Related papers: On the notions of singular domination and (multi-)…
We develop a complete description of the class of conformal relativistic dissipative fluids of divergence form, following the formalism carried out by Geroch, Lindblom and Pennisi. This type of theories is fully described in terms of…
The formulation of combinatorial differential forms, proposed by Forman for analysis of topological properties of discrete complexes, is extended by defining the operators required for analysis of physical processes dependent on scalar…
The global approach to control systems which we have been pursuing in other work favours the study of dynamics achievable through control. It employs certain globally defined geometric objects and attempts to describe them in the general…
We discuss a unified flow theory which in a single system of hyperbolic partial differential equations (PDEs) can describe the two main branches of continuum mechanics, fluid dynamics, and solid dynamics. The fundamental difference from the…
This paper develops a unified analytical framework for determinant identities under finite-rank perturbations of square matrices that remains valid without invertibility assumptions. In contrast to classical inverse-based formulations, the…
We give a survey on some aspects of the topological investigation of isolated singularities of complex hypersurfaces by means of Picard-Lefschetz theory. We focus on the concept of distinguished bases of vanishing cycles and the concept of…
A perturbative way to investigate superfluid properties of various systems under nonuniform potential is presented. We derive the perturbation expansion of the superfluid fraction, which indicates how liquid exhibits nonclassical rotational…
The Poincar\'e-Alexander Theorem states that holomorphic mappings defined on an open subset of the unit ball of $C^n$ may, under certain conditions, be extended to a biholomorphism of the unit ball. In a complex manifold, every strongly…
We consider an autonomous system of partial differential equations for one-dimensional distributed medium with periodic boundary conditions. Dynamics in time consists of alternating birth and death of patterns with spatial phases…
We revisit the theory of first-order quasilinear systems with diagonalizable principal part and only real eigenvalues, what is commonly referred to as strongly hyperbolic systems. We provide a self-contained and simple proof of local…
Monopole dominance for the nonperturbative features in QCD is studied both in the continuum and the lattice gauge theories. First, we study the dynamical chiral-symmetry breaking (D$\chi $SB) in the dual Higgs theory using the effective…
We provide explicit criteria for blow-up solutions of autonomous ordinary differential equations. Ideas are based on the quasi-homogeneous desingularization (blowing-up) of singularities and compactifications of phase spaces, which suitably…
We consider a model of steady, incompressible non-Newtonian flow with neglected convective term under external forcing. Our structural assumptions allow for certain non-degenerate power-law or Carreau-type fluids. We provide the full-range…
This paper is a survey of the generalized Hamiltonian gradient flow (GHGF) framework for Hamilton-Jacobi equations, with an emphasis on the propagation of singularities and its connections to weak KAM theory, optimal transport and mean…
We propose a new network reliability measure for some particular kind of service networks, which we refer to as domination reliability. We relate this new reliability measure to the domination polynomial of a graph and the coverage…
We consider a discrete dynamical system on a pseudo-Riemannian manifold and we determine the concept of a hyperbolic set for it. We insert a condition in the definition of a hyperbolic set which implies to the unique decomposition of a part…
We introduce measure-theoretic definitions of {\it hyperbolic structure for measure-preserving automorphisms}. A wide class of $K$-automorphisms possesses a hyperbolic structure; we prove that all $K$-automorphisms have a slightly weaker…
Loop quantum gravity is an approach to quantum gravity that starts from the Hamiltonian formulation in terms of a connection and its canonical conjugate. Quantization proceeds in the spirit of Dirac: First one defines an algebra of basic…
Using an approach due to Bowen, Franco showed that continuous expansive flows with specification have unique equilibrium states for potentials with the Bowen property. We show that this conclusion remains true using weaker non-uniform…
The well-known notion of domination in a graph abstracts the idea of protecting locations with guards. This paper introduces a new graph invariant, the autonomous domination number, which abstracts the idea of defending a collection of…