Estimation of density and hazard rate is very important to the reliability analysis of a system. In order to estimate the density and hazard rate of a hazard rate monotonously decreasing system, a new nonparametric es...Estimation of density and hazard rate is very important to the reliability analysis of a system. In order to estimate the density and hazard rate of a hazard rate monotonously decreasing system, a new nonparametric estimator is put forward. The estimator is based on the kernel function method and optimum algorithm. Numerical experiment shows that the method is accurate enough and can be used in many cases.展开更多
This paper deals with Mckean-Vlasov backward stochastic differential equations with weak monotonicity coefficients.We first establish the existence and uniqueness of solutions to Mckean-Vlasov backward stochastic diff...This paper deals with Mckean-Vlasov backward stochastic differential equations with weak monotonicity coefficients.We first establish the existence and uniqueness of solutions to Mckean-Vlasov backward stochastic differential equations.Then we obtain a comparison theorem in one-dimensional situation.展开更多
This paper deals with the monotonicity of limit wave speed c0(h)to a perturbed g KdV equation.We show the decrease of c0(h)by combining the analytic method and the numerical technique.Our results solve a special case ...This paper deals with the monotonicity of limit wave speed c0(h)to a perturbed g KdV equation.We show the decrease of c0(h)by combining the analytic method and the numerical technique.Our results solve a special case of the open question presented by Yan et al.,and the method potentially provides a way to study the monotonicity of c0(h)for general m∈N^(+).展开更多
The purpose of this article is to introduce a new method with a self-adaptive stepsize for approximating a common solution of monotone inclusion problems and variational inequality problems in reflexive Banach spaces....The purpose of this article is to introduce a new method with a self-adaptive stepsize for approximating a common solution of monotone inclusion problems and variational inequality problems in reflexive Banach spaces.The strong convergence result for our method is established under some standard assumptions without any requirement of the knowledge of the Lipschitz constant of the mapping.Several numerical experiments are provided to verify the advantages and efficiency of proposed algorithms.展开更多
Interval-valued pre-aggregation functions are a hot topic in the research of aggregation functions and have received considerable attention in recent years.As a special class of interval-valued pre-aggregation functio...Interval-valued pre-aggregation functions are a hot topic in the research of aggregation functions and have received considerable attention in recent years.As a special class of interval-valued pre-aggregation functions,(light)interval-valued pre-t-norms were initially proposed by Wang and Hu,but their properties were not further discussed by the authors.The main purpose of this paper is to study in depth the properties and generation of(light)intervalvalued pre-t-norms.Firstly,several properties of(light)interval-valued pre-t-norms and their relationship with(light)pre-t-norms are presented.Then,two different generation methods for(light)interval-valued pre-t-norms are introduced.Finally,it demonstrates a specific application of(light)interval-valued pre-t-norms in constructing interval-valued directional monotonic fuzzy implications,namely,using the(light)interval-valued pre-t-norm IT,interval-valued fuzzy negations IN,and(light)interval-valued pre-t-conorm IS to construct interval-valued QL-directional monotonic operations.展开更多
Stress relaxation is a time-dependent phenomenon in rocks,characterized by a gradual decrease in stress magnitude while strain remains constant with time.This study introduces a novel experimental approach to investig...Stress relaxation is a time-dependent phenomenon in rocks,characterized by a gradual decrease in stress magnitude while strain remains constant with time.This study introduces a novel experimental approach to investigate deformation processes during the primary and secondary stages of stress relaxation and to differentiate the damage mechanisms occurring during relaxation from those under monotonic loading.To this end,the deformation behavior of prismatic-shaped homogeneous Stanstead granite(SG)rock specimens was monitored using two-dimensional digital image correlation(2D-DIC)in-sync with active ultrasonic sensing during stress relaxation and monotonic loading conditions.In particular,the SG specimens were allowed to undergo stress relaxation starting at a driving stress(σd)just above the crack damage(CD)threshold of the specimens,while their deformation characteristics were evaluated via 2D-DIC full-field strain maps and ultrasonic characteristics.The results indicate that the primary stage of relaxation is marked by accumulation of tensile damage at a decreasing rate,and the rate of damage accumulation reaches a steady state during the secondary stage of relaxation.Likewise,the ultrasonic amplitude reduced at a decreasing rate during the primary stage of relaxation and attained a constant rate of reduction during secondary relaxation.Additionally,a comparison of rock behavior during stress relaxation and monotonic loading conditions quantitatively demonstrated that SG dilates more during relaxation than under monotonic loading over a given range of damage values.This is interpreted to be associated with the fact that local extensional strains are diffuse under relaxation,in contrast with the more localized nature of damage under monotonic loading conditions.展开更多
