Grandi’s paradox, which was posed for a real function of the form <span style="white-space:nowrap;">1/(1+ x), has been resolved and extended to complex valued functions. Resolution of this approximate...Grandi’s paradox, which was posed for a real function of the form <span style="white-space:nowrap;">1/(1+ x), has been resolved and extended to complex valued functions. Resolution of this approximately three-hundred-year-old paradox is accomplished by the use of a consistent truncation approach that can be applied to all the series expansions of Grandi-type functions. Furthermore, a new technique for improving the convergence characteristics of power series with alternating signs is introduced. The technique works by successively averaging a series at different orders of truncation. A sound theoretical justification of the successive averaging method is demonstrated by two different series expansions of the function <span style="white-space:nowrap;">1/(1+ e<sup>x </sup>) . Grandi-type complex valued functions such as <span style="white-space:nowrap;">1/(i + x) are expressed as consistently-truncated and convergence-improved forms and Fagnano’s formula is established from the series expansions of these functions. A Grandi-type general complex valued function <img src="Edit_f4efd7cd-6853-4ca4-b4dc-00f0b798c277.png" width="80" height="24" alt="" /> is introduced and expanded to a consistently truncated and successively averaged series. Finally, an unorthodox application of the successive averaging method to polynomials is presented.展开更多
We consider the space X of all analytic functionsof two complex variables s1 and s2, equipping it with the natural locally convex topology and using the growth parameter, the order of f as defined recently by the auth...We consider the space X of all analytic functionsof two complex variables s1 and s2, equipping it with the natural locally convex topology and using the growth parameter, the order of f as defined recently by the authors. Under this topology X becomes a Frechet space Apart from finding the characterization of continuous linear functionals, linear transformation on X, we have obtained the necessary and sufficient conditions for a double sequence in X to be a proper bases.展开更多
The 300 msw Simulated Saturation Diving Chamber Complex was designed and built by ourselves. It was completed at the end of 1985. A 300 msw trimixed saturation diving experiment was successfully conducted in the compl...The 300 msw Simulated Saturation Diving Chamber Complex was designed and built by ourselves. It was completed at the end of 1985. A 300 msw trimixed saturation diving experiment was successfully conducted in the complex by Chinese Underwater Technology Institute(CUTI) from May 22 to June 12 of 1987. During the experiment, 4 divers habitated in the complex for 20 days, and they performed 16 person-time excursion dives and 8 other tests. The result of the experiment indicates that the complex is well designed, suitably configurated, wholly integrated and steadily run, as well as of low leakage. The main functions of the complex have approached to those of the same kind in the world. The complex can be used as a basic facility for serving the nation's saturation diving technology, underwater operation, personnel training, etc.展开更多
For series manufacture of pressure sensors, stage of technological tests is performed, related to a definition of the manufacturing accuracy of the sensors. Technological test plan of pressure sensors involves testing...For series manufacture of pressure sensors, stage of technological tests is performed, related to a definition of the manufacturing accuracy of the sensors. Technological test plan of pressure sensors involves testing the sensors on certain fixed temperature and pressure points available in the table. According to a test results, we determine transformation function mathematical model coefficients of sensors and accordance by the claimed accuracy class, of the manufactured sensors. The cost of pressure sensors mostly depends on the cost of this step and determined by the complexity of the used transformation function model. The analysis of a contemporary works associated with the choice of transformation functions for smart pressure sensors. A new proposed indicator of model complexity of a sensor transformation function. In details shown features of the complexity indicator use and given an example. In the article was set and resolved the task to reduce the cost of the tests for commercially available sensors, by reducing the number of temperature points, without compromising the accuracy of the sensor measurement ability.展开更多
