Search results for "Predicate logic"
showing 10 items of 170 documents
When a convergence of filters is measure-theoretic
2022
Abstract Convergence almost everywhere cannot be induced by a topology, and if measure is finite, it coincides with almost uniform convergence and is finer than convergence in measure, which is induced by a metrizable topology. Measures are assumed to be finite. It is proved that convergence in measure is the Urysohn modification of convergence almost everywhere, which is pseudotopological. Extensions of these convergences from sequences to arbitrary filters are discussed, and a concept of measure-theoretic convergence is introduced. A natural extension of convergence almost everywhere is neither measure-theoretic, nor finer than a natural extension of convergence in measure. A straightforw…
Ray-Space-Based Multichannel Nonnegative Matrix Factorization for Audio Source Separation
2021
Nonnegative matrix factorization (NMF) has been traditionally considered a promising approach for audio source separation. While standard NMF is only suited for single-channel mixtures, extensions to consider multi-channel data have been also proposed. Among the most popular alternatives, multichannel NMF (MNMF) and further derivations based on constrained spatial covariance models have been successfully employed to separate multi-microphone convolutive mixtures. This letter proposes a MNMF extension by considering a mixture model with Ray-Space-transformed signals, where magnitude data successfully encodes source locations as frequency-independent linear patterns. We show that the MNMF alg…
Heat Kernel Measure on Central Extension of Current Groups in any Dimension
2006
We define measures on central extension of current groups in any dimension by using infinite dimensional Brownian motion.
Response properties with explicitly correlated coupled-cluster methods using a Slater-type correlation factor and cusp conditions
2009
The recently proposed extension of the explicitly correlated coupled-cluster ansatz using cusp conditions [A. Kohn, J. Chem. Phys. 130, 104104 (2009)] is tested for suitability in the calculation of response properties. For this purpose, static and dynamic electrical properties up to ESHG hyperpolarizabilities as well as optical rotations have been computed within the CCSD(F12) model. It is shown that effectively converged correlation contributions can reliably be obtained using augmented quadruple zeta basis sets already. The ansatz is optionally equipped with an extension capable of reducing the one-electron basis set error. A further simplification of the method specific Lagrangian aimed…
Stochastic multicriteria acceptability analysis using the data envelopment model
2006
Abstract Data envelopment analysis (DEA) and stochastic multicriteria acceptability analysis (SMAA-2) are methods for evaluating alternatives based on multiple criteria. While DEA is mainly an ex-post tool used for classifying alternatives into efficient and inefficient ones, SMAA-2 is an ex-ante tool for supporting multiple criteria decision-making. Both methods use a kind of value function where the importance of criteria is modeled using weights. Unlike many other methods, neither DEA nor SMAA-2 requires decision-makers’ weights as input. Instead, these so-called non-parametric methods explore the weight space in order to identify weights favorable for each alternative. This paper introd…
Extension of the Applicability of Jäntti's Method to the Fast Calculation of Desorption Data
2000
The time for sorption measurements may be reduced substantially by measuring several values at short time intervals at the beginning of a kinetic curve and extrapolating them to the equilibrium value. The method used by Jäntti for simple adsorption processes has been extended to complicated processes described by a second-order differential equation. A simulated example is provided.
Uncertainty measures—Problems concerning additivity
2009
Additivity of an uncertainty measure on an MV-algebra has a clear meaning. If the divisibility is dropped, we come up to a so-called Girard algebra. There we discuss strong resp. weak additivity based on so-called divisible disjoint unions resp. on additivity for all sub-MV-algebras. We obtain a description of those extensions from additive measures on an MV-algebra to the canonical Girard algebra extension of pairs which are strongly additive and valuation measures. Finally, we prove the non-existence of strongly additive measure extensions, if the underlying MV-algebra is a finite chain with more than two non-trivial elements.
On certain extension theorems in the mixed Borel setting
2004
Abstract Given two sequences M 1 and M 2 of positive numbers, we give necessary and sufficient conditions under which the inclusions Λ { M 1 } ⊂ f (j) (0) j∈ N 0 : f∈ D { M 2 } [−1,1] , Λ ( M 1 ) ⊂ f (j) (0) j∈ N 0 : f∈ D ( M 2 ) [−1,1] hold, by means of explicit constructions. This answers a question raised by Chaumat and Chollet (Math. Ann. 298 (1994) 7–40). We also consider the case when [−1,1] is replaced by [−1,1]m as well as the possibility to get ultraholomorphic extensions.
Analytic Extension of Non Quasi - Analytic Whitney Jets of Beurling Type
1998
Let (Mr)r∈ℕ0 be a logarithmically convex sequence of positive numbers which verifies M0 = 1 as well as Mr ≥ 1 for every r ∈ ℕ and defines a non quasi - analytic class. Let moreover F be a closed proper subset of ℝn. Then for every function f on ℝn belonging to the non quasi - analytic (Mr)-class of Beurling type, there is an element g of the same class which is analytic on ℝ,nF and such that Dαf(x) = Dαg(x) for every α ∈ ℕn0 and x ∈ F.
Graph connectivity and monadic NP
2002
Ehrenfeucht games are a useful tool in proving that certain properties of finite structures are not expressible by formulas of a certain type. In this paper a new method is introduced that allows the extension of a local winning strategy for Duplicator, one of the two players in Ehrenfeucht games, to a global winning strategy. As an application it is shown that graph connectivity cannot be expressed by existential second-order formulas, where the second-order quantification is restricted to unary relations (monadic NP), even, in the presence of a built-in linear order. As a second application it is stated, that, on the other hand, the presence of a linear order increases the power of monadi…