Stability for the manifolds of equilibrium states of a generalized Birkhoff system is studied. A theorem for the stability of the manifolds of equilibrium states of the general autonomous system is used to the general...Stability for the manifolds of equilibrium states of a generalized Birkhoff system is studied. A theorem for the stability of the manifolds of equilibrium states of the general autonomous system is used to the generalized BirkhoiYian system and two propositions on the stability of the manifolds of equilibrium states of the system are obtained. An example is given to illustrate the application of the results.展开更多
We propose a new out of equilibrium thermodynamic approach to Schiff Electrodynamics aimed to generalize in rotating frames a recent reformulation of extended Ahranov-Bohm electrodynamic model.In accordance with these...We propose a new out of equilibrium thermodynamic approach to Schiff Electrodynamics aimed to generalize in rotating frames a recent reformulation of extended Ahranov-Bohm electrodynamic model.In accordance with these theories,we introduce a gauge breaking scalar field S linearly dependent on a thermal field T generated by a chopped laser beam,showing that under particular hypotheses it satisfies the hyperbolic telegraph equation.Exploiting then a particular gauge generalized condition suggested recently,we deduce that T and S are proportional to a thermoelectric scalar field which satisfies a Klein-Gordon equation,suggesting it can be interpreted as a dynamic Thomson voltage induced by rotation.We then illustrate briefly a more general theory of anisotropic heat diffusion on rotating conductors exposed to a chopped polarized laser beam formulated and developed in the Ph.D.thesis of the author.We show the existence of new helicoidal thermal waves that satisfy a telegraphist dissipative equation,whose isothermal wavefronts are quantized.We give a simple stationary estimate of a new dynamic Thomson effect induced by the chopped laser beam on the rotating conductors which is similar to a rotational Tolman effect.Finally,it is briefly outlined the relevance of the new anisotropic wavelike heat diffusion model proposed for paving the way to a new dynamic approach to thermal management and to future implementation of tunable thermal emissivity on thermal metamaterials bypassing conventional Kirchoff reciprocity law.展开更多
For a family of vector-valued bifunctions,we introduce the notion of sequentially lower monotonity,which is strictly weaker than the lower semi-continuity of the second variables of the bifunctions.Then,we give a gene...For a family of vector-valued bifunctions,we introduce the notion of sequentially lower monotonity,which is strictly weaker than the lower semi-continuity of the second variables of the bifunctions.Then,we give a general version of vectorial Ekeland variational principle(briefly,denoted by EVP) for a system of equilibrium problems,where the sequentially lower monotone objective bifunction family is defined on products of sequentially lower complete spaces(concerning sequentially lower complete spaces,see Zhu et al(2013)),and taking values in a quasi-ordered locally convex space.Besides,the perturbation consists of a subset of the ordering cone and a family {p_i}_(i∈I) of negative functions satisfying for each i∈I,p_i(x_i,y_i) = 0 if and only if x_i=y_i.From the general version,we can deduce several particular equilibrium versions of EVP,which can be applied to show the existence of solutions for countable systems of equilibrium problems.In particular,we obtain a general existence result of solutions for countable systems of equilibrium problems in the setting of sequentially lower complete spaces.By weakening the compactness of domains and the lower semi-continuity of objective bifunctions,we extend and improve some known existence results of solutions for countable system of equilibrium problems in the setting of complete metric spaces(or Fréchet spaces).When the domains are non-compact,by using the theory of angelic spaces(see Floret(1980)),we generalize some existence results on solutions for countable systems of equilibrium problems by extending the framework from reflexive Banach spaces to the strong duals of weakly compactly generated spaces.展开更多
Under certain load pattern, the geometrically indeterminate pin-jointed mechanisms will present certain shapes to keep static equalization. This paper proposes a matrix-based method to determine the mobility and equil...Under certain load pattern, the geometrically indeterminate pin-jointed mechanisms will present certain shapes to keep static equalization. This paper proposes a matrix-based method to determine the mobility and equilibrium stability of mechanisms according to the effects of the external loads. The first and second variations of the potential energy function of mechanisms under conservative force field are analyzed. Based on the singular value decomposition (SVD) method, a new crite- rion for the mobility and equilibrium stability of mechanisms can be concluded by analyzing the equilibrium matrix. The mobility and stability of mechanisms can be classified by unified matrix formulae. A number of examples are given to demonstrate the proposed criterion. In the end, criteria are summarized in a table.展开更多
