Defined terms in geometry

axiomatic structure of a mathematical system in Geometry particular: (a) defined terms; (b) undefined terms; (c) postulates; and (d) theorems

AXIOMATIC STRUCTURE OF MATHEMATICAL SYSTEM IN GEOMETRY particular: (a) defined terms; (b) undefined terms; (c) postulates; and (d) theorems

Axiomatic structure of mathematical system in geometry particularly (a) defined terms; (b) undefined terms; (c) postulates; and (d) theorems.

New Trends in Agriculture Extension approaches Extension has been, and still is, under attack from a wide spectrum of politicians and economists over its cost and financing. As a result, Extension Systems have had to make changes, by restating the system’s mission, developing a new vision for the future, and formulating plans for the necessary transition to achieve the desired change. 1. Privatization of Agricultural Extension Service Privatization: Process of funding and delivering the extension services by private individual or organization is called Private Extension. Concept: Privatization of extension refers to services rendered in rural area & allied aspects of extension personnel working in private agencies or organization for which farmers are expected to pay a fee & it can be viewed as supplementary or alternative to public extension services (Sarvanan & Shivalinge 1980). Privatization approaches ➢ Share cropping system ➢ Village extension contract system ➢ Public extension through private delivery ➢ Service for vouchers Strengths of Private Extension System ➢ More demand - driven rather than supply – driven ➢ High quality of services in terms of satisfying information needs of clientele, trained manpower, sustained finances and resource allocation ➢ Provides for an information mix and choices available to farmers ➢ Enhanced efficiency of staff ➢ Assure continuous supply and quality agricultural products ➢ More effective because farmer can select an adviser who is the best able to help ➢ Healthy competition among service provider will lead to better quality and lower costs for service Weakness of Private Extension System ➢ Concentrate on area having favorable physical environment ➢ More face-to-face contacts (person oriented) ➢ Increased dependence of farmers and hence exploitation ➢ No education role ➢ Deprivation of small farmers ➢ Hamper the free flow of information 2. Cyber Extension or e-extension Concepts Cyber space: it is the imaginary or virtual space of computers connected with each other on Networks, across the Globe. Cyber extension: it means 'using the power of online networks, computer communications and digital interactive multimedia to facilitate dissemination of agriculture technology. Cyber Extension thus can be defined as the extension over cyber space. Important tools of cyber extension E-Mail, Telnet, File Transfer Protocol (FTP), Gopher, Archie and World Wide Web (WWW) Strengths of Cyber Extension ➢ Access to the astounding information and continuously available ➢ Information rich and instantaneously available of information ➢ Interactive communication ➢ The information is available from any point on the globe ➢ Communication is dynamic ➢ Cut steps from traditional process ➢ Save money, time and effort ➢ Multiplicity of purpose Issues and Concerns of Cyber Extension ➢ Lack of Reliable Telecom Infrastructure in Rural Areas ➢ Erratic or no Power Supply ➢ Lack of ICT Trained manpower (willing to serve) in Rural Areas ➢ Lack of content (locally relevant and in local languages) ➢ Lack of Information Services to Rural Clientele ➢ Low Purchasing power of the Rural communities ➢ Lack of Holistic Approaches ➢ Issues of Sustainability Application of cyber extension ➢ Village information shops Dr. M.S. SwaminathanResearch Foundation, Chennai ➢ Information villagers MANAGE in Ranga Reddy District in Andhra pradesh ➢ Gyandoot net initiative of District Dhar, Madhya Pradesh. ➢ Warna wired village of National Informatics Center (NIC) in Kolhapur- Sangli Districts of Maharashtra 3. Market-Led-Extension (MLE) Concepts Market: A congregation of prospective buyers & sellers with a common motive of trading a particular commodity. Extension: It is the spreading/reaching out to the mass Market-led-extension: Agriculture & economics coupled with extension is the perfect blend for reaching at the door steps of common man with the help of technology. Dimensions of market-led