Volume 72, Issue 2

Generalized orthomodular posets were introduced recently by D. Fazio, A. Ledda and the first author of the present paper in order to establish a useful tool for studying the logic of quantum mechanics. They investigated structural properties of these posets. In the present paper, we study logical and algebraic properties of these posets. In particular, we investigate conditions under which they can be converted into operator residuated structures. Further, we study their representation by means of algebras (directoids) with everywhere defined operations. We prove congruence properties for the class of algebras assigned to generalized orthomodular posets and, in particular, for a subvariety of this class determined by a simple identity. Finally, in contrast to the fact that the Dedekind-MacNeille completion of an orthomodular poset need not be an orthomodular lattice, we show that the Dedekind-MacNeille completion of a stronger version of a generalized orthomodular poset is nearly an orthomodular lattice.

In this paper, the notion of some new classes of EQ-algebras which are called integral, O-local, and locally finite EQ-algebras are introduced, and relationships between locally finite EQ-algebras and maximal prefilters are described. Also, the notion of integral prefilters are introduced and several characteristics of them are presented. Moreover, relation among integral prefilters and some type of other prefilter such as positive implicative, maximal, prime, and fantastic prefilters in EQ-algebras are studied. Finally, Boolean prefilters in bounded lattice EQ-algebras are introduced, and it is proved that a filter of a prelinear involutive EQ-algebra L is a Boolean filter if and only if L / F is a Boolean algebra.

In this paper, we study the class of modules with fusion and implication based over distributive lattices , or FIDL - modules , for short. We introduce the concepts of FIDL-subalgebra and FIDL-congruence as well as the notions of simple and subdirectly irreducible FIDL-modules. We give a bi-sorted Priestley-like duality for FIDL-modules and moreover, as an application of such a duality, we provide a topological bi-spaced description of the FIDL-congruences. This result will allows us to characterize the simple and subdirectly irreducible FIDL-modules.

k -rough Heyting algebras were introduced by Eric San Juan in 2008 as an algebraic formalism for reasoning on finite increasing sequences over Boolean algebras in general and on generalizations of rough set concepts in particular. In 2020, we defined and studied the variety of k × j -rough Heyting algebras. These algebras constitute an extension of Heyting algebras and in the case j = 2 they coincide with k -rough Heyting algebras. In this note, we introduce the notion of k × j -ideal on k × j -rough Heyting algebras which allows us to consider a topology of them. Besides, we define the concept of 𝓕-multiplier, where 𝓕 is a topology on a k × j -rough Heyting algebra A , which is used to construct the localization k × j -rough Heyting algebras A 𝓕 . Furthermore, we prove that the k × j -rough Heyting algebras of fractions A S associated with a ∧ -closed subset S of A is a k × j -rough Heyting algebra of localization. Finally, in the finite case we prove that A S is isomorphic to a special subalgebra of A . Since 3-valued Łukasiewicz –Moisil algebras are a particular case of k × j -rough Heyting algebras, all these results generalize those obtained in 2005 by Chirtes and Busneag.

We study meet infinite distributivity (MID) in congruence lattices of direct sums of algebras. The main result of this note is that in a congruence distributive variety the MID of congruence lattices is preserved by direct sums of algebras, it means that the congruence lattice of a direct sum of algebras is MID if and only if a congruence lattice of every constituent algebra is MID.

Let D be a nonsquare integer, and let k be an integer with | k | ≥ 1 and gcd( D , k ) = 1. In the part I of this paper, using some properties on the representation of integers by binary quadratic primitive forms with discriminant 4 D , M.-H. Le gave a series of explicit formulas for the integer solutions ( x , y , z ) of the equation x 2 – Dy 2 = k z , gcd( x , y ) = 1, z > 0 for 2 ∤ k or | k | is a power of 2. In this part, we give similar results for the other cases of k .

The Open Door Lemma is the well-known famous result due to Miller and Mocanu that provides a sufficient condition for an analytic function on the unit disk to have positive real part. This lemma has already been corrected by Kuroki and Owa for non-real initial point. Also, Li and Sugawa extended the Open Door Lemma in a such way that an analytic function takes its values in the given symmetric sector. Now, by the same methods, we provide a sufficient condition for an analytic function to take its values in the asymmetric arbitrary sector.

In this paper, we prove a lemma on logarithmic derivative for holomorphic curves from annuli into Kähler compact manifolds. As its application, a second main theorem for holomophic curves from annuli into semi-Abelian varieties intersecting with only one divisor is given.

