In this paper we establish some Ostrowski type inequalities for double integral mean of absolutely continuous functions. An application for special means is given as well.
We prove the weak consistency of the trimmed least square estimator of the covariance parameter of an AR(1) process with stable errors.
The ultrapower T* of an arbitrary ordered set T is introduced as an infinitesimal extension of T. It is obtained as the set of equivalence classes of the sequences in T, where the corresponding relation is generated by a free ultrafilter on the set of natural numbers. It is established that T* always satisfies Cantor’s property, while one can give the necessary and sufficient conditions for T so that T* would be complete or it would fulfill the open completeness property, respectively. Namely, the density of the original set determines the open completeness of the extension, while independently, the completeness of T* is determined by the cardinality of T.
We introduce a Floer homotopy version of the contact invariant introduced by Kronheimer–Mrowka–Ozsváth–Szabó. Moreover, we prove a gluing formula relating our invariant with the first author’s Bauer–Furuta type invariant, which refines Kronheimer–Mrowka’s invariant for 4-manifolds with contact boundary. As an application, we give a constraint for a certain class of symplectic fillings using equivariant KO-cohomology.
We extend the construction of Y-type invariants to null-homologous knots in rational homology three-spheres. By considering m-fold cyclic branched covers with m a prime power, this extension provides new knot concordance invariants
We prove a theorem on the preservation of inequalities between functions of a special form after differentiation on an ellipse. In particular, we obtain generalizations of the Duffin–Schaeffer inequality and the Vidensky inequality for the first and second derivatives of algebraic polynomials to an ellipse.
In this paper we work out a Riemann–von Mangoldt type formula for the summatory function
A congruence is defined for a matroid. This leads to suitable versions of the algebraic isomorphism theorems for matroids. As an application of the congruence theory for matroids, a version of Birkhoff’s Theorem for matroids is given which shows that every nontrivial matroid is a subdirect product of subdirectly irreducible matroids.
Let (M, [g]) be a Weyl manifold and TM be its tangent bundle equipped with Riemannian g−natural metrics which are linear combinations of Sasaki, horizontal and vertical lifts of the base metric with constant coefficients. The aim of this paper is to construct a Weyl structure on TM and to show that TM cannot be Einstein-Weyl even if (M, g) is fiat.
We give all functions ƒ , E: ℕ → ℂ which satisfy the relation
for every a, b, c ∈ ℕ, where h ≥ 0 is an integers and K is a complex number. If n cannot be written as a2 + b2 + c2 + h for suitable a, b, c ∈ ℕ, then ƒ (n) is not determined. This is more complicated if we assume that ƒ and E are multiplicative functions.