Creative Mathematics and Informatics: Celebrating a quarter century of publication

Author: Vasile Berinde

Abstract: In order to mark the 25th anniversary of the journal Creative Mathematics and Informatics, we give a brief account on the main facts on its evolution since the previous anniversary notice published 5 years ago [Berinde, V., Creative Mathematics and Informatics: Celebrating 20 years of publication, Creat. Math. Inform., 20 (2011), No. 2, i - vi].
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Supra soft $b$-connectedness I: Supra soft $b$-irresoluteness and separateness

Author: A. M. Abd El-latif

Abstract: This work is divided into two parts. In this part, we introduce and study the notion of supra soft connectedness based on the notion of supra $b$-open soft sets and give basic definitions and theorems about it. Further, we introduce the notion of supra $b$-irresolute soft functions as a generalization to the supra $b$-continuous soft function and study their properties in detail. Finally, we show that, the surjective supra $b$-irresolute soft image of supra soft $b$-connected space is also supra soft $b$-connected.
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An empirical study of the convergence area and convergence speed of Agarwal et al. fixed point iteration procedure

Author: Gheorghe Ardelean and Laszlo Balog

Abstract: We present an empirical study of the convergence area and speed of Agarwal et al. fixed point iterative procedure in the particular case of the Newton's method associated to the complex polynomials $p_{3}(z)=z^3-1$ and $p_{8}(z)=z^8-1$. In order to obtain an analytical expression for the experimental data related to the mean number of iterations (MNI) and convergence area index (CAI), we use regression analysis and find some linear and nonlinear bi-variable models with good correlation coefficients.
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On the generalized Boolean sum Schurer-Stancu approximation formula

Author: Dan BÄƒrbosu and Ovidiu T. Pop

Abstract: In this paper, the Schurer-Stancu generalized Boolean sum (GBS, for short) approximation formula is consi\-dered and
it's remainder term is expressed in terms of bivariate divided
differences. When the approximated function is sufficiently
smooth, an upper bound estimation for the remainder term
is also established. As particular cases, GBS Schurer and respectively
GBS Bernstein approximation formulas are obtained and the
expressions of their remainder are explicitly given.
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Development of a QSPR model for predicting octane number of alkanes using SD topological index

Author: ZoiÈ›a-MÄƒrioara Berinde, Claudia Butean and Thomas Dippong

Abstract: The octane number (ON, MON and PON) for the molecular structures of 18 octane isomers have been correlated using the quantitative structure-property relationship (QSPR) method, with topological index $SD$. For single parameter correlation the index $SD$ shows poor results (RON, $r = 0.406$; MON, $r =0.490$; PON, $r =0.448$), whereas for two-parameter correlation almost any combination among the above $D_C$ was found to give relatively high $r$ value. The best correlation coefficients are as follows: for RON, $r = 0.993$; MON, $r =0.968$; PON, $r =0.985$.
For RON, the best model obtained by our regression analysis is
$$
RON = -227.218 + 7.63 * SD - 37.111 * D_C \text{, with } r = 0.993,\, s = 4.8,\, F = 534.
$$
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Relationship between open sets with respect to an ideal

Author: Carlos Carpintero, Jackeline Pacheco and Ennis Rosas

Abstract: In this article, we obtain the relationship between the open sets with respect to an ideal defined by [ Michael, F. I., On some open sets with respect to an ideal, Eur. J. Pure Appl. Math, 6 (2013), No. 1, 53--58.], [Rodyna, A. Hosny and Deena, Al-Kadi, Types of Generalized Open Sets with Ideal, Int J Comput Appl., 80 (2013), No. 4, 97-112.], [Rodyna, A. Hosny, Pre-open sets respect ideal, Eur. J. Sci. Res., 104 (2013), No. 1, 99--101.], and the open sets with respect to an ideal defined by [Rosas, E., Carpintero, C., Munoz, A., Pacheco, J., Some Remarks on Semi Open Sets with Respect to an Ideal, Eur. J. Pure Appl. Math, 7 (2014), No. 4, 437--441.] and [Arafa A. N., Mareay, R. Michael, F. I., Idealization of Some Topological Concepts, Eur. J. Pure Appl. Math, 8 (2015), No. 3, 389--394.]. Also we introduce another class of open sets with respect to an ideal called $I$-$b$-open set and we give the relationships between the three last one.
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An improvement of Batir's asymptotic formula and some\ estimates related to the gamma function

Author: Valentin Gabriel Cristea and Sorinel Dumitrescu

Abstract: In this article, we improve Batir's asymptotic formula related to
the gamma function. We prove the monotonicity of some functions related to
the gamma function.
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An elementary proof for $\sin x=x-\frac{x^3}6+{o}(x^3)$

Author: Radu Gologan

Abstract: Using only elementary trigonometrical calculations we prove the power series development for the $\sin$ and $\cos$ functions up to the terms of power three and four respectively.
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Linear relations on the coefficients of the linking polynomial

