Berechung von Isotopieeffekten in den spezifischen Geschwindigkeitskonstanten k(E) für Zerfallsreaktionen

Für die Moleküle NO₂, SO₂, CO₂, werden Dissoziationswahrscheinlichkeiten und Isotopieeffekte derselben in Abhängigkeit von der Anregungsenergie und dem Drehimpulszustand berechnet (¹¹N/¹⁵N; ¹⁶O/¹⁸O; ³²S/³⁴S; ¹²C/¹³C). Die Verhütnisse der spezifischen Geschwindigkeitskonstanten für Paare isotopensubstituierter Moleküle nehmen in Abhängigkeit von der Anregungsenergie zum Teil beträchtliche Werte an, weisen ein oszillalorisches Verhalten auf und zeigen auch inverse Isotopieeffekte.     

Laminar Natural Convection in a Square Cavity with a Partition on the Heated Vertical Wall

Abstract

The laminar natural convection in an air-filled square cavity with a partition on the heated vertical wall was experimentally investigated. Temperature measurements and flow visualizations were performed for cases with heated and cooled vertical walls (corresponding to a global Grashof number Gr _H of approximately 1.4 × 10⁸) and non dimensional top wall temperatures θ _T of 0.57 (insulated) to 2.3. Experiments were performed with an aluminum partition with non dimensional height H _P /H of 0.0625 and 0.125 attached to the heated vertical wall at y/H = 0.65 and 0.95. The blockage effect and/or the thermal effect of the partition resulted in changes to the temperature and flow fields but were mainly limited to the vicinity of the partition. For the cases with the heated top wall, the change in the height of the partition at y/H = 0.95 resulted in changes to the ambient temperature outside the boundary layer due to the reduction of the size of the recirculating flow in the corner region. The changes in the partition height and the top wall temperature affected the blockage effect of the partition, resulting in the local Nusselt number near the corner region to be affected. The local Nusselt number over most of the heated vertical wall of the partitioned cavity (y/H < 0.7) was correlated to the local Rayleigh number in the form Nu = C · Ra ⁿ .     

On a Question of Glasby,Praeger, and Xia

A Jordan partition λ(m, n, p) = (λ₁, λ₂, … , λ _m ) is a partition of mn associated with the expression of a tensor V _m  ? V _n of indecomposable KG-modules into a sum of indecomposables, where K is a field of characteristic p and G a cyclic group of p-power order. It is standard if λ _i  = m + n ? 2i + 1 for all i. We answer a recent question of Glasby, Praeger, and Xia who asked for necessary and sufficient conditions for λ(m, n, p) to be standard.     

Pilot‐scale ion‐exchange centrifugal partition chromatography: Purification of sinalbin from white mustard seeds

The purification of p‐hydroxybenzylglucosinolate (sinalbin) on a multigram scale from a crude aqueous extract of white mustard seeds (Sinapis alba var. concerta) was successfully achieved by scaling up a strong ion‐exchange centrifugal partition chromatography (SIXCPC) laboratory procedure. Thus, the one‐step sinalbin purification was performed with 2.35 g of crude extract in ?170 min (830 mg/h) up to 70.3 g in ?160 min (26.3 g/h) by switching from a 200 mL laboratory scale column to a 5.7 L pilot‐scale column. The required biphasic solvent system contained ethyl acetate, n‐butanol, and water in 3:2:5 v/v/v proportions, Aliquat 336® (trioctylmethyl ammonium chloride) was added to the organic stationary phase (80 mM) and acted as ion‐exchanger. Potassium iodide in the aqueous mobile phase (80 mM) was used as sinalbin displacer. The 28.5 mass scale factor arose from the increase in mobile phase flow‐rate (from 2 to 50 mL/min), from the higher mass of injected white mustard seed extract (from 12 to 350 g), and from the calculated productivity (from 830 mg to 26.3 g). These results demonstrate that industry scale production of glucosinolates is easily performed by SIXCPC, thus providing pure reference standards for pharmacology studies.     

The Andrews-Stanley partition function and Al-Salam-Chihara polynomials

For any partition λ let ω(λ) denote the four parameter weight

ω(λ)=a^{∑_i≥1⌈λ_2i−1/2⌉}b^{∑_i≥1⌊λ_2i−1/2⌋}c^{∑_i≥1⌈λ_2i/2⌉}d^{∑_i≥1⌊λ_2i/2⌋},     

Pairs of noncrossing free Dyck paths and noncrossing partitions

Using the bijection between partitions and vacillating tableaux, we establish a correspondence between pairs of noncrossing free Dyck paths of length 2n and noncrossing partitions of [2n+1] with n+1 blocks. In terms of the number of up steps at odd positions, we find a characterization of Dyck paths constructed from pairs of noncrossing free Dyck paths by using the Labelle merging algorithm.     

Labeled partitions with colored permutations

In this paper, we extend the notion of labeled partitions with ordinary permutations to colored permutations. We use this structure to derive the generating function of the indices of colored permutations. We further give a combinatorial treatment of a relation on the q-derangement numbers with respect to colored permutations. Based on labeled partitions, we provide an involution that implies the generating function formula due to Gessel and Simon for signed q-counting of the major indices. This involution can be extended to signed permutations. This gives a combinatorial interpretation of a formula of Adin, Gessel and Roichman.