Binary search trees (BST) are a popular type of data structure when dealing with ordered data. Indeed, they enable one to access and modify data efficiently, with their height corresponding to the worst retrieval time. From a probabilistic point of view, binary search trees associated with data arriving in a uniform random order are well understood...
A complete characterisation is given of all the linear isometries of the Fréchet space of all holomorphic functions on the unit disc, when it is given one of the two standard metrics: these turn out to be weighted composition operators of a particular form. Operators similar to an isometry are also classified. Further, the larger class of operators...
The virtual braid group $VB_n$, the virtual twin group $VT_n$ and the virtual triplet group $VL_n$ are extensions of the symmetric group $S_n$, which are motivated by the Alexander-Markov correspondence for virtual knot theories. The kernels of natural epimorphisms of these groups onto the symmetric group $S_n$ are the pure virtual braid group $VP_...
This paper introduces a novel optimization approach for stain separation in digital histopathological images. Our stain separation cost function incorporates a smooth total variation regularization and is minimized by using a projected gradient algorithm. To enhance computational efficiency and enable supervised learning of the hyperparameters, we ...
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This paper studies the number of limit cycles that may bifurcate from an equilibrium of an autonomous system of differential equations. The system in question is assumed to be of dimension n, have a zero-Hopf equilibrium at the origin, and consist only of homogeneous terms of order m. Denote by Hk(n, m) the maximum number of limit cycles of the sys...
We deal here with a general 2-commodity flow model over a time expanded network designed for the management of a shared mobility systems. The model involves an integral flow vector that represents carriers together with an integral flow vector that represents the items transported by those carriers. It simultaneously copes with temporal and resourc...
In this article we consider a Bloch electron in a crystal lattice subject to slowy varying external magnetic fields. We offer an explanation of de Haas-van Alfven oscillations in terms of energy levels of approximate eigenfunctions for the magnetic Schrödinger operator by using a gaussian beam construction for a small enough magnetic field.
This article is focused on the design of an LMI‐based observer for the class of disturbance‐affected nonlinear systems. Two novel LMI conditions are derived by deploying a more general form of the matrix multiplier compared to the one used in the literature. The first method is based on the use of the criterion, while the second one utilizes an ISS...
The number of spanning trees is an important graph invariant related to different topological and dynamic properties of the graph, such as its reliability, synchronization capability and diffusion properties. In 2007, Chang et al. proposed two conjectures on the number of spanning trees of Sierpiński triangle graphs and its spanning tree entropy. I...
