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In the present paper, we deepen the works of L. Abatangelo, V. Felli, L. Hillairet and C. Léna on the asymptotic estimates of the eigenvalue variation under removal of segments from the domain in \mathbb {R}^2. We get a sharp asymptotic estimate when the eigenvalue is simple and the removed segment is tangent to a nodal line of the associated eigenfunction. Moreover, we extend their results to the case when the eigenvalue is not simple. [ABSTRACT FROM AUTHOR]

In this paper, we investigate applications of the ordinary derivative operator, instead of the q-derivative operator, to the theory of q-series. As main results, many new summation and transformation formulas are established which are closely related to some well-known formulas such as the q-binomial theorem, Ramanujan's {}_1\psi _1 formula, the quintuple product identity, Gasper's q-Clausen product formula, and Rogers' {}_6\phi _5 formula, etc. Among these results is a finite form of the Rogers-Ramanujan identity and a short way to Eisenstein's theorem on Lambert series. [ABSTRACT FROM AUTHOR]

The geproci property is a recent development in the world of geometry. We call a set of points Z\subseteq \mathbb {P}_k^3 an (a,b)-geproci set (for GEneral PROjection is a Complete Intersection) if its projection from a general point P to a plane is a complete intersection of curves of degrees a\leq b. Nondegenerate examples known as grids have been known since 2011. Nondegenerate nongrids were first described in 2018, working in characteristic 0. Almost all of these new examples are of a special kind called half grids. In this paper, based partly on the author's thesis, we use a feature of geometry in positive characteristic to give new methods of producing geproci half grids and non-half grids. [ABSTRACT FROM AUTHOR]

In this paper we consider 0-th order pseudodifferential operators on the circle. We show that inside any interval disjoint from the critical values of the principal symbol, the spectrum is absolutely continuous with possibly finitely many embedded eigenvalues. We also give an example of embedded eigenvalues. [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]

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]

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]

In this paper, we prove a vanishing theorem concerning the periods of cuspidal automorphic sheaves for \operatorname {GL}_{m+n} along the Levi subgroup \operatorname {GL}_{m}\times \operatorname {GL}_{n} for m \neq n. [ABSTRACT FROM AUTHOR]

In this paper we provide a detailed topological and measure-theoretic study of Lebesgue measure-preserving continuous circle maps that are composed with independent rotations on each of the sides. In particular, we analyze the stability of the locally eventually onto and measure-theoretic mixing properties. [ABSTRACT FROM AUTHOR]

The upper and lower solution method is a recently developed and currently the most effective tool for determining the sign of bistable traveling wave. However, for systems with nonlocal diffusion terms, it is extremely challenging to find upper and lower solutions. In this paper, we develop a new idea for constructing the upper and lower solutions to establish the explicit conditions for obtaining positive or negative wave speed for a Lotka-Volterra competitive system with bistable nonlinearity. The theoretical results are demonstrated by directly integrating the considered system. This method can be used to improve or correct the related results in the known references. [ABSTRACT FROM AUTHOR]

In this paper, we prove embedding theorems for the Möbius invariant space \mathcal {Q}_p on the open unit ball of \mathbb {C}^n into logarithmic tent spaces in the Bergman metric. [ABSTRACT FROM AUTHOR]

In this paper, using the method of blow-up analysis, we establish a trace Trudinger-Moser inequality involving L^p-norm and obtain the corresponding extremal on a compact Riemann surface with a smooth boundary. The result generalizes those of Li-Liu [Math. Z. 250 (2005), pp. 363–686] and Zhang [Commun. Pure Appl. Anal. 20 (2021), pp. 1721–1735]. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the monotonicity of the functions t \mapsto \frac {\sum _{k=0}^\infty a_k w_k(t)}{\sum _{k=0}^\infty b_k w_k(t)} and x \mapsto \frac {\int _\alpha ^\beta f(t) w(t,x) \mathrm {d} t}{\int _\alpha ^\beta g(t) w(t,x) \mathrm {d} t}, focusing on case where the monotonicity of a_k/b_k and f(t)/g(t) change once. The results presented also provide insights into the monotonicity of the ratios of two power series, two \mathcal {Z}-transforms, two discrete Laplace transforms, two discrete Mellin transforms, two Laplace transforms, and two Mellin transforms. Finally, we employ these monotonicity rules to present several applications in the realm of special functions and stochastic orders. [ABSTRACT FROM AUTHOR]

