Starting from Giaquinta’s counterexample [Gi] we introduce the class of splitting functionals being of (p, q)-growth with exponents p ≤ q < ∞ and show for the scalar case that locally bounded local minimizers are of class C. Note that to our knowledge the only C-results without imposing a relation between p and q concern the case of two independent variables as it is outlined in Marcellini’s pa...

This paper describes a prototype multilingual Q&A system that we have designed to participate in the Q&A Track of TREC-12. The system answer concrete responses, then we participate in the Q&A main task for factoid questions. The main areas of our system are: (1) Inductive Logic Programming to learn the question type, (2) Clustering of Named Entities to improve Information Retrieval and (3) Sema...

We discuss how to extract the polarized parton densities and fragmentation functions in a model independent way from SIDIS, and present results for D + u,d,s. There are two types of processes that give information on polarized parton densities in nucleon. The polarized asymmetry in DIS of longitudinally polarized leptons on longitudinally polarized nucleons: ∆A N = 2y(2− y) 1 + (1− y) ∆σ N σ N ...

Investigated is the relativistic periodic Toda chain, to each site of which the ultra-local Weyl algebra is associated. Weyl's q we are considering here is restricted to be inside the unit circle. Quantum Lax operators of the model are intertwined by six vertex R-matrix. Both independent Baxter's Q-operators are constructed explicitly as seria over local Weyl generators. The operator-valued wro...

Kronecker’s theorem states that if 1, θ1, . . . , θn are real algebraic numbers, linearly independent over Q, and if α ∈ R, then for any > 0 there are q ∈ Z and p ∈ Z such that |qθi − αi − pi| < . Here, a bound on q is given in terms of the dimension n, of the precision , of the degree of the θi’s and of their height. A possible connection to the square-root sum problem is discussed.

We investigate the low-energy behavior of the four-point Green's function ? describing virtual Compton scattering oo the nucleon. Using Lorentz invariance, gauge invariance, and crossing symmetry, we derive the leading terms of an expansion of the operator in the four-momenta q and q 0 of the initial and nal photon, respectively. The model-independent result is expressed in terms of the electro...

For each natural number $n$, we define $\omega^*(n)$ to be the of primes $p$ such that $p-1$ divides $n$. We show in contrast Hardy-Ramanujan theorem which asserts $\omega(n)$ prime divisors $n$ has a normal order $\log\log n$, function does not have order. conjecture for some positive constant $C$, $$\sum_{n\leq x} \omega^*(n)^2 \sim Cx(\log x). $$ Another related this emerges, seems independe...

The Tsallis $q$-Gaussian distribution is a powerful generalization of the standard Gaussian and commonly used in various fields, including non-extensive statistical mechanics, financial markets image processing. It belongs to $q$-distribution family, which characterized by non-additive entropy. Due their versatility practicality, $q$-Gaussians are natural choice for modeling input quantities me...

Suppose independent observations Xi , i = 1, . . . , n are observed from a mixture model f (x;Q) ≡ ∫ f (x; ) dQ( ), where is a scalar and Q( ) is a nondegenerate distribution with an unspecified form. We consider to estimate Q( ) by nonparametric maximum likelihood (NPML) method under two scenarios: (1) the likelihood is penalized by a functional g(Q); and (2) Q is under a constraint g(Q) = g0....