The Factorization of Adjoint Polynomials of E^G（i）-class Graphs and Chromatically Equivalence Analysis

Let Sn be the star with n vertices, and let G be any connected graph with p vertices. We denote by Eτp＋（r-1）^G（i） the graph obtained from Sr and rG by coinciding the i-th vertex of G with the vertex of degree r - 1 of S,, while the i-th vertex of each component of （r - 1）G be adjacented to r - 1 vertices of degree 1 of St, respectively. By applying the properties of adjoint polynomials, We prove that factorization theorem of adjoint polynomials of kinds of graphs Eτp＋（r-1）^G（i）∪（r - 1）K1 （1 ≤i≤p）. Furthermore, we obtain structure characteristics of chromatically equivalent graphs of their complements.

Chromatically Equivalent Graphs with P(G, λ) = (λ- λ_1)(λ-λ_2)λ￣(n+1)

The author finds out all of the graphs with the same chromatic polynomial and proves some relevant theorems and corollaries.

On Chromatically Equivalence of a Class of Graphs

A class of new graphs is defined. A sufficient condition for pairs of these graphs to be chromatically equivalent is proven.

Non-uniqueness and stability of two-family fiber-reinforced incompressible hyper-elastic sheet under equibiaxial loading

The problems on the non-uniqueness and stability of a two-family fiber- reinforced anisotropic incompressible hyper-elastic square sheet under equibiaxial tensile dead loading are examined within the framework of finite elasticity. For a two-family fiber-reinforced square sheet, which is in-plane symmetric and subjected to the in-plane symmetric tension in dead loading on the edges, three symmetrically deformed configu- rations and six asymmetrically deformed configurations are possible for any values of the loading. Moreover, another four bifurcated asymmetrically deformed configurations are possible for the loading beyond a certain criticM value. The stability of all the solutions is discussed in comparison with the energy of the sheet. It is shown that only one of the symmetric solutions is stable when the loading is less than the critical value. However, this symmetric solution will become unstable when the loading is larger than the critical value, while one of the four bifurcated asymmetric solutions will be stable.

Study on Non-Uniqueness of Taylor Vortex Flow Changing Inner Cylinder Acceleration Time

In concentrically rotating double cylinders consisting of a stationary outer cylinder a rotating inner cylinder, Taylor vortex flow appears. Taylor vortex flow occurs in journal bearings, various fluid machineries, containers for chemical reaction, and other rotating components. Therefore, the analysis of the flow structure of Taylor vortex flow is highly effective for its control. The main parameters that determine the modes of Taylor vortex flow of a finite length are the aspect ratio, Reynolds number Re. Aspect ratio is defined as the ratio of the cylinder length to the gap length between cylinders, and Re is determined on the basis of the angular speed of the inner cylinder. Aspect ratio was set to be 4.0, and Re to be values in the range from 100 to 1000 at intervals of 100. Thus far, a large number of studies on Taylor vortex flow have been carried out;however, the effects of the differences in initial conditions have not yet been sufficiently clarified. In this study, we changed the acceleration time of the inner cylinder in a numerical analysis, and examined the resulting changes in the mode formation and bifurcation processes. The acceleration time was changed from 1.0 s to 10.0 s. As a result, a difference was observed in the final mode depending on the difference in the acceleration time. From this finding, non-uniqueness, which is a major characteristic of Taylor vortex flow, was confirmed. However, no regularities regarding the difference in mode formation were found and the tendency of the mode formation process was not specified. Moreover, the processes of developing the vortex resulting in different final modes were monitored over time by visual observation. Similar flow behaviors were initially observed after the start of the calculation. Then, a bifurcation point, at which the flow changed to a mode depending on the acceleration time observed, and finally the flow became steady. In addition, there was also a difference in the time taken for the well-developed flow to reach the steady state. Both EFD (Experimental Fluid Dynamics) and CFD (Computational Fluid Dynamics) results show good agreement qualitatively.