This paper classifies the global dynamics of a 4D competitive Lotka-Volterra system (1.3) with two positive parameters k_1,\ k_2 via carrying simplex. It is proved that the interior of the carrying simplex is filled with periodic orbits except equilibria and each interior trajectory is persistent and tends to either a periodic orbit or an equilibrium if k_1/k_2=2. Otherwise, the system admits two 2D carrying simplices \Delta _i on x_1=i for i=0,\ 1, which are filled with periodic orbits surrounding an equilibrium. All interior orbits go in the long run to \Delta _1 if k_1/k_2>2. If 0

In this note, we prove the existence of homogeneous gradient solitons for the G_2-Laplacian flow by providing the first known example of this type. This result singles out the G_2-Laplacian flow as the first known geometric flow admitting homogeneous gradient solitons on spaces that are one-dimensional extensions in the sense of Petersen and Wylie [Differential Geom. Appl. 84 (2022), Paper No. 101929, 29]. [ABSTRACT FROM AUTHOR]

In this paper, we prove a result similar to results of Itoh [J. Algebra 150 (1992), pp. 101–117] and Hong-Ulrich [J. Lond. Math. Soc. (2) 90 (2014), pp. 861–878], proving that integral closure of an ideal is compatible with specialization by a general element of that ideal for ideals of height at least two in a large class of rings. Moreover, we show integral closure of sufficiently large powers of the ideal is compatible with specialization by a general element of the original ideal. In a polynomial ring over an infinite field, we give a class of squarefree monomial ideals for which the integral closure is compatible with specialization by a general linear form. [ABSTRACT FROM AUTHOR]

Let F be a field of characteristic 2. Our aim in this paper is to prove that the extension given by the function field of a singular conic is excellent for bilinear forms. We also give examples showing that in general this extension is not excellent for quadratic forms of arbitrary dimension. [ABSTRACT FROM AUTHOR]

Let \mathcal L=-\Delta _{\mathbb {G}}+\Upsilon be a Schrödinger operator with a nonnegative potential \Upsilon belonging to the reverse Hölder class B_{Q/2}, where Q is the homogeneous dimension of the stratified Lie group \mathbb {G}. Inspired by Shen's pioneer work and Li's work, we study fundamental solutions of the Schrödinger operator \mathcal L on the stratified Lie group \mathbb {G} in this paper. By proving an exponential decreasing variant of mean value inequality, we obtain the exponential decreasing upper estimates, the local Hölder estimates and the gradient estimates of the fundamental solutions of the Schrödinger operator \mathcal L on the stratified Lie group. As two applications, we obtain the De Giorgi-Nash-Moser theory on the improved Hölder estimate for the weak solutions of the Schrödinger equation and a Liouville-type lemma for \mathcal {L}-harmonic functions on \mathbb {G}. [ABSTRACT FROM AUTHOR]

The B-operators (abbreviation for Brownian-type operators) are upper triangular 2\times 2 block matrix operators that satisfy certain algebraic constraints. The purpose of this paper is to characterize the weak, the strong and the uniform stability of B-operators, respectively. This is achieved by giving equivalent conditions for the convergence of powers of a B-operator in each of the corresponding topologies. A more subtle characterization is obtained for B-operators with subnormal (2,2) entry. The issue of the strong stability of the adjoint of a B-operator is also discussed. [ABSTRACT FROM AUTHOR]

In this work, we consider Dirac-type operators with a constant delay less than two-fifths of the interval and not less than one-third of the interval. For our considered Dirac-type operators, an incomplete inverse spectral problem is studied. Specifically, when two complex potentials are known a priori on a certain subinterval, reconstruction of the two potentials on the entire interval is studied from complete spectra of two boundary value problems with one common boundary condition. The uniqueness of the solution of the inverse problem is proved. A constructive method is developed for the solution of the inverse problem. [ABSTRACT FROM AUTHOR]

