Efficiency and duality for a vector of quotients of curvilinear functionals on the first-order jet bundle

2017 ◽  
Vol 38 (6) ◽  
pp. 1227-1238
Author(s):  
Indira P. Debnath ◽  
S. K. Gupta
Keyword(s):  
Jet Bundle ◽  
First Order

scholarly journals PRE-MULTISYMPLECTIC CONSTRAINT ALGORITHM FOR FIELD THEORIES

2005 ◽  
Vol 02 (05) ◽  
pp. 839-871 ◽  
Author(s):  
MANUEL DE LEÓN ◽  
JESÚS MARÍN-SOLANO ◽  
JUAN CARLOS MARRERO ◽  
MIGUEL C. MUÑOZ-LECANDA ◽  
NARCISO ROMÁN-ROY
Keyword(s):  
Fiber Bundle ◽  
General Framework ◽  
Vector Fields ◽  
Classical Field ◽  
Field Theories ◽  
Second Step ◽  
Field Equations ◽  
Jet Bundle ◽  
First Order ◽  
Classical Field Theories

We present a geometric algorithm for obtaining consistent solutions to systems of partial differential equations, mainly arising from singular covariant first-order classical field theories. This algorithm gives an intrinsic description of all the constraint submanifolds. The field equations are stated geometrically, either representing their solutions by integrable connections or, what is equivalent, by certain kinds of integrable m-vector fields. First, we consider the problem of finding connections or multivector fields solutions to the field equations in a general framework: a pre-multisymplectic fiber bundle (which will be identified with the first-order jet bundle and the multi-momentum bundle when Lagrangian and Hamiltonian field theories are considered). Then, the problem is stated and solved in a linear context, and a pointwise application of the results leads to the algorithm for the general case. In a second step, the integrability of the solutions is also studied. Finally, the method is applied to Lagrangian and Hamiltonian field theories and, for the former, the problem of finding holonomic solutions is also analyzed.

AFFINE DUALITY AND LAGRANGIAN AND HAMILTONIAN SYSTEMS

2011 ◽  
Vol 08 (03) ◽  
pp. 669-697 ◽  
Author(s):  
OLGA KRUPKOVÁ ◽  
DAVID J. SAUNDERS
Keyword(s):  
Hamiltonian Systems ◽  
Arbitrary Order ◽  
Variational Problems ◽  
Higher Order ◽  
Jet Bundle ◽  
Jet Bundles ◽  
First Order ◽  
Variational Form ◽  
Independent Variable

We use affine duals of jet bundles to describe how Legendre maps may be used to provide Hamiltonian representations of variational problems in a single independent variable. Such a problem may be given as a Lagrangian (of first-order or of higher-order), or alternatively as a locally variational form on a jet bundle of arbitrary order with no preferred Lagrangian.

scholarly journals Burgers’ Equations in the Riemannian Geometry Associated with First-Order Differential Equations

2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Z. Ok Bayrakdar ◽  
T. Bayrakdar
Keyword(s):  
Vector Fields ◽  
Integral Manifold ◽  
Integrability Condition ◽  
Three Dimensional ◽  
Dimensional Manifold ◽  
Jet Bundle ◽  
First Order ◽  
Burgers Equations ◽  
Integral Curves ◽  
Metric Connection

We construct metric connection associated with a first-order differential equation by means of the generator set of a Pfaffian system on a submanifold of an appropriate first-order jet bundle. We firstly show that the inviscid and viscous Burgers’ equations describe surfaces attached to an ODE of the form dx/dt=u(t,x) with certain Gaussian curvatures. In the case of PDEs, we show that the scalar curvature of a three-dimensional manifold encoding a system of first-order PDEs is determined in terms of the integrability condition and the Gaussian curvatures of the surfaces corresponding to the integral curves of the vector fields which are annihilated by the contact form. We see that an integral manifold of any PDE defines intrinsically flat and totally geodesic submanifold.

Dual systems for all: Higher-order, role-based relational reasoning as a uniquely derived feature of human cognition

2019 ◽  
Vol 42 ◽  
Author(s):  
Daniel J. Povinelli ◽  
Gabrielle C. Glorioso ◽  
Shannon L. Kuznar ◽  
Mateja Pavlic
Keyword(s):  
Temporal Reasoning ◽  
Higher Order ◽  
Important Case ◽  
Human Cognition ◽  
Relational Reasoning ◽  
Dual Systems ◽  
First Order ◽  
Reasoning System ◽  
Role Based

Abstract Hoerl and McCormack demonstrate that although animals possess a sophisticated temporal updating system, there is no evidence that they also possess a temporal reasoning system. This important case study is directly related to the broader claim that although animals are manifestly capable of first-order (perceptually-based) relational reasoning, they lack the capacity for higher-order, role-based relational reasoning. We argue this distinction applies to all domains of cognition.

