Generalized tachyonic dark energy

In this paper, a generalized tachyonic dark energy scenario is presented in the framework of a homogeneous and isotropic Friedmann–Lemaître–Robertson–Walker (FLRW) flat universe, in which a noncanonical scalar field is coupled to gravity nonminimally. By utilizing the Noether symmetry method, we found the explicit form of both potential density and coupling function, as a function of the scalar field. It is found that the tachyon field acts as the source of inflation and accelerates the evolution of the universe in the early times considerably. While, in the late times, gravitational sources are a pressureless matter field together with the tachyon field, which is the nature of dark energy and plays an essential role in the deceleration-acceleration phase transition of the universe. Further, the role of the coefficient function of tachyon potential, alongside the potential, is considered in the evolution of the universe. It is shown that this model involves a cosmological degeneracy in the sense that different coupling parameters and tachyonic potentials may be equivalent to the same cosmological standards such as the cosmic acceleration, age, equation of state and mean Hubble of the FLRW universe. The physical characteristics of the main cosmological observables are studied in detail, which suggests that the generalized tachyon field is a remarkable dark energy candidate.

Functional Regression

This chapter deals with the main theoretical fundamentals and practical issues of using functional regression in the context of genomic prediction. We explain how to represent data in functions by means of basis functions and considered two basis functions: Fourier for periodic or near-periodic data and B-splines for nonperiodic data. We derived the functional regression with a smoothed coefficient function under a fixed model framework and some examples are also provided under this model. A Bayesian version of functional regression is outlined and explained and all details for its implementation in glmnet and BGLR are given. The examples take into account in the predictor the main effects of environments and genotypes and the genotype × environment interaction term. The examples are done with small data sets so that the user can run them on his/her own computer and can understand the implementation process.

The Adaptive Damping Technique: Improving the Simulation Accuracy of Hydraulic Transients

Hydraulic surges are transient events frequently observed in various industrial and laboratory flow situations. Understanding surge physics and its accurate numerical prediction is crucial to the safety of flow systems. The maximum accuracy achievable for transient surge simulations is limited by the inefficiencies in the mathematical models used. In this work, we propose a mathematical model that incorporates an adaptive damping technique for the accurate prediction of hydraulic surges. This model also takes the compressibility effects in the liquid during the surge process into account. The novel approach of using the local pressure fluctuation data from the flow to adjust the unsteady friction for controlling the dissipation is introduced in this paper. The adaptive-dissipation is actualized through a unique 'variable pressure wave damping coefficient' function definition. Numerical simulation of three different valve-induced surge experiments demonstrates the reliability and robustness of the mathematical model. Numerical results from the proposed model show an excellent match with the experimental data by closely reproducing both the frequency and the amplitude of transient pressure oscillations. A comparative study explains the improvement in the simulation accuracy achieved by replacing the constant damping coefficient with the proposed variable coefficient. The superiority of the new model with the adaptive damping capability over the similar models in literature and those used in commercial software packages is also well established through this study.

Vertical Plane Buoyant Jets and Fountains in a Uniform Stagnant Ambient Revisited

Planar, vertical buoyant jets are of particular interest, both for research and practical purposes for being related to the disposal of the effluent from wastewater treatment plants or saline, a by-product from desalination plants into a body of stagnant fluid. Analytical, closed form solution is derived for plane buoyant jets based on a buoyant jet width parameter proposed by List and Imberger (1973), and compares to earlier laboratory experiments satisfactorily. The derived entrainment coefficient as a function of the local Richardson number of the flow, takes two asymptotic values for jet-like and plume-like flows, while in fountains it takes values lower than that in jets. Laboratory experiments were performed to measure the penetration height of vertical plane fountains with initial Froude number in the range 20 to 130 using shadowgraph and Planar Laser Induced Fluorescence (PLIF) techniques. Interest was focused on the maximum and terminal, steady-state penetration height before the flow direction reversed. The flow was found to be in a state of unstable equilibrium, as it deviated from the vertical axis, swinging on either side. The equations of motion have been solved numerically using the derived entrainment coefficient function, and the results are congruent to earlier and present experiment for vertical fountains.

