• Nonlinear Functional Analysis and Applications
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• 제28권2호
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• pp.449-471
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• 2023

In this paper, we study a linear system of homogeneous commensurate /incommensurate fractional-order differential equations by developing a new semi-analytical scheme. In particular, by decoupling the system into two fractional-order differential equations, so that the first equation of order (δ + γ), while the second equation depends on the solution for the first equation, we have solved the under consideration system, where 0 < δ, γ ≤ 1. With the help of using the Adomian decomposition method (ADM), we obtain the general solution. The efficiency of this method is verified by solving several numerical examples.

• 대한수학회논문집
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• 제19권3호
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• pp.557-567
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• 2004

We prove the sufficient conditions for optimality in differential inclusion problem by using the value function. For this purpose, we assume at first that the value function is locally Lipschitz. Secondly, without this assumption, we use the viability theory.

• Kyungpook Mathematical Journal
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• 제51권2호
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• pp.145-164
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• 2011

In the paper, we study with weighted sharing method the uniqueness of entire functions concerning nonlinear differential polynomials sharing one value and prove two uniqueness theorems, first one of which generalizes some recent results in [10] and [16]. Our second theorem will supplement a result in [17].

• Asian Pacific Journal of Cancer Prevention
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• 제14권11호
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• pp.6331-6335
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• 2013

Objective:To evaluate the performance of combined quantitative analysis of thyroid blood flow and static imaging data in the differential diagnosis of thyroid nodules. Method: Thyroid blood flow and static imaging were performed in 165 patients with thyroid nodules. Patients were divided into a benign thyroid nodule group (BTN, n=135) and a malignant thyroid nodule group (MTN, n=30) based on the results of post-surgical pathologic examination. Carotid artery thyroid transit times (CTTT), perfusion ratio of thyroid nodule blood/thyroid blood (TNB/TB), and perfusion ratio of thyroid nodule blood/carotid artery blood (TNB/CAB) were measured using thyroid blood flow imaging. The ratios between thyroid nodule and ipsilateral submandibular gland (TN/SG) and thyroid nodule and normal thyroid tissue (TN/T) were measured from thyroid static imaging. The differences between the BTN and MTN groups were compared. Results: 1) CTTT was markedly lower in the MTN group than the BTN group, the difference being statistically significant. 2) TNB/TB and TNB/CAB were both significantly higher in MTN than BTN groups. 3) TN/T was significantly lower in MTN group than BTN group. 4) TN/SG was lower in MTN group than BTN group, but the difference was not statistically significant. 5) Using the combination of CTTT and TN/T, the sensitivity, specificity and accuracy were 93.1%, 95.3% and 94.9% respectively for the diagnosis of MTN. Using the combination of CTTT, TNB/TB and TN/T, the sensitivity, specificity and accuracy changed to 89.7%, 100%, and 98.1% respectively. 6) Correlation analysis demonstrated a significant correlation between TN/T and TNB/TB (r=-0.384, P=0.036) and TNB/CAB (r=-0.466, P=0.009) in the MTN group. Conclusion: The combination of quantitative markers from thyroid blood flow and thyroid static imaging had high specificity and accuracy in differential diagnosis of benign and malignant thyroid nodules, thus providing an important imaging diagnostic approach.

• Journal of applied mathematics & informatics
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• 제32권1_2호
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• pp.39-53
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• 2014

In this paper, a non-asymptotic method is presented for solving singularly perturbed delay differential equations whose solution exhibits a boundary layer behavior. The second order singularly perturbed delay differential equation is replaced by an asymptotically equivalent first order neutral type delay differential equation. Then, Simpson's integration formula and linear interpolation are employed to get three term recurrence relation which is solved easily by Discrete Invariant Imbedding Algorithm. Some numerical examples are given to validate the computational efficiency of the proposed numerical scheme for various values of the delay and perturbation parameters.

• Journal of applied mathematics & informatics
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• 제19권1_2호
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• pp.281-295
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• 2005

The purpose of this paper is to study a class of delay differential equations with two delays. First, we consider the existence of periodic solutions for some delay differential equations. Second, we investigate the local stability of the zero solution of the equation by analyzing the corresponding characteristic equation of the linearized equation. The exponential stability of a perturbed delay differential system with a bounded lag is studied. Finally, by choosing one of the delays as a bifurcation parameter, we show that the equation exhibits Hopf and saddle-node bifurcations.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제24권2호
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• pp.229-242
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• 2020

Functional fractional differential inclusions with impulse effects in general Banach spaces are studied. We discuss the situation when the semigroup generated by the linear part is equicontinuous and the multifunction is Caratheodory. First, we define the PC-mild solutions for functional fractional semilinear impulsive differential inclusions. We then prove the existence of PC-mild solutions for such inclusions by using the fixed point theorem, multivalued properties and applications of NCHM (noncompactness Hausdorff measure). Eventually, we enhance the acquired results by giving an example.

• Structural Engineering and Mechanics
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• 제24권2호
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• pp.247-268
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• 2006

The parts of pile, above the soil and embedded in the soil are called the first region and second region, respectively. The forth order differential equations of both region for critical buckling load of partially embedded pile with shear deformation are obtained using the small-displacement theory and Winkler hypothesis. It is assumed that the behavior of material of the pile is linear-elastic and that axial force along the pile length and modulus of subgrade reaction for the second region to be constant. Shear effect is included in the differential equations by considering shear deformation in the second derivative of the elastic curve function. Critical buckling loads of the pile are calculated for by differential transform method (DTM) and analytical method, results are given in tables and variation of critical buckling loads corresponding to relative stiffness of the pile are presented in graphs.

• Journal of information and communication convergence engineering
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• 제19권3호
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• pp.155-160
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• 2021

Differential evolution is an efficient algorithm for solving continuous optimization problems. However, its performance deteriorates rapidly, and the runtime increases exponentially when differential evolution is applied for solving large-scale optimization problems. Hence, a novel cooperative coevolution differential evolution based on Spark (known as SparkDECC) is proposed. The divide-and-conquer strategy is used in SparkDECC. First, the large-scale problem is decomposed into several low-dimensional subproblems using the random grouping strategy. Subsequently, each subproblem can be addressed in a parallel manner by exploiting the parallel computation capability of the resilient distributed datasets model in Spark. Finally, the optimal solution of the entire problem is obtained using the cooperation mechanism. The experimental results on 13 high-benchmark functions show that the new algorithm performs well in terms of speedup and scalability. The effectiveness and applicability of the proposed algorithm are verified.

• 소음진동
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• 제2권3호
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• pp.203-211
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• 1992

The main purpose of this paper is to present both the natural frequencies and the first critical loads of tapered columns. The ordinary differential equation governing the free vibration for tapered columns under compressive axial force is derived. Three kinds of cross sectional shape are considered in the governing 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. Additionally, the bisection method is used to determine the critical loads. In numerical examples, the effects of compressive axial force on the natural frequencies of tapered columns are investigated varying the end conditions. The first critical loads of tapered columns are determined on the basis of dynamic concepts. The first critical loads of tapered columns are determined on the basis of dynamic concept. The effects of cross sectional shapes are shown and some typical mode shapes are also presented.