The Energy Dependence of the Saturation Scale

At low $x \cong Q^2/W^2 << 1$, in deep inelastic scattering, the photon fluctuates into a $q \bar q$ vector state that interacts via two gluons with the proton. The energy dependence is determined by the saturation scale, in our approach given by $\Lambda^2_{sat} (W^2) \sim (W^2)^{C_2}$. Imposing DGLAP evolution, we find $C_2^{theory} = 0.27$ in agreement with the model-independent analysis of the HERA data. Different values of the exponent $C_2$ are correlated with different ratios of the longitudinal to transverse structure function. This stresses the need for experiments to separate longitudinal and transverse contributions in deep inelastic scattering.Comment: To appear in the proceedings of "PHOTON2005 International Conference on the Structure and Interactions of the Photon including the 16th International Workshop on Photon-Photon Collisions", Warsaw, 200

A Design Method for Pin Holding Type Jig

Multi-item flexible manufacturing systems have been spread to correspond the short life-cycle and the diversification of products. Part handling plays an important role to operate multi-functional robot efficiently in these systems, and many jigs are widely used to hold a part. They should be exchanged at once according to changing products. In this paper, we propose a pin jig which holds a part with two pins, and design method of the position, length and diameter of those pins for a cylindrical part. This jig has the following characteristics. As a surface of the jig is inclined to use gravity, the part can be fixed without any external forces. Therefore the structure of jig becomes simple, and loading and unloading of a part becomes easy for a robot hand

J/Psi photo- and electroproduction, the saturation scale and the gluon structure function

Our approach to low-x deep inelastic scattering based on the ell-perp factorization of perturbative QCD (the color-dipole picture) yields parameter-free absolute predictions for J/Psi production. The connection of J/Psi production to the low-x saturation scale and to the gluon structure function is clarified.Comment: 14 pages with 4 figures, with some comments on skewness etc adde

On e+e- --> W+W- --> 4f(+gamma) at LEP2

The results on e+e- --> W+W- --> 4f(+gamma) obtained by different groups are compared with each other. Differences in the results for the total cross section of up to about 0.6% are traced back to different ways of implementing the double-pole approximation.Comment: 11 pages, late

The Color Dipole Picture and the ratio of R(W, Q) = sigma L/sigma T

The transverse size of q q-bar fluctuations of the longitudinal photon is reduced relative to the transverse size of q q-bar fluctuations of the transverse photon. This implies R(W2, Q2) = 0.375 or, equivalently, FL/F2 = 0.27 at x<<0.1 and Q2 sufficiently large, while R(W2, Q2) = 0.5, if this effect is not taken into account. Forthcoming experimental data from HERA will allow to test this prediction.Comment: 13 pages, 1 figur

Fractional time differential equations as a singular limit of the Kobayashi-Warren-Carter system

This paper is concerned with a singular limit of the Kobayashi-Warren-Carter system, a phase field system modelling the evolutions of structures of grains. Under a suitable scaling, the limit system is formally derived when the interface thickness parameter tends to zero. Different from many other problems, it turns out that the limit system is a system involving fractional time derivatives, although the original system is a simple gradient flow. A rigorous derivation is given when the problem is reduced to a gradient flow of a single-well Modica-Mortola functional in a one-dimensional setting.Comment: 24 page