On (2,2)-decomposable genus 4 Jacobians

We consider the question of when a Jacobian of a curve of genus $2g$ admits a $(2,2)$-isogeny to two polarized dimension $g$ abelian varieties. We find that one of them must be a Jacobian itself and, if the associated curve is hyperelliptic, so is the other. For $g=2$ this allows us to describe $(2,2)$-decomposable genus $4$ Jacobians in terms of Prym varieties. We describe the locus of such genus $4$ curves in terms of the geometry of the Igusa quartic threefold. We also explain how our characterization relates to Prym varieties of unramified double covers of plane quartic curves, and we describe this Prym map in terms of $6$ and $7$ points in $\mathbb{P}^3$. We also investigate which genus $4$ Jacobians admit a $2$-isogeny to the square of a genus $2$ Jacobian and give a full description of the hyperelliptic ones. While most of the families we find are of the expected dimension $1$, we also find a family of unexpectedly high dimension~$2$.Comment: 22 pages; comments welcom

pp-Adic Integral Geometry

We prove a $p$-adic version of the integral geometry formula for averaging the intersection of two $p$-adic projective varieties. We apply this result to give bounds on the number of points in the modulo $p^m$ reduction of a projective variety (reproving a result by Oesterlé) and to the study of random $p$-adic polynomial systems of equations

Proximal humerus fractures operated with PHILOS plate: 4 year prospective study

Background: Fractures of proximal humerus are still an unsolved problem in many ways. Locked plating is becoming more common; precise knowledge of and experience with the surgical technique is required to maximize clinical outcomes. However the goal of proximal humerus fracture fixation should be stable reduction allowing early mobilization. This study is conducted to study the results and complications of proximal humeral fractures treated by anatomic locking compression plate (PHILOS- proximal humerus interlocking system) and PHLP- Pro.Methods: This is a 4 year prospective study, conducted in the department of Orthopaedics in Shri B M Patil Medical College & Hospital, Vijaypur. Displaced two part, three part and four part fractures of proximal humerus with or without shoulder dislocation including fractures involving osteopenic bone were included. The functional assessment was done according to constant Murley score and DASH score at the end of 6 months.Results: Out of 60 patients, 56 were available for follow-up: 24 patients having excellent results (4 are 2 part, 20 are 3 part fractures), 32 patients having good results (22 are 3 part, 10 are 4 part fractures).  None of the patients had fair or poor results. Conclusions: In conclusion, the internal fixation of proximal humeral fractures with the use of anatomic locking compression plates yields reliable results when utilized correctly. We believe that, provided the correct surgical technique is used by competent surgeon, the anatomic locking compression plate is suitable for the stabilization of proximal humeral fractures and can lead to a good functional outcome

A study of published Literature on ERP: An attempt to find Gaps for further research

According to the APICS* dictionary, Enterprise Resource Planning (ERP) is a: “…framework for organizing, defining, and standardizing the business processes necessary to effectively plan and control an organization so the organization can use its internal knowledge to seek external advantage.â€Enterprise resource planning (ERP) is defined as the ability to deliver an integrated suite of business applications. ERP tools share a common process and data model, covering broad and deep operational end-to-end processes, such as those found in finance, HR, distribution, manufacturing, service and the supply chain.(www.gartner.com/it-glossary/) ERP systems are very complex systems which are integrated in nature, huge and address the needs of all the departments across the organization. These systems are a deviation from the traditional way of functioning where by organizations followed separate individual systems for each department. HR system for example used to be a separate system and the inventory management system used to be a separate system. Sales department had a separate billing system while there was a separate system for production. This traditional way of working and the modern day ERP systems are eons apart in their approach to address the system needs of the organization. This huge difference in the way of working results in a huge impact on the organization as well as the individuals working in the organization.This impact gives rise to various issues which deserve a study giving rise to various research areas

QoS Parameter Analysis on AODV and DSDV Protocols in a Wireless Network

Wireless networks are characterized by a lack of infrastructure, and by a random and quickly changing network topology; thus the need for a robust dynamic routing protocol that can accommodate such an environment. To improve the packet delivery ratio of Destination-Sequenced Distance Vector (DSDV) routing protocol in mobile ad hoc networks with high mobility, a message exchange scheme for its invalid route reconstruction is being used. Two protocols AODV and DSDV simulated using NS-2 package and were compared in terms throughput, end to end delay and packet faction delivery varying number of nodes, speed and time. Simulation results show that DSDV compared with AODV, DSDV routing protocol consumes more bandwidth, because of the frequent broadcasting of routing updates. While the AODV is better than DSDV as it doesn’t maintain any routing tables at nodes which results in less overhead and more bandwidth. AODV perform better under high mobility simulations than DSDV. High mobility results in frequent link failures and the overhead involved in updating all the nodes with the new routing information as in DSDV is much more than that involved AODV, where the routes are created as and when required. AODV use on -demand route discovery, but with different routing mechanics. AODV uses routing tables, one route per destination, and destination sequence numbers

Nonarchimedean integral geometry

Let $K$ be a nonarchimedean local field of characteristic zero with valuation ring $R$, for instance, $K=\mathbb{Q}_p$ and $R=\mathbb{Z}_p$. We prove a general integral geometric formula for $K$-analytic groups and homogeneous $K$-analytic spaces, analogous to the corresponding result over the reals. This generalizes the $p$-adic integral geometric formula for projective spaces recently discovered by Kulkarni and Lerario, e.g., to the setting of Grassmannians. Based on this, we outline the construction of a nonarchimedean probabilistic Schubert Calculus. For this purpose, we characterize the relative position of two subspaces of $K^n$ by a position vector, a nonarchimedean analogue of the notion of principal angles, and we study the probability distribution of the position vector for random uniform subspaces. We then use this to compute the volume of special Schubert varieties over $K$. As a second application of the general integral geometry formula, we initiate the study of random fewnomial systems over nonarchimedean fields, bounding, and in some cases exactly determining, the expected number of zeros of such random systems.Comment: This version is different from the first version of the paper posted on arxiv, which also contained proofs of the nonarchimedean coarea formula and Sard's Lemma (which now are put in the appendix). The current version has also been restructured so to give more emphasis to the new result