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–peridyna...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.展开更多
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 ...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.展开更多
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, B...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)展开更多
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 ...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.展开更多
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 ∈...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.展开更多
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 obtai...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.展开更多
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 HSrmande...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.展开更多
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 fac...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.展开更多
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 reve...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.展开更多
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 Offlo...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.展开更多
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 pa...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.展开更多
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, antino...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.展开更多
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 ge...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.展开更多
We consider the weighted composition operators between Hardy spaces on the unit ball, and obtain some sufficient and necessary conditions of bounded or compact weighted composition operators. We also prove that the op...We consider the weighted composition operators between Hardy spaces on the unit ball, and obtain some sufficient and necessary conditions of bounded or compact weighted composition operators. We also prove that the operator from H^1 to H^1 is compact if and only if it is weakly compact. Meanwhile, we get the analogue on the Bergman spaces.展开更多
In this paper, Leibniz' formula of generalized divided difference with respect to a class of differential operators whose basic sets of solutions have power form, is considered. The recurrence formula of Green fun...In this paper, Leibniz' formula of generalized divided difference with respect to a class of differential operators whose basic sets of solutions have power form, is considered. The recurrence formula of Green function about the operators is also given.展开更多
We characterize the boundedness and compactness of weighted composition operators on weighted Dirichlet spaces in terms of Nevanlinna counting functions and Caxleson measure.
In the theory of random fractal, there are two important classes of random sets, one is the class of fractals generated by the paths of stochastic processes and another one is the class of factals generated by statist...In the theory of random fractal, there are two important classes of random sets, one is the class of fractals generated by the paths of stochastic processes and another one is the class of factals generated by statistical contraction operators. Now we will introduce some things about the probability basis and fractal properties of fractals in the last class. The probability basis contains (1) the convergence and measurability of a random recursive setK(ω) as a random element, (2) martingals property. The fractal properties include (3) the character of various similarity, (4) the separability property, (5) the support and zero-one law of distributionP k =P·K ?1, (6) the Hausdorff dimension and Hausdorff exact measure function.展开更多
We are all aware that our experience is structured into left and right, up and down, and we can understand from our own experience that consciousness is unified into a singular whole. Although we can understand such b...We are all aware that our experience is structured into left and right, up and down, and we can understand from our own experience that consciousness is unified into a singular whole. Although we can understand such basic phenomenological axioms of experience, there are many more principles that we cannot elucidate from our natural perspective alone. In this article, we review potential principles of consciousness revealed by prominent consciousness models, theories, and experimental observations such as the Default Space?Theory, Operational Architectonics Theory, and Integrated Information Theory,?which reveal biological and phenomenological foundations upon which consciousness is formed and maintained. The fundamental concepts we explore and consider worthy have largely emerged from commonalties shared by the various models which have gained attention. The concepts we review include the unity of consciousness, bioelectric operations as the substrate of consciousness, the emergence of a virtual 3D matrix, and the top-down dominance of perception.展开更多
This paper explores the integration of Standard Operating Procedures (SOPs) using virtual reality and smart glasses technology in food manufacturing. The study employs a thorough methodology, combining observational i...This paper explores the integration of Standard Operating Procedures (SOPs) using virtual reality and smart glasses technology in food manufacturing. The study employs a thorough methodology, combining observational insights to develop a comprehensive SOP. Implementation at different firms resulted in significant improvements, reducing product waste and enhancing overall efficiency. The use of virtual reality further augments SOP adoption. The findings underscore SOPs’ transformative influence, offering a tangible solution to challenges in the food production sector. Recommendations include regular SOP reviews and ongoing training for sustained success. Different firms exemplify SOPs as indispensable tools for operational excellence.展开更多
文摘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.
文摘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.
基金Supported in part by the National Natural Science Foundation of China(11271359)the Fundamental Research Funds for the Central Universities(2014-Ia-037and 2015-IVA-069)
文摘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)
基金Supported by the National Natural Science Foundation of China (10771064)the Natural Science Foundation of Zhejiang province (Y6090036+1 种基金Y7080197,Y606197)the Foundation of Department of Education of Zhejiang Province (20070482)
文摘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.
文摘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.
基金supported by Vietnam National Foundation for Science and Technology Development(101.02-2014.51)
文摘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.
基金partially supported by the NSFC(11631011,11626251)
文摘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.
文摘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.
文摘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.
文摘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.
文摘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.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 10775097 and 10874174)
文摘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.
文摘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.
基金Supported in part by 973 plan and NSF of Zhejiang Province of China(Gl999075105)
文摘We consider the weighted composition operators between Hardy spaces on the unit ball, and obtain some sufficient and necessary conditions of bounded or compact weighted composition operators. We also prove that the operator from H^1 to H^1 is compact if and only if it is weakly compact. Meanwhile, we get the analogue on the Bergman spaces.
文摘In this paper, Leibniz' formula of generalized divided difference with respect to a class of differential operators whose basic sets of solutions have power form, is considered. The recurrence formula of Green function about the operators is also given.
基金This work was supported by NSF of China(11171203,11201280)New Teacher’s Fund for Doctor Stations,Ministry of Education(20114402120003)NSF of Guangdong Province(10151503101000025,S2011010004511,S2011040004131)
文摘We characterize the boundedness and compactness of weighted composition operators on weighted Dirichlet spaces in terms of Nevanlinna counting functions and Caxleson measure.
文摘In the theory of random fractal, there are two important classes of random sets, one is the class of fractals generated by the paths of stochastic processes and another one is the class of factals generated by statistical contraction operators. Now we will introduce some things about the probability basis and fractal properties of fractals in the last class. The probability basis contains (1) the convergence and measurability of a random recursive setK(ω) as a random element, (2) martingals property. The fractal properties include (3) the character of various similarity, (4) the separability property, (5) the support and zero-one law of distributionP k =P·K ?1, (6) the Hausdorff dimension and Hausdorff exact measure function.
文摘We are all aware that our experience is structured into left and right, up and down, and we can understand from our own experience that consciousness is unified into a singular whole. Although we can understand such basic phenomenological axioms of experience, there are many more principles that we cannot elucidate from our natural perspective alone. In this article, we review potential principles of consciousness revealed by prominent consciousness models, theories, and experimental observations such as the Default Space?Theory, Operational Architectonics Theory, and Integrated Information Theory,?which reveal biological and phenomenological foundations upon which consciousness is formed and maintained. The fundamental concepts we explore and consider worthy have largely emerged from commonalties shared by the various models which have gained attention. The concepts we review include the unity of consciousness, bioelectric operations as the substrate of consciousness, the emergence of a virtual 3D matrix, and the top-down dominance of perception.
文摘This paper explores the integration of Standard Operating Procedures (SOPs) using virtual reality and smart glasses technology in food manufacturing. The study employs a thorough methodology, combining observational insights to develop a comprehensive SOP. Implementation at different firms resulted in significant improvements, reducing product waste and enhancing overall efficiency. The use of virtual reality further augments SOP adoption. The findings underscore SOPs’ transformative influence, offering a tangible solution to challenges in the food production sector. Recommendations include regular SOP reviews and ongoing training for sustained success. Different firms exemplify SOPs as indispensable tools for operational excellence.