Euler’s First-Order Explicit Method–Peridynamic Differential Operator for Solving Population Balance Equations of the Crystallization Process

Using Euler’s first-order explicit(EE)method and the peridynamic differential operator(PDDO)to discretize the time and internal crystal-size derivatives,respectively,the Euler’s first-order explicit method–peridynamic differential operator(EE–PDDO)was obtained for solving the one-dimensional population balance equation in crystallization.Four different conditions during crystallization were studied:size-independent growth,sizedependent growth in a batch process,nucleation and size-independent growth,and nucleation and size-dependent growth in a continuous process.The high accuracy of the EE–PDDO method was confirmed by comparing it with the numerical results obtained using the second-order upwind and HR-van methods.The method is characterized by non-oscillation and high accuracy,especially in the discontinuous and sharp crystal size distribution.The stability of the EE–PDDO method,choice of weight function in the PDDO method,and optimal time step are also discussed.

GENERALIZED FORELLI-RUDIN TYPE OPERATORS BETWEEN SEVERAL FUNCTION SPACES ON THE UNIT BALL OF C^(N)

In this paper,we investigate sufficient and necessary conditions such that generalized Forelli-Rudin type operators T_(λ,τ,k),S_(λ,τ,k),Q_(λ,τ,k)and R_(λ,τ,k)are bounded between Lebesgue type spaces.In order to prove the main results,we first give some bidirectional estimates for several typical integrals.

Inverse Differential Operators in Time and Space

When one function is defined as a differential operation on another function, it’s often desirable to invert the definition, to effectively “undo” the differentiation. A Green’s function approach is often used to accomplish this, but variations on this theme exist, and we examine a few such variations. The mathematical analysis of is sought in the form if such an inverse operator exists, but physics is defined by both mathematical formula and ontological formalism, as I show for an example based on the Dirac equation. Finally, I contrast these “standard” approaches with a novel exact inverse operator for field equations.

Exploration on the Incentive Mechanism of Regional Ecological Capital Operation from the Perspective of Principal Agent

Ecological capital operation is a major means for innovation of ecological environment protection,and provides ecological security for sustainable economic and social development.In this paper,key factors for construction of incentive mechanism of ecological capital operation are explored from government cognition,enterprise attitude and public awareness.Via model building and parameter setting,incentive mechanism system of single objective is established effectively,to promote effective realization of regional ecological capital operation.

Incentive operation characteristics and influence feedback of existing building energy-saving renovation market development

The quality of the existing building energy-saving renovation market determines the inherent inevitability of incentive,while unique requirements for the incentive should be satisfied by stage characteristics and individualization of the three entities of the existing building energy-saving renovation market development.Firstly,the analysis of internal and external factors’composition and system influencing the existing construction market development incentive structure was performed.Then,system dynamics was implemented to build the feedback model of incentive effects of market development of existing buildings energy-saving reconstruction.Discussions on the realization path of the incentive for the development of the existing energy-saving building market were also pointed out.Finally,this paper conducted the analysis of the dynamic feedback characteristics and key incentive factors of the incentive for the development of the existing building energy-saving renovation market.Based on the analyses and discussions above,this paper provides methodological guidance and implementation approach for the incentive path selection and policy-making of the existing building energy-saving transformation market,trying to help improve the incentive effectiveness of the market,and also promote healthy and sustainable development of the existing building energy-saving renovation market.

The Interpolation of Operators between Weighted Hardy Spaces and Weighted L^p Spaces

The paper is given the interpolation of operators between weighted Hardy spaces and weighted L p spaces when w∈A 1 by Calderon Zygmund decomposition.

CARLESON MEASURES,RIEMANN-STIELTJES OPERATORS AND MULTIPLIERS ON F(p,q,s)SPACES IN THE UNIT BALL OF C^n

This paper is devoted to characterizing the Riemann-Stieltjes operators and pointwise multipliers on F（p, q, s） spaces in the unit ball of C^n which contain many classical function spaces, such as the Bloch space, BMOA and Q8 spaces. The boundedness and compactness of these operators on F（p, q, s） spaces are characterized by means of an embedding theorem, i.e., F（p,q, s） spaces boundedly embedded into the tent-type spaces Tp,s^∞（μ）

Weighted composition operators from F(p,q,s) spaces to Bers-type spaces in the unit ball

This paper deals with the boundedness and compactness of the weighted composition operators from the F（p, q, s） spaces, including Hardy space, Bergman space, Qp space, BMOA space, Besov space and α-Bloch space, to Bers-type spaces Hv^∞（ or little Bers-type spaces Hv,o∞ ）, where v is normal.