In this paper,we introduce a qualitative analysis in order to study the monotonicity and comparability properties of a single-server retrial queueing model with Bernoulli feedback and negative customers,relative to st...In this paper,we introduce a qualitative analysis in order to study the monotonicity and comparability properties of a single-server retrial queueing model with Bernoulli feedback and negative customers,relative to stochastic orderings.Performance measures of such a system are available explicitly,while their forms are cumbersome(these formulas include integrals of Laplace transform,solutions of functional equations,etc.).Therefore,they are not exploitable from the application point of view.To overcome these difficulties,we present stochastic comparison methods in order to get qualitative estimates of these measures.In particular,we prove the monotonicity of the transition operator of the embedded Markov chain.In addition,we establish conditions for which transition operators as well as stationary probabilities,associated with two embedded Markov chains,having the same structure but with different parameters,are comparable relative to the given stochastic orderings.Further,numerical examples are carried out to illustrate the theoretical results.展开更多
It is known that monotone recurrence relations can induce a class of twist homeomorphisms on the high-dimensional cylinder,which is an extension of the class of monotone twist maps on the annulus or two-dimensional cy...It is known that monotone recurrence relations can induce a class of twist homeomorphisms on the high-dimensional cylinder,which is an extension of the class of monotone twist maps on the annulus or two-dimensional cylinder.By constructing a bounded solution of the monotone recurrence relation,the main conclusion in this paper is acquired:The induced homeomorphism has Birkhoff orbits provided there is a compact forward-invariant set.Therefore,it generalizes Angenent's results in low-dimensional cases.展开更多
Complex numbers play a pivotal role in both mathematics and physics,particularly in quantum mechanics,and are extensively utilized to depict the behavior of microscopic particles.Recognizing the significance of comple...Complex numbers play a pivotal role in both mathematics and physics,particularly in quantum mechanics,and are extensively utilized to depict the behavior of microscopic particles.Recognizing the significance of complex numbers,a framework of imaginarity resource theory has recently been established.In this work,we propose two types of imaginarity monotones induced by the unified(α,β)-relative entropy and investigate their properties.Moreover,we give explicit examples to illustrate our results.展开更多
Aiming at the pulse response sequence of a kind of repetitive linear discrete-time singular systems unavailable,the paper explores a data-driven adaptive iterative learning control(DDAILC)strategy that interacts with ...Aiming at the pulse response sequence of a kind of repetitive linear discrete-time singular systems unavailable,the paper explores a data-driven adaptive iterative learning control(DDAILC)strategy that interacts with the pulse response iterative correction(PRIC).The mechanism is to formulate the correction performance index as a linear summation of the quadratic correction error of the pulse response and the quadratic tracking error.The correction algorithm of the pulse response arrives and the correction error goes down in a monotonic way.It also discusses the conditional relationship between the declining rate of the correction error and the correction ratio.A DDAILC algorithm is designed by means of substituting the exact pulse response of the gain-optimized iterative learning control(GOILC)with its approximated one updated in the correction algorithm.The convergences regarding tracking error and correction error are obtained monotonically.Finally,numerical simulation verifies the validity and effectiveness.展开更多
This paper concerns the monotonicity of limit wave speed c0(h) for the perturbed g Kd V equation with general even m.We show that c0(h) is decreasing.Our results give partial answer to the open problem presented by Ya...This paper concerns the monotonicity of limit wave speed c0(h) for the perturbed g Kd V equation with general even m.We show that c0(h) is decreasing.Our results give partial answer to the open problem presented by Yan et al.(Math.Model.Anal.,19,537-555,2014).展开更多
Optical phase transfer via fiber optics is the most effective method for optical frequency standard comparison on the scale below thousands of kilometers.However,the monotonic phase discrimination range of conventiona...Optical phase transfer via fiber optics is the most effective method for optical frequency standard comparison on the scale below thousands of kilometers.However,the monotonic phase discrimination range of conventional optical phase-locked loops is limited,and link delays restrict the control bandwidth,which makes it a challenge to achieve a continuously reliable optical link.This paper presents an event-timing-based phase detection method that overcomes the monotonic phase discrimination range limitation of conventional phase-locked loops through dual-edge timestamp recording,achieving an optical phase measurement resolution on the order of 10 attoseconds.With such a technique,we established a 7-segment-cascaded optical link over 1402km of commercial fiber while sharing dense wavelength division multiplexing(DWDM)channels with live telecom traffic.The system maintained continuous operation for 11.7 days without phase cycle slips despite encountering 15 km aerial fiber noise up to 21000 rad^(2)·Hz^(−1)·km^(−1)at 1 Hz.Relative instabilities of the link are 3.7×10^(−15)at 1 s and 3.9×10^(−20)at 100000 s.展开更多
