buletinul institutului politehnic din iaşi bulletin of the polytechnic ...

BULETINUL INSTITUTULUI POLITEHNIC DIN IAŞI
BULLETIN OF THE POLYTECHNIC INSTITUTE OF IAŞI
Tomul LVII (LXI), Fasc. 3 2011
MATHEMATICS. THEORETICAL MECHANICS. PHYSICS
C O N T E N T S
Pp.
GHEORGHE EDUARD ŢARĂ, n-Rainbow Archetypal Permutations and
Strings (English, Romanian summary). . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
NICOLETA NEGOESCU, Résultats sur les points communs de deux
opérateurs contractifs (French, Romanian summary) . . . . . . . . . . . . . . . 19
MITICĂ CRAUS, VLAD BÎRLESCU and MARICEL AGOP, High
Performance Computing − A New Perspective through Fractal
Computers (I) (English, Romanian summary). . . . . . . . . . . . . . . . . . . . . . 25
VLAD BÎRLESCU, MITICĂ CRAUS, IOAN GOTTLIEB and MARICEL
AGOP, High Performance Computing − A New Perspective through
Fractal Computers (II) Fractality and Feynman’s Path-Integral Type
(English, Romanian summary). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
IOAN GOTTLIEB, CLEOPATRA MOCIUŢCHI, VLAD BÎRLESCU,
MITICĂ CRAUS, DANIELA MAGOP and MARICEL AGOP, High
Performance Computing − A New Perspective through Fractal
Computers (III) Elements of Fractal Theory (English, Romanian
summary) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
IOAN GOTTLIEB, CLEOPATRA MOCIUŢCHI, VLAD BÎRLESCU,
MITICĂ CRAUS, RODICA VIVIANA RADU and MARICEL AGOP,
High Performance Computing − A New Perspective through Fractal
Computers (IV) Fractal Approximation of Motion (English, Romanian
summary) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
TATIANA DANDU BIBIRE, VLAD BÎRLESCU, IOAN GOTTLIEB,
CLEOPATRA MOCIUŢCHI, MITICĂ CRAUS and MARICEL AGOP,
High Performance Computing − A New Perspective through Fractal
Computers (V) Considerations on the Average Value in the Fractals
Theory (English, Romanian summary) . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

PAUL DANIEL MĂTĂSARU, TLM with Random Walk vs. Probabilistic
Approach Using Fractal Generation (English, Romanian summary). .
89
OVIDIU BUHUCIANU, MARINA-AURA DARIESCU and CIPRIAN
DARIESCU, Graphene-Like Fermions in Uniform Magnetic Fields
(English, Romanian summary). . . . .. . . . . . . . . . . . . . . . . . . . . . . 97
MUGUR B. RĂUŢ, The Generalized Gravitational Potential (English,
Romanian summary) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
GINA TIRON, STELUŢA GOSAV and DANA ORTANSA DOROHOI,
Comparative Analysis of ANN and PCA-ANN Systems for Rainfall
Estimation Based on Radar Data and Numerical Weather Prediction
ALADIN Model (English, Romanian summary). . . . . . . . .. . . . . . . 115
IRINA GRĂDINARU, ELENA RALUCA BACIU, ANDREEA VELEA,
MARIA BACIU and DANIELA CALAMAZ, Study Concerning the
Wear Behaviour of Some Restorative Glass Ionomer Materials Used in
Dental Practice (English, Romanian summary ). . . . . . . . . . . . . . . . 127
n-RAINBOW ARCHETYPAL PERMUTATIONS AND STRINGS
by
GHEORGHE EDUARD ŢARĂ
Abstract. New notion related to coloured permutations are
introduced here. We define the n-rainbow permutation and the string of
an n-rainbow permutation as a closed curve in R 3 . We define the
fundamental n-rainbow permutation as an equivalence class related to the
equivalence in strings. We establish an algorithm to identify the n-
rainbow archetypal permutations and strings. We present the formula for
the number of n-rainbow archetypal permutations and strings, n≥3.
Key words: coloured permutation group, knot.
RÉSULTATS SUR LES POINTS COMMUNS
DE DEUX OPÉRATURS CONTRACTIFS
by
NICOLETA NEGOESCU