WEYL'S TYPE THEOREMS AND HYPERCYCLIC OPERATORS

For a bounded operator T acting on an infinite dimensional separable Hilbert space H, we prove the following assertions： （i） If T or T＊ ∈ SC, then generalized a- Browder＇s theorem holds for f（T） for every f ∈ Hol（σ（T））. （ii） If T or T＊ ∈ HC has topological uniform descent at all λ ∈ iso（a（T））, then generalized Weyl＇s theorem holds for f（T） for every f ∈ Hol（σ（T））. （iii） If T ∈ HC has topological uniform descent at all λ ∈（T）, then T satisfies generalized Weyl＇s theorem. （iv） Let T ∈ HC. If T satisfies the growth condition Gd（d 〉 1）, then generalized Weyl＇s theorem holds for f（T） for every f ∈ Hol（σ（T））. （v） If T ∈ SC, then, f（OssF＋ （T）） = aSBF＋ （f（T）） for all f ∈ Hol（σ（T））. （vi） Let T be a-isoloid such that T＊ ∈ HC. If T - AI has finite ascent at every A ∈ Eσ（T） and if F is of finite rank on Hsuch that TF = FT, then T ∈ F obeys generalized a-Weyl＇s theorem.

NEW WEIGHTED MULTILINEAR OPERATORS AND COMMUTATORS OF HARDY-CESàRO TYPE

This paper deals with a general class of weighted multilinear Hardy-Cesaro op- erators that acts on the product of Lebesgue spaces and central Morrey spaces. Their sharp bounds are also obtained. In addition, we obtain sufficient and necessary conditions on weight functions so that the commutators of these weighted multilinear Hardy-Cesaro oper- ators （with symbols in central BMO spaces） are bounded on the product of central Morrey spaces. These results extends known results on multilinear Hardy operators.

LOWER BOUNDS OF DIRICHLET EIGENVALUES FOR A CLASS OF FINITELY DEGENERATE GRUSHIN TYPE ELLIPTIC OPERATORS

Let Ω be a bounded open domain in Rn with smooth boundary Ω, X =（X1,X2,... ,Xm） be a system of real smooth vector fields defined on Ω and the bound-ary Ω is non-characteristic for X. If X satisfies the HSrmander＇s condition, then the vectorfield is finitely degenerate and the sum of square operator △X =m∑j=1 X2 j is a finitely de-generate elliptic operator. In this paper, we shall study the sharp estimate of the Dirichlet eigenvalue for a class of general Grushin type degenerate elliptic operators △x on Ω.

Recording the direct surgeon’s view with an operating microscopic view improves microscopic ophthalmic surgery training

AIM:To establish a recording system with a direct view of the surgeon to supplement video recording under an operating microscope,which lacks information on the movement and position of the surgeon’s hands,and to facilitate the reproduction of a skilled surgeon’s technique by a surgeon in training.METHODS:A small camera was attached to the operating microscope with a custom adapter.Microscopic surgeon’s view and direct surgeon’s view through this new camera were recorded in the surgical recording system.Both movies were synchronized and analyzed how do surgeons handle the instruments.RESULTS:A small camera attached to the operating microscope allowed the surgeon’s hands motion to be recorded without interfering with the surgeon’s movements.Different surgeons used different methods to manipulate the ultrasound handpiece and the irrigation/aspiration device.Even in the simple paracentesis procedure,different surgeons used different methods.Surgeons-in-training were able to identify and improve their weaknesses by watching synchronized movies of their hand motions and microscopic view.CONCLUSION:Simultaneous recording the surgical field out of the operating microscopic view by a small camera set on the microscope is comprehensive and improves surgeons-in-training understanding and learning surgeries.

Several Properties of p-w-hyponormal Operators

In this paper, let T be a bounded linear operator on a complex Hilbert H. We give and prove that every p-w-hyponormal operator has Bishop's property(β) and spectral properties; Quasi-similar p-w-hyponormal operators have equal spectra and equal essential spectra. Finally, for p-w-hyponormal operators, we give a kind of proof of its normality by use of properties of partial isometry.

