Lie symmetry analysis is applied to a(3+1)-dimensional Virasoro integrable model and the corresponding similarity reduction equations are obtained with the different infinitesimal generators.Invariant solutions with a...Lie symmetry analysis is applied to a(3+1)-dimensional Virasoro integrable model and the corresponding similarity reduction equations are obtained with the different infinitesimal generators.Invariant solutions with arbitrary functions for the(3+1)-dimensional Virasoro integrable model,including the interaction solution between a kink and a soliton,the lump-type solution and periodic solutions,have been studied analytically and graphically.展开更多
Effects of berberine (Ber) on platelet aggregation and TXB2 and 6 keto PGF1a plasma levels were studied in rabbits with uncomplete cerebral ischemia. Ber inhibited uncomplete cerebral ischemic rabbit platelet aggreg...Effects of berberine (Ber) on platelet aggregation and TXB2 and 6 keto PGF1a plasma levels were studied in rabbits with uncomplete cerebral ischemia. Ber inhibited uncomplete cerebral ischemic rabbit platelet aggregation triggered by collagen, ADP, and arachidonic acid (AA) with the IC 50 of 0.15, 0.46, and 0.51 mg·ml 1 , respectively. In rabbits, Ber 25, or 50 mg·kg 1 iv 30 min after uncomplete cerebral ischemia, restrained the collagen ADP and AA induced platelet aggregation determined 90 min later. With radioimmunoassay, we measured the thromboxane B2 (TXB 2) and 6 ketoprostaglandin F 1α (6 keto PGF 1α ) contents in rabbit plasma. The results indicated that the TXB 2 level in rabbit 120 min after uncomplete cerebral ischemia (921±539 pg·ml 1 ) was higher than that (230±71 pg·ml 1 ) in normal rabbits ( P < 0.01), but 6 keto PGF 1α level after ischemia (73±23pg·ml 1 ) was lower than that (262±988pg·ml 1 ) in normal rabbit. Ber (5, 25 or 50 mg·kg 1 ) reduced obviously the plasma TXB 2 level in rabbit with uncomplete cerebral ischemia (504±196, 386±174, or 272±183 vs 921±539 pg·ml 1 , respectively, P < 0.01). We conclude that the decrease of TXB 2 content is one of the possible mechanisms of Ber anti cerebral ischemic effect.展开更多
Notch pathway activation maintains neural stem cells in a proliferating state and increases nerve repair capacity. To date, studies have rarely focused on changes or damage to signal transduc- tion pathways during cer...Notch pathway activation maintains neural stem cells in a proliferating state and increases nerve repair capacity. To date, studies have rarely focused on changes or damage to signal transduc- tion pathways during cerebral hemorrhage. Here, we examined the effect of acupuncture in a rat model of cerebral hemorrhage. We examined four groups： in the control group, rats received no treatment. In the model group, cerebral hemorrhage models were established by infusing non-hep-arinized blood into the Brain. In the acupuncture group, modeled rats had Baihui （DU20） and Qubin （GBT） acupoints treated once a day for 30 minutes. In the DAPT group, modeled rats had 0.15 μg/mL DAPT solution （10 mL） infused into the brain. Immunohistochemistry and western blot results showed that acupuncture effectively inhibits Notch 1 and Hesl protein expression in rat basal ganglia. These inhibitory effects were identical to DAPT, a Notch signaling pathway inhibitor. Our results suggest that acupuncture has a neuroprotective effect on cerebral hemorrhage by in- hibiting Notch-Hes signaling pathway transduction in rat basal ganglia after cerebral hemorrhage.展开更多
In this paper, the modified CK＇s direct method to find symmetry groups of nonlinear partial differential equation is extended to （2＋1）-dimensional variable coeffficient canonical generalized KP （VCCGKP） equation...In this paper, the modified CK＇s direct method to find symmetry groups of nonlinear partial differential equation is extended to （2＋1）-dimensional variable coeffficient canonical generalized KP （VCCGKP） equation. As a result, symmetry groups, Lie point symmetry group and Lie symmetry for the VCCGKP equation are obtained. In fact, the Lie point symmetry group coincides with that obtained by the standard Lie group approach. Applying the given Lie symmetry, we obtain five types of similarity reductions and a lot of new exact solutions, including hyperbolic function solutions, triangular periodic solutions, Jacobi elliptic function solutions and rational solutions, for the VCCGKP equation.展开更多
A modified direct method is developed to find finite symmetry groups of nonlinear mathematical physicssystems.Applying the modified direct method to the well-known (2+1)-dimensional BKP equation we get its symmetry.Fu...A modified direct method is developed to find finite symmetry groups of nonlinear mathematical physicssystems.Applying the modified direct method to the well-known (2+1)-dimensional BKP equation we get its symmetry.Furthermore,the exact solutions of (2+1)-dimensional BKP equation are obtained through symmetry analysis.展开更多
