THREE KINDS OF DENTABILITIES IN BANACH SPACES AND THEIR APPLICATIONS

In this paper,we study some dentabilities in Banach spaces which are closely related to the famous Radon-Nikodym property.We introduce the concepts of the weak^(*)-weak denting point and the weak^(*)-weak^(*)denting point of a set.These are the generalizations of the weak^(*)denting point of a set in a dual Banach space.By use of the weak^(*)-weak denting point,we characterize the very smooth space,the point of weak^(*)-weak continuity,and the extreme point of a unit ball in a dual Banach space.Meanwhile,we also characterize an approximatively weak compact Chebyshev set in dual Banach spaces.Moreover,we define the nearly weak dentability in Banach spaces,which is a generalization of near dentability.We prove the necessary and sufficient conditions of the reflexivity by nearly weak dentability.We also obtain that nearly weak dentability is equivalent to both the approximatively weak compactness of Banach spaces and the w-strong proximinality of every closed convex subset of Banach spaces.

Influence of element substitutions on poisoning behavior of ZrV_(2)alloy:theoretical and experimental investigations

A ZrV_(2)alloy is typically susceptible to poisoning by impurity gases,which causes a considerable reduction in the hydrogen storage properties of the alloy.In this study,the adsorption characteristics of oxygen on ZrV_(2)surfaces doped with Hf,Ti,and Pd are investigated,and the effect of oxygen on the hydrogen storage performance of the alloy was discussed.Subsequently,the adsorption energy,bond-length change,density of states,and differential charge density of the alloy before and after doping are analyzed using the first-principles method.The theoretical results show that Ti doping has a limited effect on the adsorption of oxygen atoms on the ZrV_(2)surface,whereas Hf doping decreases the adsorption energy of oxygen on the ZrV_(2)surface.Oxygen atoms are more difficult to adsorb at most adsorption sites on Pd-substituting surfaces,which indicates that Pd has the best anti-poisoning properties,followed by Hf.The analysis of the differential charge density and partial density of states show that the electron interaction between the oxygen atom and surface atom of the alloys is weakened,and the total energy is reduced after Hf and Pd doping.Based on theoretical calculations,the hydrogen absorption kinetics of ZrV_(2),Zr_(0.9)Hf_(0.1)V_(2),and Zr(V_(0.9)Pd_(0.1))_(2) alloys are studied in a hydrogen-oxygen mixture of 0.5 vol%O_(2) at 25℃.The experimental results show that the hydrogen storage capacities of ZrV_(2),Zr_(0.9)Hf_(0.1)V_(2),and Zr(V_(0.9)Pd_(0.1))_(2) decrease to 19%,69%,and 80%of their original values,respectively.The order of alloy resistance to 0.5 vol%O_(2) poisoning is Zr(V_(0.9)Pd_(0.1))_(2)>Zr_(0.9)Hf_(0.1)V_(2)>ZrV_(2).Pd retains its original hydrogen absorption performance to a greater extent than undoped surfaces,and it has the strongest resistance to poisoning,which is consistent with previous theoretical calculations.

Effects of cross-Kerr coupling on transmission spectrum of double-cavity optomechanical system

We theoretically study the transmission spectrum of the cavity field in a double-cavity optomechanical system with cross-Kerr(CK) effect. The system consists of two tunneling coupling optomechanical cavities with a mechanical resonator as a coupling interface. By doping CK medium into the mechanical resonator, CK couplings between the cavity fields and the mechanical resonator are introduced. We investigate the effects of CK coupling strength on the transmission spectrum of the cavity field, including the transmission rate, nonreciprocity and four-wave mixing(FWM). We find that the transmission spectrum of the probe field can show two obvious transparent windows, which can be widened by increasing the CK coupling strength. For the transmission between the two cavity fields, the perfect nonreciprocity and reciprocity are present and modulated by CK coupling and phase difference between two effective optomechanical couplings. In addition, the effects of the optomechanical and CK couplings on FWM show that the single peak of FWM is split into three symmetrical peaks due to the introduction of the CK effect.

