Monte Carlo Studies of the Fundamental Limits of the Intrinsic Hyperpolarizability

The off-resonant hyperpolarizability is calculated using the dipole-free sum-over-stats expression from a randomly chosen set of energies and transition dipole moments that are forced to be consistent with the sum rules. The process is repeated so that the distribution of hyperpolarizabilities can be determined. We find this distribution to be a cycloid-like function. In contrast to variational techniques that when applied to the potential energy function yield an intrinsic hyperpolarizability less than 0.71, our Monte Carlo method yields values that approach unity. While many transition dipole moments are large when the calculated hyperpolarizability is near the fundamental limit, only two excited states dominate the hyperpolarizability - consistent with the three-level ansatz.Comment: 7 pages, 5 figure

Investigating scientific literacy: Scientist’s habits of mind as evidenced by their rationale of science and religious beliefs

Science and technology have been incredibly success¬ful in purely technical terms. For instance, international air travel, space flight, and curing of hitherto untreatable medical illnesses all are now routine events. One feature of the incredible (and seemingly ever increasing) advance of science and technology is a sense of unease amongst the general population of science’s potential to change our lives, in sometimes unpredictable and alarming ways. Public understanding of science, or scientific literacy, is of increasing concern worldwide according to much recent literature

A note on Khovanov-Rozansky sl2sl_2-homology and ordinary Khovanov homology

In this note we present an explicit isomorphism between Khovanov-Rozansky $sl_2$-homology and ordinary Khovanov homology. This result was originally stated in Khovanov and Rozansky's paper \cite{KRI}, though the details have yet to appear in the literature. The main missing detail is providing a coherent choice of signs when identifying variables in the $sl_2$-homology. Along with the behavior of the signs and local orientations in the $sl_2$-homology, both theories behave differently when we try to extend their definitions to virtual links, which seemed to suggest that the $sl_2$-homology may instead correspond to a different variant of Khovanov homology. In this paper we describe both theories and prove that they are in fact isomorphic by showing that a coherent choice of signs can be made. In doing so we emphasize the interpretation of the $sl_2$-complex as a cube of resolutions.Comment: 19 pages, 11 figures. Expanded introduction and abstract. Remark added to end of section 4.

Young influences

The major environmental issues in Malta are related to its small size and high population density, which is augmented by an influx of visitors each year. Not much is known about the environmental knowledge of young people in the Maltese islands, or of the main actors that are responsible for the acquisition and development of environmental knowledge amongst young Maltese. Research was undertaken during 2007 and 2008 to address this gap, comprising a class administered questionnaire survey completed by 447 students in the post secondary age range. Stratified sampling was used within the studied colleges and schools to ensure that youth studying languages, sciences, business, and humanities were represented according to the actual percentages at the school level.peer-reviewe

Congruence successions in compositions

A \emph{composition} is a sequence of positive integers, called \emph{parts}, having a fixed sum. By an \emph{$m$-congruence succession}, we will mean a pair of adjacent parts $x$ and $y$ within a composition such that $x\equiv y(\text{mod} m)$. Here, we consider the problem of counting the compositions of size $n$ according to the number of $m$-congruence successions, extending recent results concerning successions on subsets and permutations. A general formula is obtained, which reduces in the limiting case to the known generating function formula for the number of Carlitz compositions. Special attention is paid to the case $m=2$, where further enumerative results may be obtained by means of combinatorial arguments. Finally, an asymptotic estimate is provided for the number of compositions of size $n$ having no $m$-congruence successions

Comptroller\u27s Review of the Costs of Real Property Tax Assessment in Erie County

The New York State Office of Real Property Services (“NYSORPS”) has stated that “New York\u27s property tax system is, arguably, the most complex and confusing in the country.” NYSORPS data show that there are 1,133 distinct assessing units in New York State, as contrasted with 59 in California. Only the State of Michigan has more assessing units than New York State. In Erie County, thirty (30) municipal governments consisting of cities, towns and villages assess real property. For many years, NYSORPS has been encouraging local governments across the state to consider terminating their assessment functions and utilizing other, more efficient potentialities, including countywide assessment. Recently, elected state leaders have joined this movement