In this paper we study the convergence nf a class of means on H^p(G)(0<p<1),the means take the Bochner-Riesz means in[1],the generalized Bochner-Riesz means in[2],and the operators T^(Φ_r)in[3]as special cases....In this paper we study the convergence nf a class of means on H^p(G)(0<p<1),the means take the Bochner-Riesz means in[1],the generalized Bochner-Riesz means in[2],and the operators T^(Φ_r)in[3]as special cases.We obtain weak-type estimates for the associated maximal operators and the maximal mean boundedness for the means.展开更多
Starting from general Jacobi polynomials we derive for the Ul-traspherical polynomials as their special case a set of related polynomials which can be extended to an orthogonal set of functions with interesting proper...Starting from general Jacobi polynomials we derive for the Ul-traspherical polynomials as their special case a set of related polynomials which can be extended to an orthogonal set of functions with interesting properties. It leads to an alternative definition of the Ultraspherical polynomials by a fixed integral operator in application to powers of the variable u in an analogous way as it is possible for Hermite polynomials. From this follows a generating function which is apparently known only for the Legendre and Chebyshev polynomials as their special case. Furthermore, we show that the Ultraspherical polynomials form a realization of the SU(1,1) Lie algebra with lowering and raising operators which we explicitly determine. By reordering of multiplication and differentiation operators we derive new operator identities for the whole set of Jacobi polynomials which may be applied to arbitrary functions and provide then function identities. In this way we derive a new “convolution identity” for Jacobi polynomials and compare it with a known convolution identity of different structure for Gegenbauer polynomials. In short form we establish the connection of Jacobi polynomials and their related orthonormalized functions to the eigensolution of the Schrödinger equation to Pöschl-Teller potentials.展开更多
In the novel What I Saw and How I Lied （2008）, Judy Blundell presents readers a world of noir where so many lies are around the innocent protagonist, 15-year-old girl Evie. It is a challenge for Evie to probe into t...In the novel What I Saw and How I Lied （2008）, Judy Blundell presents readers a world of noir where so many lies are around the innocent protagonist, 15-year-old girl Evie. It is a challenge for Evie to probe into the heart of the deceptions and make ethical choices between good and evil. After experiencing the path from error to truth, from confusion to clarity, and unconsciousness to consciousness, Evie comes to realize the corruption and evils of the society and in an epiphany, obtains a self-knowledge which leads to her initiation. Through analyzing the ethical predicament and ethical choices of the protagonist Evie as well as the negative living environment around her, the present paper aims to interrogate the moral issues of truth, lie, justice, greed, fidelity, and betrayal so as to give readers a better understanding of the theme of initiation in the novel.展开更多
We consider the following (1 + 3)-dimensional P(1,4)-invariant partial differential equations (PDEs): the Eikonal equation, the Euler-Lagrange-Born-Infeld equation, the homogeneous Monge-Ampère equation, the inho...We consider the following (1 + 3)-dimensional P(1,4)-invariant partial differential equations (PDEs): the Eikonal equation, the Euler-Lagrange-Born-Infeld equation, the homogeneous Monge-Ampère equation, the inhomogeneous Monge-Ampère equation. The purpose of this paper is to construct and classify the common invariant solutions for those equations. For this aim, we have used the results concerning construction and classification of invariant solutions for the (1 + 3)-dimensional P(1,4)-invariant Eikonal equation, since this equation is the simplest among the equations under investigation. The direct checked allowed us to conclude that the majority of invariant solutions of the (1 + 3)-dimensional Eikonal equation, obtained on the base of low-dimensional (dimL ≤ 3) nonconjugate subalgebras of the Lie algebra of the Poincaré group P(1,4), satisfy all the equations under investigation. In this paper, we present obtained common invariant solutions of the equations under study as well as the classification of those invariant solutions.展开更多
文摘Lie symmetry analysis is applied to a(3+1)-dimensional Virasoro integrable model and the corresponding similarity reduction equations are obtained with the different infinitesimal generators.Invariant solutions with arbitrary functions for the(3+1)-dimensional Virasoro integrable model,including the interaction solution between a kink and a soliton,the lump-type solution and periodic solutions,have been studied analytically and graphically.
