• Journal of Applied and Pure Mathematics
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• v.4 no.3_4
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• pp.85-97
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• 2022

Let a graph G = (V, E) be a (p, q) graph. Define $${\rho}\;=\;\{\array{{\frac{p}{2}}&p\text{ is even}\\{\frac{p-1}{2}}\;&p\text{ is odd,}}$$ and M = {±1, ±2, ⋯ ± 𝜌} called the set of labels. Consider a mapping λ : V → M by assigning different labels in M to the different elements of V when p is even and different labels in M to p - 1 elements of V and repeating a label for the remaining one vertex when p is odd. The labeling as defined above is said to be a pair mean cordial labeling if for each edge uv of G, there exists a labeling $\frac{{\lambda}(u)+{\lambda}(v)}{2}$ if λ(u) + λ(v) is even and $\frac{{\lambda}(u)+{\lambda}(v)+1}{2}$ if λ(u) + λ(v) is odd such that ${\mid}\bar{\mathbb{S}}_{{\lambda}_1}-\bar{\mathbb{S}}_{{\lambda}^c_1}{\mid}{\leq}1$ where $\bar{\mathbb{S}}_{{\lambda}_1}$ and $\bar{\mathbb{S}}_{{\lambda}^c_1}$ respectively denote the number of edges labeled with 1 and the number of edges not labeled with 1. A graph G for which there exists a pair mean cordial labeling is called a pair mean cordial graph. In this paper, we investigate the pair mean cordial labeling of graphs which are obtained from path and cycle.

• Bulletin of the Korean Mathematical Society
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• v.60 no.1
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• pp.1-22
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• 2023

Let L(s, χ) be the Dirichlet L-series associated with an f-periodic complex function χ. Let P(X) ∈ ℂ[X]. We give an expression for ∑^f_n=1 χ(n)P(n) as a linear combination of the L(-n, χ)'s for 0 ≤ n < deg P(X). We deduce some consequences pertaining to the Chowla hypothesis implying that L(s, χ) > 0 for s > 0 for real Dirichlet characters χ. To date no extended numerical computation on this hypothesis is available. In fact by a result of R. C. Baker and H. L. Montgomery we know that it does not hold for almost all fundamental discriminants. Our present numerical computation shows that surprisingly it holds true for at least 65% of the real, even and primitive Dirichlet characters of conductors less than 10⁶. We also show that a generalized Chowla hypothesis holds true for at least 72% of the real, even and primitive Dirichlet characters of conductors less than 10⁶. Since checking this generalized Chowla's hypothesis is easy to program and relies only on exact computation with rational integers, we do think that it should be part of any numerical computation verifying that L(s, χ) > 0 for s > 0 for real Dirichlet characters χ. To date, this verification for real, even and primitive Dirichlet characters has been done only for conductors less than 2·10⁵.

• International Journal of Advanced Culture Technology
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• v.11 no.2
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• pp.202-209
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• 2023

This study attempted to identify the ethical principles of nurses who realized care in the war field with a nurse's unique professional spirit, and to explore a more specialized and subdivided concept of ethical nursing in the future. War has occurred frequently in history, and the outcome has always been tragic. There are always different opinions about what it means to discuss the ethics of these wars. Despite these controversies, the ethics of nursing, which always takes care of the sick at the scene of war, is interpreted regardless of war. The ethical spirit of nursing is to respect life and take care of those who need help. Whether the person asking for help is a soldier or a civilian, it doesn't matter where it is or what the purpose of the war is. Nursing practiced nursing based on the principle of bioethics for all, even in war scenes where there was no ethical reference point. This study explains that it is necessary to inherit the spirit of nursing, which practiced ethical care even in such cruel scenes of the past, and to protect the ethical fundamental spirit of nursing even in the changing environment in the future society.

• Journal of Digestive Cancer Research
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• v.11 no.1
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• pp.1-8
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• 2023

Pancreatic cancer treatment has advanced. In particular, effective chemotherapy regimen development has fundamentally altered the therapeutic concept and strategy for pancreatic cancer treatment. Consequently, the prognosis of patients with pancreatic cancer has gradually improved. Conversion surgery for locally advanced pancreatic cancer may offer long-term survival or even a full recovery in some individuals. In contrast, metastatic pancreatic cancer has long been considered a surgical contraindication because aggressive surgical resection of the metastatic lesions does not prolong patient survival. Unexpectedly positive benefits of anticancer therapy in recent clinical experience were observed even with metastatic pancreatic cancer. To date, little evidence presented the success of surgical resection for metastatic pancreatic cancer treatment in such rare cases. However, hope and concern are growing that surgical intervention, even in patients with metastatic cancer, may result in favorable outcomes. Several studies suggested different surgical intervention effects depending on metastasis sites and patterns. Thus, this review summarizes the current status of surgery in the multidisciplinary treatment of oligometastatic pancreatic cancer and discusses future perspectives.

