When Are Torsionless Modules Projective?

In this paper, we study the problem when a finitely generated torsionless module is projective. Let $\Lambda$ be an Artinian local algebra with radical square zero. Then a finitely generated torsionless $\Lambda$-module $M$ is projective if ${\rm Ext^1_\Lambda}(M,M)=0$. For a commutative Artinian ring $\Lambda$, a finitely generated torsionless $\Lambda$-module $M$ is projective if the following conditions are satisfied: (1) ${\rm Ext}^i_{\Lambda}(M,\Lambda)=0$ for $i=1,2,3$; and (2) ${\rm Ext}^i_{\Lambda}(M,M)=0$ for $i=1,2$. As a consequence of this result, we have that for a commutative Artinian ring $\Lambda$, a finitely generated Gorenstein projective $\Lambda$-module is projective if and only if it is selforthogonal.Comment: 10 page

A note on the resolution of the entropy discrepancy

It was found by Hung, Myers and Smolkin that there is entropy discrepancy for the CFTs in 6-dimensional space-time, between the field theoretical and the holographic analysis. Recently, two different resolutions to this puzzle have been proposed. One of them suggests to utilize the anomaly-like entropy and the generalized Wald entropy to resolve the HMS puzzle, while the other one initiates to use the entanglement entropy which arises from total derivative terms in the Weyl anomaly to explain the HMS mismatch. We investigate these two proposals carefully in this note. By studying the CFTs dual to Einstein gravity, we find that the second proposal can not solve the HMS puzzle. Moreover, the Wald entropy formula is not well-defined on horizon with extrinsic curvatures, in the sense that, in general, it gives different results for equivalent actions.Comment: 12 pages, no figures, accepted by PL

Investigating Structure-Activity Relationships Of SL11 To Develop A Better Prostate Cancer Diagnostic

Prostate cancer is now the second leading cause of cancer death in American men. Since many of the diagnostics either have high false results or risky, it’s important to have better diagnostics and earlier diagnosis of prostate cancer. Aberrant glycosylation is a hallmark of cancer. When cancer occurs, aberrant glycosylation occurs, therefore, glycosylation patterns may provide information about different cancer types and metastatic potential. In order to study and use these glycosylation patterns, the boronic acid functionalized synthetic lectins that can interact with glycans have been developed. The work described here focuses on 1) the structure activities of synthetic lectins (SLs), especially SL11 which is selected against the prostate cancer cell line PC3, for developing a structure-activity relationship for the SL11 with both purified glycoproteins and proteins from prostate cell lines, 2) study the ability of an array of SLs to classify prostate cancer cell lines and colon cancer cell lines

A study of gender differences - the travel behaviour of Chinese international students studying in the UK

This research note provides some preliminary findings of a study examining the behaviour of male and female international students while they are travelling. It is based on information collected about the behaviour of Chinese international students during their holiday in the UK. This work is required because of the importance of international students to the tourism industry and the paucity of previous research about this population. The study focused on the intersection of three key social characteristics: gender (comparing male and female), age (young students) and ethnicity (Chinese) has produced some interesting preliminary conclusions