scholarly journals Glue-and-cut at five loops

2021 ◽  
Vol 2021 (9) ◽  
Author(s):  
Alessandro Georgoudis ◽  
Vasco Goncalves ◽  
Erik Panzer ◽  
Raul Pereira ◽  
Alexander V. Smirnov ◽  
...  
Keyword(s):  
Momentum Space ◽  
Dimensional Regularization ◽  
First Order ◽  
Complete Set ◽  
Expansion Coefficients

Abstract We compute ε-expansions around 4 dimensions of a complete set of master integrals for momentum space five-loop massless propagator integrals in dimensional regularization, up to and including the first order with contributions of transcendental weight nine. Our method is the glue-and-cut technique from Baikov and Chetyrkin, which proves extremely effective in that it determines all expansion coefficients to this order in terms of recursively one-loop integrals and only one further integral. We observe that our results are compatible with conjectures that predict π-dependent contributions.

Scattering of elastic waves near an explosion

1993 ◽  
Vol 83 (4) ◽  
pp. 1277-1293
Author(s):  
Donald Leavy
Keyword(s):  
Displacement Field ◽  
Elastic Waves ◽  
Near Field ◽  
Static Solution ◽  
Simple Relation ◽  
Perturbation Solution ◽  
First Order ◽  
Scattering Of Elastic Waves ◽  
Harmonic Decomposition ◽  
Complete Set

Abstract We use the method of small perturbation to study the scattered waves generated by an arbitrary 3D inhomogeneous medium around a spherically symmetric compressional source. We consider two models of the medium inside the source: a homogeneous solid and a fluid. The results from these two models differ only when scattering occurs within a few source's radii from the explosion. We find that there is a simple relation between the structure of the first order scattered waves and the structure of the medium, namely that a given harmonic of the medium parameters excites only the same harmonic of the two spheroidal potentials. When scattering occurs within a wavelength from the source, we find that the quadrantal terms in the spherical harmonic decomposition of the field have the lowest frequency dependence. They depend on frequency only through the spectrum of the source. Thus, in the far field, the dominant scattered waves generated near an explosion are similar to the primary waves generated by an earthquake. However, when the displacement field is observed in the near field of the explosion, the static solution reveals that a complete set of harmonics may be required to properly account for the displacement field. We compare the perturbation solution with the exact solution of the scattering by a sphere located within a wavelength from the source. This suggests that the perturbation solution has a fairly wide domain of practical applicability. We attempt to apply these results to the Love wave generated near the Boxcar nuclear explosion.

Momentum space atomic first-order density matrices and ‘‘exchange-only’’ correlation factors

1990 ◽  
Vol 42 (5) ◽  
pp. 2622-2626 ◽  
Author(s):  
Rajeev K. Pathak ◽  
Sudhir A. Kulkarni ◽  
Shridhar R. Gadre
Keyword(s):  
Momentum Space ◽  
Density Matrices ◽  
First Order ◽  
Correlation Factors

A system of logic for partial functions under existence-dependent kleene equality

1988 ◽  
Vol 53 (3) ◽  
pp. 834-839 ◽  
Author(s):  
H. Andréka ◽  
W. Craig ◽  
I. Németi
Keyword(s):  
Practical Interest ◽  
Order Logic ◽  
First Order Logic ◽  
Basic Relation ◽  
Equational Logic ◽  
Partial Functions ◽  
First Order ◽  
Complete Set ◽  
The Subject ◽  
Relationship Of

Ordinary equational logic is a connective-free fragment of first-order logic which is concerned with total functions under the relation of ordinary equality. In [AN] (see also [AN1]) and in [Cr] it has been extended in two equivalent ways into a near-equational system of logic for partial functions. The extension given in [Cr] deals with partial functions under two relationships: a relationship of existence-dependent existence and one of existence-dependent Kleene equality. For the language that involves both relationships a set of rules was given that is complete. Those rules in the set that involve only existence-dependent existence turned out to be complete for the sublanguage that involves this relationship only. In the present paper we give a set of rules that is complete for the other sublanguage, namely the language of partial functions under existence-dependent Kleene equality.This language lacks a certain, often needed, power of expressing existence and fails, in particular, to be an extension of the language that underlies ordinary equational logic. That it possesses a fairly simple complete set of rules is therefore perhaps more of theoretical than of practical interest. The present paper is thus intended to serve as a supplement to [Cr] and, less directly, to [AN]. The subject is further rounded out, and some contrast is provided, by [Rob]. The systems of logic treated there are based on the weaker language in which partial functions are considered under the more basic relation of Kleene equality.

