Binding Number and Fractional k-Factors of Graphs

In this paper, we consider the relationship between the binding number and the existence of fractional k-factors of graphs. The binding number of G is defined by Woodall as bind(G)=min{ | NG(X) || X |:∅≠X⊆V(G) }. It is proved that a graph G has a fractional 1-factor if bind(G)≥1and has a fractional k-factor if bind(G)≥k−1k. Furthermore, it is showed that both results are best possible in some sense.

关于图的Fractional控制数

研究了图的Fractional控制问题,主要给出了关于联图的Fractional控制数的1个上界,由此确定了几类特殊联图的Fractional控制数,并推广了部分已知的结果.

图的Fractional边控制与Fractional边全控制

设G=(V,E)是一个图,一个函数f:E→[0,1]如果对所有的边e∈E(G),都有∑e∈N(e')f(e)≥1成立,则称f为图G的一个Fractional边全控制函数,简记为F边全控制函数,此处N(e')表示G中与边e'相关联的边集。图G的F边全控制数定义为γ'tf(G)=min{∑e∈E(G)f(e)f是G的一个F边全控制函数}.本文得到了一般图的F边全控制数的若干界限,还确定了一些特殊图的F边全控制数。

图的Fractional边全控制

设G=(V,E)是一个无孤立边的图,一个实值函数f:E(G)→[0,1]若对所有的边e∈E(G),均有Σe∈N(e)f(e)≥1成立,则称f为图G的一个F ractional边全控制函数。图G的Fractional边全控制数定义为γft′(G)=min{Σe∈Ef(e)|f为图G的一个Fractional边全控制函数}。确定了一般图的F ractional边全控制数若干界限,同时也研究了几类特殊图F ractional边全控制问题,给出了一些特殊图的Fractional边全控制数。

关于几类图的Fractional全控制数

设G=(V,E)是一个无孤立点的图,一个实值函数f:V→[0,1]满足∑v∈N(u)f(v)≥1对一切u∈V(G)都成立,则称f为图G的一个Fractional全控制函数。图的Fractional全控制数定义为γ0f()G=min{f(V)|f为图G的Fractional全控制函数},文章中研究了图的Fractional全控制问题,主要给出了关于联图的Fractional全控制数的一个上界,由此确定了几类特殊图的Fractional全控制数,并推广了部分已知结果。

Circular Chromatic Numbers of Some Distance Graphs

The circular chromatic number of a graph is an important parameter of a graph. The distance graph G(Z,D) , with a distance set D , is the infinite graph with vertex set Z={0,±1,±2,...} in which two vertices x and y are adjacent iff y-x∈D . This paper determines the circular chromatic numbers of two classes of distance graphs G(Z,D m,k,k+1 ) and G(Z,D m,k,k+1,k+2 ).

Bounds on Fractional Domination of Some Products of Graphs

Let γ f(G) and γ~t f(G) be the fractional domination number and fractional total domination number of a graph G respectively. Hare and Stewart gave some exact fractional domination number of P n×P m (grid graph) with small n and m . But for large n and m , it is difficult to decide the exact fractional domination number. Motivated by this, nearly sharp upper and lower bounds are given to the fractional domination number of grid graphs. Furthermore, upper and lower bounds on the fractional total domination number of strong direct product of graphs are given.

Bondage and Reinforcement Number of γ_f for Complete Multipartite Graph

The bondage number of γ f, b f(G) , is defined to be the minimum cardinality of a set of edges whose removal from G results in a graph G′ satisfying γ f(G′)> γ f(G) . The reinforcement number of γ f, r f(G) , is defined to be the minimum cardinality of a set of edges which when added to G results in a graph G′ satisfying γ f(G′)< γ f(G) . G.S.Domke and R.C.Laskar initiated the study of them and gave exact values of b f(G) and r f(G) for some classes of graphs. Exact values of b f(G) and r f(G) for complete multipartite graphs are given and some results are extended.

