ON f-EDGE COVER-COLOURING OF SIMPLE GRAPHS

An f-edge cover-colouring of a graph G = (V, E) is an assignment of colours to the edges of G such that every colour appears at each vertex v ∈ V at least f(v) times. The maximum number of colours needed to f-edge cover colour G is called the f-edge cover chromatic index of G, denoted by Xfc(G). This paper gives that min[d(v)-1/f(v)]≤xfc(G)≤

Colouring of COVID-19 Affected Region Based on Fuzzy Directed Graphs

Graph colouring is the system of assigning a colour to each vertex of a graph.It is done in such a way that adjacent vertices do not have equal colour.It is fundamental in graph theory.It is often used to solve real-world problems like traffic light signalling,map colouring,scheduling,etc.Nowadays,social networks are prevalent systems in our life.Here,the users are considered as vertices,and their connections/interactions are taken as edges.Some users follow other popular users’profiles in these networks,and some don’t,but those non-followers are connected directly to the popular profiles.That means,along with traditional relationship(information flowing),there is another relation among them.It depends on the domination of the relationship between the nodes.This type of situation can be modelled as a directed fuzzy graph.In the colouring of fuzzy graph theory,edge membership plays a vital role.Edge membership is a representation of flowing information between end nodes of the edge.Apart from the communication relationship,there may be some other factors like domination in relation.This influence of power is captured here.In this article,the colouring of directed fuzzy graphs is defined based on the influence of relationship.Along with this,the chromatic number and strong chromatic number are provided,and related properties are investigated.An application regarding COVID-19 infection is presented using the colouring of directed fuzzy graphs.

A Note on Acyclic Edge Colouring of Star Graph Families

A proper edge colouring f of a graph G is called acyclic if there are no bichromatic cycles in the graph. The acyclic edge chromatic number or acyclic chromatic index, denoted by , is the minimum number of colours in an acyclic edge colouring of G. In this paper, we discuss the acyclic edge colouring of middle, central, total and line graphs of prime related star graph families. Also exact values of acyclic chromatic indices of such graphs are derived and some of their structural properties are discussed.

Effect of colouring green stage zirconia on the adhesion of veneering ceramics with different thermal expansion coefficients

This study evaluated the adhesion of zirconia core ceramics with their corresponding veneering ceramics, having different thermal expansion coefficients （TECs）, when zirconia ceramics were coloured at green stage. Zirconia blocks （N=240; 6 mm x 7 mm x 7 mm） were manufactured from two materials namely, ICE Zirconia （Group 1） and Prettau Zirconia （Group 2）. In their green stage, they were randomly divided into two groups. Half of the specimens were coloured with colouring liquid （shade A2）, Three different veneering ceramics with different TEC （ICE Ceramic, GC Initial Zr and IPS e.max Ceram） were fired on both coloured and non-coloured zirconia cores. Specimens of high noble alloys （Esteticor Plus） veneered with ceramic （VM 13） （n= 16） acted as the control group. Core-veneer interface of the specimens were subjected to shear force in the Universal Testing Machine （0.5 mm-min-1）. Neither the zirconia core material （P=0.318） nor colouring （P=0.188） significantly affected the results （three-way analysis of variance, Tukey＇s test）. But the results were significantly affected by the veneering ceramic （P=0.000）. Control group exhibited significantly higher mean bond strength values （45.7__.8） MPa than all other tested groups （（27.1__.4.1）-（39.7__.4.7） and （27.4__.5.6）-（35.9___4.7） MPa with and without colouring, respectively） （P^0.001）. While in zirconia-veneer test groups, predominantly mixed type of failures were observed with the veneering ceramic covering ~ 1/3 of the substrate surface, in the metal-ceramic group, veneering ceramic was left adhered 1/3 of the metal surface. Colouring zirconia did not impair adhesion of veneering ceramic, but veneering ceramic had a significant influence on the core-veneer adhesion. Metal-ceramic adhesion was more reliable than all zirconia-veneer ceramics tested.

