Existence of nonoscillatory solutions of higher-order neutral delay difference equations with variable coefficients

AbstractIn this paper, we consider the following higher-order neutral delay difference equations with positive and negative coefficients: Δm(xn + cxn−k) + pnxn−r − qnxn−l = 0, n≥n0, where c ϵ R, m ⩾ 1, k ⩾ 1, r, l ⩾ 0 are integers, and {pn}∞n=n0 and {qn}n=n0∞ are sequences of nonnegative real numbers. We obtain the global results (with respect to c) which are some sufficient conditions for the existences of nonoscillatory solutions

Comparison Theorems and Oscillation Criteria for Difference Equations

AbstractFirst, we establish the equivalence of the oscillation of the delay difference equationΔxn+pnxn−k=0,and the second-order difference equationΔ2yn−1+2k+1kkk+1pn−kkk+1k+1yn=0,where {pn} is a sequence of nonnegative real numbers and k is a positive integer. Next, we obtain some sharp conditions for oscillations and nonoscillations of the first equation

On the oscillation of solutions and existence of positive solutions of neutral difference equations

AbstractWe obtain sufficient conditions for the oscillation of all solutions and existence of positive solutions of the neutral difference equation Δ(xn + cxn − m) + pnxn − k = 0, n = 0, 1, 2, …, where c and pn are real numbers, m and k are integers, and pn, m and k are nonnegative

Energy loss in high energy heavy ion collisions from the Hydro+Jet model

We investigate the effect of energy loss of jets in high energy heavy ion collisions by using a full three-dimensional space-time evolution of a fluid combined with (mini-)jets that are explicitly evolved in space-time. In order to fit the pi^0 data for the Au+Au collisions at sqrt(s_{NN}) = 130 GeV, the space-time averaged energy loss dE/dx(tau <= 3 fm/c) = 0.36 GeV/fm is extracted within the model. It is found that most energy loss occurs at the very early time less than 2 fm/c in the QGP phase and that energy loss in the mixed phase is negligible within our parameterization for jet energy loss. This is a consequence of strong expansion of the system.Comment: 4 pages, 5 figures; one figure adde

The Maximum Mass of Star Clusters

When an universal untruncated star cluster initial mass function (CIMF) described by a power-law distribution is assumed, the mass of the most massive star cluster in a galaxy (M_max) is the result of the size-of-sample (SoS) effect. This implies a dependence of M_max on the total number of star clusters (N). The SoS effect also implies that M_max within a cluster population increases with equal logarithmic intervals of age. This is because the number of clusters formed in logarithmic age intervals increases (assuming a constant cluster formation rate). This effect has been observed in the SMC and LMC. Based on the maximum pressure (P_int) inside molecular clouds, it has been suggested that a physical maximum mass (M_max[phys]) should exist. The theory predicts that M_max[phys] should be observable, i.e. lower than M_max that follows from statistical arguments, in big galaxies with a high star formation rate. We compare the SoS relations in the SMC and LMC with the ones in M51 and model the integrated cluster luminosity function (CLF) for two cases: 1) M_max is determined by the SoS effect and 2) M_max=M_max[phys]=constant. The observed CLF of M51 and the comparison of the SoS relations with the SMC and LMC both suggest that there exists a M_max[phys] of 5*10^5 M_sun in M51. The CLF of M51 looks very similar to the one observed in the ``Antennae'' galaxies. A direct comparison with our model suggests that there M_max[phys]=2*10^6 M_sun.Comment: 4 pages, contribution to "Globular Clusters: Guides to Galaxies", March 6th-10th, 200

