Failure Mode and Effects Analysis Based on Z-Numbers and the Graded Mean Integration Representation

Failuremode and effects analysis(FMEA)is a widely used safety assessmentmethod inmany fields.Z-number was previously applied in FMEA since it can take both possibility and reliability of information into consideration.However,the use of fuzzy weighted mean to integrate Z-valuations may have some drawbacks and is not suitable for some situations.In this paper,an improved method is proposed based on Z-numbers and the graded mean integration representation(GMIR)to deal with the uncertain information in FMEA.First,Z-numbers are constructed based on the evaluations of risk factors O,S,D for each failure mode by different experts.Second,weights of the three risk factors and experts are determined.Third,the integration representations of Z-numbers are obtained by a newmethod based on the GMIRmethod.Finally,risk priorities of the failure modes are derived considering the weights of experts and risk factors.Two examples and a case study are given to show the use of the proposed method and comparison with other methods.The results show that the proposed method is more reasonable,universal and simple in calculation.

On AP-Henstock Integrals of Interval-Valued Functions and Fuzzy-Number-Valued Functions

In 2000, Wu and Gong [1] introduced the thought of the Henstock integrals of inter-valvalued functions and fuzzy-number-valued functions and obtained a number of their properties. The aim of this paper is to introduce the thought of the AP- Henstock integrals of interval-valued functions and fuzzy-number-valued functions which are extensions of [1] and investigate a number of their properties.

The Generalization and Proof of “Square Root of 2 Is Not a Rational Number” on the Integral Domain

In this paper, the traditional proof of “square root of 2 is not a rational number” has been reviewed, and then the theory has been generalized to “if n is not a square, square root of n is not a rational number”. And then some conceptions of ring, integral domain, ideal, quotient ring in Advanced algebra, have been introduced. Integers can be regarded as an integral domain, the rational numbers can be regard as a fractional domain. Evens and odds are principal ideals in integral domain. The operations on evens and odds are operations on quotient ring. After introducing “the minimalist form” in fraction ring. The paper proves the main conclusion: in a integral domain, multiplicative subset S produces a fraction ring S−1R, and n is not a square element in R, then to every element a∈R, a2≠n.

On Henstock-Stieltjes Integrals of Interval-Valued Functions and Fuzzy-Number-Valued Functions

In this paper we introduce the notion of the Henstock-Stieltjes (HS) integrals of interval-valued functions and fuzzy-number-valued functions and discuss some of their properties.

对MIBS算法的Integral攻击

MIBS是M.Izadi等人在2009开发研制的轻量级分组密码算法,它广泛用于电子标签和传感器网络等环境.本文给出了对MIBS算法Integral攻击的4.5轮区分器,利用该区分器对MIBS算法进行了8轮和9轮的Integral攻击,并利用密钥编排算法中轮密钥之间的关系,结合"部分和"技术降低了攻击的时间复杂度.攻击结果如下:攻击8轮MIBS-64的数据复杂度和时间复杂度分别为238.6和224.2;攻击9轮MIBS-80的数据复杂度和时间复杂度分别为239.6和268.4.本文攻击的数据复杂度和时间复杂度都优于穷举攻击.这是对MIBS算法第一个公开的Integral攻击.

Existence of supremum and infimum in E^- and relations of (M) integral and (G) integra

Proves the existence of supremum and infimum in the noncompact fuzzy number space E ～, redefines E ～ valued (M) integral, and then discusses the relations between (M) integral and (G) integral of E ～ valued functions.

The Powers Sums, Bernoulli Numbers, Bernoulli Polynomials Rethinked

Utilizing translation operators we get the powers sums on arithmetic progressions and the Bernoulli polynomials of order munder the form of differential operators acting on monomials. It follows that (d/dn-d/dz) applied on a power sum has a meaning and is exactly equal to the Bernoulli polynomial of the same order. From this new property we get the formula giving powers sums in term of sums of successive derivatives of Bernoulli polynomial multiplied withprimitives of the same order of n. Then by changing the two arguments z,n into Z=z(z-1), λ where λ designed the 1st order power sums and proving that Bernoulli polynomials of odd order vanish for arguments equal to 0, 1/2, 1, we obtain easily the Faulhaber formula for powers sums in term of polynomials in λ having coefficients depending on Z. These coefficients are found to be derivatives of odd powers sums on integers expressed in Z. By the way we obtain the link between Faulhaber formulae for powers sums on integers and on arithmetic progressions. To complete the work we propose tables for calculating in easiest manners possibly the Bernoulli numbers, the Bernoulli polynomials, the powers sums and the Faulhaber formula for powers sums.

