Related papers: Flett's mean value theorem: a survey
Research on power values of power sums has gained much attention of late, partially due to the explosion of refinements in multiple advanced tools in (computational) Number Theory in recent years. In this survey, we present the key tools…
We give an abstract approach to the results of Adams and Nobel, [1]. It allows to exhibit a new property of VC classes. It should be stressed that the basic ideas of proofs can be found in [1].
This work is dedicated to the promotion of the results Hadamard, Landau E., Walvis A., Estarmann T and Paul R. Chernoff for pseudo zeta functions. The properties of zeta functions are studied, these properties can lead to new regularities…
This work is the continuation of the earlier efforts to apply the mean field approximation to the world sheet formulation of planar phi^3 theory. The previous attempts were either simple but without solid foundation or well founded but…
We introduce a Bayesian mean-value approach for ranking all college football teams using only win-loss data. This approach is unique in that the prior distribution necessary to handle undefeated and winless teams is calculated…
This paper re-examines the first normalized incomplete moment, a well-established measure of inequality with wide applications in economic and social sciences. Despite the popularity of the measure itself, existing statistical inference…
Initially motivated by their relevance in foundations of quantum mechanics and more recently by their applications in different contexts of quantum information science, violations of Bell inequalities have been extensively studied during…
Survey written for the Proceedings of the AMS Meeting on Algebraic Geometry, Seattle, 2005. Based on the talk delivered at this occasion, but a few comments on recent developments are added.
The paper provides a new test of convergence and divergence of positive series. In particular, it extends the known test by Margaret Martin [%\emph{Bull. Amer. Math. Soc.} \textbf{47} (6), 452--457 (1941)]. \emph{Bull. Amer. Math. Soc.}…
The Median of Means (MoM) is a mean estimator that has gained popularity in the context of heavy-tailed data. In this work, we analyze its performance in the task of simultaneously estimating the mean of each function in a class…
For the mean vector test in high dimension, Ayyala et al.(2017,153:136-155) proposed new test statistics when the observational vectors are M dependent. Under certain conditions, the test statistics for one-same and two-sample cases were…
We present a characterization of sets for which Cartwright's theorem holds true. The connection is discussed between these sets and sampling sets for entire functions of exponential type.
This paper aims to question the suitability of the Turing Test, for testing machine intelligence, in the light of advances made in the last 60 years in science, medicine, and philosophy of mind. While the main concept of the test may seem…
We generalize the well-known mean value inequality of subharmonic functions for a slightly more general function class. We also apply this generalized mean value inequality to weighted boundary behavior and nonintegrability questions of…
In this work, using the well-known mean-value theorem (Lagrange's theorem) we obtain an inequality for n-th order differential equations with retarded argument. If the retarded argument vanishes then the inequality turns to an inequality…
We study Cantor's powerset theorem from a graph-theoretic perspective, consider some alternative proofs to Cantor's original, and provide a new proof.
We show how one can ascertain the values of a complete set of mutually complementary observables of a prime degree of freedom.
In recent years, partially observable functional data has gained significant attention in practical applications and has become the focus of increasing interest in the literature. In this thesis, we build upon the concept of data…
We introduce the notion of a random mean generated by a random variable and give a construction of its expected value. We derive some sufficient conditions under which strong laws of large numbers and some limit theorems hold for random…
New estimators for the mean and the covariance function for partially observed functional data are proposed using a detour via the fundamental theorem of calculus. The new estimators allow for a consistent estimation of the mean and…