With the help of the symbolic computation system, Maple and Riccati equation （ξ＇ = ao ＋ a1ξ＋ a2ξ2）, expansion method, and a linear variable separation approach, a new family of exact solutions with q = lx ＋ ...With the help of the symbolic computation system, Maple and Riccati equation （ξ＇ = ao ＋ a1ξ＋ a2ξ2）, expansion method, and a linear variable separation approach, a new family of exact solutions with q = lx ＋ my ＋ nt ＋ Г（x,y, t） for the （2＋1）-dimensional generalized Calogero-Bogoyavlenskii-Schiff system （GCBS） are derived. Based on the derived solitary wave solution, some novel localized excitations such as fusion, fission, and annihilation of complex waves are investigated.展开更多
Starting from an improved mapping approach and a linear variable separation approach, a new family of exact solutions （including solitary wave solutions, periodic wave solutions and rational function solutions） with...Starting from an improved mapping approach and a linear variable separation approach, a new family of exact solutions （including solitary wave solutions, periodic wave solutions and rational function solutions） with arbitrary functions for a general （2＋1）-dimensional Korteweg de solutions, we obtain some novel dromion-lattice solitons, system Vries system （GKdV） is derived. According to the derived complex wave excitations and chaotic patterns for the GKdV展开更多
The extended Riccati mapping approach^[1] is further improved by generalized Riccati equation, and combine it with variable separation method, abundant new exact complex solutions for the （2＋1）-dimensional modified...The extended Riccati mapping approach^[1] is further improved by generalized Riccati equation, and combine it with variable separation method, abundant new exact complex solutions for the （2＋1）-dimensional modified dispersive water-wave （MDWW） system are obtained. Based on a derived periodic solitary wave solution and a rational solution, we study a type of phenomenon of complex wave.展开更多
By virtue of the comparability between the wave superposition method and the dynamic analysis of structures, a general format for overcoming the non-uniqueness of solution induced by the wave superposition method at t...By virtue of the comparability between the wave superposition method and the dynamic analysis of structures, a general format for overcoming the non-uniqueness of solution induced by the wave superposition method at the eigenfrequencies of the corresponding interior problems is proposed. By adding appropriate damp to the virtual source system of the wave superposition method, the unique solutions for all wave numbers can be ensured. Based on this thought, a novel method-wave superposition method with complex radius vector is constructed. Not only is the computational time of this method approximately equal to that of the standard wave superposition method, but also the accuracy is much higher compared with other correlative methods. Finally, by taking the pulsating sphere and oscillating sphere as examples, the results of calculation show that the present method can effectively overcome the non-uniqueness problem.展开更多
Starting from the extended mapping approach and a linear variable separation method, we find new families of variable separation solutions with some arbitrary functions for the （3＋1）-dimensionM Burgers system. Then...Starting from the extended mapping approach and a linear variable separation method, we find new families of variable separation solutions with some arbitrary functions for the （3＋1）-dimensionM Burgers system. Then based on the derived exact solutions, some novel and interesting localized coherent excitations such as embedded-solitons, taper-like soliton, complex wave excitations in the periodic wave background are revealed by introducing appropriate boundary conditions and/or initial qualifications. The evolutional properties of the complex wave excitations are briefly investigated.展开更多
Starting from an improved projective method and a linear variable separation approach, new families of variable separation solutions （including solltary wave solutlons, periodic wave solutions and rational function s...Starting from an improved projective method and a linear variable separation approach, new families of variable separation solutions （including solltary wave solutlons, periodic wave solutions and rational function solutions） with arbitrary functions [or the （2＋ 1）-dimensional general/zed Broer-Kaup （GBK） system are derived. Usually, in terms of solitary wave solutions and/or rational function solutions, one can find abundant important localized excitations. However, based on the derived periodic wave solution in this paper, we reveal some complex wave excitations in the （2＋1）-dimensional GBK system, which describe solitons moving on a periodic wave background. Some interesting evolutional properties for these solitary waves propagating on the periodic wave bactground are also briefly discussed.展开更多
