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The classification and representations of positive definite ternary quadratic forms of level 4N
Yifan Luo, Haigang Zhou
https://arxiv.org/abs/2402.17443 ht…

The classification and representations of positive definite ternary quadratic forms of level 4N
Classifications and representations are two main topics in the theory of quadratic forms. In this paper, we consider these topics of ternary quadratic forms. For a given squarefree integer $N$, first we give the classification of positive definite ternary quadratic forms of level $4N$ explicitly. Second, we give explicit formulas of the weighted sum of representations over each class in every genus of ternary quadratic forms of level $4N$, which are involved with modified Hurwitz class number. …

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Darmstadt 98 und ENTEGA nehmen größte Photovoltaik-Anlage in Darmstadt in Betrieb – Erneuerbare Energie entsteht auf den Dächern des Merck-Stadions am Böllenfalltor | DarmstadtNews.de
Der SV Darmstadt 98 hat mit seinem langjährigen Partner, dem Ökoenergie- und Telekommunikationsversorger ENTEGA, auf den Dächern der Haupttribüne und der Gegengerade des Merck-Stadions am Böllenfalltor auf einer Fläche von insgesamt knapp 5.700 Quadratmetern rund 2.900 Photovoltaik-Module installieren lassen. Die Anlage konnte nun Mitte März 2024 in Betrieb gehen. Die Photovoltaik-Anlage ist fast so groß

This https://arxiv.org/abs/2311.06144 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csRO_…

Multi-Agent Reinforcement Learning for the Low-Level Control of a Quadrotor UAV
By leveraging the underlying structures of the quadrotor dynamics, we propose multi-agent reinforcement learning frameworks to innovate the low-level control of a quadrotor, where independent agents operate cooperatively to achieve a common goal. While single-agent reinforcement learning has been successfully applied in quadrotor controls, training a large monolithic network is often data-intensive and time-consuming. Moreover, achieving agile yawing control remains a significant challenge due …

Characterization of quadratic $\varepsilon$-CNS polynomials (extended version)
Borka Jadrijevi\'c, Kristina Mileti\'c
https://arxiv.org/abs/2402.16588

Characterization of quadratic $\varepsilon$-CNS polynomials (extended version)
In this paper, we give characterization of quadratic $\varepsilon-$canonical number system ($\varepsilon-$CNS) polynomials for all values $\varepsilon \in\lbrack0,1)$. Our characterization provides a unified view of the well-known characterizations of the classical quadratic CNS polynomials ($\varepsilon=0$) and quadratic SCNS polynomials ($\varepsilon=1/2$). This result is a consequence of our new characterization results of $\varepsilon -$shift radix systems ($\varepsilon-$SRS) in the two-dim…

Der #SVDarmstadt98 hat mit seinem langjährigen Partner, dem Ökoenergie- und Telekommunikationsversorger ENTEGA, auf den Dächern der Haupttribüne und der Gegengerade des Merck-Stadions am Böllenfalltor auf einer Fläche von insgesamt knapp 5.700 Quadratmetern rund 2.900 #Photovoltaik Module…

Darmstadt 98 und ENTEGA nehmen größte Photovoltaik-Anlage in Darmstadt in Betrieb – Erneuerbare Energie entsteht auf den Dächern des Merck-Stadions am Böllenfalltor | DarmstadtNews.de
Der SV Darmstadt 98 hat mit seinem langjährigen Partner, dem Ökoenergie- und Telekommunikationsversorger ENTEGA, auf den Dächern der Haupttribüne und der Gegengerade des Merck-Stadions am Böllenfalltor auf einer Fläche von insgesamt knapp 5.700 Quadratmetern rund 2.900 Photovoltaik-Module installieren lassen. Die Anlage konnte nun Mitte März 2024 in Betrieb gehen. Die Photovoltaik-Anlage ist fast so groß

Characterization of quadratic $\varepsilon$-CNS polynomials (extended version)
Borka Jadrijevi\'c, Kristina Mileti\'c
https://arxiv.org/abs/2402.16588

Characterization of quadratic $\varepsilon$-CNS polynomials (extended version)
In this paper, we give characterization of quadratic $\varepsilon-$canonical number system ($\varepsilon-$CNS) polynomials for all values $\varepsilon \in\lbrack0,1)$. Our characterization provides a unified view of the well-known characterizations of the classical quadratic CNS polynomials ($\varepsilon=0$) and quadratic SCNS polynomials ($\varepsilon=1/2$). This result is a consequence of our new characterization results of $\varepsilon -$shift radix systems ($\varepsilon-$SRS) in the two-dim…

This https://arxiv.org/abs/2402.05599 has been replaced.
link: https://scholar.google.com/scholar?q=a

A Quadratic Curve Analogue of the Taniyama-Shimura Conjecture
For quadratic curves over $Q$ in $F_p$, the number of solutions, which is governed by an analogue of the Mordell-Weil group, is expressed with the Legendre symbol of a coefficient of quadratic curves. Focusing on the number of solutions, a quadratic curve analogue of the modular form in the Taniyama-Shimura conjecture is proposed. This modular form yields the Gaussian sum and also possesses some modular transformation structure.

This https://arxiv.org/abs/2402.05599 has been replaced.
link: https://scholar.google.com/scholar?q=a

A Quadratic Curve Analogue of the Taniyama-Shimura Conjecture
For quadratic curves over $Q$ in $F_p$, the number of solutions, which is governed by an analogue of the Mordell-Weil group, is expressed with the Legendre symbol of a coefficient of quadratic curves. Focusing on the number of solutions, a quadratic curve analogue of the modular form in the Taniyama-Shimura conjecture is proposed. This modular form yields the Gaussian sum and also possesses some modular transformation structure.

This https://arxiv.org/abs/1103.5906 has been replaced.
link: https://scholar.google.com/scholar?q=a<…

Torsion groups of elliptic curves over quadratic fields
We describe methods to determine all the possible torsion groups of an elliptic curve that actually appear over a fixed quadratic field. We use these methods to find, for each group that can appear over a quadratic field, the field with the smallest absolute value of it's discriminant such that there exists an elliptic curve with that torsion. We also examine the interplay of the torsion and rank over a fixed quadratic field and see that what happens is very different than over $\Q$. Finally we…