scholarly journals On Certain Approximation Problem Connected with the Sums of Subseries

2013 ◽  
Vol 55 (1) ◽  
pp. 37-45
Author(s):  
Roman Wituła ◽  
Konrad Kaczmarek ◽  
Edyta Hetmaniok ◽  
Damian Słota
Keyword(s):  
Approximation Problem ◽  
Real Numbers ◽  
The Real ◽  
The Given

Abstract In this paper a problem of approximating the real numbers by using the series of real numbers is considered. It is proven that if the given family of sequences of real numbers satisfies some conditions of set-theoretical nature, like being closed under initial subsequences and (additionally) possessing properties of adding and removing elements, then it automatically possesses some approximating properties, like, for example, reaching supremum of the set of sums of subseries.

Shuffling of Linear Orders

1995 ◽  
Vol 38 (2) ◽  
pp. 223-229
Author(s):  
John Lindsay Orr
Keyword(s):  
Ordered Set ◽  
Linear Orders ◽  
Real Numbers ◽  
The Real ◽  
Linearly Ordered Set

AbstractA linearly ordered set A is said to shuffle into another linearly ordered set B if there is an order preserving surjection A —> B such that the preimage of each member of a cofinite subset of B has an arbitrary pre-defined finite cardinality. We show that every countable linearly ordered set shuffles into itself. This leads to consequences on transformations of subsets of the real numbers by order preserving maps.

Kleinian characterization of asymptotic symmetries of real general relativity

1993 ◽  
Vol 441 (1913) ◽  
pp. 465-471 ◽  
Keyword(s):  
General Relativity ◽  
Automorphism Group ◽  
Group Action ◽  
Radon Transform ◽  
Symmetry Groups ◽  
Asymptotic Symmetry ◽  
The Real ◽  
The Given ◽  
Asymptotic Symmetries

According to Klein’s Erlanger programme, one may (indirectly) specify a geometry by giving a group action. Conversely, given a group action, one may ask for the corresponding geometry. Recently, I showed that the real asymptotic symmetry groups of general relativity (in any signature) have natural ‘projective’ classical actions on suitable ‘Radon transform’ spaces of affine 3-planes in flat 4-space. In this paper, I give concrete models for these groups and actions. Also, for the ‘atomic’ cases, I give geometric structures for the spaces of affine 3-planes for which the given actions are the automorphism group.

scholarly journals A question of van den Dries and a theorem of Lipshitz and Robinson; Not everything is standard

2007 ◽  
Vol 72 (1) ◽  
pp. 119-122 ◽  
Author(s):  
Ehud Hrushovski ◽  
Ya'acov Peterzil
Keyword(s):  
Real Numbers ◽  
The Real ◽  
First Order ◽  
Real Closed Fields ◽  
Minimal Structure ◽  
Closed Fields ◽  
New Construction ◽  
The Relationship

AbstractWe use a new construction of an o-minimal structure, due to Lipshitz and Robinson, to answer a question of van den Dries regarding the relationship between arbitrary o-minimal expansions of real closed fields and structures over the real numbers. We write a first order sentence which is true in the Lipshitz-Robinson structure but fails in any possible interpretation over the field of real numbers.

On expressible sets and p-adic numbers

2011 ◽  
Vol 54 (2) ◽  
pp. 411-422
Author(s):  
Jaroslav Hančl ◽  
Radhakrishnan Nair ◽  
Simona Pulcerova ◽  
Jan Šustek
Keyword(s):  
Haar Measure ◽  
Real Numbers ◽  
The Real ◽  
Expressible Set

AbstractContinuing earlier studies over the real numbers, we study the expressible set of a sequence A = (an)n≥1 of p-adic numbers, which we define to be the set EpA = {∑n≥1ancn: cn ∈ ℕ}. We show that in certain circumstances we can calculate the Haar measure of EpA exactly. It turns out that our results extend to sequences of matrices with p-adic entries, so this is the setting in which we work.

Models of the Real Numbers

2020 ◽  
pp. 203-221
Author(s):  
Lorenz Halbeisen ◽  
Regula Krapf
Keyword(s):  
Real Numbers ◽  
The Real

The Real Numbers

2020 ◽  
pp. 29-54
Author(s):  
Daniel W. Cunningham
Keyword(s):  
Real Numbers ◽  
The Real

scholarly journals 1,2,31,2,3, some inductive real sequences and a beautiful algebraic pattern

Analysis ◽  
2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Sarsengali Abdygalievich Abdymanapov ◽  
Serik Altynbek ◽  
Anton Begehr ◽  
Heinrich Begehr
Keyword(s):  
Computer Algebra ◽  
Real Line ◽  
Recurrence Relations ◽  
Real Numbers ◽  
The Real

Abstract By rewriting the relation 1 + 2 = 3 {1+2=3} as 1 2 + 2 2 = 3 2 {\sqrt{1}^{2}+\sqrt{2}^{2}=\sqrt{3}^{2}} , a right triangle is looked at. Some geometrical observations in connection with plane parqueting lead to an inductive sequence of right triangles with 1 2 + 2 2 = 3 2 {\sqrt{1}^{2}+\sqrt{2}^{2}=\sqrt{3}^{2}} as initial one converging to the segment [ 0 , 1 ] {[0,1]} of the real line. The sequence of their hypotenuses forms a sequence of real numbers which initiates some beautiful algebraic patterns. They are determined through some recurrence relations which are proper for being evaluated with computer algebra.

scholarly journals Real Representations of Finite Symplectic Groups over Fields of Characteristic Two

2018 ◽  
Vol 2020 (5) ◽  
pp. 1281-1299 ◽  
Author(s):  
C Ryan Vinroot
Keyword(s):  
Irreducible Representation ◽  
Generating Function ◽  
Prime Power ◽  
Symplectic Groups ◽  
Real Numbers ◽  
The Real ◽  
Characteristic Two ◽  
Finite Symplectic Groups

Abstract We prove that when q is a power of 2 every complex irreducible representation of $\textrm{Sp}\big (2n, \mathbb{F}_{q}\big )$ may be defined over the real numbers, that is, all Frobenius–Schur indicators are 1. We also obtain a generating function for the sum of the degrees of the unipotent characters of $\textrm{Sp}\big(2n, \mathbb{F}_{q}\big )$, or of $\textrm{SO}\big(2n+1,\mathbb{F}_{q}\big )$, for any prime power q.

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