We find recursive formulae for the number of perfect matchings in a graph G by splitting G into subgraphs H and Q. We use these formulas to count perfect matching of P hypercube Qn. We also apply our formulas to prove that the number of perfect matching in an edge-transitive graph is , where denotes the number of perfect matchings in G, is the graph constructed from by deleting edges with an en...

We prove an asymptotic formula for the number of rational points of bounded height on projective equivariant compactifications of H\G, where H is a connected simple algebraic group embedded diagonally into G := H. Introduction Let X ⊂ P be a smooth projective variety over a number field F . Fix a height function (1) H : P(F )→R>0 and consider the counting function N(X,T ) := {x ∈ X(F ) |H(x) ≤ ...

Cross sections for electron impact excitation of atoms are important for modeling of low temperature plasmas and gases. While there are many experimental and theoretical results for excitation to the first excited states, little information is available for excitation to higher states. We present here calculations of excitations from the ground state to the np levels of sodium (n = 3 through 11...

We have developed a new approach to the theory of linear dichroism in partially ordered systems. The description of the partially ordered ensemble uses a density of states function, D(theta, phi, approximately delta), which gives the probability that the direction of polarization for incident polarized light has spherical angles theta and phi in an axis system fixed with respect to the molecule...

We derive general formulas for photon and dilepton production rates from an arbitrary non-equilibrated medium from first principles in quantum field theory. At lowest order in the electromagnetic coupling constant, these relate the rates to the unequal-time in-medium photon polarization tensor and generalize the corresponding expressions for a system in thermodynamic equilibrium. We formulate t...

Because of special structure, a dual reflector antenna has beam rotation capability in azimuth and elevation directions. In this structure, the antenna beam can be placed in any point in the space by mechanical movement of twist reflector which it is the most important ability of the antenna. Due to the antenna structure, if the polarization of incident wave is linear, it is expected that the p...

let $g$ be a connected graph, and let $d[g]$ denote the double graph of $g$. in this paper, we first derive closed-form formulas for different distance based topological indices for $d[g]$ in terms of that of $g$. finally, as illustration examples, for several special kind of graphs, such as, the complete graph, the path, the cycle, etc., the explicit formulas for some distance based topologica...

the option-pricing problem is always an important part in modern finance. assuming that the stock diffusion is a constant, some literature has introduced many stock models and given corresponding option pricing formulas within the framework of the uncertainty theory. in this paper, we propose a new stock model with uncertain stock diffusion for uncertain markets. some option pricing formulas on...

Explicit formulas for solutions of recurrence relations for 3–loop vacuum integrals are generalized for the n-loop case. Recently [1] a new approach to implement recurrence relations [2] for vacuum integrals was suggested. Such relations connect Feynman integrals with various degrees of their denominators. In many cases they provide a possibility to express an integral with given degrees of den...