In order to study rpp semigroups, in particular, some special cases, several facts on (l)-Green’s relations and strongly rpp semigroups are given as some remarks.
Green's relations and generalized Green's relations play a fundamental role in the study of semigroups.GV-semigroups are the generalizations of completely regular semigroups in the range of π-regular semigrou...Green's relations and generalized Green's relations play a fundamental role in the study of semigroups.GV-semigroups are the generalizations of completely regular semigroups in the range of π-regular semigroups.In this paper,Green's relations and generalized Green's relations on GV-semigroups are considered by the structure of GV-semigroups.D=j and D C D* on GV-semigroups will be proved.展开更多
The solution of Poisson’s Equation plays an important role in many areas, including modeling high-intensity and high-brightness beams in particle accelerators. For the computational domain with a large aspect ratio, ...The solution of Poisson’s Equation plays an important role in many areas, including modeling high-intensity and high-brightness beams in particle accelerators. For the computational domain with a large aspect ratio, the integrated Green’s function method has been adopted to solve the 3D Poisson equation subject to open boundary conditions. In this paper, we report on the efficient implementation of this method, which can save more than a factor of 50 computing time compared with the direct brute force implementation and its improvement under certain extreme conditions.展开更多
We compare Newton’s force law of universal gravitation with a corrected simple approach based on Bhandari’s recently presented work, where the gravitation constant G is maintained. A reciprocity relation exists betw...We compare Newton’s force law of universal gravitation with a corrected simple approach based on Bhandari’s recently presented work, where the gravitation constant G is maintained. A reciprocity relation exists between both alternative gravity formulas with respect to the distances between mass centers. We conclude a one-to-one mapping of the two gravitational formulas. We don’t need Einstein’s construct of spacetime bending by matter.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
In this paper, we introduce the definition of (m, n)0-regularity in Г-semigroups. we in- vestigate and characterize the 20-regular class of F-semigroups using Green's relations. Extending and generalizing the Croi...In this paper, we introduce the definition of (m, n)0-regularity in Г-semigroups. we in- vestigate and characterize the 20-regular class of F-semigroups using Green's relations. Extending and generalizing the Croisot's Theory of Decomposition for F-semigroups, we introduce and study the absorbent and regular absorbent Г-semigroups. We approach this problem by examining quasi-ideals using Green's relations.展开更多
The possible exotic nuclear properties in the neutron-rich Ca,Ni,Zr,and Sn isotopes are examined with the continuum Skyrme Hartree-Fock-Bogoliubov theory in the framework of the Green’s function method.The pairing co...The possible exotic nuclear properties in the neutron-rich Ca,Ni,Zr,and Sn isotopes are examined with the continuum Skyrme Hartree-Fock-Bogoliubov theory in the framework of the Green’s function method.The pairing correlation,the couplings with the continuum,and the blocking effects for the unpaired nucleon in odd-A nuclei are properly treated.The Skyrme interaction SLy4 is adopted for the ph channel and the density-dependentinteraction is adopted for the pp chan-nel,which well reproduce the experimental two-neutron separation energies S_(2n)and one-neutron separation energies Sn.It is found that the criterion S_(n)>0 predicts a neutron drip line with neutron numbers much smaller than those for S_(2n)>0.Owing to the unpaired odd neutron,the neutron pairing energies−E_(pair)in odd-A nuclei are much lower than those in the neighbor-ing even-even nuclei.By investigating the single-particle structures,the possible halo structures in the neutron-rich Ca,Ni,and Sn isotopes are predicted,where sharp increases in the root-mean-square(rms)radii with significant deviations from the traditional rA^(1∕3)rule and diffuse spatial density distributions are observed.Analyzing the contributions of various partial waves to the total neutron densityρlj(r)∕ρ(r)reveals that the orbitals located around the Fermi surface-particularly those with small angular momenta-significantly affect the extended nuclear density and large rms radii.The number of neutrons Nλ(N_(0))occupying above the Fermi surfacen(continuum threshold)is discussed,whose evolution as a function of the mass number A in each isotope is consistent with that of the pairing energy,supporting the key role of the pairing correlation in halo phenomena.展开更多
In this paper,we obtain Green’s functions of two-dimensional(2D)piezoelectric quasicrystal(PQC)in half-space and bimaterials.Based on the elastic theory of QCs,the Stroh formalism is used to derive the general soluti...In this paper,we obtain Green’s functions of two-dimensional(2D)piezoelectric quasicrystal(PQC)in half-space and bimaterials.Based on the elastic theory of QCs,the Stroh formalism is used to derive the general solutions of displacements and stresses.Then,we obtain the analytical solutions of half-space and bimaterial Green’s functions.Besides,the interfacial Green’s function for bimaterials is also obtained in the analytical form.Before numerical studies,a comparative study is carried out to validate the present solutions.Typical numerical examples are performed to investigate the effects of multi-physics loadings such as the line force,the line dislocation,the line charge,and the phason line force.As a result,the coupling effect among the phonon field,the phason field,and the electric field is prominent,and the butterfly-shaped contours are characteristic in 2D PQCs.In addition,the changes of material parameters cause variations in physical quantities to a certain degree.展开更多
