Exact inequalities for sums of asymmetric random variables, with applications

Let be independent identically distributed random variables each having the standardized Bernoulli distribution with parameter . Let if and . Let . Let f be such a function that f and f′′ are nondecreasing and convex. Then it is proved that for all nonnegative numbers one has the inequality where . The lower bound on m is exact for each . Moreover, is Schur-concave in . A number of corollaries are obtained, including upper bounds on generalized moments and tail probabilities of (super)martingales with differences of bounded asymmetry, and also upper bounds on the maximal function of such (super)martingales. Applications to generalized self-normalized sums and t-statistics are given.      

Linearity of Space-Time Transformations¶Without the One-to-One, Line-onto-Line, or Constancy-of-Speed-of-Light Assumptions

Using a version of the fundamental theorem of geometry without the 1-to-1 assumption, recently obtained by the authors, the following is proved: Let n≥ 2 and T be a mapping ofℝ ⁿ onto itself which maps every timelike lineℓ into an arbitrary line so that the image of every future ray ofℓcontains at least two distinct points or the same holds for every past ray ofℓ. Then T is affine. A version of the Pappus theorem under minimal assumptions is also given, which is then used as a tool in this paper. Related results have been obtained by Borchers and Hegerfeldt. Received: 3 May 1999 / Accepted: 7 July 2000     

Criterion for complete determinacy for concave-convexlike games

Translated from Matematicheskie Zametki, Vol. 49, No. 3, pp. 73–76, March, 1991.     

Contribution of higher gluon condensates to light-quark vacuum polarization

A method of classifying quark operators in QCD sum rules is suggested. The expansion coefficients of all thed≦8 bilinear quark condensates in gluon condensates are calculated. The coefficient functions at the gluon operators withd≦8 in the polarization operator ∏(q ²) of the light-quark vector current are obtained. A comparison is performed with the calculations in the covariantly constant fields and self-dual fields. The results obtained can be used in the sum rules for the ρ, ω and ? families.     

Positive-part moments via characteristic functions,and more general expressions

A unifying and generalizing approach to representations of the positive-part and absolute moments \({{\mathsf {E}}} X_+^p\) and \({{\mathsf {E}}}|X|^p\) of a random variable X for real p in terms of the characteristic function (c.f.) of X, as well as to related representations of the c.f. of \(X_+\), generalized moments \({{\mathsf {E}}} X_+^p e^{iuX}\), truncated moments, and the distribution function, is provided. Existing and new representations of these kinds are all shown to stem from a single basic representation. Computational aspects of these representations are addressed.     

Mitochondrial respiratory chain is involved in insulin-stimulated hydrogen peroxide production and plays an integral role in insulin receptor autophosphorylation in neurons

Background  

Accumulated evidence suggests that hydrogen peroxide (H₂O₂) generated in cells during insulin stimulation plays an integral role in insulin receptor signal transduction. The role of insulin-induced H₂O₂ in neuronal insulin receptor activation and the origin of insulin-induced H₂O₂ in neurons remain unclear. The aim of the present study is to test the following hypotheses (1) whether insulin-induced H₂O₂ is required for insulin receptor autophosphorylation in neurons, and (2) whether mitochondrial respiratory chain is involved in insulin-stimulated H₂O₂ production, thus playing an integral role in insulin receptor autophosphorylation in neurons.     

Fundamental theorem of geometry without the 1-to-1 assumption

It is proved that any mapping of an -dimensional affine space over a division ring onto itself which maps every line into a line is semi-affine, if and . This result seems to be new even for the real affine spaces. Some further generalizations are also given. The paper is self-contained, modulo some basic terms and elementary facts concerning linear spaces and also - if the reader is interested in other than , , or - division rings.

     

Cyclic polygons with given edge lengths: Existence and uniqueness

Let a₁, ..., a_n be positive numbers satisfying the condition that each of the a_i’s is less than the sum of the rest of them; this condition is necessary for the a_i’s to be the edge lengths of a (closed) polygon. It is proved that then there exists a unique (up to an isometry) convex cyclic polygon with edge lengths a₁, ..., a_n. On the other hand, it is shown that, without the convexity condition, there is no uniqueness—even if the signs of all central angles and the winding number are fixed, in addition to the edge lengths.     

Nonnegative sum-symmetric matrices and optimal-score partitions

Positivity - The main result of the note describes certain optimal-score partitions. This result is based on the fact that any nonnegative square matrix whose column sums are the same as the...