Related papers: Developing Takeuti-Yasumoto forcing
Let $F$ be a totally real field and $K$ a finite abelian CM extension of $F$. Using class field theory, we show that our previous result giving a strong form of the Brumer-Stark conjecture implies the minus part of the equivariant Tamagawa…
The aim of the work is to construct new polynomial systems, which are solutions to certain functional equations which generalize the second-order differential equations satisfied by the so called classical orthogonal polynomial families of…
In a recent preprint, Y. Namikawa proposed a conjecture on Q-factorial terminalizations and their birational geometry of nilpotent orbits. He proved his conjecture for classical simple Lie algebras. In this note, we prove his conjecture for…
We develop the local theory of the generalized doubling method for the $m$-fold central extension $Sp_{2n}^{(m)}$ of Matsumoto of the symplectic group. We define local $\gamma$-, $L$- and $\epsilon$-factors for pairs of genuine…
The derivation of Marko and Siggia's interpolation formula for the force-extension relation of the Worm-Like Chain Model (C.Bustamante, J.F.Marko, E.D.Siggia, and S.Smith, Science Vol.265, p.1599 (1994); J.F.Marko and E.D.Siggia,…
We introduce weakenings of two of the more prominent open problems in the classification of $\mathrm{C}^*$-algebras, namely the quasidiagonality problem and the UCT problem. We show that the a positive solution of the conjunction of the two…
In this paper, we develop a Hamilton-Jacobi theory for forced Hamiltonian and Lagrangian systems. We study the complete solutions, particularize for Rayleigh systems and present some examples. Additionally, we present a method for the…
We continue the development of the theory of construction schemes over $\omega_1$ as introduced by the third author by studying their relation with forcing axioms. Formally, we introduce the cardinals $\mathfrak{m}^n_{\mathcal{F}}$ and use…
We derive the global existence of weak solutions of the Shigesada-Kawasaki-Teramoto systems in space dimension less or equal to 4 with a rather general condition on the coefficients. The existence is established using finite differences in…
A Mizohata-Takeuchi type estimate is a type of weighted Fourier restriction estimate. Using tools from high dimensional probability, we construct a large class of weights that satisfy sharp estimates of Mizohata-Takeuchi type. One can…
Calculi with control operators have been studied as extensions of simple type theory. Real programming languages contain datatypes, so to really understand control operators, one should also include these in the calculus. As a first step in…
It is well-known since the work of Pardoux and Peng [12] that Backward Stochastic Differential Equations provide probabilistic formulae for the solution of (systems of) second order elliptic and parabolic equations, thus providing an…
As explained in detail in the prologue to this manuscript, boundedness of weak solutions for general classes of elliptic equations in divergence form is a classic tool for achieving higher regularity. We propose here some global boundedness…
Formally self-adjoint, conformally covariant, polydifferential operators provide a general framework for studying variational problems, such as prescribing the scalar, $Q$-, or $\sigma_2$-curvatures, within a conformal class. We describe…
In an earlier work, we considered a family of restriction problems for classical groups (over local and global fields) and proposed precise answers to these problems using the local and global Langlands correspondence. These restriction…
Since Littlewood works in the 1960's, the boundedness of solutions of Duffing-type equations $\ddot{x}+g(x)=p(t)$ has been extensively investigated. More recently, some researches have focused on the family of non-smooth forced oscillators…
Recent work of Pickett has given a construction of self-dual normal bases for extensions of finite fields, whenever they exist. In this article we present these results in an explicit and constructive manner and apply them, through computer…
We introduce an iterative scheme to prove the Yamabe problem $ - a\Delta_{g} u + S u = \lambda u^{p-1} $, firstly on open domain $ (\Omega, g) $ with Dirichlet boundary conditions, and then on closed manifolds $ (M, g) $ by local argument.…
In this paper the elliptic genus for a general Calabi-Yau fourfold is derived. The recent work of Kawai calculating N=2 heterotic string one-loop threshold corrections with a Wilson line turned on is extended to a similar computation where…
In a seminal paper Richard Stanley derived Pieri rules for the Jack symmetric function basis. These rules were extended by Macdonald to his now famous symmetric function basis. The original form of these rules had a forbidding complexity…