• Kyungpook Mathematical Journal
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• v.63 no.2
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• pp.155-166
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• 2023

In 2018, Andrews introduced the partition functions ${\mathfrak{EO}}$(n) and ${\bar{\mathfrak{EO}}}$(n). The first of these denotes the number of partitions of n in which every even part is less than each odd part, and the second counts the number of partitions enumerated by the first in which only the largest even part appears an odd number of times. In 2021, Pore and Fathima introduced a new partition function ${\mathfrak{EO}}_e$(n) which counts the number of partitions of n which are enumerated by ${\bar{\mathfrak{EO}}}$(n) together with the partitions enumerated by ${\bar{\mathfrak{EO}}}$(n) where all parts are odd and the number of parts is even. They also proved some particular congruences for ${\bar{\mathfrak{EO}}}$(n) and ${\mathfrak{EO}}_e$(n). In this paper, we establish infinitely many families of congruences modulo 2, 4, 5 and 8 for ${\bar{\mathfrak{EO}}}$(n) and modulo 4 for ${\mathfrak{EO}}_e$(n). For example, if p ≥ 5 is a prime with Legendre symbol $({\frac{-3}{p}})=-1$, then for all integers n ≥ 0 and α ≥ 0, we have ${\bar{\mathfrak{EO}}}(8{\cdot}p^{2{\alpha}+1}(pn+j)+{\frac{19{\cdot}p^{2{\alpha}+2}-1}{3}}){\equiv}0$ (mod 8); 1 ≤ j ≤ (p - 1).

• Journal of Applied and Pure Mathematics
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• v.5 no.3_4
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• pp.237-253
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• 2023

Let a graph G = (V, E) be a (p, q) graph. Define $${\rho}=\{\array{{\frac{p}{2}} & \;\;p\text{ is even} \\ {\frac{p-1}{2}} & \;\;p\text{ is odd,}$$ and M = {±1, ±2, … ± ρ} called the set of labels. Consider a mapping λ : V → M by assigning different labels in M to the different elements of V when p is even and different labels in M to p - 1 elements of V and repeating a label for the remaining one vertex when p is odd. The labeling as defined above is said to be a pair mean cordial labeling if for each edge uv of G, there exists a labeling ${\frac{{\lambda}(u)+{\lambda}(v)}{2}}$ if λ(u) + λ(v) is even and ${\frac{{\lambda}(u)+{\lambda}(v)+1}{2}}$ if λ(u) + λ(v) is odd such that ${\mid}{\bar{{\mathbb{S}}}}_{\lambda}{_1}-{\bar{{\mathbb{S}}}}_{{\lambda}^c_1}{\mid}{\leq}1$ where ${\bar{{\mathbb{S}}}}_{\lambda}{_1}$ and ${\bar{{\mathbb{S}}}}_{{\lambda}^c_1}$ respectively denote the number of edges labeled with 1 and the number of edges not labeled with 1. A graph G for which there exists a pair mean cordial labeling is called a pair mean cordial graph. In this paper, we investigate the pair mean cordial labeling behavior of few graphs including the closed helm graph, web graph, jewel graph, sunflower graph, flower graph, tadpole graph, dumbbell graph, umbrella graph, butterfly graph, jelly fish, triangular book graph, quadrilateral book graph.

• Journal of Korean Neurosurgical Society
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• v.65 no.3
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• pp.370-379
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• 2022

Abusive head trauma (AHT) is the most severe form of physical abuse in children. Such injury involves traumatic damage to the head and/or spine of infants and young children. The term AHT was introduced to include a wider range of injury mechanisms, such as intentional direct blow, throw, and even penetrating trauma by perpetuator(s). Currently, it is recommended to replace the former term, shaken baby syndrome, which implicates shaking as the only mechanism, with AHT to include diverse clinical and radiological manifestations. The consequences of AHT cause devastating medical, social and financial burdens on families, communities, and victims. The potential harm of AHT to the developing brain and spinal cord of the victims is tremendous. Many studies have reported that the adverse effects of AHT are various and serious, such as blindness, mental retardation, physical limitation of daily activities and even psychological problems. Therefore, appropriate vigilance for the early recognition and diagnosis of AHT is highly recommended to stop and prevent further injuries. The aim of this review is to summarize the relevant evidence concerning the early recognition and diagnosis of AHT. To recognize this severe type of child abuse early, all health care providers maintain a high index of suspicion and vigilance. Such suspicion can be initiated with careful and thorough history taking and physical examinations. Previously developed clinical prediction rules can be helpful for decision-making regarding starting an investigation when considering meaningful findings. Even the combination of biochemical markers may be useful to predict AHT. For a more confirmative evaluation, neuroradiological imaging is required to find AHT-specific findings. Moreover, timely consultation with ophthalmologists is needed to find a very specific finding, retinal hemorrhage.