The frequency–space（f–x） empirical mode decomposition（EMD） denoising method has two limitations when applied to nonstationary seismic data. First, subtracting the first intrinsic mode function（IMF） results in ...The frequency–space（f–x） empirical mode decomposition（EMD） denoising method has two limitations when applied to nonstationary seismic data. First, subtracting the first intrinsic mode function（IMF） results in signal damage and limited denoising. Second, decomposing the real and imaginary parts of complex data may lead to inconsistent decomposition numbers. Thus, we propose a new method named f–x spatial projection-based complex empirical mode decomposition（CEMD） prediction filtering. The proposed approach directly decomposes complex seismic data into a series of complex IMFs（CIMFs） using the spatial projection-based CEMD algorithm and then applies f–x predictive filtering to the stationary CIMFs to improve the signal-to-noise ratio. Synthetic and real data examples were used to demonstrate the performance of the new method in random noise attenuation and seismic signal preservation.展开更多
Surface irregularities,such as hills and ridges,can significantly amplify ground motion caused by earthquakes.Therefore,in this study,we propose an analytical solution model to investigate the interaction between an a...Surface irregularities,such as hills and ridges,can significantly amplify ground motion caused by earthquakes.Therefore,in this study,we propose an analytical solution model to investigate the interaction between an asymmetric triangular hill on Earth and SH waves.Firstly,based on the development of wave functions and regional matching techniques,we introduce a semi-circular artificial auxiliary boundary,dividing the solution model into a semi-infinite body containing a semi-circular depression and an asymmetric fan-shaped region.Secondly,we derive the domain function form applicable to solving asymmetric problems.Utilizing the theory of complex variables,we establish a well-posed matrix for solving domain functions within the same coordinate system.Numerical results demonstrate that the scattering of SH waves by a protuberance is jointly influenced by the geometric parameters of the hill and the angle of incidence.Additionally,the frequency of the incident wave also has a certain degree of impact on the displacement amplitude.This study elucidates the scattering mechanism of SH waves by complex boundaries,providing a theoretical reference for building site selection and seismic design.In practical problems,the asymmetric assumption is more applicable than the symmetry assumption.展开更多
This study is to determine the support mechanism of pre-stressed expandable props for the stope roof in room- and-pillar mining, which is crucial for maintaining stability and preventing roof collapse in mines. Utiliz...This study is to determine the support mechanism of pre-stressed expandable props for the stope roof in room- and-pillar mining, which is crucial for maintaining stability and preventing roof collapse in mines. Utilizing an engineering case from a gold mine in Dandong, China, a laboratory-based similar test is conducted to extract the actual roof characteristic curve. This test continues until the mining stope collapses due to a U-shaped failure. Concurrently, a semi-theoretical method for obtaining the roof characteristic curve is proposed and verified against the actual curve. The semi-theoretical method calculated that the support force and vertical displacement at the demarcation point between the elastic and plastic zones of the roof characteristic curve are 5.0 MPa and 8.20 mm, respectively, corroborating well with the laboratory-based similar test results of 0.22 MPa and 0.730 mm. The weakening factor for the plastic zone in the roof characteristic curve was semi-theoretically estimated to be 0.75. The intersection between the actual roof characteristic curve and the support characteristic curves of expandable props, natural pillars, and concrete props indicates that the expandable prop is the most effective “yielding support” for the stope roof in room-and-pillar mining. That is, the deformation and failure of the stope roof can be effectively controlled with proper release of roof stress. This study provides practical insights for optimizing support strategies in room-and-pillar mining, enhancing the safety and efficiency of mining operations.展开更多
