ENO-wavelet transforms for piecewise smooth functions

We have designed an adaptive essentially nonoscillatory (ENO)-wavelet transform for approximating discontinuous functions without oscillations near the discontinuities. Our approach is to apply the main idea from ENO schemes for numerical shock capturing to standard wavelet transforms. The crucial point is that the wavelet coefficients are computed without differencing function values across jumps. However, we accomplish this in a different way than in the standard ENO schemes. Whereas in the standard ENO schemes the stencils are adaptively chosen, in the ENO-wavelet transforms we adaptively change the function and use the same uniform stencils. The ENO-wavelet transform retains the essential properties and advantages of standard wavelet transforms such as concentrating the energy to the low frequencies, obtaining maximum accuracy, maintained up to the discontinuities, and having a multiresolution framework and fast algorithms, all without any edge artifacts. We have obtained a rigorous approximation error bound which shows that the error in the ENO-wavelet approximation depends only on the size of the derivative of the function away from the discontinuities. We will show some numerical examples to illustrate this error estimate

Ground-state configuration space heterogeneity of random finite-connectivity spin glasses and random constraint satisfaction problems

We demonstrate through two case studies, one on the p-spin interaction model and the other on the random K-satisfiability problem, that a heterogeneity transition occurs to the ground-state configuration space of a random finite-connectivity spin glass system at certain critical value of the constraint density. At the transition point, exponentially many configuration communities emerge from the ground-state configuration space, making the entropy density s(q) of configuration-pairs a non-concave function of configuration-pair overlap q. Each configuration community is a collection of relatively similar configurations and it forms a stable thermodynamic phase in the presence of a suitable external field. We calculate s(q) by the replica-symmetric and the first-step replica-symmetry-broken cavity methods, and show by simulations that the configuration space heterogeneity leads to dynamical heterogeneity of particle diffusion processes because of the entropic trapping effect of configuration communities. This work clarifies the fine structure of the ground-state configuration space of random spin glass models, it also sheds light on the glassy behavior of hard-sphere colloidal systems at relatively high particle volume fraction.Comment: 26 pages, 9 figures, submitted to Journal of Statistical Mechanic

Quantum integrability and exact solution of the supersymmetric U model with boundary terms

The quantum integrability is established for the one-dimensional supersymmetric $U$ model with boundary terms by means of the quantum inverse scattering method. The boundary supersymmetric $U$ chain is solved by using the coordinate space Bethe ansatz technique and Bethe ansatz equations are derived. This provides us with a basis for computing the finite size corrections to the low lying energies in the system.Comment: 4 pages, RevTex. Some cosmetic changes. The version to appear in Phys. Rev.

Determination of organic acids evolution during apple cider fermentation using an improved HPLC analysis method

An efficient method for analyzing ten organic acids in food, namely citric, pyruvic, malic, lactic, succinic, formic, acetic, adipic, propionic and butyric acids, using HPLC was developed. Boric acid was added into the mobile phase to separate lactic and succinic acids, and a post-column buffer solution [5 mmol/L p-toluensulfonic acid (p-TSA) + 20 mmol/L bis (2-hydroxyethyl) iminotris (hydroxymethyl) methane (bis¿tris) + 100 ¿mol/L sodium ethylenediaminetetraacetic (EDTA-2Na)] was used to improve the sensitivity of detection. The average spiked recoveries for the ten organic acids ranged from 82.9 to 127.9% with relative standard deviations of 1.44¿4.71%. The linear ranges of determination were from 15 to 1,000 mg/L with correlation coefficients of 0.9995¿0.9999. The metabolism of organic acids in cider, and the effect of nutrients including diammonium phosphate (DAP), thiamine, biotin, niacinamide and pantothenic acid on their metabolism, were studied using this method of analysis. We found that before cider brewing, additions of 200 mg/L DAP and 0.3 mg/L thiamine to apple juice concentrate results in a high quality cider