• Journal of Koreanology Reviews
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• v.1 no.2
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• pp.1-9
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• 2022

Due in large part to the success of 'Korean Wave' (Hallyu) entertainment commodities, there was much discussion concerning the increasing recognition of Korean culture. With the government's help, South Korean pop culture has spread all over the globe, and Korean businesses have flourished thanks to their global competitiveness. The media in the surrounding areas were quick to catch on, and they all but declared the arrival of Hallyu. Despite a tragic and brutal history of invasions, wars, and dictatorships, South Korea has the 14th largest economy and is the 15th most significant country in terms of soft power. This is largely attributable to the country's leadership in technological and cultural revolutions. The enormous economic and political gains South Korea has experienced from its Hallyu phenomenon remain impressive and even threatening to other countries competing with it for cultural dominance. This is even though media figures in the country must constantly keep in mind new ways to maintain relevance and even enhance their favorability, as pop culture trends are transient and sometimes unpredictable. As South Korean culture spread to the West, Hallyu facilitated the export of several cultural artifacts, including classical music, theater, art, literature, and dance. The Baby Shark music video and song were both created by the Korean business Pink Fong.

• Journal of Applied and Pure Mathematics
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• v.6 no.1_2
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• pp.55-69
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• 2024

Let a graph G = (V, E) be a (p, q) graph. Define $${\rho}=\{\array{{\frac{p}{2}} && p\;\text{is even} \\ {\frac{p-1}{2}} && p\;\text{is odd,}}$$ and M = {±1, ±2, … ± 𝜌} called the set of labels. Consider a mapping λ : V → M by assigning different labels in M to the different elements of V when p is even and different labels in M to p - 1 elements of V and repeating a label for the remaining one vertex when p is odd. The labeling as defined above is said to be a pair mean cordial labeling if for each edge uv of G, there exists a labeling $\frac{{\lambda}(u)+{\lambda}(v)}{2}$ if λ(u) + λ(v) is even and $\frac{{\lambda}(u)+{\lambda}(v)+1}{2}$ if λ(u) + λ(v) is odd such that ${\mid}\bar{\mathbb{s}}_{{\lambda}_1}-\bar{\mathbb{s}}_{{\lambda}^c_1}{\mid}\,{\leq}\,1$ where $\bar{\mathbb{s}}_{{\lambda}_1}$ and $\bar{\mathbb{s}}_{{\lambda}^c_1}$ respectively denote the number of edges labeled with 1 and the number of edges not labeled with 1. A graph G with a pair mean cordial labeling is called a pair mean cordial graph. In this paper, we investigate the pair mean cordial labeling behavior of some union of graphs.

• The Korean Journal of Pain
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• v.30 no.4
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• pp.272-280
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• 2017

Background: The high cost of intrathecal morphine pump (ITMP) implantation may be the main obstacle to its use. Since July 2014, the Korean national health insurance (NHI) program began paying 50% of the ITMP implantation cost in select refractory chronic pain patients. The aims of this study were to investigate the financial break-even point and patients' satisfaction in patients with ITMP treatment after the initiation of the NHI reimbursement. Methods: We collected data retrospectively or via direct phone calls to patients who underwent ITMP implantation at a single university-based tertiary hospital between July 2014 and May 2016. Pain severity, changes in the morphine equivalent daily dosage (MEDD), any adverse events, and patients' satisfaction were determined. We calculated the financial break-even point of ITMP implantation via investigating the patient's actual medical costs and insurance information. Results: During the studied period, 23 patients received ITMP implantation, and 20 patients were included in our study. Scores on an 11-point numeric rating scale (NRS) for pain were significantly reduced compared to the baseline value (P < 0.001). The MEDD before ITMP implantation was 0.59 [IQR: 0.55-0.82]. The total MEDD increased steadily to 0.77 [IQR: 0.53-1.08] at 1 year, which was 126% of the baseline (P < 0.001). More than a half (60%) responded that the ITMP therapy was somewhat satisfying. The financial break-even point was 28 months for ITMP treatment after the NHI reimbursement policy. Conclusions: ITMP provided effective chronic pain management with improved satisfaction and reasonable financial break-even point of 28 months with 50% financial coverage by NHI program.