We introduce the concepts of unitary, almost unitary and strongly almost unitary subset of an ordered semigroup. For the notions of almost unitary and strongly almost unitary subset of an ordered semigroup, we use the...We introduce the concepts of unitary, almost unitary and strongly almost unitary subset of an ordered semigroup. For the notions of almost unitary and strongly almost unitary subset of an ordered semigroup, we use the notion of translational hull of an ordered semigroup. If (S,⋅,≤) is an ordered semigroup having an element e such that e ≤ e<sup>2</sup> and U is a nonempty subset of S such that u ≤ eu, u ≤ ue for all u ∈ U, we show that U is almost unitary in S if and only if U is unitary in . Also if (S,⋅,≤) is an ordered semigroup, e ∉ S, U is a nonempty subset of S, S<sup>e</sup>:= S ∪ {e} and U<sup>e</sup>:= U ∪ {e}, we give conditions that an (“extension” of S) ordered semigroup and the subset U<sup>e</sup> of S<sup>e</sup> must satisfy in order for U to be almost unitary or strongly almost unitary in S (in case U is strongly almost unitary in S, then the given conditions are equivalent).展开更多
In recent years,fractional-order chaotic maps have been paid more attention in publications because of the memory effect.This paper presents a novel variable-order fractional sine map(VFSM)based on the discrete fracti...In recent years,fractional-order chaotic maps have been paid more attention in publications because of the memory effect.This paper presents a novel variable-order fractional sine map(VFSM)based on the discrete fractional calculus.Specially,the order is defined as an iterative function that incorporates the current state of the system.By analyzing phase diagrams,time sequences,bifurcations,Lyapunov exponents and fuzzy entropy complexity,the dynamics of the proposed map are investigated comparing with the constant-order fractional sine map.The results reveal that the variable order has a good effect on improving the chaotic performance,and it enlarges the range of available parameter values as well as reduces non-chaotic windows.Multiple coexisting attractors also enrich the dynamics of VFSM and prove its sensitivity to initial values.Moreover,the sequence generated by the proposed map passes the statistical test for pseudorandom number and shows strong robustness to parameter estimation,which proves the potential applications in the field of information security.展开更多
Pedestrian self-organizing movement plays a significant role in evacuation studies and architectural design.Lane formation,a typical self-organizing phenomenon,helps pedestrian system to become more orderly,the majori...Pedestrian self-organizing movement plays a significant role in evacuation studies and architectural design.Lane formation,a typical self-organizing phenomenon,helps pedestrian system to become more orderly,the majority of following behavior model and overtaking behavior model are imprecise and unrealistic compared with pedestrian movement in the real world.In this study,a pedestrian dynamic model considering detailed modelling of the following behavior and overtaking behavior is constructed,and a method of measuring the lane formation and pedestrian system order based on information entropy is proposed.Simulation and analysis demonstrate that the following and avoidance behaviors are important factors of lane formation.A high tendency of following results in good lane formation.Both non-selective following behavior and aggressive overtaking behavior cause the system order to decrease.The most orderly following strategy for a pedestrian is to overtake the former pedestrian whose speed is lower than approximately 70%of his own.The influence of the obstacle layout on pedestrian lane and egress efficiency is also studied with this model.The presence of a small obstacle does not obstruct the walking of pedestrians;in contrast,it may help to improve the egress efficiency by guiding the pedestrian flow and mitigating the reduction of pedestrian system orderliness.展开更多
In an effort to clarify the formation mechanism of LPSO structure in Mg-Y-Zn alloy,the chemical environment and structural ordering in liquid Mg-rich Mg-Y-Zn system are investigated with the aid of ab-initio molecular...In an effort to clarify the formation mechanism of LPSO structure in Mg-Y-Zn alloy,the chemical environment and structural ordering in liquid Mg-rich Mg-Y-Zn system are investigated with the aid of ab-initio molecular dynamics simulation.In liquid Mg-rich Mg-Y alloys,the strong Mg-Y interaction is determined,which promotes the formation of fivefold symmetric local structure.For Mg-Zn alloys,the weak Mg-Zn interaction results in the fivefold symmetry weakening in the liquid structure.Due to the coexistence of Y and Zn,the strong attractive interaction is introduced in liquid Mg-Y-Zn ternary alloy,and contributes to the clustering of Mg,Y,Zn launched from Zn.What is more,the distribution of local structures becomes closer to that in pure Mg compared with that in binary Mg-Y and Mg-Zn alloys.These results should relate to the origins of the Y/Zn segregation zone and close-packed stacking mode in LPSO structure,which provides a new insight into the formation mechanism of LPSO structure at atomic level.展开更多
