Algebre senza base finita (II)

Sunto. Si finiscono di passare in rassegna i teoremi più importanti della teoria delle algebre a base finita, quale è esposta dalloScorza, lasciando cadere l'ipotesi della limitazione della base. Dei teoremi che restano validi si dà la dimostrazione solo quand'essa è necessariamente diversa da quella delloScorza: nel caso di teoremi la cui dimostrazione verte essenzialmente nella finitezza della base sono dati esempi di algebre per cui essi cadono in difetto. Estratto dalla tesi di laurea (Pisa, Scuola Normale Superiore, 1942).     

Algebre senza base finita (I)

Sunto. Si tratta assiomaticamente dei sistemi lineari sopra un corpo qualsiasi, con particolare riguardo alla separazione delle proprietà derivanti dal postulato della scelta. Estratto dalla tesi di laurea (Pisa, Scuola Normale Superiore, 1942).     

Spazi\mathfrak{L}^{(p,\theta )} (\Omega , \delta ) e loro proprietà(Ω, δ) e loro proprietà

Sommario Si definiscono gli spazi , dove δ è una metrica inℝ ⁿ non necessariamente euclidea, e si generalizzano dei risultati di Campanato e Meyers relativi al caso della metrica euclidea. Lavoro eseguito nell'ambito del Gruppo di RicercaC del Comitato Nazionale per la matematica del C.N.R.     

(e)-convergence and related problem

We answer negatively to a question of Zorboska (2003) [13], which is concerned to the boundary behavior of Berezin symbols of Bergman space operators. We also introduce the notions of (e)-summability of sequences and series of complex numbers, and study some of their properties. As a corollary, we obtain the classical Abel theorems of summability theory.     

半群上的Green(e)-关系

半群上的Green(e)-关系是半群上通常Green's关系的一种推广.借助半群的左(右)S-系及半群的双系深入研究了Green(e)-关系的代数性质,证明了每个H(e)-类R(e)e∩L(e)f为一个强无挠的(H(e)e,H(e)f)-双系,其中e,f为幂等元,并给出了每个含幂等元的D(e)-类的代数结构.     

Tauberian-type theorem for (e)-convergent sequences

We prove a Tauberian-type theorem for (e)-convergent sequences, which were introduced by the author in Karaev (2010) [4]. Our proof is based on the Berezin symbols technique of operator theory in the reproducing kernel Hilbert space.     

Free Completely J~(e)-simple Semigroups

A semigroup is called completely J~((e))-simple if it is isomorphic to some Rees matrix semigroup over a left cancellative monoid and each entry of whose sandwich matrix is in the group of units of the left cancellative monoid.It is proved that completely J~((e))-simple semigroups form a quasivarr ity.Moreover,the construction of free completely J~((e))-simple semigroups is given.It is found that a free completely J~((e))-simple semigroup is just a free completely J~*-simple semigroup and also a full subsemigroup of some completely simple semigroups.     

带形状参数的T-Bézier曲线

给出了n阶带形状参数的三角多项式T-Bézier基函数.由带形状参数的三角多项式T-Bézier基组成的带形状参数的T-Bézier曲线,可通过改变形状参数的取值而调整曲线形状,随着形状参数的增加,带形状参数的T-Bézier曲线将接近于控制多边形,并且可以精确表示圆、螺旋线等曲线.阶数的升高,形状参数的取值范围将扩大.     

Canonical models of arithmetic (1; e)-curves

The Fuchsian groups of signature (1; e) are the simplest class of Fuchsian groups for which the calculation of the corresponding quotient of the upper half plane presents a challenge. This paper considers the finite list of arithmetic (1; e)-groups. We define canonical models for the associated quotients by relating these to genus 1 Shimura curves. These models are then calculated by applying results on the ${\mathfrak{p}}$ -adic uniformization of Shimura curves and Hilbert modular forms.     

Subregular Spreads of PG (5, 2e)

The theory of subregular spreads of PG(3,q) was developed by R.H. Bruck (1969, in “Combinatorial Mathematics and Its Applications,” Chap. 27, pp. 426–514. Univ. of North Carolina Press, Chapel Hill). An extension of these results was provided to the higher-dimensional case by the author (1998, Finite Fields Appl.4, 362–380); however, examples of such spreads were only constructed in PG(5, q) for q odd. In this paper, we give a construction of subregular spreads for PG(5, q), where q is even.     

多元矩阵Pad(e)逼近的代数性质

本文证明多元矩阵Pade逼近与一元矩阵Pade逼近一样具有函数值变换下的不变性.     

Equazioni quasi ellittiche e spaziL p, θ (ω, δ) (I)

Summary Regularity theorems inL ^{2, θ} (ω, δ) spaces are proved for weak solutions of quasielliptic differential equations. In particular, regularization results are obtained in the class of holder continuous functions (with respect to a suitable metric related to the operator). As a consequence, we obtain results and estimates in L^p andL ^{p, θ} spaces for the solution of the Dirichlet problem.

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Lavoro eseguito nell’ambito del Gruppo di Ricerca n^o 46 del Comitato per la Matematica del C N.R.     

On antipodal Euclidean tight (2e + 1)-designs

Neumaier and Seidel (1988) generalized the concept of spherical designs and defined Euclidean designs in ℝ ⁿ . For an integer t, a finite subset X of ℝ ⁿ given together with a weight function w is a Euclidean t-design if holds for any polynomial f(x) of deg(f)≤ t, where {S _i , 1≤ i ≤ p} is the set of all the concentric spheres centered at the origin that intersect with X, X _i = X∩ S _i , and w:X→ ℝ_{> 0}. (The case of X⊂ S ⁿ⁻¹ with w≡ 1 on X corresponds to a spherical t-design.) In this paper we study antipodal Euclidean (2e+1)-designs. We give some new examples of antipodal Euclidean tight 5-designs. We also give the classification of all antipodal Euclidean tight 3-designs, the classification of antipodal Euclidean tight 5-designs supported by 2 concentric spheres.