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In this paper, we study normal magnetic curves in $C$-manifolds. We prove that magnetic trajectories with respect to the contact magnetic fields are indeed $\theta_{\alpha }$-slant curves with certain curvature functions. Then, we give the…
Quantum (step-like) magnetization curves are studies for a spin pair with antiferromagnetic coupling in the presence of a magnetic field parallel to the easy axis of the magnetic anisotropy. The consideration is done both analytically and…
Polymerized quantum spin chains (i.e. spin chains with a periodic modulation of the coupling constants) exhibit plateaux in their magnetization curves when subjected to homogeneous external magnetic fields. We argue that the strong-coupling…
We describe an approximate solution to the Heisenberg operator equations of motion for an atom in a laser field. The solution is based on a quantum generalization of the physical picture given by the well-known Simple Man Model (SMM). We…
We prove the existence of Alexandrov embedded closed magnetic geodesics on closed hyperbolic surfaces. Closed magnetic geodesics correspond to closed curves with prescribed geodesic curvature.
A folklore result due to M.W. Hirsch states that most competitive maps admit a carrying simplex, i.e., an invariant hypersurface which attracts all nontrivial orbits. The common approach in the study of these maps is to focus on the…
Recently, we systematically studied the basic theory of Bregman circumcenters in another paper. In this work, we aim to apply Bregman circumcenters to optimization algorithms. Here, we propose the forward Bregman monotonicity which is a…
We address an optimal reachability problem for a planar manipulator in a constrained environment. After introducing the optmization problem in full generality, we practically embed the geometry of the workspace in the problem, by…
We consider the Riemann problem for relativistic flows of polytropic fluids and find relations for the flow characteristics. Evolution of physical quantities take especially simple form for the case of cold magnetized plasmas. We find…
Closure problems are omnipresent when simulating multiscale systems, where some quantities and processes cannot be fully prescribed despite their effects on the simulation's accuracy. Recently, scientific machine learning approaches have…
Designing mechanical devices, called linkages, that draw a given plane curve has been a topic that interested engineers and mathematicians for hundreds of years, and recently also computer scientists. Already in 1876, Kempe proposed a…
We prove that among all unit-speed paths, a straight line minimises the expected escape time from a ball in $\mathbf{R}^n$, solving the min-mean variant of Bellman's Lost~in~a~Forest problem for ball-shaped forests. The proof uses the…
We present a systematic small-correlation expansion to solve the inverse Ising problem: find a set of couplings and fields corresponding to a given set of correlations and magnetizations. Couplings are calculated up to the third order in…
It is shown that in 2+1 dimensions the Fermi-Walker gauge allows the general solution of the problem of determining the metric from the sources in terms of simple quadratures. This technique is used to solve the problem of the occurrence of…
This paper poses a question about a simple localization problem. The question is if an {\em oblivious} walker on a line-segment can localize the middle point of the line-segment in {\em finite} steps observing the direction (i.e., Left or…
Converting a parametric curve into the implicit form, which is called implicitization, has always been a popular but challenging problem in geometric modeling and related applications. However, the existing methods mostly suffer from the…
Eigenvalue problems are fundamental to mathematics and science. We present a simple algorithm for determining eigenvalues and eigenfunctions of the Laplace--Beltrami operator on rather general curved surfaces. Our algorithm, which is based…
This paper devotes to providing rigorous theoretical analysis of the wellposedness of the direct problem and the uniqueness of the inverse problem of electromagnetic scattering in a parallel-plate waveguide. The direct problem is reduced to…
We consider an $\mathcal{MP}$-system, that is, a compact Riemannian manifold with boundary, endowed with a magnetic field and a potential. On simple $\mathcal{MP}$-systems, we study the $\mathcal{MP}$-ray transform in order to obtain new…
The recently established generalized Gell-Mann--Low theorem is applied in lowest perturbative order to bound-state calculations in a simple scalar field theory with cubic couplings. The approach via the generalized Gell-Mann--Low Theorem…