The strain-gradient and non-Euclidean continuum theories are employed for construction of non- classical solutions of continuum models. The linear approximation of both models＇ results in identical structures in term...The strain-gradient and non-Euclidean continuum theories are employed for construction of non- classical solutions of continuum models. The linear approximation of both models＇ results in identical structures in terms of their kinematic and stress characteristics. The solutions obtained in this study exhibit a critical behaviour with respect to the external loading parameter. The conclusions are obtained based on an investigation of the solution for the scalar curvature in the non-Euclidean continuum theory, The proposed analysis enables us to use different theoretical approaches for description of rock critical behaviour under different loading conditions.展开更多
The compositional model is often used to describe multicomponent multiphase porous media flows in the petroleum industry.The fully implicit method with strong stability and weak constraints on time-step sizes is commo...The compositional model is often used to describe multicomponent multiphase porous media flows in the petroleum industry.The fully implicit method with strong stability and weak constraints on time-step sizes is commonly used in mainstream commercial reservoir simulators.In this paper,we develop an efficient multistage preconditioner for the fully implicit compositional flow simulation.The method employs an adaptive setup phase to improve the parallel efficiency on GPUs.Furthermore,a multicolor Gauss-Seidel algorithm based on the adjacency matrix is applied in the algebraic multigrid methods for the pressure part.Numerical results demonstrate that the proposed algorithm achieves good parallel speedup while yielding the same convergence behavior as the corresponding sequential version.展开更多
AIM： To assess the usefulness of FibroTest to forecast scores by constructing decision trees in patients with chronic hepatitis C.METHODS： We used the C4.5 classification algorithm to construct decision trees with d...AIM： To assess the usefulness of FibroTest to forecast scores by constructing decision trees in patients with chronic hepatitis C.METHODS： We used the C4.5 classification algorithm to construct decision trees with data from 261 patients with chronic hepatitis C without a liver biopsy. The FibroTest attributes of age, gender, bilirubin, apolipoprotein, haptoglobin, α2 macroglobulin, and γ-glutamyl transpeptidase were used as predictors, and the FibroTest score as the target. For testing, a 10-fold cross validation was used.RESULTS： The overall classification error was 14.9% （accuracy 85.1%）. FibroTest＇s cases with true scores of FO and F4 were classified with very high accuracy （18/20 for FO, 9/9 for FO-1 and 92/96 for F4） and the largest confusion centered on F3. The algorithm produced a set of compound rules out of the ten classification trees and was used to classify the 261 patients. The rules for the classification of patients in FO and F4 were effective in more than 75% of the cases in which they were tested.CONCLUSION： The recognition of clinical subgroups should help to enhance our ability to assess differences in fibrosis scores in clinical studies and improve our understanding of fibrosis progression,展开更多
This paper is dedicated to the study of viscous compressible barotropic fluids in dimension N ≥ 2. We address the question of well-posedness for large data having critical Besov regularity. Our result improves N the...This paper is dedicated to the study of viscous compressible barotropic fluids in dimension N ≥ 2. We address the question of well-posedness for large data having critical Besov regularity. Our result improves N the analysis of Danchin and of the author inasmuch as we may take initial density in BN/p p,1 with 1 ≤ p 〈 ＋∞. Our result relies on a new a priori estimate for the velocity, where we introduce a new unknown called effective velocity to weaken one of the couplings between the density and the velocity. In particular, our result is the first in which we obtain uniqueness without imposing hypothesis on the gradient of the density.展开更多
A set of techniques for well treatment aimed to enhance oil recovery are considered in the present study.These are based on the application of elastic waves of various types(dilation-wave,vibro-wave,or other acoustica...A set of techniques for well treatment aimed to enhance oil recovery are considered in the present study.These are based on the application of elastic waves of various types(dilation-wave,vibro-wave,or other acoustically induced effects).In such a context,a new technique is proposed to predict the effectiveness of the elastic-wave well treatment using the rank distribution according to Zipf’s law.It is revealed that,when the results of elastic wave well treatments are analyzed,groups of wells exploiting various geological deposits can differ in terms of their slope coefficients and free members.As the slope coefficient increases,the average increase in the well oil production rate(after the well treatment)becomes larger.An equation is obtained accordingly for estimating the slope coefficient in the Zipf’s equation from the frequency of the elastic wave.The obtained results demonstrate the applicability of the Zipf’s law in the analysis of the technological efficiency of elastic-wave well treatment methods.展开更多
