q-Analogue of Shock Soliton Solution

By using Jackson's q-exponential function we introduce the generating function, the recursive formulas and the second order q-differential equation for the q-Hermite polynomials. This allows us to solve the q-heat equation in terms of q-Kampe de Feriet polynomials with arbitrary N moving zeroes, and to find operator solution for the Initial Value Problem for the q-heat equation. By the q-analog of the Cole-Hopf transformation we construct the q-Burgers type nonlinear heat equation with quadratic dispersion and the cubic nonlinearity. In q -> 1 limit it reduces to the standard Burgers equation. Exact solutions for the q-Burgers equation in the form of moving poles, singular and regular q-shock soliton solutions are found.Comment: 13 pages, 5 figure

Elastic softening of leucite and the lack of polar domain boundaries

Elastic properties of leucite have been investigated using resonant ultrasound spectroscopy over a temperature range from 300 to 1400 K. According to these measurements, elastic moduli soften by ~50% at the Ia3d-I41/acd ferroelastic transition temperature Tc1 = 940 K relative to the value at 1400 K. A second softening is observed at Tc2 = 920 K, corresponding to the structural change from the space group I41/acd to I41/a. These elastic anomalies are analyzed in a simple model under the assumption that the transitions observed at Tc1 and Tc2 can be approximated by a single pseudoproper ferroelastic transition. The two phase transitions are accompanied by a single peak in mechanical damping attributed to the high mobility of twin walls in the intermediate phase followed by pinning in the low-temperature phase. To determine whether twin walls in tetragonal leucite are polar, resonant piezoelectric spectroscopy and second harmonic generation measurements were performed, but no evidence of polarity was found

B Physics on the Lattice: Present and Future

Recent experimental measurements and lattice QCD calculations are now reaching the precision (and accuracy) needed to over-constrain the CKM parameters $\bar\rho$ and $\bar\eta$. In this brief review, I discuss the current status of lattice QCD calculations needed to connect the experimental measurements of $B$ meson properties to quark flavor-changing parameters. Special attention is given to $B\to\pi\ell\nu$, which is becoming a competitive way to determine $|V_{ub}|$, and to $B^0-\bar{B^0}$ mixings, which now include reliable extrapolation to the physical light quark mass. The combination of the recent measurement of the $B_s$ mass difference and current lattice calculations dramatically reduces the uncertainty in $|V_{td}|$. I present an outlook for reducing dominant lattice QCD uncertainties entering CKM fits, and I remark on lattice calculations for other decay channels.Comment: Invited brief review for Mod. Phys. Lett. A. 15 pages. v2: typos corrected, references adde

High-Accuracy Calculations of the Critical Exponents of Dyson's Hierarchical Model

We calculate the critical exponent gamma of Dyson's hierarchical model by direct fits of the zero momentum two-point function, calculated with an Ising and a Landau-Ginzburg measure, and by linearization about the Koch-Wittwer fixed point. We find gamma= 1.299140730159 plus or minus 10^(-12). We extract three types of subleading corrections (in other words, a parametrization of the way the two-point function depends on the cutoff) from the fits and check the value of the first subleading exponent from the linearized procedure. We suggest that all the non-universal quantities entering the subleading corrections can be calculated systematically from the non-linear contributions about the fixed point and that this procedure would provide an alternative way to introduce the bare parameters in a field theory model.Comment: 15 pages, 9 figures, uses revte

Correlations between Elastic, Calorimetric, and Polar Properties of Ferroelectric PbSc0.5Ta0.5O3 (PST)

Calorimetric, elastic, and polar properties of ferrolectric lead scandium tantalate PbSc0.5Ta0.5O3 (PST) with 65% cation order have been investigated in the vicinity of the paraelectric-ferroelectric transition at Ttrans = 295K. Comparison of temperature dependencies of the excess specific heat and elastic properties indicate that both anomalies stem from ther- mal fluctuations of order parameters in three dimensions. These fluctuations are consistent with tweed microstructure. This transition is driven by several coupled thermodynamic order parameters, as evidenced by a strongly non-linear scaling of the excess entropy with the squared ferroelectric polarization.National Natural Science Foundation of China (51850410520, 51320105014 and 51621063

Non-Gaussian numerical errors versus mass hierarchy

We probe the numerical errors made in renormalization group calculations by varying slightly the rescaling factor of the fields and rescaling back in order to get the same (if there were no round-off errors) zero momentum 2-point function (magnetic susceptibility). The actual calculations were performed with Dyson's hierarchical model and a simplified version of it. We compare the distributions of numerical values obtained from a large sample of rescaling factors with the (Gaussian by design) distribution of a random number generator and find significant departures from the Gaussian behavior. In addition, the average value differ (robustly) from the exact answer by a quantity which is of the same order as the standard deviation. We provide a simple model in which the errors made at shorter distance have a larger weight than those made at larger distance. This model explains in part the non-Gaussian features and why the central-limit theorem does not apply.Comment: 26 pages, 7 figures, uses Revte

