Exact inequalities for sums of asymmetric random variables, with applications

Let be independent identically distributed random variables each having the standardized Bernoulli distribution with parameter . Let if and . Let . Let f be such a function that f and f′′ are nondecreasing and convex. Then it is proved that for all nonnegative numbers one has the inequality where . The lower bound on m is exact for each . Moreover, is Schur-concave in . A number of corollaries are obtained, including upper bounds on generalized moments and tail probabilities of (super)martingales with differences of bounded asymmetry, and also upper bounds on the maximal function of such (super)martingales. Applications to generalized self-normalized sums and t-statistics are given.      

A Study of L-Lactide Ring-Opening Polymerization Kinetics

Summary: The paper presents an experimental study of L-lactide polymerization in molten state using as initiator the Stannous Octoate. The experiments were performed in a Haake mixer. The operating temperatures were between 170 and 195°C, the reaction time up to 60 min and monomer to initiator initial molecular ratio between 10² and 5 · 10³. The conversion was determined by using ¹H NMR and the molecular weights distributions by SEC. A preliminary mathematical modeling study was also performed, based on experimental data and a previously published reaction scheme.     

Linearity of Space-Time Transformations¶Without the One-to-One, Line-onto-Line, or Constancy-of-Speed-of-Light Assumptions

Using a version of the fundamental theorem of geometry without the 1-to-1 assumption, recently obtained by the authors, the following is proved: Let n≥ 2 and T be a mapping ofℝ ⁿ onto itself which maps every timelike lineℓ into an arbitrary line so that the image of every future ray ofℓcontains at least two distinct points or the same holds for every past ray ofℓ. Then T is affine. A version of the Pappus theorem under minimal assumptions is also given, which is then used as a tool in this paper. Related results have been obtained by Borchers and Hegerfeldt. Received: 3 May 1999 / Accepted: 7 July 2000     

Heat invariants of Riemannian manifolds

We calculate heat invariants of arbitrary Riemannian manifolds without boundary. Every heat invariant is expressed in terms of powers of the Laplacian and the distance function. Our approach is based on a multidimensional generalization of the Agmon-Kannai method. An application to computation of the Korteweg-de Vries hierarchy is also presented.     

Gamma-Ray Transitions Induced in Nuclear Spin Isomers by X-Rays

Because of the high density of energy storage and the large cross section for its release, nuclear spin isomers have attracted considerable recent interest. The triggering of induced gamma emission from them has encouraged efforts to develop intense sources of short-wavelength radiation. One of the more interesting examples is the 16⁺ 4-qp isomer of ¹⁷⁸Hf which stores 2.445 MeV for a half-life of 31 years meaning that as a material, such isomeric ¹⁷⁸Hf would store 1.3 GJ/g. Recently, a sample containing 6.3×10¹⁴ nuclei of the isomer of ¹⁷⁸Hf was irradiated with X-ray pulses derived from a device operated at 15 mA to produce bremsstrahlung radiation with end point energies set to values between 60 and 90 keV. Emission of gamma radiation from the sample was increased by 1–2% above the quiescent value of spontaneous emission. Such an accelerated decay of the ¹⁷⁸Hf isomer is consistent with an integrated cross section of 2.2×10⁻²² cm² keV if the resonant absorption of the X-rays takes place below 20 keV as indicated by the use of selective absorbing filters in the irradiating beam. The work reported here describes the current experimental focus and results recently obtained with the use of coincident detection of emitted gamma photons by several detectors. This revised version was published online in July 2006 with corrections to the Cover Date.     

Low-temperature magnetic ordering in the perovskites Pr1−xAxCoO3 (A=Ca,Sr)

The magnetic and electrical properties of polycrystalline Pr_1?xA_xCoO₃ cobaltites with A=Ca, Sr and 0≤x≤0.5 were studied in the temperature range 4 K≤T≤1000 K and field up to 7 T. The X-ray analyses show the presence of only one phase having monoclinic or orthorhombic symmetry. The magnetic measurements indicate that the Ca-doped samples have at low temperatures, similar properties to the frustrated magnetic materials. PrCoO₃ is a paramagnetic insulator in the range from 4 to 1000 K. The Sr-doped cobaltites exhibit two phase transitions: a paramagnetic–ferromagnetic (or magnetic phase separated state) phase transition at about 240 K and a second one at about 100 K. The magnetic measurements suggest the presence of magnetic clusters and a change in the nature of magnetic coupling between Co ions at low temperatures. A semiconducting type behavior and high negative magnetoresistance was found for the Ca-doped samples, while the Sr-doped ones were metallic and with negligible magnetoresistance. The results are analyzed in the frame of a phase separation scenario in the presence of the spin-state transitions of Co ions.     

Magnetic cluster developement in In1−x Mn x Sb semiconductor alloys

X-ray Diffraction (XRD), X-ray Photoelectron Spectroscopy (XPS), Transmission Electron Microscopy (TEM) and magnetic measurements as a function of applied magnetic field and temperature for In_1?x Mn _x Sb (0.05≤x≤0.2) system are reported. Magnetic measurements performed at high and small magnetic field in ZFC and FC indicate the coexistence of ferromagnetic In_1?x Mn _x Sb solid solution and two types of magnetic cluster: ferromagnetic MnSb and ferrimagnetic Mn₂Sb. XPS valence band and Mn 2p core level spectra have confirmed the presence of MnSb and Mn₂Sb phases. TEM images show some manganese antimonide phase microinclusions with dimension between (30–40) nm.     

Positive-part moments via characteristic functions,and more general expressions

A unifying and generalizing approach to representations of the positive-part and absolute moments \({{\mathsf {E}}} X_+^p\) and \({{\mathsf {E}}}|X|^p\) of a random variable X for real p in terms of the characteristic function (c.f.) of X, as well as to related representations of the c.f. of \(X_+\), generalized moments \({{\mathsf {E}}} X_+^p e^{iuX}\), truncated moments, and the distribution function, is provided. Existing and new representations of these kinds are all shown to stem from a single basic representation. Computational aspects of these representations are addressed.     

Algebraic Theories of Brackets and Related (Co)Homologies

A general theory of the Frölicher–Nijenhuis and Schouten–Nijenhuis brackets in the category of modules over a commutative algebra is described. Some related structures and (co)homology invariants are discussed, as well as applications to geometry.     

In situ, time-resolved reflectance spectroscopy in the microsecond domain: oxidation of adsorbed carbon monoxide on polycrystalline pt microelectrodes in aqueous solutions

The dynamics of the electrooxidation of adsorbed CO, COads, on polycrystalline Pt microelectrodes has been examined in CO-saturated 0.5 M H2SO4 and 0.5 M HClO4 aqueous solutions, using in situ, time-resolved, normalized differential reflectance spectroscopy lambda = 633 nm). Attention was focused on the unique dependence of COads oxidation on the potential at which the adsorbed full CO monolayer is assembled (i.e., hydrogen adsorption/desorption vs the double-layer region) using both fast linear scan voltammetry and potential step techniques. As evidenced from the data collected, COads oxidation at a fixed potential proceeds at slower rates when the monolayer is formed in the double- layer region compared to when it is formed in the hydrogen adsorption/desorption region. Possible explanations for this effect are discussed.