Utilizing Gamma-Beta function, we can build one series involving reciprocal of non-central binomial coefficients, then We can structure several new series of reciprocals of non-central binomial coefficients by item sp...Utilizing Gamma-Beta function, we can build one series involving reciprocal of non-central binomial coefficients, then We can structure several new series of reciprocals of non-central binomial coefficients by item splitting, these new created denominator of series contain 1 to 4 odd factors of binomial coefficients. As the result of splitting items, some identities of series of numbers values of reciprocals of binomial coefficients are given. The method of splitting terms offered in this paper is a new combinatorial analysis way and elementary method to create new series.展开更多
By applying the theory of formal power series,the author obtains the closed forms for two kinds of infinite series involving the reciprocals of binomial coefficients,and the author gets another closed form for the inf...By applying the theory of formal power series,the author obtains the closed forms for two kinds of infinite series involving the reciprocals of binomial coefficients,and the author gets another closed form for the infinite series Σr≥m tn＋r/（n＋rr）.展开更多
The sum of reciprocals of Mersenne primes converges to 0.51645417894078856533···, which is an example of a probably infinite subset of primes whose sum of reciprocals is finite and can be computed accur...The sum of reciprocals of Mersenne primes converges to 0.51645417894078856533···, which is an example of a probably infinite subset of primes whose sum of reciprocals is finite and can be computed accurately. This value is larger than , where ?is the set of perfect powers of prime numbers.展开更多
This paper discusses the approximation by reciprocals of polynomials with positive coefficients in Orlicz spaces and proved that if f（x） ∈ L^＊M[0, 1], changes its sign at most once in （0, 1）, then there exists ...This paper discusses the approximation by reciprocals of polynomials with positive coefficients in Orlicz spaces and proved that if f（x） ∈ L^＊M[0, 1], changes its sign at most once in （0, 1）, then there exists x0 ∈ （0, 1） and a polynomial Pn∈ Fin（＋） such that ｜｜f（x）-x-x0/Pn（x）｜｜M≤Cω（f,n-1/2）M, where Пn（＋） indicates the set of all polynomials of degree n with positive coefficients展开更多
By applying the method of on summation by parts,the purpose of this paper is to give several reciprocal summations related to squares of products of the Fibonacci numbers.
Let S^1-1,q≥2,be the surface of the unit sphere in the Euclidean space R^1,f（x）∈L^p（S^q-1）,f（x）≥0,f absohutely unegual to 0,1≤p≤＋∞,Then,it is proved in the present paper that there is a spherical harmonic...Let S^1-1,q≥2,be the surface of the unit sphere in the Euclidean space R^1,f（x）∈L^p（S^q-1）,f（x）≥0,f absohutely unegual to 0,1≤p≤＋∞,Then,it is proved in the present paper that there is a spherical harmonics PN（x） of order≤N and a constant C〉0 such that where ω（f,δ）L^p=sup 0〈t≤δ‖St（f）-f‖L^p is a kind of moduli of continuity and ^‖f-1/PN‖L^p≤Cω（f,N^-1）L^p,St（f,μ）=1/｜S^q-2｜Sin^2λt ∫-μμ’=t f（μ＇）dμ＇ is a translation operator.展开更多
This paper presents an analogical study between electromagnetic and elastic wave fields,with a one-to-one correspondence principle established regarding the basic wave equations,the physical quantities and the differe...This paper presents an analogical study between electromagnetic and elastic wave fields,with a one-to-one correspondence principle established regarding the basic wave equations,the physical quantities and the differential operations.Using the electromagnetic-to-elastic substitution,the analogous relations of the conservation laws of energy and momentum are investigated between these two physical fields.Moreover,the energy-based and momentum-based reciprocity theorems for an elastic wave are also derived in the time-harmonic state,which describe the interaction between two elastic wave systems from the perspectives of energy and momentum,respectively.The theoretical results obtained in this analysis can not only improve our understanding of the similarities of these two linear systems,but also find potential applications in relevant fields such as medical imaging,non-destructive evaluation,acoustic microscopy,seismology and exploratory geophysics.展开更多
Quantum nonreciprocity, such as nonreciprocal photon blockade, has attracted a great deal of attention due to its unique applications in quantum information processing. Its implementation primarily relies on rotating ...Quantum nonreciprocity, such as nonreciprocal photon blockade, has attracted a great deal of attention due to its unique applications in quantum information processing. Its implementation primarily relies on rotating nonlinear systems, based on the Sagnac effect. Here, we propose an all-optical approach to achieve nonreciprocal photon blockade in an on-chip microring resonator coupled to a V-type Rb atom, which arises from the Zeeman splittings of the atomic hyperfine sublevels induced by the fictitious magnetic field of a circularly polarized control laser. The system manifests single-photon blockade or multi-photon tunneling when driven from opposite directions. This nonreciprocity results from the directional detunings between the countercirculating probe fields and the V-type atom, which does not require the mechanical rotation and facilitates integration. Our work opens up a new route to achieve on-chip integrable quantum nonreciprocity, enabling applications in chiral quantum technologies.展开更多
