• Title/Summary/Keyword: representation numbers

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GOODSTEIN'S GENERALIZED THEOREM: FROM ROOTED TREE REPRESENTATIONS TO THE HYDRA GAME

  • LEONARDIS, A.;D'ATRI, G.;ZANARDO, E.
    • Journal of applied mathematics & informatics
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    • v.40 no.5_6
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    • pp.883-896
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    • 2022
  • A hereditary base-b representation, used in the celebrated Goodstein's theorem, can easily be converted into a labeled rooted tree. In this way it is possible to give a more elementary geometric proof of the aforementioned theorem and to establish a more general version, geometrically proved. This view is very useful for better understanding the underlying logical problems and the need to use transfinite induction in the proof. Similar problems will then be considered, such as the so-called "hydra game".

REPRESENTATION OF SOLUTIONS OF A SYSTEM OF FIVE-ORDER NONLINEAR DIFFERENCE EQUATIONS

  • BERKAL, M.;BEREHAL, K.;REZAIKI, N.
    • Journal of applied mathematics & informatics
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    • v.40 no.3_4
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    • pp.409-431
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    • 2022
  • In this paper, we deal with the existence of solutions of the following system of nonlinear rational difference equations with order five $x_{n+1}=\frac{y_{n-3}x_{n-4}}{y_n(a+by_{n-3}x_{n-4})}$, $y_{n+1}=\frac{x_{n-3}y_{n-4}}{x_n(c+dx_{n-3}y_{n-4})}$, n = 0, 1, ⋯, where parameters a, b, c and d are not executed at the same time and initial conditions x-4, x-3, x-2, x-1, x0, y-4, y-3, y-2, y-1 and y0 are non zero real numbers.

NOTES ON SOME IDENTITIES INVOLVING THE RIEMANN ZETA FUNCTION

  • Lee, Hye-Rim;Ok, Bo-Myoung;Choi, June-Sang
    • Communications of the Korean Mathematical Society
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    • v.17 no.1
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    • pp.165-173
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    • 2002
  • We first review Ramaswami's find Apostol's identities involving the Zeta function in a rather detailed manner. We then present corrected, or generalized formulas, or a different method of proof for some of them. We also give closed-form evaluation of some series involving the Riemann Zeta function by an integral representation of ζ(s) and Apostol's identities given here.

ON REGULARITY OF SOME FINITE GROUPS IN THE THEORY OF REPRESENTATION

  • Park, Eun-Mi
    • Communications of the Korean Mathematical Society
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    • v.9 no.4
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    • pp.773-782
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    • 1994
  • Investigation of the number of representations as well as of projective representations of a finite group has been important object since the early of this century. The numbers are very related to the number of conjugacy classes of G, so that this gives some informations on finite groups and on group characters. A generally well-known fact is that the number of non-equivlaent irreducible representations, which we shall write as n.i.r. of G is less than or equal to the number of conjugacy classes of G, and the equality holds over an algebraically closed field of characteristic not dividing $\mid$G$\mid$. A remarkable result on the numbers due to Reynolds can be stated as follows.

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Random number sensitivity in simulation of wind loads

  • Kumar, K. Suresh
    • Wind and Structures
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    • v.3 no.1
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    • pp.1-10
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    • 2000
  • Recently, an efficient and practical method has been developed for the generation of univariate non-Gaussian wind pressure time histories on low building roofs; this methodology requires intermittent exponential random numbers for the simulation. On the other hand, the conventional spectral representation scheme with random phase is found suitable for the generation of univariate Gaussian wind pressure time histories on low building roofs; this simulation scheme requires uniform random numbers. The dependency of these simulation methodologies on the random number generator is one of the items affecting the accuracy of the simultion result; therefore, an attempt has been made to investigate the issue. This note presents the observed sensitivity of random number sets in repetitive simulations of Gaussian and non-Gaussian wind pressures.

