DSpace Collection: Mathematica Balkanica New Series, Vol. 27, 2013, Fasc. 1-2
http://hdl.handle.net/10525/2546
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Letter to the Editor. Remarks on Some Inequalities for Polynomials
http://hdl.handle.net/10525/2616
Title: Letter to the Editor. Remarks on Some Inequalities for Polynomials<br/><br/>Authors: Hachani, M. A.<br/><br/>Abstract: In the present article, I point out serious errors in a paper published in Mathematica Balkanica three years ago. These errors seem to go unnoticed because some mathematicians are applying the results stated in this paper to prove other results, which should not continue.<br/><br/>Description: MSC 2010: 30A10, 30C10, 30C80, 30D15, 41A17.Extention of Apolarity and Grace Theorem
http://hdl.handle.net/10525/2614
Title: Extention of Apolarity and Grace Theorem<br/><br/>Authors: Sendov, Blagovest; Sendov, Hristo<br/><br/>Abstract: The classical notion of apolarity is defined for two algebraic polynomials of equal degree. The main property of two apolar polynomials p and q is the classical Grace theorem: Every circular domain containing all zeros of p contains at least one zero of q and vice versa. In this paper, the definition of apolarity is extended to polynomials of different degree and an extension of the Grace theorem is proved. This leads to simplification of the conditions of several well-known results about apolarity.<br/><br/>Description: MSC 2010: 30C10Sensor Location Problem for a Multigraph
http://hdl.handle.net/10525/2613
Title: Sensor Location Problem for a Multigraph<br/><br/>Authors: Pilipchuk, L. A.; Vishnevetskaya, T. S.; Pesheva, Y. H.<br/><br/>Abstract: We introduce sparse linear underdetermined systems with embedded network structure. Their structure is inherited from the non-homogeneous network ow programming problems with nodes of variable intensities. One of the new applications of the researched underdetermined systems is the sensor location problem (SLP) for a multigraph. That is the location of the minimum number of sensors in the nodes of the multigraph, in order to determine the arcs ow volume and variable intensities of nodes for the whole multigraph. Research of the rank of the sparse matrix is based on the constructive theory of decomposition of sparse linear systems.<br/><br/>Description: MSC 2010: 05C50, 15A03, 15A06, 65K05, 90C08, 90C35On the Mixed Modulus of Smoothness and a Class of Double Fourier Series
http://hdl.handle.net/10525/2611
Title: On the Mixed Modulus of Smoothness and a Class of Double Fourier Series<br/><br/>Authors: Krasniqi, Xhevat Z.<br/><br/>Abstract: In this paper we have defined a new class of double numerical sequences. If the coefficients of a double cosine or sine trigonometric series belong to the such classes, then it is verified that they are Fourier series or equivalently their sums are integrable functions. In addition, we obtain an estimate for the mixed modulus of smoothness of a double sine Fourier series whose coefficients belong to the new class of sequences mention above.<br/><br/>Description: MSC 2010: 42A32; 42A20The Lower Estimate for Bernstein Operator
http://hdl.handle.net/10525/2610
Title: The Lower Estimate for Bernstein Operator<br/><br/>Authors: Gal, Sorin G.; Tachev, Gancho T.<br/><br/>Abstract: For functions belonging to the classes C2[0; 1] and C3[0; 1], we establish the lower estimate with an explicit constant in approximation by Bernstein polynomials in terms of the second order Ditzian-Totik modulus of smoothness. Several applications to some concrete examples of functions are presented.<br/><br/>Description: MSC 2010: 41A10, 41A15, 41A25, 41A36Another Generalization of Arhangel'skii's Theorem
http://hdl.handle.net/10525/2609
Title: Another Generalization of Arhangel'skii's Theorem<br/><br/>Authors: Ergun, Nurettin<br/><br/>Description: MSC 2010: 54A25, 54A35.On Generalized Models and Singular Products of Distributions in Colombeau Algebra G(R)
http://hdl.handle.net/10525/2607
Title: On Generalized Models and Singular Products of Distributions in Colombeau Algebra G(R)<br/><br/>Authors: Damyanov, Blagovest P.<br/><br/>Abstract: Modelling of singularities given by discontinuous functions or distributions by means of generalized functions has proved useful in many problems posed by physical phenomena. We introduce in a systematic way generalized functions of Colombeau that model such singularities. Moreover, we evaluate some products of singularity-modelling generalized functions whenever the result admits an associated distribution.<br/><br/>Description: MSC 2010: 46F30, 46F10On Majorization for Matrices
http://hdl.handle.net/10525/2606
Title: On Majorization for Matrices<br/><br/>Authors: Khan, M. Adil; Latif, Naveed; Pecaric, J.; Peric, I.<br/><br/>Abstract: In this paper, we give several results for majorized matrices by using continuous convex function and Green function. We obtain mean value theorems for majorized matrices and also give corresponding Cauchy means, as well as prove that these means are monotonic. We prove positive semi-definiteness of matrices generated by differences deduced from majorized matrices which implies exponential convexity and log-convexity of these differences and also obtain Lypunov's and Dresher's type inequalities for these differences.