Nonreciprocal optical devices are essential for laser protection,modern optical communication and quantum information processing by enforcing one-way light propagation.The conventional Faraday magneto-optical nonrecip...Nonreciprocal optical devices are essential for laser protection,modern optical communication and quantum information processing by enforcing one-way light propagation.The conventional Faraday magneto-optical nonreciprocal devices rely on a strong magnetic field,which is provided by a permanent magnet.As a result,the isolation direction of such devices is fixed and severely restricts their applications in quantum networks.In this work,we experimentally demonstrate the simultaneous one-way transmission and unidirectional reflection by using a magneto-optical Fabry-Pérot cavity and a magnetic field strength of 50 mT.An optical isolator and a three-port quasi-circulator are realized based on this nonreciprocal cavity system.The isolator achieves an isolation ratio of up to 22 dB and an averaged insertion loss down to 0.97 dB.The quasi-circulator is realized with a fidelity exceeding 99% and an overall survival probability of 89.9%,corresponding to an insertion loss of~0.46 dB.The magnetic field is provided by an electromagnetic coil,thereby allowing for reversing the light circulating path.The reversible quasi-circulator paves the way for building reconfigurable quantum networks.展开更多
Controlling the size and distribution of potential barriers within a medium of interacting particles can unveil unique collective behaviors and innovative functionalities.We introduce a unique superconducting hybrid d...Controlling the size and distribution of potential barriers within a medium of interacting particles can unveil unique collective behaviors and innovative functionalities.We introduce a unique superconducting hybrid device using a novel artificial spin ice structure composed of asymmetric nanomagnets.This structure forms a distinctive superconducting pinning potential that steers unconventional motion of superconducting vortices,thereby inducing a magnetic nonreciprocal effect,in contrast to the electric nonreciprocal effect commonly observed in superconducting diodes.Furthermore,the polarity of the magnetic nonreciprocity is in situ reversible through the tunable magnetic patterns of artificial spin ice.Our findings demonstrate that artificial spin ice not only precisely modulates superconducting characteristics but also opens the door to novel functionalities,offering a groundbreaking paradigm for superconducting electronics.展开更多
This paper develops a quadratic function convex approximation approach to deal with the negative definite problem of the quadratic function induced by stability analysis of linear systems with time-varying delays.By i...This paper develops a quadratic function convex approximation approach to deal with the negative definite problem of the quadratic function induced by stability analysis of linear systems with time-varying delays.By introducing two adjustable parameters and two free variables,a novel convex function greater than or equal to the quadratic function is constructed,regardless of the sign of the coefficient in the quadratic term.The developed lemma can also be degenerated into the existing quadratic function negative-determination(QFND)lemma and relaxed QFND lemma respectively,by setting two adjustable parameters and two free variables as some particular values.Moreover,for a linear system with time-varying delays,a relaxed stability criterion is established via our developed lemma,together with the quivalent reciprocal combination technique and the Bessel-Legendre inequality.As a result,the conservatism can be reduced via the proposed approach in the context of constructing Lyapunov-Krasovskii functionals for the stability analysis of linear time-varying delay systems.Finally,the superiority of our results is illustrated through three numerical examples.展开更多
Amid the growing interest in triboelectric nanogenerators(TENGs)as novel energy-harvesting devices,several studies have focused on direct current(DC)TENGs to generate a stable DC output for operating electronic device...Amid the growing interest in triboelectric nanogenerators(TENGs)as novel energy-harvesting devices,several studies have focused on direct current(DC)TENGs to generate a stable DC output for operating electronic devices.However,owing to the working mechanisms of conventional DC TENGs,generating a stable DC output from reciprocating motion remains a challenge.Accordingly,we propose a bidirectional rotating DC TENG(BiR-TENG),which can generate DC outputs,regardless of the direction of rotation,from reciprocating motions.The distinct design of the BiR-TENG enables the mechanical rectification of the alternating current output into a rotational-direction-dependent DC output.Furthermore,it allows the conversion of the rotational-direction-dependent DC output into a unidirectional DC output by adapting the configurations depending on the rotational direction.Owing to these tailored design strategies and subsequent optimizations,the BiR-TENG could generate an effective unidirectional DC output.Applications of the BiR-TENG for the reciprocating motions of swinging doors and waves were demonstrated by harnessing this output.This study demonstrates the potential of the BiR-TENG design strategy as an effective and versatile solution for energy harvesting from reciprocating motions,highlighting the suitability of DC outputs as an energy source for electronic devices.展开更多
