Reliability-based Robust Optimization Design of Automobile Components with Non-normal Distribution Parameters

In the reliability designing procedure of the vehicle components, when the distribution styles of the random variables are unknown or non-normal distribution, the result evaluated contains great error or even is wrong if the reliability value R is larger than 1 by using the existent method, in which case the formula is necessary to be revised. This is obviously inconvenient for programming. Combining reliability-based optimization theory, robust designing method and reliability based sensitivity analysis, a new method for reliability robust designing is proposed. Therefore the influence level of the designing parameters’ changing to the reliability of vehicle components can be obtained. The reliability sensitivity with respect to design parameters is viewed as a sub-objective function in the multi-objective optimization problem satisfying reliability constraints. Given the first four moments of basic random variables, a fourth-moment technique and the proposed optimization procedure can obtain reliability-based robust design of automobile components with non-normal distribution parameters accurately and quickly. By using the proposed method, the distribution style of the random parameters is relaxed. Therefore it is much closer to the actual reliability problems. The numerical examples indicate the following: (1) The reliability value obtained by the robust method proposed increases (】0.04%) comparing to the value obtained by the ordinary optimization algorithm; (2) The absolute value of reliability-based sensitivity decreases (】0.01%), and the robustness of the products’ quality is improved accordingly. Utilizing the reliability-based optimization and robust design method in the reliability designing procedure reduces the manufacture cost and provides the theoretical basis for the reliability and robust design of the vehicle components.

A new early warning method for dam displacement behavior based on non-normal distribution function

Traditional methods for early warning of dam displacements usually assume that residual displacements follow a normal distribution.This assumption deviates from the reality,thereby affecting the reliability of early warning results and leading to misjudgments of dam displacement behavior.To solve this problem,this study proposed an early warning method using a non-normal distribution function.A new early warning index was developed using cumulative distribution function(CDF)values.The method of kernel density estimation was used to calculate the CDF values of residual displacements at a single point.The copula function was used to compute the CDF values of residual displacements at multiple points.Numerical results showed that,with residual displacements in a non-normal distribution,the early warning method proposed in this study accurately reflected the dam displacement behavior and effectively reduced the frequency of false alarms.This method is expected to aid in the safe operation of dams.

Riemann Boundary Value Problem of Non-Normal Type on the Infinite Straight Line

Various kinds of Riemann boundary value problems (BVPs) for analytic functions on closed curves or on open arc, doubly periodic Riemann BVPs, doubly quasi-periodic Riemann BVPs, and BVPs for polyanalytic functions have been widely investigated in [1-8]. The main ap- proach is to use the decomposition of polyanalytic functions and their generalization to transform the boundary value problems to their corresponding boundary value problems for analytic functions. Recently, inverse Riemann BVPs for generalized analytic functions or bianalytic functions have been investigated in [9-12]. In this paper, we consider a kind of Riemann BVP of non-normal type on the infinite straight line and discuss the solvable conditions and the general solution for it.

Non-normal Hasemann Boundary Value Problem

We will discuss the non-normal Hasemann boundary value problem: we may find these results are coincided with those of normal Hasemann boundary value problem and non-normal Riemann boundary value problem.

Doubly Periodic Riemann Boundary Value Problem of Non-Normal Type for Analytic Functions on Two Parallel Curves

In this paper, we present and study a kind of Riemann boundary value problem of non-normal type for analytic functions on two parallel curves. Making use of the method of complex functions, we give the method for solving this kind of doubly periodic Riemann boundary value problem of non-normal type and obtain the explicit expressions of solutions and the solvable conditions for it.

压缩机突尖失速的研究综述

Spike-stall is a fast stall mode of both axial and centrifugal compressors. It can very quickly lead to surge and interrupt the normal operation of compressors. Despite decades' efforts, we still do not have a clear picture of how it starts and develops, let alone predicting it. This paper reviews the research works on this instability of compressors, describes the progress made, discusses the shortcomings of current research, and proposes some new concepts that may lead to breakthroughs. It is pointed out that current methods of predicting spike-stall are mostly based on classic stability concept which is incapable of handling the transient growth and diminution of disturbances in short length scales that typify spike-stall. Modern transient instability concept is proposed that establishes the link between the maximum amplification of the system to initial perturbations and time. The non-normality of compressor system is also emphasised.

