rss_2.0Sciendo RSS Feed for Communications in Applied and Industrial Mathematicshttps://sciendo.com/journal/CAIMhttps://www.sciendo.comhttps://sciendo-parsed.s3.eu-central-1.amazonaws.com/6471181a2b88470fbea1510d/cover-image.jpghttps://sciendo.com/journal/CAIM140216https://sciendo.com/article/10.2478/caim-2024-0008<abstract> <title style='display:none'>Abstract</title> <p>The Weierstrass‘ theory of one-dimensional Lagrangian systems and a quasi-continuum approach are employed to study the propagation of solitary waves in tensegrity mass-spring chains, which exhibit softening-type elastic response in the large displacement regime and are subject to external pre-compression. The presented study analytically derives the shape of the traveling rarefaction pulses, and limiting values of the speeds of such pulses. Use is made of a tensegrity-like interaction potential that captures the main features of the real force-displacement response of the examined units. The Weierstrass approach is validated through numerical applications that establish comparisons between the theory developed in the present work and previous results available in literature.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/caim-2024-00082024-10-12T00:00:00.000+00:00https://sciendo.com/article/10.2478/caim-2024-0013<abstract> <title style='display:none'>Abstract</title> <p>We investigate the numerical calculation of the general Heun equation using Wolfram Mathematica’s functions, comparing the numerical solutions with hypergeometric and explicit solutions. This exploration sheds light on the efficacy and accuracy of the numerical algorithm implemented in Mathematica for computing Heun functions.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/caim-2024-00132024-10-12T00:00:00.000+00:00https://sciendo.com/article/10.2478/caim-2024-0010<abstract> <title style='display:none'>Abstract</title> <p>In this article, we introduce a new class of polynomials, known as Apostol Hermite Bernoulli-type polynomials, and explore some of their algebraic properties, including summation formulas and their determinant form. The majority of our results are proven using generating function methods. Additionally, we investigate the monomiality principle related to these polynomials and identify the corresponding derivative and multiplicative operators.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/caim-2024-00102024-10-12T00:00:00.000+00:00https://sciendo.com/article/10.2478/caim-2024-007<abstract> <title style='display:none'>Abstract</title> <p>In this paper we study linear fractional differential equations involving tempered Caputo-type derivatives in the hyperbolic space. We consider in detail the three-dimensional case for its simple and useful structure. We also discuss the probabilistic meaning of our results in relation to the distribution of an hyperbolic Brownian motion time-changed with the inverse of a tempered stable subordinator. The generalization to an arbitrary dimension <italic>n</italic> can be easily obtained. We also show that it is possible to construct a particular solution for the non-linear porous-medium type tempered equation by using elementary functions.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/caim-2024-0072024-10-12T00:00:00.000+00:00https://sciendo.com/article/10.2478/caim-2024-0011<abstract> <title style='display:none'>Abstract</title> <p>This article explores some properties of degenerate hypergeometric Bernoulli polynomials, which are defined through the following generating function <disp-formula> <alternatives> <graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_caim-2024-0011_eq_001.png"/> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="block"><mml:mrow><mml:mfrac><mml:mrow><mml:msup><mml:mrow><mml:mi>t</mml:mi></mml:mrow><mml:mi>m</mml:mi></mml:msup><mml:msubsup><mml:mrow><mml:mi>e</mml:mi></mml:mrow><mml:mi>λ</mml:mi><mml:mi>x</mml:mi></mml:msubsup><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:msubsup><mml:mrow><mml:mi>e</mml:mi></mml:mrow><mml:mi>λ</mml:mi><mml:mi>x</mml:mi></mml:msubsup><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>-</mml:mo><mml:msubsup><mml:mo>∑</mml:mo><mml:mrow><mml:mi>l</mml:mi><mml:mo>=</mml:mo><mml:mn>0</mml:mn></mml:mrow><mml:mrow><mml:mi>m</mml:mi><mml:mo>-</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msubsup><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mn>1</mml:mn><mml:mo>)</mml:mo></mml:mrow><mml:mi>l</mml:mi><mml:mo>,</mml:mo><mml:mi>λ</mml:mi><mml:mfrac><mml:mrow><mml:msup><mml:mrow><mml:mi>t</mml:mi></mml:mrow><mml:mi>l</mml:mi></mml:msup></mml:mrow><mml:mrow><mml:mi>l</mml:mi><mml:mo>!