Search results for "Computer Science::General Literature"
showing 8 items of 18 documents
đ¸1-contractibility of affine modifications
2019
We introduce KorasâRussell fiber bundles over algebraically closed fields of characteristic zero. After a single suspension, this exhibits an infinite family of smooth affine [Formula: see text]-contractible [Formula: see text]-folds. Moreover, we give examples of stably [Formula: see text]-contractible smooth affine [Formula: see text]-folds containing a BrieskornâPham surface, and a family of smooth affine [Formula: see text]-folds with a higher-dimensional [Formula: see text]-contractible total space.
Double points in families of map germs from â2 to â3
2020
We show that a 1-parameter family of real analytic map germs [Formula: see text] with isolated instability is topologically trivial if it is excellent and the family of double point curves [Formula: see text] in [Formula: see text] is topologically trivial. In particular, we deduce that [Formula: see text] is topologically trivial when the Milnor number [Formula: see text] is constant.
Lattice of closure endomorphisms of a Hilbert algebra
2019
A closure endomorphism of a Hilbert algebra [Formula: see text] is a mapping that is simultaneously an endomorphism of and a closure operator on [Formula: see text]. It is known that the set [Formula: see text] of all closure endomorphisms of [Formula: see text] is a distributive lattice where the meet of two elements is defined pointwise and their join is given by their composition. This lattice is shown in the paper to be isomorphic to the lattice of certain filters of [Formula: see text], anti-isomorphic to the lattice of certain closure retracts of [Formula: see text], and compactly generated. The set of compact elements of [Formula: see text] coincides with the adjoint semilattice of âŚ
Stability conditions and related filtrations for $(G,h)$-constellations
2017
Given an infinite reductive algebraic group $G$, we consider $G$-equivariant coherent sheaves with prescribed multiplicities, called $(G,h)$-constellations, for which two stability notions arise. The first one is analogous to the $\theta$-stability defined for quiver representations by King and for $G$-constellations by Craw and Ishii, but depending on infinitely many parameters. The second one comes from Geometric Invariant Theory in the construction of a moduli space for $(G,h)$-constellations, and depends on some finite subset $D$ of the isomorphy classes of irreducible representations of $G$. We show that these two stability notions do not coincide, answering negatively a question raiseâŚ
On the empirical spectral distribution for certain models related to sample covariance matrices with different correlations
2021
Given [Formula: see text], we study two classes of large random matrices of the form [Formula: see text] where for every [Formula: see text], [Formula: see text] are iid copies of a random variable [Formula: see text], [Formula: see text], [Formula: see text] are two (not necessarily independent) sets of independent random vectors having different covariance matrices and generating well concentrated bilinear forms. We consider two main asymptotic regimes as [Formula: see text]: a standard one, where [Formula: see text], and a slightly modified one, where [Formula: see text] and [Formula: see text] while [Formula: see text] for some [Formula: see text]. Assuming that vectors [Formula: see tâŚ
LĂŠvyâKhintchine decompositions for generating functionals on algebras associated to universal compact quantum groups
2018
We study the first and second cohomology groups of the $^*$-algebras of the universal unitary and orthogonal quantum groups $U_F^+$ and $O_F^+$. This provides valuable information for constructing and classifying L\'evy processes on these quantum groups, as pointed out by Sch\"urmann. In the case when all eigenvalues of $F^*F$ are distinct, we show that these $^*$-algebras have the properties (GC), (NC), and (LK) introduced by Sch\"urmann and studied recently by Franz, Gerhold and Thom. In the degenerate case $F=I_d$, we show that they do not have any of these properties. We also compute the second cohomology group of $U_d^+$ with trivial coefficients -- $H^2(U_d^+,{}_\epsilon\Bbb{C}_\epsilâŚ
On nature of mathematics. On mathematics and reality Par matemÄtikas dabu. Par matemÄtiku un realitÄti
2007
Idea that mathematics should be considered as creative order in nature is considered.
Finite groups with all minimal subgroups solitary
2016
We give a complete classification of the finite groups with a unique subgroup of order p for each prime p dividing its order. All the groups considered in this paper will be finite. One of the most fruitful lines in the research in abstract group theory during the last years has been the study of groups in which the members of a certain family of subgroups satisfy a certain subgroup embedding property. The family of the subgroups of prime order (also called minimal subgroups) has attracted the interest of many mathematicians. For example, a well-known result of ItËo (see [8, Kapitel III, Satz 5.3; 9]) states that a group of odd order with all minimal subgroups in the center is nilpotent. ThâŚ