Improved projection-based energy weighting for spectral CT

Purpose Conventional X-ray CT scanners have limited ability to distinguish low-contrast substances.However,spectral CTs with photon counting detectors can identify photon energy and utilize spectral information,which is expected to achieve improved contrast.Energy weighting is a kind of reconstruction method for spectral CT.By assigning appropriate weight for each energy channel,the image contrast can be improved.Hence,how to determine the optimal weights is very important.Methods In this paper,we developed an improved projection-based energy weighting model for spectral CT.In this model,the object thickness of low-density materials is assumed as a constant,and the measured spectrum distribution is used to calculate the weight coefficients.Both phantom and tissue experiments were conducted in spectral CT scanner.Results The results showed that the thickness of low-density materials has little influence on the energy weight,so it can be regarded as a constant.For low-contrast phantom,the contrast-to-noise ratio was improved~32%by the proposed projectionbased weighting method.Conclusions The improved projection-based energy weighting model is effective in practice.It can increase the contrast of low-density materials.

Improved Region Energy Based Image Fusion Rule for Multi-focus Image Fusion

In this paper,we propose a novel improved region energy based image fusion rule.The original images are firstly decomposed by using the lifting scheme of wavelet transform into four sub-bands:LL,LH,HL,HH,by studying principles and characteristics of the wavelet subbands,and we put emphasis on the high frequency subbands.Thus HH,HL,LH sub-bands,which represent three direction of high frequency details,are weighted by different size of three direction Gaussian kernel,then the energy based image fusion rule is applied with a optional size of window,thus the activity level of high frequency subbands are obtained,followed by a local region matching degree in the corresponding direction and resolution,an activity level of low frequency subband is calculated,then perform consistency verification on the selected wavelet coefficients,by doing the inverse wavelet transform the fused image is obtained.The performance of the proposed novel image fusion scheme is conducted and compared with a few existing image fusion algorithm,the experimental results show that the proposed method is an effective multi-focus image fusion algorithm.

New developments in the multiscale hybrid energy density computational method

Further developments in the hybrid multiscale energy density method are proposed on the basis of our previous papers. The key points are as follows. （i） The theoretical method for the determination of the weight parameter in the energy coupling equation of transition region in multiscale model is given via constructing underdetermined equations. （ii） By applying the developed mathematical method, the weight parameters have been given and used to treat some problems in homogeneous charge density systems, which ,＇ire directly related with multiscale science. （iii） A theoretical algorithm has also been presented for treating non-homogeneous systems of charge density. The key to the theoretical computational methods is the decomposition of the electrostatic energy in the total energy of density functional theory for probing the spanning characteristic at atomic scale, layer by layer, by which the choice of chemical elements and the defect complex effect can be understood deeply. （iv） The＇numerical computational program and design have also been presented.

GLOBAL STABILITY OF TRAVELING WAVEFRONTS FOR NONLOCAL REACTION-DIFFUSION EQUATIONS WITH TIME DELAY

This paper is concerned with the stability of traveling wavefronts for a population dynamics model with time delay. Combining the weighted energy method and the comparison principle, the global exponential stability of noncritical traveling wavefronts （waves with speeds c 〉 c＊, where c=c＊ is the minimal speed） is established, when the initial perturbations around the wavefront decays to zero exponentially in space as x → -∞, but it can be allowed arbitrary large in other locations, which improves the results in[9, 18, 21].

THE STABILITY OF STATIONARY SOLUTION FOR OUTFLOW PROBLEM ON THE NAVIER-STOKES-POISSON SYSTEM

In this article, we are concerned with the stability of stationary solution for outflow problem on the Navier-Stokes-Poisson system. We obtain the unique existence and the asymptotic stability of stationary solution. Moreover, the convergence rate of solution towards stationary solution is obtained. Precisely, if an initial perturbation decays with the algebraic or the exponential rate in space, the solution converges to the corresponding stationary solution as time tends to infinity with the algebraic or the exponential rate in time. The proof is based on the weighted energy method by taking into account the effect of the self-consistent electric field on the viscous compressible fluid.

