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We present the sufficient condition for a classical two-class problem from Fisher discriminant analysis has a solution. Actually, the solution was presented up to our knowledge with a necessary condition only. We use an extended Cauchy–Schwarz inequality as a tool.
Let be a Schrödinger operator on the Heisenberg group
where
and
Where
Based on this inequality and known results for the Lusin area integral
In this paper, a relationship between the zeros and critical points of a polynomial p(z) is established. The relationship is used to prove Sendov’s conjecture in some special cases.
A fluid queueing system in which the fluid flow in to the buffer is regulated by the state of the background queueing process is considered. In this model, the arrival and service rates follow chain sequence rates and are controlled by an exponential timer. The buffer content distribution along with averages are found using continued fraction methodology. Numerical results are illustrated to analyze the trend of the average buffer content for the model under consideration. It is interesting to note that the stationary solution of a fluid queue driven by a queue with chain sequence rates does not exist in the absence of exponential timer.
In this paper, we define an orthonormal basis for 2-*-inner product space and obtain some useful results. Moreover, we introduce a 2-norm on a dense subset of a 2-*-inner product space. Finally, we obtain a version of the Selberg, Buzano’s and Bessel inequality and its results in an A-2-inner product space.
Abstract
We provide a Maltsev characterization of congruence distributive varieties by showing that a variety 𝓥 is congruence distributive if and only if the congruence identity
Abstract
Fix 2 < n < ω and let CA
n
denote the class of cyindric algebras of dimension n. Roughly CA
n
is the algebraic counterpart of the proof theory of first order logic restricted to the first n variables which we denote by Ln
. The variety RCA
n
of representable CA
n
s reflects algebraically the semantics of Ln
. Members of RCA
n
are concrete algebras consisting of genuine n-ary relations, with set theoretic operations induced by the nature of relations, such as projections referred to as cylindrifications. Although CA
n
has a finite equational axiomatization, RCA
n
is not finitely axiomatizable, and it generally exhibits wild, often unpredictable and unruly behavior. This makes the theory of CA
n
substantially richer than that of Boolean algebras, just as much as Lω,ω
is richer than propositional logic. We show using a so-called blow up and blur construction that several varieties (in fact infinitely many) containing and including the variety RCA
n
are not atom-canonical. A variety V of Boolean algebras with operators is atom canonical, if whenever
Abstract
Let 𝔄 be a unital Banach algebra and ℜ its Jacobson radical. This paper investigates Banach algebras satisfying some chain conditions on closed ideals. In particular, it is shown that a Banach algebra 𝔄 satisfies the descending chain condition on closed left ideals then 𝔄/ℜ is finite dimensional. We also prove that a C *-algebra satisfies the ascending chain condition on left annihilators if and only if it is finite dimensional. Moreover, other auxiliary results are established.
Abstract
We give two new simple characterizations of the Cauchy distribution by using the Möbius and Mellin transforms. They also yield characterizations of the circular Cauchy distribution and the mixture Cauchy model.
Abstract
In this paper we present different variants of the well-known Hermite–Hadamard inequality, in a generalized context. We consider general fractional integral operators for h-convex and r-convex functions.
