Semigroup of Weakly Continuous Operators Associated to a Generalized Schrödinger Equation

In this work, we prove the existence and uniqueness of the solution of the generalized Schrödinger equation in the periodic distributional space P’. Furthermore, we prove that the solution depends continuously respect to the initial data in P’. Introducing a family of weakly continuous operators, we prove that this family is a semigroup of operators in P’. Then, with this family of operators, we get a fine version of the existence and dependency continuous theorem obtained. Finally, we provide some consequences of this study.

Group of Weakly Continuous Operators Associated to a Generalized Schrödinger Type Homogeneous Model

In this work, we prove the existence and uniqueness of the solution of the generalized Schrödinger type homogeneous model in the periodic distributional space P’. Furthermore, we prove that the solution depends continuously respect to the initial data in P’. Introducing a family of weakly continuous operators, we prove that this family is a group of operators in P’. Then, with this family of operators, we get a fine version of the existence and dependency continuous theorem obtained. Finally, we give some remarks derived from this study.

Elements and Experiments of Shenzhen Continuous Operating Reference Stations (SZCORS) System

Real-time kinematic GPS precise positioning has been playing an increasing role in both surveying and navigation. Based on the city’s fibre LAN network, Shenzhen Continuous Operating Reference Stations (SZCORS) system has been established and consists of GPS reference stations, system control center, user’s data center, and real-time datacom network. The SZCORS system provides users the real-time centimeter positioning or post-processing millimeter positioning. This paper makes discussion on the structure of SZCORS system. Some experiments have been made to test the usablity, and then the data has been analyzed.

Simulation of Continuous Esterification Process of Polyester Polyols

Based on the kinetic and thermodynamic equations, a comprehensive mathematical model for the con- tinuous esterification process of polyester polyols was developed, which was carried out in an innovational bub- bling reactive distillation tower （BRDT） at atmospheric pressure. In this new type of reactor, direct esterification between ethylene glycol and adipic acid was accomplished efficiently and rapidly. A bench BRDT with the height of 2 m was applied for the esteriflcation process of l^oly （ethylene adlpate） （P＇EA）. In the continuous operation, Hn- ear oligomers were discharged from the bottom of the column, while water passed a few column trays and a pack- ing section as a condensation byproduct. The influence of major operating conditions on reactor performance was also simulated. Simulation results were in good agreement with experimental data, providing a strategy for devel- oping and optimizing this process.

Design and operation strategies of the system for destroying time-sensitive target based on system effectiveness

To improve the effect of destroying time-sensitive target （TST）, a method of operational effectiveness evaluation is presented and some influential factors are analyzed based on the combat flow of system for destroying TST. Considering the possible operation modes of the system, a waved operation mode and a continuous operation mode are put forward at first. At the same time, some relative formulas are modified. In examples, the influential factors and operation modes are analyzed based on the system effectiveness. From simulation results, some design and operation strategies of the system for destroying time sensitive targets are concluded, which benefit to the improvement of the system effectiveness.

Some New Fixed Point Theorems in Probabilistic Metric Spaces

In this paper, we introduce the concept of the Z-M-PN space and obtain somenew fixed point theorems in probabilistic metric spaces Meanwhile,some famous fixedpoint theorems are generalized in probabilistic metric spaces, such a.s fixed point theorem of Schauder, Guo's theorem and fixed point theorem of Petryshyn are generalized in Menger PN-space. And fixed point theorem of Altman is also generalized in the Z-M-PN space.

Quasi-real time inversion method of three-dimensional epicenter coordinate, trigger time, and magnitude based on CORS

This study explores the quasi-real time inversion principle and precision estimation of three-dimensional coordinates of the epicenter, trigger time and magnitude of earthquakes with the aim to improve traditional methods, which are flawed due to missing information or distortion in the seismograph records. The epicenter, trigger time and magnitude from the Lushan earthquake are inverted and analyzed based on high-frequency GNSS data. The inversion results achieved a high precision, which are consistent with the data published by the China Earthquake Administration. Moreover, it has been proven that the inversion method has good theoretical value and excellent application prospects.

