Two notable examples of dual functionals in approximation theory and computer-aided geometric design are the blossom and the divided difference operator. Both of these dual functionals satisfy a similar set of formulas and identities. Moreover, the d...
Let H_1=SL(5), H_2=SL(3), H=H_1 \times H_2. It is known that (G,V) is a prehomogeneous vector space (see [22], [26], [25], for the definition of prehomogeneous vector spaces). A non-constant polynomial δ(x) on V is called a relative invariant poly...
Let (G,V) be an irreducible prehomogeneous vector space defined over a number field k, P in k[V] a relative invariant polynomial, and X a rational character of G such that P(gx)=X(g)P(x). Let V_k^{ss}={x \in V_k such that P(x) is not equal to 0}. F...
Crime of passion Concubinage Erotic humiliation Male dominance (BDSM) Netorare Open marriage Polyamory Polygyny Swinging Coleman, Julie (1 January 1999)
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Two-dimensional (2D) Fe-chalcogenides with rich structures, magnetisms and superconductivities are highly desirable to reveal the torturous transition mechanism and explore their potential applications in spintronics and nanoelectronics. Hydrostatic...
The main mathematical focus of this paper is a class of parametrised polynomial systems that we refer to as being tropically transverse. We show how their generic number of solutions can be expressed as the mixed volume of a modified system. We then...
OSCAR is an innovative new computer algebra system which combines and extends the power of its four cornerstone systems - GAP (group theory), Singular (algebra and algebraic geometry), Polymake (polyhedral geometry), and Antic (number theory). Here,...
After reconsidering the theorem of continuity of the roots of a polynomial in terms of its coefficients in the deformation framework, we study the stability of the greater common divisor of two polynomials compared to perturbations on their roots. We...
Compute contour polygons using marching squares. (⭐ 516)
Optimization over $l\times m\times n$ integer $3$-way tables with given line-sums is NP-hard already for fixed $l=3$, but is polynomial time solvable with both $l,m$ fixed. In the {\em huge} version of the problem, the variable dimension $n$ is encod...
We give almost-linear-time algorithms for constructing sparsifiers with $n\ poly(\log n)$ edges that approximately preserve weighted $(\ell^{2}_2 + \ell^{p}_p)$ flow or voltage objectives on graphs. For flow objectives, this is the first sparsifier c...
We present faster high-accuracy algorithms for computing $\ell_p$-norm minimizing flows. On a graph with $m$ edges, our algorithm can compute a $(1+1/\text{poly}(m))$-approximate unweighted $\ell_p$-norm minimizing flow with $pm^{1+\frac{1}{p-1}+o(1)...
We give an example showing that the product and linearization formulas for the Wick product versions of the $q$-Charlier polynomials in (Anshelevich 2004) are incorrect. Next, we observe that the relation between monomials and several families of Wic...
“Oh, what list?” Zoey walked up with Mira. “There’s the nice list, the naughty list, the top ten Kpop groups list-“ “Wait, how do the naughty and nice list come before that one?” Mira a...
This paper presents a fairness-audited and interpretable machine learning framework for predicting polycystic ovary syndrome (PCOS), designed to evaluate model performance and identify diagnostic disparities across patient subgroups. The framework in...
Here we continue to list the differential operators invariant with respect to the 15 exceptional simple Lie superalgebras of polynomial vector fields. A part of the list (for operators acting on tensors with finite dimensional fibers) was earlier o...
Owing to several applications in large scale learning and vision problems, fast submodular function minimization (SFM) has become a critical problem. Theoretically, unconstrained SFM can be performed in polynomial time [IFF 2001, IO 2009]. However, t...
In 1956 Marguerite Frank and Paul Wolfe proved that a quadratic function which is bounded below on a polyhedron $P$ attains its infimum on $P$. In this work we search for larger classes of sets $F$ with this Frank-and-Wolfe property. We establish the...
For a unital spectral triple $(\mathcal{A}, H,D)$, we study when its truncation converges to itself. The spectral truncation is obtained by using the spectral projection $P_Λ$ of $D$ onto $[-Λ,Λ]$ to deal with the case where only a finite range of...