Beam profile engineering, where a desired optical intensity distribution can be generated by an array of phase shifting (or amplitude changing) elements is a promising approach in laser material processing. For example, a spatial light modulator (SLM...
We consider the problem of estimating community memberships of nodes in a network, where every node is associated with a vector determining its degree of membership in each community. Existing provably consistent algorithms often require strong assum...
This paper considers the problem of modeling and estimating community memberships of nodes in a directed network where every row (column) node is associated with a vector determining its membership in each row (column) community. To model such direct...
A tool for learning vector representations of words and entities from Wikipedia (⭐ 964)
Dec 26, 2025 · (See e.g. Linear functional is continuous $\implies$ it is bounded for a proof that a continuous linear functional on a normed vector space must be bounded. This is also on Wikipedia.)
A necessary condition for a connection in a vector bundle to be locally metric is for its curvature matrix, which consists of $2$ forms, to be skew symmetric with respect to some local frame. In this paper we give a simple algorithm that can be used...
jQuery.Feyn is a tool for drawing Feynman diagrams with Scalable Vector Graphics (SVG), written in JavaScript and runs in modern browsers. It features predefined propagator styles, vertex types, and symbols. Math formulae can be included as external...
We proposed a purely 3-D geometrical solution to Mathematics Magazine Problem 2065. Let $\mathcal{Q}$ be a cube centered at the origin of $\mathbb{R}^3$. Choose a unit vector $(a,b,c)$ uniformly at random on the surface of the unit sphere $a^2+b^2+c^...
Plant breeders and agricultural researchers can increase crop productivity by identifying desirable features, disease resistance, and nutritional content by analysing the Dry Bean dataset. This study analyses and compares different Support Vector Mac...
Missing bound-state solutions for fermions in the background of a Cornell potential consisting of a mixed scalar-vector-pseudoscalar coupling is examined. Charge-conjugation operation, degeneracy and localization are discussed....
Pion emitting decays and radiative ones of D^{*+,0} and D_s^{*+} are studied. As the result, the full-width of D^{*0} is predicted, by assuming the isospin symmetry. In addition, the isospin non-conserving D_s^{*+} --> D_s^+ pi^0 decay is investigate...
and mathematical physics, a coordinate basis or holonomic basis for a differentiable manifold M is a set of basis vector fields {e1, ..., en} defined at
In mathematics, a set B of elements of a vector space V is called a basis (pl.: bases) if every element of V can be written in a unique way as a finite
We generalize a semi-norm for the Alexander polynomial of a connected, compact, oriented 3-manifold on its first cohomology group to a semi-norm for an arbitrary Laurent polynomial f on the dual vector space to the space of exponents of f. We deter...
We revisit the Emergence Proposal in 4d ${\cal N}=2$ vector multiplet sectors that arise from type II string Calabi--Yau compactifications, with emphasis on the role of axionic fundamental strings, or EFT strings. We focus on large-volume type IIA co...
The particle discrete element simulation of the instability and failure process of the granular slope accumulator model when the metal plate continues downward is obtained, and the two-dimensional total velocity vector of soil particle velocity and s...
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Moduli spaces of real bundles over a real curve arise naturally as Lagrangian submanifolds of the moduli space of semi-stable bundles over a complex curve. In this paper, we adapt the methods of Atiyah-Bott's "Yang-Mills over a Riemann Surface" to co...
We consider the inhomogeneous div-curl system (i.e.\ to find a vector field with prescribed div and curl) in a bounded star-shaped domain in $\mathbb{R}^3$. An explicit general solution is given in terms of classical integral operators, completing pr...
For a bounded Lipschitz domain with Lipschitz interface we show the following compactness theorem: Any $L^2$-bounded sequence of vector fields with $L^2$-bounded rotations and $L^2$-bounded divergences as well as $L^2$-bounded tangential traces on on...