Related papers: A note comprising a negative resolution of the Eff…
These notes are a self-contained short proof of the stability of persistence diagrams.
The aim of this note is to record a proof that the estimate $$\max{\{|A+A|,|A:A|\}}\gg{|A|^{12/11}}$$ holds for any set $A\subset{\mathbb{F}_q}$, provided that $A$ satisfies certain conditions which state that it is not too close to being a…
In this note, we consider the problem of aggregation of estimators in order to denoise a signal. The main contribution is a short proof of the fact that the exponentially weighted aggregate satisfies a sharp oracle inequality. While this…
The main result of this paper, as previously presented to arxiv, was incorrect. See the full text for details and for reference to the remaining results.
The purpose of this note is to give counterexamples to the containment $I^{(3)}\subset I^2$ over the real numbers.
A strongly damped wave equation including the displacement depending nonlinear damping term and nonlinear interaction function is considered. The main aim of the note is to show that under the standard dissipativity restrictions on the…
We present a number of examples and counterexamples to illustrate the results on cost-efficiency in an incomplete market obtained in [BS24]. These examples and counterexamples do not only illustrate the results obtained in [BS24], but show…
This short note provides a sharper upper bound of a well known inequality for the sum of divisors function. This is a problem in pure mathematics related to the distribution of prime numbers. Furthermore, the technique is completely…
A conjecture is given that, if true, could lead to an algorithm for computing definite sums of rational functions.
This note gives a short proof on characterizations of a forest to be equitably k-colorable.
The authors are not satisfied about the analysis.
We have dealt with the Euler's alternating series of the Riemann zeta function to define a regularized ratio appeared in the functional equation even in the critical strip and showed some evidence to indicate the hypothesis. We briefly…
In this note we provide a simple formula of general term of recurrent sequence.
We study the ex-ante minimization of market inefficiency, defined in terms of minimum deviation of market prices from fundamental values, from a centralized planner's perspective. Prices are pressured from exogenous trading actions of…
This short note presents a peculiar generalization of the Riemann hypothesis, as the action of the permutation group on the elements of continued fractions. The problem is difficult to attack through traditional analytic techniques, and…
A method is presented for using the consistent part of inconsistent axiomatic systems.
The paper has benn withdrawn because the computation of the external virial contains an error which invalidate the main result.
A nonlinear parabolic differential equation is presented which has at least one equilibrium. This equilibrium is shown to have a negative definite linearization, but a spectrum which includes zero. An elementary construction shows that the…
The note is a continuation of the previous paper ``On q-analogues of Riemann's zeta'' (math.QA/980499). It contains an output of the computer program calculating the zeros of the ``sharp'' q-zeta function.
In this note we answer a question concerning lineability of the set of non-absolutely summing operators.