Abstract. One proves some common fixed point theorems for two
operators defined on a complete metric space satisfying some contractive
inequalities.
Key words: common fixed point, contractive inequality, complete
metric space.
HIGH PERFORMANCE COMPUTING – A NEW PERSPECTIVE
THROUGH FRACTAL COMPUTERS (I)
by
MITICĂ CRAUS, VLAD BÎRLESCU and MARICEL AGOP
Abstract. A short synthesis on the quantum computing and
their correspondence with fractal geometry are established. In such
conjecture a new class of computers (fractal computers) can be
intuited.
Key words: quantum computing, quantum mechanics, fractal.
HIGH PERFORMANCE COMPUTING – A NEW PERSPECTIVE
THROUGH FRACTAL COMPUTERS
II. FRACTALITY AND FEYNMAN’S PATH-INTEGRAL TYPE
by
VLAD BÎRLESCU, MITICĂ CRAUS, IOAN GOTTLIEB and
MARICEL AGOP
Abstract. In the Nottale’s approach, a correlation between
fractality and Feynman’s path integral type is established. In this way,
Schrödinger type equations at all spatiotemporal scales can be generated.
Key words: quantum mechanics, fractal, path integral.
HIGH PERFORMANCE COMPUTING – A NEW PERSPECTIVE
THROUGH FRACTAL COMPUTERS
III. ELEMENTS OF FRACTAL THEORY
by
IOAN GOTTLIEB, CLEOPATRA MOCIUŢCHI, VLAD BÎRLESCU,
MITICĂ CRAUS, DANIELA MAGOP and MARICEL AGOP

Abstract. A systematization of fractals as well as their definitions is
proposed. Within the framework of this definition, we now divide the
theory of fractals into two branches, with fractals as mutual name. An
approximate procedure has also been defined considering fractals.
Starting from a set, the inverse of this procedure allows us to perform a
fractal extension. The so-called fractal we obtained has the given set as
an approximation. These results have multiple applications, because a
suit of sets (the Brownian motion, the ferns, etc.) are studied through
their fractal extension.
Key words: fractal, self-similarity, fractal dimension, Cantor set.
HIGH PERFORMANCE COMPUTING – A NEW PERSPECTIVE
THROUGH FRACTAL COMPUTERS
IV. FRACTAL APPROXIMATION OF MOTION
by
IOAN GOTTLIEB, CLEOPATRA MOCIUŢCHI, VLAD BÎRLESCU,
MITICĂ CRAUS, RODICA VIVIANA RADU and MARICEL AGOP
Abstract. It is developed a theory of dynamic systems, considering
that the motion of the particles occurs on fractal curves. With this
occasion we will show that quantum mechanics is equivalent to a motion
on Peano curves, in fractal dimension D F = 2, at Compton resolution
scale. In this way we will fundament a new class of computers, more
generally than the quantum ones, namely fractal computers.
Key words: fractals, quantum mechanics, scale relativity theory.
HIGH PERFORMANCE COMPUTING – A NEW PERSPECTIVE
THROUGH FRACTAL COMPUTERS
V. CONSIDERATIONS ON THE AVERAGE VALUE IN THE
FRACTALS THEORY
by
TATIANA DANDU BIBIRE, VLAD BÎRLESCU, IOAN GOTTLIEB,
CLEOPATRA MOCIUŢCHI, MITICĂ CRAUS and MARICEL AGOP

Abstract. It is generalized the notion of the average of a
function dependent on the resolution scale over fractal space-time.
The result is more general than that of Nottale's from (1996).
Key words: average values, fractal.
TLM WITH RANDOM WALK VS. PROBABILISTIC
APPROACH
USING FRACTAL GENERATION
by
PAUL DANIEL MĂTĂSARU
Abstract. Considering that the charge carrier movements take
place on fractal curves, the following paper is highlighting the
similarities between the TLM method with random walk and the
generation of a certain type of fractal. The TLM numerical method in
electromagnetism is presented, with the particular case of random walk
in a rectangular waveguide. Basic notions on fractals are also introduced.
It is shown that random walk can be replaced by generating a Heighway
dragon fractal curve.
Keywords: fractals, TLM, random walk, Heighway dragon.
GRAPHENE-LIKE FERMIONS IN UNIFORM
MAGNETIC FIELDS
by
OVIDIU BUHUCIANU, MARINA-AURA DARIESCU and CIPRIAN
DARIESCU
Abstract. In the present paper, we deal with quasi-particles in
graphene evolving in a static magnetic field, B 0 || Oz . We solve the Dirac
equation and express its solutions in terms of the Hermite associated
functions. Finally, using the wavefunctions of chiral fermions, we
compute the conserved current components.
Key words: grapheme, Dirac equation, Hermite associated
functions.
THE GENERALIZED GRAVITATIONAL POTENTIAL
by

