Regularity of the Solution to Nonlinear Anisotropic Elliptic Equations with Variable Exponents and Irregular Data

In this paper, we prove the existence and regularity of weak solutions for a class of nonlinear anisotropic elliptic equations with \(p_i(x)\) growth conditions and \(L^m\) data, with m being small. The functional setting involves Lebesgue–Sobolev spaces with variable exponents. Our results are generalizations of the corresponding results in the constant exponent case and some results given in Bendahmane et al. (Commun Pure Appl Anal 12:1201–1220, 2013).     

The Decay of 140La to Levels in 140Ce

The decay of ¹⁴⁰La to levels in ¹⁴⁰Ce has been studied in detail using a GMX-Ge and Hp-Ge coincidence spectrometer. Singles gamma-ray spectra as well as gamma-gamma coincidence were carried out to determine some γ-transitions and to insure others. Energies and relative intensities of 36 γ-transitions in the range from 26 to 3319 keV have been measured. The doubted γ-lines 936.7, 1087.9, 1303.5, 1404.2, 1415.3 and 2533.4 keV were confirmed, while other ones at 798.3, 902.0, 907.0, 1521.8 and 2494.0 keV were not observed. The two γ-lines at 1924 and 2082 keV which were a source of large discrepancies in the previous studies are confirmed in the present work to be sum peaks. Special care was paid in identifying the weak γ-transitions 936.7, 1087.9, 1415.3 and 2533.4 keV.

Es wurde der Zerfall von ¹⁴⁰La in Energienivcaus des ^l40Ce unter Verwendung eines GMX-Ge und Hp-Ge-Koinzidenzspeklrometers untersucht. Es werden einzclne Gammaspektren r und Gamma-Gamma-Koinzidenzen aufgenommen, um einige Gamma-Übergänge zu bestimmen und andere abzusichern. Die Energien und die relativen Intcnsitäten von 36 Gamma-Übergangen im Bereich von 26 … 3319 keV wurden vermessen. Die unsicheren Gamma-Linien 936,7, 1087,9, 1303,5, 1404,2, 1415,3 und 2533,4 keV wurden bestätigt, während die Linien 798,3, 902,0, 907,0, 1521,8 und 2494,0 keV nicht beobachtet werden konnten. Die zwei Gamma-Linien bei 1924 und 2082 keV, die eine Quclle groβer Unstimmigkeiten in früheren Untersuchungen gewesen sind, konnten als Summenpeaks bestätigt werden. Besondere Beachtung wurde der Zuordnung der schwachen Gamma-Übergange bei 936,7, 1087,9, 1415,3 und 2533,4 keV geschenkt.     

Geometric representation of the mean–variance–skewness portfolio frontier based upon the shortage function

The literature suggests that investors prefer portfolios based on mean, variance and skewness rather than portfolios based on mean–variance (MV) criteria solely. Furthermore, a small variety of methods have been proposed to determine mean–variance–skewness (MVS) optimal portfolios. Recently, the shortage function has been introduced as a measure of efficiency, allowing to characterize MVS optimal portfolios using non-parametric mathematical programming tools. While tracing the MV portfolio frontier has become trivial, the geometric representation of the MVS frontier is an open challenge. A hitherto unnoticed advantage of the shortage function is that it allows to geometrically represent the MVS portfolio frontier. The purpose of this contribution is to systematically develop geometric representations of the MVS portfolio frontier using the shortage function and related approaches.     

Mineralization of aqueous phenolate solutions: A combination of irradiation treatment and wet oxidation

Wet oxidation (high-temperature, high-pressure oxidation of organic wastes in aqueous solution) and radiation technology were combined in γ-ray and electron beam induced oxidation of 4×10^?4–1×10^?2 mol dm^?3 Na-phenolate solutions in a wide O₂ concentration (1–20 bar pressure) and absorbed dose (0–50 kGy) range. Most experiments were made in stainless steel high pressure autoclave equipped with magnetic stirrer. The rate of oxidation was followed by chemical oxygen demand and total organic carbon content measurements. The rate was similar in γ-ray and pulsed electron beam irradiation and increased with O₂ concentration in the liquid.     

Analogues of Miyachi, cowling-price and Morgan theorems for compact extensions of ℝ n

Let K be a compact subgroup of automorphisms of ? ⁿ . We formulate and prove an analogue of Miyachi’s theorem for the semi-direct product K ? ? ⁿ . This allows us to solve the sharpness problems in the theorem of Cowling-Price and in the L ^p ? L ^q analogue of Morgan theorem for any compact extension of ? ⁿ . These upshots are proved using the representations theory and the Plancherel formula for the group Fourier transform.     

Generalized logarithmic Gauss map and its relation to (co)amoebas

We define the generalized logarithmic Gauss map for algebraic varieties of the complex algebraic torus of any codimension. Moreover, we describe the set of critical points of the logarithmic mapping restricted to our variety, and we show an analogous of Mikhalkin's result on the critical points of the logarithmic map restricted to a hypersurface.     

Integer valued polynomials on lower triangular integer matrices

Let $D$ be an integral domain with quotient field $K$ . In this paper we study the algebra of polynomials in $K[x]$ which map the set of lower triangular $n\times n$ matrices with coefficients in $D$ into itself and show that it coincides with the algebra of polynomials whose divided differences of order $k$ map $D^{k+1}$ into $D$ for every $k< n$ . Using this result we describe the polynomial closure of this set of matrices when $D$ is the ring of integers in a global field.     

WCDS‐DCR: an energy‐efficient data‐centric routing scheme for wireless sensor networks

Wireless sensor networks (WSNs) typically consist of a large number of battery‐constrained sensors often deployed in harsh environments with little to no human control, thereby necessitating scalable and energy‐efficient techniques. This paper proposes a scalable and energy‐efficient routing scheme, called WCDS‐DCR, suitable for these WSNs. WCDS‐DCR is a fully distributed, data‐centric, routing technique that makes use of an underlying clustering structure induced by the construction of WCDS (Weakly Connected Dominating Set) to prolong network lifetime. It aims at extending network lifetime through the use of data aggregation (based on the elimination of redundant data packets) by some particular nodes. It also utilizes both the energy availability information and the distances (in number of hops) from sensors to the sink in order to make hop‐by‐hop, energy‐aware, routing decisions. Simulation results show that our solution is scalable, and outperforms existing schemes in terms of network lifetime. Copyright © 2010 John Wiley & Sons, Ltd.     

Benchmarking mean-variance portfolios using a shortage function: the choice of direction vector affects rankings!

In addition to its use in data envelopment analysis models, the shortage function has been proposed as a tool to gauge performance in multi-moment portfolio models. An open issue is how the choice of direction vector affects the efficiency measurement, especially when some of the data can be negative and, from a practical point of view, whether and how the resulting league tables are affected. This paper illustrates empirically how the choice of direction vector affects the relative ranking of mean-variance portfolios. This result is relevant to all frontier-based applications, especially those where some of the data can be naturally negative.