In this paper,we establish characterizations of α-Bloch functions and little α-Bloch functions on the unit ball as well as the unit polydisk of C^(m),which generalize and improve results of Aulaskari-Lappan,Minda,Au...In this paper,we establish characterizations of α-Bloch functions and little α-Bloch functions on the unit ball as well as the unit polydisk of C^(m),which generalize and improve results of Aulaskari-Lappan,Minda,Aulaskari-Wulan,and Wu.Some examples are also given to complement our theory.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
In this paper, the multistability issue is discussed for delayed complex-valued recurrent neural networks with discontinuous real-imaginary-type activation functions. Based on a fixed theorem and stability definition,...In this paper, the multistability issue is discussed for delayed complex-valued recurrent neural networks with discontinuous real-imaginary-type activation functions. Based on a fixed theorem and stability definition, sufficient criteria are established for the existence and stability of multiple equilibria of complex-valued recurrent neural networks. The number of stable equilibria is larger than that of real-valued recurrent neural networks, which can be used to achieve high-capacity associative memories. One numerical example is provided to show the effectiveness and superiority of the presented results.展开更多
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
In this paper, we present a new representation of gamma function as a series of complex delta functions. We establish the convergence of this representation in the sense of distributions. It turns out that the gamma f...In this paper, we present a new representation of gamma function as a series of complex delta functions. We establish the convergence of this representation in the sense of distributions. It turns out that the gamma function can be defined over a space of complex test functions of slow growth denoted by Z. Some properties of gamma function are discussed by using the properties of delta function.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
To solve the problem in dispute about a Schrdinger equation with time-depenelent mass and frequency, by means of a simple transformation of variables, the time-dependent Schrdinger equation is transformed into the tim...To solve the problem in dispute about a Schrdinger equation with time-depenelent mass and frequency, by means of a simple transformation of variables, the time-dependent Schrdinger equation is transformed into the time-independent one first and then an exact wave function can be found.展开更多
Near infrared spectroscopy(NIRS)is generally accepted as a functional brain imaging technology for brain activation study.With multichannel highly sensitive NIRS instruments,it has become possible to assess functional...Near infrared spectroscopy(NIRS)is generally accepted as a functional brain imaging technology for brain activation study.With multichannel highly sensitive NIRS instruments,it has become possible to assess functional connectivity of different brain negions by NIRS.However,the feasibility needs to be validated in complex cognitive activities.In this study,we recorded the hemodynamic activity of the bilateral prefrontal cortex(PFC)during a color-word matching Stroop task.Wavelet transform coberence(WTC)analysis was applied to ascss the functional conectivity of all homologous channel pairs within the left/right PFC.Both the behavioral and brain activ ation results showed signifcant Stroop effects.The results of WTC analysis revealed that,bilateral functional connectivity was significantly stronger during both the incongruent stimuli and neutral stimuli compared to that of the rest period.It also showed significant Stroop effect.Our findings demonstrate that,NIRS bcomes a valuable tool to elucidate the functional conectivity of brain cortex in complex cognitive activities.展开更多
Green’s function for the T-stress near a crack tip is addressed with an analytic function method for a semi-infinite crack lying in an elastical, isotropic, and infinite plate. The cracked plate is loaded by a single...Green’s function for the T-stress near a crack tip is addressed with an analytic function method for a semi-infinite crack lying in an elastical, isotropic, and infinite plate. The cracked plate is loaded by a single inclined concentrated force at an interior point. The complex potentials are obtained based on a superposition principle, which provide the solutions to the plane problems of elasticity. The regular parts of the potentials are extracted in an asymptotic analysis. Based on the regular parts, Green’s function for the T-stress is obtained in a straightforward manner. Furthermore, Green’s functions are derived for a pair of symmetrically and anti-symmetrically concentrated forces by the superimposing method. Then, Green’s function is used to predict the domain-switch-induced T-stress in a ferroelectric double cantilever beam （DCB） test. The T-stress induced by the electromechanical loading is used to judge the stable and unstable crack growth behaviors observed in the test. The prediction results generally agree with the experimental data.展开更多
