Characteristic Surface Data for the Eikonal Equation

A method of solving the eikonal equation, in either flat or curved space-times, with arbitrary Cauchy data, is extended to the case of data given on a characteristic surface. We find a beautiful relationship between the Cauchy and characteristic data for the same solution, namely they are related by a Legendre transformation. From the resulting solutions, we study and describe their associated wave-front singularities.Comment: 16 pages, no figures, Scientific Work-Place 2.5, tex, Corrected typo

Supergravity Analysis of Hybrid Inflation Model from D3--D7 System

The slow-roll inflation is a beautiful paradigm, yet the inflaton potential can hardly be sufficiently flat when unknown gravitational effects are taken into account. However, the hybrid inflation models constructed in D = 4 N = 1 supergravity can be consistent with N = 2 supersymmetry, and can be naturally embedded into string theory. This article discusses the gravitational effects carefully in the string model, using D = 4 supergravity description. We adopt the D3--D7 system of Type IIB string theory compactified on K3 x T^2/Z_2 orientifold for definiteness. It turns out that the slow-roll parameter can be sufficiently small despite the non-minimal Kahler potential of the model. The conditions for this to happen are clarified in terms of string vacua. We also find that the geometry obtained by blowing up singularity, which is necessary for the positive vacuum energy, is stabilized by introducing certain 3-form fluxes.Comment: 21 pages; v3. a typo corrected, and some changes made in sections 4.1 and 4.2, accordingl

Footwear

The natural is the beautiful. Failure to recognize this truth has resulted in strange fashions. We have all seen or heard of styles which cause deformity. We wonder at the African tribes who go thru torture to elongate the lobes of their ears; we send missionaries to China to Christianize them, and one of the first acts of the missionary is to teach them to refrain from binding the feet. And yet at home we are binding our feet, deforming them by the type of shoe we wear. A distorted, malformed foot is no more beautiful than a misshapen head, elongated ears, or tattooed skin, yet stand any day on a street corner and watch the women passing by and it will show conclusively that foot binding is still practiced among us. We do not really believe that pinched toes, flat feet, bunions, and corns are beautiful; still we wear and admire the conventional shoe which causes these deformities. The human bones are not strong enough to stand the clamping effects of these shoes, and in the end the very structure of the foot is changed

Letter Written by Katherine Trickey to Her Folks Dated October 28, 1945

[Transcription begins] 28 Oct 45 10.30 P.M. Dear Folks, Have had a beautiful day – The weather was wonderful – sunny & warm – Woke up about 9 and read in bed till 1.30 – Had nice fried chicken dinner in the Mess Hall at 2 and then went for a long walk in the woods with Marjorie, Minnie and a couple others. We were out all the afternoon – and enjoyed ourselves thoroughly. We even found some Pecans to eat. I am sending my tennis racket and the flat iron & a few other things – (in two boxes) by Railway Express tomorrow; They’ll come COD. I hope they won’t be too much. I’m too broke to send any money for them until Wed. payday! – The way the work is going I doubt if I get out much before the first of January, but I’m still hoping to get out near the first of December. Isn’t Bob’s job just the thing? I can’t think of any that would be better for him. You’ll miss them all, I know. – but I’ll be home soon so you won’t be quite so lonesome. This is a hasty letter – there really is very little new this week. Love Kay [Transcription ends