Quasi-bound state resonances of charged massive scalar fields in the near-extremal Reissner–Nordström black-hole spacetime

The quasi-bound states of charged massive scalar fields in the near-extremal charged Reissner–Nordström black-hole spacetime are studied analytically. These discrete resonant modes of the composed black-hole-field system are characterized by the physically motivated boundary condition of ingoing waves at the black-hole horizon and exponentially decaying (bounded) radial eigenfunctions at spatial infinity. Solving the Klein–Gordon wave equation for the linearized scalar fields in the black-hole spacetime, we derive a remarkably compact analytical formula for the complex frequency spectrum which characterizes the quasi-bound state resonances of the composed Reissner–Nordström-black-hole-charged-massive-scalar-field system.     

Littlewood polynomials with high order zeros

Let be the minimal length of a polynomial with coefficients divisible by . Byrnes noted that for each , and asked whether in fact . Boyd showed that for all , but . He further showed that , and that is one of the 5 numbers , or . Here we prove that . Similarly, let be the maximal power of dividing some polynomial of degree with coefficients. Boyd was able to find for . In this paper we determine for .

     

Rapid Antibiotic Susceptibility Determination for <Emphasis Type="Italic">Yersinia pestis</Emphasis> Using Flow Cytometry Spectral Intensity Ratio (SIR) Fluorescence Analysis

Rapid antimicrobial susceptibility tests (ASTs) are essential tool for proper treatment of patients infected by Yersinia pestis (Y. pestis), the causative agent of plague, or for post-exposure prophylaxis of a population exposed to a naturally acquired or deliberately prepared resistant variant. The standard AST of Y. pestis is based on bacterial growth and requires 24–48 h of incubation in addition to the time required for prior isolation of a bacterial culture from the clinical or environmental sample, which may take an additional 24–48 h. In this study, we present a new and rapid AST method based on a fluorescence determination of the minimum inhibitory concentration (MIC). Our method includes the incubation of bacteria with an antibiotic, followed by staining of the bacteria with oxonol dye (SynaptoGreen C4/FM1–43), which enables the rapid detection of an antibiotic’s effect on bacterial viability. We show that stained, non-viable bacteria exhibit a spectral redshift and an increase in fluorescence intensity compared to intact control bacteria. Based on these criteria, we developed a rapid flow cytometer measurement procedure and a unique spectral intensity ratio (SIR) analysis that enables determination of antibiotic susceptibility for Y. pestis within 6 h instead of the 24 to 48 h required for the standard AST. This new rapid determination of antibiotic susceptibility could be crucial for reducing mortality and preventing the spread of disease.     

Can Special Relativity Be Derived from Galilean Mechanics Alone?

Special relativity is based on the apparent contradiction between two postulates, namely, Galilean vs. c-invariance. We show that anomalies ensue by holding the former postulate alone. In order for Galilean invariance to be consistent, it must hold not only for bodies’ motions, but also for the signals and forces they exchange. If the latter ones do not obey the Galilean version of the Velocities Addition Law, invariance is violated. If, however, they do, causal anomalies, information loss and conservation laws’ violations are bound to occur. These anomalies are largely remedied by introducing waves and fields that disobey Galilean invariance. Therefore, from these inconsistencies within classical mechanics, electromagnetism could be predicted before experiment proved its existence. Special relativity, it might be argued, would then follow naturally, either as a resolution of the resulting conflict or as an extrapolation of the path between the theories. We conclude with a review of earlier attempts to base SR on a single postulate, and point out the originality of the present work.     

Miscibility and deformation behavior in some thermoplastic polymer blends containing poly(styrene-co-acrylonitrile)

