Volume 74, Issue 4

This article is concerned with bounded partially ordered sets P such that for every p ∈ P ∖ {1} there exists q ∈ P ∖ {0} such that 0 is the only lower bound of { p , q }. The posets P such that P ≅ Q if and only if P and Q have isomorphic zero-divisor graphs are completely characterized. In the case of finite posets, this result is generalized by proving that posets with isomorphic zero-divisor graphs form an interval under the partial order given by P ≲ Q if and only if there exists a bijective poset-homomorphism P → Q . In particular, the singleton intervals correspond to the posets that are completely determined by their zero-divisor graphs. These results are obtained by exploring universal and couniversal orderings with respect to posets that have isomorphic zero-divisor graphs.

In this paper, we prove the existence of small and big Ramsey degrees of classes of finite unary algebras in an arbitrary (not necessarily finite) algebraic language Ω. Our results generalize some Ramsey-type results of M. Sokić concerning finite unary algebras over finite languages. To do so, we develop a completely new strategy that relies on the fact that right adjoints preserve the Ramsey property. We then treat unary algebras as Eilenberg-Moore coalgebras for a functor with comultiplication, and using pre-adjunctions transport the Ramsey properties, we are interested in from the category of finite or countably infinite chains of order type ω . Moreover, we show that finite objects have finite big Ramsey degrees in the corresponding cofree structures over countably many generators.

In this paper, we show that there is no polynomial D ( n )-quadruple in ℤ[ X ] for some polynomials n ∈ ℤ[ X ] that are not representable as a difference of squares of two polynomials in ℤ[ X ].

In this paper, we consider some properties of commutative diagrams of Rees short exact sequences, and we also investigate the sufficient and necessary condition under which the induced sequences by functors − ⊗ M for the left S -act M . The main conclusions extend some known results. Further, we investigate preenvelopes and precovers in the category 𝓔 S of Rees short exact sequences of right S -acts.

Grüss inequality is subject of interest for many authors due to its effectiveness in predicting bounds in several quadrature problems. In the present article, we give weighted treatment of the discrete Čebyšev and Grüss type inequalities pertaining two n -tuples of real numbers in which the bounding constants are mobilised with bounding sequences of real numbers. As an application estimations of discrete Ostrowski type inequalities are provided. Finally, by practicing obtained results along with Jensen’s difference, a wide range of estimations are formalised by considering Jensen-Grüss differences.

For normalized starlike functions f : 𝔻 → ℂ, we consider the analytic functions g : 𝔻 → ℂ defined by g ( z ) = (1 + z ( f ″( z ))/ f ′( z ))/( zf ′( z )/ f ( z )) and g ( z ) = (1 − α )( zf ′( z ))/ f ( z ) + α (1 + ( zf ″( z ))/ f ′( z )), 0 ≤ α ≤ 1. We determine the largest radius ρ with 0 < ρ ≤ 1 such that g ( ρ z ) is subordinate to various functions with positive real part.

In this paper, we study the existence of positive solutions for a fourth order boundary value problem coupled to functional perturbed clamped beam boundary conditions. Our main ingredient is the classical fixed point index. The problem investigated is an extension of other problems studied in previous papers by covering very general nonlocal perturbed conditions on the boundary.

This paper deals with the oscillation and asymptotic behaviour of even order nonlinear differential equations with mixed nonlinear neutral terms. The findings are obtained via utilising an integral criterion as well as a comparison theorem with the oscillatory properties of a first order advanced and/or delay differential equation. We provide novel oscillation criteria that improve, extend, and simplify previously published ones. The results are illustrated by two examples.

In this paper we show that the following four-dimensional system of difference equations xn+1=ynα zn− 1β ,yn+1=znγ tn− 1δ ,zn+1=tnϵ xn− 1μ ,tn+1=xnξ yn− 1ρ ,n∈ N0, $$\begin{array}{} \displaystyle x_{n+1}=y_{n}^{\alpha}z_{n-1}^{\beta}, \quad y_{n+1}=z_{n}^{\gamma}t_{n-1}^{\delta}, \quad z_{n+1}=t_{n}^{\epsilon}x_{n-1}^{\mu}, \quad t_{n+1}=x_{n}^{\xi}y_{n-1}^{\rho}, \qquad n\in \mathbb{N}_{0}, \end{array}$$ where the parameters α , β , γ , δ , ϵ , μ , ξ , ρ ∈ ℤ and the initial values x – i , y – i , z – i , t – i , i ∈ {0, 1}, are real numbers, can be solved in closed forms, extending further some results in literature.

