• Journal of the Korean Mathematical Society
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• v.53 no.6
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• pp.1331-1345
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• 2016

A K-g-frame is a generalization of a g-frame. It can be used to reconstruct elements from the range of a bounded linear operator K in Hilbert spaces. K-g-frames have a certain advantage compared with g-frames in practical applications. In this paper, the interchangeability of two g-Bessel sequences with respect to a K-g-frame, which is different from a g-frame, is discussed. Several construction methods of K-g-frames are also proposed. Finally, by means of the methods and techniques in frame theory, several results of the stability of K-g-frames are obtained.

• Journal of applied mathematics & informatics
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• v.39 no.5_6
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• pp.859-882
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• 2021

In the proposed paper, a new algorithm based on Nonlinear Feedback Shift Register (NLFSR) and modified RC4A (Rivest Cipher 4A) cipher is introduced. NLFSR is used for image pixel scrambling while modified RC4A algorithm is used for pixel substitution. NLFSR used in this algorithm is of order 27 with maximum period 2^27-1 which was found using Field Programmable Gate Arrays (FPGA), a searching method. Modified RC4A algorithm is the modification of RC4A and is modified by introducing non-linear rotation operator in the Key Scheduling Algorithm (KSA) of RC4A cipher. Analysis of occlusion attack (up to 62.5% pixels), noise (salt and pepper, Poisson) attack and key sensitivity are performed to assess the concreteness of the proposed method. Also, some statistical and security analyses are evaluated on various images of different size to empirically assess the robustness of the proposed scheme.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.23 no.3
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• pp.203-210
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• 2019

We present the three-dimensional volume reconstruction model using the modified Cahn-Hilliard equation with a fractional Laplacian. From two-dimensional cross section images such as computed tomography, magnetic resonance imaging slice data, we suggest an algorithm to reconstruct three-dimensional volume surface. By using Laplacian operator with the fractional one, the dynamics is changed to the macroscopic limit of Levy process. We initialize between the two cross section with linear interpolation and then smooth and reconstruct the surface by solving modified Cahn-Hilliard equation. We perform various numerical experiments to compare with the previous research.

• Kyungpook Mathematical Journal
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• v.59 no.2
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• pp.301-314
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• 2019

The aim of this article is to make a connection between the Pascal distribution series and some subclasses of normalized analytic functions whose coefficients are probabilities of the Pascal distribution. For these functions, for linear combinations of these functions and their derivatives, for operators defined by convolution products, and for the Alexander-type integral operator, we find simple sufficient conditions such that these mapping belong to a general class of functions defined and studied by Goodman, Rønning, and Bharati et al.

• Communications for Statistical Applications and Methods
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• v.25 no.6
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• pp.591-604
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• 2018

The accelerated failure time (AFT) model is a linear model under the log-transformation of survival time that has been introduced as a useful alternative to the proportional hazards (PH) model. In this paper we propose variable-selection procedures of fixed effects in a parametric AFT model using penalized likelihood approaches. We use three popular penalty functions, least absolute shrinkage and selection operator (LASSO), adaptive LASSO and smoothly clipped absolute deviation (SCAD). With these procedures we can select important variables and estimate the fixed effects at the same time. The performance of the proposed method is evaluated using simulation studies, including the investigation of impact of misspecifying the assumed distribution. The proposed method is illustrated with a primary biliary cirrhosis (PBC) data set.

• Journal of the Korean Mathematical Society
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• v.58 no.1
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• pp.91-107
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• 2021

A bounded linear operator T on a separable infinite dimensional Banach space X is called strongly hypercyclic if $$X{\backslash}\{0\}{\subseteq}{\bigcup_{n=0}^{\infty}}T^n(U)$$ for all nonempty open sets U ⊆ X. We show that if T is strongly hypercyclic, then so are Tn and cT for every n ≥ 2 and each unimodular complex number c. These results are similar to the well known Ansari and León-Müller theorems for hypercyclic operators. We give some results concerning multiplication operators and weighted composition operators. We also present a result about the invariant subset problem.

• Nonlinear Functional Analysis and Applications
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• v.26 no.3
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• pp.451-474
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• 2021

In this paper, we investigate a hybrid algorithm for finding zeros of the sum of maximal monotone operators and Lipschitz continuous monotone operators which is also a common fixed point problem for finite family of relatively quasi-nonexpansive mappings and split feasibility problem in uniformly convex real Banach spaces which are also uniformly smooth. The iterative algorithm employed in this paper is design in such a way that it does not require prior knowledge of operator norm. We prove a strong convergence result for approximating the solutions of the aforementioned problems and give applications of our main result to minimization problem and convexly constrained linear inverse problem.

• Journal of applied mathematics & informatics
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• v.40 no.3_4
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• pp.657-668
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• 2022

In the present paper we introduce and study Euler sequence spaces of fractional difference and backward difference operators. We make an effort to prove that these spaces are BK-spaces and linearly isomorphic. Further, Schauder basis for Euler fractional difference sequence spaces $e^{\varsigma}_{0,p}({\Delta}^{(\tilde{\beta})},\;{\nabla}^m)$ and $e^{\varsigma}_{c,p}({\Delta}^{(\tilde{\beta})},\;{\nabla}^m)$ are also elaborate. In addition to this, we determine the 𝛼-, 𝛽- and 𝛾- duals of these spaces.

• Nonlinear Functional Analysis and Applications
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• v.27 no.2
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• pp.405-432
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• 2022

Cracks in beams and shallow arches are modeled by massless rotational springs. First, we introduce a specially designed linear operator that "absorbs" the boundary conditions at the cracks. Then the equations of motion are derived from the first principles using the Extended Hamilton's Principle, accounting for non-conservative forces. The variational formulation of the equations is stated in terms of the subdifferentials of the bending and axial potential energies. The equations are given in their abstract (weak), as well as in classical forms.

• Communications of the Korean Mathematical Society
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• v.38 no.4
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• pp.1127-1139
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• 2023

We investigate an extension of Schauder's theorem by studying the relationship between various s-numbers of an operator T and its adjoint T^*. We have three main results. First, we present a new proof that the approximation number of T and T^* are equal for compact operators. Second, for non-compact, bounded linear operators from X to Y, we obtain a relationship between certain s-numbers of T and T^* under natural conditions on X and Y . Lastly, for non-compact operators that are compact with respect to certain approximation schemes, we prove results for comparing the degree of compactness of T with that of its adjoint T^*.