scholarly journals The regular state in higher order gravity

2016 ◽  
Vol 31 (23) ◽  
pp. 1650130 ◽  
Author(s):  
Spiros Cotsakis ◽  
Seifedine Kadry ◽  
Dimitrios Trachilis
Keyword(s):  
Evolution Equations ◽  
Power Series Expansion ◽  
Type System ◽  
Higher Order ◽  
Initial Value ◽  
First Order ◽  
Higher Order Gravity ◽  
Build Time ◽  
The Right ◽  
Formal Power

We consider the higher-order gravity theory derived from the quadratic Lagrangian [Formula: see text] in vacuum as a first-order (ADM-type) system with constraints, and build time developments of solutions of an initial value formulation of the theory. We show that all such solutions, if analytic, contain the right number of free functions to qualify as general solutions of the theory. We further show that any regular analytic solution which satisfies the constraints and the evolution equations can be given in the form of an asymptotic formal power series expansion.

Exponentially Convergent Parallel Discretization Methods for the First Order Evolution Equations

2001 ◽  
Vol 1 (4) ◽  
pp. 333-355 ◽  
Author(s):  
Ivan Gavrilyuk ◽  
Vladimir L. Makarov
Keyword(s):  
Evolution Equations ◽  
Operator Coefficient ◽  
Cauchy Integral ◽  
Initial Value ◽  
Discretization Methods ◽  
First Order ◽  
Finite Set ◽  
The Right ◽  
Sinc Quadrature ◽  
Complex Coefficients

AbstractWe propose a new discretization of an initial value problem for differen- tial equations of the first order in a Banach space with a strongly P-positive operator coefficient. Using the strong positiveness, we represent the solution as a Dunford- Cauchy integral along a parabola in the right half of the complex plane, then transform it into real integrals over (−∞,∞), and finally apply an exponentially convergent Sinc quadrature formula to this integral. The integrand values are the solutions of a finite set of elliptic problems with complex coefficients, which are independent and may be solved in parallel.

scholarly journals An Optimized 5-Point Block Formula for Direct Numerical Solution of First Order Stiff Initial Value Problems

2020 ◽  
Vol 3 (2) ◽  
pp. 158-167
Author(s):  
VO Atabo ◽  
PO Olatunji
Keyword(s):  
Approximate Solution ◽  
Test Performance ◽  
Initial Value Problems ◽  
Power Series Expansion ◽  
Initial Value ◽  
First Order ◽  
Research Article ◽  
Error Constant ◽  
Direct Numerical Solution ◽  
Collocation Approach

In this research article, we focus on the formulation of a 5-point block formula for solving first order ordinary differential equations (ODEs). The method is formulated via interpolation and collocation approach using power series expansion as the approximate solution. It has been established that the derived method is of order six. Basic properties such zero and absolute stabilities, convergence, order and error constant have also been investigated. The accuracy of the method was verified on some selected stiff IVPs, compared with some existing methods (DIBBDF, SDIBBDF, BBDF(4), BBDF(5) and odes15s) and test performance showed that the new method is viable.

scholarly journals On the Versatility of Open Logical Relations

2020 ◽  
pp. 56-83 ◽  
Author(s):  
Gilles Barthe ◽  
Raphaëlle Crubillé ◽  
Ugo Dal Lago ◽  
Francesco Gavazzo
Keyword(s):  
Programming Languages ◽  
Automatic Differentiation ◽  
Type System ◽  
Order Type ◽  
Higher Order ◽  
Base Case ◽  
Logical Relation ◽  
First Order ◽  
Differentiable Functions ◽  
The One

