This paper gives the definition of λ-cut sets and studies the structure of fuzzy rough sets. Based on the concept of rough sets, this paper proposes the representation theorem of fuzzy rough sets.
Based on the Cayley-Hamilton theorem and fixed-point method,we provide an elementary proof for the representation theorem of analytic isotropic tensor functions of a second-order tensor in a three-dimensional(3D)inner...Based on the Cayley-Hamilton theorem and fixed-point method,we provide an elementary proof for the representation theorem of analytic isotropic tensor functions of a second-order tensor in a three-dimensional(3D)inner-product space,which avoids introducing the generating function and Taylor series expansion.The proof is also extended to any finite-dimensional inner-product space.展开更多
In a paper published in Acta Mathematica Sinica(2016,59(4))we obtained some representation theorems for the conjugate spaces of some l^(0) type F-normed spaces.In this pa-per,for a sequence of normed spaces(X_(i)),we ...In a paper published in Acta Mathematica Sinica(2016,59(4))we obtained some representation theorems for the conjugate spaces of some l^(0) type F-normed spaces.In this pa-per,for a sequence of normed spaces(X_(i)),we study the representation problems of conjugate spaces of some l^(0)({X_(i)})type F-normed spaces,obtain the algebraic representation continued equalities(l^(0)({X_(i)}))^(*)=^(A)(c00^(0)({X_(i)}))^(*)=Ac00({X_(i)^(*)}),(l^(0)(X))^(*)=^(A)(c0^(0)(X))^(*)=^(A)(c00^(0)(X))^(*)=^(A)C00(X^(0)),and the topological representation((c00^(0)({X_(i)}))^(*),sw^(*))=c00^(0)({X_(i)^(*)}),where sw^(*)is the sequen-tial weak star topology.For the sequences of inner product spaces and number fields with the usual topology,the concrete forms of the basic representation theorems are obtained at last.展开更多
By representing random conjugate spaces a general representation theorem on classical duals is proved. For application, we unify and improve many known important representation theorems of the dual of Lebesgue-Bochner...By representing random conjugate spaces a general representation theorem on classical duals is proved. For application, we unify and improve many known important representation theorems of the dual of Lebesgue-Bochner function spaces.展开更多
In this paper, we establish a general representation theorem for generator of backward stochastic differential equation（BSDE）, whose generator has a quadratic growth in z. As some applications, we obtain a general c...In this paper, we establish a general representation theorem for generator of backward stochastic differential equation（BSDE）, whose generator has a quadratic growth in z. As some applications, we obtain a general converse comparison theorem of such quadratic BSDEs and uniqueness theorem, translation invariance for quadratic g-expectation.展开更多
In this paper, we prove that the generator g of a class of backward stochastic differential equations （BSDEs） can be represented by the solutions of the corresponding BSDEs at point （t, y, z）, when the terminal da...In this paper, we prove that the generator g of a class of backward stochastic differential equations （BSDEs） can be represented by the solutions of the corresponding BSDEs at point （t, y, z）, when the terminal data is in Lp spaces, for 1 〈 p ≤ 2.展开更多
The representation theorem and the viability property for backward stochastic differential equations(BSDEs)require further exploration,given their widespread use in both theory and practical applications.In this study...The representation theorem and the viability property for backward stochastic differential equations(BSDEs)require further exploration,given their widespread use in both theory and practical applications.In this study,we present a positive answer to the long-standing open question of whether the representation theorem still holds in the L^(2)-sense under the standard assumptions of square integrability and Lipschitzian continuity on the generators of BSDEs.In the process,the multidimensional case is considered.Subsequently,based on the representation theorem,we obtain a necessary and sufficient condition for the viability property of the BSDEs under standard conditions on the generators.This removes the requirement for the generator to possess the properties of stronger integrability and continuity with respect to time variables.As an application of these results,we conduct various types of comparisons and converse comparisons for the solutions of multidimensional BSDEs,and several properties of the multidimensional g-expectation are obtained.展开更多
Let B be a separable real Banach space and X(t) be a symmetric conservative diffusionprocess taking values in B. In this paper, we decompose the functional u(X(t),t) into a sumof a square integrable martingale and a r...Let B be a separable real Banach space and X(t) be a symmetric conservative diffusionprocess taking values in B. In this paper, we decompose the functional u(X(t),t) into a sumof a square integrable martingale and a regular 0-quadratic variation process. On this basis, weestablish the predictable representation theorem of X(t).展开更多
In this paper,we shall exploit the Freud method in the Classical operator approximation theory to im- prove known quantitative estimalions with an emphasis on Calculah' on the generic constants.
