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Let S be the polynomial ring on the space of non-square generic matrices or the space of odd-sized skew-symmetric matrices, and let I be the determinantal ideal of maximal minors or Pf the ideal of sub-maximal Pfaffians, respectively. Using desingularizations and representation theory of the general linear group we expand upon work of Raicu–Weyman–Witt [Adv. Math. 250 (2014), pp. 596–610] to determine the S-module structures of Ext^j_S(S/I^t, S) and Ext^j_S(S/Pf^t, S), from which we get the degrees of generators of these Ext modules. As a consequence, via graded local duality we answer a question of Wenliang Zhang [J. Pure Appl. Algebra 225 (2021), Paper No. 106789] on the socle degrees of local cohomology modules of the form H^j_\mathfrak {m}(S/I^t). [ABSTRACT FROM AUTHOR]

We show that the celebrated operad of pre-Lie algebras is very rigid: it has no "non-obvious" degrees of freedom from either of the three points of view: deformations of maps to and from the "three graces of operad theory", homotopy automorphisms, and operadic twisting. Examining the latter, it is possible to answer two questions of Markl from 2005 [Czechoslovak Math. J. 57 (2007), pp. 253–268; J. Lie Theory 17 (2007), pp. 241–261], including a Lie-theoretic version of the Deligne conjecture. [ABSTRACT FROM AUTHOR]

Lei and Lin [Comm. Pure Appl. Math. 64 (2011), pp. 1297–1304] have recently given a proof of a global mild solution of the three-dimensional Navier-Stokes equations in function spaces based on the Wiener algebra. An alternative proof of existence of these solutions was then developed by Bae [Proc. Amer. Math. Soc. 143 (2015), pp. 2887–2892], and this new proof allowed for an estimate of the radius of analyticity of the solutions at positive times. We adapt the Bae proof to prove existence of the Lei-Lin solution in the spatially periodic setting, finding an improved bound for the radius of analyticity in this case. [ABSTRACT FROM AUTHOR]

By a classical result of Kadec and Pełczyński (1962), every normalized weakly null sequence in Lp, p > 2, contains a subsequence equivalent to the unit vector basis of ℓ² or to the unit vector basis of ℓp. In this paper we investigate the case 1 ≤ p < 2 and show that a necessary and sufficient condition for the first alternative in the Kadec-Pełczyński theorem is that the limit random measure μ of the sequence satisfies ∫∨x²dμ(x) ∈ Lp/2. [ABSTRACT FROM AUTHOR]

In this paper, we extend the holomorphic L² torsion introduced by Carey, Farber and Mathai to the case without the determinant class condition. We compute the metric variation formula for the holomorphic L² torsion in our case. We also study the asymptotics of the holomorphic L² torsion associated with a power of a positive line bundle. [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]

For a given positive integer m, let A = {0, 1,… , m} and q ∈ (m,m+1). A sequence (ci) = c1c2 …. consisting of elements in A is called an expansion of x if ∑ ∞i=1 ciq-i = x. It is known that almost every x belonging to the interval [0,m/(q - 1)] has uncountably many expansions. In this paper we study the existence of expansions (di) of x satisfying the inequalities ∑n i=1 diq-i ⩾ ∑n i=1 ciq-i , n = 1, 2,… , for each expansion (ci) of x. [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 maximal nilpotent and supersoluble automorphism groups of Riemann surfaces were given in earlier papers by this author. In this note the author wishes to correct the necessity of the condition given in Theorem (4.3) of \textit{Bounds for the order of supersoluble automorphism groups of Riemann surfaces} (Proc. Amer. Math. Soc. {\bf108} (1990), 587--600), which was left out at the time of writing the paper. The author also wishes to apologize to the readers for that. [ABSTRACT FROM AUTHOR]

We provide a complete answer to the problem of characterizing left Artinian rings which satisfy the (left or right) MacWilliams extension theorem for linear codes, generalizing results of Iovanov [J. Pure Appl. Algebra 220 (2016), pp. 560–576] and Schneider and Zumbrägel [Proc. Amer. Math. Soc. 147 (2019), pp. 947–961] and answering the question of Schneider and Zumbragel [Proc. Amer. Math. Soc. 147 (2019), pp. 947–961]. We show that they are quasi-Frobenius rings, and are precisely the rings which are a product of a finite Frobenius ring and an infinite quasi-Frobenius ring with no non-trivial finite modules (quotients). For this, we give a more general "minimal test for injectivity" for a left Artinian ring A: we show that if every injective morphism \Sigma _k\rightarrow A from the k'th socle of A extends to a morphism A\rightarrow A, then the ring is quasi-Frobenius. We also give a general result under which if injective maps N\rightarrow M from submodules N of a module M extend to endomorphisms of M (pseudo-injectivity), then all such morphisms N\rightarrow M extend (quasi-injectivity) and obtain further applications. [ABSTRACT FROM AUTHOR]

Let G x X → X be an action of the connected algebraic group G on the irreducible, affine variety X. We discuss the relationship between [k[X]G] and k(X)G, where [k[X]G] denotes the quotient field of k[X]G. We are particularly interested in the following three questions. (1) When is the inclusion [k[X]G] ⊆k(X)G a finite extension of fields? (2) What is the role of G-invariant divisors? (3) What is the exact characterization of "observable in codimension one"? [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]

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]

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]

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]