This paper is a continuation of recent work by Guo-Xiang-Zheng[10].We deduce the sharp Morrey regularity theory for weak solutions to the fourth order nonhomogeneous Lamm-Rivière equation △^{2}u=△(V▽u)+div(w▽...This paper is a continuation of recent work by Guo-Xiang-Zheng[10].We deduce the sharp Morrey regularity theory for weak solutions to the fourth order nonhomogeneous Lamm-Rivière equation △^{2}u=△(V▽u)+div(w▽u)+(▽ω+F)·▽u+f in B^(4),under the smallest regularity assumptions of V,ω,ω,F,where f belongs to some Morrey spaces.This work was motivated by many geometrical problems such as the flow of biharmonic mappings.Our results deepens the Lp type regularity theory of[10],and generalizes the work of Du,Kang and Wang[4]on a second order problem to our fourth order problems.展开更多
In this paper,we consider entire solutions of higher order homogeneous differential equations with the entire coefficients having the same order,and prove that the entire solutions are of infinite lower order.The prop...In this paper,we consider entire solutions of higher order homogeneous differential equations with the entire coefficients having the same order,and prove that the entire solutions are of infinite lower order.The properties on the radial distribution,the limit direction of the Julia set and the existence of a Baker wandering domain of the entire solutions are also discussed.展开更多
In this paper,we investigate the reverse order law for Drazin inverse of three bound-ed linear operators under some commutation relations.Moreover,the Drazin invertibility of sum is also obtained for two bounded linea...In this paper,we investigate the reverse order law for Drazin inverse of three bound-ed linear operators under some commutation relations.Moreover,the Drazin invertibility of sum is also obtained for two bounded linear operators and its expression is presented.展开更多
The novel Fe-N co-doped ordered mesoporous carbon with high catalytic activity in m-cresol removal was prepared by urea-assisted impregnation and simple pyrolysis method.During the preparation of the Fe-NC catalyst,th...The novel Fe-N co-doped ordered mesoporous carbon with high catalytic activity in m-cresol removal was prepared by urea-assisted impregnation and simple pyrolysis method.During the preparation of the Fe-NC catalyst,the complexation of N elements in urea could anchor Fe,and the formation of C3N4during urea pyrolysis could also prevent migration and aggregation of Fe species,which jointly improve the dispersion and stability of Fe.The FeN4sites and highly dispersed Fe nanoparticles synergistically trigger the dual-site peroxymonosulfate (PMS) activation for highly efficient m-cresol degradation,while the ordered mesoporous structure of the catalyst could improve the mass transfer rate of the catalytic process,which together promote catalytic degradation of m-cresol by PMS activation.Reactive oxygen species (ROS) analytic experiments demonstrate that the system degrades m-cresol by free radical pathway mainly based on SO_(4)^(-)·and·OH,and partially based on·OH as the active components,and a possible PMS activation mechanism by 5Fe-50 for m-cresol degradation was proposed.This study can provide theoretical guidance for the preparation of efficient and stable catalysts for the degradation of organic pollutants by activated PMS.展开更多
The 975 nm multimode diode lasers with high-order surface Bragg diffraction gratings have been simulated and calcu-lated using the 2D finite difference time domain(FDTD)algorithm and the scattering matrix method(SMM)....The 975 nm multimode diode lasers with high-order surface Bragg diffraction gratings have been simulated and calcu-lated using the 2D finite difference time domain(FDTD)algorithm and the scattering matrix method(SMM).The periods and etch depth of the grating parameters have been optimized.A board area laser diode(BA-LD)with high-order diffraction grat-ings has been designed and fabricated.At output powers up to 10.5 W,the measured spectral width of full width at half maxi-mum(FWHM)is less than 0.5 nm.The results demonstrate that the designed high-order surface gratings can effectively nar-row the spectral width of multimode semiconductor lasers at high output power.展开更多
Nuclear power plants exhibit non-linear and time-variable dynamics.Therefore,designing a control system that sets the reactor power and forces it to follow the desired load is complicated.A supercritical water reactor...Nuclear power plants exhibit non-linear and time-variable dynamics.Therefore,designing a control system that sets the reactor power and forces it to follow the desired load is complicated.A supercritical water reactor(SCWR)is a fourth-generation conceptual reactor.In an SCWR,the non-linear dynamics of the reactor require a controller capable of control-ling the nonlinearities.In this study,a pressure-tube-type SCWR was controlled during reactor power maneuvering with a higher order sliding mode,and the reactor outgoing steam temperature and pressure were controlled simultaneously.In an SCWR,the temperature,pressure,and power must be maintained at a setpoint(desired value)during power maneuvering.Reactor point kinetics equations with three groups of delayed neutrons were used in the simulation.Higher-order and classic sliding mode controllers were separately manufactured to control the plant and were compared with the PI controllers speci-fied in previous studies.The controlled parameters were reactor power,steam temperature,and pressure.Notably,for these parameters,the PI controller had certain instabilities in the presence of disturbances.The classic sliding mode controller had a higher accuracy and stability;however its main drawback was the chattering phenomenon.HOSMC was highly accurate and stable and had a small computational cost.In reality,it followed the desired values without oscillations and chattering.展开更多
