Multiple Linear Regressions by Maximizing the Likelihood under Assumption of Generalized Gauss-Laplace Distribution of the Error

Casorati Inequalities for Statistical Submanifolds in Kenmotsu Statistical Manifolds of Constant ϕ-Sectional Curvature with Semi-Symmetric Metric Connection

In this paper, we prove some inequalities between intrinsic and extrinsic curvature invariants, namely the normalized δ-Casorati curvatures and the scalar curvature of statistical submanifolds in Kenmotsu statistical manifolds of constant ϕ-sectional curvature that are endowed with semi-symmetric metric connection. Furthermore, we investigate the equality cases of these inequalities. We also describe an illustrative example.

Bayesian P-Splines Quantile Regression of Partially Linear Varying Coefficient Spatial Autoregressive Models

This paper deals with spatial data that can be modelled by partially linear varying coefficient spatial autoregressive models with Bayesian P-splines quantile regression. We evaluate the linear and nonlinear effects of covariates on the response and use quantile regression to present comprehensive information at different quantiles. We not only propose an empirical Bayesian approach of quantile regression using the asymmetric Laplace error distribution and employ P-splines to approximate nonparametric components but also develop an efficient Markov chain Monte Carlo technique to explore the joint posterior distributions of unknown parameters. Monte Carlo simulations show that our estimators not only have robustness for different spatial weight matrices but also perform better compared with quantile regression and instrumental variable quantile regression estimators in finite samples at different quantiles. Finally, a set of Sydney real estate data applications is analysed to illustrate the performance of the proposed method.

Radius of Star-Likeness for Certain Subclasses of Analytic Functions

In this paper, we investigate a normalized analytic (symmetric under rotation) function, f, in an open unit disk that satisfies the condition ℜfzgz>0, for some analytic function, g, with ℜz+1−2nzgz>0,∀n∈N. We calculate the radius constants for different classes of analytic functions, including, for example, for the class of star-like functions connected with the exponential functions, i.e., the lemniscate of Bernoulli, the sine function, cardioid functions, the sine hyperbolic inverse function, the Nephroid function, cosine function and parabolic star-like functions. The results obtained are sharp.

A Relation-Theoretic Metrical Fixed Point Theorem for Rational Type Contraction Mapping with an Application

In this article, we discuss the relation theoretic aspect of rational type contractive mapping to obtain fixed point results in a complete metric space under arbitrary binary relation. Furthermore, we provide an application to find a solution to a non-linear integral equation.

The Double Phospho/Dephosphorylation Cycle as a Benchmark to Validate an Effective Taylor Series Method to Integrate Ordinary Differential Equations

The double phosphorylation/dephosphorylation cycle consists of a symmetric network of biochemical reactions of paramount importance in many intracellular mechanisms. From a network perspective, they consist of four enzymatic reactions interconnected in a specular way. The general approach to model enzymatic reactions in a deterministic fashion is by means of stiff Ordinary Differential Equations (ODEs) that are usually hard to integrate according to biologically meaningful parameter settings. Indeed, the quest for model simplification started more than one century ago with the seminal works by Michaelis and Menten, and their Quasi Steady-State Approximation methods are still matter of investigation nowadays. This work proposes an effective algorithm based on Taylor series methods that manages to overcome the problems arising in the integration of stiff ODEs, without settling for model approximations. The double phosphorylation/dephosphorylation cycle is exploited as a benchmark to validate the methodology from a numerical viewpoint.

Fuzzy Sawi Decomposition Method for Solving Nonlinear Partial Fuzzy Differential Equations

The main goal of this paper is to propose a new decomposition method for finding solutions to nonlinear partial fuzzy differential equations (NPFDE) through the fuzzy Sawi decomposition method (FSDM). This method is a combination of the fuzzy Sawi transformation and Adomian decomposition method. For this purpose, two new theorems for fuzzy Sawi transformation regarding fuzzy partial gH-derivatives are introduced. The use of convex symmetrical triangular fuzzy numbers creates symmetry between the lower and upper representations of the fuzzy solution. To demonstrate the effectiveness of the method, a numerical example is provided.

