scholarly journals Affirmative solution of a conjecture related to a sequence of shanks

1991 ◽  
Vol 67 (3) ◽  
pp. 70-72
Author(s):  
R. A. Mollin ◽  
H. C. Williams
Keyword(s):  
Affirmative Solution

CRITERION OF PROPER ACTIONS FOR 3-STEP NILPOTENT LIE GROUPS

2007 ◽  
Vol 18 (07) ◽  
pp. 783-795 ◽  
Author(s):  
TARO YOSHINO
Keyword(s):  
Homogeneous Space ◽  
Lie Groups ◽  
Lie Group ◽  
Closed Subgroup ◽  
Nilpotent Lie Groups ◽  
Nilpotent Lie Group ◽  
Proper Actions ◽  
Affirmative Solution

For a nilpotent Lie group G and its closed subgroup L, Lipsman [13] conjectured that the L-action on some homogeneous space of G is proper in the sense of Palais if and only if the action is free. Nasrin [14] proved this conjecture assuming that G is a 2-step nilpotent Lie group. However, Lipsman's conjecture fails for the 4-step nilpotent case. This paper gives an affirmative solution to Lipsman's conjecture for the 3-step nilpotent case.

The algebraic approach to Bernstein's problem on Mendelian models of inheritance

1980 ◽  
Vol 12 (01) ◽  
pp. 9
Author(s):  
R. W. K. Odoni
Keyword(s):  
Subject Matter ◽  
Gene Locus ◽  
Second Generation ◽  
Single Gene ◽  
Algebraic Approach ◽  
Partial Solution ◽  
Joint Paper ◽  
Genotype Frequencies ◽  
The Subject ◽  
Affirmative Solution

Consider a single gene locus for which the associated character is not sex-linked, and suppose that the character is exhibited as one of alleles. Under the Mendelian model of inheritance, if genotype frequencies are constant, the distribution of zygotes is stable from the second generation on, regardless of the value of n. (This is the celebrated Hardy–Weinberg law—see Hardy (1908).) In 1924 Bernstein raised the question of whether the Mendelian model is, in fact, a necessary consequence of the assumption that the zygote distribution is stable from the second generation on; when n = 2 or 3 Bernstein gave an affirmative solution, using elementary but tedious manipulation of probabilities. Lyubich (1971) used methods of convex analysis to obtain a partial solution of Bernstein's problem for general n. Holgate (1975) introduced algebraic methods in order to present a clearer picture of the underlying structures, and to relate Bernstein's problem to the algebras studied by Etherington (1939), Schafer (1949) and others. The purpose of this paper is to expound recent work of the author and others, building on Holgate's and Lyubich's ideas. The subject-matter of the paper is contained in a forthcoming joint paper by the author and A. E. Stratton.

scholarly journals On the affirmative solution to Salem’s problem

Analysis ◽  
2019 ◽  
Vol 39 (4) ◽  
pp. 135-149
Author(s):  
Semyon Yakubovich
Keyword(s):  
Linear Combination ◽  
Special Functions ◽  
Type Problem ◽  
Classical Analysis ◽  
Question Mark ◽  
Affirmative Solution ◽  
Minkowski Question Mark Function ◽  
Stieltjes Transforms

Abstract The Salem problem to verify whether Fourier–Stieltjes coefficients of the Minkowski question mark function vanish at infinity is solved recently affirmatively. In this paper by using methods of classical analysis and special functions we solve a Salem-type problem about the behavior at infinity of a linear combination of the Fourier–Stieltjes transforms. Moreover, as a consequence of the Salem problem, some asymptotic relations at infinity for the Fourier–Stieltjes coefficients of a power {m\in\mathbb{N}} of the Minkowski question mark function are derived.

scholarly journals Operator System Structures and Extensions of Schur Multipliers

2020 ◽  
Author(s):  
Ying-Fen Lin ◽  
Ivan G Todorov
Keyword(s):  
Extension Problem ◽  
Schur Multiplier ◽  
Dual Operator ◽  
Minimal Operator ◽  
Operator System ◽  
C Algebra ◽  
Schur Multipliers ◽  
Affirmative Solution

Abstract For a given C*-algebra $\mathcal{A}$, we establish the existence of maximal and minimal operator $\mathcal{A}$-system structures on an AOU $\mathcal{A}$-space. In the case $\mathcal{A}$ is a W*-algebra, we provide an abstract characterisation of dual operator $\mathcal{A}$-systems and study the maximal and minimal dual operator $\mathcal{A}$-system structures on a dual AOU $\mathcal{A}$-space. We introduce operator-valued Schur multipliers and provide a Grothendieck-type characterisation. We study the positive extension problem for a partially defined operator-valued Schur multiplier $\varphi $ and, under some richness conditions, characterise its affirmative solution in terms of the equality between the canonical and the maximal dual operator $\mathcal{A}$-system structures on an operator system naturally associated with the domain of $\varphi $.

