About Division by 1

The Euclidean division of two formal series in one variable produces a sequence of series that we obtain explicitly, remarking that the case where one of the two initial series is 1 is sufficiently generic. As an application, we define a Wronskian of symmetric functions.Comment: 7 page

Photobase Generator Enabled Pitch Division: A Progress Report

Pitch division lithography (PDL) with a photobase generator (PBG) allows printing of grating images with twice the pitch of a mask. The proof-of-concept has been published in the previous paper[1, 2] and demonstrated by others[1]. Forty five nm half-pitch (HP) patterns were produced using a 90nm HP mask, but the image had line edge roughness (LER) that does not meet requirements. Efforts have been made to understand and improve the LER in this process. Challenges were summarized toward low LER and good performing pitch division. Simulations and analysis showed the necessity for an optical image that is uniform in the z direction in order for pitch division to be successful. Two-stage PBGs were designed for enhancement of resist chemical contrast. New pitch division resists with polymer-bound PAGs and PBGs, and various PBGs were tested. This paper focuses on analysis of the LER problems and efforts to improve patterning performance in pitch division lithography.Chemical Engineerin

An octonionic formulation of the M-theory algebra

We give an octonionic formulation of the N = 1 supersymmetry algebra in D = 11, including all brane charges. We write this in terms of a novel outer product, which takes a pair of elements of the division algebra A and returns a real linear operator on A. More generally, with this product comes the power to rewrite any linear operation on R^n (n = 1,2,4,8) in terms of multiplication in the n-dimensional division algebra A. Finally, we consider the reinterpretation of the D = 11 supersymmetry algebra as an octonionic algebra in D = 4 and the truncation to division subalgebras

On the Complexity of Chore Division

We study the proportional chore division problem where a protocol wants to divide an undesirable object, called chore, among $n$ different players. The goal is to find an allocation such that the cost of the chore assigned to each player be at most $1/n$ of the total cost. This problem is the dual variant of the cake cutting problem in which we want to allocate a desirable object. Edmonds and Pruhs showed that any protocol for the proportional cake cutting must use at least $\Omega(n \log n)$ queries in the worst case, however, finding a lower bound for the proportional chore division remained an interesting open problem. We show that chore division and cake cutting problems are closely related to each other and provide an $\Omega(n \log n)$ lower bound for chore division

An Assessment of the Division of Juvenile Justice's Use of the Youth Level of Services/ Case Management Inventory

In June, 2010, the Alaska Division of Juvenile Justice (Division) invited the Alaska Judicial Council and the Institute of Social and Economic Research (ISER) at University of Alaska Anchorage to assist “in understanding how scores on the Division’s assessment instrument for juveniles, the Youth Level of Service/Case Management Inventory (YLS/CMI), reflect the actual recidivism of juveniles who’ve received services from the Division.” Other states had shown that YLS/CMI scores could be helpful in predicting recidivism among the youths they served, but Alaska had not yet done the comparable research. ISER and the Council agreed that the questions proposed would provide valuable information and help the Division to better address the reasons for youth recidivism.The Division of Juvenile Justice.Executive Summary / Introduction / Part 1: Research background and design / Part 2: Findings / Part 3: Summary and Conclusions / Appendice

Remarks on Vector Space Generated by the Multiplicative Commutators of a Division Ring

Let D be a division ring with centre F. Let T(D) be the vector space over F generated by all multiplicative commutators in D. In [1], authors have conjectured that every division ring is generated as a vector space over its centre by all of its multiplicative commutators. In this note it is shown that if D is centrally finite, then the conjecture holds