Reciprocal transformations of the space-time shifted nonlocal short pulse equations are elaborated.Covariance of dependent and independent variables involved in the reciprocal transformations is investigated.Exact sol...Reciprocal transformations of the space-time shifted nonlocal short pulse equations are elaborated.Covariance of dependent and independent variables involved in the reciprocal transformations is investigated.Exact solutions of the space-time shifted nonlocal short pulse equations are given in terms of double Wronskians.Realness of independent variables involved in the reciprocal transformations is verified.Dynamics of some obtained solutions are illustrated.展开更多
Scalar-tensor theories of gravity are considered to be competitors to Einstein's theory of general relativity for the description of classical gravity,as they are used to build feasible models for cosmic inflation...Scalar-tensor theories of gravity are considered to be competitors to Einstein's theory of general relativity for the description of classical gravity,as they are used to build feasible models for cosmic inflation.These theories can be formulated both in the Jordan and Einstein frame,which are related by a Weyl transformation with a field transformation,known together as a frame transformation.These theories formulated in the above two frames are often considered to be equivalent from the point of view of classical theory.However,this is no longer true from the quantum field theoretical perspective.In the present article,we show that the Ward identities derived in the above two frames are not connected through the frame transformation.This shows that the quantum field theories formulated in these two frames are not equivalent to each other.Moreover,this inequivalence is also shown by comparing the effective actions derived in these two frames.展开更多
This paper presents an extension of certain forms of the real Paley-Wiener theorems to the Minkowski space-time algebra. Our emphasis is dedicated to determining the space-time valued functions whose space-time Fourie...This paper presents an extension of certain forms of the real Paley-Wiener theorems to the Minkowski space-time algebra. Our emphasis is dedicated to determining the space-time valued functions whose space-time Fourier transforms(SFT) have compact support using the partial derivatives operator and the Dirac operator of higher order.展开更多
The Hawking effect in the Vaidya-Bonner space-time can be considered as a compensate effect of the scale transformation of coordinate time.The gauge potential is the contraction of the affine connection.It is found th...The Hawking effect in the Vaidya-Bonner space-time can be considered as a compensate effect of the scale transformation of coordinate time.The gauge potential is the contraction of the affine connection.It is found that the rate of change of temperature can be obtained as the pure gauge potential of the compensate field,in addition to the Hawking temperature which was known from the stationary black holes.展开更多
The equations governing incompressible and compressible inviscid flows and written in the physical frame ( t,x,y,z ) are known to be linearly well posed and exhibit elliptic or hyperbolic nature. The linear well posed...The equations governing incompressible and compressible inviscid flows and written in the physical frame ( t,x,y,z ) are known to be linearly well posed and exhibit elliptic or hyperbolic nature. The linear well posedness is considered here for these equations under a space time transformation ( t,x,y,z)→(τ,ξ,η,ζ ), where the pseudo time τ and the new space coordinate ( ξ,η,ζ ) all depend on ( t,x,y,z ). Such a transformation could be useful for uniformly treating problems in which the flow is fast unsteady somewhere and slow unsteady or steady elsewhere. It is found that the transformation may alter the ellipticity, the hyperbolicty, and even the well posedness of the original equations. In one dimension, the transformed incompressible flow equations become weakly hyperbolic and the compressible ones could degenerate to elliptical equations. In high dimensions there are conditions such that the transformed equations become ill posed.展开更多
Ensuring digital media security through robust image watermarking is essential to prevent unauthorized distribution,tampering,and copyright infringement.This study introduces a novel hybrid watermarking framework that...Ensuring digital media security through robust image watermarking is essential to prevent unauthorized distribution,tampering,and copyright infringement.This study introduces a novel hybrid watermarking framework that integrates Discrete Wavelet Transform(DWT),Redundant Discrete Wavelet Transform(RDWT),and Möbius Transformations(MT),with optimization of transformation parameters achieved via a Genetic Algorithm(GA).By combining frequency and spatial domain techniques,the proposed method significantly enhances both the imper-ceptibility and robustness of watermark embedding.The approach leverages DWT and RDWT for multi-resolution decomposition,enabling watermark insertion in frequency subbands that balance visibility and resistance to attacks.RDWT,in particular,offers shift-invariance,which improves performance under geometric transformations.Möbius transformations are employed for spatial