Abstract:
:In telecommunication a Wireless communication is the transfer of information between two or more points that are not connected by an electrical conductor .Wireless operations permit services, such as long-range communications, that are impossible or impractical to implement with the use of wires. The term is commonly used in the telecommunications industry to refer to telecommunications systems which use some form of energy to transfer information without the use of wires. Information is transferred in this manner over both short and long distances. In this paper we are reviewing different wireless technologies and discussing about the future of wireless technologies used for cellular or mobile networks.

Abstract:
As we know that R.K. Narayan created an imaginary place Malgudi in his works. And most of the novels and stories take place in this venue. Narayan depicted the Indian society scenario through his works on the land of Malgudi. Narayan's craftsmanship lies not only in the conventional life of Malgudi but also in the leaving attention he devotes to building up a real picture of Malgudi and its inhabitants. Malgudi is his greatest Character with its Mempi Hills, tiger haunted jungles, Natraj Printing shop, Jagan's sweet emporium, Johansian Character's like Mr. Sampath and Natraj. Narayan finds plenty of comedy in the normal life of Malgudi. His attitude towards Malgudi remains lovingly sympathetic. He loves to depict the traditional life of Malgudi with all its backwardness gentle-teasing and deep understanding.

Abstract:
This paper deals with the cost-benefit analysis of a system of two identical units-one is operative and the other is kept as cold standby. There is a single server who attends the system immediately whenever needed. The unit becomes degraded after repair. The server inspects the degraded unit at its failure to see the feasibility of repair. If the repair of the degraded unit is not feasible, it is replaced by new unit which gets priority in operation as well as in repair over the degraded unit. The system is considered in up-state if either of new/degraded unit is operative. The distributions of failure time of the units are taken as negative exponential while that of inspection and repair times are taken as arbitrary such as exponential distribution, Erlang distribution and Weibull distribution etc. Various reliability measures of system effectiveness are obtained by using semi-Markov process and regenerative point technique. The behavior of mean time to system failure (MTSF), availability and profit of the system have also been studied through graphs.

Abstract:
A sequence of rational numbers as a generalization of the sequence of Bernoulli numbers is introduced. Sums of products involving the terms of this generalized sequence are then obtained using an application of Faà di Bruno's formula. These sums of products are analogous to the higher order Bernoulli numbers and are used to develop the closed form expressions for the sums of products involving the power sums which are defined via the M？bius function μ and the usual power sum of a real or complex variable . The power sum is expressible in terms of the well-known Bernoulli polynomials by . 1. Introduction Singh [1] introduced the power sum of real or complex variable and positive integer defined by the generating function from which he derived the following closed form formula for these power sums: for all where are the Bernoulli numbers and runs over all prime divisors of . In particular, gives the sum of th power of those positive integers which are less than and relatively prime to . We will call as M？bius-Bernoulli power sums. Present work is aimed at describing sums of products of the power sums via introducing yet another sequence of rational numbers which we will call as the sequence of M？bius-Bernoulli numbers. The rational sequence that appears in (2) is defined via the generating function , , and was known to Faulhaber and Bernoulli. Many explicit formulas for the Bernoulli numbers are also well known in the literature. One such formula is as follows [2]: The rest of the paper is organized as follows. M？bius Bernoulli numbers are introduced in Section 2 and their sums of products are discussed via Faà di Bruno’s formula. In Section 3 sums of products of power sums of integers are obtained in closed form using sums of products of M？bius Bernoulli numbers. 2. M？bius-Bernoulli Numbers Definition 1. We define M？bius-Bernoulli numbers , , via the generating function We immediately notice from (4) that the M？bius-Bernoulli numbers are given by Note that, for a fixed , the M？bius Bernoulli number is a multiplicative function of . Singh [1] has obtained the following identity relating the function to the M？bius-Bernoulli numbers. , from which we observe that , , and for all , where is Euler’s totient. Use of M？bius Bernoulli numbers is inherent in studies recently done by Alkan [3] on averages of Ramanujan sums which are defined for any complex number and integer by , where . M？bius Bernoulli numbers are also related to Jordan’s totient (a generalization of Euler’s totient) by , where is the square free part of . The notion of Bernoulli polynomials

