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1.
Disturbing Fuzzy Propositional Logic and its Operators 总被引:1,自引:0,他引:1
Xin Liu 《Fuzzy Optimization and Decision Making》2006,5(2):163-175
In this paper, the concept of disturbing fuzzy propositional logic is introduced, and the operators of disturbing fuzzy propositions
is defined. Then the 1-dimensional truth value of fuzzy logic operators is extended to be two-dimensional operators, which
include disturbing fuzzy negation operators, implication operators, “and” and “or” operators and continuous operators. The
properties of these logic operators are studied. 相似文献
2.
In this paper, by discovering a new fact that the Lebesgue boundedness of a class of pseudo- differential operators implies the Sobolev boundedness of another related class of pseudo-differential operators, the authors establish the boundedness of pseudo-differential operators with symbols in Sρ,δ^m on Sobolev spaces, where ∈ R, ρ≤ 1 and δ≤ 1. As its applications, the boundedness of commutators generated by pseudo-differential operators on Sobolev and Bessel potential spaces is deduced. Moreover, the boundedness of pseudo-differential operators on Lipschitz spaces is also obtained. 相似文献
3.
Very recently Deo, in the paper “Simultaneous approximation by Lupas operators with weighted function of Szasz operators”
[J. Inequal. Pure Appl. Math., 5, No. 4 (2004)] claimed to introduce the integral modifications of Lupas operators. These operators were first introduced
in 1993 by Gupta and Srivastava. They estimated the simultaneous approximation for these operators and called them Baskakov-Szasz
operators. There are several misprints in the paper by Deo. This motivated us to perform subsequent investigations in this
direction. We extend the study and estimate a saturation result in simultaneous approximation for the linear combinations
of these summation-integral-type operators.
Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 8, pp. 1135–1139, August, 2007. 相似文献
4.
Aim of this paper is to provide new examples of H?rmander operators L{\mathcal{L}} to which a Lie group structure can be attached making L{\mathcal{L}} left invariant. Our class of examples contains several subclasses of operators appearing in literature and arising both in
theoretical and in applied fields: evolution Kolmogorov operators, degenerate Ornstein–Uhlenbeck operators, Mumford and Fokker–Planck
operators, Ornstein–Uhlenbeck operators with time-dependent periodic coefficients. Our examples basically come from exponential
of matrices, as well as from linear constant-coefficient ODE’s, in
\mathbbR{\mathbb{R}} or in
\mathbbC{\mathbb{C}} . Furthermore, we describe how these groups can be combined together to obtain new structures and new operators, also having
an interest in the applied field. 相似文献
5.
In this paper we consider operators acting on a subspace ℳ of the space L
2 (ℝm; ℂm) of square integrable functions and, in particular, Clifford differential operators with polynomial coefficients. The subspace
ℳ is defined as the orthogonal sum of spaces ℳs,k of specific Clifford basis functions of L
2(ℝm; ℂm).
Every Clifford endomorphism of ℳ can be decomposed into the so-called Clifford-Hermite-monogenic operators. These Clifford-Hermite-monogenic
operators are characterized in terms of commutation relations and they transform a space ℳs,k into a similar space ℳs′,k′. Hence, once the Clifford-Hermite-monogenic decomposition of an operator is obtained, its action on the space ℳ is known.
Furthermore, the monogenic decomposition of some important Clifford differential operators with polynomial coefficients is
studied in detail. 相似文献
6.
T. A. Bouma 《Advances in Applied Clifford Algebras》2001,11(2):231-238
Given an automorphism and an anti-automorphism of a semigroup of a Geometric Algebra, then for each element of the semigroup
a (generalized) projection operator exists that is defined on the entire Geometric Algebra. A single fundamental theorem holds
for all (generalized) projection operators. This theorem makes previous projection operator formulas [2] equivalent to each
other. The class of generalized projection operators includes the familiar subspace projection operation by implementing the
automorphism ‘grade involution’ and the anti-automorphism ‘inverse’ on the semigroup of invertible versors. This class of
projection operators is studied in some detail as the natural generalization of the subspace projection operators. Other generalized
projection operators include projections ontoany invertible element, or a weighted projection ontoany element. This last projection operator even implies a possible projection operator for the zero element. 相似文献
7.
