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81.
Philip A. Ernst Wilfrid S. Kendall Gareth O. Roberts Jeffrey S. Rosenthal 《Stochastic Processes and their Applications》2019,129(2):355-380
Classical coupling constructions arrange for copies of the same Markov process started at two different initial states to become equal as soon as possible. In this paper, we consider an alternative coupling framework in which one seeks to arrange for two different Markov (or other stochastic) processes to remain equal for as long as possible, when started in the same state. We refer to this “un-coupling” or “maximal agreement” construction as MEXIT, standing for “maximal exit”. After highlighting the importance of un-coupling arguments in a few key statistical and probabilistic settings, we develop an explicit MEXIT construction for stochastic processes in discrete time with countable state-space. This construction is generalized to random processes on general state-space running in continuous time, and then exemplified by discussion of MEXIT for Brownian motions with two different constant drifts. 相似文献
82.
Wolfgang Bock Vyacheslav Futorny Mikhail Neklyudov 《Journal of Pure and Applied Algebra》2021,225(3):106535
A realization by linear vector fields is constructed for any Lie algebra which admits a biorthogonal system and for its any suitable representation. The embedding into Lie algebras of linear vector fields is in analogue to the classical Jordan—Schwinger map. A number of examples of such Lie algebras of linear vector fields is computed. In particular, we obtain examples of the twisted Heisenberg-Virasoro Lie algebra and the Schrödinger-Virasoro Lie algebras among others. More generally, we construct an embedding of an arbitrary locally convex topological algebra into the Cuntz algebra. 相似文献
83.
84.
We illustrate the usefulness of Jordan-algebraic techniques for nonconvex optimization by considering a potential-reduction
algorithm for a nonconvex quadratic function over the domain obtained as the intersection of a symmetric cone with an affine
subspace. 相似文献
85.
Feng Cheng Chang 《Applied mathematics and computation》2005,160(3):402
An analytical function f(A) of an arbitrary n×n constant matrix A is determined and expressed by the “fundamental formula”, the linear combination of constituent matrices. The constituent matrices Zkh, which depend on A but not on the function f(s), are computed from the given matrix A, that may have repeated eigenvalues. The associated companion matrix C and Jordan matrix J are then expressed when all the eigenvalues with multiplicities are known. Several other related matrices, such as Vandermonde matrix V, modal matrix W, Krylov matrix K and their inverses, are also derived and depicted as in a 2-D or 3-D mapping diagram. The constituent matrices Zkh of A are thus obtained by these matrices through similarity matrix transformations. Alternatively, efficient and direct approaches for Zkh can be found by the linear combination of matrices, that may be further simplified by writing them in “super column matrix” forms. Finally, a typical example is provided to show the merit of several approaches for the constituent matrices of a given matrix A. 相似文献
86.
We show that under perturbations by a rank-one typical operator, a fixed eigenvalue loses one Jordan block of maximal order, while the orders of the other Jordan blocks remain unchanged. We construct the first-order perturbation theory for the new eigenvalues and the zero-order approximations to the corresponding eigenvectors. 相似文献
87.
AN ALGORITHM FOR JORDAN CANONICAL FORM OF A QUATERNION MATRIX 总被引:2,自引:0,他引:2
In this paper, we first introduce a concept of companion vector, and study the Jordan canonical forms of quaternion matrices by using the methods of complex rep resentation and companion vector, not only give out a practical algorithm for Jordan canonical form J of a quaternion matrix A, but also provide a practical algorithm for corresponding nonsingular matrix P with P-1AP = J. 相似文献
88.
We study properties of Jordan representations ofH-dissipative operators in a finite-dimensional indefiniteH-space. An algebraic proof is given of the fact that such operators always have maximal semidefinite invariant subspaces.
Translated fromMatematicheskie Zametki, Vol. 63, No. 2, pp. 163–169, February, 1998.
The authors axe grateful to Professor A. A. Shkalikov for useful discussions.
The research of the first author was supported by INTAS under grant No. 93-0249. The research of the second author was supported
by the International Science Foundation and the Russian Government under grant No. NZP300. 相似文献
89.
Yuuki Hirayama Kentaro Yamaguchi Shigeru Sakamoto Michiko Iwamura 《Tetrahedron letters》2005,46(6):1027-1030
A new AB2 type building block for synthesis of dendritic compounds is made starting from Michael addition of 2 equiv of 3-hydroxyacetophenone to acrylate, followed by decarboxylation and deprotection of either carboxyl or hydroxyl protecting groups. [G1]-[G4] dendrons and [G2] dendrimer were synthesized by the reiterative [hydrogenolysis then DCC/DPTS coupling] sequence using a combination of convergent and divergent growth methods. 相似文献
90.
Bo Kågström 《BIT Numerical Mathematics》1977,17(1):39-57
Some new types of bounds and perturbation bounds, based on the Jordan normal form, for the matrix exponential are derived. These bounds are compared to known bounds, both theoretically and by numerical examples. Some recent results on the matrix exponential and the logarithmic norm are also included. 相似文献