Representation of solutions of delayed differential equations with multiple delays and periodic coefficients is established. Consequently, results on stabilizability of weakly delayed closed-loop systems and stability of non-weakly delayed periodic systems are proved. The stabilizability result is an extension of the classical Brunovský theorem for linear periodic systems of ordinary differential equations to a class of delay differential equations with pairwise permutable matrix functions.

In this paper, the semi-group method is used to discuss the existence and uniqueness of solutions for fractional and partial integro differential equations (F-PIDEs) of heat type in Banach space E . In addition, the stability of the solutions for F-PIDEs are discussed. Moreover, the Adomian decomposition method (ADM) is used to obtain the solutions numerically. Finally, numerical results of each case are obtained, and the difference of results between the fractional partial integro differential equation and partial integro differential equation are explained. Furthermore, the error is computed in each case.

By using comparison theorems, the authors investigate the oscillatory and asymptotic behavior of solutions tothe third-order quasi-linear neutral difference equation Δ a ( n ) Δ 2 z ( n ) α + q ( n ) x β ( σ ( n ) ) = 0 , $$\begin{array}{}\displaystyle\Delta\left(a(n)\left(\Delta^2 z(n) \right)^\alpha \right)+q(n)x^\beta(\sigma(n))=0,\end{array}$$ where z ( n ) = x ( n ) + px ( n − k ). Under less restrictive conditions on the coefficient functions and on the delay argument σ ( n ) than currently found in the literature, their criteria improve a number of known related results. The results are illustrated with examples.

In this paper, we study the Kantorovich variant of Chlodowsky Szász operators induced by Boas-Buck type polynomials and prove a Korovkin type theorem. Also, we present the Voronovskaya type theorem and Grüss-Voronovskaya type theorem. In the last section, we estimate the rates of pointwise approximation of Kantorovich variant of Chlodowsky Szász operators induced by Boas-Buck type polynomials for functions with derivatives of bounded variation.

We introduce and study statistical versions of recently introduced concepts of semi- α convergence, semi exhaustiveness and semi uniform convergence of sequences of functions between metric spaces. We prove some basic results and establish a connection between them. Also, we give some examples to ensure deviation of established notions.

In this paper, new common fuzzy fixed point theorems for sequence of fuzzy set-valued maps in the framework of complete b -metric spaces are established. Consequently, corresponding fixed point theorems in the setting of point-to-set-valued and single-valued mappings are deduced. A few nontrivial examples which dwell upon the generality of our results are provided. Moreover, following the fact that most available Ulam-Hyers type stability results deal with crisp mappings, we initiate the study of stability and well-posedness of functional inclusions involving fuzzy set-valued maps. It is well-known that solution of any functional inclusion is a subset of an appropriate ambient space. With this information, fuzzy fixed point problem for which the right-hand-side is a cut set of a fuzzy set-valued map is introduced. Furthermore, sufficient conditions for existence of solutions of Cantilever Beam Problem and integral inclusions are investigated to indicate the usability of our obtained results.

In this paper, we investigate the geometry of affine Killing and two-Killing vector fields on Riemannian manifolds. More specifically, a new characterization of an Euclidean space via the affine Killing vector fields are given. Some conditions for an affine Killing and two-Killing vector field to be a conformal (homothetic) or Killing one are provided.

In this paper, two linear predictors of the fractional k th upper record-value based on two-parameter exponential distribution are proposed. Moreover, a free scale-location predictive interval is constructed for the future fractional k th upper record-value. The prediction results are formulated in a general set-up relying on two fractional k th upper record-values. Some important distributional properties for each point predictor are revealed. Furthermore, the mean square error and Pitman’s measure of closeness are used to compare the point predictors. Finally, a simulation study is carried out and a real data set is analyzed to explore the efficiency of the suggested methods.

In this work, we study the distributional and moment properties of concomitants of dual generalized order statistics and consequently generalized order statistics. When the parameters are assumed to be pairwise different from Bairamov-Kotz-Becki Farlie-Gumbel-Morgenstern (BKB-FGM) family. Furthermore, an example of progressive type-II censored order statistics of BKB-FGM family under uniform distribution is obtained. Moreover, the joint distribution of dual generalized order statistics and record values of concomitants for this family are discussed. Finally, an application is given for some well-known distributions such as exponential, Pareto, and power function distributions.

In this paper, we introduce one-parameter generalization of dual-hyperbolic Pell numbers – dual-hyperbolic r -Pell numbers. We give some identities for them related to Catalan identity, Cassini identity, d’Ocagne identity and convolution identity. Moreover, we define their matrix generators.