Related papers: An Improved Harmonic Map Ansatz

Let f_\beta = h_\beta+\bar{g}_\beta and F_a = H_a +\bar{G}_a be harmonic mappings obtained by shearing of analytic mappings h_\beta +g_\beta = 1/(2i\sin\beta)log((1 + ze^{i\beta})/(1 + ze^{-i\beta})), 0<\beta<\pi and H_a+G_a = z/(1-z),…

Harmonic maps are nonlinear extensions of harmonic functions. They are critical points of natural energy functionals between Riemannian manifolds. Such type of problems appear in Physics, Geometry of Finance and the study of regularity and…

Modern density functional approximations achieve moderate accuracy at low computational cost for many electronic structure calculations. Some background is given relating the gradient expansion of density functional theory to the WKB…

Structural properties of finite digraphs $R$ and $S$ are studied which enforce $\# {\cal H}(G,R) \leq \# {\cal H}(G,S)$ for every finite digraph $G \in \mathfrak{ D }'$, where ${\cal H}(G,H)$ is the set of homomorphisms from $G$ to $H$, and…

In this paper, we develop a loop group description of harmonic maps $\mathcal{F}: M \rightarrow G/K$ of finite uniton number, from a Riemann surface $M,$ compact or non-compact, into inner symmetric spaces of compact or non-compact type. As…

Let $X$ be a simply connected CW complex with finite rational cohomology. For the finite quotient set of rationalized orbit spaces of $X$ obtained by almost free toral actions, ${\mathcal T}_0(X)=\{[Y_i] \}$, induced by an equivalence…

Recently, Hirayama and Yamashita have presented an ansatz that allows us to construct a class of solutions for the SU(2) Skyrme model. Though these solutions are not solitonic, they provide us with an example on how the plane wave solutions…

We consider the 2 Higgs Doublet Model (2HDM) and compare two effective field theory (EFT) approaches to it, according to whether the heavy degrees of freedom are integrated out before (SMEFT) or after (HEFT) spontaneous symmetry breaking.…

Domain-general model-based planners often derive their generality by constructing search heuristics through the relaxation or abstraction of symbolic world models. We illustrate how abstract interpretation can serve as a unifying framework…

If $C_n(\mathbb{R}^d)$ denotes the configuration space of $n$ distinct points in $\mathbb{R}^d$, we construct a sequence of maps $(f_m),$ $m \geq 1$, where \[f_m: C_n(\mathbb{R}^d) \times \mathbb{R}^d \to \mathbb{R}^d\] is real analytic,…

This paper is devoted to the problem of minimizing a sum of rational functions over a basic semialgebraic set. We provide a hierarchy of sum of squares (SOS) relaxations that is dual to the generalized moment problem approach due to…

We propose to extend ``invertibility'' to ``regularity'' for categories in general abstract algebraic manner. Higher regularity conditions and ``semicommutative'' diagrams are introduced. Distinction between commutative and…

Section 1 refines the theory of harmonic and potential maps. Section 2 defines a generalized Lorentz world-force law and shows that any PDEs system of order one generates such a law in suitable geometrical structure. In other words, the…

We apply our abstract gradient inequalities developed by the authors in arXiv:1510.03817 to prove Lojasiewicz--Simon gradient inequalities for the harmonic map energy function using Sobolev spaces which impose minimal regularity…

By combining two different techniques to construct multi-soliton solutions of the (3+1)-dimensional Skyrme model, the generalized hedgehog and the rational map ansatz, we find multi-Skyrmion configurations in $AdS_{2}\times S_{2}$. We…

This paper considers the problem of minimizing the ordered weighted average (or ordered median) function of finitely many rational functions over compact semi-algebraic sets. Ordered weighted averages of rational functions are not, in…

Energy minimizing maps (E.M.M.s) play a central role in the calculus of variations, partial differential equations (PDEs), and geometric analysis. These maps are often embedded into $C^\infty$ Riemannian manifolds to minimize the Dirichlet…

In this paper, we investigate some topics around the closed image $S$ of a rational map $\lambda$ given by some homogeneous elements $f_1,...,f_n$ of the same degree in a graded algebra $A$. We first compute the degree of this closed image…

We prove that for an arbitrary field $k,$ a complete, associative $k^r$-algebra $\hat H$ augmented over $k^r$ has exactly $r$ maximal two-sided ideals and deserves the name $r$-pointed. If $A$ is any $k$-algebra, $M=\{M_i\}_{i=1}^r$ is a…

Let S be an essentially smooth scheme over a field of characteristic exponent c. Let MGL and HZ denote the algebraic cobordism spectrum and the motivic cohomology spectrum over S, respectively. We show that the canonical map MGL/(a1, a2,…