Representation of Uncertain Geometric Robot Environment Using Fuzzy Numbers

  • Kim, Wan-Joo-;Ko, Joong-Hyup;Chung, Myung-Jin
    • Proceedings of the Korean Institute of Intelligent Systems Conference
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    • 1993.06a
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    • pp.1211-1214
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    • 1993
  • In this paper, we present a fuzzy-number-oriented methodology to model uncertain geometric robot environment and to manipulate geometric uncertainty between robot coordinate frames. We describe any geometric primitive of robot environment as a parameter vector in parameter space. Not only ill-known values of the parameterized geometric primitive but the uncertain quantities of coordinate transformation are represented by means of fuzzy numbers restricted to appropriate membership functions. For consistent interpretation about geometric primitives between different coordinate frames, we manipulate these uncertain quantities using fuzzy arithmetic.

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Mixed Reality Visualization of Financial Accounting Data

  • Tanlamai, Uthai;Savetpanuvong, Phannaphatr;Kunarittipol, Wisit
    • Journal of Information Technology Applications and Management
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    • v.18 no.1
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    • pp.1-14
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    • 2011
  • Mixed reality (MR) representation of accounting numbers is used as an alternative way of virtually engaging users of real three dimensional graphics of financialdata. An experiment was conducted to compare the usability and knowledge drawn from utilizing a table of numbers versus MR representations. The results showed that when MR was used, the participants' ratings of the firm's financial status and performance were more congruent with those of experts than when a table was employed. Also, MR was seen as providing less complex information with a shorter amount of time being spent and was perceived as being easy and useful.

IMBEDDINGS OF MANIFOLDS DEFINED ON AN 0-MINIMAL STRUCTURE ON (R,+,.,<)

  • Kawakami, Tomohiro
    • Bulletin of the Korean Mathematical Society
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    • v.36 no.1
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    • pp.183-201
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    • 1999
  • Let M be an 0-minimal structure on the standard structure :=( , +, ,<) of the field of real numbers. We study Cr -G manifolds (0$\leq$r$\leq$w) which are generalizations of Nash manifolds and Nash G manifolds. We prove that if M is polynomially bounded, then every Cr -G (0$\leq$r<$\infty$) manifold is Cr -G imbeddable into some n, and that if M is exponential and G is a compact affine Cw -G group, then each compact $C\infty$ -G imbeddable into some representation of G.

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COMPACTLY SUPPORTED WAVELET AND THE NUMERICAL SOLUTION OF THE VLASOV EQUATION

  • Benhadid, Yacine
    • Journal of applied mathematics & informatics
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    • v.24 no.1_2
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    • pp.17-30
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    • 2007
  • A new scheme for solving the Vlasov equation using a compactly supported wavelets basis is proposed. We use a numerical method which minimizes the numerical diffusion and conserves a reasonable time computing cost. So we introduce a representation in a compactly supported wavelet of the derivative operator. This method makes easy and simple the computation of the coefficients of the matrix representing the operator. This allows us to solve the two equations which result from the splitting technique of the main Vlasov equation. Some numerical results are exposed using different numbers of wavelets.

ON COMPARISON OF PERFORMANCES OF SYNTHETIC AND NON-SYNTHETIC GENERALIZED REGRESSION ESTIMATIONS FOR ESTIMATING LOCALIZED ELEMENTS

  • SARA AMITAVA
    • Journal of the Korean Statistical Society
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    • v.34 no.1
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    • pp.73-83
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    • 2005
  • Thompson's (1990) adaptive cluster sampling is a promising sampling technique to ensure effective representation of rare or localized population units in the sample. We consider the problem of simultaneous estimation of the numbers of earners through a number of rural unorganized industries of which some are concentrated in specific geographic locations and demonstrate how the performance of a conventional Rao-Hartley-Cochran (RHC, 1962) estimator can be improved upon by using auxiliary information in the form of generalized regression (greg) estimators and then how further improvements are also possible to achieve by adopting adaptive cluster sampling.