1. Secret Sharing Schemes and Syndrome Decoding

    Selda Çalkavur

    Math Dept, Kocaeli University, Kocaeli, Turkey.

    Abstract: Error correcting codes are used to correct errors when messages are transmitted through a noisy communication channel. Syndrome decoding is a method of correcting errors. Secret sharing is an important topic in cryptography. In this paper, we explore some relations between secret sharing schemes based on the binary linear code which is a single error correcting and syndrome decoding. Then we obtain some results using this relation.

    Pages: 741 – 750 | Full PDF Paper
  2. Conceptual Issues Related to the Definition of Government Debt

    João Cadete de Matos1, Sérgio Branco2, Filipe Morais3

    1. Statistics Department, Banco de Portugal, Lisbon, Portugal – jcmatos@bportugal.pt
    2. Statistics Department, Banco de Portugal, Lisbon, Portugal – jscbranco@bportugal.pt
    3. Statistics Department, Banco de Portugal, Lisbon, Portugal – fmmorais@bportugal.pt

    This paper discusses several concepts with regard to the definition of public debt, in particular possible changes related to the delimitation of the public sector and to the range of financial instruments included and its valuation.
    Firstly, it describes the different definitions of government debt that can be found in macroeconomic statistics. It considers the advantages and disadvantages of the various concepts, namely by taking into account the different coverage of entities and instruments and the different ways to value them.
    This analysis is supplemented by looking at net debt measures, which are especially relevant in times of financial crisis, when governments tend to hold more financial assets. From here, the paper examines the arguments that support possible changes in the government debt definition, in particular on some conceptual issues raised recently regarding the definition of the so-called Maastricht debt, which is the concept commonly used in Europe to measure the indebtedness level of a country’s general government. In this respect, recent discussion focused on the possible inclusion of trade credits in the definition of the Maastricht debt and the possible valuation of debt at nominal value rather than face value.
    Possible advantages of taking into account, for fiscal policy purposes, the debt of the whole public sector rather than just the debt of the general government sector are also analysed. In a nutshell, we can say that the latter indicator may be seen as showing a more comprehensive and accurate portrait of the financial position of governments. Finally, the challenge that contingent liabilities may pose to the definition of public debt is addressed.

    Keywords: public debt, national accounts, financial accounts, government finance statistics.

    Pages: 751 – 759 | Full PDF Paper
  3. On q-Baskakov-Durrmeyer-Stancu Operators in Approximation Theory

    Prerna Maheshwari Sharma1, Sangeeta Garg

    1. Department of Mathematics; SRM Univ., Ghaziabad (Uttar Pradesh), India.
    2. Research Scholar; Mewar University, Chittorgarh (Rajasthan), India.

    Abstract: This paper is the extension of Aral-Gupta [1] by the use of Stancu type generalization of q-Baskakov-Durrmeyer operators. We establish some important relations for these operators which provide an approximation process in the polynomial weighted space of continuous functions on [0, ∞). The rate of convergence and weighted approximation properties are also obtained.

    Keywords: q-Baskakov-Durrmeyer operators, Stancu type generalization, Rate of Convergence, Modulus of continuity, Weighted approximation.

    Pages: 760 – 774 | Full PDF Paper
  4. Pedagogical Implications of Bhaskaracharya’s Lilavati

    Sudhakar C Agarkar1, Dr Bedekar Vidya Mandir2, Naupada2

    1. VPM’s Academy of International Education and Research.
    2. Thane, 400602, Maharashtra State, India.

    Abstract: Bhaskaracharya, a celebrated Indian mathematician wrote a mathematical treatise entitled “Lilavati” in 12th century. It contains theorems and problems in elementary Arithmetic, Algebra and Geometry. Written in poetic form with ample use of alliterations metaphors, pun and tenderness the treatise displays various pedagogical characteristics like gender equity, motivational anecdotes, rapport building, content relevance etc. As a part of a year long celebration of 900th birth anniversary, 65 workshops were conducted based on Lilavati in the academic year 2014-15 both in rural as well as urban parts of India. The participants for the workshops were drawn from primary, secondary as well as tertiary level of education. It has been observed that the teaching techniques advocated in Lilavati proved useful in creating interest among students towards mathematics. They not only remove the fear of mathematics but motivates them to to undertake problem solving exercises with zeal and enthusiasm. This paper brings out pedagogical characteristics of Bhaskaracharya’s Lilavati and indicates their relevance for teaching school mathematics in 21st century.

    Pages: 775 – 780 | Full PDF Paper
  5. Local Atmospheric Pollution Evolution through Time Series Analysis

    Giuliana Passamani*, Paola Masotti

    Department of Economics and Management, University of Trento, Trento, Italy.

    Abstract: The monitoring and improvement of air quality are fundamental issues, given the possible effects of air pollution on human health. The analysis, in an Alpine Italian province, of the dynamic pattern of mutual relations among air pollutants is the main aim of the present study. In particular, the interest is the proposal of a procedure that can be used to analyse the pollution level trend. The procedure is: first, the estimation of an unobserved common component that we consider a pollution indicator and, then, the analysis of the component evolution in order to assess whether any improvement in the pollution level has been observed during the last decade. The empirical analysis is conducted through a dynamic multiple time series model with a common autoregressive stochastic factor. The results show that some improvement in the level of air pollution has been achieved, especially in the most recent years.

    Keywords: air quality, air pollutants, dynamic-factor model, unobserved common factor, double-exponential smoothing.

    Pages: 781 – 788 | Full PDF Paper