Mathematics

The Sudbury neutrino observatory (SNO) detects 8 B solar neutrino fluxes from both the D 2 O and Salt detector. In the present analysis we have taken into consideration the flux data from 2nd November, 1999 to 27th May, 2001 from the D 2 O detector and that from 26th July, 2001 to 28th August, 2003 from the Salt detector. We have applied Delay Vector Variance analysis, 17 18 M. H. Khondekar et al.

Co-operation is ubiquitous in social life. Here we try to explore how the mechanism of co-operation can generate income among the high-risk, low-income clients. In this paper we have suggested a model of the operation of microcredit institution by analyzing both borrowings & delinquency in the microcredit groups. The paper starts with a brief definition of microcredit and its history in Indian context, the difference of microcredit and general banking, microcredit and microfinance, role of Grameen Bank, women's empowerment, concept of Self-Help Group, loan schemes, process of loan repayment and types of costs associated and afterwards a plan model is demonstrated on target group and organization building. A mathematical model is proposed to understand the break-even point related to loan size and interest rates. We have also proposed a mathematical model of borrowing group creditworthiness. Corresponding risk coefficient is also measured for the entire process.

Each year a large number of people all over the world die from HIV/AIDS. Although there are many complicating factors behind the spread of HIV, we still believe that relevant mathematical models can provide a good insight of the dynamics of the spread of it. If we can provide a satisfactory profile of this dynamics it will certainly help government officials to make timely remedial actions. In the present work we have established a mathematical model of epidemiology for the spread of HIV. We have made a search for equilibrium points for the system and discussed about their stabilities. Efforts have been made to find the solution of the proposed system. On the basis of extensive analysis relevant comments are made on mutual coexistence of the group infected by HIV and the group not infected by that.

Periodogram analysis of the solar neutrino flux data from 1) 5-day-long samples from Super-Kamiokande-I detector during the period from June, 1996 to July, 2001; 2) 10day-long samples from the same detector during the same period and 3) 45-day-long samples from the same detector during the same period. (1) exhibits periodicity around 0.21-0.22, 0.67-0.77, 1.15-1.98, 6.72-6.95, 12. 05-13.24, 22.48-24.02, 33.50 and 40.73 months.

In this paper, we propose a modified version of the k-nearest neighbor (kNN) algorithm. We first introduce a new affinity function for distance measure between a test point and a training point which is an approach based on local learning. A new similarity function using this affinity function is proposed next for the classification of the test patterns. The widely used convention of k, i.e., k = [

In contact binaries mass transfer is usually non-conservative which ends into loss of mass as well as angular momentum in the system. In the present work we have presented a new mathematical model of the non-conservative mass transfer with a uniform mass accretion rate in a contact binary system with lower angular momentum. The model has been developed under the consideration of reverse mass transfer which may occur simultaneously with the original mass transfer as a result of the large scale circulations encircling the entire donor and a significant portion of the gainer. These circulations in contact binaries with lower angular momentum are caused by the overflow of the critical equipotential surface by both components of the binary system making the governing system more intricate and uncertain.

In order to ascertain the dynamics of temperature variation in India, the scaling properties of the daily mean temperature time series obtained from seven different weather stations viz. Kolkata, Chennai, New Delhi, Mumbai, Bhopal, Agartala and Ahmadabad representing different geographical zones in India has been studied. Scaling properties of the temperature profile across India has been estimated from the calculation of Hurst-Exponent parameter obtained from five different scaling methods. Hurst Exponent values confirm that all temperature time series are Fractional Brownian Motion (FBM), statistically self-affine, anti-persistent and Short Range Dependent (SRD) self similar. As SRD self similarity is a common signature of a nonlinear dynamical process, further investigation has been made to discover the presence of any nonlinear behaviour of the temperature profile of Indian climate using Delay Vector Variance (DVV) method and the present calculation confirms a deterministic nonlinear profile of the same.

In this paper, a search is made to detect any sort of nonlinearity and chaos in the solar irradiance data from the Earth Radiation Budget Satellite during the time period from October 15, 1984 to October 15, 2003 in order to investigate the inherent complexity in it. In this paper, delay vector variance analysis has been applied to trace the nonlinearity; whereas 0-1 test, correlation dimension analysis, information entropy, recurrence plot, and recurrence quantification analysis have been used to explore the signature of chaos in the present time series. Present investigation reveals that though nonlinearity is significantly present in the signal, chaotic behavior is not really observed in it.

Forbush decrease is a rapid decrease in the observed galactic cosmic ray intensity pattern followed by a coronal mass ejection. In the present paper we have analyzed the daily sampled Forbush decrease indices from January, 1967 to December, 2003 generated in IZMIRAN, Russia. Prediction of this astrophysical parameter has been performed using Takagi-Sugeno type Adaptive Neuro-Fuzzy Inference Systems (ANFIS) that allows reduction both in statistical and systematic uncertainties. The visual observation based on the graphical comparison between observed and predicted values and the qualitative performance assessment of the model indicates that this method can be used effectively for minimum Forbush decrease indices predictions. In this work, bell-shaped Gauss type membership functions have been found suitable and Hybrid Learning Algorithm method has been used for the optimization. To judge the predictive capability of the developed methodology, based on ANFIS model, the performance indicators show that root mean square error value is 0.002505 for training and 0.002502 for testing period. So, it may establish that the Forbush effect as a storm in cosmic rays is interestingly very much predictable in short senses.

Presence of outliers critically affects many pattern classification tasks. In this paper, we propose a novel dynamic outlier detection method based on neighborhood rank difference. In particular, reverse and the forward nearest neighbor rank difference is employed to capture the variations in densities of a test point with respect to various training points. In the first step of our method, we determine the influence space for a given dataset. A score for outlierness is proposed in the second step using the rank difference as well as the absolute density within this influence space. Experiments on synthetic and some UCI machine learning repository datasets clearly indicate the supremacy of our method over some recently published approaches.

In the present work, we have considered the daily signal of Solar Radio flux of 2800 Hz cited by National Geographic Data Center, USA during the period from 29 th October, 1972 to 28 th February, 2013. We have applied Savitzky-Golay nonlinear phase filter on the present discrete signal to denoise it and after denoising Finite Variance Scaling Method has been applied to investigate memory pattern in this discrete time variant signal. Our result indicates that the present signal of solar radio flux is of short memory which may in turn suggest the multi-periodic and/or pseudo-periodic behaviour of the present signal. Index Terms-solar radio flux, Savitzky-Golay nonlinear phase filter, finite variance scaling method, Hurst exponent, short memory process.

In the present work we have studied daily data of NASDAQ during the period 5 th February 1971 to 31 st January 2009, daily data of Dow Jones during the period 1 st October 1928 to 31 st January 2009 and daily data of SENSEX during 1 st July 1997 to 31 st January 2009 in order to investigate the relationship between USA and Indian stock markets. These three time series are here processed through Finite Variance Scaling Method which is a form of scaling in order to find the corresponding Hurst exponents. Study reveals that all the three series exhibit anti-persistent behaviour (short-memory process). Interestingly it is observed that the corresponding values of Hurst exponents are not significantly different from each other. We have also studied the autocorrelations with different lags for all these three series and study reveals that we have steady negative profile for autocorrelations of all the three indices.