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The generalized Riccati equation mapping is extended with the basic(G'/G)-expansion method which is powerful and straightforward mathematical tool for solving nonlinear partial differential equations. In this paper, we construct twenty-seven traveling wave solutions for the (2+1)-dimensional modified Zakharov-Kuznetsovequation by applying this method. Further, the auxiliary equation G'(?)=ω+uG(?)+νG2(?) is executed with arbitrary constant coefficients andcalled the generalized Riccati equation. The obtained solutions including solitons and periodic solutions are illustrated through the hyperbolic functions, thetrigonometric functions, and the rational functions. In addition, it is worth declaring that one of our solutions is identical for special case with already established result which verifies our other solutions. Moreover, some of obtained solutions are depicted in the figures with the aid of Maple. [ABSTRACT FROM AUTHOR]

Soft set theory, initiated by Molodtsov, can be used as a new mathematical tool for dealing with imprecise, vague, and uncertain problems. In this paper, the concepts of two types of generalised interval-valued fuzzy soft set are proposed and their basic properties are studied. The lattice structures of generalised interval-valued fuzzy soft set are also discussed. Furthermore, an application of the new approach in decision making based on generalised interval-valued fuzzy soft set is developed. [ABSTRACT FROM AUTHOR]

In 2011 Alkhazaleh and Salleh defined the concept of soft expert sets where the user can know the opinion of all the experts in one model and give an application of this concept in decision-making problems. Also, they introduced the concept of the fuzzy soft expert set as a combination between the soft expert set and the fuzzy set. In 2010 Majumdar and Samanta presented the concept of a generalized fuzzy soft sets. The purpose of this paper is to combine the work of Alkhazaleh and Salleh (2011) and Majumdar and Samanta (2010), from which we can obtain a new concept: generalized fuzzy soft expert sets (GFSES).We also introduce its operations, namely, complement, union intersection, "AND" and "OR", and study their properties. The generalized fuzzy soft expert sets are used to analyze a decision-making problem. Also in our model the user can know the opinion of all experts in one model. In this work we also introduce the concept of a generalized fuzzy soft expert sets with multiopinions four opinions(, which will be more effective and useful. Finally, we give an application of this concept in decision-making problem. [ABSTRACT FROM AUTHOR]

This paper investigated the spacing threshold of nonsubmerged spur dikes with alternate layout to classify the impact scale of spur dikes. A mathematical model was built based on standard k-ε model, finite volume method (FVM), and rigid lid assumption and was verified by experimental data. According to dimensional analysis, three indices, that is, Fr (Froude number), B/b (channel width to dike length), and B/b (channel width to water depth), were identified as the influencing factors on the spacing threshold, based on which fifteen sets of conditions were simulated. The calculation results indicate that B/h is themost influencing parameter on Sc/b (spacing threshold to dike length), followed by B/b and Fr. A dimensionless empirical formula of spacing threshold is fitted by multivariate regression. The results of four sets of additional conditions illustrate that the generalization of empirical formula is satisfactory and the precision of interpolation is higher than that of extrapolation. Furthermore, the spacing threshold of alternate spur dikes is generally smaller than ipsilateral spur dikes. [ABSTRACT FROM AUTHOR]

We investigate a class of generalized weighted scale-free networks, where the new vertex connects to m pairs of vertices selected preferentially. The key contribution of this paper is that, from the standpoint of random processes, we provide rigorous analytic solutions for the steady state distributions, including the vertex degree distribution, the vertex strength distribution and the edge weight distribution. Numerical simulations indicate that this network model yields three power law distributions for the vertex degrees, vertex strengths and edge weights, respectively. [ABSTRACT FROM AUTHOR]

In this paper, we offer the generalization of the known technique of the construction of the gradient of the residual functional based on the statement of the conjugate problem for the case when the unknown function is complex valued. The notion of the reference frequency of the medium is introduced. Knowing the value of the reference frequency lets us judge the possibility of simultaneous definition of the dielectric permittivity and conductivity. [ABSTRACT FROM AUTHOR]

The aim of this paper is to present the point of coincidence and common fixed point for three mappings in cone metric spaces over normal cone which satisfy a different contractive condition. Our result generalizes the recent related results proved by Stojan Radenović (2009) and Rangamma and Prudhvi (2012). [ABSTRACT FROM AUTHOR]

Some new limit contractive conditions in fuzzy metric spaces are introduced, by using property (E.A), some common fixed point theorems for four maps are proved in GV-fuzzy metric spaces. As an application of our results, some new contractive conditions are presented, and some common fixed point theorems are proved under these contractive conditions. The contractive conditions presented in this paper contain or generalize many contractive conditions that appeared in the literatures. Some examples are given to illustrate that our results are real generalizations for the results in the references and to show that our limit contractive conditions are important for the existence of fixed point. [ABSTRACT FROM AUTHOR]

We studied the global stability and boundedness results of third-order nonlinear differential equations of the form xx+xx(xx, xxx, xx)xx+ xx(xx, xxx, xx) = xx(xx, xx, xxx, xx). Particular cases of this equation have been studied by many authors over years. However, this particular form is a generalization of the earlier ones. A Lyapunov function was used for the proofs of the two main theorems: one with P ≡ 0 and the other with P ≠ 0. The results in this paper generalize those of other authors who have studied particular cases of the differential equations. Finally, a concrete example is given to check our results. [ABSTRACT FROM AUTHOR]

We consider the dual of the generalized Erlang (n) risk model with a barrier dividend strategy. We derive integro-differential equations with boundary conditions satisfied by the expectation of the sum of discounted dividends until ruin and the moment-generating function of the discounted dividend payments until ruin, respectively. The results are illustrated by several examples. [ABSTRACT FROM AUTHOR]