文摘Effects of berberine (Ber) on platelet aggregation and TXB2 and 6 keto PGF1a plasma levels were studied in rabbits with uncomplete cerebral ischemia. Ber inhibited uncomplete cerebral ischemic rabbit platelet aggregation triggered by collagen, ADP, and arachidonic acid (AA) with the IC 50 of 0.15, 0.46, and 0.51 mg·ml 1 , respectively. In rabbits, Ber 25, or 50 mg·kg 1 iv 30 min after uncomplete cerebral ischemia, restrained the collagen ADP and AA induced platelet aggregation determined 90 min later. With radioimmunoassay, we measured the thromboxane B2 (TXB 2) and 6 ketoprostaglandin F 1α (6 keto PGF 1α ) contents in rabbit plasma. The results indicated that the TXB 2 level in rabbit 120 min after uncomplete cerebral ischemia (921±539 pg·ml 1 ) was higher than that (230±71 pg·ml 1 ) in normal rabbits ( P < 0.01), but 6 keto PGF 1α level after ischemia (73±23pg·ml 1 ) was lower than that (262±988pg·ml 1 ) in normal rabbit. Ber (5, 25 or 50 mg·kg 1 ) reduced obviously the plasma TXB 2 level in rabbit with uncomplete cerebral ischemia (504±196, 386±174, or 272±183 vs 921±539 pg·ml 1 , respectively, P < 0.01). We conclude that the decrease of TXB 2 content is one of the possible mechanisms of Ber anti cerebral ischemic effect.
基金supported by the National Natural Science Foundation of China,No.81273824,30772840Ministry of Education Doctoral Fund in China,No.20102327110003+1 种基金the Natural Science Foundation of Heilongjiang Province in China,No.ZD201204Special funds for Technological Innovation Research of Harbin,China,No.2012RFXXS062
文摘Notch pathway activation maintains neural stem cells in a proliferating state and increases nerve repair capacity. To date, studies have rarely focused on changes or damage to signal transduc- tion pathways during cerebral hemorrhage. Here, we examined the effect of acupuncture in a rat model of cerebral hemorrhage. We examined four groups： in the control group, rats received no treatment. In the model group, cerebral hemorrhage models were established by infusing non-hep-arinized blood into the Brain. In the acupuncture group, modeled rats had Baihui （DU20） and Qubin （GBT） acupoints treated once a day for 30 minutes. In the DAPT group, modeled rats had 0.15 μg/mL DAPT solution （10 mL） infused into the brain. Immunohistochemistry and western blot results showed that acupuncture effectively inhibits Notch 1 and Hesl protein expression in rat basal ganglia. These inhibitory effects were identical to DAPT, a Notch signaling pathway inhibitor. Our results suggest that acupuncture has a neuroprotective effect on cerebral hemorrhage by in- hibiting Notch-Hes signaling pathway transduction in rat basal ganglia after cerebral hemorrhage.
