Hyperelastic curves along immersions

Hyperelastic curves in a Riemannian manifold are solutions of a constrained vari-ational problem and characterized by Euler-Lagrange equations. We study the effect of hyper-elastic curves on the geometry of isometric immersions. We investigate the relation between hyperelastic curves and umbilical submanifolds and apply the results to analyze classical elastic curves. The case of a Riemannian manifold with constant sectional curvature is also discussed and some applications are presented for illustrating the results

A Study On Geometry of Spatial Kinematics in Lorentzian Space

Bu çalışmada, dual sayı ve split kuaterniyon yardımıyla Lorenz uzayında spatial kinematiklerin dönüşümlerinin geometrisi ele alınmıştır. Ayrıca, bu uzayda bir $$ ortogonal dönüşüm matrisi, Rodrigues ve Euler parametrelerine göre  verilmiştir. Son olarak, Study'nin "soma" olarak isimlendirdiği dönüşüm uzayı geliştirilmiş ve bu yapı bir dual Lorenz projektif uzayın noktaları içinde spatial kinematiklerin dönüşümünü tanımlamak için kullanılmıştır

A Financial Ratio Analysis on BIST Information and Technology Index (XUTEK) Using AHP-weighted Grey Relational Analysis

The financial ratio analysis is an important issue for the stock exchange markets which have many sub-sectoral indexes. During Industry 4.0 revolution and transition, the sector of information and technology is shown as one of the sectors that have great strategic importance in the global change and development process. So, the performance of the information and technology sector provides a significant added value to the economies. In this study, multi-criteria decision-making (MCDM) approaches will be used to determine the weights of the criteria with considering the experts’ opinions used in the evaluation of the financial performance of the companies operating in the field of Information and Technology Sector of BIST Stock Index (XUTEK). In order to measure the financial performance of companies with MCDM methods, the ratios of the liquidity, operational/activity, financial structure, and profitability are obtained from the financial statements are frequently applied in the scientific literature. In the study, criteria weights were determined by using the pairwise comparison feature of the analytical hierarchy process method and expert opinions. Then, the smallest and largest values of the financial ratio values in quarterly periods in 2020 and the uncertainty formed were evaluated with the gray relational analysis method. After all; XUTEK stocks to be included in the priority investment portfolio in terms of financial performance have been determined

Lorentz Uzaylarında Anti-simetrik Matrisler ve İntegral Eğrileri İçinMatlab Uygulamaları

[8] de, yazarlar (2n1) boyutlu Lorentz uzayında, A matrisi A lineer dönüşümüne karşılık gelen anti-simetrik matris olmak üzere, A(x)0 denkleminin sıfırdan farklı çözümlerini ve x vektörünün kosul karakterlerine göre A anti-simetrik matrisinin normal formlarını elde ettiler. Bu çalışmada, A matrisinin yapısı göz önüne alınarak, antisimetrik matrislerin normal formları için bazı Matlab uygulamaları ve Matlab kodları üretildi. Ayrıca bu uzayda çözümleri lineer vektör alanlarının integral eğrilerine karşılık gelen birinci mertebeden lineer diferansiyel denklem sistemleri için Matlab kodları verildi. Dahası özel durumlar ve x vektörünün kosul karakterlerine göre Matlab uygulamaları yapıldı.In [8], the authors obtained the non-zero solutions of the equation A(x)0, 2 1 1 , n x E ? ? in Lorentzian space 2 1 1 , n E ? where A is a skew-symmetric matrix corresponding to the linear map A and got normal forms of the skewsymmetric matrix A, depending on the causal characters of the vector x. Taking into consideration the structure of the matrix A, we generate Matlab codes and make some Matlab applications for normal form of skew-symmetric matrix. Also, we give some Matlab codes for the linear first order system of differantial equations which the solution of the system gives rise to integral curves of linear vector fields in such a space. Moreover, we give some application with respect to special case of n and causal characters of the vector x for Matlab

P898, Quattro reami / Federico Frezzi. Image 073

https://repository.wellesley.edu/p898/1072/thumbnail.jp

Hyperelastic curves along Riemannian maps

The main purpose of this paper is to examine what kind of information the smooth Riemannian map defined between two Riemannian manifolds provides about the character of the Riemannian map when a horizontal hyperelastic curve on the total manifold is carried to a hyperelastic curve on the base manifold. For the solution of the mentioned problem, firstly, the behavior of an arbitrary horizontal curve on the total manifold under a Riemannian map is investigated and the equations related to pullback connection are obtained. The necessary conditions are given for the Riemannian map to be h-isotropic or totally umbilical when a horizontal Frenet curve in the total manifold transforms to a hyperelastic curve on the base manifold. Then, the concept of the h-hyperelastic Riemannian map is defined and using these findings, the Riemannian map along horizontal hyperelastic curves is characterized.Scientific and Technological Research Council of Turkey (TUBITAK) [119F025]This paper is supported by the Scientific and Technological Research Council of Turkey (TUBITAK) with the number 119F025

Asymptotic Frame Fields of Rational Bézier Curves

Bézier curves are a type of curves used in computer aided design and related fields. The curves can be defined with the help of De Casteljau algorithm, which is one of the most basic elements of curve and surface design, and Bernstein polynomials, which facilitate theoretical developments. A rational Bézier curve may be evaluated by applying the de Casteljau algorithm to both numerator and denominator and finally dividing through. The curves are defined by suitable control points and corresponding scalar weights. In this work, we constitute the asymptotic orthonormal frame field of a spacelike quadratic rational Bézier curve at all points on 2 and 3- dimensional lightlike cones which are degenerate surfaces in Minkowski 3 and 4-spaces. We get the formulas of curvatures for a spacelike quadratic rational Bézier curve 2 and 3-dimensional lightlike cones