The crank moments weighted by the parity of cranks

In this note, we introduce the 2kth crank moment \(\mu _{2k}(-1,n)\) weighted by the parity of cranks and show that \((-1)^n \mu _{2k}(-1,n)>0\) for \(n\ge k \ge 0\). When \(k=0\), the inequality \((-1)^n \mu _{2k}(-1,n)>0\) reduces to Andrews and Lewis’s inequality \((-1)^n(M_e(n)-M_o(n))>0\) for \(n\ge 0\), where \(M_e(n)\) (resp. \(M_o(n)\)) denotes the number of partitions of n with even (resp. odd) crank. Several generating functions of \(\mu _{2k}(-1,n)\) are also studied in order to show the positivity of \((-1)^n\mu _{2k}(-1,n)\).     

Would weighted-student funding enhance intra-district equity in Texas? A simulation using DEA

We use data envelopment analysis to model the educational production function, and then explore how a shift to weighted student funding using the student weights embedded in the Texas School Finance Formula would alter the allocation of inputs and potential outputs. School outputs are measured as value-added reading and math scores on standard achievement tests. We find that if school districts allocated their resources efficiently, then they would not allocate their resources to campuses according to the funding model weights. Policies that promote greater efficiency would also enhance equity in educational outcomes.     

Six-Membered Nitrogen Heterocycles from Xylaramide and Ribaramide

Abstract

N,N'-Diacetyl-tri-O-acetylxylaramide (8) and N,N'-diacetyl-tri-O-acetylribaramide (20) were directly converted to the nitrogen heterocycle 6-acetamido-2,6-diacetyloxy-aza-1,4-cyclohexadlen-3-one (9) with sodium acetate in acetic anhydride. Treatment of tri-O-acetylxylaramide (7) or tri-O-acetylribaramide (19) with the same solvent-base combination gave the highly crystalline 2,3,5,6-tetraacetyloxypyridlne (30) as the principal product. Mechanistic considerations for the formation of these nitrogen heterocycles are presented.     

Stability of Optically Injected Two‐State Quantum‐Dot Lasers

Simultaneous two‐state lasing is a unique property of semiconductor quantum‐dot (QD) lasers. This not only changes steady‐state characteristics of the laser device but also its dynamic response to perturbations. In this paper we investigate the dynamic stability of QD lasers in an external optical injection setup. Compared to conventional single‐state laser devices, we find a strong suppression of dynamical instabilities in two‐state lasers. Furthermore, depending on the frequency and intensity of the injected light, pronounced areas of bistability between both lasing frequencies appear, which can be employed for fast optical switching in all‐optical photonic computing applications. These results emphasize the suitability of QD semiconductor lasers in future integrated optoelectronic systems where a high level of stability is required.     

The Measurement of Time: Children's Construction of Transitivity,Unit Iteration,and Conservation of Speed

One hundred twenty children in kindergarten and grades 2, 4, and 6 were individually interviewed with five Piagetian tasks to determine the grade level at which most have constructed transitive reasoning, unit iteration, and the conservation of speed. The responses were categorized as “successful,”“unsuccessful,” or “transitional.” By combining the “successful” and “transitional” categories, it was found that the children reasoned transitively by second grade (70.0%) and demonstrated unit iteration and conservation of speed by sixth grade (70.0% and 83.3%, respectively). It was concluded that the construction of the logic necessary to make sense of the measurement of time is generally not complete before sixth grade.     

Elektroanalyse

Ohne Zusammenfassung     

Synthesis of an AIE-active fluorogen and its application in cell imaging

A fluorogen named 1-decyl-1-methyl-2,5-bis{4-[(N,N-diethylamino)methyl]phenyl}-3,4-diphenylsilole (3) was synthesized. It emitted weakly as isolated molecule but strongly as supramolecular aggregate, showing a characteristic behavior of aggregation-induced emission (AIE). The molecules of 3 formed highly emissive nanoparticles in aqueous media, which quickly and selectively marked cytoplasm of HeLa cells and posed no toxicity to the living cells. The fluorogen is thus a promising candidate material for cell imaging as a sensitive, selective and cytocompatible biosensor. Supported by the Research Grants Council of Hong Kong (Grant Nos. 603008, 601608 and 602707), the National Natural Science Foundation of China (Grant No. 20634020) and the CAO GuangBiao Foundation of Zhejiang University.