The strength of the mould cavity in sand casting is very much significant to attain high-quality castings. Optimization of green sand process parameters plays a vital role in minimizing casting defects. In the present...The strength of the mould cavity in sand casting is very much significant to attain high-quality castings. Optimization of green sand process parameters plays a vital role in minimizing casting defects. In the present research work, the effect of process parameters such as AFS grain fineness number, water, molasses, bentonite, fly ash, and ramming, and their levels on the resultant mould properties were investigated and optimized using Taguchi based grey relational analysis. The Taguchi L18 orthogonal array and analysis of variance(ANOVA) were used. The quality characteristics viz., green compression strength, permeability, bulk density, mould hardness and shatter index of green sand mould were optimized using grey relational grade, based on the experiments designed using Taguchi's Design of Experiments. ANOVA analysis indicated that water content is the most influential parameter followed by bentonite, and degree of ramming that contributes to the quality characteristics. The results are confirmed by calculating confidence intervals, which lies within the interval limits. Finally, microstructure observations and X-ray diffraction analysis have been performed for the optimal sand parametric combination. Results show that presence of maximum amount of SiO_2, which might be the reason for enhancement of the physical properties of the sand.展开更多
The pointwise space-time behaviors of the Green’s function and the global solution to the Vlasov-Poisson-Fokker-Planck(VPFP)system in three dimensional space are studied in this paper.It is shown that the Green’s fu...The pointwise space-time behaviors of the Green’s function and the global solution to the Vlasov-Poisson-Fokker-Planck(VPFP)system in three dimensional space are studied in this paper.It is shown that the Green’s function consists of the diffusion waves decaying exponentially in time but algebraically in space,and the singular kinetic waves which become smooth for all(t,x,v)when t>0.Furthermore,we establish the pointwise space-time behaviors of the global solution to the nonlinear VPFP system when the initial data is not necessarily smooth in terms of the Green’s function.展开更多
Vegetation greening has long been acknowledged,but recent studies have pointed out that vegetation greening is possibly stalled or even reversed.However,detailed analyses about greening reversal or increased browning ...Vegetation greening has long been acknowledged,but recent studies have pointed out that vegetation greening is possibly stalled or even reversed.However,detailed analyses about greening reversal or increased browning of vegetation remain scarce.In this study,we utilized the normalized difference vegetation index(NDVI)as an indicator of vegetation to investigate the trends of vegetation greening and browning(monotonic,interruption,and reversal)through the breaks for the additive season and trend(BFAST)method across China’s drylands from 1982 to 2022.It also reveals the impacts of ecological restoration programs(ERPs)and climate change on these vegetation trends.We find that the vegetation displays an obvious pattern of east-greening and west-browning in China’s drylands.Greening trends mainly exhibits monotonic greening(29.8%)and greening with setback(36.8%),whereas browning shows a greening to browning reversal(19.2%).The increase rate of greening to browning reversal is 0.0342/yr,which is apparently greater than that of greening with setback,0.0078/yr.This research highlights that,under the background of widespread vegetation greening,vegetation browning is pro-gressively increasing due to the effects of climate change.Furthermore,the ERPs have significantly increased vegetation coverage,with the increase rate in 2000-2022 being twice as much as that of 1982-1999 in reveg-etation regions.Vegetation browning in southwestern Qingzang Plateau is primarily driven by adverse climatic factors and anthropogenic disturbances,which offset the efforts of ERPs.展开更多
