Rough solutions

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  • This is the first in a series of papers in which we initiate the study of very rough solutions to the initial value problem for the Einstein-vacuum equations expressed relative to wave coordinates. By very rough we mean solutions which cannot be constructed by the classical techniques of energy estimates and Sobolev inequalities. Following [Kl-Ro] we develop new analytic methods based on Strichartz-type inequalities which result in a gain of half a derivative relative to the classical result. ...

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  • This is the second in a series of three papers in which we initiate the study of very rough solutions to the initial value problem for the Einstein vacuum equations expressed relative to wave coordinates. By very rough we mean solutions which cannot be constructed by the classical techniques of energy estimates and Sobolev inequalities. In this paper we develop the geometric analysis of the Eikonal equation for microlocalized rough Einstein metrics. This is a crucial step in the derivation of the decay estimates needed in the first paper. ...

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  • Case-based reasoning (CBR) and rule-based reasoning (RBR) are two important methods in the knowledge engineering to support decision making (see [2, 7, 8, and 9]) in decision support systems (DSS). In rule-based reasoning the computer examines historical cases and generates rules, which are chained (forward or backward) to solve problems.

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  • The research of optimal condition for etching silicon in TMAH solution with controlled etch rate and low surface roughness is the purpose of this study. The investigation on the influence of temperature, agitation, size of etch-window, etch time on etch rate and the surface roughness were carried out. With the TMAH concentration of 20% in weight, the optimal etching conditions were as follows: temperature of about 80 – 90 oC, agitation of 150 - 200 rpm. The etch rate is controlled in range of 0.49 – 0.72 µm/min. ...

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  • This is the fifth book containing examples from the Theory of Complex Functions. In this volume we shall consider the Laurent series, which are, roughly speaking, complex power series in which we also allow negative exponents. We shall only consider the the series and their relationship to the general theory, and finally the technique of solving linear differential equations with polynomial coefficients by means of Laurent series.

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  • All solutions to engineering problems start with a calculation or estimation of the duty which must be met (i.e., quantifying the problem). The purpose of heating and cooling load calculations, then, is to quantify the heating and/or cooling loads in the space(s) to be conditioned. Rough estimates of load may be made during the concept design phase.

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  • Leonard and Durrant-Whyte [1991] summarized the general problem of mobile robot navigation by three questions: “Where am I?,” “Where am I going?,” and “How should I get there?.” This report surveys the state-of-the-art in sensors, systems, methods, and technologies that aim at answering the first question, that is: robot positioning in its environment. Perhaps the most important result from surveying the vast body of literature on mobile robot positioning is that to date there is no truly elegant solution for the problem.

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  • Constructivism is the bedrock on which the whole reform movement, especially the three NCTM volumes [N1]-[N3], rests. Roughly, this is the education philosophy which holds that the acquisition of knowledge takes place only when the external input has been internalized and integrated into one’s own mind. Thus learning requires the construction of a mental image in response to the external input.

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  • The facts of silicon (Si) in plant life are one thing; the concepts regarding Si in plant physiology are another thing altogether. Most terrestrial plants grow in media dominated by silicates, and the soil solution bathing roots contains Si at concentrations exceeding those of phosphorus (P) by roughly a factor of 100. Plants absorb the element, and their Si content is of the same order of magnitude as that of the macronutrient elements.

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  • One authorized urologist (M.M.) performed all the operations. We used a standard TURP setup with an irrigation pressure of 80 cmH2O and an irrigation rate of 250 ml/min using D-sorbitol solution. After a rough resection of almost all the transition and central zone, we tried to resect and fulgurate the peripheral zone as completely as possible, especially where cancer was detected by biopsy. The resection was continued until adipose tissue, venous sinus or the external sphincter was identified.

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  • Roughly 80% of WSBI member savings banks in Africa are somehow involved in the remittances often as agents of money transfer operators (MTOs). And for a while, they partnered up exclusively with dominant MTOs (Western Union, Money Gram). Today, savings banks have developed business coop- eration with new and promising MTOs (Money Express, Choice Money Transfer, Eurogiro, etc.

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  • Most large text-understanding systems have been designed under the assumption that the input text will be in reasonably "neat" form, e.g., newspaper stories and other edited texts. However, a great deal of natural language texts e.g.~ memos, rough drafts, conversation transcripts~ etc., have features that differ significantly from "neat" texts, posing special problems for readers, such as misspelled words, missing words, poor syntactic constructlon, missing periods, etc.

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  • Generation of heating water. Cogeneration systems capture excess heat from the engine, which can be used to generate heating water that can then be utilized by local or district heating systems to cover their basic heat requirements. Peak heat demand can be covered through the combined use of a buffer and a peak boiler. Due to varying heat demands during the year, multi-engine- installations are the preferred solution for district heating systems. Steam production and drying processes.

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