In this paper, some properties of the monotone set function defined by theChoquet integral are discussed. It is shown that several important structural characteristics of theoriginal set function, such as weak null-ad...In this paper, some properties of the monotone set function defined by theChoquet integral are discussed. It is shown that several important structural characteristics of theoriginal set function, such as weak null-additivity, strong order continuity, property (s) andpseudomelric generating property, etc., are preserved by the new set function. It is also shown thatC-integrability assumption is inevitable for the preservations of strong order continuous andpseudometric generating property.展开更多
With using the cone and partial ordering t heory and mixed monotone operator theory, the existence and uniqueness for solut ion of systems of non-monotone binary nonliear operator equations are discussed. And the it...With using the cone and partial ordering t heory and mixed monotone operator theory, the existence and uniqueness for solut ion of systems of non-monotone binary nonliear operator equations are discussed. And the iterative sequences which converge to solution of systems of operator e quations and the error estimates are also given. Some corresponding results for the mixed monotone operations and the unary operator equations are improved and generalized.展开更多
On the basis of the paoers[3—7],this paper study the monotonicity problems for the positive semidefinite generalized inverses of the positive semidefinite self-conjugate matrices of quaternions in the Lowner partial ...On the basis of the paoers[3—7],this paper study the monotonicity problems for the positive semidefinite generalized inverses of the positive semidefinite self-conjugate matrices of quaternions in the Lowner partial order,give the explicit formulations of the monotonicity solution sets A{1;≥,T_1;≤B^(1)}and B{1;≥,T_2≥A^(1)}for the(1)-inverse,and two results of the monotonicity charac teriaztion for the(1,2)-inverse.展开更多
Aim The existence of generalized solution for a class of nonlinear partial differential equations with nonhanogeneous boundary condition was investigated. This problem arises from polymer processing concerned with the...Aim The existence of generalized solution for a class of nonlinear partial differential equations with nonhanogeneous boundary condition was investigated. This problem arises from polymer processing concerned with the first initial-boundary value problem or the nonstationary floW of non-Newtonian viscous incompressiblee fluid through the slit dice. MethodsThe monotone operator theory and the Schauder's fixal point theorem were used. Results and Conclusion The existence theorem of generalized solutions for a the of nonlinear partial differential equations with nonhormogeneous boundary condition is proved under reasonable conditions展开更多
文摘Estimation of density and hazard rate is very important to the reliability analysis of a system. In order to estimate the density and hazard rate of a hazard rate monotonously decreasing system, a new nonparametric estimator is put forward. The estimator is based on the kernel function method and optimum algorithm. Numerical experiment shows that the method is accurate enough and can be used in many cases.
基金Supported by the National Natural Science Foundation of China(12001074)the Research Innovation Program of Graduate Students in Hunan Province(CX20220258)+1 种基金the Research Innovation Program of Graduate Students of Central South University(1053320214147)the Key Scientific Research Project of Higher Education Institutions in Henan Province(25B110025)。
文摘This paper deals with Mckean-Vlasov backward stochastic differential equations with weak monotonicity coefficients.We first establish the existence and uniqueness of solutions to Mckean-Vlasov backward stochastic differential equations.Then we obtain a comparison theorem in one-dimensional situation.
基金Supported by the National Natural Science Foundation of China(12071162)the Natural Science Foundation of Fujian Province(2021J01302)the Fundamental Research Funds for the Central Universities(ZQN-802)。
文摘This paper deals with the monotonicity of limit wave speed c0(h)to a perturbed g KdV equation.We show the decrease of c0(h)by combining the analytic method and the numerical technique.Our results solve a special case of the open question presented by Yan et al.,and the method potentially provides a way to study the monotonicity of c0(h)for general m∈N^(+).
基金Supported by NSFC(No.12171062)the Natural Science Foundation of Chongqing(No.CSTB2022NSCQ-JQX0004)+1 种基金the Chongqing Talent Support Program(No.cstc2024ycjh-bgzxm0121)Science and Technology Project of Chongqing Education Committee(No.KJZD-M202300503)。
文摘The purpose of this article is to introduce a new method with a self-adaptive stepsize for approximating a common solution of monotone inclusion problems and variational inequality problems in reflexive Banach spaces.The strong convergence result for our method is established under some standard assumptions without any requirement of the knowledge of the Lipschitz constant of the mapping.Several numerical experiments are provided to verify the advantages and efficiency of proposed algorithms.
