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Journal articles on the topic 'Homotopy technical'

Author: Grafiati

Published: 8 June 2024

Last updated: 31 July 2025

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1

Fegan, H. D., and B. Steer. "Second Order Operators on a Compact Lie Group." Canadian Journal of Mathematics 57, no. 1 (2005): 99–113. http://dx.doi.org/10.4153/cjm-2005-005-7.

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AbstractWe describe the structure of the space of second order elliptic differential operators on a homogenous bundle over a compact Lie group. Subject to a technical condition, these operators are homotopic to the Laplacian. The technical condition is further investigated, with examples givenwhere it holds and others where it does not. Since many spectral invariants are also homotopy invariants, these results provide information about the invariants of these operators.

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Bhattacharya, Subhrajit, Maxim Likhachev, and Vijay Kumar. "Search-Based Path Planning with Homotopy Class Constraints in 3D." Proceedings of the AAAI Conference on Artificial Intelligence 26, no. 1 (2021): 2097–99. http://dx.doi.org/10.1609/aaai.v26i1.8435.

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Homotopy classes of trajectories, arising due to the presence of obstacles, are defined as sets of trajectories that can be transformed into each other by gradual bending and stretching without colliding with obstacles. The problem of exploring/finding the different homotopy classes in an environment and the problem of finding least-cost paths restricted to a specific homotopy class (or not belonging to certain homotopy classes) arises frequently in such applications as predicting paths for unpredictable entities and deployment of multiple agents for efficient exploration of an environment. In

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3

Iwase, Norio. "H-spaces with generating subspaces." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 111, no. 3-4 (1989): 199–211. http://dx.doi.org/10.1017/s0308210500018515.

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SynopsisFor an H-space with a generating subspace, we construct a space whose K-cohomology is a direct sum of a truncated polynomial algebra and an ideal, which enables technical restrictions to be removed from several known results in the homotopy theory of H-spaces.

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4

Fresse, Benoit. "Props in model categories and homotopy invariance of structures." gmj 17, no. 1 (2010): 79–160. http://dx.doi.org/10.1515/gmj.2010.007.

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Abstract We prove that any category of props in a symmetric monoidal model category inherits a model structure. We devote an appendix, about half the size of the paper, to the proof of the model category axioms in a general setting. We need the general argument to address the case of props in topological spaces and dg-modules over an arbitrary ring, but we give a less technical proof which applies to the category of props in simplicial sets, simplicial modules, and dg-modules over a ring of characteristic 0. We apply the model structure of props to the homotopical study of algebras over a prop

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5

Editorial, E. "Retraction: Solution of Burgers' equation appears in fluid mechanics by multistage optimal homotopy asymptotic method, doi https://doi.org/10.2298/TSCI23S1087W." Thermal Science, no. 00 (2023): 160. http://dx.doi.org/10.2298/tsci230724160e.

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Editor-in-Chief of the journal Thermal Science request that it is necessary to retract paper SOLUTION OF BURGERS' EQUATION APPEARS IN FLUID MECHANICS BY MULTISTAGE OPTIMAL HOMOTOPY ASYMPTOTIC METHOD DOI: https://doi.org/10.2298/TSCI23S1087W by Fuzhang WANG, Niaz ALI SHAH, Imtiaz AHMAD Hijaz AHMAD, Muhammad Kamran ALAM, and Phatiphat THOUNTHONG published in the journal Thermal Science, Vol. 27, Year 2023, Special Issue 1, S87-S92 since by technical error of the Editorial staff, this paper has already been published in the journal Thermal Science Vol.26, Part 1B, pp. 815-821, 2022 https://doi.or

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6

Pym, Brent, and Pavel Safronov. "Shifted Symplectic Lie Algebroids." International Mathematics Research Notices 2020, no. 21 (2018): 7489–557. http://dx.doi.org/10.1093/imrn/rny215.