Geometric Constants in Banach Spaces Related to the Inscribed Quadrilateral of Unit Balls

We introduce a new geometric constant Jin(X) based on a generalization of the parallelogram law, which is symmetric and related to the length of the inscribed quadrilateral side of the unit ball. We first investigate some basic properties of this new coefficient. Next, it is shown that, for a Banach space, Jin(X) becomes 16 if and only if the norm is induced by an inner product. Moreover, its properties and some relations between other well-known geometric constants are studied. Finally, a sufficient condition which implies normal structure is presented.

An Online Iterative Linear Quadratic Approach for a Satisfactory Working Point Attainment at FERMI

The attainment of a satisfactory operating point is one of the main problems in the tuning of particle accelerators. These are extremely complex facilities, characterized by the absence of a model that accurately describes their dynamics, and by an often persistent noise which, along with machine drifts, affects their behaviour in unpredictable ways. In this paper, we propose an online iterative Linear Quadratic Regulator (iLQR) approach to tackle this problem on the FERMI free-electron laser of Elettra Sincrotrone Trieste. It consists of a model identification performed by a neural network trained on data collected from the real facility, followed by the application of the iLQR in a Model-Predictive Control fashion. We perform several experiments, training the neural network with increasing amount of data, in order to understand what level of model accuracy is needed to accomplish the task. We empirically show that the online iLQR results, on average, in fewer steps than a simple gradient ascent (GA), and requires a less accurate neural network to achieve the goal.

The Censored Beta-Skew Alpha-Power Distribution

This paper introduces a new family of distributions for modelling censored multimodal data. The model extends the widely known tobit model by introducing two parameters that control the shape and the asymmetry of the distribution. Basic properties of this new family of distributions are studied in detail and a model for censored positive data is also studied. The problem of estimating parameters is addressed by considering the maximum likelihood method. The score functions and the elements of the observed information matrix are given. Finally, three applications to real data sets are reported to illustrate the developed methodology.

Solution of Some Impulsive Differential Equations via Coupled Fixed Point

In this article, we employ the notion of coupled fixed points on a complete b-metric space endowed with a graph to give sufficient conditions to guarantee a solution of system of differential equations with impulse effects. We derive recisely some new coupled fixed point theorems under some conditions and then apply our results to achieve our goal.

Slurry-phase ethylene polymerization processes: a review on multiscale modeling and simulations

Slurry polymerization processes using Zeigler–Natta catalysts, are most widely used for the production of polyethylene due to their several advantages over other processes. Significant advancements have been made in the modeling of these processes to obtain high-quality final products. The modeling work in this field has a very wide scope due to the great diversity of the catalyst types, polymerization processes, polymerization conditions, product qualities and microstructures that exist at the commercial scale. In this article, we have reviewed and discussed the slurry polymerization processes for the production of polyethylene and the multiscale modeling and simulation framework in slurry reactors. The multiscale modeling framework mainly comprises of the kinetic model, single-particle diffusion models, multiphase hydrodynamics, phase equilibria, reactor residence time distribution and the overall mass and heat balances. Guidelines to implement the multiscale mathematical modeling and simulation in slurry-phase olefin polymerization processes are proposed. Special focus is given on the need to reduce the computational effort for the simulation of industrial reactors so that the models can be used as an effective tool-kit for optimization studies using state-of-art algorithms.

A Philos-Type Oscillation Criteria for Fourth-Order Neutral Differential Equations

Some sufficient conditions are established for the oscillation of fourth order neutral differential equations of the form r t z ‴ t α ′ + q t x β σ t = 0 , where z t : = x t + p t x τ t . By using the technique of Riccati transformation and integral averaging method, we get conditions to ensure oscillation of solutions of this equation. Symmetry ideas are often invisible in these studies, but they help us decide the right way to study them, and to show us the correct direction for future developments. Moreover, the importance of the obtained conditions is illustrated via some examples.

