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In this paper, we investigate the global asymptotic stability of an age-structured population dynamics model with a Ricker's type of birth function. This model is a hyperbolic partial differential equation with a nonlinear and nonlocal boundary condition. We prove a uniform persistence result for the semiflow generated by this model. We obtain the existence of global attractors and we prove the global asymptotic stability of the positive equilibrium by using a suitable Lyapunov functional. Furthermore, we prove that our global asymptotic stability result is sharp, in the sense that Hopf bifurcation may occur as close as we want from the region global stability in the space of parameter. [ABSTRACT FROM AUTHOR]

In this paper, we consider the anisotropic curvature flow of smooth, origin-symmetric, uniformly convex hypersurfaces in \mathbb {R}^{n+1}. The flow exists for all time and converges smoothly to a solution of the even Orlicz Christoffel-Minkowski problem. Our proof also gives an approach to the solution of the L_p Christoffel-Minkowski problem. [ABSTRACT FROM AUTHOR]

In a recent series of important works Wei-Zhang [Adv. Math. 380 (2021), Paper No. 107606, 45; Proc. Lond. Math. Soc. (3) 124 (2022), pp. 106–131; Laplacian vanishing theorem for quantized singular Liouville equation , Preprint, arXiv:2202.10825, 2022] proved several vanishing theorems for non-simple blow-up solutions of singular Liouville equations. It is well known that a non-simple blow-up situation happens when the spherical Harnack inequality is violated near a quantized singular source. In this article, we further strengthen the conclusions of Wei-Zhang by proving that if the spherical Harnack inequality does hold, there exist blow-up solutions with non-vanishing coefficient functions. [ABSTRACT FROM AUTHOR]

Characterization of simultaneous similarity for commuting m- tuples of operators is an open problem even in finite-dimensional spaces; known as "A wild problem in linear algebra". In this paper we offer a criterion for simultaneous similarity of m-tuples of k-cyclic commuting operators on an arbitrary Banach space. Moreover, we obtain an additional equivalence condition in the case of finite dimensional Banach spaces, which extends the result found by Shekhtman [Math. Stat. 1 (2013), pp. 157–161] for pairs of cyclic commuting matrices. We also present two applications of our results, one in the case of general multiplication operators on Banach spaces of analytic function, and one for m-tuples of commuting square matrices. [ABSTRACT FROM AUTHOR]

It is well-known that the research of linear combination of composition operators has become a topic of increasing interest. Recently, Choe, Koo and Wang proved that the compactness of combinations composition operators induced by the symbols satisfying the condition (CNC) implies that each difference is compact on the weighted Bergman space. Motivated by that work, in this paper, we discuss which difference is compact on the weighted Bergman space when the coefficients do not satisfy the condition (CNC). [ABSTRACT FROM AUTHOR]

Upper triangular, and more generally, block-triangular matrices, are rather important in Linear Algebra, and also in Ring theory, namely in the theory of PI algebras (algebras that satisfy polynomial identities). The group gradings on such algebras have been extensively studied during the last decades. In this paper we prove that for any group grading on a block-triangular matrix algebra, over an arbitrary field, the Jacobson radical is a graded (homogeneous) ideal. As noted by F. Yasumura [Arch. Math. (Basel) 110 (2018), pp. 327–332] this yields the classification of the group gradings on these algebras and confirms a conjecture made by A. Valenti and M. Zaicev [Arch. Math. (Basel) 89 (2007), pp. 33–40]. [ABSTRACT FROM AUTHOR]

In this paper, we give the affirmative answer to a long-standing open problem of Reich in fixed point theory following the restatement of Jachymski. [ABSTRACT FROM AUTHOR]

In this paper, we will compute the non-abelian cohomology of the universal complete curve in positive characteristic. This extends Hain's result on the non-abelian cohomology of generic curves in characteristic zero to positive characteristics. Furthermore, we will prove that the exact sequence of etale fundamental groups of the universal n-punctured curve in positive characteristic does not split. [ABSTRACT FROM AUTHOR]

The intrinsic square functions including the Lusin area function, Littlewood-Paley g-function and g^\ast _\lambda-function dominate pointwisely the classical Littlewood-Paley functions and can be used to characterize the weighted Hardy spaces and more general Musielak-Orlicz Hardy spaces etc. This paper shows that for b\in \mathrm {BMO(\mathbb {R}^n)}, the commutators generated by these intrinsic square functions with b are bounded from H^p_\omega (\mathbb {R}^n) to L^p_\omega (\mathbb {R}^n) for some 0

Let \mathcal M be a semifinite factor with a faithful normal semifinite tracial weight \tau, and \mathscr P the set of all projections in \mathcal M. Denote by \mathscr P_{c} the Grassmann space of all projections in \mathscr P with trace c, where c is a positive real number. A map \psi : \mathscr P_c\rightarrow \mathscr P_c is called an ortho-isomorphism if \psi is a bijection of \mathscr P_c onto \mathscr P_c satisfying, for all P,Q\in \mathscr P_c, P\perp Q if and only if \psi (P)\perp \psi (Q). The aim of this paper is to establish a version of Uhlhorn's theorem in the setting of semifinite factors. We give a complete characterization of ortho-isomorphisms on Grassmann space \mathscr P_c in a semifinite factor. And we show that an ortho-isomorphism \psi : \mathscr P_c\rightarrow \mathscr P_c can be extended to a Jordan *-isomorphism \rho of \mathcal M onto \mathcal M. As an application, we obtain the structure of surjective isometries on \mathscr P_c with respect to strictly increasing unitarily invariant norms. [ABSTRACT FROM AUTHOR]

In this paper, we establish a general recursive formula via the usual telescoping method for certain bilateral truncated sum which may serve as a common source for Ramanujan's {}_1\psi _1, Bailey's very-well-poised {}_6\psi _6, and Rogers' {}_6\phi _5 summation formulas. The corresponding derivations for these summation formulas are presented in details. [ABSTRACT FROM AUTHOR]

This document is a retraction notice published in the Proceedings of the American Mathematical Society. The author, Khadime Salame, apologizes to the mathematical community and withdraws three papers related to fixed point theory. The papers attempted to address the question of whether left amenable semitopological semigroups have a certain fixed point property, but each paper contains errors. The author acknowledges these errors and suggests that Lau's conjecture should be regarded as an open question. The author hopes that this question will be resolved in the future. [Extracted from the article]

In Theorem 0.1 of the paper "A Severi type theorem for surfaces in \mathbb {P}^6" [Proc. Amer. Math. Soc. 149 (2021), pp. 591–605], we claimed to have given a complete classification of smooth surfaces in \mathbb {P}^6 with one 4-secant plane through the general point of \mathbb {P}^6, but the classification is still incomplete. [ABSTRACT FROM AUTHOR]