ORTHOGONALITY IN FINSLER C^*-MODULES

Amyari, Maryam,Hassanniah, Reyhaneh Korean Mathematical Society 2018 대한수학회논문집 Vol.33 No.2

In this paper, we introduce some notions of orthogonality in the setting of Finsler $C^*$-modules and investigate their relations with the Birkhoff-James orthogonality. Suppose that ($E,{\rho}$) and ($F,{\rho}^{\prime}$) are Finsler modules over $C^*$-algebras $\mathcal{A}$ and $\mathcal{B}$, respectively, and ${\varphi}:{\mathcal{A}}{\rightarrow}{\mathcal{B}}$ is a *-homomorphism. A map ${\Psi}:E{\rightarrow}F$ is said to be a ${\varphi}$-morphism of Finsler modules if ${\rho}^{\prime}({\Psi}(x))={\varphi}({\rho}(x))$ and ${\Psi}(ax)={\varphi}(a){\Psi}(x)$ for all $a{\in}{\mathcal{A}}$ and all $x{\in}E$. We show that each ${\varphi}$-morphism of Finsler $C^*$-modules preserves the Birkhoff-James orthogonality and conversely, each surjective linear map between Finsler $C^*$-modules preserving the Birkhoff-James orthogonality is a ${\varphi}$-morphism under certain conditions. In fact, we state a version of Wigner's theorem in the framework of Finsler $C^*$-modules.

20면체계획과 12면체계획의 통계적 성질에 관한 연구

김혁주(Hyuk Joo Kim) 한국자료분석학회 2020 Journal of the Korean Data Analysis Society Vol.22 No.6

설명변수가 3개인 반응표면분석에서 사용될 수 있는 실험계획 중 20면체계획과 12면체계획이 있다. 이 계획들은 모수의 값을 조정함으로써 반응표면 실험계획이 갖출 수 있는 바람직한 성질들을 쉽게 가질 수 있다는 장점이 있다. 본 논문에서는 20면체계획과 12면체계획의 직교성, 회전성 및 기울기회전성에 관하여 복합적으로 연구하였다. 구체적으로, 중심점 수의 여러 경우에 따라 직교성을 갖는 20면체계획과 12면체계획을 구하였고, 또한 회전성과 근사적인 직교성을 동시에 갖는 12면체계획을 구하였으며, 직교성과 기울기회전성을 동시에 갖는 20면체계획, 그리고 직교성과 근사적인 기울기회전성을 동시에 갖는 12면체계획을 구하였다. 그리고 직교성을 갖는 20면체계획과 12면체계획 및 회전성을 갖는 20면체계획과 12면체계획에 Park, Kim(1992)의 기울기회전성의 측도를 적용하여 그 결과를 관찰하였다. 직교성을 갖는 20면체계획과 12면체계획의 경우 기울기회전성의 측도의 값을 표로 작성하였고, 회전성을 갖는 20면체계획과 12면체계획의 경우 정확한 기울기회전성을 동시에 가질 수는 없지만 중심점의 수가 증가할수록 기울기회전계획에 가까워지는 것으로 밝혀졌다. The icosahedral and dodecahedral designs are response surface experimental designs which can be used for the case of three explanatory variables. One of the advantages of these designs is that they can easily have desirable properties separately by controlling the values of the design parameters. In this paper, we compositely studied orthogonality, rotatability and slope rotatability of the icosahedral and dodecahedral designs. Specifically, we obtained orthogonal icosahedral and dodecahedral designs for various numbers of the center points, and dodecahedral designs which simultaneously have rotatability and approximate orthogonality. We also obtained icosahedral designs which simultaneously have orthogonality and slope rotatability, and dodecahedral designs which simultaneously have orthogonality and approximate slope rotatability. Furthermore, we applied Park and Kim (1992) s measure of slope rotatability to orthogonal icosahedral and dodecahedral designs and rotatable icosahedral and dodecahedral designs, and observed the resultant facts. We tabulated the values of the measure of slope rotatability for orthogonal icosahedral and dodecahedral designs. As for rotatable icosahedral and dodecahedral designs, they cannot have exact slope rotatability, but turned out to be close to slope-rotatable designs as the number of the center points increases.

R-ORTHOGONALITY OF LATIN SQUARES USING BIVARIATE PERMUTATION POLYNOMIALS

VADIRAJA BHATTA G. R.,SHANKAR B. R.,PRASANNA POOJARY 장전수학회 2022 Proceedings of the Jangjeon mathematical society Vol.25 No.2

Cryptographic applications of Latin squares require to study them in various aspects. In this paper, the formation and observation of Latin squares using bivariate permutation polynomials over some finite rings are established with respect to their properties like self orthogonalization, r-orthogonalization, and r- mirror orthogonalization. We also identified why some particular cases fail to form self orthogonal Latin squares, and we illustrate it by giving examples.

