REDUCED MINIMAL NUMERICAL RANGES OF OPERATORS ON A HILBERT SPACE

In this note,the reduced minimal numerical ranges of a bounded linear oper- ators on a Hilbert space are defined and some of its properties are established.

The Interior of Numerical Ranges of Operators

In this note, some properties of the interior of numerical ranges of operators are established, and an alternative proof of Embry's theorem associated with the interior of a numerical ranges of an operator is given(see [3]).

Generalized Numerical Radius of Real Quaternion Matrices with Symmetric Function

In the paper the generalized numerical radiuses of real quaternion matrices with symmetric function are defined and theirs inequalities are given.

A Note on Numerical Radius Operator Spaces

In this paper, we first study some -completely bounded maps between various numerical radius operator spaces. We also study the dual space of a numerical radius operator space and show that it has a dual realization. At last, we define two special numerical radius operator spaces and which can be seen as a quantization of norm space E.

Stability of T. Chan’s Preconditioner from Numerical Range

A matrix is said to be stable if the real parts of all the eigenvalues are negative. In this paper, for any matrix An, we discuss the stability properties of T. Chan’s preconditioner cU (An) from the viewpoint of the numerical range. An application in numerical ODEs is also given.

REDUCED MINIMAL NUMERICAL RANGES OF OPERATORS ON A HILBERT SPACE

In this note,the reduced minimal numerical ranges of a bounded linear oper- ators on a Hilbert space are defined and some of its properties are established.

Joint product numerical range and geometry of reduced density matrices

The reduced density matrices of a many-body quantum system form a convex set, whose three-dimensional projection is convex in R3. The boundary of may exhibit nontrivial geometry, in particular ruled surfaces. Two physical mechanisms are known for the origins of ruled surfaces： symmetry breaking and gapless. In this work, we study the emergence of ruled surfaces for systems with local Hamiltonians in infinite spatial dimension, where the reduced density matrices are known to be separable as a consequence of the quantum de Finetti＇s theorem. This allows us to identify the reduced density matrix geometry with joint product numerical range II of the Hamiltonian interaction terms. We focus on the case where the interaction terms have certain structures, such that a ruled surface emerges naturally when taking a convex hull of ∏. We show that, a ruled surface on sitting in ∏ has a gapless origin, otherwise it has a symmetry breaking origin. As an example, we demonstrate that a famous ruled surface, known as the oloid, is a possible shape of , with two boundary pieces of symmetry breaking origin separated by two gapless lines.

Numerical analysis of factors affecting the range of heat transfer in earth surrounding three subways

In order to examine the factors which affect the range of heat transfer in earth surrounding subways, FLAC3D was adopted in this study to analyze these factors, under different conditions, in a systematic manner. When we compare these numerical tests, the results show that the main factors, affecting the heat transfer range are the thermal properties of the surrounding earth, the initial ground temperature and the temperature in the tunnel. The heat transfer coefficient between air and linings has little effect on the temperature distribution around the tunnel. The current results can provide a reference for improving the thermal environment in subways and optimizing the design of subwav ventilation and air conditioning.

Coupling mechanism of THM fields and SLG phases during the gas extraction process and its application in numerical analysis of gas occurrence regularity and effective extraction radius

The analysis of the coupling mechanism of thermal-hydraulic-mechanical(THM)fields,and solid-liquidgas(SLG)phases during gas extraction process is of profound significance to explore its numerical application in the gas occurrence regularity and its effective extraction radius.In this study,the Hudi coal mine in Qinshui basin is taken as the research area,the influencing factors of gas occurrence were analyzed,the differences in overburden load for gas pressure distribution and the factors influencing the effective extraction radius were further discussed by using the COMSOL software.The results show that the derivation of mathematical model in gas extraction shows that the process is a process the THM fields restrict each other,and the SLG phases influence each other.The longer the extraction time,the larger the influencing range of borehole,and the better the extraction effect.The larger the diameter of borehole,the larger the effective extraction radius,and the influence on gas extraction effect is smaller in the early stage and larger in the late stage.The borehole arrangement should be flexibly arranged according to the actual extraction situation.The higher the porosity,the higher the permeability,the better the gas extraction effect.The larger the overburden load of reservoir,the stronger the effective stress,which will result in the more severe the strain,and the closure of pore and fracture,which in turn will lead to the decrease of permeability and slow down the gas extraction.The relationship among extraction time,borehole diameter,negative pressure of gas extraction,permeability with effective extraction radius is exponential.This study has important theoretical and practical significance for clarifying and summarizing the gas occurrence regularity and its engineering practice.

