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Vol.19 No.2
Abstract
In this paper, we consider the Fourier-type functionals introduced in [16]. We then establish the analytic Feynman integral for the Fourier-type functionals. Further, we get a series expansion of the analytic Feynman integral for the Fourier-type functional <TEX>$[{\Delta}^kF]^{\^}$</TEX>. We conclude by applying our series expansion to several interesting functionals.
Abstract
The existence and uniqueness of T-periodic solutions for the following p-Laplacian equations: <TEX>$$({\phi}_p(x^{\prime}))^{\prime}+{\alpha}(t)x^{\prime}+g(t,x)=e(t),\;x(0)=x(T),x^{\prime}(0)=x^{\prime}(T)$$</TEX> are investigated, where <TEX>${\phi}_p(u)={\mid}u{\mid}^{p-2}u$</TEX> with <TEX>$p$</TEX> > 1 and <TEX>${\alpha}{\in}C^1$</TEX>, <TEX>$e{\in}C$</TEX> are T-periodic and <TEX>$g$</TEX> is continuous and T-periodic in <TEX>$t$</TEX>. By using coincidence degree theory, some existence and uniqueness results are obtained.
Abstract
In this paper, we introduce the notion of a slant lightlike submanifold of an indefinite Sasakian manifold. We provide a non-trivial example and obtain necessary and sufficient conditions for the existence of a slant lightlike submanifold. Also, we prove some characterization theorems.
Abstract
In this paper, we introduce the notion of an implicative vague filter in BE-algebras, and investigate some properties of them. Also we give conditions for a vague set to be an implicative vague filter, and we characterize implicative vague filters in BE-algebras. We define the notion of <TEX>$n$</TEX>-fold implicative vague filters in BE-algebras and we give characterizations of <TEX>$n$</TEX>-fold implicative vague filters and <TEX>$n$</TEX>-fold implicative BE-algebras.
Abstract
While investigating the Lauricella's list of 14 complete second-order hypergeometric series in three variables, Srivastava noticed the existence of three additional complete triple hypergeometric series of the second order, which were denoted by <TEX>$H_A$</TEX>, <TEX>$H_B$</TEX> and <TEX>$H_C$</TEX>. Each of these three triple hypergeometric functions <TEX>$H_A$</TEX>, <TEX>$H_B$</TEX> and <TEX>$H_C$</TEX> has been investigated extensively in many different ways including, for example, in the problem of finding their integral representations of one kind or the other. Here, in this paper, we aim at presenting further integral representations for the Srivatava's triple hypergeometric function <TEX>$H_B$</TEX>.
Abstract
We introduce a Heaviside-function formulation of the interaction between incompressible two-phase fluid and a non-deformable solid. Fluid and solid interact in two ways : fluid satises the Dirichlet boundary condition imposed by the velocity field of solid, and solid is accelerated by the surface traction exerted by fluid. The two-way couplings are formulated by the Heaviside function to the interface between solid and fluid. The cumbersome treatment of interface is taken care of by the Heaviside function, and the interaction is discretized in a simple manner. The discretization results in a stable and accurate projection method.
Abstract
The main purpose of this paper is to investigate <TEX>$h$</TEX>-stability of the nonlinear perturbed differential systems using the notion of <TEX>$t_{\infty}$</TEX>-similarity. As results, we generalize some previous <TEX>$h$</TEX>-stability results on this topic.
Abstract
We find the solution minimizing the shortfall risk by using the Lagrange-multiplier method. The conventional duality method in the expected utility maximization problem is used and we get the same results as in the paper [21].
Abstract
We show that every unbounded approximate Pexiderized exponential type function has the exponential type. That is, we obtain the superstability of the Pexiderized exponential type functional equation <TEX>$$f(x+y)=e(x,y)g(x)h(y)$$</TEX>. From this result, we have the superstability of the exponential functional equation <TEX>$$f(x+y)=f(x)f(y)$$</TEX>.
Abstract
For a locally compact higher rank graph <TEX>${\Lambda}$</TEX>, we construct a two-sided path space <TEX>${\Lambda}^{\Delta}$</TEX> with shift homeomorphism <TEX>${\sigma}$</TEX> and its corresponding path groupoid <TEX>${\Gamma}$</TEX>. Then we find equivalent conditions of aperiodicity, cofinality and irreducibility of <TEX>${\Lambda}$</TEX> in (<TEX>${\Lambda}^{\Delta}$</TEX>, <TEX>${\sigma}$</TEX>), <TEX>${\Gamma}$</TEX>, and the groupoid algebra <TEX>$C^*({\Gamma})$</TEX>.