scholarly journals Unification of Higher-order Patterns modulo Simple Syntactic Equational Theories

2000 ◽  
Vol Vol. 4 no. 1 ◽  
Author(s):  
Alexandre Boudet
Keyword(s):  
Higher Order ◽  
Unification Algorithm ◽  
First Order ◽  
Equational Theories ◽  
Order Case ◽  
International Audience ◽  
Syntactic Theories

International audience We present an algorithm for unification of higher-order patterns modulo simple syntactic equational theories as defined by Kirchner [14]. The algorithm by Miller [17] for pattern unification, refined by Nipkow [18] is first modified in order to behave as a first-order unification algorithm. Then the mutation rule for syntactic theories of Kirchner [13,14] is adapted to pattern E-unification. If the syntactic algorithm for a theory E terminates in the first-order case, then our algorithm will also terminate for pattern E-unification. The result is a DAG-solved form plus some equations of the form λ øverlinex.F(øverlinex) = λ øverlinex. F(øverlinex^π ) where øverlinex^π is a permutation of øverlinex When all function symbols are decomposable these latter equations can be discarded, otherwise the compatibility of such equations with the solved form remains open.

scholarly journals SUBGEOMETRICALLY ERGODIC AUTOREGRESSIONS

2020 ◽  
pp. 1-27
Author(s):  
Mika Meitz ◽  
Pentti Saikkonen
Keyword(s):  
Unit Root ◽  
Transition Probability ◽  
Higher Order ◽  
Time Series Models ◽  
Probability Measures ◽  
First Order ◽  
Markov Chain Theory ◽  
Mixing Coefficients ◽  
Order Case ◽  
Chain Theory

In this paper, we discuss how the notion of subgeometric ergodicity in Markov chain theory can be exploited to study stationarity and ergodicity of nonlinear time series models. Subgeometric ergodicity means that the transition probability measures converge to the stationary measure at a rate slower than geometric. Specifically, we consider suitably defined higher-order nonlinear autoregressions that behave similarly to a unit root process for large values of the observed series but we place almost no restrictions on their dynamics for moderate values of the observed series. Results on the subgeometric ergodicity of nonlinear autoregressions have previously appeared only in the first-order case. We provide an extension to the higher-order case and show that the autoregressions we consider are, under appropriate conditions, subgeometrically ergodic. As useful implications, we also obtain stationarity and $\beta $ -mixing with subgeometrically decaying mixing coefficients.

scholarly journals General solutions depending algebraically on arbitrary constants

1989 ◽  
Vol 113 ◽  
pp. 1-6 ◽  
Author(s):  
Keiji Nishioka
Keyword(s):  
Differential Equations ◽  
Higher Order ◽  
General Solutions ◽  
Algebraic Differential Equations ◽  
First Order ◽  
Order Case ◽  
Rational Dependence ◽  
Strong Normality ◽  
Solutions Of Equations ◽  
The Given

In his famous lectures [7] Painlevé investigates general solutions of algebraic differential equations which depend algebraically on some of arbitrary constants. Although his discussions are beyond our understanding, the rigorous and accurate interpretation to make his intuition true would be possible. Successful accomplishments have been done by some authors, for example, Kimura [1], Umemura [8, 9]. From differential algebraic viewpoint in [5] the author introduces the notion of rational dependence on arbitrary constants of general solutions of algebraic differential equations, and in [6] clarifies the relation between it and the notion of strong normality. Here we aim at generalizing to higher order case the result in [4] that in the first order case solutions of equations depend algebraically on those of equations free from moving singularities which are determined uniquely as the closest ones to the given. Part of our result can be seen in [7].

scholarly journals A Resolution Calculus for Second-order Logic with Eager Unification

10.29007/zpg2 ◽  
2018 ◽  
Author(s):  
Alexander Leitsch ◽  
Tomer Libal
Keyword(s):  
Higher Order ◽  
Second Order ◽  
Order Logic ◽  
Higher Order Logic ◽  
Unification Algorithm ◽  
Efficient Search ◽  
First Order ◽  
Unification Algorithms ◽  
Second Order Logic ◽  
Resolution Calculus

