• East Asian mathematical journal
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• 제31권5호
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• pp.653-658
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• 2015

In this paper, we consider split quaternionic functions defined on an open set of split quaternions and give the split quaternionic functions whose each inverse function is sp-hyperholomorphic almost everywhere on ${\Omega}$. Also, we describe the definitions and notions of pseudoholomorphic functions for split quaternions.

• East Asian mathematical journal
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• 제32권3호
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• pp.311-317
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• 2016

In this paper, we investigate several properties of quaternionic functions. We research some dierentials of quaternionic functions, and relations between the dierentials and the corresponding Cauchy Riemann system in Clifford analysis

• East Asian mathematical journal
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• 제29권3호
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• pp.293-302
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• 2013

We research properties of ternary numbers and hyperholomorphic functions with values in $\mathbb{C}$(2). We represent reduced quaternion numbers and obtain some propertries in dual reduced quaternion systems in view of Clifford analysis. Moreover, we obtain Cauchy theorems with respect to dual reduced quaternions.

• East Asian mathematical journal
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• 제32권5호
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• pp.641-649
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• 2016

In this paper, using three types of conjugations in a bicomplex number filed $\mathcal{T}$, we provide some basic definitions of bicomplex number and definitions of regular functions for each differential operators. And we investigate the corresponding Cauchy-Riemann systems and the corresponding Cauchy theorems in $\mathcal{T}$ in Clifford analysis.

• 대한수학회보
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• 제53권2호
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• pp.507-518
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• 2016

In this paper, using forms of conjugations, we give some algebraic properties of bicomplex numbers. We research differential operators, elementary functions and the analogous Cauchy-Riemann system in bicomplex number systems. Also, we investigate the definition and properties of regular functions with values in bicomplex settings in Clifford analysis.

• Korean Journal of Mathematics
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• 제30권3호
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• pp.491-502
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• 2022

In this paper we investigate some sufficient conditions to guarantee the existence and uniqueness of Stepanov-like weighted pseudo almost periodic solutions of cellular neural networks on Clifford algebra for non-automomous cellular neural networks with multi-proportional delays. Our analysis is based on the differential inequality techniques and the Banach contraction mapping principle.

• 호남수학학술지
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• 제38권4호
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• pp.685-692
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• 2016

The aim of this paper is to investigate the differentials of the hypercomplex valued functions in Clifford analysis. Like as the differentials defined by the naïve approach in one complex variable analysis, we define the differentials of functions with values in ternary number functions by same ways. And we survey the properties of each differential with respect to a non-commutativity of the skew field.

• East Asian mathematical journal
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• 제31권1호
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• pp.127-134
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• 2015

We give a rth conic regular functions with conic quaternion variables in $\mathbb{C}^2$ and obtain a hyper-conjugate harmonic function of conic regular function in conic quaternions in the sense of Clifford analysis.

• 호남수학학술지
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• 제36권3호
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• pp.543-553
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• 2014

The aim of this paper is to define hyperholomorphic functions with dual octonion variables on $\mathbb{C}^4{\times}\mathbb{C}^4$ in another way. Using condition of harmonicity, we research properties of functions of dual octonion variables in Clifford analysis.

• Journal of Periodontal and Implant Science
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• 제52권5호
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• pp.352-369
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• 2022

The aim of this systematic review was to evaluate clinical and microbiological outcomes with the use of azithromycin as an adjunct to non-surgical subgingival professional mechanical plaque removal (PMPR) in the treatment of grade C periodontitis. Online database searches using high-level MeSH terms in a PICO structure were conducted along with hand-searching of relevant periodontal journals. Titles and abstracts of identified studies were independently reviewed by both authors and the full texts of studies meeting the inclusion criteria were independently reviewed. In total, 122 studies were identified through searches, of which 6 were included in the qualitative analysis and 4 in the meta-analysis. Three studies included in the meta-analysis were deemed at low risk of bias and 1 at serious risk. There were conflicting results on whether azithromycin reduced the number of subgingival pathogens or detectable subgingival Aggregatibacter actinomycetemcomitans between the included studies. The meta-analysis revealed a statistically significant probing depth reduction difference in favour of azithromycin compared to the control at 3 months (weighted mean difference [WMD]=-0.39 mm; 95% confidence interval [CI], -0.66 to -0.13 mm; I²=0%) and 12 months (WMD=-1.32 mm; 95% CI, -1.71 to -0.93 mm; I²=0%). The clinical attachment level change was also statistically significant in favour of azithromycin compared to the control at 3 months (WMD=-0.61 mm; 95% CI, -1.13 to -0.10 mm; I²=71%) and 12 months (WMD=-0.88 mm; 95% CI, -1.32 to -0.44 mm; I²=0%). Based upon these results, azithromycin offers additional improvements in some clinical parameters when used in conjunction with subgingival PMPR in patients with aggressive periodontitis over control groups. These improvements appear to be maintained for up to 12 months after treatment completion. However, due to a lack of well-designed studies, the conclusions that can be drawn from the available evidence are limited.