Le Matematiche (Dipartimento di Matematica e Informatica, Università degli Studi di Catania)
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ON THE MAXIMUM PRINCIPLE FOR VISCOSITY SOLUTIONS OF FULLY NONLINEAR ELLIPTIC EQUATIONS IN GENERAL DOMAINS
Get PDFWe analyze the validity of the Maximum Principle for viscosity solutions of fully nonlinear second order elliptic equations in general unbounded domains under suitable structure conditions on the equation allowing notably quadratic growth in the gradient terms.We analyze the validity of the Maximum Principle for viscosity solutions of fully nonlinear second order elliptic equations in general unbounded domains under suitable structure conditions on the equation allowing notably quadratic growth in the gradient terms
ZEROS OF BESSEL FUNCTIONS: MONOTONICITY, CONCAVITY, INEQUALITIES
Get PDFWe present a survey of the most important inequalities and monotonicity, concavity (convexity) results of the zeros of Bessel functions. The results refer to the definition Jνκ of the zeros of Cν (x) = Jν (x) cosα −Yν (x) sinα, formulated in [6], where κ is a continuous variable. Sometimes, also the Sturm comparison theorem is an important tool of our results.We present a survey of the most important inequalities and monotoni-city, concavity (convexity) results of the zeros of Bessel functions. Theresults refer to the definition Jνκ of the zeros of Cν (x) = Jν (x) cosα −Yν (x) sinα, formulated in [6], where κ is a continuous variable. Sometimes, also the Sturm comparison theorem is an important tool of our results
On the energy functional for nonlinear stability of the classic Bénard problem
No full textNonlinear stability of motionless state of the classical Bénard problem in case of stress-free boundaries is studied for 2-dimensional disturbances, by the Liapunov’s second method. For Rayleigh number smaller than 27π^4 /4 the motionless state is proved to be unconditionally and exponentially stable with respect to a new Liapunov function which is essentially stronger than the kinetic energy
ON A THEOREM OF FALTINGS ON FORMAL FUNCTIONS
Get PDFIn 1980, Faltings proved, by deep local algebra methods, a local resultregarding formal functions which has the following global geometric factas a consequence. Theorem. − Let k be an algebraically closed field (ofany characteristic). Let Y be a closed subvariety of a projective irreduciblevariety X defined over k. Assume that X ⊂ P^n , dim(X) = d > 2 and Yis the intersection of X with r hyperplanes of P^n , with r ≤ d − 1. Then,every formal rational function on X along Y can be (uniquely) extended toa rational function on X . Due to its importance, the aim of this paper is toprovide two elementary global geometric proofs of this theorem.In 1980, Faltings proved, by deep local algebra methods, a local resultregarding formal functions which has the following global geometric factas a consequence. Theorem. − Let k be an algebraically closed field (ofany characteristic). Let Y be a closed subvariety of a projective irreducible variety X defined over k. Assume that X C P^n, dim(X) = d > 2 and Y is the intersection of X with r hyperplanes of P^n, with r ≤ d − 1. Then, every formal rational function on X along Y can be (uniquely) extended to a rational function on X. Due to its importance, the aim of this paper is to provide two elementary global geometric proofs of this theorem
MULTI-VARIABLE GOULD-HOPPER AND LAGUERRE POLYNOMIALS
Get PDFThe monomiality principle was introduced by G. Dattoli, in order to derive the properties of special or generalized polynomials starting from the corresponding ones of monomials. In this article we show a general technique to extend themonomiality approach tomulti-index polynomials in several variables. Application to the case of Hermite, Laguerre-type and mixed-type (i.e. between Laguerre and Hermite) are derived.The monomiality principle was introduced by G. Dattoli, in order toderive the properties of special or generalized polynomials starting fromthe corresponding ones of monomials. In this article we show a generaltechnique to extend themonomiality approach tomulti-index polynomials in several variables. Application to the case of Hermite, Laguerre-type and mixed-type (i.e. between Laguerre and Hermite) are derived
APPLICATION OF THE RESIDUE THEOREM TO BILATERAL HYPERGEOMETRIC SERIES
Get PDFThe application of the residue theorem to bilateral hypergeometric series identities is systematically reviewed by exemplifying three classes of summation theorems due to Dougall (1907), Jackson (1949, 1952) and Slater-Lakin (1953).The application of the residue theorem to bilateral hypergeometric series identities is systematically reviewed by exemplifying three classes of summation theorems due to Dougall (1907), Jackson (1949, 1952) and Slater-Lakin (1953)
DISCRETE MATHEMATICS, DISCRETE PHYSICS AND NUMERICAL METHODS
Get PDFDiscrete mathematics has been neglected for a long time. It has been put in the shade by the striking success of continuous mathematics in the last two centuries, mainly because continuous models in physics proved very reliable, but also because of the greater difficulty in dealing with it. This perspective has been rapidly changing in the last years owing to the needs of the numerical analysis and, more recently, of the so called discrete physics. In this paper, starting from some sentences of Fichera about discrete and continuous world, we shall present some considerations about discrete phenomena which arise when designing numerical methods or discrete models for some classical physical problems.Discrete mathematics has been neglected for a long time. It has beenput in the shade by the striking success of continuous mathematics in the last two centuries, mainly because continuous models in physics proved very reliable, but also because of the greater difficulty in dealing with it. This perspective has been rapidly changing in the last years owing to the needs of the numerical analysis and, more recently, of the so called discrete physics. In this paper, starting from some sentences of Fichera about discrete and continuous world, we shall present some considerations about discrete phenomena which arise when designing numerical methods or discrete models for some classical physical problems
New approach in stability to the comparison method applied to the Liapunov direct method
Get PDFIn this paper we deal with the stability of the stationary solution of the Lagrange equations for holonomic-rehonomic mechanical systems, by applying the comparison method to the direct Liapunov method. The stability criteria are based on the lemma given in Section 2 , where we show that the eventual stability of the zero solution of the comparison equation can imply the stability of the stationary solution of the Lagrange equations
On properties of the numbers coprime with the primes up to p_n
Get PDFIn this paper we investigate about the effective distribution of the numbers coprime with the primes up to p_n . More precisely we prove that these numbers form a periodically monotone sequence . Then we examine some properties of this sequence which, in a certain sense, are transferred to the sequence of primes. Moreover we study the distribution of twin and cousin terms within the above sequence . This study also makes furthermore strongly plausible that the set of twin primes as well as the set of cousin primes is infinite
GROUPS WITH FINITELY MANY NORMALIZERS OF NON-SUBNORMAL SUBGROUPS
Get PDFoai:ojs.www.dmi.unict.it:article/10It is proved that a group G has finitely many normalizers of non-subnormal subgroups if and only if each subgroup of G either is subnormal or has finitely many conjugates; groups with this latter property have been completely described in [8]. Moreover, groups with finitely many normalizers of infinite non-subnormal subgroups are described.It is proved that a group G has finitely many normalizers of non-subnormal subgroups if and only if each subgroup of G either is subnormal or has finitely many conjugates; groups with this latter property have been completely described in [8]. Moreover, groups with finitely many normalizers of infinite non-subnormal subgroups are described