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Padovan or Perrin numbers that are concatenations of two distinct base b repdigits Math. Slovaca (IF 1.6) Pub Date : 2023-02-16 Kouèssi N. Adédji, Virgile Dossou-yovo, Salah E. Rihane, Alain Togbé
Let {P n } n⩾0 be the Padovan sequence with initial conditions P 0=0, P 1=1, and P 2=1 and the recurrence relation P n+3=P n+1 + P n . Its companion sequence is known as the Perrin sequence {E n } n⩾0 that satisfies the same above recurrence relation with the initial conditions E 0=3, E 1=0 and E 2=2. In this paper, we determine all Padovan and Perrin numbers that are concatenations of two distinct
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A topological duality for dcpos Math. Slovaca (IF 1.6) Pub Date : 2023-02-16 Liping Zhang, Xiangnan Zhou
In this paper, a Stone-type duality for directed complete posets with a top element is developed by using a class of special subsets, named prime Scott open subsets. Following this idea, a topological duality for complete lattices is also obtained.
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Addendum to “A generalization of a result on the sum of element orders of a finite group” Math. Slovaca (IF 1.6) Pub Date : 2023-02-16 Mihai-Silviu Lazorec, Marius Tărnăuceanu
Let G be a group of order n and H be a subgroup of order m of G. Denote by ψ H (G) the sum of element orders relative to H of G. It is known that if G is nilpotent, then ψ H ( G ) ≤ ψ H m ( C n ) $ \psi_H(G) \leq\psi_{H_m}(C_n) $ , where H m is the unique subgroup of order m of C n . In this note, we show that this inequality does not hold for infinitely many finite solvable groups.
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Remarks on w-distances and metric-preserving functions Math. Slovaca (IF 1.6) Pub Date : 2023-02-16 Thanakorn Prinyasart, Suchat Samphavat
In this paper, we define new classes of functions related to metrics and w-distances. We also provide characterizations of functions in these classes. As a consequence, we obtain relations between all classes.
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Radically principal MV-algebras Math. Slovaca (IF 1.6) Pub Date : 2023-02-16 Olivier A. Heubo-Kwegna, Jean B. Nganou
An MV-algebra A is radically principal if every prime ideal P of A is radically principal, i.e., there exists a principal ideal I of A such that Rad ( P ) = Rad ( I ) $ \text{Rad}(P)=\text{Rad}(I) $ . We investigate radically principal MV-algebras and provide some characterizations as well as some classes of examples. We prove a Cohen-like theorem, precisely, an MV-algebra is radically principal if
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Solution of logarithmic coefficients conjectures for some classes of convex functions Math. Slovaca (IF 1.6) Pub Date : 2023-02-16 Ebrahim Analouei Adegani, Teodor Bulboacă, Nafya Hameed Mohammed, Paweł Zaprawa
In [Logarithmic coefficient bounds and coefficient conjectures for classes associated with convex functions, J. Funct. Spaces 2021 (2021), Art. ID 6690027], Alimohammadi et al. presented a few conjectures for the logarithmic coefficients γ n of the functions f belonging to some well-known classes like C ( 1 + α z ) $ \mathcal{C}(1+\alpha z) $ for α ∈ (0, 1], and C V h p l ( 1 / 2 ) $ \mathcal{CV}_{hpl}(1/2)
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Schur m-power convexity for general geometric Bonferroni mean of multiple parameters and comparison inequalities between several means Math. Slovaca (IF 1.6) Pub Date : 2023-02-16 Yi-Ting Wu, Feng Qi
In the paper, the authors present the Schur m-power convexity and concavity for the general geometric Bonferroni mean of multiple parameters and establish comparison inequalities for bounding the general geometric Bonferroni mean in terms of the arithmetic, geometric, and harmonic means. These Schur convexity and concavity provide a unified generalization of the Schur convexity and concavity for the
