• Journal of applied mathematics & informatics
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• v.36 no.5_6
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• pp.447-458
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• 2018

In this paper, we investigate the uniqueness problems of certain types of difference polynomials sharing a small function. The results of the paper improve and generalize the recent results due to H.P. Waghamore [Tbilisi Math. J. 11(2018), 1-13], P. Sahoo and B. Saha [App. Math. E-Notes. 16(2016), 33-44].

• The Pure and Applied Mathematics
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• v.29 no.1
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• pp.37-50
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• 2022

The purpose of the paper is to study the uniqueness problems of certain type of difference polynomials sharing a small function. With the concept of weakly weighted sharing and relaxed weighted sharing we obtain some results which extend and generalize some results due to P. Sahoo and G. Biswas [Tamkang Journal of Mathematics, 49(2)(2018), 85-97].

• Korean Journal of Mathematics
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• v.28 no.3
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• pp.489-507
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• 2020

In this paper we discussed some growth properties of entire functions of several complex variables on the basis of (p, q)-𝜑 relative Gol'dberg type and (p, q)-𝜑 relative Gol'dberg weal type where p, q are positive integers and 𝜑(R) : [0, +∞) → (0, +∞) is a non-decreasing unbounded function.

• Korean Journal of Mathematics
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• v.6 no.1
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• pp.127-135
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• 1998

Let ${\rho}(A)$ and ${\rho}(B)$ denote the orders of entire functions $A(z)$ and $B(z)$ respectively. Suppose that ${\rho}(A)$ > 1 and 0 < ${\rho}(B){\leq}\frac{1}{2}$, and that ${\rho}$(A) is not an integer. Then it is shown that every nonconstant solution $f$ of $f^{{\prime}{\prime}}+A(z)f^{\prime}+B(z)f=0$ is of infinite order if all the zeros of $A(z)$ lie in a certain angular sector depending on its genus. In addition, we investigate some growth properties of $A(z)$.

• Journal of the Korean Mathematical Society
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• v.48 no.3
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• pp.499-512
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• 2011

The purpose of this paper is twofold. The first is to establish a uniqueness theorem for entire function sharing two polynomials with its ${\kappa}$-th derivative, by using the theory of normal families. Meanwhile, the theorem generalizes some related results of Rubel and Yang and of Li and Yi. Several examples are provided to show the conditions are necessary. The second is to generalize the Br$\"{u}$-ck conjecture with the idea of sharing polynomial.

• Nuclear Engineering and Technology
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• v.30 no.3
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• pp.202-211
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• 1998

Interfacial stresses at two-material interfaces and initial displacement field over the entire domain are obtained by modifying the potential energy functional with a penalty function, which enforces continuity of the stresses at the interface of two materials. Based on the initial displacement field and interfacial stresses, a new methodology to generate a continuous stress field over the entire domain has been proposed by combining the modified projection method of stress-smoothing and Loubignac's iterative method of improving the displacement field. Stress analysis is carried out on two examples made of dissimilar materials : one is a two-material cantilever composed of highly dissimilar materials and the other is a zirconium-lined cladding tube made of slightly dissimilar materials. Results of the analysis show that the proposed method provides an improved continuous stress field over the entire domain, and accurately predicts the nodal stresses at the interface, while the conventional displacement-based finite element method produces significant stress discontinuities at the interface. In addition, the total strain energy evaluated from the improved continuous stress field converges to the exact value in a few iterations.

• Bulletin of the Korean Mathematical Society
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• v.58 no.4
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• pp.983-1002
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• 2021

We investigate the non-existence of finite order transcendental entire solutions of Fermat-type differential-difference equations [f(z)f'(z)]ⁿ + P²(z)f^m(z + 𝜂) = Q(z) and [f(z)f'(z)]ⁿ + P(z)[∆_𝜂f(z)]^m = Q(z), where P(z) and Q(z) are non-zero polynomials, m and n are positive integers, and 𝜂 ∈ ℂ \ {0}. In addition, we discuss transcendental entire solutions of finite order of the following Fermat-type differential-difference equation P²(z) [f^(k)(z)]² + [αf(z + 𝜂) - 𝛽f(z)]² = e^r(z), where $P(z){\not\equiv}0$ is a polynomial, r(z) is a non-constant polynomial, α ≠ 0 and 𝛽 are constants, k is a positive integer, and 𝜂 ∈ ℂ \ {0}. Our results generalize some previous results.

• Structural Engineering and Mechanics
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• v.39 no.1
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• pp.47-75
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• 2011

An accurate substructural synthesis method including random responses synthesis, frequency-response functions synthesis and mid-order modes synthesis is developed based on rigorous substructure description, dynamic condensation and coupling. An entire structure can firstly be divided into several substructures according to different functions, geometric and dynamic characteristics. Substructural displacements are expressed exactly by retained mid-order fixed-interfacial normal modes and residual constraint modes. Substructural interfacial degree-of-freedoms are eliminated by interfacial displacements compatibility and forces equilibrium between adjacent substructures. Then substructural mode vibration equations are coupled to form an exact-condensed synthesized structure equation, from which structural mid-order modes are calculated accurately. Furthermore, substructural frequency-response function equations are coupled to yield an exact-condensed synthesized structure vibration equation in frequency domain, from which the generalized structural frequency-response functions are obtained. Substructural frequency-response functions are calculated separately by using the generalized frequency-response functions, which can be assembled into an entire-structural frequency-response function matrix. Substructural power spectral density functions are expressed by the exact-synthesized substructural frequency-response functions, and substructural random responses such as correlation functions and mean-square responses can be calculated separately. The accuracy and capacity of the proposed substructure synthesis method is verified by numerical examples.

• Structural Engineering and Mechanics
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• v.49 no.1
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• pp.111-128
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• 2014

The stochastic response surface method (SRSM) and the response surface method (RSM) are often used for structural reliability analysis, especially for reliability problems with implicit performance functions. This paper aims to compare these two methods in terms of fitting the performance function, accuracy and efficiency in estimating probability of failure as well as statistical moments of system output response. The computational procedures of two response surface methods are briefly introduced first. Then their capabilities are demonstrated and compared in detail through two examples. The results indicate that the probability of failure mainly reflects the accuracy of the response surface function (RSF) fitting the performance function in the vicinity of the design point, while the statistical moments of system output response reflect the accuracy of the RSF fitting the performance function in the entire space. In addition, the performance function can be well fitted by the SRSM with an optimal order polynomial chaos expansion both in the entire physical and in the independent standard normal spaces. However, it can be only well fitted by the RSM in the vicinity of the design point. For reliability problems involving random variables with approximate normal distributions, such as normal, lognormal, and Gumbel Max distributions, both the probability of failure and statistical moments of system output response can be accurately estimated by the SRSM, whereas the RSM can only produce the probability of failure with a reasonable accuracy.

• Proceedings of the KSME Conference
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• 2008.11a
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• pp.1057-1062
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• 2008

Representing a complex, three-dimensional shape, such as an automobile, requires a large amount of CAD data consisting of millions of approximated discontinuous points, which makes it difficult or even impossible to efficiently optimize the entire shape. For this reason, in this paper, function based design method is proposed to optimize the external shape of an automobile. A vehicle modeling function was defined in the form of a Bernstein polynomial to smoothly express the complex 2D and 3D automobile configurations. The sub-sectional parts of the vehicle modeling function are defined as section functions through classifying each subsection of a box model. It is shown that the use of the vehicle modeling functions has the useful advantages in an aerodynamic shape optimization.