In this paper, we propose mixed generalized Hermite-Legendre spectral method for partial differential equation set in an infinite strip. We investigate mixed generalized Hermite-Legendre approximation. We propose the new algorithm for various boundary condition problems with variable coefficient. The global convergence of proposed algorithms is proved. Numerical results demonstrate the spectral...

In this paper, we first establish the regularity theorem for suitable weak solutions to the EricksenLeslie system in R2. Building on such a regularity, we then establish the existence of a global weak solution to the Ericksen-Leslie system in R2 for any initial data in the energy space, under the physical constraint conditions on the Leslie coefficients ensuring the dissipation of energy of the...

A 3-D inverse medium problem in the frequency domain is considered. Another name for this problem is Coefficient Inverse Problem. The goal is to reconstruct spatially distributed dielectric constants from scattering data. Potential applications are in detection and identification of explosive-like targets. A single incident plane wave and multiple frequencies are used. A new numerical method is...

Complex networks have been successfully employed to represent different levels of biological systems, ranging from gene regulation to protein-protein interactions and metabolism. Network-based research has mainly focused on identifying unifying structural properties, such as small average path length, large clustering coefficient, heavy-tail degree distribution and hierarchical organization, vi...

Linguistic alignment has emerged as an important property of conversational language and a driver of mutual understanding in dialogue. While various computational measures of linguistic alignment in corpus and experimental data have been devised, a systematic evaluation of them is missing. In this study, we first evaluate the sensitivity and distributional properties of three measures, indiscri...

In this short note we show that the space of all ∂̄-free maps of any complex manifold Vc into Cn is always homotopically equivalent to the space of all sections of the corresponding bundle in the space of jets of smooth maps Vc → Cn. In particular, the space of all linear ordinary differential equations with complex-valued coefficients on an elliptic curve with the identical monodromy (defined a...

In this paper, we deal with the problem of description of nonsingular pairs of compatible flat metrics for the general N -component case. We describe the scheme of the integrating the nonlinear equations describing nonsingular pairs of compatible flat metrics (or, in other words, nonsingular flat pencils of metrics). This scheme was announced in our previous paper [1]. It is based on the reduci...

Artificial intelligence in games often leads to the problem of parameter tuning. Some heuristics may have coefficients, and they should be tuned to maximize the win rate of the program. A possible approach is to build local quadratic models of the win rate as a function of program parameters. Many local regression algorithms have already been proposed for this task, but they are usually not rob...

A bstrac t. We present an empirical st udy of th e required training time for neural networks to learn to compute the parity function using the back -propagation learning algorithm, as a function of t he numb er of inp uts. The parity funct ion is a Boolean predica te whose order is equal to th e number of inpu t s. \Ve find t hat t he t rain ing time behaves roughly as 4" I where n is the num ...

The Frequency Assignment Problem (FAP) is an important problem that arises in the design of radio networks, when a channel has to be assigned to each transceiver of the network. This problem is a generalization of the graph coloring problem. In this paper we study a general version of the FAP that can include adjacent frequency constraints. Using concepts from landscapes’ theory, we prove that ...