An extension of the Semimicroscopic Algebraic Cluster Model (SACM) is proposed, based on pseudo-SU(3) model. The Hamiltonian and spectroscopic factor operator model are presented a procedure constructing space. Because huge number SU(3) irreducible representations (irrep) appear, one has to be careful in designing practical, consistent path reduce Hilbert concept forbiddenness, taking into acco...

Abstract We compute the generator rank of a subhomogeneous $C^*\!$ -algebra in terms covering dimension pieces its primitive ideal space corresponding to irreducible representations fixed dimension. deduce that every $\mathcal {Z}$ -stable approximately algebra has one, which means generic element such an is generator. This leads strong solution problem for classifiable, simple, nuclear -algebr...

An analogue of the Eisenstein irreducibility criterion is developed for linear differential operators, or, more generally, noncommutative polynomials, and is applied to a few simple examples. Introduction. The question of the irreducibility of an ordinary linear differential operator is of interest in the Picard-Vessiot theory (see Kolchin [1, §22]). Indeed, the operator is irreducible if and o...

The purpose of this research is to provide a deeper understanding of the planar high- symmetry configuration instability. In the ideal case, the distortion corresponds to the movements of nuclei along normal modes that belong to non-totally symmetric irreps of the high symmertry (HS) point group of molecule. The analysis of the structural distortion from the HS nuclear arrangements of the JT ac...

‎‎here we construct and count all ordinary irreducible characters of sylow $p$-subgroups of the steinberg triality groups ${}^3d_4(p^{3m})$.

Let K be a complete field with a discrete valuation v, ring of integers OK , and maximal ideal (πK). Let k := OK/(πK) be the residue field, assumed to be separably closed of characteristic p ≥ 0. LetX/K be a smooth proper geometrically irreducible curve of genus g ≥ 1. Let X /OK denote a regular model of X/K. Let Xk = ∑v i=1 riCi be its special fiber, where Ci/k is an irreducible component of X...

Let $\mathfrak{g}$ be a semisimple Lie algebra. We establish new relation between the Goldie rank of primitive ideal $\mathcal{J}\subset U(\mathfrak{g})$ and dimension corresponding irreducible representation $V$ an appropriate finite W-algebra. Namely, we show that $\operatorname{Grk}(\mathcal{J}) \leqslant \dim V/d_V$, where $d_V$ is index suitable equivariant Azumaya algebra on homogeneous s...

T then it is proved that (1) ) ( ) ( ) ( 0 1 2 A N A N A N A    (2) N0(A) = A2, N1(A) is a semiprime ideal of T containing A, N2(A) = A4 are equivalent, where No(A) = The set of all A-potent elements in T, N1(A) = The largest ideal contained in No(A), N2(A) = The union of all A-potent ideals. If A is a semipseudo symmetric ideal of a ternary semigroup then it is proved that N0(A) = N1(A) = N...

Let A be a polynomial ring in n+ 1 variables over an arbitrary infinite field k. It is proved that for all sufficiently large n and d there is a homogeneous prime ideal p ⊂ A satisfying the following conditions. The ideal p corresponds to a component, defined over k and irreducible over s k, of a projective algebraic variety given by a system of homogeneous polynomial equations with polynomials...

Let J be the ideal of vertex covers of a graph G. We give a graph theoretical characterization of the minimal generators of the symbolic Rees algebra of J . If G is perfect, it is shown that the Rees algebra of J is normal and we compute the irreducible representation of the Rees cone of J in terms of cliques. Then we prove that if G is perfect and unmixed, then the Rees algebra of J is a Goren...