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integrable

integrable

integrable Sentence Examples

  • If we adopt this hypothesis, and substitute s= 2C T, where c is a constant, in the fundamental equation (9), we obtain at once d 2 E/d T 2 = - 2 (c' -c"), which is immediately integrable, and gives dE/dt=p = 2 (t ° -t) (c'-c") .1 (m) E1_,'=(t-t') (c'-c") 12to-(t-}-t')1 (11) where t o is the temperature of the neutral point at which dE/dt = o.

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  • If c is the velocity of radiation in free space and, u the refractive index of a transparent body, V= c/�; thus it is the expression c2 f� 2 (u'dx-}-v'dy+w'dz) that is to be integrable explicitly, where now (u',v',w') is what is added to V owing to the velocity (u,v,w) of the medium.

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  • Now the expression above given cannot be integrable exactly, under all circumstances and whatever be the axes of co-ordinates, unless (�2u',�2vi,�2w') is the gradient of a continuous function.

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  • If we eliminate P, Q, R from (22), the resulting equations are integrable with respect to t; thus Moa - M0a.

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  • Hamiltonian theory is an important element of integrable systems, whether discrete, ordinary differential or partial differential equations.

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  • integrable lattice equations, which are the difference analogs of the soliton equations.

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  • integrable systems to surface theory.

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  • integrable quantum field theory in the Hilary term of 2006.

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  • integrable maps.

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  • integrable functions over the space with respect to the prior measure.

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  • integrable QFT in presence of a boundary.

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  • They soon realized that the three body problem is not integrable, which means that no exact solution can ever be found.

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  • We study the homoclinic orbits of the completely integrable discrete sine-Gordon.

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  • singularity analysis The Painlevé property has been used in many hundreds of papers to identify integrable cases of equations.

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  • torusroof that homoclinic trajectories in the form of pinched tori imply monodromy in two degree of freedom integrable systems has also been given.

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  • If c is the velocity of radiation in free space and, u the refractive index of a transparent body, V= c/�; thus it is the expression c2 f� 2 (u'dx-}-v'dy+w'dz) that is to be integrable explicitly, where now (u',v',w') is what is added to V owing to the velocity (u,v,w) of the medium.

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  • Now the expression above given cannot be integrable exactly, under all circumstances and whatever be the axes of co-ordinates, unless (�2u',�2vi,�2w') is the gradient of a continuous function.

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  • If we eliminate P, Q, R from (22), the resulting equations are integrable with respect to t; thus Moa - M0a.

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  • If we adopt this hypothesis, and substitute s= 2C T, where c is a constant, in the fundamental equation (9), we obtain at once d 2 E/d T 2 = - 2 (c' -c"), which is immediately integrable, and gives dE/dt=p = 2 (t ° -t) (c'-c") .1 (m) E1_,'=(t-t') (c'-c") 12to-(t-}-t')1 (11) where t o is the temperature of the neutral point at which dE/dt = o.

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  • Exact solutions and singularity analysis The Painlevé property has been used in many hundreds of papers to identify integrable cases of equations.

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  • A proof that homoclinic trajectories in the form of pinched tori imply monodromy in two degree of freedom integrable systems has also been given.

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