Volume 69, Issue 4

After the establishment of the finite embeddability property for integral and commutative residuated ordered monoids by Blok and Van Alten in 2002, the finite embeddability property for some other types of residuated ordered algebraic structures have been extensively studied. The main purpose of this paper is to construct a finite quantale X̂ F from a finite partial subalgebra F of an increasing quantum B-algebra X so that F can be embedded into X̂ F , that is, the class of increasing quantum B-algebras has the finite embeddability property.

In contrast to the abundance of “direct” Ramsey results for classes of finite structures (such as finite ordered graphs, finite ordered metric spaces and finite posets with a linear extension), in only a handful of cases we have a meaningful dual Ramsey result. In this paper we prove a dual Ramsey theorem for finite ordered oriented graphs. Instead of embeddings, which are crucial for “direct” Ramsey results, we consider a special class of surjective homomorphisms between finite ordered oriented graphs. Since the setting we are interested in involves both structures and morphisms, all our results are spelled out using the reinterpretation of the (dual) Ramsey property in the language of category theory.

The paper deals with an algebraic extension of MV-semirings based on the definition of generalized Boolean algebras. We propose a semiring-theoretic approach to EMV-algebras based on the connections between such algebras and idempotent semirings. We introduce a new algebraic structure, not necessarily with a top element, which is called an EMV-semiring and we get some examples and basic properties of EMV-semiring. We show that every EMV-semiring is an EMV-algebra and every EMV-semiring contains an MV-semiring and an MV-algebra. Then, we study EMV-semiring as a lattice and prove that any EMV-semiring is a distributive lattice. Moreover, we define an EMV-semiring homomorphism and show that the categories of EMV-semirings and the category of EMV-algebras are isomorphic. We also define the concepts of G I -simple and DLO-semiring and prove that every EMV-semiring is a G I -simple and a DLO-semiring. Finally, we propose a representation for EMV-semirings, which proves that any EMV-semiring is either an MV-semiring or can be embedded into an MV-semiring as a maximal ideal.

We introduce a nonsymmetric matrix defined by q -integers. Explicit formulæ are derived for its LU -decomposition, the inverse matrices L −1 and U −1 and its inverse. Nonsymmetric variants of the Filbert and Lilbert matrices come out as consequences of our results for special choices of q and parameters. The approach consists of guessing the relevant quantities and proving them later by traditional means.

Let σ = { σ i ∣ i ∈ I } be some partition of the set of all primes ℙ, G be a finite group and σ ( G ) = { σ i ∣ σ i ∩ π ( G ) ≠ ∅}. G is said to be σ - primary if ∣ σ ( G )∣ ≤ 1. A subgroup H of G is said to be σ - subnormal in G if there exists a subgroup chain H = H 0 ≤ H 1 ≤ … ≤ H t = G such that either H i −1 is normal in H i or H i /( H i −1 ) H i is σ -primary for all i = 1, …, t . A set 𝓗 of subgroups of G is said to be a complete Hall σ - set of G if every non-identity member of 𝓗 is a Hall σ i -subgroup of G for some i and 𝓗 contains exactly one Hall σ i -subgroup of G for every σ i ∈ σ ( G ). Let 𝓗 be a complete Hall σ -set of G . A subgroup H of G is said to be 𝓗- permutable if HA = AH for all A ∈ 𝓗. We say that a subgroup H of G is weakly 𝓗- permutable in G if there exists a σ -subnormal subgroup T of G such that G = HT and H ∩ T ≤ H 𝓗 , where H 𝓗 is the subgroup of H generated by all those subgroups of H which are 𝓗-permutable. By using the weakly 𝓗-permutable subgroups, we establish some new criteria for a group G to be σ -soluble and supersoluble, and we also give the conditions under which a normal subgroup of G is hypercyclically embedded.

In this paper, with a new approach, a new fractional Hermite-Hadamard type inequalities for convex functions is obtained by using only the left Riemann-Liouville fractional integral. Also, to have new fractional trapezoid and midpoint type inequalities for the differentiable convex functions, two new equalities are proved. Our results generalize earlier studies. We expect that this study will be lead to the new fractional integration studies for Hermite-Hadamard type inequalities.

We obtained a version of Hardy-Rellich type inequality in a domain Ω ∈ ℝ n which involves the distance to the boundary, the diameter and the volume of Ω. Weight functions in the inequalities depend on the “mean-distance” function and on the distance function to the boundary of Ω. The proved inequalities connect function to first and second order derivatives.

In this paper we introduce a new concept of Choquet-Stieltjes integral of f with respect to g on intervals, as a limit of Choquet integrals with respect to a capacity μ . For g ( t ) = t , one reduces to the usual Choquet integral and unlike the old known concept of Choquet-Stieltjes integral, for μ the Lebesgue measure, one reduces to the usual Riemann-Stieltjes integral. In the case of distorted Lebesgue measures, several properties of this new integral are obtained. As an application, the concept of Choquet line integral of second kind is introduced and some of its properties are obtained.

Under a certain condition, we propose a uniqueness theorem about meromorphic functions sharing four distinct small functions on an annulus. Two counter examples are given in order to show the certain condition is necessary. Our results generalize or improve the previous theorems due to T. B. Cao et al. and N. Wu et al.

Making use of Ruscheweyh q -differential operator, we define a new subclass of uniformly convex functions and corresponding subclass of starlike functions with negative coefficients. The main object of this paper is to obtain, coefficient estimates, closure theorems and extreme point for the functions belonging to this new class. The results are generalized to families with fixed finitely many coefficients.

The aim of this paper is to bring together two areas of studies in the theory of analytic functions: functions of bounded variation and functions related to domains bounded by conic sections. Some relevant properties are indicated.

