Related papers: The Affine BV-capacity
Several well known polytopal constuctions are examined from the functorial point of view. A naive analogy between the Billera-Sturmfels fiber polytope and the abelian kernel is disproved by an infinite explicit series of polytopes. A…
This paper extends our earlier results to higher dimensions using a different approach, based on the rigidity of complex structures on certain domains.
The study of affine Deligne-Lusztig varieties originally arose from arithmetic geometry, but many problems on affine Deligne-Lusztig varieties are purely Lie-theoretic in nature. This survey deals with recent progress on several important…
Here, we propose a new modified quantum mechanics and its new algorithms of atomic fine-structure,asymmetric variational method based on hydrogen-like atom orbit. In addition, as we all know, the ab initio calculation of atomic…
All attempts to quantize gravity face several difficult problems. Among these problems are: (i) metric positivity (positivity of the spatial distance between distinct points), (ii) the presence of anomalies (partial second-class nature of…
The primary objective of the present paper is to develop the theory of quantization dimension of an invariant measure associated with an iterated function system consisting of finite number of contractive infinitesimal similitudes in a…
We provide new characterizations of Sobolev ad BV spaces in doubling and Poincare metric spaces in the spirit of the Bourgain-Brezis-Mironescu and Nguyen limit formulas holding in domains of R^N.
Main ideas of the differential geometry on affine bundles are presented. Affine counterparts of Lie algebroid and Poisson structures are introduced and discussed. The developed concepts are applied in a frame-independent formulation of the…
We prove a highest weight theorem classifying irerducible finite--dimensional representations of quantum affine algebras and survey what is currently known about the structure of these representations.
This paper is devoted to the construction of new type of f(R) theories of gravity that are based on the principle of detailed balance. We discuss two versions of these theories with and without the projectability condition.
In order to prevent ``unavoidable'' break-down of the ``peaceful coexistence'' between foundations of quantum theory and relativity I propose a new type of a quantum gauge theory (superrelativity). This differs from ordinary gauge theories…
If nature realizes $TeV$ scale gravity, we are entering a very exciting period in which we could be able to address, experimentally, some questions on quantum gravity, strings, branes and other exotic aspects of the fundamental theory of…
An overview of the recent developments in plurifine potential theory.
We introduce an image based algorithmic tool for analyzing multi-component shapes here. Due to the generic concept of multi-component shapes, our method can be applied to the analysis of a wide spectrum of applications where real objects…
In order to determine the ratio of CKM matrix elements |V_{ub}/V_{cb}| (and |V_{ub}|), we propose a new model-independent method based on the heavy quark effective theory, which is theoretically described by the phase space factor and the…
Motivated by variational models for fracture, we provide a new proof of compactness for $GSBV^p$ functions without a priori bounds on the function itself. Our proof is based on the classical idea of concentration-compactness, making it…
In this paper we study the geometric structure of affine Deligne-Lusztig varieties for $GL_n$ and $b$ basic. We introduce a new condition on $\lambda$. If this is satisfied, then the corresponding affine Deligne-Lusztig variety is the…
The precise determination of the CKM elements $V_{cb}$ and $V_{ub}$ is crucial for any new physics analysis in the flavour sector. Their values can be determined from several tree-level decays: $V_{cb}$ can be extracted from $B\to D\ell\nu$…
A general field-antifield BV formalism for antisymplectic first class constraints is proposed. It is as general as the corresponding symplectic BFV-BRST formulation and it is demonstrated to be consistent with a previously proposed…
This is a PhD thesis on a categorical generalization of the $BF$ model called the $BFCG$ theory. The new theory is equivalent to General Relativity at the classical level but, at the quantum level, seeks to address the problem of the…