Objective:The aim of this research was to evaluate the efficiency of reciprocating morcellation for removing giant benign prostatic hyperplasia during holmium laser enucleation of the prostate,investigate whether perf...Objective:The aim of this research was to evaluate the efficiency of reciprocating morcellation for removing giant benign prostatic hyperplasia during holmium laser enucleation of the prostate,investigate whether performing morcellation as a two-stage procedure improves tissue retrieval efficiency,and seek to determine the optimal interval between the two surgeries.Methods:This study included nine cases of holmium laser enucleation of the prostate with an enucleated prostate weight exceeding 200 g,indicative of substantial prostate enlargement.Morcellation was performed on Day 0(n=4),Day 4(n=1),Day 6(n=1),and Day 7(n=3).The intervals were compared regarding the morcellation efficiency,beach ball presence,and pathology.Results:The mean estimated prostate volume was 383(range 330e528)mL;the median enucleation weight was 252(interquartile range[IQR]222,342)g;and the median enucleation time was 83(IQR 62,100)min.The mean morcellation efficiency was 1.44(SD 0.55)g/min on Day 0 and 13.69(SD 2.46)g/min on day 7.The morcellation efficiency was 4.15 g/min and 10.50 g/min on Day 4 and Day 6,respectively,with significantly higher in the two-stage group compared to one-stage group(11.0 g/min vs.1.5 g/min;p=0.014).Efficiency was strongly correlated with intervals(p<0.001);the incidences of beach balls were 100%(4/4)and 60%(3/5)in the immediate and two-stage surgery groups,respectively.Conclusion:The efficiency of two-stage morcellation with reciprocating morcellators was highly related to the postoperative interval,with the maximum efficiency reached on Day 7.展开更多
Let G be a connected graph of order n and m_(RD)^(L)_(G)I denote the number of reciprocal distance Laplacian eigenvaluesof G in an interval I.For a given interval I,we mainly present several bounds on m_(RD)^(L)_(G)I ...Let G be a connected graph of order n and m_(RD)^(L)_(G)I denote the number of reciprocal distance Laplacian eigenvaluesof G in an interval I.For a given interval I,we mainly present several bounds on m_(RD)^(L)_(G)I in terms of various structuralparameters of the graph G,including vertex-connectivity,independence number and pendant vertices.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
We consider the inverse electromagnetic scattering problem of determining the shape of a perfectly conducting core inside a penetrable chiral body. We prove the well-posedness of the corresponding direct scattering pr...We consider the inverse electromagnetic scattering problem of determining the shape of a perfectly conducting core inside a penetrable chiral body. We prove the well-posedness of the corresponding direct scattering problem by the variational method. We focus on a uniqueness result for the inverse scattering problem that is under what conditions an obstacle can be identified by the knowledge of the electric far-field pattern corresponding to all time-harmonic incident planes waves with a fixed wave number. To this end, we establish a chiral mixed reciprocity relation that connects the electric far-field pattern of a spherical wave with the scattered field of a plane wave.展开更多
Dear Editor,This letter examines the stability issue of generalized neural networks(GNNs) with time-varying delay based on a novel reciprocally convex combination(RCC). By considering a new matrix polynomial, the prop...Dear Editor,This letter examines the stability issue of generalized neural networks(GNNs) with time-varying delay based on a novel reciprocally convex combination(RCC). By considering a new matrix polynomial, the proposed novel reciprocally convex method leads to a tight bound for integral inequality combination and encompasses several existing approaches as special cases.展开更多
文摘Utilizing Gamma-Beta function, we can build one series involving reciprocal of non-central binomial coefficients, then We can structure several new series of reciprocals of non-central binomial coefficients by item splitting, these new created denominator of series contain 1 to 4 odd factors of binomial coefficients. As the result of splitting items, some identities of series of numbers values of reciprocals of binomial coefficients are given. The method of splitting terms offered in this paper is a new combinatorial analysis way and elementary method to create new series.