Crystallization behaviors of bayerite from sodium chromate alkali solutions

In order to clean production of chromium compounds, it is a critical process to remove aluminates and utilize aluminum compounds from artificial chromate alkali solutions. The effects of Na2 Cr O4 on the neutralization curve, Al（OH）3 precipitation efficiency and induction period of bayerite were investigated. The results indicate that the neutralization curve of the artificial chromate alkali solutions shows three distinct regions and its induction period is longer than that of pure sodium aluminate solutions at the same aluminum concentration. And the decreased temperature and volume fraction of CO2 enhance the particle size of bayerite β-Al（OH）3. Bayerite composed of agglomerates of rods and cone frustums was obtained from alkali metal chromate solutions with 28.5% CO2（volume fraction） at temperatures ranging from 50 °C to 70 °C. Coarse bayerite with particle size（d50） from 24.2 μm to 29.3 μm extremely has few impurities, which is suitable for comprehensive utilization.

Crystallization of gibbsite from synthetic chromate leaching solution in sub-molten salt process

For the clean and economical production of chromium compounds, it is crucial to remove aluminates from chromate alkali solutions and utilize aluminum-containing compounds. In this work, carbonization was used to remove aluminates from a synthetic chromate leaching solution containing a high K2O/Al2O3 mole ratio. The influence of reaction temperature, carbonization time, flow rate of carbon dioxide, and seed ratio on the precipitation of Al was investigated. The optimal output was obtained under the following experimental conditions： a reaction temperature of 50 °C, a carbonization time of 100 min, a carbon dioxide flow rate of 0.1 L/min, and a seed ratio of 1.0. Gibbsite was obtained following carbonization. The structure and morphology of the gibbsite were characterized by X-ray diffraction （XRD）, scanning electron microscopy （SEM）, and laser particle size analyzer. The particle size distribution and morphology of the gibbsite were significantly influenced by the experimental conditions. The gibbsite had a mean particle size （d50） of 16.72μm. The thermal decomposition of the gibbsite was analyzed by XRD and the decomposition path was determined. The obtained coarseα-Al2O3 precipitate, which contains 0.08% Cr2O3 and 0.10% K2O, was suitable for subsequent utilization.

Preparation of potassium chromate by roasting of carbon ferrochrome

The oxidizing roasting process of carbon ferrochrome to prepare potassium chromate in the presence of potassium carbonate and air was investigated. The effects of reaction temperature, reaction time, mole ratio of potassium carbonate to carbon ferrochrome were studied, and thermodynamics and kinetics were also discussed. It was observed that the reaction temperature and reaction time had a significant influence on the roasting reaction of carbon ferrochrome. The reaction mechanism changed greatly as the temperature varied. A two-stage roasting process was favorable for the roasting reaction, and a chromium recovery rate of 97.06% was obtained through this two-stage roasting method. The chromium residue yielded from this method was only 1/3 of the product. Moreover, the component of Fe in the residue was as high as 55.04%. Therefore, it can be easily recovered to produce sponge iron, realizing complete detoxication and zero-emission of chromium residue.

Estimation of illumination chromaticity via adaptive reduced relevance vector machine

A new regression algorithm of an adaptive reduced relevance vector machine is proposed to estimate the illumination chromaticity of an image for the purpose of color constancy. Within the framework of sparse Bayesian learning, the algorithm extends the relevance vector machine by combining global and local kernels adaptively in the form of multiple kernels, and the improved locality preserving projection （LLP） is then applied to reduce the column dimension of the multiple kernel input matrix to achieve less training time. To estimate the illumination chromaticity, the algorithm is trained by fuzzy central values of chromaticity histograms of a set of images and the corresponding illuminants. Experiments with real images indicate that the proposed algorithm performs better than the support vector machine and the relevance vector machine while requiring less training time than the relevance vector machine.

