Results 131 to 140 of about 575,831 (281)

An extension to rational functions of a theorem of J. L. Walsh on differences of interpolating polynomials [PDF]

, 1981
Edward B. Saff, A. Sharma, R. S. Varga
openalex   +1 more source

High‐Fidelity Information Transmission Through the Turbulent Atmosphere Utilizing Partially Coherent Cylindrical Vector Beams

Advanced Photonics Research, EarlyView.
A novel free‐space optical communication protocol that combines the benefits of partially coherent light sources with the decoding capabilities of convolutional neural networks is proposed. This approach establishes a robust communication link that can withstand atmospheric turbulence.
Linxuan Yao, Hui Zhang, Yangsheng Yuan, Yaru Gao, Chunhao Liang, Sergey A. Ponomarenko, Yangjian Cai   +6 more
wiley   +1 more source

Computation of Difference Grobner Bases [PDF]

Computer Science Journal of Moldova, 2012
This paper is an updated and extended version of our note \cite{GR'06} (cf.\ also \cite{GR-ACAT}). To compute difference \Gr bases of ideals generated by linear polynomials we adopt to difference polynomial rings the involutive algorithm based on Janet ...
Vladimir P. Gerdt, Daniel Robertz
doaj  

On the Differential-Difference Properties of the Extended Jacobi Polynomials [PDF]

, 1985
Stanisław Lewanowicz
openalex   +1 more source

Stimulated Raman Scattering with Optical Vortex Beams

Advanced Photonics Research, EarlyView.
This study presents exact analytical expressions for stimulated Raman scattering with Laguerre‐Gaussian beams, revealing signal dependence on topological and hyperbolic momentum. The results provide a theoretical foundation for coherent Raman imaging and detecting orbital angular momentum of light via structured light in nonlinear optics.
Minhaeng Cho
wiley   +1 more source

Bernoulli Polynomials in Several Variables and Summation of Monomials over Lattice Points of a Rational Parallelotope

Известия Иркутского государственного университета: Серия "Математика", 2016
The Bernoulli polynomials for natural x were first considered by J.Berno\-ulli (1713) in connection with the problem of summation of the powers of consecutive positive integers. For arbitrary $x$ these polynomials were studied by L.Euler.
O. Shishkina
doaj  

Research Progress on Atmospheric Turbulence Perception and Correction Based on Adaptive Optics and Deep Learning

Advanced Photonics Research, EarlyView.
This work presents a systematic review of atmospheric turbulence fundamentals, including theoretical formulations and adaptive optics‐based mitigation strategies. This includes an in‐depth examination of the devices, theories, and methodologies associated with traditional correction approaches.
Qinghui Liu, Yihang Di, Mengmeng Zhang, Zhenbo Ren, Jianglei Di, Jianlin Zhao   +5 more
wiley   +1 more source

Twin neural network regression

Applied AI Letters, Volume 3, Issue 4, December 2022., 2022
We propose to reformulate a regression problem into predicting differences between target values. This allows for leveraging consistency conditions which can be used as uncertainty estimates and enable the production of an ensemble of predictions while training only a single neural network.
Sebastian Johann Wetzel, Kevin Ryczko, Roger Gordon Melko, Isaac Tamblyn   +3 more
wiley   +1 more source

Partial sharing of small functions with exact difference

Ratio Mathematica
We have proven certain uniqueness results related owing to the partial sharing of small functions of $f$ with difference polynomials of the form $L(f)=b_k(z)f(z+kc)+\ldots +b_0(z)f(z)$, where $b_i$ are small functions of $f$.
Audrija Choudhury, Rupa Pal
doaj   +1 more source

Derandomizing Multivariate Polynomial Factoring for Low Degree Factors [PDF]

arXiv
For a polynomial $f$ from a class $\mathcal{C}$ of polynomials, we show that the problem to compute all the constant degree irreducible factors of $f$ reduces in polynomial time to polynomial identity tests (PIT) for class $\mathcal{C}$ and divisibility tests of $f$ by constant degree polynomials.
arxiv