Related papers: A note on a variance bound for the multinomial and…

In this note, we give an explicit expression for the quantile of a mixture of two random variables. We carefully examine all possible cases of discrete and continuous variables with possibly unbounded support. The result is useful for…

In this paper, we prove an inequality regarding the differential polynomial. This improves some recent results.

The aim of this note is to provide a variant statement of Mumford's theorem. This variant states that for a general variety, all Chow groups are "as large as possible", in the sense that they cannot be supported on a divisor.

This paper introduces a new discrete distribution suggested by curtailed sampling rules common in early-stage clinical trials. We derive the distribution of the smallest number of independent Bernoulli(p) trials needed in order to observe…

We study the shape of the probability mass function of the Markov binomial distribution, and give necessary and sufficient conditions for the probability mass function to be unimodal, bimodal or trimodal. These are useful to analyze the…

In this note, we derive a Leibniz rule for difference quotient.

This work sheds some light on the relationship between a distribution's standard deviation and its range, a topic that has been discussed extensively in the literature. While many previous studies have proposed inequalities or relationships…

We give a distribution-dependent concentration inequality for functions of independent variables. The result extends Bernstein's inequality from sums to more general functions, whose variation in any argument does not depend too much on the…

In this note we give a new lower bound on the virtual crossing number via the writhe polynomial, which refines a result of B. Mellor. The proof is based on a new interpretation of the writhe polynomial. The characterization of the writhe…

We obtain a lower bound for a number of primes in tuples. As applications, we obtain a lower bound for the Romanoff type representation functions.

In this paper, we derive optimality conditions (Chebyshev approximation) for multivariate functions. The theory of Chebyshev (uniform) approximation for univariate functions is very elegant. The optimality conditions are based on the notion…

We give an exposition and numerical studies of upper hedging prices in multinomial models from the viewpoint of linear programming and the game-theoretic probability of Shafer and Vovk. We also show that, as the number of rounds goes to…

In this short note we explain how one can use established results to prove various versions of the positive mass theorem for initial data sets with boundary, in dimensions less than 8.

In this paper we prove existence and multiplicity results of unbounded critical points for a general class of weakly lower semicontinuous functionals. We will apply a suitable nonsmooth critical point theory.

We survey results on Chebyshev polynomials centered around the work of H. Widom. In particular, we discuss asymptotics of the polynomials and their norms and general upper and lower bounds for the norms. Several open problems are also…

A new lower bound for the maximal length of a multivector is obtained. It is much closer to the best known upper bound than previously reported lower bound estimates. The maximal length appears to be unexpectedly large for $n$-vectors, with…

A variational formula for the asymptotic variance of general Markov processes is obtained. As application, we get a upper bound of the mean exit time of reversible Markov processes, and some comparison theorems between the reversible and…

In this work, considering a general subclass of bi-univalent functions and using the Chebyshev polynomials, we obtain coefficient expansions for functions in this class.

Let X_1,..., X_n be independent Bernoulli random variables and $f$ a function on {0,1}^n. In the well-known paper (Talagrand1994) Talagrand gave an upper bound for the variance of f in terms of the individual influences of the X_i's. This…

We provide an index bound for character sums of polynomials over finite fields. This improves the Weil bound for high degree polynomials with small indices, as well as polynomials with large indices that are generated by cyclotomic mappings…