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1.
Roberto Cignoli 《Soft Computing - A Fusion of Foundations, Methodologies and Applications》2008,12(4):315-320
Given a variety of bounded residuated lattices satisfying the Stone identity , the free algebras in over a set X of cardinality |X| are represented as weak Boolean products over the Cantor space 2|X| of a family of free algebras in an associated variety of (not necessarily bounded) residuated lattices with a bottom added. 相似文献
2.
Jialu Zhang Guojun Wang Mingdi Hu 《Soft Computing - A Fusion of Foundations, Methodologies and Applications》2008,12(6):585-591
This paper introduces the concepts of R
0 valuation, R
0 semantic, countable R
0 category , R
0 fuzzy topological category , etc. It is established in a natural way that the fuzzy topology δ and its cut topology on the set Ω
M
consisting of all R
0 valuations of an R
0 algebra M, and some properties of fuzzy topology δ and its cut topology are investigated carefully. Moreover, the representation theorem
for R
0 algebras by means of fuzzy topology is given, that is to say the category is equivalent to the category . By studying the relation between valuations and filters, the Loomis–Sikorski theorem for R
0 algebras is obtained. As an application, K-compactness of the R
0 logic is discussed. 相似文献
3.
Avram Sidi 《Journal of scientific computing》2007,31(3):391-417
Variable transformations for numerical integration have been used for improving the accuracy of the trapezoidal rule. Specifically,
one first transforms the integral via a variable transformation that maps [0,1] to itself, and then approximates the resulting transformed integral by the trapezoidal rule. In this work, we propose a new class of symmetric and nonsymmetric variable transformations which
we denote , where r and s are positive scalars assigned by the user. A simple representative of this class is . We show that, in case , or but has algebraic (endpoint) singularities at x = 0 and/or x = 1, the trapezoidal rule on the transformed integral produces exceptionally high accuracies for special values of r and s. In particular, when and we employ , the error in the approximation is (i) O(h
r
) for arbitrary r and (ii) O(h
2r
) if r is a positive odd integer at least 3, h being the integration step. We illustrate the use of these transformations and the accompanying theory with numerical examples.
相似文献
4.
5.
John P. Boyd 《Journal of scientific computing》2006,29(1):1-24
In constructing local Fourier bases and in solving differential equations with nonperiodic solutions through Fourier spectral algorithms, it is necessary to solve the Fourier Extension Problem. This is the task of extending a nonperiodic function, defined on an interval
, to a function
which is periodic on the larger interval
. We derive the asymptotic Fourier coefficients for an infinitely differentiable function which is one on an interval
, identically zero for
, and varies smoothly in between. Such smoothed “top-hat” functions are “bells” in wavelet theory. Our bell is (for x ≥ 0)
where
where
. By applying steepest descents to approximate the coefficient integrals in the limit of large degree j, we show that when the width L is fixed, the Fourier cosine coefficients a
j
of
on
are proportional to
where Λ(j) is an oscillatory factor of degree given in the text. We also show that to minimize error in a Fourier series truncated after the Nth term, the width should be chosen to increase with N as
. We derive similar asymptotics for the function f(x)=x as extended by a more sophisticated scheme with overlapping bells; this gives an even faster rate of Fourier convergence 相似文献
6.
Jiří Močkoř 《Soft Computing - A Fusion of Foundations, Methodologies and Applications》2009,13(6):591-596
We investigate interpretations of formulas ψ in a first order fuzzy logic in models which are based on objects of a category SetR(Ω) which consists of Ω-sets, i.e. sets with similarity relations with values in a complete MV-algebra Ω and with morphisms
defined as special fuzzy relations between Ω-sets. The interpretations are then morphisms in a category SetR(Ω) from some Ω-set to the object . We define homomorphisms between models in a category SetR(Ω) and we prove that if is a (special) homomorphism of models in a category SetR(Ω) then there is a relation between interpretations of a formula ψ in models .
Supported by MSM6198898701, grant 201/07/0191 of GAČR and grant 1M0572. 相似文献
7.
8.
Gerard Renardel de Lavalette Barteld Kooi Rineke Verbrugge 《Journal of Logic, Language and Information》2008,17(1):69-87
Propositional dynamic logic () is complete but not compact. As a consequence, strong completeness (the property ) requires an infinitary proof system. In this paper, we present a short proof for strong completeness of relative to an infinitary proof system containing the rule from [α; β
n
]φ
for all
, conclude
. The proof uses a universal canonical model, and it is generalized to other modal logics with infinitary proof rules, such
as epistemic knowledge with common knowledge. Also, we show that the universal canonical model of lacks the property of modal harmony, the analogue of the Truth lemma for modal operators. 相似文献
9.
