for any nonnegative integers n, s, t with 2 ∤ t, where [k]q = (1−q)/(1−q); this is a q-analogue of Stern’s congruence E2n+2s ≡ E2n +2 (mod 2s+1). We also prove that (−q; q)n = ∏ 0<k6n(1 + q ) divides S2n(q) and the numerator of C2n(q); this extends Carlitz’s result that 2 divides the Salié number S2n and the numerator of the Carlitz number C2n. Our result on q-Salié numbers implies a conjecture...

We interpret geometrically a variant of the Robinson-Schensted correspondence which links Brauer diagrams with updown tableaux, in the spirit of Steinberg’s result [32] on the original Robinson-Schensted correspondence. Our result uses the variety of all (N , ω, V) where V is a complete flag in C2n, ω is a nondegenerate alternating bilinear form on C2n, and N is a nilpotent element of the Lie a...

for any nonnegative integers n, s, t with 2 ∤ t, where [k]q = (1−q)/(1−q), this is a q-analogue of Stern’s congruence E2n+2s ≡ E2n +2 (mod 2s+1). We also prove that (−q; q)n = ∏ 0<k6n(1 + q ) divides S2n(q) and the numerate of C2n(q), this extends Carlitz’s result that 2 divides the Salié number S2n and the numerate of the Carlitz number C2n. For q-Salié numbers we also confirm a conjecture of ...

for any nonnegative integers n, s, t with 2 ∤ t, where [k]q = (1−q)/(1−q); this is a q-analogue of Stern’s congruence E2n+2s ≡ E2n +2 (mod 2s+1). We also prove that (−q; q)n = ∏ 0<k6n(1 + q ) divides S2n(q) and the numerate of C2n(q); this extends Carlitz’s result that 2 divides the Salié number S2n and the numerate of the Carlitz number C2n. Our result on q-Salié numbers implies a conjecture o...

for any nonnegative integers n, s, t with 2 ∤ t, where [k]q = (1−q)/(1−q), this is a q-analogue of Stern’s congruence E2n+2s ≡ E2n +2 (mod 2s+1). We also prove that (−q; q)n = ∏ 0<k6n(1 + q ) divides S2n(q) and the numerate of C2n(q), this extends Carlitz’s result that 2 divides the Salié number S2n and the numerate of the Carlitz number C2n. For q-Salié numbers we also confirm a conjecture of ...

The H+3 ion plays a key role in the chemistry of dense interstellar gas clouds where stars and planets are forming. The low temperatures and high extinctions of such clouds make direct observations of H+3 impossible, but lead to large abundances of H2D + and D2H, which are very useful probes of the early stages of star and planet formation. The ground-state rotational ortho-D2H 11,1–00,0 transi...

We consider the two-scale refinement equation f(x) = ∑N n=0 cnf(2x − n) with ∑ n c2n = ∑ n c2n+1 = 1 where c0, cN 6= 0 and the corresponding subdivision scheme. We study the convergence of the subdivision scheme and the cascade algorithm when all cn ≥ 0. It has long been conjectured that under such an assumption the subdivision algorithm converge, as well as the cascade algorithm converge unifo...

Hermitian Clifford analysis deals with the simultaneous null solutions of the orthogonal Dirac operators ∂x and its twisted counterpart ∂x|, introduced below. For a thorough treatment of this higher-dimensional function theory, we refer the reader to, for example, 1–5 . Let e1, . . . , e2n be an orthonormal basis of the Euclidean space R2n. Consider the complex Clifford algebra C2n constructed ...

Probing the gas and dust in proto-planetary disks is central for understanding the process of planet formation. In disks surrounding solar type protostars, the bulk of the disk mass resides in the outer midplane, which is cold (≤20 K), dense (≥ 107 cm−3) and depleted of CO. Observing the disk midplane has proved, therefore, to be a formidable challenge. Ceccarelli et al. (2004) detected H2D emi...

Abstract Accounting for variability in generation and load strategies to tackle cost-efficiently are key components of investment models modern electricity systems. This work presents evaluates the Hours-to-Decades (H2D) model, which builds upon a novel approach account manage variations system covering several days, variation management is particular relevance wind power integration. The model...