A Stronger Reflection Principle for Temperature Functions

2000 ◽  
Vol 61 (2) ◽  
pp. 543-554
Author(s):  
Soon-Yeong Chung
Keyword(s):  
Reflection Principle

scholarly journals NOTES ON BOUNDED INDUCTION FOR THE COMPOSITIONAL TRUTH PREDICATE

2017 ◽  
Vol 10 (3) ◽  
pp. 455-480 ◽  
Author(s):  
BARTOSZ WCISŁO ◽  
MATEUSZ ŁEŁYK
Keyword(s):  
Reflection Principle ◽  
Peano Arithmetic ◽  
Truth Predicate ◽  
Base Theory ◽  
Modified Theory ◽  
Induction Scheme

AbstractWe prove that the theory of the extensional compositional truth predicate for the language of arithmetic with Δ0-induction scheme for the truth predicate and the full arithmetical induction scheme is not conservative over Peano Arithmetic. In addition, we show that a slightly modified theory of truth actually proves the global reflection principle over the base theory.

scholarly journals Further properties of the Bergman spaces of slice regular functions

2015 ◽  
Vol 15 (4) ◽  
Author(s):  
Fabrizio Colombo ◽  
J. Oscar González-Cervantes ◽  
Irene Sabadini
Keyword(s):  
Unit Ball ◽  
Half Space ◽  
Half Plane ◽  
Bergman Kernel ◽  
Bergman Spaces ◽  
Reflection Principle ◽  
Slice Regular Functions ◽  
Regular Functions ◽  
Complex Half Plane ◽  
Schwarz Reflection Principle

AbstractWe continue the study of Bergman theory for the class of slice regular functions. In the slice regular setting there are two possibilities to introduce the Bergman spaces, that are called of the first and of the second kind. In this paperwe mainly consider the Bergman theory of the second kind, by providing an explicit description of the Bergman kernel in the case of the unit ball and of the half space. In the case of the unit ball, we study the Bergman-Sce transform. We also show that the two Bergman theories can be compared only if suitableweights are taken into account. Finally,we use the Schwarz reflection principle to relate the Bergman kernel with its values on a complex half plane.

Time Series Models

2021 ◽  
pp. 255-270
Author(s):  
James Davidson
Keyword(s):  
Time Series ◽  
Random Walk ◽  
Time Series Analysis ◽  
Poisson Process ◽  
Final Section ◽  
Reflection Principle ◽  
Time Series Models ◽  
Wold Decomposition ◽  
Linear Processes ◽  
Series Analysis

This chapter reviews some important ideas from time series analysis. The concepts of stationarity, independence, and exchangeability are defined and illustrated with examples. The Poisson process is examined in detail and then the class of linear processes, noting the implications of the Wold decomposition. The final section studies the random walk and the reflection principle.

A direct derivation of the Catalan formula

2013 ◽  
Vol 97 (538) ◽  
pp. 53-60 ◽  
Author(s):  
Gerry Leversha
Keyword(s):  
Generating Functions ◽  
Recurrence Relations ◽  
Reflection Principle ◽  
Catalan Numbers ◽  
Equal Size ◽  
Alternative Form ◽  
Direct Derivation ◽  
Image Position

Many readers will be familiar with the sequence of Catalan numbers {Cn: n ≥ 0} and the formulawith its alternative formThese can be proved by using recurrence relations, generating functions or André's reflection principle. A good reference for all of these methods is Martin Griffiths' book [1].However, none of these approaches strikes me as being naturally combinatorial. A formula such as (1) is often derived by making a list of all the ways of doing something, and then subdividing this list into classes of equal size, so that either one class consists entirely of ‘valid’ cases or there is exactly one ‘valid’ case in each list.

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