A problem of Rosser and Turquette

1958 ◽  
Vol 23 (3) ◽  
pp. 271-279 ◽  
Author(s):  
Angelo Margaris
Keyword(s):  
Positive Result ◽  
Negative Results ◽  
A Value ◽  
Truth Value ◽  
Affirmative Solution ◽  
Present Section

In this paper an affirmative solution is given for the following problem in many-valued logic posed by Rosser and Turquette in [6] p. 110:For every triple ‹s, t, m› with 1 ≤ s < t < m, is it possible to define a system of m-valued logic which satisfies the following conditions? I. Every statement which always takes values ≦ s is provable. II. No statement which ever takes a value > t is provable. III. Of those statements which always take values ≤ t and sometimes take a value > s, some are provable and some are not.We state now, temporarily deferring comment, a more demanding alternative to Condition III: III′. For every truth value k such that s < k ≦ t, there are statements P and Q such that each takes the value k at least once, but never takes a value > k, and P is provable and Q is not.In § 2 a solution is given on the level of the statement calculus. The remainder of the present section is devoted to some negative results which serve to clarify the problem, and one positive result which shall cause us to replace Condition III by III′. We confine our attention to the statement calculus.

scholarly journals $$\varvec{m}$$–Isometric Composition Operators on Directed Graphs with One Circuit

2021 ◽  
Vol 93 (5) ◽  
Author(s):  
Zenon Jan Jabłoński ◽  
Jakub Kośmider
Keyword(s):  
Composition Operators ◽  
Directed Graphs ◽  
Weighted Shifts ◽  
Completion Problem ◽  
Affirmative Solution

AbstractThe aim of this paper is to investigate m–isometric composition operators on directed graphs with one circuit. We establish a characterization of m–isometries and prove that complete hyperexpansivity coincides with 2–isometricity within this class. We discuss the m–isometric completion problem for unilateral weighted shifts and for composition operators on directed graphs with one circuit. The paper is concluded with an affirmative solution of the Cauchy dual subnormality problem in the subclass with circuit containing one element.

scholarly journals Mixed foliate CR-submanifolds in a complex hyperbolic space are non-proper

1988 ◽  
Vol 11 (3) ◽  
pp. 507-515 ◽  
Author(s):  
Bang-Yen Chen ◽  
Bao-Qiang Wu
Keyword(s):  
Hyperbolic Space ◽  
Complex Hyperbolic Space ◽  
Real Submanifolds ◽  
Complex Submanifolds ◽  
Affirmative Solution ◽  
Totally Real ◽  
Cr Submanifolds

It was conjectured in [1 II] (also in [2]) that mixed foliate CR-submanifolds in a complex hyperbolic space are either complex submanifolds or totally real submanifolds. In this paper we give an affirmative solution to this conjecture.

scholarly journals On the Berger-Coburn-Lebow Problem for Hardy Submodules

2004 ◽  
Vol 47 (3) ◽  
pp. 456-467 ◽  
Author(s):  
Michio Seto
Keyword(s):  
Affirmative Solution

AbstractIn this paper we shall give an affirmative solution to a problem, posed by Berger, Coburn and Lebow, for C*-algebras on Hardy submodules.

scholarly journals Operator system quotients of matrix algebras and their tensor products

2012 ◽  
Vol 111 (2) ◽  
pp. 210 ◽  
Author(s):  
Douglas Farenick ◽  
Vern I. Paulsen
Keyword(s):  
Tensor Products ◽  
Operator System ◽  
Linear Map ◽  
Order Isomorphism ◽  
Matrix Algebras ◽  
C Algebras ◽  
Tridiagonal Matrices ◽  
Quotient Maps ◽  
Operator Systems ◽  
Affirmative Solution

{If} $\phi:\mathcal{S}\rightarrow\mathcal{T}$ is a completely positive (cp) linear map of operator systems and if $\mathcal{J}=\ker\phi$, then the quotient vector space $\mathcal{S}/\mathcal{J}$ may be endowed with a matricial ordering through which $\mathcal{S}/\mathcal{J}$ has the structure of an operator system. Furthermore, there is a uniquely determined cp map $\dot{\phi}:\mathcal{S}/\mathcal{J} \rightarrow\mathcal{T}$ such that $\phi=\dot{\phi}\circ q$, where $q$ is the canonical linear map of $\mathcal{S}$ onto $\mathcal{S}/\mathcal{J}$. The cp map $\phi$ is called a complete quotient map if $\dot{\phi}$ is a complete order isomorphism between the operator systems $\mathcal{S}/\mathcal{J}$ and $\mathcal{T}$. Herein we study certain quotient maps in the cases where $\mathcal{S}$ is a full matrix algebra or a full subsystem of tridiagonal matrices. Our study of operator system quotients of matrix algebras and tensor products has applications to operator algebra theory. In particular, we give a new, simple proof of Kirchberg's Theorem $\operatorname{C}^*(\mathbf{F}_\infty)\otimes_{\min}\mathcal{B}(\mathcal{H})=\operatorname{C}^*(\mathbf{F}_\infty)\otimes_{\max}\mathcal{B}(\mathcal{H})$, show that an affirmative solution to the Connes Embedding Problem is implied by various matrix-theoretic problems, and give a new characterisation of unital $\operatorname{C}^*$-algebras that have the weak expectation property.

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