Showing papers in "Canadian Mathematical Bulletin in 1997"
TL;DR: In this article, it was shown that the scaling limit of lattice trees is the integrated super-Brownian excursion (ISE), as conjectured by Aldous, in all dimensions.
Abstract: This article discusses our recent proof that above eight dimensions the scaling limit of sufficiently spread-out lattice trees is the variant of super-Brownian motion called integrated super-Brownian excursion (ISE), as conjectured by Aldous. The same is true for nearest-neighbour lattice trees in sufficiently high dimensions. The proof, whose details will appear elsewhere, uses the lace expansion. Here, a related but simpler analysis is applied to show that the scaling limit of a mean-field theory is ISE, in all dimensions. A connection is drawn between ISE and certain generating functions and critical exponents, which may be useful for the study of high-dimensional percolation models at the critical point.
43 citations
TL;DR: In this article, the Luxemburg norm and K-monotonicity of local uniform rotundity in Orlicz-Lorentz spaces with the Luxembourg norm are discussed.
Abstract: Criteria for local uniform rotundity and midpoint local uniform rotun- dity in Orlicz-Lorentz spaces with the Luxemburg norm are given. Strict K-monotonicity and Kadec-Klee property are also discussed. Introduction. A function : R+ R+ is said to be an Orlicz function if is convex, (0) = 0, and (u) 0f or all u 0. Let (Ω Σ ) denote a complete -finite measure space and let L 0 = L 0 (Ω Σ ) denote the space of all (equivalence classes of) -measurable real-valued functions, equipped with the topology of convergence in measure on -finite sets. For any f L 0 the nonincreasing rearrangementof f is the function f defined by
35 citations
TL;DR: In this article, sufficient conditions are given for the quasilinear elliptic inequality to have no positive entire solutions when p has radial symmetry, and the existence of positive entire solution can be characterized by some known results.
Abstract: This paper treats the quasilinear elliptic inequality where N ≥ 2, m > 1, σ > m − 1, and p:ℝN → (0, ∞) is continuous. Sufficient conditions are given for this inequality to have no positive entire solutions. When p has radial symmetry, the existence of positive entire solutions can be characterized by our results and some known results.
27 citations
TL;DR: In this paper, a general proof of the Cauchy formula about the length of a plane curve is given in two ways: as the integral of the variation of orthogonal projections of the curve, and as a double integr ral of the number of intersections of a curve with an arbitrary line of the plan.
Abstract: plan. ABSTRACT. We give a general proof of the Cauchy formula about the length of a plane curve. The formula is given in two ways: as the integral of the variation of orthogonal projections of the curve, and as a double integ ral of the number of intersections of the curve with an arbitrary line of the plan e.
22 citations
TL;DR: In this paper, a short self-contained proof of Euler's relation with combinatorics is presented. The ingredients of this proof are (i) th e principle of inclusion and exclusion of combinatorsics and (ii) the Euler characterist ic.
Abstract: The purpose of this paper is to present a short, self-contain ed proof of Euler's relation. The ingredients of this proof are (i) th e principle of inclusion and exclusion of combinatorics and (ii) the Euler characterist ic; a development of the Euler characteristic is included.
21 citations
TL;DR: In this paper, the main result is that a Z-frame is E-projective if and only if it is stably Z-continuous, for a naturally arising collection E of morphisms.
Abstract: This paper deals with the projective objects in the category of all Z-frames, where the latter is a common generalization of different types of frames. The main result obtained here is that a Z-frame is E-projective if and only if it is stably Z-continuous, for a naturally arising collection E of morphisms.
20 citations
TL;DR: The question of the existence of compact separable radial spaces which are not Frwas first asked by Chertanov (see as mentioned in this paper ) and was first answered by Nyikos (see (Arh78)).
Abstract: IfA andB are disjoint ideals on , there is a tower preserving - centered forcing which introduces a subset of which meets every infinite member of A in an infinite set and is almost disjoint from every member ofB. We can then produce a model in which all compact separable radial spaces are Frthus answering a question of P. Nyikos. The question of the existence of compact ccc radial spaces which are not Frwas first asked by Chertanov (see (Arh78)).
20 citations
TL;DR: In this paper, the η-invariant for a cusped hyperbolic 3-manifold is defined and discussed, and some of its applications are discussed.
Abstract: In this paper, we define the η-invariant for a cusped hyperbolic 3-manifold and discuss some of its applications. Such an invariant detects the chirality of a hyperbolic knot or link and can be used to distinguish many links with homeomorphic complements.
