Related papers: A Note on Nonuniform versus Uniform ACC^k Circuits…

We study the compactification of nonautonomous systems with autonomous limits and related dynamics. Although the $C^{1}$ extension of the compactification was well established, a great number of problems arising in bifurcation and stability…

We consider edge decompositions of $K_v^{(3)}-I$, the complete 3-uniform hypergraph of order $v$ minus a 1-factor (parallel class, packing of $v/3$ disjoint edges). We prove that a decomposition into tight 6-cycles exists if and only if…

Let R be a unitary ring of finite cardinality P^k, where p is a prime number and $p\nmid k$. We show that if the group of units of $R$ has at most one subgroup of order $p$, then $R\cong A\bigoplus B,$ where $B$ is a finite ring of order…

It has been long recognized that the task of semiclassical evaluation of quantum spectra for the classically nonintegrable systems is fundamentally more complex than for the classically integrable ones. Below it is argued that the quantum…

In this paper, the space complexity of nonuniform quantum computations is investigated. The model chosen for this are quantum branching programs, which provide a graphic description of sequential quantum algorithms. In the first part of the…

In this paper, we continue the study of unit reducible fields as introduced in \cite{LPL23} for the special case of cyclotomic fields. Specifically, we deduce that the cyclotomic fields of conductors $2,3,5,7,8,9,12,15$ are all unit…

A square matrix is nonderogatory if its Jordan blocks have distinct eigenvalues. We give canonical forms (i) for nonderogatory complex matrices up to unitary similarity and (ii) for pairs of complex matrices up to similarity, in which one…

Assuming the Generalised Riemann Hypothesis (GRH), we show that for all k, there exist polynomials with coefficients in $\MA$ having no arithmetic circuits of size O(n^k) over the complex field (allowing any complex constant). We also build…

Let $n \in \mathbb{N}_{\geq 2}$. We prove that for every $k \geq 4$ there exist uniform but non-homogeneous Steiner bundles on $\mathbb{P}^n$ of $k$-type with disconnected splitting type, and we further investigate almost-uniform Steiner…

Nonuniform background electromagnetic fields, once implemented in lattice quantum chromodynamics calculations of hadronic systems, provide a means to constrain a large class of electromagnetic properties of hadrons and nuclei, from their…

We evaluate the particular performance of different quantum machine learning networks on a graph classification task. Quantum circuits with varying internal symmetry that completely, partially and not at all confer to the symmetry of the…

We show that for each non-negative integer k, every bipartite tournament either contains k arc-disjoint cycles or has a feedback arc set of size at most 7(k - 1).

I find an explicit description of modular units in terms of Siegel functions for the modular curves $X^+_{ns}(p^k)$ associated to the normalizer of a non-split Cartan subgroup of level $p^k$ where $p\not=2,3$ is a prime. The Cuspidal…

In this article some noncommutative topological objects such as NC mapping cone and NC mapping cylinder are introduced. We will see that these objects are equipped with the NCCW complex structure of [PEDERSEN]. As a generalization we…

We describe theoretically the acoustoconductance (AC) of quantum contacts. One characteristic of a contact which distinguishes it from a long, uniform wire is a strong, energy-dependent transmission probability. This has several…

It is shown that at one-loop order a neutrino charge radius (NCR) may be defined, which is ultraviolet finite, does not depend on the gauge-fixing parameter, nor on properties of the target other than its electric charge. This is…

We give an example of $C^k$-integrable almost complex structure that does not admit a corresponding $C^{k+1}$-complex coordinate system.

Let R be a finite unitary ring whose group of units is not solvable but all groups of units of all its proper subrings are solvable. In this paper we classify these rings and show that all finite rings of order $p^n$ for $n < 5$ and some of…

We introduce the first complete equational theory for quantum circuits. More precisely, we introduce a set of circuit equations that we prove to be sound and complete: two circuits represent the same unitary map if and only if they can be…

It is well known that the set of possible degree sequences for a graph on $n$ vertices is the intersection of a lattice and a convex polytope. We show that the set of possible degree sequences for a $k$-uniform hypergraph on $n$ vertices is…