Related papers: B-Spline Quarklets and Biorthogonal Multiwavelets
In this paper we prove that under some conditions on the parameters the one-dimensional Triebel-Lizorkin spaces $ F^{s}_{r,q}(\mathbb{R}) $ can be described in terms of quarklets. So for functions from Triebel-Lizorkin spaces we obtain a…
Wavelets, known to be useful in non-linear multi-scale processes and in multi-resolution analysis, are shown to have a q-deformed algebraic structure. The translation and dilation operators of the theory associate with any scaling equation…
In this paper we deduce new characterizations for bivariate Bessel-Potential spaces defined on the unit square via B-spline quarklets. For that purpose in a first step we use univariate boundary adapted quarklets to describe univariate…
Vector spaces of (framed) BPS states of Lagrangian four-dimensional N=2 field theories can be defined in semiclassical chambers in terms of the $L^2$-cohomology of Dirac-like operators on monopole moduli spaces. This was spelled out…
We consider the spectrum of BPS saturated states in $N = 2$ gauge theories in four dimensions. This spectrum may be discontinuous across real codimension one submanifolds of marginal stability in the moduli space of vacua. An example, which…
By the use of complete orthonormal sets of nonrelativistic scalar orbitals introduced by the author in previous papers the new complete orthonormal basis sets for two-and four-component spinor wave functions, and Slater spinor orbitals…
We show that compactly supported wavelets in L^2(R) of scale N may be effectively parameterized with a finite set of spin vectors in C^N, and conversely that every set of spin vectors corresponds to a wavelet. The characterization is given…
By the use of complete orthonormal sets of nonrelativistic scalar orbitals introduced by the author in previous papers the new complete orthonormal basis sets for two- and four-component spinor wave functions, and Slater spinor orbitals…
(Bi)orthogonal (multi)wavelets on the real line have been extensively studied and employed in applications with success. A lot of problems in applications are defined on bounded intervals or domains. Therefore, it is important in both…
Tile B-splines in $\mathbb{R}^d$ are defined as autoconvolutions of the indicators of tiles, which are special self-similar compact sets whose integer translates tile the space $\mathbb{R}^d$. These functions are not piecewise-polynomial,…
We consider the bipartite boolean quadric polytope (BQP) with multiple-choice constraints and analyse its combinatorial properties. The well-studied BQP is defined as the convex hull of all quadric incidence vectors over a bipartite graph.…
We introduce B-splines on the line of quaternionic order $B_q$ ($q$ in the algebra of quaternions) for the purposes of multi-channel signal and image analysis. The functions $B_q$ are defined first by their Fourier transforms, then as the…
In the heavy-quark limit, the decay spectrum for radiative and semileptonic inclusive B-meson decays is determined by a universal structure function, i.e. the shape function. We study the constraints on the bilocal heavy-quark operator for…
We discuss the non-relativistic multichannel quark model and describe the techniques developed to solve the resulting equations. We then investigate some simple solutions to demonstrate how the model unifies meson-meson scattering with…
The statistical distribution of eigenvalues of pairs of coupled random matrices can be expressed in terms of integral kernels having a generalized Christoffel--Darboux form constructed from sequences of biorthogonal polynomials. For…
The spectra and form factors of exclusive semi-leptonic decays of B-meson are analyzed, taking account of confined effects of quarks by the Covariant Oscillator Quark Model. The predicted B --> (D*,D)l nubar_l spectra with the conventional…
In this article a series of solutions with higher baryon numbers in the chiral quark soliton model are reported. The chiral quark soliton model is a simple quark model that incorporates the basic features of QCD. The B=2 axially symmetric…
The shearlets are a special case of the wavelets with composite dilation that, among other things, have a basis-like structure and multi resolution analysis properties. These relatively new representation systems have encountered wide range…
Normal multi-scale transform [4] is a nonlinear multi-scale transform for representing geometric objects that has been recently investigated [1, 7, 10]. The restrictive role of the exact order of polynomial reproduction $P_e$ of the…
Semileptonic and nonleptonic decays of the B_c meson to B_s and B mesons, caused by the c\to s,d quark transitions, are studied in the framework of the relativistic quark model. The heavy quark expansion in inverse powers of the active c…