Effect of Colouring Process on Pitting Susceptibility of Austenitic Stainless Steel

Colouring of the austenitic stainless steel alloy （20.45% Cr, 8.57% Ni） was carried out in NaNO3-KNO3 eutectic melt without and with additions of Na2O2, NaCl and their mixtures at different temperatures ranging from 400-600℃, under open-circuit and galvanostatic anodic polarization conditions. The produced colours greatly depend on the thickness of oxide films, which in turn depends on the composition of the molten bath and its temperature. The more attractive, bright, adherent and uniform coloured oxide films can be obtained at 400, 450 and 500℃ in molten nitrate bath containing NaCl and Na2O2 mixtures. The pitting corrosion susceptibility of the coloured oxide films was tested in FeCl3 and NaCl as corrosive media. The obtained results indicate that the pitting corrosion susceptibility of the coloured oxide films greatly depends on the previous operating conditions of the colouring process of the stainless steel specimens such as the composition of molten bath, temperature and technique of colouring process.

Complexity of Injective Homomorphisms to Small Tournaments, and of Injective Oriented Colourings

Several possible definitions of local injectivity for a homomorphism of an oriented graph G to an oriented graph H are considered. In each case, we determine the complexity of deciding whether there exists such a homomorphism when G is given and H is a fixed tournament on three or fewer vertices. Each possible definition leads to a locally-injective oriented colouring problem. A dichotomy theorem is proved in each case.

THE STUDY ON COLOURING MECHANISM OF THE COLOUR-TRANSITION GLAZE

The colour-transition glazed brick has been made under suitable conditions and the expected result has been-obtained.The chemical compositions of the glaze have been given. The structures of Na_2O(K_2O)-CaO(MgO)-Al_2O_3 -SiO_2 system,parent glaze and colour-transition glaze have been invesitigated by SME,Visible spec- trum,IR spectrum and Raman spectrum.A brief exp- lanation to colouring mechanism of colour-transi- tion glaze was given in accordance with theory of optical absorption and scattering. For all specimens,liquid phase separation structures were observed generally be SEM and acomparison between parent glaze and colour-transi- tion glaze was made by Visible specta.Hence an inference can be drawn from these results that the liquid phase droplets contain Nd^(3+),Pr^(3+) ions, which cause coloration selective absorbing and scattering of incident light waves.

Colouring pictures:the First Step to Learn Painting

Many of the primary school students are interested in painting.However, few of them know how to learn painting.Many primary school students think that they can begin their painting by imitating.In fact, the first step to learn painting is to colour the pictures, for you can make the pictures more beautiful by colouring them.Also, you can feel how the pictures were drawn by colouring them.

Intraspecific floral colour variation in three Pedicularis species

Flower constancy describes the phenomenon that pollinators tend to successively visit flowers of a single species during foraging,reducing reproductive interference in natural communities.The extent of flower constancy is largely determined by the floral traits of co-flowering species.Both higher inter-specific and lower intraspecific differences of floral traits should contribute to a higher level of flower constancy.However,previous studies mainly focused on interspecific difference,and the intraspecific variation(consistency)of floral traits received much less attention.We hypothesise that selection may favour lower intraspecific floral trait variation in communities composed of multiple co-flowering congeners.We investigated the floral colour variation of three focal Pedicularis species that share pollinators in 19communities composed of either single or multiple Pedicularis species.Colour was quantified using image-based colour analysis as perceived by pollinators.We found that most of the intrapopulation floral colour variation was below the colour discrimination threshold of bumblebees,implying strongly constrained by the visual selection by pollinators.Contrary to the hypothesis,there is no significant difference in intraspecific floral colour variation between different community contexts.It may be due to the relatively large interspecific floral colour differences of most co-flowering species.The influence of community context on intraspecific variation may be reflected in floral traits other than colours.

“Water-Colouring” and Geomorphologic Features of the Marl Hills in Changing Quality of Soil and Water

Water scarcity has always been one of the most important obstacles in the process of agricultural development in arid and low-rainfall climates. In farming, the water quality also plays an important role;as the poor quality of water can be one of the limiting factors in this sector that in addition to the agricultural problems has also caused soil problems. In this paper, we introduce and study an indigenous method of water conservation and soil protection in the east of Iran termed as “water-colouring” and the role of geomorphologic features of marl hills in one of the rivers located in the southern slopes of the Joghtay Mountain (Kalateh-Sadat Watershed). In this study, field observation, sampling and analysis of water and sediment, physicochemical experiments, SPSS software for statistical analysis and satellite images have been used to produce digital models. Finally, the effects of muddy water and clear water have been compared in terms of chemical quality and productivity of agricultural land. The results show that the method of water-colouring is the best indigenous-economical method for moisture retention and regeneration of the agricultural land soil. Given the statistical reasons and studying the other researches in this field, water-colouring causes change texture and soil composition, fertility of agricultural land and reduce the losses due to evaporation and infiltration.

