• Journal of applied mathematics & informatics
• /
• 제40권3_4호
• /
• pp.657-668
• /
• 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.

• Korean Journal of Mathematics
• /
• 제30권3호
• /
• pp.459-465
• /
• 2022

We exhibit various properties of the weighted Berezin operator T_α and its iteration T^k_α on L^p(𝜏), where α > -1 and 𝜏 is the invariant measure on the complex unit ball B_n. Iterations of T_α on L¹_R(𝜏) the space of radial integrable functions have performed important roles in proving 𝓜-harmonicity of bounded functions with invariant mean value property. We show differences between the case of 1 < p < ∞ and p = 1, ∞ under the infinite iteration of T_α or the infinite summation of iterations, most of which are extensions or related assertions to the propositions of the previous results.

• Journal of Applied and Pure Mathematics
• /
• 제4권1_2호
• /
• pp.9-26
• /
• 2022

The purpose of this work is to study the existence and continuous dependence on neutral stochastic partial integrodifferential equations with impulsive effects, perturbed by a fractional Brownian motion with Hurst parameter $H{\in}({\frac{1}{2}},\;1)$. We use the theory of resolvent operators developed in Grimmer [19] to show the existence of mild solutions. Further, we establish a new impulsive-integral inequality to prove the exponential stability of mild solutions in the mean square moment. Finally, an example is presented to illustrate our obtained results.

• Journal of applied mathematics & informatics
• /
• 제41권6호
• /
• pp.1181-1191
• /
• 2023

This paper investigates Young inequalities for matrices, a problem closely linked to operator theory, mathematical physics, and the arithmetic-geometric mean inequality. By obtaining new inequalities for unitarily invariant norms, we aim to derive a fresh Young inequality specifically designed for matrices.To lay the foundation for our study, we provide an overview of basic notation related to matrices. Additionally, we review previous advancements made by researchers in the field, focusing on Young improvements.Building upon this existing knowledge, we present several new enhancements of the classical Young inequality for nonnegative real numbers. Furthermore, we establish a matrix version of these improvements, tailored to the specific characteristics of matrices. Through our research, we contribute to a deeper understanding of Young inequalities in the context of matrices.

• 호남수학학술지
• /
• 제45권4호
• /
• pp.585-597
• /
• 2023

We introduce the rotational hypersurface x = x(u, v, s, t) constructed by double rotation in five dimensional Euclidean space 𝔼⁵. We reveal the first and the second fundamental form matrices, Gauss map, shape operator matrix of x. Additionally, defining the i-th curvatures of any hypersurface via Cayley-Hamilton theorem, we compute the curvatures of the rotational hypersurface x. We give some relations of the mean and Gauss-Kronecker curvatures of x. In addition, we reveal Δx=𝓐x, where 𝓐 is the 5 × 5 matrix in 𝔼⁵.

• Korean Journal of Mathematics
• /
• 제32권2호
• /
• pp.213-218
• /
• 2024

Assume that at a certain locus there are three genotypes and that for every one progeny produced by an I^AI^A homozygote, the heterozygote I^AI^B produces. W. Choi found the adapted partial differential equations for the density and operator of the frequency for one gene and applied this adapted partial differential equations to several diploid model. Also, he found adapted partial differential equations for the diploid model against recessive homozygotes and in case that the alley frequency occurs after one generation of selection when there is no dominance. (see. [1, 2]). In this paper, we find the adapted partial equations for the model of selection against heterozygotes and in case that the allele frequency changes after one generation of selection when there is overdominance. Finally, we shall find the partial differential equation of general type of selection at diploid model and it also shall apply to actual examples. This is a very meaningful result in that it can be applied in any model.

• International Journal of Fuzzy Logic and Intelligent Systems
• /
• 제15권2호
• /
• pp.102-110
• /
• 2015

The main source of noise in computed tomography (CT) images is a quantum noise, which results from statistical fluctuations of X-ray quanta reaching the detector. This paper proposes a neural network (NN) based hybrid filter for removing quantum noise. The proposed filter consists of bilateral filters (BFs), a single or multiple neural edge enhancer(s) (NEE), and a neural filter (NF) to combine them. The BFs take into account the difference in value from the neighbors, to preserve edges while smoothing. The NEE is used to clearly enhance the desired edges from noisy images. The NF acts like a fusion operator, and attempts to construct an enhanced output image. Several measurements are used to evaluate the image quality, like the root mean square error (RMSE), the improvement in signal to noise ratio (ISNR), the standard deviation ratio (MSR), and the contrast to noise ratio (CNR). Also, the modulation transfer function (MTF) is used as a means of determining how well the edge structure is preserved. In terms of all those measurements and means, the proposed filter shows better performance than the guided filter, and the nonlocal means (NLM) filter. In addition, there is no severe restriction to select the number of inputs for the fusion operator differently from the neuro-fuzzy system. Therefore, without concerning too much about the filter selection for fusion, one could apply the proposed hybrid filter to various images with different modalities, once the corresponding noise characteristics are explored.

