On the embedding of core-free projective images of normal subgroups

Sunto Siano G e due gruppi, : GG una proiettività e N un sottogruppo normale di G. Vengono provati alcuni risultati sulle proprietà di immersions in e G rispettivamente, del gruppi , la chiusura normale di N in modulo il nocciolo di N in , e .

---

---

Supported by a C.N.R. grant.     

An Elementary Approach to an Eigenvalue Estimate for Matrices

A celebrated result of Johnson, Maurey, König and Retherford from 1977 states that for every complex matrix satisfies the following eigenvalue estimate:

Semilinear Dirichlet problem involving critical exponent for the Kohn Laplacian

The paper is concerned with the Dirichlet problem

Su un problema di tipo nuovo relativo alle equazioni paraboliche d'ordine superiore al secondo

Sunto Si studia il problema della determinazione di una soluzione dell'equazione a_k(x)∂^ku/∂x^k=f(x, y) entro la semistriscia a≤x≤b, y≥0, che assuma assegnati valori per y=0 e per x=a, x₁, x₂, b (a<x₁<x₂<b). Analogamente si studia il problema della determinazione di una soluzione dell' equazione a_k(x)∂^ku/∂x^k+b(x)∂u/∂y=f(x,y), entro la medesima semistriscia, cha assuma assegnati valori per y=0 e per x=a, x₁, x₂, b e la cui ∂/∂y assuma assegnati valori per y=0. A Giovanni Sansone nel suo 70^mo compleanno.     

Lipschitz and darbo conditions for the superposition operator in some non-ideal spaces of smooth functions

Let X be a Banach space of differentiable functions and A: XX be a superposition operator. We consider for A the conditions

Caratterizzazione delle tracce per spazi con peso

Sunto Si prova un teorema di tracce per spazi di funzioni, definite su R ₊ ⁿ , con norme del tipo . Entrata in Redazione il 23 luglio 1969. Lavoro eseguito nell'ambito dei gruppi di ricerca del Comitato Nazionale per la Matematica del C.N.R.     

Einbettungen Steinscher Mannigfaltigkeiten

A well-known conjecture in geometric function theory is the conjecture of Forster, namely that there exists an embedding of a Stein manifold of dimension n in an affine space . A first step to prove this was a theorem of Forster, which gives an embedding of a Stein manifold of dimension n into for n—6. The goal of this paper is an amelioration of Forster's result. It follows the main lines of Forster's proof. It is proved that the conjecture holds asymptotically.     

Асимптотические фор мулы для нулей функци и типа Миттаг-Леффлера

The paper is devoted to study the asymptotic behaviour of zerosz _n of an entire function of Mittag-Leffler's type

The expected number of parts in a partition ofn

Forn a positive integer letp(n) denote the number of partitions ofn into positive integers and letp(n,k) denote the number of partitions ofn into exactlyk parts. Let , thenP(n) represents the total number of parts in all the partitions ofn. In this paper we obtain the following asymptotic formula for .     

Self-diffusion in a non-uniform one dimensional system of point particles with collisions

Summary We generalize the results of Spitzer, Jepsen and others [1–4] on the motion of a tagged particle in a uniform one dimensional system of point particles undergoing elastic collisions to the case where there is also an external potential U(x). When U(x) is periodic or random (bounded and statistically translation invariant) then the scaled trajectory of a tagged particle converges, as A , to a Brownian motion W _D (t) with diffusion constant , where is the average density, is the mean absolute velocity and ^–1 the temperature of the system. When U(x) is itself changing on a macroscopic scale, i.e. , then the limiting process is a spatially dependent diffusion. The stochastic differential equation describing this process is now non-linear, and is particularly simple in Stratonovich form. This lends weight to the belief that heuristics are best done in that form.Dedicated to Frank Spitzer on the occasion of his 60th birthdayWork supported in part by NSF Grants No. PHY 8201708 and No. DMR 81-14726Heisenberg-fellowAlso Department of Physics     

XXZ Spin Chain with the Asymmetry Parameter Δ = −1/2: Evaluation of the Simplest Correlators