Abstract:
The simple shooting method is revisited in order to solve nonlinear two-point BVP numerically. The BVP of the type is considered where components of are known at one of the boundaries and components of are specified at the other boundary. The map is assumed to be smooth and satisfies the Lipschitz condition. The two-point BVP is transformed into a system of nonlinear algebraic equations in several variables which, is solved numerically using the Newton method. Unlike the one-dimensional case, the Newton method does not always have quadratic convergence in general. However, we prove that the rate of convergence of the Newton iterative scheme associated with the BVPs of present type is at least quadratic. This indeed justifies and generalizes the shooting method of Ha (2001) to the BVPs arising in the higher order nonlinear ODEs. With at least quadratic convergence of Newton's method, an explicit application in solving nonlinear Rayleigh-Bénard convection in a horizontal fluid layer heated from the below is discussed where rapid convergence in nonlinear shooting essentially plays an important role. 1. Introduction Let ,？？ , be a vector valued function defined by , where each map , , is smooth over the interval . We consider the following vector differential equation satisfied by : Throughout, the map is assumed to be smooth and satisfying the Lipschitz condition on a closed rectangle with a Lipschitz constant s.t. for all？？ and ; furthermore, the components of are assumed to satisfy initial conditions at first boundary given by and -conditions at the other boundary which are given by where is a permutation of the symmetric group . Equations (1)–(4) lead to a two-point boundary value problem whose solution is not known a priori at either of the boundaries. Such BVPs are a common object of study in mathematics, physics, engineering, stochastic analysis, and optimization. In general, it is not possible to solve these BVPs analytically, and one needs to look for their numerical solutions in order to unfold the inherent dynamics. To do so, the vector differential equation may be reduced to a set of nonlinear algebraic equations by approximating the solution with a (finite) Galerkin expansion in terms of a suitably chosen set of orthogonal functions already satisfying the conditions of the BVP in hand. The resulting set of the nonlinear algebraic equations is solved numerically for the unknown Galerkin coefficients using iterative methods such as the Newton-Raphson scheme. Despite its general applicability, the Galerkin method becomes handy as the number of

Abstract:
Without assuming the field structure on the additive group of real numbers $\mathbb{R}$ with the usual order $<,$ we explore the fact that every proper subgroup of $\mathbb{R}$ is either closed or dense. This property of subgroups of the additive group of reals is special and well known (see Abels and Monoussos [4]). However, by revisiting it, we provide another direct proof. We also generalize this result to arbitrary topological groups in the sense that, any topological group having this property of the subgroups in a given topology is either connected or totally disconnected.

Abstract:
For any two arithmetic functions $f,g$ let $\bullet$ be the commutative and associative arithmetic convolution $(f\bullet g)(k):=\sum_{m=0}^k \left( \begin{array}{c} k m \end{array} \right)f(m)g(k-m)$ and for any $n\in\mathbb{N},$ $f^n=f\bullet \cdots\bullet f$ be $n-$fold product of $f\in \mathcal{S}.$ For any $x\in\mathbb{C},$ let $\mathcal{S}_0=e$ be the multiplicative identity of the ring $(\mathcal{S},\bullet,+)$ and $\mathcal{S}_x(k):=\frac{\mathcal{B}_{x+1}(k+1)-\mathcal{B}_{1}(k+1)}{k+1},~x\neq 0$ denote the power sum defined by Bernoulli polynomials $\mathcal{B}_x(k)=B_k(x).$ We consider the sums of products $\mathcal{S}_x^N(k),~N\in\mathbb{N}_0.$ A closed form expression for $\mathcal{S}^N_x(k)(x)$ generalizing the classical Faulhaber formula, is derived. Furthermore, some properties of $\alpha-$Euler numbers \cite{JS9}(a variant of Apostol Bernoulli numbers) and their sums of products, are considered using which a closed form expression for the sums of products of infinite series of the form $\eta_\alpha(k):=\sum_{n=0}^{\infty}\alpha^n n^k,~0<|\alpha|<1,~k\in\mathbb{N}_0$ and the related Abel sums, is obtained which in particular, gives a closed form expression for well known Bernoulli numbers. A generalization of the sums of products of power sums to the sums of products of alternating power sums is also obtained. These considerations generalize in a unified way to define sums of products of power sums for all $k\in\mathbb{N}$ hence connecting them with zeta functions.

Abstract:
The Cauchy-type product of two arithmetic functions $f$ and $g$ on nonnegative integers is defined as $(f\bullet g)(k):=\sum_{m=0}^{k} {k\choose m}f(m)g(k-m)$. We explore some algebraic properties of the aforementioned convolution, which is a fundamental-characteristic of the identities involving the Bernoulli numbers, the Bernoulli polynomials, the power sums, the sums of products, henceforth.

Abstract:
Effect of an axially applied magnetic field on the stability of a ferrofluid flow in an annular space between two coaxially rotating cylinders with nonaxisymmetric disturbances has been investigated numerically. The critical value of the ratio Ω∗ of angular speeds of the two cylinders, at the onset of the first nonaxisymmetric mode of disturbance, has been observed to be affected by the applied magnetic field.