The indirect voltammetric determination of trace sulfate (2.0×10^(-6)～4.0×10^(-5) mol/L ) with the adsorptive complex wave of lead(Ⅱ)-tetrakis (4-trimethylammonium phenyl) porphyrin (PbTTMAPP) is reported....The indirect voltammetric determination of trace sulfate (2.0×10^(-6)～4.0×10^(-5) mol/L ) with the adsorptive complex wave of lead(Ⅱ)-tetrakis (4-trimethylammonium phenyl) porphyrin (PbTTMAPP) is reported.This method has been used for the analysis of natural waters with satisfactory results.展开更多
The Big Bang theory states that the universe was created from pure energy, although matter, in general, is also pure energy and there is no known physical existence that is not pure energy in accordance with the mass-...The Big Bang theory states that the universe was created from pure energy, although matter, in general, is also pure energy and there is no known physical existence that is not pure energy in accordance with the mass-energy equation. All known energy is situated in a field, and it can be questioned whether also the Big Bang was situated in a field in the primordial moment it inflated into the subsequent cosmic expansion that so far lets us observe a 93-billion-light-year-wide spherical volume of the universe. In this study, the Big Bang’s gravitational influence, particularly in the form of an externally radiated gravitational wave, is considered in connection to its situation in a surrounding field with a different expansion rate than itself. The results suggest that the least possible size of the universe can be predicted by the expression of the gravitational wave produced by Big Bang, revealing that the universe has a significantly greater size than the observable, and further that Big Bang might be the production of only one of many cosmic galaxies situated together in a cosmological wave complex (CWC) where the amplitude is self-maintained by inflations.展开更多
Arrhythmia is ubiquitous worldwide and cardiologists tend to provide solutions from the recent advancements in medicine.Detecting arrhythmia from ECG signals is considered a standard approach and hence,automating this...Arrhythmia is ubiquitous worldwide and cardiologists tend to provide solutions from the recent advancements in medicine.Detecting arrhythmia from ECG signals is considered a standard approach and hence,automating this process would aid the diagnosis by providing fast,costefficient,and accurate solutions at scale.This is executed by extracting the definite properties from the individual patterns collected from Electrocardiography(ECG)signals causing arrhythmia.In this era of applied intelligence,automated detection and diagnostic solutions are widely used for their spontaneous and robust solutions.In this research,our contributions are two-fold.Firstly,the Dual-Tree Complex Wavelet Transform(DT-CWT)method is implied to overhaul shift-invariance and aids signal reconstruction to extract significant features.Next,A neural attention mechanism is implied to capture temporal patterns from the extracted features of the ECG signal to discriminate distinct classes of arrhythmia and is trained end-to-end with the finest parameters.To ensure that the model’s generalizability,a set of five traintest variants are implied.The proposed model attains the highest accuracy of 98.5%for classifying 8 variants of arrhythmia on the MIT-BIH dataset.To test the resilience of the model,the unseen(test)samples are increased by 5x and the deviation in accuracy score and MSE was 0.12%and 0.1%respectively.Further,to assess the diagnostic model performance,AUC-ROC curves are plotted.At every test level,the proposed model is capable of generalizing new samples and leverages the advantage to develop a real-world application.As a note,this research is the first attempt to provide neural attention in arrhythmia classification using MIT-BIH ECG signals data with state-of-the-art performance.展开更多
