Related papers: More on the corner-vector construction for spheric…

A recent paper of Arnold, Falk, and Winther [Bull AMS, 47 (2010)] showed that a large class of mixed finite element methods can be formulated naturally on Hilbert complexes, where using a Galerkin-like approach, one solves a variational…

We obtain a construction of the total spherical perspective with ruler, compass, and nail. This is a generalization of the spherical perspective of Barre and Flocon to a 360 degree field of view. Since the 1960s, several generalizations of…

In this paper we propose a heuristic technique for distributing points on the surface of a unit n-dimensional Euclidean sphere, generated as the orbit of a finite cyclic subgroup of orthogonal matrices, the so called cyclic group codes.…

We describe a polynomial complexity algorithm for reducing transition matrices, for vector bundles glued along a clutching-type cover of a real anisotropic conic, to canonical block diagonal forms. This is a generalization, to the real…

We analyse topological orbifold conformal field theories on the symmetric product of a complex surface M. By exploiting the mathematics literature we show that a canonical quotient of the operator ring has structure constants given by…

This paper establishes a rigorous geometrical framework for spherical origami, origami using spherical sheets based on spherical geometry. Two settings are treated: origami restricted to the unit sphere ($\mathbb{S}^2$), and…

In \cite{HK}, an integration theory for valued fields was developed with a Grothendieck group approach. It was shown that the semiring of semi-algebraic sets with measure preserving morphisms is isomorphic to a certain semiring formed out…

Let R be a ring. A construction method for flexible quadratic algebras with scalar involution over R is presented which unifies various classical constructions in the literature, in particular those to construct composition algebras.

We apply the geometric quantization method with real polarizations to the quantization of a symplectic torus. By quantizing with half-densities we canonically associate to the symplectic torus a projective Hilbert space and prove that the…

Consider a component of the Hilbert scheme whose general point corresponds to a degree d genus g smooth irreducible and nondegenerate curve in a projective variety X. We give lower bounds for the dimension of such a component when X is P^3,…

We develop geometry-of-numbers methods to count orbits in coregular vector spaces having bounded invariants over any global field. We apply these techniques to bound the average ranks and determine average Selmer group sizes of elliptic…

We give an inequality on the packing of vectors/lines in quaternionic Hilbert space $\Hd$, which generalises those of Sidelnikov and Welch for unit vectors in $\Rd$ and $\Cd$. This has a parameter $t$, and depends only on the vectors up to…

We discuss the reconstruction of generic 3+1-dimensional space-time geometries from covariant quantum spaces as backgrounds in the IKKT matrix model. An explicit recipe to realize generic classical geometries is provided. Even though this…

Quantum algorithms for electronic-structure simulations are actively being developed, yet many hybrid quantum-classical approaches are bottlenecked by the measurement overhead associated with large molecular Hamiltonians. Here we introduce…

This note presents a procedure of constructing a higher dimensional sphere map from a lower dimensional one and gives an explicit formula for smooth sphere map with a given degree. As an application a new proof of a generalized…

This work develops a geometric framework for constructing quantum error-correcting codes from weighted projective and orbifold structures, integrating algebraic geometry, divisor theory, and the CSS stabilizer formalism. Beginning with…

In this work we show how to get advantage from the Riemann--Hilbert analysis in order to obtain first and second order differential equations for the orthogonal polynomials and associated functions with a weight on the unit circle. We…

Combinatorial $t$-designs have been an interesting topic in combinatorics for decades. It was recently reported that the image sets of a fixed size of certain special polynomials may constitute a $t$-design. Till now only a small amount of…

This paper is a continuation to the study of generalized quasi contractive operators, essentially due to Akhtar et al. [A multi-step implicit iterative process for common fixed points of generalized C^{q}-operators in convex metric spaces,…

Computational analysis with the finite element method requires geometrically accurate meshes. It is well known that high-order meshes can accurately capture curved surfaces with fewer degrees of freedom in comparison to low-order meshes.…