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In the present paper, we characterize Lie (Jordan) σ-centralizers of generalized matrix algebras. More precisely, we obtain some conditions under which every Lie σ-centralizer of a generalized matrix algebra can be expressed as the sum of a σ-centralizer and a center- valued mapping. Further, it is shown that under certain appropriate assumptions every Jordan σ-centralizer of a generalized matrix algebra is a σ-centralizer. Finally, the main results are applied to triangular algebras. [ABSTRACT FROM AUTHOR]

The exponential space, which is a Banach function space, can be defined with two very differently looking, but equivalent norms. In this paper, we give estimates for the best constants of the ratio of these two norms. Our result answers a question of C. Bennett, and R. Sharpley. [ABSTRACT FROM AUTHOR]

The concept of a tolerance relation, shortly called tolerance, was studied on various algebras since the seventies of the twentieth century by B. Zelinka and the first author (see e.g. [6] and the monograph [1] and the references therein). Since tolerances need not be transitive, their blocks may overlap and hence in general the set of all blocks of a tolerance cannot be converted into a quotient algebra in the same way as in the case of congruences. However, G. Czédli ([7]) showed that lattices can be factorized by means of tolerances in a natural way, and J. Grygiel and S. Radeleczki ([8]) proved some variant of an Isomorphism Theorem for tolerances on lattices. The aim of the present paper is to extend the concept of a tolerance on a lattice to posets in such a way that results similar to those obtained for tolerances on lattices can be derived. [ABSTRACT FROM AUTHOR]

In this paper, we study the existence and stability of solutions for impulsive pantograph fractional integro-differential equation via ψ-Hilfer fractional derivative in a appropriate Banach space. Our approach is based on fixed point theorems of Darbo’s and Mönch via Kuratowski measure of non-compactness. An example is given to illustrate our approach. [ABSTRACT FROM AUTHOR]

The Malliavin calculus is an extension of the classical calculus of variations from deterministic functions to stochastic processes. In this paper we aim to show in a practical and didactic way how to calculate the Malliavin derivative, the derivative of the expectation of a quantity of interest of a model with respect to its underlying stochastic parameters, for four problems found in mechanics. The non-intrusive approach uses the Malliavin Weight Sampling (MWS) method in conjunction with a standard Monte Carlo method. The models are expressed as ODEs or PDEs and discretised using the finite difference or finite element methods. Specifically, we consider stochastic extensions of; a 1D Kelvin-Voigt viscoelastic model discretised with finite differences, a 1D linear elastic bar, a hyperelastic bar undergoing buckling, and incompressible Navier-Stokes flow around a cylinder, all discretised with finite elements. A further contribution of this paper is an extension of the MWS method to the more difficult case of non-Gaussian random variables and the calculation of second-order derivatives. We provide open-source code for the numerical examples in this paper. [ABSTRACT FROM AUTHOR]

The objective of this paper is to investigate and extend some Pachpatte type dynamic inequalities on time scales in three independent variables which provide explicit bounds on unknown functions and their derivatives. Some applications are also discussed here in order to illustrate the usefulness of our results. [ABSTRACT FROM AUTHOR]

Abstract The aim of this paper is to discuss Maimon's criticism of Kant's doctrine of mathematical cognition. In particular, we will focus on the consequences of this criticism for the problem of the possibility of metaphysics as a science. Maimon criticizes Kant's explanation of the synthetic a priori character of mathematics and develops a philosophical interpretation of differential calculus according to which mathematics and metaphysics become deeply interwoven. Maimon establishes a parallelism between two relationships: on the one hand, the mathematical relationship between the integral and the differential and on the other, the metaphysical relationship between the sensible and the supersensible. Such a parallelism will be the clue to the Maimonian solution to the Kantian problem of the possibility of metaphysics as a science. Highlights • Maimon's criticism of Kant's doctrine of mathematical cognition is analyzed. • Said criticism sheds light on the relationship between mathematics and metaphysics. • Maimon finds in differential calculus the key to the cognition of the supersensible. • Maimon's solution to the Kantian problem of metaphysics as a science is discussed. [ABSTRACT FROM AUTHOR]

