Granite is one of the most important components of the continental crust on our Earth; it thus has been an enduring studied subject in geology. According to present knowledge, granite shows a great deal of heterogenei...Granite is one of the most important components of the continental crust on our Earth; it thus has been an enduring studied subject in geology. According to present knowledge, granite shows a great deal of heterogeneity in terms of its texture,structure, mineral species and geochemical compositions at different scales from small dike to large batholith. However, the reasons for these variations are not well understood although numerous interpretations have been proposed. The key point of this debate is whether granitic magma can be effectively differentiated through fractional crystallization, and, if so, what kind of crystallization occurred during the magmatic evolution. Although granitic magma has high viscosity because of its elevated SiO2 content, we agree that fractional crystallization is effectively processed during its evolution based on the evidence from field investigation,mineral species and its chemical variations, and geochemical compositions. These data indicate that crystal settling by gravitation is not the only mechanism dominating granitic differentiation. On the contrary, flow segregation or dynamic sorting may be more important. Accordingly, granite can be divided into unfractionated, fractionated(including weakly fractionated and highly fractionated) and cumulated types, according to the differentiation degree. Highly fractionated granitic magmas are generally high in primary temperature or high with various volatiles during the later stage, which make the fractional crystallization much easier than the common granitic melts. In addition, effective magmatic differentiation can be also expected when the magma emplaced along a large scale of extensional structure. Highly fractionated granitic magma is easily contaminated by country rocks due to its relatively prolonged crystallization time. Thus, granites do not always reflect the characteristics of the source areas and the physical and chemical conditions of the primary magma. We proposed that highly fractionated granites are an important sig展开更多
This paper presents a new method for the detection and parameter estimation of multicomponent LFM signals based on the fractional Fourier transform. For the optimization in the fractional Fourier domain, an algorithm ...This paper presents a new method for the detection and parameter estimation of multicomponent LFM signals based on the fractional Fourier transform. For the optimization in the fractional Fourier domain, an algorithm based on Quasi-Newton method is proposed which consists of two steps of searching, leading to a reduction in computation without loss of accuracy. And for multicomponent signals, we further propose a signal separation technique in the fractional Fourier domain which can effectively suppress the interferences on the detection of the weak components brought by the stronger components. The statistical analysis of the estimate errors is also performed which perfects the method theoretically, and finally, simulation results are provided to show the validity of our method.展开更多
The fractional Fourier transform is a generalization of the classical Fourier transform, which is introduced from the mathematic aspect by Namias at first and has many applications in optics quickly. Whereas its poten...The fractional Fourier transform is a generalization of the classical Fourier transform, which is introduced from the mathematic aspect by Namias at first and has many applications in optics quickly. Whereas its potential appears to have remained largely unknown to the signal processing community until 1990s. The fractional Fourier transform can be viewed as the chirp-basis expansion directly from its definition, but essentially it can be interpreted as a rotation in the time-frequency plane, i.e. the unified time-frequency transform. With the order from 0 increasing to 1, the fractional Fourier transform can show the characteristics of the signal changing from the time domain to the frequency domain. In this research paper, the fractional Fourier transform has been comprehensively and systematically treated from the signal processing point of view. Our aim is to provide a course from the definition to the applications of the fractional Fourier transform, especially as a reference and an introduction for researchers and interested readers.展开更多
