A Note on Quantum Bell Nonlocality and Quantum Entanglement for High Dimensional Quantum Systems

We study the Bell nonlocality of high dimensional quantum systems based on quantum entanglement. A quantitative relationship between the maximal expectation value B of Bell operators and the quantum entanglement concurrence C is obtained for even dimension pure states, with the upper and lower bounds of B governed by C.

     

A New Sufficient Degree Condition for a Graphic Sequence to Be Forcibly k-Edge-Connected

A graphic sequence π =(d₁, d₂,..., d_n) is said to be forcibly k-edge-connected if every realization of π is k-edge-connected. In this paper, we obtain a new sufficient degree condition for π to be forcibly k-edgeconnected. We also show that this new sufficient degree condition implies a strongest monotone degree condition for π to be forcibly 2-edge-connected and a conjecture about a strongest monotone degree condition for π to be forcibly 3-edge-connected due to...     

Face-Directed Assembly of Molecular Cubes: In Situ Substitution of a Predetermined Concave Cluster

Systematic design and self-assembly of metal–organic polyhedra with predictable configurations has been a long-standing challenge in crystal engineering. Herein a concave polyoxovanadate cluster, [V₆O₆(OCH₃)₉(SO₄)₄]⁵⁻, which can be generated in situ under specific reaction conditions, is reported. Based on this cluster, a potential trivalent molecular building block, [V₆O₆(OCH₃)₉(SO₄)(CO₂)₃]²⁻, can be obtained by the bridging-ligand-substitution strategy and it possesses appropriate angle information for the design of molecular cubes. Utilizing the face-directed assembly of the trivalent molecular building block and a diverse set of tetratopic carboxylate linkers, a series of metal–organic cubes ( VMOC-1 – VMOC-5 ) with the same topology but different functionalities and dimensions were designed and constructed. An inclusion study using VMOC-3 shows that they are potential molecular receptors for selective capture of size-matching polycyclic aromatic hydrocarbon guest molecules.     

Component ordering strategies in assembly systems with uncertain capacity and random yield

Sourcing components in a complex global supplier network may lead to a high degree of supply uncertainty. Events, such as unexpected production defects or insufficient supplier capacity, can cause unexpected shortages of required components and halt the assembly of final products. Accordingly, the assembly enterprises must effectively manage various supply uncertainties in their component ordering decisions to avoid such component shortfalls. These issues have guided this research to investigate the optimal ordering strategies of an assembler facing the following two types of supply uncertainty: the uncertain production capacity of a standard component (component 1) and the random production yield of a core component (component 2). The assembler makes the component ordering decisions before these supply uncertainties are realized. We characterize the optimal ordering decision and find that the assembler should order components 1 and 2 according to a fixed ratio, which only depends on the random yield of component 2 and the production cost of component 1, but not on the uncertain capacity of component 1. A case study is presented to further explore the intertwined effects of these two uncertainties in an assembly system. Finally, the model is extended to consider a secondary option of buying additional component 1 s after observing some or all of the supply uncertainties, and this secondary option endows the firm with different capabilities in counteracting the supply uncertainties.     

椰心叶甲虫综合防治脉冲动力学模型的周期解

椰心叶甲虫是棕榈科植物最主要的害虫之一.论文针对两类寄生蜂攻击椰心叶甲虫不同年龄阶段的特点,建立了阶段结构的脉冲定期喷洒药物和释放天敌的综合防治模型.通过重合度理论和分析工具,证明了该模型周期解的存在性,给出了周期解存在的充分条件,并通过数值模拟验证了理论结果的有效性.     

Study on the Relationship between Emulsion Properties and Interfacial Rheology of Sugar Beet Pectin Modified by Different Enzymes

The contribution of rheological properties and viscoelasticity of the interfacial adsorbed layer to the emulsification mechanism of enzymatic modified sugar beet pectin (SBP) was studied. The component content of each enzymatic modified pectin was lower than that of untreated SBP. Protein and ferulic acid decreased from 5.52% and 1.08% to 0.54% and 0.13%, respectively, resulting in a decrease in thermal stability, apparent viscosity, and molecular weight (Mw). The dynamic interfacial rheological properties showed that the interfacial pressure and modulus (E) decreased significantly with the decrease of functional groups (especially proteins), which also led to the bimodal distribution of particle size. These results indicated that the superior emulsification property of SBP is mainly determined by proteins, followed by ferulic acid, and the existence of other functional groups also promotes the emulsification property of SBP.     

Regular/abnormal variation in the strength and nature of the halogen bond between H2Te and the dihalogens: Prominent effect of methyl substituents

The halogen-bonded complexes between H₂Te/Me₂Te and the dihalogen molecules XY (XY = F₂, Cl₂, Br₂, I₂, ClF, ClBr, BrF, BrCl, BrI, IF, ICl, IBr) have been studied to investigate the dependence of its strength and nature on the halogen donor X and its adjoining atom Y, as well as the methyl groups in the electron donor. The interaction energy varies between −1.7 and − 43.5 kcal/mol, indicating that the Te atom in H₂Te/Me₂Te has a strong affinity for the dihalogen molecules. For the H₂Te-XY complex, the halogen bond is stronger for the heavier halogen donor X atom and the strong electron-withdrawing group Y. However, for Me₂Te-XY, the halogen bond is stronger for the lighter halogen donor X atom. The H₂Te/Me₂Te-F₂ complex has the largest interaction energy, although the σ-hole on F₂ is the smallest in magnitude. In most of the complexes, the electrostatic and polarization contributions to the binding strength are similar in magnitude. However, for H₂Te/Me₂Te-F₂, the polarization contribution is much larger than the electrostatic contribution, with a significant contribution from charge transfer.     

On a Problem of Potentially Pancyclic-graphic Sequences Due to S.B. Rao

Acta Mathematicae Applicatae Sinica, English Series - A non-increasing sequence π = (d1, d2,..., dn) of nonnegative integers is said to be potentially hamiltonian-graphic (resp. potentially...