In this paper we prove a group theoretic analogue of the well known local nilpotence theorem for sandwich Lie algebras due to Kostrikin and Zel'manov [Trudy Mat. Inst. Steklov. 183 (1990), pp. 106–111, 225]. We introduce the notion of a strong left 3-Engel element of a group G and show that these are always in the locally nilpotent radical of G. This generalises a previous result of Jabara and Traustason [Proc. Amer. Math. Soc. 147 (2019), pp. 1921–1927] that showed that a left 3-Engel element a of a group G is in the locally nilpotent radical of G whenever a is of odd order. [ABSTRACT FROM AUTHOR]

In this paper, we present two sufficient conditions keeping the total energy and cross-helicity conservation in spaces \underline {B}^{\alpha }_{3,VMO}(\Omega) and B^{\beta }_{3,\infty }(\Omega) for the ideal magnetohydrodynamic equations in a bounded domain. This generalizes the sufficient criteria for conserved quantities recently obtained by Bardos, Gwiazda, Świerczewska Gwiazda, Titi and Wiedemann [Proc. A. 475 (2019), 18 pp.] and by Wang and Zuo [J. Differential Equations 268 (2020), pp. 4079–4101]. [ABSTRACT FROM AUTHOR]

In this paper, we introduce k-Young tableaux and their g-indices. We first present certain expansions of (c(x)D)^n in terms of inversion sequences as well as k-Young tableaux, where c(x) is a smooth function in the indeterminate x and D is the derivative with respect to x. By studying the connections between k-Young tableaux and standard Young tableaux, we then present combinatorial interpretations of Eulerian polynomials, second-order Eulerian polynomials, and André polynomials in terms of standard Young tableaux. [ABSTRACT FROM AUTHOR]

We provide a corrected proof of one of the two main results (Theorem 3.2) of the paper "The space of persistence diagrams on n points coarsely embeds into Hilbert space" [Proc. Amer. Math. Soc. 149 (2021), pp. 2693–2703]. [ABSTRACT FROM AUTHOR]

Let \mu (n) be the Möbius function and e(\alpha)=e^{2\pi i\alpha }. In this paper, we study upper bounds of the classical sum \[ S(x,\alpha)≔\sum _{1\leq n\leq x}\mu (n)e(\alpha n). \] We can improve some classical results of Baker and Harman [J. London Math. Soc. (2) 43 (1991), pp. 193–198]. [ABSTRACT FROM AUTHOR]

In this paper, we focus on the nonlocal dispersal monostable equation with seasonal succession, which can be used to describe the dynamics of species in an environment alternating between bad and good seasons. We first prove the existence and uniqueness of global positive solution, and then discuss the long time behaviors of solution. It is shown that its dynamics is completely determined by the sign of the principal eigenvalue, i.e., the time periodic problem has no positive solution and the solution of the initial value problem tends to zero when principal eigenvalue is non-negative, while the time periodic positive solution exists uniquely and is globally asymptotically stable when principal eigenvalue is negative. [ABSTRACT FROM AUTHOR]

Let (A,\mathfrak {m}) be an excellent normal domain of dimension two containing a field k \cong A/\mathfrak {m}. An \mathfrak {m}-primary ideal I is a p_g-ideal if the Rees algebra A[It] is a Cohen-Macaulay normal domain. If k is algebraically closed then Okuma, Watanabe and Yoshida proved that A has p_g-ideals and furthermore product of two p_g-ideals is a p_g ideal. Previously we showed that if k has characteristic zero then A has p_g-ideals. In this paper we prove that if k is perfect field of positive characteristic then also A has p_g ideals. [ABSTRACT FROM AUTHOR]

