Bimodule Deformations, Picard Groups and Contravariant Connections

We study deformations of invertible bimodules and the behavior of Picard groups under deformation quantization. While K ₀-groups are known to be stable under formal deformations of algebras, Picard groups may change drastically. We identify the semiclassical limit of bimodule deformations as contravariant connections and study the associated deformation quantization problem. Our main focus is on formal deformation quantization of Poisson manifolds by star products.     

On orbit equivalence of borel automorphisms

LetE andF be two Borel sets of the countable productZ of the two point space {0,1}. Assume thatE andF are invariant sets for the odometer transformationR and thatE andF are of measure zero with respect to the unique finiteR-invariant measure onZ. We show thatE andF areR-orbit equivalent in a strict sense.     

COST-BENEFIT ANALYSIS APPLIED TO WILDERNESS PRESERVATION—OPTION VALUE UNCERTAINTY AND DITONICITY

It has been recognized for some time that when cost-benefit analysis is applied to irreversible environmental decisions, such as that of developing or preserving wilderness land, there can be an option value associated with the preservation decision, which arises when there is future uncertainty with respect to the benefits of development or preservation. In this paper the provenance of option value is examined and it is shown that an important cause is a special kind of uncertainty, viz. the possibility of reversals in direction of the relative valuations of wilderness land and developed land, a property we refer to as ditonicity. It is shown that the more ditonic the relative valuation process the greater the deviance between the certainty-equivalence development policy and the stochastically optimal one, and thus by implication the greater the option value. In the two cases with zero ditonicity, when relative wilderness valuations always increase or always decrease (even though in a stochastic fashion), there is zero option value. The model used assumes that service flows from wilderness and developed land are size-dependent, with future relative values known only in terms of a stochastic process, which can take jumps up or down of the same proportional size, at random times. Development can be partial or total and can occur in impulses at any time over an infinite time horizon.     

Indestructibility and level by level equivalence and inequivalence

If κ < λ are such that κ is indestructibly supercompact and λ is 2^λ supercompact, it is known from [4] that

• {δ < κ | δ is a measurable cardinal which is not a limit of measurable cardinals and δ violates level by level equivalence between strong compactness and supercompactness}

must be unbounded in κ. On the other hand, using a variant of the argument used to establish this fact, it is possible to prove that if κ < λ are such that κ is indestructibly supercompact and λ is measurable, then

• {δ < κ | δ is a measurable cardinal which is not a limit of measurable cardinals and δ satisfies level by level equivalence between strong compactness and supercompactness}

must be unbounded in κ. The two aforementioned phenomena, however, need not occur in a universe with an indestructibly supercompact cardinal and sufficiently few large cardinals. In particular, we show how to construct a model with an indestructibly supercompact cardinal κ in which if δ < κ is a measurable cardinal which is not a limit of measurable cardinals, then δ must satisfy level by level equivalence between strong compactness and supercompactness. We also, however, show how to construct a model with an indestructibly supercompact cardinal κ in which if δ < κ is a measurable cardinal which is not a limit of measurable cardinals, then δ must violate level by level equivalence between strong compactness and supercompactness. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Constructing unextendible product bases from multiqubit ones

The construction of multipartite unextendible product bases(UPBs) is a basic problem in quantum information.We respectively construct two families of 2 × 2× 4 and 2 × 2 × 2 × 4 UPBs of size eight by using the existing four-qubit and five-qubit UPBs.As an application,we construct novel families of multipartite positive-partial-transpose entangled states,as well as their entanglement properties in terms of the geometric measure of entanglement.     

预应力锚杆肋梁在深基坑支护中的应用

本文系统介绍了预应力锚杆肋梁的受力特点,分析了预应力锚杆肋梁的受力机理,并应用于深基坑支护工程,采用有限元方法对预应力锚杆肋梁支护的基坑进行数值计算,得出纵横梁的弯矩及面层的位移,弥补了传统方法的不足,将计算结果与传统的锚桩支护方法进行对比,表明在护坡桩桩端无法嵌入的情况下,采用预应力锚杆肋梁支护是一种经济、可靠的方式。     

Anti‐inflammatory bioactive equivalence of combinatorial components β‐carboline alkaloids identified in Arenaria kansuensis by two‐dimensional chromatography and solid‐phase extraction coupled with liquid–liquid extraction enrichment technology

Bioactive equivalent combinatorial components play a critical role in herbal medicines. However, how to discover and enrich them efficiently is a question for herbal pharmaceuticals researchers. In our work, a novel two‐dimensional reversed‐phase/hydrophilic interaction high‐performance liquid chromatography method was established to perform real‐time components trapping and combining for preparation and isolation of coeluting components. Arenaria kansuensis was taken as an example, and solid‐phase extraction coupled with liquid–liquid extraction as a simple and efficient method for enriching trace components, reversed phase column coupled with hydrophilic interaction liquid chromatography XAmide column as two‐dimensional chromatography technology for isolation and preparation of coeluting constituents, enzyme‐linked immune‐sorbent assay as bio‐guided assay, and anti‐inflammatory bioactivity evaluation for bioactive constituents. A combination of 12 β‐carboline alkaloids was identified as anti‐inflammatory bioactive equivalent combinatorial components from A. kansuensis , which accounts for 1.9% w/w of original A. kansuensis . This work answers the key question of which are real anti‐inflammatory components from A. kansuensis and provides a fast and efficient approach for discovering and enriching trace β‐carboline alkaloids from herbal medicines for the first time. More importantly, the discovery of bioactive equivalent combinatorial components could improve the quality control of herbal products and inspire a herbal medicine based on combinatorial therapeutics.     

Characterization of canonical classes for systems of linear ODEs

The equivalence group is determined for systems of linear ordinary differential equations in both the standard form and the normal form. It is then shown that the normal form of linear systems reducible by an invertible point transformation to the canonical form y ⁽ⁿ⁾=0 consists of copies of the same iterative scalar equation. It is also shown that contrary to the scalar case, an iterative vector equation need not be reducible to the canonical form by an invertible point transformation. Other properties of iterative linear systems are also derived, as well as a simple algebraic formula for their general solution. Copyright © 2017 John Wiley & Sons, Ltd.     

基于集对分析联系数的区间数型多属性决策投影模型及其在基坑支护方案评价中的应用

多属性决策时因掌握的信息有限,加之问题本身的复杂性、不确定性以及人类思维的模糊性,其属性的精确值往往难以获取,常用区间数形式表示针对多属性决策中各指标区间数不能直接进行大小比较的问题,提出一种基于集对分析联系数的区间数型多属性决策投影模型.模型用备择方案在理想方案上的投影进行集结,根据区间数的误差分布形式,沟通区间数与联系数的关系,根据a+bi型联系数大小比较法则,综合评价方案优劣.以某大厦基坑支护拟用的4种方案优化选择为例,说明方法的应用与模糊优化理论模型和灰色物元分析优化模型进行了对比,得到的结果一致.     

A thermodynamic approach with internal variables using Lagrange formalism. Part II. Continuous symmetries in the case of the time–temperature equivalence

In the first part of this contribution, the Lie-symmetries of the principle of least action associated to the constitutive equations of the DNLR formalism of relaxation have been presented. We examine in this second part the continuous symmetries corresponding to the simple case of stress relaxation under isothermal conditions. The well-known principle of time/temperature equivalence is discussed in terms of variational symmetry for the Jacobi’s action functional, and connected to the Onsager’s relation near the thermodynamic equilibrium.