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Asymptotic stability of nonlinear neutral delay integro-differential equations Math. Slovaca (IF 1.6) Pub Date : 2023-02-16 Grzegorz Nowak, Samir H. Saker, Aneta Sikorska-Nowak
In this paper, by using Sadovskii’s fixed point theorem and the properties of the measure of noncompactness, we establish some sufficient conditions for the asymptotic stability results of nonlinear neutral integro-differential equations with variable delays. The results presented in this paper improve and generalize some results in the literature. An example is considered to illustrate our main results
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Conditions forcing the existence of relative complements in lattices and posets Math. Slovaca (IF 1.6) Pub Date : 2023-02-16 Ivan Chajda, Helmut Länger
It is elementary and well known that if an element x of a bounded modular lattice L $ \mathbf L $ has a complement in L $ \mathbf L $ then x has a relative complement in every interval [a, b] containing x. We show that the relatively strong assumption of modularity of L $ \mathbf L $ can be replaced by a weaker one formulated in the language of so-called modular triples. We further show that, in general
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Quantum ostrowski type inequalities for pre-invex functions Math. Slovaca (IF 1.6) Pub Date : 2022-12-21 Muhammad Aamir Ali, Hüseyin Budak, Mehmet Zeki Sarikaya, Erhan Set
In this paper, using the quantum derivatives and quantum integrals, we prove some new quantum Ostrowski’s type inequalities for pre-invex functions. Furthermore, in the special cases of newly developed inequalities, we obtain different new and existing Ostrowski’s type inequalities.
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Strengthenings of Young-type inequalities and the arithmetic geometric mean inequality Math. Slovaca (IF 1.6) Pub Date : 2022-12-21 Yonghui Ren, Pengtong Li
In this paper, we present some generalizations and further refinements of Young-type inequality due to Choi [Math. Inequal. Appl. 21 (2018), 99–106], which strengthen the results obtained by Ighachane et al. [Math. Inequal. Appl. 23 (2020), 1079–1085]. As applications of these scalars results, we can get some inequalities for determinants, trace and p-norms of τ-measurable operators.
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Induced mappings on symmetric products of Hausdorff spaces Math. Slovaca (IF 1.6) Pub Date : 2022-12-21 Yolanda García, David Maya
The symbol 𝓕 n (X) denotes the hyperspace of all nonempty subsets of a Hausdorff space X having at most n points. This hyperspace is endowed with the Vietoris topology. For a mapping between Hausdorff spaces f : X → Y, define the induced mapping fn : 𝓕 n (X) → 𝓕 n (Y) by fn (A) = f(A) (the image of A under f). In this paper, we study the relationship between the condition f belongs to a class of
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A new extension of the beta generator of distributions Math. Slovaca (IF 1.6) Pub Date : 2022-12-21 Mustapha Muhammad, Lixia Liu
In this paper, we introduced a new extension of the beta generator of distributions. Some important properties of the model are discussed, such as the series representation, quantile function, moments, Rényi entropy, and order statistics. Three special members are discussed, namely, the new extended beta exponential (NEBE), new extended beta uniform (NEBU), and new extended beta half logistic (NEBH)
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Hermite-Hadamard type inequalities for interval-valued fractional integrals with respect to another function Math. Slovaca (IF 1.6) Pub Date : 2022-12-21 Tuba Tunç
In this paper, first we define interval-valued left-sided and right-sided fractional integrals of a function with respect to the another function. Then, we handle Hermite-Hadamard type inequalities via these definitions.
