A restriction theorem for the quaternion Heisenberg group

We prove that the restriction operator for the sublaplacian on the quaternion Heisenberg group is bounded from L^p to L^p＇ if 1 ≤ p ≤4/3. This is different from the Heisenberg group, on which the restriction operator is not bounded from Lp to Lp＇ unless p = 1.

A systematic strategy for multi-period heat exchanger network retrofit under multiple practical restrictions

A systematic strategy for retrofit of the multi-period heat exchanger network （HEN） on the basis of the multi- objective optimization is developed. In this three-stage procedure, a simplified multi-objective optimization model of the multi-period lIEN is first established and then solved to target the retrofit, aiming to minimizing the total annual cost and total annual CO2 emissions. The obtained Pareto front represents series of retrofit targets under different emission limitations, from which the most desirable one can be selected. The matching of the existing and the required heat exchangers is further implemented to finalize the retrofit, which will meet the practical retrofit requirements and matching restrictions. The application of the proposed procedure is illustrated through a case study of a HEN in a vacuum gas oil hydro-treating unit.

A restriction theorem for Grushin operators

We study the Grushin operators acting on Rx d1× Rt d2 and defined by the formula L -∑ j d1=1 xj-∑ j d1=1｜xj｜2 ∑ k d2=1 2 tk. We establish a restrictiontheorem associated with the considered operators. Our result is an analogue of the restriction theorem on the Heisenberg group obtained by D. Muller [Ann. ofMath., 1990, 131： 567-587].

Efficient Array Coding Scheme for Large-Scale Storage Systems

A family of array codes with a maximum distance separable（MDS） property, named L codes, is proposed. The greatest strength of L codes is that the number of rows（columns） in a disk array does not be restricted by the prime number, and more disks can be dynamically appended in a running storage system. L codes can tolerate at least two disk erasures and some sector loss simultaneously, and can tolerate multiple disk erasures（greater than or equal to three） under a certain condition. Because only XOR operations are needed in the process of encoding and decoding, L codes have very high computing efficiency which is roughly equivalent to X codes. Analysis shows that L codes are particularly suitable for large-scale storage systems.

Restriction Theorems on Métiver Groups Associated to Joint Functional Calculus

The authors get on Metivier groups the spectral resolution of a class of operators m（L, -Δ）, the joint functional calculus of the sub-Laplacian and Laplacian on the centre, and then give some restriction theorems together with their asymptotic estimates, asserting the mix-norm boundedness of the spectral projection operators Pμ^m for two classes of functions re（a, b） =（a^α＋b^β）^γ or （1＋a^α＋b^β）^γ,with α,β〉0,γ≠0.

OPERATOR AND MATRIX REPRESENTATION FOR THE GENERALIZED INVERSE A_(T,S)^(2)

This paper presents the matrix representation for extension of inverse of restriction of a linear operator to a subspace, on the basis of which we establish useful representations in operator and matrix form for the generalized inverse A(T,S)^(2) and give some of their applications.