Abstract: Using the notion of operations on a generalized topological space (X, µ) and a hereditary class we have introduced the notion of γµ-compactness modulo a hereditary class ℋ termed as γµℋ -compactness. We have studied γµℋ-compact spaces and γµℋ-compact sets relative to µ. PubDate: Sun, 25 Sep 2022 00:00:00 GMT

Abstract: The classic method of solving the cubic and the quartic equations using Tschirnhaus transformation yields true as well as false solutions. Recently some papers on this topic are published, in which methods are given to get only the true solutions of cubic and quartic equations. However these methods have some limitations. In this paper the author presents a method of solving cubic and quartic equations using Tschirnhaus transformation, which yields only the true solutions. The proposed method is much simpler than the methods published earlier. PubDate: Sun, 25 Sep 2022 00:00:00 GMT

Abstract: BCK-sequences and n-commutative BCK-algebras were introduced by T. Traczyk, together with two related problems. The first one, whether BCK-sequences are always prolongable. The second one, if the class of all n-commutative BCK-algebras is characterised by one identity. W. A. Dudek proved that the answer to the former question is positive in some special cases, e.g. when BCK-algebra is linearly ordered. T. Traczyk showed that the answer to the latter is a˚rmative for n = 1, 2. Nonetheless, by providing counterexamples, we proved that the answers to both those open problems are negative. PubDate: Sun, 25 Sep 2022 00:00:00 GMT

Abstract: In this work, we characterize the class of compact matrix operators from c0(Q), c(Q) and ℓ∞ (Q) into c0, c and ℓ∞, respectively, with the notion of the Hausdorff measure of noncompactness. Moreover, we determine some geometric properties of the sequence space ℓp(Q). PubDate: Mon, 12 Sep 2022 00:00:00 GMT

Abstract: The aim of this paper is to present background information in relation with some fractional-order type operators in the complex plane, which is designed by the fractional-order derivative operator(s). Next we state various implications of that operator and then we show some interesting-special results of those applications. PubDate: Thu, 03 Mar 2022 00:00:00 GMT

Abstract: Let L be a not necessarily saturated lattice in ℤn with a defining matrix B. We explicitly compute the set of circuits of L in terms of maximal minors of B. This has a variety of applications from toric to tropical geometry, from Gröbner to Graver bases, and from linear to binomial ideals. PubDate: Fri, 21 Jan 2022 00:00:00 GMT

Abstract: We study the property of continuous Castelnuovo-Mumford regularity, for semihomogeneous vector bundles over a given Abelian variety, which was formulated in A. Küronya and Y. Mustopa [Adv. Geom. 20 (2020), no. 3, 401-412]. Our main result gives a novel description thereof. It is expressed in terms of certain normalized polynomial functions that are obtained via the Wedderburn decomposition of the Abelian variety’s endo-morphism algebra. This result builds on earlier work of Mumford and Kempf and applies the form of the Riemann-Roch Theorem that was established in N. Grieve [New York J. Math. 23 (2017), 1087-1110]. In a complementary direction, we explain how these topics pertain to the Index and Generic Vanishing Theory conditions for simple semihomogeneous vector bundles. In doing so, we refine results from M. Gulbrandsen [Matematiche (Catania) 63 (2008), no. 1, 123–137], N. Grieve [Internat. J. Math. 25 (2014), no. 4, 1450036, 31] and D. Mumford [Questions on Algebraic Varieties (C.I.M.E., III Ciclo, Varenna, 1969), Edizioni Cremonese, Rome, 1970, pp. 29-100]. PubDate: Thu, 28 Oct 2021 00:00:00 GMT

Abstract: In this article we define a metrizable space of multivalued maps. We show that the metric defined in this space is closely related to the homo-topy of multivalued maps. Moreover, we study properties of this space and give a few practical applications of the new metric. PubDate: Fri, 01 Oct 2021 00:00:00 GMT

Abstract: We prove that certain Fano fourfolds of K3 type constructed by Fatighenti–Mongardi have a multiplicative Chow–Künneth decomposition. We present some consequences for the Chow ring of these fourfolds. PubDate: Thu, 31 Dec 2020 00:00:00 GMT

