Results 31 to 40 of about 2,222 (176)

Phase Singularities in Complex Arithmetic Random Waves [PDF]

, 2023
Complex arithmetic random waves are stationary Gaussian complex-valued solutions of the Helmholtz equation on the two-dimensional flat torus. We use Wiener-It\^o chaotic expansions in order to derive a complete characterization of the second order high ...
Nourdin, Ivan, Rossi, Maurizia, Dalmao, Federico, Peccati, Giovanni   +3 more
core   +2 more sources

Sum of small arithmetic functions in a floor function set

Gulf Journal of Mathematics
In this paper, we derive asymptotic formulas for the summation of small arithmetic functions over a floor function set. Our results are obtained under assumptions on the size of the floor function set and its alignment with a given arithmetic progression.
T. Srichan, Traiwat Intarawong, Boonrod Yuttanan   +2 more
semanticscholar   +1 more source

RESEARCH ON SMARANDACHE PROBLEMS IN NUMBER THEORY (VOL. II) [PDF]

, 2005
The research on Smarandache Problems plays a key role in the development of number theory. Therefore, many mathematicians show their interest in the Smarandache problems and they conduct much research on them.
Duansen, Liu, Junzhuang, Li, Wenpeng, Zhang   +2 more
core   +1 more source

Asymptotic formulas for certain arithmetic functions

, 2008
This is an extended summary of a talk given by the last named author at the Czecho-Slovake Number Theory Conference 2005, held at Malenovice in September 2005.
M. Garaev, M. Kühleitner, Florian Luca, W. Nowak   +3 more
semanticscholar   +1 more source

On the ergodic Waring–Goldbach problem [PDF]

, 2022
We prove an asymptotic formula for the Fourier transform of the arithmetic surface measure associated to the Waring–Goldbach problem and provide several applications, including bounds for discrete spherical maximal functions along the primes and ...
Kumchev, Angel, Hughes, Kevin, Cook, Brian, Anderson, Theresa C.   +3 more
core   +1 more source

On Additive Divisor Sums and minorants of divisor functions [PDF]

, 2022
We establish asymptotic formulae for various correlations involving general divisor functions $d_k(n)$ and partial divisor functions $d_l(n,A)=\sum_{q|n:q\leq n^A}d_{l-1}(q)$, where $A\in[0,1]$ is a parameter and $k,l\in\mathbb{N}$ are fixed. Our results
Smith, Kevin, Andrade, Julio
core   +1 more source

On Matrix‐Based Cryptography Using Matrix Norm and Special Integer Sequences

Mathematische Nachrichten, EarlyView.
ABSTRACT In this paper, a novel matrix‐based encryption approach based on the Affine Hill cipher is presented. The key matrix is constructed using the Narayana integer sequence, and the Frobenius norm of the key matrix is used as a scaling factor in the key construction.
Melih Göcen, Sümeyye Hacer Büyükakyol   +1 more
wiley   +1 more source

On tau functions associated with linear systems [PDF]

, 2012
\noindent {\bf Abstract} This paper considers the Fredholm determinant $\det (I-\Gamma_x)$ of a Hankel integral operator on $L^2(0, \infty )$ with kernel $\phi (s+t+2x)$, where $\phi$ is a matrix scattering function.
Samantha L. Newsham, Gordon Blower, Newsham, Samantha, Blower, Gordon   +3 more
core  

Feedback Linearisation with State Constraints

International Journal of Robust and Nonlinear Control, EarlyView.
ABSTRACT Feedback Linearisation (FBL) is a widely used technique that applies feedback laws to transform input‐affine nonlinear control systems into linear control systems, allowing for the use of linear controller design methods such as pole placement.
Songlin Jin, Yuanbo Nie, Morgan Jones
wiley   +1 more source

Asymptotic formulae for certain arithmetic functions produced by fractional linear transformations [PDF]

, 2014
K.T. Atanassov introduced the two arithmetic functions \[ I(n) = \prod_{\nu=1}^k p_\nu^{1/\alpha_\nu} \qquad \text{and}\qquad R(n) = \prod_{\nu=1}^k p_\nu^{\alpha_v - 1} \] called the irrational factor and the strong restrictive factor, respectively.
Spiegelhalter, Paul
core