Set Of Colors Research Articles

Polya enumeration theorems in algebraic geometry

We generalize a formula due to Macdonald that relates the singular Betti numbers of $X^{n}/G$ to those of $X$, where $X$ is a compact manifold and $G$ is any subgroup of the symmetric group $S_{n}$ acting on $X^{n}$ by permuting coordinates. Our result is completely axiomatic: in a general setting, given an endomorphism on the cohomology $H^{\bullet}(X)$, it explains how we can explicitly relate the Lefschetz series of the induced endomorphism on $H^{\bullet}(X^{n})^{G}$ to that of the given endomorphism on $H^{\bullet}(X)$ in the presence of the Kunneth formula with respect to a cup product. For example, when $X$ is a compact manifold, we take the Lefschetz series given by the singular cohomology with rational coefficients. On the other hand, when $X$ is a projective variety over a finite field $\mathbb{F}_{q}$, we use the $l$-adic etale cohomology with a suitable choice of prime number $l$. We also explain how our formula generalizes the Polya enumeration theorem, a classical theorem in combinatorics that counts colorings of a graph up to given symmetries, where $X$ is taken to be a finite set of colors. When $X$ is a smooth projective variety over $\mathbb{C}$, our formula also generalizes a result of Cheah that relates the Hodge numbers of $X^{n}/G$ to those of $X$. We will also see that our result generalizes the following facts: 1. the generating function of the Poincare polynomials of symmetric powers of a compact manifold $X$ is rational; 2. the generating function of the Hodge-Deligne polynomials of symmetric powers of a smooth projective variety $X$ over $\mathbb{C}$ is rational; 3. the zeta series of a projective variety $X$ over $\mathbb{F}_{q}$ is rational. We also prove analogous rationality results when we replace $S_{n}$ with $A_{n}$, alternating groups.

Edge homogeneous colorings

We explore four kinds of edge colorings defined by the requirement of equal number of colors appearing, in particular ways, around each vertex or each edge. We obtain the characterization of graphs colorable in such a way that the ends of each edge see (not regarding the edge color itself) \(q\) colors (resp. one end sees \(q\) colors and the color sets for both ends are the same), and a sufficient condition for 2-coloring a graph in a way that the ends of each edge see (with the omission of that edge color) altogether \(q\) colors. The relations of these colorings to \(M_q\)-colorings and role colorings are also discussed; we prove an interpolation theorem for the numbers of colors in edge coloring where all edges around each vertex have \(q\) colors.

Optimal Control of Colored Timed Petri Nets Under Generalized Mutual Exclusion Temporal Constraints

A coloured Petri net (CPN) is widely used to model discrete event systems due to its compact representation of the system by colour sets associated with places, transitions and I/O arcs. For real-world systems such as manufacturing systems, transportation systems, and communication protocols, a coloured timed Petri net (CTPN) is proposed to model timed behaviours. To control a discrete event system with a desired control specification, it is important to describe the control specification formally. For the CPN, a class of specification called coloured generalized mutual exclusion constraints (cGMEC) is utilized to specify the behaviours. However, cGMEC can only represent safety constraints and not temporal constraints. Therefore, in this paper, we propose a novel temporal logic based constraint called a coloured generalized mutual exclusion temporal constraint (cGMETC). The cGMETC is described by a signal temporal logic (STL) formula where each atomic predicate represents a cGMEC. We propose a method for optimal control of the CTPN under a given cGMETC. In particular, we formulate an optimal control problem and solve the problem by transforming it into an integer linear programming problem. Through a simulation of an optimal control problem of a manufacturing system, we demonstrate the effectiveness of the proposed approach.

AVD proper edge-coloring of some families of graphs

Adjacent vertex-distinguishing proper edge-coloring is the minimum number of colors required for the proper edge-coloring of [Formula: see text] in which no two adjacent vertices are incident to edges colored with the same set of colors. The minimum number of colors required for an adjacent vertex-distinguishing proper edge-coloring of [Formula: see text] is called the adjacent vertex-distinguishing proper edge-chromatic index. Adjacent vertex-distinguishing proper edge-chromatic indices of the middle graph, splitting graph and shadow graph of path and cycle are determined. Adjacent vertex-distinguishing proper edge-chromatic indices of the triangular grid [Formula: see text], [Formula: see text]-graph and generalized [Formula: see text]-graph are also determined.

Visualization and Maneuverability Features of a Robotic Arm Three-Dimensional Exoscope and Operating Microscope for Clipping an Unruptured Intracranial Aneurysm: Video Comparison and Technical Evaluation.