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Gini index on generalized r-partitions Math. Slovaca (IF 1.6) Pub Date : 2022-12-21 Toufik Mansour, Matthias Schork, Mark Shattuck, Stephan Wagner
The Gini index of a set partition π of size n is defined as 1 − δ ( π ) n 2 , $1-\frac{\delta (\pi )}{{{n}^{2}}},$ where δ(π) is the sum of the squares of the block cardinalities of π. In this paper, we study the distribution of the δ statistic on various kinds of set partitions in which the first r elements are required to lie in distinct blocks. In particular, we derive the generating function for
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Approximity of asymmetric metric spaces Math. Slovaca (IF 1.6) Pub Date : 2022-12-21 Sanjoy Ghosal, Sourav Mandal, Mandobi Banerjee
In this present work, we perceive the ideas of rough weighted statistical limit set as well as rough weighted statistical cluster points set and originate these conceptions into asymmetric metric spaces. On this context we frame out several results which substantially intensify these perceptions. While explicating such notions in terms of their asymmetric concepts, this generalization despite unfollows
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A new family of compound exponentiated logarithmic distributions with applications to lifetime data Math. Slovaca (IF 1.6) Pub Date : 2022-12-21 Nooshin Hakamipour, Yuanyuan Zhang, Saralees Nadarajah
The logarithmic distribution and a given lifetime distribution are compounded to construct a new family of lifetime distributions. The compounding is performed with respect to maxima. Expressions are derived for lifetime properties like moments and the behavior of extreme values. Estimation procedures for the method of maximum likelihood are also derived and their performance assessed by a simulation
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A bivariate extension of the Omega distribution for two-dimensional proportional data Math. Slovaca (IF 1.6) Pub Date : 2022-12-21 Ömer Özbilen, Alі İ. Genç
When data generating mechanism generates two correlated data sets both defined on the unit interval, a bivariate probabilistic distribution defined on the unit square is needed for modelling the data. For this purpose, we give a Marshall-Olkin type bivariate extension of an omega distribution in this paper. This is in fact a bivariate unit-exponentiated-half-logistic distribution. We study its mathematical
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Generalizations of the steffensen integral inequality for pseudo-integrals Math. Slovaca (IF 1.6) Pub Date : 2022-12-21 Jing Guo, Xianzhong Zhou
In this paper, our aim is to prove certain kinds of Steffensen type integral inequalities for the pseudo-integral and the discrete pseudo-integral. The observations concern two cases of the real semiring with pseudo-operations with respect to pseudo-integrals: the first semiring, where pseudo-operations are defined via a monotone and continuous function g, the second semiring, when pseudo-operations
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Bernstein polynomials based iterative method for solving fractional integral equations Math. Slovaca (IF 1.6) Pub Date : 2022-12-21 Zoltan Satmari, Alexandru Mihai Bica
A novel iterative numerical method is constructed for solving second kind Volterra fractional integral equations. The method uses at each iterative step a Bernstein spline interpolation procedure combined with the corresponding quadrature formula. In this way, based on the nice approximation and shape preserving properties of the Bernstein polynomials, we propose an alternative to the classical product
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On some applications of Duhamel operators Math. Slovaca (IF 1.6) Pub Date : 2022-12-21 Ramiz Tapdigoglu, Najla Altwaijry
Let 𝔻 = {z ∈ C : |z| < 1} be the unit disk and Hol(𝔻 × 𝔻) be the space of all holomorphic functions on the bi-disc 𝔻 × 𝔻. We consider the double convolution operator 𝒦 f on the subspace Hol zw (𝔻 × 𝔻) := {f ∈ Hol(𝔻 × 𝔻) : f(z,w) = g(zw) for some g ∈ Hol(𝔻)} defined by K f h ( z w ) = ( f ∗ h ) ( z w ) := ∫ 0 z ∫ 0 w f ( ( z − u ) ( w − v ) ) h ( u v ) d v d u . $$\left( {{\mathcal{K}}_{f}}h
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The Teissier-G family of distributions: Properties and applications Math. Slovaca (IF 1.6) Pub Date : 2022-12-21 Joseph Thomas Eghwerido, Lawrence Chukwudumebi Nzei, Adebola Evelyn Omotoye, Friday Ikechukwu Agu
