Related papers: On two conjectures for M&m sequences
It has been long congectured that the crossing number of $C_m\times C_n$ is $(m-2)n$ for $2<m<=n$. In this paper we proved that conjecture is true for all but finitely many $n$ for each $m$. More specifically we proved conjecture for…
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…
We study characteristics which might distinguish two-graphs by introducing different numerical measures on the collection of graphs on $n$ vertices. Two conjectures are stated, one using these numerical measures and the other using the deck…
The famous (3n + 1) or Collatz conjecture has admitted some progress over the last several decades towards the conclusion that the conjecture is true (i.e. that all Collatz sequences will eventually reach a value of one), but has stubbornly…
We study quenched mixing rates for two classes of random interval maps characterized by the presence of two indifferent fixed points and singular points. Using a random tower construction we prove the existence of an equivariant absolutely…
Using algebraic transformations and equivalent reformulations we derive a number of new results from some earlier ones (by the author) in more accepted terms closely related to well-known conjectures of Bondy and Jung including a number of…
When testing for the mean vector in a high dimensional setting, it is generally assumed that the observations are independently and identically distributed. However if the data are dependent, the existing test procedures fail to preserve…
Seemingly unrelated linear regression models are introduced in which the distribution of the errors is a finite mixture of Gaussian components. Identifiability conditions are provided. The score vector and the Hessian matrix are derived.…
We take the first steps to develop Conley-Zehnder Theory, as conjectured by Arnold, in the world of probability. As far as we know, this paper provides the first probabilistic theorems about the density of fixed points of symplectic twist…
We obtain new average results on the conjectures of Lang-Trotter and Sato-Tate about elliptic curves.
Quotients and comprehension are fundamental mathematical constructions that can be described via adjunctions in categorical logic. This paper reveals that quotients and comprehension are related to measurement, not only in quantum logic,…
On being told that a piece of work he thought was his discovery had duplicated an earlier mathematician's work, Larry Shepp once replied "Yes, but when {\em I} discovered it, it {\em stayed} discovered". In this spirit we give discussion…
We report the emergence of a striking new phenomenon in arithmetic, which we call murmurations. First observed experimentally through averages over large arithmetic datasets, murmurations can be detected and analyzed using standard…
In the last 15 years, White and Huisken-Sinestrari developed a far-reaching structure theory for the mean curvature flow of mean convex hypersurfaces. Their papers provide a package of estimates and structural results that yield a precise…
We explore the recent results announced in "Robust machine learning by median-of-means: theory and practice" by G. Lecu\'e and M. Lerasle. We show that these results are, in fact, almost obvious outcomes of the machinery developed in [4]…
Assuming a $q$-variant of the prime $k$-tuple conjecture uniformly, we compute mixed moments of the number of primes in disjoint short intervals and progressions, respectively. This involves estimating the mean of singular series along…
Collatz Conjecture sequences increase and decrease in seemingly random fashion. By identifying and analyzing the forms of numbers, we discover that Collatz sequences are governed by very specific, well-defined rules, which we call cascades.
In this paper we explore a family of congruences over $\N^\ast$ from which one builds a sequence of symmetric matrices related to the Mertens function. From the results of numerical experiments, we formulate a conjecture about the growth of…
In the unidimensional unfolding model, given m objects in general position there arise 1+m(m-1)/2 rankings. The set of rankings is called the ranking pattern of the m given objects. By changing these m objects, we can generate various…
In this note, we present a conjecture on intersections of set families, and a rephrasing of the conjecture in terms of principal downsets of Boolean lattices. The conjecture informally states that, whenever we can express the measure of a…