Research in mathematics and science education reveals a disconnect for students as they attempt to apply their mathematical knowledge to science and engineering. With this conclusion in mind, this paper investigates a particular calculus topic that is used frequently in science and engineering: the definite integral. The results of this study demonstrate that certain conceptualizations of the definite integral, including the area under a curve and the values of an anti-derivative, are limited in their ability to help students make sense of contextualized integrals. In contrast, the Riemann sum-based “adding up pieces” conception of the definite integral (renamed in this paper as the “multiplicatively-based summation” conception) is helpful and useful in making sense of a variety of applied integral expressions and equations. Implications for curriculum and instruction are discussed. [ABSTRACT FROM AUTHOR]

Let n ≥ 1 be a fixed positive integer and R be a ring. A permuting n-additive map Ω : Rn → R is known to be permuting generalized n-derivation if there exists a permuting n-derivation Δ : Rn → R such that Ω(x1, x2, ⋯,xixi⋯,xn) = Ω(x1, x2, ⋯,xi,⋯xn)xi + xi Δ(x1, x2, ⋯,xi⋯xn) holds for all xi, xi ∈ R. A mapping δ : R → R defined by δ(x) = Δ(x, x, ⋯, x) for all x ∈ R is said to be the trace of Δ. The trace &# of can be defined in ω of Ω can be defined in the similar way. The main result of the present paper states that if R is a (n+1)!-torsion free semi-prime ring which admits a permuting n-derivation Δ such that the trace δ of Δ satisfies [[δ(x), x], x] ∈ Z (R) for all x ∈ R, then ͐ is commuting on R. Besides other related results it is also shown that in a n-torsion free prime ring if the trace ω of a permuting generalized n-derivation is centralizing on R, then ω is commuting on R. [ABSTRACT FROM AUTHOR]

In this paper, we generalize some earlier well known results by considering polynomials of lacunary type having some zeros at origin and rest of the zeros on or outside the boundary of a prescribed disk. [ABSTRACT FROM AUTHOR]

In this paper, some subordination and superordination results for higher-order derivatives of certain p-valent analytic functions in the open unit disc are derived. Relevant connection of the results, which are obtained in this paper, with various known results are also considered. [ABSTRACT FROM AUTHOR]

In this paper, is defined the operator Dλ,ν,nα,β : A → A, given by Dλ,ν,nα,β f(z) = (1 - α - β)RνDnf(z) + αRνΩλzf(z) + βDnΩλzf(z), for z ∈ U, where Rν is the Ruscheweyh derivative, Dn is the Sălăgean operator, Ωλz is a fractional differintegral operator introduced by S. Owa and H. M. Srivastava, A = {f ∈ H(U) : f(z) = z + a2z² + a3z³ + ..., z ∈ U}, α, β ≥ 0, ν > -1, n ∈ N0 = {0, 1, 2, 3, ...}, -∞ < λ < 2. A certain subclass of analytic functions in the open unit disk, Rλ,ν,nα,β (δ), where 0 ≤ δ ≤ 1, is introduced using the new operator. Are obtained some properties of the class Rλ,ν,nα,β (δ) and some differential subordinations using the operator Dλ,ν,nα,β. [ABSTRACT FROM AUTHOR]

Purpose |!|#8211; Solving the non-linear equation f(x)=0 has nice applications in various branches of physics and engineering. Sometimes the applications of the numerical methods to solve non-linear equations depending on the second derivatives are restricted in physics and engineering. The purpose of this paper is to propose two new modified Newton|!|#39;s method for solving non-linear equations. Convergence results show that the order of convergence of the proposed iterative methods for a simple root is four. The iterative methods are free from second derivative and can be used for solving non-linear equations without computing the second derivative. Finally, several numerical examples are given to illustrate that proposed iterative algorithms are effective. Design/methodology/approach |!|#8211; In this paper, first the authors introduce two new approximations for the definite integral arising from Newton|!|#39;s theorem. Then by considering these approximations, two new iterative methods are provided with fourth-order convergence which can be used for solving non-linear equations without computing second derivatives. Findings |!|#8211; In this paper, the authors propose two new iterative methods without second derivatives for solving the non-linear equation f(x)=0. From numerical results, it is observed that the new methods are comparable with various iterative methods. Also numerical results corroborate the theoretical analysis. Originality/value |!|#8211; The best property of these schemes is that they are second derivative free. Also from numerical results, it is observed that the new methods are comparable with various iterative methods. The numerical results corroborate the theoretical analysis. [ABSTRACT FROM AUTHOR]

