Canadian Mathematical Bulletin
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Oscillation Criteria for Matrix Differential Inequalities(1)
Canadian Mathematical Bulletin - Tập 16 Số 1 - Trang 5-10 - 1973
Several authors have recently considered the problem of obtaining sufficient
conditions for the oscillation of the quasilinear matrix differential
equation(1)and the associated inequality VTLV ≤ 0 (as a form). Here A, B, and V
are m x m matrix functions, A(x) is symmetric, positive semidefinite and
continuous in an interval [a, ∞) and B(x,V, V') is symmetric and continuous in
a≤ x < ∞ for all V an...
A Note on a Theorem of Ky Fan
Canadian Mathematical Bulletin - Tập 22 Số 4 - Trang 513-515 - 1979
Fan ([2, Theorem 2]) has proved the following theorem:Let K be a nonempty
compact convex set in a normed linear space X. For any continuous map f from K
into X, there exists a point u∈K such thatIn this note, we prove that the above
theorem is true for a continuous condensing map defined on a closed ball in a
Banach space. We also prove that it is true for a continuous condensing map
defined on a ...
Matrices with Prescribed Principal Elements and Singular Values
Canadian Mathematical Bulletin - Tập 14 Số 2 - Trang 247-249 - 1971
We shall be concerned with the following problem. Let a11, …, ann be complex
numbers and λ1, …, λn nonnegative real numbers. Under what conditions does there
exist an n × n complex matrix A with a11, …, ann as principal elements and λ1,
…, λn as singular values? This problem has been suggested in [3] but, to our
knowledge, has not yet been solved.
A Note on Whitney Maps
Canadian Mathematical Bulletin - Tập 23 Số 3 - Trang 373-374 - 1980
In his recent book [3] Nadler observes that the property of admitting a Whitney
map is of fundamental importance in studying the internal structure of
hyperspaces, especially their arc structure. Nadler presents three distinct
methods of constructing a Whitney map on the hyperspace 2X of nonempty closed
subsets of a continuum.A partially ordered space is a topological space X
endowed with a partia...
Obstructions to 𝒵-Stability for Unital Simple C*-Algebras
Canadian Mathematical Bulletin - Tập 43 Số 4 - Trang 418-426 - 2000
AbstractLet 𝒵 be the unital simple nuclear infinite dimensional C*-algebra
which has the same Elliott invariant as ℂ, introduced in [9]. A C*-algebra is
called 𝒵-stable if A ≅ A ⊗ 𝒵. In this note we give some necessary conditions
for a unital simple C*-algebra to be 𝒵-stable.
Relations Between the Genera and Between the Hasse-Witt Invariants of Galois Coverings of Curves
Canadian Mathematical Bulletin - Tập 28 Số 3 - Trang 321-327 - 1985
AbstractLet G ⊂ Aut (C) be a (finite) group of automorphisms of a curve C
defined over a field K and, for each subgroup H ≤ G, let gH denote the genus of
the quotient curve CH = C/H (briefly: quotient genus of H).In this paper we show
that certain idempotent relations in the rational group ring [G] imply relations
between the quotient genera {gH}H=G this generalizes two theorems of Accola.
Moreove...
B-Stable Ideals in the Nilradical of a Borel Subalgebra
Canadian Mathematical Bulletin - Tập 48 Số 3 - Trang 460-472 - 2005
AbstractWe count the number of strictly positive B-stable ideals in the
nilradical of a Borel subalgebra and prove that the minimal roots of any
B-stable ideal are conjugate by an element of the Weyl group to a subset of the
simple roots. We also count the number of ideals whose minimal roots are
conjugate to a fixed subset of simple roots.
A Generalization of a Fixed Point Theorem of Reich
Canadian Mathematical Bulletin - Tập 16 Số 2 - Trang 201-206 - 1973
The following theorem is the principal result of this paper.Let (M, d) be a
metric space and T a self-mapping of M satisfying the condition for x,y ∊
M1where a, b, c, e,f are nonnegative and we set α=a+b+c+e+f.
An Asymptotic Bound on the Composition Number of Integer Sums of Squares Formulas
Canadian Mathematical Bulletin - Tập 56 Số 1 - Trang 70-79 - 2013
AbstractLet σZ(k) be the smallest n such that there exists an identity , with
f1, . . . , fn being polynomials with integer coefficients in the variables x1,
. . . , xk and y1, . . . , yk. We prove that σℤ(k) ≥ (k6/5).
Rings all of Whose Pierce Stalks are Local
Canadian Mathematical Bulletin - Tập 22 Số 2 - Trang 159-164 - 1979
The aim of this paper is to give a number of characterizations of the rings of
the title. In particular, these turn out to be precisely those exchange rings
whose idempotents are all central. They are also those rings in which every
element is the sum of a unit and a central idempotent.
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