Le Matematiche (Dipartimento di Matematica e Informatica, Università degli Studi di Catania)
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On stability of shock waves in a compressible viscous gas
Get PDFOn the example of the Navier-Stokes model, this paper discusses the approach in which the surface of a strong discontinuity in a a compressible viscous gas is considered as a shock wave. It is proved that this approach contains essential lacks. This conclusion follows from existence of special exponentially increasing solutions to the problem on shock wave stability
On the convolution product of the distributional families related to the diamond operator
Get PDFIn this paper, we introduce a distributional family K_{α,β} which is related to the Diamond operator ♦^k iterated k-times. At first we study the properties of K_{α,β} and then we give a sense to the convolution product of K_{α,β}∗ K_{α\u27,β\u27}
Families of lines in Fano varieties complete intersection in a Grassmannian
Get PDFIn this paper we determine all Fano varieties which are complete intersections of hypersurfaces in a Grassmannian. Then, in the case Fano\u27s conjecture is satisfied, we give a formula in order to compute the dimension of the Hilbert scheme that parametrises their lines
L^{p,λ} regularity for divergence form elliptic equations with discontinuous coefficients
Get PDFWe will prove L^{p,λ} regularity results for the gradient of the solution to Dirichlet problem for some equations equations with coefficients in particular spaces
On fractional calculus operator N^{\ni_1,\ni_2} and p-transformation
No full textIn this paper, the set {N^{ν1 ν2} } of fractional calculus is discussed. It is shown that the set is an Abelian product group for f(z1 , z2 ) = f ∈ F={ f ; 0 \ne |f_{ ν1ν2} | < ∞, ν1, ν2 ∈ R} with continuous indexes ν1 , ν2 , [1]. A new P-transformation is being introduced for the functions of two variables
Varieties of simultaneous sums of power for binary forms
Get PDFThe problem of simultaneous decomposition of binary forms as sums of powers of linear forms is studied. For generic forms the minimal number of linear forms needed is found and the space parametrizing all the possible decompositions is described. More generally the variety parametrizing the 0-dimensional schemes apolar to a set of generic binary forms is described. These results are applied to the study of particular secant spaces of rational curves
The second dual variety of rational conic bundles
Get PDFThe second dual variety of a Segre-Hirzebruch surface linearly normally embedded in a projective space as a 2-regular rational conic bundle is studied by relating it to the classical dual variety of another linearly normal embedding of the underlying surface. These varieties are shown to be birational, and an upper bound on the dimensions of their singular loci is given
A note on twin practical numbers
Get PDFA positive integer m is a practical number if every positive integer n < m is a sum of distinct divisors of m. Let P_2 (x) be the counting function of the pairs (m, m + 2) of twin practical numbers. Margenstern gave a conjecture on P_2 (x). We prove a new result
Two criteria for trascendental sequences
No full textThe concept of trascendental sequence is defined in this contribution by means of the related trascendental series. The main results are two criteria for when certain sequences are trascendental. Several applications are presented
On a degeneration of the symmetric product of a curve with general moduli
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