• Title/Summary/Keyword: Function Representation

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EVALUATION OF INTEGRAL FORMULAS ASSOCIATED WITH THE PRODUCT OF GENERALIZED BESSEL FUNCTION WITH ORTHOGONAL POLYNOMIALS

  • Khan, Nabiullah;Nadeem, Raghib;Usman, Talha;Khan, Abdul Hakim
    • Honam Mathematical Journal
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    • v.41 no.1
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    • pp.135-152
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    • 2019
  • In the last decades, various integral formulas associated with Bessel functions of different kinds as well as Bessel functions themselves, have been studied and a noteworthy amount of work can be found in the literature. Following up, we present two definite integral formulas involving the product of generalized Bessel function associated with orthogonal polynomials. Also, some intriguing special cases of our main results have been discussed.

Above bandgap optical properties of ZnS grown by hot-wall epitaxy

  • Lee, M.S.;Koo, M.S.;Kim, T.J.;Kim, Y.D.;Yoo, Y.M.;O, B.;Choi, Y.D.
    • Journal of Korean Vacuum Science & Technology
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    • v.3 no.2
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    • pp.112-115
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    • 1999
  • The real ($\varepsilon$1) and imaginary ($\varepsilon$2) parts of the dielectric function of ZnS have been measured by spectroscopic ellipsometry (SE) in the 3.7-6.0 eV photon-energy range at room temperature. The obtained dielectric function spectra reveal distinct structures at energies E0/(E0+$\Delta$0) and E1 critical points. The spectrum after chemical treatment to remove surface oxide overlayer showed that these data seem to be the best representation of the dielectric function of ZnS, having the largest $\varepsilon$2 value at E1 peak region reported so far by SE. Dielectric-related optical constants of ZnS, such as the complex refractive indices (n+n=ik), absorption coefficient, and reflectance, are also presented.

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Analysis of Misunderstood Types Relate to Trigonometric Function and Its Teaching Method (삼각함수에 관한 오류 유형 분석과 그 지도 방법)

  • 강윤수;박수정
    • Journal of the Korean School Mathematics Society
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    • v.6 no.1
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    • pp.101-113
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    • 2003
  • The purpose of this study is to analyze students misunderstood types relate to trigonometric function and to devise its teaching method using GSP. To do this, we performed several steps as followings: First, we performed questionnaire survey to 70 students belong to second year at high school to find students comprehension degree about radian angle representation and trigonometric function graph. Second, we devised the teaching-learning materials relate to trigonometric function graph using GSP. And then, we used them in the class of 35 students who are at the time to learn trigonometric function in the first year at high school. Third, we conducted Questionnaire survey to students studied through teaching and learning materials using GSP. As a result of doing the survey, we found that general students were interested in the class using GSP and they could also operate computer without difficulty.

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Cross-architecture Binary Function Similarity Detection based on Composite Feature Model

  • Xiaonan Li;Guimin Zhang;Qingbao Li;Ping Zhang;Zhifeng Chen;Jinjin Liu;Shudan Yue
    • KSII Transactions on Internet and Information Systems (TIIS)
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    • v.17 no.8
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    • pp.2101-2123
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    • 2023
  • Recent studies have shown that the neural network-based binary code similarity detection technology performs well in vulnerability mining, plagiarism detection, and malicious code analysis. However, existing cross-architecture methods still suffer from insufficient feature characterization and low discrimination accuracy. To address these issues, this paper proposes a cross-architecture binary function similarity detection method based on composite feature model (SDCFM). Firstly, the binary function is converted into vector representation according to the proposed composite feature model, which is composed of instruction statistical features, control flow graph structural features, and application program interface calling behavioral features. Then, the composite features are embedded by the proposed hierarchical embedding network based on a graph neural network. In which, the block-level features and the function-level features are processed separately and finally fused into the embedding. In addition, to make the trained model more accurate and stable, our method utilizes the embeddings of predecessor nodes to modify the node embedding in the iterative updating process of the graph neural network. To assess the effectiveness of composite feature model, we contrast SDCFM with the state of art method on benchmark datasets. The experimental results show that SDCFM has good performance both on the area under the curve in the binary function similarity detection task and the vulnerable candidate function ranking in vulnerability search task.