14 citations
TL;DR: In this article, the authors studied the topology of the space of harmonic maps from S2 to CP2 and proved that the subspaces consisting of maps of a fixed degree and energy are path connected.
Abstract: In this paper we study the topology of the space of harmonic maps from S2 to CP2. We prove that the subspaces consisting of maps of a fixed degree and energy are path connected. By a result of Guest and Ohnita it follows that the same is true for the space of harmonic maps to CPn for n 1⁄2 2. We show that the components of maps to CP2 are complex manifolds. Research partially supported by NSERC fellowship. Received by the editors January 4, 1996; revised April 9, 1996. AMS subject classification: Primary: 58E20; secondary: 58D27. c Canadian Mathematical Society 1997.
13 citations
TL;DR: In this article, the authors consider rings as in the title and find the precise obstacle for them not to be Quasi-Frobenius, thus shedding new light on an old open question in Ring Theory.
Abstract: Abstract We consider rings as in the title and find the precise obstacle for them not to be Quasi-Frobenius, thus shedding new light on an old open question in Ring Theory. We also find several partial affirmative answers for that question.
13 citations
TL;DR: For positive integers p and q with (p − 2)(q − 2) > 4, there is a group [p, q] generated by reflections in the three sides of a triangle ABC with angles π /p, π/q,π/2.
Abstract: For positive integers p and q with (p − 2)(q − 2) > 4 there is, in the hyperbolic plane, a group [p, q] generated by reflections in the three sides of a triangle ABC with angles π/p, π/q, π/2. Hyperbolic trigonometry shows that the side AC has length ψ, where cosh ψ = c/s, c = cos π/q, s = sin π/p. For a conformal drawing inside the unit circle with centre A, we may take the sides AB and AC to run straight along radiiwhile BC appears as an arc of a circle orthogonal to the unit circle. The circle containing this arc is found to have radius 1/ sinh ψ = s/z, where z = , while its centre is at distance 1/ tanh ψ = c/z from A. In the hyperbolic triangle ABC, the altitude from AB to the right-angled vertex C is ζ, where sinh ζ = z.
TL;DR: For positive integers s and t, the authors showed that f (s t) = 4(s + t) + 1 whenever s g and t g are not congruent to 0 (modulo 4), where g = gcd(s t).
Abstract: For positive integers s and t, let f (s t) denote the smallest positive integer N such that every 2-colouring of (1 N) = 1 2 N has a monochromatic homothetic copy of 1 1 + s 1 + s + t . We show that f (s t) = 4(s + t) + 1 whenever s g and t g are not congruent to 0 (modulo 4), where g = gcd(s t). This can be viewed as a generalization of part of van der Waerden's theorem on arithmetic progressions, sinc e the 3-term arithmetic progressions are the homothetic copies of 1 1 + 1 1 + 1 + 1 . We also show that f (s t) = 4(s + t) + 1 in many other cases (for example, whenever s 2t 2 and t does not divide s), and that f (s t) 4(s + t) + 1 for all s, t. Thus the set of homothetic copies of 1 1 + s 1 + s + t is a set of triples with a particularly simple Ramsey function (at least for the case of two colours), and one wonders what other "natural" sets of triples, quadruples, etc., have simple (or easily estimated) Ramsey functions.
TL;DR: In this paper, a shorter proof of the existence of index pairs for discrete dynamical systems is given, and the index pairs defined in that proof are stable with respect to small perturbations of the generating map.
Abstract: A new shorter proof of the existence of index pairs for discrete dynamical systems is given. Moreover, the index pairs defined in that proof are stable with respect to small perturbations of the generating map. The existence of stable index pairs was previously known in the case of diffeomorphisms and flows generated by smooth vector fields but it was an open question in the general discrete case. Received by the editors May 23, 1995; revised November 28, 1995. The first author was supported by a grant from NSERC of Canada. The second author was partially supported by KBN grant no. 0449/P3/94/06. AMS subject classification: Primary: 54H20; secondary: 54C60, 34C35. c Canadian Mathematical Society 1997. 448
TL;DR: In this article, it was shown that if A is a torsion-free word hyperbolic group which belongs to class (Q), that all finitely generated subgroups of A are quasiconvex in A, then any maximal cyclic subgroup U of A is also a Burns subgroup of A.
