A class of nonlinear and continuous type Leontief model and its corresponding conditional input-output equation are introduced, and two basic problems under the so called positive or negative boundary assumption are p...A class of nonlinear and continuous type Leontief model and its corresponding conditional input-output equation are introduced, and two basic problems under the so called positive or negative boundary assumption are presented. By approaches of nonlinear analysis some solvability results of this equation and continuous perturbation properties of the relative solution sets are obtained, and some economic significance are illustrated by the remark.展开更多
Aim To analyze the fragmentation patterns of diquaternary dipiperaziniumscontaining dithiocarboxyl groups. Methods Positive ion electrospray ionization mass spectrometry inconjunction with tandem mass spectrometry (ES...Aim To analyze the fragmentation patterns of diquaternary dipiperaziniumscontaining dithiocarboxyl groups. Methods Positive ion electrospray ionization mass spectrometry inconjunction with tandem mass spectrometry (ESI-MS^n) was used. Results The fragment ion [M^(2+) Cl^-]^+ showed characteristic double peaks with high intensity instead of the parent molecular ionbeing detected. And [M^(2+) - CH_3^+ ]^+ ion had relatively low intensity. Meanwhile, [M^(2+) Cl^- -Cl^- - PhCH_2^+ ]^+ species had the highest intensity as the base peak, which was originated from[M^(2+) Cl^- ]^+, The detailed fragmentation mechanisms are supported with the tandem massspectrometry.展开更多
This paper presents truncation errors among Corrector Formula for left Rectangular rule and Corrector Formula for middle Rectangular rule respectively. It also displays an analysis on convergence order of compound cor...This paper presents truncation errors among Corrector Formula for left Rectangular rule and Corrector Formula for middle Rectangular rule respectively. It also displays an analysis on convergence order of compound corrector formulas for rectangular rule. Examples of numerical calculation have validated theoretical analysis.展开更多
Using the high-speed camera the time sequences of the classical flow patterns of horizontal gas-liquid pipe flow are recorded, from which the average gray-scale values of single-frame images are extracted. Thus obtain...Using the high-speed camera the time sequences of the classical flow patterns of horizontal gas-liquid pipe flow are recorded, from which the average gray-scale values of single-frame images are extracted. Thus obtained gray-scale time series is decomposed by the Empirical Mode Decomposition (EMD) method, the various scales of the signals are processed by Hurst exponent method, and then the dual-fractal characteristics are obtained. The scattered bubble and the bubble cluster theories are applied to the evolution analysis of two-phase flow patterns. At the same time the various signals are checked in the chaotic recursion chart by which the two typical characteristics (diagonal average length and Shannon entropy) are obtained. Resulting term of these properties, the dynamic characteristics of gas-liquid two-phase flow patterns are quantitatively analyzed. The results show that the evolution paths of gas-liquid two-phase flow patterns can be well characterized by the integrated analysis on the basis of the gray-scale time series of flowing images from EMD, Hurst exponents and Recurrence Plot (RP). In the middle frequency section (2nd, 3rd, 4th scales), three flow patterns decomposed by the EMD exhibit dual fractal characteristics which represent the dynamic features of bubble cluster, single bubble, slug bubble and scattered bubble. According to the change of diagonal average lengths and recursive Shannon entropy characteristic value, the structure deterministic of the slug flow is better than the other two patterns. After the decomposition by EMD the slug flow and the mist flow in the high frequency section have obvious peaks. Anyway, it is an effective way to understand and characterize the dynamic characteristics of two-phase flow patterns using the multi-scale non-linear analysis method based on image gray-scale fluctuation signals.展开更多
The near crack line analysis method was used to investigate a crack loaded by a pair of point shear forces in an infinite plate in an elastic-perfectly plastic solid. The analytical solution was obtained, that is the ...The near crack line analysis method was used to investigate a crack loaded by a pair of point shear forces in an infinite plate in an elastic-perfectly plastic solid. The analytical solution was obtained, that is the elastic-plastic fields near crack line and law that the length of the plastic zone along the crack line is varied with external loads. The results are sufficiently precise near the crack line and are not confined by small scale yielding conditions.展开更多
