We study the homotopy types of spaces of algebraic (rational) maps from real projective spaces into complex projective spaces. It was already shown in [1] that the inclusion of the first space into the second one is a homotopy equivalence. In this paper we prove that the homotopy types of the terms of the natural ‘degree’ filtration approximate closer and closer the homotopy type of the space o...

This paper proves that the functor C(∗) that sends pointed, simply-connected CW-complexes to their chain-complexes equipped with diagonals and iterated higher diagonals, determines their integral homotopy type — even inducing an equivalence of categories between the category of CW-complexes up to homotopy equivalence and a certain category of chain-complexes equipped with higher diagonals. Cons...

2 Homotopy λ-calculus 16 1 Type systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2 Homotopy λ-calculus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 3 Basic layer syntax . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 4 Basic layer semantics in Top . . . . . . . . . . . . . . . . . . . . . . . . ...

We develop a homotopy theory of categories enriched in a monoidal model category V. In particular, we deal with homotopy weighted limits and colimits, and homotopy local presentability. The main result, which was known for simplicially-enriched categories, links homotopy locally presentable V-categories with combinatorial model V-categories, in the case where all objects of V are cofibrant.

This paper is the second part of a series of papers about a new notion of T-homotopy of flows. It is proved that the old definition of T-homotopy equivalence does not allow the identification of the directed segment with the 3-dimensional cube. This contradicts a paradigm of dihomotopy theory. A new definition of T-homotopy equivalence is proposed, following the intuition of refinement of obser...

This article analyzes a strongly nonlinear oscillator with cubic and harmonic restoring force and proposes an efficient analytical technique based on the modified energy balance method (MEBM). The proposed method incorporates higher-order approximations. After applying the proposed MEBM, a set of complicated higher-order nonlinear algebraic equations are obtained. Higher-order nonlinear algebra...

In this article to prove existence of solution of infinite system of nonlinear integral equations, we consider the space of solution containing all convergence sequences with a finite limit, as with a suitable norm is a Banach space. By creating a generalization of Meir-Keeler condensing operators which is named as F-generalized Meir-Keeler condensing operators and measure of noncompactness, we...

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We present a definition of homotopy algebra for an operad, and explore its consequences. The paper should be accessible to topologists, category theorists, and anyone acquainted with operads. After a review of operads and monoidal categories, the definition of homotopy algebra is given. Specifically, suppose that M is a monoidal category in which it makes sense to talk about algebras for some o...