On the transcendence degree of the differential field generated by Siegel modular forms

It is a classical fact that the elliptic modular functions satisfies an algebraic differential equation of order 3, and none of lower order. We show how this generalizes to Siegel modular functions of arbitrary degree. The key idea is that the partial differential equations they satisfy are governed by Gauss--Manin connections, whose monodromy groups are well-known. Modular theta functions provide a concrete interpretation of our result, and we study their differential properties in detail in the case of degree 2.Comment: 21 pages, AmSTeX, uses picture.sty for 1 LaTeX picture; submitted for publicatio

Brans-Dicke gravity and the capture of stars by black holes: some asymptotic results

In the context of star capture by a black hole, a new noticeable difference between Brans-Dicke theory and general relativity gravitational radiation is pointed out. This feature stems from the non-stationarity of the black hole state, barring Hawking's theorem.Comment: 4 pages. Submitted to Classical and Quantum Gravit

Saddle-splay modulus of a particle-laden fluid interface

The scaled-particle theory equation of state for the two-dimensional hard-disk fluid on a curved surface is proposed and used to determine the saddle-splay modulus of a particle-laden fluid interface. The resulting contribution to saddle-splay modulus, which is caused by thermal motion of the adsorbed particles, is comparable in magnitude with the saddle-splay modulus of a simple fluid interface.Comment: 10 pages, 2 figure

Preliminary Geomorphological Studies of the Lime Creek Area & Preliminary Report on the Lime Creek Sites: New Evidence of Early Man in Southwestern Nebraska

PALEONTOLOGICAL and archaeological discoveries were made near Cambridge, Nebraska, by the University of Nebraska State Museum field party in the spring of 1947 (Schultz and Frankforter, 1948, pp. 279-280) . Fossils and artifacts were found in situ at the base of a fifty-foot terrace on Lime Creek (University of Nebraska State Museum Localities Ft-41 and Ft-42) and on Medicine Creek just below the mouth of Lime Creek (Ft-50). Lime Creek is located (Fig. 1) in southwestern Nebraska in the southeastern part of Frontier County. It is a tributary of Medicine Creek which in turn is a tributary to the Republican River. The paleontological material from this site reveals new information on the Pliocene-Pleistocene boundary line problem-a fundamental problem in the over-all Pleistocene history of the region. A series of five topographic benches\u27 or terraces is developed (see Figs. 4 and 5) along the Republican River and its tributaries. Field studies indicate that these represent cycles of alluviation interrupted by erosional periods. A similarly developed series of terrace-fills in a contiguous region has been provisionally correlated with the sub-stages of the Wisconsin stage of Pleistocene continental glaciation (Lueninghoener, 1946). I N THE natural course of paleontological and geological explorations in Pleistocene deposits the fossil hunter often discovers evidence of man\u27s early occupation of North America. Artifacts and other cultural evidence are frequently found in direct association with the fossilized bones of various species of animals. Some of these remains represent extinct species while others can be referred to those found in North America today. Much is yet to be learned concerning the stratigraphic distribution of vertebrate life of the Pleistocene and the time of extinction of certain forms, but new evidence (see Schultz, Lueninghoener, and Frankforter, Part 1, Fig. 6 of this report) is constantly being accumulated which aids in clarifying the picture. In 1932 the University of Nebraska State Museum commenced a research program (Lugn, 1934, pp. 319-356; Schultz, 1934, pp. 357-393) in the field and laboratory relating to the stratigraphic distribution of the Pleistocene mammals and the study of extinction in the Great Plains. Since that time the major portion of the Museum\u27s field work has been directed to problems relating to the Pleistocene. The significance of terraces to the problems has been pointed out in Part 1 of this report (also in Schultz and Stout, 1945; 1948)

Satellite material contaminant optical properties

The Air Force Wright Research and Development Center and the Arnold Engineering Development Center are continuing a program for measuring optical effects of satellite material outgassing products on cryo-optic surfaces. Presented here are infrared (4000 to 700 cm(-1)) transmittance data for contaminant films condensed on a 77 K geranium window. From the transmittance data, the contaminant film refractive and absorptive indices (n, k) were derived using an analytical thin-film interference model with a nonlinear least-squares algorithm. To date 19 materials have been studied with the optical contents determined for 13 of those. The materials include adhesives, paints, composites, films, and lubricants. This program is continuing and properties for other materials will be available in the future

Qualitative Analysis of Partially-observable Markov Decision Processes

We study observation-based strategies for partially-observable Markov decision processes (POMDPs) with omega-regular objectives. An observation-based strategy relies on partial information about the history of a play, namely, on the past sequence of observations. We consider the qualitative analysis problem: given a POMDP with an omega-regular objective, whether there is an observation-based strategy to achieve the objective with probability~1 (almost-sure winning), or with positive probability (positive winning). Our main results are twofold. First, we present a complete picture of the computational complexity of the qualitative analysis of POMDP s with parity objectives (a canonical form to express omega-regular objectives) and its subclasses. Our contribution consists in establishing several upper and lower bounds that were not known in literature. Second, we present optimal bounds (matching upper and lower bounds) on the memory required by pure and randomized observation-based strategies for the qualitative analysis of POMDP s with parity objectives and its subclasses

The homotopy theory of dg-categories and derived Morita theory

The main purpose of this work is the study of the homotopy theory of dg-categories up to quasi-equivalences. Our main result provides a natural description of the mapping spaces between two dg-categories $C$ and $D$ in terms of the nerve of a certain category of $(C,D)$-bimodules. We also prove that the homotopy category $Ho(dg-Cat)$ is cartesian closed (i.e. possesses internal Hom's relative to the tensor product). We use these two results in order to prove a derived version of Morita theory, describing the morphisms between dg-categories of modules over two dg-categories $C$ and $D$ as the dg-category of $(C,D)$-bi-modules. Finally, we give three applications of our results. The first one expresses Hochschild cohomology as endomorphisms of the identity functor, as well as higher homotopy groups of the \emph{classifying space of dg-categories} (i.e. the nerve of the category of dg-categories and quasi-equivalences between them). The second application is the existence of a good theory of localization for dg-categories, defined in terms of a natural universal property. Our last application states that the dg-category of (continuous) morphisms between the dg-categories of quasi-coherent (resp. perfect) complexes on two schemes (resp. smooth and proper schemes) is quasi-equivalent to the dg-category of quasi-coherent complexes (resp. perfect) on their product.Comment: 50 pages. Few mistakes corrected, and some references added. Thm. 8.15 is new. Minor corrections. Final version, to appear in Inventione

Topological transition in a two-dimensional model of liquid crystal

Simulations of nematic-isotropic transition of liquid crystals in two dimensions are performed using an O(2) vector model characterised by non linear nearest neighbour spin interaction governed by the fourth Legendre polynomial $P\_4$. The system is studied through standard Finite-Size Scaling and conformal rescaling of density profiles of correlation functions. A topological transition between a paramagnetic phase at high temperature and a critical phase at low temperature is observed. The low temperature limit is discussed in the spin wave approximation and confirms the numerical results