相关论文: Analytical Structure of the Generalized $\lambda-$…

We study generalized permutohedra and supermodular functions. Specifically we analyze decomposability and irreducibility for these objects and establish some asymptotic behavior. We also study a related problem on irreducibility for…

We develop deformation theory of algebras over quadratic operads where the parameter space is a commutative local algebra. We also give a construction of a distinguised deformation of an algebra over a quadratic operad with a complete local…

Co lombeau's construction of generalized functions (in its special variant) is extended to a theory of generalized sections of vector bundles. As particular cases, generalized tensor analysis and exterior algebra are studied. A point value…

The success of the identification of the planar dilatation operator of N=4 SYM with an integrable spin chain Hamiltonian has raised the question if this also is valid for a deformed theory. Several deformations of SYM have recently been…

In this thesis, we study deformations of compact holomorphic Poisson manifolds and algebraic Poisson schemes in the framework of Kodaira-Spencer's analytic deformation theory and Grothendieck's algebraic deformation theory.

Lecture 1: Projective and K\"ahler Manifolds, the Enriques classification, construction techniques. Lecture 2: Surfaces of general type and their Canonical models. Deformation equivalence and singularities. Lecture 3: Deformation and…

Generalized Procrustes Analysis (GPA) is the problem of bringing multiple shapes into a common reference by estimating transformations. GPA has been extensively studied for the Euclidean and affine transformations. We introduce GPA with…

A class of spherical functions is studied which can be viewed as the matrix generalization of Bessel functions. We derive a recursive structure for these functions. We show that they are only special cases of more general radial functions…

A unified description of the relationship between the Hamiltonian structure of a large class of integrable hierarchies of equations and W-algebras is discussed. The main result is an explicit formula showing that the former can be…

Generalised geometry studies structures on a d-dimensional manifold with a metric and 2-form gauge field on which there is a natural action of the group SO(d,d). This is generalised to d-dimensional manifolds with a metric and 3-form gauge…

We prove that if X is a separable, reflexive space which is asymptotic l_p, then X embeds into a reflexive space Z having an asymptotic l_p finite-dimensional decomposition. This result leads to an intrinsic characterization of subspaces of…

The aim of this paper is to give an overview and to compare the different deformation theories of algebraic structures. We describe in each case the corresponding notions of degeneration and rigidity. We illustrate these notions with…

In a recent series of papers by Lou et al., it was conjectured that higher dimensional integrable equations may be constructed by utilizing some conservation laws of (1 + 1)-dimensional systems. We prove that the deformation algorithm…

It is a basic introduction to differential graded Lie algebras, Maurer-Cartan equation and associated deformation functors.

We generalize some of the functional (hyper-circle) a posteriori estimates from finite element settings to general graphs or Hilbert space settings. We provide several theoretical results in regard to the generalized a posteriori error…

We present a generalization of the notion of an algebra norm relevant to real finite-dimensional unital associative algebras. Among other things, this leads to a novel set of algebra isomorphism invariants, some of which are computationally…

We show that every compact complex analytic space endowed with a fine logarithmic structure and every morphism between such spaces admit a semi-universal deformation. These results generalize the analogous results in complex analytic…

This paper is the sequel to [PTVV] (IHES Vol. 117, 2013). We develop a general and flexible context for differential calculus in derived geometry, including the de Rham algebra and polyvector fields. We then introduce the formalism of…

The decomposition of the linear-order metric perturbation is discussed in the context of the higher-order gauge-invariant perturbation theory. We show that the linear order metric perturbation is decomposed into gauge-invariant and…

An integrable deformation of the known integrable model of two interacting p-dimensional and q-dimensional spherical tops is considered. After reduction this system gives rise to the generalized Lagrange and the Kowalevski tops. The…