We deal with the following fractional generalization of the Laplace equation for rectangular domains x, y ∈ x0, X0 × y0, Y0 ⊂ R × R , which is associated with the Riemann-Liouville fractional derivativesΔu x, y λu x, y ,Δ : D1 α x0 D 1 β y0 , where λ ∈ C, α, β ∈ 0, 1 × 0, 1 . Reducing the left-hand side of this equation to the sum of fractional integrals by x and y, we then use the operational ...

M. Kohda, 2 V. Lechner, Y. Kunihashi, T. Dollinger, P. Olbrich, C. Schönhuber, I. Caspers, V.V. Bel’kov, L.E. Golub, D. Weiss, K. Richter, J. Nitta, and S.D. Ganichev ∗ Department of Materials Science, Tohoku University, Sendai 980-8579, Japan PRESTO, Japan Science and Technology Agency, Saitama 332-0012, Japan Institut für Experimentelle und Angewandte Physik, Universität Regensburg, D-93040 R...

We present progress results of a new survey for bright QSOs (V < 14.5, R < 15.4, BJ < 15.2) covering the whole sky at |b| > 30. The surface density of QSOs brighter than BJ = 14.8 turns out to be 2.9±0.8·10deg. The optical Luminosity Function at 0.04 < z ≤ 0.3 shows significant departures from the standard pure luminosity evolution, providing new insights in the modelling of the QSO phenomenon.

The main aim of this paper is to establish two generalized integral formulas involving the extended Mittag-Leffler function based on the well known Lavoie and Trottier integral formula and the obtain results are express in term of extended Wright-type function. Also, we establish certain special cases of our main result.

The well-known tendency of the lawyer engaged in the drafting of conveyances is to adhere as closely as possible to the beaten paths; to follow the forms handed down from the fathers; to view with suspicion and close scrutiny any departure therefrom, and to insert new clauses and covenants only when convinced that they are demanded by the necessities engendered by tonditions and enterprises unk...

This paper’s aim is to discuss the concept of width of a proof put forward by Timothy Gowers. It explains what this concept means and attempts to show how it relates to other concepts discussed in the existing literature on proof and proving. It also explores how the concept of width of a proof might be used productively in the mathematics curriculum and how it might fit with the various perspe...

Working in the F-basis provided by the factorizing F-matrix, the scalar products of Bethe states for the supersymmetric t-J model are represented by determinants. By means of these results, we obtain determinant representations of correlation functions for the model.

In this paper we further develop the theory of matrices over the extended tropical semiring. Introducing a notion of tropical linear dependence allows for a natural definition of matrix rank in a sense that coincides with the notions of tropical regularity and invertibility.