An interesting example of the deep interrelation between Physics and Mathematics is obtained when trying to impose mathematical boundary conditions on physical quantum fields. This procedure has recently been re-examined with care. Comments on that and previous analysis are here provided, together with considerations on the results of the purely mathematical zeta-function method, in an attempt ...

It is well known that for a mixed initial-boundary hyberbolic system to be well-defined it is necessary to impose additional boundary conditions only on the inflow eigenspace of the problem. We prove the discrete analogue of the above concerning difference approximations to such a system; that is, imposing numerical boundary conditions which are at least zeroth-order accurate with an inflow par...

While there exist now formulations of initial boundary value problems for Einstein’s field equations which are well posed and preserve constraints and gauge conditions, the question of geometric uniqueness remains unresolved. For two different approaches we discuss how this difficulty arises under general assumptions. So far it is not known whether it can be overcome without imposing conditions...

Abstract— In this article we show that a Code Division Multiple Access (CDMA) system employing long codes can be interpreted as a Multiple Input Multiple Output system where the transmit filters are time-varying. We derive conditions for existence of zero-forcing equalizers and verify through simulations that these conditions are useful guidelines for the design of appropriate solution in the p...

the optimization of process conditions for the degradation of acid blue 193 by uv/peroxydisulfate was investigated using response surface methodology (rsm). the effects of four parameters namely initial k2s2o8 concentration, uv irradiation, temperature, and initial dye concentration on two process responses, color removal and the rate constants of the first-order kinetic equations, were investi...

The map illustrates the geographic variation across counties and shows that counties with the highest prevalence of Medicare beneficiaries with 6 or more chronic conditions are located predominantly in southern states (eg, Texas, Florida, Kentucky) and northeastern states (eg, New York, Pennsylvania). Counties with the lowest prevalence are found mostly in western states (eg, Oregon, Montana, W...

Our domain G = (0,L) is an interval of length L. The boundary ∂G = {0,L} are the two endpoints. We consider here as an example the case (DD) of Dirichlet boundary conditions: Dirichlet conditions at x = 0 and x = L. For other boundary conditions (NN), (DN), (ND) one can proceed similarly. In one dimension the Laplace operator is just the second derivative with respect to x: ∆u(x, t) = uxx(x, t)...