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Auch neue Häuser in Bremen brauchen jetzt Solaranlage
Kein Neubau ohne Solaranlage: Bremen verschärft ab Juli die Regeln für Hausdächer. Sind diese mindestens 25 Quadratmeter groß, greift die Solarpflicht.

Quadratic forms and their duals
Hans Havlicek
https://arxiv.org/abs/2506.23613 https://arxiv.org/pdf/2506.23613

Quadratic forms and their duals
There are many specific results, spread over the literature, regarding the dualisation of quadrics in projective spaces and quadratic forms on vector spaces. In the present work we aim at generalising and unifying some of these. We start with a quadratic form $Q$ that is defined on a subspace $S$ of a finite-dimensional vector space $V$ over a field $F$. Whenever $Q$ satisfies a certain condition, which comes into effect only when $F$ is of characteristic two, $Q$ gives rise to a dual quadratic…

Averaging quadratically twisted $L$-values and their derivatives
Tinghao Huang
https://arxiv.org/abs/2507.00179 https://arxiv.org/pdf…

Averaging quadratically twisted $L$-values and their derivatives
In this paper, we unconditionally establish an asymptotic formula for the product of the quadratically twisted central $L$-value associated to a holomorphic cusp form $f$, and the quadratically twisted central $L$-derivative to a distinct holomorphic cusp form $g$. This result may be viewed as an extension of \cite{Li-MR4768632}, \cite{Kumar.etc-MR4765788} and \cite{zhou2025momentderivativesquadratictwists}.

Boundary bilinear control of semilinear parabolic PDEs: quadratic convergence of the SQP method
Eduardo Casas, Mariano Mateos
https://arxiv.org/abs/2505.24237

Boundary bilinear control of semilinear parabolic PDEs: quadratic convergence of the SQP method
We analyze a bilinear control problem governed by a semilinear parabolic equation. The control variable is the Robin coefficient on the boundary. First-order necessary and second-order sufficient optimality conditions are derived. A sequential quadratic programming algorithm is then proposed to compute local solutions. Starting the iterations from an initial point in an $L^2$-neighborhood of the local solution we prove stability and quadratic convergence of the algorithm in $L^p$ ($p < \infty$)…

Quadratic Bureau-Guillot systems with the first and second Painlev\'e transcendents in the coefficients. Part I: geometric approach and birational equivalence
Marta Dell'Atti, Galina Filipuk
https://arxiv.org/abs/2506.22896

Quadratic Bureau-Guillot systems with the first and second Painlevé transcendents in the coefficients. Part I: geometric approach and birational equivalence
Bureau proposed a classification of systems of quadratic differential equations in two variables which are free of movable critical points, which was recently revised by Guillot. We revisit the quadratic Bureau-Guillot systems with the first and second Painlevé transcendent in the coefficients. We explain their birational equivalence by using the geometric approach of Okamoto's spaces of initial conditions and the method of iterative polynomial regularisation, solving the Painlevé equivalence…

Quadrature Over-the-Air-Computing for Multimodal Dual-Stream Signal Processing
Hyeon Seok Rou, Kengo Ando, Giuseppe Thadeu Freitas de Abreu, David Gonz\'alez G
https://arxiv.org/abs/2507.00508

Quadrature Over-the-Air-Computing for Multimodal Dual-Stream Signal Processing
We propose a novel quadrature over-the-air computing (Q-OTAC) framework that enables the simultaneously computation of two independent functions and/or data stream within a single transmission. In contrast to conventional OTAC schemes, where a single function is computed by treating each complex signal as a single component, the proposed Q-OTAC exploits both in-phase and quadrature (IQ) components of a complex signal, encoding two distinct functions and/or data streams at the edge devices (EDs)…

Efficient Numerical Integration for Finite Element Trunk Spaces in 2D and 3D using Machine Learning: A new Optimisation Paradigm to Construct Application-Specific Quadrature Rules
Tomas Teijeiro, Pouria Behnoudfar, Jamie M. Taylor, David Pardo, Victor M. Calo
https://arxiv.org/abs/2506.23741…

Efficient Numerical Integration for Finite Element Trunk Spaces in 2D and 3D using Machine Learning: A new Optimisation Paradigm to Construct Application-Specific Quadrature Rules
Finite element methods usually construct basis functions and quadrature rules for multidimensional domains via tensor products of one-dimensional counterparts. While straightforward, this approach results in integration spaces larger than necessary, especially as the polynomial degree $p$ or the spatial dimension increases, leading to considerable computational overhead. This work starts from the hypothesis that reducing the dimensionality of the polynomial space can lead to quadrature rules wi…

The shape of quadratic Gauss paths
Justine Dell, Djordje Mili\'cevi\'c
https://arxiv.org/abs/2508.21707 https://arxiv.org/pdf/2508.21707

The shape of quadratic Gauss paths
We consider the distribution of quadratic Gauss paths, polygonal paths joining partial sums of quadratic Gauss sums to square-free fundamental discriminant moduli in a dyadic range [Q,2Q]. We prove that this striking ensemble converges in law, as Q->\infty, to a random Fourier series we explicitly describe, and we prove a convergence in probability result and a classification result for the limiting shapes that explain the visually remarkable properties of these Gauss paths.

A general approach to permutation polynomials from quadratic forms
Ruikai Chen
https://arxiv.org/abs/2506.24012 https://arxiv.org/pdf…

A general approach to permutation polynomials from quadratic forms
We investigate a family of permutation polynomials of finite fields of characteristic 2. Through a connection between permutation polynomials and quadratic forms, a general treatment is presented to characterize these permutation polynomials. By determining some character sums associated with quadratic forms, we explicitly describe several classes of permutation polynomials.

Extending bounds on minimal ranks of universal quadratic lattices to larger number fields
Mat\v{e}j Dole\v{z}\'alek
https://arxiv.org/abs/2507.23338 https://

Extending bounds on minimal ranks of universal quadratic lattices to larger number fields
There exist numerous results in the literature proving that within certain families of totally real number fields, the minimal rank of a universal quadratic lattice over such a field can be arbitrarily large. Kala introduced a technique of extending such results to larger fields -- e.g. from quadratic fields to fields of arbitrary even degree -- under some conditions. We present improvements to this technique by investigating the structure of subfields within composita of number fields, using b…