Homotopy continuation is an efficient tool for solving polynomial systems. Its efficiency relies on utilizing adaptive stepsize and adaptive precision path tracking, and endgames. In this article, we apply homotopy continuation to solve steady state problems of hyperbolic conservation laws. A third-order accurate finite difference weighted essentially non-oscillatory (WENO) scheme with Lax-Frie...

The classical infinite loopspace machines in fact induce an equivalence of categories between a localization of the category of symmetric monoidal categories and the stable homotopy category of -1-connective spectra. Introduction Since the early seventies it has been known that the classifying spaces of small symmetric monoidal categories are infinite loop spaces, the zeroth space in a spectrum...

Naturally occurring diagrams in algebraic topology are commutative up to homotopy, but not on the nose. It was quickly realized that very little can be done with this information. Homotopy coherent category theory arose out of a desire to catalog the higher homotopical information required to restore constructibility (or more precisely, functoriality) in such “up to homotopy” settings. The firs...

Let f : X → Y be a based map of simply connected spaces. The corresponding evaluation map ω : map(X, Y ; f)→ Y induces a homomorphism of homotopy groups whose image in πn(Y ) is called the nth evaluation subgroup of f . The nth Gottlieb group of X occurs as the special case in which Y = X and f = 1X . We identify the homomorphism induced on rational homotopy groups by this evaluation map, in te...

In telescopic homotopy theory, a space or spectrum X is approximated by a tower of localizations LnX, n ≥ 0, taking account of vn-periodic homotopy groups for progressively higher n. For each n ≥ 1, we construct a telescopic Kuhn functor Φn carrying a space to a spectrum with the same vn-periodic homotopy groups, and we construct a new functor Θn left adjoint to Φn. Using these functors, we sho...

in this article, we demonstrate an analytic-numeric solution for some dynamical systems using the multistagehomotopy perturbation method. the method yields results that are in complete agreement with their numericalcounterparts.

A functor is constructed from the category of globular CW-complexes to that of flows. It allows the comparison of the S-homotopy equivalences (resp. the T-homotopy equivalences) of globular complexes with the S-homotopy equivalences (resp. the T-homotopy equivalences) of flows. Moreover, it is proved that this functor induces an equivalence of categories from the localization of the category of...

A fresh look at diffractive J/ψ photoproduction at HERA, with predictions for THERA. Abstract A new analysis of the photoproduction of the J/ψ-family is presented incorporating our recent model for the dipole cross section. The relative contributions from small and large transverse size fluctuations of the photon are clear and explicitly illustrate the mixing of pertur-bative and non-perturbati...

The temperature phase transition in the N-component scalar field theory with the spontaneous symmetry breaking is investigated in the pertur-bative approach.The second Legendre transform and consideration of the gap equations in the extrema of the free energy functional is used. The super daisy and beyond resummations are applied. In the super daisy approximation a first order phase transition ...