Quantum coherence and correlation dynamics of two-qubit system in spin bath environment

The quantum entanglement,discord,and coherence dynamics of two spins in the model of a spin coupled to a spin bath through an intermediate spin are studied.The effects of the important physical parameters including the coupling strength of two spins,the interaction strength between the intermediate spin and the spin bath,the number of bath spins and the temperature of the system on quantum coherence and correlation dynamics are discussed in different cases.The frozen quantum discord can be observed whereas coherence does not when the initial state is the Bell-diagonal state.At finite temperature,we find that coherence is more robust than quantum discord,which is better than entanglement,in terms of resisting the influence of environment.Therefore,quantum coherence is more tenacious than quantum correlation as an important resource.

SOME METRIC AND TOPOLOGICAL PROPERTIES OF NEARLY STRONGLY AND NEARLY VERY CONVEX SPACES

We obtain characterizations of nearly strong convexity and nearly very convexity by using the dual concept of S and WS points,related to the so-called Rolewicz’s property(α).We give a characterization of those points in terms of continuity properties of the identity mapping.The connection between these two geometric properties is established,and finally an application to approximative compactness is given.

The dying accretion and jet in a powerful radio galaxy of Hercules A

Hercules A(Her A)is one of a rare class of dying and transition-type objects,which has a pair of giant,powerful radio lobes and a weak radio core.We reduce and analyze the radio data of Her A that were observed by the Expanded Very Large Array(EVLA)during 2010-2011 at C band.The intensity distribution is very smooth along the edge of the lobe front and the intensity also sharply decreases at the edge,which supports that magnetic fields may play an important role in radio lobes.The spectrum of the weak core is very steep and the core flux becomes weaker by about ten percent when compared to what was observed twenty years ago,which suggest that the central engine is still dying quickly.Her A deviates a lot from the relation between[O III]luminosity and low-frequency 178 MHz luminosity(LO III-L178 MHz)as defined by other FR I/II sources.However,when only radio core emission is considered,it roughly follows an LO III-L178 MHzcorrelation.This result supports that the black-hole accretion and large-scale jet in Her A did not evolve simultaneously,and indicates that although the large-scale jet is still powerful,the accretion and inner jet have changed into an inactive state.Based on the estimated Bondi accretion rate,we model the spectrum of Her A with a radiatively inefficient accretion flow and jet model.

A NOTE IN APPROXIMATIVE COMPACTNESS AND MIDPOINT LOCALLY K-UNIFORM ROTUNDITY IN BANACH SPACES

In this article, we prove the following results： （1） A Banach space X is weak midpoint locally k-uniformly rotund if and only if every closed ball of X is an approximatively weakly compact k-Chebyshev set; （2） A Banach space X is midpoint locally k-uniformly rotund if and only if every closed ball of X is an approximatively compact k-Chebyshev set.

SOME EQUIVALENT CONDITIONS OF PROXIMINALITY IN NONREFLEXIVE BANACH SPACES

In this paper,we discuss the relation between τ-strongly Chebyshev,approximatively τ-compact k-Chebyshev,approximatively τ-compact,τ-strongly proximinal and proximinal sets,where τ is the norm or the weak topology.We give some equivalent conditions regarding the above proximinality.Furthermore,we also propose the necessary and sufficient conditions that a half-space is τ-strongly proximinal,approximatively τ-compact and τ-strongly Chebyshev.

Improvement of Nickel-Stanogermanide Contact Properties by Platinum Interlayer

We report an effective method to improve the formation of nickel stanogermanide（Ni Ge Sn） by the incorporation of a platinum（Pt） interlayer. After the Ni/Pt/Ge Sn samples are annealed we obtain uniform Ni Ge Sn thin films,which are characterized by means of sheet resistance, atomic force microscopy, scanning electron microscopy,cross-section transmission electron microscopy, and energy dispersive x-ray spectroscopy. These results show that the presence of Pt increases the smoothness and uniform morphology of Ni Ge Sn films.

