In this paper we investigate the continuity property of several invariant sets J, J+ and J* of the H & eacute;non map Hc,a(x, y) = (x2 + c + ay, ax) as the parameters (c, a) E C2 vary. More precisely, we show that, if a sequence of parameters (cn, an) converges horocyclically to (c*, a*) such that Hc*,a* has a semi-parabolic fixed point and |a*|is sufficiently small, then the corresponding invariant sets converge to those of Hc*,a*. This in particular generalizes the previous result of Radu and Tanase (Trans. Amer. Math. Soc. 370(6) (2018), 3949-3996) to the case of horocyclic convergence.
This paper studies the harmonic means of positive functions on weighted Herz-Morrey spaces. We establish the norm inequalities for the harmonic means of positive functions on weighted Herz-Morrey spaces. This result is an extension of the harmonic means of positive functions on weighted Lebesgue spaces. As a special case of the main result, we have the norm inequalities of the harmonic means of positive functions on weighted Herz spaces.
Let BG be the classifying space of an algebraic group G over a subfield k of the complex numbers & Copf;. We compute a new stable birational invariant defined by Benoist and Ottem [Duke Math. J. 170 (2021), 2719-2753] as the difference of two coniveau filtrations of a smooth projective (Ekedahl) approximation X of BG & times; & Popf;infinity. Then we show (without and with the unramified cohomology) that in many cases X are not stable rational.
A simply connected rational CW complex X is called an F-0-space if it has finite-dimensional homotopy, finite-dimensional cohomology, and positive Euler characteristic. Making use of Whitehead's certain exact sequence, this paper aims to study the group E(X) of self-homotopy equivalences of X and its subgroup E-*(X) constituted by elements inducing the identity on the homology groups. Specifically, we prove that E-*(X) is trivial and E(X) is isomorphic to a certain subgroup of Q* x E(Xm-1), where m is the formal dimension of X, Xm-1 is its (m-1)-skeleton, and Q* = Q\{0}.
We give some formulas for the degree-two part of the LMO (Le-Murakami-Ohtsuki) invariant of cyclic branched covers of some genus-one knots with trivial Alexander polynomial. More concretely, we present them by using several Vassiliev invariants, where we use the 3-loop polynomial for their proofs. Furthermore, we show the existence of knots whose values of 3-loop invariant cannot be reduced. This paper is a sequel to the author's previous paper (J. Knot Theory Ramifications 33 33(7) (2024), 2450023).
In the present paper, we determine the algebraic relations among the tractable coordinates of logarithms of Anderson t-modules constructed by taking the tensor product of Drinfeld modules of rank r defined over the algebraic closure of the rational function field and their (r-1)-st exterior powers with the Carlitz tensor powers. Our results, in the case of the tensor powers of the Carlitz module, generalize the work of Chang and Yu on the algebraic independence of polylogarithms.
For k >= 2, we let A = (a1, a2, . . . , ak) be a k-tuple of positive integers with gcd(a1, a2, ... , ak) = 1 and, for a non-negative integers, the generalized Frobenius number of A, g(A; s) = g(a1, a2, . . . , ak; s), the largest integer that has at most s representations in terms of a1, a2, ... , ak with non-negative integer coefficients. In this paper, we give a formula for the generalized Frobenius number of three positive integers (a1, a2, a3) with certain conditions.
The main purpose of this paper is to introduce a new smooth version of a CW complex named a fat CW complex, and to show that it includes all closed manifolds, because existing smooth versions of CW complexes (e.g. [Iwa22]) do not have such property. We also verify that de Rham theorem holds for a fat CW complex and that a regular CW complex is reflexive in the sense of Y. Karshon, J. Watts and P. I-Zemmour. Further, any topological CW complex is topologically homotopy equivalent to a fat CW complex. So, a fat CW complex enjoys many nice properties.
Let G be a finite non-solvable group. According to R. Oliver's theory (Comment. Math. Helv. 50 (1975) 155-177; J. Algebra 50 (1978), 44-62), we have a unique natural number dG such that the n-dimensional disk has an effective smooth G-action without G-fixed points if and only if n is greater than or equal to dG. It implies that the n-dimensional sphere has an effective topological G-action with exactly one G-fixed point if n is greater than or equal to dG. However, smooth G-actions on the n-dimensional sphere are less flexible than topological G-actions on the sphere, and it is interesting to study the set & Nopf;G consisting of all natural numbers n such that there is an effective smooth G-action on the n-dimensional sphere with exactly one G-fixed point. In this paper we present a theory for obtaining a subset of & Nopf;G for G with a specified solvable normal subgroup N. This is done by first giving a sufficient condition for the existence of a desired G-action on the n-dimensional sphere in terms of tangential G-representation at the G-fixed point, and then constructing such G-representations by using real G/N-representations which can be the tangential G/N-representations of smooth G/N-actions on homology spheres with exactly one G/N-fixed point. As a consequence, we completely determine the sets & Nopf;G for G isomorphic to SL(2, 5), TL(2, 5), or A5 & times; Zr with Zr cyclic of order r = 2, or r prime to 30.
