Related papers: A Unified Non-Strict Finsler Lemma

In this paper, we prove a Morse index theorem for the index form of even order linear Hamiltonian systems on the closed interval with reasonable self-adjoint boundary conditions. The highest order term is assumed to be nondegenerate.

We extend calculus from smooth manifolds to topological manifolds making use of a theory of generalized functions developed for this aim. Actually such extension fits into a boarder context: the universal construction of a site containing…

Prompted by an observation about the integral of exponential functions of the form $f(x)=\lambda e^{\alpha x}$, we investigate the possibility to exactly integrate families of functions generated from a given function by scaling or by…

This article is concerned with the approximation of unbounded convex sets by polyhedra. While there is an abundance of literature investigating this task for compact sets, results on the unbounded case are scarce. We first point out the…

We improve an isoperimetric inequality due to Panos Papasoglu. We also generalize this inequality to the Finsler case by proving an optimal Finsler version of the Besicovitch's lemma which holds for any notion of Finsler volume.

Linear mixed models (LMMs) are suitable for clustered data and are common in biometrics, medicine, survey statistics and many other fields. In those applications, it is essential to carry out valid inference after selecting a subset of the…

In this paper, a kind of non regular constraints and a principle for seeking critical point under the constraint are presented, where no Lagrange multiplier is involved. Let $E, F$ be two Banach spaces, $g: E\rightarrow F$ a $c^1$ map…

We prove a general nonlinear projection theorem for Assouad dimension. This theorem has several applications including to distance sets, radial projections, and sum-product phenomena. In the setting of distance sets we are able to…

Mennicke--Newman lemma for unimodular rows was used by W. van der Kallen to give a group structure on the orbit set $\frac{Um_{n}(R)}{E_{n}(R)}$ for a commutative noetherian ring of dimension $d\leq 2n-4.$ In this paper, we generalise the…

This paper develops a uniformly valid and asymptotically nonconservative test based on projection for a class of shape restrictions. The key insight we exploit is that these restrictions form convex cones, a simple and yet elegant structure…

The proof of Brouwer's fixed-point theorem based on Sperner's lemma is often presented as an elementary combinatorial alternative to advanced proofs based on algebraic topology. The goal of this note is to show that: (i) the combinatorial…

Nonconvex optimization is central to modern machine learning, but the general framework of nonconvex optimization yields weak convergence guarantees that are too pessimistic compared to practice. On the other hand, while convexity enables…

Generalizations and variations of the fundamental lemma by Willems et al. are an active topic of recent research. In this note, we explore and formalize the links between kernel regression and some known nonlinear extensions of the…

It is well-understood that the robustness of mechanical and robotic control systems depends critically on minimizing sensitivity to arbitrary application-specific details whenever possible. For example, if a system is defined and performs…

We obtain an extended Reich fixed point theorem for the setting of generalized cone rectangular metric spaces without assuming the normality of the underlying cone. Our work is a generalization of the main result in \cite{AAB} and…

In this paper by using $W_{n}$-mapping, we introduce a composite iterative method for finding a common fixed point for infinite family of nonexpansive mappings and a solution of a certain variational inequality. Furthermore, the strong…

We prove Holder regularity for solutions of non divergence integro-differential equations with non necessarily even kernels. The even/odd decomposition of the kernel can be understood as a sum of a diffusion and a drift term. In our case we…

We present a generalization of the spinor and twistor geometry for on (pseudo) Riemannian manifolds enabled with nonholonomic distributions or for Finsler-Cartan spaces modelled on tangent Lorentz bundles. Nonholonomic (Finsler) twistors…

We introduce a new consistency-based approach for defining and solving nonnegative/positive matrix and tensor completion problems. The novelty of the framework is that instead of artificially making the problem well-posed in the form of an…

We derive a generalized Stokes' theorem, valid in any dimension and for arbitrary loops, even if self intersecting or knotted. The generalized theorem does not involve an auxiliary surface, but inherits a higher rank gauge symmetry from the…