We consider a finite XXZ spin chain with periodic boundary conditions and an odd number of sites. It appears that for the special value of the asymmetry parameter = –1/2, the ground state of this system described by the Hamiltonian has the energy E ₀ = –3N/2. Although the ground state is antiferromagnetic, we can find the corresponding solution of the Bethe equations. Specifically, we can explicitly construct a trigonometric polynomial Q(u) of degree n = (N–1)/2, whose zeros are the parameters of the Bethe wave function for the ground state of the system. As is known, this polynomial satisfies the Baxter T–Q equation. This equation also has a second independent solution corresponding to the same eigenvalue of the transfer matrix T. We use this solution to find the derivative of the ground-state energy of the XXZ chain with respect to the crossing parameter . This derivative is directly related to one of the spin–spin correlators, which appears to be . In turn, this correlator gives the average number of spin strings for the ground state of the chain, . All these simple formulas fail if the number N of chain sites is even.     

Laplace approximations for sums of independent random vectors

Summary LetX _i,iN, be i.i.d.B-valued random variables whereB is a real separable Banach space, and a mappingB R. Under some conditions an asymptotic evaluation of is possible, up to a factor (1+o(1)). This also leads to a limit theorem for the appropriately normalized sums under the law transformed by the density exp .     

Remarks on Mean Convergence (Boundedness) of Partial Sums of Trigonometric Series

Fairly general conditions on the coefficients of even and odd trigonometric Fourier series under which L-convergence (boundedness) of partial sums of the series is equivalent to the relation are given.     

On Bohr’s inequality

It is established that H. Bohr’s inequality \(\sum\nolimits_{k = 0}^\infty {\left| {{{f^{\left( k \right)} \left( 0 \right)} \mathord{\left/ {\vphantom {{f^{\left( k \right)} \left( 0 \right)} {\left( {2^{{k \mathord{\left/ {\vphantom {k 2}} \right. \kern-\nulldelimiterspace} 2}} k!} \right)}}} \right. \kern-\nulldelimiterspace} {\left( {2^{{k \mathord{\left/ {\vphantom {k 2}} \right. \kern-\nulldelimiterspace} 2}} k!} \right)}}} \right| \leqslant \sqrt 2 \left\| f \right\|_\infty }\) is sharp on the class H _∞.     

Group generated by two elements of orders 2 and 4 acting on real quadratic fields

Coset diagrams for the orbit of the groupG=〈x,y∶x ²=y ⁴ =1〉 acting on real quadratic fields give some interesting information. By using these coset diagrams, we show that in the orbitpG, where , the non-square positive integern does not change its value and the real quadratic irrational numbers of the formp, wherep and its algebraic conjugate have different signs, are finite in number and that part of the coset diagram containing such numbers forms a single closed path, which is the only closed path in the orbit ofp.     

Comparison of Exact Constants in Inequalities for Derivatives of Functions Defined on the Real Axis and a Circle

We investigate the relationship between the constants K(R) and K(T), where is the exact constant in the Kolmogorov inequality, R is the real axis, T is a unit circle,

AnL p Semigroup Approach to Degenerate Parabolic Boundary Value Problems

The Crandall-Liggett theorem is applied to

Partial regularity for minimisers of certain functionals having nonquadratic growth

We prove partial regularity results for local minimisers of

Some generalized theorems onp-hyponormal operators

A bounded linear operatorT is calledp-Hyponormal if (T ^*T)^p(TT ^*)^p, 0<p1. In Aluthge [1], we studied the properties of p-hyponormal operators using the operator . In this work we consider a more general operator , and generalize some properties of p-hyponormal operators obtained in [1].     

On Rounding Error Sums Related to the Circle Problem

For a large real parameter t and 0 a b we consider sums where is the rounding error function, i.e. (z) = z - [z] - 1/2. We generalize Huxley's well known estimate by showing that holds uniformly in 0 a b . Fruther, we investigate an analogous question related to the divisor problem and show that the inequality , which (due to Huxley) holds uniformly in 0 a b , and which is in general not true for 1 a b t, is true uniformly in 0 a b .