The Evaluation of the Dietary Habits Influence on the Microhardness of Gingiva-Coloured Composite and Acrylic Denture Base Materials

Purpose: The study investigated the impact of dietary habits, specifically soda, milk kefir, water kefir, almond milk, and distilled water (control) consumption, on the microhardness of gingiva-coloured composite and acrylic denture bases. Methods: Materials included gingiva-coloured composite (Fusion Universal G1), acrylic (Imicryl), and subdivided Procryla group. Subgroups comprised 15 and 30-minute heat polymerized (Pro15, Pro30), and 1 wt% (Pro1Z) and 3 wt% (Pro3Z) zirconium added groups. Immersed in beverages for 1, 7, and 14 days, pH and microhardness were assessed. SEM examined random samples. Statistical analysis used repeated measures ANOVA, and post hoc tests (p Results: The gingiva-coloured composites displayed noteworthy time-associated microhardness changes (p 0.05). Despite variable pH levels in beverages, no substantial group interaction effects were observed (p > 0.05). Initial microhardness rankings shifted after a 14-day immersion. Conclusions: Gingiva-coloured composite exhibited the highest microhardness pre- and post-immersion, followed by Procryla30 and Imicryl groups. .

关于正整数有序分拆的一些恒等式和n-colour有序分拆的两个组合性质

研究了正整数的无序分拆与有序分拆的关系.给出了正整数的无序分拆与有序分拆的一些恒等式.并且利用菲波拉契数与正整数n分拆成不含分部量1的有序分拆数的关系给出了n-colour有序分拆的两个组合性质.

都用What colour吗?

英语中表示颜色的形容词很多，同学们学过的有black，red，yellow，blue，white，green，purple，brown，orange，grey等词。由于这些词在句中所作的成分不同，故提问的方式也不同。请看下面三道对划线部分提问的题：

An Analysis of the Melancholy Colour in Robert Frost’s Poerty

Although a man stricken numerous times by pains and sufferings, Robert Frost had made the most excellent works in his lifetime. By carrying out a retrospection to Frost's rough life experiences and his times in light of their inseparable connection to and influence on his writing and analyzing the melancholy color presented in the main themes of "time"、"barrier"and "alienation and loneliness"which are concrete embodiments supporting the main element"melancholy", this thesis argues that Frost influenced his readers by inputting the element of melancholy into minds invisibly. With all the above efforts, the author of this thesis attempts to show a different side of Frost in a more specific and systematical way, and hopes it can help Frost readers understand him and read his poetry from a new angle.

Response of colour and hygroscopic properties of Scots pine wood to thermal treatment

The effect of heat treatment on the surface colour and hygro- scopic properties of pine wood were investigated in this study. Boards of Scots pine wood （Pinus sylvestris L.） were subjected to thermal treatment at 200℃, for 4, 6, and 8 h. The change of equilibrium moisture content and density values of the specimens in order to facilitate the understand- ing of the treated material behavior. The colour parameters L＊ a＊ and b＊, used to depict the total colour change （dE） of wood surface, were shown to change proportionally to the treatment intensity. Moreover, swelling in the tangential and radial directions and absorption of the specimens ap- peared to be enhanced in great extent by the thermal treatment process. The mean value of swelling percentage in the tangential direction de- creased 10.26%, 17.22%, and 19.60% for specimens treated for 4, 6, and 8 h, respectively, referring to the final measurement after 72 h of immer- sion. In radial direction, mean value of swelling percentage decreased 19.56%, 32.75%, and 34.65% for treated for 4, 6 and 8 h, respectively, after 72 h immersion, which attests the decrease in swelling and im- provement in the hygroscopic behavior of Scots pine wood.

