Volume 72, Issue 3

Let XY L , T consist of all countable L -structures M that satisfy the axioms T and in which all homomorphisms of type X (these could be plain homomorphisms, monomorphisms, or isomorphisms) between finite substructures of M are restrictions of an endomorphism of M of type Y (for example, an automorphism or a surjective endomorphism). Lockett and Truss introduced 18 such classes for relational structures. For a given pair L , T however, two or more morphism-extension properties may define the same class of structures. In this paper, we establish all equalities and inequalities between morphism-extension classes of countable graphs.

In this paper, we introduce the notion of state monadic BL-algebras and we investigate their properties. We define the concept of state monadic filters and study certain types of state monadic filters; we define and charaterize maximal and prime state monadic filters. Characterizations of local, simple and semisimple state monadic BL-algebras are also explored in the paper as well.

Batch verification for digital signature scheme is a method to verify multiple signatures simultaneously. The complex exponent test (CE test for short) proposed by Cheon and Lee is one of the most efficient batch verification tests for several digital signature schemes on certain types of elliptic curves (including Koblitz curves). The security of the CE test relies essentially on the cardinality of a subset of a residue ring of the endomorphism ring of an elliptic curve over an ideal. They have evaluated the cardinality of the above subset, and have illustrated the effectiveness of the CE test by using the evaluation. The aim of this paper is to point out that their evaluation contains a flaw. The flaw is generally related to two roots of a quadratic equation which is used in their argument. We mend the flaw of their evaluation. Our correct evaluation shows that the CE test can achieve the same security as the underlying signature scheme on Koblitz curves. As a result, the CE test is a secure batch verification when the underlying signature scheme uses Koblitz curves.

Let f ( x ) ∈ ℤ[ x ] be monic and irreducible over ℚ, with deg( f ) = n . Let K = ℚ( θ ), where f ( θ ) = 0, and let ℤ K denote the ring of integers of K . We say f ( x ) is monogenic if {1, θ , θ 2 , …, θ n −1 } is a basis for ℤ K . Otherwise, f ( x ) is called non-monogenic . In this article, we give necessary and sufficient conditions for a certain class of polynomials to be monogenic. Using these conditions allows us to generate infinite families of non-monogenic polynomials. In particular, for quadrinomials our results show that there exist infinitely many primes p ≥ 3, and integers t ≥ 1 coprime to p , such that f ( x ) = x p − 2 ptx p −1 + p 2 t 2 x p −2 + 1 is non-monogenic. Finally, we illustrate this situation with an explicit example.

Let P k and Q k be the k -th terms of the Pell and Pell-Lucas sequences respectively. In this paper, we find all the solutions of the Diophantine equations P n + 1 x ± P n − 1 x = Q m $$\begin{array}\displaystyleP_{n+1}^x\pm P_{n-1}^x=Q_m\end{array}$$ in nonnegative integer variables ( m , n , x ).

We shall prove a variety of results on certain types of Putcha semigroups such as: left weakly commutative semigroups, 𝓡-commutative semigroups, 𝓡𝓒-commutative semigroups, generalized conditionally commutative semigroups.

In this paper, under some conditions on weighted function K , we give some new equivalent characterizations of inner functions in Q K spaces. Meanwhile, we also studied inner functions in Q K spaces as multipliers of C 𝓑 ( Q K ) ∩ BMOA , where C 𝓑 ( Q K ) denoted the closure of Q K spaces in Bloch spaces.

In this paper, we extend the idea of q -derivative (or q -difference) operator for meromorphic p -valent functions and introduce certain new subclasses of meromorphic multivalent q -starlike and q -convex functions. We investigate subordination properties, coefficient inequalities, convolution properties and integral representations. We also derive sufficient conditions for meromorphic multivalent q -starlike and q -convex functions and highlight some known consequence of our main results.

In this article, we will show some algebraic dependence theorems for meromorphic mappings into a projective space sharing few hyperplanes. Our result is an improvement of many previous results in this topic.

In this work, sufficient conditions are established for oscillation of all unbounded solutions of a class of fourth order neutral differential equations of the form ( r ( t ) ( y ( t ) + p ( t ) y ( t − τ ) ) ″ ) ″ + q ( t ) G ( y ( t − α ) ) − h ( t ) H ( y ( t − σ ) ) = 0 $$\begin{array}{}\displaystyle (r(t)(y(t)+p(t)y(t-\tau))'')''+q(t)G(y(t-\alpha))-h(t)H(y(t-\sigma)) = 0\end{array} $$ under the non-canonical type assumption ∫ 0 ∞ t r ( t ) d t < ∞ $$\begin{array}{}\displaystyle \int\limits_{0}^{\infty}\frac{t}{r(t)}{\rm d} t \lt \infty\end{array} $$ for various ranges of p ( t ) with ∣ p ( t )∣ < ∞.

The existence of at least one positive radial solution of the p -biharmonic problem Δ H n ( w ( ξ ) | Δ H n u | p − 2 Δ H n u ) + R ( ξ ) w ( ξ ) | u | p − 2 u = ∑ i = 1 m a i ( | ξ | H n ) | u | q i − 2 u − ∑ j = 1 k b j ( | ξ | H n ) | u | r j − 2 u , $$\begin{array}{}\displaystyle\Delta_{\mathbb{H}^n}\big(w(\xi)|\Delta_{\mathbb{H}^n}u|^{p-2}\Delta_{\mathbb{H}^n}u\big)+ R (\xi)w(\xi) |u|^{p-2} u=\sum_{i=1}^ma_i (|\xi|_{\mathbb{H}^n}) |u|^{q_i-2} u -\sum_{j=1}^k b_j (|\xi|_{\mathbb{H}^n}) |u|^{r_j-2}u,\end{array}$$ with Navier boundary condition on a Korányi ball is proved, where w ∈ A s is a Muckenhoupt weight function and Δ Hn,p2$\begin{array}{}\displaystyle\Delta^2_{\mathbb{H}^n, p}\end{array}$ is the Heisenberg p -biharmonic operator.

