For certain subsets S and T of A = { · · · , (0, 2), (0, 1), (0, 0), (1, 0), (2, 0), · · · } and factor spaces C S [X, Y ], C +S,T [X, Y, Z,W ] and C − S,T [X, Y, Z,W ], bitableaux bases are constructed that are indexed by pairs of standard tableaux and sequences in the collections ΥψS and ΥψT . These bases give combinatorial interpretations to the appropriate Hilbert series of these spaces as ...

In the title mol-ecule, C(11)H(12)N(2)O, the pyridazine ring has a skew-boat conformation. The dihedral angle between the phenyl ring [r.m.s deviation = 0.0039 (15) Å] and the best mean-plane of the pyridazine ring [r.m.s deviations = 0.2629 (15) Å] is 53.27 (10)°. In the crystal, mol-ecules are linked by C-H⋯O hydrogen bonds and C-H⋯π inter-actions involving the methyl group and the phenyl rin...

For k a field of arbitrary characteristic, and R a k-algebra, we show that the PI degree of an iterated skew polynomial ring R[x1; τ1, δ1] · · · [xn; τn, δn] agrees with the PI degree of R[x1; τ1] · · · [xn; τn] when each (τi, δi) satisfies a qi-skew relation for qi ∈ k and extends to a higher qi-skew τi-derivation. We confirm the quantum Gel’fand-Kirillov conjecture for various quantized coord...

A theorem of Christol states that a power series over a finite field is algebraic over the polynomial ring if and only if its coefficients can be generated by a finite automaton. Using Christol’s result, we prove that the same assertion holds for generalized power series (whose index sets may be arbitrary well-ordered sets of nonnegative rationals).

We introduce circulant matrices that capture the structure of a skew-polynomial ring F[x; θ] modulo the left ideal generated by a polynomial of the type x − a. This allows us to develop an approach to skew-constacyclic codes based on such circulants. Properties of these circulants are derived, and in particular it is shown that the transpose of a certain circulant is a circulant again. This rec...

Tris paper, through analy3is to the specific power of the compressor, indicates that to reduce the power loss caused by friction is an important way to reduce the specific power of the compressor, investigates the realizability employing a single piston ring or a piston ring with small elasticity in the high speed double acting compressor, and raises a standpoint for a high speed double acting ...

5 Hopf Rings 11 5.1 What is a Hopf ring? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 5.2 DS as a co-Hopf ring spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 5.3 Rational Morava E-theory of DS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 6 EDS is a formal power series ring under ? 12 6.1 Determining...