The spt-Crank for Ordinary Partitions

The spt-function $spt(n)$ was introduced by Andrews as the weighted counting of partitions of $n$ with respect to the number of occurrences of the smallest part. Andrews, Garvan and Liang defined the spt-crank of an $S$-partition which leads to combinatorial interpretations of the congruences of $spt(n)$ mod 5 and 7. Let $N_S(m,n)$ denote the net number of $S$-partitions of $n$ with spt-crank $m$. Andrews, Garvan and Liang showed that $N_S(m,n)$ is nonnegative for all integers $m$ and positive integers $n$, and they asked the question of finding a combinatorial interpretation of $N_S(m,n)$. In this paper, we introduce the structure of doubly marked partitions and define the spt-crank of a doubly marked partition. We show that $N_S(m,n)$ can be interpreted as the number of doubly marked partitions of $n$ with spt-crank $m$. Moreover, we establish a bijection between marked partitions of $n$ and doubly marked partitions of $n$. A marked partition is defined by Andrews, Dyson and Rhoades as a partition with exactly one of the smallest parts marked. They consider it a challenge to find a definition of the spt-crank of a marked partition so that the set of marked partitions of $5n+4$ and $7n+5$ can be divided into five and seven equinumerous classes. The definition of spt-crank for doubly marked partitions and the bijection between the marked partitions and doubly marked partitions leads to a solution to the problem of Andrews, Dyson and Rhoades.Comment: 22 pages, 6 figure

Transient Sub-Poissonian Distribution for Single-Mode Lasers

In this paper, the transient photon statistics for single-mode lasers is investigated by making use of the theory of quantum electrodynamics. By taking into account of the transitive time l,we obtain the master equation for Jaynes-Cummings model. The relation between the Mandel factor and the time is obtained by directly solving the master equation. The result shows that a transient phenomenon from the transient super-Poissonian distribution to the transient sub-Poissonian distribution occurs for single-mode lasers. In addition, the influences of the thermal light field and the cavity loss on the transient sub-Poissonian distribution are also studied

Global axisymmetric stability analysis for a composite system of two gravitationally coupled scale-free discs

In a composite system of gravitationally coupled stellar and gaseous discs, we perform linear stability analysis for axisymmetric coplanar perturbations using the two-fluid formalism. The background stellar and gaseous discs are taken to be scale-free with all physical variables varying as powers of cylindrical radius $r$ with compatible exponents. The unstable modes set in as neutral modes or stationary perturbation configurations with angular frequency $\omega=0$.Comment: 7 pages using AAS styl

Decreasing erucic acid level by RNAi-mediated silencing of fatty acid elongase 1 (BnFAE1.1) in rapeseeds (Brassica napus L.)

The β-ketoacyl CoA synthase encoded by fatty acid elongase 1 gene (BnFAE1.1) is a rate-limiting enzyme regulating biosynthesis of erucic acid in rapeseeds (Brassica napus). To develop low level of erucic acid in rapeseeds by intron-spliced hairpin RNA, an inverted repeat unit of a partial BnFAE1.1 gene interrupted by a spliceable intron was cloned into pCAMBIA3301, and a seed-specific (Napin) promoter was used to control the transcription of the transgene. Four transgenic plants harboring a single copy of transgene were generated. Expression of endogenous BnFAE1.1 gene in developing T3 seeds was significantly reduced. In mature T3 seeds, erucic acid was decreased by 60.8 to 99.1% compared with wild type seeds, and accounted for 0.36 to 15.56% of total fatty acids. The level of eicosenoic acid was also greatly decreased. Furthermore, it resulted in a significant increase in the level of oleic acid, but total fatty acid content in T3 seeds was the same with that in wild type seeds. In conclusion, the expression of endogenous BnFAE1.1 was efficiently silenced by the designed RNAi silencer, causing a significant down-regulation in the level of erucic acid. Therefore, the RNAi-mediated post-transcriptional silencing of FAE1 gene to reduce oleic acid in rapeseeds was an efficient method to breed some new B. napus lines.Key words: Brassica napus L., fatty acid elongase, intron-spliced hairpin RNA, down-regulation, erucic acid

Composite Polarons in Ferromagnetic Narrow-band Metallic Manganese Oxides

A new mechanism is proposed to explain the colossal magnetoresistance and related phenomena. Moving electrons accompanied by Jahn-Teller phonon and spin-wave clouds may form composite polarons in ferromagnetic narrow-band manganites. The ground-state and finite-temperature properties of such composite polarons are studied in the present paper. By using a variational method, it is shown that the energy of the system at zero temperature decreases with the formation of composite polaron; the energy spectrum and effective mass of the composite polaron at finite temperature is found to be strongly renormalized by the temperature and the magnetic field. It is suggested that the composite polaron contribute significantly to the transport and the thermodynamic properties in ferromagnetic narrow-band metallic manganese oxides.Comment: Latex, no figur

Prediction of a High Temperature Bonding Condition at the Interface for the Hot-Rolled Stainless Steel Clad Plate on Rolling

The stainless steel-carbon steel clad plate was investigated using the theoretical analysis of various factors influencing the high-temperature interfacial bonding during its rolling. Phenomenological prediction analysis model of interfacial bonding strength at high temperature which considers the vacuum depth, rolling temperature, and rolling reduction, was established. The specific thermal simulation experiment was designed, the bonding strength of carbon steel and stainless steel at 1000~1200°C and compression degree of 10~30% was measured by a Gleeble 3500 thermal simulator, as a result, the interfacial bonding ratio was obtained. The results show that the bonding ratio is 0.5-0.65 at the experimental temperature and compression degree. The numerical simulation method was used to analyze the influence of the compression degree of the first pass for a 2000×1500×100 mm stainless steel clad plate under the interfacial bonding condition. The simulation results show that the optimum compression degree of the first pass is 15-20% at the rolling temperature of 1200°C.Листовая углеродистая сталь, плакированная нержавеющей сталью, исследована с помощью теоретического анализа различных факторов, влияющих на высокотемпературное межповерхностное сцепление при ее прокатке, феноменологической модели прогнозного анализа прочности межповерхностного сцепления при высокой температуре, которая учитывает глубину разрежения, температуру прокатки и обжатие при прокатке. Подготовлен специальный эксперимент с моделированием температурного режима, прочность сцепления углеродистой и нержавеющей сталей при 1000–1200°С и степени обжатия 10~30% измерена с помощью моделирующего устройства с регулируемым температурным режимом Gleeble 3500, получена относительная прочность межповерхностного сцепления. Показано, что при температуре и степени обжатия, принятых в эксперименте, относительная прочность сцепления составляет 0.50–0.65. Метод численного моделирования использован для анализа влияния степени обжатия за первый пропуск пластины плаплакированной нержавеющей сталью размером 2000×1500×100 мм на межповерхностное сцепление. Оптимальная степень обжатия за первый пропуск составляет 15–20% при температуре прокатки 1200°С