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In this paper, we study the uniqueness of nodal radial solutions to nonlinear elliptic equations in the unit ball in ℝ3$$ {\mathrm{\mathbb{R}}}^3 $$. Under suitable conditions, we prove that, for any given positive integer k$$ k $$, the problem we considered has at most one solution possessing exactly k−1$$ k-1 $$ nodes. Together with the results presented by Nagasaki [J. Fac. Sci. Univ. Tokyo Sect. IA Math. 36 (2): 211–232, 1989] and Tanaka [Proc. Roy. Soc. Edinburgh Sect. A. 138 (6): 1331–1343, 2008], we can prove that more types of nonlinear elliptic equations have the uniqueness of nodal radial solutions. [ABSTRACT FROM AUTHOR]

This study introduces a novel approach for synthesizing Benzoxazine‐centered Polychiral Polyheterocycles (BPCPHCs) via an innovative asymmetric carbene‐alkyne metathesis‐triggered cascade. Overcoming challenges associated with intricate stereochemistry and multiple chiral centers, the catalytic asymmetric Carbene Alkyne Metathesis‐mediated Cascade (CAMC) is employed using dirhodium catalyst/Brønsted acid co‐catalysis, ensuring precise stereo control as validated by X‐ray crystallography. Systematic substrate scope evaluation establishes exceptional diastereo‐ and enantioselectivities, creating a unique library of BPCPHCs. Pharmacological exploration identifies twelve BPCPHCs as potent Nav ion channel blockers, notably compound 8 g. In vivo studies demonstrate that intrathecal injection of 8 g effectively reverses mechanical hyperalgesia associated with chemotherapy‐induced peripheral neuropathy (CIPN), suggesting a promising therapeutic avenue. Electrophysiological investigations unveil the inhibitory effects of 8 g on Nav1.7 currents. Molecular docking, dynamics simulations and surface plasmon resonance (SPR) assay provide insights into the stable complex formation and favorable binding free energy of 8 g with C5aR1. This research represents a significant advancement in asymmetric CAMC for BPCPHCs and unveils BPCPHC 8 g as a promising, uniquely acting pain blocker, establishing a C5aR1‐Nav1.7 connection in the context of CIPN. [ABSTRACT FROM AUTHOR]

Graph similarity learning is a significant and fundamental issue in the theory and analysis of graphs, which has been applied in a variety of fields, including object tracking, recommender systems, similarity search, and so on. Recent methods for graph similarity learning that utilize deep learning typically share two deficiencies: (1) they leverage graph neural networks as backbones for learning graph representations but have not well captured the complex information inside data, and (2) they employ a cross-graph attention mechanism for graph similarity learning, which is computationally expensive. Taking these limitations into consideration, a method for graph similarity learning is devised in this study, namely, Contrastive Graph Similarity Network (CGSim). To enhance graph similarity learning, CGSim makes use of the complementary information of two input graphs and captures pairwise relations in a contrastive learning framework. By developing a dual contrastive learning module with a node-graph matching and a graph-graph matching mechanism, our method significantly reduces the quadratic time complexity for cross-graph interaction modeling to linear time complexity. Jointly learning in an end-to-end framework, the graph representation embedding module and the well-designed contrastive learning module can be beneficial to one another. A comprehensive series of experiments indicate that CGSim outperforms state-of-the-art baselines on six datasets and significantly reduces the computational cost, which demonstrates our CGSim model's superiority over other baselines. [ABSTRACT FROM AUTHOR]

In this paper, the nonlinear Schrödinger‐type equation −(∇+iA)2u+u+λIα∗K|u|2Ku=af(|u|)|u|uinℝ3$$ -{\left(\nabla + iA\right)}^2u+u+\lambda \left[{I}_{\alpha}\ast \left(K{\left|u\right|}^2\right)\right] Ku=a\frac{f\left(|u|\right)}{\mid u\mid }u\kern.5em \mathrm{in}\kern.5em {\mathrm{\mathbb{R}}}^3 $$is considered in the presence of magnetic field, where A∈C1(ℝ3,ℝ3)$$ A\in {C}^1\left({\mathrm{\mathbb{R}}}^3,{\mathrm{\mathbb{R}}}^3\right) $$, α∈(0,3)$$ \alpha \in \left(0,3\right) $$, Iα$$ {I}_{\alpha } $$ denotes the Riesz potential, K∈Lp(ℝ3)$$ K\in {L}^p\left({\mathrm{\mathbb{R}}}^3\right) $$ is a positive potential for some p∈(6/(1+α),∞]$$ p\in \left(6/\left(1+\alpha \right),\infty \right] $$, a∈Lq(ℝ3)\{0}$$ a\in {L}^q\left({\mathrm{\mathbb{R}}}^3\right)\backslash \left\{0\right\} $$ is a nonnegative potential for some q∈(3/2,∞]$$ q\in \left(3/2,\infty \right] $$, and f∈C(ℝ,[0,∞))$$ f\in C\left(\mathrm{\mathbb{R}},\right[0,\infty \left)\right) $$ is assumed to be asymptotically linear at infinity. Under suitable assumptions regarding A$$ A $$, K$$ K $$, a$$ a $$, and f$$ f $$, variational methods are used to establish the existence of ground‐state solutions of the above equation for sufficiently small values of the parameter λ$$ \lambda $$. [ABSTRACT FROM AUTHOR]