Backlund Transformations for a Class of Systems of Differential Equation.
Bäcklund transformations for several cases of a type of generalized KdV equation.
Bäcklund-Darboux transformation for non-isospectral canonical system and Riemann-Hilbert problem.
Backpropagation generalized delta rule for the selective attention Sigma-if artificial neural network
In this paper the Sigma-if artificial neural network model is considered, which is a generalization of an MLP network with sigmoidal neurons. It was found to be a potentially universal tool for automatic creation of distributed classification and selective attention systems. To overcome the high nonlinearity of the aggregation function of Sigma-if neurons, the training process of the Sigma-if network combines an error backpropagation algorithm with the self-consistency paradigm widely used in physics....
Back-scattering and nonlinear Radon transformation
Baroclinic Kelvin Waves in a Rotating Circular Basin
A linear, uniformly stratified ocean model is used to investigate propagation of baroclinic Kelvin waves in a cylindrical basin. It is found that smaller wave amplitudes are inherent to higher mode individual terms of the obtained solutions that are also evanescent away of a costal line toward the center of the circular basin. It is also shown that the individual terms if the obtained solutions can be visualized as spinning patterns in rotating stratified fluid confined in a circular basin. Moreover,...
Basic singularities in the theory of internal waves with surface tension.
Bellman approach to some problems in harmonic analysis
The stochastic optimal control uses the differential equation of Bellman and its solution - the Bellman function. Recently the Bellman function proved to be an efficient tool for solving some (sometimes old) problems in harmonic analysis.
Benjamin–Ono periodic bifurcating water waves in presence of an essential spectrum
Bergmannsche Polynom-Erzeugende erster Art.
Bernoulli's free-boundary problem, qualitative theory and numerical approximation.
Bethe ansatz solutions to quasi exactly solvable difference equations.
Bifurcating solutions to the monodomain model equipped with FitzHugh-Nagumo kinetics.
Bifurcation and symmetry in problems of capillary-gravity waves.
Bifurcation de Hopf d’ondes de choc pour les équations de Navier-Stokes compressible
Bifurcation for some semilinear elliptic equations when the linearization has no eigenvalues
We prove existence and bifurcation results for a semilinear eigenvalue problem in , where the linearization — has no eigenvalues. In particular, we show...
Bigèbres de Lie, doubles et carrés
Bi-integrable and tri-integrable couplings of a soliton hierarchy associated withSO(4)
In our paper, the theory of bi-integrable and tri-integrable couplings is generalized to the discrete case. First, based on the six-dimensional real special orthogonal Lie algebra SO(4), we construct bi-integrable and tri-integrable couplings associated with SO(4) for a hierarchy from the enlarged matrix spectral problems and the enlarged zero curvature equations. Moreover, Hamiltonian structures of the obtained bi-integrable and tri-integrable couplings are constructed by the variational identities....
Bilevel Approach of a Decomposed Topology Optimization Problem
In topology optimization problems, we are often forced to deal with large-scale numerical problems, so that the domain decomposition method occurs naturally. Consider a typical topology optimization problem, the minimum compliance problem of a linear isotropic elastic continuum structure, in which the constraints are the partial differential equations of linear elasticity. We subdivide the partial differential equations into two subproblems posed...
Bilinear estimates related to the KP equations
We survey some recent results for the KP-II equation. We also give an idea for treating the “bad frequency interactions” of the bilinear estimates in the Fourier transform restriction spaces related to the KP-I equation.