• Journal of applied mathematics & informatics
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• v.39 no.1_2
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• pp.83-91
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• 2021

In this paper, we introduce the concepts of q-cosine tangent polynomials and q-sine tangent polynomials. From these polynomials, we find some identities and properties by using q-numbers and q-trigonometric functions.

• Investigative Magnetic Resonance Imaging
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• v.20 no.1
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• pp.36-43
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• 2016

Visualization of the tissue loss tangent property can provide distinct contrast and offer new information related to tissue electrical properties. A method for non-invasive imaging of the electrical loss tangent of tissue using magnetic resonance imaging (MRI) was demonstrated, and the effect of loss tangent was observed through simulations assuming a hyperthermia procedure. For measurement of tissue loss tangent, radiofrequency field maps ($B_1{^+}$ complex map) were acquired using a double-angle actual flip angle imaging MRI sequence. The conductivity and permittivity were estimated from the complex valued $B_1{^+}$ map using Helmholtz equations. Phantom and ex-vivo experiments were then performed. Electromagnetic simulations of hyperthermia were carried out for observation of temperature elevation with respect to loss tangent. Non-invasive imaging of tissue loss tangent via complex valued $B_1{^+}$ mapping using MRI was successfully conducted. Simulation results indicated that loss tangent is a dominant factor in temperature elevation in the high frequency range during hyperthermia. Knowledge of the tissue loss tangent value can be a useful marker for thermotherapy applications.

• Journal of the Korean Mathematical Society
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• v.46 no.6
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• pp.1255-1265
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• 2009

We show that the Riemannian geometry of a tangent sphere bundle of a Riemannian manifold (M, g) of constant radius $\gamma$ reduces essentially to the one of unit tangent sphere bundle of a Riemannian manifold equipped with the respective induced Sasaki metrics. Further, we provide some applications of this theorem on the $\eta$-Einstein tangent sphere bundles and certain related topics to the tangent sphere bundles.

• Journal of applied mathematics & informatics
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• v.35 no.1_2
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• pp.113-120
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• 2017

In this paper, we introduce degenerate tangent numbers ${\mathcal{T}}^{(k)}_{n,q}({\lambda})$ and tangent polynomials ${\mathcal{T}}^{(k)}_{n,q}(x,{\lambda})$ of higher order. Finally, we obtain interesting properties of these numbers and polynomials.

• Journal of applied mathematics & informatics
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• v.38 no.3_4
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• pp.301-309
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• 2020

Recently, M. Masjed-Jamai et al. in ([6]-[7]) and Srivastava et al. in ([15]-[16]) considered the parametric type of the Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi polynomials. They proved some theorems and gave some identities and relations for these polynomials. In this work, we define the parametric poly-tangent numbers and polynomials. We give some relations and identities for the parametric poly-tangent polynomials.

• The Mathematical Education
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• v.53 no.3
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• pp.313-327
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• 2014

'Tangent' is one of the most important concepts in the middle and high school mathematics, especially in dealing with calculus. The concept of tangent in the current textbook consists of the ways which make use of discriminant or differentiation. These ways, however, do not present dynamic view points, that is, the concept of variation. In this paper, after applying 'Roberval's way of finding tangent using vectors in terms of kinematics to parabola, ellipse, circle, hyperbola, cycloid, hypocycloid and epicycloid, we will identify that this is the tangent of those curves. This trial is the educational link of mathematics and physics, and it will also suggest the appropriate example of applying vector. We will also help students to understand the tangent by connecting this method to the existing ones.

• Journal of applied mathematics & informatics
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• v.35 no.5_6
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• pp.495-504
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• 2017

In this paper we construct the Carlitz's type q-tangent numbers $T_{n,q}$ and polynomials $T_{n,q}(x)$. From these numbers and polynomials, we establish some interesting identities and relations.

• Journal of applied mathematics & informatics
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• v.32 no.3_4
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• pp.315-322
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• 2014

In this paper, we observe the behavior of complex roots of the tangent polynomials $T_n(x)$, using numerical investigation. By means of numerical experiments, we demonstrate a remarkably regular structure of the complex roots of the tangent polynomials $T_n(x)$. Finally, we give a table for the solutions of the tangent polynomials $T_n(x)$.

• Journal of Applied and Pure Mathematics
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• v.5 no.5_6
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• pp.291-301
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• 2023

In this paper, we investigate the zeros of the fully modified q-poly-tangent polynomials of the first type.

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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• 2002.08a
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• pp.109-122
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• 2002

The standard capacitor must have not only precise value of the capacitance but also the basic properties of low dielectric loss tangent. In the reforming process of capacitors, the dielectric loss tangent must be also reformed. In this paper, the development of standard capacitors of 10 and 100pF for the dielectric loss tangent standard using $Al_{2}O_{3}$ Crystal and the measurement of dielectric loss tangent are discussed. The dielectric loss tangent depends upon the surface between electrode and dielectric in capacitor. With using the Electric Field Simulator, precise design values of electrode are simulated. For the purpose of measuring capacitance effect just in the dielectric, 3-Terminal and 4-Terminal Pair configuration are applied respectively at the electrode and the connector for the measuring equipment. As stated above method, the standard capacitors of 10 and l00pF for the establishment of the dielectric loss tangent standard using the $Al_{2}O_{3}$ Crystal are made with low dielectric loss tangent less than 10-4.