Showing papers in "Ricerche Di Matematica in 2021"

Abstract: Recently Qiu [6] have introduced residual extropy as measure of uncertainty in residual lifetime distributions analogues to residual entropy (see, e.g. [3]). Also, they obtained some properties and applications of that. In this paper, we study the extropy to measure the uncertainty in a past lifetime distribution. This measure of uncertainty is called past extropy. Also it is showed a characterization result about the past extropy of largest order statistics.

Abstract: In this paper, we consider a rarefied polyatomic gas with a non-polytropic equation of state. We use the variational procedure of maximum entropy principle (MEP) to obtain the closure of the binary hierarchy of 14 moments associated with the Boltzmann equation in which the distribution function depends also on the energy of internal modes. The closed partial differential system is symmetric hyperbolic and the Cauchy problem is well-posed. In the limiting case of polytropic gas in which the internal energy is a linear function of the temperature, we find, as a special case, the previous results of Pavic et al. (Physica A 392:1302–1317, 2013). This paper, therefore, completes the equivalence between the closure obtained in the phenomenological rational extended thermodynamics theory and the one obtained by the MEP for general non-polytropic gas.

Abstract: We investigate the relaxation to equilibrium of the solution of a class of one-dimensional linear Fokker–Planck type equations that have been recently considered in connection with the study of addiction phenomena in a system of individuals. The steady states of these equations belong to the class of generalized Gamma densities. As a by-product of the relaxation analysis, we prove new weighted Poincare and logarithmic Sobolev type inequalities for this class of densities.

Abstract: The mathematical description of poikilothermic organisms’ life cycle, of insects in particular, is a widely discussed argument, above all for its application in decision support systems. The increasing interest among agricultural industries in obtaining products with minor quantities of chemical inputs has led entomologists and model scientists to study in greater depth not only the biology and behaviour of the insects, but also the way to translate these mechanisms into mathematical language. The aim of this work is to provide a new instrument to describe insect pests’ population density. In particular, the study analyses insects’ development through the life stages driven by environmental factors. This has led researchers to consider physiological age, instead of the more widely used chronological age. In addition to mortality and fertility rates, the possibility of improving the simulation by inserting as a boundary condition results from previous field monitoring or the links with diapause models has been considered. The work is validated in the case of the European grapevine moth Lobesia botrana.

Abstract: This paper introduce and study weakly 1-absorbing prime ideals in commutative rings. Let $$A\ $$ be a commutative ring with a nonzero identity $$1 e 0.$$ A proper ideal $$P\ $$ of $$A\ $$ is said to be a weakly 1-absorbing prime ideal if for every nonunits $$x,y,z\in A\ $$ with $$0 e xyz\in P,\ $$ then $$xy\in P$$ or $$z\in P.\ $$ In addition to give many properties and characterizations of weakly 1-absorbing prime ideals, we also determine rings in which every proper ideal is weakly 1-absorbing prime. Furthermore, we investigate weakly 1-absorbing prime ideals in C(X), which is the ring of continuous functions of a topological space $$X.\ $$

Abstract: In this paper, a family of mean past weighted ($$\hbox {MPW}_{\alpha }$$) distributions of order $$\alpha $$ is introduced. For the construction of this family, the concepts of the mean inactivity time and cumulative $$\alpha $$-class past entropy are used. Distributional properties and stochastic comparisons with other known weighted distributions are given. Furthermore, an upper bound for the k-order moment of the random variables associated with the new family and a characterization result are obtained. Generalized discrete mixtures that involve $$\hbox {MPW}_{\alpha }$$ distributions and other weighted distributions are also explored.

Abstract: In physics, phenomena of diffusion and wave propagation have great relevance; these physical processes are governed in the simplest cases by partial differential equations of order 1 and 2 in time, respectively. It is known that whereas the diffusion equation describes a process where the disturbance spreads infinitely fast, the propagation velocity of the disturbance is a constant for the wave equation. By replacing the time derivatives in the above standard equations with pseudo-differential operators interpreted as derivatives of non integer order (nowadays misnamed as of fractional order) we are lead to generalized processes of diffusion that may be interpreted as slow diffusion and interpolating between diffusion and wave propagation. In mathematical physics, we may refer these interpolating processes to as fractional diffusion-wave phenomena. The use of the Laplace transform in the analysis of the Cauchy and Signalling problems leads to special functions of the Wright type. In this work we analyze and simulate both the situations in which the input function is a Dirac delta generalized function and a box function, restricting ourselves to the Cauchy problem. In the first case we get the fundamental solutions (or Green functions) of the problem whereas in the latter case the solutions are obtained by a space convolution of the Green function with the input function. In order to clarify the matter for the non-specialist readers, we briefly recall the basic and essential notions of the fractional calculus (the mathematical theory that regards the integration and differentiation of non-integer order) with a look at the history of this discipline.