Although the concept of interval fuzzy set and its properties have been defined, its three theorems and their effectiveness are not proved. Therefore, the knowledge presentation and its operation rules of interval fuz...Although the concept of interval fuzzy set and its properties have been defined, its three theorems and their effectiveness are not proved. Therefore, the knowledge presentation and its operation rules of interval fuzzy set are studied firstly, and then the cut set of interval fuzzy set is proposed. Moreover, the decomposition theo- rem, the representation theorem and the extension theorem of interval fuzzy set are presented. Finally, examples are given to demonstrate that the classical fuzzy set is a special case of interval fuzzy set and interval fuzzy set is an effective expansion of the classical fuzzy set.展开更多
In this paper,we consider the measure determined by a fractional OrnsteinUhlenbeck process.For such a measure,we establish an explicit form of the martingale representation theorem and consequently obtain an explicit ...In this paper,we consider the measure determined by a fractional OrnsteinUhlenbeck process.For such a measure,we establish an explicit form of the martingale representation theorem and consequently obtain an explicit form of the Logarithmic-Sobolev inequality.To this end,we also present the integration by parts formula for such a measure,which is obtained via its pull back formula and the Bismut method.展开更多
In this paper, we prove that a kind of second order stochastic differential op- erator can be represented by the limit of solutions of BSDEs with uniformly continuous coefficients. This result is a generalization of t...In this paper, we prove that a kind of second order stochastic differential op- erator can be represented by the limit of solutions of BSDEs with uniformly continuous coefficients. This result is a generalization of the representation for the uniformly continuous generator. With the help of this representation, we obtain the corresponding converse comparison theorem for the BSDEs with uniformly continuous coefficients, and get some equivalent relationships between the properties of the generator g and the associated solutions of BSDEs. Moreover, we give a new proof about g-convexity.展开更多
Extending the results of an article published in(Acta Mathematica Sinica(2016,59(4))by the author,for a sequence of normed spaces{X_(i)},the representation problem of conjugate spaces of some l^(0)({X_(i)})type F-norm...Extending the results of an article published in(Acta Mathematica Sinica(2016,59(4))by the author,for a sequence of normed spaces{X_(i)},the representation problem of conjugate spaces of some l^(0)({X_(i)})type F-normed spaces are studied in this paper.The algebraic representation continued equalities l^(0)({X_(i)})*A=c^(0)_(00)({X_(i)})*A=c_(00)({X^(*)_(i)}),(l^(0)(X))^(*)A=(c^(0)(X))^(*)A=(c^(0)_0(X))^(*)A=(c^(0)_(00)(X))^(*)A=c_(00)(X^(*))are obtained in the first part.Under weak-star topology,the topological representation c^(0)_(00)({X_(i)})^(*),w^(*)=c^(0)_(00)({X^(*)_(i)})is obtained in the second part.For the sequence of inner product spaces and number fields with the usual topology,the concrete forms of the basic representation theorems are obtained at last.展开更多
This paper presents a nonlinear micropolar nonclassical continuum theory (MPNCCT) for finite deformation, finite strain deformation physics of thermosviscoelastic solid medium with memory (polymeric micropolar solids)...This paper presents a nonlinear micropolar nonclassical continuum theory (MPNCCT) for finite deformation, finite strain deformation physics of thermosviscoelastic solid medium with memory (polymeric micropolar solids) based on classical rotations cΘand their rates. Contravariant second Piola-Kirchhoff stress and moment tensors, in conjunction with finite deformation measures derived by the authors in recent paper, are utilized in deriving the conservation and balance laws and the constitutive theories based on conjugate pairs in entropy inequality and the representation theorem. This nonlinear MPNCCT for TVES with rheology: 1) incorporates nonlinear ordered rate dissipation mechanism based on Green’s strain rates up to order n;2) also incorporates an additional ordered rate dissipation mechanism due to microconstituents, the viscosity of the medium and the rates of the symmetric part of the rotation gradient (of cΘ) tensor up to order n, referred to as micropolar dissipation or micropolar viscous dissipation mechanism;3) incorporates the primary mechanism of memory or rheology due to long chain molecules of the polymer and the viscosity of the medium by using the contravaraint second Piola-Kirchhoff stress tensor and its rates up to order m, resulting in a relaxation spectrum;4) incorporates second mechanism of memory or rheology due to nonclassical physics, interaction of microconstituents with the viscous medium and long chain molecules by considering rates of the contravariant second Piola-Kirchhoff moment tensor up to order m, resulting in relaxation of second Piola-Kirchhoff moment tensor. This results in another relaxation spectrum for the second Piola-Kirchhoff moment tensor due to microconstituents, referred to as micropolar relaxation spectrum consisting of micropolar relaxation time constants of the material. This nonlinear MPNCCT for TVES with memory is thermodynamically and mathematically consistent, and the mathematical model consisting of conservation and balance laws and the constitutive theories has closure and naturally reduces to linear MPNCCT based on infinitesimal deformation assumption. BMM is the essential balance law for all MPNCCT and is used in the present work as well. In the absence of this balance law, a valid thermodynamically and mathematically consistent nonlinear MPNCCT is not possible. The nonlinear MPNCCT based on rotations (cΘ+αΘ) and αΘ(ignoring cΘ) is not considered due to the fact that even the linear MPNCCT based on these rotations is invalid and is thermodynamically and mathematically inconsistent MPNCCT.展开更多
