Supersymmetric Matrix model on Z-orbifold

We find that the IIA Matrix models defined on the non-compact $C^3/Z_6$, $C^2/Z_2$ and $C^2/Z_4$ orbifolds preserve supersymmetry where the fermions are on-mass-shell Majorana-Weyl fermions. In these examples supersymmetry is preserved both in the orbifolded space and in the non-orbifolded space at the same time. The Matrix model on $C^3/Z_6$ orbifold has the same ${\cal N}=2$ supersymmetry as the case of $C^3/Z_3$ orbifold which was pointed out previously. On the other hand the Matrix models on $C^2/Z_2$ and $C^2/Z_4$ orbifold have a half of the ${\cal N}=2$ supersymmetry. We further find that the Matrix model on $C^2/Z_2$ orbifold with a parity-like identification preserves ${\cal N}=2$ supersymmetry.Comment: 21 pages, no figur

A simultaneous spin/eject mechanism for aerospace payloads

A simultaneous spin/eject mechanism was developed for aerospace applications requiring a compact, passive device which would accommodate payload support and controlled-release functions, and which would provide a highly accurate spin-ejection motion to the payload. The mechanism satisfied the requirements and is adaptable to other deployment applications

Almost all palindromes are composite

We study the distribution of palindromic numbers (with respect to a fixed base $g\ge 2$) over certain congruence classes, and we derive a nontrivial upper bound for the number of prime palindromes $n\le x$ as $x\to\infty$. Our results show that almost all palindromes in a given base are composite.Comment: 19 page

Instantons, Scale Invariance and Lorentz Invariance in Matrix Theory

In this paper we consider features of graviton scattering in Matrix theory compactified on a 2-torus. The features which interest us can only be determined by nonperturbative effects in the corresponding 2+1 dimensional super Yang Mills theory. We show that the superconformal symmetry of strongly coupled Super Yang Mills Theory in 2+1 dimensions almost determines low energy, large impact parameter ten dimensional graviton scattering at zero longitudinal momentum in the Matrix model of IIB string theory. We then show that amplitudes involving arbitrary transverse momentum transfer are governed by instanton processes similar to the Polchinski Pouliot process. Finally we consider the influence of instantons on a conjectured nonrenormalization theorem. This theorem is violated by instanton processes. Far from being a problem, this fact is seen to be crucial to the consistency of the IIB interpretation. We suggest that the SO(8) invariance of strongly coupled SYM theory may lead to a proof of eleven dimensional Lorentz invariance.Comment: 11 pages (phyzzx

A note on Gauge Theories Coupled to Gravity

We analyze the bound on gauge couplings $e\geq m/m_p$, suggested by Arkani-Hamed et.al. We show this bound can be derived from simple semi-classical considerations and holds in spacetime dimensions greater than or equal to four. Non abelian gauge symmetries seem to satisfy the bound in a trivial manner. We comment on the case of discrete symmetries and close by performing some checks for the bound in higher dimensions in the context of string theory.Comment: 15 pages, 1 figure, Late

Ten Dimensional Black Hole and the D0-brane Threshold Bound State

We discuss the ten dimensional black holes made of D0-branes in the regime where the effective coupling is large, and yet the 11D geometry is unimportant. We suggest that these black holes can be interpreted as excitations over the threshold bound state. Thus, the entropy formula for the former is used to predict a scaling region of the wave function of the latter. The horizon radius and the mass gap predicted in this picture agree with the formulas derived from the classical geometry.Comment: 11 pages, harvmac; v2: typos corrected, argument for the convergence of two integrals improved, v3: one ref. adde

Twisted supersymmetry and the topology of theory space

We present examples of four dimensional, non-supersymmetric field theories in which ultraviolet supersymmetry breaking effects, such as bose-fermi splittings and the vacuum energy, are suppressed by $(\alpha/4 \pi)^{N}$, where $\alpha$ is a weak coupling factor and $N$ can be made arbitrarily large. The particle content and interactions of these models are conveniently represented by a graph with sites and links, describing the gauge theory space structure. While the theories are supersymmetric ``locally'' in theory space, supersymmetry can be explicitly broken by topological obstructions.Comment: 9 pages, revtex

The Nicolas and Robin inequalities with sums of two squares

In 1984, G. Robin proved that the Riemann hypothesis is true if and only if the Robin inequality $\sigma(n)<e^\gamma n\log\log n$ holds for every integer $n>5040$, where $\sigma(n)$ is the sum of divisors function, and $\gamma$ is the Euler-Mascheroni constant. We exhibit a broad class of subsets \cS of the natural numbers such that the Robin inequality holds for all but finitely many n\in\cS. As a special case, we determine the finitely many numbers of the form $n=a^2+b^2$ that do not satisfy the Robin inequality. In fact, we prove our assertions with the Nicolas inequality $n/\phi(n)<e^{\gamma}\log \log n$; since $\sigma(n)/n1$ our results for the Robin inequality follow at once.Comment: 21 page

Breaking the Rayleigh-Plateau instability limit using thermocavitation within a droplet

We report on the generation of liquid columns that extend far beyond the traditional Rayleigh-Plateau instability onset. The columns are driven by the acoustic pressure wave emitted after bubble collapse. A high-speed video imaging device, which records images at a rate of up to 105 fps, was employed to follow their dynamics. These bubbles, commonly termed thermocavitation bubbles, are generated by focusing a midpower (275 mW) continuous wavelength laser into a highly absorbing liquid droplet. A simple model of the propagation of the pressure wavefront emitted after the bubble collapse shows that focusing the pressure wave at the liquid-air interface drives the evolution of the liquid columns. Control over the aspect ratio of the liquid column is realized by adjusting the cavitation bubble's size, beam focus position, and droplet volume. © 2013 by Begell House, Inc