Related papers: The Jordan-Brouwer theorem for the digital normal …
Weight-equitable partitions of graphs, which are a natural extension of the well-known equitable partitions, have been shown to be a powerful tool to weaken the regularity assumption in several well-known eigenvalue bounds. In this work we…
We develop a theory of \emph{reduced} Gromov-Witten and stable pair invariants of surfaces and their canonical bundles. We show that classical Severi degrees are special cases of these invariants. This proves a special case of the MNOP…
In this paper, we first present spectral conditions for the existence of $C_{n-1}$ in graphs (2-connected graphs) of order $n$, which are motivated by a conjecture of Erd\H{o}s. Then we prove spectral conditions for the existence of…
It is shown that the Jordan frame and its conformally transformed version, the Einstein frame of nonminimally coupled theories of gravity, are actually equivalent at the quantum level. The example of the theory taken up is the Brans-Dicke…
The divisor theory of the complete graph $K_n$ is in many ways similar to that of a plane curve of degree $n$. We compute the splitting types of all divisors on the complete graph $K_n$. We see that the possible splitting types of divisors…
In this paper, we present an equitable partition theorem of tensors, which gives the relations between $H$-eigenvalues of a tensor and its quotient equitable tensor and extends the equitable partitions of graphs to hypergraphs. Furthermore,…
We classify $n$-dimensional geometric graph manifolds with nonnegative scalar curvature, and first show that if $n>3$, the universal cover splits off a codimension 3 Euclidean factor. We then proceed with the classification of the…
In this paper we prove the following Liouville-type theorem: any anisotropic minimal graph with free boundary in the half-space must be flat, provided that the graph function has at most one-sided linear growth. This extends the classical…
We prove that an analogue of Jordan's theorem on finite subgroups of general linear groups holds for the groups of biregular automorphisms of algebraic surfaces. This gives a positive answer to a question of Vladimir L. Popov.
Physical systems, characterized by an ensemble of interacting elementary constituents, can be represented and studied by different algebras of observables or operators. For example, a fully polarized electronic system can be investigated by…
We define and discuss the utility of two equivalence graph classes over which a spectral projector-based graph Fourier transform is equivalent: isomorphic equivalence classes and Jordan equivalence classes. Isomorphic equivalence classes…
Jordan algebras arise naturally in (quantum) information geometry, and we want to understand their role and their structure within that framework. Inspired by Kirillov's discussion of the symplectic structure on coadjoint orbits, we provide…
We introduce a connection between a near-term quantum computing device, specifically a Gaussian boson sampler, and the graph isomorphism problem. We propose a scheme where graphs are encoded into quantum states of light, whose properties…
Topological strings on toric Calabi--Yau threefolds can be defined non-perturbatively in terms of a free Fermi gas of N particles. Using this approach, we propose a definition of quantum mirror curves as quantum distributions on phase…
We characterize the space of restrictions of real rational functions to certain algebraic Jordan curves in the plane via the Dirichlet-to-Neumann map associated to the domain in the complex plane bounded by the curve and its Bergman kernel.…
We provide a unified description of Heinz-type mean curvature estimates under an assumption on the gradient bound for space-like graphs and time-like graphs in the Lorentz-Minkowski space. As a corollary, we give a unified vanishing theorem…
In this paper we study the Plateau problem for disk-type surfaces contained in conic regions of $\mathbb{R}^{3}$ and with prescribed mean curvature $H$. Assuming a suitable growth condition on $H$, we prove existence of a least energy…
The Theorem on Invariance of Domain due to L.E.J. Brouwer states that one connected, compact (Hausdorff) m-dimensional manifold embedded into another actually realizes a homeomorphism. This fundamental result is relevant to Functional…
A manifold is a space that locally looks like the smooth space $\mathbf{R}^{n}$. It is usually also assumed that the underlying topological space of a manifold is hausdorff. However, there are natural examples of manifolds for which the…
A special class of Jordan algebras over a field $F$ of characteristic zero is considered. Such an algebra consists of an $r$-dimensional subspace of the vector space of all square matrices of a fixed order $n$ over $F$. It contains the…