scholarly journals Air Puff System Fundamentals for Reproducible Eyeblink Conditioning Research

2019 ◽  
Vol 2 (1) ◽  
pp. 14
Author(s):  
Frederick Reitz
Keyword(s):  
Eyeblink Conditioning ◽  
Near Field ◽  
Turbulent Jet ◽  
Compressible Medium ◽  
Order Of Approximation ◽  
Pressure Source ◽  
First Order ◽  
Velocity Peak ◽  
The One ◽  
Hydraulic Analogy

Air puff systems are at once trivially straightforward and dauntingly complex. On the one hand, they are little but a pressure source, valve, and tube connected together. On the other, the air passing through them is a compressible medium, expanding approximately adiabatically while travelling at high velocity through a compliant tube, and exiting as a turbulent jet with velocity peak and profile varying non-linearly in its near-field. This complexity puts precise mathematical prediction of puff properties out of reach of most labs. There are, however, a number of phenomena fundamental to air puff system design that are worth understanding to a first order of approximation, or at least qualitatively. Using a simplified, “electronic–hydraulic analogy” model, this paper discusses these phenomena in just enough depth for the reader to confidently specify parts for an air puff delivery system, to measure its key parameters, and/or to describe a given system unambiguously in publications, thus maximizing reproducibility.

scholarly journals Higher Dimensional Holonomy Map for Rules Submanifolds in Graded Manifolds

2020 ◽  
Vol 8 (1) ◽  
pp. 68-91
Author(s):  
Gianmarco Giovannardi
Keyword(s):  
Characteristic Direction ◽  
Fixed Degree ◽  
One Dimensional ◽  
First Order ◽  
Natural Choice ◽  
Higher Dimensional ◽  
Graded Manifold ◽  
The One ◽  
Graded Manifolds ◽  
Holonomy Map

AbstractThe deformability condition for submanifolds of fixed degree immersed in a graded manifold can be expressed as a system of first order PDEs. In the particular but important case of ruled submanifolds, we introduce a natural choice of coordinates, which allows to deeply simplify the formal expression of the system, and to reduce it to a system of ODEs along a characteristic direction. We introduce a notion of higher dimensional holonomy map in analogy with the one-dimensional case [29], and we provide a characterization for singularities as well as a deformability criterion.

Relational Chase Procedures Interpreted as Resolution with Paramodulation1

1991 ◽  
Vol 15 (2) ◽  
pp. 123-138
Author(s):  
Joachim Biskup ◽  
Bernhard Convent
Keyword(s):  
Alternative Interpretation ◽  
Order Logic ◽  
First Order Logic ◽  
Inference Problem ◽  
First Order ◽  
Inference Problems ◽  
The One ◽  
The Relationship ◽  
Theoretical Foundations ◽  
Insight Into

In this paper the relationship between dependency theory and first-order logic is explored in order to show how relational chase procedures (i.e., algorithms to decide inference problems for dependencies) can be interpreted as clever implementations of well known refutation procedures of first-order logic with resolution and paramodulation. On the one hand this alternative interpretation provides a deeper insight into the theoretical foundations of chase procedures, whereas on the other hand it makes available an already well established theory with a great amount of known results and techniques to be used for further investigations of the inference problem for dependencies. Our presentation is a detailed and careful elaboration of an idea formerly outlined by Grant and Jacobs which up to now seems to be disregarded by the database community although it definitely deserves more attention.

Ring-diagram summations in the finite-temperature effective potential

1993 ◽  
Vol 71 (5-6) ◽  
pp. 227-236 ◽  
Author(s):  
M. E. Carrington
Keyword(s):  
Phase Transition ◽  
Standard Model ◽  
Effective Potential ◽  
Finite Temperature ◽  
Electroweak Phase Transition ◽  
First Order ◽  
Ring Diagram ◽  
First Order Phase Transition ◽  
The Standard Model ◽  
The One

There has been much recent interest in the finite-temperature effective potential of the standard model in the context of the electroweak phase transition. We review the calculation of the effective potential with particular emphasis on the validity of the expansions that are used. The presence of a term that is cubic in the Higgs condensate in the one-loop effective potential appears to indicate a first-order electroweak phase transition. However, in the high-temperature regime, the infrared singularities inherent in massless models produce cubic terms that are of the same order in the coupling. In this paper, we discuss the inclusion of an infinite set of these terms via the ring-diagram summation, and show that the standard model has a first-order phase transition in the weak coupling expansion.

