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Title:

Wronskian Addition Formula and Darboux-Pöschl-Teller Potentials

Description:

For the famous Darboux-Pöschl-Teller equation, we present new wronskian representation both for the potential and the related eigenfunctions. The simplest application of this new formula is the explicit description of dynamics of the DPT potentials and the action of the KdV hierarchy. The key point of the proof is some evaluation formulas for sp...

For the famous Darboux-Pöschl-Teller equation, we present new wronskian representation both for the potential and the related eigenfunctions. The simplest application of this new formula is the explicit description of dynamics of the DPT potentials and the action of the KdV hierarchy. The key point of the proof is some evaluation formulas for special wronskian determinant. Minimize

Publisher:

Journal of Mathematics

Year of Publication:

2013

Document Type:

Research Article

Language:

en

Rights:

Copyright © 2013 Pierre Gaillard and Vladimir Matveev.

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Title:

Quadratically integrable geodesic flows on the torus and on the Klein bottle

Description:

1. If the geodesic flow of a metric G on the torus T 2 is quadratically integrable then the torus T 2 isometrically covers a torus with a Liouville metric on it. 2. The set of quadratically integrable geodesic flows on the Klein bottle is described. x1. Introduction Let M 2 be a smooth close surface with a Riemannian metric G on it. The metric a...

1. If the geodesic flow of a metric G on the torus T 2 is quadratically integrable then the torus T 2 isometrically covers a torus with a Liouville metric on it. 2. The set of quadratically integrable geodesic flows on the Klein bottle is described. x1. Introduction Let M 2 be a smooth close surface with a Riemannian metric G on it. The metric allows to canonically identify the tangent and the co-tangent bundles of the surface M 2 . Therefore we have a scalar product and a norm in every co-tangential plane. Definition 1 Hamiltonian system on the co-tangent plane with the Hamiltonian H def = jpj 2 is called the geodesic flow of the metric G. It is known that the trajectories of the geodesic flow project (under the natural projection ß, ß(x; p) def = x) in the geodesics. Definition 2 A geodesic flow is called integrable if it is integrable as the Hamiltonian system. That is there exists a function F : T M 2 ! R such that: ffl F is constant on the trajectories, ff. Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2009-04-11

Source:

http://www-nonlinear.physik.uni-bremen.de/nlp/publications/./matveev/BOR_TEX/BOR_ENG.ps.gz

http://www-nonlinear.physik.uni-bremen.de/nlp/publications/./matveev/BOR_TEX/BOR_ENG.ps.gz Minimize

Document Type:

text

Language:

en

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Metadata may be used without restrictions as long as the oai identifier remains attached to it.

Metadata may be used without restrictions as long as the oai identifier remains attached to it. Minimize

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Title:

Jacobi vector fields of integrable geodesic flows

Description:

We show that an invariant surface allows to construct the Jacobi vector field along a geodesic and construct the formula for the normal component of the Jacobi field. If a geodesic is the transversal intersection of two invariant surfaces (such situation we have, for example, if the geodesic is hyperbolic), then we can construct a fundamental so...

We show that an invariant surface allows to construct the Jacobi vector field along a geodesic and construct the formula for the normal component of the Jacobi field. If a geodesic is the transversal intersection of two invariant surfaces (such situation we have, for example, if the geodesic is hyperbolic), then we can construct a fundamental solution of the the Jacobi-Hill equation ü = −K(u)u. This is done for quadratically integrable geodesic flows. §1. Introduction. 1.1. Definitions. Suppose G = (gij) is a Riemanian metric on a surface P 2, a curve γ: [a, b] → P 2 is a geodesic. We will assume that the parameter t ∈ [a, b] of the geodesic γ is natural or natural, multiplied by a constant. Minimize

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2012-12-05

Source:

http://arxiv.org/pdf/dg-ga/9712017v1.pdf

http://arxiv.org/pdf/dg-ga/9712017v1.pdf Minimize

Document Type:

text

Language:

en

Rights:

Metadata may be used without restrictions as long as the oai identifier remains attached to it.

Metadata may be used without restrictions as long as the oai identifier remains attached to it. Minimize

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Title:

Jacobi Vector Fields of Integrable Geodesic Flows

Description:

We show that an invariant surface allows to construct the Jacobi vector field along a geodesic and construct the formula for the normal component of the Jacobi field. If a geodesic is the transversal intersection of two invariant surfaces (such situation we have, for example, if the geodesic is hyperbolic), then we can construct a fundamental so...

We show that an invariant surface allows to construct the Jacobi vector field along a geodesic and construct the formula for the normal component of the Jacobi field. If a geodesic is the transversal intersection of two invariant surfaces (such situation we have, for example, if the geodesic is hyperbolic), then we can construct a fundamental solution of the the Jacobi-Hill equation u = \GammaK (u)u. This is done for quadratically integrable geodesic flows. x1. Introduction. 1.1. Definitions. Suppose G = (g ij ) is a Riemanian metric on a surface P 2 , a curve fl : [a; b] ! P 2 is a geodesic. We will assume that the parameter t 2 [a; b] of the geodesic fl is natural or natural, multiplied by a constant. Definition 1 Geodesic variation of a geodesic fl is called the smooth mapping \Gamma : [\Gamma"; "] \Theta [a; b] ! P 2 such that 1) for any fixed s 0 2 [\Gammaffl; ffl] the curve \Gamma(s 0 ; t) : [a; b] ! P 2 (as the curve of parameter t 2 [a; b]) is a geodesic, 2) fo. Minimize

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2009-04-13

Source:

http://www-nonlinear.physik.uni-bremen.de/nlp/publications/./matveev/CON_ENG/CON_ENG.ps.gz

http://www-nonlinear.physik.uni-bremen.de/nlp/publications/./matveev/CON_ENG/CON_ENG.ps.gz Minimize

Document Type:

text

Language:

en

DDC:

516 Geometry *(computed)*

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Metadata may be used without restrictions as long as the oai identifier remains attached to it.