The lottery has long captivated the imagination of players worldwide, offering the tantalizing possibility of life-changing wins. While winning the lottery is largely a matter of chance, as lottery drawings are typica...The lottery has long captivated the imagination of players worldwide, offering the tantalizing possibility of life-changing wins. While winning the lottery is largely a matter of chance, as lottery drawings are typically random and unpredictable. Some people use the lottery terminal randomly generates numbers for them, some players choose numbers that hold personal significance to them, such as birthdays, anniversaries, or other important dates, some enthusiasts have turned to statistical analysis as a means to analyze past winning numbers identify patterns or frequencies. In this paper, we use order statistics to estimate the probability of specific order of numbers or number combinations being drawn in future drawings.展开更多
This paper analyzes how artificial intelligence (AI) automation can improve warehouse management compared to emerging technologies like drone usage. Specifically, we evaluate AI’s impact on crucial warehouse function...This paper analyzes how artificial intelligence (AI) automation can improve warehouse management compared to emerging technologies like drone usage. Specifically, we evaluate AI’s impact on crucial warehouse functions—inventory tracking, order fulfillment, and logistics efficiency. Our findings indicate AI automation enables real-time inventory visibility, optimized picking routes, and dynamic delivery scheduling, which drones cannot match. AI better leverages data insights for intelligent decision-making across warehouse operations, supporting improved productivity and lower operating costs.展开更多
The main purpose of this paper is to generalize the effect of two-phased demand and variable deterioration within the EOQ (Economic Order Quantity) framework. The rate of deterioration is a linear function of time. Th...The main purpose of this paper is to generalize the effect of two-phased demand and variable deterioration within the EOQ (Economic Order Quantity) framework. The rate of deterioration is a linear function of time. The two-phased demand function states the constant function for a certain period and the quadratic function of time for the rest part of the cycle time. No shortages as well as partial backlogging are allowed to occur. The mathematical expressions are derived for determining the optimal cycle time, order quantity and total cost function. An easy-to-use working procedure is provided to calculate the above quantities. A couple of numerical examples are cited to explain the theoretical results and sensitivity analysis of some selected examples is carried out.展开更多
To solve the first-order differential equation derived from the problem of a free-falling object and the problem arising from Newton’s law of cooling, the study compares the numerical solutions obtained from Picard’...To solve the first-order differential equation derived from the problem of a free-falling object and the problem arising from Newton’s law of cooling, the study compares the numerical solutions obtained from Picard’s and Taylor’s series methods. We have carried out a descriptive analysis using the MATLAB software. Picard’s and Taylor’s techniques for deriving numerical solutions are both strong mathematical instruments that behave similarly. All first-order differential equations in standard form that have a constant function on the right-hand side share this similarity. As a result, we can conclude that Taylor’s approach is simpler to use, more effective, and more accurate. We will contrast Rung Kutta and Taylor’s methods in more detail in the following section.展开更多
This work presents the “n<sup>th</sup>-Order Feature Adjoint Sensitivity Analysis Methodology for Nonlinear Systems” (abbreviated as “n<sup>th</sup>-FASAM-N”), which will be shown to be the...This work presents the “n<sup>th</sup>-Order Feature Adjoint Sensitivity Analysis Methodology for Nonlinear Systems” (abbreviated as “n<sup>th</sup>-FASAM-N”), which will be shown to be the most efficient methodology for computing exact expressions of sensitivities, of any order, of model responses with respect to features of model parameters and, subsequently, with respect to the model’s uncertain parameters, boundaries, and internal interfaces. The unparalleled efficiency and accuracy of the n<sup>th</sup>-FASAM-N methodology stems from the maximal reduction of the number of adjoint computations (which are considered to be “large-scale” computations) for computing high-order sensitivities. When applying the n<sup>th</sup>-FASAM-N methodology to compute the second- and higher-order sensitivities, the number of large-scale computations is proportional to the number of “model features” as opposed to being proportional to the number of model parameters (which are considerably more than the number of features).When a model has no “feature” functions of parameters, but only comprises primary parameters, the n<sup>th</sup>-FASAM-N methodology becomes identical to the extant n<sup>th</sup> CASAM-N (“n<sup>th</sup>-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Nonlinear Systems”) methodology. Both the n<sup>th</sup>-FASAM-N and the n<sup>th</sup>-CASAM-N methodologies are formulated in linearly increasing higher-dimensional Hilbert spaces as opposed to exponentially increasing parameter-dimensional spaces thus overcoming the curse of dimensionality in sensitivity analysis of nonlinear systems. Both the n<sup>th</sup>-FASAM-N and the n<sup>th</sup>-CASAM-N are incomparably more efficient and more accurate than any other methods (statistical, finite differences, etc.) for computing exact expressions of response sensitivities of any order with respect to the model’s features and/or primary uncertain parameters, boundaries, and internal interfaces.展开更多
