In this paper, we are concerned with the following fractional Schrödinger-Poisson system:    (−∆s)u + u + λφu = µf(u) +|u|p−2|u|, x ∈R3 (−∆t)φ = u2, x ∈R3 where λ,µ are two parameters, s,t ∈ (0,1] ,2t + 4s > 3 ,1 < p ≤ 2∗ s and f : R → R is continuous function. Using some critical point theorems and truncation technique, we obtain the existence and multiplicity of non-trivial solutions with ...

A Legendre wavelet method is presented for numerical solutions of stochastic Volterra-Fredholm integral equations. The main characteristic of the proposed method is that it reduces stochastic Volterra-Fredholm integral equations into a linear system of equations. Convergence and error analysis of the Legendre wavelets basis are investigated. The efficiency and accuracy of the proposed method wa...

We present complete solutions of K-matrix for the quantum Mikhailov-Shabat model. It has been known that there are three diagonal solutions with no free parameters, one being trivial identity solution, the others non-trivial. The most general solutions which we found consist of three families corresponding to each diagonal solutions. One family of solutions depends on two arbitrary parameters. ...

For k ≥ 3 let A ⊂ [1, N ] be a set not containing a solution to a1x1 + · · · + akxk = a1xk+1 + · · · + akx2k in distinct integers. We prove that there is an ε > 0 depending on the coefficients of the equation such that every such A has O(N) elements. This answers a question of I. Ruzsa. Introduction The problems of estimating the size of a largest subset of [1, N ] not containing a solution to ...

Feature selection and feature transformation, the two main ways to reduce dimensionality, are often presented separately. In this paper, a feature selection method is proposed by combining the popular transformation based dimensionality reduction method Linear Discriminant Analysis (LDA) and sparsity regularization. We impose row sparsity on the transformation matrix of LDA through l2,1-norm re...

Let D(G) be the maximal cardinality of a set A ⊆ G that contains no non-trivial solution to x1 + · · · + xs − sxs+1 = 0 with xi ∈ A (1 ≤ i ≤ s + 1). Let d(n) = sup rk(H)≥n D(H) |H| , where rk(H) is the rank of H. We prove that for any n ∈ N, d(n) ≤ C ns−2 , where C is a fixed constant depending only on s.

We have developed a new agent-based simulation tool to model social dilemmas for the case of a large number of not necessarily rational decision-makers (Szilagyi and Szilagyi, 2000). The combination of various personalities with stochastic learning makes it possible to simulate the multi-person Prisoners’ Dilemma game for realistic situations. A variety of personality profiles and their arbitra...

The existence of non-trivial solutions X to matrix equations of the form F (X,A1,A2, · · · ,As) = G(X,A1,A2, · · · ,As) over the real numbers is investigated. Here F and G denote monomials in the (n × n)-matrix X = (xij) of variables together with (n × n)-matrices A1,A2, · · · ,As for s ≥ 1 and n ≥ 2 such that F and G have different total positive degrees in X. An example with s = 1 is given by...