Volume 73, Issue 2

ABSTRACT We prove that the notion of a voltage graph lift comes from an adjunction between the category of voltage graphs and the category of group labeled graphs.

For a partial lattice L the so-called two-point extension is defined in order to extend L to a lattice. We are motivated by the fact that the one-point extension broadly used for partial algebras does not work in this case, i.e. the one-point extension of a partial lattice need not be a lattice. We describe these two-point extensions and prove several properties of them. We introduce the concept of a congruence on a partial lattice and show its relationship to the notion of a homomorphism and its connections with congruences on the corresponding two-point extension. In particular we prove that the quotient L / E of a partial lattice L by a congruence E on L is again a partial lattice and that the two-point extension of L / E is isomorphic to the quotient lattice of the two-point extension L * of L by the congruence on L * generated by E . Several illustrative examples are enclosed.

In the present paper, we consider the generalized arithmetic triangle called GAT which is structurally identical to Pascal’s triangle for which we keep the Pascal’s rule of addition and we replace both legs by two sequences ( a n ) n ≥1 and ( b n ) n ≥1 with a 0 = b 0 = Ω. Our goal is to describe the recurrence relation associated to the sum of elements lying along a finite ray in this triangle. As consequences, we obtain some combinatorial properties and we establish that the sum of elements lying along a main rising diagonal is a convolution of generalized Fibonacci sequence and another sequence which one will determine. We also precise the corresponding generating function. Further, we establish some nice identities by using the Morgan-Voyce phenomenon. Finally, we generalize the Golden ratio.

The paper investigates the asymptotic behavior of the geometric polynomials, when the polynomial degree tends to infinity. Using the contour integration technique, we obtain an asymptotic formula, given explicitly in terms of the polynomial degree and variable. This type of asymptotics will be applied to derive limit theorems for combinatorial numbers.

In this paper, we consider two new conjectures concerning D (4)-quadruples and prove some special cases that support their validity. The main result is a proof that { a, b, c } and { a + 1, b, c } cannot both be D (4)-triples.

Hardy-Leindler type inequalities and their converses for multiple integrals on time scales are proved by using Fubini’s theorem and induction principle. Some generalized versions of Hardy, Wirtinger and Leindler inequalities in both continuous and discrete cases are also derived in seek of applications.

In this paper, we establish a new variant of q -Hermite-Hadamard inequality for convex functions via left and right q -integrals. Moreover, we prove some new q -midpoint and q -trapezoid type inequalities for left and right q -differentiable functions. To illustrate the newly established inequalities, we give some particular examples of convex functions.

ABSTRACT This paper mainly discusses the existence and finite-time stability of solutions for impulsive fractional stochastic differential equations (IFSDEs). By applying the Picard-Lindelöf iteration method of successive approximation scheme, we establish the existence results of solutions. Subsequently, the uniqueness of solution is derived by the method of contradiction. In addition, we investigate the finite-time stability by means of the generalized Grönwall-Bellman inequality. As an application, examples are provided to expound our theoretical conclusions.

We investigate certain properties of tilted (oblique) domains, associated with the Janow- ski function (1 + Az )/(1 + Bz ), where A, B ∈ ℂ with A ≠ B and | B | ≤ 1. We find several bounds for these oblique domains and also establish various subordination, radius, argument estimates involving Janowski function with complex parameters. Moreover, some results also generalize earlier well-known results pertaining to Janowski function.

For a ∈ (0, 1/2], r ∈ (0, 1), let 𝒦 a ( r ) ( 𝒦 ( r )) be the generalized (complete) elliptic integral of the first kind. In the article, we prove some monotonicity properties of certain combination of functions involving 𝒦 a ( r ), and thus establish its two sharp inequalities, which extend and improve some well-known results of 𝒦 ( r ).

The article delves into the task of formulation of meticulous sequence spaces whose elements’ convergence is a generalized version of the Cauchy convergence in the setting of intuitionistic fuzzy norm. The task of attaining a finite limit is attained via an infinite matrix operator, namely, Jordan totient operator. We discuss some topological and algebraic properties and establish some inclusion relations between the spaces.

In this paper, we aim to study about the estimation of norm of ( p , q )-Bernstein operators Bp,qn$\mathcal{B}_{p,q}^{n}$ in C [0,1] for the case q > p > 1 by applying ( p , q )-calculus and divided difference analogue of ( p , q )-Bernstein operators. Some basic theorem and related results are also discussed in this paper. Here, the extra parameter p shows more flexibility by choosing the value of p .