This work highlights the unparalleled efficiency of the “n<sup>th</sup>-Order Function/ Feature Adjoint Sensitivity Analysis Methodology for Nonlinear Systems” (n<sup>th</sup>-FASAM-N) by con...This work highlights the unparalleled efficiency of the “n<sup>th</sup>-Order Function/ Feature Adjoint Sensitivity Analysis Methodology for Nonlinear Systems” (n<sup>th</sup>-FASAM-N) by considering the well-known Nordheim-Fuchs reactor dynamics/safety model. This model describes a short-time self-limiting power excursion in a nuclear reactor system having a negative temperature coefficient in which a large amount of reactivity is suddenly inserted, either intentionally or by accident. This nonlinear paradigm model is sufficiently complex to model realistically self-limiting power excursions for short times yet admits closed-form exact expressions for the time-dependent neutron flux, temperature distribution and energy released during the transient power burst. The n<sup>th</sup>-FASAM-N methodology is compared to the extant “n<sup>th</sup>-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Nonlinear Systems” (n<sup>th</sup>-CASAM-N) showing that: (i) the 1<sup>st</sup>-FASAM-N and the 1<sup>st</sup>-CASAM-N methodologies are equally efficient for computing the first-order sensitivities;each methodology requires a single large-scale computation for solving the “First-Level Adjoint Sensitivity System” (1<sup>st</sup>-LASS);(ii) the 2<sup>nd</sup>-FASAM-N methodology is considerably more efficient than the 2<sup>nd</sup>-CASAM-N methodology for computing the second-order sensitivities since the number of feature-functions is much smaller than the number of primary parameters;specifically for the Nordheim-Fuchs model, the 2<sup>nd</sup>-FASAM-N methodology requires 2 large-scale computations to obtain all of the exact expressions of the 28 distinct second-order response sensitivities with respect to the model parameters while the 2<sup>nd</sup>-CASAM-N methodology requires 7 large-scale computations for obtaining these 28 second-order sensitivities;(iii) the 3<sup>rd</sup>-FASAM-N methodology is even more efficient than the 3<sup>rd</sup>-CASAM-N methodology: only 2 large-scale computations are needed to obtain the exact expressions of the 84 distinct third-order response sensitivities with respect to the Nordheim-Fuchs model’s parameters when applying the 3<sup>rd</sup>-FASAM-N methodology, while the application of the 3<sup>rd</sup>-CASAM-N methodology requires at least 22 large-scale computations for computing the same 84 distinct third-order sensitivities. Together, the n<sup>th</sup>-FASAM-N and the n<sup>th</sup>-CASAM-N methodologies are the most practical methodologies for computing response sensitivities of any order comprehensively and accurately, overcoming the curse of dimensionality in sensitivity analysis.展开更多
This paper is concerned with the following fourth-order three-point boundary value problem , where , we discuss the existence of positive solutions to the above problem by applying to the fixed point theory in cones a...This paper is concerned with the following fourth-order three-point boundary value problem , where , we discuss the existence of positive solutions to the above problem by applying to the fixed point theory in cones and iterative technique.展开更多
This work presents the mathematical framework of the “Fifth-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Nonlinear Systems (5<sup>th</sup>-CASAM-N),” which generalizes and extends all...This work presents the mathematical framework of the “Fifth-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Nonlinear Systems (5<sup>th</sup>-CASAM-N),” which generalizes and extends all of the previous works performed to date on this subject. The 5<sup>th</sup>-CASAM-N enables the exact and efficient computation of all sensitivities, up to and including fifth-order, of model responses to uncertain model parameters and uncertain boundaries of the system’s domain of definition, thus enabling, inter alia, the quantification of uncertainties stemming from manufacturing tolerances. The 5<sup>th</sup>-CASAM-N provides a fundamental step towards overcoming the curse of dimensionality in sensitivity and uncertainty analysis.展开更多
The development of quantum optics theory based on the method of integration within an ordered product of operators(IWOP)has greatly stimulated the study of quantum states in the light field,especially non-Gaussian sta...The development of quantum optics theory based on the method of integration within an ordered product of operators(IWOP)has greatly stimulated the study of quantum states in the light field,especially non-Gaussian states with various non-classical properties.In this paper,the two-mode squeezing operator is derived with integral theory within the Weyl ordering product of operators using a combinatorial field in which one mode is a chaotic field and the other mode is a vacuum field.The density operator of the new light field,its entanglement property and photon number distribution are analyzed.We also note that tracing a three-mode pure state can yield this new light field.These methods represent a theoretical approach to investigating new density operators of light fields.展开更多