extension ➢ Marketing mix: A planned mix of the controllable elements of a product's marketing plan commonly termed as 4Ps: product, price, place, and promotion. These four elements are adjusted until the right combination is found that serves the needs of the product's customers, while generating optimum income. ➢ Marketing plan: A marketing plan is a comprehensive document that outlines a business and marketing efforts for the coming year. It describes business activities involved in accomplishing specific marketing objectives within a set time frame. A marketing plan also includes a description of the current marketing position of a business, a discussion of the target market and a description of the marketing mix that a business will use to achieve their marketing goals. ➢ Market Intelligence: It is the information relevant to a company’s markets, gathered and analyzed specifically for the purpose of accurate and confident decision making. Market intelligence includes the process of gathering data from the company’s external environment, whereas the business intelligence process is primarily based on internal recorded events – such as sales, shipments and purchases. ➢ Market oriented production ➢ Use of Technology Strengths of market-led extension ➢ SWOT analysis of the market ➢ Organization of Farmers’ Interest Groups (FIGs) ➢ Enhancing the interactive and communication skills of the farmers ➢ Establishing marketing and agro-processing linkages ➢ Advice on product planning ➢ Educating the farming community ➢ Direct marketing ➢ Acquiring complete market intelligence ➢ Publication of agricultural market information Production of video films of success stories ➢ Challenges to market-led extension ➢ Gigantic size of extension system ➢ Information technology Diverse conditions ➢ Market intelligence ➢ Reforms in agricultural extension system Government Initiatives ➢ Central warehousing Corporation-1965 ➢ MSP by Commission for Agricultural Cost and Price (CACP) ➢ Food Corporation of India ➢ Then some others as: Cotton Corporation of India (CCI), Jute Corporation of India (JCI), National Dairy Development Board (NDDB), Agriculture and Processed food Export Development Authority (APEDA) etc. 4. Farmer--Led-Extension (FLE) Farmer--led-extension is defined as 'the provision of training by farmers to farmers, often through the creation of a structure of farmer promoters and farmer trainers' (Scarborough et al., 1997). Philosophy and principles ➢ Farmers and local institutions (e.g. producer organizations or village leaders) should play a key role in selecting farmer-trainers and monitoring and evaluating them. This helps make the programmes more accountable to the community or groups that they serve. ➢ Farmer-trainers are ‘of the community’; they communicate in local languages and are more sensitive to local cultures, mannerisms, farming practices, and farmers’ needs. ➢ Farmer-trainers should be selected on the basis of their skills and interest in sharing information, not just on their farming expertise. ➢ Farmer-trainers need strong linkages with and support from development agents (whether government, non-government organization (NGO), or private), the people who train and backstop them. Farmer-trainers generally serve as a complement to existing extension systems, rather than being a substitute for them. ➢ Facilitating organizations and local institutions need to be proactive in ensuring that women as well as men become farmer-trainers. ➢ Simple and appropriate reference materials should be made available to the farmer trainers. Essential Elements of Farmer--led-extension ➢ The group ➢ The Field ➢ The Facilitator ➢ The curriculum ➢ Programme leader ➢ Financing Special features of Farmer--led-extension ➢ All learning is field based & it is primary venue for learning ➢ FLE group learning constantly over the experimentation period ➢ FLE promotes healthy decisions & quality decisions ➢ Farmers conduct their own field studies with comparisons or treatments ➢ Facilitates Farmer-to-Farmer communication ➢ Field staff serve as facilitators ➢ FLE is a unique way to educate farmers ➢ It is an effective platform for sharing of experiences and collectively solving agriculture related problems. 