manipulation,providing conformal mapping and spatial dispersion that fortify watermark resilience against rotation,scaling,and translation.The GA dynamically optimizes the Möbius parameters,selecting configurations that maximize robustness metrics such as Peak Signal-to-Noise Ratio(PSNR),Structural Similarity Index Measure(SSIM),Bit Error Rate(BER),and Normalized Cross-Correlation(NCC).Extensive experiments conducted on medical and standard benchmark images demonstrate the efficacy of the proposed RDWT-MT scheme.Results show that PSNR exceeds 68 dB,SSIM approaches 1.0,and BER remains at 0.0000,indicating excellent imperceptibility and perfect watermark recovery.Moreover,the method exhibits exceptional resilience to a wide range of image processing attacks,including Gaussian noise,JPEG compression,histogram equalization,and cropping,achieving NCC values close to or equal to 1.0.Comparative evaluations with state-of-the-art watermarking techniques highlight the superiority of the proposed method in terms of robustness,fidelity,and computational efficiency.The hybrid framework ensures secure,adaptive watermark embedding,making it highly suitable for applications in digital rights management,content authentication,and medical image protection.The integration of spatial and frequency domain features with evolutionary optimization presents a promising direction for future watermarking technologies.展开更多
This paper proposes a new step-by-step Chebyshev space-time spectral method to analyze the force vibration of functionally graded material structures.Although traditional space-time spectral methods can reduce the acc...This paper proposes a new step-by-step Chebyshev space-time spectral method to analyze the force vibration of functionally graded material structures.Although traditional space-time spectral methods can reduce the accuracy mismatch between tem-poral low-order finite difference and spatial high-order discre tization,the ir time collocation points must increase dramatically to solve highly oscillatory solutions of structural vibration,which results in a surge in computing time and a decrease in accuracy.To address this problem,we introduced the step-by-step idea in the space-time spectral method.The Chebyshev polynomials and Lagrange's equation were applied to derive discrete spatial goverming equations,and a matrix projection method was used to map the calculation results of prev ious steps as the initial conditions of the subsequent steps.A series of numerical experiments were carried out.The results of the proposed method were compared with those obtained by traditional space-time spectral methods,which showed that higher accuracy could be achieved in a shorter computation time than the latter in highly oscillatory cases.展开更多
With respect to oceanic fluid dynamics,certain models have appeared,e.g.,an extended time-dependent(3+1)-dimensional shallow water wave equation in an ocean or a river,which we investigate in this paper.Using symbolic...With respect to oceanic fluid dynamics,certain models have appeared,e.g.,an extended time-dependent(3+1)-dimensional shallow water wave equation in an ocean or a river,which we investigate in this paper.Using symbolic computation,we find out,on one hand,a set of bilinear auto-Backlund transformations,which could connect certain solutions of that equation with other solutions of that equation itself,and on the other hand,a set of similarity reductions,which could go from that equation to a known ordinary differential equation.The results in this paper depend on all the oceanic variable coefficients in that equation.展开更多
When we study Lorentz transformation in the framework of quantum gauge theory of gravity, we will find that the vacuum gravitational gauge field will be changed under gravitational gauge transformation, which will cha...When we study Lorentz transformation in the framework of quantum gauge theory of gravity, we will find that the vacuum gravitational gauge field will be changed under gravitational gauge transformation, which will change the structure of the physical space-time and cause clock dilation effect. The study in this paper provides us with new insights to understand the essential and intrinsic relation between special relativity and general relativity. It provides us with a new way to unify special relativity and general relativity.展开更多
Existing orthogonal space-time block coding(OSTBC)schemes for backscatter communication systems cannot achieve a full transmission code rate when the tag is equipped with more than two antennas.In this paper,we propos...Existing orthogonal space-time block coding(OSTBC)schemes for backscatter communication systems cannot achieve a full transmission code rate when the tag is equipped with more than two antennas.In this paper,we propose a quasi-orthogonal spacetime block code(QOSTBC)that can achieve a full transmission code rate for backscatter communication systems with a four-antenna tag and then extend the scheme to support tags with 2i antennas.Specifically,we first present the system model for the backscatter system.Next,we propose the QOSTBC scheme to encode the tag signals.Then,we provide the corresponding maximum likelihood detection algorithms to recover the tag signals.Finally,simulation results are provided to demonstrate that our proposed QOSTBC scheme and the detection algorithm can achieve a better transmission code rate or symbol error rate performance for backscatter communication systems compared with benchmark schemes.展开更多
