Subjects -> MATHEMATICS (Total: 1013 journals)     - APPLIED MATHEMATICS (92 journals)    - GEOMETRY AND TOPOLOGY (23 journals)    - MATHEMATICS (714 journals)    - MATHEMATICS (GENERAL) (45 journals)    - NUMERICAL ANALYSIS (26 journals)    - PROBABILITIES AND MATH STATISTICS (113 journals) MATHEMATICS (714 journals)                  1 2 3 4 | Last

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 Bollettino dell'Unione Matematica ItalianaJournal Prestige (SJR): 0.676 Citation Impact (citeScore): 1Number of Followers: 0      Subscription journal ISSN (Print) 1972-6724 - ISSN (Online) 2198-2759 Published by Springer-Verlag  [2467 journals]
• Old perturbative methods for a new problem in Celestial Mechanics: the
space debris dynamics

Abstract: Abstract Perturbative methods have been developed and widely used in the XVIII and XIX century to study the behavior of N-body problems in Celestial Mechanics. Such methods apply to nearly-integrable Hamiltonian systems and they have the remarkable property to be constructive. A well-known application of perturbative techniques is represented by the construction of the so-called proper elements, which are quasi-invariants of the dynamics, obtained by removing the perturbing function to higher orders. They have been used to identify families of asteroids; more recently, they have been used in the context of space debris, which is the main core of this work. We describe the dynamics of space debris, considering a model including the Earth’s gravitational attraction, the influence of Sun and Moon, and the Solar radiation pressure. We construct a Lie series normalization procedure and we compute the proper elements associated to the orbital elements. To provide a concrete example, we analyze three different break-up events with nearby initial orbital elements. We use the information coming from proper elements to successfully group the fragments; the clusterization is supported by statistical data analysis and by machine learning methods. These results show that perturbative methods still play an important role in the study of the dynamics of space objects.
PubDate: 2023-01-24

• Reversibility, irreversibility, friction and nonequilibrium ensembles in
N–S equations

Abstract: Abstract Viscosity, as a physical property of fluids, reflects an average effect over a chaotic microscopic motion described by Hamiltonian equations. It is proposed, as an example, that stationary states of an incompressible fluid subject to a constant force, can be described via several ensembles, in strict analogy with equilibrium Statistical Mechanics.
PubDate: 2023-01-18

• Some fixed point theorems and applications in Busemann spaces

Abstract: Abstract In this paper, we prove a generalized version of the Darbo–Sadovskii fixed point theorem in Busemann spaces and as an application, we prove the famous Petryshyn’s theorem for k-set contraction in hyperbolic spaces for $$k\in [0,\frac{1}{2})$$ . We also obtain fixed point results for certain general classes of mappings in Busemann spaces.
PubDate: 2023-01-17

• Chaotic light scattering around extremal black holes

Abstract: Abstract We show that the scattering of light in the field of $$N\ge 3$$ static extremal black holes is chaotic in the planar case. The relativistic dynamics of such extremal objects reduce to that of a classical Hamiltonian system. Certain values of the dilaton coupling then allow one to apply techniques from symbolic dynamics and classical potential scattering. This results in a lower bound on the topological entropy of order $$\log (N-1)$$ , thus proving the emergence of chaotic scattering for $$N \ge 3$$ black holes.
PubDate: 2023-01-05

• Normal form and dynamics of the Kirchhoff equation

Abstract: Abstract We summarize some recent results on the Cauchy problem for the Kirchhoff equation \begin{aligned} \partial _{tt} u - \Delta u \Bigg ( 1 + \int _{{{\mathbb {T}}}^d} \nabla u ^2 \Bigg ) = 0 \end{aligned} on the d-dimensional torus $${{\mathbb {T}}}^d$$ , with initial data u(0, x), $$\partial _t u(0,x)$$ of size $$\varepsilon$$ in Sobolev class. While the standard local theory gives an existence time of order $$\varepsilon ^{-2}$$ , a quasilinear normal form allows to give a lower bound on the existence time of the order of $$\varepsilon ^{-4}$$ for all initial data, improved to $$\varepsilon ^{-6}$$ for initial data satisfying a suitable nonresonance condition. We also use such a normal form in an ongoing work with F. Giuliani and M. Guardia to prove existence of chaotic-like motions for the Kirchhoff equation.
PubDate: 2022-12-29

• Stochastic and statistical stability of the classical Lorenz flow under
perturbations modeling anthropogenic type forcing

Abstract: Abstract We review the results obtained in Gianfelice et al. (Commun Math Phys 313:745–779, 2012) and Gianfelice and Vaienti (J Stat Phys 181(1):163–211, 2020) on the stochastic and statistical stability of the classical Lorenz flow, where, looking at the Lorenz’63 ODE system as a simple—yet non trivial—model of the atmospheric circulation, the perturbation schemes introduced in these papers are designed to represent the effect of the so called anthropogenic forcing on the dynamic of the atmosphere.
PubDate: 2022-12-28