The optimization problem is considered in which the objective function is pseudolinear（both pseudoconvex and pseudoconcave） and the constraints are linear. The general expression for the optimal solutions to the pro...The optimization problem is considered in which the objective function is pseudolinear（both pseudoconvex and pseudoconcave） and the constraints are linear. The general expression for the optimal solutions to the problem is derived with the representation theorem of polyhedral sets, and the uniqueness condition of the optimal solution and the computational procedures to determine all optimal solutions （if the uniqueness condition is not satisfied ） are provided. Finally, an illustrative example is also given.展开更多
Fifth-order isotropic descartes tensor and its existence theorem and representation problems are researched, then a general representation formula of fifth-order isotropic descartes tensor is got.
This paper is concerned with a class of uncertain backward stochastic differential equations （UBSDEs） driven by both an m-dimensional Brownian motion and a d-dimensional canonical process with uniform Lipschitzian c...This paper is concerned with a class of uncertain backward stochastic differential equations （UBSDEs） driven by both an m-dimensional Brownian motion and a d-dimensional canonical process with uniform Lipschitzian coefficients. Such equations can be useful in mod- elling hybrid systems, where the phenomena are simultaneously subjected to two kinds of un- certainties： randomness and uncertainty. The solutions of UBSDEs are the uncertain stochastic processes. Thus, the existence and uniqueness of solutions to UBSDEs with Lipschitzian coeffi- cients are proved.展开更多
In this paper, we discuss completely positive definite maps over topological algebras. A Schwarz type inequality for n-positive definite maps, and the Stinespring representation theorem for completely positive definit...In this paper, we discuss completely positive definite maps over topological algebras. A Schwarz type inequality for n-positive definite maps, and the Stinespring representation theorem for completely positive definite maps over topological algebras are given.展开更多
This paper presents ordered rate nonlinear constitutive theories for thermoviscoelastic fluids based on Classical Continuum Mechanics (CCM). We refer to these fluids as classical thermoviscoelastic polymeric fluids. T...This paper presents ordered rate nonlinear constitutive theories for thermoviscoelastic fluids based on Classical Continuum Mechanics (CCM). We refer to these fluids as classical thermoviscoelastic polymeric fluids. The conservation and balance laws of CCM constitute the core of the mathematical model. Constitutive theories for the Cauchy stress tensor are derived using the conjugate pair in the entropy inequality, additional desired physics, and the representation theorem. The constitutive theories for the Cauchy stress tensor consider convected time derivatives of Green’s strain tensor or the Almansi strain tensor up to order n and the convected time derivatives of the Cauchy stress tensor up to order m. The resulting constitutive theories of order (m, n) are based on integrity and are valid for dilute as well as dense polymeric, compressible, and incompressible fluids with variable material coefficients. It is shown that Maxwell, Oldroyd-B, and Giesekus constitutive models can be described by a single constitutive theory. It is well established that the currently used Maxwell and Oldroyd-B models predict zero normal stress perpendicular to the flow direction. It is shown that this deficiency is a consequence of not retaining certain generators and invariants from the integrity (complete basis) in the constitutive theory and can be corrected by including additional generators and invariants in the constitutive theory. Similar improvements are also suggested for the Giesekus constitutive model. Model problem studies are presented for BVPs consisting of fully developed flow between parallel plates and lid-driven cavities utilizing the new constitutive theories for Maxwell, Oldroyd-B, and Giesekus fluids. Results are compared with those obtained from using currently used constitutive theories for the three polymeric fluids.展开更多
In this article, we give a new proof of the Itôformula for some integral processes related to the space-time Lévy noise introduced in [1] [2] as an alternative for the Gaussian white noise perturbing an...In this article, we give a new proof of the Itôformula for some integral processes related to the space-time Lévy noise introduced in [1] [2] as an alternative for the Gaussian white noise perturbing an SPDE. We discuss two applications of this result, which are useful in the study of SPDEs driven by a space-time Lévy noise with finite variance: a maximal inequality for the p-th moment of the stochastic integral, and the Itôrepresentation theorem leading to a chaos expansion similar to the Gaussian case.展开更多
基金Supported by the National Natural Science Foundation of China (No. 69803007)
文摘This paper gives the definition of λ-cut sets and studies the structure of fuzzy rough sets. Based on the concept of rough sets, this paper proposes the representation theorem of fuzzy rough sets.
