England, 1966. x +401 pages.
p. 314-315
Computation: Finite and infinite machines, by Marvin Minsky. Englewood Cliffs, N. J., Prentice Hall, xvii + 317 pages . $12.00.
p. 342-343
Geometry revisited, by H. S. M. Coxeter and S. L. Greitzer. Volume 19 of the "New Mathematical Library", Random House, 1967. $1. 95.
p. 318-319
Analytic functions of several complex variables, by R. C. Gunning and Hugo Rossi, Prentice-Hall, 1965. $12.95.
p. 336-339
Discovering modern algebra, by K.L. Gardner. Oxford University Press, London, 1966. 260 pages.
p. 353
Finite functions: an introduction to combinatorial mathematics, by Henry Sharp Jr. Prentice-Hall, Englewood Cliffs, N. J., 1965. vii + 97 pages. $4.25.
p. 352
Elementary Differential Geometry by Barret O'Neill. Academic Press, 1966.
p. 315-316
Algebraic structure theory of sequential machines, by J. Hartmanis and R. E. Stearns Prentice-Hall, Inc., Englewood Cliffs, N. J., 1966. viii + 211 pages . $11.50.
p. 324
Statement of Policy of the Canadian Mathematical Bulletin
p. 310
Elementary partial differential equations, by Paul W. Berg and James L. McGregor. Holden-Day Inc., San Francisco, 1966. xv + 421 pages. $11. 95.
p. 327
Oeuvres mathématiques, by Raphael Salem. Hermann, Paris, 1967. 648 pages. 90 F .
p. 343-345
Fourier transforms and the theory of distributions, by J. Arsac. Translated by Allen Nussbaum and Gretchen C. Heim. Prentice-Hall, Inc., Englewood Cliffs, N. J., 1966. xv + 318 pages. $10.00.
p. 360
News From the Departments
p. 365-366
Notes on differential geometry, by Noel J. Hicks. D. Van Nostrand, Princeton, New Jersey, 1965. vi + 183 pages. $2.98.
p. 356
Quasi-uniform topological spaces, by M.G. Murdeshwar and S.A. Naimpally. Series A: Preprints of Research Papers. No.4, vol. 2. (Février 1966). Nordhoff. $2.00 (Stechert).
p. 332-334
From Frege to Gödel, edited by Jean van Heijenoort. (A source book in mathematical logic, 1879-1931). Cambridge, Mass., Saunders of Toronto, 1967. x+660 pages. $18.50.
p. 346-348
Topics in optimization, edited by G. Leitmann. Academic Press, 1967. Vol. 31 of the series Maths in Science and Engineering. $18.00.
p. 334-335
Introduction to Cybernetics, by V.M. Glushkov. Academic Press, 1966. Originally published as "Vvedeniye v Kibernetiku" Ukr. Acad, of Sci. Kiev, 1964. 322 pages. $11.75.
p. 339
Mathematics for the physical sciences, by L. Schwartz. Hermann, Editeurs des Sciences et des Arts, Paris, and Addison-Wesley Publishing Company, Reading, Mass., 1966. 358 pages. $14.00.
p. 323-324
Problems for Solution
p. 304-305
Elementary topology: A combinatorial and algebraic approach, par Donald Blackett. Academic Press. $9.50.
p. 335-336

