Comment on "Two notes on imbedded prime divisors"

In this note, we show that a part of [5, Remark 2.2] is not correct. Some conditions are given under which the same holds

Superimposing theta structure on a generalized modular relation

A generalized modular relation of the form $F(z, w, \alpha)=F(z, iw,\beta)$, where $\alpha\beta=1$ and $i=\sqrt{-1}$, is obtained in the course of evaluating an integral involving the Riemann $\Xi$-function. It is a two-variable generalization of a transformation found on page $220$ of Ramanujan's Lost Notebook. This modular relation involves a surprising generalization of the Hurwitz zeta function $\zeta(s, a)$, which we denote by $\zeta_w(s, a)$. While $\zeta_w(s, 1)$ is essentially a product of confluent hypergeometric function and the Riemann zeta function, $\zeta_w(s, a)$ for $0<a<1$ is an interesting new special function. We show that $\zeta_w(s, a)$ satisfies a beautiful theory generalizing that of $\zeta(s, a)$ albeit the properties of $\zeta_w(s, a)$ are much harder to derive than those of $\zeta(s, a)$. In particular, it is shown that for $0<a<1$ and $w\in\mathbb{C}$, $\zeta_w(s, a)$ can be analytically continued to Re$(s)>-1$ except for a simple pole at $s=1$. This is done by obtaining a generalization of Hermite's formula in the context of $\zeta_w(s, a)$. The theory of functions reciprocal in the kernel $\sin(\pi z) J_{2 z}(2 \sqrt{xt}) -\cos(\pi z) L_{2 z}(2 \sqrt{xt})$, where $L_{z}(x)=-\frac{2}{\pi}K_{z}(x)-Y_{z}(x)$ and $J_{z}(x), Y_{z}(x)$ and $K_{z}(x)$ are the Bessel functions, is worked out. So is the theory of a new generalization of $K_{z}(x)$, namely, ${}_1K_{z,w}(x)$. Both these theories as well as that of $\zeta_w(s, a)$ are essential to obtain the generalized modular relation.Comment: 78 pages, submitted for publication. Comments are welcom

A Survey on Resilient Machine Learning

Machine learning based system are increasingly being used for sensitive tasks such as security surveillance, guiding autonomous vehicle, taking investment decisions, detecting and blocking network intrusion and malware etc. However, recent research has shown that machine learning models are venerable to attacks by adversaries at all phases of machine learning (eg, training data collection, training, operation). All model classes of machine learning systems can be misled by providing carefully crafted inputs making them wrongly classify inputs. Maliciously created input samples can affect the learning process of a ML system by either slowing down the learning process, or affecting the performance of the learned mode, or causing the system make error(s) only in attacker's planned scenario. Because of these developments, understanding security of machine learning algorithms and systems is emerging as an important research area among computer security and machine learning researchers and practitioners. We present a survey of this emerging area in machine learning

Game-theoretic perspective of Ping-Pong Protocol

We analyse Ping-Pong protocol from the point of view of a game. The analysis helps us in understanding the different strategies of a sender and an eavesdropper to gain the maximum payoff in the game. The study presented here characterizes strategies that lead to different Nash equilibriums. We further demonstrate the condition for Pareto optimality depending on the parameters used in the game. Moreover, we also analysed LM05 protocol and compared it with PP protocol from the point of view of a generic two-way QKD game with or without entanglement. Our results provide a deeper understanding of general two-way QKD protocols in terms of the security and payoffs of different stakeholders in the protocol

A note on pairs of rings with same prime ideals

We study the ring extensions R \subseteq T having the same set of prime ideals provided Nil(R) is a divided prime ideal. Some conditions are given under which no such T exist properly containing R. Using idealization theory, the examples are also discussed to strengthen the results.Comment: 10 page

Upper Bound on Singlet Fraction of Two Qubit Mixed Entangled States

We demonstrate the possibility of achieving the maximum possible singlet fraction using a entangled mixed two-qubit state as a resource. For this, we establish a tight upper bound on singlet fraction and show that the maximal singlet fraction obtained in \cite{Verstraete} does not attain the obtained upper bound on the singlet fraction. Interestingly, we found that the required upper bound can in fact be achieved using local filtering operations.Comment: 4 pages, 1 figur

On minimal ring extensions

Let $R$ be a commutative ring with identity. The ring $R\times R$ can be viewed as an extension of $R$ via the diagonal map $\Delta: R \hookrightarrow R\times R$, given by $\Delta(r) = (r, r)$ for all $r\in R$. It is shown that, for any $a, b\in R$, the extension $\Delta(R)[(a,b)] \subset R\times R$ is a minimal ring extension if and only if the ideal $$ is a maximal ideal of $R$. A complete classification of maximal subrings of $R(+)R$ is also given. The minimal ring extension of a von Neumann regular ring $R$ is either a von Neumann regular ring or the idealization $R(+)R/\mathfrak{m}$ where $\mathfrak{m}\in \text{Max}(R)$. If $R\subset T$ is a minimal ring extension and $T$ is an integral domain, then $(R:T) = 0$ if and only if $R$ is a field and $T$ is a minimal field extension of $R$, or $R_J$ is a valuation ring of altitude one and $T_{J}$ is its quotient field

Analysis Of SnS2 Buffer Layer And SnS Back Surface Layer Based CZTS Solar Cells Using SCAPS

A Copper-Zinc-Tin-Sulphide (CZTS)based solar cell with a modified ce3ll configuration of Mo/SnS/CZTS/SnS2/ZnO is simulated using SCAPS. An SnS2 buffer layer is used in simulation instead of the standard CdS layer. An additional back surface passivation layer of SnS is added in the modified cell configuration. An improvement in the solar cell efficiency compared to the standard CdS buffer based solar cell configuration Mo/CZTS/CdS/ZnO is found. The observations suggest the possibility of using SnS2 as a potential replacement of CdS. In addition, the use of a back surface passivation layer leads to improved solar cell performance

Role of contact work function, back surface field and conduction band offset in CZTS solar cell

We employ simulation based approach for enhancing the efficiency of Cu2ZnSnS4 (CZTS) based solar cells. Initial benchmarking of simulation with the experimentally reported solar cell in literature is performed by incorporating a suitable defect model. We then explore the effects of: (a) conduction band offset (CBO) at CZTS/CdS junction, (b) back surface field (BSF) due to an additional layer with higher carrier density, and (c) high work function back contact. Efficiency is observed to improve by about 70% upon optimizing the above three parameters. We also observe that utilizing BSF in the configuration can reduce the high work function requirement of the back contact. A work function of 5.2 eV (e.g., using Ni), a BSF layer (e.g., using SnS), and a CBO of 0.1 eV (e.g., using ZnS) constitute an optimal configuration.Comment: 30 pages, 4 tables, 10 figure

Multi-particle entanglement and generalized N-particle teleportation using quantum statistical correlations

Construction of multi-particle entangled states and direct teleportation of N-(spin 1/2) particles are important areas of quantum information processing. A number of different schemes which have been presented already, address the problem through controlled teleportation. In this article, a criterion based on standard quantum statistical correlations employed in the many body virial expansions is used to determine maximum entanglement for a N-particle state. These states remain entangled through proper traces to states for a smaller number of particles and can be generalized for arbitrary number of particles. It is shown that they are quite useful in generalized, N-particle, direct teleportation. The corresponding quantum gates are also indicated for teleportation schemes from simple computational basis states.Comment: 50 pages, 12 Tables, 9 figures and 38 reference