Certain results on starlike and convex functions
OMA-Vol. 4 (2020), Issue 2, pp. 1 – 14 Open Access Full-Text PDF
Pardeep Kaur, Sukhwinder Singh Billing
Abstract: Using the technique of differential subordination, we here, obtain certain sufficient conditions for starlike and convex functions. In most of the results obtained here, the region of variability of the differential operators implying starlikeness and convexity of analytic functions has been extended. The extended regions of the operators have been shown pictorially.
Numerical analysis of least squares and perceptron learning for classification problems
ODAM-Vol. 3 (2020), Issue 2, pp. 30 – 49 Open Access Full-Text PDF
Larisa Beilina
Abstract: This work presents study on regularized and non-regularized versions of perceptron learning and least squares algorithms for classification problems. The Fréchet derivatives for least squares and perceptron algorithms are derived. Different Tikhonov’s regularization techniques for choosing the regularization parameter are discussed. Numerical experiments demonstrate performance of perceptron and least squares algorithms to classify simulated and experimental data sets.
On the solution of fractional Riccati differential equations with variation of parameters method
EASL-Vol. 3 (2020), Issue 3, pp. 1 – 9 Open Access Full-Text PDF
Ehtasham Ul Haq, Mazhar Ali, Abdullah Saeed Khan
Abstract: In this paper, Variation of Parameters Method (VPM) is used to find the analytical solutions of non-linear fractional order quadratic Riccati differential equation. The given method is applied to initial value problems of the fractional order Riccati differential equations. The proposed technique has no discretization, linearization, perturbation, transformation, preventive suspicions and it is also free from Adomian,s polynomials. The obtained results are compare with analytical solutions by graphical and tabular form.
Einstein equations for a Finsler-Larange space with canonical N-linear connections
OMS-Vol. 4 (2020), Issue 1, pp. 240 – 247 Open Access Full-Text PDF
Roopa M. K, Narasimhamurthy S. K
Abstract: This paper is devoted to study the geometry of Einstein equations of Finsler-Lagrange with \((\alpha, \beta)\)-metrics. We characterized the Einstein equations of Finsler Lagrange space with Randers metric, by using canonical N-metrical connection.
Valuations and their generalizations for UP-algebras
OMS-Vol. 4 (2020), Issue 1, pp. 220 – 239 Open Access Full-Text PDF
Siriwan Pawai, Tararat Khamsang, Aiyared Iampan
Abstract: In this paper, we introduce the notions of a weak pseudo-valuation, a \(0\)-weak pseudo-valuation, a weak valuation, a near pseudo-valuation, a near valuation, a pseudo-valuation, and a valuation and induce a pseudo-metric without triangle inequality, a quasi pseudo-metric, a pseudo-metric, and a metric by some these mappings on a UP-algebra. We also prove that the binary operation defined on a UP-algebra is uniformly continuous under the induced metric by a valuation in some conditions.
Existence of the golden ratio in Tanjavur Brihadeeshwarar temple
OMS-Vol. 4 (2020), Issue 1, pp. 211 – 219 Open Access Full-Text PDF
C. Velmurugan, R. Kalaivanan
Abstract: In this study, we discussed the existence of golden ratio in Brihadeeshwarar temple, Tanjavur, Tamil Nadu, India, built in 1010 AD. It is listed on the UNESCO’s world heritage site of the Chola temples in southern India. This temple represents an outstanding creative achievement in the architectural idea of the pure form of the Dravida temples. Golden ratio has great influence in architecture, mathematics and art. We analyzed existence of the Golden ratio in structural design of Tanjavur Brihadeeshwarar temple prakaram. We used the Phi Grid and Phi Spiral software to measure the golden ratio and verified our result.
