We consider the family of nonlinear difference equations: xn 1 ∑ 3 i 1fi xn, . . . , xn−k f4 xn, . . . , xn−k f5 xn, . . . , xn−k / f1 xn, . . . , xn−k f2 xn, . . . , xn−k ∑ 5 i 3fi xn, . . . , xn−k , n 0, 1, . . . , where fi ∈ C 0, ∞ k , 0, ∞ , for i ∈ {1, 2, 4, 5}, f3 ∈ C 0, ∞ k , 0, ∞ , k ∈ {1, 2, . . . } and the initial values x−k, x−k 1, . . . , x0 ∈ 0, ∞ . We give sufficient conditions un...

In the present study the thermal structure evolution is reviewed for known nonlinear optical borates such as β-BaB2O4, LiB3O5, CsLiB6O10, Li2B4O7, K2Al2B2O7, and α-BiB3O6, based on single-crystal and powder X-ray diffraction data collected over wide temperature ranges. Temperature-dependent measurements of further borates are presented for the first time: α-BaB2O4 (295–673 K), β-BaB2O4 (98–693 ...

We propose a discontinuous Galerkin finite element method for convection diffusion equations that involves a new methodology handling the diffusion term. Test function derivative numerical flux term is introduced in the scheme formulation to balance the solution derivative numerical flux term. The scheme has a nonsymmetric structure. For general nonlinear diffusion equations, nonlinear stabilit...

It is well known that good bounds for solutions of nonlinear diierential equations are diicult to obtain. In this paper, we establish a theorem comparing non-negative solutions (having identical initial values) of the equations u 00 (t) + q(t)u p (t) + r(t)u(t) = 0 and v 00 (t) + k(t)q(t)v p (t) + r(t)u(t) = 0, respectively. If q(t); r(t) 0, k(t) 1, k(t) is non-decreasing, and the rst equation ...

A one-equation linear turbulence model and a two-equation nonlinear explicit algebraic stress model (EASM) are applied to the ow over a multielement airfoil. The e ect of the K-" and K-! forms of the two-equation model are explored, and the K-" form is shown to be de cient in the wallbounded regions of adverse pressure gradient ows. A new K-! form of EASM is introduced. Nonlinear terms present ...

In this paper, we propose an extremely simple deep model for the unsupervised nonlinear dimensionality reduction – deep distributed random samplings. First, its network structure is novel: each layer of the network is a group of mutually independent k-centers clusterings. Second, its learning method is extremely simple: the k centers of each clustering are only k randomly selected examples from...

This paper is focused on the following nonlinear impulsive neutral differential equation k 0 t t , t t 0, (t))) f(x(γ t q(t) (t))) f(x(β t p(t) ] t))) c(t)g(x(α([x(t) ≠ ≥ = − + ′ + 1,2,3,... k , f(x(s))ds s (s)) q(γ f(x(s))ds s (s)) p(β) a (1) x(t a) x(t k k k k t) γ(t 1 t) β(t 1 k k k k Sufficient conditions are obtained for every solution of (*) to tends to a constant as t → ∞.

Unitarity cannot be perserved order by order in ordinary perturbation theory because the constraint UU † = 1 is nonlinear. However, the corresponding constraint for K = ln U , being K = −K†, is linear so it can be maintained in every order in a perturbative expansion of K. The perturbative expansion of K may be considered as a non-abelian generalization of the linked-cluster expansion in probab...

By exploiting a causality property of the nonlinear Fourier transform, a novel decisionfeedback detection strategy for nonlinear frequency-division multiplexing (NFDM) systems is introduced. The performance of the proposed strategy is investigated both by simulations and by theoretical bounds and approximations, showing that it achieves a considerable performance improvement compared to previou...

Travelling wave solutions are important in nonlinear science. These solutions describe phenomena such as vibrations, solitons and propagation with finite speed. In recent years, direct search for exact solutions of nonlinear partial differential equations (PDEs) has become more and more attractive, partly due to the availability of computer systems like Maple or Mathematica, which allow to perf...