摘要 :
We establish sufficient conditions for the completeness of a part of root vectors of one class of the second-order operator bundles corresponding to the characteristic numbers from a certain sector and prove the theorem on complet...
展开
We establish sufficient conditions for the completeness of a part of root vectors of one class of the second-order operator bundles corresponding to the characteristic numbers from a certain sector and prove the theorem on completeness of a system of elementary holomorphic solutions of the corresponding second-order homogeneous operator differential equations. We also indicate the conditions of correct and unique solvability of a boundary-value problem for the analyzed equation with linear operator in the boundary condition and estimate the norm of the operator of the intermediate derivative in the perturbed part of the equation.
收起
摘要 :
We establish sufficient conditions for the completeness of a part of root vectors of one class of the second-order operator bundles corresponding to the characteristic numbers from a certain sector and prove the theorem on complet...
展开
We establish sufficient conditions for the completeness of a part of root vectors of one class of the second-order operator bundles corresponding to the characteristic numbers from a certain sector and prove the theorem on completeness of a system of elementary holomorphic solutions of the corresponding second-order homogeneous operator differential equations. We also indicate the conditions of correct and unique solvability of a boundary-value problem for the analyzed equation with linear operator in the boundary condition and estimate the norm of the operator of the intermediate derivative in the perturbed part of the equation.
收起
摘要 :
A completeness theorem is proved involving a system of integro-differential equations with some lambda-depending boundary conditions. Also some sufficient conditions for the root functions to form a Riesz basis are established.
摘要 :
We consider the constrained vector optimization problem min(C) f(x), g(x) epsilon-K, where f : R-n -> R-m and g : R-n -> R-p are C-1,C-1 functions, and C subset of R-m and K subset of R-p are closed convex cones with nonempty inte...
展开
We consider the constrained vector optimization problem min(C) f(x), g(x) epsilon-K, where f : R-n -> R-m and g : R-n -> R-p are C-1,C-1 functions, and C subset of R-m and K subset of R-p are closed convex cones with nonempty interiors. Two type of solutions are important for our considerations, namely w-minimizers (weakly efficient points) and i-minimizers (isolated minimizers). We formulate and prove in terms of the Dini directional derivative second-order necessary conditions for a point x(0) to be a w-minimizer and second-order sufficient conditions for x(0) to be an i-minimizer of order two. We discuss the reversal of the sufficient conditions under suitable constraint qualifications of Kuhn-Tucker type. The obtained results improve the ones in Liu, Neittaanmraki, Krizek [21].
收起
摘要 :
A differential inequality technique is used to determine a lower bound on the blow-up time for solutions to the heat equation subject to a nonlinear boundary condition when blow-up of the solution does occur. In addition, a suffic...
展开
A differential inequality technique is used to determine a lower bound on the blow-up time for solutions to the heat equation subject to a nonlinear boundary condition when blow-up of the solution does occur. In addition, a sufficient condition which implies that blow-up does occur is determined.
收起
摘要 :
We obtain necessary and sufficient conditions for the solvability of the strong matrix Hamburger moment problem. We describe all solutions of the moment problem by using the fundamental results of A. V. Shtraus on generalized reso...
展开
We obtain necessary and sufficient conditions for the solvability of the strong matrix Hamburger moment problem. We describe all solutions of the moment problem by using the fundamental results of A. V. Shtraus on generalized resolvents of symmetric operators.
收起
摘要 :
We address the problem whether a given set of expectation values is compatible with the first and second moments of the generic spin operators of a system with total spin j. Those operators appear as the Stokes operator in quantum...
展开
We address the problem whether a given set of expectation values is compatible with the first and second moments of the generic spin operators of a system with total spin j. Those operators appear as the Stokes operator in quantum optics, as well as the total angular momentum operators in the atomic ensemble literature. We link this problem to a particular extension problem for bipartite qubit states; this problem is closely related to the symmetric extension problem that has recently drawn much attention in different contexts of the quantum information literature. We are able to provide operational, approximate solutions for very large spin numbers, and in fact the solution becomes exact in the limiting case of infinite spin numbers. Solutions for low spin numbers are formulated in terms of a hyperplane characterization, similar to entanglement witnesses, which can be efficiently solved with semidefinite programming.
收起
摘要 :
Molecular motors and cytoskeletal filaments work collectively most of the time under opposing forces. This opposing force may be due to cargo carried by motors or resistance coming from the cell membrane pressing against the cytos...
展开
Molecular motors and cytoskeletal filaments work collectively most of the time under opposing forces. This opposing force may be due to cargo carried by motors or resistance coming from the cell membrane pressing against the cytoskeletal filaments. Some recent studies have shown that the collective maximum force (stall force) generated by multiple cytoskeletal filaments or molecular motors may not always be just a simple sum of the stall forces of the individual filaments or motors. To understand this excess or deficit in the collective force, we study a broad class of models of both cytoskeletal filaments and molecular motors. We argue that the stall force generated by a group of filaments or motors is additive, that is, the stall force of N number of filaments (motors) is N times the stall force of one filament (motor), when the system is reversible at stall. Conversely, we show that this additive property typically does not hold true when the system is irreversible at stall. We thus present a novel and unified understanding of the existing models exhibiting such non-addivity, and generalise our arguments by developing new models that demonstrate this phenomena. We also propose a quantity similar to thermodynamic efficiency to easily predict this deviation from stall-force additivity for filament and motor collectives.
收起
摘要 :
We explore sufficient conditions for inseparability in mixed states with a globally conserved charge, such as aparticle number. We argue that even separable states may contain entanglement in fixed charge sectors, as longas the st...
展开
We explore sufficient conditions for inseparability in mixed states with a globally conserved charge, such as aparticle number. We argue that even separable states may contain entanglement in fixed charge sectors, as longas the state cannot be separated into charge-conserving components. As a witness of symmetric inseparabilitywe study the number entanglement (NE), ΔS_m, defined as the entropy change due to a subsystem's chargemeasurement. Whenever ΔS_m > 0, there exist inseparable charge sectors, having finite (logarithmic) negativity,even when the full state either is separable or has vanishing negativity. We demonstrate that the NE is not onlya witness of symmetric inseparability, but also an entanglement monotone. Finally, we study the scaling of ΔS_m in thermal one-dimensional systems combining high-temperature expansion and conformal field theory.
收起
摘要 :
The boson sampler proposed by Aaronson and Arkhipov is a nonuniversal quantum computer, which can serve as evidence against the extended Church-Turing thesis. It samples the probability distribution at the output of a linear unita...
展开
The boson sampler proposed by Aaronson and Arkhipov is a nonuniversal quantum computer, which can serve as evidence against the extended Church-Turing thesis. It samples the probability distribution at the output of a linear unitary optical network with indistinguishable single photons at the input. Four experimental groups have already tested their small-scale prototypes with up to four photons. A boson sampler with a few dozens of single photons is believed to be hard to simulate on a classical computer. For scalability of a realistic boson sampler with current technology it is necessary to know the effect of the photon mode mismatch on its operation. Here a nondeterministic model of the boson sampler is analyzed, which employs partially indistinguishable single photons emitted by identical sources. A sufficient condition on the average mutual fidelity of the single photons is found, which guarantees that the realistic boson sampler outperforms the classical computer. Moreover, the boson-sampler computer with partially indistinguishable single photons is scalable and has more power than classical computers when the single-photon mode mismatch 1 - scales as O(N~(-3/2)) with the total number of photons N.
收起
原文获取