On Darboux-Treibich-Verdier potentials

It is shown that the four-parameter family of elliptic functions $$u_D(z)=m_0(m_0+1)\wp(z)+\sum_{i=1}^3 m_i(m_i+1)\wp(z-\omega_i)$$ introduced by Darboux and rediscovered a hundred years later by Treibich and Verdier, is the most general meromorphic family containing infinitely many finite-gap potentials.Comment: 8 page

Multidimensional Conservation Laws: Overview, Problems, and Perspective

Some of recent important developments are overviewed, several longstanding open problems are discussed, and a perspective is presented for the mathematical theory of multidimensional conservation laws. Some basic features and phenomena of multidimensional hyperbolic conservation laws are revealed, and some samples of multidimensional systems/models and related important problems are presented and analyzed with emphasis on the prototypes that have been solved or may be expected to be solved rigorously at least for some cases. In particular, multidimensional steady supersonic problems and transonic problems, shock reflection-diffraction problems, and related effective nonlinear approaches are analyzed. A theory of divergence-measure vector fields and related analytical frameworks for the analysis of entropy solutions are discussed.Comment: 43 pages, 3 figure

On the Inverse Scattering Method for Integrable PDEs on a Star Graph

© 2015, Springer-Verlag Berlin Heidelberg. We present a framework to solve the open problem of formulating the inverse scattering method (ISM) for an integrable PDE on a star-graph. The idea is to map the problem on the graph to a matrix initial-boundary value (IBV) problem and then to extend the unified method of Fokas to such a matrix IBV problem. The nonlinear Schrödinger equation is chosen to illustrate the method. The framework unifies all previously known examples which are recovered as particular cases. The case of general Robin conditions at the vertex is discussed: the notion of linearizable initial-boundary conditions is introduced. For such conditions, the method is shown to be as efficient as the ISM on the full-line

Entropy Stable Finite Volume Approximations for Ideal Magnetohydrodynamics

This article serves as a summary outlining the mathematical entropy analysis of the ideal magnetohydrodynamic (MHD) equations. We select the ideal MHD equations as they are particularly useful for mathematically modeling a wide variety of magnetized fluids. In order to be self-contained we first motivate the physical properties of a magnetic fluid and how it should behave under the laws of thermodynamics. Next, we introduce a mathematical model built from hyperbolic partial differential equations (PDEs) that translate physical laws into mathematical equations. After an overview of the continuous analysis, we thoroughly describe the derivation of a numerical approximation of the ideal MHD system that remains consistent to the continuous thermodynamic principles. The derivation of the method and the theorems contained within serve as the bulk of the review article. We demonstrate that the derived numerical approximation retains the correct entropic properties of the continuous model and show its applicability to a variety of standard numerical test cases for MHD schemes. We close with our conclusions and a brief discussion on future work in the area of entropy consistent numerical methods and the modeling of plasmas

Retrospective analysis of energy use and conservation trends: 1972-1982. Appendix

This appendix contains the detailed documentation corresponding to the end-use sectoral analyses presented in the main report. The data and methods used to calculate alternative scenarios for estimating energy savings in four economic sectors are provided in this volume. Appendix A contains the detailed documentation for the residential sector analysis. The methodology used to prepare estimates of building energy savings in the commercial sector is provided in Appendix B. Finally, Appendices C and D discuss the data and explain the analytical techniques used to derive estimates of energy savings in the industrial and transportation sectors, respectively. 9 refs., 14 figs., 86 tabs

Retrospective analysis of energy use and conservation trends: 1972-1982

The primary objective of the research reported here is to analyze energy use trends for the entire economy and by end-use sector (residential, commercial, and industrial, and transportation). In particular, an examination of energy trends was undertaken for the period 1972 through 1982 to determine the magnitude of ''energy savings'' attributable to: (1) changes in economic activity; (2) efficiency improvements relative to the 1972 stock (including structures and capital equipment); and (3) efficiency improvements relative to 1960 to 1972 trends. In addition to identifying the measures of energy savings described above, the causes of efficiency improvement relative to 1972 are explored. For example, energy savings due to efficiency improvements in the residential sector are explained by such activities as changes in household size, migration, improved shell and appliance efficiencies, and increased wood use. For this research, Pacific Northwest Laboratory (PNL) developed a consistent methodology for analyzing energy use trends by end-use sector. Alternative measures of energy use trends (i.e., alternative base cases) were developed for the purpose of measuring energy savings. The energy use trends were calculated as the product of economic activity levels (number of households in the residential sector, square feet of floor space in the commercial sector, output in the industrial sector, and person-miles/ton-miles traveled in the transportation sector) and energy use intensities (energy use per household, energy use per square foot of commercial floor space, energy use per unit of industrial output, and energy use per mile traveled). Energy savings were then defined as differences between alternative estimates of energy use. Data and methods used to derive the alternative estimates are contained in a separate volume of this report (PNL-5026-App.)

Antifeedant and toxicity effects of thiophenes from four Echinops species against the Formosan subterranean termite, Coptotermes formosanus

Over 220 crude extracts from repositories generated from plants native to Greece and Kazakhstan were evaluated for termiticidal activity against the Formosan subterranean termite, Coptotermes formosanus Shiraki (Isoptera: Rhinotermitidae). Emerging from this screening effort were bioactive extracts from two Greek species (Echinops ritro L. and Echinops spinosissimus Turra subsp. spinosissimus) and extracts from two Kazakhstan species (Echinops albicaulis Kar. & Kir. and Echinops transiliensis Golosh.). Fractionation and isolation of constituents from the most active extracts from each of the four species has been completed, resulting in the isolation of eight thiophenes possessing varying degrees of termiticidal activity. 2,2′:5′, 2″-Terthiophene and 5′-(3-buten-1-ynyl)-2,2′-bithiophene demonstrated 100% mortality against C. formosanus within 9 days at 1 and 2 wt% concentrations respectively. In addition, all but two of the eight compounds tested were significantly different from the solvent controls in the filter paper consumption bioassay. © 2006 Society of Chemical Industry

The purchase of information technology products by Dutch SMEs : problem resolution

This research focuses on the purchase of information technology (IT) products by small and medium-sized enterprises (SMEs) in the Netherlands. Based on nationwide representative survey data (a total of 1,252 IT transactions), the research considers the problems that Dutch SMEs are faced with and the way in which these problems are dealt with. On average, 28 percent of transaction are completed without problems. If problems are encountered, they mostly involve inadequate documentation (45 percent of all transactions). Frequently mentioned problems, such as incompatibility with other IT products and being over budget, occur much less frequently (about 25 percent of all transactions). Moreover, strong support was found for the existence of a specific sequence in dealing with ex-post problems. Nearly all SMEs at least communicate the problem to the supplier; if that does not solve the issue, it is almost always followed by active deliberation with the supplier about a solution. If that does not help, about half of the SMEs impose some kind of sanction (most of the time delaying the payment). If that still does not settle the issue, virtually all SMEs give up on it. Third parties, such as arbitration committees or the courts, are rarely invoked