An effective approach for numerical solution of linear and nonlinear singular boundary value problems

In this study, an effective approach is presented to obtain a numerical solution of linear and nonlinear singular boundary value problems. The proposed method is constructed by combining reproducing kernel and Legendre polynomials. Legendre basis functions are used to get the kernel function, and then the approximate solution is obtained as a finite series sum. Comparison of numerical results is made with the results obtained by other methods available in the literature. Furthermore, efficiency and accuracy of the method are demonstrated in tabulated results and plotted graphs. The numerical outcomes demonstrate that our method is very effective, applicable, and convenient.     

On the Singular Set of Free Interface in an Optimal Partition Problem

We study the singular set of free interface in an optimal partition problem for the Dirichlet eigenvalues. We prove that its upper (n − 2) -dimensional Minkowski content, and consequently its (n − 2) -dimensional Hausdorff measure, are locally finite. We also show that the singular set is countably (n − 2) -rectifiable; namely, it can be covered by countably many C¹ -manifolds of dimension (n − 2) , up to a set of (n − 2) -dimensional Hausdorff measure zero. Our results hold for optimal partitions on Riemannian manifolds and harmonic maps into homogeneous trees as well. © 2019 Wiley Periodicals, Inc.     

Pointwise Comparison of PCM and Σ Δ Quantization

A quantitative comparison of Pulse Code Modulation (PCM) and Sigma–Delta (Σ Δ) quantization methods is made in the setting of finite frames. Frames allow for redundant, overcomplete signal decompositions. PCM and Σ Δ are two industry-standard quantization methods, and the setting of finite frames is appropriate for a host of modern applications. Previous results for this comparison are known for upper error bounds, where Σ Δ performs better in the setting of frames, as opposed to orthonormal bases, where PCM is optimal. We answer the following question: For which signals x is the PCM error, that is, the norm of the difference between x and its PCM approximant, less than the Σ Δ error? We prove that, typically, in the setting of frames, Σ Δ outperforms PCM, but not always.     

An experimental and three dimensional numerical study on the wind-related heat transfer from a rectangular flat plate model collector flush mounted on the roof of a model house

Experimental and three dimensional numerical work was performed to evaluate the average heat transfer coefficients for forced convection heat transfer from the surface of a rectangular flat plate model collector flush mounted on the roof of a model residential house. Examined parameters are the roof tilt angle, windward and leeward orientations. Experiments were carried out for mass transfer using the naphthalene sublimation technique. The final results were presented in terms of heat transfer parameters using the analogy between heat and mass transfer. Numerical study was performed using Ansys Fluent 6.3. Results of experimental study are in good agreement with that of numerical study. It is observed that heat transfer coefficient decreases very slowly with increasing angle of attack and it can be stated that angle of attack does not have a strong effect on heat transfer coefficients in the range investigated. It is also observed that heat transfer coefficients on the leeward orientation are lower than those of the windward orientation. Flow separation was observed on collector surface in leeward orientation.     

Spectrophotometric multicomponent determination of sunset yellow, tartrazine and allura red in soft drink powder by double divisor-ratio spectra derivative, inverse least-squares and principal component regression methods

Double divisor-ratio spectra derivative (graphical method), classical least-squares and principal component regression (two numerical methods) methods were developed for the spectrophotometric multicomponent analysis of soft drink powders and synthetic mixtures containing three colorants without any chemical separation. The graphical method is based on the use of derivative signals of the ratio spectra using double divisor. In this method, the linear determination ranges were 2-8 mug ml(-1) sunset yellow, 4-18 mug ml(-1) tartrazine and 2-8 mug ml(-1) allura red in 0.1 M HCl. In the numerical methods, a training set was randomly prepared by using 18 samples containing between 0 and 8 mug ml(-1) of sunset yellow, 0-18 mug ml(-1) of tartrazine and 0-8 mug ml(-1) of allura red. The chemometric calibrations were calculated by using the prepared training set and its absorbances at seven points (from 375.0 to 550.0 nm) in the spectral region 325-584 nm. The proposed methods were validated by using synthetic ternary mixtures and applied to the simultaneous determination of three colorants in soft drink powders. The obtained results were statistically compared with each other.     