Maps Preserving Numerical Radius or Cross Norms of Products of Self-adjoint Operators

Let H be a complex Hilbert space with dimH ≥3, Bs（H） the （real） Jordan algebra of all self-adjoint operators on H. Every surjective map Ф ： Bs（H）→13s（H） preserving numerical radius of operator products （respectively, Jordan triple products） is characterized. A characterization of surjective maps on Bs （H） preserving a cross operator norm of operator products （resp. Jordan triple products of operators） is also given.

The ‘Two oceans and one sea' extended range numerical prediction system with an ultra-high resolution atmosphere-ocean-land regional coupled model

The‘Two Oceans and One Sea’area(West Pacific,Indian Ocean,and South China Sea;15°S–60°N,39°–178°E)is a core strategic area for the‘21st Century Maritime Silk Road’project,as well as national defense.With the increasing demand for disaster prevention and mitigation,the importance of 10–30-day extended range prediction,between the conventional short-term(around seven days)and the climate scale(longer than one month),is apparent.However,marine extended range prediction is still a‘blank point’in China,making the early warning of marine disasters almost impossible.Here,the authors introduce a recently launched Chinese national project on a numerical forecasting system for extended range prediction in the‘Two Oceans and One Sea’area based on a regional ultra-high resolution multi-layer coupled model,including the scientific aims,technical scheme,innovation,and expected achievements.The completion of this prediction system is of considerable significance for the economic development and national security of China.

Numerical Modeling of Basin-Range Tectonics Related to Continent-Continent Collision

Continent-continent collision is the most important driving mechanism for the occurrence of various geological processes in the continental lithosphere. How to recognize and determine continent-continent collision, especially its four-dimensional temporal-spatial evolution, is a subject that geological communities have long been concerned about and studied. Continent-continent collision is mainly manifested by strong underthrusting (subduction) of the underlying block along an intracontinental subduction zone and continuous obduction (thrusting propagation) of the overlying block along the intracontinental subduction zone, the occurrence of a basin-range tectonic framework in a direction perpendicular to the subduction zone and the flexure and disruption of the Moho. On the basis of numerical modeling, the authors discuss in detail the couplings between various amounts and rates of displacement caused by basin subsidence, mountain uplift and Moho updoming and downflexure during obduction (thrusting propagation) and subduction and the migration pattern of basin centers. They are probably indications or criteria for judgment or determination of continent-continent collision.

Wind-sand flow simulation and radius optimization of highway embankment under different vertical curve radius

It is of great practical value to explore the correlation between the vertical curve radius of desert highway and the increase of sand accumulation in local lines,and to select the appropriate vertical curve radius for reducing the risk of sand accumulation.In this study,three-dimensional models of desert highway embankments with different vertical curve radii were constructed,and Fluent software was used to simulate the wind-sand flow field and sand accumulation distribution of vertical curve embankments.The results show that:(1)Along the direction of the road,the concave and the convex vertical curve embankments have the effect of collecting and diverging the wind-sand flow,respectively.When the radius of the concave vertical curve is 3000 m,5000 m,8000 m,10000 m and 20000 m,the wind velocity in the middle of the vertical curve is 31.76%,22.58%,10.78%,10.53%and 10.44%,higher than that at both ends.When the radius of the convex vertical curve is 6500 m,8000 m,10000 m,20000 m and 30000 m,the wind velocity at both ends of the vertical curve is 14.06%,9.99%,6.14%,3.22%and 2.41%,higher than that in the middle.The diversion effect also decreases with the increase of the radius.(2)The conductivity of the concave and convex vertical curve embankments with different radii is greater than 1,which is the sediment transport roadbed.The conductivity increases with the increase of radius and gradually tends to be stable.When the radius of the concave and convex vertical curves reaches 8000 m and 20000 m respectively,the phenomenon of sand accumulation is no longer serious.Under the same radius condition,the concave vertical curve embankment is more prone to sand accumulation than the convex one.(3)Considering the strength of the collection and diversion of the vertical curve embankment with different radii,and the sand accumulation of the vertical curve embankment in the desert section of Wuma Expressway,the radius of the concave vertical curve is not less than 8000 m,and the radius of the convex vertical curve is not less than 20000 m,which can effectively reduce the sand accumulation of the vertical curve embankment.In the desert highway area,the research results of this paper can provide reference for the design of vertical curve to ensure the safe operation of desert highway.

