Estimating the first zero of a characteristic function

For a characteristic function (Fourier transform of a probability distribution), the first zero encodes important information. We present a general lower bound estimation of the first zero in terms of a moment of any order. The result proves the complementary nature between the first zero and moments, and has interesting implications for quantum mechanical uncertainty relations. To cite this article: S. Luo, Z. Zhang, C. R. Acad. Sci. Paris, Ser. I 338 (2004).     

Rings containing a field of characteristic zero

Let K be a field of characteristic zero, and let R be a ring containing K. Then either \(R^\times = K^\times \) or \(K^\times \) is a subgroup of infinite index in \(R^\times \).     

On a desingularization of the moduli space of noncommutative tori

It is shown that the moduli space of the noncommutative tori admits a natural desingularization by the group . Namely, we prove that the moduli space of pairs is homeomorphic to a punctured two-dimensional sphere. The proof is based on a correspondence (a covariant functor) between the complex and noncommutative tori.

     

Desingularization of quasi-excellent schemes in characteristic zero

Grothendieck proved in EGA IV that if any integral scheme of finite type over a locally noetherian scheme X admits a desingularization, then X is quasi-excellent, and conjectured that the converse is probably true. We prove this conjecture for noetherian schemes of characteristic zero. Namely, starting with the resolution of singularities for algebraic varieties of characteristic zero, we prove the resolution of singularities for noetherian quasi-excellent Q-schemes.     

Thermodynamic limit for the invariant measures in supercritical zero range processes

We prove a strong form of the equivalence of ensembles for the invariant measures of zero range processes conditioned to a supercritical density of particles. It is known that in this case there is a single site that accomodates a macroscopically large number of the particles in the system. We show that in the thermodynamic limit the rest of the sites have joint distribution equal to the grand canonical measure at the critical density. This improves the result of Großkinsky, Schütz and Spohn, where convergence is obtained for the finite dimensional marginals. We obtain as corollaries limit theorems for the order statistics of the components and for the fluctuations of the bulk.     

Characteristic subgroups of the Jonquere group over a field of characteristic zero

The lattice of characteristic subgroups of the Jonquere group over a field of characteristic zero is described.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 1, pp. 111–113, January, 1995.     

Normal structure of the jonquere group over a field of characteristic zero

The lattice of normal divisors of the Jonquere group over a field of characteristic zero is described. Kiev University, Kiev. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 6, pp. 692–698, June, 1994.     

The polynomial identities of matrices in characteristic zero

The multilinear identities of the k×k matrices F₂ are studied in terms of the cocharacters and codimension sequences. For F₂ the estimates are fairly good, while for k≥3 only partial results are obtained.     

Effect of the third stress invariant on the characteristic curves of a material

The effect of the third invariant of the stress tensor (deviator) on the stress-strain intensity curve and the Lode diagram is investigated.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, Vol. 4, No. 4, pp. 612–617, July–August, 1968.     

Polynomial-time computation of the degree of a dominant morphism in zero characteristic. IV

Consider a projective algebraic variety W that is an irreducible component of the set of all common zeros of a family of homogeneous polynomials of degrees less than d in n + 1 variables in zero characteristic. Consider a dominant rational morphism from W to W′ given by homogeneous polynomials of degree d′. We suggest algorithms for constructing objects in general position related to this morphism. These algorithms are deterministic and polynomial in (dd′) ⁿ and the size of the input. This work concludes a series of four papers. Bibliography: 13 titles. Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 360, 2008, pp. 260–294.     

Polynomial-time computation of the degree of a dominant morphism in zero characteristic. III

Consider a projective algebraic variety W that is an irreducible component of the set of all common zeros of a family of homogeneous polynomials of degrees less than d in n + 1 variables in zero characteristic. Consider a dominant rational morphism from W to W′ given by homogeneous polynomials of degree d′. We suggest algorithms for constructing objects in general position related to this morphism. These algorithms are deterministic and polynomial in (dd′)ⁿ and the size of the input. Bibliography: 13 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 344, 2007, pp. 203–239.