This can of course be solved using algebra. The rst treatise on algebra was written by Diophantus of Alexandria in the 3rd century AD. The term derives from the Arabic al-jabr or literally \the reunion of broken parts." As well as its mathematical meaning, the word also means the surgical treatment of fractures. It gained widespread use through the title of a book ilm al-jabr wa'l-mukabala|the ...

We use Brownian motion ideas to study Schriidinger operators H = +A + V on Lp(R”). In particular: (a) We prove that limt+m t-l In /I e&H j111.9 is p-independent for a very large class of V’s where 11 A ll,,,n = norm of A as an operator from L’ to L”. (b) For Y > 3 and V E LY/~--E n L”Ip+c, we show that sup jl eetH Ilm,m -: (D if and only if H has no negative eigenvalues or zero energy resonance...

The ‘Abb®sid caliphs al-Ma’m‚n and al-Mu‘ta◊im, who between them reigned from 198 to 227 A.H. (813-842 A.D.) are best-known to historians of philosophy for two things. First, they supported a massive translation project that had already begun in the previous century with al-Ma’m‚n’s grandfather, al-Man◊‚r. The result was that many of the most important works of Greek philosophy and science were...

The Frege-Russell view is that existence is a second-order property rather than a property of individuals. One of the most compelling arguments for this view is based on the premise that there is an especially close connection between existence and number. The most promising version of this argument is by C.J.F. Williams (1981, 1992). In what follows, I argue that this argument fails. I then de...

Surface samples have been collected from Kerala coast, Valapatanam-Azhikode deposit of northern Kerala coast. The average heavy minerals percentage shows 30.32 %. The heavy mineral assemblage of samples from area showed an appreciable percentage of opaque followed by sillimanite and zircon. The chemical analysis carried out for the present investigation, is detailed as Ferrian ilmenite. X-ray d...

A recent physiological finding of neural coding for border ownership (BO) that defines the direction of a figure with respect to the border has provided a possible basis for figure-ground segregation. To explore the underlying neural mechanisms of BO, we investigated stimulus configurations that activate BO circuitry through psychophysical investigation of the BO-dependent tilt aftereffect (BO-...

The time is generally a challenging task. All issues in relation to time can be better supported using temporal data models. Almost all enterprise database systems have implemented temporal data, partly according to the model specified in the SQL:2011 standard and partly according to other, older temporal models. In this article five temporal concepts will be used to investigate their implement...

We introduce a mixed-initiative approach for document reconstruction that can significantly reduce the amount of time and effort required to reassemble a document from shredded pieces or an artifact from broken fragments. We focus in particular on the hardest subproblem, which is the problem of identifying a matching neighbor for any given piece. Our approach, called hallucination, combines hum...

In this study the fish assemblages of the silted Aguas Claras stream (AC) was compared with that of a reference, the São Carlos stream (SC), so as to identify potential fish indicators of integrity or degradation. Both streams, located about 5 km from one another, are part of the Upper Paraná river basin, Brazil, and present similar physiographical features. Twenty-one species were collected in...