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
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
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
In this paper,we study the N=2a=1 supersymmetric KdV equation.We construct its Darboux transformation and the associated B?cklund transformation.Furthermore,we derive a nonlinear superposition formula,and as applicati...In this paper,we study the N=2a=1 supersymmetric KdV equation.We construct its Darboux transformation and the associated B?cklund transformation.Furthermore,we derive a nonlinear superposition formula,and as applications we calculate some solutions for this supersymmetric KdV equation and recover the related results for the Kersten-Krasil'shchik coupled KdV-mKdV system.展开更多
Agile Transformations are challenging processes for organizations that look to extend the benefits of Agile philosophy and methods beyond software engineering.Despite the impact of these transformations on orga-nizati...Agile Transformations are challenging processes for organizations that look to extend the benefits of Agile philosophy and methods beyond software engineering.Despite the impact of these transformations on orga-nizations,they have not been extensively studied in academia.We conducted a study grounded in workshops and interviews with 99 participants from 30 organizations,including organizations undergoing transformations(“final organizations”)and companies supporting these processes(“consultants”).The study aims to understand the motivations,objectives,and factors driving and challenging these transformations.Over 700 responses were collected to the question and categorized into 32 objectives.The findings show that organizations primarily aim to achieve customer centricity and adaptability,both with 8%of the mentions.Other primary important objectives,with above 4%of mentions,include alignment of goals,lean delivery,sustainable processes,and a flatter,more team-based organizational structure.We also detect discrepancies in perspectives between the objectives identified by the two kinds of organizations and the existing agile literature and models.This misalignment highlights the need for practitioners to understand with the practical realities the organizations face.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
The Lorentz transformations are the mathematical basis of Einstein’s theory of special relativity. We conduct a thorough examination of the method of derivation of the Lorentz transformations used by Einstein and ide...The Lorentz transformations are the mathematical basis of Einstein’s theory of special relativity. We conduct a thorough examination of the method of derivation of the Lorentz transformations used by Einstein and identify the cause of the incorrect implementation of the method. The cause is related to the incorrect proof of the equality φ(v)=1for the unknown function φ(v)arising in the process of derivation of the Lorentz transformations. We develop proof of the equality φ(v)=1and eliminate the cause of the incorrect implementation of the method of derivation of the Lorentz transformations used by Einstein.展开更多
Starting from the characteristics of modernization in three different historical stages since the founding of the People’s Republic of China,this paper analyses the internal changes in the professional name,subordina...Starting from the characteristics of modernization in three different historical stages since the founding of the People’s Republic of China,this paper analyses the internal changes in the professional name,subordinate disciplines and categories,and professional mission of the environmental design profession,and summarizes the changes in the characteristics of the environmental design profession in 10 aspects such as subordinate disciplines,design objects,design types,cultural characteristics,and aesthetic values on the basis of the results of the analysis,and explores five transformations of the environmental design profession in the process of China’s development in the future.The five transformations in the future development of China are to serve the harmony and beauty of the three major urban and rural spaces with“small and micro-renewal and reconstruction”;to serve the transmission of Chinese culture and the spread of Chinese civilization with“spatial heritage and innovation”;to serve the balance and sufficiency of the four functions of urban and rural settlements with“friendliness and equilibrium”;to serve the intelligence,wisdom,and enjoyment of indoor and outdoor living environment space with“scientific and technological achievements”;and to serve the co-construction,co-management,and sharing of indoor and outdoor public space in urban and rural areas with“public participation.”展开更多
The canonical transformation and Poisson theory of dynamical systems with exponential,power-law,and logarithmic non-standard Lagrangians are studied,respectively.The criterion equations of canonical transformation are...The canonical transformation and Poisson theory of dynamical systems with exponential,power-law,and logarithmic non-standard Lagrangians are studied,respectively.The criterion equations of canonical transformation are established,and four basic forms of canonical transformations are given.The dynamic equations with non-standard Lagrangians admit Lie algebraic structure.From this,we es-tablish the Poisson theory,which makes it possible to find new conservation laws through known conserved quantities.Some examples are put forward to demonstrate the use of the theory and verify its effectiveness.展开更多
