This talk will present an effort to formalize Taylor Models in the Coq proof assistant. Machinecheckable correctness proofs are facilitated by an abstract viewpoint: Taylor models can be generalized to balls in the Chebyshev metric. Extensions of elementary functions are then explained as compositions of such balls. This approach also accommodates other polynomial approximation methods than Tay...

On asymptotically complex hyperbolic (ACH) Einstein manifolds, we consider a certain variational problem for almost structures compatible with the metric, which linearized Euler-Lagrange equation at K\"ahler-Einstein is given by Dolbeault Laplacian acting on $(0,1)$-forms values in holomorphic tangent bundle. A deformation result of ACH metrics associated critical this given. It also shown that...

It is vital to select an appropriate distance metric for many learning algorithm. Cosine distance is an efficient metric for measuring the similarity of descriptors in classification task. However, the cosine similarity metric learning (CSML)[1] is not widely used due to the complexity of its formulation and time consuming. In this paper, a Quasi Cosine Similarity Metric Learning (QCSML) is pro...

We consider spacetime to be a connected real 4-manifold equipped with a Lorentzian metric and an affine connection. The 10 independent components of the (symmetric) metric tensor and the 64 connection coefficients are the unknowns of our theory. We introduce an action which is quadratic in curvature and study the resulting system of Euler–Lagrange equations. In the first part of the paper we lo...

In this paper we formulate a geometric theory of the mechanics of growing solids. Bulk growth is modeled by a material manifold with an evolving metric. The time dependence of the metric represents the evolution of the stress-free (natural) configuration of the body in response to changes in mass density and “shape”. We show that the time dependency of the material metric will affect the energy...

In [7] a fast-reaction limit for linear reaction-diffusion system consisting of two diffusion equations coupled by reaction is performed. The understood as gradient flow the free energy in space probability measures equipped with geometric structure, which contains Wasserstein metric part and cosh-type functions part. done on level proving EDP-convergence tilting. induces Lagrange multipliers s...

Abstract We perform a fast-reaction limit for linear reaction-diffusion system consisting of two diffusion equations coupled by reaction. understand the as gradient flow free energy in space probability measures equipped with geometric structure, which contains Wasserstein metric part and cosh-type functions reaction part. The is done on level structure proving EDP-convergence tilting. induces ...

In this paper, we study the stochastic Hamiltonian flow in Wasserstein manifold, probability density space equipped with $$L^2$$ -Wasserstein metric tensor, via Wong–Zakai approximation. We begin our investigation by showing that Euler–Lagrange equation, regardless it is deduced from either variational principle or particle dynamics, can be interpreted as kinetic flows manifold. further propose...

the euler-lagrange equation plays an important role in the minimization problems of the calculus of variations. this paper employs the differential transformation method (dtm) for finding the solution of the euler-lagrange equation which arise from problems of calculus of variations. dtm provides an analytical solution in the form of an infinite power series with easily computable components. s...