In recent years, three-dimensional (3D) digital exoscope systems have been developed and reported to form an adequate alternative to the conventional operating microscope. To illustrate essential and practical features in a surgical video comparing a robotic arm 3D digital exoscope and a conventional operating microscope to clip a middle cerebral artery aneurysm. We used a mouth switch-controlled operating microscope (OPMI PENTERO 900; Carl Zeiss Meditec AG) and robotic arm-controlled 3D digital Aeos exoscope (Aesculap Inc). We assessed the following visualization and optical features: overall visualization quality, color and contrast quality, range and quality of magnification, and adjustment of focus. In addition, we assessed maneuverability for changing surgical site within and viewing angle of the surgical field. We found that both modalities are suitable for this surgery and offer distinct qualities. The microscope enables faster magnification adjustment and continuous mouth switch-controlled focus adjustments. The advantages of the exoscope include the adaptation of color and contrast settings, and the surgeon can keep both hands in the surgical field while the camera pivots around its working field. The exoscope and operating microscope offer a similar high-quality visualization of, and smooth maneuvering within, the surgical field. The method of visualization and maneuvering is, however, very distinct. Therefore, a surgeon's acquaintance and experience with the specific features and how to optimally use them in surgery are of utmost importance. Further analyses of both systems are needed to evolve these tools.

Burning Karen’s Headquarters: Gender, Race, & the United Daughters of the Confederacy Headquarters

In the early morning hours of 31 May 2020 in Richmond, Virginia, along with graffiti to the monuments lining the city’s historic Monument Avenue, the nearby headquarters of the United Daughters of the Confederacy was covered in colorful graffiti and set aflame. This article explores the gendered and raced critiques of the United Daughters of the Confederacy’s memory work communicated by this protest action, using the “Karen meme” as its point of departure. Invocations of “Karen” on Twitter in response to the Richmond protest made pointed arguments about narrative, place, and aesthetics, critiquing not only the Daughters’ role in remembering the Confederacy but the “Southern lady” trope within American public memory. Rather than an oblique reference, the Karen meme, this article argues, underscored Twitter’s potential as a site of anti-racist resistance during times of crisis.

INTERVAL VERTEX-COLORINGS OF CACTUS GRAPHS WITH RESTRICTIONS ON VERTICES

An interval vertex-coloring of a graph $G$ is a coloring of the vertices of the graph with intervals of integers such that the intervals of any two adjacent vertices do not intersect. In this paper we consider the case, where for each vertex $v$ there is a length $l(v)$ and a set of colors $S(v),$ from which the colors should be and it is required to find an interval vertex-coloring $\gamma$ such that for each vertex $v$ the restrictions are met, i.e. $|\gamma(v)|=l(v),\gamma(v) \subseteq S(v) $. We will provide a pseudo-polynomial algorithm for cactus graphs. If it is impossible to have an interval vertex-coloring that satisfies all the restrictions, then the algorithm will tell that as well.

Color in web banner advertising: The influence of analogous and complementary colors on attitude and purchase intention

• This study focuses on color combinations in the context of web banner advertising. • Two experimental studies extend research on analogous and complementary colors. • Blue-green analogous color set tend to elicit more positive attitudes. • Blue-green analogous color set tend to elicit higher purchase intention. • Results were partially confirmed for Study 1 and (totally) confirmed for Study 2. The purpose of this paper is to study how color contrast (complementary vs. analogous colors) affect individuals’ attitude and purchase intention in the context of web banner advertising. Previous research on the effect of color in marketing stated that color is one of the most important factors for fast decisions regarding product choice. However, the study of color has mainly focused on isolated colors (hue) and color temperature (cool vs. warm colors). Thus, color contrast studies are lacking. Two experimental studies ( N total = 409) were conducted in the context of web banner advertising. Study 1 involved a service setting (a wireless internet service provider) and Study 2 focused on a product category (a wireless headphone set). Findings revealed that the blue-green analogous color set tend to elicit higher levels of both attitude towards the ad and purchase intention. The results were partially confirmed for Study 1 and (totally) confirmed for Study 2. This research work contributes to shed some light into color perception and e-commerce strategy thus helping marketers and designers to create more effective web banner advertisements.

I/O-optimal categorical 3-sided skyline queries

The skyline of a set of two-dimensional points is the subset of points not dominated by any other point. In this paper, we consider a set of two-dimensional points (in rank space) that are assigned an additional category, or color. The goal is to preprocess these points so that given a three-sided region of the form [a,b]×[τ,∞] we can return the set of distinct colors on the skyline of the queried region. We approach this problem in the external memory model and present an I/O-optimal data structure that answers a query using O(1+kB) I/Os and requires O(nlog⁎⁡n) words of space, where n is the number of points, k is the size of the solution, and B is the block size. Additionally, we provide a space-time trade-off by presenting a data structure that answers a query using O((log⁎⁡n)2+kB) I/Os and requires O(n) words of space.

