Flexural-Torsional Vibration of Thin-Walled Beams Subjected to Combined Initial Axial Load and End Bending Moment: Application to the Design of Saw Tooth Blades by Van Binh Phung, Anh Tuan Nguyen, Hoang Minh Dang, Thanh-Phong Dao, V. N. Duc

“…The analytical expressions for the first natural frequencies of thin-walled beams were derived by two methods that are a method based on the existence of the roots theorem of differential equation systems and the Rayleigh method. In particular, the stability boundary of a beam can be determined directly from its first natural frequency expression. …”
Get full text

The discontinuous solutions of Lame�s equations for a conical defect by O. Reut, N. Vaysfeld

“…A discontinuous solution of a certain differential equation in the partial derivatives is a solution that satisfies this equation throughout the region of determining an unknown function, with the exception of the defect points. …”
Get full text

Quantum Tunnelling for Hawking Radiation from Both Static and Dynamic Black Holes by Subenoy Chakraborty, Subhajit Saha

“…It is found that different order correction terms satisfy identical differential equation and are solved by a typical technique. …”
Get full text

A mathematical model of weight change with adaptation by Diana M. Thomas, Ashley Ciesla, James A. Levine, John G. Stevens, Corby K. Martin

“…Key factors are an adaptation of resting metabolic rate, non-exercise activity thermogenesis and dietary induced thermogenesis. We develop a differential equation model based on the first law of thermodynamics that incorporates all three adjustments along with natural age related reduction of the resting metabolic rate. …”
Get full text

NONLINEAR PRIMARY RESONANCE OF A CIRCULAR SANDWICH PLATE UNDER STATIC LOAD by GUO Wei, DU GuoJun, HU YuDa

“…The axisymmetric nonlinear vibration differential equation of the plate under static load is obtained by Galerkin method. …”
Get full text

Shaping Single Offset Reflector Antennas Using Local Axis-Displaced Confocal Quadrics by Rafael A. Penchel, José R. Bergmann, Fernando J. S. Moreira

“…This work investigates a novel numerical procedure for the solution of an exact formulation for the Geometrical Optics synthesis of a single reflector antenna by simultaneously imposing Snell’s Law and Conservation of Energy in a tube of rays, yielding a second-order nonlinear partial differential equation of Monge-Ampère type, which can be solved as a boundary value problem. …”
Get full text

Dynamics of a Single Species in a Fluctuating Environment under Periodic Yield Harvesting by Mustafa Hasanbulli, Svitlana P. Rogovchenko, Yuriy V. Rogovchenko

“…We discuss the effect of a periodic yield harvesting on a single species population whose dynamics in a fluctuating environment is described by the logistic differential equation with periodic coefficients. This problem was studied by Brauer and Sánchez (2003) who attempted the proof of the existence of two positive periodic solutions; the flaw in their argument is corrected. …”
Get full text

Achieving Synchronization in Arrays of Coupled Differential Systems with Time-Varying Couplings by Xinlei Yi, Wenlian Lu, Tianping Chen

“…We study complete synchronization of the complex dynamical networks described by linearly coupled ordinary differential equation systems (LCODEs). Here, the coupling is timevarying in both network structure and reaction dynamics. …”
Get full text

The discontinuous solutions of Lame’s equations for a conical defect by Natalya D. Vaysfel'd, O. Reut

“…A discontinuous solution of a certain differential equation in the partial derivatives is a solution that satisfies this equation throughout the region of determining an unknown function, with the exception of the defect points. …”
Get full text

Creeping Ray Tracing Algorithm for Arbitrary NURBS Surfaces Based on Adaptive Variable Step Euler Method by Song Fu, Yun-Hua Zhang, Si-Yuan He, Xi Chen, Guo-Qiang Zhu

“…In differential geometry, geodesic paths satisfy geodesic differential equation (GDE). Hence, in this paper, a general and efficient adaptive variable step Euler method is introduced for solving the GDE on arbitrarilyshaped NURBS surfaces. …”
Get full text

A Study of the Impact of Underground Economy on Integral Tax Burden in the Proportional Growth Model under Uncertainty by Akif Musayev, Aygun Musayeva