文摘We introduce the concepts of unitary, almost unitary and strongly almost unitary subset of an ordered semigroup. For the notions of almost unitary and strongly almost unitary subset of an ordered semigroup, we use the notion of translational hull of an ordered semigroup. If (S,⋅,≤) is an ordered semigroup having an element e such that e ≤ e<sup>2</sup> and U is a nonempty subset of S such that u ≤ eu, u ≤ ue for all u ∈ U, we show that U is almost unitary in S if and only if U is unitary in . Also if (S,⋅,≤) is an ordered semigroup, e ∉ S, U is a nonempty subset of S, S<sup>e</sup>:= S ∪ {e} and U<sup>e</sup>:= U ∪ {e}, we give conditions that an (“extension” of S) ordered semigroup and the subset U<sup>e</sup> of S<sup>e</sup> must satisfy in order for U to be almost unitary or strongly almost unitary in S (in case U is strongly almost unitary in S, then the given conditions are equivalent).
基金Project supported by the National Natural Science Foundation of China(Grant Nos.62071496,61901530,and 62061008)the Natural Science Foundation of Hunan Province of China(Grant No.2020JJ5767).
文摘In recent years,fractional-order chaotic maps have been paid more attention in publications because of the memory effect.This paper presents a novel variable-order fractional sine map(VFSM)based on the discrete fractional calculus.Specially,the order is defined as an iterative function that incorporates the current state of the system.By analyzing phase diagrams,time sequences,bifurcations,Lyapunov exponents and fuzzy entropy complexity,the dynamics of the proposed map are investigated comparing with the constant-order fractional sine map.The results reveal that the variable order has a good effect on improving the chaotic performance,and it enlarges the range of available parameter values as well as reduces non-chaotic windows.Multiple coexisting attractors also enrich the dynamics of VFSM and prove its sensitivity to initial values.Moreover,the sequence generated by the proposed map passes the statistical test for pseudorandom number and shows strong robustness to parameter estimation,which proves the potential applications in the field of information security.
基金Project supported by the National Natural Science Foundation of China(Grant No.71603146).
文摘Pedestrian self-organizing movement plays a significant role in evacuation studies and architectural design.Lane formation,a typical self-organizing phenomenon,helps pedestrian system to become more orderly,the majority of following behavior model and overtaking behavior model are imprecise and unrealistic compared with pedestrian movement in the real world.In this study,a pedestrian dynamic model considering detailed modelling of the following behavior and overtaking behavior is constructed,and a method of measuring the lane formation and pedestrian system order based on information entropy is proposed.Simulation and analysis demonstrate that the following and avoidance behaviors are important factors of lane formation.A high tendency of following results in good lane formation.Both non-selective following behavior and aggressive overtaking behavior cause the system order to decrease.The most orderly following strategy for a pedestrian is to overtake the former pedestrian whose speed is lower than approximately 70%of his own.The influence of the obstacle layout on pedestrian lane and egress efficiency is also studied with this model.The presence of a small obstacle does not obstruct the walking of pedestrians;in contrast,it may help to improve the egress efficiency by guiding the pedestrian flow and mitigating the reduction of pedestrian system orderliness.
基金supported by National Natural Science Foundation of China,China(No.51901117,51801116)Youth Innovation and Technology Support Program of Shandong Provincial Colleges and Universities,China(No.2020KJA002)+2 种基金Youth Fund of Shandong Academy of Sciences,China(2020QN0021)Innovation Pilot Project for Fusion of Science,Education and Industry(International Cooperation)from Qilu University of Technology(Shandong Academy of Sciences),China(No.2020KJC-GH03)Several Policies on Promoting Collaborative Innovation and Industrialization of Achievements in Universities and Research Institutes,China(No.2019GXRC030)。
文摘In an effort to clarify the formation mechanism of LPSO structure in Mg-Y-Zn alloy,the chemical environment and structural ordering in liquid Mg-rich Mg-Y-Zn system are investigated with the aid of ab-initio molecular dynamics simulation.In liquid Mg-rich Mg-Y alloys,the strong Mg-Y interaction is determined,which promotes the formation of fivefold symmetric local structure.For Mg-Zn alloys,the weak Mg-Zn interaction results in the fivefold symmetry weakening in the liquid structure.Due to the coexistence of Y and Zn,the strong attractive interaction is introduced in liquid Mg-Y-Zn ternary alloy,and contributes to the clustering of Mg,Y,Zn launched from Zn.What is more,the distribution of local structures becomes closer to that in pure Mg compared with that in binary Mg-Y and Mg-Zn alloys.These results should relate to the origins of the Y/Zn segregation zone and close-packed stacking mode in LPSO structure,which provides a new insight into the formation mechanism of LPSO structure at atomic level.
