The concurrent FE2-method is a very powerful and flexible computational tool for multi-scale problems. However the effort high. conventional, staggered (“nested Newton”) solution scheme solves microscopic problem iteratively within each macroscopic Newton-Raphson (NR) iteration, although deformation gradients as boundary conditions at micro scale are only estimates. In this contribution monolit...

Currently more and more agents are involved in human routine activities and a mixed human-agent society is thus formed by the humans and the agents involved. The relationship between humans and agents in this mixed society is subtle and it is vital to explore the influence that agents bring into the society. In this paper, we try to investigate a few questions: will humans act differently towar...

Let X1,X2, . . . , be independent random variables with EXi = 0 and write Sn = ∑ n i=1 Xi and V 2 n = ∑ n i=1 X i . This paper provides an overview of current developments on the functional central limit theorems (invariance principles), absolute and relative errors in the central limit theorems, moderate and large deviation theorems and saddle-point approximations for the self-normalized sum S...

Light-emitting dendrimers are a new distinct class of material for OLEDs. Dendrimers consist of a light-emitting core, dendrons and surface groups. Dendrimers are designed for solution coating and have a number of advantages over conjugated polymers. We report our recent results for solution processed green dendrimer OLEDs. The OLEDs were fabricated by spin-coating a blend of first generation d...

We present efficient algorithms for solving Legendre equations over Q (equivalently, for finding rational points on rational conics) and parametrizing all solutions. Unlike existing algorithms, no integer factorization is required, provided that the prime factors of the discriminant are known.

The modeling of physical systems often leads to partial differential equations (PDEs). Usually, the equations or the domain where the equations are posed are so complicated that the analytic solution cannot be found. Thus, the equations must be solved using numerical methods. In order to do this, the PDEs are first discretized using the finite element method (FEM) or the finite difference metho...

A cake is a metaphor for a heterogeneous, divisible good, such as land. A perfect division of cake is efficient (also called Pareto-optimal), envyfree, and equitable. We give an example of a cake in which it is impossible to divide it among three players such that these three properties are satisfied, however many cuts are made. It turns out that two of the three properties can be satisfied by ...

Fair Division, unlike most research on fairness in the social sciences and mathematics, is devoted solely to the analysis of constructive procedures for actually dividing things up and resolving disputes, including...