In this work we define, analyze, and compare different numerical schemes that can be used to study the ground state properties of Bose-Fermi systems, such as mixtures of different atomic species under external forces or self-bound quantum droplets. The bosonic atoms are assumed to be condensed and are described by the generalized Gross-Pitaevskii equation. The fermionic atoms, on the other hand, are treated individually, and each atom is associated with a wave function whose evolution follows the Hartree-Fock equation. We solve such a formulated set of equations using a variety of methods, including those based on adiabatic switching of interactions and the imaginary time propagation technique combined with the Gram-Schmidt orthonormalization or the diagonalization of the Hamiltonian matrix. We show how different algorithms compete at the numerical level by studying the mixture in the range of parameters covering the formation of self-bound quantum Bose-Fermi droplets.

We present a new approach to nicotinic receptor kinetics and a new model explaining random variabilities in the duration of open events. The model gives new interpretation on brief and long receptor openings and predicts (for two identical binding sites) the presence of three components in the open time distribution: two brief and a long. We also present the physical model of the receptor block. This picture naturally and universally explains receptor desensitization, the phenomenon of central importance in cellular signaling. The model is based on single-channel experiments concerning the effects of hydrocortisone (HC) on the kinetics of control wild-type (WT) and mutated alphaD200Q mouse nicotinic acetylcholine receptors (nAChRs), expressed in HEK 293 cells. The appendix contains an original result from probability renewal theory: a derivation of the probability distribution function for the duration of a process performed by two independent servers.

Let $\Gamma_k(V)$ be the Grassmann graph whose vertex set ${\mathcal G}_{k}(V)$is formed by all$k$-dimensional subspaces of an$n$-dimensional vector space $V$ over the finite field $F_q$ consisting of $q$ elements. We discuss its subgraph $\Gamma(n,k)_q$ with the vertex set ${\mathcal C}(n,k)_q$ consisting of all non-degenerate linear $[n, k]_q$ codes. %We assume that $1

The acquisition of accurately coloured, balanced images in an optical microscope can be a challenge even for experienced microscope operators. This article presents an entirely automatic mechanism for balancing the white level that allows the correction of the microscopic colour images adequately. The results of the algorithm have been confirmed experimentally on a set of two hundred microscopic images. The images contained scans of three microscopic specimens commonly used in pathomorphology. Also, the results achieved were compared with other commonly used white balance algorithms in digital photography. The algorithm applied in this work is more effective than the classical algorithms used in colour photography for microscopic images stained with hematoxylin-phloxine-saffron and for immunohistochemical staining images.

The article presents, in an elementary way, but with mathematical precision and without harm to the intuition, the path from the integral representation to the Dirac delta, starting with Schwartz's functional approach. Next, the considered representation is presented in a more intuitive sequential approach, formulated by Mikusiński and Sikorski. Finally, we present the third regularization that can be related to Sato's approach to distributions.