scholarly journals Classification of bi-Hamiltonian pairs extended by isometries

2021 ◽  
Vol 477 (2251) ◽  
pp. 20210185
Author(s):  
Maxim V. Pavlov ◽  
Pierandrea Vergallo ◽  
Raffaele Vitolo
Keyword(s):  
Type System ◽  
Local Part ◽  
First Order ◽  
Hydrodynamic Type System ◽  
Dependent Variables ◽  
Particular Solution ◽  
Non Local ◽  
Hamiltonian Operators ◽  
Hamiltonian Pair

The aim of this article is to classify pairs of the first-order Hamiltonian operators of Dubrovin–Novikov type such that one of them has a non-local part defined by an isometry of its leading coefficient. An example of such a bi-Hamiltonian pair was recently found for the constant astigmatism equation. We obtain a classification in the case of two dependent variables, and a significant new example with three dependent variables that is an extension of a hydrodynamic-type system obtained from a particular solution of the Witten–Dijkgraaf–Verlinde–Verlinde equations.

Comparison of Nonlinear Spatial Correlation Models by the Influence of the Data Augmentation to the Classification Risk

2002 ◽  
Vol 7 (1) ◽  
pp. 31-42
Author(s):  
J. Šaltytė ◽  
K. Dučinskas
Keyword(s):  
Spatial Correlation ◽  
Random Fields ◽  
Data Augmentation ◽  
Gaussian Random Fields ◽  
Classification Rule ◽  
Numerical Comparison ◽  
First Order ◽  
Bayesian Risk ◽  
Correlation Models

The Bayesian classification rule used for the classification of the observations of the (second-order) stationary Gaussian random fields with different means and common factorised covariance matrices is investigated. The influence of the observed data augmentation to the Bayesian risk is examined for three different nonlinear widely applicable spatial correlation models. The explicit expression of the Bayesian risk for the classification of augmented data is derived. Numerical comparison of these models by the variability of Bayesian risk in case of the first-order neighbourhood scheme is performed.

scholarly journals Correction to: Classification of non-local rings with genus two zero-divisor graphs

2021 ◽  
Vol 25 (4) ◽  
pp. 3355-3356
Author(s):  
T. Asir ◽  
K. Mano ◽  
T. Tamizh Chelvam
Keyword(s):  
Zero Divisor ◽  
Local Rings ◽  
Non Local ◽  
Genus Two

Some logical and syntactical observations concerning the first-order dependent type system λP

1999 ◽  
Vol 9 (4) ◽  
pp. 335-359 ◽  
Author(s):  
HERMAN GEUVERS ◽  
ERIK BARENDSEN
Keyword(s):  
Predicate Logic ◽  
Type System ◽  
Logical Framework ◽  
First Order ◽  
Logical Derivation ◽  
Dependent Type ◽  
First Order Predicate Logic

We look at two different ways of interpreting logic in the dependent type system λP. The first is by a direct formulas-as-types interpretation à la Howard where the logical derivation rules are mapped to derivation rules in the type system. The second is by viewing λP as a Logical Framework, following Harper et al. (1987) and Harper et al. (1993). The type system is then used as the meta-language in which various logics can be coded.We give a (brief) overview of known (syntactical) results about λP. Then we discuss two issues in some more detail. The first is the completeness of the formulas-as-types embedding of minimal first-order predicate logic into λP. This is a remarkably complicated issue, a first proof of which appeared in Geuvers (1993), following ideas in Barendsen and Geuvers (1989) and Swaen (1989). The second issue is the minimality of λP as a logical framework. We will show that some of the rules are actually superfluous (even though they contribute nicely to the generality of the presentation of λP).At the same time we will attempt to provide a gentle introduction to λP and its various aspects and we will try to use little inside knowledge.