scholarly journals Generic Noninteger Order Controller for Time-Delay Systems

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Sami Hafsi ◽  
Sadem Ghrab ◽  
Kaouther Laabidi
Keyword(s):  
Time Delay ◽  
Stability Region ◽  
Delay Systems ◽  
Pid Controllers ◽  
Time Delay Systems ◽  
First Order ◽  
Industrial Utilization ◽  
Complete Set ◽  
Order Representation ◽  
Fractional Controller

This paper focuses on the problem of fractional controller P I stabilization for a first-order time-delay systems. For this reason, we utilize the Hermite–Biehler and Pontryagin theorems to compute the complete set of the stabilizing P I λ parameters. The widespread industrial utilization of PID controllers and the potentiality of their noninteger order representation justify a timely interest in P I λ tuning techniques. Step responses are calculated through K p , K i , l a m b d a parameters inside and outside stability region to prove the method efficiency.

Phase Transition Studies in PMBAB and PEBAB

1984 ◽  
Vol 39 (7) ◽  
pp. 696-699 ◽  
Author(s):  
V. G. K. M. Pisipati ◽  
N. V. S. Rao
Keyword(s):  
Phase Transition ◽  
Thermal Expansion ◽  
Molar Volume ◽  
Ultrasonic Velocity ◽  
Adiabatic Compressibility ◽  
First Order ◽  
Thermal Expansion Coefficients ◽  
Methylene Unit ◽  
Expansion Coefficients ◽  
Transition Studies

The variation of density and ultrasonic velocity with temperature in N-(p-methoxybenzylidene)- p-aminobenzonitrile (PMBAB) and N-(p-ethoxybenzylidene)-p-aminobenzonitrile (PEBAB) are presented. The density jumps and thermal expansion coefficients suggest the nematic-isotropic transition of both compounds to be of first order. The adiabatic compressibility βad, molar sound velocity Rn and molar compressibility Aw are computed. The contribution of a methylene unit to the molar volume is found to be higher than literature values. The anomalous ultrasonic velocity dip at the nematic-isotropic transition for both compounds is found to be high; the value is many times those found for other nematic-isotropic or nematicsmectic A transitions.

Complete theories with countably many rigid nonisomorphic models

1975 ◽  
Vol 40 (3) ◽  
pp. 389-392 ◽  
Author(s):  
Jerome Malitz
Keyword(s):  
Standard Model ◽  
Predicate Calculus ◽  
Rigid Structure ◽  
First Order ◽  
Nontrivial Automorphism ◽  
Rigid Model ◽  
Complete Set ◽  
Complete Theories ◽  
The Universe ◽  
Order Predicate Calculus

Here we prove the following:Theorem. For every N ≤ ω there is a complete theory Tn having exactly n nonisomorphic rigid models and no uncountable rigid models. Moreover, each non-rigid model admits a nontrivial automorphism.The Tn are theories in the first-order predicate calculus and a rigid structure is a structure with no nontrivial endomorphisms, i.e., the only endomorphism of the structure into itself is the identity. The theorem answers a question of A. Ehrenfeucht.For the most part we use standard model theoretic notation with Th denoting the set of sentences true in and meaning . A complete set of sentences is one of the form Th for some . The universe of a structure may be denoted by ∣∣. An n-ary relation on X is a set of n tuples (x0, …, xn−1) with each xi ∈ X. All the structures encounted here will be relational. If P is an n-ary relation then P ↾ Y, the restriction of P to Y, is {(x0, …, xn−1): (x0, …, xn−1) ∈ P and x0, …, xn−1Y}.