The intensive care unit(ICU)is a complex setting by nature,and some have described it as bizarre due to its numerous sirens that sound when anything is dangerous,constant activity,equipment,bright lights,and high fata...The intensive care unit(ICU)is a complex setting by nature,and some have described it as bizarre due to its numerous sirens that sound when anything is dangerous,constant activity,equipment,bright lights,and high fatality rate.The demands placed on nurses to care for critically ill patients in this environment frequently prevent nurses and other health‑care professionals from acknowledging the feelings of patient’s relatives or family caregivers,resulting in a hostile environment from the patient’s relative’s perspective.When a patient’s family enters the ICU,they feel that hospital administrators do little to nothing to alleviate their discomfort and fear.Despite research demonstrating the importance of providing a homely environment for patients’families,In Nigeria ICU is still far behind how a conventional ICU environment should be structured to accommodate patient’s relations in the unit.The goal of this study was to look at the patient’s relative’s perspective on providing care for a critically ill patient in an ICU,with a focus on the unit’s complexity and overall experience.Based on the findings of this study,we recommend that hospital administrators ensure that the environment of the upcoming ICU is designed to meet the needs of patient’s relatives by addressing identified environmental concerns,like caring neglect,by providing a friendly and stress‑free environment.展开更多
At present China-U.S.trade relations are in a state of confusion.Although both countries have gained tremendous benefits from the bilateral trade relationship,some Americans have intentionally distorted some basic fac...At present China-U.S.trade relations are in a state of confusion.Although both countries have gained tremendous benefits from the bilateral trade relationship,some Americans have intentionally distorted some basic facts regarding China-U.S.trade relations. Based on an analysis of some official and nonofficial research reports published in the United States,this article holds that the China-U.S.trade imbalance is the symptom of a bigger issue stemming from the contradiction between the United States as the world's sole superpower and China as an emerging power.Economic globalisation came about due to the needs of western developed countries represented by the United States to boost economic development.Only by seizing the opportunities of economic globalisation, has China gained strong economic growth. Such a development is changing the world political,economic,military and cultural landscape that have been shaped since the post-cold-war era,and has to some extent raised doubt or suspicion on the part of the United States and its western allies.This is a manifestation of how unprepared some people in the United States and other western countries are in the face of China's rapid development and rising status.So,their immediate reaction has been to seek protection for themselves,and try their utmost to prevent China's rapid growth from impacting on the international framework and their vested interests.展开更多
This research investigates the determinants of green supply chain management(GSCM)adoption and its impact on organizational performance,while considering the potential moderating factors influencing GSCM adoption.Desp...This research investigates the determinants of green supply chain management(GSCM)adoption and its impact on organizational performance,while considering the potential moderating factors influencing GSCM adoption.Despite the growing prevalence of GSCM practices among Korean firms,the factors driving their adoption have not received sufficient attention.To bridge this gap,the study uses structural equation modeling,integrating stakeholder theory and resource-based theory to explore how green entrepreneurial orientation(GEO),institutional pressure,and relational capital affect GSCM adoption.Additionally,the study explores the effects of GSCM implementation on competitiveness and economic performance.Drawing data from a sample of 213 Korean manufacturing firms,the PLS-SEM analysis highlights the significant influence of GEO,institutional pressure,and relational capital on GSCM adoption.Additionally,the study emphasizes the positive impact of GSCM implementation on firm competitiveness.These findings provide valuable insights for enhancing sustainability in supply chain management and are applicable to similar context countries such as Taiwan,China,Japan,and the Netherlands.展开更多
China is in Africa in a vigorous way,and doing business in several countries like Sudan,Congo DRC,Angola,South Africa,and Nigeria.In the short term,the relationship may appear to be mutually beneficial.This paper seek...China is in Africa in a vigorous way,and doing business in several countries like Sudan,Congo DRC,Angola,South Africa,and Nigeria.In the short term,the relationship may appear to be mutually beneficial.This paper seeks to address the issue of Africa's perspectives on China-Africa Relations and the FOCAC and examine the concept of strategic partnerships,determine the state of China-Africa relations,examines FOCAC and draw conclusion as well as recommendation on possible ways and issues for future engageme...展开更多
Classical reciprocity relations have wide applications in acoustics, from field representation to generalized optical theorem. In this paper we introduce our recent results on the applications and generalization of cl...Classical reciprocity relations have wide applications in acoustics, from field representation to generalized optical theorem. In this paper we introduce our recent results on the applications and generalization of classical Rayleigh reciprocity relation: higher derivative reciprocity relations as a generalization of the classical one and a theoretical proof on the Green's function retrieval from volume noises.展开更多
基金The research of the second author was supported by the NSFC (10871161)
文摘In order to study rpp semigroups, in particular, some special cases, several facts on (l)-Green’s relations and strongly rpp semigroups are given as some remarks.
