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We consider involutory virtual biracks with good involutions, also known as symmetric involutory virtual biracks. Any good involution on an involutory virtual birack defines an enhancement of the counting invariant. We provide examples…
We generalize two classical formulas for complete intersection curves by introducing the the complete intersection discrepancy of a curve as a correction term. The first is a well-known multiplicity formula in singularity theory, due to…
A notion of dual curve for pseudoholomorphic curves in 4--manifolds turns out to be possible only if the notion of almost complex structure structure is slightly generalized. The resulting structure is as easy (perhaps easier) to work with,…
While the earliest applications of AI methodologies to pure mathematics and theoretical physics began with the study of Hodge numbers of Calabi-Yau manifolds, the topology type of such manifold also crucially depend on their intersection…
In this paper we are concerned with the existence of invariant curves of planar twist mappings which are almost periodic in a spatial variable. As an application of this result to differential equations we will discuss the existence of…
Ring artifacts in X-ray micro-CT images are one of the primary causes of concern in their accurate visual interpretation and quantitative analysis. The geometry of X-ray micro-CT scanners is similar to the medical CT machines, except the…
Reconstructing the missing parts of a curve has been the subject of much computational research, with applications in image inpainting, object synthesis, etc. Different approaches for solving that problem are typically based on processes…
This is the second paper devoted to the numerical version of Signature-inverse Theorem in terms of the underlying joint invariants. Signature Theorem and its Inverse guarantee any application of differential invariant signature curves to…
The traditional study of plane and space algebraic curves by looking at their tangent vectors, curvatures and torsions provides geometric, but unfortunately not sufficient information about individual curves in order to be able to…
It is shown that the squared operation of the Dirac equation which is widely applied may create new solutions and moreover may change the inner nature of original equation. Some illustrating examples are considered as well.
The effects of computer-assisted and distance learning of geometric modeling and computer aided geometric design are studied. It was shown that computer algebra systems and dynamic geometric environments can be considered as excellent tools…
Detecting vehicles in aerial images is difficult due to complex backgrounds, small object sizes, shadows, and occlusions. Although recent deep learning advancements have improved object detection, these models remain susceptible to…
When studying turbulence, it is often desirable to be able to estimate the local spatial gradient of a vector quantity using in situ measurements from a small number of irregularly spaced points. While previous studies have focused on the…
We define refined invariants which "count" nodal curves in sufficiently ample linear systems on surfaces, conjecture that their generating function is multiplicative, and conjecture explicit formulas in the case of K3 and abelian surfaces.…
Let $g \colon S \looparrowright N$ be a properly immersed $\pi_1$--injective surface in a non-geometric $3$--manifold $N$. We compute the distortion of $\pi_1(S)$ in $\pi_1(N)$ and show that how it is related to separability of $\pi_1(S)$…
We investigate modified Makar-Limanov and Derksen invariants of an affine algebraic variety. The modified Makar-Limanov invariant is the intersection of kernels of all locally nilpotent derivations with slices and the modified Derksen…
Artefacts in quantum-mimic Optical Coherence Tomography are considered detrimental because they scramble the images even for the simplest objects. They are a side effect of autocorrelation which is used in the quantum entanglement mimicking…
We study streaking artifacts caused by beam-hardening effects in X-ray computed tomography (CT). The effect is known to be nonlinear. We show that the nonlinearity can be recovered from the observed artifacts for strictly convex bodies. The…
The inelasticity in nucleus-nucleus collisions at high energies is calculated in the framework of geometrical multichain model. The very fast increase of the inelasticity is found as a result of a second-stage cascading process. The same…
A formula for the Arf invariant of a link is given in terms of the singularities of an immersed surface bounded by the link. This is applied to study the computational complexity of quantum invariants of 3--manifolds.