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In this article we discuss three different notions of linearity: syntactical, operational and denotational. We briefly define each notion of linearity, pointing out some of the main results in the area, and describe applications o...
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In this article we discuss three different notions of linearity: syntactical, operational and denotational. We briefly define each notion of linearity, pointing out some of the main results in the area, and describe applications of linear languages and type systems.
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We prove the existence of small amplitude quasi-periodic solutions for quasi-linear and fully nonlinear forced perturbations of the linear Airy equation. For Hamiltonian or reversible nonlinearities we also prove their linear stab...
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We prove the existence of small amplitude quasi-periodic solutions for quasi-linear and fully nonlinear forced perturbations of the linear Airy equation. For Hamiltonian or reversible nonlinearities we also prove their linear stability. The key analysis concerns the reducibility of the linearized operator at an approximate solution, which provides a sharp asymptotic expansion of its eigenvalues. For quasi-linear perturbations this cannot be directly obtained by a KAM iteration. Hence we first perform a regularization procedure, which conjugates the linearized operator to an operator with constant coefficients plus a bounded remainder. These transformations are obtained by changes of variables induced by diffeomorphisms of the torus and pseudo-differential operators. At this point we implement a Nash-Moser iteration (with second order Melnikov non-resonance conditions) which completes the reduction to constant coefficients.
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In this paper we consider linear sufficiency and linear completeness in the context of estimating the estimable parametric function K'beta under the general Gauss-Markov model (y,X beta, sigma V-2). We give new characterizations f...
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In this paper we consider linear sufficiency and linear completeness in the context of estimating the estimable parametric function K'beta under the general Gauss-Markov model (y,X beta, sigma V-2). We give new characterizations for linear sufficiency, and define and characterize linear completeness in a case of estimation of K'beta. Also, we consider a predictive approach for obtaining the best linear unbiased estimator of K'beta and subsequently, we give the linear analogues of the Rao-Blackwell and Lehmann-Scheffe Theorems in the context of estimating K'beta.
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The linear Rayleigh-Taylor (RT) instability in an incompressible quantum plasma is investigated on the basis of quantum magnetohydrodynamic model. It is shown that the occurrence of RT instability depends on density-temperature in...
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The linear Rayleigh-Taylor (RT) instability in an incompressible quantum plasma is investigated on the basis of quantum magnetohydrodynamic model. It is shown that the occurrence of RT instability depends on density-temperature inhomogeneity (characteristic lengths) on one hand, and the system layer size on the other. It is also observed that the combined effects of external magnetic field, diffusivity, and quantum pressure significantly modify the dispersion properties of system in both the parallel and perpendicular directions. For any case, the imaginary and real parts of dispersion relation are presented and the possibility and conditions for the instability growth rate are discussed.
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We introduce the definition of linear relative n-width and find estimates of linear relative n-widths for linear operators preserving the intersection of cones of p-monotonicity functions.
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Generalizing a linear expression over a vector space, we call a term of an arbitrary type tau linear if its every variable occurs only once. Instead of the usual superposition of terms and of the total many-sorted clone of all ter...
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Generalizing a linear expression over a vector space, we call a term of an arbitrary type tau linear if its every variable occurs only once. Instead of the usual superposition of terms and of the total many-sorted clone of all terms in the case of linear terms, we define the partial many-sorted superposition operation and the partial many-sorted clone that satisfies the superassociative law as weak identity. The extensions of linear hypersubstitutions are weak endomorphisms of this partial clone. For a variety V of one-sorted total algebras of type tau, we define the partial many-sorted linear clone of V as the partial quotient algebra of the partial many-sorted clone of all linear terms by the set of all linear identities of V. We prove then that weak identities of this clone correspond to linear hyperidentities of V.
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In this paper a new variant of the linear cryptanalysis method for block ciphers is proposed. It is based on the existing method of multidimensional linear cryptanalysis, but offers the option of discarding a whole half-space of l...
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In this paper a new variant of the linear cryptanalysis method for block ciphers is proposed. It is based on the existing method of multidimensional linear cryptanalysis, but offers the option of discarding a whole half-space of linear approximations that do not contribute to statistical nonrandomness of the multidimensional linear cryptanalysis, and keep only the information extracted from an affine subspace for statistical inference. Also the connections of the new affine cryptanalysis with conditional linear cryptanalysis and multiple linear cryptanalysis are described and demonstrated in the context of state-of-the-art ciphers.
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A bounded linear relation T on a complex Banach space X is called a relatively regular linear relation, if TBT = T and T(0) subset of N(B) for some bounded operator B on X. This paper contains some properties, characterizations an...
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A bounded linear relation T on a complex Banach space X is called a relatively regular linear relation, if TBT = T and T(0) subset of N(B) for some bounded operator B on X. This paper contains some properties, characterizations and decomposably results of relatively regular linear relation.
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The linearization of non-linear differential equations is a significant problem in analysis and synthesis of non-linear state equations. There are many methods of linearization, that leads to linear equation, which is an approxima...
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The linearization of non-linear differential equations is a significant problem in analysis and synthesis of non-linear state equations. There are many methods of linearization, that leads to linear equation, which is an approximation of non-linear equation. Considering many different features of particular linearization methods a very important problem is how to choose a method to obtain the best results. In presented paper there are proposed criteria that make possible classifying of linearization methods. Considerations are illustrated by the example of non-linear model of electrical circuit.
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A linear k-forest of a undirected graph G is a subgraph of G whose components are paths with lengths at most k. The linear k-arboricity of G, denoted by la_k(G), is the minimum number of linear k-forests needed to partition the ed...
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A linear k-forest of a undirected graph G is a subgraph of G whose components are paths with lengths at most k. The linear k-arboricity of G, denoted by la_k(G), is the minimum number of linear k-forests needed to partition the edge set E(G) of G. In case that the lengths of paths are not restricted, we then have the linear arboricity of G, denoted by la(G). In this paper, we first prove that a conjecture by Habib and Peroche holds when G is K_n or K_(n,n) and k is not less than half the order. Secondly, I(G) = min{k|la_k(G) = la(G)} is determined for G is K_n or K_(n,n).
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