基金Supported by the NNSF of China(10771093)Supported by the NSF of Henan Province(0511010300)
文摘By applying the theory of formal power series,the author obtains the closed forms for two kinds of infinite series involving the reciprocals of binomial coefficients,and the author gets another closed form for the infinite series Σr≥m tn＋r/（n＋rr）.
文摘The sum of reciprocals of Mersenne primes converges to 0.51645417894078856533···, which is an example of a probably infinite subset of primes whose sum of reciprocals is finite and can be computed accurately. This value is larger than , where ?is the set of perfect powers of prime numbers.
基金Supported by Inner Mongolia Natural Science Foundations of China (200408020108).
文摘This paper discusses the approximation by reciprocals of polynomials with positive coefficients in Orlicz spaces and proved that if f（x） ∈ L^＊M[0, 1], changes its sign at most once in （0, 1）, then there exists x0 ∈ （0, 1） and a polynomial Pn∈ Fin（＋） such that ｜｜f（x）-x-x0/Pn（x）｜｜M≤Cω（f,n-1/2）M, where Пn（＋） indicates the set of all polynomials of degree n with positive coefficients
基金Supported by the Natural Science Foundation of Henan Province(0511010300)Supported by the Natural Science Foundation of Education Department of Henan Province(2008B110011)
文摘By applying the method of on summation by parts,the purpose of this paper is to give several reciprocal summations related to squares of products of the Fibonacci numbers.
基金Supported by the National Natural Science Foundation of China （No.10371024）, the Natural Science of Zhejiang Province （No. Y604003） and the Doctor Foundation of Ningbo City （No.2004A620017）.
文摘Let S^1-1,q≥2,be the surface of the unit sphere in the Euclidean space R^1,f（x）∈L^p（S^q-1）,f（x）≥0,f absohutely unegual to 0,1≤p≤＋∞,Then,it is proved in the present paper that there is a spherical harmonics PN（x） of order≤N and a constant C〉0 such that where ω（f,δ）L^p=sup 0〈t≤δ‖St（f）-f‖L^p is a kind of moduli of continuity and ^‖f-1/PN‖L^p≤Cω（f,N^-1）L^p,St（f,μ）=1/｜S^q-2｜Sin^2λt ∫-μμ’=t f（μ＇）dμ＇ is a translation operator.
基金funded by the National Natural Science Foundation of China(Grant No.12404507)the Natural Science Research of Jiangsu Higher Education Institutions of China(Grant No.24KJB140013)the Scientific Startup Foundation of Nanjing Normal University(Grant No.184080H201B49).
文摘This paper presents an analogical study between electromagnetic and elastic wave fields,with a one-to-one correspondence principle established regarding the basic wave equations,the physical quantities and the differential operations.Using the electromagnetic-to-elastic substitution,the analogous relations of the conservation laws of energy and momentum are investigated between these two physical fields.Moreover,the energy-based and momentum-based reciprocity theorems for an elastic wave are also derived in the time-harmonic state,which describe the interaction between two elastic wave systems from the perspectives of energy and momentum,respectively.The theoretical results obtained in this analysis can not only improve our understanding of the similarities of these two linear systems,but also find potential applications in relevant fields such as medical imaging,non-destructive evaluation,acoustic microscopy,seismology and exploratory geophysics.
基金supported by the National Natural Science Foundation of China (Grant Nos.12305020 and 92365107)the National Key R&D Program of China (Grant No.2019YFA0308700)+2 种基金the Program for Innovative Talents and Teams in Jiangsu (Grant No.JSSCTD202138)China Postdoctoral Science Foundation (Grant No.2023M731613)Jiangsu Funding Program for Excellent Postdoctoral Talent (Grant No.2023ZB708)。
文摘Quantum nonreciprocity, such as nonreciprocal photon blockade, has attracted a great deal of attention due to its unique applications in quantum information processing. Its implementation primarily relies on rotating nonlinear systems, based on the Sagnac effect. Here, we propose an all-optical approach to achieve nonreciprocal photon blockade in an on-chip microring resonator coupled to a V-type Rb atom, which arises from the Zeeman splittings of the atomic hyperfine sublevels induced by the fictitious magnetic field of a circularly polarized control laser. The system manifests single-photon blockade or multi-photon tunneling when driven from opposite directions. This nonreciprocity results from the directional detunings between the countercirculating probe fields and the V-type atom, which does not require the mechanical rotation and facilitates integration. Our work opens up a new route to achieve on-chip integrable quantum nonreciprocity, enabling applications in chiral quantum technologies.
