The issues of stability the symmetrical equilibrium position floating barges in liquid, which have trapezoidal and pentagonal sections, are discussed paper. basic principles static analysis necessary for studying bodies given. exact expression potential energy a body is constructed its quadratic approximation calculated near investigated state both problems under consideration. Stability condit...

the edge szeged index is a new molecular structure descriptor equal to the sum of products mu(e)mv(e) over all edges e = uv of the molecular graph g, where mu(e) is the number of edges which its distance to vertex u is smaller than the distance to vertex v, and nv(e) is defined analogously. in this paper, the edge szeged index of one-pentagonal carbon nanocone cnc5[n] is computed for the first ...

Polyoxometalates (POMs) have potential in nanoscience due to the range of available building blocks that can allow the assembly of new nano-objects with configurable architectures. This, in turn, promises to lead to nanosystems with predefined functions, applications, and the discovery of new phenomena. Heteropolyoxometalates are an important subset of POMs. Within this class, the choice of the...

The B3LYP/6-31++G** density functional calculations were used to obtain minimum geometries and interaction energies between the molecular hydrogen and nanostructures of fullerenes, C20 (cage), C20 (bowl), C19Si (bowl, penta), C19Si (bowl, hexa). The H2 molecule is set as adsorbed in the distance of 3Å at vertical position from surface above the pentagonal and hexagonal sites of nanostructures. ...

The theory of congruences for the partition function p(n) depends heavily on the properties of half-integral weight Hecke operators. The subject has been complicated by the absence of closed formulas for the Hecke images P (z) | T (`), where P (z) is the relevant modular generating function. We obtain such formulas using Euler’s Pentagonal Number Theorem and the denominator formula for the Mons...

It is shown that coherence conditions for monoidal categories concerning associativity are analogous to coherence conditions for strict symmetric monoidal categories, where associativity arrows are identities. Mac Lane’s pentagonal coherence condition for associativity is decomposed into conditions concerning commutativity, among which we have a condition analogous to naturality and a degenerat...