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I was wondering if there is a smooth (sophisticated) way to associate algebras of global functions of formal groupoid associated to Lie-Rinehart algebra (considered as 1-stack) to its Chevalley-Eilenberg complex, that could be generalized to Lie algebroids and even Lie infinity algebroids. So far, (at least when a Lie-Rinehart A-algebra L is free as A-module)Read more

The formal group law associated with a generating function $ f(x) = x + \sum_{n=1}^\infty a_n \frac{x^n}{n!}$ is $ $ f(f^{-1}(x) + f^{-1}(y)).$ $ In my thesis, I found a large number of examples of formal group laws that have combinatorial interpretations and thus have nonnegative coefficients. In Sec 9.1 I conjectured the following characterizationRead more

Let $ M$ be a compact manifold with boundary. If we have two vector bundles $ E, F \to M$ with inner products and a differential operator $ D: C^{\infty}(E) \to C^{\infty}(F)$ then $ D$ admits a formal adjoint $ D^*: C^{\infty}(F) \to C^{\infty}(E)$ . This satisfies, for smooth sections with compact support in theRead more

If $ F:V\to W$ is a smooth at $ a\in V$ function between finite-dimensional vector spaces over $ \mathbb{R}$ , then we have $ $ F(x) = \sum_{k=0}^N\frac{1}{k!}(D^kF)(a)[(x-a)^{\otimes k}]+\text{remainder}, $ $ where $ (D^kF)(a):\mathrm{Sym}^k(V)\to W$ are $ \mathbb{R}$ -linear maps. Algebraically, this is a statement about writing tuples of homogeneous polynomials of same degree asRead more

What is software aging? Is there a subfield within computer engineering that studies this phenomenon? If they do, then what are the kinds of abstractions they employ? What are some of the different mechanisms through which software can age? What are some of the classic resources on the topic?Read more

$ \delta$ is a positive number. Is this Taylor expansion of some function?Read more