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 Annali dell'Universita di FerraraJournal Prestige (SJR): 0.429 Number of Followers: 0      Hybrid journal (It can contain Open Access articles) ISSN (Print) 0430-3202 - ISSN (Online) 1827-1510 Published by Springer-Verlag  [2658 journals]
• Generalization of Titchmarsh theorem in the deformed Hankel setting

Abstract: In this paper, by using the generalized symmetric difference $$\Delta _{h}^{m}$$ of order m and step $$h>0$$ , we obtain a generalization of Titchmarsh’s Theorem for deformed Hankel transform.
PubDate: 2021-10-11

• Multiplicative Lie triple derivation of triangular 3-matrix rings

Abstract: Let $${\mathfrak {T}}={\mathfrak {T}}_3(\mathrm {R}_i, \mathrm {M}_{ij})$$ be a triangular 3-matrix ring. In the present paper, we study of multiplicative Lie triple derivation on triangular 3-matrix rings and prove that every multiplicative Lie triple derivation on triangular 3-matrix rings can be written as a sum of an additive derivation and a center valued map vanishing at each second commutator.
PubDate: 2021-09-25

• On an operator preserving inequalities between polynomials

Abstract: Let P(z) be a polynomial of degree at most n. We consider an operator N, which carries a polynomial P(z) into \begin{aligned} N[P](z):=\sum \limits _{j=0}^{m}\lambda _j\bigg (\frac{nz}{2}\bigg )^j\frac{P^{(j)}(z)}{j!}, \end{aligned} where $$\lambda _0,\lambda _1,\ldots ,\lambda _m$$ are such that all the zeros of \begin{aligned} u(z)=\sum \limits _{j=0}^{m}\left( {\begin{array}{c}n\\ j\end{array}}\right) \lambda _jz^j \end{aligned} lie in the half plane \begin{aligned} z \le \bigg z-\frac{n}{2}\bigg . \end{aligned} In this paper, we estimate the minimum and maximum modulii of N[P(z)] on $$z =1$$ with restrictions on the zeros of P(z) and thereby obtain compact generalizations of some well known polynomial inequalities.
PubDate: 2021-09-20

• On the irreducibility of the extensions of Burau and Gassner
representations

Abstract: Let $$Cb_n$$ be the group of basis conjugating automorphisms of a free group $$\mathbb {F}_n$$ , and $$C_n$$ the group of conjugating automorphisms of $$\mathbb {F}_n$$ . Valerij G. Bardakov has constructed representations of $$Cb_n$$ , $$C_n$$ in the groups $$GL_n(\mathbb {Z}[{t_1}^{\pm 1}, \ldots ,{t_n}^{\pm 1}])$$ and in $$GL_n(\mathbb {Z}[{t}^{\pm 1}])$$ respectively, where $$t_1, \ldots , t_n, t$$ are indeterminate variables. We show that these representations are reducible and we determine the irreducible components of the representations in $$GL_n(\mathbb {C})$$ , which are obtained by giving values to the variables above. Next, we consider the tensor product of the representations of $$Cb_n$$ , $$C_n$$ and study their irreduciblity in the case $$n=3$$ .
PubDate: 2021-09-18

• A family of derivative-free methods for solving nonlinear equations

Abstract: We propose a two-parameter derivative-free family of methods with memory of convergence order 1.84 for finding the real roots of nonlinear equations. The new methods require only one function evaluation per iteration, so efficiency index is also 1.84. The process is carried out by approximating the derivative in Newton’s iteration using general quadratic equation $$\alpha u^2+\beta v^2+\alpha _1 u+\beta _1 v+\delta =0$$ in terms of coefficients $$\alpha , \beta$$ . Various options of $$\alpha , \beta$$ correspond to various quadratic forms viz. circle, ellipse, hyperbola and parabola. The application of new methods is validated on Kepler’s problem, Isentropic supersonic flow problem, L-C-R circuit problem and Population growth problem. In addition, a comparison of the performance of new methods with existing methods of same nature is also presented to check the consistency.
PubDate: 2021-09-13

• Attractors for Navier–Stokes equation with fractional operator in
the memory term

Abstract: In this paper, we study the long-time dynamics of Navier–Stokes equations with a fractional operator in the memory term and external forces \begin{aligned} \partial _tu-\nu \Delta u +\displaystyle \int _{0}^{\infty }g(s)(-\Delta )^\alpha u(t-s)\,\mathrm{d}s +(u\cdot \nabla )u+\nabla p=\epsilon f(x) \end{aligned} on a bounded domain $$\Omega$$ in $$\mathbb {R}^2$$ with smooth boundary. We establish the existence of global attractor for the associated dynamical system. We prove the continuity of global attractors with respect to forcing parameter $$\epsilon$$ in a residual dense set. Moreover, the upper-semicontinuity with respect to parameter $$\epsilon$$ of global attractors is shown.
PubDate: 2021-08-21