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Abstract Shifted symplectic Lie and $L_{\infty }$ algebroids model formal neighborhoods of manifolds in shifted symplectic stacks and serve as target spaces for twisted variants of the classical topological field theory defined by Alexandrov--Kontsevich--Schwarz--Zaboronsky. In this paper, we classify zero-, one-, and two-shifted symplectic algebroids and their higher gauge symmetries, in terms of classical geometric “higher structures”, such as Courant algebroids twisted by $\Omega ^{2}$-gerbes. As applications, we produce new examples of twisted Courant algebroids from codimension-two cycles

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7

Ramadevu, Syamala, Vijayakumar Prathi, Nageswara Rao Thota, Ibrahim Shaik Mohammed, and Jyothsna Kanithi. "Analysis of Chemically Radiative Casson Nanofluid Flow over a Porous Nonlinear Stretching Sheet using the Buongiorno Model: HAM-Based Solutions." Journal of Advanced Research in Numerical Heat Transfer 31, no. 1 (2025): 76–103. https://doi.org/10.37934/arnht.31.1.76103.

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Casson nanofluid flow has drawn substantial interest due to its industrial uses, including textile industry, paints and coatings biomedical application, drilling muds, cement slurries, tissue engineering, etc. In this article, we analyse the chemically radiative Casson fluid model across a porous sheet undergoing nonlinear stretching. It evaluates the implications regarding heat generation along with viscous dissipation. The scientific nanofluid framework laid out by Buongiorno has been exploited. Through employing the proper similarity transformations, the partial differential equations which

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8

Chen, Cui, Jiahui Hong, and Kai Zhao. "Global propagation of singularities for discounted Hamilton-Jacobi equations." Discrete & Continuous Dynamical Systems 42, no. 4 (2022): 1949. http://dx.doi.org/10.3934/dcds.2021179.

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<p style='text-indent:20px;'>The main purpose of this paper is to study the global propagation of singularities of the viscosity solution to discounted Hamilton-Jacobi equation</p><p style='text-indent:20px;'><disp-formula> <label/> <tex-math id="FE333"> \begin{document}$ \begin{align} \lambda v(x)+H( x, Dv(x) ) = 0 , \quad x\in \mathbb{R}^n. \quad\quad\quad (\mathrm{HJ}_{\lambda})\end{align} $\end{document} </tex-math></disp-formula></p><p style='text-indent:20px;'>with fixed constant <inline-formula><tex-math id="M1">\be

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9

Merkulov, Sergei, and Thomas Willwacher. "Classification of universal formality maps for quantizations of Lie bialgebras." Compositio Mathematica 156, no. 10 (2020): 2111–48. http://dx.doi.org/10.1112/s0010437x20007381.

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We settle several fundamental questions about the theory of universal deformation quantization of Lie bialgebras by giving their complete classification up to homotopy equivalence. Moreover, we settle these questions in a greater generality: we give a complete classification of the associated universal formality maps. An important new technical ingredient introduced in this paper is a polydifferential endofunctor ${\mathcal {D}}$ in the category of augmented props with the property that for any representation of a prop ${\mathcal {P}}$ in a vector space $V$ the associated prop ${\mathcal {D}}{

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10

BARNES, DAVID, and CONSTANZE ROITZHEIM. "STABLE LEFT AND RIGHT BOUSFIELD LOCALISATIONS." Glasgow Mathematical Journal 56, no. 1 (2013): 13–42. http://dx.doi.org/10.1017/s0017089512000882.

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AbstractWe study left and right Bousfield localisations of stable model categories which preserve stability. This follows the lead of the two key examples: localisations of spectra with respect to a homology theory and A-torsion modules over a ring R with A a perfect R-algebra. We exploit stability to see that the resulting model structures are technically far better behaved than the general case. We can give explicit sets of generating cofibrations, show that these localisations preserve properness and give a complete characterisation of when they preserve monoidal structures. We apply these

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11

XU, BIN. "COMPACT LIE GROUP ACTIONS ON CLOSED MANIFOLDS OF NON-POSITIVE CURVATURE." International Journal of Mathematics 17, no. 01 (2006): 119–27. http://dx.doi.org/10.1142/s0129167x06003369.

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Borel proved that, if a finite group F acts effectively and continuously on a closed aspherical manifold M with centerless fundamental group π1(M), then a natural homomorphism ψ from F to the outer automorphism group Out π1(M) of π1(M), called the associated abstract kernel, is a monomorphism. In this paper, we investigate to what extent Borel's theorem holds for a compact Lie group G acting effectively and smoothly on a particular orientable aspherical manifold N admitting a Riemannian metric g0 of non-positive curvature in case that π1(N) has a non-trivial center. It turns out that if G atta

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12

Brunner, Ilka, Nils Carqueville, Pantelis Fragkos, and Daniel Roggenkamp. "Truncated Affine Rozansky–Witten Models as Extended Defect TQFTs." Communications in Mathematical Physics 406, no. 2 (2025). https://doi.org/10.1007/s00220-024-05164-7.

