Related papers: Application of Renormalization Techniques to the C…
Regular chains and triangular decompositions are fundamental and well-developed tools for describing the complex solutions of polynomial systems. This paper proposes adaptations of these tools focusing on solutions of the real analogue:…
Tropical geometry is sensitive to embeddings of algebraic varieties inside toric varieties. The purpose of this paper is to advertise tropical modifications as a tool to locally repair bad embeddings of plane curves, allowing the…
Offset curves for planar trajectories are interesting in the generation of tool paths for numerically controlled industrial machines and in trajectory planning methods for autonomous driving systems. Theoretical offset curves may exhibit…
The problem of renormalization procedure is re-examined from the viewpoint of Micro-Macro duality.
In this paper we obtain, for a semilinear elliptic problem in R^N, families of solutions bifurcating from the bottom of the spectrum of $-\Delta$. The problem is variational in nature and we apply a nonlinear reduction method which allows…
An implementation of the Reverse Monte Carlo algorithm is presented for the study of amorphous tetrahedral semiconductors. By taking into account a number of constraints that describe the tetrahedral bonding geometry along with the radial…
We discuss how renormalisation group equations can be consistently formulated using the algebraic renormalisation framework, in the context of a dimensionally-renormalised chiral field theory in the BMHV scheme, where the BRST symmetry,…
In part I general aspects of the renormalization of a spontaneously broken gauge theory have been introduced. Here, in part II, two-loop renormalization is introduced and discussed within the context of the minimal Standard Model.…
In this paper we prove two results, one semi-historical and the other new. The semi-historical result, which goes back to Thurston and Riley, is that the geometrization theorem implies that there is an algorithm for the homeomorphism…
A new method for solving systems of linear algebraic equations of a special type arising in solving problems of image reconstruction has been proposed. This method, due to a certain symmetry of the matrix and the choice of the voxel…
We illustrate the dimensional regularization technique using a simple problem from elementary electrostatics. We contrast this approach with the cutoff regularization approach, and demonstrate that dimensional regularization preserves the…
Reconstructing a complete object from its parts is a fundamental problem in many scientific domains. The purpose of this article is to provide a systematic survey on this topic. The reassembly problem requires understanding the attributes…
Employing two distinct types of regularization terms, we propose two regularized extragradient methods for solving equilibrium problems on Hadamard manifolds. The sequences generated by these extragradient algorithms converge to a solution…
The Pythagorean Theorem has been proved in hundreds of ways, yet it inspires fresh insights through geometry and trigonometry. In this paper, we offer a new proof based on three circles that circumscribe the sides of a right triangle.…
The inverse conductivity problem aims at determining the unknown conductivity inside a bounded domain from boundary measurements. In practical applications, algorithms based on minimizing a regularized residual functional subject to PDE…
We provide an analytical approximation to the dynamics in each of the three most important low order secondary resonances (1:1, 2:1, and 3:1) bifurcating from the synchronous primary resonance in the gravitational spin-orbit problem. To…
One considers a system on $\mathbb{C}^2$ close to an invariant curve which can be viewed as a generalization of the semi-standard map to a trigonometric polynomial with many Fourier modes. The radius of convergence of an analytic…
We introduce tropical dual numbers as an extension of tropical semiring. By this innovation, one can work with honest ideals, instead of congruences, and recover the Euclidean topology on affine tropical spaces similar to Zariski's approach…
Recovering a signal from auto-correlations or, equivalently, retrieving the phase linked to a given Fourier modulus, is a wide-spread problem in imaging. This problem has been tackled in a number of experimental situations, from optical…
In this article, a new method for segmentation and restoration of images on two-dimensional surfaces is given. Active contour models for image segmentation are extended to images on surfaces. The evolving curves on the surfaces are…