MUGUR B. RĂUŢ
Abstract. This paper suggests a general form for the gravitational
potential generated by a spherical shell. Some properties of this potential
are discussed from Earnshow’s theorem perspective. The general form of
the Poisson equation is obtained for this potential, then this equation is
solved and the domain of viability for the solutions is established.
Key words: Yukawa-type potentials; algebraic potentials;
gravitational potential.
COMPARATIVE ANALYSIS OF ANN AND PCA-ANN SYSTEMS
FOR RAINFALL ESTIMATION BASED ON RADAR DATA AND
NUMERICAL WEATHER PREDICTION ALADIN MODEL
by
GINA TIRON, STELUŢA GOSAV and DANA ORTANSA DOROHOI
Abstract. Rainfall estimation on the ground based on radar
measurements is a challenging problem due on the space-time variability
on the rainfall fields. Recent research has shown that neural network
techniques can be successfully used for ground rainfall estimation from
radar measurements. The radar data used in this study were measured by
the WSR-98 D S-band Doppler radar located in Barnova (north-east of
Romania), and from rain gauges within Romania weather station.
In this paper we present a comparative analysis between several
expert systems built for rainfall estimation from reflectivity of radar
observations and ALADIN model parameters. The systems were built
using Artificial Neural Networks (ANNs) and Principal Component
Analysis (PCA) method. We have built two types of expert systems:
pure ANN systems which use as inputs reflectivity data and ALADIN
model parameters, and hybrid PC-ANN systems (artificial neural
network coupled with principal component analysis system) which use as
inputs the scores of principal component obtained by the original data i.e.
reflectivity data and ALADIN model parameters. The validation results
of all expert systems are analyzed.
Keywords: ANN, principal component analysis, rainfall
estimation, radar data, ALADIN model.

STUDY CONCERNING THE WEAR BEHAVIOUR OF SOME
RESTORATIVE GLASS IONOMER MATERIALS USED IN
DENTAL PRACTICE
by
IRINA GRĂDINARU, ELENA RALUCA BACIU, ANDREEA
VELEA,
MARIA BACIU and DANIELA CALAMAZ
Abstract. Glass ionomer cements have a wide range of usages in
dental practice. The aim of the present work was to study the wear
resistance of different glass ionomer cements frequently used in the
restoring dental medicine. Experimental researches related to the
abrasive wear behaviour were run for 2 glass ionomer cements, out of
which a conventional one (Kavitan Plus- Spofa Dental) and one
reinforced with silver (Silvercem- W+P Dental). The abrasive wear
behaviour of the dental materials under analysis was highlighted by the
determination of the mass wear, the intensity and speed of mass wear.
The statistic analysis of data was made by means of SPSS programme for
Windows 12, using the “pair” t test. From the analysis of the
experimental data we notice that Silvercem exhibits the lowest values of
absolute mass loss when using the force of 30 N. The behaviour of
Silvercem glass ionomer may be explained by the incorporation of Silver
particles in its composition giving it a superior wear resistance as
compared to the classic glass ionomers such as Kavitan Plus which in
this study obtained slightly inferior results of the wear resistance when
using the force of 30 N. Thus, Kavitan Plus exhibits values almost
identical of the wear resistance in the first two thirds of the friction
layout, the mass loss decreasing in the last part. Kavitan Plus glass
ionomer cement exhibits the highest wear resistance during the tests with
10 N forces, when it registered the lowest values of substance absolute
loss. As the force increases, this material is outrun by Silvercem.
Key words: glass ionomer cements, wear behaviour, dental
materials, dental medicine.