This paper mainly discusses fractional differential approach to detecting textural features of digital image and its fractional differential filter. Firstly, both the geo- metric meaning and the kinetic physical meani...This paper mainly discusses fractional differential approach to detecting textural features of digital image and its fractional differential filter. Firstly, both the geo- metric meaning and the kinetic physical meaning of fractional differential are clearly explained in view of information theory and kinetics, respectively. Secondly, it puts forward and discusses the definitions and theories of fractional stationary point, fractional equilibrium coefficient, fractional stable coefficient, and fractional grayscale co-occurrence matrix. At the same time, it particularly discusses frac- tional grayscale co-occurrence matrix approach to detecting textural features of digital image. Thirdly, it discusses in detail the structures and parameters of nxn any order fractional differential mask on negative x-coordinate, positive x-coordi- nate, negative y-coordinate, positive y-coordinate, left downward diagonal, left upward diagonal, right downward diagonal, and right upward diagonal, respectively. Furthermore, it discusses the numerical implementation algorithms of fractional differential mask for digital image. Lastly, based on the above-mentioned discus- sion, it puts forward and discusses the theory and implementation of fractional differential filter for digital image. Experiments show that the fractional differential-based image operator has excellent feedback for enhancing the textural details of rich-grained digital images.展开更多
In this paper,it was proved that the commutator H_(β,b)generated by an n-dimensional fractional Hardy operator and a locally integrable function b is bounded from L^(p1)(R^n)to L^(p2)(R^n)if and only if b is a CMO(R^...In this paper,it was proved that the commutator H_(β,b)generated by an n-dimensional fractional Hardy operator and a locally integrable function b is bounded from L^(p1)(R^n)to L^(p2)(R^n)if and only if b is a CMO(R^n)function,where 1/p1-1/p2=β/n,1<p1<∞,0≤β<n.Furthermore, the characterization of H_(β,b)on the homogenous Herz space K_q^(α,p)(R^n)was obtained.展开更多
Background The computational fluid dynamics(CFD)approach has been frequently applied to compute the fractional flow reserve(FFR)using computed tomography angiography(CTA).This technique is efficient.We developed the D...Background The computational fluid dynamics(CFD)approach has been frequently applied to compute the fractional flow reserve(FFR)using computed tomography angiography(CTA).This technique is efficient.We developed the DEEPVESSEL-FFR platform using the emerging deep learning technique to calculate the FFR value out of CTA images in five minutes.This study is to evaluate the DEEPVESSEL-FFR platform using the emerging deep learning technique to calculate the FFR value from CTA images as an efficient method.Methods A single-center,prospective study was conducted and 63 patients were enrolled for the evaluation of the diagnostic performance of DEEPVESSEL-FFR.Automatic quantification method for the three-dimensional coronary arterial geometry and the deep learning based prediction of FFR were developed to assess the ischemic risk of the stenotic coronary arteries.Diagnostic performance of the DEEPVESSEL-FFR was assessed by using wire-based FFR as reference standard.The primary evaluation factor was defined by using the area under receiver-operation characteristics curve(AUC)analysis.Results For per-patient level,taking the cut-off value<0.8 referring to the FFR measurement,DEEPVESSEL-FFR presented higher diagnostic performance in determining ischemia-related lesions with area under the curve of 0.928 compare to CTA stenotic severity 0.664.DEEPVESSEL-FFR correlated with FFR(R=0.686,P<0.001),with a mean di&ference of-0.006士0.0091(P=0.619).The secondary evaluation factors,indicating per vessel accuracy,sensitivity,specificity,positive predictive value,and negative predictive value were 87.3%,97.14%,75%,82.93%,and 95.45%,respectively.Conclusion DEEPVESSEL-FFR is a novel method that allows efficient assessment of the functional significance of coronary stenosis.展开更多
The generalized fractional element networks are presented in this paper. In order to extend the structure of the model solutions to the generalized function space and make it contain more physical meanings, the restri...The generalized fractional element networks are presented in this paper. In order to extend the structure of the model solutions to the generalized function space and make it contain more physical meanings, the restriction on the parameters of the fractional element proposed by Schiessel et al. is eliminated and a 'compatibility equation' is added. The discretization method for solving the inverse Laplace transform is used and developed. The generalized solutions of the model equations are given. At the same time the generalized fractional element network--Zener and Poyinting-Thomson models are discussed in detail. It is shown that all the results obtained previously about the models of single parameter with fractional order and the classical models with integer order can be contained as the special cases of the results of this paper.展开更多
The velocity field of generalized second order fluid with fractional anomalous diiusion caused by a plate moving impulsively in its own plane is investigated and the anomalous diffusion problems of the stress field an...The velocity field of generalized second order fluid with fractional anomalous diiusion caused by a plate moving impulsively in its own plane is investigated and the anomalous diffusion problems of the stress field and vortex sheet caused by this process are studied. Many previous and classical results can be considered as particular cases of this paper, such as the solutions of the fractional diffusion equations obtained by Wyss; the classical Rayleigh’s time-space similarity solution; the relationship between stress field and velocity field obtained by Bagley and co-worker and Podlubny’s results on the fractional motion equation of a plate. In addition, a lot of significant results also are obtained. For example, the necessary condition for causing the vortex sheet is that the time fractional diffusion index β must be greater than that of generalized second order fluid α; the establiihment of the vorticity distribution function depends on the time history of the velocity profile at a given point, and the time history can be described by the fractional calculus.展开更多
