分数次积分的多线性换位子(英文)

设L是L2(Rn)上解析半群的无穷小生成算子,其积分核具有高斯界,L-α/2表示L的分数次积分算子,其中0<α<n.对自然数m,若bi(i=1,2,…,m)表示Rn上有界平均振荡函数,则由分数次积分L-α/2与bi(i=1,2,…,m)生成多线性交换子是从Lp(Rn)到Lq(Rn)是有界的,其中1<p<α/n,1/q=1/p-α/n.

有1结合环的交换性条件

证明了有1结合环的两个交换性定理,推广了 Mohd Asharf 和 Gir-i.R.D 中的结果。

One-Step Realization of SWAP Gate with Superconducting Quantum-Interference Devices and Atoms in Cavity QED

We put forward a simple scheme for one-step realization of a two-qubit SWAP gate with SQUIDs （superconducting quantum-interference devices） in cavity QED via Raman transition. In this scheme, the cavity field is only virtually excited and thus the cavity decay is suppressed. The SWAP gate is realized by using only two lower fiux states of the SQUID system and the excited state would not be excited. Therefore, the effect of decoherence caused from the levels of the SQUID system is possibly minimized. The scheme can also be used to implement the SWAP gate with atoms.

On Quantum Mechanics on Noncommutative Quantum Phase Space

In this work,we develop a general framework in which Noncommutative Quantum Mechanics (NCQM), characterized by a space noncommutativity matrix parameter θ=∈_(ji)~kθ_k and a momentum noncommutativity matrix parameter β_(ij)=∈_(ij)~kβ_k,is shown to be equivalent to Quantum Mechanics (QM) on a suitable transformed Quantum Phase Space (QPS).Imposing some constraints on this particular transformation,we firstly find that the product of the two parameters θ and β possesses a lower bound in direct relation with Heisenberg incertitude relations,and secondly that the two parameters are equivalent but with opposite sign,up to a dimension factor depending on the physical system under study.This means that noncommutativity is represented by a unique parameter which may play the role of a fundamental constant characterizing the whole NCQPS.Within our framework,we treat some physical systems on NCQPS:free particle,harmonic oscillator,system of two-charged particles,Hydrogen atom.Among the obtained results, we discover a new phenomenon which consists of a free particle on NCQPS viewed as equivalent to a harmonic oscillator with Larmor frequency depending on β,representing the same particle in presence of a magnetic field=q~(-1).For the other examples,additional correction terms depending on β appear in the expression of the energy spectrum.Finally,in the two-particle system case,we emphasize the fact that for two opposite charges noncornmutativity is effectively feeled with opposite sign.

A novel two-stage Lagrangian decomposition approach for refinery production scheduling with operational transitions in mode switching

To address large scale industrial processes,a novel Lagrangian scheme is proposed to decompose a refinery scheduling problem with operational transitions in mode switching into a production subproblem and a blending and delivery subproblem.To accelerate the convergence of Lagrange multipliers,some auxiliary constraints are added in the blending and delivery subproblem.A speed-up scheme is presented to increase the efficiency for solving the production subproblem.An initialization scheme of Lagrange multipliers and a heuristic algorithm to find feasible solutions are designed.Computational results on three cases with different lengths of time horizons and different numbers of orders show that the proposed Lagrangian scheme is effective and efficient.

HILBERT-DIRAC OPERATORS IN CLIFFORD ANALYSIS

Around the central theme of 'square root' of the Laplace operator it is shown that the classical Riesz potentials of the first and of the second kind allow for an explicit expression of so-called Hilbert-Dirac convolution operators involving natural and complex powers of the Dirac operator.

Differences and relations of objectives, constraints, and decision parameters in the optimization of individual heat exchangers and thermal systems

Performance improvement of heat exchangers and the corresponding thermal systems benefits energy conservation, which is a multi-parameters, multi-objectives and multi-levels optimization problem. However, the optimized results of heat exchangers with improper decision parameters or objectives do not contribute and even against thermal system performance improvement. After deducing the inherent overall relations between the decision parameters and designing requirements for a typical heat exchanger network and by applying the Lagrange multiplier method, several different optimization equation sets are derived, the solutions of which offer the optimal decision parameters corresponding to different specific optimization objectives, respectively. Comparison of the optimized results clarifies that it should take the whole system, rather than individual heat exchangers, into account to optimize the fluid heat capacity rates and the heat transfer areas to minimize the total heat transfer area, the total heat capacity rate or the total entropy generation rate, while increasing the heat transfer coefficients of individual heat exchangers with different given heat capacity rates benefits the system performance. Besides, different objectives result in different optimization results due to their different intentions, and thus the optimization objectives should be chosen reasonably based on practical applications, where the inherent overall physical constraints of decision parameters are necessary and essential to be built in advance.