基金supported by the National Natural Science Foundation of China(12271296,12271195).
文摘This paper is a continuation of recent work by Guo-Xiang-Zheng[10].We deduce the sharp Morrey regularity theory for weak solutions to the fourth order nonhomogeneous Lamm-Rivière equation △^{2}u=△(V▽u)+div(w▽u)+(▽ω+F)·▽u+f in B^(4),under the smallest regularity assumptions of V,ω,ω,F,where f belongs to some Morrey spaces.This work was motivated by many geometrical problems such as the flow of biharmonic mappings.Our results deepens the Lp type regularity theory of[10],and generalizes the work of Du,Kang and Wang[4]on a second order problem to our fourth order problems.
基金supported partly by the National Natural Science Foundation of China(11926201,12171050)the National Science Foundation of Guangdong Province(2018A030313508)。
文摘In this paper,we consider entire solutions of higher order homogeneous differential equations with the entire coefficients having the same order,and prove that the entire solutions are of infinite lower order.The properties on the radial distribution,the limit direction of the Julia set and the existence of a Baker wandering domain of the entire solutions are also discussed.
基金supported by the NNSF of China(12261065)the NSF of Inner Mongolia(2022MS01005)+1 种基金the Basic Science Research Fund of the Universities Directly under the Inner Mongolia Autonomous Re-gion(JY20220084)the Program for Innovative Research Team in Universities of Inner Mongolia Autonomous Region(NMGIRT2317).
文摘In this paper,we investigate the reverse order law for Drazin inverse of three bound-ed linear operators under some commutation relations.Moreover,the Drazin invertibility of sum is also obtained for two bounded linear operators and its expression is presented.
基金gratefully acknowledge the financial support of the National Natural Science Foundation of China(22108145 and 21978143)the Shandong Province Natural Science Foundation(ZR2020QB189)+1 种基金State Key Laboratory of Heavy Oil Processing(SKLHOP202203008)the Talent Foundation funded by Province and Ministry Co-construction Collaborative Innovation Center of Eco-chemical Engineering(STHGYX2201).
文摘The novel Fe-N co-doped ordered mesoporous carbon with high catalytic activity in m-cresol removal was prepared by urea-assisted impregnation and simple pyrolysis method.During the preparation of the Fe-NC catalyst,the complexation of N elements in urea could anchor Fe,and the formation of C3N4during urea pyrolysis could also prevent migration and aggregation of Fe species,which jointly improve the dispersion and stability of Fe.The FeN4sites and highly dispersed Fe nanoparticles synergistically trigger the dual-site peroxymonosulfate (PMS) activation for highly efficient m-cresol degradation,while the ordered mesoporous structure of the catalyst could improve the mass transfer rate of the catalytic process,which together promote catalytic degradation of m-cresol by PMS activation.Reactive oxygen species (ROS) analytic experiments demonstrate that the system degrades m-cresol by free radical pathway mainly based on SO_(4)^(-)·and·OH,and partially based on·OH as the active components,and a possible PMS activation mechanism by 5Fe-50 for m-cresol degradation was proposed.This study can provide theoretical guidance for the preparation of efficient and stable catalysts for the degradation of organic pollutants by activated PMS.
基金supported by the National Key R&D Program of China,No.2022YFB4601201.
文摘The 975 nm multimode diode lasers with high-order surface Bragg diffraction gratings have been simulated and calcu-lated using the 2D finite difference time domain(FDTD)algorithm and the scattering matrix method(SMM).The periods and etch depth of the grating parameters have been optimized.A board area laser diode(BA-LD)with high-order diffraction grat-ings has been designed and fabricated.At output powers up to 10.5 W,the measured spectral width of full width at half maxi-mum(FWHM)is less than 0.5 nm.The results demonstrate that the designed high-order surface gratings can effectively nar-row the spectral width of multimode semiconductor lasers at high output power.
