The error-sum function of alternating Sylvester series is introduced. Some elementary properties of this function are studied. Also, the hausdorff dimension of the graph of such function is determined.
The purpose of this article is to provide the inversion relationships between the reciprocal sum S（1, 2,…, m） and the alternating sum T（1, 2,…, m） for generalized Lucas numbers which generalizes the Melham＇s re...The purpose of this article is to provide the inversion relationships between the reciprocal sum S（1, 2,…, m） and the alternating sum T（1, 2,…, m） for generalized Lucas numbers which generalizes the Melham＇s results.展开更多
We consider some new alternating double binomial sums. By using the Lagrange inversion formula, we obtain explicit expressions of the desired results which are related to a third-order linear recursive sequence. Furth...We consider some new alternating double binomial sums. By using the Lagrange inversion formula, we obtain explicit expressions of the desired results which are related to a third-order linear recursive sequence. Furthermore, their recursive relation and generating functions are obtained.展开更多
Let p be an odd prime, the harmonic congruence such as <img alt="" src="Edit_843b278d-d88a-45d3-a136-c30e6becf142.bmp" />, and many different variations and generalizations have been studied ...Let p be an odd prime, the harmonic congruence such as <img alt="" src="Edit_843b278d-d88a-45d3-a136-c30e6becf142.bmp" />, and many different variations and generalizations have been studied intensively. In this note, we consider the congruences involving the combination of alternating harmonic sums, <img alt="" src="Edit_e97d0c64-3683-4a75-9d26-4b371c2be41e.bmp" /> where P<sub>P </sub>denotes the set of positive integers which are prime to p. And we establish the combinational congruences involving alternating harmonic sums for positive integer n=3,4,5.展开更多
The error-sum function of alternating Lǖroth series is introduced, which, to some extent, discerns the superior or not of an expansion comparing to other expansions. Some elementary properties of this function are st...The error-sum function of alternating Lǖroth series is introduced, which, to some extent, discerns the superior or not of an expansion comparing to other expansions. Some elementary properties of this function are studied. Also, the Hausdorff dimension of graph of such function is determined.展开更多
Dear Editor,This letter addresses the impulse game problem for a general scope of deterministic,multi-player,nonzero-sum differential games wherein all participants adopt impulse controls.Our objective is to formulate...Dear Editor,This letter addresses the impulse game problem for a general scope of deterministic,multi-player,nonzero-sum differential games wherein all participants adopt impulse controls.Our objective is to formulate this impulse game problem with the modified objective function including interaction costs among the players in a discontinuous fashion,and subsequently,to derive a verification theorem for identifying the feedback Nash equilibrium strategy.展开更多
Let f,g and h be three distinct primitive holomorphic cusp forms of even integral weights k_(1),k_(2)and k_(3)for the full modular groupΓ=SL(2,Z),and denote byλ_(f)(n),λ_(g)(n),λ_(h)(n)the corresponding normalized...Let f,g and h be three distinct primitive holomorphic cusp forms of even integral weights k_(1),k_(2)and k_(3)for the full modular groupΓ=SL(2,Z),and denote byλ_(f)(n),λ_(g)(n),λ_(h)(n)the corresponding normalized Fourier coefficients,respectively.In this paper,we investigate the correlations of triple sums associated to these Fourier coefficientsλ_(f)(n),λ_(g)(n),λ_(h)(n)over certain polynomials,and obtain some power-saving asymptotic estimates which beat the trivial bounds.展开更多
The complete convergence for weighted sums of sequences of independent,identically distributed random variables under sublinear expectation space is studied.By moment inequality and truncation methods,we establish the...The complete convergence for weighted sums of sequences of independent,identically distributed random variables under sublinear expectation space is studied.By moment inequality and truncation methods,we establish the equivalent conditions of complete convergence for weighted sums of sequences of independent,identically distributed random variables under sublinear expectation space.The results complement the corresponding results in probability space to those for sequences of independent,identically distributed random variables under sublinear expectation space.展开更多
In this paper,by utilizing the Marcinkiewicz-Zygmund inequality and Rosenthal-type inequality of negatively superadditive dependent(NSD)random arrays and truncated method,we investigate the complete f-moment convergen...In this paper,by utilizing the Marcinkiewicz-Zygmund inequality and Rosenthal-type inequality of negatively superadditive dependent(NSD)random arrays and truncated method,we investigate the complete f-moment convergence of NSD random variables.We establish and improve a general result on the complete f-moment convergence for Sung’s type randomly weighted sums of NSD random variables under some general assumptions.As an application,we show the complete consistency for the randomly weighted estimator in a nonparametric regression model based on NSD errors.展开更多
