We show an area law in the mutual information for the maximally-mixed state Ω in the ground space of general Hamiltonians, which is independent of the underlying ground space degeneracy. Our result assumes the existence of a ‘good’ approximation to the ...

Quantum computing technologies are undergoing rapid development. The different qubit modalities being considered for quantum computing each have their strengths and weaknesses, making it challenging to compare their performance relative to each other and ...

In this paper, a three-dimensional conservative system is proposed. By analyzing the Hamiltonian energy, it is concluded that it is a non-Hamiltonian conservative system. By changing the values of the parameters b, c, the system presents ...

• In this paper, a three-dimensional conservative system is proposed. It is proved to be a non-Hamiltonian three-dimensional conservative system by Hamiltonian energy analysis.
• Successful implementation of Multisim simulation and FPGA ...

Let D be a digraph with vertex set V(D) and arc set A(D). An antidirected Hamiltonian path (resp. cycle) of D is a Hamiltonian path (resp. cycle) in which consecutive arcs have opposite directions and each arc of D occurs exactly once. Let ${\alpha }_2(D)=...$$$${}_{\mathrm{}}$${}_{\mathrm{}}\mathrm{}$$\mathcal{}$$\mathcal{}$$\mathcal{}\mathcal{}$${}_{\mathrm{}}\mathrm{}$$\mathcal{}\mathcal{}$

A graph is called supereulerian if it has a spanning eulerian subgraph. A connected even [2, 2s]-factor of a graph G is a connected factor with all vertices of even degree $i(i\in \{2,4,\dots ,2s\})$, where $s\ge 1$ is an integer. Let $W_{s,t}$ be the graph obtained ...${}_{\mathrm{}}$$\mathrm{}{}_{\mathrm{}}$${}_{\mathrm{}}$${}_{\mathrm{}}$${}_{\mathrm{}}$$\mathrm{}$${}_{\mathrm{}\mathrm{}}$${}_{\mathrm{}}$$\mathrm{}$$\mathrm{}\mathrm{}$$\mathcal{}$$\mathcal{}$$$\begin{array}{c}\hfill \mathcal{}{}_{\mathrm{}\mathrm{}\mathrm{}}{}_{\mathrm{}}{}_{\mathrm{}}{}_{\mathrm{}\mathrm{}}{}_{\mathrm{}}{}_{\mathrm{}\mathrm{}}\end{array}$$$\mathrm{}\mathrm{}$$\mathrm{}\mathrm{}$$\mathcal{}{}_{\mathrm{}\mathrm{}\mathrm{}}{}_{\mathrm{}}{}_{\mathrm{}}{}_{\mathrm{}\mathrm{}}$$\mathcal{}$

In the design of an interconnection network, one of the most fundamental considerations is the reliability of the network, which can be usually characterized by the fault tolerance of the network. Embedding paths into a network topology is crucial ...${}^{}$${}_{\mathrm{}}$${}_{\mathrm{}}$${}^{}$${}_{\mathrm{}}$${}_{\mathrm{}}$${}^{}$${}^{}$$$${}^{}$$$${}_{}$${}^{}$$\mathrm{}$$\mathrm{}$${}_{}$

• The Darwin particle-in-cell method is a non-separable canonical Hamiltonian system.

A new approach to Darwin particle-in-cell plasma simulation is described. Using a finite-element approach, the vector potential is assured to be exactly solenoidal. This allows writing the system of multi-species particles as an action-...

A robot control system is a multivariable, nonlinear automatic control system, as well as a dynamic coupling system. To address the difficult problem of data prediction under a chaotic system, a data-driven physical law learning model (DPM) is ...

For a connected graph F of order at least three, we say that a graph G is F-free if G does not contain an induced subgraph isomorphic to F. We call a connected graph G a split graph if the vertex set of G can be partitioned into a clique and an ...

It is proven that for any integer g ≥ 0 and k ∈ { 0 , … , 10 }, there exist infinitely many 5-regular graphs of genus g containing a 1-factorisation with exactly k pairs of 1-factors that are perfect, i.e. form a hamiltonian cycle. For ...

Dynamic systems are usually described by differential equations, but formulating these equations requires a high level of expertise and a detailed understanding of the observed system to be modelled. In this work, we present a data-driven approach,...

Around there, we new examination has been done on past investigations of perhaps the main numerical models that portray the worldwide monetary development and that is depicted as a non-straight fragmentary monetary model of mindfulness, where the ...

Quantum computation has emerged as a powerful computational medium of our time, having demonstrated the remarkable efficiency in factoring a positive integer and searching databases faster than any currently known classical computing ...

The equation A u = f with a linear symmetric positive definite operator A : D ( A ) ⊂ H → H having a discrete spectrum and dense image in a complex Hilbert space H is considered. This equation is transferred into the Hilbert space of finite ...

In this article, we introduce new field equations for incompressible non-viscous fluids, which can be treated similarly to Maxwell’s electromagnetic equations based on artificial intelligence algorithms. Lagrangian and Hamiltonian formulations are ...

The paper is devoted to Lagrange problem of optimal control theory with higher-order differential inclusions (HODI) and special boundary conditions. Optimality conditions are derived for HODIs, as well as for their discrete analogy. In this case, ...

In 1984, Matthews and Sumner conjectured that every 4-connected, claw-free graph contains a Hamiltonian cycle. This still unresolved conjecture has been the motivation for research into the existence of other cycle structures. In this ...

We present OIM (Oscillator Ising Machines), a new way to make Ising machines using networks of coupled self-sustaining nonlinear oscillators. OIM is theoretically rooted in a novel result that establishes that the phase dynamics of coupled ...

Quadratic functions play an important role in applied mathematics. In this paper, we consider the problem of minimizing the integral of a (not necessarily convex) quadratic function in a bounded subset of nonnegative integrable functions defined ...

A matroid M with a distinguished element $$e_0 \in E(M)$$ is a rooted matroid with $$e_0$$ being the root. We present a characterization of all connected binary rooted matroids whose root lies in at most three circuits, and a characterization of ...