Complex-valued neural networks(CVNNs)have shown their excellent efficiency compared to their real counterparts in speech enhancement,image and signal processing.Researchers throughout the years have made many efforts ...Complex-valued neural networks(CVNNs)have shown their excellent efficiency compared to their real counterparts in speech enhancement,image and signal processing.Researchers throughout the years have made many efforts to improve the learning algorithms and activation functions of CVNNs.Since CVNNs have proven to have better performance in handling the naturally complex-valued data and signals,this area of study will grow and expect the arrival of some effective improvements in the future.Therefore,there exists an obvious reason to provide a comprehensive survey paper that systematically collects and categorizes the advancement of CVNNs.In this paper,we discuss and summarize the recent advances based on their learning algorithms,activation functions,which is the most challenging part of building a CVNN,and applications.Besides,we outline the structure and applications of complex-valued convolutional,residual and recurrent neural networks.Finally,we also present some challenges and future research directions to facilitate the exploration of the ability of CVNNs.展开更多
Computational calculation was performed to investigate the mechanism of trifluoromethylation reactions of iodobenzene with well-defined N-heterocyclic carbene （NHC）-supported Cu~ trifiuor- omethyl complexes. Four pr...Computational calculation was performed to investigate the mechanism of trifluoromethylation reactions of iodobenzene with well-defined N-heterocyclic carbene （NHC）-supported Cu~ trifiuor- omethyl complexes. Four proposed reaction pathways, namely cr-bond metathesis （BM）, concerted oxidative addition-reductive elimination （OARE）, iodine atom transfer （IAT） and single-electron transfer （SET）, have been computed by density functional theory （DFT）. The result indicated that the concerted OARE mechanism is favored among the four reaction pathways, suggesting the trifluoromethylation may occur via concerted OARE mechanism involving Ar-X oxidative addition to the Cu（1） center as the rate determining step.展开更多
This paper presents a multi-ANN approximation approach to approximate complex non-linear function. Comparing with single-ANN methods the proposed approach improves and increases the approximation and generalization ab...This paper presents a multi-ANN approximation approach to approximate complex non-linear function. Comparing with single-ANN methods the proposed approach improves and increases the approximation and generalization ability, and adaptability greatly in learning processes of networks. The simulation results have been shown that the method can be applied to the modeling and identification of complex dynamic control systems.展开更多
In order to measure complex structure transfer function and calculate inner sound field, transfer function of integration is mentioned. By establishing virtual system, transfer function of integration can be measured ...In order to measure complex structure transfer function and calculate inner sound field, transfer function of integration is mentioned. By establishing virtual system, transfer function of integration can be measured and the inner sound field can also be calculated. In the experiment, automobile body transfer function of integration is measured and experimental method of establishing virtual system is very valid.展开更多
The molecular structures of fifteen possible 2-thioxanthine（2TX） complexes with one Hg^2＋ and two Cl-ions were fully optimized using density functional theory B3PW91/6-311＋＋G^＊＊ method. The effective pseudo pot...The molecular structures of fifteen possible 2-thioxanthine（2TX） complexes with one Hg^2＋ and two Cl-ions were fully optimized using density functional theory B3PW91/6-311＋＋G^＊＊ method. The effective pseudo potential LANL2DZ basis set was used for metal Hg^2＋ion. The vibrational analysis was also carried out at the same level. The bond lengths, bond angles, zero point energies, Gibbs free energies, thermodynamic energies and relative energies of all the complexes were obtained. The NBO analysis for natural charge and the second order perturbation energy values was carried out for three stable complexes and the IR spectroscopy of the two complexes was assigned to the experimental data. The results show that the 2-thioxanthine complexes with one Hg^2＋ and two Cl^-ions were formed and the complexes resulting from the thione tautomer are more stable than that of the thiol ones. The order of three complexes with relative lower energy is 2TX（1,3,7）-Hg^2＋-2, 2 TX（1,3,7）-Hg^2＋-1 and 2 TX（1,3,9）-Hg^2＋. The calculated IR spectroscopy of the two complexes agreed with the experimental data.展开更多
Hanbury-Brown and Twiss(HBT)effect is the foundation for stellar intensity interferometry.However,it is a phase insensitive two-photon interference effect.Here we extend the HBT interferometer by mixing intensity-matc...Hanbury-Brown and Twiss(HBT)effect is the foundation for stellar intensity interferometry.However,it is a phase insensitive two-photon interference effect.Here we extend the HBT interferometer by mixing intensity-matched reference fields with the input fields before intensity correlation measurement.With the freely available coherent state serving as the reference field,we experimentally demonstrate the phase sensitive two-photon interference effect when the input fields are thermal fields in either continuous wave or non-stationary pulsed wave and measure the complete complex second-order coherence function of the input fields without bringing them together from separate locations.Moreover,we discuss how to improve the signal level by using the more realistic continuous wave broadband anti-bunched light fields as the reference field.Our investigations pave the way for developing new technology of remote sensing and interferometric imaging with applications in long baseline high-resolution astronomy.展开更多
