Related papers: On matrix generalization of Robinson's Energy Dela…
We define the state of minimum energy while the expectation values of the field operators and their time derivatives in a determined moment in such a state are constrained. As an axiom, we consider such a state as the background of the…
A new dynamics more natural than that proposed by Bouchaud and Dean is introduced to the Generalized Random Energy Model, and the master equation for the dynamics is solved exactly to calculate the time correlation function. Although our…
This paper proves a new general K-network constrained energy reliability global factorization theorem. As in the unconstrained case, beside its theoretical mathematical importance the theorem shows how to do parallel processing in exact…
In a previous paper [1] it was discussed the viability of functional analysis using as a basis a couple of generic functions, and hence vectorial decomposition. Here we complete the paradigm exploiting one of the analysis methodologies…
We give an elementary proof of a generalization of Bourgain and Tzafriri's Restricted Invertibility Theorem, which says roughly that any matrix with columns of unit length and bounded operator norm has a large coordinate subspace on which…
We apply a simple decomposition to the energy of a moving particle. Based on this decomposition, we identify the potential and kinetic energies, then use them to give general definitions of momentum and the various kinds of forces exerted…
We give some details about the stationary phase lemma. We first prove a special case where the high order terms are derived explicitly. Based on that, we prove a more general case by using Morse lemma.
This simple text considers an application of Bohr-Sommerfeld quantization rule. It might be of interest for the students of physics.
An improved formulation of the one-step model of photoemission from crystal surfaces is proposed which overcomes different limitations of the original theory. Considering the results of an electronic-structure calculation, the electronic…
Network interactions between dynamical units are often subject to time delay. We develop a phase reduction method for delay-coupled oscillator networks. The method is based on rewriting the delay-differential equation as an ordinary…
We construct new invariants and give several theorems which determine in general (i) the number of physically meaningful phases in quark mass matrices and (ii) which elements of these matrices can be rendered real by rephasings. We…
We prove the following generalisation of Bohr theorem : let $K\subset\mathbb C$ a continuum, $(F_n)_n$ its Faber polynomials, $\Omega_R=\{\Phi_K<R\}, (R>1)$ the levels sets of the Green function; then there exists $R_0>1$ such that for any…
An exact calculation of the retarded electric field in the source region of a system of individual charges, expanded to third order in velocity, shows that all nonrelativistic accelerated charges in a system emit dipole electromagnetic…
Mirsky proved that, for the existence of a complex matrix with given eigenvalues and diagonal entries, the obvious necessary condition is also sufficient. We generalize this theorem to matrices over any field and provide a short proof.…
A spectral factorization theorem is proved for polynomial rank-deficient matrix-functions. The theorem is used to construct paraunitary matrix-functions with first rows given.
Textbooks frequently use the Helmholtz theorem to derive expressions for the electrostatic and magnetostatic fields but they do not usually apply this theorem to derive expressions for the time-dependent electric and magnetic fields, even…
Capacities of generalized condensers are applied to prove a two-point distortion theorem for conformal mappings. The result is expressed in terms of the Robin function and the Robin capacity with respect to the domain of definition of the…
Szalai et al. (SIAM J. on Sci. Comp. 28(4), 2006) gave a general construction for characteristic matrices for systems of linear delay-differential equations with periodic coefficients. First, we show that matrices constructed in this way…
Minimum-phase finite impulse response filters are widely used in practice, and much research has been devoted to the design of such filters. However, for the important case of Chebyshev filters there is a curious mismatch between current…
It is shown that the previous [1-3] generalization of the final-value theorem to the average (not necessarily limiting) values, can be extended to the higher-order running averages $(<>_{t}), lim_{s\rightarrow0}[sF(s)] =…