Lyapunov＇s first method, extended by V. V. Kozlov to nonlinear mechani- cal systems, is applied to the study of the instability of the position of equilibrium of a mechanical system moving in the field of conservativ...Lyapunov＇s first method, extended by V. V. Kozlov to nonlinear mechani- cal systems, is applied to the study of the instability of the position of equilibrium of a mechanical system moving in the field of conservative and dissipative forces. The mo- tion of the system is limited by ideal nonlinear nonholonomic constraints. Five cases determined by the relationship between the degree of the first nontrivial polynomials in Maclaurin＇s series for the potential energy and the functions that can be generated from the equations of nonlinear nonholonomic constraints are analyzed. In the three eases, the theorem on the instability of the position of equilibrium of nonholonomic systems with linear homogeneous constraints （V. V. Kozlov （1986）） is generalized to the case of nonlin- ear nonhomogeneous constraints. In the other two cases, new theorems are set extending the result from V. V. Kozlov （1994） to nonholonomic systems with nonlinear constraints.展开更多
Thermomechanical processing is a metallurgical operation to produce high-strength steel bars (rebars), through combining plastic deformation with thermal processes like heat treatment, water quenching, heating, and co...Thermomechanical processing is a metallurgical operation to produce high-strength steel bars (rebars), through combining plastic deformation with thermal processes like heat treatment, water quenching, heating, and cooling at various rates into a single process. Ribbed reinforcing steel bars (rebars) are used for the reinforcement of concrete structures. Tempcore is a unique process to produce high-yield-strength rebars from mild steel without addition of a high weight percentage of costly alloying elements. The strength of rebar originates from the formation of a surface layer consisting of quenched and tempered martensite that surrounds a core composed of ferrite and pearlite. The economic advantages of this process are significant in comparison to those processes requiring alloying elements or further metal working to improve the mechanical properties. However, when there is a limitation in the water-cooling capacity, the required volume fraction of the martensite layer can’t be accomplished particularly when rolling bigger diameters of 32 mm - 40 mm at a higher rolling speed to maintain high productivity. Accordingly, a small addition of microalloying elements vanadium or niobium could be used in combination with Tempcore process to obtain high-strength steel rebars. In this contribution, 0.06 weight percentage of vanadium is added to the Tempcore treated rebars to satisfy ASTM A 706 Standard of Rebar Grade 80 PSI [550 MPa]. In order to decrease the trials in the steel plant floor, thermodynamics equilibrium calculations are predicted by Thermo-Calc, CCT, TTT diagrams are calculated by JMat Pro and the kinetics evolution of the vanadium carbonitrides precipitates are predicted by the computational database Mat Calc. High yield strength and tensile strength are obtained due to the effect of fine dispersions of nanometer-scale vanadium carbonitrides precipitates inspected by transmission electron microscope.展开更多
We study the Fisher model of a competitive market from the algorithmic perspective.For that,the related convex optimization problem due to Gale and Eisenberg(Ann Math Stat 30(1):165–168,1959)is used.The latter proble...We study the Fisher model of a competitive market from the algorithmic perspective.For that,the related convex optimization problem due to Gale and Eisenberg(Ann Math Stat 30(1):165–168,1959)is used.The latter problem is known to yield a Fisher equilibrium under some structural assumptions on consumers’utilities,e.g.,homogeneity of degree 1,homotheticity.Our goal is to examine applicability of the convex optimization framework by departing from these traditional assumptions.We just assume the concavity of consumers’utility functions.For this case,we suggest a novel concept of Fisher–Gale equilibrium by using consumers’utility prices.The prices of utility transfer the utility of consumption bundle to a common numéraire.We develop a subgradient-type algorithm from Convex Analysis to compute a Fisher–Gale equilibrium via Gale’s approach.In order to decentralize prices,we additionally implement the auction design,i.e.,consumers settle and update their individual prices and producers sell at the highest offer price.Our price adjustment is based on a tatonnement procedure,i.e.,the prices change proportionally to consumers’individual excess supplies.Historical averages of consumption are shown to clear the market of goods.Our algorithm is justified by a global rate of convergence.In the worst case,the number of price updates needed to achieve anε-tolerance is proportional to 1/ε^(2).展开更多