Sommaire du Fascicule no. 3

Constructing an Automorphism From an Anti-Automorphism
p. 367-370
Notes on Splitting Extensions of Groups
p. 371-374
Duo Rings: Some Applications to Commutativity Theorems
p. 375-380
A New Characterization of Finite Prime Fields
p. 381-382
Rings of Quotients of Rings of Derivations
p. 383-398
Note on Weight Spaces of Irreducible Linear Representations
p. 399-403
A Combinatorial Interpretation of Ramanujan's Continued Fraction
p. 405-408
A Construction for Partitions Which Avoid Long Arithmetic Progressions
p. 409-414
Some Possible and Some Impossible Tripartitions of the Plane
p. 415-421
Sub-Manifolds of a Locally Product Riemannian Manifold
p. 423-435
Circumscribing an Ellipsoid about the Intersection of Two Ellipsoids
p. 437-441
On Zeros of Derivatives of Polynomials
p. 443-445
Extension of a Result of L. Lorch and P. Szego On Higher Monotonicity
p. 447-451
Almost Continuity of Mappings
p. 453-455
Some Characterizations of the Ultraspherical Polynomials
p. 457-464
Linear Functionals on Homogeneous Polynomials
p. 465-468
Unisolvence on Multidimensional Spaces
p. 469-474
Transformation of Life-Test Data
p. 475-488
More Problems Connected with Convexity
p. 489-494
A Functional Equation for the Cosine
p. 495-498
A Note on the Diameter of a Graph
p. 499-501
Note on Epi in
p. 503-504
Exercises in Mathematics, by J. Bass. Academic Press, 1966. xii + 459 pages. $14.75.
p. 507
Proceedings. United States - Japan Seminar on Differential and Functional Equations, University of Minnesota, Minneapolis, Minnesota, June 26-30, 1967, edited by William A. Harris Jr. and Yasutaka Sibuya. W.A. Benjamin, Inc., New York, Amsterdam, 1967. 500 pages. $8 50.
p. 509-512
Variétés Différentielles et analytiques, by N. Bourbaki. Hermann, Paris, 1967. 97 pages.
p. 514
The theory of splines and their applications, by J.H. Ahlberg, E.N. Nilson and J. L. Walsh. Academic Press, New York, 1967. viii + 284 pages. $13. 50.
p. 507-508
Problèmes d'Algèbre générale, par A. Bigard, M. Crestey and J. Grappy. Dunod, Paris, 1967. viii + 226 pages.
p. 515
Statement of Policy of the Canadian Mathematical Bulletin
p. 526
S. S. Wilks: Collected Papers; Contributions to mathematical statistics, edited by T.W. Anderson. John Wiley and Sons, 1967. 693 pages.
p. 517
Solutions
p. 506
Transactions of the fourth Prague conference on information theory, statistical decision functions, random processes. Academic Press, New York and London, 1967, 725 pages.
p. 517
Les fonctions généralisées ou distributions, by M. Bouix. Masson, Paris, 1964. ix + 223 pages.
p. 515
Abstracts of Theses
p. 520-524
Formulaire pour le Calcul Opérationnel, by V.A. Ditkin and A.P. Prudnikov. Masson, Paris, 1967. 468 pages.
p. 513
About vectors, by Banesh Hoffman. Prentice-Hall, 1966.
p. 516-517
Class field theory, by E. Artin and J. Tate (éd.). W.A. Benjamin Inc., New York, 1968. 286 pages. $3. 95 (paper). $9. 50 (cloth).
p. 509
Differential und Integralrechnung I, by Hans Grauert and Ingo Lieb. Heidelberger Taschenbücher Nr. 26, Springer-Verlag Berlin-Heidelberg-New York, 1967. x + 200 pages.
p. 515-516
Linear Algebra, 3rd edition (Die Grundlehren der mathematischen Wissenschaften, Vol. 97), by W.H. Greub. Springer-Verlag, New York, Inc. 1967. ix + 434 pages. $9.80 U.S. - Multilinear Algebra (Die Grundlehren der mathematischen Wissenschaften, Vol. 136), by W.H. Greub. Springer-Verlag, New York, Inc. 1967. x + 224 pages. $8.00 U.S.
p. 512-513
Announcement
p. 525
Darstellungen von Gruppen. Mit Berücksichtigung der Berdürfniese der modernen Physik. Zweite, überarbeitete Auflage. Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen, by H. Boerner. Band 74, Springer-Verlag, Berlin, Heidelberg, New York, 1967. xiv + 317 pages. DM58, $14.50 U.S.
p. 517-518
Calculus for College Students, M.H. Protter and C.B. Morrey. Addison-Wesley, 1967. 730 pages. $10.75.
p. 513
Problems for Solution
p. 505
Plane geometry and its groups, by Heinrich W. Guggenheimer. Holden-Day Inc., 1967. x + 288 pages. $9.35.
p. 508-509
Solution of equations and systems of equations, by A.M. Ostrowski. (Academic-Press, New York, London, 1966). xiv + 338 pages. $11.95.
p. 518-519

Sommaire du Fascicule no. 4

The No-Three-In-Line Problem
p. 527-531
An Edge but not Vertex Transitive Cubic Graph*
p. 533-535
On Lattice Paths with Several Diagonal Steps
p. 537-545
A Pappus Type Theorem in the Affine Group
p. 547-554
Local Near-Rings Of Cardinality P2
p. 555-561
On Compact Prime Rings and their Rings of Quotients
p. 563-568
A Note on Exact Colimits
p. 569-572
A General Selection Principle, with Applications in Analysis and Algebra
p. 573-584
Convergence of the Hausdorff Means ofDouble Fourier Series*
p. 585-591
A Note on an Oscillation Criterion for anEquation with a Functional Argument
p. 593-595
On a Theorem of Erdös and Szekeres
p. 597-598
A Banach Space of Analytic Functions For Constant Coefficient Equations of Evolution
p. 599-601
The Coreflective Subcategory of Sequential Spaces
p. 603-604
Another Proof of the Contraction Mapping Principle
p. 605-606
A Note on Polar Topologies
p. 607-609
On Zeros of Derivatives of Polynomials
p. 611
Solutions
p. 613-620
Ontario Mathematical Meetings 1968
p. 621-652
Problems for Solution
p. 612-613
Openings in Mathematics
p. 653-654

Sommaire du Fascicule no. 5

A Combinatorial Proof of a Conjecture of Goldberg and Moon
p. 655-661
A Generalization of a Theorem of Hilton
p. 663-669
Elements of Packing and Covering
p. 671-677
A Remark on the Group Rings of Order Preserving Permutation Groups
p. 679-680
On a Certain Set of Linear Inequalities
p. 681-690
Tensor Products of Banach Algebras*
p. 691-701
Some Elementary Converse Problems in Ordinary Differential Equations*
p. 703-716
A Three Dimensional Analogue of Pappus's Theorem
p. 717
A Note on Absolute Geometry
p. 719-722
An Isoperimetric Inequality for Convex Polyhedra with Triangular Faces
p. 723-727
Note on T-Minimal Complete Bipartite Graphs
p. 729-732
The Factors of a Square-Free Integer
p. 733-735
A Note on the Jacobson And Brown-McCoy Radicals
p. 737-738
On Maitland's Generalised Bessel Function
p. 739-741
Periodic Solutions by Picard's Approximations
p. 743-745
Some Remarks on a Paper of Wong
p. 747-749