In this paper, let T be a bounded linear operator on a complex Hilbert H. We give and prove that every p-w-hyponormal operator has Bishop's property(β) and spectral properties; Quasi-similar p-w-hyponormal operat...In this paper, let T be a bounded linear operator on a complex Hilbert H. We give and prove that every p-w-hyponormal operator has Bishop's property(β) and spectral properties; Quasi-similar p-w-hyponormal operators have equal spectra and equal essential spectra. Finally, for p-w-hyponormal operators, we give a kind of proof of its normality by use of properties of partial isometry.展开更多
In this paper, we investigate not only the acceleration problem of the q-Bernstein polynomials Bn(f, q; x) to B∞ (f, q; x) but also the convergence of their iterated Boolean sum. Using the methods of exact estima...In this paper, we investigate not only the acceleration problem of the q-Bernstein polynomials Bn(f, q; x) to B∞ (f, q; x) but also the convergence of their iterated Boolean sum. Using the methods of exact estimate and theories of modulus of smoothness, we get the respective estimates of the convergence rate, which suggest that q-Bernstein polynomials have the similar answer with the classical Bernstein polynomials to these two problems.展开更多
We present a Darboux transformation for Tzitzeica equation associated with 3 × 3 matrix spectral problem.The explicit solution of Tzitzeica equation is obtained,
In this paper, we first give the concept of weakly P-inversive semigroup S(P). Then we describe the strong P-congruences on S(P) in terms of their P-kernel normal systems. It is proved that there is a bijection be...In this paper, we first give the concept of weakly P-inversive semigroup S(P). Then we describe the strong P-congruences on S(P) in terms of their P-kernel normal systems. It is proved that there is a bijection between the strong P-congruences and the P-kernel normal systems. Finally, it is also prove that the lattice of strong P-congruences and the lattice of P-kernel normal systems on S(P) are isomorphic.展开更多
A kind of electric circuit is improved to optimize the linearity of edge filter demodulators in FBG .By using a logarithm amplifier and an extraction operation, the linear range of optimized edge filter demodulators h...A kind of electric circuit is improved to optimize the linearity of edge filter demodulators in FBG .By using a logarithm amplifier and an extraction operation, the linear range of optimized edge filter demodulators has been broadened effectively, and the requirement of optical filter's linear range has been reduced. Theoretical analyses and the simulation results indi-cated that the linear range of optimized edge fdter demodulator's covers the whole transition region of the edge filter, while a strict linearity of the optical filter is not necessary.展开更多
In this paper, an explicit Bgcklund transformation (BT) of the Burgers equation is obtained by using the further extended tanh method [Phys. Lett. A 307 (2003) 269; Chaos, Solitons & Fractals 17 (2003) 669]. Ba...In this paper, an explicit Bgcklund transformation (BT) of the Burgers equation is obtained by using the further extended tanh method [Phys. Lett. A 307 (2003) 269; Chaos, Solitons & Fractals 17 (2003) 669]. Based on the BT and some newly obtained seed solutions, infinite sequences of exact solutions for the Burgers equation are generated. Further more, this BT of the Burgers equation is applied to solve the variant Boussinesq equations and the approximate equations of long water wave.展开更多
In order to maintain vibration performances within the limits of the design, a vibration-based feature extraction method for dynamic characteristic using empirical mode decomposition (EMD) and wavelet analysis was p...In order to maintain vibration performances within the limits of the design, a vibration-based feature extraction method for dynamic characteristic using empirical mode decomposition (EMD) and wavelet analysis was proposed. The proposed method was verified experimentally and numerically by implementing the scheme on engine block. In the implementation process, the following steps were identified to be important: 1) EMD technique in order to solve the feature extraction of vibration signals; 2) Vibration measurement for the purpose of confirming the structural weak regions of engine block in experiment; 3) Finite element modeling for the purpose of determining dynamic characteristic in time region and frequency region to affirm the comparability of response character corresponding to improvement schemes; 4) Adopting a feature index oflMF for structural improvement based on EMD and wavelet analysis. The obtained results show that IMF of signal is more sensitive to response character corresponding to improvement schemes. Finally, examination of the results confirms that the proposed vibration-based feature extraction method is very robust, and focuses on the relative merits of modification and full-scale structural optimization of engine, together with the creation of new low-vibration designs.展开更多