Reversible waveform conversion between microwave and optical fields in a hybrid opto-electromechanical system

We present a scheme of reversible waveform conversion between microwave and optical fields in the hybrid optoelectromechanical system. As an intermediate interface, nanomechanical resonator optomechanically couples both optomechanical cavities in the optical and microwave frequency domains. We find the double-optomechanically induced transparency and achieve coherent signal waveform bi-directional transfer between microwave and optical fields based on quantum interference. In addition, we give an analytical expression of one-to-one correspondence between the microwave field and the optical output field, which intuitively shows the reversible waveform conversion relationship. In particular,by numerical simulations and approximate expression, we demonstrate the conversion effects of the three waveforms and discuss the bi-directional conversion efficiency and the bandwidth. such a hybrid opto-and electro-mechanical device has significant potential functions for electro-optic modulation and waveform conversion of quantum microwave-optical field in optical communications and further quantum networks.

On the Preconditioning Properties of RHSS Preconditioner for Saddle-Point Linear Systems

In this paper,for the regularized Hermitian and skew-Hermitian splitting(RHSS)preconditioner introduced by Bai and Benzi(BIT Numer Math 57:287–311,2017)for the solution of saddle-point linear systems,we analyze the spectral properties of the preconditioned matrix when the regularization matrix is a special Hermitian positive semidefinite matrix which depends on certain parameters.We accurately describe the numbers of eigenvalues clustered at(0,0)and(2,0),if the iteration parameter is close to 0.An estimate about the condition number of the corresponding eigenvector matrix,which partly determines the convergence rate of the RHSS-preconditioned Krylov subspace method,is also studied in this work.

Constraining evolution of magnetic field strength in the dissipation region of two BL Lac objects

With the assumption that the optical variability timescale is dominated by the cooling time of the synchrotron process for BL Lac objects,we estimate time dependent magnetic field strength of the emission region for two BL Lac objects.The average magnetic field strengths are consistent with those estimated from core shift measurement and spectral energy distribution modelling.Variation of magnetic field strength in the dissipation region is discovered.Variability of flux and magnetic field strength shows no clear correlation,which indicates the variation of magnetic field is not the dominant reason of the variability origin.The evolution of magnetic field strength can provide another approach to constrain the energy dissipation mechanism in jets.

Precise Positions of Triton in 2010–2014 based on Gaia-DR2

With unique orbital and physical characteristics,Triton is a very important target because it may contain information of the origin and evolution of the solar system.Besides space explorations,ground-based observations over long time also play a key role on research of Triton.High-precision positions of Triton obtained from ground telescopes are of great significance for studying its orbital evolution and the physical properties of Neptune.As a long-term observational target,Triton has been observed by the 1.56 m telescope of Shanghai Astronomical Observatory since 1996.In this paper,based on our AAPPDI software and with Gaia DR2 as the reference catalog,604 positions of Triton during 2010–2014 are calculated,with standard errors of 19–88 mas.A comparison between our results and the ephemeris(DE431+nep096)is also given.

On Weak Well-posedness of the Nearest Point and Mutually Nearest Point Problems in Banach Spaces

Let G be a nonempty closed subset of a Banach space X.Let B(X)be the family of nonempty bounded closed subsets of X endowed with the Hausdorff distance and B_(G)(X)={A∈B(X):A∩G=φ},where the closure is taken in the metric space(B(X),H).For x∈X and F∈B_(G)(X),we denote the nearest point problem inf{||x-g||:g∈G}by min(x,G)and the mutually nearest point problem inf{||f-g||:f∈ F,g∈G}by min(F,G).In this paper,parallel to well-posedness of the problems min(a:,G)and mm(F,G)which are defined by De Blasi et al.,we further introduce the weak well-posedness of the problems min(x,G)and min(F,G).Under the assumption that the Banach space X has some geometric properties,we prove a series of results on weak well-posedness of min(x,G)and min(F,G).We also give two sufficient conditions such that two classes of subsets of X are almost Chebyshev sets.