Most financial signals show time dependency that,combined with noisy and extreme events,poses serious problems in the parameter estimations of statistical models.Moreover,when addressing asset pricing,portfolio select...Most financial signals show time dependency that,combined with noisy and extreme events,poses serious problems in the parameter estimations of statistical models.Moreover,when addressing asset pricing,portfolio selection,and investment strategies,accurate estimates of the relationship among assets are as necessary as are delicate in a time-dependent context.In this regard,fundamental tools that increasingly attract research interests are precision matrix and graphical models,which are able to obtain insights into the joint evolution of financial quantities.In this paper,we present a robust divergence estimator for a time-varying precision matrix that can manage both the extreme events and time-dependency that affect financial time series.Furthermore,we provide an algorithm to handle parameter estimations that uses the“maximization–minimization”approach.We apply the methodology to synthetic data to test its performances.Then,we consider the cryptocurrency market as a real data application,given its remarkable suitability for the proposed method because of its volatile and unregulated nature.展开更多
In this paper it is shown that the thermodynamic limit of the partition function of the statistical models under consideration on a one-dimensional lattice with an arbitrary finite number of interacting neighbors is e...In this paper it is shown that the thermodynamic limit of the partition function of the statistical models under consideration on a one-dimensional lattice with an arbitrary finite number of interacting neighbors is expressed in terms of the principal eigenvalue of a matrix of finite size. The high sparseness of these matrices for any number of interactions makes it possible to perform an effective numerical analysis of the macro characteristics of these models.展开更多
In this paper, we investigate the flow of customers through queuing systems with randomly varying intensities. The analysis of the Kolmogorov-Chapman system of stationary equations for this model showed that it is not...In this paper, we investigate the flow of customers through queuing systems with randomly varying intensities. The analysis of the Kolmogorov-Chapman system of stationary equations for this model showed that it is not possible to construct a convenient symbolic solution. In this paper an attempt is made to circumvent this requirement by referring to the ergodicity theorems, which gives the conditions for the existence of the limit distribution in the service processes, but do not require knowledge of them.展开更多
Under the effects of electric field and chemical reaction, the problem of dispersion of aerosols in a poorly conducting fluid in a channel is solved analytically using the mixture theory together with a regular pertur...Under the effects of electric field and chemical reaction, the problem of dispersion of aerosols in a poorly conducting fluid in a channel is solved analytically using the mixture theory together with a regular perturbation technique. It is shown that the aerosols are dispersed relative to a plane moving with the mean speed of atmospheric fluid as well as the mean speed of agglomeration of aerosol with a relative diffusion coefficient, called the Taylor dispersion coefficient. This coefficient is numerically computed and the results reveal that it increases with an increase in the electric number, but decreases with increasing porous parameter. The physical explanations for the phenomena are given in this article.展开更多
This paper is dedicated to the study of viscous compressible barotropic fluids in dimension N 2.We address the question of well-posedness for large data having critical Besov regularity.Our result improves the analysi...This paper is dedicated to the study of viscous compressible barotropic fluids in dimension N 2.We address the question of well-posedness for large data having critical Besov regularity.Our result improves the analysis of Danchin and of the author inasmuch as we may take initial density in B N p p,1 with 1 p < +∞.Our result relies on a new a priori estimate for the velocity,where we introduce a new unknown called effective velocity to weaken one of the couplings between the density and the velocity.In particular,our result is the first in which we obtain uniqueness without imposing hypothesis on the gradient of the density.展开更多
Calibration and identification of the exchange effect between the karst aquifers and the underlying conduit network are important issues in order to gain a better understanding of these hydraulic systems. Based on a c...Calibration and identification of the exchange effect between the karst aquifers and the underlying conduit network are important issues in order to gain a better understanding of these hydraulic systems. Based on a coupled continuum pipe-flow(CCPF for short) model describing flows in karst aquifers, this paper is devoted to the identification of an exchange rate function, which models the hydraulic interaction between the fissured volume(matrix) and the conduit, from the Neumann boundary data, i.e., matrix/conduit seepage velocity. The authors formulate this parameter identification problem as a nonlinear operator equation and prove the compactness of the forward mapping. The stable approximate solution is obtained by two classic iterative regularization methods, namely,the Landweber iteration and Levenberg-Marquardt method. Numerical examples on noisefree and noisy data shed light on the appropriateness of the proposed approaches.展开更多
