arXiv research

Paper derives trace formula for magnetic Laplacian at zero energy.

Formula calculates volume of two-bridge knots.

It has been shown that the Alvarez-Gaum$\mathrm{\acute{e}}$-Witten miraculous anomaly cancellation formula in type IIB superstring theory and its various generalizations can be derived from modularity of certain characteristic forms. In this paper, we show that the Green-Schwarz formula and the Schwarz-Witten formula i…

Derives formula for skew stickiness ratio in asset price and volatility dynamics.

Derives integral formulae on weighted manifolds.

A simple formula approximates AUM fees' cumulative costs.

Although it is known that the dimension of the Vassiliev invariants of degree three of long virtual knots is seven, the complete list of seven distinct Gauss diagram formulas have been unknown explicitly, where only one known formula was revised without proof. In this paper, we give seven Gauss diagram formulas to pres…

The present paper produces examples of Gauss diagram formulae for virtual knot invariants which have no analogue in the classical knot case. These combinatorial formulae contain additional information about how a subdiagram is embedded in a virtual knot diagram. The additional information comes from the second author's…

We derive Verlinde's formula from the fixed point formula for loop groups proved in the companion paper "A fixed point formula for loop group actions", and extend it to compact, connected groups that are not necessarily simply-connected.

The paper derives new Gauss-Bonnet formulas for frontal bundles over surfaces with boundary.

Developed new Crofton formulas for pseudo-Riemannian spaces.

Study finds formulas for minimal submanifolds using Möbius transformations.

Unified entropy formula for real, complex, and quaternionic DLNs.

New Crofton formulae derived from existing ones.

The paper is devoted to the problem of finding explicit combinatorial formulae for the Pontryagin classes. We discuss two formulae, the classical Gabrielov-Gelfand-Losik formula based on investigation of configuration spaces and the local combinatorial formula obtained by the author in 2004. The latter formula is based…

Formula connects curvature to volume in special geometric spaces.

Wave trace singularity formula for fibre bundles generalizes Poisson summation.

Abstract: Characterizes frontals and wavefronts with formulas.

Paper proves a generalized Torres formula for twisted Reidemeister torsion.

New formula simplifies interior polynomial calculation.

Computes tube formulas for valuations in complex space forms.

Formula derived for zeta functions of 3D foliated systems.

We construct a new representation formula for indefinite improper affine spheres in terms of two para-holomorphic functions and study singularities which appear in this representation formula. As a result, it follows that cuspidal cross caps never appear as the singularities on indefinite improper affine spheres and so…

Derives formulas for differential forms on weighted manifolds.

We extend Kac-Rice formula to compute expected intersections of random submanifolds.

We present a gluing formula for Gromov-Witten invariants in the case of a triple product. This gluing formula is a simple case of a much more general gluing formula proved and stated using exploded manifolds. We present this simple case because it is relatively easy to explain without any knowledge of exploded manifold…

Author presents the second variational formula for statistical biharmonic maps.

Paper derives a Reilly type integral formula and applies it to inequalities and eigenvalue problems.

Extends Alòs' formula to Barndorff-Nielsen and Shephard model.

Extends Itô's formula for path-dependent functions in finance.

Proves Steiner and tube formulae for 3D contact sub-Riemannian surfaces.

Investigates Künneth formula for foliated de Rham cohomology, overcoming non-Hausdorff issues.

The Guillemin-Uribe trace formula is a semiclassical version of the Selberg trace formula and more general Duistermaat-Guillemin formula for elliptic operators on compact manifolds, which reflects the dynamics of magnetic geodesic flows in terms of eigenvalues of a natural differential operator (the magnetic Laplacian)…

New method verifies formulas for causal interventional distributions.

We give a new proof of a slightly weaker form of a theorem of P. Colmez. This theorem gives a formula for the Faltings height of abelian varieties with complex multiplication by a C.M. field whose Galois group over $\bf Q$ is abelian; it reduces to the formula of Chowla and Selberg in the case of elliptic curves. We sh…

We develop two types of integral formulas for the perimeter of a convex body K in planar geometries. We derive Cauchy-type formulas for perimeter in planar Hilbert geometries. Specializing to H^2 we get a formula that appears to be new. We show that it implies the standard Cauchy-Santalo formula involving a central ang…

In this article, we will discuss a localization formulas of equivariant cohomology about two Killing vector fields on the set of zero points ${\rm{Zero}}(X_{M}-\sqrt{-1}Y_{M})=\{x\in M \mid |Y_{M}(x)|=|X_{M}(x)|=0 \}.$ As application, we use it to get formulas about characteristic numbers and to get a Duistermaat-Heckm…

We give reconstruction formulas inverting the geodesic X-ray transform over functions (call it $I_0$) and solenoidal vector fields on surfaces with negative curvature and strictly convex boundary. These formulas generalize the Pestov-Uhlmann formulas in [Pestov-Uhlmann, IMRN '04] (established for simple surfaces) to ca…

Study on Killing magnetic curves in Heisenberg group geometry.

Matrix formulas for super Teichmüller spaces generalize previous work and yield super λ-lengths.

Closed form formulas for swaption prices in HJM model are derived. These formulas are used for nonparametric fit of deterministic forward volatility. It is demonstrated that this formula and non-parametric fit works very well and can be used to identify arbitrage opportunities

Graham's formula simplifies stock valuation for growth stocks.

Polterovich proved a remarkable closed formula for heat kernel coefficients of the Laplace operator on compact Riemannian manifolds involving powers of Laplacians acting on the distance function. In the case of Kähler manifolds, we prove a combinatorial formula for powers of the complex Laplacian and use it to derive a…

Abstract mathematical formulas for statistical structures and curvatures.

We compare two different bilateral counterparty valuation adjustment (BVA) formulas. The first formula is an approximation and is based on subtracting the two unilateral Credit Valuation Adjustment (CVA)'s formulas as seen from the two different parties in the transaction. This formula is only a simplified representati…

Several identities similar to the Schlaefli formula are established for tetrahedra in a space of constant curvature.

We prove an analogue of the classical Steiner formula for the $L_p$ affine surface area of a Minkowski outer parallel body for any real parameters $p$. We show that the classical Steiner formula and the Steiner formula of Lutwak's dual Brunn Minkowski theory are special cases of this new Steiner formula. This new Stein…

Turaev's shadow formula calculates the SU(2)-Reshetikhin-Turaev-Witten invariants using shadows, and its expression is somehow similar to a Euler characteristic. We give a short proof of this formula using skein theory. The formula applies to pairs (M,G) where M is a closed oriented 3-manifold and GcM is a (possibly em…