Abstract: A ternary autonomous dynamical system of FitzHugh–Rinzel type is analyzed. The system, at start, is reduced to a nonlinear integro differential equation. The fundamental solution H(x, t) is explicitly determined and the initial value problem is analyzed in the whole space. The solution is expressed by means of an integral equation involving H(x, t) . Moreover, adding an extra control term, explicit solutions are achieved.

Abstract: Similarity solutions are obtained for one-dimensional cylindrical shock wave in a self-gravitating, rotational axisymmetric non-ideal gas with azimuthal or axial magnetic field in the presence of conductive and radiative heat fluxes The total energy of the wave is non-constant It is obtained that the increase in the Cowling number, in the parameters of radiative as well as conductive heat transfer and the parameter of the non-idealness of the gas have a decaying effect on the shock wave however increase in the value of gravitational parameter has reverse effect on the shock strength It is manifested that the presence of azimuthal magnetic field removes the singularities which arise in some cases of the presence of axial magnetic field Also, it is observed that the effect of the parameter of non-idealness of the gas is diminished by increasing the value of the gravitational parameter

Abstract: The paper is concerned with the onset of bifurcations in fluid mixtures. The instability of thermal conduction state in a rotating fluid layer heated and salted from below, is analyzed. The Taylor number threshold for the transition to Hopf bifurcations, in simple closed form, is obtained. The basic property of each coefficient of the spectrum equation to drive instability and type of bifurcation, is shown and applied.

Abstract: We study the stability of laminar flows in a sheet of fluid (open channel) down an incline with constant slope angle $$\beta $$ . The basic motion is the velocity field $$U(z) \mathbf{i}$$ , where z is the coordinate of the axis orthogonal to the channel, and $$\mathbf{i}$$ is the unit vector in the direction of the flow. U(z) is a parabolic function which vanishes at the bottom of the channel and whose derivative with respect to z vanishes at the top. We study the linear stability, and prove that the basic motion is linearly stable for any Reynolds number. We also study the nonlinear Lyapunov stability by solving the Orr equation for the associated maximum problem. As in Falsaperla et al. (Phys Rev E 100(1):013113, 2019. https://doi.org/10.1103/PhysRevE.100.013113 ) we finally study the nonlinear stability of tilted rolls. This work is a preliminary investigation to model debris flows down an incline (Introduction to the physics of landslides. Lecture notes on the dynamics of mass wasting. Springer, Dordrecht, 2011. https://doi.org/10.1007/978-94-007-1122-8 ).

Abstract: We study in this work the global existence of solutions to a system of reaction cross diffusion equations appearing in the modeling of multiple sclerosis, in the one-dimensional case. Weak solutions are obtained for general initial data, and existence, uniqueness, stability and smoothness are proven when initial data are smooth.

Abstract: In this paper, we obtained the solutions of the Riemann problem for a quasilinear hyperbolic system with four equations characterizing one-dimensional planar and radially symmetric flow of van der Waals reacting gases with dust particles involving shock wave, simple wave and contact discontinuities without any restriction on the magnitude of initial states. This system is more complex due to the dust particles in van der Waals reacting gases, that is, typical irreversible exothermic reaction of real gases in the presence of dust particles. The generalised Riemann invariants are used to determine the necessary and sufficient condition for the uniqueness of solutions. The effects of non-idealness and dust particles on the compressive and rarefaction waves are also analyzed.

Abstract: The role played by magnetoelastic effects on the properties exhibited by magnetic domain walls propagating along the major axis of a thin magnetostrictive nanostrip, coupled mechanically with a thick piezoelectric actuator, is theoretically investigated. The magnetostrictive layer is assumed to be a linear elastic material belonging to the cubic crystal classes $$\bar{4}$$ 3m, 432 and m $$\bar{3}$$ m and to undergo isochoric magnetostrictive deformations. The analysis is carried out in the framework of the extended Landau–Lifshitz–Gilbert equation, which allows to describe, at the mesoscale, the spatio-temporal evolution of the local magnetization vector driven by magnetic fields and electric currents, in the presence of magnetoelastic and magnetocrystalline anisotropy fields. Through the traveling-wave transformation, the explicit expression of the key features involved in both steady and precessional regimes is provided and a qualitative comparison with data from the literature is also presented.