Some Stylized Facts of Short-Term Stock Prices of Selected Nigerian Banks

This paper examines presence of some stylized facts of short-term stock prices in the banking sector of the Nigerian Stock Market (NSM). Non-normality, lack of autocorrelation in the returns at first lag and significant positive autocorrelation in higher magnitude returns, widely studied in other markets, are investigated using daily closing stock prices of the four major Nigerian banks (Access, First, Guaranty Trust and United Bank for Africa (UBA)), from 2001 to 2013;encompassing periods of different financial scenarios. Jarque-Bera (JB), Doonik-Hansen, Kolmogrov-Smirnov and Ljung-Box (Q) test statistics are applied. Our findings reveal that the four banks stocks behave slightly different, but generally possess the stylized facts found in other markets. Observed is that, while the distributions of the returns for two of these banks (First and UBA) are approximately symmetric and leptokurtic;those of Access and Guaranty Trust banks are significantly non-symmetric and leptokurtic, thus non-normally distributed. Also established is that, while autocorrelation functions of daily returns are either negative or zero, those of both absolute returns and the squared returns are mostly positive. The autocorrelations of absolute returns are found to be predominantly positive and more persistent than those of the squared returns;indicating volatility clustering. Consequently, we conclude that the short-term stock prices of these banks behave like those of other markets. Some implications of the results for financial investment and stock market behaviour in the banking sector of NSM are discussed.

ST-metric Estimation of Factor Exposures

Non-parametric methods are treasured in data analysis,particularly in finance.ST-metric is a new concept,introduced by Tulunay(2017).It offers non-parametric methods and a new geometric view to data analysis.In that paper,ST-metric concept has been applied to performance measures of portfolios.In this current paper,we purpose another ST-metric method for finding factor exposures in the five-style-factors model.Here the style factors are value,size,minimum volatility,quality and momentum.The main idea is to find the factor exposures(weights)of the five-factors-model by minimizing the ST-metric between benchmark returns and the constructed factor model returns.We compare ST-metric method with Tracking Error method(TE-method)which is used for factor analysis of major indexes,decomposed into the style factors(tradable via Exchange Traded Funds(ETFs))by Ang et al.(2018).We show that ST-metric method gives better estimation of the factor exposures(weights)than tracking error method,in general,and further how ST-metric values vary with respect to fluctuations.This explains the reason behind the efficiency of the ST-metric method.We support this idea with empirical evidences.

A Simulation Based Comparison of Correlation Coefficients with Regard to Type I Error Rate and Power

In this simulation study, five correlation coefficients, namely, Pearson, Spearman, Kendal Tau, Permutation-based, and Winsorized were compared in terms of Type I error rate and power under different scenarios where the underlying distributions of the variables of interest, sample sizes and correlation patterns were varied. Simulation results showed that the Type I error rate and power of Pearson correlation coefficient were negatively affected by the distribution shapes especially for small sample sizes, which was much more pronounced for Spearman Rank and Kendal Tau correlation coefficients especially when sample sizes were small. In general, Permutation-based and Winsorized correlation coefficients are more robust to distribution shapes and correlation patterns, regardless of sample size. In conclusion, when assumptions of Pearson correlation coefficient are not satisfied, Permutation-based and Winsorized correlation coefficients seem to be better alternatives.

New Common Fixed Point Results for Four Maps on Cone Metric Spaces

In this paper, some new existence and uniqueness of common fixed points for four mappings are obtained, which do not satisfy continuity and commutation on non-normal cone metric spaces. These results improve and generalize several well-known comparable results in the literature.

New Fixed Point Results of Generalized g-Quasi-Contractions in Cone b-Metric Spaces Over Banach Algebras

In this paper, we introduce the concept of generalized g-quasi-contractions in the setting of cone b-metric spaces over Banach algebras. By omitting the assump- tion of normality we establish common fixed point theorems for the generalized g- quasi-contractions with the spectral radius r（λ） of the g-quasi-contractive constant vector λ satisfying r（λ） ∈[0,1） in the setting of cone b-metric spaces over Banach al- gebras, where the coefficient s satisfies s ≥ 1. The main results generalize, extend and unify several well-known comparable results in the literature.

Common Fixed Points under Contractive Conditions in Cone Metric Spaces

In order to develop and improve the fixed point theorems in cone metric spaces, some new fixed point theorems are presented for two mappings in cone metric spaces which satisfy contractive conditions, where the cone is not necessarily normal. Our results generalize fixed point theorems of Abbas, Jungck and Stojan Radenovi in cone metric spaces.

Process Capability Indices for Shape Parameter of Weibull Distribution

Process capability analysis is used to determine the process performance as capable or incapable within a specified tolerance. Basic indices Cp, Cpk, Cpm, Cpmk initially developed for normally distributed processes showed inappropriate for processes with non-normal distributions. A number of authors worked on non-normal distributions which were most notably those of Clements, Pearn and Chen, Montgomery and Johnson-Kotz-Pearn (JKP). Obtaining PCIs based on the parameters of non-normal distributions are completely disregarded and ignored. However parameters of some non-normal distributions have significance for knowing the status of process as capable or incapable. In this article we intend to work on the shape parameter of Weibull distribution to calculate PCIs. We work on two data sets for verification and validation purpose. Efficacy of the technique is assessed by bootstrapping the results of estimate and standard error of shape parameter.