基金the National Natural Science Foundation of China(Grant No.12171294)。
文摘Interval-valued pre-aggregation functions are a hot topic in the research of aggregation functions and have received considerable attention in recent years.As a special class of interval-valued pre-aggregation functions,(light)interval-valued pre-t-norms were initially proposed by Wang and Hu,but their properties were not further discussed by the authors.The main purpose of this paper is to study in depth the properties and generation of(light)intervalvalued pre-t-norms.Firstly,several properties of(light)interval-valued pre-t-norms and their relationship with(light)pre-t-norms are presented.Then,two different generation methods for(light)interval-valued pre-t-norms are introduced.Finally,it demonstrates a specific application of(light)interval-valued pre-t-norms in constructing interval-valued directional monotonic fuzzy implications,namely,using the(light)interval-valued pre-t-norm IT,interval-valued fuzzy negations IN,and(light)interval-valued pre-t-conorm IS to construct interval-valued QL-directional monotonic operations.
基金support provided by the Indian Institute of Technology Delhi,India,and Colorado School of Mines,USA,for performing the work related to this research article is greatly appreciatedsupported by the IIT Delhi MFIRP Grant No.MI022762G+1 种基金partially by the U.S.Department of Energy,Office of Basic Energy Sciences,under Award Number DE-SC0019117support is gratefully acknowledged。
文摘Stress relaxation is a time-dependent phenomenon in rocks,characterized by a gradual decrease in stress magnitude while strain remains constant with time.This study introduces a novel experimental approach to investigate deformation processes during the primary and secondary stages of stress relaxation and to differentiate the damage mechanisms occurring during relaxation from those under monotonic loading.To this end,the deformation behavior of prismatic-shaped homogeneous Stanstead granite(SG)rock specimens was monitored using two-dimensional digital image correlation(2D-DIC)in-sync with active ultrasonic sensing during stress relaxation and monotonic loading conditions.In particular,the SG specimens were allowed to undergo stress relaxation starting at a driving stress(σd)just above the crack damage(CD)threshold of the specimens,while their deformation characteristics were evaluated via 2D-DIC full-field strain maps and ultrasonic characteristics.The results indicate that the primary stage of relaxation is marked by accumulation of tensile damage at a decreasing rate,and the rate of damage accumulation reaches a steady state during the secondary stage of relaxation.Likewise,the ultrasonic amplitude reduced at a decreasing rate during the primary stage of relaxation and attained a constant rate of reduction during secondary relaxation.Additionally,a comparison of rock behavior during stress relaxation and monotonic loading conditions quantitatively demonstrated that SG dilates more during relaxation than under monotonic loading over a given range of damage values.This is interpreted to be associated with the fact that local extensional strains are diffuse under relaxation,in contrast with the more localized nature of damage under monotonic loading conditions.
文摘In this paper,we introduce a qualitative analysis in order to study the monotonicity and comparability properties of a single-server retrial queueing model with Bernoulli feedback and negative customers,relative to stochastic orderings.Performance measures of such a system are available explicitly,while their forms are cumbersome(these formulas include integrals of Laplace transform,solutions of functional equations,etc.).Therefore,they are not exploitable from the application point of view.To overcome these difficulties,we present stochastic comparison methods in order to get qualitative estimates of these measures.In particular,we prove the monotonicity of the transition operator of the embedded Markov chain.In addition,we establish conditions for which transition operators as well as stationary probabilities,associated with two embedded Markov chains,having the same structure but with different parameters,are comparable relative to the given stochastic orderings.Further,numerical examples are carried out to illustrate the theoretical results.
基金Supported by the National Natural Science Foundation of China(12201446)the Natural Science Foundation of the Jiangsu Higher Education Institutions of China(22KJB110005)the Shuangchuang Program of Jiangsu Province(JSSCBS20220898)。
文摘It is known that monotone recurrence relations can induce a class of twist homeomorphisms on the high-dimensional cylinder,which is an extension of the class of monotone twist maps on the annulus or two-dimensional cylinder.By constructing a bounded solution of the monotone recurrence relation,the main conclusion in this paper is acquired:The induced homeomorphism has Birkhoff orbits provided there is a compact forward-invariant set.Therefore,it generalizes Angenent's results in low-dimensional cases.
