abstract

If a linear electron accelerator is installed into the SPPC (Super Proton–Proton Collider) complex, \(ep\) collision options will be available in addition to \(pp\) collisions. We consider the production of excited electrons with spin-1/2 at the future SPPC-based electron–proton colliders with center-of-mass energies of \(8.44\), \(11.66\), \(26.68\), and \(36.88\) TeV. In the \(ep\rightarrow e^{\star }X\rightarrow e\gamma X\) signal process, excited electrons are produced by contact interactions and decay into the photon channel by gauge interactions. Taking into account the corresponding background process, the pseudorapidity and transverse momentum distributions of the final-state particles are plotted. We reported on the discovery, observation, and exclusion mass limits of excited electrons by applying appropriate kinematical cuts best suited for amplifying the signal of the excited electron signature. We also investigated the highest achievable values of the compositeness scale for the discovery of excited electrons at these colliders.

abstract

Under the framework of non-extensive statistical mechanics, the optimal fund allocation of pension is studied by maximizing the expected utility of terminal wealth. In order to accurately approximate the actual financial market, the non-extensive statistical theory is employed to model prices of the risky asset, which can describe the high peak and fat tail characteristics of returns. Based on the criterion of maximizing the expected utility of terminal wealth, the Hamilton–Jacob–Bellman equation is established under the condition of the exponential utility function. Furthermore, using the duality theory, an analytical solution for the optimal investment strategy is obtained. Finally, the influence of the main model parameters on the optimal investment strategy is analyzed through numerical methods.

abstract

In th, and is study, the contact interaction search potential of the FCC-based electron–proton collider was investigated. The study was carried out by using electron–proton collisions at 3.16, 5.0, and 31.6 TeV center-of-mass energies and the cross sections of the collisions were obtained with the package of CalcHEP. The exclusion, observation, and exclusion limits were determined based on a search for deviation of the jet production cross section from the prediction of the Standard Model. The limits on the compositeness scales were obtained for constructive and destructive interferences of four different helicity structures (left–left, right–right, left–right, and right–left). The comparative analysis of the results presented in this study was performed with previous and future prospect collider options. The physics potential of the studied \(ep\) collider options was evaluated by considering different kinematic cuts and a wide range of luminosity values.

abstract

This paper presents an in-depth study of a concatenation model with power-law nonlinearity. The integral form of the original model is derived, and the corresponding dynamic system is obtained. A qualitative analysis is conducted to identify the types of equilibrium points, phase diagrams, and trajectories. From specific trajectories, we can infer that this equation has periodic and soliton solutions. To validate these conclusions, the corresponding exact solutions are constructed, and several new solutions are initially presented in this paper. Finally, by adding a specific external perturbation term, we found that this model also exhibits chaotic behavior, which is presented in this paper for the first time.