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The Noether inequalities for a foliated surface of general type
Xin Lu
https://arxiv.org/abs/2404.16293 https://arxiv.org/pdf/2404.16…

The Noether inequalities for a foliated surface of general type
Let $(\mathcal{F},S)$ be a foliated surface of general type with reduced singularities over the complex number. We establish the Noether type inequalities for $(\mathcal{F},S)$. Namely, we prove that $\mathrm{vol}(\mathcal{F}) \geq p_g(\mathcal{F})-2$, and that $\mathrm{vol}(\mathcal{F}) \geq 2p_g(\mathcal{F})-4$ if moreover the surface $S$ is also of general type. Examples show that both of the Noether type inequalities are sharp.

Conversion of Boolean and Integer FlatZinc Builtins to Quadratic or Linear Integer Problems
Armin Wolf
https://arxiv.org/abs/2404.12797 https://

Conversion of Boolean and Integer FlatZinc Builtins to Quadratic or Linear Integer Problems
Constraint satisfaction or optimisation models -- even if they are formulated in high-level modelling languages -- need to be reduced into an equivalent format before they can be solved by the use of Quantum Computing. In this paper we show how Boolean and integer FlatZinc builtins over finite-domain integer variables can be equivalently reformulated as linear equations, linear inequalities or binary products of those variables, i.e. as finite-domain quadratic integer programs. Those quadratic …

Understanding Intra-Household Educational Inequalities: Gender, Birth Order, and Ability Dynamics in Benin's Households
Christelle Zozoungbo
https://arxiv.org/abs/2404.12988 <…

Understanding Intra-Household Educational Inequalities: Gender, Birth Order, and Ability Dynamics in Benin's Households
This paper investigates the nuanced interplay of gender, birth order, and innate ability in shaping educational disparities among children within households, employing both a reduced-form analysis and a structural model of household resource allocation. By decomposing overall disparities, I identify the contributions of gender, birth order, and innate ability differences. In the context of Benin, for households with non-educated heads and mixed-gender children, total inequality comprises 50% ge…