This paper introduces a novel boundary integral approach of shape uncertainty quantification for the Helmholtz scattering problem in the framework of the so-called parametric method. The key idea is to form a low-dimensional spatial embedding within the family of uncertain boundary deformations via the Coarea formula. The embedding, essentially, encompasses any irregular behavior of the boundar...

Uncertainty theory is a branch of axiomatic mathematics that deals with human uncertainty, and uncertain variable is used tomodel the uncertain quantities. Inverse uncertainty distribution provides an easy way to calculate the functions of uncertain variables as well as their expected values. This paper mainly presents a formula to calculate the variance of an uncertain variable via the inverse...

How does demand uncertainty affect entry into skill-based competition? I investigate this question in a market entry experiment with skill-based payoffs by systematically varying two key elements of the market environment: demand risk and expected market size. Results show that people’s reactions to demand risk depend on the market size: in small markets people enter more when demand is risky, ...

Ranking decision for interval data is a very important issue in decision making analysis. In recent years, several ranking approaches based on dominance relations have been developed. In these approaches, a dominance degree and an entire dominance degree are employed. However, one cannot obtain the complete rank of objects. To address this problem, this work will propose a two-grade approach to...

A function giving the distribution of the angles of orientation of the molecular axes from the normal to the interface can be obtained if one makes use of a number of special assumptions regarding the forces of orientation. This is compared with the distribution calculated on assuming an extreme form of Langmuir's principle of independent surface action. The importance of having such a function...

We review the quaternionic Fourier transform (QFT). Using the properties of the QFT we establish an uncertainty principle for the right-sided QFT. This uncertainty principle prescribes a lower bound on the product of the effective widths of quaternion-valued signals in the spatial and frequency domains. It is shown that only a Gaussian quaternion signal minimizes the uncertainty.

Wormholes have been advanced as both a method for circumventing the limitations of the speed of light as well as a means for building a time machine (to travel to the past). Thus it is argued that General Relativity may allow both of these possibilities. In this note I argue that traversable wormholes connecting otherwise causally disconnected regions, violate two of the most fundamental princi...

A theorem of Hardy states that, if f is a function on R such that |f(x)| ≤ C e−α|x|2 for all x in R and |f̂(ξ)| ≤ C e−β|ξ|2 for all ξ in R, where α > 0, β > 0, and αβ > 1/4, then f = 0. Sitaram and Sundari generalised this theorem to semisimple groups with one conjugacy class of Cartan subgroups and to the K-invariant case for general semisimple groups. We extend the theorem to all semisimple gr...