The definition of a molecular surface which is physically sound and computationally efficient is a very interesting and long standing problem in the implicit solvent continuum modeling of biomolecular systems as well ...The definition of a molecular surface which is physically sound and computationally efficient is a very interesting and long standing problem in the implicit solvent continuum modeling of biomolecular systems as well as in the molecular graphics field.In this work,two molecular surfaces are evaluated with respect to their suitability for electrostatic computation as alternatives to the widely used Connolly-Richards surface:the blobby surface,an implicit Gaussian atom centered surface,and the skin surface.As figures of merit,we considered surface differentiability and surface area continuity with respect to atom positions,and the agreement with explicit solvent simulations.Geometric analysis seems to privilege the skin to the blobby surface,and points to an unexpected relationship between the non connectedness of the surface,caused by interstices in the solute volume,and the surface area dependence on atomic centers.In order to assess the ability to reproduce explicit solvent results,specific software tools have been developed to enable the use of the skin surface in PoissonBoltzmann calculations with the DelPhi solver.The results indicate that the skin and Connolly surfaces have a comparable performance from this last point of view.展开更多
Owing to a production error,Reference[11]was omitted in the References section,and it needs to be corrected to:[11]N.S.Bulychev,Mechanics of underground structures,Moscow,Nedra,1982.The publisher would like to apologi...Owing to a production error,Reference[11]was omitted in the References section,and it needs to be corrected to:[11]N.S.Bulychev,Mechanics of underground structures,Moscow,Nedra,1982.The publisher would like to apologise for any inconvenience caused.展开更多
A brief overview of the basic principles of geomechanics of highly compressed rocks and masses is presented.The historical path of formation of this new scientific branch of the classical geomechanics is shown.The sca...A brief overview of the basic principles of geomechanics of highly compressed rocks and masses is presented.The historical path of formation of this new scientific branch of the classical geomechanics is shown.The scales and structural levels of the geomedium failure are identified.The issues of adequate mathematical models at various geomedium structural levels developing,as well as methods for determining the parameters of these models are considered.The object,subject,methods and principles of geomechanics of highly compressed rocks and masses are formulated as a complex discipline at the intersection of classical geomechanics and mesomechanics.展开更多
Mean field theory has raised a lot of interest in the recent years (see in particular the results of Lasry-Lions in 2006 and 2007,of Gueant-Lasry-Lions in 2011,of HuangCaines-Malham in 2007 and many others).There are ...Mean field theory has raised a lot of interest in the recent years (see in particular the results of Lasry-Lions in 2006 and 2007,of Gueant-Lasry-Lions in 2011,of HuangCaines-Malham in 2007 and many others).There are a lot of applications.In general,the applications concern approximating an infinite number of players with common behavior by a representative agent.This agent has to solve a control problem perturbed by a field equation,representing in some way the behavior of the average infinite number of agents.This approach does not lead easily to the problems of Nash equilibrium for a finite number of players,perturbed by field equations,unless one considers averaging within different groups,which has not been done in the literature,and seems quite challenging.In this paper,the authors approach similar problems with a different motivation which makes sense for control and also for differential games.Thus the systems of nonlinear partial differential equations with mean field terms,which have not been addressed in the literature so far,are considered here.展开更多
We study the structure of rings which satisfy the von Neumann regularity of commutators,and call a ring R C-regularif ab-ba ∈(ab-ba)R(ab-ba)for all a,b in R.For a C-regular ring R,we prove J(R[X])=N^(*)(R[X])=N^(*)(R...We study the structure of rings which satisfy the von Neumann regularity of commutators,and call a ring R C-regularif ab-ba ∈(ab-ba)R(ab-ba)for all a,b in R.For a C-regular ring R,we prove J(R[X])=N^(*)(R[X])=N^(*)(R)[X]=W(R)[X]■Z(R[X]),where J(A),N^(*)(A),W(A),Z(A)are the Jacobson radical,upper nilradical,Wedderburn radical,and center of a given ring A,respectively,and A[X]denotes the polynomial ring with a set X of commuting indeterminates over A;we also prove that R is semiprime if and only if the right(left)singular ideal of R is zero.We provide methods to construct C-regular rings which are neither commutative nor von Neumann regular,from any given ring.Moreover,for a C-regular ring R,the following are proved to be equivalent:(i)R is Abelian;(ii)every prime factor ring of R is a duo domain;(ii)R is quasi-duo;and(iv)R/W(R)is reduced.展开更多