DECAY ESTIMATES OF PLANAR STATIONARY WAVES FOR DAMED WAVE EQUATIONS WITH NONLINEAR CONVECTION IN MULTI-DIMENSIONAL HALF SPACE

This paper is concerned with the initial-boundary value problem for damped wave equations with a nonlinear convection term in the multi-dimensional half space R n ＋ ： u tt u ＋ u t ＋ divf （u） = 0, t 〉 0, x = （x 1 , x ′ ） ∈ R n ＋ ：= R ＋ × R n 1 , u（0, x） = u 0 （x） → u ＋ , as x 1 → ＋ ∞ , u t （0, x） = u 1 （x）, u（t, 0, x ′ ） = u b , x ′ = （x 2 , x 3 , ··· , x n ） ∈ R n 1 . （I） For the non-degenerate case f ′ 1 （u ＋ ） 〈 0, it was shown in [10] that the above initialboundary value problem （I） admits a unique global solution u（t, x） which converges to the corresponding planar stationary wave φ（x 1 ） uniformly in x 1 ∈ R ＋ as time tends to infinity provided that the initial perturbation and/or the strength of the stationary wave are sufficiently small. And in [10] Ueda, Nakamura, and Kawashima proved the algebraic decay estimates of the tangential derivatives of the solution u（t, x） for t → ＋ ∞ by using the space-time weighted energy method initiated by Kawashima and Matsumura [5] and improved by Nishihkawa [7]. Moreover, by using the same weighted energy method, an additional algebraic convergence rate in the normal direction was obtained by assuming that the initial perturbation decays algebraically. We note, however, that the analysis in [10] relies heavily on the assumption that f ′ （u） 〈 0. The main purpose of this paper isdevoted to discussing the case of f ′ 1 （u b ） ≥ 0 and we show that similar results still hold for such a case. Our analysis is based on some delicate energy estimates.

User scheduling and power allocation for downlink multi-cell multi-carrier NOMA systems

In Non-Orthogonal Multiple Access(NOMA),the best way to fully exploit the benefits of the system is the efficient resource allocation.For the NOMA power domain,the allocation of power and spectrum require solving the mixed-integer nonlinear programming NP-hard problem.In this paper,we investigate user scheduling and power allocation in Multi-Cell Multi-Carrier NOMA(MCMC-NOMA)networks.To achieve that,we consider Weighted Sum Rate Maximization(WSRM)and Weighted Sum Energy Efficiency Maximization(WSEEM)problems.First,we tackle the problem of user scheduling for fixed power using Fractional Programming(FP),the Lagrange dual method,and the decomposition method.Then,we consider Successive Pseudo-Convex Approximation(SPCA)to deal with the WSRM problem.Finally,for the WSEEM problem,SPCA is utilized to convert the problem into separable scalar problems,which can be parallelly solved.Thus,the Dinkelbach algorithm and constraints relaxation are used to characterize the closed-form solution for power allocation.Extensive simulations have been implemented to show the efficiency of the proposed framework and its superiority over other existing schemes.

SMALL DATA SOLUTIONS OF 2-D QUASILINEAR WAVE EQUATIONS UNDER NULL CONDITIONS

For the 2-D quasilinear wave equation （δt2-△x）u＋2∑i,j=0gij（δu）δiju=0 satisfying null condition or both null conditions, a blowup or global existence result has been shown by Alinhac. In this paper, we consider a more general 2-D quasilinear wave equation （δt2-△x）u＋2∑i,j=0gij（δu）δiju=0 satisfying null conditions with small initial data and the coefficients depending simultaneously on u and δu. Through construction of an approximate solution, combined with weighted energy integral method, a quasi-global or global existence solution are established by continuous induction.

THE VLASOV-POISSON-BOLTZMANN SYSTEM NEAR MAXWELLIANS FOR LONG-RANGE INTERACTIONS

In this article, we are concerned with the construction of global smooth small-amplitude solutions to the Cauchy problem of the one species Vlasov-Poisson-Boltzmann system near Maxwellians for long-range interactions. Compared with the former result obtained by Duan and Liu in [12] for the two species model, we do not ask the initial perturbation to satisfy the neutral condition and our result covers all physical collision kernels for the full range of intermolecular repulsive potentials.