scholarly journals SOME CONSIDERATIONS ABOUT PODOLSKY-AXIONIC ELECTRODYNAMICS

2012 ◽  
Vol 27 (11) ◽  
pp. 1250061 ◽  
Author(s):  
PATRICIO GAETE
Keyword(s):  
Interaction Potential ◽  
Gauge Invariant ◽  
First Order ◽  
Dependent Variables ◽  
Path Dependent

For a Podolsky-axionic electrodynamics, we compute the interaction potential within the structure of the gauge-invariant but path-dependent variables formalism. The result is equivalent to that of axionic electrodynamics from a new noncommutative approach, up to first-order in θ.

scholarly journals SMT-Based System Verification with DVF

10.29007/59rn ◽  
2018 ◽  
Author(s):  
Amit Goel ◽  
Sava Krstic ◽  
Rebekah Leslie ◽  
Mark Tuttle
Keyword(s):  
Thin Layer ◽  
Type System ◽  
Transition Systems ◽  
First Order ◽  
Verification Conditions ◽  
Logic Verification ◽  
System Verification ◽  
Selected Subset ◽  
Parametric Specification

We introduce the <i>Deductive Verificaton Framework</i> (DVF), a language and a tool for verifying properties of transition systems. The language is procedural and the system transitions are a selected subset of procedures. The type system and built-in operations are consistent with SMT-LIB, as are the multisorted first-order logical formulas that may occur in DVF programs as pre- and post-conditions, assumptions, assertions, and goals. A template mechanism allows parametric specification of complex types within the confines of this logic. Verification conditions are generated from specified goals and passed to SMT engine(s). A general assume-guarantee scheme supports a thin layer of interactive proving.

scholarly journals On a solvable class of product-type systems of difference equations

Filomat ◽  
2017 ◽  
Vol 31 (19) ◽  
pp. 6113-6129 ◽  
Author(s):  
Stevo Stevic ◽  
Bratislav Iricanin ◽  
Zdenk Smarda
Keyword(s):  
Closed Form ◽  
Difference Equations ◽  
Type Systems ◽  
Product Type ◽  
Dependent Variables ◽  
Solvable Class ◽  
Solvable Product

It is shown that the following class of systems of difference equations zn+1 = ?zanwbn, wn+1 = ?wcnzdn-2, n ? N0, where a,b,c,d ? Z, ?, ?, z-2, z-1, z0,w0 ? C \ {0}, is solvable, continuing our investigation of classification of solvable product-type systems with two dependent variables. We present closed form formulas for solutions to the systems in all the cases. In the main case, when bd ? 0, a detailed investigation of the form of the solutions is presented in terms of the zeros of an associated polynomial whose coefficients depend on some of the parameters of the system.

scholarly journals On generalized Lemaitre–Tolman–Bondi metric: Fractal matter at the end of matter–antimatter recombination

2021 ◽  
pp. 2150086
Author(s):  
Sergio L. Cacciatori ◽  
Alessio Marrani ◽  
Federico Re
Keyword(s):  
Dark Matter ◽  
Relativistic Effects ◽  
Partial Explanation ◽  
First Order ◽  
Acceleration Of The Universe ◽  
Particular Solution ◽  
Ancient Times ◽  
The Universe ◽  
Recombination Epoch ◽  
Ltb Metric

Many recent researches have investigated the deviations from the Friedmannian cosmological model, as well as their consequences on unexplained cosmological phenomena, such as dark matter and the acceleration of the Universe. On one hand, a first-order perturbative study of matter inhomogeneity returned a partial explanation of dark matter and dark energy, as relativistic effects due to the retarded potentials of far objects. On the other hand, the fractal cosmology, now approximated by a Lemaitre–Tolman–Bondi (LTB) metric, results in distortions of the luminosity distances of SNe Ia, explaining the acceleration as apparent. In this work, we extend the LTB metric to ancient times. The origin of the fractal distribution of matter is explained as the matter remnant after the matter–antimatter recombination epoch. We show that the evolution of such a inhomogeneity necessarily requires a dynamical generalization of LTB, and we propose a particular solution.

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