Cooling Curve Analysis of A356 Alloy by Conventional Casting and the Effect of Stirring

The present investigation attempted to explore the effect of stirring during solidification of Aluminum A356 alloy, mainly focusing on the change from dendrite to globular structure. For this purpose samples of A356 alloy were melted in the electrical resistance furnace and cooling curves were recorded for each level agitation. The experimental curves were numerically processed by calculating first and second derivatives. From these were determined temperatures and times of start nucleation of alpha solid and eutectic reaction.

Higgs inflation and its extensions and the further refining dS swampland conjecture

On the one hand, Andriot and Roupec (Fortsch Phys, 1800105, 2019) proposed an alternative refined de Sitter conjecture, which gives a natural condition on a combination of the first and second derivatives of the scalar potential (Andriot and Roupec 2019). On the other hand, in our previous article (Liu in Eur Phys J Plus 136:901, 2021) , we have found that Palatini Higgs inflation model is in strong tension with the refined de Sitter swampland conjecture (Liu 2021). Therefore, following our previous research, in this article we examine if Higgs inflation model and its two variations: Palatini Higgs inflation and Higgs-Dilaton model (Rubio in Front Astron Space Sci, 10.3389/fspas.2018.00050, 2019) can satisfy the “further refining de Sitter swampland conjecture” or not. Based on observational data (Ade et al., Phys Rev Lett 121:221301, 2018; Akrami et al., Planck 2018 results. X. Constraints on inflation, arXiv:1807.06211 [astro-ph.CO], 2018; Aghanim et al., Planck 2018 results: VI. Cosmological parameters, arXiv:1807.06209 [astro-ph.CO], 2018), we find that these three inflationary models can always satisfy this new swampland conjecture if only we adjust the relevant parameters a, $$b = 1-a$$ b = 1 - a and q. Therefore, if the “further refining de Sitter swampland conjecture” does indeed hold, then the three inflationary models might all be in “landscape”.

CONDITIONS OF MONOTONE APPROXIMATION OF RAMSEY CURVES AND THEIR MODIFICATIONS

The algorithm for approximating the experimental data of the Ramsey curve and its modifications has been developed, which provides a monotonic increase of the approximating function in the interval [0;\infty) and an existence of a given number of inflection points. The Ramsey curve belongs to the family of logistic curves that are widely used in modeling of limited increasing processes in various subject fields. The classical Ramsey curve has two parameters and has a left constant asymmetry. It is also known that its three-parameter modification provides the possibility of displacement along the axes of ordinate. The extensive practical use of the Ramsey curve with both two and more parameters for approximating experimental dependences is restrained by the frequent loss by this curve of the logistic shape when approximating without additional restrictions on the relationships between its parameters. The article discusses modifications of the Ramsey curve with three and five parameters. The first and second derivatives of the studied modifications of the Ramsey function have a special structure. They are products of polynomial and exponential functions. This allows using Sturm's theorem on the number of polynomial roots in a given interval to control the shape of the approximating curve. It has been shown that with an increase in the number of parameters for the modified curve, the number of possible combinations of restrictions on the values of the parameters ensuring the preservation of its like shape increases significantly. The solution to the approximation problem in this case consists of solving a sequence of conditional global optimization problems with different constraints and choosing a solution that provides the smallest approximation error. Also, the studies of the accuracy of estimating the parameters of the Ramsey curve in accordance with the accuracy of the experimental data have been carried out. In order to simulate the presence of measurement errors, the values of a normally distributed random variable with a mathematical expectation equal to zero and different values of the standard deviation for different series of computational experiments were added to the values of the deterministic sequence. Computational experiments have shown a significant sensitivity of the values of the Ramsey function parameters to the measurement accuracy of experimental data.

Some perturbed inequalities of Ostrowski type for twice differentiable functions

We establish new perturbed Ostrowski type inequalities for functions whose second derivatives are of bounded variation. In addition, we obtain some integral inequalities for absolutely continuous mappings. Finally, some inequalities related to Lipschitzian derivatives are given.

On new general versions of Hermite–Hadamard type integral inequalities via fractional integral operators with Mittag-Leffler kernel

The main motivation of this study is to bring together the field of inequalities with fractional integral operators, which are the focus of attention among fractional integral operators with their features and frequency of use. For this purpose, after introducing some basic concepts, a new variant of Hermite–Hadamard (HH-) inequality is obtained for s-convex functions in the second sense. Then, an integral equation, which is important for the main findings, is proved. With the help of this integral equation that includes fractional integral operators with Mittag-Leffler kernel, many HH-type integral inequalities are derived for the functions whose absolute values of the second derivatives are s-convex and s-concave. Some classical inequalities and hypothesis conditions, such as Hölder’s inequality and Young’s inequality, are taken into account in the proof of the findings.

Inequalities for the First and Second Derivatives of Algebraic Polynomials on an Ellipse

We prove a theorem on the preservation of inequalities between functions of a special form after differentiation on an ellipse. In particular, we obtain generalizations of the Duffin–Schaeffer inequality and the Vidensky inequality for the first and second derivatives of algebraic polynomials to an ellipse.

Application of generalized equations of finite difference method to computation of bent isotropic stretched and/or compressed plates of variable stiffness under elastic foundation

The computation of bent isotropic plates, stretched and/or compressed, is a topic widely explored in the literature from both experimental and numerical point of view. We expose in this work an application of the generalized equations of Finite difference method to that topic. The strength of the proposed method is the ability to reconstruct the approximate solution with respect of eventual discontinuities involved in the investigated function as well as its first and second derivatives, including the right-hand side of the equilibrium equation. It is worth mentioning that by opposition to finite element methods our method needs neither fictitious points nor a special condensation of grid. Well-known benchmarks are used in this work to illustrate the efficiency of our numerical and the high accuracy of calculation as well. A comparison of our results with those available in the literature also shows good agreement.

New version of fractional Simpson type inequalities for twice differentiable functions

Simpson inequalities for differentiable convex functions and their fractional versions have been studied extensively. Simpson type inequalities for twice differentiable functions are also investigated. More precisely, Budak et al. established the first result on fractional Simpson inequality for twice differentiable functions. In the present article, we prove a new identity for twice differentiable functions. In addition to this, we establish several fractional Simpson type inequalities for functions whose second derivatives in absolute value are convex. This paper is a new version of fractional Simpson type inequalities for twice differentiable functions.

Algorithms for Optimal Power Flow Extended to Controllable Renewable Systems and Loads

In an effort to quantify and manage uncertainties inside power systems with penetration of renewable energy, uncertainty costs have been defined and different uncertainty cost functions have been calculated for different types of generators and electric vehicles. This article seeks to use the uncertainty cost formulation to propose algorithms and solve the problem of optimal power flow extended to controllable renewable systems and controllable loads. In a previous study, the first and second derivatives of the uncertainty cost functions were calculated and now an analytical and heuristic algorithm of optimal power flow are used. To corroborate the analytical solution, the optimal power flow was solved by means of metaheuristic algorithms. Finally, it was found that analytical algorithms have a much higher performance than metaheuristic methods, especially as the number of decision variables in an optimization problem grows.