This study introduces a parsimonious and tractable generator for continuous distribution called the Teissier-G family of distributions for continuous random variables and examines the distributions belonging to this family as the sub-models. Some general statistical characteristics and sub-models of the new generator were examined and studied. Similarly, we examined the shapes of the sub-models probability
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Approximation theorems for the new construction of Balázs operators and its applications Math. Slovaca (IF 1.6) Pub Date : 2022-12-21 Fuat Usta
Balázs operators are an influential tool that can be used to approximate a function on the unbounded interval [0, ∞). In this study, a new construction of Balázs operators which depending upon on a function ρ(x) has been introduced. The function ρ(x) plays a significant role in this construction due to the fact that the new operator preserves definitely two test functions from the set of {1, ρ(x),
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On two correlated linear models with common and different parameters Math. Slovaca (IF 1.6) Pub Date : 2022-12-21 Bo Jiang, Ming Liu, Yongge Tian
A parametric regression model may comprise several correlated individual regression equations, and these equations may have common and different unknown parameters. In such a situation, the common unknown parameter vectors in these equations can be estimated individually or simultaneously according to various available statistical inference methods. The purpose of this paper is to provide an integral
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Approximating families for lattice outer measures on unsharp quantum logics Math. Slovaca (IF 1.6) Pub Date : 2022-12-21 Mona Khare, Pratibha Pandey
The aim of the present paper is to study lattice outer measures on an unsharp quantum logic, viz. a difference poset P associated with a monotone function μ defined on a sub-difference poset L of P and an approximating family in L. Having proved a number of fundamental properties, relationships among these outer measures and eventually among corresponding families of measurable elements of P are investigated
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Coercive and noncoercive elliptic problems with variable exponent Laplacian under Robin boundary conditions Math. Slovaca (IF 1.6) Pub Date : 2022-12-21 Makkia Dammak, Abir Amor Ben Ali
In the present paper, we study the existence as well as the non-existence of some positive solutions for the equation −Δ p(x) u = λ k(x) uq ± h(x) ur under Robin boundary condition in a regular open bounded domain Ω of ℝ N , N ≥ 2. Δ p(x) is the p(x)-Laplacian operator where p ∈ C 1(Ω) and p > 1. Our proofs are based on the sub solution-super solution method and also on variational arguments.
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Kalmbach measurability In d0-algebras Math. Slovaca (IF 1.6) Pub Date : 2022-12-21 Anna Avallone, Paolo Vitolo
We introduce the notion of ∧-projection in order to extend to d0-algebras the concept of Kalmbach measurable elements with respect to an outer measure μ. We prove, in case μ is faithful, that Kalmbach measurable ∧-projections are quasi-central, thus generalizing a result known for orthomodular lattices, and recently extended to D-lattices.
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The symmetric 4-Player gambler’s problem with unequal initial stakes Math. Slovaca (IF 1.6) Pub Date : 2022-12-21 Abid Hussain, Salman A. Cheema
This research advances the 4-player gambler’s ruin problem for the case of arbitrary initial stakes. The aim of the research is attained by offering simple expressions using the difference equation approach and thus providing closed form solution to the problem. Moreover, the existing technique of Chang [A game with four players, Statist. Probab. Lett. 23(2) (1995), 111–115] dealing with equal initial
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On η-biharmonic hypersurfaces in pseudo-Riemannian space forms Math. Slovaca (IF 1.6) Pub Date : 2022-12-21 Li Du, Jinjun Ren
In this paper, η-biharmonic hypersurfaces with constant scalar curvature in 5-dimensional pseudo-Riemannian space forms are studied. We prove that such hypersurfaces with diagonalizable shape operator have constant mean curvature, which gives an affirmative partial answer to the conjecture in [Arvanitoyeorgos, A.—Kaimakamis, F. G.: Hypersurfaces of type $\begin{array}{} \displaystyle M^3_2 \end{array}$
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A note on set-star-K-Menger spaces Math. Slovaca (IF 1.6) Pub Date : 2022-12-21 Sumit Singh