In this paper, to construct exact solution of nonlinear partial differential equation, an easy-to-use approach is proposed. By means of the transformation of the independent variables and the travelling wave transform...In this paper, to construct exact solution of nonlinear partial differential equation, an easy-to-use approach is proposed. By means of the transformation of the independent variables and the travelling wave transformation, the partial differential equation is reduced to an ordinary differential equation. To solve the ordinary differential equation, we assume the soliton solution in the explicit expression and obtain the travelling wave solution. By the transformation back to the original independent variables, the soliton solution of the original partial differential equation is derived. We investigate the short wave model for the Camassa-Holm equation and the Degasperis-Procesi equation respectively. One-cusp soliton solution of the Camassa-Flolm equation is obtained. One-loop soliton solution of the Degasperis- Procesi equation is also obtained, the approximation of which in a closed form can be obtained firstly by the Adomian decomposition method. The obtained results in a parametric form coincide perfectly with those given in the present reference. This illustrates the efficiency and reliability of our approach.展开更多
This paper deals with the oscillatory properties of a class of nonlinear neutralparabolic partial differential equations with several delays. Sufficient criteria for the equa-tion to be oscillatory are obtained by mak...This paper deals with the oscillatory properties of a class of nonlinear neutralparabolic partial differential equations with several delays. Sufficient criteria for the equa-tion to be oscillatory are obtained by making use of some results of first-order functionaldifferential inequalities. These results fully reveal the essential difference between this typeand that without delays.展开更多
How lfinally lost my heart is a short story written by Doris Lessing, the winner of the 2007 Nobel Prize in Literature. This paper is intended to analyze this short story from the feminist perspective, and show the ex...How lfinally lost my heart is a short story written by Doris Lessing, the winner of the 2007 Nobel Prize in Literature. This paper is intended to analyze this short story from the feminist perspective, and show the exact process of women's emotional independence as well as the writer's concern on women's thorough liberation.展开更多
Hyponatremia, serum sodium 〈 135 mEq/L, is themost common electrolyte abnormality and is in a state of flux. Hyponatremic patients are symptomatic and should be treated but our inability to consistently determine the...Hyponatremia, serum sodium 〈 135 mEq/L, is themost common electrolyte abnormality and is in a state of flux. Hyponatremic patients are symptomatic and should be treated but our inability to consistently determine the causes of hyponatremia has hampered the delivery of appropriate therapy. This is especially applicable to differentiating syndrome of inappropriate antidiuresis (SIAD) from cerebral salt wasting (CSW) or more appropriately, renal salt wasting (RSW), because of divergent therapeutic goals, to water-restrict in SIAD and administer salt and water in RSW. Differentiating SIAD from RSW is extremely diffcult because of identical clinical parameters that defne both syndromes and the mindset that CSW occurs rarely. It is thus insuffcient to make the diagnosis of SIAD simply because it meets the defned characteristics. We review the pathophysiology of SIAD and RSW, the evolution of an algorithm that is based on determinations of fractional excretion of urate and distinctive responses to saline infusions to differentiate SIAD from RSW. This algorithm also simplifes the diagnosis of hyponatremic patients due to Addison’s disease, reset osmostat and prerenal states. It is a common perception that we cannot accurately assess the volume status of a patient by clinical criteria. Our algorithm eliminates the need to determine the volume status with the realization that too many factors affect plasma renin, aldosterone, atrial/brain natriuretic peptide or urine sodium concentration to be useful. Reports and increasing recognition of RSW occurring in patients without evidence of cerebral disease should thus elicit the need to consider RSW in a broader group of patients and to question any diagnosis of SIAD. Based on the accumulation of supporting data, we make the clinically important proposal to change CSW to RSW, to eliminate reset osmostat as type C SIAD and stress the need for a new defnition of SIAD.展开更多