Let Sψ∗$\begin{array}{} \mathcal {S}^*_\psi \end{array}$ be a subclass of starlike functions in the unit disk 𝕌, where ψ is a convex function such that ψ (0) = 1, ψ ′(0) > 0, ℜ( ψ ( ξ )) > 0 and ψ (𝕌) is symmetric with respect to the real axis. We obtain the sharp solution of Fekete-Szegö problem for the family Sψ∗$\begin{array}{} \mathcal {S}^*_\psi \end{array}$, and then extend the result to the case of corresponding subclass defined on the bounded starlike circular domain Ω in several complex variables, which give an unified answer of Fekete-Szegö problem for the kinds of subclasses of starlike mappings defined on Ω. At last, we propose two conjectures related the same problems on the unit ball in a complex Banach space and on the unit polydisk in ℂ n .

The Riccati equation method is used to establish three new oscillatory criteria for the second order linear ordinary differential equations. We show that the first of these criteria in the continuous case of the coefficient function (potential) of the equation implies the J. Deng’s oscillatory criterion. An extremal oscillatory condition for the Mathieu’s equation is obtained. The obtained results are compared with some known oscillatory criteria.

In this paper we introduce rough weighted statistical limit set and weighted statistical cluster points set which are natural generalizations of rough statistical limit set and statistical cluster points set of double sequences respectively. Some new examples are constructed to ensure the deviation of basic results. Both the sets don’t follow the usual extension properties which will be discussed here.

Let 𝓐 be a Banach algebra and let 𝓜 be a unital Banach algebra. For a homomorphism Φ from 𝓐 into 𝓜, we consider 𝓜 as a Banach right 𝓐-module and investigate when 𝓜 is a retract of 𝓐 with respect to Φ. We also give characterizations of admitting vector-valued invariant Φ-means in terms of projectivity and injectivity. Finally, we apply these results to abstract Segal algebras.

In this article we introduce binomial difference sequence spaces of fractional order α , bpr,s$\begin{array}{} b_p^{r,s} \end{array}$ (Δ ( α ) ) (1 ≤ p ≤ ∞) by the composition of binomial matrix, B r , s and fractional difference operator Δ ( α ) , defined by (Δ ( α ) x ) k = ∑i=0∞(−1)iΓ(α+1)i!Γ(α−i+1)xk−i$\begin{array}{} \displaystyle \sum\limits_{i=0}^{\infty}(-1)^i\frac{\Gamma(\alpha+1)}{i!\Gamma(\alpha-i+1)}x_{k-i} \end{array}$. We give some topological properties, obtain the Schauder basis and determine the α , β and γ -duals of the spaces. We characterize the matrix classes (bpr,s$\begin{array}{} b_p^{r,s} \end{array}$(Δ ( α ) ), Y ), where Y ∈ { ℓ ∞ , c , c 0 , ℓ 1 } and certain classes of compact operators on the space bpr,s$\begin{array}{} b_p^{r,s} \end{array}$(Δ ( α ) ) using Hausdorff measure of non-compactness. Finally, we give some geometric properties of the space bpr,s$\begin{array}{} b_p^{r,s} \end{array}$(Δ ( α ) ) (1 < p < ∞).

We obtain a refined Young type inequality in this paper. The conclusion is presented as follows: Let A , B ∈ B (𝓗) be two positive operators and p ∈ [0, 1], then A♯pB+G∗(A♯pB)G≤A∇pB−2r(A∇B−A♯B),$$\begin{array}{} \displaystyle A\sharp_p B+G^*(A\sharp_p B)G\le A\nabla_p B-2r(A\nabla B-A\sharp B), \end{array}$$ where r = min{ p , 1 – p }, G = L(2p)2$\begin{array}{} \displaystyle \frac{\sqrt{L(2p)}}{2} \end{array}$ A –1 S ( A | B ), L ( t ) is periodic with period one and L ( t ) = t221−tt2t$\begin{array}{} \displaystyle \frac{t^2}{2}\left( \frac{1-t}{t} \right)^{2t} \end{array}$ for t ∈ [0, 1]. Moreover, we give the s -th powering of two inequalities related to the above one with s > 0 which refines Lin’s work. In the mean time, we present an inequality involving Hilbert-Schmidt norm.

In this paper, we show that a class of metric spaces determined by a continuous function f , which defines on the metric space of all real, n × n -matrices m is closed under the Gromov-Hausdorff convergence. This conclusion can be used to prove some metric properties of metric space is stable under the Gromov-Hausdorff convergence. Secondly, we consider the stability problem in Gromov hyperbolic space and show that if a sequence of Gromov hyperbolic spaces ( X n , d n ) is said to converge to ( X , d ) in the sense of Gromov-Hausdorff convergence, then the Gromov hyperbolicity δ ( X n ) of ( X n , d n ) tends to the Gromov hyperbolicity δ ( X ) of ( X , d ).

We introduce and study the beta exponentiated Nadarajah-Haghighi model, which has increasing, decreasing, upside-down bathtub and bathtub shaped hazard functions. Some of its mathematical properties are determined including a power series for the quantile function. We perform a Monte Carlo simulation study to assess the finite sample behavior of the maximum likelihood estimates of the parameters. We define a new regression model based on the new distribution. The potentiality of this regression model is proved empirically by means of a real dataset related to diabetic retinopathy study.

Based on the work of A. Monteiro, A. Torrens, and D. Buşneag, in this paper we point out that the dual space of Hilbert algebras with supremum generated by chains depends, modulo the dual space of a Hilbert algebra with supremum defined by S. Celani an D. Montangie, exclusively, on the order carried out by the topological space. We use such a characterization to prove that a bounded Hilbert algebra generated by chains is determined by the monoid of its endomorphisms.