Abstract: Archimedes’ well known theorem on the area of a parabolic segment says that this area is 4/3 of the area of a certain inscribed triangle. In this paper we generalize this theorem to the n-dimensional euclidean space, n ≥ 3. It appears that the ratio of the volume of an n-dimensional solid bounded by an (n − 1)-dimensional hyper-paraboloid and an (n − 1)-dimensional hyperplane and the volume of a certain inscribed cone (we analogously repeat Archimedes’ procedure) depends only on the dimension of the euclidean space and it equals to 2n/(n +1). PubDate: Thu, 08 Jul 2021 00:00:00 GMT
Abstract: We show a simple example for ordered semigroup 𝕊 = 𝕊 (+,⩽) that 𝕊 ⊆ℝ (ℝ denotes the real line) and ]a, b[ + ]c, d[ = ]a + c, b + d[ for all a, b, c, d ∈ 𝕊 such that a < b and c < d, but the intervals are no translation invariant, that is, the equation c +]a, b[ = ]c + a, c + b[ is not always fulfilled for all elements a, b, c ∈ 𝕊 such that a < b.The multiplicative version of the above example is shown too.The product of open intervals in the ordered ring of all integers (denoted by ℤ) is also investigated. Let Ix := {1, 2, . . ., x} for all x ∈ ℤ+ and defined the function g : ℤ+ → ℤ+ byg(x):=max{ y∈ℤ+ Iy⊆Ix⋅Ix }g\left( x \right): = \max \left\{ {y \in {\mathbb{Z}_ + } {I_y} \subseteq {I_x} \cdot {I_x}} \right\}for all x ∈ ℤ+. We give the function g implicitly using the famous Theorem of Chebishev.Finally, we formulate some questions concerning the above topics. PubDate: Thu, 08 Jul 2021 00:00:00 GMT
Abstract: In this paper we establish some two point weighted Taylor’s expansions for analytic functions f : D ⊆ ℂ→ ℂ defined on a convex domain D. Some error bounds for these expansions are also provided. Examples for the complex logarithm and the complex exponential are also given. PubDate: Thu, 08 Jul 2021 00:00:00 GMT
Abstract: In real life, variability and inaccuracy are always presentand must be calculated by either possibilistic, probabilistic, polymorphic or other uncertainty approach. This benchmark study is about to construct new types of fuzzy soft ideals i.e., (∈, ∈ ∨qk)-FSR(L)Is of ordered semigroup(OSG). Based on this inception, fuzzy soft level subsets are defined which link ordinary ideals with (∈, ∈ ∨qk)-fuzzy soft left(right) ideals. Some binary operations like ◦λ, intersection ∩λ and union of fuzzy soft sets ∪λ are given and various fundamental results of ideal theory are developed through these types of fuzzy soft ideals. PubDate: Thu, 08 Jul 2021 00:00:00 GMT
Abstract: We give a stochastic order for Varma residual entropy and study several properties of it, like closure, reversed closure and preservation of this order in some stochastic models. PubDate: Thu, 08 Jul 2021 00:00:00 GMT
Abstract: In this article, two-dimensional nonlinear and multi-term time fractional diffusion equations are solved numerically by collocation method, which is used with the help of Lucas operational matrix. In the proposed method solutions of the problems are expressed in terms of Lucas polynomial as basis function. To determine the unknowns, the residual, initial and boundary conditions are collocated at the chosen points, which produce a system of nonlinear algebraic equations those have been solved numerically. The concerned method provides the highly accurate numerical solution. The accuracy of the approximate solution of the problem can be increased by expanding the terms of the polynomial. The accuracy and efficiency of the concerned method have been authenticated through the error analyses with some existing problems whose solutions are already known. PubDate: Thu, 08 Jul 2021 00:00:00 GMT
Abstract: In this paper, in the setting of Hadamard spaces, a iterative scheme is proposed for approximating a solution of the inclusion problem for a finite family of monotone operators which is a unique solution of a variational inequality. Some applications in convex minimization and fixed point theory are also presented to support the main result. PubDate: Thu, 08 Jul 2021 00:00:00 GMT
Abstract: We translate some graph properties of 𝔸𝔾(R) and Γ(R) to some topological properties of Zariski topology. We prove that the facts “(1) The zero ideal of R is an anti fixed-place ideal. (2) Min(R) does not have any isolated point. (3) Rad(𝔸𝔾 (R)) = 3. (4) Rad(Γ(R)) = 3. (5) Γ(R) is triangulated (6) 𝔸𝔾 (R) is triangulated.” are equivalent. Also, we show that if the zero ideal of a ring R is a fixed-place ideal, then dtt(𝔸𝔾 (R)) = ℬ(R) and also if in addition Min(R) > 2, then dt(𝔸𝔾 (R)) = ℬ (R) . Finally, it is shown that dt(𝔸𝔾 (R)) is finite if and only if dtt(𝔸𝔾 (R)) is finite if and only if Min(R) is finite. PubDate: Thu, 08 Jul 2021 00:00:00 GMT
Abstract: In this paper, we establish some basic results for quaternion combined impulsive matrix dynamic equation on time scales for the first time. Quaternion matrix combined-exponential function is introduced and some basic properties are obtained. Based on this, the fundamental solution matrix and corresponding Cauchy matrix for a class of quaternion matrix dynamic equation with combined derivatives and bi-directional impulses are derived. PubDate: Thu, 08 Jul 2021 00:00:00 GMT
