Hadrons Ltd.: A Limited Corporation?

We report on some recent progress in hadron spectroscopy. We centre on unquenched results from Lattice and from the Quark Model Static Approach to Quantum Chromodynamics. We also review quenched Quark Model results for the non-static part of the hadron spectrum and emphasize the role that effective hadron?Chadron components may be playing to explain spectral anomalies. Glueballs and multiquarks proposals are briefly examined.     

Vibrational analysis and thermodynamic properties of C120 nanotorus: a DFT study

Density functional theory (DFT) computational methods are applied to a C₁₂₀ carbon nanotorus studied as an isolated molecular species, using the functional GGA PW91. This toroidal form of carbon contains five fold, six fold, and sevenfold rings. The calculated cohesive energy of the nanotorus, indicates that the ground state of this structure is energetically more stable than that of fullerene C₆₀. Geometry and stability, Raman and IR vibrational analysis and thermodynamic properties have been reported and compared to the values obtained by other authors.     

From Open Quantum Systems to Open Quantum Maps

For a class of quantized open chaotic systems satisfying a natural dynamical assumption we show that the study of the resolvent, and hence of scattering and resonances, can be reduced to the study of a family of open quantum maps, that is of finite dimensional operators obtained by quantizing the Poincaré map associated with the flow near the set of trapped trajectories.     

Self-avoiding Fractional Brownian Motion��The Edwards Model

In this work we extend Varadhan??s construction of the Edwards polymer model to the case of fractional Brownian motions in ? ^d , for any dimension d??2, with arbitrary Hurst parameters H??1/d.     

M?ssbauer spectroscopy and X-ray diffraction analyses of clayey samples used as ceramic sourcing materials, in Peru

The ceramic industry is an important area of economic activity in the Ayacucho Region, in particular in the District of Quinua. As a consequence, there is a huge demand for clay to produce ceramic pastes in that region. This paper reports on results concerning the mineralogical characterization of four clayey samples, which were collected MAA and SPQA from the area Pampa de La Quinua with geographic coordinates 13° 02?? 49?? S 74° 08?? 03?? W, CE1M and CE2M from the Quinua locality 13° 03?? 07?? S 74° 08?? 31?? W, both in the District of Quinua, Province of Huamanga, Ayacucho, Peru. The chemical and mineralogical characterization of these samples was carried out with powder X-ray diffraction detecting quartz, albite, montmorillonite, kaolinite and glauconite mineral phases, Mössbauer spectroscopy detected iron in kaolinite, glauconite and montmorillonite minerals. Chemical analysis was performed through scanning electron microscopy and energy dispersive X-ray spectroscopy. Data obtained from the combination of these techniques provided relevant information about the morphology, chemical composition, and the mineralogy of samples.     

Quasi-stationary distributions for structured birth and death processes with mutations

We study the probabilistic evolution of a birth and death continuous time measure-valued process with mutations and ecological interactions. The individuals are characterized by (phenotypic) traits that take values in a compact metric space. Each individual can die or generate a new individual. The birth and death rates may depend on the environment through the action of the whole population. The offspring can have the same trait or can mutate to a randomly distributed trait. We assume that the population will be extinct almost surely. Our goal is the study, in this infinite dimensional framework, of the quasi-stationary distributions of the process conditioned on non-extinction. We first show the existence of quasi-stationary distributions. This result is based on an abstract theorem proving the existence of finite eigenmeasures for some positive operators. We then consider a population with constant birth and death rates per individual and prove that there exists a unique quasi-stationary distribution with maximal exponential decay rate. The proof of uniqueness is based on an absolute continuity property with respect to a reference measure.     

The asymptotic expansion for n! and the Lagrange inversion formula

We obtain an explicit simple formula for the coefficients of the asymptotic expansion for the factorial of a natural number, $$n!=n^n\sqrt{2\pi n}\mbox{e}^{-n}\biggl\{1+\frac{a_1}{n}+\frac{a_2}{n^2}+\frac{a_3}{n^3}+\cdots\biggr\},$$ in terms of derivatives of powers of an elementary function that we call normalized left truncated exponential function. The unique explicit expression for the a _k that appears to be known is that of Comtet in (Advanced Combinatorics, Reidel, 1974), which is given in terms of sums of associated Stirling numbers of the first kind. By considering the bivariate generating function of the associated Stirling numbers of the second kind, another expression for the coefficients in terms of them follows also from our analysis. Comparison with Comtet??s expression yields an identity which is somehow unexpected if considering the combinatorial meaning of the terms. It suggests by analogy another possible formula for the coefficients, in terms of a normalized left truncated logarithm, that in fact proves to be true. The resulting coefficients, as well as the first ones are identified via the Lagrange inversion formula as the odd coefficients of the inverse of a pair of formal series. This in particular leads to the identification of a couple of simple implicit equations, which permits us to obtain also some recurrences related to the a _k ??s.     

On K s -free subgraphs in K s+k -free graphs and vertex Folkman numbers

Extending the problem of determining Ramsey numbers Erdős and Rogers introduced the following function. For given integers 2 ≤ s < t let f _s,t (n) = min{max{|S|: S ⊆ V (H) and H[S] contains no K _s }}, where the minimum is taken over all K _t -free graphs H of order n. This function attracted a considerable amount of attention but despite that, the gap between the lower and upper bounds is still fairly wide. For example, when t=s+1, the best bounds have been of the form Ω(n ^1/2+o(1)) ≤ f _s,s+1(n) ≤ O(n ^1−ɛ(s)), where ɛ(s) tends to zero as s tends to infinity. In this paper we improve the upper bound by showing that f _s,s+1(n) ≤ O(n ^2/3). Moreover, we show that for every ɛ > 0 and sufficiently large integers 1 ≪ k ≪ s, Ω(n ^1/2−ɛ ) ≤ f _s,s+k (n) ≤ O(n ^1/2+ɛ . In addition, we also discuss some connections between the function f _s,t and vertex Folkman numbers.