Background Previous studies have demonstrated that serum uric acid （UA） is an independent predictor of incident type 2 diabetes mellitus （T2DM） in general populations. This study aimed to investigate specific char...Background Previous studies have demonstrated that serum uric acid （UA） is an independent predictor of incident type 2 diabetes mellitus （T2DM） in general populations. This study aimed to investigate specific characteristics of UA and its relationship between UA and blood glucose and other risk factors in the Chinese population.Methods A total of 946 subjects were included in this study. UA, glucose, insulin, fractional excretion of UA （FEua）,creatinine clearance rate （Ccr）, hemoglobin A1c （HbA1c）, fructosamine （FA）, blood pressure and lipids were studied and also reexamined after the patients underwent two weeks of combined therapeutics.Results UA levels were the highest in subjects with impaired glucose regulation （IGR）, followed by subjects with normoglycemia （NGT） and finally by subjects with T2DM. The level of the 2-hour postprandial insulin and the area under the curve for insulin （AUCins） showed a similar tendency. The UA levels initially increased with increasing fasting blood glucose （FBG） and postprandial blood glucose （PPBG） levels, up to 7 mmol/L and 10 mmol/L, respectively, and thereafter decreased at higher FBG and PPBG levels. Compared with subjects in the lower serum UA quartile, subjects in the upper quartile of serum UA levels had higher weights, triglyceride levels, and creatinine levels as well as lower Ccr and FEua levels. Compared with women＇s group, UA levels were higher, and FEua levels were lower in men＇s group. Sex,body mass index （BMI）, mean arterial blood pressure （MAP）, serum triglycerides （TG）, FA and Ccr were independent correlation factors of UA. UA decreased and FEua increased after the patients underwent a combined treatment.Conclusions UA increased initially and then decreased as glucose levels increased from NGT to IGR and T2DM.Compared with NGT and T2DM, IGR subjects had higher SUA levels, which related to its high levels of insulin. Under T2DM, male gender, BMI, MAP, Ccr, TG and FA are independent correlation factors展开更多
In this paper, a multiple parameters weighted fractional Fourier transform(MPWFRFT) and constellation scrambling(CS) method based physical layer(PHY) security system is proposed. The proposed scheme is executed by two...In this paper, a multiple parameters weighted fractional Fourier transform(MPWFRFT) and constellation scrambling(CS) method based physical layer(PHY) security system is proposed. The proposed scheme is executed by two steps. In the first step, MPWFRFT, implemented as the constellation beguiling(CB) method, is applied to change the signal's identity. In the second step the additional pseudo random phase information, regarded as the encryption key, is attached to the original signal to enhance the security. Typically, the pseudo random phase information can be removed effectively by the legitimate receiver. In contrast to the cryptography based encryption algorithms and the conventional PHY secrecy techniques, the main contribution of the proposed scheme is concentrated on the variation in signal's characteristics. Simulation results show that the proposed scheme can prevent the exchanging signal from eavesdroppers' classifi cation or inception. Moreover, the proposed scheme can guarantee the BER performance at a tolerate increasing in computational complexity for the legitimate receivers.展开更多
As the fractional Fourier transform has attracted a considerable amount of attention in the area of optics and signal processing, the discretization of the fractional Fourier transform becomes vital for the applicatio...As the fractional Fourier transform has attracted a considerable amount of attention in the area of optics and signal processing, the discretization of the fractional Fourier transform becomes vital for the application of the fractional Fourier transform. Since the discretization of the fractional Fourier transform cannot be obtained by directly sampling in time domain and the fractional Fourier domain, the discretization of the fractional Fourier transform has been investigated recently. A summary of discretizations of the fractional Fourier transform developed in the last nearly two decades is presented in this paper. The discretizations include sampling in the fractional Fourier domain, discrete-time fractional Fourier transform, fractional Fourier series, discrete fractional Fourier transform （including 3 main types： linear combination-type; sampling-type; and eigen decomposition-type）, and other discrete fractional signal transform. It is hoped to offer a doorstep for the readers who are interested in the fractional Fourier transform.展开更多
