scholarly journals Vector lattices over subfields of the reals

1990 ◽  
Vol 48 (3) ◽  
pp. 359-375 ◽  
Author(s):  
P. Bixler ◽  
P. Conrad ◽  
W. B. Powell ◽  
C. Tsinakis
Keyword(s):  
Vector Lattice ◽  
Scalar Multiplication ◽  
Real Numbers ◽  
The Real ◽  
Vector Lattices ◽  
Non Linear ◽  
Minimal Prime

AbstractIn this paper we consider classes of vector lattices over subfields of the real numbers. Among other properties we relate the archimedean condition of such a vector lattice to the uniqueness of scalar multiplication and the linearity of l-automorphisms. If a vector lattice in the classes considered admits an essential subgroup that is not a minimal prime, then it also admits a non-linear l-automorphism and more than one scalar multiplication. It is also shown that each l-group contains a largest archimedean convex l-subgroup which admits a unique scalar multiplication.

scholarly journals The ksmt Calculus Is a $$\delta $$-complete Decision Procedure for Non-linear Constraints

2021 ◽  
pp. 113-130
Author(s):  
Franz Brauße ◽  
Konstantin Korovin ◽  
Margarita V. Korovina ◽  
Norbert Th. Müller
Keyword(s):  
Decision Procedure ◽  
Linear Constraints ◽  
Real Numbers ◽  
Efficient Treatment ◽  
The Real ◽  
Non Linear ◽  
Transcendental Functions

Abstract is a CDCL-style calculus for solving non-linear constraints over the real numbers involving polynomials and transcendental functions. In this paper we investigate properties of the calculus and show that it is a $$\delta $$ δ -complete decision procedure for bounded problems. We also propose an extension with local linearisations, which allow for more efficient treatment of non-linear constraints.

Free Vector Lattices

1968 ◽  
Vol 20 ◽  
pp. 58-66 ◽  
Author(s):  
Kirby A. Baker
Keyword(s):  
Universal Algebra ◽  
Vector Lattice ◽  
Piecewise Linear ◽  
Continuous Functions ◽  
Real Numbers ◽  
Vector Lattices ◽  
Explicit Characterization

This note presents a useful explicit characterization of the free vector lattice FVL(ℵ) on ℵ generators as a vector lattice of piecewise linear, continuous functions on Rℵ, where ℵ is any cardinal and R is the set of real numbers. A transfinite construction of FVL(ℵ) has been given by Weinberg (14) and simplified by Holland (13, § 5). Weinberg's construction yields the fact that FVL(ℵ) is semi-simple; the present characterization is obtained by combining this fact with a theorem from universal algebra due to Garrett Birkhoff.

scholarly journals Countable vector lattices

1974 ◽  
Vol 10 (3) ◽  
pp. 371-376 ◽  
Author(s):  
Paul F. Conrad
Keyword(s):  
Vector Space ◽  
Vector Lattice ◽  
Real Vector Space ◽  
Vector Spaces ◽  
Real Vector ◽  
Real Numbers ◽  
Vector Lattices ◽  
Direct Sum ◽  
Ordered Vector Spaces ◽  
Countable Dimension

In his paper “On the structure of ordered real vector spaces” (Publ. Math. Debrecen 4 (1955–56), 334–343), Erdös shows that a totally ordered real vector space of countable dimension is order isomorphic to a lexicographic direct sum of copies of the group of real numbers. Brown, in “Valued vector spaces of countable dimension” (Publ. Math. Debrecen 18 (1971), 149–151), extends the result to a valued vector space of countable dimension and greatly simplifies the proof. In this note it is shown that a finite valued vector lattice of countable dimension is order isomorphic to a direct sum of o–simple totally ordered vector spaces. One obtains as corollaries the result of Erdös and the applications that Brown makes to totally ordered spaces.

Dynamics of a family of orbitally continuous mappings

Filomat ◽  
2017 ◽  
Vol 31 (11) ◽  
pp. 3507-3517
Author(s):  
Abhijit Pant ◽  
R.P. Pant ◽  
Kuldeep Prakash
Keyword(s):  
Fixed Points ◽  
Julia Sets ◽  
Real Numbers ◽  
Continuous Mappings ◽  
Non Linear

The aim of the present paper is to study the dynamics of a class of orbitally continuous non-linear mappings defined on the set of real numbers and to apply the results on dynamics of functions to obtain tests of divisibility. We show that this class of mappings contains chaotic mappings. We also draw Julia sets of certain iterations related to multiple lowering mappings and employ the variations in the complexity of Julia sets to illustrate the results on the quotient and remainder. The notion of orbital continuity was introduced by Lj. B. Ciric and is an important tool in establishing existence of fixed points.

scholarly journals Determinants of Non-Linear Effects of Fiscal Policy on Output: The Case of Bulgaria

2009 ◽  
Vol 4 (1) ◽  
pp. 51-61 ◽  
Author(s):  
Vladimir Vladimirov ◽  
Maria Neycheva
Keyword(s):  
Fiscal Policy ◽  
Currency Board ◽  
Main Determinant ◽  
The Real ◽  
Real Gdp ◽  
Non Linear ◽  
Short Run ◽  
Linear Effects ◽  
Policy Impacts ◽  
The Government

Determinants of Non-Linear Effects of Fiscal Policy on Output: The Case of BulgariaThe paper illuminates the non-linear effects of the government budget on short-run economic activity. The study shows that in the Bulgarian economy under a Currency Board Arrangement the tax policy impacts the real growth in the standard Keynesian manner. On the other hand, the expenditure policy exhibits non-Keynesian behavior on the short-run output: cuts in government spending accelerate the real GDP growth. The main determinant of this outcome is the size of the discretionary budgetary changes. The results imply that the balanced budget rule improves the sustainability of public finances without assuring a growth-enhancing effect.

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.

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.

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