• Journal of applied mathematics & informatics
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• v.27 no.3_4
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• pp.501-515
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• 2009

A second order nonlinear ordinary differential equation is obtained by solving the initial-boundary value problem of a class of elas-todynamics equations, which models the radially symmetric motion of a incompressible hyper-elastic solid sphere under a suddenly applied surface tensile load. Some new conclusions are presented. All existence conditions of nonzero solutions of the ordinary differential equation, which describes cavity formation and motion in the interior of the sphere, are presented. It is proved that the differential equation has singular periodic solutions only when the surface tensile load exceeds a critical value, in this case, a cavity would form in the interior of the sphere and the motion of the cavity with time would present a class of singular periodic oscillations, otherwise, the sphere remains a solid one. To better understand the results obtained in this paper, the modified Varga material is considered simultaneously as an example, and numerical simulations are given.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.9 no.3
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• pp.13-19
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• 1989

A system of coupled differential equations governing the lateral-torsional buckling of thin-walled arches subjected to pure bending moment is presented. The governing differential equations are derived using incremental form of principle of virtual displacement based on updated Lagrangian procedure. The differential equations are solved for the critical end moments of arches with I section, and then comparative studies are made with existing solutions.

• Magazine of the Korean Society of Agricultural Engineers
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• v.34 no.1
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• pp.57-65
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• 1992

The main purpose of this paper is to present both the natural frequencies and mode shapes of tapered beams under tensile axial force. The differential equation governing planar free vibration for tapered beams under tensile axial force is derived as nondimensional form. The three kinds of cross sectional shape are considered in differential equation. The Runge-Kutta method and Determinant Search method are used to perform the integration of the differential equation and to determine the natural frequencies, respectively. The hinged-hinged, hinged-clamped, clamped-clamped and constraints are applied in numerical examples. The lowest four nondimensional natural frequencies are reported as the function of nondimensional tensile axial force. The fundamental natural frequencies are presented when section ratios and nondimensional axial forces are varied. The effects of cross sectional shapes are reported and some typical mode shapes are also presented.

• Smart Structures and Systems
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• v.5 no.3
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• pp.279-290
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• 2009

Two degrees of freedom resonant systems are employed to improve the resonant property of resonant sensor, as compared to a single degree of freedom resonant system. This paper presents design, development and testing of two degrees of freedom resonant sensor. To measure absolute mass, cantilever shaped two different masses (smaller/absorber mass and bigger/drive mass) with identical resonant frequency are mechanically linked to form 2 - Degree-of-Freedom (DOF) resonator which exhibits higher amplitude of displacement at the smaller mass. The same concept is extended for measuring differential quantity, by having two bigger mass and one smaller mass. The main features of this work are the 3 - DOF resonator for differential detection and the microcontroller based closed loop electronics for resonant sensor with piezoelectric sensing and excitation. The advantage of using microcontroller is that the method can be easily extended for any range of measurand.

• Nuclear Engineering and Technology
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• v.49 no.8
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• pp.1645-1653
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• 2017

This investigation explores the thermally stratified stretchable flow of an Oldroyd-B material bounded by a linear stretched surface. Heat transfer characteristics are addressed through thermal stratification and heat generation/absorption. Formulation is arranged for mixed convection. Application of suitable transformations provides ordinary differential systems through partial differential systems. The homotopy concept is adopted for the solution of nonlinear differential systems. The influence of several arising variables on velocity and temperature is addressed. Besides this, the rate of heat transfer is calculated and presented in tabular form. It is noticed that velocity and Nusselt number increase when the thermal buoyancy parameter is enhanced. Moreover, temperature is found to decrease for larger values of Prandtl number and heat absorption parameter. Comparative analysis for limiting study is performed and excellent agreement is found.

• Kyungpook Mathematical Journal
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• v.56 no.1
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• pp.137-146
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• 2016

In this paper we study the oscillation criteria for the second order nonlinear differential equation with delay and advanced arguments of the form $$([x(t)+a(t)x(t-{\sigma}_1)+b(t)x(t+{\sigma}_2)]^{\alpha})^{{\prime}{\prime}}+q(t)x^{\beta}(t-{\tau}_1)+q(t)x^{\gamma}(t+{\tau}_2)=0,\;t{\geq}t_0$$ where ${\sigma}_1$, ${\sigma}_2$, ${\tau}_1$ and ${\tau}_2$ are nonnegative constants and ${\alpha}$, ${\beta}$ and ${\gamma}$ are the ratios of odd positive integers. Examples are provided to illustrate the main results.

• Bulletin of the Korean Mathematical Society
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• v.57 no.6
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• pp.1409-1426
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• 2020

Let 𝒜_n be the class of analytic functions f(z) of the form f(z) = z + ∑^∞_k=n+1 α_kz^k, n ∈ ℕ defined on the open unit disk 𝔻, and let $${\Omega}_n:=\{f{\in}{\mathcal{A}}_n:\|zf^{\prime}(z)-f(z)\|<{\frac{1}{2}},\;z{\in}{\mathbb{D}}\}$$. In this paper, we make use of differential subordination technique to obtain sufficient conditions for the class Ω_n. Writing Ω := Ω₁, we obtain inclusion properties of Ω with respect to functions which map 𝔻 onto certain parabolic regions and as a consequence, establish a relation connecting the parabolic starlike class 𝒮_P and the uniformly starlike UST. Various radius problems for the class Ω are considered and the sharpness of the radii estimates is obtained analytically besides graphical illustrations.

• Structural Engineering and Mechanics
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• v.73 no.1
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• pp.97-108
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• 2020

This study presents a 4 node, 11 DOF/node plate element based on higher order shear deformation theory for lamina composite plates. The theory accounts for parabolic distribution of the transverse shear strain through the thickness of the plate. Differential field equations of composite plates are obtained from energy methods using virtual work principle. Differential field equations of composite plates are obtained from energy methods using virtual work principle. These equations were transformed into the operator form and then transformed into functions with geometric and dynamic boundary conditions with the help of the Gâteaux differential method, after determining that they provide the potential condition. Boundary conditions were determined by performing variational operations. By using the mixed finite element method, plate element named HOPLT44 was developed. After coding in FORTRAN computer program, finite element matrices were transformed into system matrices and various analyzes were performed. The current results are verified with those results obtained in the previous work and the new results are presented in tables and graphs.

• Kyungpook Mathematical Journal
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• v.59 no.1
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• pp.73-82
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• 2019

In this work, we give necessary and sufficient conditions under which every solution of a class of first-order neutral differential equations of the form $$(x(t)+p(t)x({\tau}(t)))^{\prime}+q(t)Hx({\sigma}(t)))=0$$ either oscillates or converges to zero as $t{\rightarrow}{\infty}$ for various ranges of the neutral coefficient p. Our main tools are the Knaster-Tarski fixed point theorem and the Banach's contraction mapping principle.

• Communications of the Korean Mathematical Society
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• v.36 no.3
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• pp.515-526
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• 2021

The paper has been devoted to study the uniqueness problem of meromorphic function and its linear differential polynomial sharing two values. We have pointed out gaps in one of the theorem due to [1]. We have further extended the corrected form of Chen-Li-Li's result which in turn extend the an earlier result of [8] in a large extent. In fact, we have subtly use the notion of weighted sharing of values in this particular section of literature which was unexplored till now. A handful number of examples have been provided by us pertinent to different discussions. Specially we have given an example to show that one condition in a theorem can not be dropped.