A Guide to Precision Calculations in Dyson's Hierarchical Scalar Field Theory

The goal of this article is to provide a practical method to calculate, in a scalar theory, accurate numerical values of the renormalized quantities which could be used to test any kind of approximate calculation. We use finite truncations of the Fourier transform of the recursion formula for Dyson's hierarchical model in the symmetric phase to perform high-precision calculations of the unsubtracted Green's functions at zero momentum in dimension 3, 4, and 5. We use the well-known correspondence between statistical mechanics and field theory in which the large cut-off limit is obtained by letting beta reach a critical value beta_c (with up to 16 significant digits in our actual calculations). We show that the round-off errors on the magnetic susceptibility grow like (beta_c -beta)^{-1} near criticality. We show that the systematic errors (finite truncations and volume) can be controlled with an exponential precision and reduced to a level lower than the numerical errors. We justify the use of the truncation for calculations of the high-temperature expansion. We calculate the dimensionless renormalized coupling constant corresponding to the 4-point function and show that when beta -> beta_c, this quantity tends to a fixed value which can be determined accurately when D=3 (hyperscaling holds), and goes to zero like (Ln(beta_c -beta))^{-1} when D=4.Comment: Uses revtex with psfig, 31 pages including 15 figure

Clinical applications and limitations of current ovarian stem cell research: a review

The publication of a report in Nature in 2004 by the Tilly group suggesting that mouse ovaries are capable of generating oocytes de novo post-natally, has sparked interest in a problem long thought to have been resolved from classical studies in a variety of mammalian species. Within a nearly two year time period, laboratories around the world have taken up the challenge to dogma raised by this initial report, either to test this concept in an experimental basic science setting or give direction to clinical applications that could result, were the original premises of this work in the mouse valid for extrapolation to humans. This review provides a status report for this promising area of research, (1) to summarize recent findings in the literature with respect to the validity of the original hypothesis proffered by the Tilly group, and, (2) to gauge the potential utility of ovarian stem cells as a treatment for certain forms of human infertility

Vortex Images and q-Elementary Functions

In the present paper problem of vortex images in annular domain between two coaxial cylinders is solved by the q-elementary functions. We show that all images are determined completely as poles of the q-logarithmic function, where dimensionless parameter $q = r^2_2/r^2_1$ is given by square ratio of the cylinder radii. Resulting solution for the complex potential is represented in terms of the Jackson q-exponential function. By composing pairs of q-exponents to the first Jacobi theta function and conformal mapping to a rectangular domain we link our solution with result of Johnson and McDonald. We found that one vortex cannot remain at rest except at the geometric mean distance, but must orbit the cylinders with constant angular velocity related to q-harmonic series. Vortex images in two particular geometries in the $q \to \infty$ limit are studied.Comment: 17 page

Relationship among expression of basic-fibroblast growth factor, MTDH/Astrocyte elevated gene-1, adenomatous polyposis coli, matrix metalloproteinase 9,and COX-2 markers with prognostic factors in prostate carcinomas

Background: The etiopathogenesis of prostate cancer (PC) is still not clear, but hormonal, genetic, and environmental factors are thought to play a role in the tumor pathogenesis. Astrocyte elevated gene-1(AEG-1) as a novel transmembrane protein is predominantly located in the perinuclear region and endoplasmic reticulum. It has been found that AEG-1 upregulation increases the invasive ability of glioma and prostate cancer. Basic fibroblast growth factor (bFGF), matrix metalloproteinase-9 (MMP-9), cyclooxygenases-2 (COX-2), and adenomatous polyposis coli (APC) are very important in tumor progression as well. Materials and Methods: This study included 97 radical prostatectomy specimens. IHC stains for bFGF, MMP-9, COX-2, APC, and AEG-1 were performed on the tissue microarray using standard procedures. For each patient, the age, Gleason score, tumor volume, lymphovascular invasion, lymph node metastasis, surgical margin, and the invasion of vesiculoseminalis areas were assessed. Analyses were performed using the statistical PASW (ver. 18). Results: Statistically significant positive relationships were found MMP-9 and COX-2 (r = 0.242 and P = 0.017), between MMP-9 and APC (r = 0.207 and P = 0.043), and between bFGF and AEG-1 (r = 0.295 and P = 0.004). However, the relationships between age and staining results and tumor volume and staining results were not found to be significant. Although a positive correlation was found between the Gleason score and tumor volume and the Gleason score and age (r = 0.415 and P = 0.0001; r = 0.246 and P = 0.015, respectively), we did not find a statistically significant relationship between other stains and other prognostic parameters (lymphovascular invasion, lymph node metastasis, surgical margin, or vesiculoseminalis invasion). Conclusion:The relationships we found between MMP-9 and COX-2, between MMP-9, and APC and between bFGF and AEG-1 as independent prognostic parameters could be helpful in the development of new therapeutic procedures.Keywords: Adenomatous polyposis coli, astrocyte elevated gene‑1, basic fibroblast growth factor, cyclooxygenases‑2, matrix metalloproteinase‑9, prognostic parameters, prostate adenocarcinomasNigerian Journal of Clinical Practice • Oct-Dec 2013 • Vol 16 • Issue