This paper introduces a modified formal variable separation approach,showcasing a systematic and notably straightforward methodology for analyzing the B-type Kadomtsev-Petviashvili(BKP)equation.Through the application...This paper introduces a modified formal variable separation approach,showcasing a systematic and notably straightforward methodology for analyzing the B-type Kadomtsev-Petviashvili(BKP)equation.Through the application of this approach,we successfully ascertain decomposition solutions,Bäcklund transformations,the Lax pair,and the linear superposition solution associated with the aforementioned equation.Furthermore,we expand the utilization of this technique to the C-type Kadomtsev-Petviashvili(CKP)equation,leading to the derivation of decomposition solutions,Bäcklund transformations,and the Lax pair specific to this equation.The results obtained not only underscore the efficacy of the proposed approach,but also highlight its potential in offering a profound comprehension of integrable behaviors in nonlinear systems.Moreover,this approach demonstrates an efficient framework for establishing interrelations between diverse systems.展开更多
1 | BACKGROUND.A decade ago we asked the question, “Is there something inmedicine that is eternal or enduring?” Our aim was to writea manuscript entitled, “That which does not change inmedicine.” The publication b...1 | BACKGROUND.A decade ago we asked the question, “Is there something inmedicine that is eternal or enduring?” Our aim was to writea manuscript entitled, “That which does not change inmedicine.” The publication begins as follows: “The practiceof medicine involves continual change, driven by a constantstream of developments in the understanding of biologicalstructure and function relevant to human diseases, and theparallel improvements in pharmacologic and other technologicalinterventions. This change is also driven by evolvingsocial philosophies, ethical trends, and lifestyles.” [1] Thatpreamble reverberates as strongly now as then, perhapseven more so, given the velocity of technological change.When we deliberated on which aspects of medical practiceshould remain stable, we had few premonitions thatimplantable chips, robotic surgery, virtual reality, andartificial intelligence (AI) would soon become ubiquitous.The needle has clearly moved, propelled by extraordinaryadvances in bioengineering, computer and data sciences;major shifts in the governance and organization of clinicalpractice;and powerful sociocultural trends.展开更多
The standard implementation of the hybrid GMRES algorithm for solving large nonsymmetric linear systems involves a Gram-Schmidt process which is a potential source of significant numerical error. An alternative implem...The standard implementation of the hybrid GMRES algorithm for solving large nonsymmetric linear systems involves a Gram-Schmidt process which is a potential source of significant numerical error. An alternative implementation is outlined here in which orthogonalization by Householder transformations replaces the Gram-Schmidt process. Numerical experiments show that the new implementation is more stable.展开更多
The atmosphere is an evolutionary agent essential to the shaping of a planet,while in oceanic science and daily life,liquids are commonly seen.In this paper,we investigate a generalized variable-coefficient Korteweg-d...The atmosphere is an evolutionary agent essential to the shaping of a planet,while in oceanic science and daily life,liquids are commonly seen.In this paper,we investigate a generalized variable-coefficient Korteweg-de Vriesmodified Korteweg-de Vries equation for the atmosphere,oceanic fluids and plasmas.With symbolic computation,beginning with a presumption,we work out certain scaling transformations,bilinear forms through the binary Bell polynomials and our scaling transformations,N solitons(with N being a positive integer)via the aforementioned bilinear forms and bilinear auto-Bäcklund transformations through the Hirota method with some solitons.In addition,Painlevé-type auto-Bäcklund transformations with some solitons are symbolically computed out.Respective dependences and constraints on the variable/constant coefficients are discussed,while those coefficients correspond to the quadratic-nonlinear,cubic-nonlinear,dispersive,dissipative and line-damping effects in the atmosphere,oceanic fluids and plasmas.展开更多
The asymptotic theory for nonlinear transformations of fractionally integrated time series is developed. By the use of fractional Occupation Times Formula, various nonlinear functions of fractionally integrated series...The asymptotic theory for nonlinear transformations of fractionally integrated time series is developed. By the use of fractional Occupation Times Formula, various nonlinear functions of fractionally integrated series such as ARFIMA time series are studied, and the asymptotic distributions of the sample moments of such functions are obtained and analyzed. The transformations considered in this paper includes a variety of functions such as regular functions, integrable functions and asymptotically homogeneous functions that are often used in practical nonlinear econometric analysis. It is shown that the asymptotic theory of nonlinear transformations of original and normalized fractionally integrated processes is diffent from that of fractionally integrated processes, but is similar to the asymptotic theory of nonlinear transformations of integrated processes.展开更多
