A combinatorial formula of G.-C. Rota and J.A. Stein is taken to perform Wickre-ordering in quantum field theory. Wick’s theorem becomes a Hopf algebraic identity called Cliffordization. The combinatorial method relying on Hopf algebras is highly efficient in computations and yields closed algebraic expressions. AMS Subject Classifications 2000: 81R50; 16W30

We show that a linear algebraic group is the Galois group of a parameterized Picard-Vessiot extension of k(x), x′ = 1, for certain differential fields k, if and only if its identity component has no one dimensional quotient as a linear algebraic group.

In today's cities, especially metropolises, the issue of identity and its transformation has become one of the most important issues among urban authorities and designers. Mean while, Mashhad as the second religious metropolises in the world has an identity- causing and effective role among Islamic cities of Iran In recent decades, the amount of urban construction, especially in central part of...

In this paper, we investigate a mean-square stabilizing solution to a modified algebraic Riccati equation (MARE), which arises in our previous work on the linear quadratic optimal control for linear time-invariant discrete systems with random input gains. An explicit necessary and sufficient condition ensuring the existence of a mean-square stabilizing solution is given directly in terms of the...

The paper deals with the numerical treatment of stochastic differential-algebraic equations of index one with a scalar driving Wiener process. Therefore, a particularly customized stochastic Runge-Kutta method is introduced. Order conditions for convergence with order 1.0 in the mean-square sense are calculated and coefficients for some schemes are presented. The proposed schemes are stiffly ac...

We prove that, if A and B are complete normed non-associative algebras, and if B is strongly semisimple and algebraic, then dense range homomorphisms from A to B are continuous. As a consequence, we obtain that homomorphisms from complete normed algebras into a complete normed power-associative algebraic algebra B are continuous if and only if B has no nonzero elements with zero square. We also...

These lecture notes give an introduction to the algebraic renormalization of the Standard Model. We start with the construction of the tree approximation and give the classical action and its defining symmetries in functional form. These are the Slavnov-Taylor identity, Ward identities of rigid symmetry and the abelian local Ward identity. The abelian Ward identity ensures coupling of the elect...

The aim of the present study was to investigate whether, after scoring a goal, team becomes more vulnerable conceding goal soon after. A total 518 results were collected and integrated data study. independent Chi-square test used analyze data. values adjusted residue observed, all outside range -1.96 1.96 considered. All analyzes performed using α = 5%. equalizer moment happened in first-quarte...