The theory of the Riemann zeta-function ζ(s) and Dirichlet L-functions L(s, χ) abounds with unsolved problems. Chronologically the first of these, now known as the Riemann Hypothesis (RH), originated from Riemann’s remark that it is very probable that all non-trivial zeros of ζ(s) lie on the line < s = 12 . Later on Piltz conjectured the same for all of the functions L(s, χ) (GRH). The vertical...

A new theory and synthesis procedure are advanced f o r low s e n s i t i v i t y ac t i ve f i l t e r s , based on s t r uc tu ra l pass i v i t y o f bu i l d i ng blocks. Key t o t he theory and synthesis methods are t he concepts of bounded r e a l i t y and loss less bounded rea l property. Wave-active f i l t e r s which a re wel l known f o r low passband s e n s i t i v i t y t u r n o...

Learning Theory is the study of systems that implement functions from ev ident ia l states to theor ies . The theoret ica l framework developed in the theory makes possible the comparison of classes of algorithms which embody d i s t i n c t learning strategies along a var ie ty of dimensions. Such comparisons y ie ld valuable information to those concerned with inference problems in Cognit ive...

we develop a theory of stratified $lm$-filters which generalizes the theory of stratified $l$-filters. our stratification condition explicitly depends on a suitable mapping between the lattices $l$ and $m$. if $l$ and $m$ are identical and the mapping is the identity mapping, then we obtain the theory of stratified $l$-filters. based on the stratified $lm$-filters, a general theory of lattice-v...

0 ∈ Tx + λCx, where T : D(T )⊂ X → 2X is a strongly quasibounded maximal monotone operator and C : D(C)⊂ X → X∗ satisfies the condition (S+)D(C) with L⊂ D(C). The method of approach is to use a topological degree theory for (S+)L-perturbations of strongly quasibounded maximal monotone operators, recently developed by Kartsatos and Quarcoo. Moreover, applying degree theory, a variant of the Fred...

We show that for any N > 0 there exists a natural even n > N such that the discriminant of moduli of K3 surfaces of the degree n is not equal to the set of zeros of any automorphic form on the corresponding IV type domain. We give the necessary condition on a ”condition S ⊂ LK3 on Picard lattice of K3” for the corresponding moduli MS⊂LK3 of K3 to have the discriminant which is equal to the set ...