基金Leading Academic Discipline Project of SHNU,China (No.DZL803)Innovation Project of Shanghai Education Committee,China(No.12YZ081)+2 种基金General Scientific Research Project of SHNU,China (No.SK201121)National Natural Science Foundation of China(No.11001046)Fundamental Research Fundation for the Central Universities,China (No.11D10904)
文摘Green's relations and generalized Green's relations play a fundamental role in the study of semigroups.GV-semigroups are the generalizations of completely regular semigroups in the range of π-regular semigroups.In this paper,Green's relations and generalized Green's relations on GV-semigroups are considered by the structure of GV-semigroups.D=j and D C D* on GV-semigroups will be proved.
文摘The solution of Poisson’s Equation plays an important role in many areas, including modeling high-intensity and high-brightness beams in particle accelerators. For the computational domain with a large aspect ratio, the integrated Green’s function method has been adopted to solve the 3D Poisson equation subject to open boundary conditions. In this paper, we report on the efficient implementation of this method, which can save more than a factor of 50 computing time compared with the direct brute force implementation and its improvement under certain extreme conditions.
文摘We compare Newton’s force law of universal gravitation with a corrected simple approach based on Bhandari’s recently presented work, where the gravitation constant G is maintained. A reciprocity relation exists between both alternative gravity formulas with respect to the distances between mass centers. We conclude a one-to-one mapping of the two gravitational formulas. We don’t need Einstein’s construct of spacetime bending by matter.
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In this paper, we introduce the definition of (m, n)0-regularity in Г-semigroups. we in- vestigate and characterize the 20-regular class of F-semigroups using Green's relations. Extending and generalizing the Croisot's Theory of Decomposition for F-semigroups, we introduce and study the absorbent and regular absorbent Г-semigroups. We approach this problem by examining quasi-ideals using Green's relations.
基金the National Natural Science Foundation of China(No.U2032141)the Open Project of Guangxi Key Laboratory of Nuclear Physics and Nuclear Technology(No.NLK2022-02)+4 种基金the Central Government Guidance Funds for Local Scientific and Technological Development,China(Guike ZY22096024)the Natural Science Foundation of Henan Province(No.202300410479)the Guizhou Provincial Science and Technology Projects(No.ZK[2022]203)the Foundation of Fundamental Research for Young Teachers of Zhengzhou University(No.JC202041041)the Physics Research and Development Program of Zhengzhou University(No.32410217).
文摘The possible exotic nuclear properties in the neutron-rich Ca,Ni,Zr,and Sn isotopes are examined with the continuum Skyrme Hartree-Fock-Bogoliubov theory in the framework of the Green’s function method.The pairing correlation,the couplings with the continuum,and the blocking effects for the unpaired nucleon in odd-A nuclei are properly treated.The Skyrme interaction SLy4 is adopted for the ph channel and the density-dependentinteraction is adopted for the pp chan-nel,which well reproduce the experimental two-neutron separation energies S_(2n)and one-neutron separation energies Sn.It is found that the criterion S_(n)>0 predicts a neutron drip line with neutron numbers much smaller than those for S_(2n)>0.Owing to the unpaired odd neutron,the neutron pairing energies−E_(pair)in odd-A nuclei are much lower than those in the neighbor-ing even-even nuclei.By investigating the single-particle structures,the possible halo structures in the neutron-rich Ca,Ni,and Sn isotopes are predicted,where sharp increases in the root-mean-square(rms)radii with significant deviations from the traditional rA^(1∕3)rule and diffuse spatial density distributions are observed.Analyzing the contributions of various partial waves to the total neutron densityρlj(r)∕ρ(r)reveals that the orbitals located around the Fermi surface-particularly those with small angular momenta-significantly affect the extended nuclear density and large rms radii.The number of neutrons Nλ(N_(0))occupying above the Fermi surfacen(continuum threshold)is discussed,whose evolution as a function of the mass number A in each isotope is consistent with that of the pairing energy,supporting the key role of the pairing correlation in halo phenomena.