</mml:mo></mml:mrow></mml:mfrac></mml:mrow></mml:mrow></mml:mfrac><mml:mo>=</mml:mo><mml:munderover><mml:mo>∑</mml:mo><mml:mrow><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn>0</mml:mn></mml:mrow><mml:mrow><mml:msup><mml:mrow/><mml:mo>∞</mml:mo></mml:msup></mml:mrow></mml:munderover><mml:mrow><mml:msubsup><mml:mrow><mml:mi>B</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi><mml:mo>,</mml:mo><mml:mi>λ</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:mi>m</mml:mi><mml:mo>-</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mo>]</mml:mo></mml:mrow></mml:mrow></mml:msubsup></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>x</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mfrac><mml:mrow><mml:msup><mml:mrow><mml:mi>t</mml:mi></mml:mrow><mml:mi>n</mml:mi></mml:msup></mml:mrow><mml:mrow><mml:mi>n</mml:mi><mml:mo>!</mml:mo></mml:mrow></mml:mfrac><mml:mo>,</mml:mo><mml:mi> </mml:mi><mml:mi> </mml:mi><mml:mi> </mml:mi><mml:mi> </mml:mi><mml:mrow><mml:mo>|</mml:mo><mml:mi>t</mml:mi><mml:mo>|</mml:mo></mml:mrow><mml:mo>&lt;</mml:mo><mml:mo>min</mml:mo><mml:mrow><mml:mo>{</mml:mo><mml:mrow><mml:mn>2</mml:mn><mml:mi>π</mml:mi><mml:mo>,</mml:mo><mml:mfrac><mml:mn>1</mml:mn><mml:mrow><mml:mrow><mml:mo>|</mml:mo><mml:mi>λ</mml:mi><mml:mo>|</mml:mo></mml:mrow></mml:mrow></mml:mfrac></mml:mrow><mml:mo>}</mml:mo></mml:mrow><mml:mo>,</mml:mo><mml:mi>λ</mml:mi><mml:mo>∈</mml:mo><mml:mi>ℝ</mml:mi><mml:mo>\</mml:mo><mml:mrow><mml:mo>{</mml:mo><mml:mn>0</mml:mn><mml:mo>}</mml:mo></mml:mrow><mml:mo>.</mml:mo></mml:mrow></mml:math> <tex-math>{{{t^m}e_\lambda ^x\left( t \right)} \over {e_\lambda ^x\left( t \right) - \sum\nolimits_{l = 0}^{m - 1} {\left( 1 \right)l,\lambda{{{t^l}} \over {l!}}} }} = \sum\limits_{n = 0}^{^\infty } {B_{n,\lambda }^{\left[ {m - 1} \right]}} \left( x \right){{{t^n}} \over {n!}},\,\,\,\,\left| t \right| &lt; \min \left\{ {2\pi ,{1 \over {\left| \lambda \right|}}} \right\},\lambda \in \mathbb{R}\backslash \left\{ 0 \right\}.</tex-math> </alternatives> </disp-formula> We deduce their associated summation formulas and their corresponding determinant form. Also we focus our attention on the zero distribution of such polynomials and perform some numerical illustrative examples, which allow us to compare the behavior of the zeros of degenerate hypergeometric Bernoulli polynomials with the zeros of their hypergeometric counterpart. Finally, using a monomiality principle approach we present a differential equation satisfied by these polynomials.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/caim-2024-00112024-10-12T00:00:00.000+00:00https://sciendo.com/article/10.2478/caim-2024-0006ARTICLEtruehttps://sciendo.com/article/10.2478/caim-2024-00062024-10-12T00:00:00.000+00:00https://sciendo.com/article/10.2478/caim-2024-0012<abstract> <title style='display:none'>Abstract</title> <p>This article outlines an innovative procedure to improve the accessibility of Mathematics for secondary school students with visual impairments. Using LATEX, a widely used typesetting system, a transformative approach is developed that converts traditional mathematical content into three accessible formats: <italic>PDF</italic>, <italic>MathJax</italic> and <italic>LAMBDA</italic>. Central to this system is the integration of alternative text, which offers full descriptions of images and mathematical formulae and promotes a richer understanding of its content. The broader implications of this project include the introduction of novel teaching models for educators, enhanced accessibility of Mathematics programmes, and the potential to encourage the enrolment of visually impaired students in science degree courses. Ultimately, this work contributes to the creation of the conditions for the development of an inclusive and barrier-free learning environment in Mathematics education.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/caim-2024-00122024-10-12T00:00:00.000+00:00https://sciendo.com/article/10.2478/caim-2024-0009<abstract> <title style='display:none'>Abstract</title> <p>Neurophysiological signal analysis is crucial for understanding the complex dynamics of brain function and its deviations in various pathological conditions. Traditional linear methods, while insightful, often fail to capture the full spectrum of inherently non-linear brain dynamics. This review explores the efficacy and applicability of the Higuchi fractal dimension (HFD) in interpreting neurophysiological signals such as scalp electroencephalography (EEG) and stereotactic intracranial encephalography (sEEG). We focus on three case studies: i) distinguishing between Alzheimer’s disease (AD) and healthy controls; ii) classifying neurodynamics across diverse brain parcels looking for a signature of that cortical parcel; and iii) differentiating states of consciousness. Our study highlights the potential of non-linear analysis for deeper insights into brain dynamics and its potential for improving clinical diagnostics.