A L1 Regularized Logistic Regression Model for Highdimensional Questionnaire Data Analysis

The LI regularization method, or Lasso, is a technique for feature selection in high-dimensional statistical analysis. This method compresses the coefficients of the model by using the absolute value of the coefficient function as a penalty term. By adding L1 regularization to log-likelihood function of Logistic model, variable screening method based on the logistic regression model can be realized. The process of variable selection via Lasso is illustrated in Figure 1. The purpose of the experiment is to figure out the important factors that influence interviewees' subjective well-being using L1 regularized logistic regression. Experiments have been performed on CGSS 2017 data. Important features have been successfully selected by using the L1 regularization method.

Ulam stability for nonautonomous quantum equations

We establish the Ulam stability of a first-order linear nonautonomous quantum equation with Cayley parameter in terms of the behavior of the nonautonomous coefficient function. We also provide details for some cases of Ulam instability.

Solving an inverse elliptic coefficient problem by convex non-linear semidefinite programming

Several applications in medical imaging and non-destructive material testing lead to inverse elliptic coefficient problems, where an unknown coefficient function in an elliptic PDE is to be determined from partial knowledge of its solutions. This is usually a highly non-linear ill-posed inverse problem, for which unique reconstructability results, stability estimates and global convergence of numerical methods are very hard to achieve. The aim of this note is to point out a new connection between inverse coefficient problems and semidefinite programming that may help addressing these challenges. We show that an inverse elliptic Robin transmission problem with finitely many measurements can be equivalently rewritten as a uniquely solvable convex non-linear semidefinite optimization problem. This allows to explicitly estimate the number of measurements that is required to achieve a desired resolution, to derive an error estimate for noisy data, and to overcome the problem of local minima that usually appears in optimization-based approaches for inverse coefficient problems.

A semi-analytic method to compute Feynman integrals applied to four-loop corrections to the $$ \overline{\mathrm{MS}} $$-pole quark mass relation

We describe a method to numerically compute multi-loop integrals, depending on one dimensionless parameter x and the dimension d, in the whole kinematic range of x. The method is based on differential equations, which, however, do not require any special form, and series expansions around singular and regular points. This method provides results well suited for fast numerical evaluation and sufficiently precise for phenomenological applications. We apply the approach to four-loop on-shell integrals and compute the coefficient function of eight colour structures in the relation between the mass of a heavy quark defined in the $$ \overline{\mathrm{MS}} $$ MS ¯ and the on-shell scheme allowing for a second non-zero quark mass. We also obtain analytic results for these eight coefficient functions in terms of harmonic polylogarithms and iterated integrals. This allows for a validation of the numerical accuracy.

A Constructive Approach About the Existence of Positive Solutions for Minkowski Curvature Problems

In this paper, we give an existence theorem about positive solutions for the Dirichlet boundary value problem of one dimensional Minkowski curvature equations. We apply the theorem to one parameter family of problems to investigate a constructive method for numerical range of parameters where positive solutions exist. Moreover, we establish a nonexistence theorem of positive solutions for the corresponding one parameter family of problems. The coefficient function may be singular at the boundary and nonlinear term satisfies a sublinear growth condition. Main argument for the proof of existence theorem is employed by Krasnoselskii’s theorem of cone expansion and compression. We give a numerical algorithm and various examples to illustrate numerical information about ranges of the existence and nonexistence parameters which have been given only in a theoretical manner so far.

Method for synthesis of matching devices for broadband radio engineering systems with unstable load impedance based on the method of real frequencies

The aim of this work is to develop a method for the synthesis of matching devices for broadband radio engineering systems with varying impedance in different operating conditions. To achieve this goal, a criterion (complex criterion) is proposed for minimizing the value of the modulus of the sensitivity invariant of the reflection coefficient function to a change in the load impedance with restrictions on the square of the deviation of the power transmission ratio from a given level. It is proposed to use a combination of methods of real frequencies together with the shown complex criterion, which made it possible to implement an effective approach to the synthesis of matching devices for broadband radio engineering systems with an unstable load impedance. To verify the approach, a matching device was synthesized, which made it possible to reduce the loss of the power transmission factor level transmitted to the UHF/VHF antenna of the AD-44 / CW-TA-30-512 range when it is located in various operating conditions by at least 50 % in relation to losses obtained with a standard matching device.