基金supported by the National Key R&D Program of China(Grant No.2019YFA0308700)the National Natural Science Foundation of China(Grant Nos.11890704,92365107,and 12305020)+2 种基金the Program for Innovative Talents and Teams in Jiangsu(Grant No.JSSCTD202138)the Shccig-Qinling Program,the China Postdoctoral Science Foundation(Grant No.2023M731613)the Jiangsu Funding Program for Excellent Postdoctoral Talent(Grant No.2023ZB708)。
文摘Nonreciprocal optical devices are essential for laser protection,modern optical communication and quantum information processing by enforcing one-way light propagation.The conventional Faraday magneto-optical nonreciprocal devices rely on a strong magnetic field,which is provided by a permanent magnet.As a result,the isolation direction of such devices is fixed and severely restricts their applications in quantum networks.In this work,we experimentally demonstrate the simultaneous one-way transmission and unidirectional reflection by using a magneto-optical Fabry-Pérot cavity and a magnetic field strength of 50 mT.An optical isolator and a three-port quasi-circulator are realized based on this nonreciprocal cavity system.The isolator achieves an isolation ratio of up to 22 dB and an averaged insertion loss down to 0.97 dB.The quasi-circulator is realized with a fidelity exceeding 99% and an overall survival probability of 89.9%,corresponding to an insertion loss of~0.46 dB.The magnetic field is provided by an electromagnetic coil,thereby allowing for reversing the light circulating path.The reversible quasi-circulator paves the way for building reconfigurable quantum networks.
基金supported by the National Natural Science Foundation of China(Grant Nos.62288101 and 62274086)the National Key R&D Program of China(Grant No.2021YFA0718802)the Jiangsu Outstanding Postdoctoral Program。
文摘Controlling the size and distribution of potential barriers within a medium of interacting particles can unveil unique collective behaviors and innovative functionalities.We introduce a unique superconducting hybrid device using a novel artificial spin ice structure composed of asymmetric nanomagnets.This structure forms a distinctive superconducting pinning potential that steers unconventional motion of superconducting vortices,thereby inducing a magnetic nonreciprocal effect,in contrast to the electric nonreciprocal effect commonly observed in superconducting diodes.Furthermore,the polarity of the magnetic nonreciprocity is in situ reversible through the tunable magnetic patterns of artificial spin ice.Our findings demonstrate that artificial spin ice not only precisely modulates superconducting characteristics but also opens the door to novel functionalities,offering a groundbreaking paradigm for superconducting electronics.
基金the National Natural Science Foundation of China(62273058,U22A2045)the Key Science and Technology Projects of Jilin Province(20200401075GX)the Youth Science and Technology Innovation and Entrepreneurship Outstanding Talents Project of Jilin Province(20230508043RC)。
文摘This paper develops a quadratic function convex approximation approach to deal with the negative definite problem of the quadratic function induced by stability analysis of linear systems with time-varying delays.By introducing two adjustable parameters and two free variables,a novel convex function greater than or equal to the quadratic function is constructed,regardless of the sign of the coefficient in the quadratic term.The developed lemma can also be degenerated into the existing quadratic function negative-determination(QFND)lemma and relaxed QFND lemma respectively,by setting two adjustable parameters and two free variables as some particular values.Moreover,for a linear system with time-varying delays,a relaxed stability criterion is established via our developed lemma,together with the quivalent reciprocal combination technique and the Bessel-Legendre inequality.As a result,the conservatism can be reduced via the proposed approach in the context of constructing Lyapunov-Krasovskii functionals for the stability analysis of linear time-varying delay systems.Finally,the superiority of our results is illustrated through three numerical examples.
基金This work was supported by the National Research Foundation of Korea(NRF)grant funded by the Korea government(MSIT)(No.2022R1C1C1008831).This work was also supported by the Human Resources Development of the Korea Institute of Energy Technology Evaluation and Planning(KETEP)grant funded by the Ministry of Trade,Industry and Energy of Korea(No.RS-2023-00244330).S J P was supported by Basic Research Program through the National Research Foundation of Korea(NRF)funded by the Ministry of Education(No.2018R1A6A1A03025526).
