2022/1

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    Necessary conditions for hyponormality of Toeplitz operators on the Bergman space
    (Vysoké učení technické v Brně, Fakulta strojního inženýrství, Ústav matematiky, 2022) Gupta, Anuradha; Aggarwal, Amita
    In this paper, we present necessary conditions for the hyponormality of Toeplitz operator Tφ on the Bergman space L2 a(D) when the symbol φ is a polyno- mial in z and z.
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    Existence of solutions for a class of second-order boundary value problems
    (Vysoké učení technické v Brně, Fakulta strojního inženýrství, Ústav matematiky, 2022) Haghshenas, Hadi; Afrouzi, Ghasem A.
    We employ some known critical point theorems to establish results on the existence of weak solutions for an impulsive boundary value problem depending on two real parameters. One of the results ensures the existence of at least three weak solutions, while another one proves the existence of at least one.
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    A game theory explanation for menstrual synchrony: The harem paradox
    (Vysoké učení technické v Brně, Fakulta strojního inženýrství, Ústav matematiky, 2022) Haugen, Kjetil K.
    The 50th anniversary of the McClintock effect deserves a new view on the subject. This paper applies (evolutionary) game theory to gain further insight. Among interesting results are strong indications of Nash equilibria in mixed strate- gies, indicating that the effect depends on parameters characterizing both females and males in the group. As such, much of the empirical research conducted on the subject over the last 50 years may be questioned. Furthermore, the article predicts that the effect’s potential presence depends strongly on female envy/jealousy as well as male preferences on female attractiveness.
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    On some similarities and differences between deep neural networks and kernel learning machines
    (Vysoké učení technické v Brně, Fakulta strojního inženýrství, Ústav matematiky, 2022) Pei, Eddie; Fokoué, Ernest
    This paper presents a thorough computational comparison of the predic- tive performances of deep neural networks and kernel learning machines. The work featured here successfully establishes that on both real-life datasets and artificially simulated ones, kernel learning machines tend to be just as good as deep neural net- works, and quite often outperform them predictively. It turns out from the findings of this paper that while deep neural networks might have worked well on tasks for which millions of observations are available, kernel learning machines just happen to be predictively better on a wide variety of tasks with the kind of sample size that one should realistically expect to have in practice.
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    Third order differential subordination associated with Janowski functions 
    (Vysoké učení technické v Brně, Fakulta strojního inženýrství, Ústav matematiky, 2022) Jeyaraman, M. P.; Lavanya, V. Agnes S. J.; Aaishafarzana, H.
    Using the admissibility condition, we obtain certain third order differ- ential subordination results for an analytic function p with p(0) = 1 belonging to the class of Janowski functions, P[A, B]. As an application, certain second order differential inequalities involving special functions are obtained.