Aim The general arbitrary cracked problem in an elastic plane was discussed. Methods For the purpose of acquiring the solution of the problem, a new formulation on the problem was proposed. Compared with the classic...Aim The general arbitrary cracked problem in an elastic plane was discussed. Methods For the purpose of acquiring the solution of the problem, a new formulation on the problem was proposed. Compared with the classical plane elastic crack model, only the known conditions were revised in the new formulation, which are greatly convenient to solve the problem, and no other new condition was given. Results and Conclusion The general exact analytic solution is given here based on the formulation though the problem is very complicated. Furthermore, the stress intensity factors K Ⅰ, K Ⅱ of the problem are also given.展开更多
In this paper, antiplane response of an isosceles triangular hill to incident SH waves is studied based on the method of complex function and by using moving coordinate system. The standing wave function, which can sa...In this paper, antiplane response of an isosceles triangular hill to incident SH waves is studied based on the method of complex function and by using moving coordinate system. The standing wave function, which can satisfy the governing equation and boundary condition, is provided. Furthermore, numerical examples are presented; the influences of wave number and angle of the incident waves and the angle of the hill’s peak on ground motion are discussed.展开更多
Two mono iron complexes Fe（CO）2PR3（NN） （R = Cy （3）, Ph （4）, NN = o-phenylenediamine dianion ligand, N2H2Ph2-） derived from the ligand substitution of Fe（CO）3hPR3 by the NN ligand were isolated and structur...Two mono iron complexes Fe（CO）2PR3（NN） （R = Cy （3）, Ph （4）, NN = o-phenylenediamine dianion ligand, N2H2Ph2-） derived from the ligand substitution of Fe（CO）3hPR3 by the NN ligand were isolated and structurally characterized by single crystal X-ray diffraction. They have a similar first coordination sphere and oxidation state of the iron center as the [Fe]-hydrogenase active site, and can be a model of it IR demonstrated that the effect of the NN ligand on the coordinated CO stretch- ing frequencies was due to its excellent electron donating ability. The reversible protonation/deprotonation of the NN ligand was identified by infrared spectroscopy and density functional theory computation. The NN ligand is an effective proton acceptor as the internal base of the cysteine thiolate ligand in [Fe]-hydrogenase. The electrochemical properties of complexes 3, 4 were investigated by cyclic voltammograms. Complex 3 catalyzed the transfer hydrogenation of benzoquinone to hydroquinone effectively under mild conditions.展开更多
In this paper problems of collinear cracks between bonded dissimilar materials under antiplane concentrated forces are dealt with. General solutions of the problems are formulated by applying extended Schwarz principl...In this paper problems of collinear cracks between bonded dissimilar materials under antiplane concentrated forces are dealt with. General solutions of the problems are formulated by applying extended Schwarz principle integrated with the analysis of the singularity of complex stress functions. Closed-form solutions of several typical problems are obtained and the stress intensity factors are given. These solutions include a series of original results and some results of previous researches. It is found that under symmetrical loads the solutions for the dissimilar materials are the same as those for the homogeneous materia[7]展开更多
By the application of the theory of complex functions, asymmetrical dynamic propagation problems on mode Ⅲ interface crack are studied. The universal representations of analytical solutions are obtained by the approa...By the application of the theory of complex functions, asymmetrical dynamic propagation problems on mode Ⅲ interface crack are studied. The universal representations of analytical solutions are obtained by the approaches of self-similar function. The problems researched can be facilely transformed into Riemann-Hilbert problems and analytical solution to an asymmetrical propagation crack under the condition of point loads and unit-step loads, respectively, is acquired. After those solutions were used by superposition theorem, the solutions of arbitrarily complex problems could be attained.展开更多