Aiming at the problem that infrared small target detection faces low contrast between the background and the target and insufficient noise suppression ability under the complex cloud background,an infrared small targe...Aiming at the problem that infrared small target detection faces low contrast between the background and the target and insufficient noise suppression ability under the complex cloud background,an infrared small target detection method based on the tensor nuclear norm and direction residual weighting was proposed.Based on converting the infrared image into an infrared patch tensor model,from the perspective of the low-rank nature of the background tensor,and taking advantage of the difference in contrast between the background and the target in different directions,we designed a double-neighborhood local contrast based on direction residual weighting method(DNLCDRW)combined with the partial sum of tensor nuclear norm(PSTNN)to achieve effective background suppression and recovery of infrared small targets.Experiments show that the algorithm is effective in suppressing the background and improving the detection ability of the target.展开更多
Sensitivity encoding(SENSE)is a parallel magnetic resonance imaging(MRI)reconstruction model by utilizing the sensitivity information of receiver coils to achieve image reconstruction.The existing SENSE-based reconstr...Sensitivity encoding(SENSE)is a parallel magnetic resonance imaging(MRI)reconstruction model by utilizing the sensitivity information of receiver coils to achieve image reconstruction.The existing SENSE-based reconstruction algorithms usually used nonadaptive sparsifying transforms,resulting in a limited reconstruction accuracy.Therefore,we proposed a new model for accurate parallel MRI reconstruction by combining the L0 norm regularization term based on the efficient sum of outer products dictionary learning(SOUPDIL)with the SENSE model,called SOUPDIL-SENSE.The SOUPDIL-SENSE model is mainly solved by utilizing the variable splitting and alternating direction method of multipliers techniques.The experimental results on four human datasets show that the proposed algorithm effectively promotes the image sparsity,eliminates the noise and artifacts of the reconstructed images,and improves the reconstruction accuracy.展开更多
The ring-opening alternating copolymerization(ROAC)of 3,4-dihydrocoumarin(DHC)/epoxides has been successfully developed using an imidazolium salt of 1-ethyl-3-methylimidazolium chloride(EMIMCl)as a catalyst.The result...The ring-opening alternating copolymerization(ROAC)of 3,4-dihydrocoumarin(DHC)/epoxides has been successfully developed using an imidazolium salt of 1-ethyl-3-methylimidazolium chloride(EMIMCl)as a catalyst.The resulting copolymer has a molecular weight of 13.7kg·mol^(-1),a narrow molecular weight distribution of 1.03 and a strictly alternating structure.The MALDI-TOF MS characterization and DFT calculations including electrostatic potential(ESP),hydrogen-atom abstraction(HAA),independent gradient model based on hirshfeld partition(IGMH)and atoms-in-molecules(AIM)analysis were used to investigate the metal-free catalytic process.The synergistic effect of anions and cations of EMIMCl for ROAC of DHC and epoxides was demonstrated.This study provides a metal-free catalytic system for the facile synthesis of alternating polyesters from DHC.展开更多
Prefabricated twinning represents an effective strategy for optimizing the microstructure of extruded forming components and facilitating changes in texture.The study examines the incorporation of[10-12]twins into an ...Prefabricated twinning represents an effective strategy for optimizing the microstructure of extruded forming components and facilitating changes in texture.The study examines the incorporation of[10-12]twins into an AZ31 magnesium alloy billet via cold pre-upsetting deformation before alternating forward extrusion(CUAFE).The experimental results indicate that the initial presence of[10-12]twins is advantageous for the development of[10-10]and[11-20]texture components during the extrusion process.In addition,different DRX mechanisms have different influences on the evolution of basal texture.The CDRX grains tend to preferentially select the[11-20]texture orientation,weakening the[10-10]texture and enhancing the[11-20]texture.However,most DDRX grains deviate significantly from the orientation of their surrounding original grain and do not have a preferred orientation.This is reflected in the mechanical properties of the CUAFE part.The tensile strength is 323.5 MPa,while the elongation is as high as 20.1%.展开更多