基金the National Natural Science Foundation of China(Nos.11972365 and 12102458)。
文摘In this paper,we obtain Green’s functions of two-dimensional(2D)piezoelectric quasicrystal(PQC)in half-space and bimaterials.Based on the elastic theory of QCs,the Stroh formalism is used to derive the general solutions of displacements and stresses.Then,we obtain the analytical solutions of half-space and bimaterial Green’s functions.Besides,the interfacial Green’s function for bimaterials is also obtained in the analytical form.Before numerical studies,a comparative study is carried out to validate the present solutions.Typical numerical examples are performed to investigate the effects of multi-physics loadings such as the line force,the line dislocation,the line charge,and the phason line force.As a result,the coupling effect among the phonon field,the phason field,and the electric field is prominent,and the butterfly-shaped contours are characteristic in 2D PQCs.In addition,the changes of material parameters cause variations in physical quantities to a certain degree.
基金financially supported by the National Institute of Technology,Manipur,India
文摘The strength of the mould cavity in sand casting is very much significant to attain high-quality castings. Optimization of green sand process parameters plays a vital role in minimizing casting defects. In the present research work, the effect of process parameters such as AFS grain fineness number, water, molasses, bentonite, fly ash, and ramming, and their levels on the resultant mould properties were investigated and optimized using Taguchi based grey relational analysis. The Taguchi L18 orthogonal array and analysis of variance(ANOVA) were used. The quality characteristics viz., green compression strength, permeability, bulk density, mould hardness and shatter index of green sand mould were optimized using grey relational grade, based on the experiments designed using Taguchi's Design of Experiments. ANOVA analysis indicated that water content is the most influential parameter followed by bentonite, and degree of ramming that contributes to the quality characteristics. The results are confirmed by calculating confidence intervals, which lies within the interval limits. Finally, microstructure observations and X-ray diffraction analysis have been performed for the optimal sand parametric combination. Results show that presence of maximum amount of SiO_2, which might be the reason for enhancement of the physical properties of the sand.
基金supported by National Natural Science Foundation of China(11671100 and 12171104)the National Science Fund for Excellent Young Scholars(11922107)Guangxi Natural Science Foundation(2018GXNSFAA138210 and 2019JJG110010)。
文摘The pointwise space-time behaviors of the Green’s function and the global solution to the Vlasov-Poisson-Fokker-Planck(VPFP)system in three dimensional space are studied in this paper.It is shown that the Green’s function consists of the diffusion waves decaying exponentially in time but algebraically in space,and the singular kinetic waves which become smooth for all(t,x,v)when t>0.Furthermore,we establish the pointwise space-time behaviors of the global solution to the nonlinear VPFP system when the initial data is not necessarily smooth in terms of the Green’s function.
基金supported by the National Natural Science Foundation of China(Grants No.41991231,42041004,and 41888101)the China University Research Talents Recruitment Program(111 project,Grant No.B13045).
文摘Vegetation greening has long been acknowledged,but recent studies have pointed out that vegetation greening is possibly stalled or even reversed.However,detailed analyses about greening reversal or increased browning of vegetation remain scarce.In this study,we utilized the normalized difference vegetation index(NDVI)as an indicator of vegetation to investigate the trends of vegetation greening and browning(monotonic,interruption,and reversal)through the breaks for the additive season and trend(BFAST)method across China’s drylands from 1982 to 2022.It also reveals the impacts of ecological restoration programs(ERPs)and climate change on these vegetation trends.We find that the vegetation displays an obvious pattern of east-greening and west-browning in China’s drylands.Greening trends mainly exhibits monotonic greening(29.8%)and greening with setback(36.8%),whereas browning shows a greening to browning reversal(19.2%).The increase rate of greening to browning reversal is 0.0342/yr,which is apparently greater than that of greening with setback,0.0078/yr.This research highlights that,under the background of widespread vegetation greening,vegetation browning is pro-gressively increasing due to the effects of climate change.Furthermore,the ERPs have significantly increased vegetation coverage,with the increase rate in 2000-2022 being twice as much as that of 1982-1999 in reveg-etation regions.Vegetation browning in southwestern Qingzang Plateau is primarily driven by adverse climatic factors and anthropogenic disturbances,which offset the efforts of ERPs.