Abstract: In this article, the kinematics of one-dimensional motion have been applied to construct evolution equations for non-planar weak and strong shocks propagating into a non-ideal relaxing gas. The approximate value of exponent of shock velocity, at the instant of shock collapse, obtained from systematic approximation method is compared with those obtained from characteristic rule and Guderley’s scheme. Computation of exponent is carried out for different values of van der Waals excluded volume. Effects of non-ideal and relaxation parameters on the wave evolution, governed by the evolution equations, are analyzed.

Abstract: The dynamics of four component dusty plasma with nonthermal electrons and positrons are examined. The bifurcation analysis of small amplitude dust ion acoustic (DIA) waves in this multicomponent plasma is investigated. Employing the reductive perturbation technique (RPT), the two nonlinear equations viz. KdV and mKdV are derived and using the travelling wave transformation, respective planar dynamical systems are deduced. Based on the bifurcation theory of this dynamical system, all possible phase portraits, including nonlinear homoclinic orbit, nonlinear periodic orbit and supernonlinear periodic orbit are presented. The pseudopotential profiles for the nonlinear equations are plotted for different parametric values to illustrate and confirm the phase plane analysis. It is found that the system parameter values affect the bifurcation of the DIA waves. It is also shown that the system supports both nonlinear and supernonlinear DIA periodic waves.

Abstract: Let A be a positive (semidefinite) bounded linear operator on a complex Hilbert space $$\big ({\mathcal {H}}, \langle \cdot , \cdot \rangle \big )$$ . The semi-inner product induced by A is defined by $${\langle x, y\rangle }_A := \langle Ax, y\rangle $$ for all $$x, y\in {\mathcal {H}}$$ and defines a seminorm $${\Vert \cdot \Vert }_A$$ on $${\mathcal {H}}$$ . This makes $${\mathcal {H}}$$ into a semi-Hilbert space. For $$p\in [1,+\infty )$$ , the generalized A-joint numerical radius of a d-tuple of operators $${\mathbf {T}}=(T_1,\ldots ,T_d)$$ is given by $$\begin{aligned} \omega _{A,p}({\mathbf {T}}) =\sup _{\Vert x\Vert _A=1}\left( \sum _{k=1}^d|\big \langle T_kx, x\big \rangle _A|^p\right) ^{\frac{1}{p}}. \end{aligned}$$ Our aim in this paper is to establish several bounds involving $$\omega _{A,p}(\cdot )$$ . In particular, under suitable conditions on the operators tuple $${\mathbf {T}}$$ , we generalize the well-known inequalities due to Kittaneh (Studia Math 168(1):73–80, 2005).

Abstract: We discuss the structure of the shock wave solution for a system of Navier–Stokes equations, obtained as hydrodynamic limit of a BGK description of the dynamics of monoatomic gases at kinetic level. We investigate first the thickness of the transition region of the shock profile for a monoatomic gas, for varying Mach number and different physical options for the viscosity coefficient. The analysis is then extended to a binary gas mixture. Some numerical results for noble gases are presented and discussed.

Abstract: In this work we are interested in the periodic solutions of the singular problem involving variable exponent with a homogeneous Dirichlet boundary conditions modeled as $$\begin{aligned} {\partial _t u}-\varDelta u =\displaystyle \frac{f}{u^{\gamma (t,x)}}\text { in }]0,T[\times \varOmega \end{aligned}$$ Where $$\varOmega $$ is an open regular bounded subset of $${\mathbb {R}}^{N}$$ , $$T>0$$ is the period, $$\gamma (t,x)$$ is a nonnegative periodic function belonging in $${\mathcal {C}}(\overline{Q_{T}})$$ and f is a nonnegative measurable function periodic in time with period T and belonging to a certain Lebesgue space. Under suitable assumptions on $$\gamma $$ and f, we prove an existence result of a nonnegative weak time periodic solution to the considered problem.

Abstract: The paper is concerned with the IBVP of the Navier–Stokes equations. The goal is to evaluate the possible gap between the energy equality and the energy inequality deduced for a weak solution. This kind of analysis is new and the result is a natural continuation and improvement of a result obtained by the same authors in Crispo et al. (Some new properties of a suitable weak solution to the Navier–Stokes equations. arXiv:1904.07641 ).