The results of the study of the effect of partial substitution of Fe by Mn in the La Fe_(11.2-x)Mn_(x)Co_(0.7)Si_(1.1)system on magnetization,specific heat,magnetostriction and magnetocaloric effect are presented.Dire...The results of the study of the effect of partial substitution of Fe by Mn in the La Fe_(11.2-x)Mn_(x)Co_(0.7)Si_(1.1)system on magnetization,specific heat,magnetostriction and magnetocaloric effect are presented.Direct measurements of the adiabatic temperature change(ΔT_(ad))were carried out in alternating magnetic fields(AMF)using the magnetic field modulation method.Partial substitution of Fe atoms by Mn atoms leads to a shift in the Curie temperature(T_(C))towards lower temperatures without a noticeable deterioration in magnetic properties.A correlation was found between the structural component of the magnetocaloric effect and the stability of the frequency of theΔT_(ad)in the AMFs—an increase in the manganese concentration leads to a decrease in magnetostriction and to a lower dependence ofΔT_(ad)on the frequency of the magnetic field.Estimates of the specific cooling power Q_(C)as a function of the frequency of the AMF showed that the highest value of Q_(C)at f=20 Hz in a magnetic field of 12k Oe is 26.3 W g^(-1)and is observed for the composition with x=0.1.This value is higher than that of Gd,for which,under the same conditions,Q_(C)=21.6 W g^(-1).All the samples studied show stability of the value ofΔT_(ad)without any sign of deterioration of the effect up to 60,000cycles of switching on/off of the magnetic field of 12 k Oe.The discovered frequency and cyclic stability ofΔT_(ad)of the studied samples increase their prospects for application in magnetic cooling technology.展开更多
Denoising is an important preprocessing step in seismic exploration that improves the signal-to-noise ratio(SNR)and helps identify oil and minerals.Dictionary learning(DL)is a promising method for noise attenuation.Th...Denoising is an important preprocessing step in seismic exploration that improves the signal-to-noise ratio(SNR)and helps identify oil and minerals.Dictionary learning(DL)is a promising method for noise attenuation.The DL extracts sparse features from noisy seismic data using over-complete dictionaries and performs denoising based on a threshold.However,the choice of threshold in DL greatly impacts the denoising results and the improvement in output SNR.Ramanujan’s sum(s)(RS)is a signal processing tool that exhibits derivative behavior and finds applications in edge detection and noise estimation of signals.Hence,we propose a novel DL method with threshold estimation based on RS to improve the output SNR.In this work,we estimate the noise variance of seismic data based on RS and use it as a threshold value for the DL method to perform denoising.We analyze the results of the proposed work on synthetically generated and field data sets.We perform simulations on noisy seismic data across a wide range of SNR values and tabulate the denoised results using the performance metrics SNR and mean squared error.The results indicate that the proposed method provides superior SNR and reduced mean squared error compared to MAD,SURE-based,and adaptive soft-thresholding techniques.展开更多
文摘The error-sum function of alternating Sylvester series is introduced. Some elementary properties of this function are studied. Also, the hausdorff dimension of the graph of such function is determined.
基金Supported by the Natural Science Foundation of the Education Department of Henan Province(2003110009)
文摘The purpose of this article is to provide the inversion relationships between the reciprocal sum S（1, 2,…, m） and the alternating sum T（1, 2,…, m） for generalized Lucas numbers which generalizes the Melham＇s results.
基金Foundation item： Supported by the Natural Science Foundation of Zhejiang Province（YT080320, LYI2A01030） Supported by the National Natural Science Foundation of China（l1226297） Supported by the Zhejiang Univerity City College Scientific Research Foundation（J-13003）
文摘We consider some new alternating double binomial sums. By using the Lagrange inversion formula, we obtain explicit expressions of the desired results which are related to a third-order linear recursive sequence. Furthermore, their recursive relation and generating functions are obtained.
文摘Let p be an odd prime, the harmonic congruence such as <img alt="" src="Edit_843b278d-d88a-45d3-a136-c30e6becf142.bmp" />, and many different variations and generalizations have been studied intensively. In this note, we consider the congruences involving the combination of alternating harmonic sums, <img alt="" src="Edit_e97d0c64-3683-4a75-9d26-4b371c2be41e.bmp" /> where P<sub>P </sub>denotes the set of positive integers which are prime to p. And we establish the combinational congruences involving alternating harmonic sums for positive integer n=3,4,5.
文摘The error-sum function of alternating Lǖroth series is introduced, which, to some extent, discerns the superior or not of an expansion comparing to other expansions. Some elementary properties of this function are studied. Also, the Hausdorff dimension of graph of such function is determined.
基金supported in part by the National Natural Science Foundation of China(62173051)the Fundamental Research Funds for the Central Universities(2024CDJCGJ012,2023CDJXY-010)+1 种基金the Chongqing Technology Innovation and Application Development Special Key Project(CSTB2022TIADCUX0015,CSTB2022TIAD-KPX0162)the China Postdoctoral Science Foundation(2024M763865)
文摘Dear Editor,This letter addresses the impulse game problem for a general scope of deterministic,multi-player,nonzero-sum differential games wherein all participants adopt impulse controls.Our objective is to formulate this impulse game problem with the modified objective function including interaction costs among the players in a discontinuous fashion,and subsequently,to derive a verification theorem for identifying the feedback Nash equilibrium strategy.
