Related papers: The Jordan-Brouwer theorem for the digital normal …
We study the quantization of spaces whose K-theory in the classical limit is the ring of dual numbers $\mathbb{Z}[t]/(t^2)$. For a compact Hausdorff space we recall necessary and sufficient conditions for this to hold. For a compact quantum…
Ramanujan graphs are graphs whose spectrum is bounded optimally. Such graphs have found numerous applications in combinatorics and computer science. In recent years, a high dimensional theory has emerged. In this paper these developments…
In this paper we investigate the existence and uniqueness of spacelike radial graphs of prescribed mean curvature in the Lorentz-Minkowski space $\mathbb{L}^{n+1}$, for $n\geq 2$, spanning a given boundary datum lying on the hyperbolic…
A still amazing identity of the D-G doublet Raman spectra of parental and reduced graphene oxides is considered from the digital twins viewpoint. About thirty DTs, presenting different aspects of the GO structure and properties, were…
A generalization of the Borsuk-Ulam theorem to Stiefel manifolds is considered. This theorem is applied to derive bounds on $d$ that guarantee-for a given set of $m$ measures in $\mathbb{R}^d$-the existence of $k$ mutually orthogonal…
The Zero divisor Graph of a commutative ring $R$, denoted by $\Gamma[R]$, is a graph whose vertices are non-zero zero divisors of $R$ and two vertices are adjacent if their product is zero. We consider the zero divisor graph…
This paper contains an algebraic constructive and self-contained account of the invariance rule of the digital root under division for an arbitrary natural basis representation. Both the cases of repeating and non-repeating fractionals are…
We obtain a gradient estimate for the Gauss maps from complete spacelike constant mean curvature hypersurfaces in Minkowski space into the hyperbolic space. As applications, we prove a Bernstein theorem which says that if the image of the…
In this paper, we prove two Liouville-type theorems for capillary minimal graph over $\mathbb{R}^n_+$. First, if $u$ has linear growth, then for $n=2,3$ and for any $\theta\in(0,\pi)$, or $n\geq4$ and $\theta\in(\frac{\pi}6,\frac{5\pi}6)$,…
Non-Hermitian systems exhibit diverse graph patterns of energy spectra under open boundary conditions. Here we present an algebraic framework to comprehensively characterize the spectral geometry and graph topology of non-Bloch bands. Using…
An area metric is a (0,4)-tensor with certain symmetries on a 4-manifold that represent a non-dissipative linear electromagnetic medium. A recent result by Schuller, Witte and Wohlfarth provides a pointwise normal form theorem for such area…
We consider the dynamics of relativistic spin-half particles in quantum graphs with transparent branching points. The system is modeled by combining the quantum graph concept with the one of transparent boundary conditions applied to the…
We show that for a sequence of random graphs Brouwer's conjecture holds true with probability tending to one as the number of vertices tends to infinity. Surprisingly, it was found that a similar statement holds true for weighted graphs…
For oriented connected closed manifolds of the same dimension, there is a transitive relation: $M$ dominates $N$, or $M \ge N$, if there exists a continuous map of non-zero degree from $M$ onto $N$. Section 1 is a reminder on the notion of…
Multicomponent KdV-systems are defined in terms of a set of structure constants and, as shown by Svinolupov, if these define a Jordan algebra the corresponding equations may be said to be integrable, at least in the sense of having…
Hybrid quantum systems that combine discrete-variable (DV) and continuous-variable (CV) architectures represent a promising direction in quantum information science. However, transferring concepts, information and states between such…
A theory of reduction of Lie-Jordan Banach algebras with respect to either a Jordan ideal or a Lie-Jordan subalgebra is presented. This theory is compared with the standard reduction of C*-algebras of observables of a quantum system in the…
While stabilizer tableaus have proven useful as a descriptive tool for additive quantum codes, they otherwise offer little guidance for concrete constructions or algorithm analysis. We introduce a representation of stabilizer codes as…
We summarize features and results on the problem of the existence of Ground States for the Nonlinear Schr\"odinger Equation on doubly-periodic metric graphs. We extend the results known for the two--dimensional square grid graph to the…
We present a topological proof of the existence of invariant manifolds for maps with normally hyperbolic-like properties. The proof is conducted in the phase space of the system. In our approach we do not require that the map is a…