Chromatic Adaptation to Complex Field

Chromatic adaptation of human eyes to complex field is investigated using binocular asymmetric matching method. The results show that the leve of chromatic adapta- tion mainly depends on the average color of adapting field, whereas no obvious change oc- curs when the number of hues and their color differences vary in a complex field. The shifts of perceived color evoked by chromatic adaptation in CIE 1976 L U V color space are approximately proportional to the average color difference between the adapting field and reference field.

Effect of Varieties on Tea Pigment and Chromatic Aberration of Black Tea Infusion

Effects of varieties on the content of tea pigment, L＊, a＊ and b＊ value of chromatic aberration of black tea infusion was studied. The correlation relationship between content of TF, TR, TB and L＊, a＊, b＊ value was extremely significant at P＆lt;0.05. Fresh tea leaves with plucking standard of 1 bud and 2 leaves could man-ufacture black tea with higher content of tea pigment, higher a＊ and b＊ value but lower L＊ value, than those of plucking standard of 1 bud and 3 leaves. But the discrepancy of certain parameter of the two plucking standards changed with vari-eties. Varieties’ quality potential could be concealed by improper plucking standards. Six varieties were divided into four groups on the basis of gross tea polyphenols in fresh tea leaves （GTP）, consumption of tea polyphenols to gross tea polyphenols ratio （CTP/GTP） and gross tea pigment to consumption of tea polyphenols ratio （GP/CTP）. Hybrid performed the very suitability of black tea manufacturing. To en-sure high quality of made black tea, suitable variety should be chosen and reason-able plucking standard also should be taken into consideration.

Novel method to prepare sodium chromate from carbon ferrochrome

An oxidizing roasting process of carbon ferrochrome to prepare sodium chromate in the presence of sodium carbonate and air was investigated. The effects of reaction temperature, reaction time, mole ratio of sodium carbonate to carbon ferrochrome were studied, and thermodynamics and kinetics of the reaction were also discussed. It was observed that there was a sudden increase in reaction rate when the temperature rose to a certain value, and the sample with a smaller grain size could start the sudden increase at a lower temperature. The chromium recovery rate increased with the increase of mole ratio of sodium carbonate to carbon ferrochrome, and it reached up to 99.34% when mole ratio of sodium carbonate to carbon ferrochrome increased to 1.2:1. The chromium residue yielded from this method was only about 1/3 of the product. Moreover, the content of Fe in the residue was as high as 60.41%. Therefore, it can be easily recovered to produce sponge iron, realizing complete detoxication and zero-emission of chromium residue.

CIRCULAR CHROMATIC NUMBER AND MYCIELSKI GRAPHS

For a general graph G, M（G） denotes its Mycielski graph. This article gives a number of new sufficient conditions for G to have the circular chromatic number xc（M（G）） equals to the chromatic number x（M（G））, which have improved some best sufficient conditions published up to date.

N-butyl-2-cyanoacrylate, iso-amyl-2-cyanoacrylate and hypertonic glucose with 72% chromated glycerin in gastric varices

cyanoacrylate and a mixture of 72% chromated glycerinwith hypertonic glucose solution in management ofgastric varices.METHODS： Ninety patients with gastric varicespresented to Endoscopy Unit of Ain Shams UniversityHospital were included. They were randomly allocatedinto three groups; each group included 30 patients treatedwith intravariceal sclerosant injections in biweeklysessions till complete obturation of gastric varices;Group I （n-butyl-2-cyanoacrylate; Histoacryl？）, GroupII （iso-amyl-2-cyanoacrylate; Amcrylate？） and GroupIII （mixture of 72% chromated glycerin; Scleremo？with glucose solution 25%）. All the procedures wereperformed electively without active bleeding. Recruitedpatients were followed up for 3 mo.RESULTS： 26% of Scleremo group had bleeding duringpuncture vs 3.3% in each of the other two groups withsignificant difference, （P 〈 0.05）. None of Scleremogroup had needle obstruction vs 13.3% in each of theother two groups with no significant difference, （P 〉0.05）. Rebleeding occurred in 13.3% of Histoacryl andAmcrylate groups vs 0% in Scleremo group with nosignificant difference. The in hospital mortality was 6.6%in both Histoacryl and Amcrylate groups, while it was0% in Scleremo group with no significant difference. Inthe first and second sessions, the amount of Scleremoneeded for obturation was significantly high, while the amount of Histoacryl was significantly low. Scleremo was the less costly of the two treatments. CONCLUSION： All used sclerosant substances showed efficacy and success in management of gastric varices with no significant differences except in total amount,cost and bleeding during puncture.