In this paper we give the (L^p(ω~p),L^q(ω~q)) boundedness for a class of multilinear operators, which is similar to the higher-order commutator for the rough fractional integral.In our results the kernel function is...In this paper we give the (L^p(ω~p),L^q(ω~q)) boundedness for a class of multilinear operators, which is similar to the higher-order commutator for the rough fractional integral.In our results the kernel function is merely assumed on a size condition.展开更多
The fractional calculus approach in the constitutive relationship model of viscoelastic fluid is introduced.The flow near a wall suddenly set in mo- tion is studied for a non-Newtonian viscoelastic fluid with the frac...The fractional calculus approach in the constitutive relationship model of viscoelastic fluid is introduced.The flow near a wall suddenly set in mo- tion is studied for a non-Newtonian viscoelastic fluid with the fractional Maxwell model.Exact solutions of velocity and stress are obtained by using the discrete in- verse Laplace transform of the sequential fractional derivatives.It is found that the effect of the fractional orders in the constitutive relationship on the flow field is signif- icant.The results show that for small times there are appreciable viscoelastic effects on the shear stress at the plate,for large times the viscoelastic effects become weak.展开更多
The Noether and Lie symmetries as well as the conserved quantities of Hamiltonian system with fractional derivatives are es-tablished. The definitions and criteria for the fractional symmetrical transformations and qu...The Noether and Lie symmetries as well as the conserved quantities of Hamiltonian system with fractional derivatives are es-tablished. The definitions and criteria for the fractional symmetrical transformations and quasi-symmetrical transformations inthe Noether sense of Hamiltonian system are first discussed. Then, using the invariance of Hamiltonian action under the infini-tesimal transformations with respect to time, generalized coordinates and generalized momentums, the fractional Noethertheorem of the system is obtained. Further, the Lie symmetry and conserved quantity of the system are acquired. Two exam-ples are presented to illustrate the application of the results.展开更多
基金supported by the National Natural Science Foundation of China (Grant No. 41130313)by the Strategic Priority Research Program (B) of the Chinese Academy of Sciences (Grant No. XDB03010200)
文摘Granite is one of the most important components of the continental crust on our Earth; it thus has been an enduring studied subject in geology. According to present knowledge, granite shows a great deal of heterogeneity in terms of its texture,structure, mineral species and geochemical compositions at different scales from small dike to large batholith. However, the reasons for these variations are not well understood although numerous interpretations have been proposed. The key point of this debate is whether granitic magma can be effectively differentiated through fractional crystallization, and, if so, what kind of crystallization occurred during the magmatic evolution. Although granitic magma has high viscosity because of its elevated SiO2 content, we agree that fractional crystallization is effectively processed during its evolution based on the evidence from field investigation,mineral species and its chemical variations, and geochemical compositions. These data indicate that crystal settling by gravitation is not the only mechanism dominating granitic differentiation. On the contrary, flow segregation or dynamic sorting may be more important. Accordingly, granite can be divided into unfractionated, fractionated(including weakly fractionated and highly fractionated) and cumulated types, according to the differentiation degree. Highly fractionated granitic magmas are generally high in primary temperature or high with various volatiles during the later stage, which make the fractional crystallization much easier than the common granitic melts. In addition, effective magmatic differentiation can be also expected when the magma emplaced along a large scale of extensional structure. Highly fractionated granitic magma is easily contaminated by country rocks due to its relatively prolonged crystallization time. Thus, granites do not always reflect the characteristics of the source areas and the physical and chemical conditions of the primary magma. We proposed that highly fractionated granites are an important sig
文摘This paper presents a new method for the detection and parameter estimation of multicomponent LFM signals based on the fractional Fourier transform. For the optimization in the fractional Fourier domain, an algorithm based on Quasi-Newton method is proposed which consists of two steps of searching, leading to a reduction in computation without loss of accuracy. And for multicomponent signals, we further propose a signal separation technique in the fractional Fourier domain which can effectively suppress the interferences on the detection of the weak components brought by the stronger components. The statistical analysis of the estimate errors is also performed which perfects the method theoretically, and finally, simulation results are provided to show the validity of our method.
