Related papers: A local-global principle for weak approximation on…

We propose a new approach to the Fourier restriction conjectures. It is based on a discretization of the Fourier extension operators in terms of quadratically modulated wave packets. Using this new point of view, and by combining natural…

We generalise Birch's seminal work on forms in many variables to handle a system of forms in which the degrees need not all be the same. This allows us to prove the Hasse principle, weak approximation, and the Manin-Peyre conjecture for a…

Local solutions for variational and quasi-variational inequalities are usually the best type of solutions that could practically be obtained when in case of lack of convexity or else when available numerical techniques are too limited for…

We present the concept of cotorsion pairs cut along subcategories of an abelian category. This provides a generalization of complete cotorsion pairs, and represents a general framework to find approximations restricted to certain…

In this paper, we obtain sufficient conditions in terms of projective criteria under which the partial sums of a stationary process with values in ${\mathcal{H}}$ (a real and separable Hilbert space) admits an approximation, in…

Improved local and global versions of the effective Nullstellensatz for ideal sheaves on non-singular complex varieties are obtained, based on a new invariant motivated by the notion of finite type from the theory of several complex…

We investigate the "ramified descent problem": which adelic points of a smooth geometrically connected variety $X$ defined over a number field $K$ can be approximated by points that lift to a (twist of a) given ramified cover? We show that…

We prove some new relations between weak approximation and some rational equivalence relations (Brauer and R-equivalence) in algebraic groups over arithmetical fields. By using weak approximation and local - global approach, we compute…

Latent fibrations are an adaptation, appropriate for categories of partial maps (as presented by restriction categories), of the usual notion of fibration. The paper initiates the development of the basic theory of latent fibrations and…

We give soft, quantitatively optimal extensions of the classical Sphere Theorem, Wilking's connectivity principle and Frankel's Theorem to the context of ${k}$-th Ricci curvature. The hypotheses are soft in the sense that they are satisfied…

We consider parahoric Bruhat-Tits group schemes over a smooth projective curve and torsors under them. If the characteristic of the ground field is either zero or positive but not too small and the generic fiber is absolutely simple and…

In this work, we broadly connect kernel-based filtering (e.g. approaches such as the bilateral filters and nonlocal means, but also many more) with general variational formulations of Bayesian regularized least squares, and the related…

We systematically develop a theory of stratification in the context of tensor triangular geometry and apply it to classify the localizing tensor-ideals of certain categories of spectral $G$-Mackey functors for all finite groups $G$. Our…

We address the problem of weak approximation for general cubic hypersurfaces defined over number fields, with arbitrary singular locus. In particular, weak approximation is established for the smooth locus of projective, geometrically…

Let $k$ be a number field and $X$ a smooth integral affine variety equipped with a morphism $f : X \to A^1_k$ to the affine line. Assume that all fibres of $f$ are split, for instance that they are geometrically integral. Assume that the…

A compressed sensing scheme for near-field imaging of corrugations of relative sparse Fourier components is proposed. The scheme employs random sparse measurement of near field to recover the angular spectrum of the scattered field. It is…

A general reformulation of classical sharp-edge diffraction theory is proposed within paraxial approximation. The, not so much known, Poincar\'e vector potential construction is employed directly inside Fresnel's 2D integral in order for it…

Let $K$ be a global field of positive characteristic. We prove that the Brauer-Manin obstructions to the Hasse principle, to weak approximation and to strong approximation are the only ones for homogeneous spaces of reductive groups with…

Since introduced by Martinet and Rockafellar, the proximal point algorithm was generalized in many fruitful directions. More recently, in 2002, Pennanen studied the proximal point algorithm without monotonicity. A year later, Iusem and…

We present a new coherence theorem for comprehension categories, providing strict models of dependent type theory with all standard constructors, including dependent products, dependent sums, identity types, and other inductive types.…