In this paper, we made a new breakthrough, which proposes a new recursion–transform（RT） method with potential parameters to evaluate the nodal potential in arbitrary resistor networks. For the first time, we found ...In this paper, we made a new breakthrough, which proposes a new recursion–transform（RT） method with potential parameters to evaluate the nodal potential in arbitrary resistor networks. For the first time, we found the exact potential formulae of arbitrary m × n cobweb and fan networks by the RT method, and the potential formulae of infinite and semi-infinite networks are derived. As applications, a series of interesting corollaries of potential formulae are given by using the general formula, the equivalent resistance formula is deduced by using the potential formula, and we find a new trigonometric identity by comparing two equivalence results with different forms.展开更多
This paper is a further continuation of the paper [1]. In the present paper Mellin transform and Miints formula of weak functions in complex domain will be treated.
In the literature, the Bailey transform has many applications in basic hypergeometric series. In this paper, we derive many new transformation formulas for q-series by means of the Bailey transform. Meanwhile, We also...In the literature, the Bailey transform has many applications in basic hypergeometric series. In this paper, we derive many new transformation formulas for q-series by means of the Bailey transform. Meanwhile, We also obtain some new terminated identities. Furthermore, we establish a companion identity to the Rogers-Ramanujan identity labelled by number (23) on Slater’s list.展开更多
Very recently Atash and Al-Gonah [1] derived two extension formulas for Lauricella’s function of the second kind of several variables and . Now in this research paper we derive two families of transformation formulas...Very recently Atash and Al-Gonah [1] derived two extension formulas for Lauricella’s function of the second kind of several variables and . Now in this research paper we derive two families of transformation formulas for the first kind of Lauricella’s function of several variables and with the help of generalized Dixon’s theorem on the sum of the series obtained earlier by Lavoie et al. [2]. Some new and known results are also deduced as applications of our main formulas.展开更多
The purposes of this article are to discuss the symplectic transformation laws on theta series and to give some explicit formulas for the trace of the symplectic operator.
Here introduced and studied are two formulaic classes consisting of various combinatorial algebraic identities and series summation formulas. The basic ideas include utilizing properly the △-operator and Stirling num...Here introduced and studied are two formulaic classes consisting of various combinatorial algebraic identities and series summation formulas. The basic ideas include utilizing properly the △-operator and Stirling numbers for some series transformations. A variety of classic formulas and remarkable identities are shown to be the members of the classes.展开更多
In this paper, the properties of the exponential Radon transform and its dual are discussed. Furthermore, the analytical reconstruction formulas of exponential Radon transform with two different methods are developed.
In the present paper, the authors introduce a new integral transform which yields a number of potentially useful （known or new） integral transfoms as its special cases. Many fundamental results about this new integr...In the present paper, the authors introduce a new integral transform which yields a number of potentially useful （known or new） integral transfoms as its special cases. Many fundamental results about this new integral transform, which are established in this paper, in- clude （for example） existence theorem, Parseval-type relationship and inversion formula. The relationship between the new integral transform with the H-function and the H-transform are characterized by means of some integral identities. The introduced transform is also used to find solution to a certain differential equation. Some illustrative examples are also given.展开更多
This paper studies the variation of constant formulae for linear Caputo fractional delay differential systems. We discuss the exponential estimates of the solutions for linear time invariant fractional delay different...This paper studies the variation of constant formulae for linear Caputo fractional delay differential systems. We discuss the exponential estimates of the solutions for linear time invariant fractional delay differential systems by using the Gronwall＇s integral inequality. The variation of constant formula for linear time invariant fractional delay differential systems is obtained by using the Laplace transform method. In terms of the superposition principle of linear systems and fundamental solution matrix, we also establish the variation of constant formula for linear time varying fractional delay differential systems. The obtained results generalize the corresponding ones of integer-order delayed differential equations.展开更多
Here the biquaternionic model of electro-gravimagnetic field (EGM-field) has been considered, which describes the change of EGM-fields, charges and currents in their interaction. The invariance of these equations with...Here the biquaternionic model of electro-gravimagnetic field (EGM-field) has been considered, which describes the change of EGM-fields, charges and currents in their interaction. The invariance of these equations with respect to the group of Poincare-Lorentz transformations has been proved. The relativistic formulae of transformation for density of electric and gravity-magnetic charges and currents, active power and forces have been obtained.展开更多