5. Expert system Expert system is an intelligent computer program that uses knowledge and inferences procedures to solve problems (Daniel Hunt, 1986). Objectives of developing expert system ➢ To enhance the performance of agricultural extension personnel and farmer ➢ To make farming more efficient and profitable ➢ To reduce the time required in solving the problems ➢ To maintain the expert system by continuously upgrading the database Advantages of expert system ➢ Solves critical problems by making logical deductions without taking much time ➢ It combines experimental and conventional knowledge with the reasoning skills of specialists ➢ To enhance the performance of average worker to the level of an expert Limitations of expert system ➢ Expensive computer program ➢ Mostly developed not in regional languages ➢ Requires AC power and internet connection all the time ➢ Complex software requires computer skilled personnel Modules of expert system in agriculture ➢ COMAX: Integrated crop management in cotton ➢ SOYEX: Soybean oil extraction expert system ➢ PLANT/ds: Diagnosis of soybean diseases ➢ MAIZE: Maize expert system for field crop management ➢ SEMAGI: Weed control decision making in sunflowers ➢ Rice Crop Doctor: Developed by National Institute of Agricultural Extension Management (MANAGE) Difference between conventional and expert system of extension Conventional Extension ➢ Universal approachability of same information is a problem ➢ Information is given whatever is available without considering needs and resources ➢ No Cost benefit analysis ➢ Information flow depends on availability of agent ➢ Require users to draw their own conclusion from facts Expert System of Extension ➢ Universal approachability of same information is possible ➢ Information is chosen based on their needs and resources ➢ Cost benefit analysis ➢ Information through Cyber Cafe at any place at any time ➢ Conclusion is drawn based on the decision given by the expert

A solution is a mixture in which one or more substances are uniformly distributed in another substance. Solutions can be mixtures of liquids, solids, or gases. For example, plasma, the liquid part of blood, is a very complex solution. It is composed of many types of ions and large molecules, as well as gases, that are dissolved in water. A solute (SAHL-YOOT) is a substance dissolved in the solvent. The particles that compose a solute may be ions, atoms, or molecules. The solvent is the substance in which the solute is dissolved. For example, when sugar, a solute, and water, a solvent, are mixed, a solution of sugar water results. Though the sugar dissolves in the water, neither the sugar molecules nor the water molecules are altered chemically. If the water is boiled away, the sugar molecules remain and are unchanged. Solutions can be composed of various proportions of a given solute in a given solvent. Thus, solutions can vary in concentra- tion. The concentration of a solution is the amount of solute dis- solved in a fixed amount of the solution. For example, a 2 percent saltwater solution contains 2 g of salt dissolved in enough water to make 100 mL of solution. The more solute dissolved, the greater is the concentration of the solution. A saturated solution is one in which no more solute can dissolve. Aqueous (AY-kwee-uhs) solutions—solutions in which water is the solvent—are universally important to living things. Marine microorganisms spend their lives immersed in the sea, an aqueous solution. Most nutrients that plants need are in aqueous solutions in moist soil. Body cells exist in an aqueous solution of intercellu- lar fluid and are themselves filled with fluid; in fact, most chemical reactions that occur in the body occur in aqueous solutions. Copyright © by Holt, Rinehart and Winston. All rights reserved. Liquid water Solid water Ice (solid water) is less dense than liquid water because of the structure of ice crystals. The water molecules in ice are bonded to each other in a way that creates large amounts of open space between the molecules, relative to liquid water. FIGURE 2-12 solvent from the Latin solvere, meaning “to loosen” Word Roots and Origins CHEMISTRY OF LIFE 43 ACIDS AND BASES One of the most important aspects of a living system is the degree of its acidity or alkalinity. What do we mean when we use the terms acid and base? Ionization of Water As water molecules move about, they bump into one another. Some of these collisions are strong enough to result in a chemical change: one water molecule loses a proton (a