Virtual photon structure functions and positivity constraints

We study the three positivity constraints among the eight virtual photon structure functions, derived from the Cauchy-Schwarz inequality and which are hence model-independent. The photon structure functions obtained from the simple parton model show quite different behaviors in a massive quark or a massless quark case, but they satisfy, in both cases, the three positivity constraints. We then discuss an inequality which holds among the unpolarized and polarized photon structure functions $F_1^\gamma$, $g_1^\gamma$ and $W_{TT}^\tau$, in the kinematic region $\Lambda^2\ll P^2 \ll Q^2$, where $-Q^2 (-P^2)$ is the mass squared of the probe (target) photon, and we examine whether this inequality is satisfied by the perturbative QCD results.Comment: 24 pages, 13 eps figure

The Mass of the Lightest Supersymmetric Higgs Boson beyond the Leading Logarithm Approximation

We examine the radiative corrections to the mass of the lightest Higgs boson in the minimal supersymmetric extension of the standard model. We use the renormalization-group improved effective potential which includes the next-to-leading-order contributions. We find that, contrary to the result of Espinosa and Quir\'os, the higher-order corrections to the lightest Higgs boson mass are non-negligible, adding $3-11$ GeV ($3-9$ GeV) to the result in the leading logarithm approximation for the range of top quark mass $100 {\rm GeV} < m_t < 200 {\rm GeV}$ and for the supersymmetric breaking scale $M_{\rm SUSY} = 1 {\rm TeV}$ ($M_{\rm SUSY} = 10 {\rm TeV}$). Also we find that our result is stable under the change of the renormalization parameter $t$.Comment: 17 pages (2 figures not included

Nano-artifact metrics based on random collapse of resist

Artifact metrics is an information security technology that uses the intrinsic characteristics of a physical object for authentication and clone resistance. Here, we demonstrate nano-artifact metrics based on silicon nanostructures formed via an array of resist pillars that randomly collapse when exposed to electron-beam lithography. The proposed technique uses conventional and scalable lithography processes, and because of the random collapse of resist, the resultant structure has extremely fine-scale morphology with a minimum dimension below 10 nm, which is less than the resolution of current lithography capabilities. By evaluating false match, false non-match and clone-resistance rates, we clarify that the nanostructured patterns based on resist collapse satisfy the requirements for high-performance security applications

Whitney umbrellas and swallowtails

In this paper, we introduce the notions of map-germs of pedal unfolding type and normalized Legendrian map-germs; and then we show that the fundamental theorem of calculus provides a natural one to one correspondence between Whitney umbrellas of pedal unfolding type and normalized swallowtails

Spin Structure Function of the Virtual Photon Beyond the Leading Order in QCD

Polarized photon structure can be studied in the future polarized $e^{+}e^{-}$ colliding-beam experiments. We investigate the spin-dependent structure function of the virtual photon $g_1^{\gamma}(x,Q^2,P^2)$, in perturbative QCD for $\Lambda^2 \ll P^2 \ll Q^2$, where $-Q^2$ ($-P^2$) is the mass squared of the probe (target) photon. The analysis is performed to next-to-leading order in QCD. We particularly emphasize the renormalization scheme independence of the result.The non-leading corrections significantly modify the leading log result, in particular, at large $x$ as well as at small $x$. We also discuss the non-vanishing first moment sum rule of $g_1^\gamma$, where ${\cal O}(\alpha_s)$ corrections are computed.Comment: 39 pages, LaTeX, 6 Postscript Figures, eqsection.sty file include

Target Mass Effects in Polarized Virtual Photon Structure Functions

We study target mass effects in the polarized virtual photon structure functions $g_1^\gamma (x,Q^2,P^2)$, $g_2^\gamma (x,Q^2,P^2)$ in the kinematic region $\Lambda^2\ll P^2 \ll Q^2$, where $-Q^2 (-P^2)$ is the mass squared of the probe (target) photon. We obtain the expressions for $g_1^\gamma (x,Q^2,P^2)$ and $g_2^\gamma (x,Q^2,P^2)$ in closed form by inverting the Nachtmann moments for the twist-2 and twist-3 operators. Numerical analysis shows that target mass effects appear at large $x$ and become sizable near $x_{\rm max}(=1/(1+\frac{P^2}{Q^2}))$, the maximal value of $x$, as the ratio $P^2/Q^2$ increases. Target mass effects for the sum rules of $g_1^\gamma$ and $g_2^\gamma$ are also discussed.Comment: 24 pages, LaTeX, 9 eps figure

The alphaalphas2alpha alpha_s^2 corrections to the first moment of the polarized virtual photon structure function g1gamma(x,Q2,P2)g_1^gamma(x,Q^2,P^2)

We present the next-to-next-to-leading order ($alpha alpha_s^2$) corrections to the first moment of the polarized virtual photon structure function $g_1^gamma(x,Q^2,P^2)$ in the kinematical region $Lambda^2 ll P^2 ll Q^2$, where $-Q^2(-P^2)$ is the mass squared of the probe (target) photon and $Lambda$ is the QCD scale parameter. In order to evaluate the three-loop-level photon matrix element of the flavor singlet axial current, we resort to the Adler-Bardeen theorem for the axial anomaly and we calculate in effect the two-loop diagrams for the photon matrix element of the gluon operator. The $alpha alpha_s^2$ corrections are found to be about 3% of the sum of the leading order ($alpha$) andthe next-to-leading order ($alpha alpha_s$) contributions, when $Q^2=30 sim 100 {rm GeV}^2$and $P^2=3{rm GeV}^2$, and the number of active quark flavors $n_f$ is three to five.Comment: 21 page

An explanatory model for food-web structure and evolution

Food webs are networks describing who is eating whom in an ecological community. By now it is clear that many aspects of food-web structure are reproducible across diverse habitats, yet little is known about the driving force behind this structure. Evolutionary and population dynamical mechanisms have been considered. We propose a model for the evolutionary dynamics of food-web topology and show that it accurately reproduces observed food-web characteristic in the steady state. It is based on the observation that most consumers are larger than their resource species and the hypothesis that speciation and extinction rates decrease with increasing body mass. Results give strong support to the evolutionary hypothesis.Comment: 16 pages, 3 figure

Exponentiation of certain Matrices related to the Four Level System by use of the Magic Matrix

In this paper we show how to calculate explicitly the exponential of certain matrices, which are evolution operators governing the interaction of the four level system of atoms and the radiation, etc. We present a consistent method in terms of the magic matrix by Makhlin. As a closely related subject, we derive a closed form expression of the Baker-Campbell-Hausdorff formula for a class of matrices in SU(4), by use of the method developed by the present authors in quant-ph/0610009.Comment: Latex ; 13 pages ; 2 figures ; substantial changes (including the title) made. To appear in Yokohama Mathematical Journal (2007

Upper bounds on the non-random fluctuations in first passage percolation with low moment conditions

We consider first passage percolation with i.i.d. weights on edges of the d-dimensional cubic lattice. Under the assumptions that a weight is equal to zero with probability smaller than the critical probability of bond percolation in the d-dimensional cubic lattice, and has moments bigger than 1, we investigate upper bounds on the so-called non-random fluctuations of the model. In addition, we give an application of our result to a lower bound for variance of the first passage percolation in the case where the limit shape has flat edges.Comment: This is the corrected version of the paper. 11 pages, title change