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Abstract: Abstract The present paper attempts to study the almost Ricci solitons in a generalized D-conformally deformed (LCS) \(_{n}\) -manifold considering potential vector field as a solenoidal vector field, a gradient vector field or the Reeb vector field of the deformed structure and explicitly investigate the Ricci and scalar curvatures for some cases. We also determine some inequalities for the Ricci curvature of the deformed (LCS) \(_{n}\) -manifold when it admits a gradient almost Ricci soliton. PubDate: 2022-05-24

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Abstract: Abstract Our aim in this paper is to study the uniqueness of complete spacelike hypersurfaces immersed in the anti-de Sitter space \({{\mathbb {H}}}_1^{n+1}\) , through the behavior of their higher order mean curvatures. This is done by applying a suitable maximum principle concerning smooth vector fields whose norm is Lebesgue integrable on a complete Riemannian manifold. We also infer the nullity of complete r-maximal spacelike hypersurfaces and, in particular, we establish a nonexistence result concerning complete 1-maximal spacelike hypersurfaces in \({{\mathbb {H}}}_1^{n+1}\) . PubDate: 2022-05-18

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Abstract: Abstract This paper provides sufficient conditions for the stability, asymptotic stability, uniform stability, boundedness and uniformly boundedness of solutions of a certain class of second-order nonlinear vector differential equations using the second method of Lyapunov. By constructing a suitable complete Lyapunov function, which serves as a basic tool, we establish the properties mentioned above and thereby improve and complement some known results found in the literature. Lastly, the correctness of our main results is justified by the examples given. PubDate: 2022-05-03

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Abstract: Abstract We investigate the behavior of the solutions of a class of certain strictly hyperbolic equations defined on \((0,T]\times {\mathbb {R}}^n\) in relation to a class of metrics on the phase space. In particular, we study the global regularity and decay issues of the solution to an equation with coefficients polynomially bound in x with their x-derivatives and t-derivative of order \(\text {O}(t^{-\delta }),\delta \in [0,1),\) and \(\text {O}(t^{-1})\) respectively. This type of singular behavior allows coefficients to be either oscillatory or logarithmically bounded at \(t=0\) . We use the Planck function associated with the metric to subdivide the extended phase space and define an appropriate generalized parameter dependent symbol class. We report that the solution experiences a finite loss in the Sobolev space index in relation to the initial datum defined in the Sobolev space tailored to the metric. Our analysis suggests that an infinite loss is quite expected when the order of singularity of the first time derivative of the leading coefficients exceeds \(O(t^{-1})\) . We confirm this by providing a counterexample. Further, using the \(L^1\) integrability of the logarithmic singularity in t and the global properties of the operator with respect to x, we derive an anisotropic cone condition in our setting. PubDate: 2022-05-01

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Abstract: 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: 2022-05-01

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Abstract: Abstract We discuss a notion of weak solution for a semilinear wave equation that models the interaction of an elastic body with a rigid substrate through an adhesive layer, relying on results in [2]. Our analysis embraces the vector-valued case in arbitrary dimension as well as the case of non-local operators (e.g. fractional Laplacian). PubDate: 2022-04-11

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Abstract: Abstract Let R be a prime ring of char \((R)\ne 2\) , \(Q_r\) its right Martindale quotient ring and C its extended centroid, \(f(x_1,\dots , x_n)\) a multilinear polynomial over C that is noncentral-valued on R and F an X-generalized skew derivation of R. If for some \(0\ne a\in R\) , $$\begin{aligned} a[F(f(x_1,\dots , x_n)),f(x_1,\dots , x_n)]\in C \end{aligned}$$ for all \(x_1,\dots , x_n\in R\) , then one of the following holds: There exists \(\lambda \in C\) such that \(F(x) = \lambda x\) for all \(x \in R\) ; There exist \(\lambda \in C\) and \(a'\in Q_r\) such that \(F(x) =a'x+xa'+ \lambda x\) for all \(x \in R\) and \(f(x_1,\dots , x_n)^2\) is central-valued on R; R satisfies \(s_4\) and there exist \(\lambda \in C\) and \(a'\in Q_r\) such that \(F(x) =a'x+xa'+ \lambda x\) for all \(x \in R\) . PubDate: 2022-04-06