Abstract: In this paper, first we consider some partitioned matrices having some special kind of blocks, and we obtain their eigenvalues and eigenvectors. From these, we deduce several results on the eigenvalues of partitioned matrices in the literature. Next we consider an extension of a generalized join of graphs introduced by Hedetniemi (On classes of graphs defined by special cutsets of lines. In: Many facets of graph theory. Proceedings of the conference held at Western MiGammagan University, Kalamazoo/Mi, 1968. Lecture notes in mathematics, vol 110, pp 171–189, 1969), we call it the $${\mathcal {M}}$$ -join of $${\mathcal {H}}_k$$ . The spectra of partitioned matrices allow to detect the adjacency, the Laplacian and the signless Laplacian spectrum of old and new type of join of graphs. Further, we have constructed several pairs of simultaneously A-cospectral, L-cospectral and Q-cospectral graphs.

Abstract: This paper is concerned with an inverse source problem for a space-time fractional diffusion equation. We aim to identify an unknown source term from partially observed data. The employed model involves the Caputo fractional derivative in time and the non-local fractional Laplacian operator in space. The well-posedness of the forward problem is discussed. The considered ill-posed inverse source problem is formulated as a minimization one. The existence, uniqueness and stability of the solution of the minimization problem are examined. An iterative process is developed for identifying the unknown source term. A numerical implementation of the proposed approach is performed. The convergence of the discretized fractional derivatives is analyzed. The efficiency and accuracy of the proposed identification algorithm are confirmed by some numerical experiments.

Abstract: In this paper, we attain the multifractal Hewitt–Stromberg dimension functions of Moran measures associated with homogeneous Moran fractals and show that the multifractal Hewitt–Stromberg measures are mutually singular for which the multifractal functions do not necessarily coincide In particular, we give a positive answer to questions posed in Attia and Selmi (J Geom Anal 31:825-862, 2021) and discuss some interesting examples

Abstract: The Boltzmann equation for charge transport in monolayer graphene is numerically solved by using a discontinuous Galerkin method. The numerical fluxes are based on a uniform non oscillatory reconstruction. The numerical scheme has been tested by simulating the electron dynamics in a graphene field effect transistor. To the best of our knowledge the presented simulations are the first ones using a full Boltzmann equation in graphene devices.

Abstract: Let G be an abelian group The aim of this short paper is to describe a way to identify pure subgroups H of G by looking only at how the subgroup lattice $$\mathcal {L}(H)$$ embeds in $$\mathcal {L}(G)$$ It is worth noticing that all results are carried out in a local nilpotent context for a general definition of purity

Abstract: In this paper, we propose two new methods to solve large-scale systems of differential equations, which are based on the Krylov method. In the first one, the exact solution with the exponential projection technique of the matrix. In the second, we get a new problem of small size, by dropping the initial problem, and then we solve it in ways, such as the Rosenbrock and the BDF. Some theoretical results are presented such as an accurate expression of the remaining criteria. We give an expression of error report and numerical values to compare the two methods in terms of how long each method takes, and we also compare the approaches.

Abstract: Recently, Ruggeri et al. (The Riemann problem of relativistic Euler system with Synge energy, arXiv:2001.04128v1 [math-ph], 2020) studied the Riemann problem of the relativistic Euler system for rarefied monatomic and diatomic gases with a constitutive equation for the energy determined by Synge, which is the only realistic equation compatible with the kinetic theory. The aim of the present work is to consider the classical and ultrarelativistic limits of their results, showing that they are in agreement with those already present in literature.

Abstract: We fix a Finsler norm F and, using the anisotropic curvature flow, we prove that in the plane the anisotropic maximum curvature $$k^F_{\max }$$ of a smooth Jordan curve is such that $$ k^F_{\max }(\gamma )\ge \sqrt{\kappa /A}$$ , where A is the area enclosed by $$\gamma $$ and $$\kappa $$ the area of the unitary Wulff shape associated to the anisotropy F.

Abstract: We investigate the longitudinal and transversal vibrations of the viscoelastic beam with nonlinear tension and nonlinear delay term under the general decay rate for relaxation function. The existence theorem is proved by the Faedo–Galerkin method and using suitable Lyapunov functional to establish the general decay result.

Abstract: In this note, we consider a hyperbolic system of equations in a domain made up of two components. We prescribe a homogeneous Dirichlet condition on the exterior boundary and a jump of the displacement proportional to the conormal derivatives on the interface. This last condition is the mathematical interpretation of an imperfect interface. We apply a control on the external boundary and, by means of the Hilbert Uniqueness Method, introduced by J. L. Lions, we study the related boundary exact controllability problem. The key point is to derive an observability inequality by using the so called Lagrange multipliers method, and then to construct the exact control through the solution of an adjoint problem. Eventually, we prove a lower bound for the control time which depends on the geometry of the domain, on the coefficients matrix and on the proportionality between the jump of the solution and the conormal derivatives on the interface.