文摘The intensive care unit(ICU)is a complex setting by nature,and some have described it as bizarre due to its numerous sirens that sound when anything is dangerous,constant activity,equipment,bright lights,and high fatality rate.The demands placed on nurses to care for critically ill patients in this environment frequently prevent nurses and other health‑care professionals from acknowledging the feelings of patient’s relatives or family caregivers,resulting in a hostile environment from the patient’s relative’s perspective.When a patient’s family enters the ICU,they feel that hospital administrators do little to nothing to alleviate their discomfort and fear.Despite research demonstrating the importance of providing a homely environment for patients’families,In Nigeria ICU is still far behind how a conventional ICU environment should be structured to accommodate patient’s relations in the unit.The goal of this study was to look at the patient’s relative’s perspective on providing care for a critically ill patient in an ICU,with a focus on the unit’s complexity and overall experience.Based on the findings of this study,we recommend that hospital administrators ensure that the environment of the upcoming ICU is designed to meet the needs of patient’s relatives by addressing identified environmental concerns,like caring neglect,by providing a friendly and stress‑free environment.
文摘At present China-U.S.trade relations are in a state of confusion.Although both countries have gained tremendous benefits from the bilateral trade relationship,some Americans have intentionally distorted some basic facts regarding China-U.S.trade relations. Based on an analysis of some official and nonofficial research reports published in the United States,this article holds that the China-U.S.trade imbalance is the symptom of a bigger issue stemming from the contradiction between the United States as the world's sole superpower and China as an emerging power.Economic globalisation came about due to the needs of western developed countries represented by the United States to boost economic development.Only by seizing the opportunities of economic globalisation, has China gained strong economic growth. Such a development is changing the world political,economic,military and cultural landscape that have been shaped since the post-cold-war era,and has to some extent raised doubt or suspicion on the part of the United States and its western allies.This is a manifestation of how unprepared some people in the United States and other western countries are in the face of China's rapid development and rising status.So,their immediate reaction has been to seek protection for themselves,and try their utmost to prevent China's rapid growth from impacting on the international framework and their vested interests.
文摘This research investigates the determinants of green supply chain management(GSCM)adoption and its impact on organizational performance,while considering the potential moderating factors influencing GSCM adoption.Despite the growing prevalence of GSCM practices among Korean firms,the factors driving their adoption have not received sufficient attention.To bridge this gap,the study uses structural equation modeling,integrating stakeholder theory and resource-based theory to explore how green entrepreneurial orientation(GEO),institutional pressure,and relational capital affect GSCM adoption.Additionally,the study explores the effects of GSCM implementation on competitiveness and economic performance.Drawing data from a sample of 213 Korean manufacturing firms,the PLS-SEM analysis highlights the significant influence of GEO,institutional pressure,and relational capital on GSCM adoption.Additionally,the study emphasizes the positive impact of GSCM implementation on firm competitiveness.These findings provide valuable insights for enhancing sustainability in supply chain management and are applicable to similar context countries such as Taiwan,China,Japan,and the Netherlands.
文摘China is in Africa in a vigorous way,and doing business in several countries like Sudan,Congo DRC,Angola,South Africa,and Nigeria.In the short term,the relationship may appear to be mutually beneficial.This paper seeks to address the issue of Africa's perspectives on China-Africa Relations and the FOCAC and examine the concept of strategic partnerships,determine the state of China-Africa relations,examines FOCAC and draw conclusion as well as recommendation on possible ways and issues for future engageme...
文摘Classical reciprocity relations have wide applications in acoustics, from field representation to generalized optical theorem. In this paper we introduce our recent results on the applications and generalization of classical Rayleigh reciprocity relation: higher derivative reciprocity relations as a generalization of the classical one and a theoretical proof on the Green's function retrieval from volume noises.