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1
Content available remote New Semantical Insights Into Call-by-Value λ-Calculus
Manzonetto Giulio, Pagani Michele, Ronchi Della Rocca Simona
Fundamenta Informaticae
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2019
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Vol. 170, nr 1-3
241--256
EN
Despite the fact that call-by-value λ-calculus was defined by Plotkin in 1977, we believe that its theory of program approximation is still at the beginning. A problem that is often encountered when studying its operational semantics is that, during the reduction of a λ-term, some redexes remain stuck (waiting for a value). Recently, Carraro and Guerrieri proposed to endow this calculus with permutation rules, naturally arising in the context of linear logic proof-nets, that succeed in unblocking a certain number of such redexes. In the present paper we introduce a new class of models of call-by-value λ-calculus, arising from non-idempotent intersection type systems. Beside satisfying the usual properties as soundness and adequacy, these models validate the permutation rules mentioned above as well as some reductions obtained by contracting suitable λI-redexes. Thanks to these (perhaps unexpected) features, we are able to demonstrate that every model living in this class satisfies an Approximation Theorem with respect to a refined notion of syntactic approximant. While this kind of results often require impredicative techniques like reducibility candidates, the quantitative information carried by type derivations in our system allows us to provide a combinatorial proof.
2
Content available Some mixed matrix problems over several discrete valuation rings
Gubareni N.
Journal of Applied Mathematics and Computational Mechanics
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2013
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Vol. 12, nr 4
47--58
EN
This article presents some results about several district valuation rings with a common skew field of fractions. They are obtained from the approximation theorem for discrete valuation rings. These results give the possibility to solve basic mixed matrix problems for such rings. We present the solution of some mixed flat matrix problems over several district valuation rings with common skew field of fractions.
3
Content available remote An approximation theorem in Musielak-Orlicz-Sobolev spaces
Benkirane A., Douieb J., Ould Mohamedhen Val M.
Commentationes Mathematicae
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2011
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Vol. 51, [Z] 1
109-120
EN
In this paper we prove the uniform boundedness of the operators of convolution in the Musielak-Orlicz spaces and the density of C[...]in the Musielak-Orlicz-Sobolev spaces by assuming a condition of Log-Hölder type of continuity.
4
Content available remote Voronovskaja-type theorems and approximation theorems for a class of GBS operators
Pop O. T.
Fasciculi Mathematici
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2009
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Nr 42
91-108
EN
In this paper we will demonstrate a Voronovskajatype theorems and approximation theorems for GBS operators associated to some linear positive operators. Through parti- cular cases, we obtain statements verified by the GBS operators of Bernstein, Schurer, Durrmeyer, Kantorovich, Stancu, Bleimann- Butzer-Hahn, Mirakjan-Favard-Szász, Baskakov, Meyer-König and Zeller, Ismail-May.
5
Content available remote Approximation of functions of two variables by modified Szasz-Mirakyan operators
Walczak Z.
Fasciculi Mathematici
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2001
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Nr 31
117-128
EN
We consider certain modified Szasz-Mirakyan operators in the exponential weighted spaces of continuous functions of two variables. We prove theorems on the degree of approximation, the Voronovskaya type theorem and we study some differential properties of these operators. The similar results for functions of one variable were given in [1] and [2].
6
Content available remote Approximation of functions of several variables in exponential weighted spaces
Górzeńska M., Leśniewicz M., Prętki Cz.
Fasciculi Mathematici
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1999
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Nr 29
23-34
EN
In this note we define some operators Ln and U n of the Szasz-Mirakjan type in exponential weighted spaces of functions of several variables. In Sec. 2 we give some basic properties of these operators. The main theorems are given in Sec. 3. The similar results for functions belonging to polynomial weighted spaces are given in [3]. Some properties of these operators for functions of one variable with exponential weighted spaces are given in [4] .
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