In this paper, we propose and analyze a viral infection model with humoral immunity. The incidence rate is given by Hill type infection rate. We have derived two threshold parameters, R0 and R1 which completely determined the global properties of the model. By constructing suitable Lyapunov functions and applying LaSalle's invariance principle we have established the global asymptotic stability of all steady states of the model. We have proven that, if R0 ≤ 1, then the infection-free steady state is globally asymptotically stable (GAS), if R1 ≤ 1 < R0, then the chronic-infection steady state without humoral immune response is GAS, and if R1 > 1, then the chronic-infection steady state with humoral immune response is GAS. [ABSTRACT FROM AUTHOR]

In this paper, we present some new inequalities for the gamma function. The main tools are the multiple-correction method developed in [6, 7] and a generalized Mortici's lemma. [ABSTRACT FROM AUTHOR]

In this paper, we consider Choquet integrals and derivatives of non- negative, continuous and decreasing functions on the non-positive real line with respect to fuzzy measures. We prove some properties of derivatives of those functions and some examples. [ABSTRACT FROM AUTHOR]

In this paper we obtain some weighted Ostrowski type and Grüss type inequalities on time scales by using the recent theory of combined dynamic derivatives on time scales. These results extend some known results in the literature and give some other interesting inequalities as special cases. [ABSTRACT FROM AUTHOR]

In the paper, the authors establish some new inequalities of Simpson type for functions whose third derivatives are extended s-convex functions, and apply these inequalities to derive some inequalities of special means. [ABSTRACT FROM AUTHOR]

Abstract: The authors had exhibited in a previous paper a continuous strictly increasing singular function from into with a derivative that takes non-zero finite values at the points of an uncountable set. In this article, the construction is improved to encompass a dense set. [Copyright &y& Elsevier]

In this paper, we study a new class of three-point boundary value prob- lems of nonlinear second-order q-difference inclusions. Our problems con- tain different numbers of q in derivatives and integrals. By using fixed point theorems, some new existence results are obtained in the cases when the right-hand side has convex as well as noncovex values. [ABSTRACT FROM AUTHOR]

Abstract: Let be the graph obtained from by adding a new vertex corresponding to each edge of and by joining each new vertex to the end vertices of the corresponding edge, and be the graph obtained from by inserting a new vertex into every edge of and by joining by edges those pairs of these new vertices which lie on adjacent edges of . In this paper, we determine the Laplacian polynomials of and of a regular graph ; on the other hand, we derive formulae and lower bounds of the Kirchhoff index of these graphs. [Copyright &y& Elsevier]

Let $$\mathcal{A}$$ and $$\mathcal{B}$$ be unital rings, and $$\mathcal{M}$$ be an $$\left( {\mathcal{A},\mathcal{B}} \right)$$-bimodule, which is faithful as a left $$\mathcal{A}$$-module and also as a right $$\mathcal{B}$$-module. Let $$\mathcal{U} = Tri\left( {\mathcal{A},\mathcal{M},\mathcal{B}} \right)$$ be the triangular algebra. In this paper, we give some different characterizations of Lie higher derivations on $$\mathcal{U}$$. [ABSTRACT FROM AUTHOR]

In this paper, we introduce intuitionistic fuzzy derivative, intuitionistic fuzzy Gateaux derivative and intuitionistic fuzzy Fréchet derivative and some of their properties are studied. The relations between intuitionistic fuzzy Gateaux derivative and intuitionistic fuzzy Fréchet derivative are studied. [ABSTRACT FROM AUTHOR]

In this paper, some oscillation criteria for solutions of a general second order non-linear differential equations with damping of the form (a(t) ψ (x (t)) k (x' (t)))' + p (t) k (x' (t)) + q (t) f (x (t)) = 0, are given. The results obtained extend some existing results in the literature by using the refined integral averaging technique introduced by Rogovchenko and Tuncay). [ABSTRACT FROM AUTHOR]

The least squares derivative and the approximate derivative are both generalizations of the ordinary derivative. The existence of either of these generalized derivatives does not guarantee the existence of the other and it is even possible for both generalized derivatives to exist at a point but have different values. Several examples of such functions are presented in this paper. In addition, conditions for which the existence of the approximate derivative implies the existence (and equality) of the least squares derivative are stated and proved. These conditions involve the notion of Hölder continuity and a stronger version of approximate differentiability. [ABSTRACT FROM AUTHOR]