Effect of Motor Imagery Training on Somatosensory Evoked Potentials and Upper Limb Function in Stroke Patients

  • Choi, Jongbae;Yang, Jongeun
    • Journal of International Academy of Physical Therapy Research
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    • v.11 no.1
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    • pp.2005-2011
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    • 2020
  • Background: Motor imagery is the mental representation of an action without overt movement or muscle activation. However, few previous studies have demonstrated motor imagery training effects as an objective assessment tool in patients with early stroke. Objective: To investigate the effect of motor imagery training on Somatosensory Evoked Potentials (SSEP) and upper limb function of stroke patients. Design: A quasi-experimental study. Methods: Twenty-four patients with stroke were enrolled in this study. All subjects were assigned to the experimental or control group. All participants received traditional occupational therapy for 30 minutes, 5 times a week. The experimental group performed an additional task of motor imagery training (MIT) 20 minutes per day, 5 days a week, for 4 weeks. Both groups were assessed using the SSEP amplitude, Fugl-Meyer assessment of upper extremity (FMA UE) and Wolf motor function test. Results: After the intervention, the experimental group showed significant improvement in SSEP amplitude and FMA UE than did the control group. Conclusion: These findings suggest that the MIT effectively improve the SSEP and upper limb function of stroke patients.

A Study on Formation of the Process-Object Perspective of Function Using Excel to Specialized High School Math Underachievers (특성화 고등학교 수학부진 학생들의 엑셀을 활용한 함수의 과정-대상 관점 형성에 대한 연구)

  • Choi, Jiyeon;Heo, Hye Ja
    • Journal of Educational Research in Mathematics
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    • v.23 no.2
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    • pp.213-235
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    • 2013
  • The purpose of this study is to analyze how the teaching activities which used EXCEL influence the specialized high school underachieved students. They have difficulties in making use of various representations for better understanding of function. EXCEL is helpful for learning function because it enables the students to use real life materials in math learning as well as formulates Tabular, Algebraic and Graphical which represent function. Furthermore, the students in specialized high school also have the experience of using EXCEL while studying other subjects. For that reason they have no burdens and fears on using EXCEL in learning activities. Utilizing EXCEL in the classroom gives an expectation that it helps to have interests on studying function and prepare for the next learning in the end. Research classes were conducted in a group of five students who have different hopes of career and a variety of mathematical interests. Though the students couldn't transfer Algebraic to Graphical in the diagnostic evaluation, they could resolve the problem of connections between Graphical, Tabular and Algebraic in the process perspectives, and could also express graphical representation by linking object perspectives with process perspectives. Therefore, they solved the connection problem of Tabular, Algebraic and Graphical in the object perspectives. As a result, the students could make transitions between Algebraic and Graphical in object perspectives through the classes applying EXCEL. Consequently, teaching the students with underachievement utilizing EXCEL enables them to recover their interests on math and it helps them to complete their following curriculum.

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CERTAIN CLASSES OF UNIVALENT FUNCTIONS WITH NEGATIVE COEFFICIENTS

  • Lee, Sang-Keun
    • East Asian mathematical journal
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    • v.5 no.2
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    • pp.135-150
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    • 1989
  • In this paper, we define new classes $S*({\alpha},{\beta},{\gamma})$ and $C*({\alpha},{\beta},{\gamma})$ of T, the class of analytic and univalent functions with negative coefficients. We have sharp results concerning coefficients, distortion of functions belonging to these classes along with a. representation formular for the function in $S*({\alpha},{\beta},{\gamma})$ and $C*({\alpha},{\beta},{\gamma})$. Furthermore, we improve the results of Libera for the class of starlike functions having negative coefficients.

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A CLASS OF DEFINITE INTEGRALS

  • Kim, Insuk
    • Honam Mathematical Journal
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    • v.39 no.3
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    • pp.453-463
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    • 2017
  • The aim of this paper is to provide a class of six definite general integrals in terms of gamma function. The results are established with the help of generalized summation formulas obtained earlier by Rakha and Rathie. The results established in this paper are simple, interesting, easily established and may be useful potentially.

A Genetic Algorithm for Searching Shortest Path in Public Transportation Network (대중교통망에서의 최단경로 탐색을 위한 유전자 알고리즘)

  • 장인성;박승헌
    • Korean Management Science Review
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    • v.18 no.1
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    • pp.105-118
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    • 2001
  • The common shortest path problem is to find the shortest route between two specified nodes in a transportation network with only one traffic mode. The public transportation network with multiple traffic mode is a more realistic representation of the transportation system in the real world, but it is difficult for the conventional shortest path algorithms to deal with. The genetic algorithm (GA) is applied to solve this problem. The objective function is to minimize the sum of total service time and total transfer time. The individual description, the coding rule and the genetic operators are proposed for this problem.

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ON SEQUENCE OF FUNCTIONS

  • Salehbhai, Ibrahim A.;Prajapati, Jyotindra C.;Shukla, Ajay K.
    • Communications of the Korean Mathematical Society
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    • v.28 no.1
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    • pp.123-134
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    • 2013
  • Operational techniques have drawn the attention of several researchers in the study of sequence of functions and polynomials. An attempt is made to introduce a new sequence of functions by using operational techniques. Some generating relations and finite summation formulae have been obtained. The corresponding MAPLE code for obtaining above sequence of functions for different values of parameters was also discussed.