- ItemOn a subclass of bi-close-to-convex functions by means of the Gegenbauer polynomial(Vysoké učení technické v Brně, Fakulta strojního inženýrství, Ústav matematiky, 2021) Al Amoush, Adnan Ghazy; Bulut, SerapIn this paper, we express a new subcollection of bi-close-to-convex functions by means of Gegenbauer polynomials in the open unit disc U. Further, several related outcomes such as coefficient bounds and Fekete–Szegő inequalities are obtained.
- ItemTopological solutions of η-generalized vector variational-like inequality problems(Vysoké učení technické v Brně, Fakulta strojního inženýrství, Ústav matematiky, 2021) Kuma, Satish; Gupta, Ankit; Garg, Pankaj Kumar; Ratna, Dev SarmaIn this paper, we discuss several variants of the η-generalized vector variational-like inequality problem and provide existence theorems for their solutions via a topological approach. Several topological concepts like compactness, closedness, net theory and admissibility of function space topology are used for obtaining the main results. Finally, we give some topological properties of the solution set so obtained.
- ItemBradley–Terry modeling with multiple game outcomes with applications to College Hockey(Vysoké učení technické v Brně, Fakulta strojního inženýrství, Ústav matematiky, 2021) Whelan, John T.; Klein, Jacob E.The Bradley–Terry model has previously been used in both Bayesian and frequentist interpretations to evaluate the strengths of sports teams based on win-loss game results. It has also been extended to handle additional possible results such as ties. We implement a generalization which includes multiple possible outcomes such as wins or losses in regulation, overtime, or shootouts. A natural application is to ice hockey competitions such as international matches, European professional leagues, and NCAA hockey, all of which use a zero-sum point system which values overtime and shootout wins as 2/3 of a win, and overtime and shootout losses as 1/3 of a win. We incorporate this into the probability model, and evaluate the posterior distributions for the associated strength parameters using techniques such as Gaussian expansion about maximum a posteriori estimates, and Hamiltonian Monte Carlo.
- ItemOn cubic polynomials with a given discriminant(Vysoké učení technické v Brně, Fakulta strojního inženýrství, Ústav matematiky, 2021) Klaška, JiříLet D ∈ Z and let CD be the set of all monic cubic polynomials with integer coefficients and with the discriminant equal to D. In this paper we devise a method for determining the set CD. Our method is closely related to integer solutions of Mordell’s equation. A complete discussion of the case D = 0 is also included.
- ItemSome new subspaces of an FK-space and defferred Cesàro conullity(Vysoké učení technické v Brně, Fakulta strojního inženýrství, Ústav matematiky, 2021) Sezgek, Şeyda; Dağadur, İlhanIn this paper, we construct new important subspaces Dqp S, Dqp W, Dqp F and Dqp B for a locally convex FK-space X containing ϕ, the space of finite sequences. Then, we show that there is a relation among these subspaces. Also, we study deferred Cesàro conullity of one FK-space with respect to another, and we give some important results. Finally, we examine the deferred Cesàro conullity of the absolute summability domain lA, and show that if lA is deferred Cesàro conull, then A cannot be l-replaceable.