Universality of the dispersion to average multiplicity ratios in high-energy proton-nucleus interactions

It is shown that the existing data on the high-energy proton-nuclear emulsion interactions are consistent with the hypothesis that the ratio of the dispersion to the average multiplicity for different target nuclei is an energy independent constant, the same for all nuclei. Its value is found to be a = 0.58 ± 0.03 in agreement with the one found in proton-proton collisions.     

Exponential functional of Lévy processes: Generalized Weierstrass products and Wiener–Hopf factorization

In this note, we state a representation of the Mellin transform of the exponential functional of Lévy processes in terms of generalized Weierstrass products. As by-product, we obtain a multiplicative Wiener–Hopf factorization generalizing previous results obtained by Patie and Savov (2012) [14] as well as smoothness properties of its distribution.     

On possible dependence structures of a set of random variables

We give a constructive proof of existence of random vectors and discrete-time random processes with arbitrary nonsingular marginal distributions and arbitrary dependence structure. A corollary of this fact regarding Gaussian distributions is also established, as well as some abstract properties of dependence structures.     

Intermolecular central to axial chirality transfer in the self-assembled biphenyl containing amino acid-oxalamide gelators

Chiral amino acid and biphenyl incorporating oxalamide gelators 4-7 with large, 9 bond distance between chiral centres and biphenyl units have been studied. CD investigation of 4-octanol gel and the crystal structure of rac-4 reveal that efficient central to axial chirality transfer occurs by intermolecular interactions in gel and solid state assemblies.     

Variable degree polynomial splines are Chebyshev splines

Variable degree polynomial (VDP) splines have recently proved themselves as a valuable tool in obtaining shape preserving approximations. However, some usual properties which one would expect of a spline space in order to be useful in geometric modeling, do not follow easily from their definition. This includes total positivity (TP) and variation diminishing, but also constructive algorithms based on knot insertion. We consider variable degree polynomial splines of order $k\geqslant 2$ spanned by $\{ 1,x,\ldots x^{k-3},(x-x_i)^{m_i-1},(x_{i+1}-x)^{n_i-1} \}$ on each subinterval $[x_i,x_{i+1}\rangle\subset [0,1]$ , i?=?0,1, ...l. Most of the paper deals with non-polynomial case m _i ,n _i ?∈?[4,?∞?), and polynomial splines known as VDP–splines are the special case when m _i , n _i are integers. We describe VDP–splines as being piecewisely spanned by a Canonical Complete Chebyshev system of functions whose measure vector is determined by positive rational functions p(x), q(x). These functions are such that variable degree splines belong piecewisely to the kernel of the differential operator $\frac{d}{dx} p \frac{d}{dx} q \frac{d^{k-2}} {dx^{k-2}}$ . Although the space of splines is not based on an Extended Chebyshev system, we argue that total positivity and variation diminishing still holds. Unlike the abstract results, constructive properties, like Marsden identity, recurrences for quasi-Bernstein polynomials and knot insertion algorithms may be more involved and we prove them only for VDP splines of orders 4 and 5.     

A Characterization of Higher Rank Symmetric Spaces Via Bounded Cohomology

Let M be complete nonpositively curved Riemannian manifold of finite volume whose fundamental group Γ does not contain a finite index subgroup which is a product of infinite groups. We show that the universal cover is a higher rank symmetric space iff is injective (and otherwise the kernel is infinite dimensional). This is the converse of a theorem of Burger–Monod. The proof uses the celebrated Rank Rigidity Theorem, as well as a new construction of quasi-homomorphisms on groups that act on CAT(0) spaces and contain rank 1 elements. Received: September 2007, Accepted: March 2008     

Non-uniform exponential tension splines

We describe explicitly each stage of a numerically stable algorithm for calculating with exponential tension B-splines with non-uniform choice of tension parameters. These splines are piecewisely in the kernel of D ²(D ²–p ²), where D stands for ordinary derivative, defined on arbitrary meshes, with a different choice of the tension parameter p on each interval. The algorithm provides values of the associated B-splines and their generalized and ordinary derivatives by performing positive linear combinations of positive quantities, described as lower-order exponential tension splines. We show that nothing else but the knot insertion algorithm and good approximation of a few elementary functions is needed to achieve machine accuracy. The underlying theory is that of splines based on Chebyshev canonical systems which are not smooth enough to be ECC-systems. First, by de Boor algorithm we construct exponential tension spline of class C ¹, and then we use quasi-Oslo type algorithms to evaluate classical non-uniform C ² tension exponential splines.      

Coherence for closed categories with biproducts

A coherence result for symmetric monoidal closed categories with biproducts is shown in this paper. It is also explained how to prove coherence for compact closed categories with biproducts and for dagger compact closed categories with dagger biproducts by using the same technique.     

Thermal lens spectrometry under excitation of a divergent pump beam

Thermal lens spectrometry (TLS) under excitation of a divergent pump beam is discussed in both conventional and microscopic TLS instruments. A refined thermal lens (TL) model was proposed for calculating the TL signal of a “finite TL element.” Experiments as well as comparison with numerical simulations demonstrated that the effective sample length for a certain pump beam profile was about six times the confocal distance of the pump beam for laser-excited case and 1.5 mm for incoherent light source-excited case. For laser-excited conventional TLS instrument or thermal lens microscope (TLM), an empirical formula of the optimum pump beam waist radius for maximum detection sensitivity was obtained at a given sample length. At larger pump beam waist radius of 7 μm, the TL signal was found 2.5 times lower compared to the diffraction limit; however, the resulting two orders of magnitude lower power density in the sample could be quite desirable for the detection of photolabile analytes. By investigating the influence of a finite TL element on the TL signal, we found that an optimal distance between the probe beam waist and the sample was needed to assure the maximum detection sensitivity and good response linearity. Under the optimal detection scheme, limit of detection of the laser-excited TLM at 4 mW power was evaluated to be 8.6 × 10^?9 M for 100-μm-thick ferroin solution, corresponding to an absorbance of 9.5 × 10^?7 absorbance units.