In this paper, a better asymptotic order of Fourier transform on SL(2,R) is obtained by using classical analysis and Lie analysis comparing with that of [5],[6] ,and the Plancherel theorem on C2i(SL(2,R)) is also obta...In this paper, a better asymptotic order of Fourier transform on SL(2,R) is obtained by using classical analysis and Lie analysis comparing with that of [5],[6] ,and the Plancherel theorem on C2i(SL(2,R)) is also obtained as an application.展开更多
The new inversion formula of the Laplace transform is considered. In the formula we use only the positive values ofx SiCoLT（x） = c S（x）, L（S（x）） = T（x）, c = const., x 〉 O,from the real axis. Si is the sinus...The new inversion formula of the Laplace transform is considered. In the formula we use only the positive values ofx SiCoLT（x） = c S（x）, L（S（x）） = T（x）, c = const., x 〉 O,from the real axis. Si is the sinus transform, Co is the cosines transform of Fourier and L is the Laplace transform.展开更多
In this paper we consider Weinstein operator. We define and study the continuous Gabor transform associated with this operator. We prove a Plancherel formula, an inversion formula and a weak uncertainty principle for ...In this paper we consider Weinstein operator. We define and study the continuous Gabor transform associated with this operator. We prove a Plancherel formula, an inversion formula and a weak uncertainty principle for it. As applications, we obtain analogous of Heisenberg’s inequality for the generalized continuous Gabor transform. At the end we give the practical real inversion formula for the generalized continuous Gabor transform.展开更多
[Objectives] To investigate the infrared identification of ZhuQin Formula and Atractylodes polysaccharides and its effect on immune function in immunocompromised mice. [Methods] In this experiment,the structure of pol...[Objectives] To investigate the infrared identification of ZhuQin Formula and Atractylodes polysaccharides and its effect on immune function in immunocompromised mice. [Methods] In this experiment,the structure of polysaccharides was analyzed by Fourier transform infrared spectroscopy. The experiment was divided into the polysaccharide groups of high,medium and low dose of ZhuQin,the extraction group of ZhuQin,the polysaccharide group of Atractylodes,the positive drug group,the blank group and the model group. The model of immunosuppressed mice was established by intraperitoneal injection of cyclophosphamide. The carbon clearance index,immune organ index,serum hemolysin,spleen T and B lymphocyte transformation rate were determined. [Results]The results show that the polysaccharides have obvious absorption peaks of polysaccharides; Formula extracts and polysaccharides can enhance the immune function of immunosuppressive mice at a certain dose level,and the effect of formula polysaccharide is better than that of extract and single traditional Chinese medicine polysaccharides. [Conclusions] The results suggest that the polysaccharides of ZhuQin Formula and Atractylodes may be acidic polysaccharides containing pyran ring and furan ring. ZhuQin Formula polysaccharide may play an immunomodulatory role mainly by improving the specific immunity of the organism.展开更多
The purpose of this paper is to investigate the behavior of a Wiener integral along the curve C of the scale factor ρ > 0 for the Wiener integral ∫C0[0,T]F(ρx)dm(x) about the function defined on the Wiener space...The purpose of this paper is to investigate the behavior of a Wiener integral along the curve C of the scale factor ρ > 0 for the Wiener integral ∫C0[0,T]F(ρx)dm(x) about the function defined on the Wiener space C0[0,T], where θ(t,u) is a Fourier-Stieltjes transform of a complex Borel measure.展开更多
In this paper, we use the Mittag-Leffler addition formula to solve the Green function of generalized time fractional diffusion equation in the whole plane and prove the convergence of the Green function.
基金Project supported by the Natural Science Foundation of Jiangsu Province,China(Grant No.BK20161278)
文摘In this paper, we made a new breakthrough, which proposes a new recursion–transform（RT） method with potential parameters to evaluate the nodal potential in arbitrary resistor networks. For the first time, we found the exact potential formulae of arbitrary m × n cobweb and fan networks by the RT method, and the potential formulae of infinite and semi-infinite networks are derived. As applications, a series of interesting corollaries of potential formulae are given by using the general formula, the equivalent resistance formula is deduced by using the potential formula, and we find a new trigonometric identity by comparing two equivalence results with different forms.
文摘This paper is a further continuation of the paper [1]. In the present paper Mellin transform and Miints formula of weak functions in complex domain will be treated.
文摘In the literature, the Bailey transform has many applications in basic hypergeometric series. In this paper, we derive many new transformation formulas for q-series by means of the Bailey transform. Meanwhile, We also obtain some new terminated identities. Furthermore, we establish a companion identity to the Rogers-Ramanujan identity labelled by number (23) on Slater’s list.
文摘Very recently Atash and Al-Gonah [1] derived two extension formulas for Lauricella’s function of the second kind of several variables and . Now in this research paper we derive two families of transformation formulas for the first kind of Lauricella’s function of several variables and with the help of generalized Dixon’s theorem on the sum of the series obtained earlier by Lavoie et al. [2]. Some new and known results are also deduced as applications of our main formulas.
文摘The purposes of this article are to discuss the symplectic transformation laws on theta series and to give some explicit formulas for the trace of the symplectic operator.