Abstract: We show that if A is a torsion-free word hyperbolic group which belongs to class (Q), that is all finitely generated subgroups of A are quasiconvex in A, then any maximal cyclic subgroup U of A is a Burns subgroup of A. This, in particular, implies that if B is a Howson group (that is the intersection of any two finitely generated subgroups is finitely generated) then A *U B, ⧼A, t | Ut = V⧽ are also Howson groups. Finitely generated free groups, fundamental groups of closed hyperbolic surfaces and some interesting 3-manifold groups are known to belong to class (Q) and our theorem applies to them. We also describe a large class of word hyperbolic groups which are not Howson.
TL;DR: In this article, it was shown that there are infinitely many weak solutions of the p-harmonic flow with initial and boundary data f = f 0 on the parabolic boundary of a bounded smooth domain.
Abstract: If f0: Ω 2 Rm ! Sn is a weakly p-harmonic map from a bounded smooth domain Ω in Rm (with 2 U p U m) into a sphere and if f0 is not stationary p-harmonic, then there exist infinitely many weak solutions of the p-harmonic flow with initial and boundary data f0, i.e., there are infinitely many global weak solutions f : Ωð R+ ! Sn of ]tf div (jrf jp 2rf ) = jrf jpf weakly on Ωð R+ f = f0 on the parabolic boundary of Ωð R+. We also show that there exist non-stationary weakly (m 1)-harmonic maps f0: Bm ! Sm 1. This work is supported by the Swiss National Science Foundation. Received by the editors October 6, 1995. AMS subject classification: 35K40, 35K55, 35K65. c Canadian Mathematical Society 1997. 174
TL;DR: In this paper, the authors show that H1(M; Z[1/|A|][A]-module is determined as a Z[ 1/ |A|]-module by the Alexander ideals of L and certain ideal class invariants.
Abstract: Let A be a finite abelian group and M be a branched cover of an homology 3-sphere, branched over a link L, with covering group A. We show that H1(M; Z[1/|A|]) is determined as a Z[1/|A|][A]-module by the Alexander ideals of L and certain ideal class invariants.
TL;DR: In this paper, it was shown that the multipliers from BMOA, VMOA and B0 or disk algebra A are polynomial in the multiplier space, where X is BMOAs, X is VMOAs and X is a disk algebra.
Abstract: We show that the multiplier space , where X is BMOA, VMOA, B, B0 or disk algebra A. We give the multipliers from , we also give the multipliers from , C 0, BMOA, and Hp .
TL;DR: In this article, the authors consider Dirichlet series with Euler products of the form F(s) = Πp in > 1, and which are regular in ≥ 1 except for a pole of order m at s = 1.
Abstract: Abstract In this paper, we consider Dirichlet series with Euler products of the form F(s) = Πp in > 1, and which are regular in ≥ 1 except for a pole of order m at s = 1. We establish criteria for such a Dirichlet series to be nonvanishing on the line of convergence. We also show that our results can be applied to yield non-vanishing results for a subclass of the Selberg class and the Sato-Tate conjecture.
TL;DR: Clarke and Ledyaev as discussed by the authors developed a variant of the multidirectional mean value theorem applicable to locally Lipschitz functions on certai n Banach spaces, namely those that admit a C 1 -Lipschitzer continuous bump function.
Abstract: Recently, F. H. Clarke and Y. Ledyaev established a multidirectional mean value theorem applicable to lower semi-continuous functions on Hilbert spaces, a result which turns out to be useful in many applications. We develop a variant of the result applicable to locally Lipschitz functions on certai n Banach spaces, namely those that admit aC 1 -Lipschitz continuous bump function.
TL;DR: In this article, a characterisation of the range of a homomorphism between two commutative group algebras is presented which implies, among other things, that this range is closed.
Abstract: Abstract A characterisation of the range of a homomorphism between two commutative group algebras is presented which implies, among other things, that this range is closed. The work relies mainly on the characterisation of such homomorphisms achieved by P. J. Cohen.
TL;DR: In this paper, the authors give an elementary potential-theoretic proof of a theore m of G. Johnsson: all solutions of Cauchy's problems for the Lapl ace equations with an en- tire data on a sphere extend harmonically to the whole space RN except, perhaps, for the center of the sphere.
Abstract: We give an elementary potential-theoretic proof of a theore m of G. Johnsson: all solutions of Cauchy's problems for the Lapl ace equations with an en- tire data on a sphere extend harmonically to the whole space RN except, perhaps, for the center of the sphere.
TL;DR: In this paper, the restriction of the minimal representatio n of H to the closed subgroup PGL3 G2 was studied, where H is the split, adjoint group of type E6 over a p-adic field.