Stochasting modeling of planetary ring systems

1984 ◽  
Vol 75 ◽  
pp. 461-469 ◽  
Author(s):  
Robert W. Hart
Keyword(s):  
Maximum Entropy ◽  
Ring System ◽  
The Sun ◽  
Ultimate State ◽  
Interparticle Interactions ◽  
Ring Systems ◽  
First Order ◽  
Planetary Ring ◽  
Insight Into

ABSTRACTThis paper models maximum entropy configurations of idealized gravitational ring systems. Such configurations are of interest because systems generally evolve toward an ultimate state of maximum randomness. For simplicity, attention is confined to ultimate states for which interparticle interactions are no longer of first order importance. The planets, in their orbits about the sun, are one example of such a ring system. The extent to which the present approximation yields insight into ring systems such as Saturn's is explored briefly.

Morphological studies of linear (AB)n multiblock copolymers and their blends

1992 ◽  
Vol 50 (1) ◽  
pp. 384-385
Author(s):  
Richard J. Spontak ◽  
Steven D. Smith ◽  
Arman Ashraf
Keyword(s):  
Electron Microscopy ◽  
Microphase Separation ◽  
Multiblock Copolymers ◽  
First Order ◽  
Morphological Studies ◽  
Transmission Electron ◽  
First Order Phase Transition ◽  
Covalently Bonded ◽  
Total Molecular Weight ◽  
First Order Phase

Block copolymers are composed of sequences of dissimilar chemical moieties covalently bonded together. If the block lengths of each component are sufficiently long and the blocks are thermodynamically incompatible, these materials are capable of undergoing microphase separation, a weak first-order phase transition which results in the formation of an ordered microstructural network. Most efforts designed to elucidate the phase and configurational behavior in these copolymers have focused on the simple AB and ABA designs. Few studies have thus far targeted the perfectly-alternating multiblock (AB)n architecture. In this work, two series of neat (AB)n copolymers have been synthesized from styrene and isoprene monomers at a composition of 50 wt% polystyrene (PS). In Set I, the total molecular weight is held constant while the number of AB block pairs (n) is increased from one to four (which results in shorter blocks). Set II consists of materials in which the block lengths are held constant and n is varied again from one to four (which results in longer chains). Transmission electron microscopy (TEM) has been employed here to investigate the morphologies and phase behavior of these materials and their blends.

Exact First Order Finite Element Modeling for Eddy Current NDE

1991 ◽  
Vol 3 (1) ◽  
pp. 235-253 ◽  
Author(s):  
L. D. Philipp ◽  
Q. H. Nguyen ◽  
D. D. Derkacht ◽  
D. J. Lynch ◽  
A. Mahmood
Keyword(s):  
Finite Element ◽  
Finite Element Modeling ◽  
Eddy Current ◽  
Element Modeling ◽  
First Order ◽  
Eddy Current Nde

Challenging the Multidimensional Conception of Perceived Person-Environment Fit

2020 ◽  
pp. 1-9
Author(s):  
Julian M. Etzel ◽  
Gabriel Nagy
Keyword(s):  
Higher Education ◽  
University Students ◽  
Educational Outcomes ◽  
Factor Model ◽  
Higher Order ◽  
Substantial Proportion ◽  
Unique Variance ◽  
First Order ◽  
Person Environment Fit ◽  
Order Factor

Abstract. In the current study, we examined the viability of a multidimensional conception of perceived person-environment (P-E) fit in higher education. We introduce an optimized 12-item measure that distinguishes between four content dimensions of perceived P-E fit: interest-contents (I-C) fit, needs-supplies (N-S) fit, demands-abilities (D-A) fit, and values-culture (V-C) fit. The central aim of our study was to examine whether the relationships between different P-E fit dimensions and educational outcomes can be accounted for by a higher-order factor that captures the shared features of the four fit dimensions. Relying on a large sample of university students in Germany, we found that students distinguish between the proposed fit dimensions. The respective first-order factors shared a substantial proportion of variance and conformed to a higher-order factor model. Using a newly developed factor extension procedure, we found that the relationships between the first-order factors and most outcomes were not fully accounted for by the higher-order factor. Rather, with the exception of V-C fit, all specific P-E fit factors that represent the first-order factors’ unique variance showed reliable and theoretically plausible relationships with different outcomes. These findings support the viability of a multidimensional conceptualization of P-E fit and the validity of our adapted instrument.

The Clinical Analysis Questionnaire: First Order Norms

1994 ◽  
Author(s):  
A. J. Cotton
Keyword(s):  
Clinical Analysis ◽  
First Order
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