The authors deal with nonlinear elliptic and parabolic systems that are the Bellman like systems associated to stochastic differential games with mean field dependent dynamics.The key novelty of the paper is that they...The authors deal with nonlinear elliptic and parabolic systems that are the Bellman like systems associated to stochastic differential games with mean field dependent dynamics.The key novelty of the paper is that they allow heavily mean field dependent dynamics.This in particular leads to a system of PDE's with critical growth,for which it is rare to have an existence and/or regularity result.In the paper,they introduce a structural assumptions that cover many cases in stochastic differential games with mean field dependent dynamics for which they are able to establish the existence of a weak solution.In addition,the authors present here a completely new method for obtaining the maximum/minimum principles for systems with critical growths,which is a starting point for further existence and also qualitative analysis.展开更多
This study provides new insights into the nature of seasonal variations in coordinate time series of GPS sites located near active faults and methods of their modeling. Monthly averaged coordinate time series were ana...This study provides new insights into the nature of seasonal variations in coordinate time series of GPS sites located near active faults and methods of their modeling. Monthly averaged coordinate time series were analyzed for several pairs of collocated GPS sites situated near the active fault intersection area, in close proximity to the central part of the northern boundary of the Amurian plate and the vicinity of the San Andreas Fault zone. It is concluded that the observed seasonal variations are best described by a breather function which is one of the solutions of the well-known sine-Gordon equation. The obtained results suggest that, in this case, the source of seasonal variations may be caused by the appearance of solitary strain waves in the fault intersection system, which may be qualitatively treated as standing waves of compression-extension of the geological medium. Based on statistical testing, the limits of applicability of the suggested model have been established.展开更多
We prove that the mirror coupling is the unique maximal Markovian coupling of two Euclidean Brownian motions starting from single points and discuss the connection between the uniqueness of maximalMarkovian coupling o...We prove that the mirror coupling is the unique maximal Markovian coupling of two Euclidean Brownian motions starting from single points and discuss the connection between the uniqueness of maximalMarkovian coupling of Brownian motions and certain mass transportation problems.展开更多
The paper presents an approach to fast approximate estimation of conditions for spacetime structures appearing in the flows.The approach is based on combination of optimization problem computation with methods of data...The paper presents an approach to fast approximate estimation of conditions for spacetime structures appearing in the flows.The approach is based on combination of optimization problem computation with methods of data visual presentation.The visual presentation methods are applied for analysis of multidimensional array containing discrete result data.Optimization problem solution is implemented by parallel computation in a multitask form.For some cases,the approach allows to obtain for control parameter of considered problem the sought-for approximate dependence on characteristic parameters in a quasi-analytical form.展开更多
文摘The strain-gradient and non-Euclidean continuum theories are employed for construction of non- classical solutions of continuum models. The linear approximation of both models＇ results in identical structures in terms of their kinematic and stress characteristics. The solutions obtained in this study exhibit a critical behaviour with respect to the external loading parameter. The conclusions are obtained based on an investigation of the solution for the scalar curvature in the non-Euclidean continuum theory, The proposed analysis enables us to use different theoretical approaches for description of rock critical behaviour under different loading conditions.
基金supported by the Postgraduate Scientific Research Innovation Project of Hunan Province(No.CX20210607)Postgraduate Scientific Research Innovation Project of Xiangtan University(No.XDCX2021B110)+2 种基金supported by the National Science Foundation of China(No.11971472)supported by the Excellent Youth Foundation of SINOPEC(No.P20009)supported by the National Science Foundation of China(No.11971414).
文摘The compositional model is often used to describe multicomponent multiphase porous media flows in the petroleum industry.The fully implicit method with strong stability and weak constraints on time-step sizes is commonly used in mainstream commercial reservoir simulators.In this paper,we develop an efficient multistage preconditioner for the fully implicit compositional flow simulation.The method employs an adaptive setup phase to improve the parallel efficiency on GPUs.Furthermore,a multicolor Gauss-Seidel algorithm based on the adjacency matrix is applied in the algebraic multigrid methods for the pressure part.Numerical results demonstrate that the proposed algorithm achieves good parallel speedup while yielding the same convergence behavior as the corresponding sequential version.
