Level surfaces of non-degenerate functions inR n+1

We study level surfaces of non-degenerate functions inR ⁿ⁺¹. Such level surfaces are non-degenerate in the sense of affine differential geometry. In affine differential geometry, the affine normal plays an important role for the study of a non-degenerate hypersurface. In this note, being motivated by Koszul's work we take a canonical vector field for level surfaces of a non-degenerate function and give certain characterizations of when is transversal, by the shape operatorS, the transversal connection , and consider the difference between and the affine normal.     

Conformational behavior of styrene–p-chlorostyrene triblock copolymers in dilute solutions. I. Composition dependence of conformational behavior

Dilute solution properties of (styrene-p-chlorostyrene) triblock copolymers in various solvents were studied over a wide range of molecular weight and composition. Viscosity and osmotic pressure results indicate that the conformational behavior of the B_mA_nB_m and A_mB_nA_m copolymers (A = styrene; B = p-chlorostyrene; m and n denote the number of units) are similar in nonselective solvents such as toluene and 2-butanone, but different in selective solvents such as carbon tetrachloride and cumene. Short-range and long-range interaction parameters of the block copolymers were determined by applying the Stockmayer–Fixman method to viscosity data and also by application of the equation relating the osmotic virial coefficient and the excluded volume. The results show that the unperturbed dimensions of the block copolymers vary linearly with composition, and long-range interaction parameters in nonselective solvents can be expressed by those of the parent homopolymers, the chemical composition, and values of the interaction parameter β_AB between styrene and p-chlorostyrene monomeric units.     

NeK X-ray yields on Be,C, Mg,Al and Ti bombardments

NeK X-rays have been measured when various thick targets were irradiated by Ne^{+, ++} ions. For Mg, Al and Ti targets, the X-ray yield dependence on Ne energy agrees qualitatively with the electron promotion model prediction.     

Full-scale fatigue test of twin-turboprop transport

When the design work was commenced on the YS-11 transport airplane in 1959, the fatigue behavior of the structure was one of the most cardinal problems in the structural design, then the various design principles were introduced in order to overcome the fatigue problems, and the fatigue test of the full-scale airplane structure was planned to guarantee a fatigue life of 30,000 flight hours. In order to perform the fatigue test of the full-scale air-plane structure, the equipment for the wing fatigue test and for the fuselage fatigue test was developed separately. The former consisted of sixteen hydraulic actuators, controlled automatically, and a program device, being able to program the four different repeated loads; the latter was a familiar water tank in which the fuselage was pressurized by water and loaded, the external loads corresponding to gust loads, standing on the ground loads and the others by actuators. Concerning these tests, the following problems will be explained in our report:

1. 1.
   The structure and operation of the equipment of the full-scale fatigue test.     

SO(N) supergravity and unification of all fundamental forces

From the group theoretical arguments, we find that among allSO(N) supergravitiesN=10 is the minimal supersymmetry group which unifies all fundamental forces of weak, electromagnetic, strong and gravitational interactions. The (super)symmetry is broken throughSO(10)→SU(3)?SU(2)?U(1)→SU(3)?U(1). All observed particles of the low energy physics (three generations of quarks and leptons, γ,Z, W ^± and gluons) and graviton can be minimally accomodated with the correctSU(3)?SU(2)?U(1) quantum numbers. Some characteristic predictions, which can be checked in the coming high energy experiments, are briefly discussed.     

Super Yang–Mills theory from nonlinear supersymmetry

The relation between a nonlinear supersymmetric (NLSUSY) theory and a SUSY Yang–Mills (SYM) theory is studied for N=3$N=3$ SUSY in two-dimensional space–time. We explicitly show the NL/L SUSY relation for the (pure) SYM theory by means of cancellations among Nambu–Goldstone fermion self-interaction terms.     

Sinc-Galerkin method for numerical solution of the Bratu’s problems

Study of the performance of the Galerkin method using sinc basis functions for solving Bratu’s problem is presented. Error analysis of the presented method is given. The method is applied to two test examples. By considering the maximum absolute errors in the solutions at the sinc grid points are tabulated in tables for different choices of step size. We conclude that the Sinc-Galerkin method converges to the exact solution rapidly, with order, $O(\exp{(-c \sqrt{n}}))$ accuracy, where c is independent of n.