Discrete Physics and the Dirac Equation

We rewrite the 1+1 Dirac equation in light cone coordinates in two significant forms, and solve them exactly using the classical calculus of finite differences. The complex form yields ``Feynman's Checkerboard''---a weighted sum over lattice paths. The rational, real form can also be interpreted in terms of bit-strings.Comment: LaTex 16 pages, 10 figures. To obtain a copy, send e-mail to [email protected]

Berry Esseen bounds for combinatorial central limit theorems and pattern occurrences, using zero and size biasing

Berry Esseen type bounds to the normal, based on zero- and size-bias couplings, are derived using Stein's method. The zero biasing bounds are illustrated with an application to combinatorial central limit theorems where the random permutation has either the uniform distribution or one which is constant over permutations with the same cycle type and having no fixed points. The size biasing bounds are applied to the occurrences of fixed relatively ordered sub-sequences (such as rising sequences) in a random permutation, and to the occurrences of patterns, extreme values, and subgraphs on finite graphs.Comment: 23 page

Beyond Disability Civil Rights

[Excerpt] This Article argues that to be effective, both domestic and international disability rights must adopt a disability human rights paradigm. Such a framework combines the type of civil and political rights provided by antidiscrimination legislation (also called negative or first-generation rights) with the full spectrum of social, cultural, and economic measures (also called positive or second-generation rights) bestowed by many human rights treaties.16 By acting holistically, this agenda accounts for factors normally exogenous to civil rights laws and ensures that individuals can flourish and participate in their societies. Accordingly, our intention is to share some thoughts on how to best provide disabled citizens with equal opportunity rather than “merely” equal treatment. Internationally, States and civil society organizations have been developing innovative and effective equality measures. We draw on their experiences in providing examples of how disability legislation and policy can be developed to implement a more holistic human rights approach. These lessons are also pertinent for invigorating the ADA

Rocket engine injector Patent

Rocket engine injector orifice to accommodate changes in density, velocity, and pressure, thereby maintaining constant mass flow rate of propellant into rocket combustion chambe

Insert sleeve prevents tube soldering contamination

Teflon sleeve insert prevents contamination of internal tube surfaces by solder compound during soldering operations that connect and seal the tube ends. The sleeve insert is pressed into the mating tube ends with a slight interference fit