In this paper,we propose a hybrid decode-and-forward and soft information relaying(HDFSIR)strategy to mitigate error propagation in coded cooperative communications.In the HDFSIR approach,the relay operates in decode-...In this paper,we propose a hybrid decode-and-forward and soft information relaying(HDFSIR)strategy to mitigate error propagation in coded cooperative communications.In the HDFSIR approach,the relay operates in decode-and-forward(DF)mode when it successfully decodes the received message;otherwise,it switches to soft information relaying(SIR)mode.The benefits of the DF and SIR forwarding strategies are combined to achieve better performance than deploying the DF or SIR strategy alone.Closed-form expressions for the outage probability and symbol error rate(SER)are derived for coded cooperative communication with HDFSIR and energy-harvesting relays.Additionally,we introduce a novel normalized log-likelihood-ratio based soft estimation symbol(NL-SES)mapping technique,which enhances soft symbol accuracy for higher-order modulation,and propose a model characterizing the relationship between the estimated complex soft symbol and the actual high-order modulated symbol.Further-more,the hybrid DF-SIR strategy is extended to a distributed Alamouti space-time-coded cooperative network.To evaluate the~performance of the proposed HDFSIR strategy,we implement extensive Monte Carlo simulations under varying channel conditions.Results demonstrate significant improvements with the hybrid technique outperforming individual DF and SIR strategies in both conventional and distributed Alamouti space-time coded cooperative networks.Moreover,at a SER of 10^(-3),the proposed NL-SES mapping demonstrated a 3.5 dB performance gain over the conventional averaging one,highlighting its superior accuracy in estimating soft symbols for quadrature phase-shift keying modulation.展开更多
Let T:T^(d)→T^(d),defined by Tx=AX(mod 1),where A is a d×d integer matrix with eigenvalues 1<|λ_(1)|≤|λ_(2)|≤…≤|λ_(d)|,We investigate the Hausdorff dimension of the recurrence set R(ψ)={x∈T^(d):T^(n)...Let T:T^(d)→T^(d),defined by Tx=AX(mod 1),where A is a d×d integer matrix with eigenvalues 1<|λ_(1)|≤|λ_(2)|≤…≤|λ_(d)|,We investigate the Hausdorff dimension of the recurrence set R(ψ)={x∈T^(d):T^(n)x∈B(x,ψ(n))for infinitely many n}forα≥log|λ_(d)/λ_(1)|,whereψis a positive decreasing function defined onℕand its lower order at infinity isα=lim inf_(n→∞)-logψ(n)/n.In the case that A is diagonalizable overℚwith integral eigenvalues,we obtain the dimension formula.展开更多
The synthesized molecular clusters featuring the cubic[4Fe–4S]core have been studied for several decades,as they serve as true analogs of the active components in ferritin within biological systems.Such a model clust...The synthesized molecular clusters featuring the cubic[4Fe–4S]core have been studied for several decades,as they serve as true analogs of the active components in ferritin within biological systems.Such a model cluster has been extensively investigated in various fields,including structural modulation,catalysis,and self-assembly under laboratory conditions,with the aim of gaining an in-depth understanding of their roles in biological functions.Herein,we revisited three well-known[Fe_(4)S_(4)(SR)_(4)]^(2–)molecules,namely[Me_(4)N]_(2)[Fe_(4)S_(4)(SR)_(4)](R=o-MBT,m-MBT,p-MBT),and successfully established their single crystal structures that remain unknown prior to this work.Interestingly,it is revealed that the position of the substituent methyl group has an obvious steric effect on the arrangement of the ligand around the[4Fe–4S]core,which further influences their overall packing patterns in single crystals.In addition,this work unveils two new structure transformation behaviors for the[Fe_(4)S_(4)(SR)_(4)]^(2–)system:i)the monomeric[Fe(SR)_(4)]^(2–)and tetrameric[Fe_(4)S_(4)(SR)_(4)]^(2–)can be interconverted,and ii)[Fe_(4)S_(4)(SR)_(4)]^(2–)can be transferred into an intriguing iron-oxide complex Na_(2)Fe_(6)O(OMe)_(18)·6MeOH in a well-controlled oxidizing environment.展开更多
Considering the different versions of the Penrose transform on D-modules and their applications to different levels of DM-modules in coherent sheaves, we obtain a geometrical re-construction of the electrodynamical ca...Considering the different versions of the Penrose transform on D-modules and their applications to different levels of DM-modules in coherent sheaves, we obtain a geometrical re-construction of the electrodynamical carpet of the space-time, which is a direct consequence of the equivalence between the moduli spaces, that have been demonstrated in a before work. In this case, the equivalence is given by the Penrose transform on the quasi coherent Dλ-modules given by the generalized Verma modules diagram established in the Recillas conjecture to the group SO(1, n + 1), and consigned in the Dp-modules on which have been obtained solutions in field theory of electromagnetic type.展开更多
In the Kigongo area of Mwanza Region,northwest Tanzania,fishmonger Neema Aisha remembers how the morning’s fresh catch would sour while she queued for the ferry,putting her business at risk.