AbstractLogical relations are one among the most powerful techniques in the theory of programming languages, and have been used extensively for proving properties of a variety of higher-order calculi. However, there are properties that cannot be immediately proved by means of logical relations, for instance program continuity and differentiability in higher-order languages extended with real-valued functions. Informally, the problem stems from the fact that these properties are naturally expressed on terms of non-ground type (or, equivalently, on open terms of base type), and there is no apparent good definition for a base case (i.e. for closed terms of ground types). To overcome this issue, we study a generalization of the concept of a logical relation, called open logical relation, and prove that it can be fruitfully applied in several contexts in which the property of interest is about expressions of first-order type. Our setting is a simply-typed $$\lambda $$ λ -calculus enriched with real numbers and real-valued first-order functions from a given set, such as the one of continuous or differentiable functions. We first prove a containment theorem stating that for any collection of real-valued first-order functions including projection functions and closed under function composition, any well-typed term of first-order type denotes a function belonging to that collection. Then, we show by way of open logical relations the correctness of the core of a recently published algorithm for forward automatic differentiation. Finally, we define a refinement-based type system for local continuity in an extension of our calculus with conditionals, and prove the soundness of the type system using open logical relations.

scholarly journals More of me! Less of me!: Reflexive Imperativism about Affective Phenomenal Character

Mind ◽  
2019 ◽  
Vol 128 (512) ◽  
pp. 1013-1044 ◽  
Author(s):  
Luca Barlassina ◽  
Max Khan Hayward
Keyword(s):  
Phenomenal Character ◽  
Higher Order ◽  
Intentional Content ◽  
First Order ◽  
The Right ◽  
In Virtue Of

AbstractExperiences like pains, pleasures, and emotions have affective phenomenal character: they feel pleasant or unpleasant. Imperativism proposes to explain affective phenomenal character by appeal to imperative content, a kind of intentional content that directs rather than describes. We argue that imperativism is on the right track, but has been developed in the wrong way. There are two varieties of imperativism on the market: first-order and higher-order. We show that neither is successful, and offer in their place a new theory: reflexive imperativism. Our proposal is that an experience P feels pleasant in virtue of being (at least partly) constituted by a Command with reflexive imperative content (1), while an experience U feels unpleasant in virtue of being (at least partly) constituted by a Command with reflexive imperative content (2): More of P!Less of U!If you need a slogan: experiences have affective phenomenal character in virtue of commanding us Get more of me! Get less of me!

Higher Order Two-Point Efficient Family of Halley Type Methods for Simple Roots

2016 ◽  
Vol 13 (04) ◽  
pp. 1641016 ◽  
Author(s):  
Ramandeep Behl ◽  
S. S. Motsa
Keyword(s):  
Nonlinear Equations ◽  
Computational Cost ◽  
Basins Of Attraction ◽  
Higher Order ◽  
The Other ◽  
Sixth Order ◽  
Order Derivative ◽  
Initial Value ◽  
First Order ◽  
The Family

In this paper, we proposed a new highly efficient two-point sixth-order family of Halley type methods that do not require any second-order derivative evaluation for obtaining simple roots of nonlinear equations, numerically. In terms of computational cost, each member of the family requires two-function and two first-order derivative evaluations per iteration. On the account of the results obtained, it is found that our proposed methods are efficient and show better performance than existing sixth-order methods available in the literature. Further, it is also noted that larger basins of attraction belong to our methods as compared to the existing ones. On the other hand, the existing methods are slower and have darker basins while some of them are too sensitive upon the choice of the initial value.

DYNAMICS OF A PARTICULAR LORENZ TYPE SYSTEM

2010 ◽  
Vol 21 (07) ◽  
pp. 973-982 ◽  
Author(s):  
GIORGIO E. TESTONI ◽  
PAULO C. RECH
Keyword(s):  
Equilibrium Points ◽  
Three Dimensional ◽  
Type System ◽  
Equation System ◽  
Largest Lyapunov Exponent ◽  
Differential Equation System ◽  
Order Ordinary Differential Equation ◽  
First Order ◽  
The Stability ◽  
The Right

In this paper we analytically and numerically investigate the dynamics of a nonlinear three-dimensional autonomous first-order ordinary differential equation system, obtained from paradigmatic Lorenz system by suppressing the y variable in the right-hand side of the second equation. The Routh–Hurwitz criterion is used to decide on the stability of the nontrivial equilibrium points of the system, as a function of the parameters. The dynamics of the system is numerically characterized by using diagrams that associate colors to largest Lyapunov exponent values in the parameter-space. Additionally, phase-space plots and bifurcation diagrams are used to characterize periodic and chaotic attractors.

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.

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.

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