文摘Amid the growing interest in triboelectric nanogenerators(TENGs)as novel energy-harvesting devices,several studies have focused on direct current(DC)TENGs to generate a stable DC output for operating electronic devices.However,owing to the working mechanisms of conventional DC TENGs,generating a stable DC output from reciprocating motion remains a challenge.Accordingly,we propose a bidirectional rotating DC TENG(BiR-TENG),which can generate DC outputs,regardless of the direction of rotation,from reciprocating motions.The distinct design of the BiR-TENG enables the mechanical rectification of the alternating current output into a rotational-direction-dependent DC output.Furthermore,it allows the conversion of the rotational-direction-dependent DC output into a unidirectional DC output by adapting the configurations depending on the rotational direction.Owing to these tailored design strategies and subsequent optimizations,the BiR-TENG could generate an effective unidirectional DC output.Applications of the BiR-TENG for the reciprocating motions of swinging doors and waves were demonstrated by harnessing this output.This study demonstrates the potential of the BiR-TENG design strategy as an effective and versatile solution for energy harvesting from reciprocating motions,highlighting the suitability of DC outputs as an energy source for electronic devices.
文摘Objective:The aim of this research was to evaluate the efficiency of reciprocating morcellation for removing giant benign prostatic hyperplasia during holmium laser enucleation of the prostate,investigate whether performing morcellation as a two-stage procedure improves tissue retrieval efficiency,and seek to determine the optimal interval between the two surgeries.Methods:This study included nine cases of holmium laser enucleation of the prostate with an enucleated prostate weight exceeding 200 g,indicative of substantial prostate enlargement.Morcellation was performed on Day 0(n=4),Day 4(n=1),Day 6(n=1),and Day 7(n=3).The intervals were compared regarding the morcellation efficiency,beach ball presence,and pathology.Results:The mean estimated prostate volume was 383(range 330e528)mL;the median enucleation weight was 252(interquartile range[IQR]222,342)g;and the median enucleation time was 83(IQR 62,100)min.The mean morcellation efficiency was 1.44(SD 0.55)g/min on Day 0 and 13.69(SD 2.46)g/min on day 7.The morcellation efficiency was 4.15 g/min and 10.50 g/min on Day 4 and Day 6,respectively,with significantly higher in the two-stage group compared to one-stage group(11.0 g/min vs.1.5 g/min;p=0.014).Efficiency was strongly correlated with intervals(p<0.001);the incidences of beach balls were 100%(4/4)and 60%(3/5)in the immediate and two-stage surgery groups,respectively.Conclusion:The efficiency of two-stage morcellation with reciprocating morcellators was highly related to the postoperative interval,with the maximum efficiency reached on Day 7.
基金supported by the Natural Science Foundation of Xinjiang Uygur Autonomous Region of China“Graph problems of topological parameters based on the spectra of graph matrices”(2021D01C069)the National Natural Science Foundation of the People's Republic of China“The investigation of spectral properties of graph operations and their related problems”(12161085)。
文摘Let G be a connected graph of order n and m_(RD)^(L)_(G)I denote the number of reciprocal distance Laplacian eigenvaluesof G in an interval I.For a given interval I,we mainly present several bounds on m_(RD)^(L)_(G)I in terms of various structuralparameters of the graph G,including vertex-connectivity,independence number and pendant vertices.
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We consider the inverse electromagnetic scattering problem of determining the shape of a perfectly conducting core inside a penetrable chiral body. We prove the well-posedness of the corresponding direct scattering problem by the variational method. We focus on a uniqueness result for the inverse scattering problem that is under what conditions an obstacle can be identified by the knowledge of the electric far-field pattern corresponding to all time-harmonic incident planes waves with a fixed wave number. To this end, we establish a chiral mixed reciprocity relation that connects the electric far-field pattern of a spherical wave with the scattered field of a plane wave.
基金supported by the Basic Science Research Program through the National Research Foundation of Korea(NRF)funded by the Ministry of Science,Information and Communications Technology(ICT),and Future Planning(2020 R1A2C2005709)the National Natural Science Foundation of China(618255304)the Key Project of Natural Science Foundation of Hebei Province(F2021203054)。
文摘Dear Editor,This letter examines the stability issue of generalized neural networks(GNNs) with time-varying delay based on a novel reciprocally convex combination(RCC). By considering a new matrix polynomial, the proposed novel reciprocally convex method leads to a tight bound for integral inequality combination and encompasses several existing approaches as special cases.
