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Continued fractions and the density of graphs of some functions
채희준,전병흡,이정연 강원경기수학회 2017 한국수학논문집 Vol.25 No.2
We consider some simple periodic functions on the field of rational numbers with values in $\mathbb{Q}/\mathbb{Z}$ which are defined in terms of lowest-term-expression of rational numbers. We prove the density of graphs of these functions by constructing explicitly points on the graphs close to a given point using continued fractions.
Statistical convergence in partial metric spaces
Fatih Nuray 강원경기수학회 2022 한국수학논문집 Vol.30 No.1
Let $X$ be a partial metric space generated by a partial metric $p$. In this paper, we introduce the notions of statistical convergence and strongly Ces\`{a}ro summability in partial metric spaces. Also, we investigate the relations between the statistical convergence and strongly Ces\`{a}ro summability.
Liftings of absolutely summing operators on $\mathcal{L}_1^\lambda-$ spaces
강정흥 강원경기수학회 2022 한국수학논문집 Vol.30 No.1
In this article, we prove that an absolutely summing operator on $\mathcal{L}_1^{\lambda}$ spaces has a lifting under the conditions that a target Banach space is a quotient of reflexive Banach subspaces.
Gradients in a deep neural network and their Python implementations
박영호 강원경기수학회 2022 한국수학논문집 Vol.30 No.1
This is an expository article about the gradients in deep neural network. It is hard to find a place where gradients in a deep neural network are dealt in details in a systematic and mathematical way. We review and compute the gradients and Jacobians to derive formulas for gradients which appear in the backpropagation and implement them in vectorized forms in Python.
Semi-conformal $L$-harmonic maps and Liouville type theorem
Embarka Remli,Ahmed Mohammed Cherif 강원경기수학회 2022 한국수학논문집 Vol.30 No.1
In this paper, we prove that every semi-conformal harmonic map between Riemannian manifolds is $L$-harmonic map. We also prove a Liouville type theorem for $L$-harmonic maps.
r-notion of conjugacy in partial transformation semigroup
Aftab Hussain Shah,Mohd Rafiq Parray 강원경기수학회 2022 한국수학논문집 Vol.30 No.1
In this paper, we present a new definition of conjugacy that can be applied to an arbitrary semigroup and it does not reduce to the universal relation in semigroups with a zero. We compare the new notion of conjugacy with existing notions, characterize the conjugacy in subsemigroups of partial transformations through digraphs and restrictive partial homomorphisms.
Fixed point theorem via Meir-Keeler contraction in rectangular $M_b$-metric space
Mohammad Asim,Meenu 강원경기수학회 2022 한국수학논문집 Vol.30 No.1
In this paper, we present a fixed point theorem for Meir-Keeler contraction in the framework of Rectangular $M_b$-metric Space. Our main result improves some existing results in literature. An example is also adopted to exhibit the utility of our main result.
Controlled $K$-frames in Hilbert C*-modules
Ekta Rajput,Nabin Kumar Sahu,Vishnu Narayan Mishra 강원경기수학회 2022 한국수학논문집 Vol.30 No.1
Controlled frames have been the subject of interest because of their ability to improve the numerical efficiency of iterative algorithms for inverting the frame operator. In this paper, we introduce the notion of controlled $K$-frame or controlled operator frame in Hilbert $C^{*}$-modules. We establish the equivalent condition for controlled $K$-frame. We investigate some operator theoretic characterizations of controlled $K$-frames and controlled Bessel sequences. Moreover, we establish the relationship between the $K$-frames and controlled $K$-frames. We also investigate the invariance of a controlled $K$-frame under a suitable map $T$. At the end, we prove a perturbation result for controlled $K$-frame.
Arusamy Mohanapriya,Varudaraj Sivakumar,Periasamy Prakash 강원경기수학회 2021 한국수학논문집 Vol.29 No.4
This research article deals with the Mittag-Leffler-Hyers-Ulam stability of linear and impulsive fractional order differential equation which involves the Caputo derivative. The application of the generalized fractional Fourier transform method and fixed point theorem, evaluates the existence, uniqueness and stability of solution that are acquired for the proposed non-linear problems on Lizorkin space. Finally, examples are introduced to validate the outcomes of main result.
Quasi hemi-slant submanifolds of cosymplectic manifolds
Rajendra Prasad,Sandeep Kumar Verma,Sumeet Kumar,Sudhakar K Chaubey 강원경기수학회 2020 한국수학논문집 Vol.28 No.2
We introduce and study quasi hemi-slant submanifolds of almost contact metric manifolds (especially, cosymplectic manifolds) and validate its existence by providing some non-trivial examples. Necessary and sufficient conditions for integrability of distributions, which are involved in the definition of quasi hemi-slant submanifolds of cosymplectic manifolds, are obtained. Also, we investigate the necessary and sufficient conditions for quasi hemi-slant submanifolds of cosymplectic manifolds to be totally geodesic and study the geometry of foliations determined by the distributions.