Weighted norm inequalities of Bochner-Riesz means

Let w be a Muckenhoupt weight and be the weighted Hardy spaces. We use the atomic decomposition of and their molecular characters to show that the Bochner-Riesz means are bounded on for 0<p?1 and δ>max{n/p−(n+1)/2,[n/p]rw⁻¹(rw−1)−(n+1)/2}, where rw is the critical index of w for the reverse Hölder condition. We also prove the boundedness of the maximal Bochner-Riesz means for 0<p?1 and δ>n/p−(n+1)/2.     

Cutsets and anti-chains in linear lattices

Consider the poset, ordered by inclusion, of subspaces of a four-dimensional vector space over a field with 2 elements. We prove that, for this poset, any cutset (i.e., a collection of elements that intersects every maximal chain) contains a maximal anti-chain of the poset. In analogy with the same result by Duffus, Sands, and Winkler [D. Duffus, B. Sands, P. Winkler, Maximal chains and anti-chains in Boolean lattices, SIAM J. Discrete Math. 3 (2) (1990) 197-205] for the subset lattice, we conjecture that the above statement holds in any dimension and for any finite base field, and we prove some special cases to support the conjecture.     

Complexity results on restricted instances of a paint shop problem for words

We study the following problem: an instance is a word with every letter occurring twice. A solution is a 2-coloring of its letters such that the two occurrences of every letter are colored with different colors. The goal is to minimize the number of color changes between adjacent letters.This is a special case of the paint shop problem for words, which was previously shown to be NP-complete. We show that this special case is also NP-complete and even APX-hard. Furthermore, derive lower bounds for this problem and discuss a transformation into matroid theory enabling us to solve some specific instances within polynomial time.     

Charmonium results from BES

Using ～ 14 × 10^6 ψ（2S） and ～ 58 × 10^ J/ ψ data collected at BES Ⅱ/BEPC, the branching fraction of ψ（2S）→Ω-Ω^＋ is measured with about 5a statistical significance. The A electric dipole and ∧ decay parameter are studied using the decay J/ψ →∧∧→ ppπ^＋π^-. Using （106±3）× 10^6 ψ（2S） decays collected at BESⅢ/BEPC Ⅱ, we have obtained some interesting physics results. The branching fractions of XcJ→π^0π^0, ηη are measured with precision improved. The mass and width of he（l^1P1） state, together with the branching fractions of Br（ψ（2S） →π^0hc） and Br（hc →γηc） are the first measurements. Surprisingly, the decays of Xc1→φφ, ωω, and ωφ are firstly observed in BESⅢ data.     

Investigation of thermostability and phonon–phonon interactions in Mo6S3I6 nanowires by Raman scattering spectroscopy

Detailed Raman scattering measurements were performed on molybdenum–sulfur–iodine nanowires (Mo₆S₃I₆). At room temperature, 21 well‐resolved Raman modes were experimentally observed for the first time in this new compound. The phase stability and vibrational properties of the nanowires were investigated by different temperature treatments. High‐temperature Raman spectra showed that the phase separation of Mo₆S₃I₆ nanowires took place between 573 and 673 K, followed by appearance of a new mode at 819 cm⁻¹ characteristic of the MoO₃ phase. Low‐temperature Raman scattering spectra showed a significant difference in phonon–phonon interactions between internal and external Raman modes of Mo₆S₃I₆ nanowires. These interesting vibrational properties can give new insights for improved material preparation and achievement of higher conductivity and other functional properties of these otherwise interesting materials. Copyright © 2009 John Wiley & Sons, Ltd.     

Modal series solution for an epidemic model

In this article, we generalize a recently proposed method to obtain an exact general solution for the classical Susceptible, Infected, Recovered and Susceptible (SIRS) epidemic mathematical model. This generalization is based upon the nonlinear coupling of two frequencies in an infinite modal series solution. It is shown that these series provide a nonstandard approach in order to obtain an accurate analytical solution for the classical SIRS epidemic model. Numerical results of the SIRS epidemic model for real and complex frequencies are included in order to test the validity and reliability of the method. This method could be applied to a wide class of models in physics, chemistry or engineering.     

A psychophysical model of decision making

Herein we develop a psychophysical model of decision making based on the difference between objective clock time and the human brain’s perception of time. In this model the utility function is given by the survival probability, which is shown to be a generalized hyperbolic distribution. The parameters of the utility function are fit to intertemporal choice model experimental data and decision making is determined to be a 1/f-noise process.     

Probing the discrete motion of vortices with rf excitations

In this work we present experimental results on the rectification of vortices in a superconductor/ferromagnet system under a high frequency drive. The two-dimensional pinning landscape, induced by the stray fields of the ferromagnetic template, has no intrinsic asymmetry. Nevertheless, an asymmetric potential is artificially induced by an applied dc bias. The experimental results unambiguously show a biased, discrete motion of the vortices in the periodic potential at frequencies above 10 MHz. This synchronized motion is very sensitive to the external applied field. Increasing temperature leads to a reduction of the pinning potential, which in turn results in a lower ac power needed to drive the vortex lattice.     

Energy transfers between Sm and Eu in YPO4, LaP5O14 and LaP3O9 phosphates. Potential quantum cutters for red emitting phosphors

This work concerns the studies of energy transfers between Sm³⁺ and Eu³⁺ ions in some phosphates as new luminescent materials emitting in the orange-red color. The choose of ions is based on the possibility of quantum cutting process and the matrices are selected according to the 5d bands position of Sm³⁺ ion. The Sm³⁺ and Eu³⁺ doped YPO₄, LaP₅O₁₄ and LaP₃O₉ are synthesized and spectroscopic studies in ultraviolet and vacuum ultraviolet ranges have been achieved.