基金Supported by A grant of the Universidad Nacional Autonoma de Mexico SDI.PTID.05.6
文摘AIM： To assess the usefulness of FibroTest to forecast scores by constructing decision trees in patients with chronic hepatitis C.METHODS： We used the C4.5 classification algorithm to construct decision trees with data from 261 patients with chronic hepatitis C without a liver biopsy. The FibroTest attributes of age, gender, bilirubin, apolipoprotein, haptoglobin, α2 macroglobulin, and γ-glutamyl transpeptidase were used as predictors, and the FibroTest score as the target. For testing, a 10-fold cross validation was used.RESULTS： The overall classification error was 14.9% （accuracy 85.1%）. FibroTest＇s cases with true scores of FO and F4 were classified with very high accuracy （18/20 for FO, 9/9 for FO-1 and 92/96 for F4） and the largest confusion centered on F3. The algorithm produced a set of compound rules out of the ten classification trees and was used to classify the 261 patients. The rules for the classification of patients in FO and F4 were effective in more than 75% of the cases in which they were tested.CONCLUSION： The recognition of clinical subgroups should help to enhance our ability to assess differences in fibrosis scores in clinical studies and improve our understanding of fibrosis progression,
文摘This paper is dedicated to the study of viscous compressible barotropic fluids in dimension N ≥ 2. We address the question of well-posedness for large data having critical Besov regularity. Our result improves N the analysis of Danchin and of the author inasmuch as we may take initial density in BN/p p,1 with 1 ≤ p 〈 ＋∞. Our result relies on a new a priori estimate for the velocity, where we introduce a new unknown called effective velocity to weaken one of the couplings between the density and the velocity. In particular, our result is the first in which we obtain uniqueness without imposing hypothesis on the gradient of the density.
基金supported by the Government of Perm Krai,Research Project No.C-26/628 dated 05/04/2021.
文摘A set of techniques for well treatment aimed to enhance oil recovery are considered in the present study.These are based on the application of elastic waves of various types(dilation-wave,vibro-wave,or other acoustically induced effects).In such a context,a new technique is proposed to predict the effectiveness of the elastic-wave well treatment using the rank distribution according to Zipf’s law.It is revealed that,when the results of elastic wave well treatments are analyzed,groups of wells exploiting various geological deposits can differ in terms of their slope coefficients and free members.As the slope coefficient increases,the average increase in the well oil production rate(after the well treatment)becomes larger.An equation is obtained accordingly for estimating the slope coefficient in the Zipf’s equation from the frequency of the elastic wave.The obtained results demonstrate the applicability of the Zipf’s law in the analysis of the technological efficiency of elastic-wave well treatment methods.
文摘Most financial signals show time dependency that,combined with noisy and extreme events,poses serious problems in the parameter estimations of statistical models.Moreover,when addressing asset pricing,portfolio selection,and investment strategies,accurate estimates of the relationship among assets are as necessary as are delicate in a time-dependent context.In this regard,fundamental tools that increasingly attract research interests are precision matrix and graphical models,which are able to obtain insights into the joint evolution of financial quantities.In this paper,we present a robust divergence estimator for a time-varying precision matrix that can manage both the extreme events and time-dependency that affect financial time series.Furthermore,we provide an algorithm to handle parameter estimations that uses the“maximization–minimization”approach.We apply the methodology to synthetic data to test its performances.Then,we consider the cryptocurrency market as a real data application,given its remarkable suitability for the proposed method because of its volatile and unregulated nature.
文摘In this paper it is shown that the thermodynamic limit of the partition function of the statistical models under consideration on a one-dimensional lattice with an arbitrary finite number of interacting neighbors is expressed in terms of the principal eigenvalue of a matrix of finite size. The high sparseness of these matrices for any number of interactions makes it possible to perform an effective numerical analysis of the macro characteristics of these models.
文摘In this paper, we investigate the flow of customers through queuing systems with randomly varying intensities. The analysis of the Kolmogorov-Chapman system of stationary equations for this model showed that it is not possible to construct a convenient symbolic solution. In this paper an attempt is made to circumvent this requirement by referring to the ergodicity theorems, which gives the conditions for the existence of the limit distribution in the service processes, but do not require knowledge of them.
