We show that global vanishing of Massey products on a commutative differential graded algebra is not invariant under field extension. Non-vanishing triple Massey products remain non-vanishing upon ...field extension, while higher Massey products can generally vanish. If the field being extended is algebraically closed, all non-vanishing Massey products remain non-vanishing on a finite type commutative differential graded algebra.
We show that if the universal cover of a closed smooth manifold admitting a metric with non-negative Ricci curvature is formal, then the manifold itself is formal. We reprove a result of ...Fiorenza–Kawai–Lê–Schwachhöfer, that closed orientable manifolds with a non-negative Ricci curvature metric and sufficiently large first Betti number are formal. Our method allows us to remove the orientability hypothesis; we further address some cases of non-closed manifolds.
We give an exposition of Sullivan’s theorem on realizing rational homotopy types by closed smooth manifolds, including a discussion of the necessary rational homotopy and surgery theory, adapted to ...the realization problem for almost complex manifolds: namely, we give a characterization of the possible simply connected rational homotopy types, along with a choice of rational Chern classes and fundamental class, realized by simply connected closed almost complex manifolds in real dimensions six and greater. As a consequence, beyond demonstrating that rational homotopy types of closed almost complex manifolds are plenty, we observe that the realizability of a simply connected rational homotopy type by a simply connected closed almost complex manifold depends only on its cohomology ring. We conclude with some computations and examples.
Serre’s duality theorem implies a symmetry between the Hodge numbers,
=
, on a compact complex
–manifold. Equivalently, the first page of the associated Frölicher spectral sequence satisfies
for all
...,
. Adapting an argument of Chern, Hirzebruch, and Serre 3 in an obvious way, in this short note we observe that this “Serre symmetry”
holds on all subsequent pages of the spectral sequence as well. The argument shows that an analogous statement holds for the Frölicher spectral sequence of an almost complex structure on a nilpotent real Lie group as considered by Cirici and Wilson in 4.
We study the space of (orthogonal) almost complex structures on closed six-dimensional manifolds as the space of sections of the twistor space for a given metric. For a connected six-manifold with ...vanishing first Betti number, we express the space of almost complex structures as a quotient of the space of sections of a seven-sphere bundle over the manifold by a circle action, and then use this description to compute the rational homotopy theoretic minimal model of the components that satisfy a certain Chern number condition. We further obtain a formula for the homological intersection number of two sections of the twistor space in terms of the Chern classes of the corresponding almost complex structures.
We show that the only rational homology spheres which can admit almost complex structures occur in dimensions two and six. Moreover, we provide infinitely many examples of six-dimensional rational ...homology spheres which admit almost complex structures, and infinitely many which do not. We then show that if a closed almost complex manifold has sum of Betti numbers three, then its dimension must be a power of two.
The aim of this experimental research is to confirm the correctness of the proposed methodology for optimizing atmospheric gas burners. Also, the burner was tested in actual conditions. The object of ...this experimental optimization is a typical modern atmospheric gas burner for households (required heat output for average households ranges from 8-12 kW) to which the proposed methodology will be applied in order to optimize its design characteristics and performance to obtain energy efficient and an environmentally friendly device.
The paper presents results of theoretical numerical research dealing with CO and NOx emission performed in the process of optimization of the performance of low-power atmospheric burners. The ...theoretical part of this paper, whose main goals were better understanding of the complex issues of methodology and establishment of performance prediction and optimization of low-power atmospheric gas burner included numerical variation of independent parameters, such as burner geometry, the coefficients of primary and secondary air and different gaseous fuels including biogas. The findings of theoretically obtained performance prediction and optimization of atmospheric burners were experimentally investigated in purpose built test rigs for a number of variable parameters. The obtained results fully justified the proposed models of performance prediction and burner optimization.
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