Reliability modeling of three-state systems with multiple types of components

In this paper, a system consisting of three states: perfect functioning, partial functioning, and down is considered. The system is assumed to be composed of several non-identical groups of binary components. The reliability of the system states under various assumptions on the component lifetimes is investigated. For this purpose, first, a new concept of bivariate survival signature (BSS) is introduced. Then, under the assumption that the component lifetimes of each type are exchangeable dependent, representations for the joint reliability function of the state lifetimes are obtained based on the notion of BSS. In the particular case, three-state systems composed of two types of different modules such as general-series (parallel) systems and systems with component-wise redundancy are investigated. Several examples are presented to illustrate the theoretical results.

Analysis of nonlinear time-fractional Klein-Gordon equation with power law kernel

<abstract><p>We investigate the nonlinear Klein-Gordon equation with Caputo fractional derivative. The general series solution of the system is derived by using the composition of the double Laplace transform with the decomposition method. It is noted that the obtained solution converges to the exact solution of the model. The existence of the model in the presence of Caputo fractional derivative is performed. The validity and precision of the presented method are exhibited with particular examples with suitable subsidiary conditions, where good agreements are obtained. The error analysis and its corresponding surface plots are presented for each example. From the numerical solutions, we observe that the proposed system admits soliton solutions. It is noticed that the amplitude of the wave solution increases with deviations in time, that concludes the factor $ \omega $ considerably increases the amplitude and disrupts the dispersion/nonlinearity properties, as a result, may admit the excitation in the dynamical system. We have also depicted the physical behavior that states the advancement of localized mode excitations in the system.</p></abstract>

Solutions of Bernoulli Equations in the Fractional Setting

We present a general series representation formula for the local solution of the Bernoulli equation with Caputo fractional derivatives. We then focus on a generalization of the fractional logistic equation and present some related numerical simulations.

Tricomi’s Method for the Laplace Transform and Orthogonal Polynomials

Tricomi’s method for computing a set of inverse Laplace transforms in terms of Laguerre polynomials is revisited. By using the more recent results about the inversion and the connection coefficients for the series of orthogonal polynomials, we find the possibility to extend the Tricomi method to more general series expansions. Some examples showing the effectiveness of the considered procedure are shown.

The Behavior of Non-Destructive Test for Different Grade of Concrete

Rebound hammer tests are generally preferred as a non-destructive testing method as compared to destructive testing methods such as compression tests. In this study, a general series of rebound hammer tests and destructive tests were carried on in a heavy concrete laboratory. A set of concrete cubes measuring 100 x 100 x 100 mm were cast and subjected to water curing for 7, 14 and 28 days to obtain the cube strength and rebound number. Three grades of concrete, namely M20, M25 and M30 were used in this experiment. At 28 days, the minimum target strength should be 30 MPa. The rebound hammer tests were conducted before the compression tests. The data obtained for each test was evaluated and tabulated in the findings of this study. It was found that the variation between predicted strength and experimental strength for the rebound hammer test was 0.18%. This indicates that the rebound hammer test is able to predict strength with acceptable accuracy.

Benzoylthioureas: Design, Synthesis and Antimycobacterial Evaluation

Background: New drugs and strategies to treat tuberculosis (TB) are urgently needed. In this context, thiourea derivatives have a wide range of biological activities, including anti-TB. This fact can be illustrated with the structure of isoxyl, an old anti-TB drug, which has a thiourea as a pharmacophore group. Objective: The aim of this study is to describe the synthesis and the antimycobacterial activity of fifty-nine benzoylthioureas derivatives. Methods: Benzoylthiourea derivatives have been synthesized and evaluated for their activity against Mycobacterium tuberculosis using the MABA assay. After that, a structure-activity relationship study of this series of compounds has been performed. Results and Discussion: Nineteen compounds exhibited antimycobacterial activity between 423.1 and 9.6 μM. In general, we observed that the presence of bromine, chlorine and t-Bu group at the para-position in benzene ring plays an important role in the antitubercular activity of Series A. These substituents were fixed at this position in benzene ring and other groups such as Cl, Br, NO2 and OMe were introduced in the benzoyl ring, leading to the derivatives of Series B. In general, Series B was less cytotoxic than Series A, which indicates that the presence of a substituent at benzoyl ring contributes to an improvement in both antimycobacterial activity and toxicity profiles. Conclusion: Compound 4c could be considered a good prototype to be submitted to further structural modifications in the search for new anti-TB drugs, since it is 1.8 times more active than the first line anti-TB drug ethambutol and 0.65 times less active than isoxyl.

Analytical Solutions for Stress and Displacement Fields in Disks under Arbitrarily Distributed Loads

The general series solution (GSS) approach is presented, in order to determine the stress and displacement fields in disks under arbitrarily distributed normal and tangential loads. An Airy stress function in series form is selected. Stresses are expressed by infinite coefficients. Thus displacements are expressed by the infinite stress coefficients. And self-equilibrated loads acting on the side edge are extended to Fourier series. Stress coefficients are related to loading coefficients by stress boundary conditions. Then five examples show the validity of this approach. The GSS approach might lead to industrial applications in rock mechanics, petroleum and mining engineering, etc.