Non-commutative spaces in physics and mathematics

The present review aims both to offer some motivations and mathematical prerequisites for a study of NCG from the viewpoint of a theoretical physicist and to show a few applications to matrix theory and results obtained. Lectures given by the author at the TMR School on contemporary string theory and brane physics, 26 Jan--2 Feb 2000, Torino.Comment: 27 pages + figures (in .eps format), first part appeared as hep-th/9802129. submitted to Class. Quant. Gra

Local Physical Coodinates from Symplectic Projector Method

The basic arguments underlying the symplectic projector method are presented. By this method, local free coordinates on the constrait surface can be obtained for a broader class of constrained systems. Some interesting examples are analyzed.Comment: 8 page

String Theory and the Fuzzy Torus

We outline a brief description of non commutative geometry and present some applications in string theory. We use the fuzzy torus as our guiding example.Comment: Invited review for IJMPA rev1: an imprecision corrected and a reference adde

Rates of Depression and Anxiety in Cancer Patients: A Review of Cross-National Findings

Cancer is the leading cause of death worldwide. In this paper, we examine the similarities and differences between the United States (US) and the European Union (EU-27) in the incidences, deaths, types of screening, and screening rates for breast, cervical, colorectal, prostate, and lung cancers. We highlight the differences between the health care, economic, and sociopolitical systems in the US and EU-27 that result in different types of coverage, access to health care, and cancer screening. Finally, we discuss patient-directed, provider-directed, community-directed, and system-directed interventions and the outcomes of these approaches

Commutator Anomaly in Noncommutative Quantum Mechanics

In this letter, firstly, the Schr$\ddot{o}$dinger equation on noncommutative phase space is given by using a generalized Bopp's shift. Then the anomaly term of commutator of arbitrary physical observable operators on noncommutative phase space is obtained. Finally, the basic uncertainty relations for space-space and space-momentum as well as momentum-momentum operators in noncommutative quantum mechanics (NCQM), and uncertainty relation for arbitrary physical observable operators in NCQM are discussed.Comment: 7 page

Three flavors of extremal Betti tables

We discuss extremal Betti tables of resolutions in three different contexts. We begin over the graded polynomial ring, where extremal Betti tables correspond to pure resolutions. We then contrast this behavior with that of extremal Betti tables over regular local rings and over a bigraded ring.Comment: 20 page

Holographic Entropy Packing inside a Black Hole

If general relativity is spontaneously induced, the black hole limit is governed by a phase transition which occurs precisely at the would have been horizon. The exterior Schwarzschild solution then connects with a novel core of vanishing spatial volume. The Kruskal structure, admitting the exact Hawking imaginary time periodicity, is recovered, with the conic defect defused at the origin, rather than at the horizon. The entropy stored inside \textbf{any} interior sphere is universal, equal to a quarter of its surface area, thus locally saturating the 't Hooft-Susskind holographic bound. The associated Komar mass and material energy functions are non-singular.Comment: [V3] accepted to PRL (version shortened, a paragraph on singularity structure added); 10 pages, no figure