It is well known that the use of Helmholtz decomposition theorem for static vector fields , when applied to the time dependent vector fields , which represent the electromagnetic field, allows us to obtain instan...It is well known that the use of Helmholtz decomposition theorem for static vector fields , when applied to the time dependent vector fields , which represent the electromagnetic field, allows us to obtain instantaneous-like solutions all along . For this reason, some people thought (see e.g. [1] and references therein) that the Helmholtz theorem cannot be applied to time dependent vector fields and some modification is wanted in order to get the retarded solutions. However, the use of the Helmholtz theorem for static vector fields is correct even for time dependent vector fields (see, e.g. [2]), so a relation between the solutions was required, in such a way that a retarded solution can be transformed in an instantaneous one, and conversely. On this paper we want to suggest, following most of the time the mathematical formalism of Woodside in [3], that: 1) there are many Helmholtz decompositions, all equally consistent, 2) each one is naturally related to a space-time structure, 3) when we use the Helmholtz decomposition for the electromagnetic potentials it is equivalent to a gauge transformation, 4) there is a natural methodological criterion for choosing the gauge according to the structure postulated for a global space-time, 5) the Helmholtz decomposition is the manifestation at the level of the fields that a gauge is involved. So, when we relate the retarded solution to the instantaneous one what we do is to change the gauge and the space-time. And, if the Helmholtz decompositions are related to a space-time structure, and are equivalent to gauge transformations, each gauge transformation is natural for a specific space-time. In this way, a Helmholtz decomposition for Euclidean space is equivalent to the Coulomb gauge and a Helmholtz decomposition for the Minkowski space is equivalent to the Lorenz gauge. This leads us to consider that the theories defined by different gauges may be mathematically equivalent, because they can be related by means of a gauge transformation, but they are not empirically equivalent, because they have quite different observational consequences due to the different space-time structure involved.展开更多
The hydrogen-induced microstructure evolution and phase transformations in Ti-6Al-4V alloy during heating and cooling were studied.The specimens were heated to 1273 K and subsequently cooled to room temperature.The hy...The hydrogen-induced microstructure evolution and phase transformations in Ti-6Al-4V alloy during heating and cooling were studied.The specimens were heated to 1273 K and subsequently cooled to room temperature.The hydrogen content is up to 0.8%（mass fraction）.The hydrogen-induced dynamic phase transformations and the corresponding mechanisms were analyzed.When the hydrogen content increases,the β transus temperature significantly decreases and the magnitude decreases,and the volume fraction of β phase increases.During heating,the phase transformations in hydrogenated Ti-6Al-4V alloys can be divided into three stages,and the phase transformation order is δ→α＋H2↑？δ＋α′→βH？α′→αH＋βH？αH→α＋H2↑？α→β？βH→β＋H2↑.In addition,the relationship among hydrogenation and Ms and Mf of α′ martensite were determined.展开更多
Metal-organic frameworks(MOFs)have always been the focus of chemists due to their diverse structures,adjustable pore size and high stability since they came into being.In recent years,as one of the most significant ap...Metal-organic frameworks(MOFs)have always been the focus of chemists due to their diverse structures,adjustable pore size and high stability since they came into being.In recent years,as one of the most significant applications of MOFs porous materials,photocatalytic organic compounds transformation has made full-grown progress both in the preparation of the catalysts themselves and in the scope of specific applications.Herein,we summarize the research progress of MOFs catalysts for photocatalytic transformations of organic compounds in recent three years.Some outstanding works on the preparation and synthesis strategies of photocatalysts are introduced firstly,including internal optimization and modification of MOFs,POM@MOF composite and core-shell MOF@COF hybrids.The second part is about the application of diverse types of organic reactions,including dual-function organic reactions,catalytic oxidation reactions,comprehensive utilization of CO_(2) and degradation of organic pollutants.Besides,the development opportunities and some problems to be solved in this field are proposed.展开更多
