In the context of a general lattice Γ in Rn and a strictly expanding map M which preserves the lattice, we characterize all the wavelet families, all the MSF wavelets, all the multiwavelets associated with a Multiresolution Analysis (MRA) of multiplicity d ≥ 1, and all the scaling functions. Moreover, we give several examples: in particular, we construct a single, MRA and C∞(Rn) wavelet, which ...

If large-angle multigluon radiation gives significant contributions to parton showers in the LHC high-energy region, appropriate generalizations of parton branching methods are required for Monte Carlo simulations of exclusive high-multiplicity final states. We discuss the use in this context of transverse-momentum dependent kernels which factorize in the region of high energies. We give exampl...

1. Preliminaries 1 2. Multiplicity free actions 8 3. Linear multiplicity free actions 15 4. Examples of multiplicity free decompositions 21 5. A recursive criterion for multiplicity free actions 33 6. The classification of linear multiplicity free actions 37 7. Invariant polynomials and differential operators 43 8. Generalized binomial coefficients 52 9. Eigenvalues for operators in PD(V ) 61 R...

In the context of a general lattice ? in R n and a strictly expanding map M which preserves the lattice, we characterize all the wavelet families, all the MSF wavelets, all the multiwavelets associated with a Multiresolution Analysis (MRA) of multiplicity d 1; and all the scaling functions. Moreover , we give several examples: in particular, we construct a single, MRA and C 1 (R n) wavelet, whi...

| A new context-sensitive neural network, called an \EXIN" (excitatory+inhibitory) network, is described. EXIN networks self-organize in complex perceptual environments, in the presence of multiple superimposed patterns, multiple scales, and uncertainty. The networks use a new inhibitory learning rule, in addition to an excitatory learning rule, to allow superposition of multiple simultaneous n...

We take G to be an undirected graph without loops or multiple edges, with vertex set V (G) = f1; : : : ; ng, and with (0; 1)-adjacency matrix A. Let P denote the orthogonal projection of IR onto the eigenspace E( ) of A, and let fe1; : : : ; eng be the standard orthonormal basis of IR. Since E( ) is spanned by the vectors Pej (j = 1; : : : ; n) there exists X V (G) such that the vectors Pej (j ...

in this paper, we establish some results on the existence of at least three weak solutions for adirichlet problem involving p-laplacian using a variational approach.

this study attempts to examine the multilingualism in algeria, in other words, the phenomenon of linguistic diversity which characterizes the algerian reality and its relationship. for that matter the article visualizes the linguistic level of learners especially children, highlighting the characteristics of the multiplicity of its causes and manifestations. here, the descriptive methodology is...

1. Preliminaries 1 2. Multiplicity free actions 8 3. Linear multiplicity free actions 14 4. Examples of multiplicity free decompositions 21 5. A recursive criterion for multiplicity free actions 32 6. The classification of linear multiplicity free actions 36 7. Invariant polynomials and differential operators 42 8. Generalized binomial coefficients 51 9. Eigenvalues for operators in PD(V ) 59 R...