In this paper,conjugate k-holomorphic functions and generalized k-holomorphic functions are defined in the two-dimensional complex space,and the corresponding Riemann boundary value problems and the inverse problems a...In this paper,conjugate k-holomorphic functions and generalized k-holomorphic functions are defined in the two-dimensional complex space,and the corresponding Riemann boundary value problems and the inverse problems are discussed on generalized bicylinders.By the characteristics of the corresponding functions and boundary properties of the Cauchy type singular integral operators with conjugate k-holomorphic kernels,the general solutions and special solutions of the corresponding boundary value problems are studied in a detailed fashion,and the integral expressions of the solutions are obtained.展开更多
In this paper, a novel design procedure is proposed for synthesizing high-capacity auto-associative memories based on complex-valued neural networks with real-imaginary-type activation functions and constant delays. S...In this paper, a novel design procedure is proposed for synthesizing high-capacity auto-associative memories based on complex-valued neural networks with real-imaginary-type activation functions and constant delays. Stability criteria dependent on external inputs of neural networks are derived. The designed networks can retrieve the stored patterns by external inputs rather than initial conditions. The derivation can memorize the desired patterns with lower-dimensional neural networks than real-valued neural networks, and eliminate spurious equilibria of complex-valued neural networks. One numerical example is provided to show the effectiveness and superiority of the presented results.展开更多
We study the high order equilibrium distributions of a counting random variable. Properties such as moments, the probability generating function, the stop--loss transform and the mean residual lifetime, are derived. E...We study the high order equilibrium distributions of a counting random variable. Properties such as moments, the probability generating function, the stop--loss transform and the mean residual lifetime, are derived. Expressions are obtained for higher order equilibrium distribution functions under mixtures and convolutions of a counting distribution. Recursive formulas for higher order equilibrium distribution functions of the (a,b,0) -family of distributions are given.展开更多
In this paper,new infinite sequence complex solutions of the coupled Kd V equations are constructed with the help of function transformation and the second kind of elliptic equation.First of all,according to the funct...In this paper,new infinite sequence complex solutions of the coupled Kd V equations are constructed with the help of function transformation and the second kind of elliptic equation.First of all,according to the function transformation,the coupled Kd V equations are changed into the second kind of elliptic equation.Secondly,the new solutions and Bäcklund transformation of the second kind of elliptic equation are applied to search for new infinite sequence complex solutions of the coupled Kd V equations.These solutions include new infinite sequence complex solutions composed by Jacobi elliptic function,hyperbolic function and triangular function.展开更多
基金Supported by Natural Science Research Project for Colleges and Universities of Anhui Province(Grant No.2022AH050329)Yunnan Provincial Department of Education Fund(Grant No.2025J0376).
文摘In this paper,we establish characterizations of α-Bloch functions and little α-Bloch functions on the unit ball as well as the unit polydisk of C^(m),which generalize and improve results of Aulaskari-Lappan,Minda,Aulaskari-Wulan,and Wu.Some examples are also given to complement our theory.
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.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.61374094 and 61503338)the Natural Science Foundation of Zhejiang Province,China(Grant No.LQ15F030005)
文摘In this paper, the multistability issue is discussed for delayed complex-valued recurrent neural networks with discontinuous real-imaginary-type activation functions. Based on a fixed theorem and stability definition, sufficient criteria are established for the existence and stability of multiple equilibria of complex-valued recurrent neural networks. The number of stable equilibria is larger than that of real-valued recurrent neural networks, which can be used to achieve high-capacity associative memories. One numerical example is provided to show the effectiveness and superiority of the presented results.
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In this paper, we present a new representation of gamma function as a series of complex delta functions. We establish the convergence of this representation in the sense of distributions. It turns out that the gamma function can be defined over a space of complex test functions of slow growth denoted by Z. Some properties of gamma function are discussed by using the properties of delta function.
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.
文摘To solve the problem in dispute about a Schrdinger equation with time-depenelent mass and frequency, by means of a simple transformation of variables, the time-dependent Schrdinger equation is transformed into the time-independent one first and then an exact wave function can be found.
基金supported by the Science Fund for Creative Research Group of China(Grant No.61121004)National Natural Science Foundation of China(Grant No.61078072)863 Program(Grant No.2012AA02A602).
