scholarly journals Geometric theory of meromorphic functions

2004 ◽  
pp. 221-230 ◽  
Author(s):  
A. Eremenko
Keyword(s):  
Meromorphic Functions ◽  
Geometric Theory

GEOMETRIC THEORY OF MULTIDIMENSIONAL INTERPOLATION

2020 ◽  
Vol 2020 (1) ◽  
pp. 9-16
Author(s):  
Evgeniy Konopatskiy
Keyword(s):  
Response Function ◽  
Algebraic Curves ◽  
Geometric Theory ◽  
Analytical Description ◽  
Geometric Interpretation ◽  
Affine Geometry ◽  
Mathematical Apparatus ◽  
Multidimensional Interpolation ◽  
Pass Through

The paper presents a geometric theory of multidimensional interpolation based on invariants of affine geometry. The analytical description of geometric interpolants is performed within the framework of the mathematical apparatus BN-calculation using algebraic curves that pass through preset points. A geometric interpretation of the interaction of parameters, factors, and the response function is presented, which makes it possible to generalize the geometric theory of multidimensional interpolation in the direction of increasing the dimension of space. The conceptual principles of forming the tree of the geometric interpolant model as a geometric basis for modeling multi-factor processes and phenomena are described.

Further investigations on Fujimoto type strong uniqueness polynomials

Filomat ◽  
2017 ◽  
Vol 31 (16) ◽  
pp. 5203-5216
Author(s):  
Abhijit Banerjee ◽  
Bikash Chakraborty ◽  
Sanjay Mallick
Keyword(s):  
Meromorphic Functions ◽  
Future Research ◽  
Strong Uniqueness ◽  
Open Questions

Taking the question posed by the first author in [1] into background, we further exhaust-ably investigate existing Fujimoto type Strong Uniqueness Polynomial for Meromorphic functions (SUPM). We also introduce a new kind of SUPM named Restricted SUPM and exhibit some results which will give us a new direction to discuss the characteristics of a SUPM. Moreover, throughout the paper, we pose a number of open questions for future research.

Examples of theories of presheaf type

2018 ◽  
Author(s):  
Olivia Caramello
Keyword(s):  
Finite Groups ◽  
Linear Independence ◽  
Geometric Theory ◽  
Vector Spaces ◽  
Linear Orders ◽  
Locally Finite ◽  
Strong Unit ◽  
Locally Finite Groups ◽  
Simplicial Sets ◽  
Separable Extensions

This chapter discusses several classical as well as new examples of theories of presheaf type from the perspective of the theory developed in the previous chapters. The known examples of theories of presheaf type that are revisited in the course of the chapter include the theory of intervals (classified by the topos of simplicial sets), the theory of linear orders, the theory of Diers fields, the theory of abstract circles (classified by the topos of cyclic sets) and the geometric theory of finite sets. The new examples include the theory of algebraic (or separable) extensions of a given field, the theory of locally finite groups, the theory of vector spaces with linear independence predicates and the theory of lattice-ordered abelian groups with strong unit.

Flat functors and classifying toposes

2018 ◽  
Author(s):  
Olivia Caramello
Keyword(s):  
General Theory ◽  
Geometric Theory ◽  
Small Category ◽  
Independent Interest ◽  
Yoneda Lemma ◽  
Geometric Morphisms ◽  
The Way

This chapter develops a general theory of extensions of flat functors along geometric morphisms of toposes; the attention is focused in particular on geometric morphisms between presheaf toposes induced by embeddings of categories and on geometric morphisms to the classifying topos of a geometric theory induced by a small category of set-based models of the latter. A number of general results of independent interest are established on the way, including developments on colimits of internal diagrams in toposes and a way of representing flat functors by using a suitable internalized version of the Yoneda lemma. These general results will be instrumental for establishing in Chapter 6 the main theorem characterizing the class of geometric theories classified by a presheaf topos and for applying it.

On Fixed Points of Meromorphic Functions f(z) and f(z + c), Δcf(z)

2019 ◽  
Vol 39 (5) ◽  
pp. 1277-1289
Author(s):  
Shuangting Lan ◽  
Zongxuan Chen
Keyword(s):  
Fixed Points ◽  
Meromorphic Functions

scholarly journals Joseph Fourier 250thBirthday: Modern Fourier Analysis and Fourier Heat Equation in Information Sciences for the XXIst Century

Entropy ◽  
2019 ◽  
Vol 21 (3) ◽  
pp. 250
Author(s):  
Frédéric Barbaresco ◽  
Jean-Pierre Gazeau
Keyword(s):  
Fourier Analysis ◽  
Heat Equation ◽  
Harmonic Analysis ◽  
Lie Groups ◽  
Coherent States ◽  
Geometric Theory ◽  
Plancherel Formula ◽  
Group Representations ◽  
Modern Development ◽  
Xxist Century

For the 250th birthday of Joseph Fourier, born in 1768 at Auxerre in France, this MDPI special issue will explore modern topics related to Fourier analysis and Fourier Heat Equation. Fourier analysis, named after Joseph Fourier, addresses classically commutative harmonic analysis. The modern development of Fourier analysis during XXth century has explored the generalization of Fourier and Fourier-Plancherel formula for non-commutative harmonic analysis, applied to locally compact non-Abelian groups. In parallel, the theory of coherent states and wavelets has been generalized over Lie groups (by associating coherent states to group representations that are square integrable over a homogeneous space). The name of Joseph Fourier is also inseparable from the study of mathematics of heat. Modern research on Heat equation explores geometric extension of classical diffusion equation on Riemannian, sub-Riemannian manifolds, and Lie groups. The heat equation for a general volume form that not necessarily coincides with the Riemannian one is useful in sub-Riemannian geometry, where a canonical volume only exists in certain cases. A new geometric theory of heat is emerging by applying geometric mechanics tools extended for statistical mechanics, for example, the Lie groups thermodynamics.

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