CT법을 이용한 진직도 및 직각도 측정에 관한 연구

이승수,김민주,박정보,전언찬 한국공작기계학회 2002 한국생산제조학회지 Vol.11 No.1

As high-precision parts are needed with manufacturing techniques improved, the demand of high-precision machine tools has been increasing. They are made to developed the precision measuring skill to maintenance the accuracy of themselves as a matte of course. We on the paper measured straightness and orthogonality of the square to verify that is possible for CT(circular test) method by 2-dimensional probe and the square to measure orthogonality. Furthermore, we compared the result of the study with the computer simulation's to prove its possibility, and made an improvement of measuring method.

q-SOBOLEV ORTHOGONALITY OF THE q-LAGUERRE POLYNOMIALS {L_n^(-N)(·q)}_n=0^∞ FOR POSITIVE INTEGERS N

Moreno, Samuel G.,Garcia-Caballe, Esther M. Korean Mathematical Society 2011 대한수학회지 Vol.48 No.5

The family of q-Laguerre polynomials $\{L_n^{(\alpha)}({\cdot};q)\}_{n=0}^{\infty}$ is usually defined for 0 < q < 1 and ${\alpha}$ > -1. We extend this family to a new one in which arbitrary complex values of the parameter ${\alpha}$ are allowed. These so-called generalized q-Laguerre polynomials fulfil the same three term recurrence relation as the original ones, but when the parameter ${\alpha}$ is a negative integer, no orthogonality property can be deduced from Favard's theorem. In this work we introduce non-standard inner products involving q-derivatives with respect to which the generalized q-Laguerre polynomials $\{L_n^{(-N)}({\cdot};q)\}_{n=0}^{\infty}$, for positive integers N, become orthogonal.

q-SOBOLEV ORTHOGONALITY OF THE q-LAGUERRE POLYNOMIALS <수식> FOR POSITIVE INTEGERS N

Samuel G. Moreno,Esther M. Garcia-Caballero 대한수학회 2011 대한수학회지 Vol.48 No.5

The family of q-Laguerre polynomials <수식> is usually defined for 0 < q < 1 and α > -1. We extend this family to a new one in which arbitrary complex values of the parameter α are allowed. These so-called generalized q-Laguerre polynomials fulfil the same three term recurrence relation as the original ones, but when the parameter α is a negative integer, no orthogonality property can be deduced from Favard's theorem. In this work we introduce non-standard inner products involving q-derivatives with respect to which the generalized q-Laguerre polynomials <수식>, for positive integers N, become orthogonal.

Novel Beamforming and User Scheduling Algorithm for Inter-cell Interference Cancellation

Kyunghoon Kim,Jinhua Piao,Seungwon Choi 대한전자공학회 2016 IEIE Transactions on Smart Processing & Computing Vol.5 No.5

Coordinated multi-point transmission is a candidate technique for next-generation cellular communications systems. We consider a system with multiple cells in which base stations coordinate with each other by sharing user channel state information, which mitigates inter-cell interference (ICI), especially for users located at the cell edge. We introduce a new user scheduling method that considers both ICI and intra-cell orthogonality. Due to the influence of ICI cancellation and the loss reduction of effective channel gain during the beamforming process, the proposed method improves the system sum rate, when compared to the conventional method, by an average of 0.55bps/Hz for different numbers of total users per cell.

Autocorrelation Coefficient for Detecting the Frequency of Bio-Telemetry

Yoshiya Muraki,Yukako Yagi,Kiyoshi Kurokawa,Isao Nakajima 한국멀티미디어학회 2022 The journal of multimedia information system Vol.9 No.3

A MATLAB program was developed to calculate the half-wavelength of a sine-curve baseband signal with white noise by using an autocorrelation function, a SG filter, and zero-crossing detection. The frequency of the input signal can be estimated from 1) the first zero-crossing (corresponding to ¼λ) and 2) the R value (the Y axis of the correlogram) at the center of the segment. Thereby, the frequency information of the preceding segment can be obtained. If the segment size were optimized, and a portion with a large zero-crossing dynamic range were obtained, the frequency discrimination ability would improve. Furthermore, if the values of the correlogram for each frequency prepared on the CPU side were prepared in a table, the volume of calculations can be reduced by 98%. As background, period detection by autocorrelation coefficients requires an integer multiple of 1/2λ (when using a sine wave as the object of the autocorrelation function), otherwise the correlogram drawn by R value will not exhibit orthogonality. Therefore, it has not been used in bio-telemetry where the frequencies move around.

A GENERALIZATION OF THE LAGUERRE POLYNOMIALS

Ali, Asad Korean Mathematical Society 2021 대한수학회논문집 Vol.36 No.2

The main aim of this paper is to introduce and study the generalized Laguerre polynomials and prove that these polynomials are characterized by the generalized hypergeometric function. Also we investigate some properties and formulas for these polynomials such as explicit representations, generating functions, recurrence relations, differential equation, Rodrigues formula, and orthogonality.

General Orthogonality for Orthogonal Polynomials

Sun, Hosung Korean Chemical Society 2013 Bulletin of the Korean Chemical Society Vol.34 No.1

The bound state wave functions for all the known exactly solvable potentials can be expressed in terms of orthogonal polynomials because the polynomials always satisfy the boundary conditions with a proper weight function. The orthogonality of polynomials is of great importance because the orthogonality characterizes the wave functions and consequently the quantum system. Though the orthogonality of orthogonal polynomials has been known for hundred years, the known orthogonality is found to be inadequate for polynomials appearing in some exactly solvable potentials, for example, Ginocchio potential. For those potentials a more general orthogonality is defined and algebraically derived. It is found that the general orthogonality is valid with a certain constraint and the constraint is very useful in understanding the system.