Results 41 to 50 of about 10,296,479 (327)

QED in external fields, a functional point of view [PDF]

, 2001
A functional partial differential equation is set for the proper graphs generating functional of QED in external electromagnetic fields. This equation leads to the evolution of the proper graphs with the external field amplitude and the external field ...
C. J. Burden, C. J. Burden, D. Fliegner, D.-S. Lee, E. J. Ferrer, J. Alexandre, J. Alexandre, J. Schwinger, K. Farakos, L. D. Landau, L. F. Abbott, L. F. Abbott, V. P. Gusynin, V. P. Gusynin, V. Skalozub, W. Dittrich, W. Heisenberg   +16 more
core   +2 more sources

On the functional equation of the Siegel series [PDF]

, 2015
It is well-known that the Fourier coefficients of Siegel-Eisenstein series can be expressed in terms of the Siegel series. The functional equation of the Siegel series of a quadratic form over $\mathbb{Q}_p$ was first proved by Katsurada.
T. Ikeda
semanticscholar   +1 more source

Numerical Calculations to Grasp a Mathematical Issue Such as the Riemann Hypothesis

Information, 2020
This article presents the use of data processing to apprehend mathematical questions such as the Riemann Hypothesis (RH) by numerical calculation. Calculations are performed alongside graphs of the argument of the complex numbers ζ ( x + i y ...
Michel Riguidel
doaj   +1 more source

Axiomatic Characterizations of Information Measures

Entropy, 2008
Axiomatic characterizations of Shannon entropy, Kullback I-divergence, and some generalized information measures are surveyed. Three directions are treated: (A) Characterization of functions of probability distributions suitable as information measures. (
Imre Csiszár
doaj   +1 more source

On the equation F(nᵏ-1) = D [PDF]

Notes on Number Theory and Discrete Mathematics
We prove that if F is a completely multiplicative function and k∈{2,3} such that the equation F(nᵏ-1) = 1 holds for every n∈ℕ, n>1, then F is the identity function.
I. Kátai, B. M. M. Khanh, B. M. Phong
doaj   +1 more source

On the Notion of Reproducibility and Its Full Implementation to Natural Exponential Families

Mathematics, 2021
Let F=Fθ:θ∈Θ⊂R be a family of probability distributions indexed by a parameter θ and let X1,⋯,Xn be i.i.d. r.v.’s with L(X1)=Fθ∈F. Then, F is said to be reproducible if for all θ∈Θ and n∈N, there exists a sequence (αn)n≥1 and a mapping gn:Θ→Θ,θ⟼gn(θ ...
Shaul K. Bar-Lev
doaj   +1 more source

Hyperstability of general linear functional equation

Aequationes Mathematicae, 2016
Our purpose is to investigate criteria for hyperstability of linear type functional equations. We prove that a function satisfying the equation approximately in some sense, must be a solution of it.
A. Bahyrycz, J. Olko
semanticscholar   +1 more source

A Linear Evolution for Non-Linear Dynamics and Correlations in Realistic Nuclei

, 2003
A new approach to high energy evolution based on a linear equation for QCD generating functional is developed. This approach opens a possibility for systematic study of correlations inside targets, and, in particular, inside realistic nuclei.
Adcox, Adcox, Adler, Adler, Adloff, Adloff, Ayala, Ayala, Ayala, Back, Back, Back, Back, Back, Balitsky, Balitsky, Balitsky, Bartels, Bartels, Bartels, Bartels, Bartels, Bazilevsky, Bearden, Bearden, Breitweg, Breitweg, Chekanov, Collins, Dunlop, E. Levin, Eskola, Ewerz, Golec-Biernat, Golec-Biernat, Golec-Biernat, Golec-Biernat, Gotsman, Gotsman, Gotsman, Gribov, Iancu, Jalilian-Marian, Jalilian-Marian, Jalilian-Marian, Jalilian-Marian, Kharzeev, Kharzeev, Kharzeev, Kharzeev, Kovchegov, Kovchegov, Kovchegov, Kovchegov, Kovchegov, Kovner, Kowalski, Kuraev, Kwiecinski, Laenen, Levin, Levin, Levin, Lipatov, M. Lublinsky, McLerran, McLerran, McLerran, McLerran, McLerran, Milov, Mioduszewski, Mueller, Mueller, Mueller, Mueller, Mueller, Mueller, Munier, Munier, Sakaguci, Schwimmer, Stasto, Weigert, Xu   +84 more
core   +2 more sources

Some Best Proximity Theorems for Generalized Proximal $\mathcal{Z}$-Contraction Maps in $b$-Metric Spaces with Applications [PDF]

Sahand Communications in Mathematical Analysis
The simulation function and the notion of $\mathcal{Z}$-contraction concerning $\zeta$ which generalizes the Banach contraction principle and unifies several known types of contractions involving the combination of $d(fx, fy)$ and $d(x, y)$.
Dasari Ratna Babu
doaj   +1 more source

Chains of fundamental mutually homogeneous functions with a common real eigenvalue

St. Petersburg Polytechnical University Journal: Physics and Mathematics, 2020
This work continues the study of the properties of mutually homogeneous functions, which are a generalization of Euler homogeneous functions and can be used in the synthesis of electric and magnetic fields of electron and ion-optical systems with special
Berdnikov Alexander, Solovyev Konstantin, Krasnova Nadezhda   +2 more
doaj   +1 more source