the second law of thermodynamic (entropy principle) is of special theo-philosophical importance. it seems that this law, which is renowned as “the death of software design” and despite the order in the world, is like an incompatible universal. this article examines the concept of entropy in the three temperature, statistic, and information applications and addresses the contradiction of the sec...

in this paper, the dual area vector of a closed dual spherical curve is kinematically generatedand the dual steineer vector of a motion are extensively studied by the methods of differential geometry.jacobi’s theorems, known for real curves, are investigated for closed dual curves. the closed trajectorysurfaces generated by an oriented line are fixed in a moving rigid body in ir3 , in which the...

We prove an analogue of the L\"uck Approximation Theorem in positive characteristic for certain residually finite rationally soluble (RFRS) groups including right-angled Artin and Bestvina--Brady groups. Specifically, we that mod $p$ homology growth equals dimension group with coefficients a universal division ring this is independent choice residual chain. For general RFRS obtain inequality be...

Symplectic methods, like the Verlet method, are a standard tool for the long term integration of Hamiltonian systems as they arise, for example, in molecular dynamics. One of the reasons for the popularity of symplectic methods is the conservation of energy over very long periods of time up to small fluctuations that scale with the order of the method. In this paper, we discuss a qualitative fe...

Symplectic methods, like the Verlet method, are a standard tool for the long term integration of Hamiltonian systems as they arise, for example , in molecular dynamics. One of the reasons for the popularity of symplectic methods is the conservation of energy over very long periods of time up to small uctuations that scale with the order of the method. In this paper, we discuss a qualitative fea...

The ring of graph invariants is spanned by the basic graph invariants which calculate the number of subgraphs isomorphic to a given graph in other graphs. Sets of basic graph invariants form ensembles where each graph in the set induces the corresponding invariant calculating the number of subgraphs isomorphic to this graph in other graphs. It is well known that all other graph invariants such ...

A symmetric two-delta-function model spectral density is used to estimate several topological indices of alternant hydrocarbons, namely: the total n-electron energy (E.), the modified topological index (Z), the HOlVIO-LUMO separation (XHL) and the spectral radius of adjacency matrix (R). It is found, that the invariants defined by integration (like E. and Z) are reproduced much better than the ...

This is the long version of the ICM2014 proceedings. It consists in a short overview of the ”topological recursion”, a relation appearing in the asymptotic expansion of many integrable systems and in enumerative problems. We recall how computing large size asymptotics in random matrices, has allowed to discover some fascinating and ubiquitous geometric invariants. Specializations of this method...

‎In this paper we prove that a simplicial complex is determined‎ ‎uniquely up to isomorphism by its barycentric subdivision as well as‎ ‎its comparability graph‎. ‎We also put together several algebraic‎, ‎combinatorial and topological invariants of simplicial complexes‎.