相关论文: Partial Signatures and the Yoshida-Nicolaescu Theo…
A well-known property of the signature of closed oriented 4n-dimensional manifolds is Novikov additivity, which states that if a manifold is split into two manifolds with boundary along an oriented smooth hypersurface, then the signature of…
Zeckendorf's Theorem states that any positive integer can be uniquely decomposed into a sum of distinct, non-adjacent Fibonacci numbers. There are many generalizations, including results on existence of decompositions using only even…
Recent work alludes to various `controversies' associated with signature change in general relativity. As we have argued previously, these are in fact disagreements about the (often unstated) assumptions underlying various possible…
The main aim of the paper is to prove a fountain theorem without assuming the $\tau$-upper semicontinuity condition on the variational functional. Using this improved fountain theorem, we may deal with more general strongly indefinite…
This article shows a very elementary and straightforward proof of the Implicit Function Theorem for differentiable maps $F(x,y)$ defined on a finite-dimensional Euclidean space. There are no hypothesis on the continuity of the partial…
In this paper, we first present simple proofs of Choi's results [4], then we give a short alternative proof for Fiedler and Markham's inequality [6]. We also obtain additional matrix inequalities related to partial determinants.
In this paper we consider images of (ordinary) noncommutative polynomials on matrix algebras endowed with a graded structure. We give necessary and sufficient conditions to verify that some multilinear polynomial is a central polynomial, or…
We present a version of Krasnosel'skii fixed point theorem for operators acting on Cartesian products of normed linear spaces, under cone-compression and cone-expansion conditions of norm type. Our approach, based on the fixed point index…
In the theory of conditional sets, many classical theorems from areas such as functional analysis, probability theory or measure theory are lifted to a conditional framework, often to be applied in areas such as mathematical economics or…
A $D_{\infty}$-topological Markov chain is a topological Markov chain provided with an action of the infinite dihedral group $D_{\infty}$. It is defined by two zero-one square matrices $A$ and $J$ satisfying $AJ=JA^{\textsf{T}}$ and…
In this short note we give an alternative proof of Glivenko's Theorem, stating that a formula $\phi$ is provable in classical propositional logic if and only if $\neg\neg\phi$ is provable in intuitionistic propositional logic. We work in…
We prove new Skoda-type division, or ideal membership, theorems. We work in a geometric setting of line bundles over Kahler manifolds that are Stein away from an analytic subvariety. (This includes complex projective manifolds.) Our…
We give in this paper a short semantical proof of the strong normalization for full propositional classical natural deduction. This proof is an adaptation of reducibility candidates introduced by J.-Y. Girard and simplified to the classical…
We prove global stability for a system of nonlinear wave equations satisfying a generalized null condition. The generalized null condition allows for null forms whose coefficients have bounded $C^k$ norms. We prove both pointwise decay and…
A method for deriving the asymptotic behaviour of any physical field is presented. This leads to a geometrically meaningful derivation of the peeling properties for arbitrary values of the cosmological constant. Application to the…
We prove some Liouville type theorems on smooth compact Riemannian manifolds with nonnegative sectional curvature and strictly convex boundary. This gives a nonlinear generalization in low dimension of the recent sharp lower bound of the…
We present two novel, explicit representations of Cholesky factor of a nonsingular correlation matrix. The first representation uses semi-partial correlation coefficients as its entries. The second, uses an equivalent form of the square…
A formula for the partial trace of a full symmetrizer is obtained. The formula is used to provide an inductive proof of the well-known formula for the dimension of a full symmetry class of tensors.
The paper establishes an analog Whittaker-Shannon-Kotelnikov sampling theorem with fast decreasing coefficient, as well as a new modification of the corresponding interpolation formula applicable for general type non-vanishing bounded…
A proof of the continuous martingale convergence theorem is provided. It relies on a classical martingale inequality and the almost sure convergence of a uniformly bounded non-negative super-martingale, after a truncation argument.