Abstract: The aim of this paper is to analyse the potential impact of multiple current interventions in communities with limited resources in order to obtain optimal control strategies and provide a basis for future predictions of the most effective control measures against the spread of malaria. We developed a population-based model of malaria transmission dynamics to investigate the effectiveness of five different interventions. The model captured both the human and the mosquito compartments. The control interventions considered were: educational campaigns to mobilise people for diagnostic test and treatment and to sleep under bed nets; treatment through mass drug administration; indoor residual spraying(IRS) with insecticide to reduce malaria transmission; insecticide treated net (ITN) to reduce morbidity; and regular destruction of mosquito breeding sites to reduce the number of new mosquito and bites/contact at dusks and dawn. Analysis of the potential impact of the multiple control interventions were carried out and the optimal control strategies that minimized the number of infected human and mosquito and the cost of applying the various control interventions were determined. PubDate: Thu, 08 Jul 2021 00:00:00 GMT
Abstract: Let R be a commutative ring with identity and S be a multiplicative subset of R. In this paper, we introduce the concept of weakly S-prime ideals which is a generalization of weakly prime ideals. Let P be an ideal of R disjoint with S. We say that P is a weakly S-prime ideal of R if there exists an s ∈ S such that, for all a, b ∈ R, if 0 ≠ ab ∈ P, then sa ∈ P or sb ∈ P. We show that weakly S-prime ideals have many analog properties to these of weakly prime ideals. We also use this new class of ideals to characterize S-Noetherian rings and S-principal ideal rings. PubDate: Thu, 08 Jul 2021 00:00:00 GMT
Abstract: Let ℕ be the set of all positive integers. In this paper, using some known results on various types of Diophantine equations, we solve a couple of special cases of the ternary equation x2 − y2m = zn, x, y, z, m, n ∈ ℕ, gcd(x, y) = 1, m ≥ 2, n ≥ 3. PubDate: Thu, 08 Jul 2021 00:00:00 GMT
Abstract: In the paper, the concept of Lp-dual three-mixed quermassintegrals is introduced. The formula for the Lp-dual three-mixed quermassintegrals with respect to the p-radial addition is proved. Inequalities of Lp-Minkowski, and Brunn-Minkowski type for the Lp-dual three-mixed quermassintegrals are established. The new Lp-Minkowski inequality is obtained that generalize a family of Minkowski type inequalities. The Lp-Brunn-Minkowski inequality is used to obtain a series of Brunn-Minkowski type inequalities. PubDate: Thu, 08 Jul 2021 00:00:00 GMT
Abstract: The aim of this paper is to consider the extensibility of the Diophantine triple {2, b, c}, where 2 < b < c, and to prove that such a set cannot be extended to an irregular Diophantine quadruple. We succeed in that for some families of c’s (depending on b). As corollary, for example, we prove that for b/2 − 1 prime, all Diophantine quadruples {2, b, c, d} with 2 < b < c < d are regular. PubDate: Thu, 08 Jul 2021 00:00:00 GMT
Abstract: Over finite local Frobenius non-chain rings of length 5 and nilpotency index 4 and when the length of the code is relatively prime to the characteristic of the residue field of the ring, the structure of the dual of γ-constacyclic codes is established and the algebraic characterization of self-dual, reversible γ-constacyclic codes and γ-constacyclic codes with complementary dual are given. PubDate: Thu, 08 Jul 2021 00:00:00 GMT
Abstract: In this paper, at first we study strong Sheffer stroke NMV-algebra. For getting more results and some classification, the notions of filters and subalgebras are introduced and studied. Finally, by a congruence relation, we construct a quotient strong Sheffer stroke NMV-algebra and isomorphism theorems are proved. PubDate: Tue, 13 Apr 2021 00:00:00 GMT
Abstract: In this article, we are going to look at the convergence properties of the integral ∫01(ax+b)cx+ddx\int_0^1 {{{\left( {ax + b} \right)}^{cx + d}}dx}, and express it in series form, where a, b, c and d are real parameters. PubDate: Tue, 13 Apr 2021 00:00:00 GMT
Abstract: We consider the second-order linear homogeneous quaternion recurrence solutions for some new curiosity bivariate quadratic quaternionic equations. PubDate: Tue, 13 Apr 2021 00:00:00 GMT
Abstract: In this paper we introduce the functions which count the number of generalized Lucas and Pell-Lucas sequence terms not exceeding a given value x and, under certain conditions, we derive exact formulae (Theorems 3 and 4) and establish asymptotic limits for them (Theorem 6). We formulate necessary and sufficient arithmetic conditions which can identify the terms of a-Fibonacci and a-Lucas sequences. Finally, using a deep theorem of Siegel, we show that the aforementioned sequences contain only finitely many perfect powers. During the process we also discover some novel integer sequences. PubDate: Tue, 13 Apr 2021 00:00:00 GMT
Abstract: In this paper, we study the reducibility property of special hyper-groups, called Corsini hypergroups, named after the mathematician who introduced them. The concept of reducibility was introduced by Jantosciak, who noticed that it can happen that hyperproduct does not distinguish between a pair of elements. He defined a certain equivalences in order to identify elements which play the same role with respect to the hyperoperation. First we will determine specific conditions under which the Corsini hypergroups are reduced. Next, we will present some properties of these hypergroups necessary for studying the fuzzy reducibility property. The fuzzy reducibility will be considered with respect to the grade fuzzy set μ̃, used for defining the fuzzy grade of a hypergroup. Finally, we will study the reducibility and the fuzzy reducibility of the direct product of Corsini hypergroups. PubDate: Tue, 13 Apr 2021 00:00:00 GMT
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