Related papers: Recent developments in the theory of separately ho…
Recent developments in the theory of heavy quarks are reviewed. In the area of heavy quark fragmentation, there has been progress in the study of both pertubative and nonperturbative processes, including the identification of new observable…
Tight maps was introduced along tight homomorphisms by Burger, Iozzi and Wienhard with aims towards maximal representations. In this paper we classify tight maps into classical Hermitian symmetric spaces and give a partial result for the…
This paper presents a survey of recent and not so recent results concerning the study of smooth homeomorphisms of the circle with a finite number of non-flat critical points, an important topic in the area of One-dimensional Dynamics. We…
We offer a new perspective on the closed graph theorem and the open mapping theorem for separated barrelled spaces and fully complete spaces.
We investigate the geometry of holomorphic curves and complex surfaces from the perspective of singularity theory. We show that, with a suitable choice of a complex bilinear symmetric form, the families of functions and mappings that…
The paper suggests a short survey of integration algorithms which evolved since 1982. These theorems and algorithms form discrete versions of the calculus theorems.
When inclusions in a composite are separated by a very small gap, high contrast between the inclusion and matrix properties can induce strong amplification of the underlying field inside the narrow region. Quantifying this field…
In this paper, we define the notion of a mapping on soft classes and study several properties of images and inverse images of soft sets supported by examples and counterexamples. Finally, these notions have been applied to the problem of…
The unusual magnetic materials are significant in both science and technology. However, because of the strongly correlated effects, it is difficult to understand their novel properties from theoretical aspects. Holographic duality offers a…
In this article, we discuss some properties of holomorphic fibrations in the complex analytic setting.
The last decade has seen the development of a wide set of tools, such as wavefront shaping, computational or fundamental methods, that allow to understand and control light propagation in a complex medium, such as biological tissues or…
We use topological methods to study complexity of deep computations and limit computations. We use topology of function spaces, specifically, the classification Rosenthal compacta, to identify new complexity classes. We use the language of…
Semistable reduction theorem for projective morphisms in the category of complex analytic spaces is established.
Recently, the theory concerning piecewise smooth vector fields (PSVFs for short) have been undergoing important improvements. In fact, many results obtained do not have an analogous for smooth vector fields. For example, the chaoticity of…
A new concept called multilevel contours is introduced through this article by the author. Theorems on contours constructed on a bundle of complex planes are stated and proved. Multilevel contours can transport information from one complex…
In this paper we study the set of projective maps between compact proper convex real projective manifolds. We show that this set contains only finitely many distinct homotopy classes and each homotopy class has the structure of a real…
We provide a short introduction to the field of topological data analysis and discuss its possible relevance for the study of complex systems. Topological data analysis provides a set of tools to characterise the shape of data, in terms of…
Our paper develops a theory of Poisson slices and a uniform approach to their partial compactifications. The theory in question is loosely comparable to that of symplectic cross-sections in real symplectic geometry.
The continuity, in a suitable topology, of algebraic and geometric operations on real analytic manifolds and vector bundles is proved. This is carried out using recently arrived at seminorms for the real analytic topology. A new…
This set of lecture notes gives an introduction to holomorphic function spaces as used in mathematical physics. The emphasis is on the Segal-Bargmann space and the canonical commutation relations. Later sections describe more advanced…