scholarly journals LINEAR CONNECTIONS ON THE TWO-PARAMETER QUANTUM PLANE

1996 ◽  
Vol 08 (08) ◽  
pp. 1055-1060 ◽  
Author(s):  
YVON GEORGELIN ◽  
JEAN-CHRISTOPHE WALLET ◽  
THIERRY MASSON
Keyword(s):  
Differential Forms ◽  
Linear Connection ◽  
Quantum Plane ◽  
Specific Relation ◽  
Linear Connections ◽  
Definition Of ◽  
Two Parameters ◽  
Two Parameter

We apply a recently proposed definition of a linear connection in non-commutative geometry based on the natural bimodule structure of the algebra of differential forms to the case of the two-parameter quantum plane. We find that there exists a non-trivial family of linear connections only when the two parameters obey a specific relation.

Two parameters are required for a Budyko function to describe the land-atmosphere interaction

2021 ◽  
Author(s):  
Daeha Kim ◽  
Jong Ahn Chun
Keyword(s):  
Land Surface ◽  
River Basins ◽  
Control Surface ◽  
Primary Control ◽  
Evaporative Demand ◽  
Atmosphere Interaction ◽  
The Mean ◽  
Two Parameters ◽  
Two Parameter ◽  
Surface Changes

<p>While the Budyko framework has been a simple and convenient tool to assess runoff (Q) responses to climatic and surface changes, it has been unclear how parameters of a Budyko function represent the vertical land-atmosphere interactions. Here, we explicitly derived a two-parameter equation by correcting a boundary condition of the Budyko hypothesis. The correction enabled for the Budyko function to reflect the evaporative demand (E<sub>p</sub>) that actively responds to soil moisture deficiency. The derived two-parameter function suggests that four physical variables control surface runoff; namely, precipitation (P), potential evaporation (E<sub>p</sub>), wet-environment evaporation (E<sub>w</sub>), and the catchment properties (n). We linked the derived Budyko function to a definitive complementary evaporation principle, and assessed the relative elasticities of Q to climatic and land surface changes. Results showed that P is the primary control of runoff changes in most of river basins across the world, but its importance declined with climatological aridity. In arid river basins, the catchment properties play a major role in changing runoff, while changes in E<sub>p</sub> and E<sub>w</sub> seem to exert minor influences on Q changes. It was also found that the two-parameter Budyko function can capture unusual negative correlation between the mean annual Q and E<sub>p</sub>. This work suggests that at least two parameters are required for a Budyko function to properly describe the vertical interactions between the land and the atmosphere.</p>

Vertical Chern Type Classes on Complex Finsler Bundles

2011 ◽  
Vol 57 (2) ◽  
pp. 377-386
Author(s):  
Cristian Ida
Keyword(s):  
Differential Forms ◽  
Linear Connection ◽  
Curvature Form ◽  
Cohomology Groups ◽  
Finsler Manifolds ◽  
Invariance Properties ◽  
Type Classes

Vertical Chern Type Classes on Complex Finsler BundlesIn the present paper, we define vertical Chern type classes on complex Finsler bundles, as an extension of thev-cohomology groups theory on complex Finsler manifolds. These classes are introduced in a classical way by using closed differential forms with respect to the conjugated vertical differential in terms of the vertical curvature form of Chern-Finsler linear connection. Also, some invariance properties of these classes are studied.

Duality on the quantum space(3) with two parameters

Open Physics ◽  
2012 ◽  
Vol 10 (5) ◽  
Author(s):  
Muttalip Özavşar ◽  
Gürsel Yeşilot
Keyword(s):  
Hopf Algebra ◽  
Lie Algebra ◽  
Differential Forms ◽  
Quantum Space ◽  
Dual Algebra ◽  
Commutation Relations ◽  
Dual Hopf Algebra ◽  
Invariant Differential ◽  
Leibniz Rules ◽  
Two Parameters

AbstractIn this study, we introduce a dual Hopf algebra in the sense of Sudbery for the quantum space(3) whose coordinates satisfy the commutation relations with two parameters and we show that the dual algebra is isomorphic to the quantum Lie algebra corresponding to the Cartan-Maurer right invariant differential forms on the quantum space(3). We also observe that the quantum Lie algebra generators are commutative as those of the undeformed Lie algebra and the deformation becomes apparent when one studies the Leibniz rules for the generators.

scholarly journals Adaptabilidade de Objetos de Aprendizagem usando Calibragem e Sequenciamento Adaptativo de Exercícios

2018 ◽  
Vol 26 (1) ◽  
pp. 70
Author(s):  
Rômulo César Silva ◽  
Alexandre Ibrahim Direne ◽  
Diego Marczal ◽  
Ana Carla Borille ◽  
Paulo Ricardo Bittencourt Guimarães ◽  
...  
Keyword(s):  
Problem Solving ◽  
Empirical Study ◽  
Cognitive Skills ◽  
Learning Objects ◽  
Skill Level ◽  
Problem Solution ◽  
Algebraic Expressions ◽  
Student Skill ◽  
Definition Of ◽  
Two Parameters

The work approaches theoretical and implementation issues of a framework for creating and executing Learning Objects (LOs) where problem-solving tasks are ordered according to the matching of two parameters, both calculated automatically: (1) student skill level and (2) problem solution difficulty. They are formally defined as algebraic expressions. The definition of skill level is achieved through a rating-based measure that resembles the ones of game mastery scales, while the solution difficulty is based on mistakes and successes of learners to deal with the problem. An empirical study based on existing students data demonstrated the suitability of the formulas. Besides, the motivational aspects of learning are considered in depth. In this sense, it is important to propose activities according to the student’s level of expertise, which is achieved through presenting students with exercises that are compatible with the difficulty degree of their cognitive skills. Also, the results of an experiment conducted with four highschool classes using the framework for the domain of logarithmic properties are presented.