基金Project supported by the Department of Science of Technology of India (Grant No. SR/S4-AS-237/2004-05)the Research Grants Council of the Hong Kong Special Administrative Region, China, (Grant Nos. HKU 715609E, HKU 715510E)supported by the University of Hong Kong through the Seed Funding Programme for Basic Research (Grant No. 200911159024)
文摘Under the effects of electric field and chemical reaction, the problem of dispersion of aerosols in a poorly conducting fluid in a channel is solved analytically using the mixture theory together with a regular perturbation technique. It is shown that the aerosols are dispersed relative to a plane moving with the mean speed of atmospheric fluid as well as the mean speed of agglomeration of aerosol with a relative diffusion coefficient, called the Taylor dispersion coefficient. This coefficient is numerically computed and the results reveal that it increases with an increase in the electric number, but decreases with increasing porous parameter. The physical explanations for the phenomena are given in this article.
文摘This paper is dedicated to the study of viscous compressible barotropic fluids in dimension N 2.We address the question of well-posedness for large data having critical Besov regularity.Our result improves the analysis of Danchin and of the author inasmuch as we may take initial density in B N p p,1 with 1 p < +∞.Our result relies on a new a priori estimate for the velocity,where we introduce a new unknown called effective velocity to weaken one of the couplings between the density and the velocity.In particular,our result is the first in which we obtain uniqueness without imposing hypothesis on the gradient of the density.
基金supported by the National Natural Science Foundation of China(Nos.91330202,11301089,91130004)Chinese Ministry of Education(No.20110071120001)the Programme of Introducing Talents of Discipline to Universities of China(No.B08018)
文摘Calibration and identification of the exchange effect between the karst aquifers and the underlying conduit network are important issues in order to gain a better understanding of these hydraulic systems. Based on a coupled continuum pipe-flow(CCPF for short) model describing flows in karst aquifers, this paper is devoted to the identification of an exchange rate function, which models the hydraulic interaction between the fissured volume(matrix) and the conduit, from the Neumann boundary data, i.e., matrix/conduit seepage velocity. The authors formulate this parameter identification problem as a nonlinear operator equation and prove the compactness of the forward mapping. The stable approximate solution is obtained by two classic iterative regularization methods, namely,the Landweber iteration and Levenberg-Marquardt method. Numerical examples on noisefree and noisy data shed light on the appropriateness of the proposed approaches.
基金supported by NIGMS,NIH,grant number,1R01GM093937-01.
文摘The definition of a molecular surface which is physically sound and computationally efficient is a very interesting and long standing problem in the implicit solvent continuum modeling of biomolecular systems as well as in the molecular graphics field.In this work,two molecular surfaces are evaluated with respect to their suitability for electrostatic computation as alternatives to the widely used Connolly-Richards surface:the blobby surface,an implicit Gaussian atom centered surface,and the skin surface.As figures of merit,we considered surface differentiability and surface area continuity with respect to atom positions,and the agreement with explicit solvent simulations.Geometric analysis seems to privilege the skin to the blobby surface,and points to an unexpected relationship between the non connectedness of the surface,caused by interstices in the solute volume,and the surface area dependence on atomic centers.In order to assess the ability to reproduce explicit solvent results,specific software tools have been developed to enable the use of the skin surface in PoissonBoltzmann calculations with the DelPhi solver.The results indicate that the skin and Connolly surfaces have a comparable performance from this last point of view.
文摘Owing to a production error,Reference[11]was omitted in the References section,and it needs to be corrected to:[11]N.S.Bulychev,Mechanics of underground structures,Moscow,Nedra,1982.The publisher would like to apologise for any inconvenience caused.
基金funded by Foundation of Far Eastern Federal University(No.D-231-22 dated July 05,2022).
文摘A brief overview of the basic principles of geomechanics of highly compressed rocks and masses is presented.The historical path of formation of this new scientific branch of the classical geomechanics is shown.The scales and structural levels of the geomedium failure are identified.The issues of adequate mathematical models at various geomedium structural levels developing,as well as methods for determining the parameters of these models are considered.The object,subject,methods and principles of geomechanics of highly compressed rocks and masses are formulated as a complex discipline at the intersection of classical geomechanics and mesomechanics.
