Related papers: The Butterfly lemma
We show that every sheaf on the site of smooth manifolds with values in a stable (infinity,1)-category (like spectra or chain complexes) gives rise to a differential cohomology diagram and a homotopy formula, which are common features of…
A general expression for the optical theorem for probe sources given in terms of propagation invariant beams is derived. This expression is obtained using the far field approximation for Rayleigh regime. In order to illustrate this results…
This work provides a complete characterization of the solutions of a linear interpolation problem for vector polynomials. The interpolation problem consists in finding n scalar polynomials such that an equation involving a linear…
We dig out a deeper mathematical structure of the quantum Hall system from a perspective of the Langlands program. An algebraic expression of the Hamiltonian with the quantum group is a cornerstone. The Langlands duality of the quantum…
In a recent letter, new representations were proposed for the pair of sequences ($\gamma,\delta$), as defined formally by Bailey in his famous lemma. Here we extend and prove this result, providing pairs ($\gamma,\delta$) labelled by the…
Mathematical diffraction theory is concerned with the analysis of the diffraction image of a given structure and the corresponding inverse problem of structure determination. In recent years, the understanding of systems with continuous and…
Uniform interpolation is the property that, for any formula and set of atoms, there exists the strongest consequence omitting those atoms. It plays a central role in knowledge representation and reasoning tasks such as knowledge update and…
A general theory of permutation orbifolds is developed for arbitrary twist groups. Explicit expressions for the number of primaries, the partition function, the genus one characters, the matrix elements of modular transformations and for…
We study birational quasi-isomorphisms between normal Noetherian domains endowed with cluster structures of geometric type. We prove an analogue of the Starfish lemma that allows one to transfer various cluster and algebraic properties of…
A novel refinement of the conventional treatment of Kadanoff--Baym equations is suggested. Besides the Boltzmann equation another differential equation is used for calculating the evolution of the non-equilibrium two-point function.…
The multivariate covering lemma states that given a collection of $k$ codebooks, each of sufficiently large cardinality and independently generated according to one of the marginals of a joint distribution, one can always choose one…
One studies Cremona monomial maps by combinatorial means. Among the results is a simple integer matrix theoretic proof that the inverse of a Cremona monomial map is also defined by monomials of fixed degree, and moreover, the set of…
We discuss an interesting duality known to occur for certain complex reflection groups, namely the duality groups. Our main construction yields a concrete, representation theoretic realisation of this duality. This allows us to naturally…
We consider the problem of uniform interpolation of functions with values in a complex inner product space of finite dimension. This problem can be casted within a modified weighted pluripotential theoretic framework. Indeed, in the…
The elegance and usefulness of a complex formulation of the basic lensing equations is demonstrated with a number of applications. Using standard tools of complex function theory, we present, for instance, a new proof of the fact that the…
Perturbing the external control parameters of nonlinear systems leads to dramatic changes of its bifurcations. A branch of singular theory, the catastrophe theory, analyses the generating function that depends on state and control…
We present a unified approach to (bi-)orthogonal basis sets for gravitating systems. Central to our discussion is the notion of mutual gravitational energy, which gives rise to the self-energy inner product on mass densities. We consider a…
The paper [GLZ] "L-functions of Carlitz modules, resultantal varieties and rooted binary trees" is devoted to a description of some resultantal varieties related to L-functions of Carlitz modules. It contains a conjecture that some of these…
The Kernel Complex Lemma states that given commutative diagram with exact rows and exact columns which covers the region under a $\Gamma$-shape, then the kernel sequence on the top and the kernel sequence at the left have in each position…
We present a slightly more general version of Boole's additive formula for factorials as a simple consequence of Lagrange's Interpolating Polynomial theorem.