Vehicle ad-hoc networks have developed rapidly these years,whose security and privacy issues are always concerned widely.In spite of a remarkable research on their security solutions,but in which there still lacks con...Vehicle ad-hoc networks have developed rapidly these years,whose security and privacy issues are always concerned widely.In spite of a remarkable research on their security solutions,but in which there still lacks considerations on how to secure vehicleto-vehicle communications,particularly when infrastructure is unavailable.In this paper,we propose a lightweight certificateless and oneround key agreement scheme without pairing,and further prove the security of the proposed scheme in the random oracle model.The proposed scheme is expected to not only resist known attacks with less computation cost,but also as an efficient way to relieve the workload of vehicle-to-vehicle authentication,especially in no available infrastructure circumstance.A comprehensive evaluation,including security analysis,efficiency analysis and simulation evaluation,is presented to confirm the security and feasibility of the proposed scheme.展开更多
Based on the homogenous balance method and with the help of mathematica, the Backlund transformation and the transfer heat equation are derived. Analyzing the heat-transfer equation, the multiple soliton solutions and...Based on the homogenous balance method and with the help of mathematica, the Backlund transformation and the transfer heat equation are derived. Analyzing the heat-transfer equation, the multiple soliton solutions and other exact analytical solution for Whitham-Broer-Kaup equations(WBK) are derived. These solutions contain Fan's, Xie's and Yan's results and other new types of analytical solutions, such as rational function solutions and periodic solutions. The method can also be applied to solve more nonlinear differential equations.展开更多
Complex dynamics are studied in the T system, a three-dimensional autonomous nonlinear system. In particular, we perform an extended Hopf bifurcation analysis of the system. The periodic orbit immediately following th...Complex dynamics are studied in the T system, a three-dimensional autonomous nonlinear system. In particular, we perform an extended Hopf bifurcation analysis of the system. The periodic orbit immediately following the Hopf bifurcation is constructed analytically for the T system using the method of multiple scales, and the stability of such orbits is analyzed. Such analytical results complement the numerical results present in the literature. The analytical results in the post-bifurcation regime are verified and extended via numerical simulations, as well as by the use of standard power spectra, autocorrelation functions, and fractal dimensions diagnostics. We find that the T system exhibits interesting behaviors in many parameter regimes.展开更多
文摘A class of nonlinear and continuous type Leontief model and its corresponding conditional input-output equation are introduced, and two basic problems under the so called positive or negative boundary assumption are presented. By approaches of nonlinear analysis some solvability results of this equation and continuous perturbation properties of the relative solution sets are obtained, and some economic significance are illustrated by the remark.
文摘Aim To analyze the fragmentation patterns of diquaternary dipiperaziniumscontaining dithiocarboxyl groups. Methods Positive ion electrospray ionization mass spectrometry inconjunction with tandem mass spectrometry (ESI-MS^n) was used. Results The fragment ion [M^(2+) Cl^-]^+ showed characteristic double peaks with high intensity instead of the parent molecular ionbeing detected. And [M^(2+) - CH_3^+ ]^+ ion had relatively low intensity. Meanwhile, [M^(2+) Cl^- -Cl^- - PhCH_2^+ ]^+ species had the highest intensity as the base peak, which was originated from[M^(2+) Cl^- ]^+, The detailed fragmentation mechanisms are supported with the tandem massspectrometry.