Sugars and Sweeteners: Structure, Properties and In Silico Modeling

Several studies report the effects of excessive use of sugars and sweeteners in the diet. These include obesity, cardiac diseases, diabetes, and even lymphomas, leukemias, cancers of the bladder and brain, chronic fatigue syndrome, Parkinson's disease, Alzheimer's disease, multiple sclerosis, autism, and systemic lupus. On the other hand, each sugar and sweetener has a distinct metabolic assimilation process, and its chemical structure plays an important role in this process. Several scientific papers present the biological effects of the sugars and sweeteners in relation to their chemical structure. One important issue dealing with the sugars is the degree of similarity in their structures, focusing mostly on optical isomerism. Finding and developing new sugars and sweeteners with desired properties is an emerging research area, in which in silico approaches play an important role.

Exact Solutions to the Maxmin Problem max‖Ax‖ Subject to ‖Bx‖≤1

In this manuscript we provide an exact solution to the maxmin problem max ∥ A x ∥ subject to ∥ B x ∥ ≤ 1 , where A and B are real matrices. This problem comes from a remodeling of max ∥ A x ∥ subject to min ∥ B x ∥ , because the latter problem has no solution. Our mathematical method comes from the Abstract Operator Theory, whose strong machinery allows us to reduce the first problem to max ∥ C x ∥ subject to ∥ x ∥ ≤ 1 , which can be solved exactly by relying on supporting vectors. Finally, as appendices, we provide two applications of our solution: first, we construct a truly optimal minimum stored-energy Transcranian Magnetic Stimulation (TMS) coil, and second, we find an optimal geolocation involving statistical variables.

Some New Observations and Results for Convex Contractions of Istratescu’s Type

The purpose is to ensure that a continuous convex contraction mapping of order two in b-metric spaces has a unique fixed point. Moreover, this result is generalized for convex contractions of order n in b-metric spaces and also in almost and quasi b-metric spaces.

Key Factors Determining the Expected Benefit of Customers When Using Bank Cards: An Analysis on Millennials and Generation Z in Romania

The purpose of this article is to define the level of significance of the different indicators that influence the benefits expected by the customers when deciding on a bank card. The most important indicators that affect the expectations when using the bank card were considered: The level of the credit limit, the existence of rewards programs, the costs associated with the card, the existence of associated services of type e-banking/m-banking, the image and the social status, the possibility to perform ATM cash operations, customer service, ease of use and volume of information on the card. The research was carried out on a sample of 148 bank cardholders in Romania from the Millennials and Generation Z. The values of the indicators for different categories of users of bank cards and different age categories can be determined based on the obtained results and the tests performed. The determined values of the indicators represent the basic elements for building a regression model that will help bank managers to optimize their personalized offers in relation to customer expectations.

Medical Diagnostic Tests: A Review of Test Anatomy, Phases, and Statistical Treatment of Data

Diagnostic tests are approaches used in clinical practice to identify with high accuracy the disease of a particular patient and thus to provide early and proper treatment. Reporting high-quality results of diagnostic tests, for both basic and advanced methods, is solely the responsibility of the authors. Despite the existence of recommendation and standards regarding the content or format of statistical aspects, the quality of what and how the statistic is reported when a diagnostic test is assessed varied from excellent to very poor. This article briefly reviews the steps in the evaluation of a diagnostic test from the anatomy, to the role in clinical practice, and to the statistical methods used to show their performances. The statistical approaches are linked with the phase, clinical question, and objective and are accompanied by examples. More details are provided for phase I and II studies while the statistical treatment of phase III and IV is just briefly presented. Several free online resources useful in the calculation of some statistics are also given.