From discrete flow of Beckner to continuous flow of Janson in complex hypercontractivity

On the basis of the theory of algebraic curves, the continuous flow and discrete flow related to the relativistic Toda hierarchy are straightened out using the Abel–Jacobi coordinates. The meromorphic function and the Baker–Akhiezer function are introduced on the hyperelliptic curve. Quasi-periodic solutions of the relativistic Toda hierarchy are constructed with the help of the asymptotic properties and the algebro-geometric characters of the meromorphic function and the hyperelliptic curve.

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Modeling of word translation: Activation flow from concepts to lexical items

Bilingualism Language and Cognition ◽

10.1017/s1366728912000612 ◽

2012 ◽

Vol 16 (2) ◽

pp. 343-353 ◽

Cited By ~ 5

Author(s):

ARDI ROELOFS ◽

TON DIJKSTRA ◽

SVETLANA GERAKAKI

Keyword(s):

Continuous Flow ◽

Computational Models ◽

Word Production ◽

Discrete Models ◽

Empirical Observation ◽

Bilingual Speakers ◽

Continuous Models ◽

Discrete Flow ◽

Word Translation ◽

Lexical Items

Whereas most theoretical and computational models assume a continuous flow of activation from concepts to lexical items in spoken word production, one prominent model assumes that the mapping of concepts onto words happens in a discrete fashion (Bloem & La Heij, 2003). Semantic facilitation of context pictures on word translation has been taken to support the discrete-flow model. Here, we report results of computer simulations with the continuous-flow WEAVER++ model (Roelofs, 1992, 2006) demonstrating that the empirical observation taken to be in favor of discrete models is, in fact, only consistent with those models and equally compatible with more continuous models of word production by monolingual and bilingual speakers. Continuous models are specifically and independently supported by other empirical evidence on the effect of context pictures on native word production.

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Homotopy Groups of Transformation Groups

Canadian Journal of Mathematics ◽

10.4153/cjm-1969-123-x ◽

1969 ◽

Vol 21 ◽

pp. 1123-1136 ◽

Cited By ~ 1

Author(s):

F. Rhodes

Keyword(s):

Phase Space ◽

Continuous Flow ◽

Homotopy Group ◽

Transformation Group ◽

Group Extension ◽

Transformation Groups ◽

Necessary Condition ◽

Homotopy Groups ◽

Split Extension ◽

Discrete Flow

In a previous paper (2) I defined the fundamental group σ(X, x0, G) of a group Gof homeomorphisms of a space X, and showed that if the transformation group admits a family of preferred paths, then σ(X, x0, G) can be represented as a group extension of π1(X, x0) by G. In this paper the homotopy groups of a transformation group are defined. The nth absolute homotopy group of a transformation group which admits a family of preferred paths is shown to be representable as a split extension of the nth absolute torus homotopy group τn(X, x0) by G.In § 6 it is shown that the action of G on X induces a homomorphism of Ginto a quotient group of a subgroup of the group of automorphisms of τn(X, x0). This homomorphism is used to obtain a necessary condition for the embedding of one transformation group in another, in particular, for the embedding of a discrete flow in a continuous flow with the same phase space.

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The embedding of a linear discrete flow in a continuous flow

Colloquium Mathematicum ◽

10.4064/cm-15-2-263-270 ◽

1966 ◽

Vol 15 (2) ◽

pp. 263-270

Author(s):

W. R. Utz

Keyword(s):

Continuous Flow ◽

Discrete Flow

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DECOMPOSITION AND STRAIGHTENING OUT OF THE DISCRETE KAUP–NEWELL FLOWS

International Journal of Modern Physics B ◽

10.1142/s021797921105922x ◽

2011 ◽

Vol 25 (32) ◽

pp. 4513-4531 ◽

Cited By ~ 4

Author(s):

XIANGUO GENG ◽

TING SU

Keyword(s):

Differential Equations ◽

Ordinary Differential Equations ◽

Finite Order ◽

Continuous Flow ◽

Algebraic Curve ◽

Explicit Solutions ◽

Order Expansion ◽

Discrete Flow

A coupled 2+1-dimensional discrete Chen–Lee–Liu equation is proposed, which together with two 1+1-dimensional discrete Kaup–Newell equations is decomposed into solvable ordinary differential equations with the help of the resulting Lax matrix and its finite-order expansion. Based on the theory of the algebraic curve, the Abel–Jacobi coordinates are introduced to straighten out the corresponding continuous flow and discrete flow, by which explicit solutions for the coupled 2+1-dimensional discrete Chen–Lee–Liu equation and the 1+1-dimensional discrete Kaup–Newell equations are obtained in the Abel–Jacobi coordinates.

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Quasi-periodic solutions of the Belov–Chaltikian lattice hierarchy

Reviews in Mathematical Physics ◽

10.1142/s0129055x17500258 ◽

2017 ◽

Vol 29 (08) ◽

pp. 1750025 ◽

Cited By ~ 2

Author(s):

Xianguo Geng ◽

Xin Zeng

Keyword(s):

Asymptotic Behavior ◽

Meromorphic Function ◽

Periodic Solutions ◽

Continuous Flow ◽

Jacobian Variety ◽

Trigonal Curve ◽

Essential Properties ◽

Discrete Flow ◽

Abel Map ◽

Matrix Spectral Problem

Utilizing the characteristic polynomial of Lax matrix for the Belov–Chaltikian (BC) lattice hierarchy associated with a [Formula: see text] discrete matrix spectral problem, we introduce a trigonal curve with three infinite points, from which we establish the associated Dubrovin-type equations. The essential properties of the Baker–Akhiezer function and the meromorphic function are discussed, that include their asymptotic behavior near three infinite points on the trigonal curve and the divisor of the meromorphic function. The Abel map is introduced to straighten out the continuous flow and the discrete flow in the Jacobian variety, from which the quasi-periodic solutions of the entire BC lattice hierarchy are obtained in terms of the Riemann theta function.

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Catalyst- and oxidant-free electrochemical para-selective hydroxylation of N-arylamides in batch and continuous-flow

Green Chemistry ◽

10.1039/d0gc02294b ◽

2020 ◽

Vol 22 (19) ◽

pp. 6437-6443

Author(s):

Cheng-Kou Liu ◽

Meng-Yi Chen ◽

Xin-Xin Lin ◽

Zheng Fang ◽

Kai Guo

Keyword(s):

Ammonium Salt ◽

Quaternary Ammonium ◽

Continuous Flow ◽

Quaternary Ammonium Salt ◽

Selective Hydroxylation

A catalyst-, oxidant-, acidic solvent- and quaternary ammonium salt-free electrochemical para-selective hydroxylation of N-arylamides at rt in batch and continuous-flow was developed.

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