A space X is said to have the set-star-K-Menger property if for each nonempty subset A of X and for each sequence (𝓤 n : n ∈ ℕ) of collections of open sets in X such that for each n ∈ ℕ, A ⊆ ⋃ 𝓤 n , there is a sequence (Kn : n ∈ ℕ) of compact subsets of X such that A ⊆ $\begin{array}{} \bigcup\limits_{n \in \mathbb{N}} \end{array} $ St(Kn , 𝓤 n ). In this paper, we prove that: There exists a T 1
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Solvability of mixed problems for heat equations with two nonlocal conditions Math. Slovaca (IF 1.6) Pub Date : 2022-12-21 Onur Alp İlhan, Danyal Soybaş, Shakirbay G. Kasimov, Farhod D. Rakhmanov
In this study, the solvability of a problem of the heat conduction theory with two nonlocal boundary conditions is investigated. Systems of eigenfunctions of the corresponding operator with two nonlocal boundary conditions are taken into consideration. A theorem on the solvability of the problem of the theory of heat conduction with two nonlocal boundary conditions is given
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Multiplicative functions of special type on Piatetski-Shapiro sequences Math. Slovaca (IF 1.6) Pub Date : 2022-12-21 Teerapat Srichan
Let f k ( n ) := ∑ d k ∣ n Φ ( d ) , $$ f_k(n):=\sum\limits_{d^k \mid n} \Phi(d), $$ where Φ(d) is a multiplicative function, Φ(d) = O(dε ). We study asymptotic behaviour of the sum T f k c ( N ) := ∑ n ≤ N f k n c , 1 < c < 2 , $$ T_{f_k}^c(N):=\sum\limits_{n \leq N} f_k\left(\left\lfloor n^c\right\rfloor\right), \quad 1
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On variational approaches for fractional differential equations Math. Slovaca (IF 1.6) Pub Date : 2022-12-21 Amjad Salari, Nader Biranvand, Saeed Hashemi Sababe
This paper deals with the existence and numerical estimates of solutions for a class of fractional differential equations, while the nonlinear part of the problem admits some Special hypotheses. In particular, for a precise localization of the parameter, the existence of a non-zero solution is established requiring the sublinearity of nonlinear part at origin and infinity. Moreover, theoretical and
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Ideals of functions with compact support in the integer-valued case Math. Slovaca (IF 1.6) Pub Date : 2022-12-21 Themba Dube, Oghenetega Ighedo, Batsile Tlharesakgosi
For a zero-dimensional Hausdorff space X, denote, as usual, by C(X, ℤ) the ring of continuous integer-valued functions on X. If f ∈ C(X, ℤ), denote by Z(f) the set of all points of X that are mapped to 0 by f. The set $$\begin{array}{} \displaystyle C_K(X,\mathbb Z)=\{f\in C(X,\mathbb Z)\mid \text{cl}_X(X\smallsetminus \mathsf Z(f))\text{ is compact}\} \end{array}$$ is the integer-valued analogue of
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Enveloping action: Convergence spaces Math. Slovaca (IF 1.6) Pub Date : 2022-12-21 Bernd Losert, Gary Richardson
Given a partial action, an enveloping action in the context of convergence spaces is studied. Whenever the enveloping action space is not Hausdorff (T 3), a related enveloping action on a Hausdorff (T 3) space is developed. Invariance of quotient (proper, open) maps to the related space is also discussed.
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Triangular numbers and generalized fibonacci polynomial Math. Slovaca (IF 1.6) Pub Date : 2022-12-21 Adem Şahіn
In the present paper, we study triangular numbers. We focus on the linear homogeneous recurrence relation of degree 3 with constant coefficients for triangular numbers. Then we deal with the relationship between generalized Fibonacci polynomials and triangular numbers. We show that different properties of triangular numbers can be obtained by using this relationship. Finally, we examine the properties
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Quantifiers on L-algebras Math. Slovaca (IF 1.6) Pub Date : 2022-12-21 Lavinia Corina Ciungu
In this paper, we introduce the notion of monadic L-algebras and we study properties of these new structures. We define and investigate the monadic ideals of a monadic L-algebra, and we characterize the monadic ideal generated by a subset of a monadic L-algebra. We define the existential and universal quantifiers on semiregular L-algebras with negation, and we investigate certain properties of these
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On some classical properties of normed spaces via generalized vector valued almost convergence Math. Slovaca (IF 1.6) Pub Date : 2022-12-21 Mahmut Karakuş, Feyzi Başar