基金supported by the National Natural Science Foundation of China(Grant Nos.60232010 and 60572094)the Teaching and Research Award for 0utstanding Young Teachers in Higher Education Institutions of M0E,P.R.C.the Ministerial Foundation of China(Grant No.6140445).
文摘The fractional Fourier transform is a generalization of the classical Fourier transform, which is introduced from the mathematic aspect by Namias at first and has many applications in optics quickly. Whereas its potential appears to have remained largely unknown to the signal processing community until 1990s. The fractional Fourier transform can be viewed as the chirp-basis expansion directly from its definition, but essentially it can be interpreted as a rotation in the time-frequency plane, i.e. the unified time-frequency transform. With the order from 0 increasing to 1, the fractional Fourier transform can show the characteristics of the signal changing from the time domain to the frequency domain. In this research paper, the fractional Fourier transform has been comprehensively and systematically treated from the signal processing point of view. Our aim is to provide a course from the definition to the applications of the fractional Fourier transform, especially as a reference and an introduction for researchers and interested readers.
基金Supported by China Postdoctoral Science Foundation (Grant No. 20060401016), Fondation Franco-Chinoise Pour La Science Et Ses Applications (FFCSA)the National Natural Science Foundation of China (Grant No. 60572033)the Doctor Foundation of China National Education Department (Grant No. 20060610021)
文摘This paper mainly discusses fractional differential approach to detecting textural features of digital image and its fractional differential filter. Firstly, both the geo- metric meaning and the kinetic physical meaning of fractional differential are clearly explained in view of information theory and kinetics, respectively. Secondly, it puts forward and discusses the definitions and theories of fractional stationary point, fractional equilibrium coefficient, fractional stable coefficient, and fractional grayscale co-occurrence matrix. At the same time, it particularly discusses frac- tional grayscale co-occurrence matrix approach to detecting textural features of digital image. Thirdly, it discusses in detail the structures and parameters of nxn any order fractional differential mask on negative x-coordinate, positive x-coordi- nate, negative y-coordinate, positive y-coordinate, left downward diagonal, left upward diagonal, right downward diagonal, and right upward diagonal, respectively. Furthermore, it discusses the numerical implementation algorithms of fractional differential mask for digital image. Lastly, based on the above-mentioned discus- sion, it puts forward and discusses the theory and implementation of fractional differential filter for digital image. Experiments show that the fractional differential-based image operator has excellent feedback for enhancing the textural details of rich-grained digital images.
基金This work was partially supported by the National Natural Science Foundation of China(Grant Nos.10571014,10371080)the Doctoral Programme Foundation of Institute of Higher Education of China(Grant No.20040027001)
文摘In this paper,it was proved that the commutator H_(β,b)generated by an n-dimensional fractional Hardy operator and a locally integrable function b is bounded from L^(p1)(R^n)to L^(p2)(R^n)if and only if b is a CMO(R^n)function,where 1/p1-1/p2=β/n,1<p1<∞,0≤β<n.Furthermore, the characterization of H_(β,b)on the homogenous Herz space K_q^(α,p)(R^n)was obtained.