文摘This paper presents truncation errors among Corrector Formula for left Rectangular rule and Corrector Formula for middle Rectangular rule respectively. It also displays an analysis on convergence order of compound corrector formulas for rectangular rule. Examples of numerical calculation have validated theoretical analysis.
基金Supported by the National Natural Science Foundation of China (50976018) the Natural Science Foundation of JilinProvince (20101562)
文摘Using the high-speed camera the time sequences of the classical flow patterns of horizontal gas-liquid pipe flow are recorded, from which the average gray-scale values of single-frame images are extracted. Thus obtained gray-scale time series is decomposed by the Empirical Mode Decomposition (EMD) method, the various scales of the signals are processed by Hurst exponent method, and then the dual-fractal characteristics are obtained. The scattered bubble and the bubble cluster theories are applied to the evolution analysis of two-phase flow patterns. At the same time the various signals are checked in the chaotic recursion chart by which the two typical characteristics (diagonal average length and Shannon entropy) are obtained. Resulting term of these properties, the dynamic characteristics of gas-liquid two-phase flow patterns are quantitatively analyzed. The results show that the evolution paths of gas-liquid two-phase flow patterns can be well characterized by the integrated analysis on the basis of the gray-scale time series of flowing images from EMD, Hurst exponents and Recurrence Plot (RP). In the middle frequency section (2nd, 3rd, 4th scales), three flow patterns decomposed by the EMD exhibit dual fractal characteristics which represent the dynamic features of bubble cluster, single bubble, slug bubble and scattered bubble. According to the change of diagonal average lengths and recursive Shannon entropy characteristic value, the structure deterministic of the slug flow is better than the other two patterns. After the decomposition by EMD the slug flow and the mist flow in the high frequency section have obvious peaks. Anyway, it is an effective way to understand and characterize the dynamic characteristics of two-phase flow patterns using the multi-scale non-linear analysis method based on image gray-scale fluctuation signals.
基金National Natural Science Foundation ofChina( No.5 98790 12 )
文摘The near crack line analysis method was used to investigate a crack loaded by a pair of point shear forces in an infinite plate in an elastic-perfectly plastic solid. The analytical solution was obtained, that is the elastic-plastic fields near crack line and law that the length of the plastic zone along the crack line is varied with external loads. The results are sufficiently precise near the crack line and are not confined by small scale yielding conditions.
基金Natural Science and Education Foundation of Henan Province(2007110016)
文摘In this paper, let T be a bounded linear operator on a complex Hilbert H. We give and prove that every p-w-hyponormal operator has Bishop's property(β) and spectral properties; Quasi-similar p-w-hyponormal operators have equal spectra and equal essential spectra. Finally, for p-w-hyponormal operators, we give a kind of proof of its normality by use of properties of partial isometry.
文摘In this paper, we investigate not only the acceleration problem of the q-Bernstein polynomials Bn(f, q; x) to B∞ (f, q; x) but also the convergence of their iterated Boolean sum. Using the methods of exact estimate and theories of modulus of smoothness, we get the respective estimates of the convergence rate, which suggest that q-Bernstein polynomials have the similar answer with the classical Bernstein polynomials to these two problems.
基金The project supported by National Natural Science Foundation of China under Grant No. 10471132 and the Special Foundation for the State Key Basic Research Program "Nonlinear Sciencc"
文摘We present a Darboux transformation for Tzitzeica equation associated with 3 × 3 matrix spectral problem.The explicit solution of Tzitzeica equation is obtained,
基金the Science Research Foundation of Qingdao Technological University(C2002-214)
文摘In this paper, we first give the concept of weakly P-inversive semigroup S(P). Then we describe the strong P-congruences on S(P) in terms of their P-kernel normal systems. It is proved that there is a bijection between the strong P-congruences and the P-kernel normal systems. Finally, it is also prove that the lattice of strong P-congruences and the lattice of P-kernel normal systems on S(P) are isomorphic.
