Acta et Commentationes Universitatis Tartuensis de Mathematica 2020-05-26T14:30:24+00:00 Enno Kolk Open Journal Systems <p><em>Acta et Commentationes Universitatis Tartuensis de Mathematica&nbsp;</em>(ACUTM) is an international journal of pure and applied mathematics.</p> Some new Hermite–Hadamard type inequalities for functions whose n<sup>th</sup> derivatives are convex 2020-05-26T14:30:24+00:00 B. Meftah M. Merad N. Ouanas A. Souahi <p>We first create an integral identity for <em>n</em>-times differentiable functions. Relying on this identity, we establish some new Hermite–Hadamard type inequalities for functions whose <em>n<sup>th</sup></em> derivatives are convex.</p> 2020-01-14T00:00:00+00:00 ##submission.copyrightStatement## On singular systems of nonlinear equations involving 3n-Caputo derivatives 2020-05-26T14:30:23+00:00 Amele Taïeb <p>We study singular fractional systems of nonlinear differential equations involving 3<em>n</em>-Caputo derivatives. We investigate existence and uniqueness results using the contraction mapping principle. We also discuss the existence of at least one solution by means of Schauder fixed point theorem. Moreover, we define and discuss the Ulam–Hyers stability and the generalized Ulam–Hyers stability of solutions for such systems. To illustrate the main results, we present some examples.</p> 2020-01-14T00:00:00+00:00 ##submission.copyrightStatement## Simpson’s type inequalities for η-convex functions via k-Riemann–Liouville fractional integrals 2020-05-26T14:30:22+00:00 Seth Kermausuor <p>We introduce some Simpson's type integral inequalities via <em>k</em>-Riemann–Liouville fractional integrals for functions whose derivatives are <em>η</em>-convex. These results generalize some results in the literature.</p> 2020-01-14T00:00:00+00:00 ##submission.copyrightStatement## Certain sufficient conditions for close-to-convexity and starlikeness of multivalent functions 2020-05-26T14:30:22+00:00 Mohamed K. Aouf Teodor Bulboacă Adela O. Mostafa <p>By using Jack's lemma, we derive simple sufficient conditions for analytic functions to be multivalent close-to-convex and multivalent starlike.</p> 2020-01-14T00:00:00+00:00 ##submission.copyrightStatement## On generalized Lagrange–Hermite–Bernoulli and related polynomials 2020-05-26T14:30:21+00:00 Waseem A. Khan M. A. Pathan <p>We introduce a new class of generalized polynomials, ascribed to the family of Hermite, Lagrange, Bernoulli, Miller–Lee, and Laguerre polynomials and of their associated forms. These polynomials can be expressed in the form of generating functions, which allow a high degree of exibility for the formulation of the relevant theory. We develop a point of view based on generating relations, exploited in the past, to study some aspects of the theory of special functions. We propose a fairly general analysis allowing a transparent link between different forms of special polynomials.</p> 2020-01-14T17:09:39+00:00 ##submission.copyrightStatement## Multi-objective global optimization of grillage-type engineering structures using advanced metaheuristics 2020-05-26T14:30:21+00:00 Rimantas Belevičius Darius Mačiūnas Dmitrij Šešok <p>The purpose of the paper is to present the method implemented for a global optimization of grillage-type pile foundations introducing two advanced metaheuristics: AAGA and AGADS. The suggested new optimization algorithm including the synergy of AAGA and AGADS demonstrates improved results comparing with former AGA and GADS. Compromise objective function to be minimized involves the maximum reactive force in piles and maximum bending moment in the connecting beams. The feasibility of a simple weighting technique for the objective function is proved by numerical investigation of objective function domain for several different topologies of foundations. Sizing problem of connecting beams is solved together with the optimization problem. The original finite element program was employed for solution of direct problem.</p> 2020-01-14T17:16:08+00:00 ##submission.copyrightStatement## Estimating probability of fatigue failure of steel structures 2020-05-26T14:30:20+00:00 Z. Kala <p>The article deals with the analysis of failure probability of the effect of random factors in uencing fatigue crack propagation in a steel element under bending moment. The theoretical model of fatigue crack progression is based on linear fracture mechanics. When determining the required degree of failure probability, it is possible to specify the time of the first inspection of the construction, which will focus on the fatigue damage. Using a conditional probability, subsequent inspection times are specified. The failure probability is examined using a fairly new sensitivity analysis subordinated to a contrast. The importance ranking of the input random variables to the failure probability is investigated. Fatigue properties of steel are taken from recent experimental research. Numerical results are obtained using the Monte Carlo simulation.</p> 2020-01-14T17:22:22+00:00 ##submission.copyrightStatement## Comparison between finite element analysis and rheological models for chip formation 2020-05-26T14:30:20+00:00 Olga Liivapuu Jüri Olt Tanel Tärgla <p>In the process of cutting, often the selection of cutting parameters is done considering empirical methods. This approach is more expensive and does not usually lead to the best solutions. Numerical methods for simulating the chip formation have been under development over the last thirty years. The aim of the present research is to compare models based on rheological properties of metals with 2D Finite Element Models of chip formation process.</p> 2020-01-14T17:27:36+00:00 ##submission.copyrightStatement## Theoretical description of large deformations in criss-cross composites (with application to Tensylon®) 2020-05-26T14:30:19+00:00 Pavel S. Mostovykh <p>A theoretical model of an anisotropic material, Tensylon®, under large strains is proposed. This model is capable to describe the material’s response in in-plane tension at different angles to the fibrils. At 0° and at 90°, i.e., along the fibrils in either “criss” or “cross” plies, it quantitatively predicts the experimentally observed elastic behaviour until failure. At 45° to the fibrils, it quantitatively describes the experi- mental data in the elastic and plastic domains. The description remains accurate up to strains of 35%, that corresponds to 30÷40% of deforma- tion gradient components. The infinitesimal strains model would give at least 25% of error under such circumstances.</p> 2020-01-14T17:33:58+00:00 ##submission.copyrightStatement## A new characterization of the simple groups C4(q), by its order and the largest order of elements 2020-05-26T14:30:18+00:00 Behnam Ebrahimzadeh Reza Mohammadyari Miryousef Sadeghi <p>We prove that the simple group <em>C</em><sub>4</sub>(<em>q</em>), where <em>q</em> &gt; 2 and (<em>q</em><sup>4</sup> + 1)=2 are prime numbers, can be uniquely determined by its order and the largest order of elements.</p> 2020-01-14T17:39:49+00:00 ##submission.copyrightStatement## Some competing nonresponse adjustment estimators 2020-05-26T14:30:17+00:00 Imbi Traat <p>The nonresponse adjustment estimator, derived in this paper by standard regression tools, is surprising by its form. The weights of the new estimator, called the f-estimator, are (general) inverses of the respective weights in the classical linear calibration estimator and propensity adjusted estimator. In a simulation experiment on real data, the new estimator is the best for several study variables.</p> 2020-01-14T17:43:12+00:00 ##submission.copyrightStatement##