J. Sakalauskaitė 《Lithuanian Mathematical Journal》2007,47(3):266-276
In this paper, we consider branching time temporal logic CT L with epistemic modalities for knowledge (belief) and with awareness operators. These logics involve the discrete-time linear
temporal logic operators “next” and “until” with the branching temporal logic operator “on all paths”. In addition, the temporal
logic of knowledge (belief) contains an indexed set of unary modal operators “agent i knows” (“agent i believes”). In a language of these logics, there are awareness operators. For these logics, we present sequent calculi with
a restricted cut rule. Thus, we get proof systems where proof-search becomes decidable. The soundness and completeness for
these calculi are proved.
Published in Lietuvos Matematikos Rinkinys, Vol. 47, No. 3, pp. 328–340, July–September, 2007. 相似文献
8.
A local lifting theorem for bounded operators that intertwine a pair of jointly subnormal families of unbounded operators
is proved. Each family in question is assumed to be composed of operators defined on a common invariant domain consisting
of “joint” analytic vectors. This result can be viewed as a generalization of the local lifting theorem proved by Sebestyén,
Thomson and the present authors for pairs of bounded subnormal operators. 相似文献
9.
10.
Ivan Chajda 《Central European Journal of Mathematics》2011,9(5):1185-1191
We introduce two unary operators G and H on a relatively pseudocomplemented lattice which form an algebraic axiomatization of the tense quantifiers “it is always
going to be the case that” and “it has always been the case that”. Their axiomatization is an extended version for the classical
logic and it is in accordance with these operators on many-valued Łukasiewicz logic. Finally, we get a general construction
of these tense operators on complete relatively pseudocomplemented lattice which is a power lattice via the so-called frame. 相似文献
11.
For a domain
with singular points on the boundary, we consider a C
*
-algebra
of operators acting in the weighted space
. It is generated by the operators of multiplication by continuous functions on
and the operators
where σ is a homogeneous function. We show that the techniques of limit operators apply to define a symbol algebra for
. When combined with the local principle, this leads to describing the Fredholm operators in
.
Received: 21 December 2000 相似文献
12.
V. P. Maslov 《Theoretical and Mathematical Physics》2000,125(2):1552-1567
We develop the theory of averaging the operators in a Fock space, introduced in our previous papers. We find the algebra of
mean operators. We introduce the quantum entropy and quantum free energy using the function f(z)=zlog(z) of the mean unit
operator (the “measure” of mean operators). Such a “quantum thermodynamics” determines the temperature dependence of the critical
speed (“the Landau criterion”) and the temperature distribution at which the speed of a superfluid system is nonzero even
at zero temperature. We generalize the consideration to the case where sparsely distributed bosons form clusters.
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 125, No. 2, pp. 297–314, November, 2000. 相似文献
13.
A. K. Kitover 《Journal of Mathematical Sciences》1981,16(3):1184-1186
One considers “weighted translation” operators in ideal Banach spaces. It is proved that if the translation is aperiodic (the
set of periodic points has measure zero), then the spectrum of such an operator is rotationinvariant. This result can be extended
(under certain additional restrictions) to “weighted translation” operators acting in regular subspaces of ideal spaces, in
particular, to operators in Hardy spaces.
In this note we prove the rotation-invariance of the spectrum of aperiodic operators of “weighted translation” in ideal spaces
and uniform B-algebras.
Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR,
Vol. 65, pp. 196–198, 1976. 相似文献
14.
S. P. Khekalo 《Journal of Mathematical Sciences》2007,147(1):6543-6549
As is known, in mathematical physics there are differential operators with constant coefficients whose fundamental solutions
can be constructed explicitly; such operators are said to be exactly solvable. In this paper, the problem of adding lower-order
terms with variable coefficients to exactly solvable operators in such a way that the new operators (deformations) admit constructing
fundamental solutions in explicit form is posed. This problem is directly related to Hadamard’s problem of describing differential
operators satisfying the Huygens’ principle. On the basis of the Fourier method of separation of variables and the method
of gauge-equivalent operators, an effective method for finding exactly solvable deformations depending on one variable is
constructed. An application of such deformations to constructing Huygens’ differential operators associated with the cone
of real symmetric positive-definite matrices is suggested.
