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1

On oscillatory behaviour of third-order half-linear dynamic equations on time scales

Grace Said R., Chhatria Gokula Nanda

Opuscula Mathematica

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2022

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Vol. 42, no. 6

849--865

EN

In this work, we study the oscillation and asymptotic behaviour of third-order nonlinear dynamic equations on time scales. The findings are obtained using an integral criterion as well as a comparison theorem with the oscillatory properties of a first-order dynamic equation. As a consequence, we give conditions which guarantee that all solutions to the aforementioned problem are only oscillatory, different from any other result in the literature. We propose novel oscillation criteria that improve, extend, and simplify existing ones in the literature. The results are associated with a numerical example. We point out that the results are new even for the case T = R or T = Z.

2

A method for comparison of large deflection in beams

Taghipour Yasser, Darfarin Sara

International Journal of Applied Mechanics and Engineering

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2022

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Vol. 27, no. 4

179--193

EN

The deflection analysis of beams has been recently an active area of research. The large deflection of beams refers to deflections occurring due to large displacements and small strains. This type of deflection has been one of the areas of interest in the development of beam deformation methods. The wide diversity of beam deformation methods highlights the importance of their comparison to further elucidate the properties and features of each method and determine their benefits and limitations. In this study, a new comparison model is introduced which involves three steps, instead of only comparing final results for verification in common studies. In the first step, a complete comparison is made based on the assumptions and approximations of each method of the kinematics of deformation, displacement, and strain fields. After selecting the most accurate method in the first step, the displacement functions are determined by polynomial approximation under different loading and support conditions based on the selected method. In the third step, the displacement functions are used to calculate the strains in each method. The conclusion is based on comparing the strains. This comparative model can be used as a benchmark to compare different theories of deformation analysis.

3

Logistic Regression Realized with Artificial Neuron and Estimation Formulas

Korohoda P., Grabska-Chrząstowska J.

Image Processing & Communications

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2012

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Vol. 17, no. 4

265--274

EN

In the paper an experiment is described, that was designed and conducted to verify hypothesis that artificial neuron with sigmoidal activation function can efficiently solve the task of logistic regression in the case when the explaining variable is one-dimensional, and the explained variable is binomial. Computations were performed with 12 sets of statistical parameters, assumed for the generation of 65356 sets of data in each case. Comparative analysis of the obtained results with use of the reference values for the regression coefficients indicated that the investigated neuron can satisfactory perform the task, with efficiency similar to that obtained with classical logistic regression algorithm, when the teaching sets of input data, corresponding with output values 0 and 1, do not allow for simple separation. Moreover, it has been discovered that the simple formulas estimating the statistical distributions parameters from the samples, offer statistically superior assessment of the regression coefficient parameters.

4

On the oscillation of certain advanced functional differential equations using comparison methods

Agarwal R. P., Grace S. R., O'Regan D.

Fasciculi Mathematici

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2005

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Nr 35

5-22

EN

Some new criteria for the oscillation of advanced functional differential equations of the form are presented in this paper. A discussion of neutral equations will also be included.