Tootfinder

Putin um 11.00 Uhr Ortszeit in Anchorage erwartet
Der russische Präsident Putin wird um 11.00 Uhr Ortszeit (21.00 Uhr MESZ) in Anchorage in Alaska erwartet. US-Präsident Trump werde ihn an seinem Flugzeug begrüßen, sagte Kreml-Sprecher Dmitri Peskow im russischen Staatsfernsehen.
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Ukraine-Liveblog: ++ Trump gegen NATO-Sicherheitsgarantien für Ukraine ++
Auf dem Weg zum Treffen mit Russlands Präsident Putin hat sich US-Präsident Trump gegen Sicherheitsgarantien der NATO für die Ukraine ausgesprochen. Der ukrainische Präsident Selenskyj appellierte an Trump: "Wir zählen auf Amerika."

In #Grafing startet der Bau eines 4,2-MW-Solarparks im Ortsteil #Nettelkofen.
Das kommunale Unternehmen #Eberwerk will damit rund 1.300 Haushalte mit regionalem

Eberwerk baut Solarpark Grafing für regionale Energiewende – Spatenstich bei Nettelkofen
Im Grafinger Ortsteil Nettelkofen entsteht eine PV-Anlage mit Gesamtleistung von 4,2 Megawatt von Eberwerk für regionale Energiewende und Klimaschutz.

Deciding Whether a C-Q Channel Preserves a Bit is QCMA-Complete
Kiera Hutton, Arthur Mehta, Andrej Vukovic
https://arxiv.org/abs/2508.10664 https://arxiv.o…

Deciding Whether a C-Q Channel Preserves a Bit is QCMA-Complete
We prove that deciding whether a classical-quantum (C-Q) channel can exactly preserve a single classical bit is QCMA-complete. This "bit-preservation" problem is a special case of orthogonality-constrained optimization tasks over C-Q channels, in which one seeks orthogonal input states whose outputs have small or large Hilbert-Schmidt overlap after passing through the channel. Both problems can be cast as biquadratic optimization with orthogonality constraints. Our main technical contribution u…

Modular differential equations and orthogonal polynomials
Khalil Besrour, Hicham Saber, Abdellah Sebbar
https://arxiv.org/abs/2508.10788 https://arxiv.org/…

Modular differential equations and orthogonal polynomials
We study second-order modular differential equations whose solutions transform equivariantly under the modular group. In the reducible case, we construct all such solutions using an explicit ansatz involving Eisenstein series and the $J$-invariant, reducing the problem to an algebraic system. We show that the roots of this system are captured by orthogonal polynomials satisfying a Fuchsian differential equation. Their recurrence, norms, and weight function are derived, completing the classifica…

Approximation and orthogonality on fully symmetric domains
Yuan Xu
https://arxiv.org/abs/2509.10342 https://arxiv.org/pdf/2509.10342

Approximation and orthogonality on fully symmetric domains
We study orthogonal polynomials on a fully symmetric planar domain $Ω$ that is generated by a certain triangle in the first quadrant. For a family of weight functions on $Ω$, we show that orthogonal polynomials that are even in the second variable on $Ω$ can be identified with orthogonal polynomials on the unit disk composed with a quadratic map, and the same phenomenon can be extended to the domain generated by the rotation of $Ω$ in higher dimensions. The connection allows an immediate de…

Orthogonality between cellulose nanocrystals and a low-molecular weight gelator
Thuy-Linh Phi (LCMCP-SMiLES), Eero Kontturi (LCMCP-SMiLES), Niki Baccile (LCMCP-SMiLES)
https://arxiv.org/abs/2509.10020 …

Orthogonality between cellulose nanocrystals and a low-molecular weight gelator
The development of multicomponent hydrogels has gained a lot of attention in the field of soft matter, as precise tuning of the chemical nature and colloidal properties of each component brings mechanical and functional benefits compared to one-component gels. Within the field, orthogonality between a self-assembled low-molecular weight gelator (LMWG) and a colloid is a domain that has received little attention. In this study, orthogonal LMWG-colloid hydrogels were developed with the additional…

Faster algorithms for k-Orthogonal Vectors in low dimension
Anita D\"urr, Evangelos Kipouridis, Karol W\k{e}grzycki
https://arxiv.org/abs/2507.11098 h…

Faster algorithms for k-Orthogonal Vectors in low dimension
In the Orthogonal Vectors problem (OV), we are given two families $A, B$ of subsets of $\{1,\ldots,d\}$, each of size $n$, and the task is to decide whether there exists a pair $a \in A$ and $b \in B$ such that $a \cap b = \emptyset$. Straightforward algorithms for this problem run in $\mathcal{O}(n^2 \cdot d)$ or $\mathcal{O}(2^d \cdot n)$ time, and assuming SETH, there is no $2^{o(d)}\cdot n^{2-\varepsilon}$ time algorithm that solves this problem for any constant $\varepsilon > 0$. William…

Information Retention in Iterative Random Projection of Convex Bodies to Lower Dimensions
Nazanin Mirhosseini
https://arxiv.org/abs/2508.10218 https://arxi…

Information Retention in Iterative Random Projection of Convex Bodies to Lower Dimensions
In this paper, we consider a bounded convex body $K_0 \subset \mathbb{R}^{n}$ subjected to two successive random orthogonal projections onto $\mathbb{R}^{n-1}$ and $\mathbb{R}^{n-2}$, respectively. First, we project $K_0$ orthogonally onto $U_{1}^{\perp}$, the orthogonal complement of $\mbox{\boldmath $U$}_1$, where $\mbox{\boldmath $U$}_1$ is uniformly distributed on the unit sphere $S^{n-1}$. This yields a random convex body $K_1 = \mathrm{Proj}_{{U_1}^{\perp}}(K_0) \subset \mathbb{R}^{n-1}$.…

Markov dualities via the spectral decompositions of the two Markov generators in their bi-orthogonal basis of right and left eigenvectors
Cecile Monthus
https://arxiv.org/abs/2507.11041

Markov dualities via the spectral decompositions of the two Markov generators in their bi-orthogonal basis of right and left eigenvectors
The notion of Markov duality between two Markov processes that can live in two different configurations spaces $(x,{\tilde x})$ is revisited via the spectral decompositions of the two Markov generators in their bi-orthogonal basis of right and left eigenvectors. In this formulation, the two generators should have the same eigenvalues $(-E)$ that may be complex, while the duality function $Ω(x,{\tilde x})$ can be considered as a mapping between the right and the left eigenvectors of the two mod…

Orthogonal polynomials, quantum walks and the Prouhet-Tarry-Escott problem
Frederico Can\c{c}ado, Gabriel Coutinho, Thom\'as Jung Spier
https://arxiv.org/abs/2509.09948 http…

Orthogonal polynomials, quantum walks and the Prouhet-Tarry-Escott problem
This paper is motivated by the following problem. Define a quantum walk on a positively weighted path (linear chain). Can the weights be tuned so that perfect state transfer occurs between the first vertex and any other position? We do not fully answer this question - in fact, we show that a particular case of this problem is equivalent to a solution of a particular case of the well known Prouhet-Tarry-Escott problem, deeming our original task certainly harder than anticipated. In our journey, …