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### An approximate wave solution for perturbed KDV and dissipative NLS equations: weighted residual method

In the present work, we modified the conventional "weighted residual method" to some nonlinear evolution equations and tried to obtain the approximate progressive wave solutions for these evolution equations. For the illustration of the method we studied the approximate progressive wave solutions for the perturbed KdV and the dissipative NLS equations. The results obtained here are in complete agreement with the solutions of inverse scattering method. The present solutions are even valid when the dissipative effects are considerably large. The results obtained are encouraging and the method can be used to study the cylindrical and spherical evolution equations.Publisher's Versio

### On generalized sarmanov bivariate distributions

A class of bivariate distributions which generalizes the Sarmanov class is introduced. This class possesses a simple analytical form and desirable dependence properties. The admissible range for association parameter for given bivariate distributions are derived and the range for correlation coefficients are also presented.Publisher's Versio

### Construction of shift invariant m-band tight framelet packets

Framelets and their promising features in applications have attracted a great deal of interest and effort in recent years. In this paper, we outline a method for constructing shift invariant M-band tight framelet packets by recursively decomposing the multiresolution space VJ for a fixed scale J to level 0 with any combined mask m = [m0, m1, . . . , mL] satisfying some mild conditions.Publisher's Versio

### A note on line graphs

The line graph and 1-quasitotal graph are well-known concepts in graph theory. In Satyanarayana, Srinivasulu, and Syam Prasad [13], it is proved that if a graph G consists of exactly m connected components Gi (1 ≤ i ≤ m) then L(G) = L(G1) = L(G2) ⊕ ... ⊕ L(Gm) where L(G) denotes the line graph of G, and ⊕ denotes the ring sum operation on graphs. In [13], the authors also introduced the concept 1- quasitotal graph and obtained that Q1(G) = G⊕L(G) where Q1(G) denotes 1-quasitotal graph of a given graph G. In this note, we consider zero divisor graph of a finite associate ring R and we will prove that the line graph of Kn−1 contains the complete graph on n vertices where n is the number of elements in the ring R.Publisher's Versio

### The minimum mean monopoly energy of a graph

The motivation for the study of the graph energy comes from chemistry, where the research on the so-called total pi - electron energy can be traced back until the 1930s. This graph invariant is very closely connected to a chemical quantity known as the total pi - electron energy of conjugated hydro carbon molecules. In recent times analogous energies are being considered, based on Eigen values of a variety of other graph matrices. In 1978, I.Gutman [1] defined energy mathematically for all graphs. Energy of graphs has many mathematical properties which are being investigated. The ordinary energy of an undirected simple finite graph G is defined as the sum of the absolute values of the Eigen values of its associated matrix. i.e. if mu(1), mu(2), ..., mu(n) are the Eigen values of adjacency matrix A(G), then energy of graph is Sigma(G) = Sigma(n)(i=1) vertical bar mu(i)vertical bar Laura Buggy, Amalia Culiuc, Katelyn Mccall and Duyguyen [9] introduced the more general M-energy or Mean Energy of G is then defined as E-M (G) = Sigma(n)(i=1)vertical bar mu(i) - (mu) over bar vertical bar, where (mu) over bar vertical bar is the average of mu(1), mu(2), ..., mu(n). A subset M subset of V (G), in a graph G (V, E), is called a monopoly set of G if every vertex v is an element of (V - M) has at least d(v)/2 neighbors in M. The minimum cardinality of a monopoly set among all monopoly sets in G is called the monopoly size of G, denoted by mo(G) Ahmed Mohammed Naji and N.D.Soner [7] introduced minimum monopoly energy E-MM [G] of a graph G. In this paper we are introducing the minimum mean monopoly energy, denoted by E-MM(M) (G), of a graph G and computed minimum monopoly energies of some standard graphs. Upper and lower bounds for E-MM(M) (G)are also established.Publisher's Versio

### A numerical solution of the modified regularized long wave (MRLW) equation using quartic B-splines

In this paper, a numerical solution of the modified regularized long wave (MRLW) equation is obtained by subdomain finite element method using quartic B-spline functions. Solitary wave motion, interaction of two and three solitary waves and the development of the Maxwellian initial condition into solitary waves are studied using the proposed method. Accuracy and efficiency of the proposed method are tested by calculating the numerical conserved laws and error norms L₂ and L∞. The obtained results show that the method is an effective numerical scheme to solve the MRLW equation. In addition, a linear stability analysis of the scheme is found to be unconditionally stable.Publisher's Versio

### Jacobsthal family modulo m

In this study, we investigate sets of remainder of the Jacobsthal and JacobsthalLucas numbers modulo m for some positive integers m. Also some properties related to these sets and a new method to calculate the length of period modulo m is given.Publisher's Versio

### A note on discrete frames of translates in Cᴺ

In this note, we present necessary and sufficient conditions with explicit frame bounds for a discrete system of translates of the form {Tkφ}k∈Zᴺ to be a frame for the unitary space Cᴺ.Publisher's Versio

### Certain generating functions involving the incomplete I-functions

In this paper, we have derived a set of generating functions for incomplete I-functions. Bilateral along with linear generating relations are derived for incomplete I-functions. The results obtained are of a general nature, as special cases, the generating relations obtained for the incomplete I-functions.Publisher's Versio

### Free surface flow over a triangular depression

Two-dimensional steady free-surface flows over an obstacle is considered. The fluid is assumed to be inviscid, incompressible and the flow is irrotational. Both gravity and surface tension are included in the dynamic boundary conditions. Far upstream, the flow is assumed to be uniform. Triangular obstruction is located at the channel bottom. In this paper, the fully nonlinear problem is formulated by using a boundary integral equation technique. The resulting integro-differential equations are solved iteratively by using Newton’s method. When surface tension and gravity are included, there are two additional parameters in the problem known as the Weber number and Froude number. Finally, solution diagrams for all flow regimes are presented.Publisher's Versio