A linearization‐based approach of homotopy analysis method for non‐linear time‐fractional parabolic PDEs
Sign Up to like & getrecommendations! Published in 2019 at "Mathematical Methods in the Applied Sciences"
DOI: 10.1002/mma.5829
Abstract: In this paper, a novel approach, namely, the linearization‐based approach of homotopy analysis method, to analytically treat non‐linear time‐fractional PDEs is proposed. The presented approach suggests a new optimized structure of the homotopy series solution… read more here.
Keywords: non linear; homotopy analysis; approach; homotopy ... See more keywords
Orbispaces, orthogonal spaces, and the universal compact Lie group
Sign Up to like & getrecommendations! Published in 2019 at "Mathematische Zeitschrift"
DOI: 10.1007/s00209-019-02265-1
Abstract: This paper identifies the homotopy theories of topological stacks and orbispaces with unstable global homotopy theory. At the same time, we provide a new perspective by interpreting it as the homotopy theory of ‘spaces with… read more here.
Keywords: lie group; universal compact; homotopy; compact lie ... See more keywords
Fiber product homotopy method for multiparameter eigenvalue problems
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DOI: 10.1007/s00211-021-01215-6
Abstract: We develop a new homotopy method for solving multiparameter eigenvalue problems (MEPs) called the fiber product homotopy method. It requires deformation of exponentially fewer equations compared to existing homotopy methods for MEPs. We show that… read more here.
Keywords: fiber product; homotopy method; method; homotopy ... See more keywords
Gcd-monoids arising from homotopy groupoids
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DOI: 10.1007/s00233-018-9950-5
Abstract: The interval monoid $$\Upsilon ({P})$$Υ(P) of a poset P is defined by generators [x, y], where $$x\le y$$x≤y in P, and relations $$[x,x]=1$$[x,x]=1, $$[x,z]=[x,y]\cdot [y,z]$$[x,z]=[x,y]·[y,z] for $$x\le y\le z$$x≤y≤z. It embeds into its universal group $$\Upsilon ^{\pm }({P})$$Υ±(P), the interval… read more here.
Keywords: group; homotopy; mathrm; monoid upsilon ... See more keywords
Morphisms of Rational Motivic Homotopy Types
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DOI: 10.1007/s10485-020-09618-6
Abstract: We investigate several interrelated foundational questions pertaining to the study of motivic dga’s of Dan-Cohen and Schlank (Rational motivic path spaces and Kim’s relative unipotent section conjecture. arXiv:1703.10776 ) and Iwanari (Motivic rational homotopy type.… read more here.
Keywords: motivic homotopy; homotopy; motivic dga; rational motivic ... See more keywords
A new probability-one homotopy method for solving minimum-time low-thrust orbital transfer problems
Sign Up to like & getrecommendations! Published in 2018 at "Astrophysics and Space Science"
DOI: 10.1007/s10509-018-3420-0
Abstract: Homotopy methods have been widely utilized to solve low-thrust orbital transfer problems, however, it is not guaranteed that the optimal solution can be obtained by the existing homotopy methods. In this paper, a new homotopy… read more here.
Keywords: probability one; thrust orbital; low thrust; homotopy ... See more keywords
The homotopy groups of a homotopy group completion
Sign Up to like & getrecommendations! Published in 2019 at "Israel Journal of Mathematics"
DOI: 10.1007/s11856-019-1914-2
Abstract: Let $M$ be a topological monoid with homotopy group completion $\Omega BM$. Under a strong homotopy commutativity hypothesis on $M$, we show that $\pi_k (\Omega BM)$ is the quotient of the monoid of free homotopy… read more here.
Keywords: homotopy groups; group completion; homotopy; homotopy group ... See more keywords
Topology of scrambled simplices
Sign Up to like & getrecommendations! Published in 2018 at "Journal of Homotopy and Related Structures"
DOI: 10.1007/s40062-018-0214-6
Abstract: In this paper we define a family of topological spaces, which contains and vastly generalizes the higher-dimensional Dunce hats. Our definition is purely combinatorial, and is phrased in terms of identifications of boundary simplices of a standard… read more here.
Keywords: topology scrambled; topology; scrambled simplices; homotopy ... See more keywords
A theorem on multiplicative cell attachments with an application to Ravenel’s X(n) spectra
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DOI: 10.1007/s40062-018-0222-6
Abstract: We show that the homotopy groups of a connective $$\mathbb {E}_k$$Ek-ring spectrum with an $$\mathbb {E}_k$$Ek-cell attached along a class $$\alpha $$α in degree n are isomorphic to the homotopy groups of the cofiber of… read more here.
Keywords: theorem multiplicative; homotopy groups; ravenel spectra; mathbb ... See more keywords
Weight decompositions of Thom spaces of vector bundles in rational homotopy
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DOI: 10.1007/s40062-019-00243-2
Abstract: Motivated by the theory of representability classes by submanifolds, we study the rational homotopy theory of Thom spaces of vector bundles. We first give a Thom isomorphism at the level of rational homotopy, extending work… read more here.
Keywords: rational homotopy; thom spaces; homotopy; vector bundles ... See more keywords
Derived representation theory of Lie algebras and stable homotopy categorification of sl
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DOI: 10.1016/j.aim.2018.10.044
Abstract: We set up foundations of representation theory over $S$, the sphere spectrum, which is the `initial ring' of stable homotopy theory. In particular, we treat $S$-Lie algebras and their representations, characters, $gl_n(S)$-Verma modules and their… read more here.
Keywords: homotopy; stable homotopy; lie algebras; representation theory ... See more keywords