Calculating Quenching Weights

We calculate the probability (``quenching weight'') that a hard parton radiates an additional energy fraction due to scattering in spatially extended QCD matter. This study is based on an exact treatment of finite in-medium path length, it includes the case of a dynamically expanding medium, and it extends to the angular dependence of the medium-induced gluon radiation pattern. All calculations are done in the multiple soft scattering approximation (Baier-Dokshitzer-Mueller-Peign\'e-Schiff--Zakharov ``BDMPS-Z''-formalism) and in the single hard scattering approximation (N=1 opacity approximation). By comparison, we establish a simple relation between transport coefficient, Debye screening mass and opacity, for which both approximations lead to comparable results. Together with this paper, a CPU-inexpensive numerical subroutine for calculating quenching weights is provided electronically. To illustrate its applications, we discuss the suppression of hadronic transverse momentum spectra in nucleus-nucleus collisions. Remarkably, the kinematic constraint resulting from finite in-medium path length reduces significantly the transverse momentum dependence of the nuclear modification factor, thus leading to consistency with the data measured at the Relativistic Heavy Ion Collider (RHIC).Comment: 45 pages LaTeX, 20 eps-figure

Collective Properties of Low-lying Octupole Excitations in 82208Pb126^{208}_{82}Pb_{126}, 2060Ca40^{60}_{20}Ca_{40} and 828O20^{28}_{8}O_{20}

The octupole strengths of $\beta$-stable nucleus $^{208}_{82}Pb_{126}$, a neutron skin nucleus $^{60}_{20}Ca_{40}$ and a neutron drip line nucleus $^{28}_{8}O_{20}$ are studied by using the self-consistent Hartree-Fock calculation plus the random phase approximation (RPA) with Skyrme interaction. The collective properties of low-lying excitations are analyzed by using particle-vibration coupling. The results show that the lowest isoscalar states above threshold in $^{60}_{20}Ca_{40}$ and $^{28}_{8}O_{20}$ are the superpositions of collective excitations and unperturbed transitions from bound state to nonresonance states. For these three nuclei, both the low-lying isoscalar states and giant isoscalar resonance carry isovector strength. The ratio B(IV)/B(IS) is checked. It is found that, for $^{208}_{82}Pb_{126}$, the ratios are equal to $(\frac{N-Z}{A})^2$ in good accuracy, while for $^{60}_{20}Ca_{40}$ and $^{28}_{8}O_{20}$, the ratios are much larger than $(\frac{N-Z}{A})^2$. This results from the excess neutrons with small binding energies in $^{60}_{20}Ca_{40}$ and $^{28}_{8}O_{20}$.Comment: 14 pages, 10 figure

Distribution of MHC class II alleles in primary systemic vasculitis

Distribution of MHC class II alleles in primary systemic vasculitis. Previous studies have shown a number of different associations between major histocompatibility complex (MHC) alleles and primary systemic vasculitis. Disease heterogeneity and the lack of specificity of certain MHC typing techniques may have contributed to the lack of consistency in those studies. We therefore studied a relatively homogeneous group of 94 patients with Wegener's granulomatosis, microscopic polyangiitis, or renal-limited vasculitis using molecular techniques that allow more precise assignment of MHC genotype. DNA was prepared from peripheral blood and DRB1 genotype determined by Taq restriction fragment length polymorphism. DQB1 and DPB1 genotype were assigned by polymerase chain reaction amplification followed by probing with allele-specific oligonucleotides. Specificity of associated anti-neutrophil cytoplasm antibodies (ANCA) was determined where possible by solid phase immunoassays using purified proteinase 3 (PR3) and myeloperoxidase (MPO). After correction for multiple comparisons there were no significant differences in the distribution of DRB1, DQB1 and DPB1 alleles between a local control group (N = 90 for DRB1, N = 50 for DQB1 and DPB1) and the patient group as a whole (N = 94) or two a priori defined subgroups (anti-PR3 positive, N = 35; anti-MPO positive, N = 22). We have therefore found no significant association between primary systemic vasculitis and any MHC class II allele. This, together with the fact that previous smaller studies have shown no consistent association, suggests that any such association is very weak, if it exists at all

Is Schr\"{o}dinger's Conjecture for the Hydrogen Atom Coherent States Attainable

We construct the most general SO(4,2) hydrogen atom coherent states which are the counterpart of Schr\"{o}dinger's harmonic oscillator coherent states. We show that these states cannot be localized and cannot follow the classical orbits. Thus, Schr\"{o}dinger's conjecture for the hydrogen atom coherent states is unattainable.Comment: 10 pages, report