It is difficult to recover chrysocolla from sulfidation flotation which is closely related to the mineral surface composition.In this study,the effects of fluoride roasting on the surface composition of chrysocolla we...It is difficult to recover chrysocolla from sulfidation flotation which is closely related to the mineral surface composition.In this study,the effects of fluoride roasting on the surface composition of chrysocolla were investigated,its impact on sulfidation flotation was explored,and the mechanisms involved in both fluoride roasting and sulfidation flotation were discussed.With CaF_(2)as the roasting reagent,Na_(2)S·9H_(2)O as the sulfidation reagent,and sodium butyl xanthate(NaBX)as the collector,the results of the flotation experiments showed that fluoride roasting improved the floatability of chrysocolla,and the recovery rate increased from 16.87%to 82.74%.X-ray diffraction analysis revealed that after fluoride roasting,approximately all the Cu on the chrysocolla surface was exposed in the form of CuO,which could provide a basis for subsequent sulfidation flotation.The microscopy and elemental analyses revealed that large quantities of"pagoda-like"grains were observed on the sulfidation surface of the fluoride-roasted chrysocolla,indicating high crystallinity particles of copper sulfide.This suggests that the effect of sulfide formation on the chrysocolla surface was more pronounced.X-ray photoelectron spectroscopy revealed that fluoride roasting increased the relative contents of sulfur and copper on the surface and that both the Cu~+and polysulfide fractions on the surface of the minerals increased.This enhances the effect of sulfidation,which is conducive to flotation recovery.Therefore,fluoride roasting improved the effect of copper species transformation and sulfidation on the surface of chysocolla,promoted the adsorption of collectors,and improved the recovery of chrysocolla from sulfidation flotation.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11875040 and 12171308)
文摘Reciprocal transformations of the space-time shifted nonlocal short pulse equations are elaborated.Covariance of dependent and independent variables involved in the reciprocal transformations is investigated.Exact solutions of the space-time shifted nonlocal short pulse equations are given in terms of double Wronskians.Realness of independent variables involved in the reciprocal transformations is verified.Dynamics of some obtained solutions are illustrated.
文摘Scalar-tensor theories of gravity are considered to be competitors to Einstein's theory of general relativity for the description of classical gravity,as they are used to build feasible models for cosmic inflation.These theories can be formulated both in the Jordan and Einstein frame,which are related by a Weyl transformation with a field transformation,known together as a frame transformation.These theories formulated in the above two frames are often considered to be equivalent from the point of view of classical theory.However,this is no longer true from the quantum field theoretical perspective.In the present article,we show that the Ward identities derived in the above two frames are not connected through the frame transformation.This shows that the quantum field theories formulated in these two frames are not equivalent to each other.Moreover,this inequivalence is also shown by comparing the effective actions derived in these two frames.
基金supported by the Deanship of Scientific Research at King Khalid University,Saudi Arabia (R.G.P.1/207/43)。
文摘This paper presents an extension of certain forms of the real Paley-Wiener theorems to the Minkowski space-time algebra. Our emphasis is dedicated to determining the space-time valued functions whose space-time Fourier transforms(SFT) have compact support using the partial derivatives operator and the Dirac operator of higher order.