Pythagoreans Figurative Numbers: The Beginning of Number Theory and Summation of Series

In this article we shall examine several different types of figurative numbers which have been studied extensively over the period of 2500 years, and currently scattered on hundreds of websites. We shall discuss their computation through simple recurrence relations, patterns and properties, and mutual relationships which have led to curious results in the field of elementary number theory. Further, for each type of figurative numbers we shall show that the addition of first finite numbers and infinite addition of their inverses often require new/strange techniques. We sincerely hope that besides experts, students and teachers of mathematics will also be benefited with this article.

Strong Laws of Large Numbers for Weighted Sums of Ч-mixing Sequence

In this paper, strong laws of large numbers for weighted sums of ■-mixing sequence are investigated. Our results extend the corresponding results for negatively associated sequence to the case of ■-mixing sequence.

Effects of Seed Viability and Number of Generations on Genetic Integrity of Soybean Germplasm Zhonghuang 18 by AFLP Markers

The seeds of a soybean cultivar Zhonghuang 18 were subjected to accelerated aging for 0(population G_0-1), 112(population G_0-2), 154(population G_0-3) and 196 d(population G_0-4), whose germination percentage was found to be 98.0%, 95.0%, 81.0%, and 79.0%, respectively. Then, the four populations were regenerated twice in the field. The first descendant populations were marked as G_1-1, G_1-2, G_1-3 and G_1-4, and the second were marked as G_2-1, G_2-2, G_2-3 and G_2-4, respectively. The genetic variation between the control population(G_0-1) and the experimental populations was analyzed using 12 AFLP primer combinations. The results showed that there was no significant difference in genetic similarity between the 11 experimental populations and the control population G_0-1. The genetic similarity between population G_2-4 and G_0-1 was still as high as 0.933 3, indicating that the F_2 generation of the population whose germination percentage was only 79.0% still had a high genetic similarity to the control population. The results of t-tests revealed that the populations G_1-1, G_2-1, G_1-2 and G_2-2 showed no significant difference from the control population G_0-1 in effective number of alleles per locus(Ae), genetic diversity index(H) and Shannon's diversity index(I), while these indices of populations G_0-3, G_0-4, G_1-3, G_1-4, G_2-3 and G_2-4 were significantly reduced. χ~2 tests indicated that the populations G_1-1 and G_2-1 showed little difference, and the populations G_0-2, G_0-3, G_0-4, G_1-2, G_1-3, G_1-4, G_2-2, G_2-3, and G_2-4 showed great difference in allele frequency distribution from the control population G_0-1, and the difference was greater when the seed viability was lower. Compared with the control population G_0-1, the number of rare alleles(Nr) of the populations G_0-2, G_1-1, G_2-1, G_1-2 and G_2-2 showed no significant difference, while that of the populations G_0-3, G_0-4, G_1-3, G_1-4, G_2-3 and G_2-4 declined obviously. These results revealed that compared with the control population, the genetic diversity and Nr for the descendant populations of the populations with 98.0% and 95.0% germination percentages did not change significantly, but declined greatly for the descendant populations of the populations with 81.0.% and 79.0% percentages. The results suggested that the decline in seed viability has a greater impact than the number of generations on genetic structure of soybean germplasm. So, it is suggested that soybean seed with an initial germination percentage of 98.0% should be regenerated before its germination percentage declines to 81.0%.

Sums of Squares of Fibonacci Numbers with Prime Indices

In this paper we present some identities for the sums of squares of Fibonacci and Lucas numbers with consecutive primes, using maximal prime gap G(x)~log2x, as indices.

Integral Sequences of Infinite Length Whose Terms Are Relatively Prime

It is given in Weil and Rosenlicht ([1], p. 15) that (resp. 2) for all non-negative integers m and n with m≠n if c is any even (resp. odd) integer. In the present paper we generalize this. Our purpose is to give other integral sequences such that G.C.D.(ym,yn)=1 for all positive integers m and n with m≠n. Roughly speaking we show the following 1) and 2). 1) There are infinitely many polynomial sequences such that G.C.D.(fm(a),fn(a))=1 for all positive integers m and n with with m≠n and infinitely many rational?integers a. 2) There are polynomial sequences such that G.C.D.(gm(a,b),gn(a,b))=1 for all positive integers m and n with m≠n and arbitrary (rational or odd) integers a and b with G.C.D.(a,b)=1. Main results of the present paper are Theorems 1 and 2, and Corollaries 3, 4 and 5.

