Structure formation in turbulence as an instability of effective quantum plasma

Structure formation in turbulence can be understood as an instability of “plasma” formed by fluctuations serving as effective particles. These “particles” are quantumlike in the sense that their wavelengths are non-negligible compared to the sizes of background coherent structures. The corresponding “kinetic equation” describes the Wigner matrix of the turbulent field, and the coherent structures serve as collective fields. This formalism is usually applied to manifestly quantumlike or scalar waves. Here, we show how to systematically extend it to more complex systems using compressible Navier–Stokes turbulence as an example. In this case, the fluctuation Hamiltonian is a five-dimensional matrix operator and diverse modulational modes are present. As an illustration, we calculate these modes for a sinusoidal shear flow and find two modulational instabilities. One of them is specific to supersonic flows, and the other one is a Kelvin–Helmholtz-type instability that is a generalization of the known zonostrophic instability. Our calculations are readily extendable to other types of turbulence, for example, magnetohydrodynamic turbulence in plasma.     

Utility maximization problem with random endowment and transaction costs: when wealth may become negative

In this article, we study the problem of maximizing expected utility from the terminal wealth with proportional transaction costs and random endowment. In the context of the existence of consistent price systems, we consider the duality between the primal utility maximization problem and the dual one, which is set up on the domain of finitely additive measures. In particular, we prove duality results for utility functions supporting possibly negative values. Moreover, we construct a shadow market by the dual optimal process and consider the utility-based pricing for random endowment.     

Summability in of a vector measure

We show a picture of the relations among different types of summability of series in the space  of integrable functions with respect to a vector measure m of relatively norm compact range. In order to do that, we study the class of the so‐called m‐1‐summing operators. We give several applications regarding the existence of copies of c ₀ in , as well as on m‐1‐summing operators which are weakly compact, Asplund or weakly precompact.     

Optimal investment strategies for participating contracts

Participating contracts are popular insurance policies, in which the payoff to a policyholder is linked to the performance of a portfolio managed by the insurer. We consider the portfolio selection problem of an insurer that offers participating contracts and has an S-shaped utility function. Applying the martingale approach, closed-form solutions are obtained. The resulting optimal strategies are compared with portfolio insurance hedging strategies (CPPI and OBPI). We also study numerical solutions of the portfolio selection problem with constraints on the portfolio weights.     

Modeling contribution behavior in fundraising: Segmentation analysis for a public broadcasting station

Funding pressures have forced many not-for-profit organizations to reduce their reliance on mass-marketing efforts, e.g., pledge drives, and increase the volume and sophistication of their direct marketing activities. The efficiency of direct marketing, however, is linked to an organization’s ability to target population segments effectively, which, in turn, has motivated the development of methodological approaches for market segmentation.     

Optimization of heterogeneous Catalyst-assisted fatty acid methyl esters biodiesel production from Soybean oil with different Machine learning methods

There is a growing attention to the bio and renewable energies due to fast depletion of fossil fuels as well as the global warming problem. Here, we developed a modeling and simulation method by means of artificial intelligence (AI) for prediction of the bioenergy production from vegetable bean oil. AI methods are well known for prediction of complex and nonlinear process. Three distinct Adaptive Boosted models including Huber regression, LASSO, and Support Vector Regression (SVR) as well as artificial neural network (ANN) were applied in this study to predict actual yield of Fatty acid methyl esters (FAME) production. All boosted utilizing the Adaptive boosting algorithm. The important influencing parameters on the biodiesel production such as the catalyst loading (CAO/Ag, wt%) and methanol to oil (Soybean oil) molar ratio were selected as the input variables of models while the yield of FAME production was selected as output. Model hyper-parameters were tuned to maintain generality while improving prediction accuracy. The models were evaluated using three distinct metrics Mean Absolute Error (MAE), Root Mean Square Error (RMSE), and R². Error rates of 8.16780E-01, 4.43895E-01, 2.06692E + 00, and 3.92713 E-01 were obtained with the MAE metric for boosted Huber, SVR, LASSO and ANN models. On the other hand, the RMSE error of these models were about 1.092E-02, 1.015E-02, 2.669E-02, and 1.01174E-02, respectively. Finally, the R-square score were calculated for boosted Huber, boosted SVR, and boosted LASSO as 0.976, 0.990, 0.872, and 0.99702, respectively. Therefore, it can be concluded that although the boosted SVR and ANN models were better models for prediction of process efficiency in terms of error, but all algorithms had high accuracy. The optimum yield of 83.77% and 81.60% for biodiesel production were observed at optimum operating values from boosted SVR and ANN models, respectively.