Related papers: New error bounds for Boole's rule
Numerical integration over the implicitly defined domains is challenging due to topological variances of implicit functions. In this paper, we use interval arithmetic to identify the boundary of the integration domain exactly, thus getting…
Nelson's stochastic quantum mechanics provides an ideal arena to test how the Born rule is established from an initial probability distribution that is not identical to the square modulus of the wave function. Here, we investigate…
This article considers the semilinear boundary value problem given by the Poisson equation, -\Delta u=f(u) in a bounded domain \Omega\subset \R^{n} with smooth boundary. For the zero boundary value case, we approximate a solution using the…
In this work we propose and analyse a numerical method for computing a family of highly oscillatory integrals with logarithmic singularities. For these quadrature rules we derive error estimates in terms of $N$, the number of nodes, $k$ the…
The algebraic derivation of the numerical limits of Bell inequalities in either three or four random variables is independent of the assumption of randomness.The limits of the inequalities follow as mathematical consequences of their…
Numerical computation of the time evolution of the mass transfer rate in a close binary can be and, in particular, has been a computational challenge. Using a simple physical model to calculate the mass transfer rate, we show that for a…
Boole polynomials play an important role in the area of number theory, algebra and umbral calculus. In this paper, we investigate some properties of Boole polynomials and consider Witt-type formulas for the Boole numbers and polynomials.…
It is shown that the Mott insulating and superfluid phases of bosons in an optical lattice may be distinguished by a non-local 'parity order parameter' which is directly accessible via single site resolution imaging. In one dimension, the…
This paper introduces a fast and numerically stable algorithm for the solution of fourth-order linear boundary value problems on an interval. This type of equation arises in a variety of settings in physics and signal processing. Our method…
In this paper, we propose new sequential estimation methods based on inclusion principle. The main idea is to reformulate the estimation problems as constructing sequential random intervals and use confidence sequences to control the…
Let $X_1,X_2,...,X_n$ be a sequence of independent or locally dependent random variables taking values in $\mathbb{Z}_+$. In this paper, we derive sharp bounds, via a new probabilistic method, for the total variation distance between the…
Simple upper and lower bounds are established for the integral $\int_0^x\mathrm{e}^{-\beta u}u^\nu t_{\mu,\nu}(u)\,\mathrm{d}u$, where $x>0$, $0<\beta<1$, $\mu+\nu>-2$, $\mu-\nu\geq-3$, and $t_{\mu,\nu}(x)$ is the modified Lommel function…
In this paper, we study the inverse problem for determining an unknown time-dependent source coefficient in a semilinear pseudo-parabolic equation with variable coefficients and Neumann boundary condition. This unknown source term is…
We present new tight bounds for averaging differential inclusions, which we apply to multi-frequency inclusions consisting of a sum of time periodic set-valued mappings. For this family of inclusions we establish an a tight estimate of…
The recent development, shows that the Bray-Curtis's formula for similarity Index (1957), has been applied in various fields like Ecology, Astrophysics, etc. In this paper, we found the possible boundary conditions for this evolved formula…
We describe methods for proving bounds on infinite-time averages in differential dynamical systems. The methods rely on the construction of nonnegative polynomials with certain properties, similarly to the way nonlinear stability can be…
Cranley and Patterson put forward the following randomization as the basis for the estimation of the error of a lattice rule for an integral of a one-periodic function over the unit cube in s dimensions. The lattice rule is randomized using…
Motivation: The comparison of diverse genomic datasets is fundamental to understanding genome biology. Researchers must explore many large datasets of genome intervals (e.g., genes, sequence alignments) to place their experimental results…
We establish bounds for the covariance of a large class of functions of infinite variance stable random variables, including unbounded functions such as the power function and the logarithm. These bounds involve measures of dependence…
The surface code is a promising candidate for fault-tolerant quantum computation, achieving a high threshold error rate with nearest-neighbor gates in two spatial dimensions. Here, through a series of numerical simulations, we investigate…