QUASI-NEUTRAL LIMIT AND THE INITIAL LAYER PROBLEM OF THE DRIFT-DIFFUSION MODEL

In this article we study quasi-neutral limit and the initial layer problem of the drift-diffusion model.Different from others studies,we consider the physical case that the mobilities of the charges are different..The quasi-neutral limit with an initial layer structure is rigorously proved by using the weighted energy method coupled with multi-scaling asymptotic expansions.

DEGENERATE BOUNDARY LAYER SOLUTIONS TO THE GENERALIZED BENJAMIN-BONAMAHONY-BURGERS EQUATION

This paper is concerned with the convergence rates of the global solutions of the generalized Benjamin-Bona-Mahony-Burgers（BBM-Burgers） equation to the corresponding degenerate boundary layer solutions in the half-space.It is shown that the convergence rate is t-（α/4） as t →∞ provided that the initial perturbation lies in H α 1 for α 〈 α（q）：= 3 ＋（2/q）,where q is the degeneracy exponent of the flux function.Our analysis is based on the space-time weighted energy method combined with a Hardy type inequality with the best possible constant introduced in [1]

Global Classical Solution and Asymptotic Behavior to a Kind of Linearly Degenerate Quasilinear Hyperbolic System

This paper is concerned with the global classical solution and the asymptotic behavior to a kind of linearly degenerate quasilinear hyperbolic system in several space variables.When the semilinear terms contain at least two waves with different propagation speeds,we can prove that the system considered admits a global classical solution by the weighted energy estimate under the small and suitable decay assumptions on the initial data.Furthermore,we can show that the solution converges to a solution of the linearized system based on the decay property of the nonlinearties.

Pointwise decaying rate of large perturbation around viscous shock for scalar viscous conservation law

In this paper, we consider the large perturbation around the viscous shock of the scalar conservation law with viscosity in one dimension case. We divide the time region into t ≤T0 and t 〉 To for a fixed constant To when applying energy method. Since To is fixed, the case t ≤ To is easy to deal with and when t 〉 To, from the decaying property of the solution, there is a priori estimate for the solution. Thus we can succeed to control the nonlinear term and get the pointwise estimate for the perturbation by the weighted energy method.

The non-cutoff Vlasov-Maxwell-Boltzmann system with weak angular singularity

We establish the global existence of small-amplitude solutions near a global Maxwellian to the Cauchy problem of the Vlasov-Maxwell-Boltzmann system for non-cutoff soft potentials with weak angular singularity. This extends the work of Duan et al.(2013), in which the case of strong angular singularity is considered, to the case of weak angular singularity.

DECAY RATES TOWARD STATIONARY WAVES OF SOLUTIONS FOR DAMPED WAVE EQUATIONS

Abstract This paper is concerned with the initial-boundary value problem for damped wave equations with a nonlinear convection term in the half space R＋{utt-txx＋ut＋f（u）x=0,t〉0,x∈R＋,u（0,x）=u0（x）→u＋,asx→＋∞,ut（0,x）=u1（x）,u（t,0）=ub.For the non-degenerate case f]（u＋） 〈 0, it is shown in [1] that the above initialboundary value problem admits a unique global solution u（t,x） which converges to the stationary wave φ（x） uniformly in x ∈ R＋ as time tends to infinity provided that the initial perturbation and/or the strength of the stationary wave are sufficiently small. Moreover, by using the space-time weighted energy method initiated by Kawashima and Matsumura [2], the convergence rates （including the algebraic convergence rate and the exponential convergence rate） of u（t, x） toward φ（x） are also obtained in [1]. We note, however, that the analysis in [1] relies heavily on the assumption that f＇（ub） 〈 0. The main purpose of this paper is devoted to discussing the case of f＇（ub）= 0 and we show that similar results still hold for such a case. Our analysis is based on some delicate energy estimates.

Stability of traveling wave fronts for nonlocal diffusive systems

This paper is concerned with stability of traveling wave fronts for nonlocal diffusive sys­tem.We adopt L^(1),-weighted,L^(1)-and L^(2)-energy estimates for the perturbation systems,and show that all solutions of the Cauchy problem for the considered systems converge exponentially to traveling wave fronts provided that the initial perturbations around the traveling wave fronts belong to a suitable weighted Sobolev spaces.