A band is a semigroup consisting of idempotents. It is proved that for any field K and any band S with finitely many components, the semigroup algebra K[S] can be embedded in upper triangular matrices over a commutative K-algebra. The proof of a theorem of Malcev [4, Theorem 10] on embeddability of algebras into matrix algebras over a field is corrected and it is proved that if S = F ∪ E is a b...

We present a comprehensive study of the effective Conformal Field Theory (CFT) describing the low energy excitations of a gas of spinless interacting fermions on a circle in the gapless regime (Luttinger liquid). Functional techniques and modular transformation properties are used to compute all correlation functions in a finite size and at finite temperature. Forward scattering disorder is tre...

Let L/K be a finite Galois extension of number fields with Galois group G. Let p be a prime and let r ≤ 0 be an integer. By examining the structure of the p-adic group ring Zp[G], we prove many new cases of the p-part of the equivariant Tamagawa number conjecture (ETNC) for the pair (h(Spec(L))(r),Z[G]). The same methods can also be applied to other conjectures concerning the vanishing of certa...

We overview numerous algorithms in computational D-module theory together with the theoretical background as well as the implementation in the computer algebra system Singular. We discuss new approaches to the computation of Bernstein operators, of logarithmic annihilator of a polynomial, of annihilators of rational functions as well as complex powers of polynomials. We analyze algorithms for l...

In this note we show that the complete symmetric polynomials are dual generators of compressed artinian Gorenstein algebras satisfying Strong Lefschetz Property. This is first example an explicit form with these properties. For forms any degree in number variables, provide upper bound for Waring rank by establishing power sum decomposition. Moreover, determine rank, cactus resolution and Proper...

In this paper, we make a comprehensive study of two classes Boolean functions whose interest originally comes from hybrid symmetric-FHE encryption (with stream ciphers like FiLIP), but which also present much for general ciphers. The in these are cheap and easy to implement, they allow the resistance all classical attacks their guess determine variants as well. We exactly main cryptographic par...

The main result of the paper is a description of the maximal ideals in the modular group algebras of the finitary symmetric and alternating groups (provided the characteristic p of the ground field is greater than 2). For the symmetric group there are exactly p − 1 such ideals and for the alternating group there are (p − 1)/2 of them. The description is obtained in terms of the annihilators of ...

We propose an integrated numerically reliable computational approach to solve fault detection and isolation (FDI) problems for periodic systems. For this purpose, a bank of periodic fault detection filters providing a structured residual set is designed using a new least order synthesis technique of periodic fault detection filters. The synthesis procedure relies on a recently developed numeric...