ABSTRACT In this paper, we analyze the existence of Weyl distance in general metric and various classes of multi-dimensional Weyl p -almost periodic functions in general metric. The main structural properties for the introduced classes of Weyl almost periodic type functions are established. We also provide some applications of our theoretical results to the abstract Volterra integro-differential equations.

ABSTRACT In this paper, we investigate the existence of φ -fixed point for Banach orbital contraction over 𝔄 -metric space. Also a fixed point result has been established via asymptotic regularity property over such generalized metric space. Our fixed point theorems have also been applied to the fixed circle problem. Moreover, we give some new solutions to the open problem raised by Özgür and Taş on the geometric properties of φ -fixed points of self-mappings and the existence and uniqueness of φ -fixed circles and φ -fixed discs for various classes of self-mappings.

We consider a Riemannian manifold ( M , g ) admitting a concurrent-recurrent vector field for which the metric g is a Yamabe soliton or a τ -quasi Yamabe gradient soliton. We show that if the metric of a Riemannian three-manifold ( M , g ) admitting a concurrent-recurrent vector field is a Yamabe soliton, then M is of constant negative curvature – α 2 . In this case, we see that the potential vector field is Killing. Next, we show that if the metric of a Riemannian manifold M admitting concurrent-recurrent vector field is a non-trivial r-quasi Yamabe gradient soliton with potential function f , then M has constant scalar curvature and is equal to – n ( n – 1) α 2 . Finally, an illustrative example is presented.

ABSTRACT In this research paper, we propose a new class of bivariate distributions called Bivariate Generalized Gamma-Lindley (BGGL) distribution with four parameters. This model is a mixture of independent Gamma random variables and bivariate generalized Lindley distribution. We investigate various properties of the new bivariate distribution such as graphical representation, joint moments and correlation. Furthermore, we derive a measure of entropy of this bivariate distribution. We also derive the distributions of the random variables X 1 + X 2 , X 1 /( X 1 + X 2 ), X 1 / X 2 and X 1 X 2 as well as the corresponding moment properties when X 1 and X 2 follow the BGGL distribution. Additionally, we address two approximations of the product of the proposed model and assess their goodness of fit. Next, we elaborate the expectation maximization (E.M) algorithm in order to estimate the BGGL model parameters. Finally, we provide two concrete examples to demonstrate the applicability of the results.

ABSTRACT The multivariate exponential power is a useful distribution for modeling departures from normality in data by means of a tail weight scalar parameter that regulates the non-normality of the model. The incorporation of a shape asymmetry vector into the model serves to account for potential asymmetries and gives rise to the multivariate skew exponential power distribution. This work is aimed at revisiting the skew exponential power distribution taking as a starting point its formulation as a scale mixture of skew-normal distributions. The paper provides some highlights and theoretical insights on the role played by its parameters to assess two complementary aspects of the multivariate non-normality such as directional asymmetry and tail weight behavior regardless of the asymmetry. The intuition behind both issues relies on well-known mathematical ideas about skewness maximization and convex transform stochastic orderings.

Let us denote by ℒℱ$[\mathcal{L}\mathcal{F}$ the class of all orthomodular lattices (OMLs) that are locally finite (i.e., L∈ℒℱ$[L\in \mathcal{L}\mathcal{F}$ provided each finite subset of L generates in L a finite subOML). In this note, we first show how one can obtain new locally finite OMLs from the initial ones and enlarge thus the class ℒℱ$[\mathcal{L}\mathcal{F}$. We find ℒℱ$[\mathcal{L}\mathcal{F}$ considerably large though, obviously, not all OMLs belong to ℒℱ$[\mathcal{L}\mathcal{F}$. Then we study states on the OMLs of ℒℱ$[\mathcal{L}\mathcal{F}$. We show that local finiteness may to a certain extent make up for distributivity. For instance, we show that if L∈ℒℱ$[L\in \mathcal{L}\mathcal{F}$ and if for any finite subOML K there is a state s : K → [0, 1] on K , then there is a state on the entire L . We also consider further algebraic and state properties of ℒℱ$[\mathcal{L}\mathcal{F}$ relevant to the quantum logic theory.