• On $$\alpha -$$ Bézier curves and surfaces

Abstract: Abstract In the given note, we present the generalization of Bézier curves depending upon the parameter $$\alpha$$ , named as $$\alpha -$$ Bézier curves. Also, we introduce tensor product $$\alpha -$$ Bézier surfaces. We study some properties and degree elevation of these curves and surfaces. In the end, we show that the parameter provides us the flexibility to modify the curves as well as surfaces. To present it, we give some numerical examples with the help of Matlab.
PubDate: 2022-12-10

• Corrected iteration

Abstract: Abstract For $$\lambda$$ inaccessible, we may consider $$(<\lambda )$$ -support iteration of some definable in fact specific $$(<\lambda )$$ -complete $$\lambda ^+$$ -c.c. forcing notions. But do we have “preservation by restricting to a sub-sequence of the iterated forcing"' To regain it we “correct" the iteration. We prove this for a characteristic case for iterations which holds by “nice” for $$\lambda = \aleph _{0}.$$ This is done generally in a work H. Horowitz and the author Shelah. This work is use in a work of the author in (Trans Am Math Soc 373(8):5351–5369, arXiv:0904.0817, 2020) where we use so called strongly $$(< \lambda ^{+})$$ -directed $${\textbf{m}}.$$ We could here restrict ourselves to reasonable $${\textbf{m}}$$ (see 2.13(3)).
PubDate: 2022-12-04

• Correction to: ACM curves in multiprojective spaces

Abstract: A Correction to this paper has been published: 10.1007/s40574-022-00319-7
PubDate: 2022-12-01
DOI: 10.1007/s40574-022-00321-z

• Affine mobi spaces

Abstract: Abstract The category of mobi algebras has been introduced as a model to the unit interval of real numbers. The notion of mobi space over a mobi algebra has been proposed as a model for spaces with geodesic paths. In this paper we analyse the particular case of affine mobi spaces and show that there is an isomorphism of categories between modules over unitary rings with 1/2 and pointed affine mobi spaces over mobi algebras with 2.
PubDate: 2022-12-01
DOI: 10.1007/s40574-022-00324-w

• Nonlinear weighted elliptic equations with Sobolev weights

Abstract: Abstract In this paper we are going to prove existence of solutions in $$W_{0}^{1,p}(\Omega )$$ for the weighted elliptic equation \begin{aligned} \left\{ \begin{array}{ll} -\mathrm{div}(s(x)\, \nabla u ^{p-2}\,\nabla u) = f(x) &{}\quad \text{ in } \Omega ,\\ u = 0 &{}\quad \text{ on } \partial \Omega , \end{array} \right. \end{aligned} under the assumption that the weight function s(x) is strictly positive and belongs to $$W^{1,p}(\Omega )$$ . The proof will be based on a new technique, which takes advantage of the fact that s(x) is in a Sobolev space, and that will also be applied to other equations.
PubDate: 2022-12-01
DOI: 10.1007/s40574-021-00314-4

• Intervals of varieties of involution semigroups with contrasting reduct
intervals

Abstract: Abstract It is known that the lattice structure of an interval of varieties of involution semigroups can be very different from that of its reduct interval of varieties of semigroups, but it is uncertain how wide this difference can be. The present article exhibits intervals to show that the difference can be between being a two-element chain and having an infinite chain. These intervals are bounded by varieties generated by an involution semigroup of order between four and six. One of the involution semigroups of order four turns out to be a smallest involution semigroup to generate a non-Specht variety. In contrast, it is long known that every semigroup of order up to four generates a Specht variety.
PubDate: 2022-12-01
DOI: 10.1007/s40574-022-00317-9

• Convergence theorems for solving a system of pseudomonotone variational
inequalities using Bregman distance in Banach spaces

Abstract: Abstract In this paper, we present two new parallel Bregman projection algorithms for finding a common solution of a system of pseudomonotone variational inequality problems in a real reflexive Banach space. The first algorithm combines a parallel Bregman subgradient extragradient method with the Halpern iterative method for approximating a common solution of variational inequalities in reflexive Banach spaces. The second algorithm involves a parallel Bregman subgradient extragradient method, Halpern iterative method and a line search procedure which aims to avoid the condition of finding prior estimate of the Lipschitz constant of each cost operator. Two strong convergence results were proved under standard assumptions imposed on the cost operators and control sequences. Finally, we provide some numerical experiments to illustrate the behaviour of the sequences generated by the proposed algorithms.
PubDate: 2022-12-01
DOI: 10.1007/s40574-022-00322-y

• The first cohomology group and weak amenability of a Morita context Banach
algebra

