In this communication we generalize some recent results of Rump to categories enriched in a commutative quantale V. Using these results, we show that every quantale-enriched multicategory admits an injective hull. Fin...
We construct infinite families of abstract regular polytopes of type {4, p1, . . ., pn−1} from extensions of centrally symmetric spherical abstract regular n-polytopes. In addition, by applying the halving operation, ...
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A conformal mapping in a plane domain locally maps circles to circles. More generally, quasiconformal mappings locally map circles to ellipses of bounded distortion. In this paper the authors study the corresponding s...
A conformal mapping in a plane domain locally maps circles to circles. More generally, quasiconformal mappings locally map circles to ellipses of bounded distortion. In this paper the authors study the corresponding situation for solutions to Stein-Weiss systems in the nD Euclidean space. We add a more precise meaning by pointing out that a generalized holomorphic function asymptotically maps the unit sphere onto explicitly characterized ellipsoids and vice versa. Ultimately, we illustrate our approach using a typical example.
Observability problem for non-autonomous systems is considered. We deduce high-order observability conditions using the techniques developed in [8] and [9] for stabilization problem, and show that the stabilizer const...
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This brief presents a general unifying perspective on the fractional calculus. It brings together results of several recent approaches in generalizing the least action principle and the EulerLagrange equations to incl...
ISBN:
(数字)9783319147567
ISBN:
(纸本)9783319147550;9783319147567
This brief presents a general unifying perspective on the fractional calculus. It brings together results of several recent approaches in generalizing the least action principle and the EulerLagrange equations to include fractional *** dependence of Lagrangians on generalized fractional operators as well as on classical derivatives is considered along with still more general problems in which integer-order integrals are replaced by fractional integrals. General theorems are obtained for several types of variational problems for which recent results developed in the literature can be obtained as special cases. In particular, the authors offer necessary optimality conditions of EulerLagrange type for the fundamental and isoperimetric problems, transversality conditions, and Noether symmetry theorems. The existence of solutions is demonstrated under Tonelli type conditions. The results are used to prove the existence of eigenvalues and corresponding orthogonal eigenfunctions of fractional SturmLiouville *** Methods in the Fractional Calculus of Variations is a self-contained text which will be useful for graduate students wishing to learn about fractional-order systems. The detailed explanations will interest researchers with backgrounds in applied mathematics, control and optimization as well as in certain areas of physics and engineering.
In this paper we present a new class of convolutional codes that admits an efficient algebraic decoding algorithm. We study some of its properties and show that it can decode interesting sequences of errors patterns. ...
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It is well known that the presence of orthogonal decompositions for Hilbert spaces is particularly important to the study of certain boundary value problems of systems of partial differential equations. During the las...
It is well known that the presence of orthogonal decompositions for Hilbert spaces is particularly important to the study of certain boundary value problems of systems of partial differential equations. During the last years, many essential results have been obtained within the framework of real quaternion and Clifford algebras. However, according to our current knowledge central questions concerning the decompositions of the complex quaternion Hilbert space remain untouched so far. In this paper, we introduce a new orthogonal decomposition of the complex quaternion Hilbert space into its subspaces of null solutions of the corresponding Dirac operator invoking orthogonality with complex potential. The corresponding orthoprojections onto the subspaces of this decomposition are studied in detail. We then apply this decomposition to prove the existence and uniqueness, and a representation formula for the solution of related Dirichlet boundary value problems. We end up evaluating the Teodorescu transform from the estimation of its kernel function.
We prove a Noether type symmetry theorem to fractional problems of the calculus of variations with classical and Riemann-Liouville derivatives. As result, we obtain constants of motion (in the classical sense) that ar...
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ISBN:
(纸本)9781467320658
We prove a Noether type symmetry theorem to fractional problems of the calculus of variations with classical and Riemann-Liouville derivatives. As result, we obtain constants of motion (in the classical sense) that are valid along the mixed classical/fractional Euler-Lagrange extremals. Both Lagrangian and Hamiltonian versions of the Noether theorem are obtained. Finally, we extend our Noether's theorem to more general problems of optimal control with classical and Riemann-Liouville derivatives.
It is shown that the reflection 2Cat → 2Preord of the category of all 2-categories into the category of 2-preorders determines a monotone-light factorization system on 2Cat and that the light morphisms are precisely ...
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