Related papers: Improved Constants for Effective Irrationality Mea…
For certain compactly supported metric and/or potential perturbations of the Laplacian on $\mathbb{H}^{n+1}$, we establish an upper bound on the resonance counting function with an explicit constant that depends only on the dimension, the…
This paper presents a formal approach to explaining change of inference in Quantitative Bipolar Argumentation Frameworks (QBAFs). When drawing conclusions from a QBAF and updating the QBAF to then again draw conclusions (and so on), our…
We prove a $\mathsf{C}^1$-elliptic estimate of the form $ \sup_{B(x,r/2)} |\mathrm{grad} (\psi) | \leq C \left\{ \sup_{B(x,r)} |\Delta \psi| + \sup_{B(x,r)} |\psi| \right\}, $ valid on any complete Riemannian manifold $M$ and for any smooth…
We continue the work of Takao Komatsu by considering the inhomogeneous approximation constant L(\theta,\phi) for Hurwitzian numbers \theta, and rationally related \phi(r \theta +m)/n in Q(\theta) +Q. The current work uses a compactness…
Let $(M,g)$ be an analytic Riemannian manifold of dimension $n \geq 5$. In this paper, we consider the so-called constant $Q$-curvature equation \[ \varepsilon^4\Delta_{g}^2 u -\varepsilon^2 b \Delta_{g} u +a u = u^{p} , \qquad \text{in }…
In this article, we deal with the fine boundary regularity, a weighted H\"{o}lder regularity of weak solutions to the problem involving the fractional $(p,q)$ Laplacian denoted by $(-\Delta)_{p}^{s} u + (-\Delta)_{q}^{s} u = f(x)$ in…
The problem of testing low-degree polynomials has received significant attention over the years due to its importance in theoretical computer science, and in particular in complexity theory. The problem is specified by three parameters:…
We found, by Hurwitz's Zeta Function, a new functional equation for Riemann Zeta Function. Considering this equation for $s=2$ and $s=1$, we determine a relation between the values of Riemann zeta Function on positive integers. The Matrix…
We propose a unified framework for establishing existence of nonparametric M-estimators, computing the corresponding estimates, and proving their strong consistency when the class of functions is exceptionally rich. In particular, the…
We find uniform with respect to parameter $p \ (1\leq p\leq\infty)$ upper estimations of best approximations by trigonometric polynomials of classes $C^{\psi}_{\beta,p}$ of periodic functions generated by sequences $\psi(k)$, that decrease…
We obtain new inequalities for certain hypergeometric functions. Using these inequalities, we deduce estimates for the hyperbolic metric and the induced distance function on a certain canonical hyperbolic plane domain.
In this paper, we present a result on using algebraic conjugates to form a sequence of approximations to an algebraic number, and in this way obtain effective irrationality measures for related algebraic numbers. From this result, we are…
We give explicit and asymptotic lower bounds for the quantity $|e^{s/t}-M/N|$ by studying a generalized continued fraction expansion of $e^{s/t}$. In cases $|s|\geq 3$ we improve existing results by extracting a large common factor from the…
A new non-parametric method based on Gaussian Processes was proposed recently to measure the Hubble constant $H_0$. The freedom in this approach comes in the chosen covariance function, which determines how smooth the process is and how…
\begin{abstract} In this paper we address the problem of finding the best constants in inequalities of the form: $$ \|\big(|P_+f|^s+|P_-f|^s\big)^{\frac{1}{s}}\|_{L^p({\mathbb{T}})}\leq A_{p,s} \|f\|_{L^p({\mathbb{T}})},$$ where $P_+f$ and…
In this paper we give an extension of the classical Caffarelli-Kohn-Nirenberg inequalities: we show that for $1<p,q<\infty$, $0<r<\infty$ with $p+q\geq r$, $\delta\in[0,1]\cap\left[\frac{r-q}{r},\frac{p}{r}\right]$ with $\frac{\delta…
The main aim of the present work is to give some interesting the $q$-analogues of various $q$-recurrence relations, $q$-recursion formulas, $q$-partial derivative relations, $q$-integral representations, transformation and summation…
Considerable progress has been made in determining the Hubble constant over the past two decades. We discuss the cosmological context and importance of an accurate measurement of the Hubble constant, and focus on six high-precision…
Pippenger ([Pippenger, 1977]) showed the existence of $(6m,4m,3m,6)$-concentrator for each positive integer $m$ using a probabilistic method. We generalize his approach and prove existence of $(6m,4m,3m,5.05)$-concentrator (which is no…
The one-loop effective action for 4-dimensional gauged supergravity with negative cosmological constant, is investigated in space-times with compact hyperbolic spatial section. The explicit expansion of the effective action as a power…