Non-Achievability of Metal-Insulator Transition in Two-Dimensional Systems

We present a simple demonstration of the nonfeasibility of metal-insulator transition in an exactly two-dimensional （2D） system. The Hartree-Fock potential in the 3D system is suitably modified and presented for the 2D case. The many body effects are included in the screening function, and binding energies of a donor are obtained as a function of impurity concentration so as to find out the possible way leading metal-insulator transition in the 2D system. While solving for the binding energy for a shallow donor in an isolated well of a GaAs/Ga1-x Als As superlattice system within the effective mass approximation, it leads to unphysical results for higher concentrations. It shows that the phase transition, the bound electron entering into the conduction band whereby （H）min=0, is not possible beyond this concentration. The results suggest thai a phase transition is impossible in 213 systems, supporting the scaling theory of localization. The results are compared with the existing data available and discussed in the light of existing literature.     

Coordinate transform invariance

A four-dimensional operator is shown to contain the operator-generators for rotation, scale, reflections, and boosts. The hypothesis is advanced that a physical system changes under this operator by at most a complex phase factor due to invariance against the choice of menial frame. A canonical transform gives a simple relation between space-time and energy-momentum. The basic conserved quantity is a four-dimensional angular momentum and/or coupling constant. The differential of this function contains a second-order differential product which is constrained as a power series in the independent variable. The analysis explores the consequences of the model and shows its degree of correspondence to the standard models.     

A techno-economic assessment of the pretreatment and fractionation steps of a biomass-to-ethanol process

Applied Biochemistry and Biotechnology - It is generally recognized that the front-end (pretreatment, fractionation, enzymatic hydrolysis) steps of a lignocellulose-to-ethanol process are both...     

The Weierstrass mean

Theorem.Let the sequences {e _i ⁽ⁿ⁾ },i=1, 2, 3,n=0, 1, 2, ...be defined by where the e ⁽⁰⁾ s satisfy and where all square roots are taken positive. Then where the convergence is quadratic and monotone and where The discussions of convergence are entirely elementary. However, although the determination of the limits can be made in an elementary way, an acquaintance with elliptic objects is desirable for real understanding.     

Local nondeterminism and local times for stable processes

Summary Our main theorem gives sufficient conditions for symmetric stable processes and fields to have a jointly continuous local time. The approach is through the L ^p representation for such processes. We develop a measure of dependence for vectors in a normed linear space and use that to analyze the probabilistic independence of the increments of a stable process. Local nondeterminism is defined for stable processes and shown to be equivalent to locally approximately independent increments. Sufficient conditions for several classes of stable processes to be local nondeterministic are given. These ideas are extended to multidimensional stable random fields and we prove existence of jointly continuous local times. The results extend most Gaussian results to their stable analogs.     

Implicitly representing arrangements of lines or segments

Anarrangement ofn lines (or line segments) in the plane is the partition of the plane defined by these objects. Such an arrangement consists ofO(n ²) regions, calledfaces. In this paper we study the problem of calculating and storing arrangementsimplicitly, using subquadratic space and preprocessing, so that, given any query pointp, we can calculate efficiently the face containingp. First, we consider the case of lines and show that with (n) space¹ and (n ^3/2) preprocessing time, we can answer face queries in (n)+O(K) time, whereK is the output size. (The query time is achieved with high probability.) In the process, we solve three interesting subproblems: (1) given a set ofn points, find a straight-edge spanning tree of these points such that any line intersects only a few edges of the tree, (2) given a simple polygonal path , form a data structure from which we can find the convex hull of any subpath of quickly, and (3) given a set of points, organize them so that the convex hull of their subset lying above a query line can be found quickly. Second, using random sampling, we give a tradeoff between increasing space and decreasing query time. Third, we extend our structure to report faces in an arrangement of line segments in (n ^1/3)+O(K) time, given(n ^4/3) space and (n ^5/3) preprocessing time. Lastly, we note that our techniques allow us to computem faces in an arrangement ofn lines in time (m ^2/3 n ^2/3+n), which is nearly optimal.The first author is pleased to acknowledge the support of Amoco Fnd. Fac. Dev. Comput. Sci. 1-6-44862 and National Science Foundation Grant CCR-8714565. Work on this paper by the fifth author has been supported by Office of Naval Research Grant N00014-87-K-0129, by National Science Foundation Grant NSF-DCR-83-20085, by grants from the Digital Equipment Corporation, and the IBM Corporation, and by a research grant from the NCRD—the Israeli National Council for Research and Development. The sixth author was supported in part by a National Science Foundation Graduate Fellowship. This work was begun while the non-DEC authors were visiting at the DEC Systems Research Center.