基金supported by National Natural Science Foundation of China(Grant No.12161056)Natural Science Foundation of Jiangxi Province(Grant No.20232ACB211003)。
文摘Complex numbers play a pivotal role in both mathematics and physics,particularly in quantum mechanics,and are extensively utilized to depict the behavior of microscopic particles.Recognizing the significance of complex numbers,a framework of imaginarity resource theory has recently been established.In this work,we propose two types of imaginarity monotones induced by the unified(α,β)-relative entropy and investigate their properties.Moreover,we give explicit examples to illustrate our results.
基金supported by the National Natural Science Foundation of China(619733380).
文摘Aiming at the pulse response sequence of a kind of repetitive linear discrete-time singular systems unavailable,the paper explores a data-driven adaptive iterative learning control(DDAILC)strategy that interacts with the pulse response iterative correction(PRIC).The mechanism is to formulate the correction performance index as a linear summation of the quadratic correction error of the pulse response and the quadratic tracking error.The correction algorithm of the pulse response arrives and the correction error goes down in a monotonic way.It also discusses the conditional relationship between the declining rate of the correction error and the correction ratio.A DDAILC algorithm is designed by means of substituting the exact pulse response of the gain-optimized iterative learning control(GOILC)with its approximated one updated in the correction algorithm.The convergences regarding tracking error and correction error are obtained monotonically.Finally,numerical simulation verifies the validity and effectiveness.
基金Supported by the National Natural Science Foundation of China (12071162)the Natural Science Foundation of Fujian Province (2025J01168)。
文摘This paper concerns the monotonicity of limit wave speed c0(h) for the perturbed g Kd V equation with general even m.We show that c0(h) is decreasing.Our results give partial answer to the open problem presented by Yan et al.(Math.Model.Anal.,19,537-555,2014).
基金supported by the National Key Research and Development Program of China(Grant No.2020YFC2200103)the Shandong Provincial Natural Science Foundation(Grant Nos.ZR2022LLZ006 and ZR2022LLZ011)+1 种基金the Innovation Program for Quantum Science and Technology(Grant Nos.2021ZD0300904 and 2021ZD0300903)the Key R&D Plan of Shandong Province(Grant No.2023CXPT105)。
文摘Optical phase transfer via fiber optics is the most effective method for optical frequency standard comparison on the scale below thousands of kilometers.However,the monotonic phase discrimination range of conventional optical phase-locked loops is limited,and link delays restrict the control bandwidth,which makes it a challenge to achieve a continuously reliable optical link.This paper presents an event-timing-based phase detection method that overcomes the monotonic phase discrimination range limitation of conventional phase-locked loops through dual-edge timestamp recording,achieving an optical phase measurement resolution on the order of 10 attoseconds.With such a technique,we established a 7-segment-cascaded optical link over 1402km of commercial fiber while sharing dense wavelength division multiplexing(DWDM)channels with live telecom traffic.The system maintained continuous operation for 11.7 days without phase cycle slips despite encountering 15 km aerial fiber noise up to 21000 rad^(2)·Hz^(−1)·km^(−1)at 1 Hz.Relative instabilities of the link are 3.7×10^(−15)at 1 s and 3.9×10^(−20)at 100000 s.
文摘In this paper, some properties of the monotone set function defined by theChoquet integral are discussed. It is shown that several important structural characteristics of theoriginal set function, such as weak null-additivity, strong order continuity, property (s) andpseudomelric generating property, etc., are preserved by the new set function. It is also shown thatC-integrability assumption is inevitable for the preservations of strong order continuous andpseudometric generating property.
文摘With using the cone and partial ordering t heory and mixed monotone operator theory, the existence and uniqueness for solut ion of systems of non-monotone binary nonliear operator equations are discussed. And the iterative sequences which converge to solution of systems of operator e quations and the error estimates are also given. Some corresponding results for the mixed monotone operations and the unary operator equations are improved and generalized.
文摘On the basis of the paoers[3—7],this paper study the monotonicity problems for the positive semidefinite generalized inverses of the positive semidefinite self-conjugate matrices of quaternions in the Lowner partial order,give the explicit formulations of the monotonicity solution sets A{1;≥,T_1;≤B^(1)}and B{1;≥,T_2≥A^(1)}for the(1)-inverse,and two results of the monotonicity charac teriaztion for the(1,2)-inverse.
文摘Aim The existence of generalized solution for a class of nonlinear partial differential equations with nonhanogeneous boundary condition was investigated. This problem arises from polymer processing concerned with the first initial-boundary value problem or the nonstationary floW of non-Newtonian viscous incompressiblee fluid through the slit dice. MethodsThe monotone operator theory and the Schauder's fixal point theorem were used. Results and Conclusion The existence theorem of generalized solutions for a the of nonlinear partial differential equations with nonhormogeneous boundary condition is proved under reasonable conditions