文摘Nuclear power plants exhibit non-linear and time-variable dynamics.Therefore,designing a control system that sets the reactor power and forces it to follow the desired load is complicated.A supercritical water reactor(SCWR)is a fourth-generation conceptual reactor.In an SCWR,the non-linear dynamics of the reactor require a controller capable of control-ling the nonlinearities.In this study,a pressure-tube-type SCWR was controlled during reactor power maneuvering with a higher order sliding mode,and the reactor outgoing steam temperature and pressure were controlled simultaneously.In an SCWR,the temperature,pressure,and power must be maintained at a setpoint(desired value)during power maneuvering.Reactor point kinetics equations with three groups of delayed neutrons were used in the simulation.Higher-order and classic sliding mode controllers were separately manufactured to control the plant and were compared with the PI controllers speci-fied in previous studies.The controlled parameters were reactor power,steam temperature,and pressure.Notably,for these parameters,the PI controller had certain instabilities in the presence of disturbances.The classic sliding mode controller had a higher accuracy and stability;however its main drawback was the chattering phenomenon.HOSMC was highly accurate and stable and had a small computational cost.In reality,it followed the desired values without oscillations and chattering.
文摘The lottery has long captivated the imagination of players worldwide, offering the tantalizing possibility of life-changing wins. While winning the lottery is largely a matter of chance, as lottery drawings are typically random and unpredictable. Some people use the lottery terminal randomly generates numbers for them, some players choose numbers that hold personal significance to them, such as birthdays, anniversaries, or other important dates, some enthusiasts have turned to statistical analysis as a means to analyze past winning numbers identify patterns or frequencies. In this paper, we use order statistics to estimate the probability of specific order of numbers or number combinations being drawn in future drawings.
文摘This paper analyzes how artificial intelligence (AI) automation can improve warehouse management compared to emerging technologies like drone usage. Specifically, we evaluate AI’s impact on crucial warehouse functions—inventory tracking, order fulfillment, and logistics efficiency. Our findings indicate AI automation enables real-time inventory visibility, optimized picking routes, and dynamic delivery scheduling, which drones cannot match. AI better leverages data insights for intelligent decision-making across warehouse operations, supporting improved productivity and lower operating costs.
文摘The main purpose of this paper is to generalize the effect of two-phased demand and variable deterioration within the EOQ (Economic Order Quantity) framework. The rate of deterioration is a linear function of time. The two-phased demand function states the constant function for a certain period and the quadratic function of time for the rest part of the cycle time. No shortages as well as partial backlogging are allowed to occur. The mathematical expressions are derived for determining the optimal cycle time, order quantity and total cost function. An easy-to-use working procedure is provided to calculate the above quantities. A couple of numerical examples are cited to explain the theoretical results and sensitivity analysis of some selected examples is carried out.
文摘To solve the first-order differential equation derived from the problem of a free-falling object and the problem arising from Newton’s law of cooling, the study compares the numerical solutions obtained from Picard’s and Taylor’s series methods. We have carried out a descriptive analysis using the MATLAB software. Picard’s and Taylor’s techniques for deriving numerical solutions are both strong mathematical instruments that behave similarly. All first-order differential equations in standard form that have a constant function on the right-hand side share this similarity. As a result, we can conclude that Taylor’s approach is simpler to use, more effective, and more accurate. We will contrast Rung Kutta and Taylor’s methods in more detail in the following section.
文摘This work presents the “n<sup>th</sup>-Order Feature Adjoint Sensitivity Analysis Methodology for Nonlinear Systems” (abbreviated as “n<sup>th</sup>-FASAM-N”), which will be shown to be the most efficient methodology for computing exact expressions of sensitivities, of any order, of model responses with respect to features of model parameters and, subsequently, with respect to the model’s uncertain parameters, boundaries, and internal interfaces. The unparalleled efficiency and accuracy of the n<sup>th</sup>-FASAM-N methodology stems from the maximal reduction of the number of adjoint computations (which are considered to be “large-scale” computations) for computing high-order sensitivities. When applying the n<sup>th</sup>-FASAM-N methodology to compute the second- and higher-order sensitivities, the number of large-scale computations is proportional to the number of “model features” as opposed to being proportional to the number of model parameters (which are considerably more than the number of features).When a model has no “feature” functions of parameters, but only comprises primary parameters, the n<sup>th</sup>-FASAM-N methodology becomes identical to the extant n<sup>th</sup> CASAM-N (“n<sup>th</sup>-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Nonlinear Systems”) methodology. Both the n<sup>th</sup>-FASAM-N and the n<sup>th</sup>-CASAM-N methodologies are formulated in linearly increasing higher-dimensional Hilbert spaces as opposed to exponentially increasing parameter-dimensional spaces thus overcoming the curse of dimensionality in sensitivity analysis of nonlinear systems. Both the n<sup>th</sup>-FASAM-N and the n<sup>th</sup>-CASAM-N are incomparably more efficient and more accurate than any other methods (statistical, finite differences, etc.) for computing exact expressions of response sensitivities of any order with respect to the model’s features and/or primary uncertain parameters, boundaries, and internal interfaces.
