A triple comparison between anticipating stochastic integrals in financial modeling

We consider a simplified version of the problem of insider trading in a financial market. We approach it by means of anticipating stochastic calculus and compare the use of the Hitsuda-Skorokhod, the Ayed-Kuo, and the Russo-Vallois forward integrals within this context. Our results give some indication that, while the forward integral yields results with a suitable financial meaning, the Hitsuda-Skorokhod and the Ayed-Kuo integrals do not provide an appropriate formulation of this problem. Further results regarding the use of the Ayed-Kuo integral in this context are also provided, including the proof of the fact that the expectation of a Russo-Vallois solution is strictly greater than that of an Ayed-Kuo solution. Finally, we conjecture the explicit solution of an Ayed-Kuo stochastic differential equation that possesses discontinuous sample paths with finite probability

Lambda-determinants and domino-tilings

Consider the $2n$-by-$2n$ matrix $M=(m_{i,j})_{i,j=1}^{2n}$ with $m_{i,j} = 1$ for $i,j$ satisfying $|2i-2n-1|+|2j-2n-1| \leq 2n$ and $m_{i,j} = 0$ for all other $i,j$, consisting of a central diamond of 1's surrounded by 0's. When $n \geq 4$, the $\lambda$-determinant of the matrix $M$ (as introduced by Robbins and Rumsey) is not well-defined. However, if we replace the 0's by $t$'s, we get a matrix whose $\lambda$-determinant is well-defined and is a polynomial in $\lambda$ and $t$. The limit of this polynomial as $t \to 0$ is a polynomial in $\lambda$ whose value at $\lambda=1$ is the number of domino tilings of a $2n$-by-$2n$ square.Comment: 4 pages; to appear in a special issue of Advances in Applied Mathematics honoring David P. Robbin

SU(3) symmetry breaking in lower fp-shell nuclei

Results of shell-model calculations for lower fp-shell nuclei show that SU(3) symmetry breaking in this region is driven by the single-particle spin-orbit splitting. However, even though states of the yrast band exhibit SU(3) symmetry breaking, the results also show that the yrast band B(E2) values are insensitive to this fragmentation of the SU(3) symmetry; specifically, the quadrupole collectivity as measured by B(E2) transition strengths between low lying members of the yrast band remain high even though SU(3) appears to be broken. Results for $^{44,46,48}Ti$ and $^{48}Cr$ using the Kuo-Brown-3 two-body interaction are given to illustrate these observations.Comment: Updated to the published versio

Cumulus convection and the terrestrial water-vapor distribution

Cumulus convection plays a significant role in determining the structure of the terrestrial water vapor field. Cumulus convection acts directly on the moisture field by condensing and precipitating water vapor and by redistributing water vapor through cumulus induced eddy circulations. The mechanisms by which cumulus convection influences the terrestrial water vapor distribution is outlined. Calculations using a theory due to Kuo is used to illustrate the mechanisms by which cumulus convection works. Understanding of these processes greatly aids the ability of researchers to interpret the seasonal and spatial distribution of atmospheric water vapor by providing information on the nature of sources and sinks and the global circulation

Drawing from Grotowski and Beyond: Kuo Pao Kun’s Discourse on Audiences in Singapore in the 1980s

Much has been researched on Kuo Pao Kun’s multilingualism and multiculturalism. However, as one of one of the most important Asian dramatists, the analysis of Kuo’s discourse on audiences remains largely unexplored. There is a pressing need to understand the ways which theatre practitioners imagine audiences as it points to issues of subjectivity, audience participation and social engagement, especially in a neoliberal society like Singapore where people are often positioned as docile economic subjects. Among the many Asian and Western dramatists Kuo drew inspiration from, Jerzy Grotowski was pivotal. This essay seeks to address this gap by examining how the latter’s ideas was crucial to understanding how Kuo envisioned theatre and audiences alongside his artistic practice

An evening of song, performed by the students of Phyllis Hoffman, December 2, 1992

This is the concert program of the An Evening of Song Performed by the Students of Phyllis Hoffman performance on Wednesday, December 2, 1992 at 8:30 p.m., at the Concert Hall, 855 Commonwealth Avenue. Works performed were Sei mia gioia by George Frideric Handel, The Grass by Vincent Persichetti, Si trai ceppi by G. F. Handel, Sonntag by Johannes Brahms, Ergiti amor by Alessandro Scarlatti, Absalom by Ned Rorem, Adieu by Gabriel Fauré, Warm as the Autumn Light by Douglas Moore, Ein Aeölsharfe by J. Brahms, Die Männer sind mechant! by Franz Schubert, "O Columbine" from "I Pagliacci" by Ruggiero Leoncavallo, The World's Highway by Charles Ives, L'Invitation au Voyage by Henri Duparc, O mio babbino caro by Giacomo Puccini, Wie Melodien zieht es mir by J. Brahms, Nebbie by Ottorino Respighi, Malinconia by Vincenzo Bellini, Per pietá by V. Bellini, Sourire by Olivier Messiaen, Chévere by Xavier Montsalvatge, Erinnerung by Gustav Mahler, and Ablösung im Sommer by G. Mahler. Digitization for Boston University Concert Programs was supported by the Boston University Humanities Library Endowed Fund