Xueling Ma Jianming Zhan Yang Xu 《Soft Computing - A Fusion of Foundations, Methodologies and Applications》2007,11(11):1079-1087
In this paper, we introduce the notions of interval valued -fuzzy filters and interval valued -fuzzy Boolean (implicative) filters in R
0-algebras and investigate some of their related properties. Some characterization theorems of these generalized fuzzy filters
are derived. In particular, we prove that an interval valued fuzzy set F in R
0-algebras is an interval valued -fuzzy Boolean filter if and only if it is an interval valued -fuzzy implicative filter. 相似文献
10.
Tobias Storch 《Genetic Programming and Evolvable Machines》2006,7(2):171-193
Different objective functions characterize different problems. However, certain fitness transformations can lead to easier problems although they are still a model of the considered problem. In this article, the class of not worsening transformations for a simple population-based evolutionary algorithm (EA) is described completely. That is the class of functions that transfers easy problems in easy ones and difficult problems in difficult ones. Surprisingly, this class for the rank-based EA equals that for all black-box algorithms. The importance of the black-box algorithms' knowledge of the transformation is also pointed out. Hence, a comparison with the class of not worsening transformations for a similar EA which applies fitness-proportional selection, shows that is a proper superset of . Moreover, is a proper subset of the corresponding class for random search. Finally, the minimal and maximal classes of not worsening transformations are described completely, too. 相似文献
11.
Relations between states and maps, which are known for quantum systems in finitedimensional Hilbert spaces, are formulated
rigorously in geometrical terms with no use of coordinate (matrix) interpretation. In a tensor product realization they are
represented simply by a permutation of factors. This leads to natural generalizations for infinite-dimensional Hilbert spaces
and a simple proof of a generalized Choi Theorem. The natural framework is based on spaces of Hilbert-Schmidt operators and the corresponding tensor products of Hilbert spaces. It is proved that the corresponding isomorphisms cannot be naturally extended to compact (or bounded)
operators, nor reduced to the trace-class operators. On the other hand, it is proven that there is a natural continuous map
from trace-class operators on (with the nuclear norm) into compact operators mapping the space of all bounded operators on into trace class operators on (with the operator-norm). Also in the infinite-dimensional context, the Schmidt measure of entanglement and multipartite
generalizations of state-maps relations are considered in the paper. 相似文献
12.
Simple a posteriori error estimators for the <Emphasis Type="Italic">h</Emphasis>-version of the boundary element method 总被引:1,自引:0,他引:1
The h-h/2-strategy is one well-known technique for the a posteriori error estimation for Galerkin discretizations of energy minimization
problems. One considers to estimate the error , where is a Galerkin solution with respect to a mesh and is a Galerkin solution with respect to the mesh obtained from a uniform refinement of . This error estimator is always efficient and observed to be also reliable in practice. However, for boundary element methods,
the energy norm is non-local and thus the error estimator η does not provide information for a local mesh-refinement. We consider Symm’s integral equation of the first kind, where the
energy space is the negative-order Sobolev space . Recent localization techniques allow to replace the energy norm in this case by some weighted L
2-norm. Then, this very basic error estimation strategy is also applicable to steer an h-adaptive algorithm. Numerical experiments in 2D and 3D show that the proposed method works well in practice. A short conclusion
is concerned with other integral equations, e.g., the hypersingular case with energy space and , respectively, or a transmission problem.
Dedicated to Professor Ernst P. Stephan on the occasion of his 60th birthday. 相似文献
13.
Chuzo Iwamoto Naoki Hatayama Yoshiaki Nakashiba Kenichi Morita Katsunobu Imai 《Acta Informatica》2007,44(5):345-359
We present translational lemmas for the three standard models of parallel computation, and apply them to obtain tight hierarchy
results. It is shown that, for arbitrarily small rational constant , (i) there is a language which can be accepted by a -uniform circuit family of depth and size but not by any -uniform circuit family of depth and size , (ii) there is a language which can be accepted by a -time -space ATM with l worktapes but not by any -time -space ATM with the same l worktapes if the number of tape symbols is fixed, and (iii) there is a language which can be accepted by a -time PRAM with processors but not by any -time PRAM with processors. Here, c > 0, d ≥ 1, r
1 > 1, and r
2 ≥ 1 are arbitrary rational constants, and l ≥ 2 is an arbitrary integer.