AVD Proper Edge-Coloring of some Cycle Related Graphs

The adjacent vertex-distinguishing proper edge-coloring is the minimum number of colors required for a proper edge-coloring of G, in which no two adjacent vertices are incident to edges colored with the same set of colors. The minimum number of colors required for an adjacent vertex-distinguishing proper edge-coloring of G is called the adjacent vertex-distinguishing proper edge-chromatic index. In this paper, I compute adjacent vertex-distinguishing proper edge-chromatic index of Anti-prism, sunflower graph, double sunflower graph, triangular winged prism, rectangular winged prism and Polygonal snake graph.

CREATIVE DESIGN OF BUILDINGS AND STRUCTURES

This article provides information on the design and efficient use of buildings and structures to improve the integration of engineering graphics and design sciences, the construction of quality housing. The article in your hand is drawing and design in a cycle of engineering graphics and design sciences on improving the integration of themes, in which architectural approaches are described by nature in relation to the set of colors used by artists as well as modest decorators, architects and designers. buildings are also covered.

Quantum Legacies: Dispatches from an Uncertain World

Quantum Legacies: Dispatches from an Uncertain World

Increasing workers comfort: experiment of the effect of color and lighting in assembly manufacture

Color and light are the main factors in the car manufacturing industry, with not much research, conducted on this topic, related to employee physical comfort. The factor affecting employee work comfort is the color factor and lighting time in their workplace environment. Color is the light, reflected by an object, then interpreted by the eye based on the light that hits the object. The value of the color wavelength in the spectrum of 380 nm to780 nm impacts worker performance. Good lighting will affect whether or not the room’s light conditions affect the illumination’s value. A good working room condition will affect the physical comfort of employees. Employee physical comfort has developed in many previous studies. However, research on the configuration of colors and lighting in the manufacturing industry’s work environment is still underdeveloped. This research aims to measure and determine the impact of color and lighting at specific color wavelengths on the illumination value and the employee’s physical comfort. It starts with studying the color, light, human comfort, then examines the effect on the manufacturing industry employees’ performance in the wiring installation assembly industry. Color and light settings are proven essential to get better human comfort. Green color with a wavelength of 490 nm to 570 can increase the highest illuminate average lux value of 12.43 %. Yellow can increase the heart rate by 4.85 %, while green can reduce Diastole by 2.95 % and Systole by 1.29 %. Pupillary size changes L by 23.17 % and R by 21.43 %. The effect of green color and lighting time can increase the value of illumination and decrease heart rate, blood pressure, and pupil size so that it impacts the physical comfort of employees.

Steganography in Color Animated Image Sequence for Secret Data Sharing Using Secure Hash Algorithm

Steganography is one of the leading strategy that is employed to hide restricted content into a cover media so that the person unaware of the fact can’t predict that the cover media can acquire some secret information. The effectiveness of any steganographic approach is appraised on imperceptibility of the stego-media, payload of the cover media, integrity of the secret information, security, and computational complexity. The work presented in this paper focuses on these important concerns of secured data transmission. The proposed steganographic approach uses multimedia files including animated image sequences as cover media for concealing secret messages. The entire secret information to be embedded is converted to a code using Secure Hash Algorithm-1 (SHA-1) (National Institute of Standards, and Technology (US). Technology Administration. Secure hash standard, 1993) and shared with the secret message to validate the authenticity of the transmitted secret information. The whole secret message is converted to its ASCII to embed them by replacing the least significant digit (LSD) (Liu et al. In Proceedings of the 2012 IEEE International Conference on Communications (ICC), IEEE, 2012). The receiver validates the transmitted information with SHA-1 again generating a code, which validates with the existing code sent over from the transmitting end. The proposed algorithm is worked upon a variety of text messages with a large set of color animated image sequences as cover media and also has been tested carefully by different parametric measures. This algorithm gives robust outputs in terms of visual imperceptibility, safety, and embedding capability.

Research on key technologies of 3D visualization of marine environmental field

In view of the slow rendering speed and poor effect of 3D visualization of marine environment field, this paper studies the 3D visualization of vector field and scalar field of marine environment based on particle system, second-order Euler integral algorithm, linear interpolation method and 3D GIS visualization technology. Firstly, the particle motion model is constructed based on the second-order Euler integration algorithm, and the multi-scale transformation model is constructed based on the perspective perception, and the multi-scale visualization model of the vector field of marine environment is established. Secondly, the mesh is generated by bilinear interpolation, and the color mapping model and the hierarchical color setting scalar field visualization model are established. Finally, based on the technology of 3D GIS, the 3D visualization of marine environment field is realized, and the rendering speed and rendering effect are improved, which provides the basis for the efficient utilization of marine environment information.

