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. .

敦煌三危山出产多色颜料的矿物学及谱学特征研究

敦煌三危山火焰沟发现一处古代多色颜料开采遗址,该遗址的发现对研究我国西北地区古代矿物颜料的来源有着一定的学术意义。为判断三危山出产颜料的矿物种属及其谱学特征,本文应用偏光显微镜、X射线衍射、激光拉曼光谱、X射线荧光光谱多种光谱分析手段对所出产多色颜料矿物开展科学分析。结果表明,三危山古矿出产矿物颜料属天然矿物,主要化学成分为Fe_(2)O_(3)(平均含量66%)和SiO_(2)等,部分样品呈现富硅铝的特征,且均存在不同程度的烧失;主要物相以赤铁矿、针铁矿为主,少许铁矾类,脉石矿物包括石英、高岭石及少许黏土矿物。同时进一步通过拉曼光谱对矿物颜料的显色物相进行分析,2号亮黄色矿物显色物相和前述主要物相一致,均为铁矾类(黄钾铁矾和黄钠铁矾)。除4号样品外,所有呈红棕色的样品主要显色物相均为α-Fe_(2)O_(3)即赤铁矿,而4号样品显色物相为针铁矿,呈色本应为黄色,但致其呈色变为红棕色是由于和赤铁矿伴生存在,且赤铁矿显色能力远强于针铁矿,故改变了4号样品的呈色。综上,该古矿遗址所出产的红色矿物颜料主要为赤铁矿,黄色矿物颜料为黄钾铁矾和黄钠铁矾。黄钾铁矾作为优良的颜料,在岩画及壁画也多有使用,但在莫高窟目前已研究的壁画上暂未发现使用,三危山古矿实证了铁矾类颜料矿物的存在,该发现在一定程度上拓宽了对西北地区黄色矿物颜料的维度。同时也为后续研究该矿冶遗址出产颜料的流向,提供了基础性的数据支撑。

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.

多糖对红葡萄酒颜色稳定性的影响研究进展

红葡萄酒颜色是判断葡萄酒品质的重要指标之一,在葡萄酒酿造和存储过程中由于光照、温度和pH等各种因素导致葡萄酒的颜色消退品质下降。多糖是存在于葡萄酒中的一大类复杂大分子,来源于葡萄细胞壁破碎和酵母细胞壁自溶。研究发现多糖对葡萄酒颜色稳定具有潜在应用价值,如何利用多糖在不影响葡萄酒品质的前提下提高葡萄酒颜色稳定性,对提升葡萄酒品质具有重要意义。该文针对多糖对葡萄酒颜色稳定性影响的相关研究进展进行综述,阐述了葡萄酒中多糖种类、结构及多糖对葡萄酒颜色影响的作用机制研究进展,最后对未来研究重点进行展望,旨在为利用多糖稳定红葡萄酒颜色工艺开发提供参考。

鸡公山野生木本观赏植物资源及开发利用策略分析

采用实地调研与文献结合的方法,根据生活型、花色、花期、果色、果实类型、观果季节和叶色,将鸡公山的野生木本观花、观果和观叶植物进行分类,分析其数量和应用情况。结果表明,研究区野生木本观花植物157种,以灌木、白色系花朵数量较多,主要在春季观花;观果植物50种,以乔木、红色果实和核果数量较多,多在秋季观果;观叶植物35种,其中槭树科、漆树科树种最多,秋色叶树种较多。关于野生木本观赏植物开发利用提出了适地适树和强化种质资源保护的策略。本研究为研究区乡土木本观赏植物应用提供参考。

基于孟塞尔色彩体系的通山县传统村落色彩风貌控制研究——以宝石村为例

湖北省咸宁市通山县位于鄂、湘、赣三省交界,其聚落布局、结构、工艺、色彩风貌皆体现出多元融合的发展态势,并最终形成极具地域特色的聚落面貌。在当代乡村振兴的国家战略背景下,针对传统村落的色彩风貌控制策略研究,有助于凝练村落特色、提升环境和谐度,尤其在部分新建民居建筑进入到传统聚落环境中时,由于建筑材料与建造工艺的改变,在最终呈现出的色彩风貌上面临着新旧关系衔接的问题。该文以通山县13个传统村落作为主要调研样本,结合通山县传统村落文献记载和实地照片等定性分析,利用孟塞尔色彩体系的色彩表达方法进行色相、彩度、明度的定量分析,解析通山县传统民居的色彩现状。以宝石村为重点研究对象,选取村落中具有代表性的街巷与典型民居建筑,根据民居搭建年代筛选出可保留的民居色彩,提出推荐色谱,为宝石村提炼出更具地域特色的色彩组成,为其后续修复与发展提供色彩风貌控制的方向与策略。

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%.