With the theory of complex functions, dynamic propagation problems concerning surfaces of asymmetrical mode Ⅲ crack subjected to moving loads are investigated. General representations of analytical solutions are obta...With the theory of complex functions, dynamic propagation problems concerning surfaces of asymmetrical mode Ⅲ crack subjected to moving loads are investigated. General representations of analytical solutions are obtained with self-similar functions. The problems can be easily converted into Riemann-Hilbert problems using this technique. Analytical solutions to stress, displacement and dynamic stress intensity factor under constant and unit-step moving loads on the surfaces of asymmetrical extension crack, respectively, are obtained. By applying these solutions, together with the superposition principle, solutions of discretionarily intricate problems can be found.展开更多
文摘Grandi’s paradox, which was posed for a real function of the form <span style="white-space:nowrap;">1/(1+ x), has been resolved and extended to complex valued functions. Resolution of this approximately three-hundred-year-old paradox is accomplished by the use of a consistent truncation approach that can be applied to all the series expansions of Grandi-type functions. Furthermore, a new technique for improving the convergence characteristics of power series with alternating signs is introduced. The technique works by successively averaging a series at different orders of truncation. A sound theoretical justification of the successive averaging method is demonstrated by two different series expansions of the function <span style="white-space:nowrap;">1/(1+ e<sup>x </sup>) . Grandi-type complex valued functions such as <span style="white-space:nowrap;">1/(i + x) are expressed as consistently-truncated and convergence-improved forms and Fagnano’s formula is established from the series expansions of these functions. A Grandi-type general complex valued function <img src="Edit_f4efd7cd-6853-4ca4-b4dc-00f0b798c277.png" width="80" height="24" alt="" /> is introduced and expanded to a consistently truncated and successively averaged series. Finally, an unorthodox application of the successive averaging method to polynomials is presented.
文摘We consider the space X of all analytic functionsof two complex variables s1 and s2, equipping it with the natural locally convex topology and using the growth parameter, the order of f as defined recently by the authors. Under this topology X becomes a Frechet space Apart from finding the characterization of continuous linear functionals, linear transformation on X, we have obtained the necessary and sufficient conditions for a double sequence in X to be a proper bases.
文摘The 300 msw Simulated Saturation Diving Chamber Complex was designed and built by ourselves. It was completed at the end of 1985. A 300 msw trimixed saturation diving experiment was successfully conducted in the complex by Chinese Underwater Technology Institute(CUTI) from May 22 to June 12 of 1987. During the experiment, 4 divers habitated in the complex for 20 days, and they performed 16 person-time excursion dives and 8 other tests. The result of the experiment indicates that the complex is well designed, suitably configurated, wholly integrated and steadily run, as well as of low leakage. The main functions of the complex have approached to those of the same kind in the world. The complex can be used as a basic facility for serving the nation's saturation diving technology, underwater operation, personnel training, etc.
文摘For series manufacture of pressure sensors, stage of technological tests is performed, related to a definition of the manufacturing accuracy of the sensors. Technological test plan of pressure sensors involves testing the sensors on certain fixed temperature and pressure points available in the table. According to a test results, we determine transformation function mathematical model coefficients of sensors and accordance by the claimed accuracy class, of the manufactured sensors. The cost of pressure sensors mostly depends on the cost of this step and determined by the complexity of the used transformation function model. The analysis of a contemporary works associated with the choice of transformation functions for smart pressure sensors. A new proposed indicator of model complexity of a sensor transformation function. In details shown features of the complexity indicator use and given an example. In the article was set and resolved the task to reduce the cost of the tests for commercially available sensors, by reducing the number of temperature points, without compromising the accuracy of the sensor measurement ability.