文摘This work highlights the unparalleled efficiency of the “n<sup>th</sup>-Order Function/ Feature Adjoint Sensitivity Analysis Methodology for Nonlinear Systems” (n<sup>th</sup>-FASAM-N) by considering the well-known Nordheim-Fuchs reactor dynamics/safety model. This model describes a short-time self-limiting power excursion in a nuclear reactor system having a negative temperature coefficient in which a large amount of reactivity is suddenly inserted, either intentionally or by accident. This nonlinear paradigm model is sufficiently complex to model realistically self-limiting power excursions for short times yet admits closed-form exact expressions for the time-dependent neutron flux, temperature distribution and energy released during the transient power burst. The n<sup>th</sup>-FASAM-N methodology is compared to the extant “n<sup>th</sup>-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Nonlinear Systems” (n<sup>th</sup>-CASAM-N) showing that: (i) the 1<sup>st</sup>-FASAM-N and the 1<sup>st</sup>-CASAM-N methodologies are equally efficient for computing the first-order sensitivities;each methodology requires a single large-scale computation for solving the “First-Level Adjoint Sensitivity System” (1<sup>st</sup>-LASS);(ii) the 2<sup>nd</sup>-FASAM-N methodology is considerably more efficient than the 2<sup>nd</sup>-CASAM-N methodology for computing the second-order sensitivities since the number of feature-functions is much smaller than the number of primary parameters;specifically for the Nordheim-Fuchs model, the 2<sup>nd</sup>-FASAM-N methodology requires 2 large-scale computations to obtain all of the exact expressions of the 28 distinct second-order response sensitivities with respect to the model parameters while the 2<sup>nd</sup>-CASAM-N methodology requires 7 large-scale computations for obtaining these 28 second-order sensitivities;(iii) the 3<sup>rd</sup>-FASAM-N methodology is even more efficient than the 3<sup>rd</sup>-CASAM-N methodology: only 2 large-scale computations are needed to obtain the exact expressions of the 84 distinct third-order response sensitivities with respect to the Nordheim-Fuchs model’s parameters when applying the 3<sup>rd</sup>-FASAM-N methodology, while the application of the 3<sup>rd</sup>-CASAM-N methodology requires at least 22 large-scale computations for computing the same 84 distinct third-order sensitivities. Together, the n<sup>th</sup>-FASAM-N and the n<sup>th</sup>-CASAM-N methodologies are the most practical methodologies for computing response sensitivities of any order comprehensively and accurately, overcoming the curse of dimensionality in sensitivity analysis.
文摘This paper is concerned with the following fourth-order three-point boundary value problem , where , we discuss the existence of positive solutions to the above problem by applying to the fixed point theory in cones and iterative technique.
文摘This work presents the mathematical framework of the “Fifth-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Nonlinear Systems (5<sup>th</sup>-CASAM-N),” which generalizes and extends all of the previous works performed to date on this subject. The 5<sup>th</sup>-CASAM-N enables the exact and efficient computation of all sensitivities, up to and including fifth-order, of model responses to uncertain model parameters and uncertain boundaries of the system’s domain of definition, thus enabling, inter alia, the quantification of uncertainties stemming from manufacturing tolerances. The 5<sup>th</sup>-CASAM-N provides a fundamental step towards overcoming the curse of dimensionality in sensitivity and uncertainty analysis.
基金Project supported by the National Natural Science Foundation of China(Grant No.11775208)the Foundation for Young Talents in College of Anhui Province,China(Grant Nos.gxyq2021210 and gxyq2019077)the Natural Science Foundation of the Anhui Higher Education Institutions of China(Grant Nos.KJ2020A0638 and 2022AH051586)。
文摘The development of quantum optics theory based on the method of integration within an ordered product of operators(IWOP)has greatly stimulated the study of quantum states in the light field,especially non-Gaussian states with various non-classical properties.In this paper,the two-mode squeezing operator is derived with integral theory within the Weyl ordering product of operators using a combinatorial field in which one mode is a chaotic field and the other mode is a vacuum field.The density operator of the new light field,its entanglement property and photon number distribution are analyzed.We also note that tracing a three-mode pure state can yield this new light field.These methods represent a theoretical approach to investigating new density operators of light fields.