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Abstract We apply the cobordism hypothesis with singularities to the case of affine Rozansky–Witten models, providing a construction of extended TQFTs that includes all line and surface defects. On a technical level, this amounts to proving that the associated homotopy 2-category is pivotal, and to systematically employing its 3-dimensional graphical calculus. This in particular allows us to explicitly calculate state spaces for surfaces with arbitrary defect networks. As specific examples we discuss symmetry defects which can be used to model non-trivial background gauge fields, as well as bo

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13

Yuan, Allen. "Integral models for spaces via the higher Frobenius." Journal of the American Mathematical Society, February 14, 2022. http://dx.doi.org/10.1090/jams/998.

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We give a fully faithful integral model for simply connected finite complexes in terms of E ∞ \mathbb {E}_{\infty } -ring spectra and the Nikolaus–Scholze Frobenius. The key technical input is the development of a homotopy coherent Frobenius action on a certain subcategory of p p -complete E ∞ \mathbb {E}_{\infty } -rings for each prime p p . Using this, we show that the data of a simply connected finite complex X X is the data of its Spanier-Whitehead dual, as an E ∞ \mathbb {E}_{\infty } -ring, together with a trivialization of the Frobenius action after completion at each prime. In producin

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14

Porcelli, Noah W. "Families of relatively exact Lagrangians, free loop spaces and generalised homology." Selecta Mathematica 30, no. 2 (2024). http://dx.doi.org/10.1007/s00029-023-00910-6.

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AbstractWe prove that (under appropriate orientation conditions, depending on R) a Hamiltonian isotopy $$\psi ^1$$ ψ 1 of a symplectic manifold $$(M, \omega )$$ ( M , ω ) fixing a relatively exact Lagrangian L setwise must act trivially on $$R_*(L)$$ R ∗ ( L ) , where $$R_*$$ R ∗ is some generalised homology theory. We use a strategy inspired by that of Hu et al. (Geom Topol 15:1617–1650, 2011), who proved an analogous result over $${\mathbb {Z}}/2$$ Z / 2 and over $${\mathbb {Z}}$$ Z under stronger orientation assumptions. However the differences in our approaches let us deduce that if L is a

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15

Freed, Daniel S., Gregory W. Moore, and Constantin Teleman. "Topological symmetry in quantum field theory." Quantum Topology, October 22, 2024. http://dx.doi.org/10.4171/qt/223.

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We introduce a definition and framework for internal topological symmetries in quantum field theory, including “noninvertible symmetries” and “categorical symmetries”. We outline a calculus of topological defects which takes advantage of well-developed theorems and techniques in topological field theory. Our discussion focuses on finite symmetries, and we give indications for a generalization to other symmetries. We treat quotients and quotient defects (often called “gauging” and “condensation defects”), finite electromagnetic duality, and duality defects, among other topics. We include an app

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16

Jarrar, Rabab, Tapas Roy, B. Rath, Prachi Prava Mohapatra, Dilip K. Maiti, and Jihad Asad. "ORIGIN OF POSITION DEPENDENT MASS IN A ROTATING PARABOLIC OR SEMI-PARABOLIC PATH: CLASSICAL AND SEMI-CLASSICAL." JOURNAL OF MECHANICS OF CONTINUA AND MATHEMATICAL SCIENCES 20, no. 06 (2025). https://doi.org/10.26782/jmcms.2025.06.00013.

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For both classical and quantum elements of the system, parabolic and semi-parabolic nature paths have been examined and analyzed. We use the most powerful semi-analytical techniques, namely the optimal and modified homotopy perturbation approach, to examine the dynamics of the particle motion with stability analysis. It is demonstrated that the particle's motion on a rotating parabolic path is precisely harmonic oscillator motion with mass depending on location. We find the exact analytical expression for the motion's frequency and amplitude. We then discuss the dependencies of amplitude and f

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17

Zhang, Peng, and Jing-Yuan Chen. "An explicit categorical construction of instanton density in lattice Yang-Mills theory." Journal of High Energy Physics 2025, no. 6 (2025). https://doi.org/10.1007/jhep06(2025)085.