hydrogen nucleus), and the other gains this proton. This reaction really occurs in two steps. First, one molecule of water pulls apart another water molecule, or dissociates, into two ions of opposite charge: H2O ∏ H OH The OH ion is known as the hydroxide ion. The free H ion can react with another water molecule, as shown in the equation below. H H2O ∏ H3O The H3O ion is known as the hydronium ion. Acidity or alkalin- ity is a measure of the relative amounts of hydronium ions and hydroxide ions dissolved in a solution. If the number of hydronium ions in a solution equals the number of hydroxide ions, the solution is said to be neutral. Pure water contains equal numbers of hydro- nium ions and hydroxide ions and is therefore a neutral solution. Acids If the number of hydronium ions in a solution is greater than the number of hydroxide ions, the solution is an acid. For example, when hydrogen chloride gas, HCl, is dissolved in water, its mol- ecules dissociate to form hydrogen ions, H, and chloride ions, Cl, as is shown in the equation below. HCl ∏ H Cl These free hydrogen ions combine with water molecules to form hydronium ions, H3O. This aqueous solution contains many more hydronium ions than it does hydroxide ions, making it an acidic solution. Acids tend to have a sour taste; how- ever, never taste a substance to test it for acidity. In concentrated forms, they are highly corrosive to some materials, as you can see in Figure 2-13. Bases If sodium hydroxide, NaOH, a solid, is dissolved in water, it dissociates to form sodium ions, Na, and hydroxide ions, OH, as shown in the equation below. NaOH ∏ Na OH Copyright © by Holt, Rinehart and Winston. All rights reserved. Eco Connection onnection Acid Precipitation Acid precipitation, more commonly called acid rain, describes rain, snow, sleet, or fog that contains high levels of sulfuric and nitric acids. These acids form when sulfur dioxide gas, SO2, and nitrogen oxide gas, NO, react with water in the atmosphere to produce sulfuric acid, H2SO4, and nitric acid, HNO3. Acid precipitation makes soil and bodies of water, such as lakes, more acidic than normal. These high acid levels can harm plant and animal life directly. A high level of acid in a lake may kill mollusks, fish, and amphibians. Even in a lake that does not have a very elevated level of acid, acid precipitation may leach aluminum and magnesium from soils, poisoning water- dwelling species. Reducing fossil-fuel consump- tion, such as occurs in gasoline engines and coal-burning power plants, should reduce high acid levels in precipitation. Sulfur dioxide, SO2, which is produced when fossil fuels are burned, reacts with water in the atmosphere to produce acid precipitation. Acid precipitation, or acid rain, can make lakes and rivers too acidic to support life and can even corrode stone, such as the face of this statue. FIGURE 2-13 44 CHAPTER 2 This solution then contains more hydroxide ions than hydronium ions and is therefore defined as a base. The adjective alkaline refers to bases. Bases have a bitter taste; however, never taste a substance to test for alkalinity. They tend to feel slippery because the OH ions react with the oil on our skin to form a soap. In fact, commercial soap is the product of a reaction between a base and a fat. pH Scientists have developed a scale for comparing the relative con- centrations of hydronium ions and hydroxide ions in a solution. This scale is called the pH scale, and it ranges from 0 to 14, as shown in Figure 2-14. A solution with a pH of 0 is very acidic, a solution with a pH of 7 is neutral, and a solution with a pH of 14 is very basic. A solution’s pH is measured on a logarithmic scale. That is, the change of one pH unit reflects a 10-fold change in the acidity or alkalinity. For example, urine has 10 times the H3O ions at a pH of 6 than water does at a pH of 7. Vinegar, has 1,000 times more H3O ions at a pH of 3 than urine at a pH of 6, and 10,000 times more H3O ions than water at a pH of 7. The pH of a solution can be measured with litmus paper or with some other chemical indicator that changes color at various pH levels. Buffers The control of pH is important for living systems. Enzymes can function only within a very narrow pH range. The control of pH in organisms is often accomplished with buffers. Buffers are chemi- cal substances that neutralize small amounts of either an acid or a base added to a solution. As Figure 2-14 shows, the composition of your internal environment—in terms of acidity and alkalinity— varies greatly. Some of your body fluids, such as stomach acid and urine, are acidic. Others, such as intestinal fluid and blood, are

