We define a semi-symmetric metric connection in an almost r-paracontact Riemannian manifold and we consider submanifolds of an almost r-paracontact Riemannian manifold endowed with a semi-symmetric metric connection and obtain Gauss and Codazzi equations, Weingarten equation and curvature tensor for submanifolds of an almost r-paracontact Riemannian manifold endowed with a semi-symmetric metric connection.

The paper studies an existence problem of a (generalized) universal covering space over a digital wedge with a compatible adjacency. In algebraic topology it is well-known that a connected, locally path connected, semilocally simply connected space has a universal covering space. Unlike this property, in digital covering theory we need to investigate its digital version which remains open.

Exton introduced 20 distinct triple hypergeometric functions whose names are Xi (i = 1,$\ldots$, 20) to investigate their twenty Laplace integral representations whose kernels include the confluent hypergeometric functions $_0F_1$, $_1F_1$, a Humbert function $\Psi_2$, a Humbert function $\Phi_2$. The object of this paper is to present 25 (presumably new) integral representations of Euler types for the Exton hypergeometric function $X_5$ among his twenty $X_i$ (i = 1,$\ldots$, 20), whose kernels include the Exton function X5 itself, the Exton function $X_6$, the Horn's functions $H_3$ and $H_4$, and the hypergeometric function F = $_2F_1$.

In this paper, we consider a preconditioned accelerated overrelaxation (PAOR) method to solve systems of linear equations. We show the convergence of the PAOR method. We also give com-parison results when the coefficient matrix is an L- or H-matrix. Finally, we provide some numerical experiments to show efficiency of PAOR method.

W. A. Dudek, M. Shabir and M. Irfan Ali discussed the properties of (${\alpha},{\beta}$)-fuzzy ideals of hemirings in [9]. In this paper, we discuss the generalization of their results on (${\alpha},{\beta}$)-fuzzy ideals of hemirings. As a generalization of the notions of $({\alpha},\;\in{\vee}q)$-fuzzy left (right) ideals, $({\alpha},\;\in{\vee}q)$-fuzzy h-ideals and $({\alpha},\;\in{\vee}q)$-fuzzy k-ideals, the concepts of $({\alpha},\;\in{\vee}q_m)$-fuzzy left (right) ideals, $({\alpha},\;\in{\vee}q_m)$-fuzzy h-ideals and $({\alpha},\;\in{\vee}q_m)$-fuzzy k-ideals are defined, and their characterizations are considered. Using a left (right) ideal (resp. h-ideal, k-ideal), we construct an $({\alpha},\;\in{\vee}q_m)$-fuzzy left (right) ideal (resp. $({\alpha},\;\in{\vee}q_m)$-fuzzy h-ideal, $({\alpha},\;\in{\vee}q_m)$-fuzzy k-ideal). The implication-based fuzzy h-ideals (k-ideals) of a hemiring are considered.

In this paper we evaluate the analogue of Wiener integral ${\int\limits}_{C[0,t]}x(t_1){\cdots}x(t_n)d\omega_\rho(x)$ where 0 = $t_0$ < $t_1$ $\cdots$ < $t_n$ $\leq$ t and the Paley-Wiener-Zygmund integral ${\int\limits}_{C[0,t]}$ exp $({\int\limits}_0^t h(s)\tilde{d}x(s))d\omega_\rho(x)$ is the analogue of Wiener measure space.

In this paper, we consider countable version of star covering properties to get interesting results about the relationship between starcompactness and countable pracompactness. We also construct examples related to countable pracompactness and H-closedness.

There are various papers on finding all the derivations of a non-associative algebra and an anti-symmetrized algebra (see [2], [3], [4], [5], [6], [10], [13], [15], [16]). We and all the derivations of the growing algebra WN($e^{{\pm}x_1x_2x_3}$, 0, 3)[1] with the set of all right annihilators $T_3$ = $\{id,\;\partial_1,\;\partial_2,\;\partial_3\}$ in the paper. The dimension of $Der_{non}$(WN($e^{{\pm}x_1x_2x_3}$, 0, 3)$_{[1]}$) of the algebra WN($e^{{\pm}x_1x_2x_3}$, 0, 3)$_{[1]}$ is one and every derivation of the algebra WN($e^{{\pm}x_1x_2x_3}$, 0, 3)$_{[1]}$ is outer. We show that there is a class P of purely outer algebras in this work.

In this paper, we investigate a generalization of the Adams-Bashforth method by using the Taylor's series. In case of m-step method, the local truncation error can be expressed in terms of m - 1 coefficients. With an appropriate choice of coefficients, the proposed method has produced much smaller error than the original Adams-Bashforth method. As an application of the generalized Adams-Bashforth method, the accuracy performance is demonstrated in the satellite orbit prediction problem. This implies that the generalized Adams-Bashforth method is applied to the orbit prediction of a low-altitude satellite. This numerical example shows that the prediction of the satellite trajectories is improved one order of magnitude.

The resultant and discriminant of composite polynomials were studied by McKay and Wang using some algebraic properties. In this paper we study the resultant and discriminant of iterate polynomials. We shall use elementary computations of matrices and block matrix determinants; this could provide not only the values but also the visual structure of resultant and discriminant from elementary matrix calculation.

In this paper, we introduced a special set, called T-part, in a Q-algebra X. We also show that the T-part of X is a subalgebra of X. By using T-part, we provide an equivalent condition that every ideal is a T-ideal.

Let $X_1,X_2,\cdots$ be identically distributed $\rho$-mixing random variables with mean zeros and positive finite variances. In this paper, we prove $$\array{\lim\\{\in}\downarrow0}{\in}^2 \sum\limits_{n=3}^\infty\frac{1}{nlogn}P({\mid}S_n\mid\geq\in\sqrt{nloglogn}=1$$, $$\array{\lim\\{\in}\downarrow0}{\in}^2 \sum\limits_{n=3}^\infty\frac{1}{nlogn}P(M_n\geq\in\sqrt{nloglogn}=2 \sum\limits_{k=0}^\infty\frac{(-1)^k}{(2k+1)^2}$$ where $S_n=X_1+\cdots+X_n,\;M_n=max_{1{\leq}k{\leq}n}{\mid}S_k{\mid}$ and $\sigma^2=EX_1^2+ 2\sum\limits{^{\infty}_{i=2}}E(X_1,X_i)=1$.