文摘Based on the Cayley-Hamilton theorem and fixed-point method,we provide an elementary proof for the representation theorem of analytic isotropic tensor functions of a second-order tensor in a three-dimensional(3D)inner-product space,which avoids introducing the generating function and Taylor series expansion.The proof is also extended to any finite-dimensional inner-product space.
基金Supported by the National Natural Science Foundation of China(Grant No.11471236)
文摘In a paper published in Acta Mathematica Sinica(2016,59(4))we obtained some representation theorems for the conjugate spaces of some l^(0) type F-normed spaces.In this pa-per,for a sequence of normed spaces(X_(i)),we study the representation problems of conjugate spaces of some l^(0)({X_(i)})type F-normed spaces,obtain the algebraic representation continued equalities(l^(0)({X_(i)}))^(*)=^(A)(c00^(0)({X_(i)}))^(*)=Ac00({X_(i)^(*)}),(l^(0)(X))^(*)=^(A)(c0^(0)(X))^(*)=^(A)(c00^(0)(X))^(*)=^(A)C00(X^(0)),and the topological representation((c00^(0)({X_(i)}))^(*),sw^(*))=c00^(0)({X_(i)^(*)}),where sw^(*)is the sequen-tial weak star topology.For the sequences of inner product spaces and number fields with the usual topology,the concrete forms of the basic representation theorems are obtained at last.
文摘By representing random conjugate spaces a general representation theorem on classical duals is proved. For application, we unify and improve many known important representation theorems of the dual of Lebesgue-Bochner function spaces.
基金The authors are supported by the National Natural Science Foundation of China(No.11571024)Natural Science Foundation of Beijing(No.1132008)supported by a program of Hebei province(No.QN2017116)
文摘In this paper, we establish a general representation theorem for generator of backward stochastic differential equation（BSDE）, whose generator has a quadratic growth in z. As some applications, we obtain a general converse comparison theorem of such quadratic BSDEs and uniqueness theorem, translation invariance for quadratic g-expectation.
基金Supported by the National Natural Science Foundation of China (No. 10921101)WCU (World Class University)program through the National Research Foundation of Korea funded by the Ministry of Education,Science and Technology (No. R31-20007)+1 种基金the National Natural Science Foundation of China (No. 11171179)the Natural Science Foundation of Shandong Province (No. ZR2009AL015)
文摘In this paper, we prove that the generator g of a class of backward stochastic differential equations （BSDEs） can be represented by the solutions of the corresponding BSDEs at point （t, y, z）, when the terminal data is in Lp spaces, for 1 〈 p ≤ 2.
基金supported by the Natural Science Foundation of Shandong Province(Grant Nos.ZR2022MA079,ZR2021MG049)the National Social Science Funding of China(Grant No.21CJY027).
文摘The representation theorem and the viability property for backward stochastic differential equations(BSDEs)require further exploration,given their widespread use in both theory and practical applications.In this study,we present a positive answer to the long-standing open question of whether the representation theorem still holds in the L^(2)-sense under the standard assumptions of square integrability and Lipschitzian continuity on the generators of BSDEs.In the process,the multidimensional case is considered.Subsequently,based on the representation theorem,we obtain a necessary and sufficient condition for the viability property of the BSDEs under standard conditions on the generators.This removes the requirement for the generator to possess the properties of stronger integrability and continuity with respect to time variables.As an application of these results,we conduct various types of comparisons and converse comparisons for the solutions of multidimensional BSDEs,and several properties of the multidimensional g-expectation are obtained.