A covariant form for the complete set of first-order electromagnetic conservation laws

1994 ◽  
Vol 320 (1-2) ◽  
pp. 96-98 ◽  
Author(s):  
I.Yu. Krivsky ◽  
V.M. Simulik ◽  
Z.Z. Torich
Keyword(s):  
Conservation Laws ◽  
Covariant Form ◽  
First Order ◽  
Complete Set

scholarly journals CURRENT DEPTH REFRACTION OF REGULAR WAVES

1984 ◽  
Vol 1 (19) ◽  
pp. 75 ◽  
Author(s):  
Ivar G. Jonsson ◽  
John B. Christoffersen
Keyword(s):  
Large Scale ◽  
Wave Motion ◽  
Regular Waves ◽  
Small Surface ◽  
First Order ◽  
Linear Waves ◽  
Sea Bed ◽  
Wave Heights ◽  
Complete Set ◽  
Bed Friction

The complete set of equations for the refraction of small surface gravity waves on large-scale currents over a gradually varying sea bed is derived and presented. Wave lengths, direction of propagation and wave heights are all determined along the so-called wave rays as solutions to ordinary, first-order differential equations. Dissipation due to bed friction in the combined current wave motion is included. The ray tracing method is used in an example. A method for the calculation of current depth refraction of weakly non-linear waves is proposed.

The stability of Poiseuille flow in a pipe of circular cross-section

1972 ◽  
Vol 54 (1) ◽  
pp. 93-112 ◽  
Author(s):  
Harold Salwen ◽  
Chester E. Grosch
Keyword(s):  
Cross Section ◽  
Poiseuille Flow ◽  
Circular Cross Section ◽  
Perturbation Velocity ◽  
The Matrix ◽  
Complete Set ◽  
Expansion Coefficients ◽  
Matrix Differential ◽  
The Stability ◽  
Axisymmetric Disturbances

The stability of Poiseuille flow in a pipe of circular cross-section to azimuthally varying as well as axisymmetric disturbances has been studied. The perturbation velocity and pressure were expanded in a complete set of orthonormal functions which satisfy the boundary conditions. Truncating the expansion yielded a matrix differential equation for the time dependence of the expansion coefficients. The stability characteristics were determined from the eigenvalues of the matrix, which were calculated numerically. Calculations were carried out for the azimuthal wavenumbersn= 0,…, 5, axial wavenumbers α between 0·1 and 10·0 and αR[les ] 50000,Rbeing the Reynolds number. Our results show that pipe flow is stable to infinitesimal disturbances for all values of α,Randnin these ranges.

STRATEGIES TO DEFEND A PROTAGONIST OF AN EVENT

2010 ◽  
Vol 19 (04) ◽  
pp. 439-464
Author(s):  
SARA BOUTOUHAMI ◽  
DANIEL KAYSER
Keyword(s):  
Natural Language ◽  
Experimental Validation ◽  
Answer Set Programming ◽  
First Order ◽  
Starting Point ◽  
First Results ◽  
Argumentative Strategies ◽  
Complete Set ◽  
Car Accident ◽  
Answer Set

We aim at controlling the biases that exist in every description, in order to give the best possible image of one of the protagonists of an event. Starting from a supposedly complete set of propositions accounting for an event, we develop various argumentative strategies (insinuation, justification, reference to customary norms) to imply the facts that cannot be simply omitted but have the "wrong" orientation w.r.t. the protagonist we defend. By analyzing these different strategies, a contribution of this work is to provide a number of relevant parameters to take into account in developing and evaluating systems aiming at understanding natural language (NL) argumentations. The source of inspiration for this work is a corpus of 160 texts where each text describes a (different) car accident. Its result, for a given accident, is a set of first-order literals representing the essential facts of a description intended to defend one of the protagonists. An implementation in Answer Set Programming is underway. A couple of examples showing how to extract, from the same starting point, a defense for the two opposite sides are provided. Experimental validation of this work is in progress, and its first results are reported.

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