Modeling bodies that can only undergo isochoric motions subject to mechanical stimuli but are compressible or expansible with respect to thermal stimuli

In this short note, we discuss a new constitutive approach to describing the response of bodies, both solid and fluid, that can only undergo isochoric motions in isothermal processes but which can undergo non-isochoric motions in arbitrary processes. Within this new framework, one finds that conditions that were perceived as constraints on the response of the body now arise naturally within the frame work of the constitutive definition of these bodies. For instance, a central approximation in fluid mechanics that is of great utility in the analysis of fluid flow problems in geophysics and astrophysics is that due to Oberbeck (Ann Phys Chem 1:271–292, 1879; Uber die bewengungsercheinungen der Atmosphare, Sitz Ber K Preuss Akad Miss, pp 383–395, 1129–1138, 1888) and Boussinesq (Theorie Analytique de la Chaleur. Gauthier-Villas, Paris, 1903) for describing the flow of fluids, which can undergo only isochoric motions in isothermal processes but which are otherwise capable of non-isochoric motions. A similar demand can be made concerning the response of solid bodies wherein one could carry out an approximation similar to that of the Oberbeck–Boussinesq equations, and such an approach might be of great value in the study of technologically relevant problems.     

A continuum-mechanical analysis of the influence of mechanical stimuli on biological tissue

Mechanical stimuli play a crucial role in the differentiation process of mesenchymal stem cells (MSC). The resulting mechanical signals are important in the regulation of various cell functions and maintenance of many tissues. The underlying molecular and biophysical mechanisms of the differentiation process are poorly understood. Present remodelling and growth models are purely phenomenological without linkage to cell mechanisms. The presented macroscopic model of MSC mechanics is based on a multiphasic-multicomponent formulation within the framework of Theory of Porous Media (TPM), where a single cell is considered as a mixture of interacting constituents. In particular, the constituents are the solid cytoskeleton saturated by a fluid phase (cytoplasm), which itself consists of a liquid solvent and mobile components, e. g., chemical messengers, proteins, etc. To demonstrate the capabilities of the developed model, first qualitative numerical simulations of the impact of external forces on MSC are presented. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

升值之言该如何听

自今年6月中国暗示将松动人民币汇率以来,人民币升值幅度仅为0．4％,这大大低于华盛顿的期待,因此,中美两国的关系日益紧张起来。随着失业率的膨胀,以及选举年即将到来,美国国会再一次将人民币汇率摆上了议事日程：9月6日,华盛顿两位高官为缓和中美关系前往北京,就人民币及其他重要问题进行高峰会晤,以期达成共识。     

From A to B to Z

Semigroup Forum - The variety generated by the Brandt semigroup $$B_2$$ can be defined within the variety generated by the semigroup $$A_2$$ by the single identity $$x^2y^2\approx y^2x^2$$ . Edmond...     

How to distribute antidote to control epidemics

We give a rigorous analysis of variations of the contact process on a finite graph in which the cure rate is allowed to vary from one vertex to the next, and even to depend on the current state of the system. In particular, we study the epidemic threshold in the models where the cure rate is proportional to the degree of the node or when it is proportional to the number of its infected neighbors. © 2010 Wiley Periodicals, Inc. Random Struct. Alg., 2010     

Learning to represent,representing to learn

This study explores how students learn to create, discuss, and reason with representations to solve problems. A summer school algebra class for seventh and eighth graders provided opportunities for students to create and use representations as problem-solving tools. This case study follows the learning trajectories of three boys. Two of the three boys had been low-achievers in their previous math classes, and one was a high achiever. Analysis of all three boys’ written work reveals how their representations became more sophisticated over time. Their small group interactions while problem-solving also show changes in how they communicated and reasoned with representations. For these boys, representation functioned as a learning practice. Through constructing and reasoning with representations, the boys were able to engage in generalizing and justifying claims, discuss quadratic growth, and collaborate and persist in problem-solving. Negotiating different student-constructed representations of a problem also gave them opportunities to act with agency, as they made choices and judgments about the validity of the different perspectives. These findings have implications for the importance of giving all students access to mathematics through representations, with representational thinking serving as a central disciplinary practice and as a learning practice that supports further mathematics learning.     

Sampling to provide or to bound: With applications to fully dynamic graph algorithms

In dynamic graph algorithms the following provide-or-bound problem has to be solved quickly: Given a set S containing a subset R and a way of generating random elements from S testing for membership in R, either (i) provide an element of R, or (ii) give a (small) upper bound on the size of R that holds with high probability. We give an optimal algorithm for this problem. This algorithm improves the time per operation for various dynamic graph algorithms by a factor of O(log n). For example, it improves the time per update for fully dynamic connectivity from O(log³n) to O(log²n). © 1997 John Wiley & Sons, Inc. Random Struct. Alg., 11 , 369–379 (1997)     

When to rebuild or when to adjust scorecards

Data-based scorecards, such as those used in credit scoring, age with time and need to be rebuilt or readjusted. Unlike the huge literature on modelling the replacement and maintenance of equipment there have been hardly any models that deal with this problem for scorecards. This paper identifies an effective way of describing the predictive ability of the scorecard and from this describes a simple model for how its predictive ability will develop. Using a dynamic programming approach one is then able to find when it is optimal to rebuild and when to readjust a scorecard. Failing to readjust or rebuild a scorecard when they aged was one of the defects in credit scoring identified in the investigations into the sub-prime mortgage crisis.     

Anstee的两个定理的订正

本文的目的有二个,其一是给出反例说明Anstee的两个定理是欠妥的,其二是订正这二个定理。为方便起见,我们沿用[2]中的有关记号和定义。 设R和S分别为m维和n维非负整数向量,P=(P_(ij))_(m×n)为每列至多有一个1的(0,1)-矩阵。令_p(R,S)是一切以R为行和向量、S为列和向量且覆盖(cover)P的(0,1)-矩阵组成的集合。一个列向量a若是_p(R,S)中某个矩阵的第k列,则称a为_p(R,S)的     

Options to expand and to contract in combination

This work presents a real options approach to the valuation of multiple investment projects, focusing on the case of option to expand and/or to contract. Proper valuation formulas are obtained by solving Black–Scholes PDE and the impact of strategic interaction among multiple options is studied.