N—H⋯N and C—H⋯π inter­actions in 4‐amino‐3‐methyl‐5‐(p‐tol­yl)‐4H‐1,2,4‐triazole and 4‐amino‐3‐methyl‐5‐phenyl‐4H‐1,2,4‐triazole

The title compounds, C₁₀H₁₂N₄, (I), and C₉H₁₀N₄, (II), have been synthesized and characterized both spectroscopically and structurally. The dihedral angles between the triazole and benzene ring planes are 26.59 (9) and 42.34 (2)°, respectively. In (I), mol­ecules are linked principally by N—H⋯N hydrogen bonds involving the amino NH₂ group and a triazole N atom, forming R₄⁴(20) and R₂⁴(10) rings which link to give a three‐dimensional network of mol­ecules. The hydrogen bonding is supported by two different C—H⋯π inter­actions from the tolyl ring to either a triazole ring or a tolyl ring in neighboring mol­ecules. In (II), inter­molecular hydrogen bonds and C—H⋯π inter­actions produce R₃⁴(15) and R₄⁴(21) rings.     

Function Computation under Privacy,Secrecy, Distortion,and Communication Constraints

The problem of reliable function computation is extended by imposing privacy, secrecy, and storage constraints on a remote source whose noisy measurements are observed by multiple parties. The main additions to the classic function computation problem include (1) privacy leakage to an eavesdropper is measured with respect to the remote source rather than the transmitting terminals’ observed sequences; (2) the information leakage to a fusion center with respect to the remote source is considered a new privacy leakage metric; (3) the function computed is allowed to be a distorted version of the target function, which allows the storage rate to be reduced compared to a reliable function computation scenario, in addition to reducing secrecy and privacy leakages; (4) two transmitting node observations are used to compute a function. Inner and outer bounds on the rate regions are derived for lossless and lossy single-function computation with two transmitting nodes, which recover previous results in the literature. For special cases, including invertible and partially invertible functions, and degraded measurement channels, simplified lossless and lossy rate regions are characterized, and one achievable region is evaluated as an example scenario.     

An Analytical Solution and Nonlinear Regression Analysis for Sandface Temperature Transient Data in the Presence of a Near-Wellbore Damaged Zone

Throughout this study, we present a dual-continuum model of transport of the natural gas in shale formations. The model includes several physical mechanisms such as diffusion, adsorption and rock stress sensitivity. The slippage has a clear effect in the low-permeability formations which can be described by the apparent permeability. The adsorption mechanism has been modeled by the Langmuir isotherm. The porosity-stress model has been used to describe stress state of the rocks. The thermodynamics deviation factor is calculated using the equation of state of Peng–Robinson. The governing differential system has been solved numerically using the mixed finite element method (MFEM). The stability of the MFEM has been investigated theoretically and numerically. A semi-implicit scheme is employed to solve the two coupled pressure equations, while the thermodynamic calculations are conducted explicitly. Moreover, numerical experiments are performed under the corresponding physical parameters of the model. Some represented results are shown in graphs including the rates of production as well as the pressures and the apparent permeability profiles.

     

Information and preference reversals in lotteries

Several approaches have been proposed for evaluating information in expected utility theory. Among the most popular approaches are the expected utility increase, the selling price and the buying price. While the expected utility increase and the selling price always agree in ranking information alternatives, Hazen and Sounderpandian [11] have demonstrated that the buying price may not always agree with the other two. That is, in some cases, where the expected utility increase would value information A more highly than information B, the buying price may reverse these preferences. In this paper, we discuss the conditions under which all these approaches agree in a generic decision environment where the decision maker may choose to acquire arbitrary information bundles.     

Synthesis of palladium complexes derived from imidazolidin‐2‐ylidene ligands and used for catalytic amination reactions

N‐Aryl amination and the Buchwald–Hartwig reaction are of great synthetic and industrial interest and scientists accept their usefulness and versatility for obtaining arylamines. In this study Ag–N‐heterocyclic carbene complexes were used as transmetallation reagents for the synthesis of Pd–N‐heterocyclic carbene complexes. The new Pd–N‐heterocyclic carbene complexes were characterized using elemental analysis and ¹H NMR, ¹³C NMR and infrared spectroscopies. The crystal structure of one, namely dichlorobis[1,3‐bis(2‐methylbenzyl)imidazolidin‐2‐yliden]palladium(II), is presented. The activity of the Pd(II) complexes in the coupling reaction of anilines or amines with bromobenzene was investigated. These complexes exhibited high catalytic activities in the direct synthesis of triarylamines and secondary amines in a single step. Copyright © 2016 John Wiley & Sons, Ltd.