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
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.
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
Fix 2 < n < ω and let CA
denote the class of cyindric algebras of dimension n. Roughly CA
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
of representable CA
s reflects algebraically the semantics of Ln
. Members of RCA
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
has a finite equational axiomatization, RCA
is not finitely axiomatizable, and it generally exhibits wild, often unpredictable and unruly behavior. This makes the theory of CA
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
are not atom-canonical. A variety V of Boolean algebras with operators is atom canonical, if whenever
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.
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.
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.