Exact Inverse Operator on Field Equations

Differential equations of electromagnetic and similar physical fields are generally solved via antiderivative Green’s functions involving integration over a region and its boundary. Research on the Kasner metric reveals a variable boundary deemed inappropriate for standard anti-derivatives, suggesting the need for an alternative solution technique. In this work I derive such a solution and prove its existence, based on circulation equations in which the curl of the field is induced by source current density and possibly changes in associated fields. We present an anti-curl operator that is believed novel and we prove that it solves for the field without integration required.

Time Evolution Caused by Hamiltonian Composed of Quadratic Combination of Canonical Operators and Time-Dependent Two-Mode Fresnel Operator

We show that the time-dependent two-mode Fresnel operator is just the time-evolutional unitary operator governed by the Hamiltonian composed of quadratic combination of canonical operators in the way of exhibiting SU（1,1） algebra. This is an approach for obtaining the time-dependent Hamiltonian from the preassigned time evolution in classical phase space, an approach which is in contrast to Lewis-Riesenfeld＇s invariant operator theory of treating timedependent harmonic oscillators.

Determination of the Response Amplitude Operator(s) of an FPSO

The driving necessities of cost reduction and the need to develop fields at ever increasing water depths have led to the use of floating structures. Among these structures are the Floating Production Storage and Offloading (FPSO) units whose motion analysis is considered in this paper. In actual environmental condition, it is required to accurately determine or predict large amplitude motion of the FPSO before any offshore operation. This paper seeks to present a detailed method of computing the Response Amplitude Operator(s) (RAOs) for the six (6) degrees of freedom using ANSYS AQWA. The results indicate for Heave motion a tendency for the heave peak value to move slightly higher dimensionless encounter-frequency as the wave moves from Head sea to Beam sea direction. A MATLAB source code was developed to validate the result for heave motion at head sea. Although a small difference in predicted heave motion occurred, it is pertinent to note that the comparisons between results generated in the MATLAB program and ANSYS AQWA demonstrate generally good agreement, and the roll response of the FPSO is noted to be critical.

The Fuzzy Synthesizing Evaluation of City's Environmental Quality Based on GIOWA Operator:A Case of 13 Cities of Jiangsu Province

In this paper, the generally induced ordered weighted averaging (GIOWA) operator is used to construct the fuzzy evaluating system of the quality of a city’s environment including air, water and noise. Based on the part data of air, water and noise of the 13 cities under the jurisdiction of Jiangsu provincial government in 2002, a case study is given. The evaluating results show that the evaluating system of the quality of a city’s environment based on the GIOWA operator can reflect the condition of pollution controlled and environmental quality of a city in a period of time.

国内S Zorb装置运行情况分析

介绍了国内S Zorb装置的分布情况以及其中28套工业装置在2023年的运行情况,通过对比不同S Zorb装置的2023年运行数据发现,不同S Zorb装置原料硫含量和烯烃含量、主要操作参数、辛烷值损失、吸附剂活性虽然存在较大的差别,但所有装置均可稳定生产满足国Ⅵ标准的汽油,说明S Zorb装置具有较好的适应性。汇总了2011年以来中国石化S Zorb装置的运行数据,结果发现,中国石化S Zorb装置的原料硫含量波动较大,烯烃含量呈逐年下降趋势,而装置脱硫率基本不变,烯烃饱和反应及辛烷值损失变化较大。

Unifying the theory of integration within normal-,Weyl- and antinormal-ordering of operators and the s-ordered operator expansion formula of density operators

By introducing the s-parameterized generalized Wigner operator into phase-space quantum mechanics we invent the technique of integration within s-ordered product of operators （which considers normally ordered, antinormally ordered and Weyl ordered product of operators as its special cases）. The s-ordered operator expansion （denoted by s…s ） formula of density operators is derived, which isρ=2/1-s∫d^2β/π〈-β｜ρ｜β〉sexp{2/s-1（s｜β｜^2-β＊α＋βa-αα）}s The s-parameterized quantization scheme is thus completely established.

BOUNDEDNESS OF STEIN'S SQUARE FUNCTIONS ASSOCIATED TO OPERATORS ON HARDY SPACES

Let （X, d,μ） be a metric measure space endowed with a metric d and a nonnegative Borel doubling measure μ. Let L be a second order non-negative self-adjoint operator on L^2（X）. Assume that the semigroup e^-tL generated by L satisfies the Davies-Gaffney estimates. Also, assume that L satisfies Plancherel type estimate. Under these conditions, we show that Stein＇s square function Gδ（L） arising from Bochner-Riesz means associated to L is bounded from the Hardy spaces HL^p（X） to L^p（X） for all 0 〈 p ≤ 1.