Mediterranean Journal of Mathematics最新文献

This paper is concerned with the existence and stability of quasi-periodic solutions for the Navier–Stokes equation on irrational tori. We prove the persistence of quasi-periodic invariant tori under the small quasi-periodic external force. Furthermore, we obtain the orbital and asymptotic stability in the appropriate Sobolev space. Using the norm estimate of the heat propagator (textrm{e}^{tDelta _{alpha }}), we get the solutions convergence exponentially to the invariant tori as (trightarrow infty ), with the rate of convergence (O(textrm{e}^{-rho t})) for any (rho in (0,1)).

In this paper, we study conformal bi-slant Riemannian submersions from locally product manifolds onto Riemannian manifold as a generalization of invariant, anti-invariant, semi-invariant, slant, semi-slant and hemi-slant Riemannian submersions. We investigate the geometry of foliations determined by vertical and horizontal distributions, and obtain the geometry of leaves of these distributions. In the end, we give a non-trivial example.

We characterize Saphar’s approximation property of order p in terms of a density of finite rank operators in the space of absolutely p-summing operators. We also study the approximation property of the tensor norm associated with the ideal of p-dominated operators.

Given a representation (varphi :B_n rightarrow G_n) of the braid group (B_n), (n ge 2) into a group (G_n), we are considering the problem of whether it is possible to extend this representation to a representation (Phi :SM_n rightarrow A_n), where (SM_n) is the singular braid monoid and (A_n) is an associative algebra, in which the group of units contains (G_n). We also investigate the possibility of extending the representation (Phi :SM_n rightarrow A_n) to a representation (widetilde{Phi } :SB_n rightarrow A_n) of the singular braid group (SB_n). On the other hand, given two linear representations (varphi _1, varphi _2 :H rightarrow GL_m(Bbbk )) of a group H into a general linear group over a field (Bbbk ), we define the defect of one of these representations with respect to the other. Furthermore, we construct a linear representation of (SB_n) which is an extension of the Lawrence–Krammer–Bigelow representation (LKBR) and compute the defect of this extension with respect to the exterior product of two extensions of the Burau representation. Finally, we discuss how to derive an invariant of classical links from the Lawrence–Krammer–Bigelow representation.

Previously, we found the strongly continuous semigroups governing

for (x,tge 0) and (a=0,1). In this paper, we do this for a variant of the above equation where (a=frac{1}{2}.) We also deal with nonautonomous versions having governing operators such as

Here (alpha , theta ,) and r are real-valued continuous functions in ([0,+infty )), (alpha (t)>0, ) (theta (t)ge 0,, r(t)ge 0,) for any (tge 0.) When (theta =0=r) on ([0,infty )), the corresponding equation reduces to a nonautonomous version of the Cox–Ingersoll–Ross (CIR) bond equation.

The objective of this study is iterative systems based on general types of curves, not only on circumference arcs. We begin by presenting some implementations and generalizations of constructions based on arcs of circumference. Then we consider constructions based on general curves and give a “universal property” relating to the primary construction that exploits arcs of circumference. With the prospect of applying these theoretical models also to coastal geomorphology in the future, and inspired by one of the best-known models on the subject, the logarithmic spiral one for the so-called headland-bay beaches (HBBs), we study geometrically some cases in which the constructions are based on arcs of the golden spiral. Simultaneously we concretely illustrate and explain the universal property above. Finally we dedicate a section to discuss the possibility of how to numerically evaluate and compare the (infinite) lengths originating from our theoretical geometric constructions. Some explicit examples, calculations and comparisons will be provided by the use of infinity computing which is one of the various possible assets that contemporary non-standard mathematics makes available.

In this paper, the boundedness and compactness of generalized integration operators (T_g^{n,k}) between different analytic tent spaces in the unit disc are completely characterized.

This paper is concerned with the existence of a closed trajectory of an autonomous planar system with constraints. In contrast to previously known results, we do not require the constraint to be convex.

In this paper, we focus on the existence of strict solutions to a class of differential equations with state-dependent nonlocal conditions. Using fixed point theorems and general Gronwall inequality, we give some new conclusions. Moreover, an example is given to illustrate our conclusions valuable.

In our previous work, we have studied the limit cycles for a class of discontinuous piecewise quadratic polynomial differential systems with a non-regular line of discontinuity, which is formed by two rays starting from the origin and forming an angle (alpha = pi /2). The unperturbed system is the quadratic uniform isochronous center (dot{x} = -y + x y), (dot{y} = x + y^2) with a family of periodic orbits surrounding the origin. In this paper, we continue to investigate this kind of piecewise differential systems, but now the angle between the two rays is (alpha in (0,pi /2)cup [3pi /2,2pi )). Using the Chebyshev theory, we prove that the maximum number of hyperbolic limit cycles that can bifurcate from these periodic orbits using the averaging theory of first order is exactly 8 for (alpha in (0,pi /2)cup [3pi /2,2pi )). Together with our previous work, which concerns on the case of (alpha =pi /2), we can conclude that using the averaging theory of first order the maximum number of hyperbolic limit cycles is exactly 8, when this quadratic center is perturbed inside the above-mentioned classes separated by a non-regular line of discontinuity with (alpha in (0,pi /2]cup [3pi /2,2pi )).