Non-probabilistic solutions of imprecisely defined fractional-order diffusion equations

The fractional diffusion equation is one of the most important partial differential equations（PDEs） to model problems in mathematical physics. These PDEs are more practical when those are combined with uncertainties. Accordingly, this paper investigates the numerical solution of a non-probabilistic viz. fuzzy fractional-order diffusion equation subjected to various external forces. A fuzzy diffusion equation having fractional order 0 〈 α≤ 1 with fuzzy initial condition is taken into consideration. Fuzziness appearing in the initial conditions is modelled through convex normalized triangular and Gaussian fuzzy numbers. A new computational technique is proposed based on double parametric form of fuzzy numbers to handle the fuzzy fractional diffusion equation. Using the single parametric form of fuzzy numbers, the original fuzzy diffusion equation is converted first into an interval-based fuzzy differential equation. Next, this equation is transformed into crisp form by using the proposed double parametric form of fuzzy numbers. Finally, the same is solved by Adomian decomposition method（ADM） symbolically to obtain the uncertain bounds of the solution. Computed results are depicted in terms of plots. Results obtained by the proposed method are compared with the existing results in special cases.

Levy Constrained Search in Fock Space：An Alternative Approach to Noninteger Electron Number

By extending the Levy wavefunction constrained search to Fock Space,one can define a wavefunction constrained search for electron densities in systems having noninteger number of electrons.For pure-state v-representable densities,the results are equivalent to what one would obtain with the zero-temperature grand canonical ensemble.In other cases,the wavefunction constrained search in Fock space presents an upper bound to the grand canonical ensemble functional.One advantage of the Fock-space wavefunction constrained search functional over the zero-temperature grand-canonical ensemble constrained search functional is that certain specific excited states(i.e.,those that are not ground-statev-representable) are the stationary points of the Fock-space functional.However,a potential disadvantage of the Fock-space constrained search functional is that it is not convex.

两类图的Fractional控制数

设G=(V,E)为一个图,如果一个实值函数f:V→[0,1],对任意u∈V(G),均有f(N[u])≥1成立,则称f为图G的一个Fractional控制函数。图G的Fractional控制数定义为γf(G)=min{f(V)|f为图G的一个Fractional控制函数}。本文给出m≥3,n≥2时乘积图K_(m)×P_(n)的Fractional控制数、Fractional全控制数和m≥5,n≥3时联图K_(m)∨P_(n)的Fractional控制数。

Experimental determination of distributions of soot particle diameter and number density by emission and scattering techniques

A diagnostics method was presented that uses emission and scattering techniques to simultaneously determine the distributions of soot particle diameter and number density in hydrocarbon flames. Two manta G-504 C cameras were utilized for the scattering measurement, with consideration of the attenuation effect in the flames according to corresponding absorption coefficients. Distributions of soot particle diameter and number density were simultaneously determined using the measured scattering coefficients and absorption coefficients under multiple wavelengths already measured with a SOC701 V hyper-spectral imaging device, according to the Mie scattering theory. A flame was produced using an axisymmetric laminar diffusion flame burner with 194 mL/min ethylene and 284 L/min air, and distributions of particle diameter and number density for the flame were presented. Consequently, the distributions of soot volume fraction were calculated using these two parameters as well, which were in good agreement with the results calculated according to the Rayleigh approximation,demonstrating that the proposed diagnostic method is capable of simultaneous determination of the distributions of soot particle diameter and number density.

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.

The Fractional Hydrogen Atom: A Paradigm for Astrophysical Phenomena

We have found that fractional principal quantum numbers are permitted in hydrogen atom which yield the conditions for neutron and white dwarf stars evolution. The number densities of neutron and white dwarf stars reveal that these systems have the maximal conductivity of 1.37×1010Ω-1m-1. They are giant perfect conductors at very high temperature and magnetic field.

A generalized set of correlations for plus fraction characterization

The importance of accurate determination of the critical properties of plus fractions in prediction of phase behaviour of hydrocarbon mixtures by equations of state is well known in the petroleum industry. It has been stated in various papers （Elsharkawy, 2001） that using the plus fraction as a single group in equation of state calculations reduces the accuracy of the results. However in this work it has been shown that using the proper values of critical temperature and pressure for the plus fraction group can estimate the properties of hydrocarbon mixtures, and they are accurate enough to be used in reservoir engineering and enhanced oil recovery calculations. In this paper, a new method is proposed for calculating the critical properties of plus fractions of petroleum fluids. One can use this method either in predicting critical pressure and temperature of single carbon numbers （SCNs） after the splitting process or in predicting critical pressure and temperature of the plus fraction as a single group. A comparison study is performed against Riazi-Daubert correlation （Riazi and Daubert, 1987） and Sancet correlations （Sancet, 2007） for 25 oil samples taken from 14 fields from southwest Iran. The results indicate the superiority of the proposed method to the Riazi-Daubert and Sancet correlations.