文摘Background The computational fluid dynamics(CFD)approach has been frequently applied to compute the fractional flow reserve(FFR)using computed tomography angiography(CTA).This technique is efficient.We developed the DEEPVESSEL-FFR platform using the emerging deep learning technique to calculate the FFR value out of CTA images in five minutes.This study is to evaluate the DEEPVESSEL-FFR platform using the emerging deep learning technique to calculate the FFR value from CTA images as an efficient method.Methods A single-center,prospective study was conducted and 63 patients were enrolled for the evaluation of the diagnostic performance of DEEPVESSEL-FFR.Automatic quantification method for the three-dimensional coronary arterial geometry and the deep learning based prediction of FFR were developed to assess the ischemic risk of the stenotic coronary arteries.Diagnostic performance of the DEEPVESSEL-FFR was assessed by using wire-based FFR as reference standard.The primary evaluation factor was defined by using the area under receiver-operation characteristics curve(AUC)analysis.Results For per-patient level,taking the cut-off value<0.8 referring to the FFR measurement,DEEPVESSEL-FFR presented higher diagnostic performance in determining ischemia-related lesions with area under the curve of 0.928 compare to CTA stenotic severity 0.664.DEEPVESSEL-FFR correlated with FFR(R=0.686,P<0.001),with a mean di&ference of-0.006士0.0091(P=0.619).The secondary evaluation factors,indicating per vessel accuracy,sensitivity,specificity,positive predictive value,and negative predictive value were 87.3%,97.14%,75%,82.93%,and 95.45%,respectively.Conclusion DEEPVESSEL-FFR is a novel method that allows efficient assessment of the functional significance of coronary stenosis.
基金the Doctoral Program Foundation of the Ministry of Education of China,the National Natural Science Foundation of China(Grant Nos.10272067 and 10002003)the Foundation for University Key Teacher by the Ministry of Education.
文摘The generalized fractional element networks are presented in this paper. In order to extend the structure of the model solutions to the generalized function space and make it contain more physical meanings, the restriction on the parameters of the fractional element proposed by Schiessel et al. is eliminated and a 'compatibility equation' is added. The discretization method for solving the inverse Laplace transform is used and developed. The generalized solutions of the model equations are given. At the same time the generalized fractional element network--Zener and Poyinting-Thomson models are discussed in detail. It is shown that all the results obtained previously about the models of single parameter with fractional order and the classical models with integer order can be contained as the special cases of the results of this paper.
基金the Doctoral Program Foundation of the Education Ministry of China the National Natural Science Foundation of China (Grant No. 10002003) Foundation for University Key Teacher by the Ministry of Education of China.
文摘The velocity field of generalized second order fluid with fractional anomalous diiusion caused by a plate moving impulsively in its own plane is investigated and the anomalous diffusion problems of the stress field and vortex sheet caused by this process are studied. Many previous and classical results can be considered as particular cases of this paper, such as the solutions of the fractional diffusion equations obtained by Wyss; the classical Rayleigh’s time-space similarity solution; the relationship between stress field and velocity field obtained by Bagley and co-worker and Podlubny’s results on the fractional motion equation of a plate. In addition, a lot of significant results also are obtained. For example, the necessary condition for causing the vortex sheet is that the time fractional diffusion index β must be greater than that of generalized second order fluid α; the establiihment of the vorticity distribution function depends on the time history of the velocity profile at a given point, and the time history can be described by the fractional calculus.
文摘Background Previous studies have demonstrated that serum uric acid （UA） is an independent predictor of incident type 2 diabetes mellitus （T2DM） in general populations. This study aimed to investigate specific characteristics of UA and its relationship between UA and blood glucose and other risk factors in the Chinese population.Methods A total of 946 subjects were included in this study. UA, glucose, insulin, fractional excretion of UA （FEua）,creatinine clearance rate （Ccr）, hemoglobin A1c （HbA1c）, fructosamine （FA）, blood pressure and lipids were studied and also reexamined after the patients underwent two weeks of combined therapeutics.Results UA levels were the highest in subjects with impaired glucose regulation （IGR）, followed by subjects with normoglycemia （NGT） and finally by subjects with T2DM. The level of the 2-hour postprandial insulin and the area under the curve for insulin （AUCins） showed a similar tendency. The UA levels initially increased with increasing fasting blood glucose （FBG） and postprandial blood glucose （PPBG） levels, up to 7 mmol/L and 10 mmol/L, respectively, and thereafter decreased at higher FBG and PPBG levels. Compared with subjects