文摘A kind of electric circuit is improved to optimize the linearity of edge filter demodulators in FBG .By using a logarithm amplifier and an extraction operation, the linear range of optimized edge filter demodulators has been broadened effectively, and the requirement of optical filter's linear range has been reduced. Theoretical analyses and the simulation results indi-cated that the linear range of optimized edge fdter demodulator's covers the whole transition region of the edge filter, while a strict linearity of the optical filter is not necessary.
基金中国博士后科学基金,国家重点基础研究发展计划(973计划),the National Key Basic Research Project of China under
文摘In this paper, an explicit Bgcklund transformation (BT) of the Burgers equation is obtained by using the further extended tanh method [Phys. Lett. A 307 (2003) 269; Chaos, Solitons & Fractals 17 (2003) 669]. Based on the BT and some newly obtained seed solutions, infinite sequences of exact solutions for the Burgers equation are generated. Further more, this BT of the Burgers equation is applied to solve the variant Boussinesq equations and the approximate equations of long water wave.
基金Project(50975192) supported by the National Natural Science Foundation of ChinaProject(10YFJZJC14100) supported by Tianjin Municipal Natural Science Foundation of China
文摘In order to maintain vibration performances within the limits of the design, a vibration-based feature extraction method for dynamic characteristic using empirical mode decomposition (EMD) and wavelet analysis was proposed. The proposed method was verified experimentally and numerically by implementing the scheme on engine block. In the implementation process, the following steps were identified to be important: 1) EMD technique in order to solve the feature extraction of vibration signals; 2) Vibration measurement for the purpose of confirming the structural weak regions of engine block in experiment; 3) Finite element modeling for the purpose of determining dynamic characteristic in time region and frequency region to affirm the comparability of response character corresponding to improvement schemes; 4) Adopting a feature index oflMF for structural improvement based on EMD and wavelet analysis. The obtained results show that IMF of signal is more sensitive to response character corresponding to improvement schemes. Finally, examination of the results confirms that the proposed vibration-based feature extraction method is very robust, and focuses on the relative merits of modification and full-scale structural optimization of engine, together with the creation of new low-vibration designs.
基金the State Key Basic Research Program of China under Grant No.2004CB318000the Research Fund for the Doctoral Program of Higher Education of China under Grant No.20060269006
文摘In this paper, to construct exact solution of nonlinear partial differential equation, an easy-to-use approach is proposed. By means of the transformation of the independent variables and the travelling wave transformation, the partial differential equation is reduced to an ordinary differential equation. To solve the ordinary differential equation, we assume the soliton solution in the explicit expression and obtain the travelling wave solution. By the transformation back to the original independent variables, the soliton solution of the original partial differential equation is derived. We investigate the short wave model for the Camassa-Holm equation and the Degasperis-Procesi equation respectively. One-cusp soliton solution of the Camassa-Flolm equation is obtained. One-loop soliton solution of the Degasperis- Procesi equation is also obtained, the approximation of which in a closed form can be obtained firstly by the Adomian decomposition method. The obtained results in a parametric form coincide perfectly with those given in the present reference. This illustrates the efficiency and reliability of our approach.
基金Supported by the National Natural Science Foundation of China(40373003, 40372121)Supported by the Youth Foundation of Cina University of Geosciences(CUGQNL0517)
文摘This paper deals with the oscillatory properties of a class of nonlinear neutralparabolic partial differential equations with several delays. Sufficient criteria for the equa-tion to be oscillatory are obtained by making use of some results of first-order functionaldifferential inequalities. These results fully reveal the essential difference between this typeand that without delays.
文摘How lfinally lost my heart is a short story written by Doris Lessing, the winner of the 2007 Nobel Prize in Literature. This paper is intended to analyze this short story from the feminist perspective, and show the exact process of women's emotional independence as well as the writer's concern on women's thorough liberation.