“…It is also assumed that dynamics of gross domestic product are modeled by fuzzy linear differential equation. An optimal value of tax burden is determined as a solution to the considered fuzzy integral equation. …”
Get full text

Effect of time delay on a detritus-based ecosystem by Nurul Huda Gazi, Malay Bandyopadhyay

“…Next, we have introduced discrete time delay due to recycling of dead organic matters and gestation of nutrients to the growth equations of various trophic levels. With delay differential equation model system we have studied the effect of time delay on the stability behaviour. …”
Get full text

Modified Homotopy Perturbation Method and Approximate Solutions to a Class of Local Fractional Integrodifferential Equations by Bo Xu, Sheng Zhang

“…In this paper, the local fractional version of homotopy perturbation method (HPM) is established for a new class of local fractional integral-differential equation (IDE). With the embedded homotopy parameter monotonously changing from 0 to 1, the special easy-to-solve fractional problem continuously deforms to the class of local fractional IDE. …”
Get full text

VIBRATION MODAL ANALYSIS AND RESEARCH OF CANTILEVER BEAM BASED ON POLY IIR METHOD by ZHANG Min, ZHANG Yi, HOU YaoHua, MA GuangXuan

“…Following to use Bernoulli Euler beam theory to calculate the beam vibration differential equation,in addition to the beam set specific boundary constraint conditions to calculate each order modal parameters,using the Workbench beam finite element simulation analysis for the first five order natural frequency and vibration mode. …”
Get full text

Asymptotic Behavior of an Optimal Investment-Reinsurance Problem with General Utility Functions by Yan Zhang, Peibiao Zhao

“…Moreover, applying the dual method along with the partial differential equation method, we verify the asymptotic behavior of the optimal control strategy, which means that the optimal investment-reinsurance strategy with the general utility functions converges to that with the power utility function at any level of the initial wealth.…”
Get full text

Global attractivity of positive periodic solutions for an impulsive delay periodic food limited population model by Jian Song

“…We will consider the following nonlinear impulsive delay differential equation N′(t)=r(t)N(t)((K(t)−N(t−mw))/(K(t)+λ(t)N(t−mw))), a.e. t>0, t≠tk, N(tk+)=(1+bk)N(tk), K=1,2,…, where m is a positive integer, r(t), K(t), λ(t) are positive periodic functions of periodic ω. …”
Get full text

Numerical Solutions to Optimal Portfolio Selection and Consumption Strategies under Stochastic Volatility by Lei Ge, Qiang Zhang

“…Based on the method of dynamic programming, this paper uses analysis methods governed by the nonlinear and inhomogeneous partial differential equation to study modern portfolio management problems with stochastic volatility, incomplete markets, limited investment scope, and constant relative risk aversion (CRRA). …”
Get full text

Coefficients of prolongations for symmetries of ODEs by Ricardo Alfaro, Jim Schaeferle

“…He found that transformations which form a continuous group and leave a differential equation invariant can be used to simplify the equation. …”
Get full text

Traverse Vibration of Axially Moving Laminated SMA Beam considering Random Perturbation by Hao Ying, Gao Minglei

“…The transverse vibration differential equation of axially moving SMA laminated beam with two simply-supported edges is obtained through the Galerkin method. …”
Get full text

Mechanism Kinematics Analysis of Two-leg Shield Hydraulic Support by Wang Hongwei, Dong Zhifeng

“…As a multi-linkage mechanism with multi-degree of freedom,the two-leg shield hydraulic support is comprised of beams,fore and rear links and hydraulic cylinders.It can realize supporting roof,protecting coal wall and moving forward under the function of hydraulic power,and plays an important role in coal mining.According to structure and operating characteristics of the two-leg shield hydraulic support,the geometrical relationship and calculations about rear link angle and shield beam angle for the supporting height,head distance,leg length and balance cylinder length are deduced.The differential equation of motion for the hydraulic support is established by the Lagrangian theory,and the support type of ZY17300/32/70 is calculated and analyzed.The relationship between angle displacement and velocity for the rear link angle and shield beam angle along with the motion characteristic of supporting height is obtained.The response characteristics of motion velocity and acceleration for top beam are discussed during the working process of lifting up and down.…”
Get full text