Preliminary versions of different parts of this paper appeared in Proc. MCU 2004 (LNCS 3354) and Proc. FCT 2005 (LNCS 3623). 相似文献
14.
We consider deterministic broadcasting in radio networks whose nodes have full topological information about the network. The aim is to design a polynomial algorithm, which, given a graph G with source s, produces a fast broadcast scheme in the radio network represented by G. The problem of finding a fastest broadcast scheme for a given graph is NP-hard, hence it is only possible to get an approximation algorithm. We give a deterministic polynomial algorithm which produces a broadcast scheme of length , for every n-node graph of diameter D, thus improving a result of Gąsieniec et al. (PODC 2005) [17] and solving a problem stated there. Unless the inclusion NP BPTIME( holds, the length of a polynomially constructible deterministic broadcast scheme is optimal.A preliminary version of this paper (with a weaker result) appeared in the Proc. 7th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems (APPROX’2004), August 2004, Harvard University, Cambridge, USA, LNCS 3122, 171–182. Research of the second author supported in part by NSERC discovery grant and by the Research Chair in Distributed Computing of the Université du Québec en Outaouais. Part of this work was done during the second author’s visit at the Max-Planck-Institut für Informatik. 相似文献
15.
Thomas Vetterlein 《Soft Computing - A Fusion of Foundations, Methodologies and Applications》2006,10(11):995-1000
Let d
ν be the metric associated with a strictly positive submeasure ν on some Boolean algebra
. If d
ν is bounded from above by 1, E
ν=1−d
ν is a (fuzzy) similarity relation on
at least w.r.t. the Lstrok ukasiewicz t-norm, but possibly also w.r.t. numerous further t-norms.In this paper, we show that under certain assumptions on
and ν, we may associate with ν in a natural way a continuous t-norm w.r.t. which E
ν is a similarity relation and which, in a certain sense, is the weakest such t-norm. Up to isomorphism, every continuous t-norm arises in this way 相似文献
16.
Christopher M. Kellett Andrew R. Teel 《Mathematics of Control, Signals, and Systems (MCSS)》2007,19(3):183-205
Difference inclusions arise naturally in the study of discrete-time or sampled-data systems. We develop two novel sufficient
conditions for robustness of a stability property referred to as -stability with respect to an arbitrary measure; i.e., where a continuous positive definite function of the solutions satisfies
a class- estimate of time and the continuous positive definite function of the initial condition.
Christopher M. Kellett was supported by the Australian Research Council under Discovery Project Grant DP0771131. Andrew R.
Teel was supported by NSF grants ECS-0324679, ECS-0622253, and AFOSR grants F49620-03-1-0203 and FA9550-06-1-0134. 相似文献
17.
In statistical analysis of measurement results it is often necessary to compute the range of the population variance when we only know the intervals of possible values of the x
i
. While can be computed efficiently, the problem of computing is, in general, NP-hard. In our previous paper “Population Variance under Interval Uncertainty: A New Algorithm” (Reliable Computing
12 (4) (2006), pp. 273–280) we showed that in a practically important case we can use constraints techniques to compute in time O(n · log(n)). In this paper we provide new algorithms that compute (in all cases) and (for the above case) in linear time O(n).
Similar linear-time algorithms are described for computing the range of the entropy when we only know the intervals of possible values of probabilities p
i
.
In general, a statistical characteristic ƒ can be more complex so that even computing ƒ can take much longer than linear time.
For such ƒ, the question is how to compute the range in as few calls to ƒ as possible. We show that for convex symmetric functions ƒ, we can compute in n calls to ƒ. 相似文献
18.
Iwona Cieślik 《Acta Informatica》2008,45(2):79-91
Kierstead et al. (SIAM J Discret Math 8:485–498, 1995) have shown 1 that the competitive function of on-line coloring for
-free graphs (i.e., graphs without induced path on 5 vertices) is bounded from above by the exponential function . No nontrivial lower bound was known. In this paper we show the quadratic lower bound . More precisely, we prove that is the exact competitive function for ()-free graphs. In this paper we also prove that 2 - 1 is the competitive function of the best clique covering on-line algorithm for ()-free graphs. 相似文献
19.
20.
In this work, we consider the problem of solving , , where b
(k+1) = f(x
(k)). We show that when A is a full matrix and , where depends on the specific software and hardware setup, it is faster to solve for by explicitly evaluating the inverse matrix A
−1 rather than through the LU decomposition of A. We also show that the forward error is comparable in both methods, regardless of the condition number of A. 相似文献