An ideal of polynomials is symmetric if it closed under permutations variables. We relate general ideals to the so called Specht generated by all a given shape. show connection between leading monomials in and contained ideal. This provides applications several contexts. Most notably, this gives information about solutions corresponding set equations. From another perspective, restricts isotypi...

We consider generalized exponents of a finite reflection group acting on a real or complex vector space V . These integers are the degrees in which an irreducible representation of the group occurs in the coinvariant algebra. A basis for each isotypic component arises in a natural way from a basis of invariant generalized forms. We investigate twisted reflection representations (V tensor a line...

A new oxoborate β -CaB4O7 has been synthesized under high-pressure/high-temperature conditions from calcium oxide and boron oxide with a Walker-type multianvil apparatus at 7.7 GPa and 1100 ◦C. Single crystal X-ray structure determination of β -CaB4O7 revealed: Pmn21, a = 1058.4(1), b = 436.9(1), c = 419.4(1) pm, Z = 2, R1 = 0.0305, wR2 = 0.0587 (all data). The compound is isotypic to the known...

Crystals of the title compound, [Fe(C(8)H(7)N(3))(3)](2)[PMo(12)O(40)]·6H(2)O, prepared under hydro-thermal conditions, are isotypic with the Mn(2+) and Cd(2+) analogues. The Fe(2+) cation is in a distorted octa-hedral coordination by six N atoms from three chelating 3-(2-pyrid-yl)-1H-pyrazole ligands. The heteropoly-anion [PMo(12)O(40)](4-) is a one-electron reduced species in which two O atom...

Single crystals of the title compound, Na(H2AsO4), were obtained by partial neutralization of arsenic acid with sodium hydroxide in aqueous solution. The crystal structure of Na(H2AsO4) is isotypic with the phosphate analogue and the asymmetric unit consists of two sodium cations and two tetra-hedral H2AsO4- anions. Each of the sodium cations is surrounded by six O atoms of five H2AsO4- groups,...

The complex Ginzburg± Landau (CGL) equation on a one-dimensional domain with periodic boundary conditions has a number of diþ erent symmetries. Solutions of the CGL equation may or may not be ® xed by the action of these symmetries. We investigate the stability of chaotic solutions with some re ̄ ectional symmetry to perturbations which break that symmetry. This can be achieved by considering th...

We introduce a tensor decomposition of the $$\ell $$ -adic Tate module an abelian variety $$A_0$$ defined over number field which is geometrically isotypic. If potentially $$\mathrm {GL}_2$$ -type and totally real field, we use this to describe its Sato–Tate group prove conjecture in certain cases.