Equilibrium constants are essential for understanding and predicting the behavior of chemical systems across various scientifc disciplines.Traditionally,these constants are computed via nonlinear regression of reactio...Equilibrium constants are essential for understanding and predicting the behavior of chemical systems across various scientifc disciplines.Traditionally,these constants are computed via nonlinear regression of reaction isotherms,which show the depend-ence of the unreacted fraction of one reactant on the total concentration of another reactant.However,while these equilibrium constants can be precise(with small random errors),they may also be grossly inaccurate(with large systematic errors),leading to potential misinterpretations.Although some statisticalmethods exist for assessing the accuracy of nonlinear regression,their limitedpracticality for molecular scientists has resulted in their neglect by this research community.The objective of this work is to develop a practical method for quantitatively assessing the accuracy of equilibrium constants that could be easily understood and immediately adopted by researchers routinely determining these constants.Our approach integrates error-propagation and regression-stability analyses to establish the accuracy confidence interval(ACI)-a range within which the true value of the computed parameter lies with a defined probability.In a proof-of-principle study,we applied this approach to develop a workflow for determining the ACI of the equilibrium dissociation constant(K_(d))of affinity complexes from a single binding isotherm.We clearly explained how the input parameters for this workflow can be determined,and finally,we have implemented this workflow in a user-friendly web application(https://aci.sci.yorku.ca)to facilitate its immediate adoption by molecular scientists,regardless of their mathematical and computer proficiency.We further conducted three case studies exemplifying the use of the ACI in the context of simultaneous assessment of precision and accuracy of determined K_(d)values.By understanding the ACI of equilibrium constants and other parameters computed through nonlinear regression,researchers can avoid misconceptions that arise from relying solely on precision.展开更多
The purpose of this paper is to prove the equilibrium of general equilibrium of market economy in China. As a consequence,it is shown that, when the governmentplanning system gradually loses its function,the correspon...The purpose of this paper is to prove the equilibrium of general equilibrium of market economy in China. As a consequence,it is shown that, when the governmentplanning system gradually loses its function,the corresponding equilibrium point sequence of planned/market mixed economy converges to the unique equilibrium point of market economy. This demonstrates that the transition of China’s planned/market mixed economy to market economy will be stable.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant Nos.10772025,10932002 and 10972127)the Natural Science Foundation of Henan Province,China(Grant No.102300410144)the Beijing Municipal Key Disciplines Fund for General Mechanics and Foundation of Mechanics,China
文摘Stability for the manifolds of equilibrium states of a generalized Birkhoff system is studied. A theorem for the stability of the manifolds of equilibrium states of the general autonomous system is used to the generalized BirkhoiYian system and two propositions on the stability of the manifolds of equilibrium states of the system are obtained. An example is given to illustrate the application of the results.
文摘We propose a new out of equilibrium thermodynamic approach to Schiff Electrodynamics aimed to generalize in rotating frames a recent reformulation of extended Ahranov-Bohm electrodynamic model.In accordance with these theories,we introduce a gauge breaking scalar field S linearly dependent on a thermal field T generated by a chopped laser beam,showing that under particular hypotheses it satisfies the hyperbolic telegraph equation.Exploiting then a particular gauge generalized condition suggested recently,we deduce that T and S are proportional to a thermoelectric scalar field which satisfies a Klein-Gordon equation,suggesting it can be interpreted as a dynamic Thomson voltage induced by rotation.We then illustrate briefly a more general theory of anisotropic heat diffusion on rotating conductors exposed to a chopped polarized laser beam formulated and developed in the Ph.D.thesis of the author.We show the existence of new helicoidal thermal waves that satisfy a telegraphist dissipative equation,whose isothermal wavefronts are quantized.We give a simple stationary estimate of a new dynamic Thomson effect induced by the chopped laser beam on the rotating conductors which is similar to a rotational Tolman effect.Finally,it is briefly outlined the relevance of the new anisotropic wavelike heat diffusion model proposed for paving the way to a new dynamic approach to thermal management and to future implementation of tunable thermal emissivity on thermal metamaterials bypassing conventional Kirchoff reciprocity law.
