In this paper we show three new results concerning dimension datum. Firstly, for two subgroups $H_{1}$($\cong U(2n+1)$) and $H_{2}$($\cong Sp(n)\times SO(2n+2)$) of $SU(4n+2)$, find a family pairs irreducible representations $(\tau_1,\tau_2)\in\hat{H_{1}}\times\hat{H_{2}}$ such that $\mathscr{D}_{H_1,\tau_1}=\mathscr{D}_{H_2,\tau_2}$. With construct examples isospectral hermitian vector bundles...

By examining the Fourier transform of the initial datum near the origin, we define the decay character of the datum and provide a method to study the lower and upper algebraic rates of decay of solutions to a wide class of dissipative system of equations.

We prove that for a given strictly increasing initial datum in C,the solution of the initial value problem is piecewise C smooth except for flux functions of nonconvex conservation laws in a certain subset of C of first category,defined in the range of the initial datum.

Traditionally, geometric dimensioning and tolerancing (GD&T) requirements have been exchanged with technical drawings. However, with the advent of computer-aided design, manufacturing, and inspection equipment, the ability to exchange these requirements in a computer-sensible manner has become increasingly more desirable. As “a data model is an effective technique to define the shareable semant...

There are numerous past and current examples of ontology-driven projects that provide auto-generated user interfaces for managing entities and relations, each presenting its own varied and complex data model. Our Datum Proof Sheet application aims to simplify the application development landscape by building community consensus about the way basic categorical, textual and numeric datum fields s...

The axis of the non-diffracting beam produced by an axicon is very stable and can be adopted as the datum line to measure the spatial straightness error in continuous working distance, which may be short, medium or long. Though combining the non-diffracting beam datum-line with LVDT displace detector, a new straightness error measurement method is developed. Because the Non-diffracting beam dat...

Given a smooth bounded domain Ω ⊆ R, we consider the equation ∆v = 2vx ∧ vy in Ω, where v : Ω → R. We prescribe Dirichlet boundary datum, and consider the case in which this datum converges to zero. An asymptotic study of the corresponding Euler functional is performed, analyzing multiple-bubbling phenomena. This allows us to settle a particular case of a question raised by H. Brezis and J.M. C...