ADVANCE OF SMARANDACHE APPROACH TO SOLVING SYSTEMS OF DIOPHANTlNE EQUATIONS

By developing F. Smarandache (algebraic) approach to solving systems of Diophantine equations we elaborate a set of new computative algorithms and analytical formulae, which may be used for fmding numerical solutions of some combinatorial and number-theoretic problems

Central Bank Governance and Challenges Posed By the Crisis

In the first section of this paper, it will be explained that though generalizations are misleading, some of the central banks, especially among the advanced and systemically important economies, may have to take some, though not entire responsibility, for causing the global financial crisis. The second section elaborates that central banks have acquitted themselves well in avoiding a financial collapse through support of respective governments, and coordination at global level enabled them to do so. The fiscal authorities were leading the coordinated actions towards managing the crisis and embanking on the stimulus on multiple fronts. It is likely that the transparency and accountability processes are also unconventional. The third section postulates that in regard to exit policies, central banks face pressures in terms of coordination among them and with fiscal authorities as well as other regulators within each country. The fourth section briefly mentions select issues arising out of reforms under contemplation in financial sector, as a consequence of the crisis. The fifth section lists the need to revisit governance issues in central banks in the light of experience with the crisis. The concluding part focuses on governance issues of special relevance to central banks in developing countries.

Fiscal policy economic reforms.

Given a parctitioner's perspective of fiscal policy and economic reforms based on his working experience from different Indian and International government institutions.Fiscal Policy ; Economic Reforms

Asymptotic analysis for personalized Web search

Personalized PageRank is used in Web search as an importance measure for Web documents. The goal of this paper is to characterize the tail behavior of the PageRank distribution in the Web and other complex networks characterized by power laws. To this end, we model the PageRank as a solution of a stochastic equation $R\stackrel{d}{=}\sum_{i=1}^NA_iR_i+B$, where $R_i$'s are distributed as $R$. This equation is inspired by the original definition of the PageRank. In particular, $N$ models the number of incoming links of a page, and $B$ stays for the user preference. Assuming that $N$ or $B$ are heavy-tailed, we employ the theory of regular variation to obtain the asymptotic behavior of $R$ under quite general assumptions on the involved random variables. Our theoretical predictions show a good agreement with experimental data

Level curvature distribution in a model of two uncoupled chaotic subsystems

We study distributions of eigenvalue curvatures for a block diagonal random matrix perturbed by a full random matrix. The most natural physical realization of this model is a quantum chaotic system with some inherent symmetry, such that its energy levels form two independent subsequences, subject to a generic perturbation which does not respect the symmetry. We describe analytically a crossover in the form of a curvature distribution with a tunable parameter namely the ratio of inter/intra subsystem coupling strengths. We find that the peak value of the curvature distribution is much more sensitive to the changes in this parameter than the power law tail behaviour. This observation may help to clarify some qualitative features of the curvature distributions observed experimentally in acoustic resonances of quartz blocks

Statistical Properties of Random Banded Matrices with Strongly Fluctuating Diagonal Elements

The random banded matrices (RBM) whose diagonal elements fluctuate much stronger than the off-diagonal ones were introduced recently by Shepelyansky as a convenient model for coherent propagation of two interacting particles in a random potential. We treat the problem analytically by using the mapping onto the same supersymmetric nonlinear $\sigma-$model that appeared earlier in consideration of the standard RBM ensemble, but with renormalized parameters. A Lorentzian form of the local density of states and a two-scale spatial structure of the eigenfunctions revealed recently by Jacquod and Shepelyansky are confirmed by direct calculation of the distribution of eigenfunction components.Comment: 7 pages,RevTex, no figures Submitted to Phys.Rev.

THE SYSTEM - GRAPHICAL ANALYSIS OF SOME NUMERICAL SMARANDACHE SEQUENCES

The system - graphical analysis results of some numerical Smarandache sequences are adduced. It is demonstrated that they possess of the big aesthetic, cognitive and applied significance

In-Degree and PageRank of web pages: why do they follow similar power laws?

PageRank is a popularity measure designed by Google to rank Web pages. Experiments confirm that PageRank values obey a power law with the same exponent as In-Degree values. This paper presents a novel mathematical model that explains this phenomenon. The relation between PageRank and In-Degree is modelled through a stochastic equation, which is inspired by the original definition of PageRank, and is analogous to the well-known distributional identity for the busy period in the $M/G/1$ queue. Further, we employ the theory of regular variation and Tauberian theorems to analytically prove that the tail distributions of PageRank and In-Degree differ only by a multiple factor, for which we derive a closed-form expression. Our analytical results are in good agreement with experimental data