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Abstract: Abstract A number of higher order Newton-like methods (i.e. the methods requiring both function and derivative evaluations) are available in literature for multiple zeros of a nonlinear function. However, higher order Traub-Steffensen-like methods (i.e. the methods requiring only function evaluations) for computing multiple zeros are rare in literature. Traub-Steffensen-like iterations are important in the circumstances when derivatives are complicated to evaluate or expensive to compute. Motivated by this fact, here we present an efficient and rapid-converging Traub-Steffensen-like algorithm to locate multiple zeros. The method achieves eighth order convergence by using only four function evaluations per iteration, therefore, this convergence rate is optimal. Performance is demonstrated by applying the method on different problems including some real life models. The computed results are compared with that of existing optimal eighth-order Newton-like techniques to reveal the computational efficiency of the new approach. PubDate: 2022-04-04

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Abstract: Abstract In this paper we have studied the model for arched beams problem $$\begin{aligned}&\rho _{1}\varphi _{tt}-k(\varphi _{x}+\psi +l\omega )_{x}-k_{0}l(\omega _{x}-l\varphi )=0,\\&\rho _{2}\psi _{tt}-b\psi _{xx}+k(\varphi _{x}+\psi +l\omega )+\gamma \theta _{tx}=0,\\&\rho _{1}\omega _{tt}-k_{0}(\omega _{x}-l\varphi )_{x}+kl(\varphi _{x} +\psi +l\omega )=0,\\&\rho _{3}\theta _{tt}-\kappa \theta _{xx}+\beta (g*\theta _{xx})+\gamma \psi _{tx}=0, \end{aligned}$$ which reduces to the classical Timoshenko system when the arch curvature \(l=0\) , the asymptotic stability of one-dimensional Timoshenko system by thermoelasticity of type III was proved by Djebabla and Tatar in Djebabla (J. Dyn. Control Syst. 16(2):189-210, 2010). The subject of this paper is to supplement these previous results by proving that the Bresse system which is considered a generalization of the Timoshenko system, is also subjected to the same sufficient condition that controls the stability of the Timoshenko system and we have shown that (exponential / polynomial) energy stability is achieved in an (exponential and polynomial) kernel function state. PubDate: 2022-04-04

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Abstract: Abstract In this paper we study the initial boundary value problem of a semilinear Klein-Gordon equation with the multiplication of logarithmic and polynomial nonlinearities. By using potential well method and energy method, we obtain the existence of global solutions and finite-time blowup solutions. PubDate: 2022-04-04

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Abstract: Abstract Talenti inequalities are a central feature in the qualitative analysis of PDE constrained optimal control as well as in calculus of variations. The classical parabolic Talenti inequality states that if we consider the parabolic equation \({\frac{\partial u}{\partial t}}-\Delta u=f=f(t,x)\) then, replacing, for any time t, \(f(t,\cdot )\) with its Schwarz rearrangement \(f^\#(t,\cdot )\) increases the concentration of the solution in the following sense: letting v be the solution of \({\frac{\partial v}{\partial t}}-\Delta v=f^\#\) in the ball, then the solution u is less concentrated than v. This property can be rephrased in terms of the existence of a maximal element for a certain order relationship. It is natural to try and rearrange the source term not only in space but also in time, and thus to investigate the existence of such a maximal element when we rearrange the function with respect to the two variables. In the present paper we prove that this is not possible. PubDate: 2022-03-23

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Abstract: Abstract Let X be an irreducible, reduced complex projective hypersurface of degree d. A uniform point for X is a point P such that the projection of X from P has maximal monodromy. We extend and improve some results concerning the finiteness of the locus of non-uniform points for projections of hypersurfaces obtained by the authors and Cuzzucoli (Ann. Mat. Pura ed Appl. 1923, 1–18 (2021)) only for P not contained in X. PubDate: 2022-02-27 DOI: 10.1007/s11565-022-00390-0