• Stability analysis for a multi-layer Hele-Shaw displacement

Abstract: A well known approximation for the displacement of two immiscible fluids in a porous medium is the Hele-Shaw model. In experiments it was observed that a liquid with variable viscosity, introduced between the two initial fluids, can minimize the Saffman-Taylor instability. In some works an attempt was made to replace the variable viscosity liquid with a sequence of several immiscible liquids with constant viscosities. We prove that the linear stability analysis of this multi-layer Hele-Shaw model leads us to an ill-posed problem.
PubDate: 2021-08-11

• Initial value problems of nonlinear fractional differential equations with
two orders

Abstract: In this paper, we use the fixed point theory to obtain the existence and uniqueness of solutions for a class of nonlinear fractional differential equations. Two examples are given to illustrate this work.
PubDate: 2021-08-07

• Helicity and regularity of weak solutions to 3D Navier–Stokes
equations

Abstract: We show that a Leray–Hopf weak solution to the three-dimensional Navier–Stokes the initial value problem is regular in (0, T] if $$\Vert \nabla u_0^+\Vert _2$$ (or $$\Vert \nabla u_0^-\Vert _2$$ ) for initial value $$u_0$$ and $$\max \{\frac{d{\mathcal H}}{dt},0\}$$ (or $$\max \{-\frac{d{\mathcal H}}{dt},0\}$$ ) are suitably small depending on the initial kinetic energy and viscosity, where $$u_0^+=\int _0^{\infty } dE_\lambda u_0$$ , $$u_0^-=\int _{-\infty }^0 dE_\lambda u_0$$ , $$\{E_\lambda \}_{\lambda \in {\mathbb R}}$$ is the spectral resolution of the $$\mathrm{curl}$$ operator and $${\mathcal H}\equiv \int _{\mathbb R^3}u\cdot \mathrm{curl} u\,dx$$ is the helicity of the fluid flow. The results suggest that the helicity change rate rather than the magnitude of the helicity itself affects regularity of the viscous incompressible flows. More precisely, an initially regular viscous incompressible flow with suitably small positive or negative maximal helical component does not lose its regularity as long as the total helical behavior of the flow with respect to time is not decreasing, or even weakened at a moderate rate in accordance with the initial kinetic energy and viscosity.
PubDate: 2021-07-31

• Rings with fine nilpotents

Abstract: A nonzero sum of a unit and a nilpotent element in a ring is called a fine element. This is a study of rings in which every nonzero nilpotent is fine, which we call NF rings.
PubDate: 2021-07-06

• Space curves, X-ranks and cuspidal projections

Abstract: Let $$X\subset \mathbb {P}^3$$ be an integral and non-degenerate curve. We say that $$q\in \mathbb {P}^3\setminus X$$ has X-rank 3 if there is no line $$L\subset \mathbb {P}^3$$ such that $$q\in L$$ and $$\#(L\cap X)\ge 2$$ . We prove that for all hyperelliptic curves of genus $$g\ge 5$$ there is a degree $$g+3$$ embedding $$X\subset \mathbb {P}^3$$ with exactly $$2g+2$$ points with X-rank 3 and another embedding without points with X-rank 3 but with exactly $$2g+2$$ points $$q\in \mathbb {P}^3$$ such that there is a unique pair of points of X spanning a line containing q. We also prove the non-existence of points of X-rank 3 for general curves of bidegree (a, b) in a smooth quadric (except in known exceptional cases) and we give lower bounds for the number of pairs of points of X spanning a line containing a fixed $$q\in \mathbb {P}^3\setminus X$$ . For all integers $$g\ge 5$$ , $$x\ge 0$$ we prove the existence of a nodal hyperelliptic curve X with geometric genus g, exactly x nodes, $$\deg (X) = x+g+3$$ and having at least $$x+2g+2$$ points of X-rank 3.
PubDate: 2021-07-01

• Asymptotic modeling of the behavior of a reinforced plate governed by a
full von Karman thermo-elastic system with nonlinear thermal coupling

