Commutative Quantum Operator Algebras

A key notion bridging the gap between {\it quantum operator algebras} \cite{LZ10} and {\it vertex operator algebras} \cite{Bor}\cite{FLM} is the definition of the commutativity of a pair of quantum operators (see section 2 below). This is not commutativity in any ordinary sense, but it is clearly the correct generalization to the quantum context. The main purpose of the current paper is to begin laying the foundations for a complete mathematical theory of {\it commutative quantum operator algebras.} We give proofs of most of the relevant results announced in \cite{LZ10}, and we carry out some calculations with sufficient detail to enable the interested reader to become proficient with the algebra of commuting quantum operators.Comment: 22 pages, Late

Development and characterization analysis of a radar polarimeter

The interaction of electromagnetic waves with natural earth surface was of interest for many years. A particular area of interest in controlled remote sensing experiments is the phenomena of depolarization. The development stages of the radar system are documented. Also included are the laboratory procedures which provides some information about the specifications of the system. The radar system developed is termed the Radar Polarimeter System. A better insight of the operation of the RPS in terms of the newly developed technique--synthetic aperture radar system is provided. System performance in tems of radar cross section, in terms of power, and in terms of signal to noise ratio are also provided. In summary, an overview of the RPS in terms of its operation and design as well as how it will perform in the field is provided

Redefining Lumpectomy Using a Modification of the “Sick Lobe” Hypothesis and Ductal Anatomy

Objectives. The “Sick Lobe” hypothesis states that breast cancers evolve from entire lobes or portions of lobes of the breast where initiation events have occurred early in development. The implication is that some cancers are isolated events and others are truly multi-focal but limited to single lobar-ductal units. Methods. This is a single surgeon retrospective review of early stage breast cancer lumpectomy patients treated from 1/2000 to 2/2005. Ductal endoscopy was used direct lumpectomy surgical margins by defining ductal anatomy and mapping proliferative changes within the sick lobe for complete excision. Results. Breast conservation surgery for stage 0–2 breast cancer with an attempt to perform endoscopy in association with therapeutic lumpectomy was performed in 554 patients (successful endoscopy in 465 cases). With an average followup of >5 years for the entire group, annual hazard rate for local failure in traditional lumpectomy without ductal mapping was 0.97%/yr. and for lumpectomy with ductal mapping and excision of entire sick lobe was 0.18%/yr. With endoscopy, 42% of patients were found to have extensive disease within their “sick lobe.” Conclusions. Targeting breast cancer lumpectomy using endoscopy and excision of regional associated proliferation seems associated with lower recurrence in this non-randomized series

Strong unitary and overlap uncertainty relations: theory and experiment

We derive and experimentally investigate a strong uncertainty relation valid for any $n$ unitary operators, which implies the standard uncertainty relation as a special case, and which can be written in terms of geometric phases. It is saturated by every pure state of any $n$-dimensional quantum system, generates a tight overlap uncertainty relation for the transition probabilities of any $n+1$ pure states, and gives an upper bound for the out-of-time-order correlation function. We test these uncertainty relations experimentally for photonic polarisation qubits, including the minimum uncertainty states of the overlap uncertainty relation, via interferometric measurements of generalised geometric phases.Comment: 5 pages of main text, 5 pages of Supplemental Material. Clarifications added in this updated versio

Algebraic and geometric structures in string backgrounds

We give a brief introduction to the study of the algebraic structures -- and their geometrical interpretations -- which arise in the BRST construction of a conformal string background. Starting from the chiral algebra \cA of a string background, we consider a number of elementary but universal operations on the chiral algebra. From these operations we deduce a certain fundamental odd Poisson structure, known as a Gerstenhaber algebra, on the BRST cohomology of \cA. For the 2D string background, the correponding G-algebra can be partially described in term of a geometrical G-algebra of the affine plane \bC^2. This paper will appear in the proceedings of {\it Strings 95}