Novel numerical techniques for the finite moment log stable computational model for European call option

Option pricing models are often used to describe the dynamic characteristics of prices in financial markets. Unlike the classical Black–Scholes (BS) model, the finite moment log stable (FMLS) model can explain large movements of prices during small time steps. In the FMLS, the second-order spatial derivative of the BS model is replaced by a fractional operator of order α which generates an α-stable Lévy process. In this paper, we consider the finite difference method to approximate the FMLS model. We present two numerical schemes for this approximation: the implicit numerical scheme and the Crank–Nicolson scheme. We carry out convergence and stability analyses for the proposed schemes. Since the fractional operator routinely generates dense matrices which often require high computational cost and storage memory, we explore three methods for solving the approximation schemes: the Gaussian elimination method, the bi-conjugate gradient stabilized method (Bi-CGSTAB) and the fast Bi-CGSTAB (FBi-CGSTAB) in order to compare the cost of calculations. Finally, two numerical examples with exact solutions are presented where we also use extrapolation techniques to achieve higher-order convergence. The results suggest that the proposed schemes are unconditionally stable and convergent, and the FMLS model is useful for pricing options.     

Calculus rules of the generalized contingent derivative and applications to set-valued optimization

Positivity - In the paper, we develop sum and chain rules of the generalized contingent derivative for set-valued mappings. Then, their applications to sensitivity analysis and optimality...     

Stable Ti3+ Defects in Oriented Mesoporous Titania Frameworks for Efficient Photocatalysis

By introducing a compatible reducing agent (2‐ethylimidazole) into a mono‐micelle assembly process, we present a type of ordered mesoporous TiO₂ microspheres that combines radially aligned mesostructure with Ti³⁺ defects in mesoporous frameworks. Such reductant acts as a building block of mesostructured frameworks and reduces Ti⁴⁺ in situ to generate defects during calcination, giving rise to the coexistence of bulk Ti³⁺ defects and an ordered mesostructure. The mesoporous TiO₂ has both excellent mesoporosity (a high surface area of 106 m² g^?1, a mean pore size of 18.4 nm) and stable defects with an extended photoresponse. Such integration of unique mesoscopic architecture and atomic vacancies provide both effective mass transportation and enhanced light utilization, leading to a remarkable increase in H₂ generation rate. A maximum H₂ evolution rate of 19.8 mmol g^?1 h^?1 can be achieved, along with outstanding stability under solar light.     

An Improved Model for Polyether Production from 1,3‐Propanediol

A dynamic mathematical model is developed for production of Cerenol polyether from 1,3‐propanediol in a batch reactor system. The model accounts for polycondensation reactions and side reactions in the liquid phase and for mass transfer of volatile species to the vapor. Parameters are estimated using measured liquid‐phase concentrations of monomer, oligomers, water, and end groups as well as the mass and composition of condensate collected from the overhead condenser system. The proposed model uses novel probability factors to keep the model equations relatively simple while accounting for the complex influence of superacid catalyst on reaction rates. The model is a significant advance over previous Cerenol models because it better accounts for mass‐transfer rates and for the dynamic behavior of the condenser. In addition, the proposed model accounts for the inhibitory influence of water on polycondensation kinetics due to hydration of hydroxyl ends. The model equations and parameter estimates provide a substantial improvement in fit to the data, especially for long reaction times and high catalyst levels, resulting in a 97% reduction in the value of the weighted least squared objective function compared to equations and parameters from a previous model.     

Optimal Control of the Instationary Three Dimensional Navier-Stokes-Voigt Equations

We study an optimal control problem with quadratic objective functional for the three dimensional Navier-Stokes-Voigt equations in bounded domains. We show the existence of optimal solutions, the necessary optimality conditions and the sufficient optimality conditions. The second-order optimality conditions obtained in the article seem to be optimal.     

Levitin–Polyak well-posedness for strong bilevel vector equilibrium problems and applications to traffic network problems with equilibrium constraints

In this paper we consider strong bilevel vector equilibrium problems and introduce the concepts of Levitin–Polyak well-posedness and Levitin–Polyak well-posedness in the generalized sense for such problems. The notions of upper/lower semicontinuity involving variable cones for vector-valued mappings and their properties are proposed and studied. Using these generalized semicontinuity notions, we investigate sufficient and/or necessary conditions of the Levitin–Polyak well-posedness for the reference problems. Some metric characterizations of these Levitin–Polyak well-posedness concepts in the behavior of approximate solution sets are also discussed. As an application, we consider the special case of traffic network problems with equilibrium constraints.     

New Scalarizing Approach to the Stability Analysis in Parametric Generalized Ky Fan Inequality Problems

This paper gives sufficient conditions for the upper and lower semicontinuities of the solution mapping of a parametric mixed generalized Ky Fan inequality problem. We use a new scalarizing approach quite different from traditional linear scalarization approaches which, in the framework of the stability analysis of solution mappings of equilibrium problems, were useful only for weak vector equilibrium problems and only under some convexity and strict monotonicity assumptions. The main tools of our approach are provided by two generalized versions of the nonlinear scalarization function of Gerstewitz. Our stability results are new and are obtained by a unified technique. An example is given to show that our results can be applied, while some corresponding earlier results cannot.     

Effective magnetic monopoles and universal conductance fluctuations

The observation of isolated positive and negative charges, but not isolated magnetic north and south poles, is an old puzzle. Instead, evidence of effective magnetic monopoles has been found in the abstract momentum space. Apart from Hall-related effects, few observable consequences of these abstract monopoles are known. Here, we show that it is possible to manipulate the monopoles by external magnetic fields and probe them by universal conductance fluctuation measurements in ferromagnets with strong spin-orbit coupling. The observed fluctuations are not noise, but reproducible quasiperiodic oscillations as a function of magnetization direction, a novel Berry phase fingerprint of the magnetic monopoles.     

Existence and Exponential Decay of Solutions for a Wave Equation with Integral Nonlocal Boundary Conditions of Memory Type

In this paper, we consider a wave equation with integral nonlocal boundary conditions of memory type. First, we establish two local existence theorems by using Faedo–Galerkin method and standard arguments of density. Next, we give a su?cient condition to guarantee the global existence and exponential decay of weak solutions. Finally, we present numerical results.     

Unprecedented hour-long residence time of a cation in a left-handed G-quadruplex

Cations are critical for the folding and assembly of nucleic acids. In G-quadruplex structures, cations can bind between stacked G-tetrads and coordinate with negatively charged guanine carbonyl oxygens. They usually exchange between binding sites and with the bulk in solution with time constants ranging from sub-millisecond to seconds. Here we report the first observation of extremely long-lived K⁺ and NH₄⁺ ions, with an exchange time constant on the order of an hour, when coordinated at the center of a left-handed G-quadruplex DNA. A single-base mutation, that switched one half of the structure from left- to right-handed conformation resulting in a right–left hybrid G-quadruplex, was shown to remove this long-lived behaviour of the central cation.

An extremely long-lived cation has been detected in left-handed G-quadruplexes.