共查询到20条相似文献,搜索用时 31 毫秒
1.
J.D.H. Smith 《Algebra Universalis》1997,38(2):175-184
The study of quasigroup homotopies reduces to the study of homomorphisms between semisymmetric quasigroups. In particular,
the study of homotopies between central quasigroups reduces to the study of homomorphisms between entropic semisymmetric quasigroups.
Received December 20, 1996; accepted in final form September 17, 1997. 相似文献
2.
Jonathan D. H. Smith 《代数通讯》2013,41(5):1878-1885
The article analyzes homotopies between central quasigroups, and their groups of autotopies. In particular, the cycle types of autotopies of central quasigroups and other group isotopes of prime order are identified. 相似文献
3.
Adel A. George Michael 《Results in Mathematics》2007,51(1-2):107-109
In this paper we generalize a theorem of McAuley-Tulley [2] to show that small homotopies of any topological space can be
lifted to small homotopies for any Hurewicz fibration between arbitrary topological spaces.
Received: July 7, 2005. Revised: July 13, 2006. 相似文献
4.
Vedran Krčadinac 《Mathematica Slovaca》2011,61(6):885-894
Napoleon’s quasigroups are idempotent medial quasigroups satisfying the identity (ab·b)(b·ba) = b. In works by V. Volenec geometric terminology has been introduced in medial quasigroups, enabling proofs of many theorems
of plane geometry to be carried out by formal calculations in a quasigroup. This class of quasigroups is particularly suited
for proving Napoleon’s theorem and other similar theorems about equilateral triangles and centroids. 相似文献
5.
《Comptes Rendus Mathematique》2019,357(9):737-742
By considering homotopies that preserve the stratification, one obtains a natural notion of homotopy for stratified spaces. In this short note, we introduce invariants of stratified homotopy, the stratified homotopy groups. We show that they satisfy a stratified version of Whitehead's theorem. As an example, we introduce a complete knot invariant defined via the stratified homotopy groups. 相似文献
6.
S.K Stein 《Journal of Combinatorial Theory, Series A》1974,16(3):391-397
A theorem in convex bodies (in fact, measure theory) and a theorem about translates of sets of integers are generalized to coverings by subsets of a finite set. These theorems are then related to quasigroups and (0, 1)-matrices. 相似文献
7.
D. A. Permyakov 《Moscow University Mathematics Bulletin》2008,63(5):208-210
In 2005, R. Nikkuni calculated the Wu invariant for immersions of graphs into a plane considered up to a regular homotopy, i.e., for homotopies that are immersions. He showed that two immersions are regularly homotopic if and only if their Wu invariants coincide. In this paper a simple combinatorial construction for this invariant is described, a theorem similar to Ryo Nikkuni’s theorem is proved, and the fact that all values of the constructed combinatorial invariant can be implemented by immersions is also proved. 相似文献
8.
9.
Quantum quasigroups provide a self-dual framework for the unification of quasigroups and Hopf algebras. This paper furthers the transfer program, investigating extensions to quantum quasigroups of various algebraic features of quasigroups and Hopf algebras. Part of the difficulty of the transfer program is the fact that there is no standard model-theoretic procedure for accommodating the coalgebraic aspects of quantum quasigroups. The linear quantum quasigroups, which live in categories of modules under the direct sum, are a notable exception. They form one of the central themes of the paper.From the theory of Hopf algebras, we transfer the study of grouplike and setlike elements, which form separate concepts in quantum quasigroups. From quasigroups, we transfer the study of conjugate quasigroups, which reflect the triality symmetry of the language of quasigroups. In particular, we construct conjugates of cocommutative Hopf algebras. Semisymmetry, Mendelsohn, and distributivity properties are formulated for quantum quasigroups. We classify distributive linear quantum quasigroups that furnish solutions to the quantum Yang-Baxter equation. The transfer of semisymmetry is designed to prepare for a quantization of web geometry. 相似文献
10.
Brent Kerby 《Journal of Combinatorial Theory, Series A》2011,118(8):2232-2245
Norton and Stein associated a number with each idempotent quasigroup or diagonalized Latin square of given finite order n, showing that it is congruent mod 2 to the triangular number T(n). In this paper, we use a graph-theoretic approach to extend their invariant to an arbitrary finite quasigroup. We call it the cycle number, and identify it as the number of connected components in a certain graph, the cycle graph. The congruence obtained by Norton and Stein extends to the general case, giving a simplified proof (with topology replacing case analysis) of the well-known congruence restriction on the possible orders of general Schroeder quasigroups. Cycle numbers correlate nicely with algebraic properties of quasigroups. Certain well-known classes of quasigroups, such as Schroeder quasigroups and commutative Moufang loops, are shown to maximize the cycle number among all quasigroups belonging to a more general class. 相似文献
11.
S. M. Malamud 《Transactions of the American Mathematical Society》2005,357(10):4043-4064
We establish an analog of the Cauchy-Poincare interlacing theorem for normal matrices in terms of majorization, and we provide a solution to the corresponding inverse spectral problem. Using this solution we generalize and extend the Gauss-Lucas theorem and prove the old conjecture of de Bruijn-Springer on the location of the roots of a complex polynomial and its derivative and an analog of Rolle's theorem, conjectured by Schoenberg.
12.
