Superposition in nonlinear wave and evolution equations

Real and bounded elliptic solutions suitable for applying the Khare-Sukhatme superposition procedure are presented and used to generate superposition solutions of the generalized modified Kadomtsev-Petviashvili equation (gmKPE) and the nonlinear cubic-quintic Schroedinger equation (NLCQSE).Comment: submitted to International Journal of Theoretical Physics, 23 pages, 2 figures, style change

A note on entropic uncertainty relations of position and momentum

We consider two entropic uncertainty relations of position and momentum recently discussed in literature. By a suitable rescaling of one of them, we obtain a smooth interpolation of both for high-resolution and low-resolution measurements respectively. Because our interpolation has never been mentioned in literature before, we propose it as a candidate for an improved entropic uncertainty relation of position and momentum. Up to now, the author has neither been able to falsify nor prove the new inequality. In our opinion it is a challenge to do either one.Comment: 2 pages, 2 figures, 2 references adde

Scattering of electromagnetic waves by rough interfaces and inhomogeneous layers

We consider a two-dimensional problem of scattering of a time-harmonic electromagnetic plane wave by an infinite inhomogeneous conducting or dielectric layer at the interface between semi-infinite homogeneous dielectric half-spaces. The magnetic permeability is assumed to be a fixed positive constant. The material properties of the media are characterized completely by an index of refraction, which is a bounded measurable function in the layer and takes positive constant values above and below the layer, corresponding to the homogeneous dielectric media. In this paper, we examine only the transverse magnetic (TM) polarization case. A radiation condition appropriate for scattering by infinite rough surfaces is introduced, a generalization of the Rayleigh expansion condition for diffraction gratings. With the help of the radiation condition the problem is reformulated as an equivalent mixed system of boundary and domain integral equations, consisting of second-kind integral equations over the layer and interfaces within the layer. Assumptions on the variation of the index of refraction in the layer are then imposed which prove to be sufficient, together with the radiation condition, to prove uniqueness of solution and nonexistence of guided wave modes. Recent, general results on the solvability of systems of second kind integral equations on unbounded domains establish existence of solution and continuous dependence in a weighted norm of the solution on the given data. The results obtained apply to the case of scattering by a rough interface between two dielectric media and to many other practical configurations

Study of the 12C+12C fusion reactions near the Gamow energy

The fusion reactions 12C(12C,a)20Ne and 12C(12C,p)23Na have been studied from E = 2.10 to 4.75 MeV by gamma-ray spectroscopy using a C target with ultra-low hydrogen contamination. The deduced astrophysical S(E)* factor exhibits new resonances at E <= 3.0 MeV, in particular a strong resonance at E = 2.14 MeV, which lies at the high-energy tail of the Gamow peak. The resonance increases the present non-resonant reaction rate of the alpha channel by a factor of 5 near T = 8x10^8 K. Due to the resonance structure, extrapolation to the Gamow energy E_G = 1.5 MeV is quite uncertain. An experimental approach based on an underground accelerator placed in a salt mine in combination with a high efficiency detection setup could provide data over the full E_G energy range.Comment: 4 Pages, 4 figures, accepted for publication in Phys. Rev. Let

A closer look at the uncertainty relation of position and momentum

We consider particles prepared by the von Neumann-L\"uders projection. For those particles the standard deviation of the momentum is discussed. We show that infinite standard deviations are not exceptions but rather typical. A necessary and sufficient condition for finite standard deviations is given. Finally, a new uncertainty relation is derived and it is shown that the latter cannot be improved.Comment: 3 pages, introduction shortened, content unchange

Grothendieck groups and a categorification of additive invariants

A topologically-invariant and additive homology class is mostly not a natural transformation as it is. In this paper we discuss turning such a homology class into a natural transformation; i.e., a "categorification" of it. In a general categorical set-up we introduce a generalized relative Grothendieck group from a cospan of functors of categories and also consider a categorification of additive invariants on objects. As an example, we obtain a general theory of characteristic homology classes of singular varieties.Comment: 27 pages, to appear in International J. Mathematic

Role of Medium- and Short-Chain L-3-Hydroxyacyl-CoA Dehydrogenase in the Regulation of Body Weight and Thermogenesis

Dysregulation of fatty acid oxidation plays a pivotal role in the pathophysiology of obesity and insulin resistance. Medium- and short-chain-3-hydroxyacyl-coenzyme A (CoA) dehydrogenase (SCHAD) (gene name, hadh) catalyze the third reaction of the mitochondrial β-oxidation cascade, the oxidation of 3-hydroxyacyl-CoA to 3-ketoacyl-CoA, for medium- and short-chain fatty acids. We identified hadh as a putative obesity gene by comparison of two genome-wide scans, a quantitative trait locus analysis previously performed in the polygenic obese New Zealand obese mouse and an earlier described small interfering RNA-mediated mutagenesis in Caenorhabditis elegans. In the present study, we show that mice lacking SCHAD (hadh(−/−)) displayed a lower body weight and a reduced fat mass in comparison with hadh(+/+) mice under high-fat diet conditions, presumably due to an impaired fuel efficiency, the loss of acylcarnitines via the urine, and increased body temperature. Food intake, total energy expenditure, and locomotor activity were not altered in knockout mice. Hadh(−/−) mice exhibited normal fat tolerance at 20 C. However, during cold exposure, knockout mice were unable to clear triglycerides from the plasma and to maintain their normal body temperature, indicating that SCHAD plays an important role in adaptive thermogenesis. Blood glucose concentrations in the fasted and postprandial state were significantly lower in hadh(−/−) mice, whereas insulin levels were elevated. Accordingly, insulin secretion in response to glucose and glucose plus palmitate was elevated in isolated islets of knockout mice. Therefore, our data indicate that SCHAD is involved in thermogenesis, in the maintenance of body weight, and in the regulation of nutrient-stimulated insulin secretion