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This paper presents a new method to prove the nonuniform dichotomy spectrum theorem. Chu et al. [Bull. Sci. Math. 139 (2015), pp. 538-557] and Zhang [J. Funct. Anal. 267 (2014), pp. 1889-1916] generalized the dichotomy spectrum in Siegmund [J. Dynam. Differential Equations 14 (2002), pp. 243-258] to the nonuniform dichotomy spectrum and the authors in these works employed linear integral manifolds (stable and unstable) to establish the spectral theorem. They then used the spectrum theorem to study reducibility. We prove the nonuniform dichotomy spectrum by way of contradiction. In particular, we employ the nonuniform kinematically similarity (nonuniform reducibility) to reduce the shift system into two blocks and then we get a contradiction based on a technique in mathematical analysis. The method in the proof is completely different from previous works. [ABSTRACT FROM AUTHOR]

This paper compares two models of the equivariant homotopy type of the smash powers of a spectrum, namely the "Bökstedt smash product" and the Hill-Hopkins-Ravenel norm. [ABSTRACT FROM AUTHOR]

In a paper by J. V. Pereira and the author it was proved that any pencil of plane curves of degree $d>1$ with irreducible generic fiber can have at most five completely reducible fibers although no examples with five such fibers had ever been found. Recently Janis Stipins has proved that if a pencil has a base of $d^2$ points, then it cannot have five completely reducible fibers. In this paper we generalize Stipins' result to arbitrary pencils. We also include into consideration more general special fibers that are the unions of lines and non-reduced curves. These fibers are important for characteristic varieties of hyperplane complements. [ABSTRACT FROM AUTHOR]

The result stated in the title is proved, thereby disproving the result shown in a 1983 paper by B. A. Barnes (Theorem 4.1). [ABSTRACT FROM AUTHOR]

Let A be an operator algebra on a Hilbert space. We say that an element G ? A is an all-derivable point of A if every derivable linear mapping ? at G (i.e. ?(ST) = ?(S)T + S?(T) for any S, T ∊ algN with ST = G) is a derivation. Suppose that N is a nontrivial complete nest on a Hilbert space H. We show in this paper that G ∊ algN is an all-derivable point if and only if G ≠ 0. [ABSTRACT FROM AUTHOR]

This paper discusses the twisted conjugacy classes in loop groups. We restrict to classical groups and give some explicit classifications. [ABSTRACT FROM AUTHOR]

In this paper, we compare the virtual fundamental classes of the stacks of (g, β, μ)-stable ramified maps ,Ug, μ(X, β) and of (g, β, μ)-log stable ramified maps Ulog g,μ(X, β). For that we will see how they are identified via virtual normalization and then apply Costello's push-forward formula. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to explicitly describe in terms of generators and relations the universal central extension of the infinite dimensional Lie algebra, $ \mathfrak{g}\otimes \mathbb{C}[t,t^{-1},u\vert u^2=(t^2-b^2)(t^2-c^2)]$ [ABSTRACT FROM AUTHOR]

In this paper we study an operator $ T$ which is $ M$ of $ E$-hypercyclic and use it to answer negatively two questions asked by Madore and Martínez-Avendaño. We also give a sufficient condition for $ T$-hypercyclic for all finite co-dimensional subspaces $ M$. [ABSTRACT FROM AUTHOR]

In this paper, a nonlinear version of the Extrapolation Theorem is proved and, as a corollary, a nonlinear version of Grothendieck's Theorem is presented. Finally, we prove that if $ T:X\to H$ being a pointed metric space and $ T(0)=0$ $ T^\char93 \vert _{H^*}$-summing $ (1\le q<\infty)$ is Lipschitz 1-summing. [ABSTRACT FROM AUTHOR]

In this paper, we compute the second variational formula for the functional $ \int_M v^{(6)}(g)dv_g$) is a strict local maximum within its conformal class unless the manifold is isometric to a round sphere with the standard metric up to a multiple of a constant. [ABSTRACT FROM AUTHOR]

In this paper, we use the Perron method to prove the existence of viscosity solutions with asymptotic behavior at infinity to Hessian equations. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to prove that there exist measures $ d\mu(x)=\gamma(x)dx$ $ \gamma(x)=\gamma_{0}(\vert x\vert)$ $ \gamma_{0}$ $ \mathcal{M}_{\mu}$ does not map $ L^{p}_{\mu}(\mathbb{R}^{n})$ $ L^{p}_{\mu}(\mathbb{R}^{n})$. This result answers an open question of P. Sjögren and F. Soria. [ABSTRACT FROM AUTHOR]

This paper is devoted to a study of geodesics of Finsler metrics via Zermelo navigation. We give a geometric description of the geodesics of the Finsler metric produced from any Finsler metric and any homothetic field in terms of navigation representation, generalizing a result previously only known in the case of Randers metrics with constant $ S$ [ABSTRACT FROM AUTHOR]