Colour and organic removal of biologically treated coffee curing wastewater by electrochemical oxidation method

The treatment of biologically treated wastewater of coffee-curing industry by the electrochemical oxidation using steel anode was investigated. Bench-scale experiments were conducted for activated sludge process on raw wastewater and the treated effluents were further treated by electrochemical oxidation method for its colour and organic content removal. The efficiency of the process was determined in terms of removal percentage of COD, BOD and colour during the course of reaction. Several operating parameters like time, pH and current density were examined to ascertain their effects on the treatment efficiency. Steel anode was found to be effective for the COD and colour removal with anode efficiency of 0.118 kgCOD\5h -1\5A -1\5m -2 and energy consumption 20.61 kWh\5kg -1 of COD at pH 9. The decrease in pH from 9 to 3 found to increase the anode efficiency from 0.118 kgCOD\5h -1\5A -1\5m -2 to 0.144 kWh\5kg -1 of COD while decrease the energy consumption from 20.61 kWh\5kg -1 of COD to 12.86 kWh\5kg -1 of COD. The pH of 5 was considered an ideal from the present treatment process as it avoids the addition of chemicals for neutralization of treated effluents and also economical with respect to energy consumption. An empirical relation developed for relationship between applied current density and COD removal efficiency showed strong predictive capability with coefficient of determination of 96.5%.

与n-colour有序分拆相关的两个组合恒等式

给出了正整数ν分拆成m个分部量的n-colour有序分拆数的递推公式,并由这些递推关系得到了两个组合恒等式.

Colour stabilities of three types of orthodontic clear aligners exposed to staining agents

The aim of this study was to evaluate and compare the colour stabilities of three types of orthodontic clear aligners exposed to staining agents in vitro. Sixty clear orthodontic aligners produced by three manufacturers （Invisalign, Angelalign, and Smartee） were immersed in three staining solutions （coffee, black tea, and red wine） and one control solution （distilled water）. After 12-h and 7-day immersions, the aligners were washed in an ultrasonic cleaner and measured with a colourimeter. The colour changes （△E＊） were calculated on the basis of the Commission Internationale de I＇Eclairage L＊a＊b＊ colour system （CIE L＊a＊b＊）, and the results were then converted into National Bureau of Standards （NBS） units. Fourier transformation infrared （FT-IR） spectroscopy and scanning electron microscopy （SEM） were conducted to observe the molecular and morphologic alterations to the aligner surfaces, respectively. The three types of aligners exhibited slight colour changes after 12 h of staining, with the exception of the Invisalign aligners stained with coffee. The Invisalign aligners exhibited significantly higher AE＊ values （ranging from 0.30 to 27.81） than those of the Angelalign and Smartee aligners （AE＊ values ranging from 0.33 to 1.89 and 0.32 to 1.61, respectively, P〈O.05）. IFT-IR analysis confirmed that the polymer-based structure of aligners did not exhibit significant chemical differences before and after the immersions. The SEM results revealed different surface alterations to the three types of aligner materials after the 7-day staining. The three types of aesthetic orthodontic appliances exhibited colour stability after the 12-h immersion, with the exception of the Invisalign aligners stained by coffee. The Invisalign aligners were more prone than the Angelalign and Smartee aligners to pigmentation. Aligner materials may be improved by considering aesthetic colour stability properties.

正整数有序分拆的几个计数公式及n-colour有序分拆的一些新的组合性质

本文首先给出了正整数分别恰含一个奇分部量和一个偶分部量的有序分拆数的计数公式.其次还利用正整数的"偶-奇"无序分拆给出了正整数的n-colour有序分拆的几个新的组合性质.

The effect of dehydrogenase enzyme activity in glycolysis on the colour stability of mutton during postmortem storage

This study investigated the influence of activities of glyceraldehyde-3-phosphate dehydrogenase （GAPDH） and lactate dehydrogenase-B （LDH-B） on the colour stability of mutton. From 60 sheep （Bayannur mutton sheep）, 15 Iongissimus dorsi （LD） muscles were selected on the basis of colour stability （R630/580 and a＊ value） during the storage and classified into three groups （5 for each group） as high colour stability （HCS）, intermediate colour stability （ICS） and low colour stability （LCS）. The activities of GAPDH and LDH-B, muscle colour attributes, nicotinamide adenine dinucleuotide （NADH） concen- tration and lactate concentration were measured. The samples in HCS had higher activities of GAPDH and LDH-B than the samples in the LCS, and the samples in the HCS group also possessed higher NADH and lower lactate concentration. The higher activity of dehydrogenase enzyme may result in higher NADH concentrations and colour stability in muscle tissue. The results suggest that the activity of GAPDH and LDH-B may also play a role in maintaining colour stability.