Related papers: Necessary and sufficient conditions for differenti…
We discuss the solvability of a fairly general class of systems of perturbed Hammerstein integral equations with functional terms that depend on several parameters. The nonlinearities and the functionals are allowed to depend on the…
For homogeneous difference equation of the second order we study the analogy of Hartman-Wintner problem on asymptotic integration of fundamental system of solutions as argument tends to infinity.
We consider a disentanglement process in which local properties of an entangled state are preserved, while the entanglement between the subsystems is erased. Sufficient conditions for a perfect disentanglement (into product states and into…
In earlier work we presented necessary conditions for a fundamental triple to be that of a 3-dimensional Poincar\'e duality pair with aspherical boundary components. We provide a construction which shows that the necessary conditions are…
We present a necessary and sufficient condition for the separability of multipartite quantum states, this criterion also tells us how to write a multipartite separable state as a convex sum of separable pure states. To work out this…
A general maximum principle (necessary and sufficient conditions) for an optimal control problem governed by a stochastic differential equation driven by an infinite dimensional martingale is established. The solution of this equation takes…
Consider a generic $r$-dimensional subspace of $\mathbb{R}^d$, $r<d$, and suppose that we are only given projections of this subspace onto small subsets of the canonical coordinates. The paper establishes necessary and sufficient…
Necessary and sufficient conditions for Lipschitzness of the Lempert and Green functions are found in terms of their boundary behaviors.
Given a matrix with partitions of its rows and columns and entries from a field, we give the necessary and sufficient conditions that it has a non--singular submatrix with certain number of rows from each row partition and certain number of…
We provide a necessary and sufficient condition for separability of Gaussian states of bipartite systems of arbitrarily many modes. The condition provides an operational criterion since it can be checked by simple computation. Moreover, it…
An algebraic approach for factorizing nonlinear partial differential equations (PDEs) and systems of PDEs is provided. In the particular case of second order linear and nonlinear PDEs and systems of PDEs, necessary and sufficient conditions…
We provide necessary and sufficient conditions for separability of mixed states of n-particle systems. The conditions are formulated in terms of maps which are positive on product states of $n-1$ particles. The method of providing of the…
We study fractional variational problems of Herglotz type of variable order. Necessary optimality conditions, described by fractional differential equations depending on a combined Caputo fractional derivative of variable order, are proved.…
Necessary conditions for separability are most easily expressed in the computational basis, while sufficient conditions are most conveniently expressed in the spin basis. We use the Hadamard matrix to define the relationship between these…
Many modern numerical methods in computational science and engineering rely on derivatives of mathematical models for the phenomena under investigation. The computation of these derivatives often represents the bottleneck in terms of…
This paper provides necessary and sufficient conditions of optimality for variational problems that deal with a fractional derivative with respect to another function. Fractional Euler--Lagrange equations are established for the fundamental…
It is a meaningful issue that under what condition neighborhoods induced by a covering are equal to the covering itself. A necessary and sufficient condition for this issue has been provided by some scholars. In this paper, through a…
The extremal index is an important parameter in the characterization of extreme values of a stationary sequence. Our new estimation approach for this parameter is based on the extremal behavior under the local dependence condition…
In a recent paper (quant-ph/0102133) Chen, Liang, Li and Huang suggest a necessary and sufficient separability criterion, which is supposedly practical in judging the separability of any mixed state. In this note we briefly recapitulate…
Using formulas for certain quantities involving stable vectors, due to I. Molchanov, and in some cases utilizing the so-called divide and color model, we prove that certain families of integrals which, ostensibly, depend on a parameter are…