基金Supported in part by NSFC(Nos.12401011,12201214)National Key Research and Development Program of China(No.2021YFA1000700)+3 种基金Shaanxi Fundamental Science Research Project for Mathematics and Physics(No.23JSQ053)Science and Technology Program for Youth New Star of Shaanxi Province(No.2025ZC-KJXX-29)Natural Science Basic Research Program of Shaanxi Province(No.2025JC-YBQN-091)Scientific Research Foundation for Young Talents of WNU(No.2024XJ-QNRC-01)。
文摘Let f,g and h be three distinct primitive holomorphic cusp forms of even integral weights k_(1),k_(2)and k_(3)for the full modular groupΓ=SL(2,Z),and denote byλ_(f)(n),λ_(g)(n),λ_(h)(n)the corresponding normalized Fourier coefficients,respectively.In this paper,we investigate the correlations of triple sums associated to these Fourier coefficientsλ_(f)(n),λ_(g)(n),λ_(h)(n)over certain polynomials,and obtain some power-saving asymptotic estimates which beat the trivial bounds.
基金supported by Doctoral Scientific Research Starting Foundation of Jingdezhen Ceramic University(Grant No.102/01003002031)Re-accompanying Funding Project of Academic Achievements of Jingdezhen Ceramic University(Grant Nos.215/20506277,215/20506341)。
文摘The complete convergence for weighted sums of sequences of independent,identically distributed random variables under sublinear expectation space is studied.By moment inequality and truncation methods,we establish the equivalent conditions of complete convergence for weighted sums of sequences of independent,identically distributed random variables under sublinear expectation space.The results complement the corresponding results in probability space to those for sequences of independent,identically distributed random variables under sublinear expectation space.
基金supported by the National Social Science Fundation(Grant No.21BTJ040)the Project of Outstanding Young People in University of Anhui Province(Grant Nos.2023AH020037,SLXY2024A001).
文摘In this paper,by utilizing the Marcinkiewicz-Zygmund inequality and Rosenthal-type inequality of negatively superadditive dependent(NSD)random arrays and truncated method,we investigate the complete f-moment convergence of NSD random variables.We establish and improve a general result on the complete f-moment convergence for Sung’s type randomly weighted sums of NSD random variables under some general assumptions.As an application,we show the complete consistency for the randomly weighted estimator in a nonparametric regression model based on NSD errors.
基金Supported by the Key Laboratory Fund for Equipment Pre-Research(6142207210202)。
文摘Aiming at the problem that infrared small target detection faces low contrast between the background and the target and insufficient noise suppression ability under the complex cloud background,an infrared small target detection method based on the tensor nuclear norm and direction residual weighting was proposed.Based on converting the infrared image into an infrared patch tensor model,from the perspective of the low-rank nature of the background tensor,and taking advantage of the difference in contrast between the background and the target in different directions,we designed a double-neighborhood local contrast based on direction residual weighting method(DNLCDRW)combined with the partial sum of tensor nuclear norm(PSTNN)to achieve effective background suppression and recovery of infrared small targets.Experiments show that the algorithm is effective in suppressing the background and improving the detection ability of the target.
基金the National Natural Science Foundation of China(No.61861023)the Yunnan Fundamental Research Project(No.202301AT070452)。
文摘Sensitivity encoding(SENSE)is a parallel magnetic resonance imaging(MRI)reconstruction model by utilizing the sensitivity information of receiver coils to achieve image reconstruction.The existing SENSE-based reconstruction algorithms usually used nonadaptive sparsifying transforms,resulting in a limited reconstruction accuracy.Therefore,we proposed a new model for accurate parallel MRI reconstruction by combining the L0 norm regularization term based on the efficient sum of outer products dictionary learning(SOUPDIL)with the SENSE model,called SOUPDIL-SENSE.The SOUPDIL-SENSE model is mainly solved by utilizing the variable splitting and alternating direction method of multipliers techniques.The experimental results on four human datasets show that the proposed algorithm effectively promotes the image sparsity,eliminates the noise and artifacts of the reconstructed images,and improves the reconstruction accuracy.