New progress on beam availability and reliability of PKU high intensity CW proton ECR ion source

The stability and reliability of an ion source and its beam availability are extremely significant for any accelerator,especially for those high current long term CW operation ones like ADS. Although the first high quality 306-hours continuous wave（CW） operating curve at 50 m A@35 ke V has been successfully obtained with a standard compact 2.45 GHz ECR ion source at Peking University（PKU）, but the uncertainties that caused beam trips before are unacceptable during an accelerator real operation and should be eliminated. Meanwhile, no permission will be given when the beam power is upgraded from 50 m A@35 ke V to 50 m A@50 ke V. To improve the PKU CW proton source quality, several upgrades were done recently. After those improvements, a new long term CW proton beam experiment at 50 m A@50 ke V was carried out in June 2016. The total running time is 300.5 hours, including near 6 hours ion source preparation and 294 hours non-disturb continuous operation. Within the continuous 13 days operation, no beam-off happened, no spark was observed,no beam drop appeared, no interrupting action was needed, and only a few beam fluctuations caused by the air conditional failure occurred. Beam availability and reliability within the 294 hours is 100%. The root-mean-square（RMS） emittance of this 50 m A@50 ke V CW proton beam is about 0.186 π.mm.mrad. A careful inspection of the ion source was done after this long term operation and no obvious damage was found. The restart experimental results obtained after the ion source inspection prove the high repeatability of PKU PMECRIS. In addition, a 130-m A H＋beam was obtained at 50 k V with duty factor of 10%（100 Hz/1 ms） with this source. Details will be presented in this paper.

SOME PROBLEMS IN THE Z-C-X SPACE

The new concepts of the Z-C-X space and excellent cone are introduced. Some problems of random semiclosed 1-set-contractive operator are investigated in the Z-C-X space. At first, an important inequality is proved. Secondly, several new conclusions are proved by means of random fixed point index in the theory of random topological degree. A random solution of a class of random operator equations under conditions of imitating the parallelogram law is obtained, famous Altman's theorem is generalized in partially ordered Z-C-X space. Therefore, some new results are obtained.

Sensitivity analysis of generalized set-valued quasi-variational inclusion in Banach spaces

The sensitivity analysis for a class of generalized set-valued quasi-variational inclusion problems is investigated in the setting of Banach spaces. By using the resolvent operator technique, without assuming the differentiability and monotonicity of the given data, equivalence of these problems to the class of generalized resolvent equations is established.

Deterministic Quantum Secure Direct Communication with Dense Coding and Continuous Variable Operations

We propose a deterministic quantum secure direct two check photon sequences are used to check the securities of the communication protocol by using dense coding. The channels between the message sender and the receiver. The continuous variable operations instead of the usual discrete unitary operations are performed on the travel photons so that the security of the present protocol can be enhanced. Therefore some specific attacks such as denial-of-service attack, intercept-measure-resend attack and invisible photon attack can be prevented in ideal quantum channel. In addition, the scheme is still secure in noise channel. Furthurmore, this protocol has the advantage of high capacity and can be realized in the experiment.

GPS-Meteorology Network in Wuhan Region

There are three aspects in the study of GPS meteorology network in the Wuhan region. The first is the comparison of the GPS precipitable water vapor between final ephemeris and ultra-rapid ephemeris for which the relative coefficient is 99.97 and the root mean squares is 0.048 mm. It can be concluded that ultra-rapid ephemeris can be used to get the GPS precipitable water vapor for the real-time prediction. The second is the comparison of precipitable water vapor of GPS stations and the distribution of water vapor in the Wuhan region is acquired. The change of GPS precipitable water vapor and rainfall in a rainfall process are compared and analyzed. The change of GPS precipitable water vapor can reflect and predict the process of rainfall.

CONSIDER SAINT-VENANT'S PRINCIPLE BY MEANS OF CHAIN MODEL

A precise background theory of computational mechanics is formed. Saint_Venant's principle is discussed in chain model by means of this precise theory. The classical continued fraction is developed into operator continued fraction to be the constrictive formulation of the chain model. The decay of effect of a self_equilibrated system of forces in chain model is decided by the convergence of operator continued fraction, so the reasonable part of Saint_Venant's principle is described as the convergence of operator continued fraction. In case of divergence the effect of a self_equilibrated system of forces may be non_zero at even infinite distant sections, so Saint_Venant's principle is not a common principle.