A fluid-structure interaction system subject to Sommerfeld＇s condition is defined as a Sommerfeld system which is divided into three categories： Fluid Sommerfeld （FS） System, Solid Sommerfeld （SS） System and Flu...A fluid-structure interaction system subject to Sommerfeld＇s condition is defined as a Sommerfeld system which is divided into three categories： Fluid Sommerfeld （FS） System, Solid Sommerfeld （SS） System and Fluid Solid Sommerfeld （FSS） System of which Sommerfeld conditions are imposed on a fluid boundary only, a solid boundary only and both fluid and solid boundaries, respectively. This paper follows the previous initial results claimed by simple examples to further mathematically investigate the natural vibrations of generalized Sommerfeld systems. A new parameter representing the speed of radiation wave for generalized 3-D problems with more complicated boundary conditions is introduced into the Sommerfeld condition which allows investigation of the natural vibrations of a Sommerfeld system involving both free surface and compressible waves. The mathematical demonstrations and selected examples confirm and reveal the natural behaviour of generalized Sommerfeld systems defined above. These generalized conclusions can be used in theoretical or engineering analysis of the vibrations of various Sommerfeld systems in engineering.展开更多
The caustic lines are formed as envelop lines of wave rays on the complex topo- graphy where conventional ray theory fails.By using the inner and outer scale method in the near region the caustic lines the singulariti...The caustic lines are formed as envelop lines of wave rays on the complex topo- graphy where conventional ray theory fails.By using the inner and outer scale method in the near region the caustic lines the singularities of the ray theory are dealt with.Using the conclusion that the phase of the ray in contact with the caustic line increases by π/2,the whole wave refraction problem is solvec except on caustic lines.展开更多
In this study,we investigate the(2+1)-dimensional Korteweg-De Vries(KdV)equation with the extension of time-dependent coefficients.A symbolic computational method,the simplified Hirota’s method,and a long-wave method...In this study,we investigate the(2+1)-dimensional Korteweg-De Vries(KdV)equation with the extension of time-dependent coefficients.A symbolic computational method,the simplified Hirota’s method,and a long-wave method are utilized to create various exact solutions to the suggested equation.The symbolic computational method is applied to create the Lump solutions and periodic lump waves.Hirota’s method and a long-wave method are implemented to explore single-,double-and triple-M-lump waves,and interaction physical phenomena such as an interaction of single-M-lump with one-,twosoliton solutions,as well as a collision of double-M-lump with single-soliton waves.Furthermore,the simplified Hirota’s method is employed to explore complex multi-soliton solutions.To realize dynamics,the gained solutions are drawn via utilizing different arbitrary variable coefficients.展开更多
基金supported by the National Natural Science Foundation of China(Grant No.11375079)the Scientific Research Fund of Zhejiang Provincial Education Department of China(Grant No.Y 201120994)the Natural Science Foundation of Zhejiang Province,China(Grant Nos.Y6100257,LY14A010005,and Y6110140)
文摘With the help of the symbolic computation system, Maple and Riccati equation （ξ＇ = ao ＋ a1ξ＋ a2ξ2）, expansion method, and a linear variable separation approach, a new family of exact solutions with q = lx ＋ my ＋ nt ＋ Г（x,y, t） for the （2＋1）-dimensional generalized Calogero-Bogoyavlenskii-Schiff system （GCBS） are derived. Based on the derived solitary wave solution, some novel localized excitations such as fusion, fission, and annihilation of complex waves are investigated.
基金Project supported by the National Natural Science Foundation of China （Grant No 10172056）, the Natural Science Foundation of Zhejiang Province, China （Grant No Y604106）, the Foundation of New Century 151 Talent Engineering of Zhejiang Province, the Scientific Research Foundation of Zhejiang Provincial Education Department of China （Grant No 20070568） and the Natural Science Foundation of Zhejiang Lishui University （Grant No KZ04008）.
文摘Starting from an improved mapping approach and a linear variable separation approach, a new family of exact solutions （including solitary wave solutions, periodic wave solutions and rational function solutions） with arbitrary functions for a general （2＋1）-dimensional Korteweg de solutions, we obtain some novel dromion-lattice solitons, system Vries system （GKdV） is derived. According to the derived complex wave excitations and chaotic patterns for the GKdV
基金Supported by Science and Technology Foundation of Guizhou Province under Grant No.20072009
文摘The extended Riccati mapping approach^[1] is further improved by generalized Riccati equation, and combine it with variable separation method, abundant new exact complex solutions for the （2＋1）-dimensional modified dispersive water-wave （MDWW） system are obtained. Based on a derived periodic solitary wave solution and a rational solution, we study a type of phenomenon of complex wave.