The efficiency of the first-order resolution calculus is impaired when lifting it to higher-order logic. The main reason for that is the semi-decidability and infinitary natureof higher-order unification algorithms, which requires the integration of unification within the calculus and results in a non-efficient search for refutations.We present a modification of the constrained resolution calculus (Huet'72) which uses an eager unification algorithm while retaining completeness. Thealgorithm is complete with regard to bounded unification only, which for many cases, does not pose a problem in practice.

scholarly journals From Kajihara’s transformation formula to deformed Macdonald–Ruijsenaars and Noumi–Sano operators

2021 ◽  
Vol 28 (2) ◽  
Author(s):  
Martin Hallnäs ◽  
Edwin Langmann ◽  
Masatoshi Noumi ◽  
Hjalmar Rosengren
Keyword(s):  
Hypergeometric Series ◽  
Basic Hypergeometric Series ◽  
Root Systems ◽  
Higher Order ◽  
Explicit Description ◽  
Transformation Formula ◽  
Inverse Limits ◽  
First Order ◽  
Order Case ◽  
Multiple Basic Hypergeometric Series

AbstractKajihara obtained in 2004 a remarkable transformation formula connecting multiple basic hypergeometric series associated with A-type root systems of different ranks. By specialisations of his formula, we deduce kernel identities for deformed Macdonald–Ruijsenaars (MR) and Noumi–Sano (NS) operators. The deformed MR operators were introduced by Sergeev and Veselov in the first order case and by Feigin and Silantyev in the higher order cases. As applications of our kernel identities, we prove that all of these operators pairwise commute and are simultaneously diagonalised by the super-Macdonald polynomials. We also provide an explicit description of the algebra generated by the deformed MR and/or NS operators by a Harish-Chandra type isomorphism and show that the deformed MR (NS) operators can be viewed as restrictions of inverse limits of ordinary MR (NS) operators.

A High-Order Solution for the Added Stability Lobes in Intermittent Machining

2000 ◽  
Author(s):  
William T. Corpus ◽  
William J. Endres
Keyword(s):  
Closed Form ◽  
High Speed ◽  
Higher Order ◽  
Second Order ◽  
Machining Processes ◽  
Analytical Technique ◽  
First Order ◽  
Order Solution ◽  
Order Case ◽  
Speed Stability

Abstract An earlier work by the authors presented a solution for the added ultrahigh-speed stability lobe that has been shown to exist for intermittent and other periodically time varying machining processes. That earlier first-order solution was not clearly extendible to a higher order. A more general analytical technique presented here does permit higher-order results. The solution is developed first for the case of zero damping for which a final closed-form symbolic result can be realized up to second order. More important than improved accuracy, the higher-order nature of the result confirms that there exist multiple added lobes and permits a mathematical description of their locations along the spindle-speed axis. A solution is then derived for the structurally damped case, where the first-order case permits a final closed-form symbolic result while the second-order case requires computational evaluation. The first-order result matches perfectly the previously published one, as expected. The second-order result improves accuracy, measured relative to numerical simulation results, and, more important, permits a second added lobe to be predicted. The second added lobe tends to cut into the region of the high-speed stability peak that is predicted under traditional zero-frequency (time-averaged) analyses. The damped solutions also indicate that structural damping of the dominant mode becomes virtually unimportant at ultrahigh speeds.

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.

Computational Models for Multilayered Composite Shells with Application to Tires

1996 ◽  
Vol 24 (1) ◽  
pp. 11-38 ◽  
Author(s):  
G. M. Kulikov
Keyword(s):  
Type Theory ◽  
Computational Models ◽  
Geometrical Nonlinearity ◽  
Higher Order ◽  
Stress Strain ◽  
Strain Fields ◽  
First Order ◽  
Timoshenko Type ◽  
Joint Influence ◽  
Discrete Layer

Abstract This paper focuses on four tire computational models based on two-dimensional shear deformation theories, namely, the first-order Timoshenko-type theory, the higher-order Timoshenko-type theory, the first-order discrete-layer theory, and the higher-order discrete-layer theory. The joint influence of anisotropy, geometrical nonlinearity, and laminated material response on the tire stress-strain fields is examined. The comparative analysis of stresses and strains of the cord-rubber tire on the basis of these four shell computational models is given. Results show that neglecting the effect of anisotropy leads to an incorrect description of the stress-strain fields even in bias-ply tires.

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