Results 41 to 50 of about 196 (142)

On the Krein-Milman theorem in vector spaces over a non-archimedean valued field K

Indagationes Mathematicae, 1990
Assume that \(K\) is a nonarchimedian complete valued field with a nontrivial valuation, and \(E\) is a Hausdorff locally convex space over \(K\). In this paper some Krein-Milman like theorems for sets in \(E\) are proved. The considered sets are absolutely convex, closed and weakly \(c'\)-compact, if \(K\) is spherically complete, and absolutely ...
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Quasi-invariant and pseudo-differentiable measures on a non-Archimedean Banach space. II. Measures with values in non-Archimedean fields

, 2001
Latex, earlier version: ICTP preprint IC/96 ...
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An analogue of Hilbert's 10th problem for fields of meromorphic functions over non-Archimedean valued fields

Journal of Number Theory, 2003
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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On the analyticity of WLUD$^\infty$ functions of one variable and WLUD$^\infty$ functions of several variables in a complete non-Archimedean valued field

, 2021
Let $\mathcal{N}$ be a non-Archimedean ordered field extension of the real numbers that is real closed and Cauchy complete in the topology induced by the order, and whose Hahn group is Archimedean. In this paper, we first review the properties of weakly locally uniformly differentiable (WLUD) functions, $k$ times weakly locally uniformly differentiable
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Definable retractions and a non-Archimedean Tietze--Urysohn theorem over Henselian valued fields

, 2018
We prove the existence of definable retractions onto arbitrary closed subsets of $K^{n}$ definable over Henselian valued fields $K$. Hence directly follows non-Archimedian analogues of the Tietze--Urysohn and Dugundji theorems on extending continuous definable functions.
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Nonlinear distance measures under the framework of Pythagorean fuzzy sets with applications in problems of pattern recognition, medical diagnosis, and COVID-19 medicine selection. [PDF]

Beni Suef Univ J Basic Appl Sci, 2023
Dutta P, Borah G, Gohain B, Chutia R.
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Summary on non-Archimedean valued fields

, 2018
This article summarizes the main properties of ultrametric spaces, valued fields, ordered fields and fields with valuations of higher rank, highlighting their similarities and differences. The most used non-Archimedean valued fields are reviewed, like a completion in the case of the p-adic numbers fields and the Levi-Civita fields, or like an algebraic
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A spectral theorem for a non-Archimedean valued field whose residue field is formally real

Extracta Mathematicae
In this paper, we will prove a spectral theorem for self-adjoint compactoid operators. Also, we will study the condition on which the coefficient field must be imposed. In order to get the theorems, we will use the Fredholm theory for compactoid operators. Moreover, the property of maximal complete field is important for our study.
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FUNCTIONALS WITH VALUES IN THE NON‐ARCHIMEDEAN FIELD OF LAURENT SERIES AND THEIR APPLICATIONS TO THE EQUATIONS OF ELASTICITY THEORY. I

Mathematical Modelling and Analysis, 2002
Functionals with values in Non‐Archimedean field of Laurent series applied to the definition of generalized solution (in the form of soliton) of the Hopf equation. Calculation method for the profile of infinitely narrow soliton is proposed. Applying this method, calculations of profiles are reduced to the nonlinear system of algebraic equations in R n ...
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A novel MCDM approach for design concept evaluation based on interval-valued picture fuzzy sets. [PDF]

PLoS One, 2023
Ma Q, Sun H, Chen Z, Tan Y.
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