For the holonomic nonconservative system, by using the Noether symmetry, a non-Noether conserved quantity is obtained directly under general infinitesimal transformations of groups in which time is variable. At first,...For the holonomic nonconservative system, by using the Noether symmetry, a non-Noether conserved quantity is obtained directly under general infinitesimal transformations of groups in which time is variable. At first,the Noether symmetry, Lie symmetry, and Noether conserved quantity are given. Secondly, the condition under which the Noether symmetry is a Lie symmetry under general infinitesimal transformations is obtained. Finally, a set of nonNoether conserved quantities of the system are given by the Noether symmetry, and an example is given to illustrate the application of the results.展开更多
This paper studies the conformal invariance by infinitesimal point transformations of non-conservative Lagrange systems. It gives the necessary and sufficient conditions of conformal invariance by the action of infini...This paper studies the conformal invariance by infinitesimal point transformations of non-conservative Lagrange systems. It gives the necessary and sufficient conditions of conformal invariance by the action of infinitesimal point transformations being Lie symmetric simultaneously. Then the Noether conserved quantities of conformal invariance are obtained. Finally an illustrative example is given to verify the results.展开更多
Various solid state phase transformations exist in metastable β-type Ti alloys,which can be employed to optimize the mechanical properties.In this paper,synchrotron X-ray diffraction(SXRD)experiments were carried out...Various solid state phase transformations exist in metastable β-type Ti alloys,which can be employed to optimize the mechanical properties.In this paper,synchrotron X-ray diffraction(SXRD)experiments were carried out to study the phase transformations of a Ti36Nb5Zr alloy subjected to different thermomechanical treatments.Furthermore,the correlation between the phase constitutions and the mechanical properties was discussed.The a" texture formed,and high-density defects were introduced after cold rolling of the solution treated specimen,leading to the decrease in Young’s modulus and the increase in strength.The cold-rolled specimens were then annealed at temperatures from 423 to 773 K for 30 min.Both the Young’s modulus and strength increased with annealing temperatures increasing up to 673 K,which resulted from the precipitation of the ω and/or α phases.With further increase in annealing temperatures to 773 K,the β→α precipitation replaced the β→ω_(iso) phase transformation,and the density of defects decreased,leading to the decrease in both the Young’s modulus and strength.These results provide theoretical basis for the design biomedical Ti alloys with both low Young’s modulus and high strength.展开更多
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 National Natural Science Foundation of China (Grant Nos.12175111,11931107 and 12171474)NSFC-RFBR (Grant No.12111530003)。
文摘In this paper,we study the N=2a=1 supersymmetric KdV equation.We construct its Darboux transformation and the associated B?cklund transformation.Furthermore,we derive a nonlinear superposition formula,and as applications we calculate some solutions for this supersymmetric KdV equation and recover the related results for the Kersten-Krasil'shchik coupled KdV-mKdV system.
基金funding from the European Commission for the Ruralities Project(grant agreement no.101060876).
文摘Agile Transformations are challenging processes for organizations that look to extend the benefits of Agile philosophy and methods beyond software engineering.Despite the impact of these transformations on orga-nizations,they have not been extensively studied in academia.We conducted a study grounded in workshops and interviews with 99 participants from 30 organizations,including organizations undergoing transformations(“final organizations”)and companies supporting these processes(“consultants”).The study aims to understand the motivations,objectives,and factors driving and challenging these transformations.Over 700 responses were collected to the question and categorized into 32 objectives.The findings show that organizations primarily aim to achieve customer centricity and adaptability,both with 8%of the mentions.Other primary important objectives,with above 4%of mentions,include alignment of goals,lean delivery,sustainable processes,and a flatter,more team-based organizational structure.We also detect discrepancies in perspectives between the objectives identified by the two kinds of organizations and the existing agile literature and models.This misalignment highlights the need for practitioners to understand with the practical realities the organizations face.
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.
文摘The Lorentz transformations are the mathematical basis of Einstein’s theory of special relativity. We conduct a thorough examination of the method of derivation of the Lorentz transformations used by Einstein and identify the cause of the incorrect implementation of the method. The cause is related to the incorrect proof of the equality φ(v)=1for the unknown function φ(v)arising in the process of derivation of the Lorentz transformations. We develop proof of the equality φ(v)=1and eliminate the cause of the incorrect implementation of the method of derivation of the Lorentz transformations used by Einstein.