基金supported financially by the National Natural Science Foundation(No.41174117)the Major National Science and Technology Projects(No.2011ZX05031–001)
文摘The frequency–space（f–x） empirical mode decomposition（EMD） denoising method has two limitations when applied to nonstationary seismic data. First, subtracting the first intrinsic mode function（IMF） results in signal damage and limited denoising. Second, decomposing the real and imaginary parts of complex data may lead to inconsistent decomposition numbers. Thus, we propose a new method named f–x spatial projection-based complex empirical mode decomposition（CEMD） prediction filtering. The proposed approach directly decomposes complex seismic data into a series of complex IMFs（CIMFs） using the spatial projection-based CEMD algorithm and then applies f–x predictive filtering to the stationary CIMFs to improve the signal-to-noise ratio. Synthetic and real data examples were used to demonstrate the performance of the new method in random noise attenuation and seismic signal preservation.
基金supported by the National Key R&D Program of China(Grant No.2022YFC3003601)Joint Funds of the National Natural Science Foundation of China Project on Earthquake Science(Grant No.U2239252)the program of the Innovative Research Team in China Earthquake Administration.
文摘Surface irregularities,such as hills and ridges,can significantly amplify ground motion caused by earthquakes.Therefore,in this study,we propose an analytical solution model to investigate the interaction between an asymmetric triangular hill on Earth and SH waves.Firstly,based on the development of wave functions and regional matching techniques,we introduce a semi-circular artificial auxiliary boundary,dividing the solution model into a semi-infinite body containing a semi-circular depression and an asymmetric fan-shaped region.Secondly,we derive the domain function form applicable to solving asymmetric problems.Utilizing the theory of complex variables,we establish a well-posed matrix for solving domain functions within the same coordinate system.Numerical results demonstrate that the scattering of SH waves by a protuberance is jointly influenced by the geometric parameters of the hill and the angle of incidence.Additionally,the frequency of the incident wave also has a certain degree of impact on the displacement amplitude.This study elucidates the scattering mechanism of SH waves by complex boundaries,providing a theoretical reference for building site selection and seismic design.In practical problems,the asymmetric assumption is more applicable than the symmetry assumption.
基金Project(2022YFC2903801) supported by the National Key Research and Development Program of ChinaProjects(52374117, 52274115) supported by the National Natural Science Foundation of China。
文摘This study is to determine the support mechanism of pre-stressed expandable props for the stope roof in room- and-pillar mining, which is crucial for maintaining stability and preventing roof collapse in mines. Utilizing an engineering case from a gold mine in Dandong, China, a laboratory-based similar test is conducted to extract the actual roof characteristic curve. This test continues until the mining stope collapses due to a U-shaped failure. Concurrently, a semi-theoretical method for obtaining the roof characteristic curve is proposed and verified against the actual curve. The semi-theoretical method calculated that the support force and vertical displacement at the demarcation point between the elastic and plastic zones of the roof characteristic curve are 5.0 MPa and 8.20 mm, respectively, corroborating well with the laboratory-based similar test results of 0.22 MPa and 0.730 mm. The weakening factor for the plastic zone in the roof characteristic curve was semi-theoretically estimated to be 0.75. The intersection between the actual roof characteristic curve and the support characteristic curves of expandable props, natural pillars, and concrete props indicates that the expandable prop is the most effective “yielding support” for the stope roof in room-and-pillar mining. That is, the deformation and failure of the stope roof can be effectively controlled with proper release of roof stress. This study provides practical insights for optimizing support strategies in room-and-pillar mining, enhancing the safety and efficiency of mining operations.
基金partially supported by the JSPS KAKENHI(JP22H03643,JP19K22891)。
文摘Complex-valued neural networks(CVNNs)have shown their excellent efficiency compared to their real counterparts in speech enhancement,image and signal processing.Researchers throughout the years have made many efforts to improve the learning algorithms and activation functions of CVNNs.Since CVNNs have proven to have better performance in handling the naturally complex-valued data and signals,this area of study will grow and expect the arrival of some effective improvements in the future.Therefore,there exists an obvious reason to provide a comprehensive survey paper that systematically collects and categorizes the advancement of CVNNs.In this paper,we discuss and summarize the recent advances based on their learning algorithms,activation functions,which is the most challenging part of building a CVNN,and applications.Besides,we outline the structure and applications of complex-valued convolutional,residual and recurrent neural networks.Finally,we also present some challenges and future research directions to facilitate the exploration of the ability of CVNNs.