Miscibility in blends of poly(styrene-co-acrylonitrile) (PSAN) with several other polymeric components has been investigated over a range of compositions by means of thermal analysis and transmission electron microscopy. Systems in vestigated were (i) PSAN/polycarbonate (PC), (ii) PSAN/styrene-maleic anhydride-methyl methacrylate terpolymer (S/MA/MM), (iii) PSAN/polynorbornene nitrile (PNN), and (iv) PSAN//S/MA/MM//PC. PSAN/PC was demonstrated to be partially miscible in all proportions over the PSAN copolymer composition range 23–70 wt % AN, while the miscibility or lack thereof of PSAN//S/MA/MM depended on the relative AN and MA contents of the PSAN and S/MA/MM, respectively. In contrast, PSAN/PNN was found to be immiscible in all proporations, while the system PSAN//S/MA/MM//PC was shown to be partially miscible. Deformation studies performed on rubber-modified versions of these blends defined deformation mode and microstructural deformation behavior. Dual extensometer tensile testing yielded relative contributions of crazing and of plastic flow, which correlated both with blend composition and with toughness. TEM observations of deformed specimens indicated a deformation process in the multiphase matrix blends consisting of craze initiation and propagation in the rubber-containing phase, craze arresting in the ductile second matrix phase, and coordinated extensive deformation of the matrix phases and of the rubber particles, where the ability to support the latter coordinated forms of deformation were observed to increase with increasing proportion of plastically deforming phase.     

Determination of polymer branching with gel-permeation chromatography. I. Theory

The effect of long-and short-chain branching in polymer molecules on gel-permeation chromatographic (GPC) separation is discussed. The calculation of calibration curves for branched polymers is developed from the universal calibration technique based on the hydrodynamic volume concept and previously established relationships for the effect of branching on molecular dimensions. Typical calibration curves are shown for different branching models and degrees of branching. As branching increases, the curves are shown to converge. Methods of characterizing branching and molecular weight distributions of franctions and whole polymers from GPC and intrinsic viscosity data are presented.     

ℓ-norm and its Application to Learning Theory

We investigate connections between an important parameter in the theory of Banach spaces called the -norm, and two properties of classes of functions which are essential in Learning Theory – the uniform law of large numbers and the Vapnik–Chervonenkis (VC) dimension. We show that if the -norm of a set of functions is bounded in some sense, then the set satisfies the uniform law of large numbers. Applying this result, we show that if X is a Banach space which has a nontrivial type, then the unit ball of its dual satisfies the uniform law of large numbers. Next, we estimate the -norm of a set of {0,1}-functions in terms of its VC dimension. Finally, we present a `Gelfand number' like estimate of certain classes of functions. We use this estimate to formulate a learning rule, which may be used to approximate functions from the unit balls of several Banach spaces.     

Gravitation, the Quantum and Bohr's Correspondence Principle

The black hole combines in some sense both thehydrogen atom and the black-bodyradiation problems of quantum gravity. Thisanalogy suggests that black-hole quantization may be thekey to a quantum theory of gravity. During the last twenty-fiveyears evidence has been mounting that black-hole surfacearea is indeed quantized, with uniformally spaced areaeigenvalues. There is, however, no general agreement on the spacing of the levels. In thisessay we use Bohr's correspondence principle to providethis missing link. We conclude that the fundamental areaunit is 4h ln 3. This is the unique spacing consistent both with the area-entropythermodynamic relation for black holes, withBoltzmann-Einstein formula in statistical physics andwith Bohr's correspondence principle.     

Effect of molecular structure on polyethylene melt rheology. II. Shear-dependent viscosity

The investigation of the effect of molecular structural variables on the melt viscosity of polyethylene was extended to the shear dependent region by application of a reduced variables treatment following, in a formal sense, that of Bueche. Viscosity–shear rate data were obtained for a series of experimentally polymerized linear polyethylene samples having a range of molecular weights and molecular weight distributions as characterized primarily by gel permeation chromatography. These data could be superimposed on a single reduced variables flow curve using parameters which were a function only of temperature, limiting Newtonian viscosity, M?_w, and M?_w/M?_n. The same treatment was successfully applied also to branched (low-density) fraction data discussed in a previous paper, with additional correction for long-chain branching. However, different reduced variables curves were obtained for the branched and linear cases.     

Time-dependent random walks and the theory of complex adaptive systems

Motivated by novel results in the theory of complex adaptive systems, we analyze the dynamics of random walks in which the jumping probabilities are time dependent. We determine the survival probability in the presence of an absorbing boundary. For an unbiased walk, the survival probability is maximized in the case of large temporal oscillations in the jumping probabilities. On the other hand, a random walker who is drifted towards the absorbing boundary performs best with a constant jumping probability. We use the results to reveal the underlying dynamics responsible for the phenomenon of self-segregation and clustering observed in the evolutionary minority game.