Recently, the authors interested some new problems on multiplier spaces of Lorentz’ almost convergence and f λ-convergence as a generalization of almost convergence. f λ-convergence is firstly introduced by Karakuş and Başar, and used for some new characterizations of completeness and barrelledness of the spaces through weakly unconditionally Cauchy series in a normed space X and its continuous dual
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Subordination-implication problems concerning the nephroid starlikeness of analytic functions Math. Slovaca (IF 1.6) Pub Date : 2022-12-21 Anbhu Swaminathan, Lateef Ahmad Wani
Let A be the set of all analytic functions f defined on the open unit disk D satisfying f(0) = f'(0) − 1 = 0. Let φNe (z) := 1 + z − z 3 =3 be the recently introduced Carathéodory function which maps the unit circle ∂ D $ \partial \mathbb{D} $ D onto a 2-cusped kidney-shaped curve called nephroid given by ( ( u − 1 ) 2 + v 2 − 4 a ) 3 − 4 v 2 2 = 0. ${{\left( {{(u-1)}^{2}}+{{v}^{2}}-\frac{4}{a} \r
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Chen’s first inequality for hemi-slant warped products in nearly trans-Sasakian manifolds Math. Slovaca (IF 1.6) Pub Date : 2022-12-21 Siraj Uddin, Lamia S. Alqahtani, Abdulqader Mustafa
In this paper, we prove that every hemi-slant warped product submanifold of the form N θ × f N ⊥ in a nearly trans-Sasakian manifold M͠ satisfies the following inequality: ∥h∥2 ≥ n 2cot2 θ(∥∇̂(ln f)∥2 – β 2), whereas the warped product by reversing these two factors, i.e., N ⊥ × f N θ satisfying the inequality: $\begin{array}{} \displaystyle \|h\|^2\geq \frac{n_1}{9}\cos^2\theta(\|\widehat\nabla(\ln
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An algebraic study of the logic S5’(BL) Math. Slovaca (IF 1.6) Pub Date : 2022-12-21 Juntao Wang, Xiaoli He, Mei Wang
P. Hájek introduced an S5-like modal fuzzy logic S5(BL) and showed that is equivalent to the monadic basic predicate logic mBL∀. Inspired by the above important results, D. Castaño et al. introduced monadic BL-algebras and their corresponding propositional logic S5’(BL), which is a simplified set of axioms of S5(BL). In this paper, we review the algebraic semantics of S5’(BL) and obtain some new results
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Fan-Hemicontinuity for the gradient of the norm in Hilbert space Math. Slovaca (IF 1.6) Pub Date : 2022-12-21 Marcel Bogdan
It was claimed in [Sadeqi, I.—Salehi Paydar, M.: A comparative study of Ky Fan hemicontinuity and Brezis pseudomonotonicity of mappings and existence results, J. Optim. Theory Appl. 165(2) (2015), 344–358] that the gradient of a convex Gâteaux differentiable function is Fanhemicontinuous. The aim of the present paper is to correct this implication by exemplifying for ∇ ‖ ⋅ ‖ $\nabla \|\cdot \|$ in
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Boundedness and almost periodicity of solutions of linear differential systems Math. Slovaca (IF 1.6) Pub Date : 2022-12-21 Dhaou Lassoued, Michal Fečkan
In this paper, we study the following linear differential system (1) x ′ ( t ) = A ( t ) x ( t ) , x ( t ) ∈ ℝ n , t ∈ ℝ , $${{x}^{\prime }}(t)=A(t)x(t),\,\,\,\,x(t)\in {{\mathbb{R}}^{n}},\quad t\in \mathbb{R},$$ where t ↦ A(t) is a matrix valued almost periodic function. We prove that if all the solutions of the above system are almost periodic, there exists an almost periodic function b : R → R n
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On a generalized Lamé-Navier system in ℝ3 Math. Slovaca (IF 1.6) Pub Date : 2022-12-21 Daniel Alfonso Santiesteban, Ricardo Abreu Blaya, Martín Patricio Árciga Alejandre
This paper is devoted to a fundamental system of equations in Linear Elasticity Theory: the famous Lamé-Navier system. The Clifford algebra language allows us to rewrite this system in terms of the Euclidean Dirac operator, which at the same time suggests a very natural generalization involving the so-called structural sets. We are interested in finding some structures in the solutions of these generalized
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A general matrix series inversion pair and associated polynomials Math. Slovaca (IF 1.6) Pub Date : 2022-12-21 Reshma R. Sanjhira, B. I. Dave
In the present work, a pair of general inverse matrix series relations is established, and thereby a general class of matrix polynomials is introduced. This class generalizes the extended Jacobi polynomials and their particular cases such as the polynomials of Brafman, Jacobi, Chebyshev, and Legendre. It is further shown that this pair also gives rise to the matrix forms of the Wilson polynomials and
