Financial market and pricing of emerging financial derivatives: A mathematical approach

Pricing has been one of the key problems of financial market theory. With the development of the modern financial market, various new financial derivatives have been created and need to be priced properly. In the thesis, we are going to use several mathematical tools to investigate the essential structure of the financial market and models for financial derivatives

A (2+1)-dimensional sine-Gordon and sinh-Gordon equations with symmetries and kink wave solutions

In this paper, a (2+1)-dimensional sine-Gordon equation and a sinh-Gordon equation are derived from the well-known AKNS system. Based on the Hirota bilinear method and Lie symmetry analysis, kink wave solutions and travelingwave solutions of the (2+1)-dimensional sine-Gordon equation are constructed. The traveling wave solutions of the (2+1)-dimensional sinh-Gordon equation can also be provided in a similar manner. Meanwhile, conservation laws are derived

Disorder induced multifractal superconductivity in monolayer niobium dichalcogenides

The interplay between disorder and superconductivity is a subtle and fascinating phenomenon in quantum many body physics. The conventional superconductors are insensitive to dilute nonmagnetic impurities, known as the Anderson's theorem. Destruction of superconductivity and even superconductor-insulator transitions occur in the regime of strong disorder. Hence disorder-enhanced superconductivity is rare and has only been observed in some alloys or granular states. Because of the entanglement of various effects, the mechanism of enhancement is still under debate. Here we report well-controlled disorder effect in the recently discovered monolayer NbSe$_2$ superconductor. The superconducting transition temperatures of NbSe$_2$ monolayers are substantially increased by disorder. Realistic theoretical modeling shows that the unusual enhancement possibly arises from the multifractality of electron wave functions. This work provides the first experimental evidence of the multifractal superconducting state

Neuromorphic Computing-Assisted Triboelectric Capacitive-Coupled Tactile Sensor Array for Wireless Mixed Reality Interaction.

Flexible tactile sensors show promise for artificial intelligence applications due to their biological adaptability and rapid signal perception. Triboelectric sensors enable active dynamic tactile sensing, while integrating static pressure sensing and real-time multichannel signal transmission is key for further development. Here, we propose an integrated structure combining a capacitive sensor for static spatiotemporal mapping and a triboelectric sensor for dynamic tactile recognition. A liquid metal-based flexible dual-mode triboelectric-capacitive-coupled tactile sensor (TCTS) array of 4 × 4 pixels achieves a spatial resolution of 7 mm, exhibiting a pressure detection limit of 0.8 Pa and a fast response of 6 ms. Furthermore, neuromorphic computing using the MXene-based synaptic transistor achieves 100% recognition accuracy of handwritten numbers/letters within 90 epochs based on dynamic triboelectric signals collected by the TCTS array, and cross-spatial information communication from the perceived multichannel tactile data is realized in the mixed reality space. The results illuminate considerable application possibilities of dual-mode tactile sensing technology in human-machine interfaces and advanced robotics