A certain class of Laplace transforms with applications to reaction and reaction-diffusion equations

A class of Laplace transforms is examined to show that particular cases of this class are associated with production-destruction and reaction-diffusion problems in physics, study of differences of independently distributed random variables and the concept of Laplacianness in statistics, alpha-Laplace and Mittag-Leffler stochastic processes, the concepts of infinite divisibility and geometric infinite divisibility problems in probability theory and certain fractional integrals and fractional derivatives. A number of applications are pointed out with special reference to solutions of fractional reaction and reaction-diffusion equations and their generalizations.Comment: LaTeX, 12 pages, corrected typo

On the practicality of time-optimal two-qubit Hamiltonian simulation

What is the time-optimal way of using a set of control Hamiltonians to obtain a desired interaction? Vidal, Hammerer and Cirac [Phys. Rev. Lett. 88 (2002) 237902] have obtained a set of powerful results characterizing the time-optimal simulation of a two-qubit quantum gate using a fixed interaction Hamiltonian and fast local control over the individual qubits. How practically useful are these results? We prove that there are two-qubit Hamiltonians such that time-optimal simulation requires infinitely many steps of evolution, each infinitesimally small, and thus is physically impractical. A procedure is given to determine which two-qubit Hamiltonians have this property, and we show that almost all Hamiltonians do. Finally, we determine some bounds on the penalty that must be paid in the simulation time if the number of steps is fixed at a finite number, and show that the cost in simulation time is not too great.Comment: 9 pages, 2 figure

Reaction-diffusion systems and nonlinear waves

The authors investigate the solution of a nonlinear reaction-diffusion equation connected with nonlinear waves. The equation discussed is more general than the one discussed recently by Manne, Hurd, and Kenkre (2000). The results are presented in a compact and elegant form in terms of Mittag-Leffler functions and generalized Mittag-Leffler functions, which are suitable for numerical computation. The importance of the derived results lies in the fact that numerous results on fractional reaction, fractional diffusion, anomalous diffusion problems, and fractional telegraph equations scattered in the literature can be derived, as special cases, of the results investigated in this article.Comment: LaTeX, 16 pages, corrected typo

Vitamin D in relation to myocardial structure and function after eight years of follow-up: the Hoorn study.

Background and Aims: To investigate associations between baseline serum 25-hydroxyvitamin D [25(OH)D] levels and myocardial structure and function after 8 years of follow-up in older Dutch subjects. Methods: We included 256 subjects of the Hoorn Study, a population-based cohort. They underwent a standardized 2-dimensional echocardiogram at baseline between 2000 and 2001, and again between 2007 and 2009. We studied the association of 25(OH)D quartiles with echocardiographic measures of the left ventricular mass index (LVMI), left ventricular systolic function and markers of diastolic function using linear regression analyses. Results: At baseline, subjects had a mean age of 67.4 ± 5.2 years and 41.4% had prior cardiovascular disease (CVD). Low serum 25(OH)D levels were only associated with higher LVMI at 8-year follow-up in subjects without prior CVD and in subjects with low kidney function (median estimated glomerular filtration rate ≤77.5 ml/min/1.73

Fractional reaction-diffusion equations

In a series of papers, Saxena, Mathai, and Haubold (2002, 2004a, 2004b) derived solutions of a number of fractional kinetic equations in terms of generalized Mittag-Leffler functions which provide the extension of the work of Haubold and Mathai (1995, 2000). The subject of the present paper is to investigate the solution of a fractional reaction-diffusion equation. The results derived are of general nature and include the results reported earlier by many authors, notably by Jespersen, Metzler, and Fogedby (1999) for anomalous diffusion and del-Castillo-Negrete, Carreras, and Lynch (2003) for reaction-diffusion systems with L\'evy flights. The solution has been developed in terms of the H-function in a compact form with the help of Laplace and Fourier transforms. Most of the results obtained are in a form suitable for numerical computation.Comment: LaTeX, 17 pages, corrected typo

Differences in biopsychosocial profiles of diabetes patients by level of glycaemic control and health-related quality of life: The Maastricht Study

Aims Tailored, patient-centred innovations are needed in the care for persons with type 2 diabetes mellitus (T2DM), in particular those with insufficient glycaemic control. Therefore, this study sought to assess their biopsychosocial characteristics and explore whether distinct biopsychosocial profiles exist within this subpopulation, which differ in health-related quality of life (HRQoL). Methods Cross-sectional study based on data from The Maastricht Study, a population-based cohort study focused on the aetiology, pathophysiology, complications, and comorbidities of T2DM. We analysed associations and clustering of glycaemic control and HRQoL with 38 independent variables (i.e. biopsychosocial characteristics) in different subgroups and using descriptive analyses, latent class analysis (LCA), and logistic regressions. Results Included were 840 persons with T2DM, mostly men (68.6%) and with a mean age of 62.6 (±7.7) years. Mean HbA1c was 7.1% (±3.2%); 308 patients (36.7%) had insufficient glycaemic control (HbA1c>7.0% [53 mmol/mol]). Compared to those with sufficient control, these patients had a significantly worse-off status on multiple biopsychosocial factors, including self-efficacy, income, education and several health-related characteristics. Two ‘latent classes’ were identified in the insufficient glycaemic control subgroup: with low respectively high HRQoL. Of the two, the low HRQoL class comprised about one-fourth of patients and had a significantly worse biopsychosocial profile. Conclusions Insufficient glycaemic control, particularly in combination with low HRQoL, is associated with a generally worse biopsychosocial profile. Further research is needed into the complex and multidimensional causal pathways explored in this study, so as to increase our understanding of the heterogeneous care needs and preferences of persons with T2DM, and translate this knowledge into tailored care and support arrangements

The Centurion 18 telescope of the Wise Observatory

We describe the second telescope of the Wise Observatory, a 0.46-m Centurion 18 (C18) installed in 2005, which enhances significantly the observing possibilities. The telescope operates from a small dome and is equipped with a large-format CCD camera. In the last two years this telescope was intensively used in a variety of monitoring projects. The operation of the C18 is now automatic, requiring only start-up at the beginning of a night and close-down at dawn. The observations are mostly performed remotely from the Tel Aviv campus or even from the observer's home. The entire facility was erected for a component cost of about 70k$ and a labor investment of a total of one man-year. We describe three types of projects undertaken with this new facility: the measurement of asteroid light variability with the purpose of determining physical parameters and binarity, the following-up of transiting extrasolar planets, and the study of AGN variability. The successful implementation of the C18 demonstrates the viability of small telescopes in an age of huge light-collectors, provided the operation of such facilities is very efficient.Comment: 16 pages, 13 figures, some figures quality was degraded, accepted for publication in Astrophysics and Space Scienc

Efficient Algorithm on a Non-staggered Mesh for Simulating Rayleigh-Benard Convection in a Box

An efficient semi-implicit second-order-accurate finite-difference method is described for studying incompressible Rayleigh-Benard convection in a box, with sidewalls that are periodic, thermally insulated, or thermally conducting. Operator-splitting and a projection method reduce the algorithm at each time step to the solution of four Helmholtz equations and one Poisson equation, and these are are solved by fast direct methods. The method is numerically stable even though all field values are placed on a single non-staggered mesh commensurate with the boundaries. The efficiency and accuracy of the method are characterized for several representative convection problems.Comment: REVTeX, 30 pages, 5 figure