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The purpose of this paper is to describe the structures of the Möbius semigroup induced by the Möbius transformation group (?, SL(2,?)). In particular, we study stabilizer subsemigoups of Möbius semigroup via the triangle semigroup. In this work, we obtained a geometric interpretation of the least contraction coefficient function of the Möbius semigroup via the triangle semigroup and investigated an extension of stabilizer subsemigoups of the Möbius semigroup. Finally, we obtained a factorization of our stabilizer subsemigoups of the Möbius semigroup. 相似文献
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We show that the Möbius function of an interval in a permutation poset where the lower bound is sum (resp. skew) indecomposable depends solely on the sum (resp. skew) indecomposable permutations contained in the upper bound, and that this can simplify the calculation of the Möbius sum. For increasing oscillations, we give a recursion for the Möbius sum which only involves evaluating simple inequalities. 相似文献
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《复变函数与椭圆型方程》2012,57(3):225-228
Let G be a non-elementary subgroup of SL(2,Г n ) containing hyperbolic elements. We show that G is the extension of a subgroup of SL(2,C) if and only if that G is conjugate in SL(2,Г n ) to a group G' with the following properties: (1) There are g 0, h ? G', where g 0 and h are hyperbolic, such that fix(g 0) = {0,∞}, fix(h)∩fix(g 0) = and fix(h) ∩ C ≠ ; (2) tr(g) ? C for each g ? G'. As an application, we show that if G contains only hyperbolic elements and uniformly parabolic elements, then G is the extension of a subgroup of SL(2,C), which also yields the discreteness of G. 相似文献
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The Ramanujan Journal - In this paper, we investigate decompositions of the partition function p(n) from the additive theory of partitions considering the famous Möbius function $$mu (n)$$... 相似文献
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Möbius invariants of general circle packings are defined in terms of cross ratios. The necessary and sufficient conditions of existence of circle packings are established by the techniques of Möbius invariants. It is shown that circle packings are uniquely determined, up to Möbius transformations, by their Möbius invariants. The rigidity of infinite circle packings with bounded degree is proved using the approach of Möbius invariants. 相似文献
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《Communications in Nonlinear Science & Numerical Simulation》2011,16(12):4698-4703
In this work, we propose a new type of activation function for a complex valued neural network (CVNN). This activation function is a special Möbius transformation classified as reflection. It is bounded outside of the unit disk and has partial continuous derivatives but not differentiable since it does not satisfy the Cauchy–Riemann equalities. However, the fixed points set of this function is a circle. Therefore, we employ this function to a specific complex valued Hopfield neural network (CVHNN) and increase the number of fixed points of the CVHNN. Using of this activation function leads us also to guarantee the existence of fixed points of the CVHNN. It is shown that the fixed points are all asymptotically stable states of the CVHNN which indicates that the information capacity is enlarged. 相似文献
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An umbilic-free hypersurface in the unit sphere is called MSbius isoparametric if it satisfies two conditions, namely, it has vanishing MSbius form and has constant MSbius principal curvatures. In this paper, under the condition of having constant MSbius principal curvatures, we show that the hypersurface is of vanishing MSbius form if and only if its MSbius form is parallel with respect to the Levi-Civita connection of its MSbius metric. Moreover, typical examples are constructed to show that the condition of having constant MSbius principal curvatures and that of having vanishing MSbius form are independent of each other. 相似文献
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In this paper we propose to develop harmonic analysis on the Poincaré ball \({{\mathbb {B}}_{t}^{n}}\), a model of the \(n\)-dimensional real hyperbolic space. The Poincaré ball \({{\mathbb {B}}_{t}^{n}}\) is the open ball of the Euclidean \(n\)-space \(\mathbb {R}^n\) with radius \(t >0\), centered at the origin of \(\mathbb {R}^n\) and equipped with Möbius addition, thus forming a Möbius gyrogroup where Möbius addition in the ball plays the role of vector addition in \(\mathbb {R}^n.\) For any \(t>0\) and an arbitrary parameter \(\sigma \in \mathbb {R}\) we study the \((\sigma ,t)\)-translation, the \((\sigma ,t)\)-convolution, the eigenfunctions of the \((\sigma ,t)\)-Laplace–Beltrami operator, the \((\sigma ,t)\)-Helgason Fourier transform, its inverse transform and the associated Plancherel’s Theorem, which represent counterparts of standard tools, thus, enabling an effective theory of hyperbolic harmonic analysis. Moreover, when \(t \rightarrow +\infty \) the resulting hyperbolic harmonic analysis on \({{\mathbb {B}}_{t}^{n}}\) tends to the standard Euclidean harmonic analysis on \(\mathbb {R}^n,\) thus unifying hyperbolic and Euclidean harmonic analysis. As an application we construct diffusive wavelets on \({{\mathbb {B}}_{t}^{n}}\). 相似文献
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Jørgensen’s inequality gives a necessary condition for a nonelementary two generator subgroup of $SL(2, {\mathbb C})$ to be discrete. By embedding $SL(2,{\mathbb C})$ into $\hat U(1,1; {\mathbb H})$ , we obtain a new type of Jørgensen’s inequality, which is in terms of the coefficients of involved isometries. We provide an example to show that this result gives an improvement over the classical Jørgensen’s inequality. 相似文献
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V. V. Aseev 《Siberian Mathematical Journal》2016,57(3):385-397
A möbius bilipschitz mapping is an η-quasimöbius mapping with the linear distortion function η(t) = Kt. We show that if an open Jordan arc γ ? C with distinct endpoints a and b is homogeneous with respect to the family FK of möbius bilipschitz automorphisms of the sphere C with K specified then γ has bounded turning RT(γ) in the sense of Rickman and, consequently, γ is a quasiconformal image of a rectilinear segment. The homogeneity of γ with respect to FK means that for all x, y ∈ γ {a, b} there exists f ∈ FK with f(γ) = γ and f(x) = y. In order to estimate RT(γ) from above, we introduce the condition BR(δ) of bounded rotation of γ, and then the explicit bound depends only on K and δ. 相似文献
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Krzysztof Witczynski 《Journal of Geometry》1994,51(1-2):187-189
H.S.M. Coxeter in his book Introduction to Geometry quotes a theorem of Möbius. In the paper two counterexamples are given. A corrected version of the theorem is stated and proved. 相似文献
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The purpose of this paper is to point out some aspects of the
relationship between combinatorial inverse semigroups and their
Möbius categories, and to explore combinatorial results arising
from combinatorial Brandt semigroups, fundamental simple inverse
-semigroups and from the free monogenic inverse
semigroup. 相似文献
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In this note, we characterize the regular probability measures satisfying the Choquet-Deny convolution equation =* on Abelian topological semigroups for a given probability measure . 相似文献