基金supported by National Natural Science Foundation of China(Nos.21073144,21173169)Fundamental Research Funds for the Central Universities(No.XDJK2013A008)
文摘Computational calculation was performed to investigate the mechanism of trifluoromethylation reactions of iodobenzene with well-defined N-heterocyclic carbene （NHC）-supported Cu~ trifiuor- omethyl complexes. Four proposed reaction pathways, namely cr-bond metathesis （BM）, concerted oxidative addition-reductive elimination （OARE）, iodine atom transfer （IAT） and single-electron transfer （SET）, have been computed by density functional theory （DFT）. The result indicated that the concerted OARE mechanism is favored among the four reaction pathways, suggesting the trifluoromethylation may occur via concerted OARE mechanism involving Ar-X oxidative addition to the Cu（1） center as the rate determining step.
文摘This paper presents a multi-ANN approximation approach to approximate complex non-linear function. Comparing with single-ANN methods the proposed approach improves and increases the approximation and generalization ability, and adaptability greatly in learning processes of networks. The simulation results have been shown that the method can be applied to the modeling and identification of complex dynamic control systems.
文摘In order to measure complex structure transfer function and calculate inner sound field, transfer function of integration is mentioned. By establishing virtual system, transfer function of integration can be measured and the inner sound field can also be calculated. In the experiment, automobile body transfer function of integration is measured and experimental method of establishing virtual system is very valid.
基金supported by the National Natural Science Foundation of China(No.21643014)the Special Natural Science Foundation of Science and Technology Bureau of Xi’an City Government(No.2016CXWL02)
文摘The molecular structures of fifteen possible 2-thioxanthine（2TX） complexes with one Hg^2＋ and two Cl-ions were fully optimized using density functional theory B3PW91/6-311＋＋G^＊＊ method. The effective pseudo potential LANL2DZ basis set was used for metal Hg^2＋ion. The vibrational analysis was also carried out at the same level. The bond lengths, bond angles, zero point energies, Gibbs free energies, thermodynamic energies and relative energies of all the complexes were obtained. The NBO analysis for natural charge and the second order perturbation energy values was carried out for three stable complexes and the IR spectroscopy of the two complexes was assigned to the experimental data. The results show that the 2-thioxanthine complexes with one Hg^2＋ and two Cl^-ions were formed and the complexes resulting from the thione tautomer are more stable than that of the thiol ones. The order of three complexes with relative lower energy is 2TX（1,3,7）-Hg^2＋-2, 2 TX（1,3,7）-Hg^2＋-1 and 2 TX（1,3,9）-Hg^2＋. The calculated IR spectroscopy of the two complexes agreed with the experimental data.
基金supported in part by the National Natural Science Foundation of China(Grant Nos.12004279,92476113 and 12074283)by City University of Hong Kong(Project No.9610522)+1 种基金the General Research Fund from Hong Kong Research Grants Council(Nos.11315822,11301624)Joint NSFC/RGC Collaborative Research Scheme(No.CRS_CityU103/24).
文摘Hanbury-Brown and Twiss(HBT)effect is the foundation for stellar intensity interferometry.However,it is a phase insensitive two-photon interference effect.Here we extend the HBT interferometer by mixing intensity-matched reference fields with the input fields before intensity correlation measurement.With the freely available coherent state serving as the reference field,we experimentally demonstrate the phase sensitive two-photon interference effect when the input fields are thermal fields in either continuous wave or non-stationary pulsed wave and measure the complete complex second-order coherence function of the input fields without bringing them together from separate locations.Moreover,we discuss how to improve the signal level by using the more realistic continuous wave broadband anti-bunched light fields as the reference field.Our investigations pave the way for developing new technology of remote sensing and interferometric imaging with applications in long baseline high-resolution astronomy.