in the lower serum UA quartile, subjects in the upper quartile of serum UA levels had higher weights, triglyceride levels, and creatinine levels as well as lower Ccr and FEua levels. Compared with women＇s group, UA levels were higher, and FEua levels were lower in men＇s group. Sex,body mass index （BMI）, mean arterial blood pressure （MAP）, serum triglycerides （TG）, FA and Ccr were independent correlation factors of UA. UA decreased and FEua increased after the patients underwent a combined treatment.Conclusions UA increased initially and then decreased as glucose levels increased from NGT to IGR and T2DM.Compared with NGT and T2DM, IGR subjects had higher SUA levels, which related to its high levels of insulin. Under T2DM, male gender, BMI, MAP, Ccr, TG and FA are independent correlation factors
基金supported by the National Basic Research Program of China under Grant 2013CB329003in part by the National Natural Science Foundation General Program of China under Grant 61171110
文摘In this paper, a multiple parameters weighted fractional Fourier transform(MPWFRFT) and constellation scrambling(CS) method based physical layer(PHY) security system is proposed. The proposed scheme is executed by two steps. In the first step, MPWFRFT, implemented as the constellation beguiling(CB) method, is applied to change the signal's identity. In the second step the additional pseudo random phase information, regarded as the encryption key, is attached to the original signal to enhance the security. Typically, the pseudo random phase information can be removed effectively by the legitimate receiver. In contrast to the cryptography based encryption algorithms and the conventional PHY secrecy techniques, the main contribution of the proposed scheme is concentrated on the variation in signal's characteristics. Simulation results show that the proposed scheme can prevent the exchanging signal from eavesdroppers' classifi cation or inception. Moreover, the proposed scheme can guarantee the BER performance at a tolerate increasing in computational complexity for the legitimate receivers.
基金the National Natural Science Foundation of China (Grant Nos.60232010 and 60572094)the National Natural Science Founda-tion of China for Distinguished Young Scholars (Grant No.60625104)
文摘As the fractional Fourier transform has attracted a considerable amount of attention in the area of optics and signal processing, the discretization of the fractional Fourier transform becomes vital for the application of the fractional Fourier transform. Since the discretization of the fractional Fourier transform cannot be obtained by directly sampling in time domain and the fractional Fourier domain, the discretization of the fractional Fourier transform has been investigated recently. A summary of discretizations of the fractional Fourier transform developed in the last nearly two decades is presented in this paper. The discretizations include sampling in the fractional Fourier domain, discrete-time fractional Fourier transform, fractional Fourier series, discrete fractional Fourier transform （including 3 main types： linear combination-type; sampling-type; and eigen decomposition-type）, and other discrete fractional signal transform. It is hoped to offer a doorstep for the readers who are interested in the fractional Fourier transform.
基金This research is supported by the NNSF (Grant:19971010)National 973 Project of China.
文摘In this paper we give the (L^p(ω~p),L^q(ω~q)) boundedness for a class of multilinear operators, which is similar to the higher-order commutator for the rough fractional integral.In our results the kernel function is merely assumed on a size condition.
基金The project supported by the National Natural Science Foundation of China (10002003)Foundation for University Key Teacher by the Ministry of EducationResearch Fund for the Doctoral Program of Higher Education
文摘The fractional calculus approach in the constitutive relationship model of viscoelastic fluid is introduced.The flow near a wall suddenly set in mo- tion is studied for a non-Newtonian viscoelastic fluid with the fractional Maxwell model.Exact solutions of velocity and stress are obtained by using the discrete in- verse Laplace transform of the sequential fractional derivatives.It is found that the effect of the fractional orders in the constitutive relationship on the flow field is signif- icant.The results show that for small times there are appreciable viscoelastic effects on the shear stress at the plate,for large times the viscoelastic effects become weak.
基金supported by the National Natural Science Foundation of China (Grant No. 11072218)
文摘The Noether and Lie symmetries as well as the conserved quantities of Hamiltonian system with fractional derivatives are es-tablished. The definitions and criteria for the fractional symmetrical transformations and quasi-symmetrical transformations inthe Noether sense of Hamiltonian system are first discussed. Then, using the invariance of Hamiltonian action under the infini-tesimal transformations with respect to time, generalized coordinates and generalized momentums, the fractional Noethertheorem of the system is obtained. Further, the Lie symmetry and conserved quantity of the system are acquired. Two exam-ples are presented to illustrate the application of the results.
