Narrow Results

In this paper, we obtain $L^{\infty }$ estimate for the Maxwell–Higgs system in the exterior region of Reissner–Nordström spacetimes. Utilizing the integrated local energy decay estimate, the Sobolev embedding theorem alongside the Gagliardo–Nirenberg–Sobolev inequality on compact Riemannian manifold, we derive the boundedness for $L^{\infty }$ norm of the Maxwell–Higgs system on Reissner–Nordström geometry.

In this paper, back-propagation (BP) neural network model with 8 hidden layers and 10 neurons was utilized to estimate corrosion behaviors of Ni-TiN coatings, deposited through pulse electrodeposition. Effects of plating parameters, namely, pulse frequency, TiN concentration and current density, on Ni-TiN coatings weight losses were discussed. Results indicated that pulse frequency, TiN concentration and current density had significant effects on weight losses of Ni-TiN coatings. Maximum mean square error of BP model was 9.10%, and this verified that the BP neural network model could accurately estimate corrosion behavior of Ni-TiN coatings. The coating fabricated at pulse frequency of 500Hz, TiN particle concentration of 8g/L and current density of 4A/dm² consisted of fine grains and compact oxides, demonstrating that the coating displayed best corrosion resistance in this corrosion test. Concentrations of Ti and Ni in Ni-TiN coating prepared at pulse frequency of 500Hz, TiN particle concentration of 8g/L and current density of 4A/dm² were 18.6at.% and 55.4at.%, respectively.

For $n\in \mathbb{N}$ the $n$th alternating harmonic number

The following sections are included:

• INTRODUCTION

• POINT ESTIMATION
  • Point Estimate, Estimator, and Estimation
  • Four Important Properties of Estimators
  • Mean-Squared Error for Choosing Point Estimator

• INTERVAL ESTIMATION

• INTERVAL ESTIMATES FOR μ WHEN IS KNOWN
  • Confidence Intervals in Terms of 20 Samples
  • Sandbags We Can Have Real Confidence In: 95 Percent and 99 Percent Confidence Intervals
  • 95 Percent Confidence Interval for the Sandbag Sample with a Smaller Sample Size
  • 95 Percent Confidence Interval for the Mean External Audit Fees for 32 Diverse Companies

• CONFIDENCE INTERVALS FOR μ WHEN IS UNKNOWN
  • 95 Percent Confidence Interval for the Average Weight of Football Players
  • 90 Percent Confidence Interval for the Average Weight of Football Players
  • Estimate for Waiting Time at a Bank
  • 95 Percent Confidence Interval for the True Mean Incremental Profit of “Successful” Trade Promotion

• CONFIDENCE INTERVALS FOR THE POPULATION PROPORTION
  • 95 Percent Confidence Interval for Voting Proportion
  • 95 Percent Confidence Interval for Commodity Preference Proportion
  • 95 Percent Confidence Interval for the Proportion of Working Adults Who Use Computer Equipment

• CONFIDENCE INTERVALS FOR THE VARIANCE
  • Confidence Intervals for

• AN OVERVIEW OF STATISTICAL QUALITY CONTROL⁵
  • The Sample Size of an Inspection
  • Acceptance Sampling and Its Alternative Plans
  • Process Control

• CONTROL CHARTS FOR QUALITY CONTROL
  • -Chart
  • -Chart and S-Chart

• FURTHER APPLICATIONS
  • Using Interval Estimates to Evaluate Donors and Donations Models
  • Shoppers’ Attitudes Toward Shoplifting and Shoplifting Prevention Devices

• Summary

• Appendix 10A Control Chart Approach for Cash Management¹⁶

• Appendix 10B Using MINITAB to Generate Control Charts

• Questions and Problems

Using the estimates of so-called Hodge decomposition of disturbed vector fields, a Caccioppoli type estimate is established for very weak Solutions of a class of nonlinear equations involved nonhomogeneous items.

Growth at infinity is given for modified Riesz potential in the half space.