Related papers: On Log-Concave Operator Acting on Sequences and Se…
We consider log-convex sequences that satisfy an additional constraint imposed on their rate of growth. We call such sequences log-balanced. It is shown that all such sequences satisfy a pair of double inequalities. Sufficient conditions…
What is Sequence Algebra? This is a question that any teacher or student of mathematics or computer science can engage with. Sequences are in Calculus, Combinatorics, Statistics and Computation. They are foundational, a step up from number…
We present a characterization of operator log-convex functions by using positive linear mappings. Moreover, we study the non-commutative f-divergence functional of operator log-convex functions. In particular, we prove that f is operator…
In this paper, we primarily deal with approximately monotone and convex sequences. We start by showing that any sequence can be expressed as the difference between two nondecreasing sequences. One of these two monotone sequences act as the…
We examine the convergence properties of sequences of nonnegative real numbers that satisfy a particular class of recursive inequalities, from the perspective of proof theory and computability theory. We first establish a number of results…
This work investigates the properties of the proximity operator for quasar-convex functions and establishes the convergence of the proximal point algorithm to a global minimizer with a particular focus on its convergence rate. In…
This paper is concerned with the convergence of power sequences and stability of Hilbert space operators, where "convergence" and "stability" refer to weak, strong and norm topologies. It is proved that an operator has a convergent power…
In this paper, we introduce operator geodesically convex and operator convex-log functions and characterize some properties of them. Then apply these classes of functions to present several operator Azc\'{e}l and Minkowski type inequalities…
Generating logical form equivalents of human language is a fresh way to employ neural architectures where long short-term memory effectively captures dependencies in both encoder and decoder units. The logical form of the sequence usually…
Given the congruence lattice L of a finite algebra A with a Mal'cev term, we look for those sequences of operations on L that are sequences of higher commutator operations of expansions of A. The properties of higher commutators proved so…
We discuss interplays between log-concave functions and log-concave sequences. We prove a Bernstein-type theorem, which characterizes the Laplace transform of log-concave measures on the half-line in terms of log-concavity of the…
Horizontal and vertical generating functions and recursion relations have been investigated by Comtet for triangular double sequences. In this paper we investigate the horizontal and vertical log-concavity of triangular sequences assigned…
The last decade has witnessed the success of the traditional feature-based method on exploiting the discrete structures such as words or lexical patterns to extract relations from text. Recently, convolutional and recurrent neural networks…
We investigate log-concavity in the context of level Hilbert functions and pure $O$-sequences, two classes of numerical sequences introduced by Stanley in the late Seventies whose structural properties have since been the object of a…
A collectively $\sigma$-Levi set of operators is a generalization of the $\sigma$-Levi operator. By use of collective order convergence, we investigate relations between collectively $\sigma$-Levi and collectively compact sets of operators.
In this paper we introduce and study some Hilbert-type operators acting from the function spaces into the sequence spaces. We give some sufficient and necessary conditions for the boundedness and compactness of these Hilbert-type operators.…
In recent years, the log-concavity of $\{\sqrt[n]{S_n}\}_{n\geq 1}$ have been received a lot of attention. Very recently, Sun posed the following conjecture in his new book: the sequences $\{\sqrt[n]{a_n}\}_{n\geq 2}$ and $\{…
We extend the exponential formula by Bender and Canfield (1996), which relates log-concavity and the cycle index polynomials. The extension clarifies the log-convexity relation. The proof is by noticing the property of a compound Poisson…
The theory of the functional sequences and series is presented; uniformly convergent, convergent in the sense of a mean square and weakly convergent sequences and series are considered. Sequential approach to constructing generalized…
We define the field $\mathbb{L}$ of logarithmic hyperseries, construct on $\mathbb{L}$ natural operations of differentiation, integration, and composition, establish the basic properties of these operations, and characterize these…