arXiv research

Constructs explicit solutions to Spin(7)-structures gradient flow.

The aim of this paper is to write an explicit orthonormal parallelization for all parallelizable products of spheres, using an explicit isomorphism with a trivial vector bundle.

Paper studies the theoretical equivalence between implicit and explicit neural networks in high dimensions.

An explicit formula for the $A$-polynomial of the knot with Conway's notation $C(2n,3)$ is obtained from the explicit Riley-Mednykh polynomial of it.

Paper proposes an efficient method to optimize neural networks without backpropagation.

This work improves neural network calibration using explicit regularization.

Explicit presentations found for asymptotically rigid mapping class groups.

The paper defines wave-front singularities using explicit analytic functions.

Proposes a new model for better speech segmentation.

We provide explicit spinor representations for Clifford algebras.

In this letter, two explicit self-similar solutions to a graph representation of time-like extremal hypersurfaces in Minkowski spacetime $\mathbb{R}^{1+3}$ are given. Meanwhile, there is an untable eigenvalue in the linearized time-like extremal hypersurfaces equation around two explicit self-similar solutions.

Researchers found explicit solutions to a complex equation in advanced geometry.

We use filtrations of the Grassmannian model to produce explicit algebraic formulae for all harmonic maps of finite uniton number from a Riemann surface, and so all harmonic maps from the 2-sphere, to the unitary group for a general class of factorizations by unitons. We show how these specialize to give explicit formu…

Study on Killing magnetic curves in Heisenberg group geometry.

We present a binary code for spinors and Clifford multiplication using non-negative integers and their binary expressions, which can be easily implemented in computer programs for explicit calculations. As applications, we present explicit descriptions of the triality automorphism of $Spin(8)$, explicit representations…

Some special solutions to the multidimensional Lamé and Bourlet type equations are constructed in an explicit form.

We extend Hoste-Shanahan's calculations for the A-polynomial of twist knots, to give an explicit formula.

Estimates Bergman kernel for positive line bundles.

Explicit formulas for pretzel knots' Alexander polynomials.

Constructs explicit $p$-harmonic functions on Grassmannians and flag manifolds.

We derive explicit, uniform, a priori interior Hessian and gradient estimates for special Lagrangian equations of all phases in dimension two.

Formula found for a specific knot's A-polynomial.

In this paper we prove explicit formulas for all Willmore surfaces of revolution and demonstrate their use in the discussion of the associated Dirichlet boundary value problems. It is shown by an explicit example that symmetric Dirichlet boundary conditions do in general not entail the symmetry of the surface. In addit…

It is "well known" that there is no explicit expression for the Black-Scholes implied volatility. We prove that, as a function of underlying, strike, and call price, implied volatility does not belong to the class of D-finite functions. This does not rule out all explicit expressions, but shows that implied volatility …

This note finds explicit representatives for moduli space of parabolic bundles.

Constructs explicit p-harmonic functions on specific Lie groups.

Using the idea of special Legendre curves, the authors obtained the explicit description of flat Lagrangian H-umbilical submanifolds in quaternion Euclidean spaces.

Study conic Laplacian on \(\mb P^1\) with explicit model and boundary data.

Research aims to ensure fair classification across explicit and implicit sensitive features.

We provide explicit, simple, geometric formulas for free involutions rho of Euclidean spheres that are not conjugate to the antipodal involution. Therefore the quotient S^n/rho is a manifold that is homotopically equivalent but not diffeomorphic to RP^n. We use these formulas for constructing explicit non-trivial eleme…

This paper provides an explicit form for symmetric differentials and their corresponding holomorphic functions.

Nonlinear kernels can be approximated using finite-dimensional feature maps for efficient risk minimization. Due to the inherent trade-off between the dimension of the (mapped) feature space and the approximation accuracy, the key problem is to identify promising (explicit) features leading to a satisfactory out-of-sam…

Develops methods to construct harmonic and wave maps into variable-curvature surfaces.

Solvable structures are exploited in order to find families of explicit solutions to evolution PDEs admitting suitable differential constraints. The effectiveness of the method is verified on several explicit examples.

We prove that, except for a few explicit roots of unity, the quantum image of any Johnson subgroup of the mapping class group contains an explicit free non-abelian subgroup.

We construct explicit solutions to continuous motion of discrete plane curves described by a semi-discrete potential modified KdV equation. Explicit formulas in terms the $τ$ function are presented. Bäcklund transformations of the discrete curves are also discussed. We finally consider the continuous limit of discrete …

Maps persistence diagrams into Hilbert and Euclidean spaces with explicit distortions.

M. F. Atiyah proved that the index of a transversally elliptic operator relative to a free action can be computed by using indices of elliptic operators on the orbit manifold. In this paper, we derive an explicit formula for the transversal indices on S^1-bundles over complex projective spaces. Using this explicit form…

Researchers provide explicit parametrizations for Sasakian space forms.

Study finds formulas for special curves in complex spaces.

We construct in an explicit algebraic form a family of complete noncompact Ricci-flat metrics which generalize Calabi metrics in real dimension $4(n+1)$ and with holonomy $SU(2(n+1))$.

Continuous-time PCD for MLE with explicit error bounds.

This paper continues arXiv.org:math.AG/0609256 and arXiv:0708.3991 Using authors's methods of 1980, 1981, some explicit finite sets of number fields containing all ground fields of arithmetic hyperbolic reflection groups in dimensions at least 4 are defined, and good explicit bounds of their degrees (over Q) are obtain…

An explicit example of an exotic symplectic $\mathbf{R}^6$ is given. Together with an earlier known example on $\mathbf{R}^4$, this yields an explicit exotic symplectic form on $\mathbf{R}^{2n}$ for all $n\geq2$.

By using the Hawking Taub-NUT metric, this note gives an explicit construction of a 3-parameter family of Einstein Finsler metrics of non-constant flag curvature in terms of navigation representation.

We prove an explicit equivalence between various hyperbolic type properties for quasi-geodesics in CAT(0) spaces. Specifically, we prove that for X a CAT(0) space and $γ$ a quasi-geodesic, the following four statements are equivalent and moreover the quantifiers in the equivalences are explicit: (i) $γ$ is S-Slim, (ii)…

We provide an explicit section for a mapping class group sequence.

Researchers found explicit formulae for special solitons in 3D spaces.