• Honam Mathematical Journal
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• v.27 no.2
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• pp.141-162
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• 2005

In this paper, by considering the notion of hyperK-algebras of order 3 (which satisfies the simple or normal condition), we state and prove some theorems which determine the relationships between (weak) hyperK-ideals and positive implicative hyperK-ideals of type $1,{\ldots},8$.

• Kyungpook Mathematical Journal
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• v.60 no.4
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• pp.797-803
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• 2020

The Brück conjecture is still open for an entire function f with hyper order of no less than 1/2, which is not an integer. In this paper, it is proved that the hyper order of solutions of a linear complex differential equation that is related to the Brüuck Conjecture is infinite. The results show that the conjecture holds in a special case when the hyper order of f is 1/2.

• Bulletin of the Korean Mathematical Society
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• v.40 no.1
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• pp.123-137
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• 2003

In this note first we define the notions of weak implicative and implicative hyper K-ideals of a hyper K-algebra H. Then we state and prove some theorems which determine the relationship between these notions and (weak) hyper K-ideals. Also we give some relations between these notions and all types of positive implicative hyper K-ideals. Finally we classify the implicative hyper K-ideals of a hyper K-algebra of order 3.

• The Pure and Applied Mathematics
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• v.16 no.1
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• pp.155-165
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• 2009

We investigate the growth of solutions of complex linear differential equations in the unit disc. We obtain properties of solutions of differential equations with entire coefficients. We use the concept of the hyper order to estimate the growth of solutions.

• Journal of information and communication convergence engineering
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• v.1 no.4
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• pp.223-228
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• 2003

In this paper, we introduce a hyper-chaos secure communication method using hyper-chaos circuit onsist of State-Controlled Cellular Neural Network SC-CNN). We make a hyper-chaos circuit using SC-CNN with the n-double scroll or Chua's oscillator. A hyper-chaos circuit is created by applying identical n-double scroll or non-identical n-double scroll and Chua's oscillator with weak coupled method to each cell. Hyper-chaos ynchronization was achieved using GS (Generalized Synchronization) method between the transmitter and receiver about each state variable in the SC-CNN. In order to secure communication, we have synthesizing the desired information with a hyper-chaos circuit by adding the information signal to the hyper-chaos signal using the SC-CNN in the transmitter. And then, transmitting the synthesized signal to the ideal channel, we confirm secure communication by separating the information signal and the hyper-chaos signal in the receiver.

• The Pure and Applied Mathematics
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• v.19 no.3
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• pp.289-295
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• 2012

We research the properties of solutions of general higher order non-homogeneous linear differential equations and apply the hyper order to obtain more precise estimation for the growth of solutions of infinite order.

• Journal of the Korean Mathematical Society
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• v.42 no.1
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• pp.85-99
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• 2005

In this paper, we investigate some properties of the entire function of the hyper order less than ${\frac}{1}{2}$ sharing one value CM with its k-th derivative.

• Journal of IKEEE
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• v.22 no.1
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• pp.14-20
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• 2018

The purpose of training a convolutional neural network (CNN) is to obtain weight factors that give high classification accuracies. The initial values of hyper-parameters affect the training results, and it is important to train a CNN with a suitable hyper-parameter set of a learning rate, a batch size, the initialization of weight factors, and an optimizer. We investigate the effects of a single hyper-parameter while others are fixed in order to obtain a hyper-parameter set that gives higher classification accuracies and requires shorter training time using a proposed VGG-like CNN for training since the VGG is widely used. The CNN is trained for four datasets of CIFAR10, CIFAR100, GTSRB and DSDL-DB. The effects of the normalization and the data transformation for datasets are also investigated, and a training scheme using merged datasets is proposed.

• The Pure and Applied Mathematics
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• v.17 no.3
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• pp.249-256
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• 2010

We research the properties of solutions of general higher order homogeneous linear differential equations and apply the hyper order to obtain more precise estimation for the growth of solutions of infinite order.

• Bulletin of the Korean Mathematical Society
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• v.61 no.1
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• pp.229-246
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• 2024

We consider the delay differential equations $$b(z)w(z+1)+c(z)w(z-1)+a(z)\frac{w'(z)}{w^k(z)}=\frac{P(z, w(z))}{Q(z, w(z))}$$, where k ∈ {1, 2}, a(z), b(z) ≢ 0, c(z) ≢ 0 are rational functions, and P(z, w(z)) and Q(z, w(z)) are polynomials in w(z) with rational coefficients satisfying certain natural conditions regarding their roots. It is shown that if this equation has a non-rational meromorphic solution w with hyper-order ρ2(w) < 1, then either deg_w(P) = deg_w(Q) + 1 ≤ 3 or max{deg_w(P), deg_w(Q)} ≤ 1. In addition, it is shown that in the case max{deg_w(P), deg_w(Q)} = 0 the equations above can have such a solution, with an additional zero density requirement, only if the coefficients of the equation satisfy certain strict conditions.