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Quantum field theories can be applied to compute various statistical properties of random tensors. In particular, signed distributions of tensor eigenvalues/vectors are the easiest, which can be computed as partition functions of four-fermi theories. Though signed distributions are different from genuine ones because of extra signs of weights, they are expected to coincide in vicinities of ends of distributions. In this paper, we perform a case study of the signed eigenvalue/vector distribution of the real symmetric order-three random tensor. The correct critical point and the correct end in the large N limit are obtained from the four-fermi theory, for which a method using the Schwinger-Dyson equation is very efficient. Since locations of ends are particularly important in applications, such as the largest eigenvalues and the best rank-one tensor approximations, signed distributions are the easiest and highly useful through the Schwinger-Dyson method. [ABSTRACT FROM AUTHOR]

In this paper, we present a new simple method for solving two integral equations of Love's type that have many applications, especially in electrostatic systems. The approach of the solution is based on an innovative technique using matrix algebra for the barycentric Lagrange interpolation. The unknown function is expressed through the product of four matrices. The kernel is interpolated twice, so we get it in the product of five matrices. Additionally, we derive an equivalent linear algebraic system to the solution by substituting the matrix-vector barycentric interpolated unknown function together with the double interpolated kernel into both sides of the integral equation. Thus, there was no need to employ the collocation method. The obtained results converge strongly with the approximate analytical solutions, in addition to being uniformly approximated, continuous, and even, which proves the validity of the solution by the presented method. [ABSTRACT FROM AUTHOR]

Regime-switching models have been heavily studied recently, as they have some clear advantages of over other non-constant volatility model to resolve the so-called smirk effect displayed when constant volatility models are used to price financial derivatives such as options. However, due to the increased model complexity, the associated computational effort usually increases as well, particularly when they are used to price American-style options. In this paper, a novel computational approach based on integral equations is presented. A distinctive feature of our approach, in comparison with other numerical approaches, is that the coupled partial differential equations (PDEs) in a PDE system have been decoupled in the Fourier space, resulting in a completely decoupled integral equation for each economical states, and thus has greatly reduced computational effort. Some examples with preliminary results for a two-state regime-switching model are used to demonstrate our approach. [ABSTRACT FROM AUTHOR]

New propulsion systems in aircrafts must meet strict regulations and emission limitations. The Flightpath 2050 goals set by the Advisory Council for Aviation Research and Innovation in Europe (ACARE) include reductions of 75%, 90%, and 65% in CO2, NOx, and noise, respectively. These goals are not fully satisfied by marginal improvements in gas turbine technology or aircraft design. A novel control design procedure for the next generation of turbofan engines is proposed in this paper to improve Full Authority Digital Engine Control (FADEC) systems and reduce the emission levels to meet the Flightpath 2050 regulations. Hence, an Adaptive Network–based Fuzzy Inference System (ANFIS), nonlinear autoregressive network with exogenous inputs (NARX) techniques, and the block-structure Hammerstein–Wiener approach are used to develop a model for a turbofan engine. The Min–Max control structure is chosen as the most widely used practical control algorithm for gas turbine aero engines. The objective function is considered to minimize the emission level for the engine in a pre-defined maneuver while keeping the engine performance in different aspects. The Genetic Algorithm (GA) is applied to find the optimized control structure. The results confirm the effectiveness of the proposed approach in emission reduction for the next generation of turbofan engines. [ABSTRACT FROM AUTHOR]

Queueing systems are modeled by equations which depend on a large number of input parameters. In practice, significant uncertainty is associated with estimates of these parameters, and this uncertainty must be considered in the analysis of the model. The objective of this paper is to propose a sensitivity analysis approach for a queueing model, presenting parameters that follow a Gaussian distribution. The approach consists in decomposing the output of the model (stationary distribution of the model) into a polynomial chaos. The sensitivity indices, allowing to quantify the contribution of each parameter to the variance of the output, are obtained directly from the coefficients of decomposition. The proposed approach is then applied to M/G/1/N queueing model. The most influential parameters are highlighted. Finally several numerical and data examples are sketched out to illustrate the accuracy of the proposed method and compare them with Monte Carlo simulation. The results of this work will be useful to practitioners in various fields of theoretical and applied sciences. [ABSTRACT FROM AUTHOR]

In this paper, we describe new hybrid genetic algorithm and particle swarm optimization to solve the sum of earliness and the number of tardy job on two-machines flow shop schedule problem is NP- hard. The study discusses a hybrid genetic algorithm and particle swarm optimization (HGA-PSO) to tackle the presented mission. Extensive experiments, based on computers, suggest that the proposed mathematical models are efficient in solving flow shop problems with GA solved to n = 3000 while PSO solved to n = 500 job. [ABSTRACT FROM AUTHOR]

The benefit of this paper is to find the circular divison of the factor group when r is an odd number, where Q2r is denoted to Quaternion group of order 4r, such that for each positive integer r, there are two generators a and b for Q2r satisfies Q2r = {ah bk, 0 ≤ h ≤ 2r − 1, k = 0, 1} which has the following properties {a2r = b4 = I, barb−1 = a−r}. [ABSTRACT FROM AUTHOR]