Abstract: In this paper, we deal with the asymptotic modeling of the behavior of a reinforced rectangular plate with a thin layer of high thermal conductivity. We focus on a thermo-elastic model described by a set of nonlinear time dependent partial differential equations, accounting for nonlinear mechanical and nonlinear thermal coupling. Our aim is to model this junction and reproduce the effect of the thin body by means of approximate boundary conditions, obtained by an asymptotic analysis with respect to the thickness of this latter. The study is carried out for two kinds of layers: Stiff and soft. Different limit behaviors occur according to the rigidity or the softness of this latter.
PubDate: 2021-06-12

• Space-time decay rate for Navier–Stokes equations with power-law
type nonlinear viscous fluid

Abstract: We investigate the space-time decay properties for strong solutions to the 3D Navier–Stokes equations with power-law type nonlinear viscous fluid. Based on the temporal decay results for this equation, we find that one can obtain decay estimate of the weight for the velocity field u by direct weighted energy estimate.
PubDate: 2021-05-31

• On the decay of a nonlinear wave equation with delay

Abstract: In this paper we consider wave equation with logarithmic nonlinearity and distributive internal delay. We establish the local existence result using the semigroup theory whereas the global existence by the well-depth method. Finally, under suitable assumptions on the weight of the delay and that of frictional damping, we prove that the system is exponentially stable.
PubDate: 2021-05-26

• Approximation by modified Szász-Kantorovich type operators based on
Brenke type polynomials

Abstract: In this paper, a modification of Szász-Kantorovich type operators based on Brenke-type polynomials is introduced, and the convergence properties of the proposed operators with the help of Korovkin’s theorem are discussed. The order of convergence of these operators with the aid of classical and second-order modulus of continuity is studied. A Voronovkaja-type theorem is also established. Lastly, the rate of convergence and error estimation of these operators compared with the existing operators with the help of some graphs and tables using Mathematica.
PubDate: 2021-05-22

• Perturbation bounds for angular sectors of spectra of unbounded operators

Abstract: Let A and $$\tilde{A}$$ be linear unbounded in general operators on a Hilbert space. We consider the following problem: let the spectrum of A lie in some angular sector. In what sector the spectrum of $$\tilde{A}$$ lies, if A and $$\tilde{A}$$ are sufficiently “close”' Illustrative examples are also presented.
PubDate: 2021-05-01

• Exponential stability of thermoelastic Timoshenko system with
Cattaneo’s law

Abstract: In this paper, we consider a one dimensional thermoelastic Timoshenko system where the thermal coupling is acting on both the shear force and the bending moment, and the heat flux is given by Cattaneo’s law. We establish an exponential stability result irrespective of the values of the coefficients of the system.
PubDate: 2021-05-01

• Some inequalities for polynomials with restricted zeros

Abstract: By using the boundary Schwarz lemma, it was shown by Dubinin (J Math Sci 143:3069–3076, 2007) that if P(z) is a polynomial of degree n having all its zeros in $$z \le 1,$$ then for all z on $$z =1$$ for which $$P(z)\ne 0,$$ \begin{aligned} Re\bigg (\frac{zP^{\prime }(z)}{P(z)}\bigg )\ge \frac{n}{2}+\frac{1}{2}\left( \frac{ a_n - a_0 }{ a_n + a_0 }\right) . \end{aligned} In this paper, by using simple techniques we generalize the above inequality, thereby give a simple proof of the above inequality. As an application of our result, we also obtain sharp refinements of some known results due to Malik (J Lond Math Soc 1:57–60, 1969), Aziz and Rather (Math Ineq Appl 1:231–238, 1998). These results take into account the size of the constant term and the leading coefficient of the polynomial P(z).
PubDate: 2021-05-01

• An approach to H-supplemented modules via noncosingular modules

Abstract: Let M be a module over a ring R. We call M, $$\gamma$$ -H-supplemented provided for every submodule N of M there is a direct summand D of M such that $$M=N+X$$ if and only if $$M=D+X$$ for every submodule X of M with M/X noncosingular. We prove that M is $$\gamma$$ -H-supplemented if and only if for every submodule N of M there exists a direct summand D of M such that $$(N+D)/N\ll _{\gamma } M/N$$ and $$(N+D)/D\ll _{\gamma } M/D$$ .
PubDate: 2021-05-01

• Approximating multiple integrals of continuous functions by $$\delta$$
δ -uniform curves

Abstract: We present a method to approximate, with controlled and arbitrarily small error, multiple intregrals over the unit cube $$[0,1]^{d}$$ by a single variable integral over [0, 1]. For this, we use the so called $$\delta$$ -uniform curves, which are a particular case of $$\alpha$$ -dense curves. Our main result improves and extends other existing methods on this subject.
PubDate: 2021-05-01

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