基金financially supported by the National Natural Science Foundation of China(No.22161040)Natural Science Foundation of Gansu(No.24JRRA125)Science Research Project of Northwest Normal University(No.NWNU-LKZD2021-3)。
文摘The ring-opening alternating copolymerization(ROAC)of 3,4-dihydrocoumarin(DHC)/epoxides has been successfully developed using an imidazolium salt of 1-ethyl-3-methylimidazolium chloride(EMIMCl)as a catalyst.The resulting copolymer has a molecular weight of 13.7kg·mol^(-1),a narrow molecular weight distribution of 1.03 and a strictly alternating structure.The MALDI-TOF MS characterization and DFT calculations including electrostatic potential(ESP),hydrogen-atom abstraction(HAA),independent gradient model based on hirshfeld partition(IGMH)and atoms-in-molecules(AIM)analysis were used to investigate the metal-free catalytic process.The synergistic effect of anions and cations of EMIMCl for ROAC of DHC and epoxides was demonstrated.This study provides a metal-free catalytic system for the facile synthesis of alternating polyesters from DHC.
基金supported by the National Natural Science Foundation of China(No.52475341).
文摘Prefabricated twinning represents an effective strategy for optimizing the microstructure of extruded forming components and facilitating changes in texture.The study examines the incorporation of[10-12]twins into an AZ31 magnesium alloy billet via cold pre-upsetting deformation before alternating forward extrusion(CUAFE).The experimental results indicate that the initial presence of[10-12]twins is advantageous for the development of[10-10]and[11-20]texture components during the extrusion process.In addition,different DRX mechanisms have different influences on the evolution of basal texture.The CDRX grains tend to preferentially select the[11-20]texture orientation,weakening the[10-10]texture and enhancing the[11-20]texture.However,most DDRX grains deviate significantly from the orientation of their surrounding original grain and do not have a preferred orientation.This is reflected in the mechanical properties of the CUAFE part.The tensile strength is 323.5 MPa,while the elongation is as high as 20.1%.
基金financially supported by Russian Science Foundation(No.24-43-00156,https://rscf.ru/en/project/24-43-00156/)the National Natural Science Foundation of China(No.52171169)the State Key Laboratory for Advanced Metals and Materials(No.2023-ZD01)。
文摘The results of the study of the effect of partial substitution of Fe by Mn in the La Fe_(11.2-x)Mn_(x)Co_(0.7)Si_(1.1)system on magnetization,specific heat,magnetostriction and magnetocaloric effect are presented.Direct measurements of the adiabatic temperature change(ΔT_(ad))were carried out in alternating magnetic fields(AMF)using the magnetic field modulation method.Partial substitution of Fe atoms by Mn atoms leads to a shift in the Curie temperature(T_(C))towards lower temperatures without a noticeable deterioration in magnetic properties.A correlation was found between the structural component of the magnetocaloric effect and the stability of the frequency of theΔT_(ad)in the AMFs—an increase in the manganese concentration leads to a decrease in magnetostriction and to a lower dependence ofΔT_(ad)on the frequency of the magnetic field.Estimates of the specific cooling power Q_(C)as a function of the frequency of the AMF showed that the highest value of Q_(C)at f=20 Hz in a magnetic field of 12k Oe is 26.3 W g^(-1)and is observed for the composition with x=0.1.This value is higher than that of Gd,for which,under the same conditions,Q_(C)=21.6 W g^(-1).All the samples studied show stability of the value ofΔT_(ad)without any sign of deterioration of the effect up to 60,000cycles of switching on/off of the magnetic field of 12 k Oe.The discovered frequency and cyclic stability ofΔT_(ad)of the studied samples increase their prospects for application in magnetic cooling technology.
文摘Denoising is an important preprocessing step in seismic exploration that improves the signal-to-noise ratio(SNR)and helps identify oil and minerals.Dictionary learning(DL)is a promising method for noise attenuation.The DL extracts sparse features from noisy seismic data using over-complete dictionaries and performs denoising based on a threshold.However,the choice of threshold in DL greatly impacts the denoising results and the improvement in output SNR.Ramanujan’s sum(s)(RS)is a signal processing tool that exhibits derivative behavior and finds applications in edge detection and noise estimation of signals.Hence,we propose a novel DL method with threshold estimation based on RS to improve the output SNR.In this work,we estimate the noise variance of seismic data based on RS and use it as a threshold value for the DL method to perform denoising.We analyze the results of the proposed work on synthetically generated and field data sets.We perform simulations on noisy seismic data across a wide range of SNR values and tabulate the denoised results using the performance metrics SNR and mean squared error.The results indicate that the proposed method provides superior SNR and reduced mean squared error compared to MAD,SURE-based,and adaptive soft-thresholding techniques.