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/caim-2024-00092024-10-12T00:00:00.000+00:00https://sciendo.com/article/10.2478/caim-2024-0005<abstract> <title style='display:none'>Abstract</title> <p>We review recent mathematical results concerning the analysis of hydrostatic equations in the context of stably stratified fluids. Beginning with the simpler and better understood setting of homogeneous fluids, we emphasize the additional mathematical challenges posed by non-homogeneous framework. We present both positive and negative results, including well-posedness and proof of the hydrostatic limit with a suitable regularization, alongside ill-posedness in the fully inviscid setting and the breakdown of the hydrostatic limit in specific scenarios.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/caim-2024-00052024-09-26T00:00:00.000+00:00https://sciendo.com/article/10.2478/caim-2024-0002<abstract> <title style='display:none'>Abstract</title> <p>Mathematics has been applied to physics and engineering in the last few centuries, substantially contributing to the various phases of the industrial revolution. Its application to biology is instead relatively more recent. In this paper we provide an overview of some problems in a few fields mainly related to ecology. The models discussed help in fighting pests in agriculture to improve crop harvesting and to combat the phenomenon of alien species invasions, that due to worldwide trading and climate changes is affecting the temperate regions, threatening the survival of the native species. A pair of examples related to primary oxygen production and fallacies of our linear way of thinking are also presented, to stress the fact that raising temperatures entail huge unforeseen problems. Finally we delve briefly in the vaste field of epidemiology, that would deserve a review on its own, to discuss models for diseases in the environment and one instance related epidemics affecting humans, prompted by the important role of asymptomatics played in them.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/caim-2024-00022024-07-17T00:00:00.000+00:00https://sciendo.com/article/10.2478/caim-2024-0003<abstract> <title style='display:none'>Abstract</title> <p>In the framework of the theory of Landscape Ecology, a review of Lotka-Volterrra type models is proposed. Such models can be considered useful tools in order to represent and evaluate the dynamical behavior and the ecological stability of an environmental system which, as known, is subjected during time to several transformations. At this purpose, after such a review and presentation of different models, an application to an important wine region in France is performed using a model recently introduced in literature.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/caim-2024-00032024-07-17T00:00:00.000+00:00https://sciendo.com/article/10.2478/caim-2024-0004<abstract> <title style='display:none'>Abstract</title> <p>The application of the Partition of Unity Method (PUM) to signal approximation on graphs represents a recent advancement of this versatile and efficient interpolation technique. Given the novelty of this approach, little is yet known regarding the role of kernel parameters employed in constructing the associated Graph Basis Functions (GBFs). In order to shed light on this aspect, this study proposes several numerical tests obtained using GBFs generated by heat kernels and variational spline kernels.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/caim-2024-00042024-07-17T00:00:00.000+00:00https://sciendo.com/article/10.2478/caim-2024-0001<abstract> <title style='display:none'>Abstract</title> <p>We study the quasistatic evolution of a linear peridynamic Kelvin-Voigt viscoelastic material. More specifically, we consider the gradient flow of a nonlocal elastic energy with respect to a nonlocal viscous dissipation. Following an evolutionary Γ-convergence approach, we prove that the solutions of the nonlocal problem converge to the solution of the local problem, when the peridynamic horizon tends to 0, that is, in the nonlocal-to-local limit.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/caim-2024-00012024-05-25T00:00:00.000+00:00https://sciendo.com/article/10.2478/caim-2023-0004<abstract> <title style='display:none'>Abstract</title> <p>The paper presents a complete (to the best of the author’s knowledge) overview on the existing literature concerning the NLS equation with point-concentrated nonlinearity. Precisely, it mainly covers the following topics: definition of the model, weak and strong local well-posedness, global well-posedness, classification and stability (orbital and asymptotic) of the standing waves, blow-up analysis and derivation from the standard NLS equation with shrinking potentials. Also some related problem is mentioned.