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On concatenations of two $k$-generalized Lucas numbers
Alex Behakanira Tumwesigye, Mahadi Ddamulira, Prosper Kaggwa
https://arxiv.org/abs/2509.24057 https://

On concatenations of two $k$-generalized Lucas numbers
For an integer \( k \geq 2 \), the sequence of \( k \)-generalized Lucas numbers is defined by the recurrence relation \( L_n^{(k)} = L_{n-1}^{(k)} + \cdots + L_{n-k}^{(k)} \) for all \( n \geq 2 \), with initial conditions \( L_0^{(k)} = 2 \), \( L_1^{(k)} = 1 \) for all \( k \geq 2 \), and \( L_{2-k}^{(k)} = \cdots = L_{-1}^{(k)} = 0 \) for \( k \geq 3 \). In this paper, we determine all \( k \)-generalized Lucas numbers that are concatenations of two terms of the same sequence and completely…

Q&A with Francis Dufay, CEO of Jumia, Africa's largest e-commerce platform, on Temu and other rivals, adding Chinese sellers to stay competitive, AI, and more (Damilare Dosunmu/Rest of World)
https://restofworld.org/2025/jumia-temu-shein-africa/

How Africa’s e-commerce giant is fighting off Shein and Temu
Jumia is capitalizing on the U.S.-China trade war as Chinese vendors are exploring new avenues to route their products into markets such as Nigeria and Côte d'Ivoire.

Gap Inhomogeneity in Cuprates: a view from Two-Dimensional Josephson Echo Spectroscopy
Alex G\'omez Salvador, Ivan Morera, Marios H. Michael, Pavel E. Dolgirev, Danica Pavicevic, Albert Liu, Andrea Cavalleri, Eugene Demler
https://arxiv.org/abs/2509.23856

Gap Inhomogeneity in Cuprates: a view from Two-Dimensional Josephson Echo Spectroscopy
Novel theoretical developments have allowed to connect microscopic disorder in bosonic collective excitations to the signatures in two-dimensional terahertz spectroscopy (Gómez Salvador et al. 2025). Here, we employ this framework to analyze the recently measured Josepshon echoes in optimally doped La$_{2-x}$Sr$_x$CuO$_4$ (Liu et al. 2024). We consider the spatial gap inhomogeneities -observed in scanning tunneling microscopy- as input for the disorder in the superfluid density, and compute th…

Momentum-resolved two-dimensional spectroscopy as a probe of nonlinear quantum field dynamics
Duilio De Santis, Alex G\'omez Salvador, Nataliia Bazhan, Sebastian Erne, Maximilian Pr\"ufer, Claudio Guarcello, Davide Valenti, J\"org Schmiedmayer, Eugene Demler
https://arxiv.org/abs/2509.25147

Momentum-resolved two-dimensional spectroscopy as a probe of nonlinear quantum field dynamics
Emergent collective excitations constitute a hallmark of interacting quantum many-body systems, yet in solid-state platforms their study has been largely limited by the constraints of linear-response probes and by finite momentum resolution. We propose to overcome these limitations by combining the spatial resolution of ultracold atomic systems with the nonlinear probing capabilities of two-dimensional spectroscopy (2DS). As a concrete illustration, we analyze momentum-resolved 2DS of the quant…

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