In the present paper, we give concrete descriptions of the canonical liftings of level two of tetrapods in characteristic three.
Fix a prime p >= 3 and let E be an algebraic extension of Ap. We construct some Wach modules over 0E[[lr]] of rank three and calculate mod-p reductions of the corresponding crystalline representations of Gal(Ap/Ap) over E. The main idea in the construction of some Wach modules is to approximate p-adically and lr-adically the conditions of Wach modules by simpler conditions. Yamashita and Yasuda (in preparation) have constructed some Wach modules of rank two by employing some approximation methods. We apply their method to construct some Wach modules of rank three.
Let r be an odd prime number, and let K be a real abelian field of conductor f(K) and class number h(K). When r inverted iota f(K), Jakubec (Abh. Math. Semin. Univ. Hambg. 63 (1993), 67-86) and Metsankyla (Manuscripta Math. 93 (1997), 481-498) gave a sufficient condition for r inverted iota h(K) in terms related to Fermat quotients associated to cyclotomic elements zeta(m) - 1 for integers m dividing f(K). We give a refined version of this result by different methods.
First, a complete classification of the generalized Ricci-Bourguignon soliton on real hypersurfaces in the complex hyperbolic space CHn = SUn,1/S(U1Un) has been given. Next as an application we give a complete classification of the gradient generalized Ricci-Bourguignon soliton on Hopf real hypersurfaces in the complex hyperbolic space CHn.
We give some sufficient and necessary conditions for the existence of fold maps of orientable 6-dimensional manifolds into I[85 with a prescribed singular set. To get the results, we study the relative half Euler characteristic of linearly independent vector fields. As a corollary we obtain that there are fold maps of S6 into I[85 whose singular sets consist of aspherical homology 4-spheres.
The non-isothermal model of compressible nematic liquid crystals in a threedimensional infinite layer is considered. We prove the existence of global strong solutions and their decay rates when the initial data is close to steady state. It turns out that the low-frequency part of the solution decays like a two-dimensional heat kernel. We can also see that the low-frequency part appears in the asymptotic reading part of the solution which is affected by nonlinear terms as t goes to infinity.
We give an explicit formula for Capelli-type identities of prehomogeneous vector spaces associated with sub-Hankel determinants. Moreover, we determine multivariate b-functions of these prehomogeneous vector spaces explicitly. As an application, we solve a conjecture on a b-function raised by Ishi and Kogiso (Seminar on Mathematical Sciences, 39. Keio University, 2016, pp. 83-93) affirmatively.
We introduce a new class of von Neumann algebras by deforming the construction of the von Neumann algebras introduced by Bo & zdot;ejko and Speicher and discuss the factoriality of the same.
In this paper, we prove that the convergence speed of certain quadratic recurrence formulas in the Arimoto-Blahut algorithm is of order O(1/N). The Arimoto-Blahut algorithm is a well-known algorithm in information theory for computing the capacity of a discrete memoryless channel. There have been many studies on exponential convergence, whereas we found previously (Nakagawa et al. IEEE Trans. Inform. Theory 67(10) (2021), 6810-6831) that there exists a channel for which the convergence is of order O(1/N). In that reference, the convergence of order O(1/N) was analyzed by using quadratic recurrence formulas consisting of the first-and second-order terms of the Taylor expansion of the defining function of the Arimoto-Blahut algorithm. However, there we assumed an infinite number of inequalities and the proof was given under this assumption. In this present paper, we prove the convergence of order O(1/N) by assuming only a finite number of inequalities. The important contribution of this paper is the novelty of the proof. A key idea of the proof is to examine a continuous-time function (i.e., a function defined over the non-negative real numbers) obtained by interpolating the discrete-time function (i.e., a sequence defined over the non-negative integers) of the quadratic recurrence formulas with line segments. The correctness of the proof is demonstrated by several numerical examples.
It will be shown that transformations of order one on the Wiener space give rise to quadratic forms as exponents of change of variables formulas, and conversely every exponentially integrable quadratic form has a transformation of order one realizing the form in such a manner. Several expressions of corresponding change of variables formulas are also discussed.
The study of homogenization results has long been a central focus in the field of mathematical analysis, particularly for equations without lower-order terms. However, the importance of studying homogenization results for parabolic equations with lower-order terms cannot be understated. In this study, we aim to extend the analysis to homogenization for the general parabolic equation with random coefficients: c7tpE-O center dot(a(epsilon x,epsilon t2)OpE)-b(epsilon x,epsilon t2)OpE-d(epsilon x,epsilon t2)pE=0. Moreover, we establish the Caccioppoli inequality and Meyers estimate for the generalized parabolic equation. By using the generalized Meyers estimate, we get the weak convergence of pE in H1.