基金Chongqing 2023 Undergraduate Colleges and Universities“Course Ideology and Politics Demonstration Course”and First-Class Undergraduate Course“Offline Course”“Environmental Space Design,”Chongqing College of Engineering 2022 Undergraduate“Course Civics and Politics Demonstration Course”and Gold Course“Offline Course”“Environmental Space Design,”Chongqing 2021 Higher Education Teaching Reform Research Project-Teaching Reform and Practice of Curriculum Civics and Politics Education Integrated into Environmental Design Professional Courses(Key Project)(202127)。
文摘Starting from the characteristics of modernization in three different historical stages since the founding of the People’s Republic of China,this paper analyses the internal changes in the professional name,subordinate disciplines and categories,and professional mission of the environmental design profession,and summarizes the changes in the characteristics of the environmental design profession in 10 aspects such as subordinate disciplines,design objects,design types,cultural characteristics,and aesthetic values on the basis of the results of the analysis,and explores five transformations of the environmental design profession in the process of China’s development in the future.The five transformations in the future development of China are to serve the harmony and beauty of the three major urban and rural spaces with“small and micro-renewal and reconstruction”;to serve the transmission of Chinese culture and the spread of Chinese civilization with“spatial heritage and innovation”;to serve the balance and sufficiency of the four functions of urban and rural settlements with“friendliness and equilibrium”;to serve the intelligence,wisdom,and enjoyment of indoor and outdoor living environment space with“scientific and technological achievements”;and to serve the co-construction,co-management,and sharing of indoor and outdoor public space in urban and rural areas with“public participation.”
基金Supported by the National Natural Science Foundation of China(12272248,11972241)。
文摘The canonical transformation and Poisson theory of dynamical systems with exponential,power-law,and logarithmic non-standard Lagrangians are studied,respectively.The criterion equations of canonical transformation are established,and four basic forms of canonical transformations are given.The dynamic equations with non-standard Lagrangians admit Lie algebraic structure.From this,we es-tablish the Poisson theory,which makes it possible to find new conservation laws through known conserved quantities.Some examples are put forward to demonstrate the use of the theory and verify its effectiveness.
基金sponsored by the National Natural Science Foundations of China(Nos.12301315,12235007,11975131)the Natural Science Foundation of Zhejiang Province(No.LQ20A010009).
文摘This paper introduces a modified formal variable separation approach,showcasing a systematic and notably straightforward methodology for analyzing the B-type Kadomtsev-Petviashvili(BKP)equation.Through the application of this approach,we successfully ascertain decomposition solutions,Bäcklund transformations,the Lax pair,and the linear superposition solution associated with the aforementioned equation.Furthermore,we expand the utilization of this technique to the C-type Kadomtsev-Petviashvili(CKP)equation,leading to the derivation of decomposition solutions,Bäcklund transformations,and the Lax pair specific to this equation.The results obtained not only underscore the efficacy of the proposed approach,but also highlight its potential in offering a profound comprehension of integrable behaviors in nonlinear systems.Moreover,this approach demonstrates an efficient framework for establishing interrelations between diverse systems.
文摘1 | BACKGROUND.A decade ago we asked the question, “Is there something inmedicine that is eternal or enduring?” Our aim was to writea manuscript entitled, “That which does not change inmedicine.” The publication begins as follows: “The practiceof medicine involves continual change, driven by a constantstream of developments in the understanding of biologicalstructure and function relevant to human diseases, and theparallel improvements in pharmacologic and other technologicalinterventions. This change is also driven by evolvingsocial philosophies, ethical trends, and lifestyles.” [1] Thatpreamble reverberates as strongly now as then, perhapseven more so, given the velocity of technological change.When we deliberated on which aspects of medical practiceshould remain stable, we had few premonitions thatimplantable chips, robotic surgery, virtual reality, andartificial intelligence (AI) would soon become ubiquitous.The needle has clearly moved, propelled by extraordinaryadvances in bioengineering, computer and data sciences;major shifts in the governance and organization of clinicalpractice;and powerful sociocultural trends.