__________
Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 38, Suzdal
Conference-2004, Part 3, 2006. 相似文献
15.
Raphaël Ponge 《Journal d'Analyse Mathématique》2010,110(1):1-30
The aim of this paper is to show that various known characterizations of traces on classical pseudodifferential operators
can actually be obtained by very elementary considerations on pseudodifferential operators, using only basic properties of
these operators. Thereby, we give a unified treatment of the determinations of the space of traces (i) on ΨDOs of non-integer
order or of regular parity-class, (ii) on integer order ΨDOs, (iii) on ΨDOs of non-positive orders in dimension ≥ 2, and (iv)
on ΨDOs of non-positive orders in dimension 1. 相似文献
16.
Miroslav Engli 《Arkiv f?r Matematik》1992,30(1):227-243
In this paper it is shown that Toeplitz operators on Bergman space form a dense subset of the space of all bounded linear
operators, in the strong operator topology, and that their norm closure contains all compact operators. Further, theC
*-algebra generated by them does not contain all bounded operators, since all Toeplitz operators belong to the essential commutant
of certain shift. The result holds in Bergman spacesA
2(Ω) for a wide class of plane domains Ω⊂C, and in Fock spacesA
2(C
N),N≧1. 相似文献
17.
S. Albeverio A. Yu. Khrennikov V.M. Shelkovich 《Journal of Fourier Analysis and Applications》2006,12(4):393-425
In this article the p-adic Lizorkin spaces of test functions and distributions are introduced. Multi-dimensional Vladimirov’s
and Taibleson’s fractional operators, and a class of p-adic pseudo-differential operators are studied on these spaces. Since
the p-adic Lizorkin spaces are invariant under these operators, they can play a key role in considerations related to fractional
operator problems. Solutions of pseudo-differential equations are also constructed. Some problems of spectral analysis of
pseudo-differential operators are studied. p-Adic multidimensional Tauberian theorems connected with these pseudo-differential
operators for the Lizorkin distributions are proved. 相似文献
18.
Ioana Ghenciu 《Monatshefte für Mathematik》2020,191(4):719-733
In this paper we introduce p-Dunford–Pettis completely continuous operators and study Banach spaces with the wp-Dunford–Pettis relative compact property (wp-DPrcP). We study the behaviour of p-Dunford–Pettis completely operators on spaces with this property. We give sufficient conditions for spaces of operators to have the wp-DPrcP. 相似文献
19.
Oliver Nowak 《Central European Journal of Mathematics》2010,8(5):890-907
Korovkin-type approximation theory usually deals with convergence analysis for sequences of positive operators. In this work
we present qualitative Korovkin-type convergence results for a class of sequences of non-positive operators, more precisely
regular operators with vanishing negative parts under a limiting process. Sequences of that type are called sequences of almost
positive linear operators and have not been studied before in the context of Korovkin-type approximation theory. As an example
we show that operators related to the multivariate scattered data interpolation technique moving least squares interpolation originally due to Lancaster and Šalkauskas [Surfaces generated by moving least squares methods, Math. Comp., 1981, 37, 141–158]
give rise to such sequences. This work also generalizes Korovkin-type results regarding Shepard interpolation [Korovkin-type
convergence results for multivariate Shepard formulae, Rev. Anal. Numér. Théor. Approx., 2009, 38, 170–176] due to the author.
Moreover, this work establishes connections and differences between the concepts of sequences of almost positive linear operators
and sequences of quasi-positive or convexity-monotone linear operators introduced and studied by Campiti in [Convexity-monotone
operators in Korovkin theory, Rend. Circ. Mat. Palermo (2) Suppl., 1993, 33, 229–238]. 相似文献
20.
Dynamic effect algebras 总被引:1,自引:0,他引:1
We introduce the so-called tense operators in lattice effect algebras. Tense operators express the quantifiers “it is always
going to be the case that” and “it has always been the case that” and hence enable us to express the dimension of time in
the logic of quantum mechanics. We present an axiomatization of these tense operators and prove that every lattice effect
algebra whose underlying lattice is complete can be equipped with tense operators. Such an effect algebra is called dynamic
since it reflects changes of quantum events from past to future. 相似文献