Chow groups of ind-schemes and extensions of Saito's filtration

Let $K$ be a field of characteristic zero and let $Sm/K$ be the category of smooth and separated schemes over $K$. For an ind-scheme $\mathcal X$ (and more generally for any presheaf of sets on $Sm/K$), we define its Chow groups $\{CH^p(\mathcal X)\}_{p\in \mathbb Z}$. We also introduce Chow groups $\{\mathcal{CH}^p(\mathcal G)\}_{p\in \mathbb Z}$ for a presheaf with transfers $\mathcal G$ on $Sm/K$. Then, we show that we have natural isomorphisms of Chow groups $$CH^p(\mathcal X)\cong \mathcal{CH}^p(Cor(\mathcal X))\qquad\forall\textrm{ }p \in \mathbb Z$$ where $Cor(\mathcal X)$ is the presheaf with transfers that associates to any $Y\in Sm/K$ the collection of finite correspondences from $Y$ to $\mathcal X$. Additionally, when $K=\mathbb C$, we show that Saito's filtration on the Chow groups of a smooth projective scheme can be extended to the Chow groups $CH^p(\mathcal X)$ and more generally, to the Chow groups of an arbitrary presheaf of sets on $Sm/\mathbb C$. Similarly, there exists an extension of Saito's filtration to the Chow groups of a presheaf with transfers on $Sm/\mathbb C$. Finally, when the ind-scheme $\mathcal X$ is ind-proper, we show that the isomorphism $CH^p(\mathcal X)\cong \mathcal{CH}^p(Cor(\mathcal X))$ is actually a filtered isomorphism.Comment: Exposition improve

L-functions for holomorphic forms on GSp(4) x GL(2) and their special values

We provide an explicit integral representation for L-functions of pairs (F,g) where F is a holomorphic genus 2 Siegel newform and g a holomorphic elliptic newform, both of squarefree levels and of equal weights. When F,g have level one, this was earlier known by the work of Furusawa. The extension is not straightforward. Our methods involve precise double-coset and volume computations as well as an explicit formula for the Bessel model for GSp(4) in the Steinberg case; the latter is possibly of independent interest. We apply our integral representation to prove an algebraicity result for a critical special value of L(s, F \times g). This is in the spirit of known results on critical values of triple product L-functions, also of degree 8, though there are significant differences.Comment: 48 pages, typos corrected, some changes in Sections 6 and 7, other minor change

Private Label Brand Choice Dynamics Logit model involving demographic and psychographic variables

Research on private label brands started with focus on explaining the choice of private label brands by simple demographics variables which later expanded into work on attitudinal and behavioral characteristics of customers. However, all these studies had never tried to integrate demographic and psychographic variables to achieve a higher explanatory power, even though researchers had suggested that such a combination is likely to have a higher explanatory power. This paper, after a review of literature, identifies the variables for private label brand proneness. This is followed by mathematical explanation which provides the mathematical model using discrete choice modeling. The paper also provides operationalization of integrated model in current Indian retail scenario and concludes with explaining the limitations.

Web Security Detection Tool

According to Government Computer News (GCN) web attacks have been marked as all- time high this year. GCN says that some of the leading security software like SOPHOS detected about 15,000 newly infected web pages daily in initial three months of 2008 [13]. This has lead to the need of efficient software to make web applications robust and sustainable to these attacks. While finding information on different types of attacks, I found that SQL injection and cross site scripting are the most famous among attackers. These attacks are used extensively since, they can be performed using different techniques and it is difficult to make a web application completely immune to these attacks. There are myriad detection tools available which help to detect vulnerabilities in web applications. These tools are mainly categorized as white-box and black-box testing tools. In this writing project, we aim to develop a detection tool which would be efficient and helpful for the users to pinpoint possible vulnerabilities in his/her PHP scripts. We propose a technique to integrate the aforementioned categories of tools under one framework to achieve better detection against possible vulnerabilities. Our system focuses on giving the developer a simple and concise tool which would help him/her to correct possible loopholes in the PHP code snippets

Heat conduction in a one-dimensional gas of elastically colliding particles of unequal masses

We study the nonequlibrium state of heat conduction in a one-dimensional system of hard point particles of unequal masses interacting through elastic collisions. A BBGKY-type formulation is presented and some exact results are obtained from it. Extensive numerical simulations for the two-mass problem indicate that even for arbitrarily small mass differences, a nontrivial steady state is obtained. This state exhibits local thermal equilibrium and has a temperature profile in accordance with the predictions of kinetic theory. The temperature jumps typically seen in such studies are shown to be finite-size effects. The thermal conductivity appears to have a very slow divergence with system size, different from that seen in most other systems.Comment: 5 pages, 4 figures, Accepted for publication in Phys. Rev. Let

Non-extensive Statistical Mechanics and Black Hole Entropy From Quantum Geometry

Using non-extensive statistical mechanics, the Bekenstein-Hawking area law is obtained from microstates of black holes in loop quantum gravity, for arbitrary real positive values of the Barbero-Immirzi parameter$(\gamma)$. The arbitrariness of $\gamma$ is encoded in the strength of the "bias" created in the horizon microstates through the coupling with the quantum geometric fields exterior to the horizon. An experimental determination of $\gamma$ will fix this coupling, leaving out the macroscopic area of the black hole to be the only free quantity of the theory.Comment: 6 pages, published versio