• 전기의세계
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• v.23 no.1
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• pp.54-60
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• 1974

To study the entire human heart function an electrical analogue has been designed, based upon fundamental properties of cardiac by starling's

• Journal of applied mathematics & informatics
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• v.25 no.1_2
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• pp.533-540
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• 2007

For a certain open set G in the complex plane $\mathbb{C}$, we construct a transcendental entire function f, such that whose translated family {$f(2^nz)$} is finitely normal exactly on the set G.

• Bulletin of the Korean Mathematical Society
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• v.48 no.5
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• pp.951-957
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• 2011

In 1996, Br$\ddot{u}$ck studied the relation between f and f' if an entire function f shares one value a CM with its first derivative f' and posed the famous Br$\ddot{u}$ck conjecture. In this work, we generalize the value a in the Br$\ddot{u}$ck conjecture to a small function ${\alpha}$. Meanwhile, we prove that the Br$\ddot{u}$ck conjecture holds for a class of meromorphic functions.

• Communications of the Korean Mathematical Society
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• v.35 no.1
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• pp.229-241
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• 2020

For a second order linear differential equation f" + A(z)f' + B(z)f = 0, with A(z) and B(z) being transcendental entire functions under some restrictions, we have established that all non-trivial solutions are of infinite order. In addition, we have proved that these solutions, with a condition, have exponent of convergence of zeros equal to infinity. Also, we have extended these results to higher order linear differential equations.

• 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.

• Korean Journal of Mathematics
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• v.29 no.1
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• pp.179-191
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• 2021

In this paper we introduce generalised logarithmic proximate order, generalised logarithmic proximate type of an entire function and prove the corresponding existence theorems. Also we investigate some theorems on the application of generalised logarithmic proximate order.

• Journal of the Korean Mathematical Society
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• v.59 no.4
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• pp.775-787
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• 2022

Sufficient conditions for the Jensen polynomials of the derivatives of a real entire function to be hyperbolic are obtained. The conditions are given in terms of the growth rate and zero distribution of the function. As a consequence some recent results on Jensen polynomials, relevant to the Riemann hypothesis, are extended and improved.

• Journal of applied mathematics & informatics
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• v.42 no.3
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• pp.549-565
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• 2024

In this paper, we investigate the uniqueness of linear difference differential polynomials sharing a small function. By using the concepts of weakly weighted and relaxed weighted sharing of transcendental entire functions with finite order, we obtained the corresponding results, which improve and extend some results of Chao Meng [14].

• Bulletin of the Korean Mathematical Society
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• v.54 no.3
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• pp.825-838
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• 2017

In this paper we study the uniqueness question of meromorphic functions whose certain differential polynomials share a small function.

• Korean Journal of Radiology
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• v.22 no.5
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• pp.759-769
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• 2021

Objective: To evaluate the application of laplacian-regularized mean apparent propagator (MAPL)-MRI to brain glioma-induced corticospinal tract (CST) injury. Materials and Methods: This study included 20 patients with glioma adjacent to the CST pathway who had undergone structural and diffusion MRI. The entire CSTs of the affected and healthy sides were reconstructed, and the peritumoral CSTs were manually segmented. The morphological characteristics of the CST (track number, average length, volume, displacement of the affected CST) were examined and the diffusion parameter values, including fractional anisotropy (FA), mean diffusivity (MD), axial diffusivity (AD), radial diffusivity (RD), mean squared displacement (MSD), q-space inverse variance (QIV), return-to-origin probability (RTOP), return-to-axis probabilities (RTAP), and return-to-plane probabilities (RTPP) along the entire and peritumoral CSTs, were calculated. The entire and peritumoral CST characteristics of the affected and healthy sides as well as those relative CST characteristics of the patients with motor weakness and normal motor function were compared. Results: The track number, volume, MD, RD, MSD, QIV, RTAP, RTOP, and RTPP of the entire and peritumoral CSTs changed significantly for the affected side, whereas the AD and FA changed significantly only in the peritumoral CST (p < 0.05). In patients with motor weakness, the relative MSD of the entire CST, QIV of the entire and peritumoral CSTs, and the AD, MD, RD of the peritumoral CST were significantly higher, whereas the RTPP of the entire and peritumoral CSTs and the RTOP of the peritumoral CST were significantly lower than those in patients with normal motor function (p < 0.05 for all). In contrast, no significant changes were found in the CST morphological characteristics, FA, or RTAP (p > 0.05 for all). Conclusion: MAPL-MRI is an effective approach for evaluating microstructural changes after CST injury. Its sensitivity may improve when using the peritumoral CST features.