相关论文: Discrete L'Hospital's rule
This paper has been withdrawn by the author due to the version of [A complete proof of Hamilton's conjecture] at arXiv:1008.1576
In this paper, we present the Leibniz rule for the $\Psi-$Hilfer ($\Psi-$H) fractional derivative in two versions, the first in relation to $\Psi-$RL fractional derivative and the second in relation to the $\Psi-$H fractional derivative. In…
Pisier's inequality is central in the study of normed spaces and has important applications in geometry. We provide an elementary proof of this inequality, which avoids some non-constructive steps from previous proofs. Our goal is to make…
Bell tests are of profound statistical nature. Besides physical considerations, the proper understanding of their implications should involve detailed statistical analyses. In this regard, recent works have shown that their consequences and…
In this paper, we obtain an analogue of the discrete Calderon condition and prove that this condition is sufficient for an orthonormal twisted wavelet system to be complete in L^{2}(R^{2}).
A discrete version of Lagrangian reduction is developed in the context of discrete time Lagrangian systems on $G\times G$, where $G$ is a Lie group. We consider the case when the Lagrange function is invariant with respect to the action of…
In this note we discuss the nature of gaps in the support of a discretely infinitely divisible distribution from the angle of compound Poisson laws/processes. The discussion is extended to infinitely divisible distributions on the…
It is well-known that the Lebesgue integral generalises the Riemann integral. However, as is also well-known but less frequently well-explained, this generalisation alone is not the reason why the Lebesgue integral is important and needs to…
The paper reviews various arithmetic analogues of Hamiltonian systems and presents some new facts suggesting ways to relate/unify these examples.
This paper has been withdrawn by the authors. There was an erroneous estimate of the degree of a transformed polynomial, making the method appear more effective than it really is. We thank an anonymous referee for pointing out this error.
The increasing availability of large collections of electronic health record (EHR) data and unprecedented technical advances in deep learning (DL) have sparked a surge of research interest in developing DL based clinical decision support…
A new discrete distribution has been proposed as a discrete analogue of the two sided power distribution [Van Drop, J. R. and Kotz, S. (2002a). A novel extension of the triangular distribution and its parameter estimation, Journal of the…
We introduce the discrete Fr\'echet gap and its variants as an alternative measure of similarity between polygonal curves. We believe that for some applications the new measure (and its variants) may better reflect our intuitive notion of…
Various adaptive randomization procedures (adaptive designs) have been proposed to clinical trials. This paper discusses several broad families of procedures, such as the play-the-winner rule and Markov chain model, randomized…
Clinical trials in specific indications require the administration of rescue medication in case a patient does not sufficiently respond to investigational treatment. The application of additional treatment on an as needed basis causes…
A non-algorithmic, generalized version of a recent result, asserting that a natural relaxation of the Koml\'os conjecture from boolean discrepancy to spherical discrepancy is true, is proved by a very short argument using convex geometry.
This paper aims to study a new stochastic order based upon discrete Laplace transforms. By this order, in a setup where the sample size is random, having discrete delta and nabla distributions, we obtain some ordering results involving…
The extended Hamilton's Principle and other methods proposed to handle non-holonomic constraints are considered. They dont agree with each other. By looking at its consistency with D'Alembert's principle for linear non-holonomic…
As the use of differential privacy (DP) becomes widespread, the development of effective tools for reasoning about the privacy guarantee becomes increasingly critical. In pursuit of this goal, we demonstrate novel relationships between DP…
We discuss some easy statements dealing with linear inhomogeneous Diophantine approximation. Surprisingly, we did not find some of them in the literature.