Can you create an evaluation using this information PHONETICS VS. PHONOLOGY Whereas phonetics is the study of sounds that occur in language, phonology is the study of how these sounds are organized and how they function in language. It uses the classifications of sounds derived from phonetics to describe and analyze how sounds occur in speech. STRUCTURALIST PHONEMICS STRUCTURALIST PHONEMICS As linguists began to study sounds in fine detail, they recognized increasingly complex aspects of phonetic organization. For example, the sound /p/ appears in different varieties in English. STRUCTURALIST PHONEMICS One of the varieties of /p/ is indicated by [ph]. This sound is produced with an accompanying puff of air called aspiration, as in the words “pill,” and “peace.” Another sound, indicated by [p•], is produced when there is little or no aspiration; this sound occurs in a word like “spill.” A third major variety for the /p/ sound is the unreleased [p– ], which may occur at the end of a word like “stop.” To deal with these variations for the /p/ sound, the structuralists suggested the existence of an abstract unit which they termed a phoneme. STRUCTURALIST PHONEMICS A phoneme was defined by the structuralists as an abstract phonological unit that represents a class of real sounds, termed the allophones of a phoneme. The phoneme /p/ in English, then, is represented by the allophones [ph], [p•], and [p– ]. STRUCTURALISTS: MINIMAL PAIRS How do we know what these abstract units of sound called phonemes are? In order to find the phonemes of a language, the structuralists developed the concept of the minimal pair, defined as any two words that: a) Contain the same number of segments b) Differ in meaning c) Exhibit only one phonetic difference. STRUCTURALISTS: MINIMAL PAIRS In practical terms, phonemes distinguish meanings; and a phoneme can also be defined as the smallest meaning-distinguishing unit of sound. For instance, the words “pin” /pɪn/ and “bin” /bɪn/ mean different things, and the only one difference in these words occurs in the initial sounds. STRUCTURALISTS: MINIMAL PAIRS By using the concept of a minimal pair, we can determine that the three variations of the /p/ sound do not represent three phonemes. Certainly, it is possible to pronounce the word cap with either an aspirated [ph ] or unreleased [p– ]; however, the two forms [kæph ] and [kæp– ] are not a minimal pair, even though they involve different sounds, because they are identical in meaning. STRUCTURALISTS: FREE VARIATION The two forms [kæph ] and [kæp– ] are, therefore, said to exhibit free variation: that is, the pronunciation may vary without signifying a change in meaning. In other words, we may conclude that the unreleased [p– ] and the aspirated [ph ] are not representations of different phonemes in English; they are, in fact, allophones of one phoneme, /p/. STRUCTURALISTS: COMPLEMENTARY DISTRIBUTION When phonemes have more than one allophone in a language, the allophones are said to be in complementary distribution. Complementary distribution means that the allophones of a phoneme occur in different phonetic environments (that is, with different sounds surrounding them). TRANSFORMATIONAL- GENERATIVE PHONOLOGY TRANSFORMATIONAL-GENERATIVE PHONOLOGY Transformational-generative phonology is a relatively recent development in linguistic theory. Chomsky launched Transformational-Generative Grammar in 1957, but the earliest studies within this framework were largely concerned with syntax. A decade later, the first comprehensive transformational-generative treatment of English phonology appeared: Chomsky and Halle’s The Sound Pattern of English (1968). TRANSFORMATIONAL-GENERATIVE PHONOLOGY Transformational-generative phonologists strongly oppose the structuralists’ phonemic level. They replace this level by a series of rules that directly relate underlying representations to observed phonetic representations. The central mechanisms in transformational-generative phonology, then, are underlying representations and phonological rules. PHONOLOGICAL RULES A rule is an operational statement in which some