Selection of Coherent and Concise Formulae on Bernoulli Polynomials-Numbers-Series and Power Sums-Faulhaber Problems

Utilizing the translation operator to represent Bernoulli polynomials and power sums as polynomials of Sheffer-type, we obtain concisely almost all their known properties as so as many new ones, especially new recursion relations for calculating Bernoulli polynomials and numbers, new formulae for obtaining power sums of entire and complex numbers. Then by the change of arguments from z into Z = z(z-1) and n into λ which is the 1st order power sum we obtain the Faulhaber formula for powers sums in term of polynomials in λ having coefficients depending on Z. Practically we give tables for calculating in easiest possible manners, the Bernoulli numbers, polynomials, the general powers sums.

Integral Transform Method for a Porous Slider with Magnetic Field and Velocity Slip

Current research is about the injection of a viscous fluid in the presence of a transverse uniform magnetic field to reduce the sliding drag.There is a slip-on both the slider and the ground in the two cases,for example,a long porous slider and a circular porous slider.By utilizing similarity transformation Navier-Stokes equations are converted into coupled equations which are tackled by Integral Transform Method.Solutions are obtained for different values of Reynolds numbers,velocity slip,and magnetic field.We found that surface slip and Reynolds number has a substantial influence on the lift and drag of long and circular sliders,whereas the magnetic effect is also noticeable.

Sums of Involving the Harmonic Numbers and the Binomial Coefficients

Let the numbers be defined by , where and are the exponential complete Bell polynomials. In this paper, by means of the methods of Riordan arrays, we establish general identities involving the numbers , binomial coefficients and inverse of binomial coefficients. From these identities, we deduce some identities involving binomial coefficients, Harmonic numbers and the Euler sum identities. Furthermore, we obtain the asymptotic values of some summations associated with the numbers by Darboux’s method.

Sums of Squares of Polygonal Numbers

Polygonal numbers and sums of squares of primes are distinct fields of number theory. Here we consider sums of squares of consecutive (of order and rank) polygonal numbers. We try to express sums of squares of polygonal numbers of consecutive orders in matrix form. We also try to find the solution of a Diophantine equation in terms of polygonal numbers.

Generalizations of Some Formulas of the Reciprocal Sum and Alternating Sum for Generalized Lucas Numbers

这篇文章的目的是提供在相互的和 S 之间的倒置关系(1， 2，， m ) 并且轮流出现的和 T (1， 2，， m ) 为概括的概括卢卡斯数字， Melham 是结果。

Simulation and Experimental Study on Influence of Multi⁃port Integrated Hydraulic Transformer Port Number on Transformer Ratio Characteristics

The integrated hydraulic transformer has a compact structure and no throttling loss in the process of pressure regulation.It is widely used in the common pressure rail hydrostatic transmission system.The integrated hydraulic transformer is realized by designing more than three ports on the distribution plate,and the voltage transformation characteristics of the integrated hydraulic transformer with different port numbers are different.In this paper,the influence of port number on the pressure ratio of integrated hydraulic transformer was studied,and the pressure ratio characteristics of 3⁃ports,4⁃ports,and 5⁃ports integrated hydraulic transformer were obtained,and an experimental platform was built for experimental verification,which shows that the simulation results are consistent with the experimental results and provides a theoretical basis for the design of integrated hydraulic transformer.

Research of Tile Type Transceiver Module Integrating with Two-Dimensional Sum Difference Network

Transceiver module and two-dimensional sum difference network are important components of phased array antenna. In this paper, multilayer printed board is used to integrate millimeter wave multi-channel transceiver circuit and sum difference network. The interconnection between them is realized through RF coaxial vertical transition. At the same time, the heat dissipation design and inter channel shielding design of the module are carried out. The RF and low frequency required by the module are completed through the wiring between and within the dielectric plate layers. Finally, 128 arrays are fabricated and verified by multi-channel passive test. The results show that the type transceiver module integrating with two-dimensional sum difference network has good performance, and 128 channels have excellent amplitude and phase characteristics. The integration technology has the characteristics of lightweight, miniaturization, high integration and low manufacturing cost. It can be widely used in miniaturized phased array antennas.

The Formula of General Term of the Sum of Equal Powers of Natural Numbers

The formula of general term of the sum of equal powers of natural numbers.