文摘Here introduced and studied are two formulaic classes consisting of various combinatorial algebraic identities and series summation formulas. The basic ideas include utilizing properly the △-operator and Stirling numbers for some series transformations. A variety of classic formulas and remarkable identities are shown to be the members of the classes.
基金Supported by the National Natural Science Foundation of China (61271398)the Ningbo Natural Science Foundation (2011A610170)the Scientific Research Fund of Zhejiang Provincial Education Department(Y201016044)
文摘In this paper, the properties of the exponential Radon transform and its dual are discussed. Furthermore, the analytical reconstruction formulas of exponential Radon transform with two different methods are developed.
文摘In the present paper, the authors introduce a new integral transform which yields a number of potentially useful （known or new） integral transfoms as its special cases. Many fundamental results about this new integral transform, which are established in this paper, in- clude （for example） existence theorem, Parseval-type relationship and inversion formula. The relationship between the new integral transform with the H-function and the H-transform are characterized by means of some integral identities. The introduced transform is also used to find solution to a certain differential equation. Some illustrative examples are also given.
基金the Programs of Educational Commission of Anhui Province(Grant Nos.KJ2011A197KJ2013Z186)
文摘This paper studies the variation of constant formulae for linear Caputo fractional delay differential systems. We discuss the exponential estimates of the solutions for linear time invariant fractional delay differential systems by using the Gronwall＇s integral inequality. The variation of constant formula for linear time invariant fractional delay differential systems is obtained by using the Laplace transform method. In terms of the superposition principle of linear systems and fundamental solution matrix, we also establish the variation of constant formula for linear time varying fractional delay differential systems. The obtained results generalize the corresponding ones of integer-order delayed differential equations.
文摘Here the biquaternionic model of electro-gravimagnetic field (EGM-field) has been considered, which describes the change of EGM-fields, charges and currents in their interaction. The invariance of these equations with respect to the group of Poincare-Lorentz transformations has been proved. The relativistic formulae of transformation for density of electric and gravity-magnetic charges and currents, active power and forces have been obtained.
文摘In this paper, a better asymptotic order of Fourier transform on SL(2,R) is obtained by using classical analysis and Lie analysis comparing with that of [5],[6] ,and the Plancherel theorem on C2i(SL(2,R)) is also obtained as an application.
文摘The new inversion formula of the Laplace transform is considered. In the formula we use only the positive values ofx SiCoLT（x） = c S（x）, L（S（x）） = T（x）, c = const., x 〉 O,from the real axis. Si is the sinus transform, Co is the cosines transform of Fourier and L is the Laplace transform.
文摘In this paper we consider Weinstein operator. We define and study the continuous Gabor transform associated with this operator. We prove a Plancherel formula, an inversion formula and a weak uncertainty principle for it. As applications, we obtain analogous of Heisenberg’s inequality for the generalized continuous Gabor transform. At the end we give the practical real inversion formula for the generalized continuous Gabor transform.
基金Supported by Public Welfare and Industry Special Fund Project of the Ministry of Agriculture(201303040-05)Natural Science Foundation Project of CQCSTC(2013FYF110600)
文摘[Objectives] To investigate the infrared identification of ZhuQin Formula and Atractylodes polysaccharides and its effect on immune function in immunocompromised mice. [Methods] In this experiment,the structure of polysaccharides was analyzed by Fourier transform infrared spectroscopy. The experiment was divided into the polysaccharide groups of high,medium and low dose of ZhuQin,the extraction group of ZhuQin,the polysaccharide group of Atractylodes,the positive drug group,the blank group and the model group. The model of immunosuppressed mice was established by intraperitoneal injection of cyclophosphamide. The carbon clearance index,immune organ index,serum hemolysin,spleen T and B lymphocyte transformation rate were determined. [Results]The results show that the polysaccharides have obvious absorption peaks of polysaccharides; Formula extracts and polysaccharides can enhance the immune function of immunosuppressive mice at a certain dose level,and the effect of formula polysaccharide is better than that of extract and single traditional Chinese medicine polysaccharides. [Conclusions] The results suggest that the polysaccharides of ZhuQin Formula and Atractylodes may be acidic polysaccharides containing pyran ring and furan ring. ZhuQin Formula polysaccharide may play an immunomodulatory role mainly by improving the specific immunity of the organism.
文摘The purpose of this paper is to investigate the behavior of a Wiener integral along the curve C of the scale factor ρ > 0 for the Wiener integral ∫C0[0,T]F(ρx)dm(x) about the function defined on the Wiener space C0[0,T], where θ(t,u) is a Fourier-Stieltjes transform of a complex Borel measure.
文摘In this paper, we use the Mittag-Leffler addition formula to solve the Green function of generalized time fractional diffusion equation in the whole plane and prove the convergence of the Green function.