基金Supported by the National Natural Science Foundation of China。
文摘The Hawking effect in the Vaidya-Bonner space-time can be considered as a compensate effect of the scale transformation of coordinate time.The gauge potential is the contraction of the affine connection.It is found that the rate of change of temperature can be obtained as the pure gauge potential of the compensate field,in addition to the Hawking temperature which was known from the stationary black holes.
基金National Natural Science F oundation of China(No.10 0 2 5 2 10 )
文摘The equations governing incompressible and compressible inviscid flows and written in the physical frame ( t,x,y,z ) are known to be linearly well posed and exhibit elliptic or hyperbolic nature. The linear well posedness is considered here for these equations under a space time transformation ( t,x,y,z)→(τ,ξ,η,ζ ), where the pseudo time τ and the new space coordinate ( ξ,η,ζ ) all depend on ( t,x,y,z ). Such a transformation could be useful for uniformly treating problems in which the flow is fast unsteady somewhere and slow unsteady or steady elsewhere. It is found that the transformation may alter the ellipticity, the hyperbolicty, and even the well posedness of the original equations. In one dimension, the transformed incompressible flow equations become weakly hyperbolic and the compressible ones could degenerate to elliptical equations. In high dimensions there are conditions such that the transformed equations become ill posed.
文摘Ensuring digital media security through robust image watermarking is essential to prevent unauthorized distribution,tampering,and copyright infringement.This study introduces a novel hybrid watermarking framework that integrates Discrete Wavelet Transform(DWT),Redundant Discrete Wavelet Transform(RDWT),and Möbius Transformations(MT),with optimization of transformation parameters achieved via a Genetic Algorithm(GA).By combining frequency and spatial domain techniques,the proposed method significantly enhances both the imper-ceptibility and robustness of watermark embedding.The approach leverages DWT and RDWT for multi-resolution decomposition,enabling watermark insertion in frequency subbands that balance visibility and resistance to attacks.RDWT,in particular,offers shift-invariance,which improves performance under geometric transformations.Möbius transformations are employed for spatial manipulation,providing conformal mapping and spatial dispersion that fortify watermark resilience against rotation,scaling,and translation.The GA dynamically optimizes the Möbius parameters,selecting configurations that maximize robustness metrics such as Peak Signal-to-Noise Ratio(PSNR),Structural Similarity Index Measure(SSIM),Bit Error Rate(BER),and Normalized Cross-Correlation(NCC).Extensive experiments conducted on medical and standard benchmark images demonstrate the efficacy of the proposed RDWT-MT scheme.Results show that PSNR exceeds 68 dB,SSIM approaches 1.0,and BER remains at 0.0000,indicating excellent imperceptibility and perfect watermark recovery.Moreover,the method exhibits exceptional resilience to a wide range of image processing attacks,including Gaussian noise,JPEG compression,histogram equalization,and cropping,achieving NCC values close to or equal to 1.0.Comparative evaluations with state-of-the-art watermarking techniques highlight the superiority of the proposed method in terms of robustness,fidelity,and computational efficiency.The hybrid framework ensures secure,adaptive watermark embedding,making it highly suitable for applications in digital rights management,content authentication,and medical image protection.The integration of spatial and frequency domain features with evolutionary optimization presents a promising direction for future watermarking technologies.
基金supported by the Advance Research Project of Civil Aerospace Technology(Grant No.D020304)National Nat-ural Science Foundation of China(Grant Nos.52205257 and U22B2083).
文摘This paper proposes a new step-by-step Chebyshev space-time spectral method to analyze the force vibration of functionally graded material structures.Although traditional space-time spectral methods can reduce the accuracy mismatch between tem-poral low-order finite difference and spatial high-order discre tization,the ir time collocation points must increase dramatically to solve highly oscillatory solutions of structural vibration,which results in a surge in computing time and a decrease in accuracy.To address this problem,we introduced the step-by-step idea in the space-time spectral method.The Chebyshev polynomials and Lagrange's equation were applied to derive discrete spatial goverming equations,and a matrix projection method was used to map the calculation results of prev ious steps as the initial conditions of the subsequent steps.A series of numerical experiments were carried out.The results of the proposed method were compared with those obtained by traditional space-time spectral methods,which showed that higher accuracy could be achieved in a shorter computation time than the latter in highly oscillatory cases.
