Cofinite Graphs and Their Profinite Completions

We generalize the idea of cofinite groups, due to B. Hartley, [2]. First we define cofinite spaces in general. Then, as a special situation, we study cofinite graphs and their uniform completions.The idea of constructing a cofinite graph starts with defining a uniform topological graph $\Gamma$, in an appropriate fashion. We endow abstract graphs with uniformities corresponding to separating filter bases of equivalence relations with finitely many equivalence classes over $\Gamma$. It is established that for any cofinite graph there exists a unique cofinite completion

In vitro Anti-Leishmanial and Anti-Tumour Activities of a Pentacyclic Triterpenoid Compound Isolated from the Fruits of Dregea volubilis Benth Asclepiadaceae

Purpose: Dregea volubilis Benth, commonly known as Jukti in Bengal, is used in the treatment of boils and abscesses from ancient times. The purpose of this study is to elucidate the active compounds and as well as their anti-leishmanial and anti-tumour activities. Methods: Dried and crushed fruits of Dregea volubilis were extracted by petroleum ether (40 - 60°C); the best solvent system had first been verified by analytical Thin Layer Chromatography (TLC). The extract was subjected to TLC and column chromatography (CC) to isolate the pure compounds. Spectradata were obtained by Infra Red pectroscopy, Mass Spectroscopy and Nuclear Magnetic Resonance - Proton Magnetic Resonance (PMR), Carbon Magnetic Resonance (CMR) and Distortionless Enhancement by Polarization Transfer (DEPT) - for structure elucidation of the isolated compound(s). One of the compounds isolated was screened for anti-leishmanial activity against promastigotes of Leishmania donovani and anti-tumour activity on K562 leukemic cell line.Results: A pentacyclic triterpenoid compound was isolated and designated as taraxerone, and then characterized as d-friedoolean-14-en, 3 one together with ß-sitosterol and a long chain lipid fraction.This compound showed in vitro anti-leishmanial activity against promastigotes of Leishmania donovani (strain AG 83) and anti-tumour activity on K562 leukemic cell line. Conclusion: A pentacyclic triterpenoid compound designated as taraxerone and characterized as Dfriedoolean-14-en, 3 one together was successfully isolated. The structure was determined on the basis of spectral analysis (IR, MASS, NMR (PMR, CMR and DEPT) and the compound demonstrated in vitro anti-leishmanial and anti-tumour activities

Multiscale interaction with topography and extreme rainfall events in the northeast Indian region

Flash floods associated with extreme rain events are a major hydrological disaster in the northeast Indian (NEI) region because of the unique topographic features of the region as well as increased frequency of occurrence of such events. Knowledge of the spatiotemporal distribution of these events in the region and an understanding of the factors responsible for them, therefore, would be immensely useful for appropriate disaster preparedness. Using daily rainfall data from 15 stations over the region for 32 years (1975-2006), it is shown that the frequency of occurrence of these events is largest not during the premonsoon thunderstorm season but during the peak monsoon months (June-July-August). This fact together with the fact that most of these events occur during long rainy spells indicate that the extreme events in the NEI region largely occur in association with the monsoon synoptic events rather than isolated thunderstorms. We also find that the aggregate of extreme rain events over the region has a significant decreasing trend in contrast to a recent finding of an increasing trend of such events in central India (Goswami et al., 2006). This decreasing trend of extreme events is consistent with observed decreasing trend in convective available potential energy and increasing convective inhibition energy over the region for the mentioned period. Examination of the structure of convection associated with the extreme rain events in the region indicates that they occur through a multiscale interaction of circulation with the local topography. It is found that at all the stations, the events are associated with a mesoscale structure of convection that is embedded in a much larger scale convective organization. We identify that this large-scale organization is a manifestation of certain phases of the tropical convergence zone associated with the northward propagating active-break phases of the summer monsoon intraseasonal oscillation. Further, it is shown that the mesoscale circulation interacting with the local topography generates southward propagating gravity waves with diurnal period. The strong updrafts associated with the gravity waves within the mesoscale organization leads to very deep convective events and the extreme rainfall. The insights provided by our study would be useful when designing models to improve the prediction of extreme events

MINIMIZATION OF LOAD BASED RESOURCES IN CLOUD COMPUTING SYSTEMS

“Cloud computing” is a term, which involves virtualization, distributed computing, networking, software and Web services. Our Objective is to develop an effective load balancing algorithm using Divisible Load Scheduling Theorem to maximize or minimize different performance parameters (throughput, latency for example) for the clouds of different sizes. Central to these issues lays the establishment of an efficient load balancing algorithm. The load can be CPU load, memory capacity, delay or network load. Load balancing is the process of distributing the load among various nodes of a distributed system to improve both resource utilization and job response time while also avoiding a situation where some of the nodes are heavily loaded while other nodes are idle or doing very little work. Load balancing ensures that all processor in the system or every node in the network does approximately the equal amount of work at any instant of time

Stopping power of hot QCD plasma

The partonic energy loss has been calculated taking both the hard and soft contributions for all the $2 \to 2$ processes, revealing the importance of the individual channels. Cancellation of the intermediate separation scale has been exhibited. Subtleties related to the identical final state partons have properly been taken into account. The estimated collisional loss is compared with its radiative counter part. We show that there exists a critical energy ($E_c$) below which the collisional loss is more than its radiative counterpart. In addition, we present closed form formulas for both the collision probabilities and the stopping power ($dE/dx$)Comment: revised version, section added, 9pages with 5 figure

New way to achieve chaotic synchronization in spatially extended systems

We study the spatio-temporal behavior of simple coupled map lattices with periodic boundary conditions. The local dynamics is governed by two maps, namely, the sine circle map and the logistic map respectively. It is found that even though the spatial behavior is irregular for the regularly coupled (nearest neighbor coupling) system, the spatially synchronized (chaotic synchronization) as well as periodic solution may be obtained by the introduction of three long range couplings at the cost of three nearest neighbor couplings.Comment: 5 pages (revtex), 7 figures (eps, included