Self-adjoint extensions of elliptic operators are used to model the solution of a partial differential equation defined in a singularly perturbed domain. The asymptotic expansion of the solution of a Laplacian with respect to a small parameter ε is first performed in a domain perturbed by the creation of a small hole. The resulting singular perturbation is approximated by choosing an appropriat...

New CP 1-soliton behaviour on a flat torus is reported. Defined by the Weierstrass elliptic function and numerically-evolved from rest, each soliton splits up in two lumps which eventually reunite, divide and get back together again, etc.. This result opens up the question of fractional topological charge.

My research concerns the theoretical foundations of topological data analysis (TDA). Work done in the last several years on theory and applications of TDA has demonstrated that TDA offers a principled, flexible, and computationally viable framework for studying coarse-scale global geometric features of data [17, 26, 13, 7, 11, 10, 8, 24]. Moreover, the tools of TDA have proven to be very well s...

Pathogenic bacteria present a large disease burden on human health. Control of these pathogens is hampered by rampant lateral gene transfer, whereby pathogenic strains may acquire genes conferring resistance to common antibiotics. Here we introduce tools from topological data analysis to characterize the frequency and scale of lateral gene transfer in bacteria, focusing on a set of pathogens of...

The Leutwyler-Smilga prediction regarding the (ir)relevance of the global topological charge for QCD in a finite box is subject to a test. To this end the lattice version of a suitably chosen analogue (massive 2-flavour Schwinger model) is analyzed in the small (V Σm≪ 1), intermediate (V Σm ≃ 1) and large (V Σm≫ 1) Leutwyler-Smilga regimes. The predictions for the small and large regimes are co...

In many engineering problems the shape of the structure is not exactly known. In that situation it is possible to consider a family of shapes which belong to the interval set Ω ∈ [Ω,Ω]. In order to find upper and lower bound of the solution, which depend on uncertain (interval) shape, it is possible to use properties of topological derivative or differentials which are positive definite (in man...

We report an investigation of electron conduction in oligophenyl based double barrier molecular device. We have carried out analytical calculations and numerical simulations on isolated molecules, consisting of aromatic π conjugated system made up of three phenyl rings separated by insulator groups −CH2−, −SiH2−, −GeH2− and −SnH2−. We show analytically as well as numerically that when the two i...

In this paper, the concept of {sl local base with  stratifiedstructure} in $I$-topological vector spaces is introduced. Weprove that every $I$-topological vector space has a balanced localbase with stratified structure. Furthermore, a newcharacterization of $I$-topological vector spaces by means of thelocal base with stratified structure is given.

In this work, we introduce notion of connectedness on fuzzy soft topological spaces and present fundamentals properties. We also investigate effect to fuzzy soft connectedness. Moreover, $C_i$-connectedness which plays an important role in fuzzy topological space extend to fuzzy soft topological spaces.

We show that the lattice of compactifications of a topological group $G$ is a complete lattice which is isomorphic to the lattice of all closed normal subgroups of the Bohr compactification $bG$ of $G$. The correspondence defines a contravariant functor from the category of topological groups to the category of complete lattices. Some properties of the compactification lattice of a topological ...