基金This project is supported by the National Natural Science Foundation of China
文摘Let B be a separable real Banach space and X(t) be a symmetric conservative diffusionprocess taking values in B. In this paper, we decompose the functional u(X(t),t) into a sumof a square integrable martingale and a regular 0-quadratic variation process. On this basis, weestablish the predictable representation theorem of X(t).
文摘In this paper,we shall exploit the Freud method in the Classical operator approximation theory to im- prove known quantitative estimalions with an emphasis on Calculah' on the generic constants.
基金Supported by the Aeronautical Science Foundation(20115868009)the Open Project Program of Key Laboratory of Intelligent Computing&Information Processing of Ministry of Education in Xiangtan University(2011ICIP04)+1 种基金the Program of 211 Innovation Engineering on Information in Xiamen University(2009-2011)the College Students Innovation Training Plan of Xianmen University~~
文摘Although the concept of interval fuzzy set and its properties have been defined, its three theorems and their effectiveness are not proved. Therefore, the knowledge presentation and its operation rules of interval fuzzy set are studied firstly, and then the cut set of interval fuzzy set is proposed. Moreover, the decomposition theo- rem, the representation theorem and the extension theorem of interval fuzzy set are presented. Finally, examples are given to demonstrate that the classical fuzzy set is a special case of interval fuzzy set and interval fuzzy set is an effective expansion of the classical fuzzy set.
基金supported by the National Natural Science Foundation of China(11801064)。
文摘In this paper,we consider the measure determined by a fractional OrnsteinUhlenbeck process.For such a measure,we establish an explicit form of the martingale representation theorem and consequently obtain an explicit form of the Logarithmic-Sobolev inequality.To this end,we also present the integration by parts formula for such a measure,which is obtained via its pull back formula and the Bismut method.
基金the partial support from the NSF of China(11171186)the NSF of Shandong Province(ZR2010AM021)the "111" project
文摘In this paper, we prove that a kind of second order stochastic differential op- erator can be represented by the limit of solutions of BSDEs with uniformly continuous coefficients. This result is a generalization of the representation for the uniformly continuous generator. With the help of this representation, we obtain the corresponding converse comparison theorem for the BSDEs with uniformly continuous coefficients, and get some equivalent relationships between the properties of the generator g and the associated solutions of BSDEs. Moreover, we give a new proof about g-convexity.
基金Supported by the National Natural Science Foundation of China(11471236)
文摘Extending the results of an article published in(Acta Mathematica Sinica(2016,59(4))by the author,for a sequence of normed spaces{X_(i)},the representation problem of conjugate spaces of some l^(0)({X_(i)})type F-normed spaces are studied in this paper.The algebraic representation continued equalities l^(0)({X_(i)})*A=c^(0)_(00)({X_(i)})*A=c_(00)({X^(*)_(i)}),(l^(0)(X))^(*)A=(c^(0)(X))^(*)A=(c^(0)_0(X))^(*)A=(c^(0)_(00)(X))^(*)A=c_(00)(X^(*))are obtained in the first part.Under weak-star topology,the topological representation c^(0)_(00)({X_(i)})^(*),w^(*)=c^(0)_(00)({X^(*)_(i)})is obtained in the second part.For the sequence of inner product spaces and number fields with the usual topology,the concrete forms of the basic representation theorems are obtained at last.
文摘This paper presents a nonlinear micropolar nonclassical continuum theory (MPNCCT) for finite deformation, finite strain deformation physics of thermosviscoelastic solid medium with memory (polymeric micropolar solids) based on classical rotations cΘand their rates. Contravariant second Piola-Kirchhoff stress and moment tensors, in conjunction with finite deformation measures derived by the authors in recent paper, are utilized in deriving the conservation and balance laws and the constitutive theories based on conjugate pairs in entropy inequality and the representation theorem. This nonlinear MPNCCT for TVES with rheology: 1) incorporates nonlinear ordered rate dissipation mechanism based on Green’s strain rates up to order n;2) also incorporates an additional ordered rate dissipation mechanism due to microconstituents, the viscosity of the medium and the rates of the symmetric part of the rotation gradient (of cΘ) tensor up to order n, referred to as micropolar dissipation or micropolar viscous dissipation mechanism;3) incorporates the primary mechanism of memory or rheology due to long chain molecules of the polymer and the viscosity of the medium by using the contravaraint second Piola-Kirchhoff stress tensor and its rates up to order m, resulting in a relaxation spectrum;4) incorporates second mechanism of memory or rheology due to nonclassical physics, interaction of microconstituents with the viscous medium and long chain molecules by considering rates of the contravariant second Piola-Kirchhoff moment tensor up to order m, resulting in relaxation of second Piola-Kirchhoff moment tensor. This results in another relaxation spectrum for the second Piola-Kirchhoff moment tensor due to microconstituents, referred to as micropolar relaxation spectrum consisting of micropolar relaxation time constants of the material. This nonlinear MPNCCT for TVES with memory is thermodynamically and mathematically consistent, and the mathematical model consisting of conservation and balance laws and the constitutive theories has closure and naturally reduces to linear MPNCCT based on infinitesimal deformation assumption. BMM is the essential balance law for all MPNCCT and is used in the present work as well. In the absence of this balance law, a valid thermodynamically and mathematically consistent nonlinear MPNCCT is not possible. The nonlinear MPNCCT based on rotations (cΘ+αΘ) and αΘ(ignoring cΘ) is not considered due to the fact that even the linear MPNCCT based on these rotations is invalid and is thermodynamically and mathematically inconsistent MPNCCT.
