Abstract:
[2+2] Photocycloaddition of olefins is a very useful reaction in synthetic organic chemistry to obtain cyclobutane-containing molecules, which are almost inaccessible by other methods. The reaction, when performed in the crystalline state, occurs more efficiently and selectively than in homogeneous solution due to tight and regular molecular arrangement in the crystal state. Despite numerous examples for the solid-state [2+2] photodimerization of monoenes, however, it is still a challenge to prepare not only dimers but also higher oligomers and polymers from conjugated polyenes, which have multiple reactive double bonds in a molecule. In our recent studies of the solid-state photoreactions of α,ω-diarylpolyenes, noncovalent intermolecular interactions in crystals were effectively utilized to prealign molecules in stacking arrangements, suitable for the [2+2] reaction. With appropriate ring-substituents, [2+2] photodimerization and photopolymerization of the polyenes took place, although the degree of polymerization was relatively low. This review will describe the details of these reactions.

Abstract:
It has been known for some time that 2-loop renormalization group (RG) equations of a dimensionless parameter can be solved in a closed form in terms of the Lambert W function. We apply the method to a generic theory with a Gaussian fixed point to construct RG invariant physical parameters such as a coupling constant and a physical squared mass. As a further application, we speculate a possible exact effective potential for the O(N) linear sigma model in four dimensions.

Abstract:
We give the large N limit of the effective potential for the O(N) linear sigma model in four dimensions in terms of the Lambert W function. The effective potential is fully consistent with the renormalization group, and it admits an asymptotic expansion in powers of a small positive coupling parameter. Careful consideration of the UV cutoff present in the model validates the physics of the large N limit.

Abstract:
The influence of organic compounds (OCs) on the head-disk interface (HDI) was investigated in hard disk drives. The drives were tested at high temperature to investigate the influence of gaseous OC and to confirm if the gaseous OC forms droplets on head or disk. In the experiment, errors occurred by readback signal jump and we observed the droplets on the disk after full stroke seek operation of the drive. Our results indicate that the gaseous OC condensed on the slider and caused flying instability resulting in drive failure due to slider contact with a droplet of liquid OC. Furthermore, this study shows that kinetic viscosity of OC is an important factor to cause drive failure using alkane reagents. 1. Introduction To achieve 1？Tb/in2 recording density, a head-disk clearance below 2？nm is required. At this small clearance flying instability, which results in a few nanometers of clearance variation, may cause read/write errors due to the high sensitivity of magnetic recording performance to clearance. In addition to direct contact between head and disk, collision between a lubricant droplet and head may cause vibrations and induce a read/write “signal jump” such as reported by Li et al. [1]. Fowler and Geiss [2] observed droplets of OC (alkane) on the head that can cause the stiction at the HDI with a visualization setup. With these references, we used model OC instead of using lubricant for accelerated testing to facilitate droplet observation as it is difficult to observe the lubricant droplet on the disk covered with the lubricant film. We found that OC, specifically hydrocarbons, can also make the flying head unstable by contact with a droplet of OC during the write operation, resulting in an unrecoverable read error. In this study, drive level test was carried out to investigate the influence of OC on reliability of head disk interface (HDI). 2. Experimental Details To investigate the influence of OC, we applied 30？mg of hydrocarbon oil to the inside top cover of test drives. The drives were placed with the top cover down to avoid dropping the hydrocarbon oil to disk. This hydrocarbon oil has a wide distribution of molecular weight from about 100 to 500 grams per mole. For the drive test, several 10000？rpm test drives were built. Tests were conducted at a controlled temperature of 55°C to volatilize components of the hydrocarbon oil. The test sequence is shown in Figure 1. First, full stroke seeks between maximum outer radius (OD) and minimum inner radius (ID) without write/read operation (no dynamic flying height control) were conducted for 10

Abstract:
We give a formula for the derivatives of a correlation function of composite operators with respect to the parameters (i.e., the strong fine structure constant and the quark mass) of QCD in four-dimensional euclidean space. The formula is given as spatial integration of the operator conjugate to a parameter. The operator product of a composite operator and a conjugate operator has an unintegrable part, and the formula requires divergent subtractions. By imposing consistency conditions we derive a relation between the anomalous dimensions of the composite operators and the unintegrable part of the operator product coefficients.

Abstract:
In a previous paper we derived a relation between the operator product coefficients and anomalous dimensions. We explore this relation in the $(\phi^4)_4$ theory and compute the coefficient functions in the products of $\phi^2$ and $\phi^4$ to first order in the parameter $\lambda$. The calculation results in two-loop beta functions.

Abstract:
In a previous paper, field theory in curved space was considered, and a formula that expresses the first order variation of correlation functions with respect to the external metric was postulated. The formula is given as an integral of the energy-momentum tensor over space, where the short distance singularities of the product of the energy-momentum tensor and an arbitrary composite field must be subtracted, and finite counterterms must be added. These finite counterterms have been interpreted geometrically as a connection for the linear space of composite fields over theory space. In this paper we will study a second order consistency condition for the variational formula and determine the torsion of the connection. A non-vanishing torsion results from the integrability of the variational formula, and it is related to the Bose symmetry of the product of two energy-momentum tensors. The massive Ising model on a curved two-dimensional surface is discussed as an example, and the short-distance singularities of the product of two energy-momentum tensors are calculated explicitly.

Abstract:
This is the first of three papers on the short-distance properties of the energy-momentum tensor in field theory. We study the energy-momentum tensor for renormalized field theory in curved space. We postulate an exact Ward identity of the energy-momentum tensor. By studying the consistency of the Ward identity with the renormalization group and diffeomorphisms, we determine the short-distance singularities in the product of the energy-momentum tensor and an arbitrary composite field in terms of a connection for the space of composite fields over theory space. We discuss examples from the four-dimensional $\phi^4$ theory. In the forthcoming two papers we plan to discuss the torsion and curvature of the connection.

Abstract:
By completing the old discussion of K.~Wilson, we express the chiral anomaly in terms of a double integral of a three-point function of chiral currents over an arbitrarily small region in the coordinate space. An integrability condition provides an important finite local counterterm to the integral.