The concept of regular matrix was introduced by Wilansky which was later used to define regular Tribonacci matrix by Yaying and Hazarika. In this paper, by using the domain of regular Tribonacci matrix A = ( a jk ) and the concept of ideal convergence, we introduce some intuitionistic fuzzy Tribonacci ideal convergent spaces. We also focus on some topological and algebraic properties of these convergent sequence spaces.

In the present paper we consider some specific properties of special series of Fourier coefficients of the Lipschitz class functions with respect to general orthonormal systems (ONS). The obtained results demonstrate that the properties of the general ONS and of the subsequence of this system are essentially different. It is shown that the problems for the general ONS are trivial for classical ONS (trigonometric, Haar and Walsh systems).

The goal of this paper is to obtain the spectra and fine spectra of the matrix Δ 3ab$\begin{array}{}\displaystyle\Delta_{3}^{ab}\end{array}$ on the Hahn space. Also, we explore some ideas of how to study the problem for a general form of the matrix, namely, the matrix Δ nab$\begin{array}{}\displaystyle\Delta _{n}^{ab}\end{array}$ where the non-zero diagonals are the entries of a n -ary repetition sequence.

In this paper, we investigate topological sphere theorems for compact minimal contact CR-submanifolds of odd dimensional unit sphere. We show that if an inequality involving the warping function and the scalar curvature of the fibers is satisfied, a compact minimal contact CR-warped product submanifold of the odd dimensional unit sphere is homeomorphic to the sphere. In particular case, for 5-dimensional unit sphere, we show that a 4-dimensional compact minimal contact CR-warped product submanifold is homeomorphic to a sphere if ∣∇ln f ∣ 2  < 1 is satisfied. By using Bonnet-Myers’s theorem we give a result about fundamental group and by Leung’s theorem we obtain a result about homology groups of a contact CR-warped submanifold.

We propose a new family of continuous distributions with two shape parameters called the Extended type I(ET1HL-G). We study some basic properties including quantile function, asymptotic, mixture for cdf and pdf, various entropies and order statistics. Then we study half-logistic distribution as special case with more details. The maximum likelihood estimates of parameters are compared with various methods of estimations by conducting a simulation study. Finally, two data sets are illustration the purposes.

In this paper, a new distribution defined on (0, 1) is introduced. It is obtained by the transformation of a positive random variable following the Chen distribution with respect to the inverted exponential function. Basic distributional properties of the newly defined distribution are studied. Then, as a statistical model, we examine different methods of estimation for related parameters. We assess the performance of the obtained estimators by a complete simulation study. Subsequently, the quantile regression model based on the proposed distribution is introduced. Applications of the proposed models to real data sets show that they have better modeling capabilities than fair competitors.

Let K be a fixed proper convex cone contained in a separable Banach space E . Our main result in this note is a construction of a fuzzy process taking values in K -positive fuzzy sets, i.e. in a cone FcconvK(E)$ \mathcal F_{\mathrm{cconv}}^{K}(E) $ of fuzzy sets contained in K . We prove that this process can be considered as a fuzzy Lévy subordinator (with values in FcconvK(E)$ \mathcal F_{\mathrm{cconv}}^{K}(E) $) or simply fuzzy FcconvK(E)$ \mathcal F_{\mathrm{cconv}}^{K}(E) $ -subordinator .

Consider the following nonparametric model: Y ni = g ( x ni )+ ε ni , 1 ⩽  i  ⩽  n , where xni∈A$ x_{ni}\in \mathbb{A} $ are the nonrandom design points and A$ \mathbb{A} $ is a compact set of ℝ m for some m =1, g (·) is a real valued function defined on A$ \mathbb{A} $, and ε n 1 , ⋅, ε nn are zero mean φ -mixing random errors with finite moment of 2+ δ order for some δ >0. Under some general conditions, we obtain the uniformly asymptotic normality of the weighted estimator of g (·). The rate of Berry-Esseen bound can approximate O ( n −1/4 ) under some appropriate conditions. The validity of the main results is partially illustrated via a numerical simulation.

Both variance and entropy are commonly used measures for uncertainty. There exists many cases where variance is infinite and entropy is finite. In this note, we derive an upper bound illustrating the relationship between variance and entropy of random variables having a special class of distributions. We also derive an upper bound for k th absolute central moment proportional to entropy power for a special class of distributions.

A. V. Arhangelskii introduced the dimension Dind and properties of this dimension have been studied for various classes of topological spaces. In this paper, we study this dimension for finite T 0 -spaces. Especially, we prove that in the realm of finite T 0 -spaces, Dind is less than or equal to the small inductive dimension ind, the large inductive dimension Ind and the covering dimension dim. We also study the “gaps” between Dind and the dimensions ind, Ind and dim, presenting various examples which shows these “gaps”. Moreover, in this field of spaces, we give characterizations of Dind, inserting the meaning of the maximal family of pairwise disjoint open sets, and study properties of this dimension.