Some limit theorems with respect to constrained permutations and partitions

It is a classical result that the ratio of the fixed point free permutations in the whole tends to 1 / e. A generalization of this limit theorem when the cycles must contain at least a given \(m>2\) number of elements is also known. In the present paper we find the limit of the fixed point free permutations with given number of cycles in the whole. In the second part of the paper similar questions are studied when we take partitions in place of permutations.     

Some imbedding theorems for block designs balanced with respect to pairs

We prove imbedding theorems for block designs balanced with respect to pairs, and with the aid of these theorems we establish the existence of (v, k, )-resolvable BIB block designs with parameters v, k, such that =k–1 [and also such that =(k–l)/2 if k is odd], k ¦(p–1) for each prime divisor p of the number v/k; we also establish an imbedding theorem for Kirkman triple systems.Translated from Matematicheskie Zametki, Vol. 16, No. 1, pp. 173–184, July, 1974.     

Restriction estimates for space curves with respect to general measures

In this paper we consider adjoint restriction estimates for space curves with respect to general measures and obtain optimal estimates when the curves satisfy a finite type condition. The argument here is new in that it doesn?t rely on the offspring curve method, which has been extensively used in the previous works. Our work was inspired by the recent argument due to Bourgain and Guth which was used to deduce linear restriction estimates from multilinear estimates for hypersurfaces.     

Bayesian estimates,stable with respect to the choice of the loss function

A family of distributions is defined for which the generalized Bayesian estimate of a real parameter , constructed according to the repeated choice, does not depend on the choice of the even convex loss function from a sufficiently wide class. It is shown that these families are a subclass of the exponential families with a sufficient statistic for the parameter of rank two.Translated from Matematicheskie Zametki, Vol. 23, No. 2, pp. 327–334, February, 1978.     

Fixed point theorems with respect to a contractive condition of integral type

We derive some fixed point theorems for mappings satisfying a contractive condition of integral type.     

Schur lemma and limit theorems in lattice groups with respect to filters

Some Schur, Nikodým, Brooks-Jewett and Vitali-Hahn-Saks-type theorems for (?)-group-valued measures are proved in the setting of filter convergence. Finally we pose an open problem.     

Rademacher chaos: tail estimates versus limit theorems

We study Rademacher chaos indexed by a sparse set which has a fractional combinatorial dimension. We obtain tail estimates for finite sums and a normal limit theorem as the size tends to infinity. The tails for finite sums may be much larger than the tails of the limit.     

Lefschetz fixed point theorems in generalized neighborhood extension spaces with respect to a map

We present several new Lefschetz fixed point results for compact self maps in new classes of spaces with respect to the map.     

Precision in the basic estimates in contour-solid theorems

Translated from Ukrainskii Matematicheskii Zhurnal. Vol. 41, No. 1, pp. 75–79, January, 1989.     

Superharmonic functions in the Heisenberg group: estimates and Liouville theorems

We state some growth conditions on non negative superharmonic functions of the Heisenberg group in intrinsic cones and prove some non existence results for non negative D_H \Delta_H polyharmonic functions and L¹D_H L^1\Delta_H superharmonic functions.     

Four theorems on uniform estimates of oscillatory integrals

Exact order uniform estimates of oscillatory integrals with monomial phase are obtained. These results are close to the hypothesis of V. I. Arnold on uniform estimates of oscillatory integrals. Namely, for absolute values of oscillatory integrals, estimates of order ρ ^?1/k ln ^n?1 τ uniform with respect to phase and amplitude are derived for every sufficiently small perturbation of phase (i.e., the monomial \(x_1^{m_1 } \ldots x_n^{m_n }\) , m _j ≤ k, 1 ≤ k, is perturbed by monomials \(x_1^{s_1 } \ldots x_n^{s_n }\) , where s _j ≤ k, 1 ≤ j ≤ n), and for each amplitude φ ∈ C ₀ ² (R ⁿ ), n > 0. In the case |m| < nk the upper uniform estimate with the same perturbation and the same amplitude has the order τ ^?1/k ln ^n?2 τ. The estimate by order τ ^?1/k ln ^n?2 τ was proved in the case when the amplitude vanishes at the origin. In the case k = 1, a uniform estimate of order τ ^?1ln ^n?2 τ is valid. This implies a uniform estimate for a polynomial phase. Previously the upper estimate of an oscillatory integral by the value 32 ⁿ τ ^?1/k ln ^n?1(τ+2) was known for the amplitude being the characteristic function of a cube and the same phase.     

Extremality of convex sets with some applications

In this paper we introduce an enhanced notion of extremal systems for sets in locally convex topological vector spaces and obtain efficient conditions for set extremality in the convex case. Then we apply this machinery to deriving new calculus results on intersection rules for normal cones to convex sets and on infimal convolutions of support functions.     

Refined theorems on the relaxation of equality constraints in an optimal control problem,linear with respect to the control

Moscow. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 31, No. 2, pp. 37–51, March–April, 1990.     

Liouville-type theorems and decay estimates for solutions to higher order elliptic equations

Liouville-type theorems are powerful tools in partial differential equations. Boundedness assumptions of solutions are often imposed in deriving such Liouville-type theorems. In this paper, we establish some Liouville-type theorems without the boundedness assumption of nonnegative solutions to certain classes of elliptic equations and systems. Using a rescaling technique and doubling lemma developed recently in Polá?ik et al. (2007) [20], we improve several Liouville-type theorems in higher order elliptic equations, some semilinear equations and elliptic systems. More specifically, we remove the boundedness assumption of the solutions which is required in the proofs of the corresponding Liouville-type theorems in the recent literature. Moreover, we also investigate the singularity and decay estimates of higher order elliptic equations.