Abstract: In this paper, we show that for every semispray $S$ on a vector
bundle $(R\times TM , \pi , R\times M),$ there are several
sequences of semisprays and correspondingly several nonlinear
connections associated to it. It is important to derive
conditions on $S,$ which guarantee that a sequence of
nonlinear connections
associated to $S$ is constant. We show that the homogeneity
condition for $S$ yields the result.
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No. of downloads: 189

Bivariate uniform approximation via bivariate Lagrange interpolation polynomials

Author: Dan Bărbosu / Ovidiu T. Pop

Abstract: In the present note, we extend some univariate uniform approximation results by means of Lagrange interpolating polynomials [Ivan, M., Elements of Interpolation Theory, Mediamira Science Publisher, Cluj-Napoca (2004)] to the bivariate case.
It is well known that generally, in the univariate case, the sequence of Lagrange interpolation polynomials does't converges to the approximated function. This fact was first observed by G. Faber (see [9]), which constructed an example when the sequence of Lagrange interpolation polynomials diverges. The result of G. Faber was more generalized by I. Muntean (see [12]). M. Ivan
established first sufficient conditions for the uniform
convergence of the sequence of Lagrange interpolation polynomials
associated to a univariate real valued function.
First, we represent the remainder term of bivariate
Lagrange interpolation formula in terms of bivariate divided
difference. Using this representation we establish sufficient
conditions for the uniform convergence of the sequence of
bivariate Lagrange interpolation polynomials to the approximated
function.
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No. of downloads: 205

A man who had known his star in the sky. A homage to Professor Eugen Grebenikov (1932-2013)

Author: Vasile Berinde

Abstract: The main aim of this note is to present some data about the education, professional activity and scientific publications of Professor Eugen Grebenikov (1932-2013), a distinguished mathematician born in 1932 at Slobozia Mare, Ismail county, Romania (now in Republic of Moldova) who was educated and had worked for most of his life time in Moscow. Some author' s personal recollections are also included.
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No. of downloads: 152

A mathematical model for the study of contamination of honey with lead and cadmium in Baia Mare area

Abstract: Eleven samples of honey collected from different locations spread in the Baia Mare area and situated at various distances from the pollution source, the company Romplumb S.A. (while it has been in operation and after its closure in January 2012) were studied to determine the presence of the Pb and Cd by electrothermal atomic absorption spectrometry. It has been found that the concentration of lead and cadmium is generally correlated with the degree of pollution of the environment with these heavy metals, as well as with the distances from the pollution source and the directions of circulation of the contaminated air. In order to characterize the contamination of honey we introduced the index of contamination (IC) that shows a medium contamination for Pb and weak contamination for Cd in the period the pollution source was active and a weak contamination for Pb and no contamination for Cd after the closure of the metallurgical plant. We obtained a mathematical model representing the concentration of Pb in honey with respect to the geographical position in case the air was also contaminated with Pb, and showing more clearly the influence of air flows on the contamination of honey.
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No. of downloads: 183

About the implementation and some applications of the FIXPOINT software minipackage

Author: Andrei Bozântan / Vasile Berinde

Abstract: The main aim of this note is to briefly present the implementation, main features and some current and potential applications of the software minipackage FIXPOINT, designed and implemented by the first author and used by the second author in solving some concrete problems.
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No. of downloads: 157

Remarks on notions of $\mu^*$-open sets

Author: Carlos Carpintero / Ennis Rosas / Margot Salas / Ivan Blanco / Martha Polo

Abstract: The purpose of this paper is to show that the construction leading from a generalized topology $\mu$ and a hereditary class of sets $\mathcal{H}$ to another generalized topology $\mu^*$ remains valid, together with a lot of properties, if the generalized topology $\mu$ and the hereditary class $\mathcal{H}$ are replaced by arbitrary classes of subsets.
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No. of downloads: 190

Fixed point theorems for multivalued generalized contractions with respect to two topologically equivalent metrics

Author: Iulia Coroian

Abstract: In this paper, we will present some fixed point results for multivalued almost contractions with respects to two topologically equivalent Hausdorff type metrics.
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No. of downloads: 148

Fixed point theorems for almost contractions in generalized metric spaces

Abstract: Fixed point theorems for almost contractions in generalized metric spaces are proved. The obtained results are extensions and generalizations, from metric space setting to generalized metric space setting, of many well-known fixed point theorems in literature.
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No. of downloads: 176

Investigating the effectiveness of advertising on declining social networks

Author: Gergely Kocsis / Imre Varga

Abstract: In this paper we aim to investigate the question if it's worth it to advertise on
declining social networks or not. Our investigations are based on computer simulations using
a previously defined and here simplified model of information spreading.
To make our results as close to the real life as possible we run simulations both on a real
network sample and on several generated networks representing as well classical scale-free-like social
topologies as declining social networks. As a result we found how the continuous destruction
of the network affects the spreading, changing also the effectiveness of the advertising.
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No. of downloads: 159

Integrability of trigonometric series with coefficients from the class ${\bf K}$

Author: Xhevat Z. Krasniqi

Abstract: In this paper we deal with a class of sine and cosine trigonometric series. We have imposed some
conditions on their coefficients so that their sums will be integrable with the exception of two points.
In fact, some estimates of the integrals of the absolute values of their sums, expressed in terms of the
coefficients, are obtain extending some results of a paper Telyakovskii, S. A., Localizing the conditions of integrability of trigonometric series,
Trudy Mat. Inst. Steklov., 210 (1995), 264--273 (Russian).
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No. of downloads: 171

Some inequalities for geometrically-arithmetically $h$-convex functions

Author: Muhammad Aslam Noor / Khalida Inayat Noor / Muhammad Uzair Awan

Abstract: In this paper, we consider a class of geometrically convex function which is called geometrically-arithmetically $h$-convex function.
Some inequalities of Hermite-Hadamard type for geometrically-arithmetically $h$-convex functions are derived. Several special cases are discussed.
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No. of downloads: 183

Fixed point theorems for multivalued generalized contractions of rational type in complete metric spaces

Author: Anca M. Oprea

Abstract: The purpose of this paper is to present some fixed point theorems for multivalued contractions of rational type. We extend the results of I. Cabrera, J. Harjani and K. Sadarangan, A fixed point theorem for contractions of rational type in partially ordered metric spaces, Annali dellâ€™Universita di Ferrara, DOI 10.1007/s11565-013-0176-x, to the case of multivalued operators.
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No. of downloads: 155

Stolarsky type means related to an extension of H\"{o}lder-type inequality

Author: Ksenija Smoljak

Abstract: In this paper linear functionals related to an extension of HÃ¶lder-type inequality are defined and their $n-$exponential
convexity is proved. Furthermore, new Stolarsky type means, using families of exponentially convex functions,
are defined and their monotonicity property is proved.
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No. of downloads: 154

Generalized Pell numbers, balancing numbers and binary quadratic forms

Author: Ahmet Tekcan / Merve Tayat

Abstract: In this work, we derive some algebraic identities on generalized Pell numbers and their relationship with balancing numbers. Also we deduce some results on binary quadratic forms involving Pell and balancing numbers.
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No. of downloads: 169

Properties and inequalities for the $\boldsymbol{h}$- and $\boldsymbol{(h,m)}$-logarithmically convex functions

Author: Bo-Yan Xi / Shu-Hong Wang / Feng Qi

Abstract: In the paper, the authors introduce definitions of $h$-logarithmically convex functions and $(h,m)$-logarithmically convex functions respectively, discuss some properties of these kinds of functions, and establish some integral inequalities for these kinds of functions.
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