We study Euclidean operator radius inequalities of d -tuple operators as well as the sum and the product of d -tuple operators. A power inequality for the Euclidean operator radius of d -tuple operators is also studied. Further, we study the Euclidean operator radius inequalities of 2 × 2 operator matrices whose entries are d -tuple operators.

This paper studies equable parallelograms whose vertices lie on the Eisenstein lattice. Using Rosenberger’s Theorem on generalised Markov equations, we show that the set of these parallelograms forms naturally an infinite tree, all of whose vertices have degree 4, bar the root which has degree 3. This study naturally complements the authors’ previous study of equable parallelograms whose vertices lie on the integer lattice.

This article is a continuation of the study of star-𝓘-Hurewicz and strongly star-𝓘-Hurewicz properties done in [Das et al.: On certain variations of 𝓘- Hurewicz property , Topology Appl. 251 (2018), 363–376]. We primarily consider and study the relative versions of star-𝓘-Hurewicz and strongly star-𝓘-Hurewicz properties. We study their relationships with the star-Hurewicz, strongly star-Hurewicz, star-𝓘-Hurewicz, strongly star-𝓘-Hurewicz and similar other properties. Few related games are also studied.

Motivated by Bonanzinga and Maesano (2022), we introduce and study the new relative versions of star-Menger property related to some properties studied lately by Kočinac et al. (2022) and Bonanzinga et al. (2023). In this paper, we provide some examples to understand their relationships with other relativizations of star selection principles. Further, we investigate the behaviour of these spaces under various mappings.

This paper proposes a new probability model called as Maxwell - Boltzmann - Exponential (MBE) distribution. The MBE distribution arises as a mixture distribution of the Maxwell-Boltzmann and exponential distributions. The statistical properties of the distributions are studied and obtained in closed-form expressions. Three methodologies are assessed and compared for the estimation of parameters in the MBE distribution. The MBE regression model is defined, with the proposed regression model being an alternative to the gamma regression model for response variables that are extremely right-skewed and bimodal. Two real data sets are used to demonstrate the applicability of the proposed models against the existing models.

The Marshall-Olkin family of probability distributions has been the inspiration of numerous research publications in the field of probability distributions. In this paper, we present several new properties of this family. In particular, we focus on stochastic orders, stress-strength reliability, Lorenz and the Leimkhuler curves, compounding, and integrated tail distribution. Two applications related to Lorenz curves and ruin theory are finally presented.

We propose a method to obtain a new class of copulas using a probability generating function (PGF) of positive-integer valued random variable. Some existing copulas in the literature are sub-families of the proposed copulas. Various dependence measures and invariant property of the tail dependence coefficient under PGF transformation are also discussed. We propose an algorithm for generating random numbers from the PGF copula. The bivariate concavity properties, such as Schur concavity and quasi-concavity, associated with the PGF copula are studied. Two new generalized FGM copulas are introduced using PGFs of geometric and discrete Mittag-Leffler distributions. The proposed two copulas improved the Spearman’s rho of FGM copula by (−0.3333, 0.4751) and (−0.3333, 0.9573). Finally, we analyse a real dataset to illustrate the practical application of the proposed copulas.

The symbol TD ( X ) denotes the hyperspace of all nonempty totally disconnected compact subsets of a Hausdorff space X . This hyperspace is endowed with the Vietoris topology. For a mapping between Hausdorff spaces f : X → Y , define the induced mapping TD ( f ) : TD ( X ) → TD ( Y ) by TD ( f )( A ) = f ( A ) (the image of A under f ). In the current paper, we study the relationships between the condition f belongs to a class of mappings between Hausdorff spaces 𝕄 and the condition TD ( f ) belongs to 𝕄.