A Comparison of Hierarchical Bayesian Models for Small Area Estimation of Counts

Small area estimation (SAE) tackles the problem of providing reliable estimates for small areas, i.e., subsets of the population for which sample information is not sufficient to warrant the use of a direct estimator. Hierarchical Bayesian approach to SAE problems offers several advantages over traditional SAE models including the ability of appropriately accounting for the type of surveyed variable. In this paper, a number of model specifications for estimating small area counts are discussed and their relative merits are illustrated. We conducted a simulation study by reproducing in a simplified form the Italian Labour Force Survey and taking the Local Labor Markets as target areas. Simulated data were generated by assuming population characteristics of interest as well as survey sampling design as known. In one set of experiments, numbers of employment/unemployment from census data were utilized, in others population characteristics were varied. Results show persistent model failures for some standard Fay-Herriot specifications and for generalized linear Poisson models with (log-)normal sampling stage, whilst either unmatched or nonnormal sampling stage models get the best performance in terms of bias, accuracy and reliability. Though, the study also found that any model noticeably improves on its performance by letting sampling variances be stochastically determined rather than assumed as known as is the general practice. Moreover, we address the issue of model determination to point out limits and possible deceptions of commonly used criteria for model selection and checking in SAE context.

On Cubic Nonsymmetric Cayley Graphs

Let be a connected Cayley graph of group G, then Γ is called normal if the right regular representation of G is a normal subgroup of , the full automorphism group of Γ. For the case where G is a finite nonabelian simple group and Γ is symmetric cubic Cayley graph, Caiheng Li and Shangjin Xu proved that Γ is normal with only two exceptions. Since then, the normality of nonsymmetric cubic Cayley graph of nonabelian simple group aroused strong interest of people. So far such graphs which have been known are all normal. Then people conjecture that all of such graphs are either normal or the Cayley subset consists of involutions. In this paper we give an negative answer by two counterexamples. As far as we know these are the first examples for the non-normal cubic nonsymmetric Cayley graphs of finite nonabelian simple groups.

ON THE NON-NORMAL OPERATORS——SEMI-HYPONORMAL OPERATORS

Let A be a linear operator in a Hilbert space H such that Q=（A*A）1/2-（AA*）1/2≥0 andlet A=UR be the polar decomposition. Then there exist opeators A+=lim U*nAUn and A-=lim Un AU*n.In this paper, the relations between the spectra of A+, A-,R and U are derived. Asingular integral model of the operator A is presented. Finally we shall prove the inequality ||Q||≤μφ（σ（A））/2π under certain conditions.

RQI DYNAMICS FOR NON-NORMAL MATRICES WITHREAL EIGENVALUES

RQI is an approach for eigenvectors of matrices. In 1974, B.N Parlett proved that it was a ''succeessful algorithm'' with cubic convergent speed for normal matrices. After then, several authors developed relevant theory and put this research into dynamical frame. [3] indicated that RQI failed for non-normal matrices with complex eigenvalues. In this paper, RQI for non-normal matrices with only real spectrum is analyzed. The authors proved that eigenvectors are super-attractive fixed points of RQI. The geometrical and topological behaviours of two periodic orbits are considered too. The existness of three or higher periodic orbits and their geometry are considered too. The existness of three or higher periodic orbits and their geometry are still open and of interest. It will be reported in our forthcomming paper.

Cyclic Division Algebras with Non-norm Elements

In this paper, we construct some cyclic division algebras （K/F,σ,γ）. We obtain a necessary and sufficient condition of a non-norm elementγ provided that F = Q and K is a subfield of a cyclotomic field Q（ζpu）, where p is a prime and ζpu is a pu th primitive root of unity. As an application for space time block codes, we also construct cyclic division algebras （K/F,σ, γ）, where F = Q（i）, i = √-1, K is a subfield of Q（ζ4pu） or Q（ζ4pu1 pu2）, and γ = 1＋i. Moreover, we describe all cyclic division algebras （K/F, σ, γ） such that F = Q（i）, K is a subfield of L = Q（ζ4pu1, pu2） and γ= 1 ＋i, where [K： F] = φ（pu1 pu2）/d, d = 2 or 4, φ is the Euler totient function, and p1,p2 ≤ 100 are distinct odd primes.

The Influence of the Number of Non-（sub）normal Non-abelian Subgroups on Solvability of Finite Groups

We obtain some sufficient conditions on the number of non-（sub）normai nonabelian subgroups of a finite group to be solvable, which extend a result of Shi and Zhang in 2011.

Ideal counting function in cubic fields

For a cubic algebraic extension K of Q, the behavior of the ideal counting function is considered in this paper. More precisely, let aK（n） be the number of integral ideals of the field K with norm n, we prove an asymptotic formula for the sum.