NEW FIXED POINT THEOREMS FOR P_1-COMPACT MAPPINGS IN BANACH SPACES

E E. Browder and W. V. Petryshyn defined the topological degree for A- proper mappings and then W. V. Petryshyn studied a class of A-proper mappings, namely, P1-compact mappings and obtained a number of important fixed point theorems by virtue of the topological degree theory. In this paper, following W. V. Petryshyn, we continue to study P1-compact mappings and investigate the boundary condition, under which many new fixed point theorems of P1-compact mappings are obtained. On the other hand, this class of A-proper mappings with the boundedness property includes completely continuous operators and so, certain interesting new fixed point theorems for completely continuous operators are obtained immediately. As a result of it, our results generalize several famous theorems such as Leray-Schauder＇s theorem, Rothe＇s theorem, Altman＇s theorem, Petryshyn＇s theorem, etc.

Structure of continuous matrix product operator for transverse field Ising model:An analytic and numerical study

We study the structure of the continuous matrix product operator(cMPO)^([1]) for the transverse field Ising model(TFIM).We prove TFIM’s cMPO is solvable and has the form T=e^(-1/2H_(F)).H_(F) is a non-local free fermionic Hamiltonian on a ring with circumferenceβ,whose ground state is gapped and non-degenerate even at the critical point.The full spectrum of H_(F) is determined analytically.At the critical point,our results verify the state–operator-correspondence^([2]) in the conformal field theory(CFT).We also design a numerical algorithm based on Bloch state ansatz to calculate the lowlying excited states of general(Hermitian)cMPO.Our numerical calculations coincide with the analytic results of TFIM.In the end,we give a short discussion about the entanglement entropy of cMPO’s ground state.

The Representation of Continuous Linear Operator by Integral

In this paper,we study the representation of linear operator on but abandom the Radon-Nikodym property and give a necessary and sufficient condition for representability of linear operator on by integral.

Regularity of Continuous Linear Operators on Banach Function Spaces

In this paper we present some characterizations of Banach function spaces on which every continuous linear operator is regular.

L^p CONTINUITY OF HRMANDER SYMBOL OPERATORS OpS_(0,0) ~m AND NUMERICAL ALGORITHM

If we use Littlewood-Paley decomposition, there is no pseudo-orthogonality for Ho¨rmander symbol operators OpS m 0 , 0 , which is different to the case S m ρ,δ （0 ≤δ 〈 ρ≤ 1）. In this paper, we use a special numerical algorithm based on wavelets to study the L p continuity of non infinite smooth operators OpS m 0 , 0 ; in fact, we apply first special wavelets to symbol to get special basic operators, then we regroup all the special basic operators at given scale and prove that such scale operator’s continuity decreases very fast, we sum such scale operators and a symbol operator can be approached by very good compact operators. By correlation of basic operators, we get very exact pseudo-orthogonality and also L 2 → L 2 continuity for scale operators. By considering the influence region of scale operator, we get H 1 （= F 0 , 2 1 ） → L 1 continuity and L ∞→ BMO continuity. By interpolation theorem, we get also L p （= F 0 , 2 p ） → L p continuity for 1 〈 p 〈 ∞ . Our results are sharp for F 0 , 2 p → L p continuity when 1 ≤ p ≤ 2, that is to say, we find out the exact order of derivations for which the symbols can ensure the resulting operators to be bounded on these spaces.

Analysis on accuracy of Engineering Star RTK in cadastral survey based on SOUTH-CORS

Currently,with the fast development of GPS technique,GPS RTK is rapidly being applied to the cadastral survey. GPS RTK technique not only improves efficiency and accelerates the rate of mapping,but also increases economic efficiency. The authors introduced a method for GPS RTK rapid positioning,which uses continuous operational reference system (CORS) as a base station to change the method of previous map drawing by obtaining real-time three-dimensional coordinates of boundary points and statistically analyzing with the three-dimensional coordinates obtained by Total Station to get the accuracy of GPS RTK real-time coordinates. The application of GPS RTK in practical measurement was discussed when the data link had been lost especially. The results show that the three-dimensional coordinates measured by total station can be replaced by real-time three-dimensional coordinates measured by Engineering Star RTK in the CORS.

Space of Operators and Property (MB)

In this paper, a new class of Banach spaces, termed as Banach spaces with property (MB), will be introduced. It is stated that a space X has property (MB) if every V -subset of X* is an L-subset of X* . We describe those spaces which have property (MB) . Also, we show that if a Banach space X has property (MB) and Banach space Y does not contain , then every operator is completely continuous.