基金financially supported by the Scientific Research Foundation of North China University of Technology(Grant Nos.11005136024XN147-87 and 110051360024XN151-86).
文摘With respect to oceanic fluid dynamics,certain models have appeared,e.g.,an extended time-dependent(3+1)-dimensional shallow water wave equation in an ocean or a river,which we investigate in this paper.Using symbolic computation,we find out,on one hand,a set of bilinear auto-Backlund transformations,which could connect certain solutions of that equation with other solutions of that equation itself,and on the other hand,a set of similarity reductions,which could go from that equation to a known ordinary differential equation.The results in this paper depend on all the oceanic variable coefficients in that equation.
文摘When we study Lorentz transformation in the framework of quantum gauge theory of gravity, we will find that the vacuum gravitational gauge field will be changed under gravitational gauge transformation, which will change the structure of the physical space-time and cause clock dilation effect. The study in this paper provides us with new insights to understand the essential and intrinsic relation between special relativity and general relativity. It provides us with a new way to unify special relativity and general relativity.
基金supported by Beijing Municipal Natural Science Foundation(L222002)the Natural Science Foundation of China(U22B2004).
文摘Existing orthogonal space-time block coding(OSTBC)schemes for backscatter communication systems cannot achieve a full transmission code rate when the tag is equipped with more than two antennas.In this paper,we propose a quasi-orthogonal spacetime block code(QOSTBC)that can achieve a full transmission code rate for backscatter communication systems with a four-antenna tag and then extend the scheme to support tags with 2i antennas.Specifically,we first present the system model for the backscatter system.Next,we propose the QOSTBC scheme to encode the tag signals.Then,we provide the corresponding maximum likelihood detection algorithms to recover the tag signals.Finally,simulation results are provided to demonstrate that our proposed QOSTBC scheme and the detection algorithm can achieve a better transmission code rate or symbol error rate performance for backscatter communication systems compared with benchmark schemes.
基金funded by the Deanship of Graduate Studies and Scientific Research at Jouf University under grant No.(DGSSR-2024-02-02160).
文摘In this paper,we propose a hybrid decode-and-forward and soft information relaying(HDFSIR)strategy to mitigate error propagation in coded cooperative communications.In the HDFSIR approach,the relay operates in decode-and-forward(DF)mode when it successfully decodes the received message;otherwise,it switches to soft information relaying(SIR)mode.The benefits of the DF and SIR forwarding strategies are combined to achieve better performance than deploying the DF or SIR strategy alone.Closed-form expressions for the outage probability and symbol error rate(SER)are derived for coded cooperative communication with HDFSIR and energy-harvesting relays.Additionally,we introduce a novel normalized log-likelihood-ratio based soft estimation symbol(NL-SES)mapping technique,which enhances soft symbol accuracy for higher-order modulation,and propose a model characterizing the relationship between the estimated complex soft symbol and the actual high-order modulated symbol.Further-more,the hybrid DF-SIR strategy is extended to a distributed Alamouti space-time-coded cooperative network.To evaluate the~performance of the proposed HDFSIR strategy,we implement extensive Monte Carlo simulations under varying channel conditions.Results demonstrate significant improvements with the hybrid technique outperforming individual DF and SIR strategies in both conventional and distributed Alamouti space-time coded cooperative networks.Moreover,at a SER of 10^(-3),the proposed NL-SES mapping demonstrated a 3.5 dB performance gain over the conventional averaging one,highlighting its superior accuracy in estimating soft symbols for quadrature phase-shift keying modulation.
基金supported by the Science Foundation of China University of Petroleum,Beijing(2462023SZBH013)the China Postdoctoral Science Foundation(2023M743878)+2 种基金the Postdoctoral Fellowship Program of CPSF(GZB20240848)supported partially by the NSFC(12271176)the Guangdong Natural Science Foundation(2024A1515010946).
文摘Let T:T^(d)→T^(d),defined by Tx=AX(mod 1),where A is a d×d integer matrix with eigenvalues 1<|λ_(1)|≤|λ_(2)|≤…≤|λ_(d)|,We investigate the Hausdorff dimension of the recurrence set R(ψ)={x∈T^(d):T^(n)x∈B(x,ψ(n))for infinitely many n}forα≥log|λ_(d)/λ_(1)|,whereψis a positive decreasing function defined onℕand its lower order at infinity isα=lim inf_(n→∞)-logψ(n)/n.In the case that A is diagonalizable overℚwith integral eigenvalues,we obtain the dimension formula.
