Abstract Several properties of subspaces $$J \subset X$$ J ⊂ X in a pair ( X , J ) with quotient lifting different types are derived, giving emphasis to order-preserving for order unit spaces and affine continuous functions on Choquet simplexes.

On the basis of the perturbation expansion for electron gas energy in the third order to the electron-ion potential the pair and irreducible three-ion interaction potentials in metallic hydrogen are calculated. The irreducible potential of three-ion interaction has attractive nature at short interionic separation and oscillates at large ones. The anisotropic character of the three-ion interacti...

Counterterms that are not reducible to ζn are generated by 3F2 hypergeometric series arising from diagrams for which triangle and uniqueness relations furnish insufficient data. Irreducible double sums, corresponding to the torus knots (4, 3) = 819 and (5, 3) = 10124, are found in anomalous dimensions at O(1/N3) in the large-N limit, which we compute analytically up to terms of level 11, corres...

There are many studies for generating irreducible polynomials (L. M. Adleman & H. W. Lenstra (1986)) − (Ian. F. Blake et al., (1993)). This is because irreducible polynomials play critical roles in the cases such as constructing extension field or generating random sequence. The problem of generating irreducible polynomial is theoretically interesting and have attracted many scientists and engi...

We give a complete description of the discrete spectra in branching law $\Pi|_{G'}$ with respect to pair $(G,G')=(O(p,q), O(p',q') \times O(p'',q''))$ for irreducible unitary representations $\Pi$ $G$ that are "geometric quantization" minimal elliptic coadjoint orbits. also construct explicitly all holographic operators and prove closed Parseval-type formula.

In this paper it is proved that the algorithms of differentiation VIII-X (introduced by A.G. Zavadskij to classify equipped posets tame representation type) induce categorical equivalences between some quotient categories, in particular, analgorithm Az introduced build with a pair ofpoints (a, b) suitable for VII such subset strong points related weak pointais not empty.

Let A and A! be dual Koszul algebras. By Positselski a filtered algebra U with grU = A is Koszul dual to a differential graded algebra (A!, d). We relate the module categories of this dual pair by a⊗−Hom adjunction. This descends to give an equivalence of suitable quotient categories and generalizes work of Beilinson, Ginzburg, and Soergel.

We produce skew loops—loops that lack any pair of parallel tangent lines—homotopic to any loop in a flat torus, or any other quotient of Rn by a discrete subgroup. The interesting case here is n = 3 . More subtly for any n , we then characterize the homotopy classes that will contain a skew loop having a specified loop τ ⊂ S as tangent indicatrix.

We construct functorially a class of algebras using the formalism of double derivations. These algebras extend to higher dimensions Crawley-Boevey and Holland’s construction of deformed preprojective algebras and encompass symplectic reflection algebras associated to wreath products. We use this construction to show that the quotient field of a symplectic reflection algebra is “rational”, confi...

We construct functorially a class of algebras using the formalism of double derivations. These algebras extend to higher dimensions Crawley-Boevey and Holland's construction of deformed preprojective algebras and encompass symplectic reflection algebras associated to wreath products. We use this construction to show that the quotient field of a symplectic reflection algebra is " rational " , co...