文摘Aim The general arbitrary cracked problem in an elastic plane was discussed. Methods For the purpose of acquiring the solution of the problem, a new formulation on the problem was proposed. Compared with the classical plane elastic crack model, only the known conditions were revised in the new formulation, which are greatly convenient to solve the problem, and no other new condition was given. Results and Conclusion The general exact analytic solution is given here based on the formulation though the problem is very complicated. Furthermore, the stress intensity factors K Ⅰ, K Ⅱ of the problem are also given.
文摘In this paper, antiplane response of an isosceles triangular hill to incident SH waves is studied based on the method of complex function and by using moving coordinate system. The standing wave function, which can satisfy the governing equation and boundary condition, is provided. Furthermore, numerical examples are presented; the influences of wave number and angle of the incident waves and the angle of the hill’s peak on ground motion are discussed.
基金supported by the National Natural Science Foundation of China(21103121,21276187)Tianjin Municipal Natural Science Foundation(13JCQNJC05800)the Specialized Research Fund for the Doctoral Program of Higher Education(20121317110009)~~
文摘Two mono iron complexes Fe（CO）2PR3（NN） （R = Cy （3）, Ph （4）, NN = o-phenylenediamine dianion ligand, N2H2Ph2-） derived from the ligand substitution of Fe（CO）3hPR3 by the NN ligand were isolated and structurally characterized by single crystal X-ray diffraction. They have a similar first coordination sphere and oxidation state of the iron center as the [Fe]-hydrogenase active site, and can be a model of it IR demonstrated that the effect of the NN ligand on the coordinated CO stretch- ing frequencies was due to its excellent electron donating ability. The reversible protonation/deprotonation of the NN ligand was identified by infrared spectroscopy and density functional theory computation. The NN ligand is an effective proton acceptor as the internal base of the cysteine thiolate ligand in [Fe]-hydrogenase. The electrochemical properties of complexes 3, 4 were investigated by cyclic voltammograms. Complex 3 catalyzed the transfer hydrogenation of benzoquinone to hydroquinone effectively under mild conditions.
文摘In this paper problems of collinear cracks between bonded dissimilar materials under antiplane concentrated forces are dealt with. General solutions of the problems are formulated by applying extended Schwarz principle integrated with the analysis of the singularity of complex stress functions. Closed-form solutions of several typical problems are obtained and the stress intensity factors are given. These solutions include a series of original results and some results of previous researches. It is found that under symmetrical loads the solutions for the dissimilar materials are the same as those for the homogeneous materia[7]
基金Project supported by the Postdoctoral Science Foundation of China (No.2005038199)the Natural Science Foundation of Heilongjiang Province of China (No.ZJG04-08)
文摘By the application of the theory of complex functions, asymmetrical dynamic propagation problems on mode Ⅲ interface crack are studied. The universal representations of analytical solutions are obtained by the approaches of self-similar function. The problems researched can be facilely transformed into Riemann-Hilbert problems and analytical solution to an asymmetrical propagation crack under the condition of point loads and unit-step loads, respectively, is acquired. After those solutions were used by superposition theorem, the solutions of arbitrarily complex problems could be attained.
基金the Post-Doctoral Science Foundation of China(No.2005038199)the Natural Science Foundation of Heilongjiang Province of China(No.ZJG04-08)
文摘With the theory of complex functions, dynamic propagation problems concerning surfaces of asymmetrical mode Ⅲ crack subjected to moving loads are investigated. General representations of analytical solutions are obtained with self-similar functions. The problems can be easily converted into Riemann-Hilbert problems using this technique. Analytical solutions to stress, displacement and dynamic stress intensity factor under constant and unit-step moving loads on the surfaces of asymmetrical extension crack, respectively, are obtained. By applying these solutions, together with the superposition principle, solutions of discretionarily intricate problems can be found.