Chromatic λ‐choosable and λ‐paintable graphs

AbstractLet be the minimum number of vertices in a non‐‐choosable ‐chromatic graph. The Ohba conjecture, confirmed by Noel, Reed and Wu, asserts that . This bound is tight if is even. If is odd, then it is known that and it is conjectured by Noel that . For a multiset of positive integers, let . For positive integer , let be the multiplicity of in , and let be the number of elements in that are odd integers. A ‐list assignment of is a list assignment such that the colour set can be partitioned into the disjoint union of sets so that for each and each vertex of , . We say is ‐choosable if is ‐colourable for any ‐list assignment of . We say is trivial if consists of copies of 1. It is easy to see that if is trivial, then ‐choosable is equivalent to ‐colourable. For any nontrivial , let be the minimum number of vertices in a non‐‐choosable ‐chromatic graph. We prove that for any nontrivial , . In particular, if , that is, contains no odd integer greater than 1, then . We also prove that . In particular, if , then . We then introduce the concept of ‐paintability of graphs, which is an online version of ‐choosability. Let be the minimum number of vertices in a non‐‐paintable ‐chromatic graph. We determine the value of when each integer in is at most 2.

Video recoloring via spatial-temporal geometric palettes

Color correction and color grading are important steps in film production. Recent palette-based approaches to image recoloring have shown that a small set of representative colors provide an intuitive set of handles for color adjustment. However, a single, static palette cannot represent the time-varying colors in a video. We introduce a spatial-temporal geometry-based approach to video recoloring. Specifically, its core is a 4D skew polytope with a few vertices that approximately encloses the video pixels in color and time, which implicitly defines time-varying palettes through slicing of the 4D skew polytope at specific time values. Our geometric palette is compact, descriptive, and provides a correspondence between colors throughout the video, including topological changes when colors merge or split. Experiments show that our method produces natural, artifact-free recoloring.

The Action of the Weyl Group on the E_8 Root System

Let varGamma be the graph on the roots of the E_8 root system, where any two distinct vertices e and f are connected by an edge with color equal to the inner product of e and f. For any set c of colors, let varGamma _c be the subgraph of varGamma consisting of all the 240 vertices, and all the edges whose color lies in c. We consider cliques, i.e., complete subgraphs, of varGamma that are either monochromatic, or of size at most 3, or a maximal clique in varGamma _c for some color set c, or whose vertices are the vertices of a face of the E_8 root polytope. We prove that, apart from two exceptions, two such cliques are conjugate under the automorphism group of varGamma if and only if they are isomorphic as colored graphs. Moreover, for an isomorphism f from one such clique K to another, we give necessary and sufficient conditions for f to extend to an automorphism of varGamma , in terms of the restrictions of f to certain special subgraphs of K of size at most 7.

МУСТАҚИЛЛИК ДАВРИДА МАҲОБАТЛИ РАНГТАСВИР

The article analyzes the features of the formation of the school of painting in Uzbekistan in the twentieth century, the harmony of painting with modern urban planning, analysis of the work of greatpainters. In particular, in the works of B. Jalolov, one of the most prominent artists in the field of monumental painting, we see that he skillfully combined the strong traditions of the academic school, the aesthetics of Western and Eastern art. His work can be seen in a series of frescoes. The interior of theTurkiston concert palace in Tashkent contains analytical information about the work of Umar Khayyam on oriental lyrics, “Nobody said why I was born” at the National Bank of Uzbekistan, as well as about his monumental works in many other regions. On the example of Samarkand, A. Isaev was one of the most versatile artists in the field of monumental painting, he also wrote “The Great Silk Road” on the walls of the foyer of the Institute of Foreign Languages and “Friendship of Peoples” for the foyer of the academic lyceum of the Institute, Examples “History of Samarkand” for the hotel “ Afrosiyab ", at the Samarkand Agricultural Institute, such as" The Generosity of Mother Earth ", 41 ceramic panels on Tashkent Street and many other monumental paintings. By the colors in the artist's works, one can imagine that the artist played the melody in a lyrical tone. The article notes that almost all compositions are characterized by a description of the artist's work, such as the observation ofwarmth, a set of warm colors, oriental colors, a patriotic mood, which is typical for all artists

Hopf Algebra Structure of Generalized Quasi-Symmetric Functions in Partially Commutative Variables

We introduce a coloured generalization $\mathrm{NSym}_A$ of the Hopf algebra of non-commutative symmetric functions described as a subalgebra of the of rooted ordered coloured trees Hopf algebra. Its natural basis can be identified with the set of sentences over alphabet $A$ (the set of colours). We present also its graded dual algebra $\mathrm{QSym}_A$ of coloured quasi-symmetric functions together with its realization in terms of power series in partially commutative variables. We provide formulas expressing multiplication, comultiplication and the antipode for these Hopf algebras in various bases — the corresponding generalizations of the complete homogeneous, elementary, ribbon Schur and power sum bases of $\mathrm{NSym}$, and the monomial and fundamental bases of $\mathrm{QSym}$. We study also certain distinguished series of trees in the setting of restricted duals to Hopf algebras.