Opérateurs de mise en mémoire et traduction de Gödel

Résumé En-calcul, la stratégie de réduction à gauche (appel par nom) a, comme on sait, de bonnes propriétés mathématiques; en particulier, elle termine toujours si on l'applique à un terme normalisable. Mais, avec cette stratégie, l'argument d'une fonction est recalculé à chaque utilisation.Pour éviter ce défaut, on définit la notion «d'opérateur de mise en mémoire» (pour un type de données). SiT est un opérateur de mise en mémoire, pour les entiers par exemple, on remplace l'évaluation, par réduction gauche, de (où est un entier et un -terme quelconque) par celle deT; et celle-ci revient à ramener d'abord à une forme réduite ₀, puis à appliquer à ₀. On a donc ainsi simulé «l'appel par valeur» dans la stratégie de réduction à gauche.Le théorème principal (Corollaire du Théorème 4.1) montre que, dans un 1-calcul typé du second ordre, en utilisant la traduction de Gödel de la logique classique en logique intuitionniste, on peut trouver un type (spécification) très simple pour les opérateurs de mise en mémoire. Il donne donc aussi un moyen d'obtenir ces opérateurs, à savoir de démontrer ce type dans le calcul des prédicats intuitionniste du second ordre.

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In-calculus, the strategy of leftmost reduction (call-by-name) is known to have good mathematical properties; in particular, it always terminates when applied to a normalizable term. On the other hand, with this strategy, the argument of a function is re-evaluated at each time it is used.To avoid this drawback, we define the notion of storage operator, for each data type. IfT is a storage operator for integers, for example, let us replace the evaluation, by leftmost reduction, of (where is an integer, and any-term) by the evaluation oft. Then, this computation is the same as the following: first compute up to some reduced form ₀, and then apply to ₀. So, we have simulated call-by-value evaluation within the strategy of leftmost reduction.The main theorem of the paper (Corollary of Theorem 4.1) shows that, in a second order-calculus, using Gödel's translation of classical intuitionistic logic, we can find a very simple type (or specification) for storage operators. Thus, it gives a way to get such operators, which is to prove this type in second order intuitionistic predicate calculus.

     

On some problems of interpolation by ℒ-splines

_n (D) — ,s — _n (D), _v (v=1, 2, ...,s/2) — . _m={0x ₀<x ₁<...<x _2m–1<2,x _2m =x ₀+2} , x _j +1–x _j <(4s max _v )^–1,j=0, 1, ..., 2m –1, ( ) 2- - _n,m 2m , _m . , L _q - (1q) W ( _n )={f ₂ :f ^(n–1)AC ₂ , _n (D)f 1} 2- - (s _n f), _m . , - - _n,m .

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The author expresses his gratitude to Yu. N. Subbotin for a useful discussion on the results of this paper.     

Замечания об ихтерполировании

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The trace to subsets ofR n of Besov spaces in the general case

R ⁿ. , , , F R ⁿ, F , R ⁿ R ⁿ . ^p,q (Rⁿ), >0, 1, q, — ( ) Rⁿ. , ^p,q (Rⁿ) ^F Rⁿ. , q B ^p,q (F), = – (n–)/, >0, — « », ad — F, . , . : , F=R ^d,F— « » F— R ⁿ, « », F. .

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This work has been supported in part by the Swedish Natural Science Research Council.     

О лагранжевом интерполировании с узлами в корнях многочленов сонина-маркова

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On the uniform (C, 1)-summability of Fourier series and integrability of series with respect to multiplicative orthonormal systems

H (G), f(g)H (G) , (, 1)- OHMC G. , OHMC, A. H. . , . , OHMC, lim supp _n=, , ,n .. . , 117 234 . . -      

Sharpening of Stečkin's theorem to strong approximation with exponentp

— , B _n , B p1., , p=1 , - . , , , p.     

Investigation of Haar and Franklin series in Hardy spaces

(L ¹,H) (, ) , ; H — . , , L ¹ . [13] , . , , , .     

Transferring estimates for zonal convolution operators

_p - , . Ad- .     

A generalization of Pal-type interpolation

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Жизнь и деятельность яноша Бояи

: . BOLYAI.     

Discretization with interpolating approximation

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Один Способ Замены Переменных В теории Параболических Уравнений и Его Применение

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On the divergence of spherical sums of double Fourier-Haar series

. : [0, +) [0, +) - , u+ (u) (u)=o(u lnu). [0, 1]² f , ¦f¦ L([0, 1]²), - [0, 1]².     

On the angular derivative and univalence

f . , , — , A f f(). , , f() 0 . , , ,A , f . , f() - f() . , , . (1976) ( ¦f(z)¦<1) . . (1969) ( ).     

On regular embedding integrally in R3 of metrics of class C4 of negative curvature

On the x₀y plane let there be specified a complete metric of negative curvature K by means of the line element ds²=dx²+B²(x, y) dy², and, in the strip _a={0xa, -4-bounded function B>0,K-²<0 ( and are constants). Then, the metric in strip _a is embedded in R³ by means of a surface of class C³.Translated from Matematicheskie Zametki, Vol. 14, No. 2, pp. 261–266, August, 1973.     

О предельном распределении для сумм независимых слууайных велиуин на бикомпактных коммутативных топологиуеских группах

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On term by term dyadic differentiability of Walsh series

. . . . : {ja _j },j=1,2,... — , f(x) , , f ^[1](x) — f .     

Finitely Valued f-Modules, An Addendum

In an -group M with an appropriate operator set it is shown that the -value set (M) can be embedded in the value set (M). This embedding is an isomorphism if and only if each convex -subgroup is an -subgroup. If (M) has a.c.c. and M is either representable or finitely valued, then the two value sets are identical. More generally, these results hold for two related operator sets ₁ and ₂ and the corresponding -value sets and . If R is a unital -ring, then each unital -module over R is an f-module and has exactly when R is an f-ring in which 1 is a strong order unit.     

Maximal inequalities,convexity inequality,and their duality. II

, , . . . [1], , . , , ., , L logL. , , . . . . [5]. , .