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It is shown that the four trefoil solitons that are described by the irreducible representations D^{3/2}_{mm'} of the quantum algebra SL_q(2) (and that may be identified with the four families of elementary fermions…
In this paper a special piecewise linear system is studied. It is shown that, under a mild assumption, the semi-smooth Newton method applied to this system is well defined and the method generates a sequence that converges linearly to a…
In this paper, we show how to split the writhe of reduced projections of oriented alternating links into two parts, called nullification writhe, or wx, and remaining writhe, or wy, such that the sum of these quantities equals the writhe w,…
We show that reducible braids which are, in a Garside-theoretical sense, as simple as possible within their conjugacy class, are also as simple as possible in a geometric sense. More precisely, if a braid belongs to a certain subset of its…
The main goal of this paper is applying the cut-off projection for solving one-dimensional backward heat conduction problem in a two-slab system with a perfect contact. In a constructive manner, we commence by demonstrating the…
We study the relation between sweeping processes with the cone of limiting normals and projection processes. We prove the existence of solution of a perturbed sweeping process with the cone of limiting normals and of nonstationary…
We introduce an unknotting-type number of knot projections that gives an upper bound of the crosscap number of knots. We determine the set of knot projections with the unknotting-type number at most two, and this result implies classical…
The problem of finding a point in the intersection of closed sets can be solved by the method of alternating projections and its variants. It was shown in earlier papers that for convex sets, the strategy of using quadratic programming (QP)…
This paper is devoted to the general problem of projection onto a polyhedral convex cone generated by a finite set of generators.This problem is reformulated into projection onto the polytope obtained by simple truncation of the original…
For many applications in signal processing and machine learning, we are tasked with minimizing a large sum of convex functions subject to a large number of convex constraints. In this paper, we devise a new random projection method (RPM) to…
We give a short proof that if a non-trivial band sum of two knots results in a tight fibered knot, then the band sum is a connected sum. In particular, this means that any prime knot obtained by a non-trivial band sum is not tight fibered.…
Two new invariants that are closely related to Milnor's curvature-torsion invariant are introduced. The first, the spiral index of a knot, captures the minimum number of maxima among all knot projections that are free of inflection points.…
Rooted plane trees are reduced by four different operations on the fringe. The number of surviving nodes after reducing the tree repeatedly for a fixed number of times is asymptotically analyzed. The four different operations include…
Let $T_n(q)$ be the ring of lower triangular matrices of order $n \geq 2$ with entries from the finite field $F(q)$ of order $q \geq 2$ and let ${^2T_n(q)}$ denote its free left module. For $n=2,3$ it is shown that the projective line over…
Nonlinear systems arising from time integrators like Backward Euler can sometimes be reformulated as optimization problems, known as incremental potentials. We show through a comprehensive experimental analysis that the widely used…
Twisted torus knots are torus knots with some full twists added along some number of adjacent strands. There are infinitely many known examples of twisted torus knots which are actually torus knots. We give eight more infinite families of…
In this paper we present a systematic method to generate prime knot and prime link minimal triple-point projections, and then classify all classical prime knots and prime links with triple-crossing number at most four. We also extend the…
We consider the quasiconformal dilatation of projective transformations of the real projective plane. For non-affine transformations, the contour lines of dilatation form a hyperbolic pencil of circles, and these are the only circles that…
Tikhonov regularization is a popular approach to obtain a meaningful solution for ill-conditioned linear least squares problems. A relatively simple way of choosing a good regularization parameter is given by Morozov's discrepancy…
In this paper we provide an efficient computation of the projection onto the cone generated by the epigraph of the perspective of any convex lower semicontinuous function. Our formula requires solving only two scalar equations involving the…