A nonlinear model for marble sulphation including surface rugosity and mechanical damage

Here we propose and analyze a mathematical model that aims to describe the marble sulphation process occurring in a given material. The model accounts for rugosity as well as for damaging effects. This model is characterized by some technical difficulties that seem hard to overcome from a theoretical viewpoint. Therefore, we introduce some physically reasonable modifications in order to establish the existence of a suitable notion of solution on a given time interval. Numerical simulations are presented and discussed, also in view of further research.     

A posteriori error analysis of a quadratic finite volume method for nonlinear elliptic problems

In this article, we construct and analyze a residual-based a posteriori error estimator for a quadratic finite volume method (FVM) for solving nonlinear elliptic partial differential equations with homogeneous Dirichlet boundary conditions. We shall prove that the a posteriori error estimator yields the global upper and local lower bounds for the alt="urn:x-wiley:0749159X:media:num22823:num22823-math-0001" loading="lazy" class="section_image" src="/cms/asset/8ae9ae84-be2f-44c2-bd2f-38067440098a/num22823-math-0001.png"> norm error of the FVM. So that the a posteriori error estimator is equivalent to the true error in a certain sense. Numerical experiments are performed to illustrate the theoretical results.     

CuI/Fe3O4 NPs@Biimidazole IL‐KCC‐1 as a leach proof nanocatalyst for the synthesis of imidazo[1,2‐a]pyridines in aqueous medium

In the present work, an innovative leach proof nanocatalyst based on dendritic fibrous nanosilica (DFNS) modified with ionic liquid loaded Fe₃O₄ NPs and CuI salts was designed and applied for the rapid synthesis of imidazo[1,2‐a]pyridines from the reaction of phenyl acetylene, 2‐aminopyridine, and aldehydes in aqueous medium. The structure of the synthesized nanocatalyst was studied by field emission scanning electron microscopy (FESEM), transmission electron microscopy (TEM), Fourier transform infrared (FT‐IR), flame atomic absorption spectroscopy (FAAS), energy‐dispersive X‐ray (EDX), and X‐ray diffraction (XRD), vapor–liquid–solid (VLS), and adsorption/desorption analysis (Brunauer–Emmett–Teller [BET] equation) instrumental techniques. CuI/Fe₃O₄NPs@IL‐KCC‐1 with high surface area (225 m² g^?1) and porous structure not only exhibited excellent catalytic activity in aqueous media but also, with its good stability, simply recovered by an external magnet and recycled for eight cycles without significant loss in its intrinsic activity. Higher catalytic activity of CuI/Fe₃O₄NPs@IL‐KCC‐1 is due to exceptional dendritic fibrous structure of KCC‐1 and the ionic liquid groups that perform as strong anchors to the loaded magnetic nanoparticles (MNPs) and avoid leaching them from the pore of the nanocatalyst. Green reaction media, shorter reaction times, higher yields (71–97%), easy workup, and no need to use the chromatographic column are the advantages of the reported synthetic method.     

Extremal generalized centralizers in matrix algebras

We describe matrices with extremal generalized centralizers over algebraically closed fields.     

On the Motion of Substance in a Channel of a Network: Extended Model and New Classes of Probability Distributions

We discuss the motion of substance in a channel containing nodes of a network. Each node of the channel can exchange substance with: (i) neighboring nodes of the channel, (ii) network nodes which do not belong to the channel, and (iii) environment of the network. The new point in this study is that we assume possibility for exchange of substance among flows of substance between nodes of the channel and: (i) nodes that belong to the network but do not belong to the channel and (ii) environment of the network. This leads to an extension of the model of motion of substance and the extended model contains previous models as particular cases. We use a discrete-time model of motion of substance and consider a stationary regime of motion of substance in a channel containing a finite number of nodes. As results of the study, we obtain a class of probability distributions connected to the amount of substance in nodes of the channel. We prove that the obtained class of distributions contains all truncated discrete probability distributions of discrete random variable ath xmlns:mml="http://www.w3.org/1998/Math/MathML" id="mm1">&amp;#x003c9;ath> which can take values ath xmlns:mml="http://www.w3.org/1998/Math/MathML" id="mm2">0,1,&amp;#x022ef;,Nath>. Theory for the case of a channel containing infinite number of nodes is presented in <a href="#app1-entropy-22-01240" rid="app1-entropy-22-01240" class=" app">Appendix Aa>. The continuous version of the discussed discrete probability distributions is described in <a href="#app2-entropy-22-01240" rid="app2-entropy-22-01240" class=" app">Appendix Ba>. The discussed extended model and obtained results can be used for the study of phenomena that can be modeled by flows in networks: motion of resources, traffic flows, motion of migrants, etc.     

Temporal freedom in mathematical thought: A philosophical–empirical enquiry

This paper seeks to introduce and elaborate on the notion of ‘temporal freedom’ in the context of mathematical thinking.The intention is to merge a philosophical and empirical discussion on this topic, and findings will be presented from a qualitative study in which 29 high-school students were invited to explore the symmetry group of a square during clinical interviews. The data indicate how the interviewees – who were given the opportunity to freely explore an unseen mathematical system – repeatedly brought past and future together in a tangible present during their investigations. In doing so they were exceptionally successful in engaging with advanced abstract algebra, far beyond what might have been expected at the outset.By using empirical data to exemplify an otherwise highly philosophical discussion, I hope to draw explicit attention to the temporal aspect of the human mind in mathematical action which instructional methods frequently fail to recognise, value and utilise.     

富里叶级数的收敛速度

对正弦和余弦富立叶级数,通过合并相邻同号项,使其重排成交错级数.讨论了重排形成的交错级数的敛散性.指出根据自变量x的不同取值,该交错级数可能是单调递减或周期递减的级数.按照莱布尼茨判定法提出了不同精度要求的级数项数的计算公式.选取一到三阶收敛的富立叶级数计算了不同比值精度及差值精度要求的级数项数.计算表明,在x的取值为2π的等分点时,富立叶级数的部分和随项数的增加单调地逼近其收敛值.在x的取值为其它点时,富立叶级数的部分和随项数的增加围绕收敛值上下变动,周期地逼近其收敛值.低收敛阶富立叶级数的收敛速度较慢.要达到0.01%的精度,一收敛阶富立叶级数需要数万项,二收敛阶富立叶级数也需要数百项.在不同计算点处,要达到相同的计算精度,需要的级数项数差别较大.