文摘Hyponatremia, serum sodium 〈 135 mEq/L, is themost common electrolyte abnormality and is in a state of flux. Hyponatremic patients are symptomatic and should be treated but our inability to consistently determine the causes of hyponatremia has hampered the delivery of appropriate therapy. This is especially applicable to differentiating syndrome of inappropriate antidiuresis (SIAD) from cerebral salt wasting (CSW) or more appropriately, renal salt wasting (RSW), because of divergent therapeutic goals, to water-restrict in SIAD and administer salt and water in RSW. Differentiating SIAD from RSW is extremely diffcult because of identical clinical parameters that defne both syndromes and the mindset that CSW occurs rarely. It is thus insuffcient to make the diagnosis of SIAD simply because it meets the defned characteristics. We review the pathophysiology of SIAD and RSW, the evolution of an algorithm that is based on determinations of fractional excretion of urate and distinctive responses to saline infusions to differentiate SIAD from RSW. This algorithm also simplifes the diagnosis of hyponatremic patients due to Addison’s disease, reset osmostat and prerenal states. It is a common perception that we cannot accurately assess the volume status of a patient by clinical criteria. Our algorithm eliminates the need to determine the volume status with the realization that too many factors affect plasma renin, aldosterone, atrial/brain natriuretic peptide or urine sodium concentration to be useful. Reports and increasing recognition of RSW occurring in patients without evidence of cerebral disease should thus elicit the need to consider RSW in a broader group of patients and to question any diagnosis of SIAD. Based on the accumulation of supporting data, we make the clinically important proposal to change CSW to RSW, to eliminate reset osmostat as type C SIAD and stress the need for a new defnition of SIAD.
基金This work was supported in part by the National Natural Science Foundation of China under Grant No.61170217,61272469,61303212,61332019,and Grant No.U1135004,and by the Fundamental Research Founds for National University,China University of Geosciences
文摘Vehicle ad-hoc networks have developed rapidly these years,whose security and privacy issues are always concerned widely.In spite of a remarkable research on their security solutions,but in which there still lacks considerations on how to secure vehicleto-vehicle communications,particularly when infrastructure is unavailable.In this paper,we propose a lightweight certificateless and oneround key agreement scheme without pairing,and further prove the security of the proposed scheme in the random oracle model.The proposed scheme is expected to not only resist known attacks with less computation cost,but also as an efficient way to relieve the workload of vehicle-to-vehicle authentication,especially in no available infrastructure circumstance.A comprehensive evaluation,including security analysis,efficiency analysis and simulation evaluation,is presented to confirm the security and feasibility of the proposed scheme.
基金Supported by the National Nature Science Foundation of China(10371070)Supported by the Nature Science Foundation of Educational Committee of Liaoning Province(2021401157)
文摘Based on the homogenous balance method and with the help of mathematica, the Backlund transformation and the transfer heat equation are derived. Analyzing the heat-transfer equation, the multiple soliton solutions and other exact analytical solution for Whitham-Broer-Kaup equations(WBK) are derived. These solutions contain Fan's, Xie's and Yan's results and other new types of analytical solutions, such as rational function solutions and periodic solutions. The method can also be applied to solve more nonlinear differential equations.
文摘Complex dynamics are studied in the T system, a three-dimensional autonomous nonlinear system. In particular, we perform an extended Hopf bifurcation analysis of the system. The periodic orbit immediately following the Hopf bifurcation is constructed analytically for the T system using the method of multiple scales, and the stability of such orbits is analyzed. Such analytical results complement the numerical results present in the literature. The analytical results in the post-bifurcation regime are verified and extended via numerical simulations, as well as by the use of standard power spectra, autocorrelation functions, and fractal dimensions diagnostics. We find that the T system exhibits interesting behaviors in many parameter regimes.