2-ρ-DERIVATIONS ON A ρ-ALGEBRA AND APPLICATIONS TO THE QUATERNIONIC ALGEBRA

2007 ◽  
Vol 04 (03) ◽  
pp. 457-469 ◽  
Author(s):  
CĂTĂLIN CIUPALĂ
Keyword(s):  
Linear Connection ◽  
Linear Connections

In this paper, we introduce 2-ρ-derivations on a ρ-algebra A, and define 2-linear connections on a ρ-bimodule M over A using these 2-derivations. Then we introduce and study the curvature of a linear connection. Our results are applied to the particular case of the quaternionic algebra ℍ.

scholarly journals Prolongations of linear connections to the frame bundle

1983 ◽  
Vol 28 (3) ◽  
pp. 367-381
Author(s):  
Luis A. Cordero ◽  
Manuel de Leon
Keyword(s):  
Linear Connection ◽  
Frame Bundle ◽  
Linear Connections ◽  
Complete Lift

In this paper we construct the prolongation of a linear connection Γ on a manifold Μ to the bundle space of its frame bundle, and show that such prolongated connection coincides with the so-called complete lift of Γ to .

scholarly journals On the Holonomy Groups of Linear Connections

1956 ◽  
Vol 10 ◽  
pp. 97-100 ◽  
Author(s):  
Jun-Ichi Hano ◽  
Hideki Ozeki
Keyword(s):  
Linear Group ◽  
Affine Space ◽  
General Linear Group ◽  
Affine Connection ◽  
Holonomy Group ◽  
Linear Connection ◽  
General Linear ◽  
Linear Connections ◽  
Holonomy Groups ◽  
Lie Subgroup

In this note we show in § 1, as the main result, that any connected Lie subgroup of the general linear group GL(n, R) can be realized as the holonomy group of a linear connection, i.e. the homogeneous holonomy group of the associeted affine connection, defined on an affine space of dimension n (n ≧ 2).

scholarly journals A simulated annealing algorithm to quantify patterns in astronomical data

2019 ◽  
Vol 490 (4) ◽  
pp. 5904-5920
Author(s):  
Maria Chira ◽  
Manolis Plionis
Keyword(s):  
Simulated Annealing ◽  
Simulated Annealing Algorithm ◽  
Cost Minimization ◽  
Dark Matter Halo ◽  
Interaction Coefficients ◽  
Astronomical Data ◽  
Robotic Vision ◽  
Minimization Algorithms ◽  
Definition Of ◽  
Two Parameters

ABSTRACT We develop an optimization algorithm, using simulated annealing for the quantification of patterns in astronomical data based on techniques developed for robotic vision applications. The methodology falls in the category of cost minimization algorithms and it is based on user-determined interaction – among the pattern elements – criteria that define the properties of the sought structures. We applied the algorithm on a large variety of mock images and we constrained the free parameters; α and k, which express the amount of noise in the image and how strictly the algorithm seeks for cocircular structures, respectively. We find that the two parameters are interrelated and also that, independently of the pattern properties, an appropriate selection for most of the images would be log k = −2 and 0 < α ≲ 0.04. The width of the effective α-range, for different values of k, is reduced when more interaction coefficients are taken into account for the definition of the patterns of interest. Finally, we applied the algorithm on N-body simulation dark-matter halo data and on the HST image of the lensing Abell 2218 cluster to conclude that this versatile technique could be applied for the quantification of structure and for identifying coherence in astronomical patterns.

On the computation of parameters that model snow avalanche motion

1981 ◽  
Vol 18 (1) ◽  
pp. 121-130 ◽  
Author(s):  
S. Bakkehøi ◽  
T. Cheng ◽  
U. Domaas ◽  
K. Lied ◽  
R. Perla ◽  
...  
Keyword(s):  
Snow Avalanche ◽  
Computational Problem ◽  
Avalanche Dynamics ◽  
Two Parameters ◽  
Two Parameter

This paper explores the computational problem of finding suitable numbers to use in a two-parameter model of snow avalanche dynamics. The two parameters are friction, μ, and a ratio of avalanche mass to drag, M/D. Given a path profile, and a maximum avalanche speed, then it is possible to compute unique values for u and M/D. If only the path profile and the stopping position are known, then it is possible to compute tables of pairs {μ, M/D} which can be tested as predictors of avalanche speeds. To generate these tables it is convenient to scale M/D in multiples of the total vertical drop of the path. The computations were tested on 136 avalanche paths. Values of {μ, M/D} were stratified, and certain values were rejected as unrealistic.

The Restricted Newton Method for Fast Nonlinear Model Predictive Control

2019 ◽  
Author(s):  
Anson Maitland ◽  
Chi Jin ◽  
John McPhee
Keyword(s):  
Model Predictive Control ◽  
Predictive Control ◽  
Newton’S Method ◽  
Newton's Method ◽  
Gradient Descent ◽  
Autonomous Vehicle ◽  
Optimization Method ◽  
Selection Strategies ◽  
Two Parameters ◽  
Two Parameter

Abstract We introduce the Restricted Newton’s Method (RNM), a basic optimization method, to accelerate model predictive control turnaround times. RNM is a hybrid of Newton’s method (NM) and gradient descent (GD) that can be used as a building block in nonlinear programming. The two parameters of RNM are the subspace on which we restrict the Newton steps and the maximal size of the GD step. We present a convergence analysis of RNM and demonstrate how these parameters can be selected for MPC applications using simple machine learning methods. This leads to two parameter selection strategies with different convergence behaviour. Lastly, we demonstrate the utility of RNM on a sample autonomous vehicle problem with promising results.

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