• 한국정보통신학회논문지
• /
• 제13권11호
• /
• pp.2277-2282
• /
• 2009

본 논문에서는 형태학적 특징 및 차 연산과 ART2 알고리즘을 이용한 차량 번호판 인식 방법을 제안하였다. 무인 카메라에서 획득된 차량 번호판 영상에서 차 연산을 이용하여 에지를 추출한 후에 블록 이진화한다. 이진화된 차량 영상에서 신 구 차량 번호판의 형태학적 특성을 8방향 윤곽선 추적 알고리즘에 적용하여 잡음 영역을 제거하고, 차량의 번호판 영역을 추출한다. 추출된 번호판 영역에 대하여 평균 이진화와 최대 최소 이진화를 적용하여 번호판의 개별 영역에 대한 형태학적 특성을 고려하여 잡음을 제거하고, Labeling 알고리즘을 적용하여 개별 문자를 추출한 후에 결합한다. 이렇게 추출되어 결합된 개별 문자 및 숫자 코드들은 ART2 알고리즘에 적용하여 학습 및 인식된다. 제안된 차량 번호판 추출 및 인식 방법의 성능을 평가하기 위해 녹색 번호판과 흰색 번호판 이미지 각각 100장을 대상으로 실험한 결과, 제안된 차량 번호판 추출 및 인식기법이 효율적임을 확인하였다.

• Journal of Dental Anesthesia and Pain Medicine
• /
• 제19권1호
• /
• pp.29-36
• /
• 2019

Background: An inability to cope with threatening dental stimuli, i.e., sight, sound, and sensation of airotor, manifests as anxiety and behavioral management problems. Behavior modification techniques involving pre-exposure to dental equipment will give children a first-hand experience of their use, sounds, and clinical effects. The aim of this study was to compare the techniques of Tell-Show-Play-doh, a smartphone dentist game, and a conventional Tell-Show-Do method in the behavior modification of anxious children in the dental operatory. Methods: Sixty children in the age group of 4-8 years, with Frankl's behavior rating score of 2 or 3, requiring Class I and II cavity restorations were divided into three groups. The groups were Group 1: Tell-Show-Play-doh; Group 2: smartphone dentist game; and Group 3: Tell-Show-Do technique and each group comprised of 20 children. Pulse rate, Facial Image Scale (FIS), Frankl's behavior rating scale, and FLACC (Face, Leg, Activity, Cry, Consolability) behavior scales were used to quantify anxious behavior. Operator compliance was recorded through a validated questionnaire. Results: The results showed lower mean pulse rates, lower FIS and FLACC scores, higher percentage of children with Frankl's behavior rating score of 4, and better operator compliance in both the Tell-Show-Play-doh and smartphone dentist game groups than in the conventional Tell-Show-Do group. Conclusion: The Tell-Show-Play-doh and smartphone dentist game techniques are effective tools to reduce dental anxiety in pediatric patients.

• Clinics in Orthopedic Surgery
• /
• 제10권4호
• /
• pp.484-490
• /
• 2018

Background: The use of three-dimensional multi-segment foot models (3D MFMs) is increasing since they have superior ability to illustrate the effect of foot and ankle pathologies on intersegmental motion of the foot compared to single-segment foot model gait analysis. However, validation of the repeatability of the 3D MFMs is important for their clinical use. Although many MFMs have been validated in normal adults, research on MFM repeatability in children is lacking. The purpose of this study is to validate the intrasession, intersession, and interrater repeatability of an MFM with a 15-marker set (DuPont foot model) in healthy children. Methods: The study included 20 feet of 20 healthy children (10 boys and 10 girls). We divided the participants into two groups of 10 each. One group was tested by the same operator in each test (intersession analysis), while the other group was tested by a different operator in each test (interrater analysis). The multiple correlation coefficient (CMC) and intraclass correlation coefficient (ICC) were calculated to assess repeatability. The difference between the two sessions of each group was assessed at each time point of gait cycle. Results: The intrasession CMC and ICC values of all parameters showed excellent or very good repeatability. The intersession CMC of many parameters showed good or better repeatability. Interrater CMC and ICC values were generally lower for all parameters than intrasession and intersession. The mean gaps of all parameters were generally similar to those of the previous study. Conclusions: We demonstrated that 3D MFM using a 15-marker set had high intrasession, intersession, and interrater repeatability in the assessment of foot motion in healthy children but recommend some caution in interpreting the hindfoot parameters.