Mean dimension may decrease after taking the natural extension. In this paper we show that mean dimension is preserved by natural extension for an endomorphism on a compact metrizable abelian group. As an application, we obtain that the mean dimension of an algebraic cellular automaton coincides with the mean dimension of its natural extension, which strengthens a result of Burguet and Shi [Israel J. Math. (to appear).] with a different proof. [ABSTRACT FROM AUTHOR]

In this paper, we study the dynamics of an operator \mathcal T naturally associated to the so-called Collatz map , which maps an integer n \geq 0 to n / 2 if n is even and 3n + 1 if n is odd. This operator \mathcal T is defined on certain weighted Bergman spaces \mathcal B ^2 _\omega of analytic functions on the unit disk. Building on previous work of Neklyudov, we show that \mathcal T is hypercyclic on \mathcal B ^2 _\omega, independently of whether the Collatz Conjecture holds true or not. Under some assumptions on the weight \omega, we show that \mathcal T is actually ergodic with respect to a Gaussian measure with full support, and thus frequently hypercyclic and chaotic. [ABSTRACT FROM AUTHOR]

A subset A of a vector space X is called \alpha-lineable whenever A contains, except for the null vector, a subspace of dimension \alpha. If X has a topology, then A is \alpha-spaceable if such subspace can be chosen to be closed. The vast existing literature on these topics has shown that positive results for lineability and spaceability are quite common. Recently, the stricter notions of (\alpha,\beta)-lineability/spaceability were introduced as an attempt to shed light on more subtle issues. In this paper, among other results, we prove some general criteria for the notion of (\alpha,\beta)-lineability/spaceability and, as applications, we extend recent results of different authors. [ABSTRACT FROM AUTHOR]

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]

In this paper, we establish the method of holomorphic handle attaching to the strongly pseudoconcave boundary of a complex surface. We use this for proving the following statements: (1) every closed connected oriented contact 3-manifold can be filled as the strongly pseudoconcave boundary of a compact complex surface; (2) any two non-empty closed connected oriented contact 3-manifolds are complex cobordant. Moreover, we show that such a complex surface (or complex cobordism) can be taken Kähler. [ABSTRACT FROM AUTHOR]

The aim of this paper is to show that the structure skew brace associated with a finite non-degenerate solution of the Yang-Baxter equation is finitely presented. [ABSTRACT FROM AUTHOR]

Given a non-positive DG-ring A, associated to it are the reduction and coreduction functors F(-) = \mathrm {H}^0(A)\otimes ^{\mathrm {L}}_A - and G(-) = \mathrm {R}\operatorname {Hom}_A(\mathrm {H}^0(A),-), considered as functors \operatorname {\mathsf {D}}(A) \to \operatorname {\mathsf {D}}(\mathrm {H}^0(A)), as well as the forgetful functor S:\operatorname {\mathsf {D}}(\mathrm {H}^0(A)) \to \operatorname {\mathsf {D}}(A). In this paper we carry a systematic study of the categorical properties of these functors. As an application, a new descent result for vanishing of \operatorname {Ext} and \operatorname {Tor} over ordinary commutative noetherian rings is deduced. [ABSTRACT FROM AUTHOR]

The hyperbolic structure on a 3–dimensional cone–manifold with a knot as singularity can often be deformed into a limiting Euclidean structure. In the present paper we show that the respective normalised Euclidean volume is always an algebraic number, which is reminiscent of Sabitov's theorem (the Bellows Conjecture). This fact also stands in contrast to hyperbolic volumes whose number–theoretic nature is usually quite complicated. [ABSTRACT FROM AUTHOR]