There are numerous application of quasigroups in cryptology. It turns out that quasigroups with the relatively small number of associative triples can be utilized in designs of hash functions. In this paper we provide both a new lower bound and a new upper bound on the minimum number of associative triples over quasigroups of a given order. 相似文献
13.
J. Berkovits 《Journal of Differential Equations》2007,234(1):289-310
We introduce a new extension of the classical Leray-Schauder topological degree in a real separable reflexive Banach space. The new class of mappings for which the degree will be constructed is obtained essentially by replacing the compact perturbation by a composition of mappings of monotone type. It turns out that the class contains the Leray-Schauder type maps as a proper subclass. The new class is not convex thus preventing the free application of affine homotopies. However, there exists a large class of admissible homotopies including subclass of affine ones so that the degree can be effectively used. We shall construct the degree and prove that it is unique. We shall generalize the Borsuk theorem of the degree for odd mappings and show that the ‘principle of omitted rays’ remains valid. To illuminate the use of the new degree we shall briefly consider the solvability of abstract Hammerstein type equations and variational inequalities. 相似文献
14.
The aim of this article is the study of right nuclei of quasigroups with right unit element. We investigate an extension process in this category of quasigroups, which is defined by a slight modification of non-associative Schreier-type extensions of groups or loops. The main results of the article give characterizations of quasigroup extensions satisfying particular nuclear conditions. We apply these results for constructions of right nuclear quasigroup extensions with right inverse property. 相似文献
15.
In this article, we study the spectrum of quasigroups all conjugates of which are distinct and pairwise orthogonal. We call such quasigroups totally conjugate orthogonal quasigroups (for brevity, totCO-quasigroups). Every totCO-quasigroup defines the complete conjugate orthogonal Latin square graph K 6. Examples of totCO-quasigroups of different orders are given. 相似文献
16.
Jonathan D. H. Smith 《Algebra Universalis》2006,55(2-3):387-406
The concept of a permutation representation has recently been extended from groups to quasigroups. Following a suggestion
of Walter Taylor, the concept is now further extended to left quasigroups. The paper surveys the current state of the theory,
giving new proofs where necessary to cover the general case of left quasigroups. Both the Burnside Lemma and the Burnside
algebra appear in this new context.
This paper is dedicated to Walter Taylor.
Received August 9, 2005; accepted in final form March 7, 2006. 相似文献
17.
《Applied mathematics and computation》1987,24(2):115-138
In a previous paper we described a new method for defining homotopies for finding all solutions to polynomial systems. A major feature of this new approach is that the start system for the homotopy need not be a “random” or “generic” system. Also, homotopy paths are strictly increasing in the homotopy parameter. In this paper we establish some principles of implementation and report on the performance of programs that use the new homotopies. A feature of our implementation is that we eliminate divergent paths entirely. We include performance statistics for homotopies derived from more traditional approaches for comparison. Generally, the new approach is faster and more reliable. 相似文献
18.
In this paper we propose a new proof of the well-known theorem by S. N. Bernstein, according to which among entire functions
which give on (−∞,∞) the best uniform approximation of order σ of periodic functions there exists a trigonometric polynomial whose order does not exceed σ. We also prove an analog of this Bernstein theorem and an analog of the Jackson theorem for uniform almost periodic functions
with an arbitrary spectrum. 相似文献
19.
Ronald D. Baker 《Aequationes Mathematicae》1978,18(1-2):296-303
A quasigroupQ is a set together with a binary operation which satisfies the condition that any two elements of the equationxy =z uniquely determines the third. A quasigroup is in indempotent when any elementx satisfies the indentityxx =x. Several types of Tactical Systems are defined as arrangement of points into “blocks” in such a way as to balance the incidence of (ordered or unordered) pairs of points, and shown to be coexistent with idempotent quasigroups satisfying certain identifies. In particular the correspondences given are: 1. totally symmetric idempotent quasigroups and Steiner triple systems, 2. semi-symmetric idempotent quasigroups and directed triple systems, 3. idempotent quasigroups satisfying Schröder's Second Law, namely (xy)(yx)=x, and triple tourna-ments, and 4. idempotent quasigroups satisfying Stein's Third Law, namely (xy)(yx)=y, and directed tournaments. These correspondences are used to obtain corollaries on the existence of such quasig-roups from constructions of the Tactical Systems. In particular this provides a counterexample to an ”almost conjecture“ of Norton and Stein (1956) concerning the existence of those quasigroups in 3 and 4 above. Indeed no idempotent qnasigroups satisfying Stein's Third Law and with order divisible by four were known to N. S. Mendelsohn when he wrote a paper on such quasigroups for the Third Waterloo Conference on Combinatorics (May, 1968). Finally, a construction for triple tournaments is interpreted as a Generalized Semi-Direct Product of idempotent quasigroups. 相似文献
20.
Jimmie D. Lawson 《Monatshefte für Mathematik》1996,121(4):309-333
We introduce the notions of causal paths and causal homotopies, modifications of the traditional notions of paths and homotopies, as more suitable for certain basic constructions in (Lie) semigroup theory. The major result is the construction in this causal context of an analogue of the universal covering semigroup and the demonstration that local homomorphisms on the given semigroup extend to global homomorphisms on it. In certain important cases, it is shown that this semigroup actually agrees with the universal covering semigroup.The author gratefully acknowledges the partial support of theNational Science Foundation. DMS 910-4582. 相似文献