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Abstract: Abstract In this paper, we generalize, with respect to the w-operation, the notions of FI-injective and FI-flat modules introduced by L. Mao and N. Ding. Let R be a ring. An R-module M is called w-FI-flat if \(\mathrm{Tor}_{1}^{R}(E,M)=0\) for any absolutely w-pure R-module E, and M is said to be w-FI-injective if \(\mathrm{Ext}_{R}^{1}(E,M)=0\) for any absolutely w-pure R-module E. The introduced modules are studied and compared with other classical modules. Among other things, we show that every module has a w-FI-flat cover. We use also the introduced modules to characterize some well known kind of rings. PubDate: 2022-02-25 DOI: 10.1007/s11565-022-00388-8

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Abstract: Abstract In 2013, Masson and Siljander determined a method to prove that the minimal p-weak upper gradient \(g_{f_\varepsilon }\) for the time mollification \(f_\varepsilon \) , \(\varepsilon >0\) , of a parabolic Newton–Sobolev function \(f\in L^p_\mathrm {loc}(0,\tau ;N^{1,p}_\mathrm {loc}(\Omega ))\) , with \(\tau >0\) and \(\Omega \) open domain in a doubling metric measure space \((\mathbb {X},d,\mu )\) supporting a weak (1, p)-Poincaré inequality, \(p\in (1,\infty )\) , is such that \(g_{f-f_\varepsilon }\rightarrow 0\) as \(\varepsilon \rightarrow 0\) in \(L^p_\mathrm {loc}(\Omega _\tau )\) , \(\Omega _\tau \) being the parabolic cylinder \(\Omega _\tau :=\Omega \times (0,\tau )\) . Their approach involved the use of Cheeger’s differential structure, and therefore exhibited some limitations; here, we shall see that the definition and the formal properties of the parabolic Sobolev spaces themselves allow to find a more direct method to show such convergence, which relies on p-weak upper gradients only and which is valid regardless of structural assumptions on the ambient space, also in the limiting case when \(p=1\) . PubDate: 2022-02-21 DOI: 10.1007/s11565-022-00389-7

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Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

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Abstract: Abstract In the space \(L^{2}({\mathbb {R}}^{2},{\mathcal {H}})\) , using the analog of the Steklov operator, we construct the generalized modulus of smoothness, and also using the Laplacian operator we define the K-functional. The main result of our article is the proof of the equivalence between K-functionals and modulus of smoothness. PubDate: 2022-01-29 DOI: 10.1007/s11565-022-00387-9

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Abstract: Abstract The concept of Hopfian modules has been extensively studied in the literature. In this paper, we introduce and study the notion of \(\delta \) -weakly Hopfian modules. The class of \(\delta \) -weakly Hopfian modules lies properly between the class of Hopfian modules and the class of weakly Hopfian modules. It is shown that over a ring R, every quasi-projective R-module is \(\delta \) -weakly Hopfian iff \(\delta (R)=J(R)\) . We prove that any weak duo module, with zero radical is \(\delta \) -weakly Hopfian. Let M be a module such that M satisfies ascending chain conditions on \(\delta \) -small submodules. Then it is shown that M is \(\delta \) -weakly Hopfian. Some other properties of \(\delta \) -weakly Hopfian modules are also obtained with examples. PubDate: 2022-01-08 DOI: 10.1007/s11565-021-00383-5

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Abstract: Abstract A model for thermal convection with generalized friction is investigated. It is shown that the linear instability threshold is the same as the global stability one. In addition, decay of the energy in the \(L^2\) norm is shown for the perturbation velocity and temperature fields. However, due to the presence of the generalized friction we establish exponential decay in the \(L^{\beta +1}\) norm for the perturbation temperature, where \(\beta >1\) . PubDate: 2021-12-17 DOI: 10.1007/s11565-021-00382-6