Related papers: On Ryser's Conjecture
We give a new proof of a lemma by L. Shepp, that was used in connection to random coverings of a circle.
We give a number new examples analytically and numerically to confirm the Kohler conjecture. It turned out that for a rather large class of nonnegative functions the equality (A) hold.
The assumptions needed to prove Cox's Theorem are discussed and examined. Various sets of assumptions under which a Cox-style theorem can be proved are provided, although all are rather strong and, arguably, not natural.
We extend Carpi's results by showing that Dejean's conjecture holds for n >= 30.
In this paper, we have obtained a necessary and suffcient condition for the series.
We introduce a necessary and sufficient criterion for determining the existence and the values of ratio limits of complex sequences generated by arbitrary linear recurrences.
This article proposes a unified analytical approach leading to a partial resolution of the Erdos-Straus, Sierpinski conjectures, and their generalization. We introduce an equivalent reformulation of these conjectures while constructing two…
We derive the necessary and sufficient condition for almost sure convergence of the sequence of measurable functions, and consider some applications in the theory of Fourier series and in the theory of random fields.
We find conditions equivalent to some commutator identities considered in Part I
We defend a new theory of statistical evidence, which we call Robust Bayesianism (RB). We prove that, under widely accepted assumptions, RB entails the law of likelihood [Royall, 1997], the likelihood principle [Berger and Wolpert, 1988],…
The first version of this paper gave another proof of the Kropholler Conjecture, which gives a relative version of Stallings Ends Theorem, following an earlier incorrect proof. It has been pointed out by Sam Shepherd that the the second…
The necessary and sufficient conditions for differentiability of a function of several real variables stated and proved and its ramifications discussed.
We give a proof of Cox's Theorem on the product rule and sum rule for conditional plausibility without assuming continuity or differentiablity of plausibility. Instead, we extend the notion of plausibility to apply to unknowns giving them…
A conjecture is given that, if true, could lead to an algorithm for computing definite sums of rational functions.
We provide a proof of the Borwein Conjecture using analytic methods.
In this paper a new conjecture equivalent to Collatz conjecture is presented. In particural, showing that (all) the solution(s) of newly introduced iterative functional equation(s) have a given property is equivalent to prove Collatz…
We prove the Milnor conjecture for Lie groups and the Friedlander conjecture for complex algebraic Lie groups.
We prove the Invariant Subspace Conjecture for separable Hilbert spaces.
Give deterministic necessary and sufficient conditions to guarantee that if a subspace fits certain partially observed data from a union of subspaces, it is because such data really lies in a subspace. Furthermore, Give deterministic…
We prove a stronger version of a termination theorem appeared in the paper "On existence of log minimal models II". We essentially just get rid of the redundant assumptions so the proof is almost the same as in there. However, we give a…