Le Matematiche (Dipartimento di Matematica e Informatica, Università degli Studi di Catania)
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Entropy solutions for nonlinear elliptic anisotropic problem with Robin boundary condition
Get PDFWe study a Robin boundary value problem of nonlinear elliptic anisotropic type. We prove the existence and uniqueness of entropy solutions for -data, via the existence and uniqueness of weak solution
An asymptotic formula of cosine power sums
Get PDFIn the paper, the authors find several accurate approximations of some cosine power sums and present an asymptotic formula for these cosine power sums
Poincaré series of monomial rings with minimal Taylor resolution
Get PDFWe give a comparison between the Poincaré series of two monomial rings: R = A/I and R_q = A/I_q where I_q is a monomial ideal generated by the q’th power of monomial generators of I. We compute the Poincaré series for a new class of monomial ideals with minimal Taylor resolution. We also discuss the structure a monomial ring with minimal Taylor resolution where the ideal is generated by quadratic monomials
Skew Hurwitz series over quasi Baer and PS-rings
Get PDFIn this paper, we consider some properties of rings which are shared by the ring R and the ring T = (HR, σ ) of skew Hurwitz series. In particular we show that:1) If R is a ring with char(R) = 0 and σ is an R -automorphism such that σ (e) = e and the left annihilator of every left ideal is σ -invariant, then the following are equivalent:i) T is a quasi Baer ring.ii) R is a quasi Baer ring.2) If R is a right PS-ring with char(R) = 0, then T is a right PS-ring
On a class of generalized analytic functions
Get PDFThis paper deals with a new generalization of analytical functions.The p-wave functions are introduced and studied. We consider their theoretical aspect and applications. Some integral representations of x^k y^l -wave functions (k, l − const. > 0), and their inversion formulas are derived. As an application of the theory, a singular Cauchy problem is formulated and solved in terms of the Bessel function of the first kind and Gauss hypergeometric function
WEAK CONVERGENCE OF JACOBIAN DETERMINANTS
Get PDFLet \Om be a bounded open set in sufficiently smooth and and mappings belong to the Sobolev space W^{1,2}(\Om,\R^2). We prove that if the sequence of Jacobians converges to a measure in sense of measures andif one allows different assumptions on the two components of and , e.g.u_k \rightharpoonup u \;\;\mbox{weakly in} \;\; W^{1,2}(\Om) \qquad \, v_k \rightharpoonup v \;\;\mbox{weakly in} \;\; W^{1,q}(\Om)for some , then\begin{equation}\label{0}d\mu=J_f\,dz.\end{equation}Moreover, we show that this result is optimal in the sense that conclusion fails for .On the other hand, we prove that \eqref{0} remains valid also if one considers the case , but it is necessary to require that weakly converges to in a Zygmund-Sobolev space with a slightly higher degree of regularity than W^{1,2}(\Om) and precisely u_k \rightharpoonup u \;\;\mbox{weakly in} \;\; W^{1,L^2 \log^\alpha L}(\Om)for some . Let \Om be a bounded open set in sufficiently smooth and and mappings belong to the Sobolev space . We prove that if the sequence of Jacobians converges to a measure in sense of measures andif one allows different assumptions on the two components of and , e.g.u_k \rightharpoonup u \;\;\mbox{weakly in} \;\; W^{1,2}(\Omega) \qquad \, v_k \rightharpoonup v \;\;\mbox{weakly in} \;\; W^{1,q}(\Omega)for some , then\begin{equation}\label{0}d\mu=J_f\,dz.\end{equation}Moreover, we show that this result is optimal in the sense that conclusion fails for .On the other hand, we prove that \eqref{0} remains valid also if one considers the case , but it is necessary to require that weakly converges to in a Zygmund-Sobolev space with a slightly higher degree of regularity than and preciselyu_k \rightharpoonup u \;\;\mbox{weakly in} \;\; W^{1,L^2 \log^\alpha L}(\Omega)for some .
Curves on a quadric surface over
No full textHere (following a paper by Giuffida, Maggioni and Re) we study the existence of curve defined over small fields and with for all integers such that and
Generalization of some inequalities for the (q_1, . . . , q_s)-gamma function
Get PDFRecently were established q-analogues of some inequalities involving the gamma functions. In this paper are presented the (q1, . . . , qs)-analogues of those inequalities
Existence of solutions to integral type BVPs for second order ODEs on the whole line
Get PDFSome integral type boundary value problems (BVPs) for second order differential equations (ODEs) with one-dimensional p-Laplacian on the whole line are discussed. Sufficient conditions to guarantee the existence of solutions are established. The emphasis is put on the one-dimensional p-Laplacian term [ρ(t)Φ(x\u27(t))]\u27 involved with the nonnegative function ρ that may satisfy , and the differential equations are defined on the whole line
On the weak Lefschetz property of graded modules over K[x, y]
Get PDFIt is known that graded cyclic modules over S = K[x, y] have the Weak Lefschetz Property (WLP). This is not true for non-cyclic modules over S. The purpose of this note is to study which conditions on S-modules ensure the WLP. We give an algorithm to test the WLP for graded modules with fixed Hilbert function. In particular, we prove that indecomposable graded modules over S with the Hilbert function (h_0, h_1) have the WLP