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This https://arxiv.org/abs/2407.15742 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

New solutions for the Lane-Emden problem on planar domains
We consider the Lane-Emden problem on planar domains. When the exponent is large, the existence and multiplicity of solutions strongly depend on the geometric properties of the domain, which also deeply affect their qualitative behavior. Remarkably, a wide variety of solutions, both positive and sign-changing, have been found when the exponent is sufficiently large. In this paper, we focus on this topic and fine new sign-changing solutions that exhibit an unexpected concentration phenomenon as …

Existence and Nonexistence of Extremals for Trudinger-Moser inequalities with $L^p$ type perturbation on any bounded planar domains
Lu Chen, Rou Jiang, Guozhen Lu, Maochun Zhu
https://arxiv.org/abs/2506.23076

Existence and Nonexistence of Extremals for Trudinger-Moser inequalities with $L^p$ type perturbation on any bounded planar domains
In this study, we investigate the perturbed Trudinger-Moser inequalities as follows:\[ S_Ω(λ,p)=\sup_{u\in H_{0}^{1}(Ω),\Vert\nabla u\Vert _{L^{2}\left( Ω\right) }\leq 1}\int_Ω\left( e^{4πu^{2}}-λ|u|^{p}\right) dx, \] where $1\leq p<\infty$ and $Ω$ is a bounded domain in $\mathbb{R}^2$. Our results demonstrate that there exists a threshold $λ^{\ast}(p)>0$ such that $S_Ω(λ,p)$ is attainable if $λ<λ^{\ast}(p)$, but unattainable if $λ>λ^{\ast}(p)$ when $p\in[1,2]$. For $p>…

Measuring Cyclic Tensile Properties of Fluids with Composite Harmonic Exponential Waveforms (CHEW)
L. A. Kroo, R. A. Nicholson, M. W Boehm, S. K. Baier, P. A. Underhill, G. H. McKinley
https://arxiv.org/abs/2506.16747

Measuring Cyclic Tensile Properties of Fluids with Composite Harmonic Exponential Waveforms (CHEW)
Building off recent advances on how to practically use exponential shear in a torsional rheometer to compute transient planar extensional viscosity (Kroo et al. 2025a), we extend the technique to cyclic tensile measurements in complex fluids and soft solids. An novel input strain waveform provides a unifying approach that smoothly interpolates between exponential shear (ES) and oscillatory shear (SAOS/MAOS/LAOS) as a flow type parameter is varied. Analogous to cyclic tensile fatigue tests in so…

A polynomial delay algorithm generating all potential maximal cliques in triconnected planar graphs
Alexander Grigoriev, Yasuaki Kobayashi, Hisao Tamaki, Tom C. van der Zanden
https://arxiv.org/abs/2506.12635

A polynomial delay algorithm generating all potential maximal cliques in triconnected planar graphs
We develop a new characterization of potential maximal cliques of a triconnected planar graph and, using this characterization, give a polynomial delay algorithm generating all potential maximal cliques of a given triconnected planar graph. Combined with the dynamic programming algorithms due to Bouchitt{é} and Todinca, this algorithm leads to a treewidth algorithm for general planar graphs that runs in time linear in the number of potential maximal cliques and polynomial in the number of vert…

This https://arxiv.org/abs/2408.06616 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Gromov-Witten invariants in family and quantum cohomology
A moduli space of stable maps to the fibers of a fiber bundle is constructed. The new moduli space is a family version of the classical moduli space of stable maps to a non-singular complex projective variety. The virtual cycle for this moduli space is also constructed, and an analogue of Gromov-Witten invariants is defined. As an application, we recover the formula for the number of rational degree d curves in P3, whose image lies in a plane in P3 (known as planar curves in P3), intersecting r…

A unifying perspective on measuring transient planar extensional viscosity from exponential shear
L. A. Kroo, R. A. Nicholson, M. W Boehm, S. K. Baier, G. H. McKinley
https://arxiv.org/abs/2506.16667

A unifying perspective on measuring transient planar extensional viscosity from exponential shear
Here we present an experimentally practical and robust method to compute the transient extensional viscosity from exponential shear on a wide variety of viscoelastic complex fluids. To achieve this, we derive an analytical, frame-invariant continuum solution for the exponential shear material function, valid over all Weissenberg numbers. Specifically, we amend the original framework of Doshi and Dealy proposed in 1987 to explicitly address the effect of rotation of material elements, due to the…