A stochastic process whose successive intervals between events form a first order Markov chain — I

1968 ◽  
Vol 5 (03) ◽  
pp. 648-668
Author(s):  
D. G. Lampard
Keyword(s):  
Markov Chain ◽  
Point Processes ◽  
Electronic Device ◽  
Statistical Properties ◽  
Time Intervals ◽  
First Order ◽  
Stochastic Point Process ◽  
Order Markov Chain ◽  
The One ◽  
Stochastic Point Processes

In this paper we discuss a counter system whose output is a stochastic point process such that the time intervals between pairs of successive events form a first order Markov chain. Such processes may be regarded as next, in order of complexity, in a hierarchy of stochastic point processes, to “renewal” processes, which latter have been studied extensively. The main virtue of the particular system which is studied here is that virtually all its important statistical properties can be obtained in closed form and that it is physically realizable as an electronic device. As such it forms the basis for a laboratory generator whose output may be used for experimental work involving processes of this kind. Such statistical properties as the one and two-dimensional probability densities for the time intervals are considered in both the stationary and nonstationary state and also discussed are corresponding properties of the successive numbers arising in the stores of the counter system. In particular it is shown that the degree of coupling between successive time intervals may be adjusted in practice without altering the one dimensional probability density for the interval lengths. It is pointed out that operation of the counter system may also be regarded as a problem in queueing theory involving one server alternately serving two queues. A generalization of the counter system, whose inputs are normally a pair of statistically independent Poisson processes, to the case where one of the inputs is a renewal process is considered and leads to some interesting functional equations.

scholarly journals Intercombination Transitions between Levels X1Σg+ and A 3Πu in C2

1987 ◽  
Vol 120 ◽  
pp. 103-105
Author(s):  
J. Le Bourlot ◽  
E. Roueff
Keyword(s):  
Transition Probabilities ◽  
Energy Levels ◽  
Wave Functions ◽  
Spin Orbit Coupling ◽  
Energy Matrix ◽  
First Order ◽  
Emission Transition ◽  
Intercombination Transition ◽  
The One ◽  
Potential Curves

We present a new calculation of intercombination transition probabilities between levels X1Σg+ and a 3Πu of the C2 molecule. Starting from experimental energy levels, we calculate RKR potential curves using Leroy's Near Dissociation Expansion (NDE) method; these curves give us wave functions for all levels of interest. We then compute the energy matrix for the four lowest states of C2, taking into account Spin-Orbit coupling between a 3Πu and A 1Πu on the one hand and X 1Σ+g and b 3Σg− on the other. First order wave functions are then derived by diagonalization. Einstein emission transition probabilities of the Intercombination lines are finally obtained.

scholarly journals Functional ASP with Intensional Sets: Application to Gelfond-Zhang Aggregates

2018 ◽  
Vol 18 (3-4) ◽  
pp. 390-405 ◽  
Author(s):  
PEDRO CABALAR ◽  
JORGE FANDINNO ◽  
LUIS FARIÑAS DEL CERRO ◽  
DAVID PEARCE
Keyword(s):  
Binary Operation ◽  
Compositional Semantics ◽  
First Order ◽  
Simple Addition ◽  
Logical Language ◽  
Extended Approach ◽  
Logical Term ◽  
New Type ◽  
The One ◽  
Logical Treatment

AbstractIn this paper, we propose a variant of Answer Set Programming (ASP) with evaluable functions that extends their application to sets of objects, something that allows a fully logical treatment of aggregates. Formally, we start from the syntax of First Order Logic with equality and the semantics of Quantified Equilibrium Logic with evaluable functions (${\rm QEL}^=_{\cal F}$). Then, we proceed to incorporate a new kind of logical term,intensional set(a construct commonly used to denote the set of objects characterised by a given formula), and to extend${\rm QEL}^=_{\cal F}$semantics for this new type of expression. In our extended approach, intensional sets can be arbitrarily used as predicate or function arguments or even nested inside other intensional sets, just as regular first-order logical terms. As a result, aggregates can be naturally formed by the application of some evaluable function (count,sum,maximum, etc) to a set of objects expressed as an intensional set. This approach has several advantages. First, while other semantics for aggregates depend on some syntactic transformation (either via a reduct or a formula translation), the${\rm QEL}^=_{\cal F}$interpretation treats them as regular evaluable functions, providing a compositional semantics and avoiding any kind of syntactic restriction. Second, aggregates can be explicitly defined now within the logical language by the simple addition of formulas that fix their meaning in terms of multiple applications of some (commutative and associative) binary operation. For instance, we can use recursive rules to definesumin terms of integer addition. Last, but not least, we prove that the semantics we obtain for aggregates coincides with the one defined by Gelfond and Zhang for the${\cal A}\mathit{log}$language, when we restrict to that syntactic fragment.

