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Vol.20 No.4
Abstract
Certain interesting single (or double) infinite series associated with hypergeometric functions have been expressed in terms of Psi (or Digamma) function <TEX>${\psi}(z)$</TEX>, for example, see Nishimoto and Srivastava [8], Srivastava and Nishimoto [13], Saxena [10], and Chen and Srivastava [5], and so on. In this sequel, with a view to unifying and extending those earlier results, we first establish two relations which some double infinite series involving hypergeometric functions are expressed in a single infinite series involving <TEX>${\psi}(z)$</TEX>. With the help of those series relations we derived, we next present two functional relations which some double infinite series involving <TEX>$\bar{H}$</TEX>-functions, which are defined by a generalized Mellin-Barnes type of contour integral, are expressed in a single infinite series involving <TEX>${\psi}(z)$</TEX>. The results obtained here are of general character and only two of their special cases, among numerous ones, are pointed out to reduce to some known results.
Abstract
Let A be an algebra and D a derivation of A. Then D is called algebraic nil if for any <TEX>$x{\in}A$</TEX> there is a positive integer n = n(x) such that <TEX>$D^{n(x)}(P(x))=0$</TEX>, for all <TEX>$P{\in}\mathbb{C}[X]$</TEX> (by convention <TEX>$D^{n(x)}({\alpha})=0$</TEX>, for all <TEX>${\alpha}{\in}\mathbb{C}$</TEX>). In this paper, we show that any algebraic nil derivation (possibly unbounded) on a commutative complex algebra A maps into N(A), where N(A) denotes the set of all nilpotent elements of A. As an application, we deduce that any nilpotent derivation on a commutative complex algebra A maps into N(A), Finally, we deduce two noncommutative versions of algebraic nil derivations inclusion range.
Abstract
We define an <TEX>${\varepsilon}$</TEX>-regular function in dual quaternions. From the properties of <TEX>${\varepsilon}$</TEX>-regular functions, we represent the Taylor series of <TEX>${\varepsilon}$</TEX>-regular functions with values in dual quaternions.
Abstract
We present a high-order potential flow model for the motion of hydrodynamic unstable interfaces in cylindrical geometry. The asymptotic solutions of the bubbles in the gravity-induced instability and the shock-induced instability are obtained from the high-order model. We show that the model gives significant high-order corrections for the solution of the bubble.
Abstract
We find an explicit <TEX>$C^{\infty}$</TEX>-continuous path of Riemannian metrics <TEX>$g_t$</TEX> on the 4-d hyperbolic space <TEX>$\mathbb{H}^4$</TEX>, for <TEX>$0{\leq}t{\leq}{\varepsilon}$</TEX> for some number <TEX>${\varepsilon}$</TEX> > 0 with the following property: <TEX>$g_0$</TEX> is the hyperbolic metric on <TEX>$\mathbb{H}^4$</TEX>, the scalar curvatures of <TEX>$g_t$</TEX> are strictly decreasing in t in an open ball and <TEX>$g_t$</TEX> is isometric to the hyperbolic metric in the complement of the ball.
Abstract
In this paper, we suggest and analyze a family of multi-step iterative methods which do not involve the high-order differentials of the function for solving nonlinear equations using a different type of decomposition (mainly due to Noor and Noor [15]). We also discuss the convergence of the new proposed methods. Several numerical examples are given to illustrate the efficiency and the performance of the new iterative method. Our results can be considered as an improvement and refinement of the previous results.
Abstract
A standard deviation has been a starting point for a mathematical definition of risk. As a remedy for drawbacks such as subadditivity property discouraging the diversification, coherent and convex risk measures are introduced in an axiomatic approach. Choquet expectation and g-expectations, which generalize mathematical expectations, are widely used in hedging and pricing contingent claims in incomplete markets. The each risk measure or expectation give rise to its own pricing rules. In this paper we investigate relationships among dynamic risk measures, Choquet expectation and dynamic g-expectations in the framework of the continuous-time asset pricing.