文摘The optimization problem is considered in which the objective function is pseudolinear（both pseudoconvex and pseudoconcave） and the constraints are linear. The general expression for the optimal solutions to the problem is derived with the representation theorem of polyhedral sets, and the uniqueness condition of the optimal solution and the computational procedures to determine all optimal solutions （if the uniqueness condition is not satisfied ） are provided. Finally, an illustrative example is also given.
文摘Fifth-order isotropic descartes tensor and its existence theorem and representation problems are researched, then a general representation formula of fifth-order isotropic descartes tensor is got.
基金Supported by National Natural Science Foundation of China(71171003,71210107026)Anhui Natural Science Foundation(10040606003)Anhui Natural Science Foundation of Universities(KJ2012B019,KJ2013B023)
文摘This paper is concerned with a class of uncertain backward stochastic differential equations （UBSDEs） driven by both an m-dimensional Brownian motion and a d-dimensional canonical process with uniform Lipschitzian coefficients. Such equations can be useful in mod- elling hybrid systems, where the phenomena are simultaneously subjected to two kinds of un- certainties： randomness and uncertainty. The solutions of UBSDEs are the uncertain stochastic processes. Thus, the existence and uniqueness of solutions to UBSDEs with Lipschitzian coeffi- cients are proved.
文摘In this paper, we discuss completely positive definite maps over topological algebras. A Schwarz type inequality for n-positive definite maps, and the Stinespring representation theorem for completely positive definite maps over topological algebras are given.
文摘This paper presents ordered rate nonlinear constitutive theories for thermoviscoelastic fluids based on Classical Continuum Mechanics (CCM). We refer to these fluids as classical thermoviscoelastic polymeric fluids. The conservation and balance laws of CCM constitute the core of the mathematical model. Constitutive theories for the Cauchy stress tensor are derived using the conjugate pair in the entropy inequality, additional desired physics, and the representation theorem. The constitutive theories for the Cauchy stress tensor consider convected time derivatives of Green’s strain tensor or the Almansi strain tensor up to order n and the convected time derivatives of the Cauchy stress tensor up to order m. The resulting constitutive theories of order (m, n) are based on integrity and are valid for dilute as well as dense polymeric, compressible, and incompressible fluids with variable material coefficients. It is shown that Maxwell, Oldroyd-B, and Giesekus constitutive models can be described by a single constitutive theory. It is well established that the currently used Maxwell and Oldroyd-B models predict zero normal stress perpendicular to the flow direction. It is shown that this deficiency is a consequence of not retaining certain generators and invariants from the integrity (complete basis) in the constitutive theory and can be corrected by including additional generators and invariants in the constitutive theory. Similar improvements are also suggested for the Giesekus constitutive model. Model problem studies are presented for BVPs consisting of fully developed flow between parallel plates and lid-driven cavities utilizing the new constitutive theories for Maxwell, Oldroyd-B, and Giesekus fluids. Results are compared with those obtained from using currently used constitutive theories for the three polymeric fluids.
基金funded by a grant from the Natural Sciences and Engineering Research Council of Canada.
文摘In this article, we give a new proof of the Itôformula for some integral processes related to the space-time Lévy noise introduced in [1] [2] as an alternative for the Gaussian white noise perturbing an SPDE. We discuss two applications of this result, which are useful in the study of SPDEs driven by a space-time Lévy noise with finite variance: a maximal inequality for the p-th moment of the stochastic integral, and the Itôrepresentation theorem leading to a chaos expansion similar to the Gaussian case.
