Abstract With the rapid development of social networks, academic networks have attracted increasing attention. In particular, providing personalized recommendations for learners considering data sparseness and cold-start scenarios is a challenging task. An important research topic to accurately discover potential friends build implicit learning groups obtain collaborative similar according cont...

The solvability in Sobolev spaces is proved for divergence form second order elliptic equations in the whole space, a half space, and a bounded Lipschitz domain. For equations in the whole space or a half space, the leading coefficients a are assumed to be measurable in one direction and have small BMO semi-norms in the other directions. For equations in a bounded domain, additionally we assume...

In this paper, we propose an e cient technique for the animation of exible thin objects. Massspring model was employed to represent the exible objects. Many techniques have used the mass-spring model to generate plausible animation of soft objects. The easiest approach to animation with mass-spring model is explicit Euler method, but the explicit Euler method has serious disadvantage that it su...

We study the automorphisms of a graph product of finitely-generated abelian groups W . More precisely, we study a natural subgroup Aut W of AutW , with Aut W = AutW whenever vertex groups are finite and in a number of other cases. We prove a number of structure results, including a semi-direct product decomposition Aut W = (InnW ⋊Out W )⋊Aut W . We also give a number of applications, some of wh...

Given a 3–manifold the second author defined functions δn : H (M ;Z) → N, generalizing McMullen’s Alexander norm, which give lower bounds on the Thurston norm. We reformulate these invariants in terms of Reidemeister torsion over a non– commutative multivariable Laurent polynomial ring. This allows us to show that these functions are semi-norms.

We consider the problem of drawing Venn diagrams for which each region’s area is proportional to some weight (e.g., population or percentage) assigned to that region. These area-proportional Venn diagrams have an enhanced ability over traditional Venn diagrams to visually convey information about data sets with interacting characteristics. We develop algorithms for drawing area-proportional Ven...

Diierential cryptanalysis is a powerful attack developed by Eli Biham and Adi Shamir. It has been successfully applied to many DES-like cryptosystems. We provide a brief introduction to their paper BS91] and show how to apply diierential cryptanalysis to attack the Data Encryption Standard (DES) reduced to 5 rounds.