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The global harnack estimates for a nonlinear heat equation with potential under finsler-geometric flow Math. Slovaca (IF 1.6) Pub Date : 2022-12-21 Shahroud Azami
Let (Mn , F(t), m), t ∈ [0, T], be a compact Finsler manifold with F(t) evolving by the Finsler-geometric flow $\begin{array}{} \displaystyle \frac{\partial g(x,t)}{\partial t}=2h(x,t), \end{array}$ where g(t) is the symmetric metric tensor associated with F, and h(t) is a symmetric (0, 2)-tensor. In this paper, we consider local Li-Yau type gradient estimates for positive solutions of the following
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Generalized hyperharmonic number sums with reciprocal binomial coefficients Math. Slovaca (IF 1.6) Pub Date : 2022-12-21 Rusen Li
In this paper, we mainly show that generalized hyperharmonic number sums with reciprocal binomial coefficients can be expressed in terms of classical (alternating) Euler sums, zeta values and generalized (alternating) harmonic numbers.
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Partial actions on convergence spaces Math. Slovaca (IF 1.6) Pub Date : 2022-08-10 Nathaniel Adu, Piotr Mikusiński, Gary Richardson
Continuous partial actions and continuous enveloping actions are investigated in the category of convergence spaces. Product and quotient constructions are considered. Further, it is shown that a continuous partial action on a convergence space can be extended to a continuous partial action on a compactification of the convergence space.
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Models, coproducts and exchangeability: Notes on states on Baire functions Math. Slovaca (IF 1.6) Pub Date : 2022-08-10 Serafina Lapenta, Giacomo Lenzi
We discuss exchangeability and independence in the setting of σ-complete Riesz MV-algebras. We define and link to each other the notions of exchangeability and distribution law for a sequence of observables (i.e. non classical random variables), as well as the notion of independence for a sequence of algebras. We obtain two categorical dualities for σ-complete Riesz MV-algebras endowed with states
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A new family of two-variable polynomials based on hermite polynomials Math. Slovaca (IF 1.6) Pub Date : 2022-08-09 Esra Erkuş-Duman, Hakan Ciftci
The aim of this paper is to introduce a new two-variable polynomials defined via Hermite polynomials. In order to construct some fundamental properties of these polynomials, we first derive a generating function relation. By using definition and this generating relation, we arrive at several recurrence relations, an integral representation, some implicit summation formulae, a symmetry identity for
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An alternative for Laplace Birnbaum-Saunders distribution Math. Slovaca (IF 1.6) Pub Date : 2022-08-09 İsmet Bίrbίçer, Alί İ. Genç
In this paper, we first propose a new general method to introduce various lifetime distributions by choosing an appropriate kernel distribution. They have some characteristics in common with the well-known Birnbaum-Saunders distribution. Then, we choose the triangular distribution as a kernel model and construct the new distribution. This distribution has its support on the positive real axis and consists
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On quasi-small loop groups Math. Slovaca (IF 1.6) Pub Date : 2022-08-09 Behrooz Mashayekhy, Hanieh Mirebrahimi, Hamid Torabi, Ameneh Babaee
In this paper, we study some properties of homotopical closeness for paths. We define the quasi-small loop group as the subgroup of all classes of loops that are homotopically close to null-homotopic loops, denoted by π 1 q s ( X , x ) $\pi_1^{qs} (X, x)$ for a pointed space (X, x). Then we prove that, unlike the small loop group, the quasi-small loop group π 1 q s ( X , x ) $\pi_1^{qs}(X, x)$ does
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Stability criteria for systems of two first-order linear ordinary differential equations Math. Slovaca (IF 1.6) Pub Date : 2022-08-09 Gevorg A. Grigorian
The Riccati equation method is used to establish stability criteria for systems of two first-order linear ordinary differential equations. Examples are presented in which the obtained result is compared with the results obtained by the Lyapunov and Bogdanov methods, by a method involving estimates of solutions in the Lozinskii logarithmic norms and by the freezing method.