Phase-dependent double optomechanically induced transparency in a hybrid optomechanical cavity system with coherently mechanical driving

We propose a scheme that can generate tunable double optomechanically induced transparency in a hybrid optomechanical cavity system.In this system, the mechanical resonator of the optomechanical cavity is coupled with an additional mechanical resonator and the additional mechanical resonator can be driven by a weak external coherently mechanical driving field.We show that both the intensity and the phase of the external mechanical driving field can control the propagation of the probe field, including changing the transmission spectrum from double windows to a single-window.Our study also provides an effective way to generate intensity-controllable, narrow-bandwidth transmission spectra, with the probe field modulated from excessive opacity to remarkable amplification.

Stochastic Stabilization for Nonhomogeneous Markovian Jump Discrete-Time Singular Systems

Stochastic stability analysis and control synthesis problems are studied for a class of nonhomogeneous Markovian jump discretetime singular systems( MJDSS). The time-varying character is considered to be the model in a polytopic sense. Based on the parameter dependent stochastic Lyapunov functional and the matrix analysis techniques, sufficient criteria are derived to ensure regularity, causality and stochastic stability of the closed-loop singular system in terms of linear matrix inequalities. Finally,one example is provided to illustrate the effectiveness of our results.

Opto-electromechanically induced transparency in a hybrid opto-electromechanical system

We study opto-electromechanically induced transparency in a hybrid opto-electromechanical system made up of an optical cavity tunneling-coupled to an opto-mechanical cavity, which is capacitively coupled to a charged mechanical oscillator by a charged and moveable mechanical cavity mirror as an interface. By studying the effects of the different parameters on the output field, we propose a scheme to modulate the opto-electromechanically induced transparency(OEMIT). Our results show that the OEMIT with the transparency windows from single to double to triple can be modulated by changing the tunneling, opto-mechanical and electrical couplings. In addition, the explanation of the OEMIT with multi-windows is given by the energy level diagram based on quantum interference. Our investigation will provide an optimal platform to manipulate the transmission of optical field via microfabricated opto-electromechanical device.

Nereid's orbit based on new precise observations

A new orbit of Triton was provided by our previous work, benefitted by new Gaia Data, both in a new precise reduction of charge-coupled device observations and in the planetary ephemeris INPOP19 a.In this paper, we provide a new ephemeris for another main Neptunian satellite, Nereid. The orbit is fitted for the newest observations, including 2 075 ground-based observations during the period 1949-2018 and 83 space observations acquired by the Voyager 2 spacecraft in 1989. The dynamical model used here is consistent with that of our previous work. For the ground-based absolute observations of Nereid, the rootmean-square deviations are 0.201′′in right ascension and 0.189′′in declination. Finally, a comparison with the HORIZONS ephemeris is made and discussed.

Edge states enhanced by long-range hopping:An analytical study

We analyze the behavior of edge states in long-range(LR)interacting systems.In terms of lattice model Hamiltonian with the LR coupling,we determine analytically the condition of existence of edge states within the transfer matrix method(TMM).The expressions we obtain are general and hold for any choice of the LR hopping.The reason why edge states can appear is the transfer matrix in the bulk different from that in the boundary layers.Our predictions are in good agreement with numerical results by exact diagonalization.Our result is helpful in solving novel edge states in oneand two-dimensional(2D)superconductors with LR hopping and pairing.

Solitary wave for a nonintegrable discrete nonlinear Schr?dinger equation in nonlinear optical waveguide arrays

We study a nonintegrable discrete nonlinear SchriSdinger （dNLS） equation with the term of nonlinear nearest-neighbor interaction occurred in nonlinear optical waveguide arrays. By using discrete Fourier transformation, we obtain numerical approximations of stationary and travelling solitary wave solutions of the nonintegrable dNLS equation. The analysis of stability of stationary solitary waves is performed. It is shown that the nonlinear nearest-neighbor interaction term has great influence on the form of solitary wave. The shape of solitary wave is important in the electric field propagating. If we neglect the nonlinear nearest-neighbor interaction term, much important information in the electric field propagating may be missed. Our numerical simulation also demonstrates the difference of chaos phenomenon between the nonintegrable dNLS equation with nonlinear nearest-neighbor interaction and another nonintegrable dNLS equation without the term.