Results 51 to 60 of about 161 (125)

New Perspectives on Generalised Lacunary Statistical Convergence of Multiset Sequences

Mathematics
This paper explores the concepts of J-lacunary statistical limit points, J-lacunary statistical cluster points, and J-lacunary statistical Cauchy multiset sequences.
María C. Listán-García, Ömer Kişi, Mehmet Gürdal   +2 more
doaj   +1 more source

On Sequences With Exponentially Distributed Gaps

Random Structures &Algorithms, Volume 66, Issue 1, January 2025.
ABSTRACT It is well known that a sequence (xn)n∈ℕ⊆[0,1]$$ {\left({x}_n\right)}_{n\in \mathbb{N}}\subseteq \left[0,1\right] $$ which has Poissonian correlations of all orders necessarily has exponentially distributed nearest‐neighbor gaps. It is natural to ask whether this implication also holds in the other direction, that is, whether a sequence with ...
Christoph Aistleitner, Manuel Hauke, Agamemnon Zafeiropoulos   +2 more
wiley   +1 more source

Absolutely continuous and pure point spectra of discrete operators with sparse potentials

Mathematical Methods in the Applied Sciences, Volume 47, Issue 17, Page 13025-13036, 30 November 2024.
We consider the discrete Schrödinger operator H=−Δ+V$$ H=-\Delta +V $$ with a sparse potential V$$ V $$ and find conditions guaranteeing either existence of wave operators for the pair H$$ H $$ and H0=−Δ$$ {H}_0=-\Delta $$ or presence of dense purely point spectrum of the operator H$$ H $$ on some interval [λ0,0]$$ \left[{\lambda}_0,0\right] $$ with λ0<
Stanislav Molchanov, Oleg Safronov, Boris Vainberg   +2 more
wiley   +1 more source

The Role of Lacunary Statistical Convergence for Double sequences in Neutrosophic Normed Spaces [PDF]

Neutrosophic Sets and Systems
This paper introduces and explores the concept of lacunary statistical convergence of double sequence within the framework neutrosophic normed spaces. Neutrosophic normed spaces extend classical normed spaces by incorporating neutrosophic numbers, which ...
Jenifer. P, Jeyaraman. M
doaj   +1 more source

Infinite‐width limit of deep linear neural networks

Communications on Pure and Applied Mathematics, Volume 77, Issue 10, Page 3958-4007, October 2024.
Abstract This paper studies the infinite‐width limit of deep linear neural networks (NNs) initialized with random parameters. We obtain that, when the number of parameters diverges, the training dynamics converge (in a precise sense) to the dynamics obtained from a gradient descent on an infinitely wide deterministic linear NN.
Lénaïc Chizat, Maria Colombo, Xavier Fernández‐Real, Alessio Figalli   +3 more
wiley   +1 more source

Generalized s r I  -statistical convergence in intuitionistic fuzzy normed linear space [PDF]

Songklanakarin Journal of Science and Technology (SJST), 2018
The notion of lacunary ideal convergence in intuitionistic fuzzy normed linear space (IFNLS) was introduced in (Debnath, 2012). As a continuation of this work, in the present paper, we introduce and study the new concept of s r I  -statistical ...
Nabanita Konwar, Pradip Debnath
doaj   +1 more source

Lacunary sequences related to statistical convergence

Annals of Communications in Mathematics, 2020
In this manuscript, our concern is to introduce the new approach of studying the lacunary almost statistical convergence and strongly almost convergence of the generalized difference sequences of fuzzy numbers. Some interesting and basic properties concerning them will be studied.
openaire   +2 more sources

On Asymptotically Lacunary Statistical Equivalent Set Sequences

Journal of Mathematics, 2013
This paper presents three definitions which are natural combination of the definitions of asymptotic equivalence, statistical convergence, lacunary statistical convergence, and Wijsman convergence.
Uğur Ulusu, Fatih Nuray
doaj   +1 more source

On some aspects of lacunary I $\mathcal{I}$ -statistical convergence and its applications in approximation theory via power series method

Journal of Inequalities and Applications
This paper introduces and systematically explores the notion of deferred I $\mathcal{I}$ -lacunary statistical convergence and strongly deferred I $\mathcal{I}$ -lacunary Cesàro convergence for sequences of real numbers, unifying deferred intervals ...
Xiu-Liang Qiu, Humma Javed Sheikh, Kuldip Raj, Qing-Bo Cai   +3 more
doaj   +1 more source