Abstract: Let H be the split, adjoint group of type E6 over a p-adic field. In this paper we study the restriction of the minimal representatio n of H to the closed subgroup PGL3 G2.
TL;DR: In this article, the classification of finite groups G satisfying the condition NG(H)/CG(H) ≅ Aut(H), for every abelian subgroup H of G, is presented.
Abstract: Abstract This note contains the classification of the finite groups G satisfying the condition NG(H)/CG(H) ≅ Aut(H) for every abelian subgroup H of G.
TL;DR: In this paper, it was shown that the main boundedness, convergence, and differentiability properties of continuous convex functions on Banach spaces do not extend to larger classes of functions.
Abstract: There is a sizeable class of results precisely relating boundedness, convergence
and differentiability properties of continuous convex functions on Banach
spaces to whether or not the space contains an isomorphic copy of ‡1. In this note,
we provide constructions showing that the main such results do not extend to natural
broader classes of functions.
TL;DR: In this article, it was shown that if f is an entire transcendental function, l a straight line in the complex plane, and n ≥ 2, then f has infinitely many repelling periodic points of period n that do not lie on l.
Abstract: Abstract It is shown that if f is an entire transcendental function, l a straight line in the complex plane, and n ≥ 2, then f has infinitely many repelling periodic points of period n that do not lie on l.
TL;DR: In this paper, real hypersurfaces of a complex space form Mn(c), c ≠ 0 under certain conditions of the Ricci tensor on the orthogonal distribution T 0.
Abstract: We study real hypersurfaces of a complex space form Mn(c), c ≠ 0 under certain conditions of the Ricci tensor on the orthogonal distribution T 0.
TL;DR: In this paper, it was shown that ï 7! Sp( f (ï)Ò g(ï)) is an analytic multivalued function, where ö denotes the spectral radius.
Abstract: RÉSUMÉ. If f and g are two analytic functions from a domain D of the complex plane into respectively the Banach spaces V+ and V , we prove that ï 7! Sp( f (ï)Ò g(ï)) is an analytic multivalued function. From this derives the subharmonicity of the functions ï 7! öV( f (ï)Ò g(ï)) and ï 7! log öV ( f (ï)Ò g(ï)) where ö denotes the spectral radius. We apply these results to obtain nice caracterizations of the radical and the socle of a Banach Jordan pair, and finally we get an algebraic structural theorem.
TL;DR: In this article, it was shown that the J0-radical of a matrix near-ring can be an intermediate ideal, which solves a conjecture p ut forward in (1).
Abstract: An example is constructed to show that theJ0-radical of a matrix near- ring can be an intermediate ideal. This solves a conjecture p ut forward in (1).
TL;DR: In this paper, it was shown that the rank of a point x belonging to the boundary of B1 or B2 is linear under some hypotheses on the ranks, and that a holomorphic mapping such that f ≥ 0 and f 0(0) is an isometry is linear.
Abstract: RESUME. Let B1 and B2 be the open unit balls of Cn1 and Cn2 for the norms k . k1 and k . k2 . Let f : B1 ! B2 be a holomorphic mapping such that f (0) ≥ 0. It is well known that, for every z 2 B1, kf (z)k2 kzk1, and kf 0(0)k 1. In this paper, I prove the converse of this result. Let f : B1 ! B2 be a holomorphic mapping such that f 0(0) is an isometry. If B2 is strictly convex, I prove that f (0) ≥ 0 and that f is linear. I also define the rank of a point x belonging to the boundary of B1 or B2. Under some hypotheses on the ranks, I prove that a holomorphic mapping such that f (0) ≥ 0 and that f 0(0) is an isometry is linear.
TL;DR: In this paper, a finite dimensional nilpotent F-algebra R whose adjoint group A(R) is not centre-by-metabelian has been constructed, in spite of the fact that R is Lie centre by metabelian and satisfies the identities x 2p = 0 when p > 2 and x 8 > 0 when P = 2.
Abstract: Abstract For every field F of characteristic p ≥ 0, we construct an example of a finite dimensional nilpotent F-algebra R whose adjoint group A(R) is not centreby- metabelian, in spite of the fact that R is Lie centre-by-metabelian and satisfies the identities x2p = 0 when p > 2 and x 8 > 0 when p = 2. The existence of such algebras answers a question raised by A. E. Zalesskii, and is in contrast to positive results obtained by Krasilnikov, Sharma and Srivastava for Lie metabelian rings and by Smirnov for the class Lie centre-by-metabelian nil-algebras of exponent 4 over a field of characteristic 2 of cardinality at least 4.