基金National Natural Science Foundation of China(Grant No. 11471236)
文摘For a family of vector-valued bifunctions,we introduce the notion of sequentially lower monotonity,which is strictly weaker than the lower semi-continuity of the second variables of the bifunctions.Then,we give a general version of vectorial Ekeland variational principle(briefly,denoted by EVP) for a system of equilibrium problems,where the sequentially lower monotone objective bifunction family is defined on products of sequentially lower complete spaces(concerning sequentially lower complete spaces,see Zhu et al(2013)),and taking values in a quasi-ordered locally convex space.Besides,the perturbation consists of a subset of the ordering cone and a family {p_i}_(i∈I) of negative functions satisfying for each i∈I,p_i(x_i,y_i) = 0 if and only if x_i=y_i.From the general version,we can deduce several particular equilibrium versions of EVP,which can be applied to show the existence of solutions for countable systems of equilibrium problems.In particular,we obtain a general existence result of solutions for countable systems of equilibrium problems in the setting of sequentially lower complete spaces.By weakening the compactness of domains and the lower semi-continuity of objective bifunctions,we extend and improve some known existence results of solutions for countable system of equilibrium problems in the setting of complete metric spaces(or Fréchet spaces).When the domains are non-compact,by using the theory of angelic spaces(see Floret(1980)),we generalize some existence results on solutions for countable systems of equilibrium problems by extending the framework from reflexive Banach spaces to the strong duals of weakly compactly generated spaces.
基金Project supported by the National Natural Science Foundation of China (Nos. 50378083 and 50638050)the Research Foundation for the Doctoral Program of Higher Education of China (No. 20050335097)
文摘Under certain load pattern, the geometrically indeterminate pin-jointed mechanisms will present certain shapes to keep static equalization. This paper proposes a matrix-based method to determine the mobility and equilibrium stability of mechanisms according to the effects of the external loads. The first and second variations of the potential energy function of mechanisms under conservative force field are analyzed. Based on the singular value decomposition (SVD) method, a new crite- rion for the mobility and equilibrium stability of mechanisms can be concluded by analyzing the equilibrium matrix. The mobility and stability of mechanisms can be classified by unified matrix formulae. A number of examples are given to demonstrate the proposed criterion. In the end, criteria are summarized in a table.
基金Project supported by the Ministry of Science and Technological Development of the Republic of Serbia (Nos. 144019, 20152, and 114052)
文摘Lyapunov＇s first method, extended by V. V. Kozlov to nonlinear mechani- cal systems, is applied to the study of the instability of the position of equilibrium of a mechanical system moving in the field of conservative and dissipative forces. The mo- tion of the system is limited by ideal nonlinear nonholonomic constraints. Five cases determined by the relationship between the degree of the first nontrivial polynomials in Maclaurin＇s series for the potential energy and the functions that can be generated from the equations of nonlinear nonholonomic constraints are analyzed. In the three eases, the theorem on the instability of the position of equilibrium of nonholonomic systems with linear homogeneous constraints （V. V. Kozlov （1986）） is generalized to the case of nonlin- ear nonhomogeneous constraints. In the other two cases, new theorems are set extending the result from V. V. Kozlov （1994） to nonholonomic systems with nonlinear constraints.
文摘Thermomechanical processing is a metallurgical operation to produce high-strength steel bars (rebars), through combining plastic deformation with thermal processes like heat treatment, water quenching, heating, and cooling at various rates into a single process. Ribbed reinforcing steel bars (rebars) are used for the reinforcement of concrete structures. Tempcore is a unique process to produce high-yield-strength rebars from mild steel without addition of a high weight percentage of costly alloying elements. The strength of rebar originates from the formation of a surface layer consisting of quenched and tempered martensite that surrounds a core composed of ferrite and pearlite. The economic advantages of this process are significant in comparison to those processes requiring alloying elements or further metal working to improve the mechanical properties. However, when there is a limitation in the water-cooling capacity, the required volume fraction of the martensite layer can’t be accomplished particularly when rolling bigger diameters of 32 mm - 40 mm at a higher rolling speed to maintain high productivity. Accordingly, a small addition of microalloying elements vanadium or niobium could be used in combination with Tempcore process to obtain high-strength steel rebars. In this contribution, 0.06 weight percentage of vanadium is added to the Tempcore treated rebars to satisfy ASTM A 706 Standard of Rebar Grade 80 PSI [550 MPa]. In order to decrease the trials in the steel plant floor, thermodynamics equilibrium calculations are predicted by Thermo-Calc, CCT, TTT diagrams are calculated by JMat Pro and the kinetics evolution of the vanadium carbonitrides precipitates are predicted by the computational database Mat Calc. High yield strength and tensile strength are obtained due to the effect of fine dispersions of nanometer-scale vanadium carbonitrides precipitates inspected by transmission electron microscope.