Fraction of Missing Information (γ) at Different Missing Data Fractions in the 2012 NAMCS Physician Workflow Mail Survey

In his 1987 classic book on multiple imputation (MI), Rubin used the fraction of missing information, γ, to define the relative efficiency (RE) of MI as RE = (1 + γ/m)?1/2, where m is the number of imputations, leading to the conclusion that a small m (≤5) would be sufficient for MI. However, evidence has been accumulating that many more imputations are needed. Why would the apparently sufficient m deduced from the RE be actually too small? The answer may lie with γ. In this research, γ was determined at the fractions of missing data (δ) of 4%, 10%, 20%, and 29% using the 2012 Physician Workflow Mail Survey of the National Ambulatory Medical Care Survey (NAMCS). The γ values were strikingly small, ranging in the order of 10?6 to 0.01. As δ increased, γ usually increased but sometimes decreased. How the data were analysed had the dominating effects on γ, overshadowing the effect of δ. The results suggest that it is impossible to predict γ using δ and that it may not be appropriate to use the γ-based RE to determine sufficient m.

Mass Constituents of a Flat Lattice Multiverse: Conclusion from Similarity between Two Universal Numbers, the Rocksalt-Type 2<i>D</i>Madelung Constant and the Golden Mean

In fairly good agreement with the consensus range of dark energy to matter this ratio of the critical density is suggested to be connected with the golden mean &phi;=0.6180339887, yielding for dark energy to matter mass fractions .?Assuming the baryonic matter to be only 4.432%, the ratio of matter to baryonic matter would be , and further the ratio of dark matter to baryonic one . If one subtracts from the dark matter a contribution of antimatter with the same mass of baryonic matter, according to the antigravity theories of Villata respectively Hajdukovic, the remaining mass ratio would yield . Replacing the “Madelung” constant α of Villata’s “lattice universe” by &phi;, one reaches again 1 + &phi;as the ratio of the repulsive mass contribution to the attractive one. Assuming instead of a 3D lattice a flat 2D one of rocksalt type, the numerical similarity between the Madelung constant and φ&minus;1 could not be just coincidence. The proposed scaling of the cosmological mass fractions with the square of the most irrational universal number &phi;may indicate that the chaotic cosmological processes have reached a quite stable equilibrium. This may be confirmed by another, but similar representation of the mass constituents by the Archimedes’ constant &pi;, giving for respectively for the dark components . However, the intimate connection of φ with its reciprocal may ignite the discussion whether our universe is intertwined with another universe or even part of a multiverse with the dark constituents contributed from there.

Goal Programming for Solving Fractional Programming Problem in Fuzzy Environment

This paper is comprised of the modeling and optimization of a multi objective linear programming problem in fuzzy environment in which some goals are fractional and some are linear. Here, we present a new approach for its solution by using α-cut of fuzzy numbers. In this proposed method, we first define membership function for goals by introducing non-deviational variables for each of objective functions with effective use of α-cut intervals to deal with uncertain parameters being represented by fuzzy numbers. In the optimization process the under deviational variables are minimized for finding a most satisfactory solution. The developed method has also been implemented on a problem for illustration and comparison.

基于超高分辨质谱的家蚕脂肪体样品处理方案优化研究

随着家蚕基因组图谱的发布,家蚕的研究逐渐进入后基因组时代,家蚕蛋白质组样品前处理方法没有统一的标准,鉴定到的蛋白质数量差异较大.基于超高分辨率质谱仪,建立冰上组织研磨器研磨提取蛋白质的方法,能极大地避免材料的损失,具有稳定和快速的优点.通过对不同提取试剂的摸索,发现尿素+DTT对家蚕组织样品的提取效果最好.通过对上样量和上样时间的摸索,确定最佳上样量为10μL,最佳上样时间为120 min.利用90%序列相似性原则构建非冗余家蚕数据库Strealine,在家蚕5龄第3 d脂肪体材料中,使用该库能鉴定到1910种蛋白质.进一步采用反相色谱柱对肽段进行分级,将鉴定到的蛋白数量提升至3986种.