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Abstract Since the inception of lattice QCD, a natural definition for the Yang-Mills instanton on lattice has been long sought for. In a recent work [1], one of authors showed the natural solution has to be organized in terms of bundle gerbes in higher homotopy theory / higher category theory, and introduced the principles for such a categorical construction. To pave the way towards actual numerical implementation in the near future, nonetheless, an explicit construction is necessary. In this paper we provide such an explicit construction for SU(2) gauge theory, with technical aspects inspired

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18

Vijayan, Lipiya, and G. Sucharitha. "Electroosmotic Effects on Peristaltic Transport of Ree‐Eyring Nanofluid with Double Diffusive Convection in Symmetric Microchannel." Advanced Theory and Simulations, June 3, 2025. https://doi.org/10.1002/adts.202500403.

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AbstractThis study examines significant applications across various domains, including microfluidics, biomedical engineering, and energy systems, focusing on the advancement of lab‐on‐a‐chip technologies, electrokinetic pumps, and micro‐scale filtration systems. A detailed investigation is conducted to explore the combined influence of peristaltic transport, double‐diffusive convection, electroosmosis, magnetohydrodynamics (MHD), Hall current, viscous dissipation, thermal radiation, and porous medium flow in the presence of a heat source. The Poisson–Boltzmann ionic distribution is approximate

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19

Naveen, K., S. Mukhtar, A. M. Mahnashi, Rasool Shah, D. G. Prakasha, and D. K. Archana. "A robust technique to study fractional model describing economic and environmental mathematical system." Engineering Computations, March 21, 2025. https://doi.org/10.1108/ec-10-2024-0932.

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PurposeThe primary goal of this study is to create a more accurate and effective mathematical model for the economic and environmental system by utilizing a non-local derivative.Design/methodology/approachThis study aims to produce results that better represent real-world complexity and dynamics. The arbitrary order of the economics and environmental mathematical model is categorised into three dynamics: the control achievement cost, the manufacturing element capability and the technical exclusion diagnostics cost. The proposed model includes a system of three equations which are studied via t

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20

Senthilvadivu, Karuppiah, Sheniyappan Eswaramoorthi, Karuppusamy Loganathan, and Mohamed Abbas. "Time-dependent Darcy–Forchheimer flow of Casson hybrid nanofluid comprising the CNTs through a Riga plate with nonlinear thermal radiation and viscous dissipation." Nanotechnology Reviews 13, no. 1 (2024). http://dx.doi.org/10.1515/ntrev-2023-0202.

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Abstract Carbon nanotubes (CNTs) are gaining popularity due to their expanding uses in industrial and technical processes, such as geothermal reservoirs, water and air filters, coatings, solar collection, ceramic material reinforcement, electrostatic dissipation, etc. In addition, the CNTs have superior electrical conductivity and biocompatibility. Based on the aforementioned applications, the current work examines the time-dependent and Darcy–Forchheimer flow of water/glycerin-based Casson hybrid nanofluid formed by single-walled CNTs and multi-walled CNTs over a Riga plate under velocity sli

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21

Elliott, Ross-Jordon S., Tiffany N. Phan, and Chima O. Oluigbo. "Technical case report: intractable focal seizures related to bifrontal transmantle heterotopia subserving peculiar homotopic motor distribution treated by responsive neurostimulation therapy." Acta Neurochirurgica, April 12, 2022. http://dx.doi.org/10.1007/s00701-022-05193-y.

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22

Budney, Ryan, and David Gabai. "On the Automorphism Groups of Hyperbolic Manifolds." International Mathematics Research Notices 2025, no. 7 (2025). https://doi.org/10.1093/imrn/rnaf083.

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Abstract Let ${\mathrm{Diff}}_{0}(N)$ represent the subgroup of diffeomorphisms that are homotopic to the identity. We show that if $N$ is a closed hyperbolic 4-manifold, then $\pi _{0}{\mathrm{Diff}}_{0}(N)$ is not finitely generated with similar results holding topologically. This proves in dimension-4 results previously known for $n$-dimensional hyperbolic manifolds of dimension $n\ge 11$ by Farrell and Jones in 1989 and $n\ge 10$ by Farrell and Ontaneda in 2010. Our proof relies on the technical result that $\pi _{0}{\mathrm{Homeo}}(S^{1}\times D^{3})$ is not finitely generated, which exte

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