文摘The standard implementation of the hybrid GMRES algorithm for solving large nonsymmetric linear systems involves a Gram-Schmidt process which is a potential source of significant numerical error. An alternative implementation is outlined here in which orthogonalization by Householder transformations replaces the Gram-Schmidt process. Numerical experiments show that the new implementation is more stable.
基金the National Natural Science Foundation of China(Grant No.11871116)the Fundamental Research Funds for the Central Universities of China(Grant No.2019XD-A11)the BUPT Innovation and Entrepreneurship Support Program,Beijing University of Posts and Telecommunications,and the National Scholarship for Doctoral Students of China.
文摘The atmosphere is an evolutionary agent essential to the shaping of a planet,while in oceanic science and daily life,liquids are commonly seen.In this paper,we investigate a generalized variable-coefficient Korteweg-de Vriesmodified Korteweg-de Vries equation for the atmosphere,oceanic fluids and plasmas.With symbolic computation,beginning with a presumption,we work out certain scaling transformations,bilinear forms through the binary Bell polynomials and our scaling transformations,N solitons(with N being a positive integer)via the aforementioned bilinear forms and bilinear auto-Bäcklund transformations through the Hirota method with some solitons.In addition,Painlevé-type auto-Bäcklund transformations with some solitons are symbolically computed out.Respective dependences and constraints on the variable/constant coefficients are discussed,while those coefficients correspond to the quadratic-nonlinear,cubic-nonlinear,dispersive,dissipative and line-damping effects in the atmosphere,oceanic fluids and plasmas.
基金Supported by National Natural Science Foundation of China(No.70471050).
文摘The asymptotic theory for nonlinear transformations of fractionally integrated time series is developed. By the use of fractional Occupation Times Formula, various nonlinear functions of fractionally integrated series such as ARFIMA time series are studied, and the asymptotic distributions of the sample moments of such functions are obtained and analyzed. The transformations considered in this paper includes a variety of functions such as regular functions, integrable functions and asymptotically homogeneous functions that are often used in practical nonlinear econometric analysis. It is shown that the asymptotic theory of nonlinear transformations of original and normalized fractionally integrated processes is diffent from that of fractionally integrated processes, but is similar to the asymptotic theory of nonlinear transformations of integrated processes.
文摘It is well known that the use of Helmholtz decomposition theorem for static vector fields , when applied to the time dependent vector fields , which represent the electromagnetic field, allows us to obtain instantaneous-like solutions all along . For this reason, some people thought (see e.g. [1] and references therein) that the Helmholtz theorem cannot be applied to time dependent vector fields and some modification is wanted in order to get the retarded solutions. However, the use of the Helmholtz theorem for static vector fields is correct even for time dependent vector fields (see, e.g. [2]), so a relation between the solutions was required, in such a way that a retarded solution can be transformed in an instantaneous one, and conversely. On this paper we want to suggest, following most of the time the mathematical formalism of Woodside in [3], that: 1) there are many Helmholtz decompositions, all equally consistent, 2) each one is naturally related to a space-time structure, 3) when we use the Helmholtz decomposition for the electromagnetic potentials it is equivalent to a gauge transformation, 4) there is a natural methodological criterion for choosing the gauge according to the structure postulated for a global space-time, 5) the Helmholtz decomposition is the manifestation at the level of the fields that a gauge is involved. So, when we relate the retarded solution to the instantaneous one what we do is to change the gauge and the space-time. And, if the Helmholtz decompositions are related to a space-time structure, and are equivalent to gauge transformations, each gauge transformation is natural for a specific space-time. In this way, a Helmholtz decomposition for Euclidean space is equivalent to the Coulomb gauge and a Helmholtz decomposition for the Minkowski space is equivalent to the Lorenz gauge. This leads us to consider that the theories defined by different gauges may be mathematically equivalent, because they can be related by means of a gauge transformation, but they are not empirically equivalent, because they have quite different observational consequences due to the different space-time structure involved.