Role of Single Word Variables in Recall of Statistical Approximations to English

1966 ◽  
Vol 19 (2) ◽  
pp. 627-634 ◽  
Author(s):  
Mari J. K. Brown
Keyword(s):  
Free Recall ◽  
Higher Order ◽  
Order Of Approximation ◽  
Single Word ◽  
First Order ◽  
Original Order ◽  
Sequential Organization ◽  
The Individual

Free recall of lists at different orders of approximation to English was compared to the recall of the same lists when the order of the words had been scrambled to destroy their sequential organization. Recall of the organized lists showed the typical improvement with increasing order of approximation. Recall of the scrambled lists was unrelated to the original order of approximation. The results indicate that increased recall with increasing order of approximation to English is not produced by systematic differences in the characteristics of the individual words comprising the approximations. When recall of the organized lists was scored in terms of the number of longer sequences present in recall, the number of recalled sequences of any given length increased as order of approximation to English increased, with the first order list showing proportionally less organization in recall than the second and higher order lists.

scholarly journals What the Tortoise Said to Achilles: Lewis Carroll’s Paradox in Terms of Hilbert Arithmetic

2021 ◽  
Author(s):  
Vasil Penchev
Keyword(s):  
Hidden Variables ◽  
Formal Structure ◽  
Lewis Carroll ◽  
First Order ◽  
Logical Paradox ◽  
Completeness Of Quantum Mechanics ◽  
The One ◽  
In Virtue Of ◽  
The Liar ◽  
Completeness Theorems

Lewis Carroll, both logician and writer, suggested a logical paradox containing furthermore two connotations (connotations or metaphors are inherent in literature rather than in mathematics or logics). The paradox itself refers to implication demonstrating that an intermediate implication can be always inserted in an implication therefore postponing its ultimate conclusion for the next step and those insertions can be iteratively and indefinitely added ad lib, as if ad infinitum. Both connotations clear up links due to the shared formal structure with other well-known mathematical observations: (1) the paradox of Achilles and the Turtle; (2) the transitivity of the relation of equality. Analogically to (1), one can juxtapose the paradox of the Liar (for Lewis Carroll’s paradox) and that of the arrow (for “Achilles and the Turtle”), i.e. a logical paradox, on the one hand, and an aporia of motion, on the other hand, suggesting a shared formal structure of both, which can be called “ontological”, on which basis “motion” studied by physics and “conclusion” studied by logic can be unified being able to bridge logic and physics philosophically in a Hegelian manner: even more, the bridge can be continued to mathematics in virtue of (2), which forces the equality (for its property of transitivity) of any two quantities to be postponed analogically ad lib and ad infinitum. The paper shows that Hilbert arithmetic underlies naturally Lewis Carroll’s paradox admitting at least three interpretations linked to each other by it: mathematical, physical and logical. Thus, it can be considered as both generalization and solution of his paradox therefore naturally unifying the completeness of quantum mechanics (i.e. the absence of hidden variables) and eventual completeness of mathematics as the same and isomorphic to the completeness of propositional logic in relation to set theory as a first-order logic (in the sense of Gödel (1930)’s completeness theorems).

scholarly journals Lagrangian Representations for Linear and Nonlinear Transport

2017 ◽  
Vol 63 (3) ◽  
pp. 418-436
Author(s):  
Stefano Bianchini ◽  
Paolo Bonicatto ◽  
Elio Marconi
Keyword(s):  
Conservation Laws ◽  
Continuity Equation ◽  
Space Dimension ◽  
Nonlinear Transport ◽  
Scalar Conservation Laws ◽  
First Order ◽  
Entropy Dissipation ◽  
Linear And Nonlinear ◽  
Scalar Conservation ◽  
The One

In this note we present a unifying approach for two classes of first order partial differential equations: we introduce the notion of Lagrangian representation in the settings of continuity equation and scalar conservation laws. This yields, on the one hand, the uniqueness of weak solutions to transport equation driven by a two dimensional BV nearly incompressible vector field. On the other hand, it is proved that the entropy dissipation measure for scalar conservation laws in one space dimension is concentrated on countably many Lipschitz curves.

Observation of a radical intermediate in the one electron oxidation of 5-methyl-1-thia-5-azacyclooctane by •Br2−

1984 ◽  
Vol 62 (9) ◽  
pp. 1874-1876 ◽  
Author(s):  
Warren Kenneth Musker ◽  
Parminder S. Surdhar ◽  
Rizwan Ahmad ◽  
David A. Armstrong
Keyword(s):  
Aqueous Solution ◽  
Rate Constant ◽  
Half Life ◽  
Cation Radical ◽  
Order Rate Constant ◽  
Type Structure ◽  
Radical Intermediate ◽  
Text Type ◽  
First Order ◽  
The One

The one electron oxidant •Br2− reacts with 5-methyl-1-thia-5-azacyclooctane (4) in aqueous solution at high pH with an overall rate constant of ~2 × 108 M s−1. The radical intermediate produced has a broad maximum at 500 nm with ε = 2400 M−1 cm−1 and at pH 10 decays with a first order rate constant of 2.3 ± 0.3 × 104 s−1, first half-life of 30 ± 5 μs. Its characteristics do not correspond to those of the [Formula: see text] species reported by Asmus and co-workers. The species appears to be the same as the cation radical reported earlier in the one electron oxidation of 4 in acetonitrile. This species is considered to have an [Formula: see text] type structure, which provides transannular stabilization.

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