基金Project supported by the National Natural Science Foundation of China (No. 10172038).
文摘By virtue of the comparability between the wave superposition method and the dynamic analysis of structures, a general format for overcoming the non-uniqueness of solution induced by the wave superposition method at the eigenfrequencies of the corresponding interior problems is proposed. By adding appropriate damp to the virtual source system of the wave superposition method, the unique solutions for all wave numbers can be ensured. Based on this thought, a novel method-wave superposition method with complex radius vector is constructed. Not only is the computational time of this method approximately equal to that of the standard wave superposition method, but also the accuracy is much higher compared with other correlative methods. Finally, by taking the pulsating sphere and oscillating sphere as examples, the results of calculation show that the present method can effectively overcome the non-uniqueness problem.
基金the Natural Science Foundation of Zhejiang Province under Grant Nos.Y604106 and Y606181the Foundation of New Century"151 Talent Engineering"of Zhejiang Provincethe Scientific Research Foundation of Key Discipline of Zhejiang Province
文摘Starting from the extended mapping approach and a linear variable separation method, we find new families of variable separation solutions with some arbitrary functions for the （3＋1）-dimensionM Burgers system. Then based on the derived exact solutions, some novel and interesting localized coherent excitations such as embedded-solitons, taper-like soliton, complex wave excitations in the periodic wave background are revealed by introducing appropriate boundary conditions and/or initial qualifications. The evolutional properties of the complex wave excitations are briefly investigated.
基金The project supported by the Natural Science Foundation of Zhejiang Province under Grant Nos. Y604106 and Y606181, the Foundation of New Century ＂151 Talent Engineering＂ of Zhejiang Province, the Scientific Research Foundation of Key Discipline of Zhejiang Province, and the Natural Science Foundation of Zhejiang Lishui University under Grant No. KZ05005 Acknowledgments The authors are in debt to Profs. J.P. Fang, H.P. Zhu, and J.F. Zhang, and Drs. Z.Y. Ma and W.H. Huang for their fruitful discussions.
文摘Starting from an improved projective method and a linear variable separation approach, new families of variable separation solutions （including solltary wave solutlons, periodic wave solutions and rational function solutions） with arbitrary functions [or the （2＋ 1）-dimensional general/zed Broer-Kaup （GBK） system are derived. Usually, in terms of solitary wave solutions and/or rational function solutions, one can find abundant important localized excitations. However, based on the derived periodic wave solution in this paper, we reveal some complex wave excitations in the （2＋1）-dimensional GBK system, which describe solitons moving on a periodic wave background. Some interesting evolutional properties for these solitary waves propagating on the periodic wave bactground are also briefly discussed.
文摘The indirect voltammetric determination of trace sulfate (2.0×10^(-6)～4.0×10^(-5) mol/L ) with the adsorptive complex wave of lead(Ⅱ)-tetrakis (4-trimethylammonium phenyl) porphyrin (PbTTMAPP) is reported.This method has been used for the analysis of natural waters with satisfactory results.
文摘The Big Bang theory states that the universe was created from pure energy, although matter, in general, is also pure energy and there is no known physical existence that is not pure energy in accordance with the mass-energy equation. All known energy is situated in a field, and it can be questioned whether also the Big Bang was situated in a field in the primordial moment it inflated into the subsequent cosmic expansion that so far lets us observe a 93-billion-light-year-wide spherical volume of the universe. In this study, the Big Bang’s gravitational influence, particularly in the form of an externally radiated gravitational wave, is considered in connection to its situation in a surrounding field with a different expansion rate than itself. The results suggest that the least possible size of the universe can be predicted by the expression of the gravitational wave produced by Big Bang, revealing that the universe has a significantly greater size than the observable, and further that Big Bang might be the production of only one of many cosmic galaxies situated together in a cosmological wave complex (CWC) where the amplitude is self-maintained by inflations.
