A new convergent algorithm to approximate potentials from fixed angle scattering data

We introduce a new iterative method to recover a real compact supported potential of the Schr\"odinger operator from their fixed angle scattering data. The method combines a fixed point argument with a suitable approximation of the resolvent of the Schr\"odinger operator by partial sums associated to its Born series. Convergence is established for potentials with small norm in certain Sobolev spaces. As an application we show some numerical experiments that illustrate this convergence.Comment: 25 pages, 6 figure

On the large N limit, W_\infty Strings, Star products, AdS/CFT Duality, Nonlinear Sigma Models on AdS spaces and Chern-Simons p-branes

It is shown that the large $N$ limit of SU(N) YM in $curved$ $m$-dim backgrounds can be subsumed by a higher $m+n$ dimensional gravitational theory which can be identified to an $m$-dim generally invariant gauge theory of diffs $N$, where $N$ is an $n$-dim internal space (Cho, Sho, Park, Yoon). Based on these findings, a very plausible geometrical interpretation of the $AdS/CFT$ correspondence could be given. Conformally invariant sigma models in $D=2n$ dimensions with target non-compact SO(2n,1) groups are reviewed. Despite the non-compact nature of the SO(2n,1), the classical action and Hamiltonian are positive definite. Instanton field configurations are found to correspond geometrically to conformal ``stereographic'' mappings of $R^{2n}$ into the Euclidean signature $AdS_{2n}$ spaces. The relation between Self Dual branes and Chern-Simons branes, High Dimensional Knots, follows. A detailed discussion on $W_\infty$ symmetry is given and we outline the Vasiliev procedure to construct an action involving higher spin massless fields in $AdS_4$. This $AdS_4$ spacetime higher spin theory should have a one-to-one correspondence to noncritical $W_\infty$ strings propagating on $AdS_4 \times S^7$.Comment: 43 pages, Tex fil

String Representation of Quantum Loops

We recover a general representation for the quantum state of a relativistic closed line (loop) in terms of string degrees of freedom.The general form of the loop functional splits into the product of the Eguchi functional, encoding the holographic quantum dynamics, times the Polyakov path integral, taking into account the full Bulk dynamics, times a loop effective action, which is needed to renormalize boundary ultraviolet divergences. The Polyakov string action is derived as an effective actionfrom a phase space,covariant,Schild action, by functionally integrating out the world-sheet coordinates.The area coordinates description of the boundary quantum dynamics, is shown to be induced by the ``zero mode'' of the bulk quantum fluctuations. Finally, we briefly comment about a ``unified, fully covariant'' description of points, loops and strings in terms of Matrix Coordinates.Comment: 16 Pages, RevTeX, no figure

On the Dynamics of Dengue Virus type 2 with Residence Times and Vertical Transmission

A two-patch mathematical model of Dengue virus type 2 (DENV-2) that accounts for vectors' vertical transmission and between patches human dispersal is introduced. Dispersal is modeled via a Lagrangian approach. A host-patch residence-times basic reproduction number is derived and conditions under which the disease dies out or persists are established. Analytical and numerical results highlight the role of hosts' dispersal in mitigating or exacerbating disease dynamics. The framework is used to explore dengue dynamics using, as a starting point, the 2002 outbreak in the state of Colima, Mexico

Applications of the hard sphere DeSantis equation of state to the estimation of the density of compressed alternative refrigerants.

19th International Congress of Refrigeration. Proceedings The Hague, the Netherlands, august 20-25, 1995.The density of liquid refrigerants is very important for the design of compression cycles in the refrigeration and air conditioning industries. The increasing concern with the environmental protection leads the governments to legislate in order to banish in the short term the use of the CFC's and in the long run the HCFC's. Considering those decisions, the industries need to find new replacements for those compounds, and suitable substitutes seam to be HFC's, fluorinated ethers, their mixtures and mixtures with small quantities of HCFC's. The only problem in using those alternative refrigerants is the lack of knowledge about their properties. Among them, the density is one of the most important. It is the propose of this paper to show the use of a model that allows the user to estimate the liquid density for the refrigerants. The uncertainty of this model is of ± 2.0 % for reduced values of temperature less then 0.95 and reduced values of density less then 1.0. This model needs the information for the critical parameters and the pressure of the saturated liquid-vapour line. The Hard-Sphere DeSantis equation of state Ref. /1/ is use to give physical support to the model. The corrections to the attractive and repulsive part, a and b, have been calculated from a few experimental pure refrigerants Ref. /1/ (HCFC 152a, HCFC 22, HCFC 142b, HCFC 123, HCFC 114)

Prediction of the vapor pressure of environmentally acceptable halocarbons.

Copyright © 2000 Plenum Publishing Corporation.The vapor pressure and its dependence on temperature of halocarbons for 0.002< p R<1 have been analyzed in terms of universal behavior. Results for CFC-114, HCFC-123, HCFC-141b, HCFC-142b, HCFC-143a, HFC-23, HFC-32, HFC-134, HFC-125, HFC-134a, and HFC-152a for reduced temperatures between 0.55 and 1.0 show that the reduced vapor pressure can be expressed as a function of 1−T R by a Padé approximant. Deviations of the correlated data from the universal function do not amount to more than ±0.06 MPa, with an average deviation of 0.025 MPa. Predictions of the saturation vapor pressures of HCFC-124, HCFC-225ca, and HCFC-225cb, which are the systems used to test the capability of this scheme, agree within 0.025 MPa, that is, within the accuracy of the corresponding states correlation. However, for HFC-236ea, the deviations are as large as -0.07 MPa. The present scheme can be used to calculate the Pitzer acentric factor, and an average value of ω=0.269±0.015 is obtained for all the fluids