Disjoint sequence methods from the theory of Riesz spaces are used to study measures of weak non-compactness in L_{1}(\mu)-spaces. A principal new result of the present paper is the following: Let E be an abstract M-space. Then \begin{align*} \omega (B)&=\sup \{\limsup \limits _{n\rightarrow \infty }\rho _{B}(x_{n}):(x_{n})_{n}\subseteq B_{E} \operatorname {disjoint} \}\\ &=\inf \{\varepsilon >0:\exists x^{*}\in E^{*}_{+} \operatorname {so}\operatorname {that} B\subseteq [-x^{*},x^{*}]+\varepsilon B_{E^{*}}\}\\ &=\sup \{\limsup \limits _{n\rightarrow \infty }\rho _{B}(x_{n}):(x_{n})_{n}\subseteq B_{E} \operatorname {weakly}\operatorname {null} \}\\ &=\sup \{\operatorname {ca}_{\rho _{B}}((x_{n})_{n}):(x_{n})_{n}\subseteq (B_{E})_{+} \operatorname {increasing} \}\\ &=\sup \{\limsup \limits _{n\rightarrow \infty }\|x^{*}_{n}\|:(x^{*}_{n})_{n}\subseteq \operatorname {Sol}(B)\operatorname {disjoint}\}\\ &=\sup \{\limsup \limits _{n\rightarrow \infty }\sup \limits _{x^{*}\in B}|\langle x^{*},x_{n}\rangle |:(x_{n})_{n}\subseteq B_{E}\operatorname {disjoint} \}\\ \end{align*} for every norm bounded subset B of E^{*}. [ABSTRACT FROM AUTHOR]

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]

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 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]

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]

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]

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

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]

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]

The study of bipartite maps (or Grothendieck's dessins d'enfants) is closely connected with geometry, mathematical physics and free probability. Here we study these objects from their permutation factorization formulation using a novel character theory approach. We first present some general symmetric function expressions for the number of products of two permutations respectively from two arbitrary, but fixed, conjugacy classes indexed by \alpha and \gamma that produce a permutation with m cycles. Our next objective is to derive explicit formulas for the cases where \alpha corresponds to full cycles, i.e., one-face bipartite maps. We prove a far-reaching explicit formula, and show that the number for any \gamma can be iteratively reduced to that of products of two full cycles, which implies an efficient dimension-reduction algorithm for building a database of all these numbers. Note that the number for products of two full cycles can be computed by the Zagier-Stanley formula. Also, in a unified way, we easily prove the celebrated Harer-Zagier formula and Jackson's formula, and we may obtain explicit formulas for several new families as well. [ABSTRACT FROM AUTHOR]

We prove that minimizers of the L^{d}-norm of the Hessian in the unit ball of \mathbb {R}^d are locally of class C^{1,\alpha }. Our findings extend previous results on Hessian-dependent functionals to the borderline case and resonate with the Hölder regularity theory available for elliptic equations in double-divergence form. [ABSTRACT FROM AUTHOR]

Consider L^0, the F-space of all equivalence classes of measurable functions on a finite measure space equipped with the topology of convergence in measure. Inspired by Nikishin's classical result on the factorization of sublinear continuous operators from a Banach space to L^0, we prove a theorem that characterizes those maps from any quasi-metric space into L^0 that factor strongly through Marcinkiewicz weighted spaces. We show applications to sublinear operators on a certain class of quasi-Banach spaces with generalized Rademacher type generated by Orlicz sequence spaces. [ABSTRACT FROM AUTHOR]

In this note, we prove that the compactly supported mapping class group of a surface containing a genus 3 subsurface has no realization as a subgroup of the homeomorphism group. We also prove that for certain surfaces with order 6 symmetries, their mapping class groups have no realization as a subgroup of the homeomorphism group. Examples of such surfaces include the plane minus a Cantor set and the sphere minus a Cantor set. [ABSTRACT FROM AUTHOR]

Let H^2(S) be the Hardy space on the unit sphere in \mathbf {C}^n. We show that there are Toeplitz operators T_f and T_g on H^2(S) such that the product T_fT_g is not compact and yet \|T_fT_gk_z\| tends to 0 as |z| \rightarrow 1. Consequently, the Berezin transform \langle T_fT_gk_z,k_z\rangle tends to 0 as |z| \rightarrow 1. [ABSTRACT FROM AUTHOR]

In this note, we obtain a Gaussian concentration inequality for a class of non-Lipschitz functions. In the one-dimensional case, our results supplement those established by Paouris and Valettas [Ann. Probab. 46 (2018), pp. 1441–1454]. [ABSTRACT FROM AUTHOR]