• Advances in Energy Research
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• v.8 no.2
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• pp.111-123
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• 2022

Solar Energy is the energy of solar radiation carried by them in the form of heat and light. It can be converted into electricity. Solar potential depends on the site's atmosphere; the solar energy distribution depends on many factors, e.g., turbidity, cloud types, pollution levels, solar altitude, etc. We estimated solar radiation with the help of the Ashrae clear-sky model for three locations in Pakistan, namely Pasni, Gwadar, and Jiwani. As these locations are close to each other as compared to the distance between the sun and earth, therefore a slight change of latitude and longitude does not make any difference in the calculation of direct beam solar radiation (BSR), diffuse solar radiation (DSR), and global solar radiation (GSR). A modified formula for declination angle is also developed and presented. We also created two different models for Ashrae constants. The values of these constants are compared with the standard Ashrae Model. A good agreement is observed when we used these constants to calculate BSR, DSR, GSR, the Root mean square error (RMSE), Mean Absolute error (MABE), Mean Absolute percent error (MAPE), and chisquare (χ²) values are in acceptance range, indicating the validity of the models.

• Kyungpook Mathematical Journal
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• v.62 no.2
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• pp.271-287
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• 2022

In this paper, starting with the geometric constants that can characterize Hilbert spaces, combined with the isosceles orthogonality of Banach spaces, the orthogonal geometric constant Ω_X(α) is defined, and some theorems on the geometric properties of Banach spaces are derived. Firstly, this paper reviews the research progress of orthogonal geometric constants in recent years. Then, this paper explores the basic properties of the new geometric constants and their relationship with conventional geometric constants, and deduces the identity of Ω_X(α) and γ_X(α). Finally, according to the identities, the relationship between these the new orthogonal geometric constant and the geometric properties of Banach Spaces (such as uniformly non-squareness, smoothness, convexity, normal structure, etc.) is studied, and some necessary and sufficient conditions are obtained.

• Kyungpook Mathematical Journal
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• v.63 no.1
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• pp.61-78
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• 2023

In this paper, we introduce two new geometric constants related to the heights of triangles: ∆_H(X) and ∆_h(X, I). We also propose two new geometric constants, ∆_m(X) and ∆_M(X), related to the midlines of equilateral triangles, and discuss the relation between the heights and midlines in equilateral triangles. We give estimates for these geometric constants in terms of other geometric parameters, and the geometric constants are used to discuss geometric properties such as uniform non-squareness, uniform normal structure, and the fixed point property.

• Journal of the Korean Mathematical Society
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• v.41 no.1
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• pp.157-174
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• 2004

In this work we discuss "plank problems" for complex Banach spaces and in particular for the classical $L^{p}(\mu)$ spaces. In the case $1\;{\leq}\;p\;{\leq}\;2$ we obtain optimal results and for finite dimensional complex Banach spaces, in a special case, we have improved an early result by K. Ball [3]. By using these results, in some cases we are able to find best possible lower bounds for the norms of homogeneous polynomials which are products of linear forms. In particular, we give an estimate in the case of a real Hilbert space which seems to be a difficult problem. We have also obtained some results on the so-called n-th (linear) polarization constant of a Banach space which is an isometric property of the space. Finally, known polynomial inequalities have been derived as simple consequences of various results related to plank problems.

• Bulletin of the Korean Mathematical Society
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• v.30 no.2
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• pp.167-170
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• 1993

In this paper, X, X$_{1}$, X$_{2}$, .. will denote any sequence of pairwise independent random variables with common distribution, and b$_{1}$, b$_{2}$.. will denote any sequence of constants. Using Chung [2, Theorem 4.2.5] and the same idea as in Chow and Robbins [1, Lemma 1 and 2] we have the following lemma.

• Journal of the Chungcheong Mathematical Society
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• v.25 no.3
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• pp.579-587
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• 2012

A fourth-order family of triparametric extensions of Jarratt's method are proposed in this paper to find a simple root of nonlinear algebraic equations. Convergence analysis including numerical experiments for various test functions apparently verifies the fourth-order convergence and asymptotic error constants.

• Journal of the Chungcheong Mathematical Society
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• v.27 no.1
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• pp.133-143
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• 2014

A new three-step quadraparametric family of eighth-order iterative methods free from second derivatives are proposed in this paper to find a simple root of a nonlinear equation. Convergence analysis as well as numerical experiments confirms the eighth-order convergence and asymptotic error constants.

• Journal of the Korean Mathematical Society
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• v.33 no.2
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• pp.455-468
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• 1996

Certain analytic behavior of geometric objects defined on a Riemannian manifold depends on some very crude properties of the manifold. Some of those crude invariants are the volume growth rate, isoperimetric constants, and the likes. However, these crude invariants sometimes exercise surprising control over the analytic behavior.

• Journal of the Chungcheong Mathematical Society
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• v.5 no.1
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• pp.65-74
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• 1992

In this note, we show that the ${\omega}$-limit mapping is continuous and the Lipschitz constants vary continuously if the flow (x, ${\pi}$) is Lipschitz stable. Moreover we analyse the ${\omega}$-limit sets under the generalized locally Lipschitz stable flows.

• Proceedings of the KIEE Conference
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• 2001.07b
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• pp.825-827
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• 2001

In this paper, we made mathematical modeling of BLDC motor system and design of PI controller. Using Apache web-server and PHP web-programming, we embodied virtual laboratory for PI controller design of BLDC Motor system by using proportional constants$(K_P)$ and constants of integration$(K_I)$.