基金Project supported by the WCU World Class University program through the National Research Foundation of Korea funded by the Ministry of Education,Science and Technology (No. R31-20007)the Research Grants Council of HKSAR (No. PolyU 5001/11P)
文摘Mean field theory has raised a lot of interest in the recent years (see in particular the results of Lasry-Lions in 2006 and 2007,of Gueant-Lasry-Lions in 2011,of HuangCaines-Malham in 2007 and many others).There are a lot of applications.In general,the applications concern approximating an infinite number of players with common behavior by a representative agent.This agent has to solve a control problem perturbed by a field equation,representing in some way the behavior of the average infinite number of agents.This approach does not lead easily to the problems of Nash equilibrium for a finite number of players,perturbed by field equations,unless one considers averaging within different groups,which has not been done in the literature,and seems quite challenging.In this paper,the authors approach similar problems with a different motivation which makes sense for control and also for differential games.Thus the systems of nonlinear partial differential equations with mean field terms,which have not been addressed in the literature so far,are considered here.
文摘We study the structure of rings which satisfy the von Neumann regularity of commutators,and call a ring R C-regularif ab-ba ∈(ab-ba)R(ab-ba)for all a,b in R.For a C-regular ring R,we prove J(R[X])=N^(*)(R[X])=N^(*)(R)[X]=W(R)[X]■Z(R[X]),where J(A),N^(*)(A),W(A),Z(A)are the Jacobson radical,upper nilradical,Wedderburn radical,and center of a given ring A,respectively,and A[X]denotes the polynomial ring with a set X of commuting indeterminates over A;we also prove that R is semiprime if and only if the right(left)singular ideal of R is zero.We provide methods to construct C-regular rings which are neither commutative nor von Neumann regular,from any given ring.Moreover,for a C-regular ring R,the following are proved to be equivalent:(i)R is Abelian;(ii)every prime factor ring of R is a duo domain;(ii)R is quasi-duo;and(iv)R/W(R)is reduced.
基金supported by the National Science Foundation(Nos.DMS 1303775,DMS 1612880)the Hong Kong SAR Research Grant Council(Nos.GRF 500113,11303316)Hausdorff Center for Mathematics at University of Bonn and the Czech Science Foundation(No.16-03230S)
文摘The authors deal with nonlinear elliptic and parabolic systems that are the Bellman like systems associated to stochastic differential games with mean field dependent dynamics.The key novelty of the paper is that they allow heavily mean field dependent dynamics.This in particular leads to a system of PDE's with critical growth,for which it is rare to have an existence and/or regularity result.In the paper,they introduce a structural assumptions that cover many cases in stochastic differential games with mean field dependent dynamics for which they are able to establish the existence of a weak solution.In addition,the authors present here a completely new method for obtaining the maximum/minimum principles for systems with critical growths,which is a starting point for further existence and also qualitative analysis.
文摘This study provides new insights into the nature of seasonal variations in coordinate time series of GPS sites located near active faults and methods of their modeling. Monthly averaged coordinate time series were analyzed for several pairs of collocated GPS sites situated near the active fault intersection area, in close proximity to the central part of the northern boundary of the Amurian plate and the vicinity of the San Andreas Fault zone. It is concluded that the observed seasonal variations are best described by a breather function which is one of the solutions of the well-known sine-Gordon equation. The obtained results suggest that, in this case, the source of seasonal variations may be caused by the appearance of solitary strain waves in the fault intersection system, which may be qualitatively treated as standing waves of compression-extension of the geological medium. Based on statistical testing, the limits of applicability of the suggested model have been established.
基金This research was supported in part by the NSF grant DMS-010479 and a Simons Foundation Collaboration Grant for Mathematicians(Hsu)and by the SFB 611 at the University of Bonn(Sturm).
文摘We prove that the mirror coupling is the unique maximal Markovian coupling of two Euclidean Brownian motions starting from single points and discuss the connection between the uniqueness of maximalMarkovian coupling of Brownian motions and certain mass transportation problems.
基金supported by RFBR grant(project number 13-01-00367A).
文摘The paper presents an approach to fast approximate estimation of conditions for spacetime structures appearing in the flows.The approach is based on combination of optimization problem computation with methods of data visual presentation.The visual presentation methods are applied for analysis of multidimensional array containing discrete result data.Optimization problem solution is implemented by parallel computation in a multitask form.For some cases,the approach allows to obtain for control parameter of considered problem the sought-for approximate dependence on characteristic parameters in a quasi-analytical form.