Abstract: We present both necessary and sufficient conditions for a convex closed shape such that for every convex function the average integral over the shape does not exceed the average integral over its boundary.It is proved that this inequality holds for n-dimensional parallelotopes, n-dimensional balls, and convex polytopes having the inscribed sphere (tangent to all its facets) with the centre in the centre of mass of its boundary. PubDate: Thu, 31 Dec 2020 00:00:00 GMT

Abstract: In the present paper, we study in the harmonic analysis associated to the Weinstein operator, the boundedness on Lp of the uncentered maximal function. First, we establish estimates for the Weinstein translation of characteristic function of a closed ball with radius ɛ centered at 0 on the upper half space ℝd–1× ]0, +∞ [. Second, we prove weak-type L1-estimates for the uncentered maximal function associated with the Weinstein operator and we obtain the Lp-boundedness of this operator for 1 < p ≤ + ∞. As application, we define a large class of operators such that each operator of this class satisfies these Lp-inequalities. In particular, the maximal operator associated respectively with the Weinstein heat semigroup and the Weinstein-Poisson semigroup belong to this class. PubDate: Thu, 31 Dec 2020 00:00:00 GMT

Abstract: This paper presents some generalizations of BCI algebras (the RM, tRM, *RM, RM**, *RM**, aRM**, *aRM**, BCH**, BZ, pre-BZ and pre-BCI algebras). We investigate the p-semisimple property for algebras mentioned above; give some examples and display various conditions equivalent to p-semisimplicity. Finally, we present a model of mereology without antisymmetry (NAM) which could represent a tRM algebra. PubDate: Thu, 31 Dec 2020 00:00:00 GMT

Abstract: In this manuscript, we study the existence, uniqueness and various kinds of Ulam stability including Ulam–Hyers stability, generalized Ulam– Hyers stability, Ulam–Hyers–Rassias stability, and generalized Ulam–Hyers– Rassias stability of the solution to an implicit nonlinear fractional differential equations corresponding to an implicit integral boundary condition. We develop conditions for the existence and uniqueness by using the classical fixed point theorems such as Banach contraction principle and Schaefer’s fixed point theorem. For stability, we utilize classical functional analysis. The main results are well illustrated with an example. PubDate: Thu, 31 Dec 2020 00:00:00 GMT

Abstract: In this paper, we derive several subordination results and integral means result for certain class of analytic functions defined by means of q-differential operator. Some interesting corollaries and consequences of our results are also considered. PubDate: Thu, 31 Dec 2020 00:00:00 GMT

Abstract: The aim of this paper is to prove the existence and stability of solutions of a system of quadratic integral equations in the Banach algebra of continuous and bounded functions on unbounded rectangle. The main tool used in our considerations is the multiple fixed point theorem which is a consequence of Darbo’s fixed point theorem and the technique associated with measures of noncompactness. We also present an illustrative example. PubDate: Thu, 31 Dec 2020 00:00:00 GMT

Abstract: This paper presents a theorem dealing with absolute matrix summability of infinite series. This theorem has been proved taking quasi β-power increasing sequence instead of almost increasing sequence. PubDate: Thu, 31 Dec 2020 00:00:00 GMT

Abstract: In this article we present the existence and uniqueness results for fractional integro-differential equations with ψ-Hilfer fractional derivative. The reasoning is mainly based upon different types of classical fixed point theory such as the Mönch fixed point theorem and the Banach fixed point theorem. Furthermore, we discuss Eα -Ulam-Hyers stability of the presented problem. Also, we use the generalized Gronwall inequality with singularity to establish continuous dependence and uniqueness of the δ-approximate solution. PubDate: Thu, 31 Dec 2020 00:00:00 GMT

Abstract: Let f be a polynomial in two complex variables. We say that f is nearly irreducible if any two nonconstant polynomial factors of f have a common zero in C2. In the paper we give a criterion of nearly irreducibility for a given polynomial f in terms of its Newton diagram. PubDate: Thu, 31 Dec 2020 00:00:00 GMT

Abstract: The n-tuples of commuting Hilbert space contractions are considered. We give a model of a commuting lifting of one contraction and investigate conditions under which a commuting lifting theorem holds for an n-tuple. A series of such liftings leads to an isometric dilation of the n-tuple. The method is tested on some class of triples motivated by Parrotts example. It provides also a new proof of the fact that a positive definite n-tuple has an isometric dilation. PubDate: Thu, 31 Dec 2020 00:00:00 GMT