Linear operators preserving the generalized decomposable numerical range

LET G be a subgroup of the symmetric group Sm. Denote by CG the set of all functions f: G→C. A function f∈CG is said to be positive semi-definite （p. s. d. ） if there exists c∈CG such that for all τ∈G. In particular, the irreducible complex characters of G are p. s. d. Let Cn×m denote the set of all n×m complex matrices. For f∈CG, the

On the Origin and Numerical Range of Bounded Operators

Numerical range has an important applications on spectrum distribution of operators. In this paper, we devoted to characterizing operators whose numerical range contains the origin. Some necessary and sufficient conditions are given by operator decomposition technique and constructive methods. Furthermore, the closeness of the numerical range of a given operator is also investigated.

Applying the Theory of Numerical Radius of Operators to Obtain Multi-observable Quantum Uncertainty Relations

Quantum uncertainty relations are mathematical inequalities that describe the lower bound of products of standard deviations of observables(i.e.,bounded or unbounded self-adjoint operators).By revealing a connection between standard deviations of quantum observables and numerical radius of operators,we establish a universal uncertainty relation for k observables,of which the formulation depends on the even or odd quality of k.This universal uncertainty relation is tight at least for the cases k=2 and k=3.For two observables,the uncertainty relation is a simpler reformulation of Schr?dinger’s uncertainty principle,which is also tighter than Heisenberg’s and Robertson’s uncertainty relations.

Numerical Simulation of Regional Short-Range Climate Anomalies

With the high-speed development of numerical weather prediction, since the later 1980's, the prediction of short-range climate anomalies has attracted worldwide meteorologists' attention . What the so called short-range refers to the time scale from one month to one season or more. In dealing with the problem of short-range climate prediction, two points are needed noticing: one is the basic research to explore or investigate the mechanism of variability of the slow varying components which mainly include internal dynamics of extratropics, external forcings and tropical dynamics, and the other is the modeling efforts to simulate the process of the long-term evolution of the signal which include the improvement of model quality, stochastic prediction and the air-sea-coupled model (Miyakoda et al.,1986). Previous researches on the numerical prediction of short-term climate anomalies are mostly concentrated in the analysis of variables with global spatial scale, especially the global general atmospheric circulation analysis.As to the simulation or prediction of regional short-term climate anomalies, there exist many difficulties and problems. Though some meteorologists are devoting themself to this field, up to now, they have not reached satisfactory results. As a primary effort, by using the 2-level general atmospheric circulation model developed in the Institute of Atmospheric Physics, Chinese Academy of Sciences (IAP-AGCM) (Zeng et al., 1989), and taking the year of 1985 as a case, a numerical simulation of regional short-term climate change is completed. We pay high attention to the predictant of anomalous summer rainfall in the Yangtze River and Yellow River valleys, especially its month to month variation.

On y-numerical Radius and Its Stability

Let A be an n×n complex matrix,and let y =(α1,...,αn) be an n-dimensional complex vector.The y-numerical radius of A,denoted by ry(A),is defined follows:r_y(A) = max {|sum form i=1 to n α_ix_i~* Ax_i|:x_i~* x_i = 1,x_i ∈ C^n},where Cn is an n-dimensional vector space over complex field C.In this paper we studynorm properties and stability of y-numerical radius.

Norm Properties of Y-numerical Radii

Given an n×n complex matrix A and an n-dimensional complex vector y=(ν1 , ··· , νn ), the y-numerical radius of A is the nonnegative quantity ry(A)=max{n∑j=1ν*jAx︱:Axj︱: x*jxj=1,xj ∈Cn}.Here Cn is an n-dimensional linear space overthe complex field C. For y = (1, 0, ··· , 0) it reduces to the classical radius r(A) =max {|x*Ax|: x*x=1}.We show that ry is a generalized matrix norm if and only ifn∑j=1νj≠ 0.Next, we study some properties of the y-numerical radius of matrices andvectors with non-negative entries.