The construction of joins and secant varieties is studied in the combinatorial context of monomial ideals. For ideals generated by quadratic monomials, the generators of the secant ideals are obstructions to graph colorings, and this leads to a commutative algebra version of the Strong Perfect Graph Theorem. Given any projective variety and any term order, we explore whether the initial ideal o...

The pre-coloring extension problem consists, given a graph G and a subset of nodes to which some colors are already assigned, in nding a coloring of G with the minimum number of colors which respects the pre-coloring assignment. This can be reduced to the usual coloring problem on a certain contracted graph. We prove that pre-coloring extension is polynomial for complements of Meyniel graphs. W...

The energy sector in Poland is currently calling for dynamic redevelopment and cleaner energy. This country world famous its high level of coal production, from which it does not want to retreat the next two decades. For this reason, safer gradually reduce use while increasing consumption gas simultaneously developing green However, Polish still dependent on Russian supplied through Yamal pipel...

We obtain the characterization of saturation class and approximation spaces for perfect spline approximation. Also, a generalized perfect spline approximation is investigated.

In an earlier paper (J. Phys. A: Math. Gen. 26 (1993) 4689) we introduced the notion of cycle percolation in the Bose gas and conjectured that it occurs if and only if there is Bose-Einstein condensation. Here we give a complete proof of this statement for the perfect and the imperfect (mean-field) Bose gas and also show that in the condensate there is an infinite number of macroscopic cycles.

It has been known since the rigorous result by Angelescu and Corciovei [A-C] that the answer to the question in the title is negative for the Perfect Bose Gas (PBG). The main result of the present paper is that the answer could become positive if the bosons are simultaneously embedded in a periodic external potential. We show that it is true for PBG, as well as for the Bose gas with a mean-fiel...

In an earlier paper (J. Phys. A: Math. Gen. 26 (1993) 4689) we introduced the notion of cycle percolation in the Bose gas and conjectured that it occurs if and only if there is Bose-Einstein condensation. Here we give a complete proof of this statement for the perfect and the imperfect (mean-field) Bose gas and also show that in the condensate there is an infinite number of macroscopic cycles.

air, and nonequilibrium air solutions to sharp cones and a sharp wedge were obtained as check cases for the UPS code. The integrated LAURA-UPS procedure is demonstrated for two slender blunted-cones. Heating rates are presented on an 8-deg sphere-cone in Mach 5 and perfect gas at 0and 4-deg angles of attack and on the Reentry-F body at Mach 20, 80,000 ft. equilibrium gas conditions for 0and 0.1...

When the stagnation temperature of the combustion chamber or ambient air increases, the specific heats and their ratio do not remain constant any more, and start to vary with this temperature. The gas remains perfect, except, it will be calorically imperfect and thermally perfect. A new generalized form of the Prandtl Meyer function is developed, by adding the effect of variation of this temper...