基金Project(51275132)supported by the National Natural Science Foundation of China
文摘The hydrogen-induced microstructure evolution and phase transformations in Ti-6Al-4V alloy during heating and cooling were studied.The specimens were heated to 1273 K and subsequently cooled to room temperature.The hydrogen content is up to 0.8%（mass fraction）.The hydrogen-induced dynamic phase transformations and the corresponding mechanisms were analyzed.When the hydrogen content increases,the β transus temperature significantly decreases and the magnitude decreases,and the volume fraction of β phase increases.During heating,the phase transformations in hydrogenated Ti-6Al-4V alloys can be divided into three stages,and the phase transformation order is δ→α＋H2↑？δ＋α′→βH？α′→αH＋βH？αH→α＋H2↑？α→β？βH→β＋H2↑.In addition,the relationship among hydrogenation and Ms and Mf of α′ martensite were determined.
基金National Natural Science Foundation of China(21701078)for the financial support of this work。
文摘Metal-organic frameworks(MOFs)have always been the focus of chemists due to their diverse structures,adjustable pore size and high stability since they came into being.In recent years,as one of the most significant applications of MOFs porous materials,photocatalytic organic compounds transformation has made full-grown progress both in the preparation of the catalysts themselves and in the scope of specific applications.Herein,we summarize the research progress of MOFs catalysts for photocatalytic transformations of organic compounds in recent three years.Some outstanding works on the preparation and synthesis strategies of photocatalysts are introduced firstly,including internal optimization and modification of MOFs,POM@MOF composite and core-shell MOF@COF hybrids.The second part is about the application of diverse types of organic reactions,including dual-function organic reactions,catalytic oxidation reactions,comprehensive utilization of CO_(2) and degradation of organic pollutants.Besides,the development opportunities and some problems to be solved in this field are proposed.
基金国家自然科学基金，湖南省自然科学基金，the Scientific Research Foundation of Education Burean of Hunan Province
文摘For the holonomic nonconservative system, by using the Noether symmetry, a non-Noether conserved quantity is obtained directly under general infinitesimal transformations of groups in which time is variable. At first,the Noether symmetry, Lie symmetry, and Noether conserved quantity are given. Secondly, the condition under which the Noether symmetry is a Lie symmetry under general infinitesimal transformations is obtained. Finally, a set of nonNoether conserved quantities of the system are given by the Noether symmetry, and an example is given to illustrate the application of the results.
基金Project supported by the National Natural Science Foundation of China (Grant Nos 10472040, 10572021 and 10772025)the Outstanding Young Talents Training Found of Liaoning Province of China (Grant No 3040005)
文摘This paper studies the conformal invariance by infinitesimal point transformations of non-conservative Lagrange systems. It gives the necessary and sufficient conditions of conformal invariance by the action of infinitesimal point transformations being Lie symmetric simultaneously. Then the Noether conserved quantities of conformal invariance are obtained. Finally an illustrative example is given to verify the results.
基金This work was financially supported by the Fundamental Research Funds for the Central Universities(No.2017QNA04)Qing-Kun Meng thanks Prof.Yu-Chen Karen Chen-Wiegart at Stony Brook University and Dr.Jian-Ming Bai,Dr.Hui Zhong and Dr.Sanjit Ghose at National Synchrotron Light Source II for their assistance in the synchrotron experiments.This research used 28-ID-2(XPD)beamline of the National Synchrotron Light Source II,a U.S.Department of Energy(DOE)Office of Science User Facility operated for the DOE Office of Science by Brookhaven National Laboratory under Contract No.DE-SC0012704.
文摘Various solid state phase transformations exist in metastable β-type Ti alloys,which can be employed to optimize the mechanical properties.In this paper,synchrotron X-ray diffraction(SXRD)experiments were carried out to study the phase transformations of a Ti36Nb5Zr alloy subjected to different thermomechanical treatments.Furthermore,the correlation between the phase constitutions and the mechanical properties was discussed.The a" texture formed,and high-density defects were introduced after cold rolling of the solution treated specimen,leading to the decrease in Young’s modulus and the increase in strength.The cold-rolled specimens were then annealed at temperatures from 423 to 773 K for 30 min.Both the Young’s modulus and strength increased with annealing temperatures increasing up to 673 K,which resulted from the precipitation of the ω and/or α phases.With further increase in annealing temperatures to 773 K,the β→α precipitation replaced the β→ω_(iso) phase transformation,and the density of defects decreased,leading to the decrease in both the Young’s modulus and strength.These results provide theoretical basis for the design biomedical Ti alloys with both low Young’s modulus and high strength.
