Related papers: Some consequences of the Karpenko-Merkurjev theore…
We prove the mean ergodic theorem of von Neumann in a Hilbert-Kaplansky space. We also prove a multiparameter, modulated, subsequential and a weighted mean ergodic theorems in a Hilbert-Kaplansky space
According to modern quantum physics, at the microlevel, the dimension of space-time is at least 11; we only observe 4 dimensions because the others are compactified: the size along each of the other dimensions is much smaller than the…
We prove a Pucci-Serrin conjecture on critical dimensions under a uniform bound on the energy. The method is based on the analysis of the Green's function of polyharmonic operators with "almost" Hardy potential.
In this work, we find base and dimension of a subspace appeared in works by V. A. Sharafutdinov. The same problem, but expressed in terms of polynomials from matrix minors, was initially solved by W. Hodge. The new result of this paper is…
Five dimensional model with extended dimensions investigated. It is shown that four dimensionality of our world is the result of stability requirement. Extra component of Einstein equations giving trapping solution for matter fields…
This small note contains some easy examples of quartic hypersurfaces that have finite-dimensional motive. As an illustration, we verify a conjecture of Voevodsky (concerning smash-equivalence) for some of these special quartics.
In this note we generalize and prove a recent conjecture of Varchenko concerning the number of critical points of a (multivalued) meromorphic function $\phi$ on an algebraic manifold. Under certain conditions, this number turns out to…
The consequences of replica-symmetry breaking on the structure of ultrametric matrices appearing in the theory of disordered systems is investigated with the help of representation theory, and the results are compared with those obtained by…
We explore a notion of pseudofinite dimension, introduced by Hrushovski and Wagner, on an infinite ultraproduct of finite structures. Certain conditions on pseudofinite dimension are identified that guarantee simplicity or supersimplicity…
The possibility of physics in multiple time dimensions is investigated. Drawing on recent work by Walter Craig and myself, I show that, contrary to conventional wisdom, there is a well-posed initial value problem--deterministic, stable…
We prove that all bounded subsets of $\mathbb{Q}_p^n$ containing a line segment of unit length in every direction have Hausdorff and Minkowski dimension $n$. This is the analogue of the classical Kakeya conjecture with $\mathbb{R}$ replaced…
We consider recent work linking majorization and trumping, two partial orders that have proven useful with respect to the entanglement transformation problem in quantum information, with general Dirichlet polynomials, Mellin transforms, and…
We study the relations between several notions of dimension for an additive set, some of which are well-known and some of which are more recent, appearing for instance in work of Schoen and Shkredov. We obtain bounds for the ratios between…
In theories which require a space of dimension d>4, there is a natural mechanism of suppressing neutrino masses: while Standard Model fields are confined to a 3-brane, right handed neutrinos live in the bulk. Due to Kaluza-Klein…
In this paper, we apply high level versions of Jacobi's derivative formula to number theory such as quarternary quadratic forms and convolution sums of some arithmetical functions.
A description of solutions of some integral equations has been obtained. A two-radii theorem is obtained as well.
Fedorchuk's fully closed (continuous) maps and resolutions are applied in constructions of non-metrizable higher-dimensional analogues of Anderson, Choquet, and Cook's continua. Certain theorems on dimension-lowering maps are proved for…
In this communication, we show that both infinite-dimensional versions of Noether's theorems, and the explanation of quantum anomalies can be obtained using similar formulas for the derivatives of functions whose values are measures…
In this work, partial answers to Reich, Mizoguchi and Takahashi, and Amini-Harandi's conjectures are presented via a light version of Caristi's fixed point theorem. Moreover, we introduce that many of known fixed point theorem can easily…
We employ the pinching theorem, ensuring that some operators A admit any sequence of contractions as an operator diagonal of A, to deduce/improve two recent theorems of Kennedy-Skoufranis and Loreaux-Weiss for conditional expectations onto…