EXPLORING SOME NEW IDEAS ON SMARANDACHE TYPE SETS, FUNCTIONS AND SEQUENCES

In this article I have defined a number of SMARANDACHE type sets ,sequences which I found very interesting. The problems and conjectures proposed would give food for thought and would pave ways for more work in this field

SMARANDACHE RECIPROCAL FUNCTION AND AN ELEMENTARY INEQUALITY

The Smarandache Function is defined as S(n) = k . Where k is the smallest integer such that n divides k

GALEX Observations of Diffuse UV Radiation at High Spatial Resolution from the Sandage Nebulosity

Using the GALEX ultraviolet imagers we have observed a region of nebulosity first identified as starlight scattered by interstellar dust by Sandage (1976). Apart from airglow and zodiacal emission, we have found a diffuse UV background of between 500 and 800 \phunit in both the \galex FUV (1350 -- 1750 \AA) and NUV (1750 -- 2850 \AA). Of this emission, up to 250 \phunit is due to \htwo fluorescent emission in the FUV band; the remainder is consistent with scattering from interstellar dust. We have estimated the optical constants to be $a = 0.3; g = 0.7$ in the FUV and $a = 0.5; g = 0.7$ in the NUV, implying highly forward scattering grains, plus an extragalactic contribution of as much as 150 \phunit. These are the highest spatial resolution observations of the diffuse UV background to date and show an intrinsic scatter beyond that expected from instrumental noise alone. Further modeling is required to understand the nature of this scatter and its implications for the ISM.Comment: Total 20 pages, Figures 9, Accepted for publication in Astrophysical Journa

SOME MORE IDEAS ON SMARANDACHE FACTOR PARTITIONS

We define here the SMARANDACHE FACTOR PARTITION FUNCTION (SFP)

ALGORITHM FOR LISTING OF SMARANDACHE FACTOR PARTITIONS

In this note an algorithm to list out all the SFPs of a number without missing any is developed

SOME MORE CONJECTURES ON PRIMES AND DIVISORS

There are an innumerable numbers of conjectures and unsolved problems in number theory predominantly on primes which have been giving sleepless nights to the mathematicians allover the world for centuries

OS Scheduling Algorithms for Memory Intensive Workloads in Multi-socket Multi-core servers

Major chip manufacturers have all introduced multicore microprocessors. Multi-socket systems built from these processors are routinely used for running various server applications. Depending on the application that is run on the system, remote memory accesses can impact overall performance. This paper presents a new operating system (OS) scheduling optimization to reduce the impact of such remote memory accesses. By observing the pattern of local and remote DRAM accesses for every thread in each scheduling quantum and applying different algorithms, we come up with a new schedule of threads for the next quantum. This new schedule potentially cuts down remote DRAM accesses for the next scheduling quantum and improves overall performance. We present three such new algorithms of varying complexity followed by an algorithm which is an adaptation of Hungarian algorithm. We used three different synthetic workloads to evaluate the algorithm. We also performed sensitivity analysis with respect to varying DRAM latency. We show that these algorithms can cut down DRAM access latency by up to 55% depending on the algorithm used. The benefit gained from the algorithms is dependent upon their complexity. In general higher the complexity higher is the benefit. Hungarian algorithm results in an optimal solution. We find that two out of four algorithms provide a good trade-off between performance and complexity for the workloads we studied