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/caim-2023-00042023-10-13T00:00:00.000+00:00https://sciendo.com/article/10.2478/caim-2023-0003<abstract> <title style='display:none'>Abstract</title> <p>We survey results concerning the problem of identifying depth profiles at coastal zone, which evolve in time due to natural as well as anthropic activities. This issue is relevant to control the modifications of the environment occurring near sea coastlines, but also in river's estuaries and harbors. One of the main goals is to predict the time evolution of the depth profile in the long-term (i.e., over years or decades, say), and to do this on the basis of <italic>real</italic> observed and measured <italic>data</italic>, available in several databases. Most mathematical models are formulated in terms of partial differential equations of the diffusive type, in one or two space dimensions. Consequently, from the mathematical standpoint, the aforementioned identification problem takes on the form of an inverse problem for some given parabolic equation associated with suitable initial and boundary conditions.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/caim-2023-00032023-09-16T00:00:00.000+00:00https://sciendo.com/article/10.2478/caim-2023-0002<abstract> <title style='display:none'>Abstract</title> <p>This paper concerns the existence of global weak solutions <italic>á la Leray</italic> for compressible Navier–Stokes–Fourier systems with periodic boundary conditions and the truncated virial pressure law which is assumed to be thermodynamically unstable. More precisely, the main novelty is that the pressure law is not assumed to be monotone with respect to the density. This provides the first global weak solutions result for the compressible Navier-Stokes-Fourier system with such kind of pressure law which is strongly used as a generalization of the perfect gas law. The paper is based on a new construction of approximate solutions through an iterative scheme and fixed point procedure which could be very helpful to design efficient numerical schemes. Note that our method involves the recent paper by the authors published in Nonlinearity (2021) for the compactness of the density when the temperature is given.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/caim-2023-00022023-06-21T00:00:00.000+00:00https://sciendo.com/article/10.2478/caim-2018-0014<abstract><title style='display:none'>Abstract</title><p> Kinetic models have so far been used to model wealth distribution in a society. In particular, within the framework of the kinetic theory for active particles, some important models have been developed and proposed. They involve nonlinear interactions among individuals that are modeled according to game theoretical tools by introducing parameters governing the temporal dynamics of the system. In this present paper we propose an approach based on optimal control tools that aims to optimize this evolving dynamics from a social point of view. Namely, we look for time dependent control variables concerning the distribution of wealth that can be managed, for instance, by the government, in order to obtain a given social profile.</p></abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/caim-2018-00142018-12-19T00:00:00.000+00:00https://sciendo.com/article/10.2478/caim-2018-0009<abstract><title style='display:none'>Abstract</title><p> In this paper the optimal control of alignment models composed by a large number of agents is investigated in presence of a selective action of a controller, acting in order to enhance consensus. Two types of selective controls have been presented: an homogeneous control filtered by a selective function and a distributed control active only on a selective set. As a first step toward a reduction of computational cost, we introduce a model predictive control (MPC) approximation by deriving a numerical scheme with a feedback selective constrained dynamics. Next, in order to cope with the numerical solution of a large number of interacting agents, we derive the mean-field limit of the feedback selective constrained dynamics, which eventually will be solved numerically by means of a stochastic algorithm, able to simulate effciently the selective constrained dynamics. Finally, several numerical simulations are reported to show the effciency of the proposed techniques.</p></abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/caim-2018-00092018-12-19T00:00:00.000+00:00https://sciendo.com/article/10.2478/caim-2018-0018<abstract><title style='display:none'>Abstract</title><p>In the present paper we propose two mathematical models describing, respectively at the microscopic level and at the mesoscopic level, a system of interacting tumor cells and cells of the immune system. The microscopic model is in terms of a Markov chain defined by the generator, the mesoscopic model is developed in the framework of the kinetic theory of active particles. The main result is to prove the transition from the microscopic to mesoscopic level of description.</p></abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/caim-2018-00182018-12-19T00:00:00.000+00:00https://sciendo.com/article/10.2478/caim-2018-0019ARTICLEtruehttps://sciendo.com/article/10.2478/caim-2018-00192018-12-19T00:00:00.000+00:00en-us-1