基金The project supported by the Natural Science Foundation of Shandong Province of China under Grant Nos. 2004zx16 and Q2005A01
文摘In this paper, the modified CK＇s direct method to find symmetry groups of nonlinear partial differential equation is extended to （2＋1）-dimensional variable coeffficient canonical generalized KP （VCCGKP） equation. As a result, symmetry groups, Lie point symmetry group and Lie symmetry for the VCCGKP equation are obtained. In fact, the Lie point symmetry group coincides with that obtained by the standard Lie group approach. Applying the given Lie symmetry, we obtain five types of similarity reductions and a lot of new exact solutions, including hyperbolic function solutions, triangular periodic solutions, Jacobi elliptic function solutions and rational solutions, for the VCCGKP equation.
基金National Natural Science Foundation of China under Grant Nos.90203001,90503006,0475055,and 10647112the Foundation of Donghua University
文摘A modified direct method is developed to find finite symmetry groups of nonlinear mathematical physicssystems.Applying the modified direct method to the well-known (2+1)-dimensional BKP equation we get its symmetry.Furthermore,the exact solutions of (2+1)-dimensional BKP equation are obtained through symmetry analysis.
文摘In this paper we study the convergence nf a class of means on H^p(G)(0<p<1),the means take the Bochner-Riesz means in[1],the generalized Bochner-Riesz means in[2],and the operators T^(Φ_r)in[3]as special cases.We obtain weak-type estimates for the associated maximal operators and the maximal mean boundedness for the means.
文摘Starting from general Jacobi polynomials we derive for the Ul-traspherical polynomials as their special case a set of related polynomials which can be extended to an orthogonal set of functions with interesting properties. It leads to an alternative definition of the Ultraspherical polynomials by a fixed integral operator in application to powers of the variable u in an analogous way as it is possible for Hermite polynomials. From this follows a generating function which is apparently known only for the Legendre and Chebyshev polynomials as their special case. Furthermore, we show that the Ultraspherical polynomials form a realization of the SU(1,1) Lie algebra with lowering and raising operators which we explicitly determine. By reordering of multiplication and differentiation operators we derive new operator identities for the whole set of Jacobi polynomials which may be applied to arbitrary functions and provide then function identities. In this way we derive a new “convolution identity” for Jacobi polynomials and compare it with a known convolution identity of different structure for Gegenbauer polynomials. In short form we establish the connection of Jacobi polynomials and their related orthonormalized functions to the eigensolution of the Schrödinger equation to Pöschl-Teller potentials.
文摘In the novel What I Saw and How I Lied （2008）, Judy Blundell presents readers a world of noir where so many lies are around the innocent protagonist, 15-year-old girl Evie. It is a challenge for Evie to probe into the heart of the deceptions and make ethical choices between good and evil. After experiencing the path from error to truth, from confusion to clarity, and unconsciousness to consciousness, Evie comes to realize the corruption and evils of the society and in an epiphany, obtains a self-knowledge which leads to her initiation. Through analyzing the ethical predicament and ethical choices of the protagonist Evie as well as the negative living environment around her, the present paper aims to interrogate the moral issues of truth, lie, justice, greed, fidelity, and betrayal so as to give readers a better understanding of the theme of initiation in the novel.
文摘We consider the following (1 + 3)-dimensional P(1,4)-invariant partial differential equations (PDEs): the Eikonal equation, the Euler-Lagrange-Born-Infeld equation, the homogeneous Monge-Ampère equation, the inhomogeneous Monge-Ampère equation. The purpose of this paper is to construct and classify the common invariant solutions for those equations. For this aim, we have used the results concerning construction and classification of invariant solutions for the (1 + 3)-dimensional P(1,4)-invariant Eikonal equation, since this equation is the simplest among the equations under investigation. The direct checked allowed us to conclude that the majority of invariant solutions of the (1 + 3)-dimensional Eikonal equation, obtained on the base of low-dimensional (dimL ≤ 3) nonconjugate subalgebras of the Lie algebra of the Poincaré group P(1,4), satisfy all the equations under investigation. In this paper, we present obtained common invariant solutions of the equations under study as well as the classification of those invariant solutions.