基金The research of Yurii Nesterov was supported by the Russian Science Foundation(No.17-11-01207).
文摘We study the Fisher model of a competitive market from the algorithmic perspective.For that,the related convex optimization problem due to Gale and Eisenberg(Ann Math Stat 30(1):165–168,1959)is used.The latter problem is known to yield a Fisher equilibrium under some structural assumptions on consumers’utilities,e.g.,homogeneity of degree 1,homotheticity.Our goal is to examine applicability of the convex optimization framework by departing from these traditional assumptions.We just assume the concavity of consumers’utility functions.For this case,we suggest a novel concept of Fisher–Gale equilibrium by using consumers’utility prices.The prices of utility transfer the utility of consumption bundle to a common numéraire.We develop a subgradient-type algorithm from Convex Analysis to compute a Fisher–Gale equilibrium via Gale’s approach.In order to decentralize prices,we additionally implement the auction design,i.e.,consumers settle and update their individual prices and producers sell at the highest offer price.Our price adjustment is based on a tatonnement procedure,i.e.,the prices change proportionally to consumers’individual excess supplies.Historical averages of consumption are shown to clear the market of goods.Our algorithm is justified by a global rate of convergence.In the worst case,the number of price updates needed to achieve anε-tolerance is proportional to 1/ε^(2).
基金supported by a York University grant to the Catalyzing Interdisciplinary Research Cluster“Technologies for Identification and Control of Infectious Diseases”and an NSERC Discovery Grant(RGPIN-2022-04563)to S.N.KAdditional support was provided by an NSERC Undergraduate Student Research Award(USRA-582491-2023)to J.La University of Münster visiting fellowship to S.N.K.We extend our gratitude to Prof.Howard A.Levin and Dr.Yeon-Jung Seo from Iowa State University and Prof.Jianhong Wu from York University for their valuable assistance in refining the manuscript.
文摘Equilibrium constants are essential for understanding and predicting the behavior of chemical systems across various scientifc disciplines.Traditionally,these constants are computed via nonlinear regression of reaction isotherms,which show the depend-ence of the unreacted fraction of one reactant on the total concentration of another reactant.However,while these equilibrium constants can be precise(with small random errors),they may also be grossly inaccurate(with large systematic errors),leading to potential misinterpretations.Although some statisticalmethods exist for assessing the accuracy of nonlinear regression,their limitedpracticality for molecular scientists has resulted in their neglect by this research community.The objective of this work is to develop a practical method for quantitatively assessing the accuracy of equilibrium constants that could be easily understood and immediately adopted by researchers routinely determining these constants.Our approach integrates error-propagation and regression-stability analyses to establish the accuracy confidence interval(ACI)-a range within which the true value of the computed parameter lies with a defined probability.In a proof-of-principle study,we applied this approach to develop a workflow for determining the ACI of the equilibrium dissociation constant(K_(d))of affinity complexes from a single binding isotherm.We clearly explained how the input parameters for this workflow can be determined,and finally,we have implemented this workflow in a user-friendly web application(https://aci.sci.yorku.ca)to facilitate its immediate adoption by molecular scientists,regardless of their mathematical and computer proficiency.We further conducted three case studies exemplifying the use of the ACI in the context of simultaneous assessment of precision and accuracy of determined K_(d)values.By understanding the ACI of equilibrium constants and other parameters computed through nonlinear regression,researchers can avoid misconceptions that arise from relying solely on precision.
文摘The purpose of this paper is to prove the equilibrium of general equilibrium of market economy in China. As a consequence,it is shown that, when the governmentplanning system gradually loses its function,the corresponding equilibrium point sequence of planned/market mixed economy converges to the unique equilibrium point of market economy. This demonstrates that the transition of China’s planned/market mixed economy to market economy will be stable.
