Related papers: On the Brannan's conjecture
The classical propositional assumption-based model is extended to incorporate probabilities for the assumptions. Then it is placed into the framework of evidence theory. Several authors like Laskey, Lehner (1989) and Provan (1990) already…
We give derivations of some basic results for the Bernstein approximation in $n$ variables that are useful in investigating copulas. It is shown that Bernstein approximations of copulas are again copulas. We exhibit a stochastic…
Bayesian inference affords scientists with powerful tools for testing hypotheses. One of these tools is the Bayes factor, which indexes the extent to which support for one hypothesis over another is updated after seeing the data. Part of…
This note gives an informal overview of the proof in our paper "Borel Conjecture and Dual Borel Conjecture", see arXiv:1105.0823.
Inspired by the recent pioneering work, dubbed "The Ramanujan Machine" by Raayoni et al. (arXiv:1907.00205), we (automatically) [rigorously] prove some of their conjectures regarding the exact values of some specific infinite continued…
We prove the Aharoni Berger Conjecture
In this paper, we state as a conjecture a vector-valued Hopf-Dunford-Schwartz lemma and give a partial answer to it. As an application of this powerful result, we prove some Fe fferman-Stein inequalities in the setting of Dunkl analysis…
The object of this paper is to generalize a theorem on the binomial coefficient [4] to the case in an arithmetic progression. We will also give a slightly stronger result than Langevin's [2].
A conjecture is given that, if true, could lead to an algorithm for computing definite sums of rational functions.
A recently proposed integral representation for permanents is rederived using only elementary combinatorics. For this proof the assumption that the matrix, for which the permanent is calculated, has an inverse is not necessary.
In this paper, we introduce the method of adding additional factors and a parameter to multiple zeta values and prove some generalizations of the duality theorem and several relations among multiple zeta values. In particular, we are able…
We provide the results of pattern recognition experiments on mathematical expressions. We give a few examples of conjectured results. None of which was thoroughly checked for novelty. We did not attempt to prove all the relations found and…
We provide a refinement of Horn's conjecture by considering spectra with repetitions. To do this we adapt P. Belkale's techniques to our context, in the form proposed by N. Berline, M. Vergne and M. Walter.
We introduce a multivariate analogue of Bernoulli polynomials and give their fundamental properties: difference and differential relations, symmetry, explicit formula, inversion formula, multiplication theorem, and binomial type formula.…
A proof of the continuous martingale convergence theorem is provided. It relies on a classical martingale inequality and the almost sure convergence of a uniformly bounded non-negative super-martingale, after a truncation argument.
In Bayesian hypothesis testing, evidence for a statistical model is quantified by the Bayes factor, which represents the relative likelihood of observed data under that model compared to another competing model. In general, computing Bayes…
A parameter estimation problem is considered for a stochastic parabolic equation with multiplicative noise under the assumption that the equation can be reduced to an infinite system of uncoupled diffusion processes. From the point of view…
We show that Pinney's equation [2] with a constant coefficient can be reduced to its linear part by a simple change of variables. Also, Pinney's original solution is simplified slightly.
Triangular distributions are a well-known class of distributions that are often used as an elementary example of a probability model. Maximum likelihood estimation of the mode parameter of the triangular distribution over the unit interval…
In this paper we have proposed a median based estimator using known value of some population parameter(s) in simple random sampling. Various existing estimators are shown particular members of the proposed estimator. The bias and mean…