Graphs‚ Groups and Surfaces 1 Introduction In this paper‚ we will discuss the interactions among graphs‚ groups and surfaces. For any given graph‚ we know that there is an automorphism group associated with it. On the other hand‚ for any group‚ we could associate with it a graph representation‚ namely a Cayley graph of presentations of the group. We will first describe such a correspondence. Also‚ a graph is always embeddable in some surface. So we will then focus on properties of graphs
Premium Group Graph theory
Chapter 1 Outlook 1. Explain the five parts of an information system‚ 2. Distinguish application software from system software‚ 3. Distinguish four types of computers‚ 4. Explain computer connectivity. 1.1 Introduction: People who use microcomputers are called “end users”. Today: • Microcomputers are common tools in all areas of life. Writers write‚ artists draw‚ engineers and scientists calculate – all on microcomputers. • With the aid of computers‚ new forms of learning
Premium Computer Computer data storage Personal computer
#1. The Emperor’s Decree to the Outer Barbarians and Letter to the English Ruler are both sent from Qing Dynasty to Great Britain. The emperor’s Decree to the Outer Barbarians was written to Britain during the flourishing period of Qing Dynasty. The emperor sent a decree to Britain as a respond to requests of Britain on trade regulations. On contrary‚ Letter to the English Ruler‚ written before Opium War occurs‚ includes “warnings” of Qing Dynasty to Britain to no longer harm their people with
Premium Edo period Samurai Tokugawa shogunate
of Nervous Tissue Exercise 1: Multipolar Neurons Paste an image found on LabPaq site or Google images of a spinal cord smear and label its basic parts using basic labeling boxes provided. Identify the cell body‚ the nucleus‚ the large nucleolus‚ and granular Nissl bodies on the slide. Try to find the axon and differentiate it from the dendrites if possible. Hint: after pasting image‚ right click on it and select “order”‚ “send to back”. cell body nucleus large nucleolus Nissl
Premium Neuron Nervous system
Affirmative action has deep roots within the American workforce as well as the schooling system. Once used as a system to prevent racism and discrimination during the civil rights era‚ affirmative action has remained a part of American culture. Although many Americans may not be entirely aware of its use‚ all of them are affected by it. The effects and uses of this system can be seen through the history‚ public opinion and finally‚ how it can be fixed or changed to better
Premium Affirmative action Discrimination Reverse discrimination
Cell Structure and Function Chapter Outline Cell theory Properties common to all cells Cell size and shape – why are cells so small? Prokaryotic cells Eukaryotic cells Organelles and structure in all eukaryotic cell Organelles in plant cells but not animal Cell junctions History of Cell Theory mid 1600s – Anton van Leeuwenhoek Improved microscope‚ observed many living cells mid 1600s – Robert Hooke Observed many cells including cork cells 1850 – Rudolf Virchow
Premium Cell Organelle Eukaryote
The plasma membrane is a fluid phospholipid bilayer. The outside of the bilayer is hydrophilic portions of porteins and phospholipids because they are exposed to water. This results in a stable membrane structure. Inside the bilayer hydrophobic portions of proteins and phospholipids because the inside of the bilayer is nonaqueous. the proteins bob in the fluid bilayer of phospholipids. The proteins also vary in structure and function. There are teh integral proteins; transmembrane
Premium Cell membrane Lipid bilayer Protein
and appears in the Rig Veda as the name of the sections of the work‚ but is also used in other Indian religions‚ particularly Buddhism. In the Tibetan branch of Vajrayana Buddhism‚ mandalas have been developed into sandpainting. They are also a key part of anuttarayoga tantra meditation practices. In various spiritual traditions‚ mandalas may be employed for focusing attention of aspirants and adepts‚ as a spiritual teaching tool‚ for establishing a sacred space‚ and as an aid to meditation and trance
Premium Buddhism Mahayana
10.6 SURFACES IN SPACE EXAMPLE 6.1 Sketching a Surface © The McGraw-Hill Companies‚ Inc. Permission required for reproduction or display. Slide 1 10.6 SURFACES IN SPACE EXAMPLE 6.1 Sketching a Surface Solution Since there are no x’s in the equation‚ the trace of the graph in the plane x = k is the same for every k. This is then a cylinder whose trace in every plane parallel to the yz-plane is the parabola z = y2. © The McGraw-Hill Companies‚ Inc. Permission required for
Premium Conic section Ellipse
Cell Organelles Nucleus Its function is to control the cell’s activities and retain the chromosomes. The nucleus is bound by a double membrane‚ the nuclear envelope. The nuclear envelope has pores in it to allow the transport of mRNA. The cytoplasm like material is called nucleoplasm which contains chromatin (coils of DNA and histone proteins)‚ it is chromatin that condenses to form chromosomes during cell division. Within the nucleus is a small spherical body called the nucleolus which
Free Cell Endoplasmic reticulum Organelle