The 2nd order renormalization group flow for non-linear sigma models in 2 dimensions

We show that for two dimensional manifolds M with negative Euler characteristic there exists subsets of the space of smooth Riemannian metrics which are invariant and either parabolic or backwards-parabolic for the 2nd order RG flow. We also show that solutions exists globally on these sets. Finally, we establish the existence of an eternal solution that has both a UV and IR limit, and passes through regions where the flow is parabolic and backwards-parabolic

Geometric variations of the Boltzmann entropy

We perform a calculation of the first and second order infinitesimal variations, with respect to energy, of the Boltzmann entropy of constant energy hypersurfaces of a system with a finite number of degrees of freedom. We comment on the stability interpretation of the second variation in this framework.Comment: 9 pages, no figure

No classical limit of quantum decay for broad states

Though the classical treatment of spontaneous decay leads to an exponential decay law, it is well known that this is an approximation of the quantum mechanical result which is a non-exponential at very small and large times for narrow states. The non exponential nature at large times is however hard to establish from experiments. A method to recover the time evolution of unstable states from a parametrization of the amplitude fitted to data is presented. We apply the method to a realistic example of a very broad state, the sigma meson and reveal that an exponential decay is not a valid approximation at any time for this state. This example derived from experiment, shows the unique nature of broad resonances

Mutual Fund Theorem for continuous time markets with random coefficients

We study the optimal investment problem for a continuous time incomplete market model such that the risk-free rate, the appreciation rates and the volatility of the stocks are all random; they are assumed to be independent from the driving Brownian motion, and they are supposed to be currently observable. It is shown that some weakened version of Mutual Fund Theorem holds for this market for general class of utilities; more precisely, it is shown that the supremum of expected utilities can be achieved on a sequence of strategies with a certain distribution of risky assets that does not depend on risk preferences described by different utilities.Comment: 17 page

Physical applications of second-order linear differential equations that admit polynomial solutions

Conditions are given for the second-order linear differential equation P3 y" + P2 y'- P1 y = 0 to have polynomial solutions, where Pn is a polynomial of degree n. Several application of these results to Schroedinger's equation are discussed. Conditions under which the confluent, biconfluent, and the general Heun equation yield polynomial solutions are explicitly given. Some new classes of exactly solvable differential equation are also discussed. The results of this work are expressed in such way as to allow direct use, without preliminary analysis.Comment: 13 pages, no figure

Towards a feasible implementation of quantum neural networks using quantum dots

We propose an implementation of quantum neural networks using an array of quantum dots with dipole-dipole interactions. We demonstrate that this implementation is both feasible and versatile by studying it within the framework of GaAs based quantum dot qubits coupled to a reservoir of acoustic phonons. Using numerically exact Feynman integral calculations, we have found that the quantum coherence in our neural networks survive for over a hundred ps even at liquid nitrogen temperatures (77 K), which is three orders of magnitude higher than current implementations which are based on SQUID-based systems operating at temperatures in the mK range.Comment: revtex, 5 pages, 2 eps figure

GPU accelerated shake and rattle algorithms for systems with holonomic constraints

The dynamic of complex fluid can be described by including viscoelastic stress tensor into the equation of Non-Newtonian fluid. Different models are used to evaluate the stress tensor at various levels, with the multi-scale model being the most effective

DERMATOLOGICAL IMAGE DENOISING USING ADAPTIVE HENLM METHOD

In this paper we propose automatic image denoising method based on Hermite functions (HeNLM). It is an extension of non-local means (NLM) algorithm. Differences between small image blocks (patches) are replaced by differences between feature vectors thus reducing computational complexity. The features are calculated in coordinate system connected with image gradient and are invariant to patch rotation. HeNLM method depends on the parameter that controls filtering strength. To chose automatically this parameter we use a no-reference denoising quality assessment method. It is based on Hessian matrix analysis. We compare the proposed method with full-reference methods using PSNR metrics, SSIM metrics, and its modifications MSSIM and CMSC. Image databases TID, DRIVE, BSD, and a set of dermatological immunofluorescence microscopy images were used for the tests. It was found that more perceptual CMSC and MSSIM metrics give worse correspondence than SSIM and PSNR to the results of information preservation by the non-reference image denoising

Fast processing of data from Sneg-2MP experiment

The following subjects are covered: Basic stages during computer processing of data from Sneg-2MP instrument, basic modes during separation and fast processing (separation of data during satellite flight, separation of burst data segments, sampling and analysis of initial burst data segment). Experimental results obtained on the basis of fast processed data are reported