The intersection lines between discontinuity surfaces and their intersection points on the visible surfaces of any engineering structure may be the instability indicators. This paper describes a new approach to modelling the intersecting lines and points that would provide the first evaluation of any instability in an engineering structure characterized by the failure modes. In this work, the i...

In recent years, determining the common information privately and efficiently between two mutually mistrusting parties have become an important issue in social networks. Many Private set intersection (PSI) protocols have been introduced to address this issue. By applying these protocols, two parties can compute the intersection between their sets without disclosing any information about compone...

Given a big divisor D on a normal complex projective variety X , we show that the restricted volume of D along a very general complete-intersection curve C ⊂ X can be read off from the Okounkov body of D with respect to an admissible flag containing C. From this we deduce that if two big divisors D1 and D2 on X have the same Okounkov body with respect to every admissible flag, then D1 and D2 ar...

‎For a set of non-negative integers~$L$‎, ‎the $L$-intersection number of a graph is the smallest number~$l$ for which there is an assignment of subsets $A_v subseteq {1,dots‎, ‎l}$ to vertices $v$‎, ‎such that every two vertices $u,v$ are adjacent if and only if $|A_u cap A_v|in L$‎. ‎The bipartite $L$-intersection number is defined similarly when the conditions are considered only for the ver...

By pure analogy with a usual three-dimensional origami, we can fold a regular octahedral material along flat faces in 4-space. The octahedron comprises four congruent tetrahedra. We will show a procedure to fold a tetrahedron along bisectors of the dihedral angles. This procedure demonstrates that each two of four surfaces of the given tetrahedron coincide with each other and that the point of ...

Nontrivial periodic solutions of Lagrange Equations are investigated. Sublinear and superlinear nonlinearity are included. Convexity assumptions are significiently relaxed. The method used is the duality developed by the authors.

Soft-body models are common in games to simulate cloth or elastic objects. To realistically simulate soft-body objects, collision detection and response is required. In addition, soft-body models must re-arrange their internal structure to react to the collision. This paper presents a new collision detection and response algorithm which can simulate a variety of soft-body material behaviors ran...