The Nonsymmetric Kaluza-Klein(Jordan-Thiry) Theory.A path to a Unified Field Theory

In the paper we consider the Nonsymmetric Kaluza-Klein(Jordan-Thiry) Theory and hierarchy of a symmetry breaking within Grand Unified Theories.In this way we try to construct Unified Field Theory.We conside alsoa quintessence and skewon fields as possible Dark Matter particles.Both particles are massive with zero and one spin.It means with scalar and pseudovector particles.They are interacting only gravitationally..They are really apart of gravity.In this way they are geometrized.We find anatural to get a cosmological constant(Dark Energy) and the fith force. We consider also an effective gravitational" constant" Geff and a test particles movement in the theory.We consider also a tower of scalar (massive) fields as additional Dark Matter derived in the paper.Comment: TeX, 146 pages ,no figures,some corrections and extension

Incremental Network Design with Minimum Spanning Trees

Given an edge-weighted graph $G=(V,E)$ and a set $E_0\subset E$, the incremental network design problem with minimum spanning trees asks for a sequence of edges $e'_1,\ldots,e'_T\in E\setminus E_0$ minimizing $\sum_{t=1}^Tw(X_t)$ where $w(X_t)$ is the weight of a minimum spanning tree $X_t$ for the subgraph $(V,E_0\cup\{e'_1,\ldots,e'_t\})$ and $T=\lvert E\setminus E_0\rvert$. We prove that this problem can be solved by a greedy algorithm.Comment: 9 pages, minor revision based on reviewer comment

On some developments in the Nonsymmetric Kaluza-Klein Theory

We consider a condition for a charge confinement and gravito-electromagnetic wave solutions in the Nonsymmetric Kaluza-Klein Theory.We consider also an influence of a cosmological constant on a static,spherically symmetric solution.We remind to the reader some fudamentals of the Nonsymmetric Kaluza-Klein Theory and a geometrcal background behind the theory.Simultaneously we give some remarks concerning misunderstanding connected to several notions of the Nonsymmetric Kaluza-Klein Theory,Einstein Unified Field Theory,geometrization and unification of physical interactions .We reconsider Dirac field in the Nonsymmetric Kaluza-Klein Theory.Comment: 60 pages, 40 figure