基金This research was partially supported by JNTU Hyderabad,India under Grant proceeding number:JNTUH/TEQIP-III/CRS/2019/CSE/08.The authors are grateful for the support provided by the TEQIP-III team.
文摘Arrhythmia is ubiquitous worldwide and cardiologists tend to provide solutions from the recent advancements in medicine.Detecting arrhythmia from ECG signals is considered a standard approach and hence,automating this process would aid the diagnosis by providing fast,costefficient,and accurate solutions at scale.This is executed by extracting the definite properties from the individual patterns collected from Electrocardiography(ECG)signals causing arrhythmia.In this era of applied intelligence,automated detection and diagnostic solutions are widely used for their spontaneous and robust solutions.In this research,our contributions are two-fold.Firstly,the Dual-Tree Complex Wavelet Transform(DT-CWT)method is implied to overhaul shift-invariance and aids signal reconstruction to extract significant features.Next,A neural attention mechanism is implied to capture temporal patterns from the extracted features of the ECG signal to discriminate distinct classes of arrhythmia and is trained end-to-end with the finest parameters.To ensure that the model’s generalizability,a set of five traintest variants are implied.The proposed model attains the highest accuracy of 98.5%for classifying 8 variants of arrhythmia on the MIT-BIH dataset.To test the resilience of the model,the unseen(test)samples are increased by 5x and the deviation in accuracy score and MSE was 0.12%and 0.1%respectively.Further,to assess the diagnostic model performance,AUC-ROC curves are plotted.At every test level,the proposed model is capable of generalizing new samples and leverages the advantage to develop a real-world application.As a note,this research is the first attempt to provide neural attention in arrhythmia classification using MIT-BIH ECG signals data with state-of-the-art performance.
文摘A fluid-structure interaction system subject to Sommerfeld＇s condition is defined as a Sommerfeld system which is divided into three categories： Fluid Sommerfeld （FS） System, Solid Sommerfeld （SS） System and Fluid Solid Sommerfeld （FSS） System of which Sommerfeld conditions are imposed on a fluid boundary only, a solid boundary only and both fluid and solid boundaries, respectively. This paper follows the previous initial results claimed by simple examples to further mathematically investigate the natural vibrations of generalized Sommerfeld systems. A new parameter representing the speed of radiation wave for generalized 3-D problems with more complicated boundary conditions is introduced into the Sommerfeld condition which allows investigation of the natural vibrations of a Sommerfeld system involving both free surface and compressible waves. The mathematical demonstrations and selected examples confirm and reveal the natural behaviour of generalized Sommerfeld systems defined above. These generalized conclusions can be used in theoretical or engineering analysis of the vibrations of various Sommerfeld systems in engineering.
文摘The caustic lines are formed as envelop lines of wave rays on the complex topo- graphy where conventional ray theory fails.By using the inner and outer scale method in the near region the caustic lines the singularities of the ray theory are dealt with.Using the conclusion that the phase of the ray in contact with the caustic line increases by π/2,the whole wave refraction problem is solvec except on caustic lines.
文摘In this study,we investigate the(2+1)-dimensional Korteweg-De Vries(KdV)equation with the extension of time-dependent coefficients.A symbolic computational method,the simplified Hirota’s method,and a long-wave method are utilized to create various exact solutions to the suggested equation.The symbolic computational method is applied to create the Lump solutions and periodic lump waves.Hirota’s method and a long-wave method are implemented to explore single-,double-and triple-M-lump waves,and interaction physical phenomena such as an interaction of single-M-lump with one-,twosoliton solutions,as well as a collision of double-M-lump with single-soliton waves.Furthermore,the simplified Hirota’s method is employed to explore complex multi-soliton solutions.To realize dynamics,the gained solutions are drawn via utilizing different arbitrary variable coefficients.
