and Applied Analysis 3 2. Results Solutions to 1.1 subject to conditions 1.2 are meant in the following weak sense. Definition 2.1. A function u ∈ Lmloc Q ∩ L p loc Q is called a weak solution to 1.1 if ∫ Q |u|φ dP ∫ S u 0, t2;x φ 0, t2;x dP2 ∫ S u t1, 0;x φ t1, 0;x dP1 − ∫

Reliability and validity are crucial issues in research. Reliability is concerned with lowered quality of data due to random errors in measurement. Validity is concerned with whether variables measure what they purport to measure or are biased by other systemic factors, excluding random errors. Strength of correlation is limited by reliability. Given the problems in measuring reliability and va...

In the preceding chapters, the effects of lensing were so strong as to leave an unmistakable imprint on a specific source, allowing a detailed treatment. However, only the densest regions of the universe are able to provide such a spectacular lensing effect. To study more representative regions of the universe, we must examine large numbers of sources statistically. This is the domain of weak l...

This paper is devoted to clarify the algorithmic definition of the weak stability boundary in the framework of the planar Restricted Three Body Problem. The role of the invariant hyperbolic manifolds associated to the central manifolds of the libration points L1 and L2, as boundary of the weak stability region, is shown.

We explain how any cofibrantly generated weak factorisation system on a category may be equipped with a universally and canonically determined choice of cofibrant replacement. We then apply this to the theory of weak ω-categories, showing that the universal and canonical cofibrant replacement of the operad for strict ω-categories is precisely Leinster’s operad for weak ω-categories.

the strategic planning of marketing and the application of marketing strategies for achieving sustainable competitive advantages are of the factors that help the survival of producers of agricultural organic products. although, there are evidences of the growth of organic farming in iran but, there are no useful information and proposals for making marketing strategies in organic production hol...

Various classes of infinite-state processes are often specified by rewrite systems. We extend Mayr’s Process Rewrite Systems (PRS) [13] by finite-state unit whose transition function satisfies some restrictions inspired by weak finite automata. We classify these models by their expressiveness and show how the hierarchy of new classes (w.r.t. bisimilarity) is related to both PRS hierarchy of May...

This paper is a study of similarities and di erences between strong and weak quantum consequence operations determined by a given class of ortholattices. We prove that the only strong orthologics which admits the deduction theorem (the only strong orthologics with algebraic semantics, the only equivalential strong orthologics, respectively) is the classical logic. In the papers concerning quant...

Double no-touch options, contracts which pay out a fixed amount provided an underlying asset remains within a given interval, are commonly traded, particularly in FX markets. In this work, we establish model-free bounds on the price of these options based on the prices of more liquidly traded options (call and digital call options). Key steps are the construction of superand sub-hedging strateg...