文摘Near infrared spectroscopy(NIRS)is generally accepted as a functional brain imaging technology for brain activation study.With multichannel highly sensitive NIRS instruments,it has become possible to assess functional connectivity of different brain negions by NIRS.However,the feasibility needs to be validated in complex cognitive activities.In this study,we recorded the hemodynamic activity of the bilateral prefrontal cortex(PFC)during a color-word matching Stroop task.Wavelet transform coberence(WTC)analysis was applied to ascss the functional conectivity of all homologous channel pairs within the left/right PFC.Both the behavioral and brain activ ation results showed signifcant Stroop effects.The results of WTC analysis revealed that,bilateral functional connectivity was significantly stronger during both the incongruent stimuli and neutral stimuli compared to that of the rest period.It also showed significant Stroop effect.Our findings demonstrate that,NIRS bcomes a valuable tool to elucidate the functional conectivity of brain cortex in complex cognitive activities.
基金Project supported by the National Natural Science Foundation of China(Nos.10702071 and 11090334)the China Postdoctoral Science Foundation(No.201003281)+2 种基金the Shanghai Postdoctoral Scientific Program(No.10R21415800)the Shanghai Leading Academic Discipline Project(No.B302)sponsored by the"Sino-German Center for Research Promotion"under a project of"Crack Growth in Ferroelectrics Driven by Cyclic Electric Loading"
文摘Green’s function for the T-stress near a crack tip is addressed with an analytic function method for a semi-infinite crack lying in an elastical, isotropic, and infinite plate. The cracked plate is loaded by a single inclined concentrated force at an interior point. The complex potentials are obtained based on a superposition principle, which provide the solutions to the plane problems of elasticity. The regular parts of the potentials are extracted in an asymptotic analysis. Based on the regular parts, Green’s function for the T-stress is obtained in a straightforward manner. Furthermore, Green’s functions are derived for a pair of symmetrically and anti-symmetrically concentrated forces by the superimposing method. Then, Green’s function is used to predict the domain-switch-induced T-stress in a ferroelectric double cantilever beam （DCB） test. The T-stress induced by the electromechanical loading is used to judge the stable and unstable crack growth behaviors observed in the test. The prediction results generally agree with the experimental data.
基金supported by the NSF of Henan Province(222300420397,242300421394)Xie’s research was supported by the NSFC(11571089,11871191).
文摘In this paper,conjugate k-holomorphic functions and generalized k-holomorphic functions are defined in the two-dimensional complex space,and the corresponding Riemann boundary value problems and the inverse problems are discussed on generalized bicylinders.By the characteristics of the corresponding functions and boundary properties of the Cauchy type singular integral operators with conjugate k-holomorphic kernels,the general solutions and special solutions of the corresponding boundary value problems are studied in a detailed fashion,and the integral expressions of the solutions are obtained.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.61503338,61573316,61374152,and 11302195)the Natural Science Foundation of Zhejiang Province,China(Grant No.LQ15F030005)
文摘In this paper, a novel design procedure is proposed for synthesizing high-capacity auto-associative memories based on complex-valued neural networks with real-imaginary-type activation functions and constant delays. Stability criteria dependent on external inputs of neural networks are derived. The designed networks can retrieve the stored patterns by external inputs rather than initial conditions. The derivation can memorize the desired patterns with lower-dimensional neural networks than real-valued neural networks, and eliminate spurious equilibria of complex-valued neural networks. One numerical example is provided to show the effectiveness and superiority of the presented results.
文摘We study the high order equilibrium distributions of a counting random variable. Properties such as moments, the probability generating function, the stop--loss transform and the mean residual lifetime, are derived. Expressions are obtained for higher order equilibrium distribution functions under mixtures and convolutions of a counting distribution. Recursive formulas for higher order equilibrium distribution functions of the (a,b,0) -family of distributions are given.
基金Supported by the Natural Natural Science Foundation of China(Grant No:11361040)Science Research Foundation of Institution of Higher Education of Inner Mongolia Autonomous Region,China(Grant No:NJZY16180)Natural Science Foundation of Inner Mongolia Autonomous Region,China(Grant No:2015MS0128)。
文摘In this paper,new infinite sequence complex solutions of the coupled Kd V equations are constructed with the help of function transformation and the second kind of elliptic equation.First of all,according to the function transformation,the coupled Kd V equations are changed into the second kind of elliptic equation.Secondly,the new solutions and Bäcklund transformation of the second kind of elliptic equation are applied to search for new infinite sequence complex solutions of the coupled Kd V equations.These solutions include new infinite sequence complex solutions composed by Jacobi elliptic function,hyperbolic function and triangular function.
