1,034 research outputs found
On twists of modules over non-commutative Iwasawa algebras
It is well known that, for any finitely generated torsion module M over the
Iwasawa algebra Z_p [[{\Gamma} ]], where {\Gamma} is isomorphic to Z_p, there
exists a continuous p-adic character {\rho} of {\Gamma} such that, for every
open subgroup U of {\Gamma}, the group of U-coinvariants M({\rho})_U is finite;
here M( {\rho}) denotes the twist of M by {\rho}. This twisting lemma was
already applied to study various arithmetic properties of Selmer groups and
Galois cohomologies over a cyclotomic tower by Greenberg and Perrin-Riou. We
prove a non commutative generalization of this twisting lemma replacing torsion
modules over Z_p [[ {\Gamma} ]] by certain torsion modules over Z_p [[G]] with
more general p-adic Lie group G.Comment: submitte
Climate Change and Disease Simulation
Climate change has manifested differential impacts on various components of the earth system. The impact of climate change is not merely limited to the climatic variable. Climate change has resulted in complex, unforeseen consequences in the biosphere of earth. The silent but gradual changes arise out of varied responses of disease-causing organism to the combination of the disease-conducive environmental variables. The change is the same for both the target hosts plant as well as the animal kingdom. There is an urgent need to look into the changing disease dynamics and the disease pathogen genome sensitivity to the changes in climatic variables. The long memory of genetic makeup of disease pathogen to capture, inherit and evolve or mutate the changed or impacted gene due to climate change in generation after generation may invite a cascading effect on the next generation of biosphere. These silent but gradual changes in the genome of disease organism are rarely investigated or included in simulation models. This also enhances the risk of quantification of uncertainties of various disease simulation models. Thus, chances and lists of black swan events in life and food insecurity are on the rise
Spatio-temporal Trends of Standardized Precipitation Index for Meteorological Drought Analysis across Agroclimatic Zones of India
1. Introduction:
Drought is a normal part of climate of India and every year it affects one or the other State. Droughts, like other meteorological phenomena, have spatial and temporal characteristics that vary significantly from one region to another. The understanding of the spatio-temporal trends of meteorological drought helps in undertaking informed decisions on their preparedness and mitigation measures. Though no significant trends have been reported in the Indian Summer Monsoon Rainfall (IMSR) over long periods, the spatio-temporal trends in drought indices reveals the anomaly in rainfall across regions over different time scales which may be related to climate change induced extreme rainfall events. So, a study was carried out to compute spatio-temporal trends in Standardized Precipitation Index (SPI), an index of rainfall anomaly, using gridded monthly rainfall datasets of CRU TS 3.0 for the 1951 – 2006 period for Indian landmass and the results are reported here.

2. Methodology:
SPI is simply the difference in standardized precipitation from its mean for a specified time period divided by the standard deviation. As precipitation is typically not normally distributed for accumulation periods of 12 months or less, SPI overcomes this disadvantage by fitting an incomplete gamma distribution and then transforming it to normal distribution. Negative values of SPI due to less than normal rainfall indicate dryness while SPI less than -1 indicate drought. Delineation of homogeneous regions for climate change / trend analysis has been a debatable matter due to unwise delineation of the homogeneous regions based on a single climatic variable, mostly the isohyets. Therefore, in this study 14 Agroclimatic Zones (ACZs) of India were selected for SPI trend analysis as homogeneous regions (Fig 1) due to commonality of climatic parameters and their extremes, soil types and water resources. The results of drought trends at ACZ level also can be directly translated into plans for agricultural sectors. SPI were computed for individual months (June, July, August and September) and for the whole Indian summer monsoon duration (June-July-August-September i.e. JJAS). Mean SPIs of various ACZs for the individual months and JJAS over a 56 year period were analyzed for temporal trends using the Mann Kendall test and regional temporal trends across all ACZ together using the Regional Kendall test.

3. Results:
Significant temporal trends in monthly & JJAS SPI at 10% or lower level of significance were observed for ACZ4 (Middle Gangetic plains), ACZ5 (Upper Gangetic plains), ACZ6 (Trans Gangetic plains), ACZ7 (Eastern plateau and hills), ACZ8 (Central plateau and hills), ACZ12 (West coast) and ACZ14 (Western dry) regions. The rest of the ACZs did not show any significant trend in SPI for the 56 year study period. In ACZ4, SPI showed a consistently negative trend for JUN, JUL, AUG and JJAS, whereas in ACZ5, SPI showed a significant negative trend for JUL, AUG & JJAS. SPI showed a significant negative trend in SEP & JJAS for ACZ7, AUG & JJAS in ACZ8, JUL in ACZ12 and AUG in ACZ14. On the other hand, a significantly positive trend in SPI was observed in JUN in ACZ6, ACZ8, and ACZ12. 
The analysis of temporal trends in SPI for all ACZs taken together using the Regional Kendall test showed a significant positive trend in JUN SPI, while significant negative trends in SPI were observed for JUL, AUG and JJAS across India. No significant trend was observed for SEP SPI. The rate of increase in JUN SPI was 0.75E-02 per year, while the rate of change of SPI for JUL, AUG, & JJAS was -0.76E-02, -0.54E-02, and -0.65E-02 per year, respectively.

4. Conclusions:
Among the different ACZ of India, there was an increase in probability of meteorological drought hazard in ACZ4, ACZ5, ACZ7 and ACZ8 covering the States of Bihar, Uttar Pradesh, Madhya Pradesh, Orissa and Eastern Rajasthan. Results also point to a significant decreasing trend in rainfall in these regions for different months as well as for the JJAS monsoon period. In the dry western parts of India (Western Rajasthan and Gujarat), which are traditionally water scare regions, there is no change in probability of occurrence of meteorological drought. 
For India as a whole, there is an increase in probability of meteorological drought in the future due to decreasing trends in rainfall for the JJAS period. The months of July and August will become drier, while June will become wetter. This change in rainfall distribution towards the early period and overall drier months of July and August have an important implication for the productivity of the main crop season of India thus impacting its food security negatively
Binary Cubic Forms and Rational Cube Sum Problem
The classical Diophantine problem of determining which integers can be
written as a sum of two rational cubes has a long history; from the earlier
works of Sylvester, Satg{\'e}, Selmer etc. and up to the recent work of
Alp{\"o}ge-Bhargava-Shnidman. In this note, we use integral binary cubic forms
to study the rational cube sum problem. We prove (unconditionally) that for any
positive integer , infinitely many primes in each of the residue classes as well as , are sums of two rational cubes. Among
other results, we prove that every non-zero residue class , for
any prime , contains infinitely many primes which are sums of two rational
cubes. Further, for an arbitrary integer , we show there are infinitely many
primes in each of the residue classes and , such
that is a sum of two rational cubes
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