linguistic entity is modified, resulting in a new linguistic entity. Rules may add elements, remove elements, or change elements. By using phonological rules, linguists attempt to demonstrate that there is order in linguistic phenomena and that linguistic patterns are systematic. PHONOLOGICAL DERIVATION A phonological derivation is an operation that begins with an underlying representation and, through the application of a set of specific rules, yields the actual sound the speaker produces. The representation of a phonological rule has the following general appearance. /A/ → [B] / C “A” changes to “B” under condition “C” PHONOLOGICAL RULE – EXAMPLE In most Southern dialects, the word ten is pronounced like the word tin. This is not an isolated fact, for den is pronounced like din and Ben is pronounced like bin, and so on. This very general fact can be represented by the phonological rule: /ɛ/ → [I] / ___ [n] den /dɛn/ → /dIn/ Ben /bɛn/ → /bIn/ ten /tɛn/ → /tIn/ /ɛ/ → [I] / ___ [n] - high - low - tense + front + high - tense + front + sonorant + anterior + coronal - continuant NOTATIONAL DEVICES IN PHONOLOGICAL RULES The statement of phonological rules can be complex, and linguists have developed several notational devices for writing them. Often, the following symbols will be necessary for stating the conditions under which rules apply: # indicates a word boundary + indicates an intraword boundary $ indicates a syllable boundary UNDERLYING REPRESENTATIONS AND RELATED ISSUES The transformational-generative description of phonology relates underlying representations to phonetic representations by rules. This can be represented in a simple example: In English, there are certain pairs of words like sign / signature, and malign / malignant that exhibit a regular alternation in their phonetic representations: [g] is present in the second member of the pairs but absent in the first member. UNDERLYING REPRESENTATIONS AND RELATED ISSUES To explain the relatedness of words such as sign / signature, we could claim that the underlying representation of the segment in all such pairs is /g/ and that a rule operates to delete /g/ before syllable-final nasals. Thus, the rule “/g/ is deleted before syllable-final nasal” would appear formally as: + voice - anterior →∅ ____ [+ nasal] $ - coronal UNDERLYING REPRESENTATIONS AND RELATED ISSUES On the left-hand side of the arrow, we place the features needed to uniquely specify /g/ among the consonants; that is, no other consonant has the features [+ voice], [- anterior], and [- coronal]. The symbols → mean that the sound /g/ changes to nothing or more properly “/g/ is deleted.” The horizontal line following the slash mark refers to the position of /g/ - namely, before a segment that is [+nasal]. Finally, this [+nasal] segment occurs before a syllable boundary, as indicated by $. A less formal way of writing this rule would be: /g/ → / _ [+nasal] $ Notice that this rule also helps describe such alternations as phlegm/phlegmatic and paradigm/paradigmatic. Application Activity: Think of other words in which this rule can be applied. Write the sound segments to prove /g/ is deleted. Another example is the process through which the prefix meaning “not” is added to words. This prefix alternates among the forms /Im/, /In/, and /Iŋ/, depending on the point of articulation of the initial segment of the following word. -If the segment begins in the extreme front part of the mouth (labials), the form is /Im/, as in improper. -If the segment begins in the extreme back part of the mouth (velars), the form is /Iŋ/, as in incomplete. -If the segment begins in the mid-region of the mouth (all other sounds), the form is /In/, as in indecent. *Exceptions:Words beginning with /r/ or /l/. Analyze the Word “in + complete,” for example. /n/ → [ŋ] / __ [k] - continuant - continuant - continuant + sonorant → + sonorant - sonorant + anterior - anterior - strident + coronal - coronal - coronal + tense THE VELAR SOFTENING RULE Still another example of alternation in English is found in pairs of words like “electric / electricity,” in which the segments /k/ and /s/ alternate. /k/ changes to [s] only before non- low, front vowels. THE VELAR SOFTENING RULE /k/ → [s] / __ - continuant + continuant - strident → - sonorant V - anterior + anterior - low - coronal + coronal - back

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