Abstract: Abstract Motivated by the elaborate works of Forrest, Marcoux, and Zhang [Trans. Amer. Math. Soc. 354 (2002), 1435–1452 and 4131–4151] on determining the first cohomology group and studying n-weak amenability of triangular and module extension Banach algebras, we investigate the same notions for a Morita context Banach algebra $$\mathbb {G}=\left[ \begin{array}{cc} \mathbb {A}&{} \ \mathbb {M}\\ \mathbb {N}&{} \ \mathbb {B}\end{array} \right] ,$$ where $$\mathbb {A}$$ and $$\mathbb {B}$$ are Banach algebras, $$\mathbb {M}$$ and $$\mathbb {N}$$ are Banach $$(\mathbb {A},\mathbb {B})$$ and $$(\mathbb {B},\mathbb {A})$$ -bimodules, respectively. We describe the $$n^{\text {t}h}$$ -dual $$\mathbb {G}^{(n)}$$ of $$\mathbb {G}$$ and characterize the structure of derivations from $$\mathbb {G}$$ to $$\mathbb {G}^{(n)}$$ for studying the first cohomology group $$\mathbf{H}^1\left( \mathbb {G}, \mathbb {G}^{(n)}\right)$$ and characterizing the n-weak amenability of $$\mathbb {G}$$ . Our study provides some improvements of certain known results on the triangular Banach algebras. The results are then applied to the full matrix Banach algebras $$\mathbb {M}_k(\mathbb {A})$$ . Some examples illustrating the results are also included, and several questions are also left undecided.
PubDate: 2022-12-01
DOI: 10.1007/s40574-022-00320-0

• Hilbert’s $$19{\text {th}}$$ problem revisited

Abstract: Abstract In this survey article we revisit Hilbert’s 19th problem concerning the regularity of minimizers of variational integrals. We first discuss the classical theory (that is, the statement and resolution of Hilbert’s problem in all dimensions). We then discuss recent results concerning the regularity of minimizers of degenerate convex functionals. Finally, we discuss some open problems. Exercises are included for the benefit of researchers who are entering the subject.
PubDate: 2022-12-01
DOI: 10.1007/s40574-021-00315-3

• ACM curves in multiprojective spaces

Abstract: Abstract We consider arithmetically Cohen–Macaulay (shortened to ACM) curves in a multiprojective space Y, i.e. curves $$T\subset Y$$ such that the restriction map $$H^0(L)\rightarrow H^0(L_{ T})$$ is surjective for all line bundles L on Y such that $$H^0(L)\ne 0$$ . We prove that there are many such curves if all factors have dimension at least 3, but that T strongly resembles a rational normal curve if Y has $$\mathbb {P}^1$$ as one of its factors.
PubDate: 2022-12-01
DOI: 10.1007/s40574-022-00319-7

• A priori Lipschitz estimates for nonlinear equations with mixed local and
nonlocal diffusion via the adjoint-Bernstein method

Abstract: Abstract We establish a priori Lipschitz estimates for equations with mixed local and nonlocal diffusion, coercive gradient terms and unbounded right-hand side in Lebesgue spaces through an integral refinement of the Bernstein method. This relies on a nonlinear, nonlocal and variational version of the Bochner identity that involves the adjoint equation of the linearization of the initial problem.
PubDate: 2022-11-05
DOI: 10.1007/s40574-022-00340-w

• Some remarks on the periodic motions of a bouncing ball

Abstract: Abstract We consider the vertical motion of a free falling ball bouncing elastically on a racket moving in the vertical direction according to a regular 1-periodic function f. For fixed coprime p, q we study existence, stability in the sense of Lyapunov and multiplicity of p periodic motions making q bounces in a period. If f is real analytic we prove that one periodic motion is unstable and give some information on the set of these motions.
PubDate: 2022-10-28
DOI: 10.1007/s40574-022-00339-3

• Uniqueness of hypersurfaces in weighted product spaces via maximum
principles for the drift Laplacian

Abstract: Abstract We apply suitable maximum principles for the drift Laplacian to obtain several uniqueness results concerning complete two-sided hypersurfaces immersed with constant f-mean curvature in a weighted product space of form $${\mathbb {R}}\times M_{f}^{n}$$ and such that its potential function f does not depend on the parameter $$t\in {\mathbb {R}}$$ . Among these results, we prove that the slices are the only complete two-sided f-minimal hypersurfaces lying in a half-space of $${\mathbb {R}}\times M_{f}^{n}$$ and such that the Bakry–Émeri–Ricci tensor is bounded from below. Furthermore, we study the f-mean curvature equation related to entire graphs defined on the base $$M^{n}$$ .
PubDate: 2022-10-11
DOI: 10.1007/s40574-022-00337-5

• Statistical and transport properties of a one-dimensional random walk with
periodically distributed trapping intervals

Abstract: Abstract Following the kind invitation of the organizers of the Fourth DinAmicI Day, I gave on December, 17, 2021, a talk concerning the study of a random walk model in a trapping environment. This paper contains an extended summary of our main results. We will describe statistical and transport properties for sequences of i.i.d. jumps with finite variance in the presence of periodically distributed traps of finite size on the real line. In particular, we will emphasise connections with strongly chaotic deterministic systems and other stochastic processes.
PubDate: 2022-10-07
DOI: 10.1007/s40574-022-00336-6

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