The integer part of some terms of a sequence of real numbers

Author: Dumitru Acu

Abstract: In this paper we generalize some problems concerning the integer
part of some terms of particular sequences of real numbers.
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Abstract: In this paper we introduce some new means, which give new
refinements for Arithmetic Mean-Geometric Mean-Harmonic Mean [AM-GM-HM] inequalities.
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Abstract: The Hamilton quaternions are usually introduced as generalisation of
complex numbers respecting the basic identities. We present a way to use
matrices to introduce quaternions and study their properties, using an
isomorphism between the two structures.
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Abstract: This set of notes is aimed at the teacher of the gifted student who wishes to be exposed to less routine techniques of induction than normally found in a standard school textbook.
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On the convergence of a sequence generated by an integral

Author: Marcelina Mocanu / Adrian Sandovici

Abstract: Some results concerning the convergence of some sequences generated by
integrals are presented. Immediate applications are also given.
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Abstract: The aim of this paper is to give two general results regarding the computation of some particular limits of real sequences which are defined by a definite integral (Proposition 1 and Proposition 2). Several applications are then presented.
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Abstract: Is this note we will demonstrate a mean-value theorem (Theorem 3), from which through
several particularizations, we will obtain the mean-value theorem of Dimitrie
Pompeiu and the mean-value theorem of Mircea Ivan.
We will also give a geometrical interpretation of Theorem 3.
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A method to determine all non-isomorphic groups of order 12

Author: Dumitru Valcan

Abstract: The present work gives a method to determine of
all non-isomorphic groups of order 12 and gives descriptions of
all these groups.
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Abstract: Often, the researcher in educational testing theory, would like to have a model that simply explains the obtained scores. In order to establish if such a model is adequate, an indicator based on the eigenvalues of the empirical covariance matrix of the scores is used.
This paper presents the standard methodology to construct this indicator, its bootstrap estimate of the standard error and its percentile bootstrap confidence interval. Finally, for a case study, a program that implements in Matlab the described algorithm provides the desired results.
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A better grading of the student's performance using the first principal

Author: Cristian Marinoiu / Iuliana Dobre

Abstract: In this paper we describe an application of the first principal component of the empirical covariance matrix of the scores in educational testing theory.
An algorithm for better grading the students' performance is implemented in Matlab and the results are provided.
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On the spline and B-spline approximation of a function

Author: Magnolia Rebeles

Abstract: The functions are main mathematical main tools in describing and
analyzing physical processes and phenomena in nature. Only in a few
cases the functions modeling these phenomena are known
explicitly, in the most of the cases there are used
approximations.
In this paper the power of the spline and B-spline
approximation for a given function is presented. A code algorithm generates a table in which the values of these two approximations can be compared. The purpose of this utility programme is to be a didactic tool on how the B-spline functions perform a better approximation than the spline functions.
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Analysis of duration and convexity of coupon obligation

Author: Vincent Soltes / Michael Soltes

Abstract: Duration and convexity of coupon bonds are analysed in this paper. There is derived new formula for duration of the coupon bonds. The proof is based on the calculation of the sum some special sequences without using derivation and integration.
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Abstract: This article presents a Java implementation of one of the
best coding algorithms for the subbands of images. The SPIHT (Set
Partitioning in Hierarchical Trees) algorithm performs a progressive coding
of the transformed images, speculating the correlation between the DWT
coefficients, with a data structure called zerotree.
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Optimal values in structures with pseudo-random generated elements

Author: Camelia Mihaela Pintea

Abstract: We propose structures with recurrent and random values. These values are called pseudo-random values. The goal is to find the optimal values for the pseudo-random values of dynamic lists, character strings and numerical sequences.
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Some methods for composing problems in mathematics

Author: Radu Bairac

Abstract: The article sustains the idea that the
mathematics education should be performed
as a continuous research and discovery, not just as a
simple transmission of already known ideas.
An essential contribution to this activity would
be the invention of new mathematical problems.
Here are some methods: paraphrasing, changing of
statement's data, analogy, generalization,
combination.
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Abstract: In this paper we present the importance of generalization in the didactics of Mathematics with an illustration starting from a problem given at a mathematics competition.
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The method of characteristic values in testing mathematical models

Author: Istvan Huba Atilla Sass

Abstract: Mathematical modeling of natural phenomena is frequently used by scientists. Since mathematical models usually involve laborious computation, there is a real
need for shortcut methods testing the suitability of the chosen model in an early stage of the modeling. In this paper we present and illustrate such a method, namely the method of characteristic values.
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Abstract: In this article we will rewiev the existence and uniqueness
results for fractal sets.
The fractals are sets having noninteger Hausdorff dimensions. In
selfsimilar case this dimension can be calculated using the similarity
dimension.
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