Metadata may be used without restrictions as long as the oai identifier remains attached to it. Minimize

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Title:

Competitive exclusion in Cladocera through elevated mortality of adults

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Abstract. The population dynamics of two cladocerans, Ceriodaphnia pulchella and Diaphanosoma brachyurum competing under laboratory conditions in lake water was analysed using cross-correlations. Both mixed and isolated populations of the two cladocerans showed delayed density-dependence in the death rates of juveniles and adults as well as in f...

Abstract. The population dynamics of two cladocerans, Ceriodaphnia pulchella and Diaphanosoma brachyurum competing under laboratory conditions in lake water was analysed using cross-correlations. Both mixed and isolated populations of the two cladocerans showed delayed density-dependence in the death rates of juveniles and adults as well as in fecundity rate. The regressions for each of the three rates on total density of competitors were compared between the two species. There were no significant differences in the slopes of regressions for fecundity rates and the death rates of juveniles. However, in the inferior competitor (Diaphanosoma) which went extinct in all treatments, the death rate of adults increased with total density much more quickly than in the superior competitor (Ceriodaphnia). The intraspecific comparisons indicated that while Cerio-daphnia adults survived better than juveniles under conditions of crowding, in Diaphanosoma, juveniles were better survivors than adults. These data suggest that the contention of higher vulnerability of cladoceran juveniles than adults to starvation and crowding may prove to be not a universal phenomenon. Minimize

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2015-01-16

Source:

http://epub.ub.uni-muenchen.de/5138/1/041.pdf

http://epub.ub.uni-muenchen.de/5138/1/041.pdf Minimize

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text

Language:

en

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Title:

Quadratically

Description:

integrable geodesic flows on the torus and on the Klein bottle

integrable geodesic flows on the torus and on the Klein bottle Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2012-12-05

Source:

http://arxiv.org/pdf/solv-int/9712019v1.pdf

http://arxiv.org/pdf/solv-int/9712019v1.pdf Minimize

Document Type:

text

Language:

en

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Title:

CHINA'S GAS POLICY IN CENTRAL ASIA

Description:

The development of China's gas industry cannot be reviewed outside the context of the development problems that have arisen throughout its entire energy sphere. The growth of the Chinese economy in the midterm is largely related to the increase in the share of consumption of efficient energy resources-natural gas, oil, hydro-, and nuclear power,...

The development of China's gas industry cannot be reviewed outside the context of the development problems that have arisen throughout its entire energy sphere. The growth of the Chinese economy in the midterm is largely related to the increase in the share of consumption of efficient energy resources-natural gas, oil, hydro-, and nuclear power, although at present their share in the production structure of energy resources is relatively small. But drawing effective energy resources into circulation is fraught with a fair number of problems. At the present time, the high rates of growth in the Chinese economy are not sustained by corresponding development in the fuel and energy complex. The PRC is increasingly becoming a net importer of energy resources. Over time, the shortage of energy resources will only rise, and meeting the needs of the national economy for them in full measure will become one of the active factors in the state's foreign policy strategy. A key facet of China's energy diplomacy is stable and guaranteed provision of the country's needs for highly efficient energy resources, meaning oil and natural gas. Due to the PRC's extensive involvement in the globalization processes, significant attention should be given to such external factors of world energy market movement as a change in the geopolitical situation and the related increase in political risks and instability in hydrocarbon production, increase in world prices for oil and gas, greater state participation in world energy resource trade, and so on. Minimize

Publisher:

Central Asia & Central Caucasus Press AB

Year of Publication:

2008

Document Type:

text

Subjects:

CHINA,CHINA''S ENERGY DIPLOMACY,CENTRAL ASIA,RUSSIA,PETROCHINA,SINOPEC,CNOOC

CHINA,CHINA''S ENERGY DIPLOMACY,CENTRAL ASIA,RUSSIA,PETROCHINA,SINOPEC,CNOOC Minimize

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Title:

Lichnerowicz-Obata conjecture in dimension two

Publisher:

Birkhäuser

Year of Publication:

2005

Source:

Commentarii Mathematici Helvetici ; 1458917-5 ; 0010-2571 ; 80 ; 2005 ; 541

Commentarii Mathematici Helvetici ; 1458917-5 ; 0010-2571 ; 80 ; 2005 ; 541 Minimize

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article

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Title:

Lichnerowicz-Obata conjecture in dimension two

Publisher:

[s.n.]

Year of Publication:

2005

Rights:

[s.n.]

[s.n.] Minimize

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Title:

There exist no locally symmetric Finsler spaces of positive or negative flag curvature

Description:

We show that the results of Foulon (1997 an 2002) and Kim (2007) (independently, Deng and Hou (2007)) about the nonexistence of locally symmetric Finsler metrics of positive or negative flag curvature are in fact local.

We show that the results of Foulon (1997 an 2002) and Kim (2007) (independently, Deng and Hou (2007)) about the nonexistence of locally symmetric Finsler metrics of positive or negative flag curvature are in fact local. Minimize

Year of Publication:

2014-06-11

Document Type:

text

Subjects:

Mathematics - Differential Geometry

Mathematics - Differential Geometry Minimize

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