<abstract xmlns="http://www.w3.org/1999/xhtml"> In this paper we study the continuous dependence and the differentiability with respect to the parameter λ ∈ [λ1, λ2] of the solution operator S : [λ1, λ2] → L2[a, b] for a mixed Fredholm-Volterra type integral equation. The main tool is the fiber Picard operators theorem (see [9], [8], [11], [3] and [2]).</abstract>

Data dependence of solutions for Fredholm-Volterra integral equations in L2[a, b]

<abstract xmlns="http://www.w3.org/1999/xhtml"> In this paper we prove some results concerning bicentric quadrilaterals. We offer a new proof of the Blundon-Eddy inequality, which we use to obtain other inequalities in bicentric quadrilaterals.</abstract>

505600 Săcele-Négyfalu, Jud. Braşov, Romania

061311 bd. Timişoara nr. 35, Ы. OD6, sc. E, et. 7 ap. 176, Sect. 6., Bucureşti, Romania

Some inequalities in bicentric quadrilateral

<abstract xmlns="http://www.w3.org/1999/xhtml"> We establish quantitative estimates for the limit q-Bernstein operator introduced in [3], via the second order Ditzian-Totik modulus of smoothness.</abstract>

Approximation by limit q-Bernstein operator

<abstract xmlns="http://www.w3.org/1999/xhtml"> In this paper we give a new proof of the famous result of E. L. Green [3], that gradings of a finite, path connected quiver are in one-to-one correspondence with Galois coverings. Namely we prove that the inverse construction to the skew group construction has as many solutions as the number of different gradings on the starting quiver.</abstract>

Galois covering and smash product of skew categories

<abstract xmlns="http://www.w3.org/1999/xhtml"> Worst, best and average number of messages and running time of leader election algorithms of different distributed systems are analyzed. Among others the known characterizations of the expected number of messages for LCR algorithm and of the worst number of messages of Hirschberg-Sinclair algorithm are improved</abstract>

Leader election in synchronous networks

<abstract xmlns="http://www.w3.org/1999/xhtml"> A result concerning the starlikeness of the image of the Alexander operator is improved in this paper. The techniques of differential subordinations are used.</abstract>

About a condition for starlikeness

<abstract xmlns="http://www.w3.org/1999/xhtml"> We survey arithmetic and asymptotic properties of the alternating sum-of-divisors function β defined by β(pa) = pa − pa−1 + pa−2 − · · · + (−1)a for every prime power pa (a ≥ 1), and extended by multiplicativity. Certain open problems are also stated.</abstract>

A survey of the alternating sum-of-divisors function

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Acta Universitatis Sapientiae, Mathematica

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