SOME MORE IDEAS ON SMARANDACHE FACTOR PARTITIONS

We define here the SMARANDACHE FACTOR PARTITION FUNCTION (SFP)

SOME NOTIONS ON LEAST COMMON MULTIPLES

There is the well known result that n! divides the product of any set of n consecutive numbers. Using this idea we define Smarandache LCM Ratio Sequence ofthe rth kind as SLRS(r)

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

Hamiltonian Theory of Disorder at 1/3

The Hamiltonian Theory of the fractional quantum Hall (FQH) regime provides a simple and tractable approach to calculating gaps, polarizations, and many other physical quantities. In this paper we include disorder in our treatment, and show that a simple model with minimal assumptions produces results consistent with a range of experiments. In particular, the interplay between disorder and interactions can result in experimental signatures which mimic those of spin textures