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Weighted composition operators from the Besov space into nth weighted type spaces Math. Slovaca (IF 1.6) Pub Date : 2022-08-09 Xiangling Zhu, Ebrahim Abbasi, Daryoush Molaei
Let φ be an analytic self-map of the open unit disk 𝔻 in the complex plane ℂ and u be an analytic function on 𝔻. The weighted composition operator is defined on the space H(𝔻) of analytic functions on 𝔻 by u C φ f = u ⋅ ( f ∘ φ ) , f ∈ H ( D ) . $$u{C_\varphi }f = u \cdot \left( {f \circ \varphi } \right),\quad f \in H\left(D\right).$$ The boundedness and the compactness of weighted composition
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Decreasing property and complete monotonicity of two functions constituted via three derivatives of a function involving trigamma function Math. Slovaca (IF 1.6) Pub Date : 2022-08-09 Feng Qi
With the aid of convolution theorem of the Laplace transforms, a monotonicity rule for the ratio of two Laplace transforms, Bernstein’s theorem for completely monotonic functions, and other analytic techniques, the author presents decreasing property of a ratio constituted via three derivatives of a sum involving trigamma function and discovers necessary and sufficient conditions for a function constituted
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Inverse tangent series involving pell and pell-lucas polynomials Math. Slovaca (IF 1.6) Pub Date : 2022-08-09 Dongwei Guo, Wenchang Chu
By means of the telescoping method, several summation formulae are established for the arctangent function with its argument being Pell and Pell–Lucas polynomials. Numerous infinite series identities involving Fibonacci and Lucas numbers are included as particular cases.
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On the solvability of a fourth-order differential evolution equation on singular cylindrical domain in R4 Math. Slovaca (IF 1.6) Pub Date : 2022-08-09 Belkacem Chaouchi, Marko Kostić
In this paper, we investigate the solvability of a fourth-order differential evolution equation on singular cylindrical domain containing a cuspidal point. Some regularity results are obtained for the classical solutions by using the Dunford operational calculus.
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A perturbed eigenvalue problem in exterior domain Math. Slovaca (IF 1.6) Pub Date : 2022-08-09 Andrei Grecu
Let Ω ⊂ R N (N ≥ 2) be a simply connected bounded domain, containing the origin, with C 2 boundary denoted by ∂Ω. Denote by Ω e x t := R N ∖ Ω ¯ $\Omega^{\mathrm{ext}}:=\mathbb{R}^{N} \backslash \bar{\Omega}$ the exterior of Ω. We consider the perturbed eigenvalue problem − Δ p u − Δ q u = μ K ( x ) | u | p − 2 u for x ∈ Ω ext u ( x ) = 0 for x ∈ ∂ Ω u ( x ) → 0 , as | x | → ∞ , $$\left\{\begin{array}{lcl}
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Refinement of seminorm and numerical radius inequalities of semi-Hilbertian space operators Math. Slovaca (IF 1.6) Pub Date : 2022-08-09 Pintu Bhunia, Raj Kumar Nayak, Kallol Paul
Let 𝓗 be a complex Hilbert space and A be a non-zero positive bounded linear operator on 𝓗. The main aim of this paper is to discuss a general method to develop A-operator seminorm and A-numerical radius inequalities of semi-Hilbertian space operators using the existing corresponding inequalities of bounded linear operators on 𝓗. Among many other inequalities we prove that if S, T, X ∈ 𝓑 A (𝓗)
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On extensions of bilinear maps Math. Slovaca (IF 1.6) Pub Date : 2022-08-09 Carlos S. Kubrusly
The paper deals with extension of bounded bilinear maps. It gives a necessary and sufficient condition for extending a bounded bilinear map on the Cartesian product of subspaces of Banach spaces. This leads to a full characterization for extension of bounded bilinear maps on the Cartesian product of arbitrary subspaces of Hilbert spaces. Applications concerning projective tensor products are also investigated