基金supported by the Fundamental Research Funds for the Central Universities(22120240204 and 22120240039)the National Natural Science Foundation of China(22301219,Z.Z.,22101205,H.H.)。
文摘The synthesized molecular clusters featuring the cubic[4Fe–4S]core have been studied for several decades,as they serve as true analogs of the active components in ferritin within biological systems.Such a model cluster has been extensively investigated in various fields,including structural modulation,catalysis,and self-assembly under laboratory conditions,with the aim of gaining an in-depth understanding of their roles in biological functions.Herein,we revisited three well-known[Fe_(4)S_(4)(SR)_(4)]^(2–)molecules,namely[Me_(4)N]_(2)[Fe_(4)S_(4)(SR)_(4)](R=o-MBT,m-MBT,p-MBT),and successfully established their single crystal structures that remain unknown prior to this work.Interestingly,it is revealed that the position of the substituent methyl group has an obvious steric effect on the arrangement of the ligand around the[4Fe–4S]core,which further influences their overall packing patterns in single crystals.In addition,this work unveils two new structure transformation behaviors for the[Fe_(4)S_(4)(SR)_(4)]^(2–)system:i)the monomeric[Fe(SR)_(4)]^(2–)and tetrameric[Fe_(4)S_(4)(SR)_(4)]^(2–)can be interconverted,and ii)[Fe_(4)S_(4)(SR)_(4)]^(2–)can be transferred into an intriguing iron-oxide complex Na_(2)Fe_(6)O(OMe)_(18)·6MeOH in a well-controlled oxidizing environment.
文摘Considering the different versions of the Penrose transform on D-modules and their applications to different levels of DM-modules in coherent sheaves, we obtain a geometrical re-construction of the electrodynamical carpet of the space-time, which is a direct consequence of the equivalence between the moduli spaces, that have been demonstrated in a before work. In this case, the equivalence is given by the Penrose transform on the quasi coherent Dλ-modules given by the generalized Verma modules diagram established in the Recillas conjecture to the group SO(1, n + 1), and consigned in the Dp-modules on which have been obtained solutions in field theory of electromagnetic type.
文摘In the Kigongo area of Mwanza Region,northwest Tanzania,fishmonger Neema Aisha remembers how the morning’s fresh catch would sour while she queued for the ferry,putting her business at risk.
基金financially supported by the National Natural Science Foundation of China(No.52374259)the Open Fund of the State Key Laboratory of Mineral Processing Science and Technology,China(No.BGRIMM-KJSKL-2023-11)the Major Science and Technology Projects in Yunnan Province,China(No.202302 AF080004)。
文摘It is difficult to recover chrysocolla from sulfidation flotation which is closely related to the mineral surface composition.In this study,the effects of fluoride roasting on the surface composition of chrysocolla were investigated,its impact on sulfidation flotation was explored,and the mechanisms involved in both fluoride roasting and sulfidation flotation were discussed.With CaF_(2)as the roasting reagent,Na_(2)S·9H_(2)O as the sulfidation reagent,and sodium butyl xanthate(NaBX)as the collector,the results of the flotation experiments showed that fluoride roasting improved the floatability of chrysocolla,and the recovery rate increased from 16.87%to 82.74%.X-ray diffraction analysis revealed that after fluoride roasting,approximately all the Cu on the chrysocolla surface was exposed in the form of CuO,which could provide a basis for subsequent sulfidation flotation.The microscopy and elemental analyses revealed that large quantities of"pagoda-like"grains were observed on the sulfidation surface of the fluoride-roasted chrysocolla,indicating high crystallinity particles of copper sulfide.This suggests that the effect of sulfide formation on the chrysocolla surface was more pronounced.X-ray photoelectron spectroscopy revealed that fluoride roasting increased the relative contents of sulfur and copper on the surface and that both the Cu~+and polysulfide fractions on the surface of the minerals increased.This enhances the effect of sulfidation,which is conducive to flotation recovery.Therefore,fluoride roasting improved the effect of copper species transformation and sulfidation on the surface of chysocolla,promoted the adsorption of collectors,and improved the recovery of chrysocolla from sulfidation flotation.