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 ).

EDGE-FACE CHROMATIC NUMBER OF 2-CONNECTED PLANE GRAPHS WITH HIGH MAXIMUM DEGREE

The edge-face chromatic number Xef （G） of a plane graph G is the least number of colors assigned to the edges and faces such that every adjacent or incident pair of them receives different colors. In this article, the authors prove that every 2-connected plane graph G with △（G）≥｜G｜ - 2≥9 has Xef（G） = △（G）.

Novel colored flames via chromaticity of essential colors

Colored flame compositions have distinctive variety of applications ranging from military signaling,rocket tracking, and illuminating devices. Certain elements and compounds when heated to high temperature are able to emit unique wavelengths in the visible region. This study, reports on the development of novel colored flames that cannot be generated by emitting atomic/molecular species. This was achieved by using chromaticity of basic colored flames. Mixing of high quality primary colored flames including Blue, Yellow, and Red in proper ratio was conducted; any interfering incandescent emission resulted from MgO was eliminated using Al metal fuel. The spectral characteristics in terms of luminous intensity, and color quality were evaluated using digital luxmeter and UV-Vis. spectrometer respectively.High quality mixed colored flames include violet, sweet pink, and marigold were developed. This study shaded the light on the state of the art for the real development of novel colored flame compositions and chromaticity of basic colored flames.

NON-CHROMATE CONVERSION COATING TREATMENT FOR MAGNESIUM ALLOY

A no pollution organic acid based conversion coating solution MIS. No.1 has been examined as to its suitability as possible replacement for chromate containing formulations on magnesium alloys. Investigations have concentrated on the formation of passive film from simple MIS. No.1 solution using immersion. The morphology of passivated surfaces was examined using scanning electron microscopy (SEM). The corrosion resistance of the passivated surfaces and the painted surface was assessed using electrochemical techniques as well as humidity and salt fog tests. It was concluded that the surface treatment magnesium alloy by MIS.No.1 solution is more effective than that by chromate coating treatment, and the MIS.No.1 coating is also suitable for painting's pretreatment.

RECURSIVE FORMULA FOR CALCULATING THE CHROMATIC POLYNOMIAL OF A GRAPH BY VERTEX DELETION

A new recursive vertex-deleting formula for the computation of the chromatic polynomial of a graph is obtained in this paper. This algorithm is not only a good tool for further studying chromatic polynomials but also the fastest among all the algorithms for the computation of chromatic polynomials.

Enhanced coking resistance of a Ni cermet anode by a chromates protective layer

Ni-based anodes of SOFCs are susceptible to coking, which greatly limits practical application of direct methane-based fuels. An indirect internal reformer is an effective way to convert methane-based fuels into syngas before they reach anode. In this work, catalytic activity of a redox-stable perovskite La0.7Sr0.3Cr0.8Fe0.2O3-δ(LSCrFO) for methane conversion was evaluated. The catalyst was fabricated as an anodic protective layer to improve coking resistance of a Ni cermet anode. Using wet CH4 as a fuel, the LSCrFO-modified cell showed excellent power output and good coking resistance with peak power density of 1.59 W cm-2 at 800℃. The cell demonstrated good durability lasting for at least 100 h. While the bare cell without the protective layer showed poor durability with the cell voltage fast dropped from 0.75 V to 0.4 V within 30 min. Under wet coal bed methane (CBM) operation, obvious performance degradation within 35 h (1.7 mV h^-1) was observed due to the influence of heavy carbon compounds in CBM. The pre-and post-mortem microstructures and carbon analysis of the anode surface and catalyst surface were further conducted.