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M. Obradovic

Publications and source records attributed to M. Obradovic.

7 recordsLinked to original sources
arXiv2025

On certain applications of grunsky coefficients in the theory of univalent functions

In this paper a survey is given of application of a method based on Grunsky coefficients for obtaining different estimates (some sharp) for the general class of univalent functions where no analytical characterisation exists. More precisely, estimates are given for the modulus of the third and the fourth logarithmic coefficients, for the modulus of the second and the third Hankel determinant for the general class of univalent functions, and for the modulus of some coefficients of the inverse function, and some coefficient differences.

math.CV↗
arXiv2025

The CMS Phase-2 Fast Beam Condition Monitor prototype test with beam

The Fast Beam Condition Monitor (FBCM) is a standalone luminometer for the High Luminosity LHC (HL-LHC) program of the CMS Experiment at CERN. The detector is under development and features a new, radiation-hard, front-end application-specific integrated circuit (ASIC) designed for beam monitoring applications. The achieved timing resolution of a few nanoseconds enables the measurement of both the luminosity and the beam-induced background. The ASIC, called FBCM23, features six channels with adjustable shaping times, enabling in-field fine-tuning. Each ASIC channel outputs a single binary asynchronous signal encoding time of arrival and time over threshold information. The FBCM is based on silicon-pad sensors, with two sensor designs presently being considered. This paper presents the results of tests of the FBCM detector prototype using both types of silicon sensors with hadron, muon, and electron beams. Irradiated FBCM23 ASICs and silicon-pad sensors were also tested to simulate the expected conditions near the end of the detector's lifetime in the HL-LHC radiation environment. Based on test results, direct bonding between the sensor and ASIC was chosen, and an optimal bias voltage and ASIC threshold for FBCM operation were proposed. The current design of the front-end test board was validated following the beam test and is now being used for the first front-end module, which is expected to be produced in summer 2025. These results represent a major step forward in validating the FBCM concept, first version of the firmware and establishing a reliable design path for the final detector.

physics.ins-det↗
arXiv2022

Univalency of certain transform of univalent functions

We consider univalency problem in the unit disc $\mathbb D$ of the function $$g(z)=\frac{(z/f(z))-1}{-a_{2}},$$ where $f$ belongs to some classes of univalent functions in ${\mathbb D}$ and $a_{2}=\frac{f''(0)}{2}\neq 0$.

math.CV↗
arXiv2021

On certain properties of the class $U(λ)$

Let ${\mathcal A}$ be the class of functions analytic in the unit disk ${\mathbb D} := \{ z\in {\mathbb C}:\, |z| < 1 \}$ and normalized such that $f(z)=z+a_2z^2+a_3z^3+\cdots$. In this paper we study the class $\mathcal{U}(λ)$, $0<λ\leq1$, consisting of functions $f$ from ${\mathcal{A}}$ satisfying \[\left|\left(\frac{z}{f(z)}\right)^2f'(z)-1\right| < λ\quad (z\in {\mathbb D}).\] and give results regarding the Zalcman Conjecture, the generalised Zalcman conjecture, the Krushkal inequality and the second and third order Hankel determinant.

math.CV↗
arXiv2014

Tests of exponentiality based on Arnold-Villasenor characterization, and their efficiencies

We propose two families of scale-free exponentiality tests based on the recent characterization of exponentiality by Arnold and Villasenor. The test statistics are based on suitable functionals of U-empirical distribution functions. The family of integral statistics can be reduced to V- or U-statistics with relatively simple non-degenerate kernels. They are asymptotically normal and have reasonably high local Bahadur efficiency under common alternatives. This efficiency is compared with simulated powers of new tests. On the other hand, the Kolmogorov type tests demonstrate very low local Bahadur efficiency and rather moderate power for common alternatives,and can hardly be recommended to practitioners. We also explore the conditions of local asymptotic optimality of new tests and describe for both families special "most favorable" alternatives for which the tests are fully efficient.

math.ST↗