Author: Koko K. Kayibi, S. Pirzada and Ahmad M. Alghamdi

Abstract: In 1972, Brylawski showed that the coefficients of the Tutte polynomial of a matroid are not independent, but they obey some linear relations. This result was extended to matroid perspectives by Vergnas in 1999. We extend this result further to all matroids pairs, and we conjecture that all the linear relations obeyed by the coefficients of the linking polynomial are linear combinations of the basic ones.
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Iterative methods for a fixed point of hemicontractive-type mapping and a solution of a variational inequality problem

Author: Tesfalem Hadush Meche, Mengistu Goa Sangago and Habtu Zegeye

Abstract: In this paper, we introduce and study an iterative process for finding a common point of the fixed point set of a Lipschitz hemicontractive-type multi-valued mapping and the solution set of a variational inequality problem for a monotone mapping. Our results improve and extend most of the results that have been proved for this class of nonlinear mappings.
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Rate of growth of polynomials with restricted zeros

Author: Abdullah Mir and Q. M. Dawood

Abstract: In this paper we consider for a fixed $\mu,$ the class of polynomials $P(z)=a_0+\sum\limits_{\nu=\mu}^{n}a_\nu z_\nu,\, 1\leq \mu \leq n, $ of degree at most $n$ not vanishing in the disk $ \left|z\right|0$. For any $\rho>\sigma\geq 1$ and $0PDF |

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On the reformulated reciprocal degree distance of graphs

Author: K. Pattabiraman and M. Vijayaragavan

Abstract: The reciprocal degree distance (RDD), defined for a connected graph $G$ as vertex-degree-weighted sum of the reciprocal distances, that is, $RDD(G) =\sum\limits_{u,v\in V(G)}\frac{(d(u) + d(v))}{d_G(u,v)}.$ The new graph invariant named reformulated reciprocal degree distance is defined for a connected graph $G$ as $\overline{R}_t(G) =\sum\limits_{u,v\in V(G)}\frac{(d(u) + d(v))}{d_G(u,v)+t},~t\geq 0.$ The reformulated reciprocal degree distance is a weight version of the $t$-Harary index, that is, $\overline{H}_t(G) =\sum\limits_{u,v\in V(G)}\frac{1}{d_G(u,v)+t},~t\geq 0.$ In this paper, the reformulated reciprocal degree distance and reciprocal degree distance of disjunction, symmetric difference, Cartesian product of two graphs are obtained. Finally, we obtain the reformulated reciprocal degree distance and reciprocal degree distance of double a graph.
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Multiplicity of positive solutions for second order Sturm-Liouville boundary value problems

Author: K. R. Prasad, N. Sreedhar and L. T. Wesen

Abstract: In this paper, we develop criteria for the existence of multiple positive solutions
for second order Sturm-Liouville boundary value problem,
$$u''+k^2u+f(t,u)=0, ~~0\leq t\leq 1, $$
$$a u(0)-bu'(0)=0 \text{~and~} c u(1)+d u'(1)=0,$$
where $k\in\bigg(0, \dfrac{\pi}{2}\bigg)$ is a constant, by an application of Avery--Henderson fixed point theorem.
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Analysis of finite-source cluster networks

Author: Adam Toth, Tamas Berczes, Attila Kuki, Bela Almasi, Wolfgang Schreiner, Jinting Wang and Fang Wang

Abstract: Nowadays the distributed heterogeneous resources of networks, like the computational grid, start to have a greater part of interest
so, the investigations of such systems are vital. Because of the more efficient utilisation of the resources, the job scheduling becomes more challenging for the system administrators. The allocation of the arriving jobs has a great impact on the efficiency and the energy consumption of the system.
In this paper, we present a finite source generalized model for the performance evaluation of scheduling
compute-intensive jobs based on the infinite model of Tien Van Do. The available computers are classified into three groups. This classification is based on two aspects: high performance priority (HP) and energy efficiency priority (EE).
We investigate three schemes (separate queue, class queue and common queue) for buffering the
jobs in a computational cluster that is built from Commercial Off-The-Shelf (COTS)
servers. Our main interest is to calculate performance measures and energy consumption of the system using the different buffering schemes and classifications.
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On orthonormal sets in inner product quasilinear spaces

Author: Ylmaz Ylmaz, Hacer Bozkurt and Sumeyye Cakan

Abstract: Aseev, S. M [Aseev, S. M., Quasilinear operators and their
application in the theory of multivalued mappings, Proc. Steklov Inst. Math., 2 (1986), 23--52] generalized linear spaces by introducing the notion of quasilinear spaces in 1986. Then, special quasilinear spaces which are called "solid floored quasilinear spaces" were defined and their some properties examined in [Cakan, S., Some New Results Related to Theory of
Normed Quasilinear Spaces, Ph.D. Thesis, Inonu University,
Malatya, 2016]. In fact, this classification was made so as to examine consistent and detailed some properties related to quasilinear spaces.
In this paper, we present some properties of orthogonal and orthonormal sets on inner product quasilinear spaces. At the same time, the mentioned classification is crucial for define some topics such as Schauder basis, complete orthonormal sequence, orthonormal basis and complete set and some related theorems. Also, we try to explain some geometric differences of inner product quasilinear spaces from the inner product (linear) spaces.
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