Eco fueling marketing report Research Paper Example | Topics and Well Written Essays - 4000 words

Eco fueling marketing report - Research Paper Example 8 3.4 Technological factors†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.......... 8 4.0 Customer Analysis†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦. 9 5.0 Competitor Analysis†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. 10 6.0 Stakeholder Analysis†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦..... 11 7.0 Internal and External Analysis (SWOT) 7.1 Strengths†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚ ¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. 11 7.2 Weaknesses†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. 12 7.3 Opportunities†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦... 12 7.4 Threats†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦......... 12 8.0 Conclusion†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦. 13 References†¦Ã¢â‚¬ ¦Ã¢ € ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦... 14 1.0 INTRODUCTION The creation of utility, the power of goods and services to satisfy wants or needs, is of utmost importance to a marketer. For a service or product to be considered valuable in the market, it has to benefit customers and offer lucrative returns to a company (Boone and Kurtz, 2009, p. 5). Critical analysis of marketing strategies is required if a company is to attain utility for its products and services. PEST, SWOT, stakeholder, customer and environmental scan analysis must be conducted to appraise current business strategies and formulate recommendations for the establishment of new strategies or improving on current... The creation of utility, the power of goods and services to satisfy wants or needs, is of utmost importance to a marketer. For a service or product to be considered valuable in the market, it has to benefit customers and offer lucrative returns to a company (Boone and Kurtz, 2009, p. 5). Critical analysis of marketing strategies is required if a company is to attain utility for its products and services. PEST, SWOT, stakeholder, customer and environmental scan analysis must be conducted to appraise current business strategies and formulate recommendations for the establishment of new strategies or improving on current ones. E-cofueling, a company based in Brisbane, is the focus of this marketing audit report. The company, which dealing in the development and distribution of ethanol co-fueling of diesel engines, as well as development of viable emission technologies, was established in 2009. Environmental scanning refers to the progressive process of gathering data regarding different phenomena in the market with a view to identify opportunities, as well as threats. As the current market remains active, changes are inevitable, which presents its fair share of threats and opportunities to a company. In order to carry out appropriate environment scans, a marketer must carry out extensive research and gather information pertaining social, technological, competitive, regulatory and economic factors that have a direct impact on market trends.

The Ego, The Superego and The Id Essay Example for Free

The Ego, The Superego and The Id Essay The structure of the personality in psychoanalytic theory is threefold. Freud divided it into the id, the ego and the superego. Only the ego is visible, or on the surface one may say, while the id and the superego remain hidden, below the surface of what we show of our personalities to others, but each has its own effects on the personality nonetheless. This essay seeks to explore these three layers of personality and how they work with one another. In Freuds structural hypothesis, the id is generally recognised as the psychic representative of the drives. (Berger 1995 p.106) The id represents biological forces and is always present in the personality. The id is governed by the pleasure principle, or notion of hedonism (seeking of pleasure). Early in the development of his theory Freud saw sexual energy, or the libido or the life instinct, as the only source of energy for the id. It was this notion that gave rise to the popular conception that psychoanalysis is all about sex. Read more: Superego examples essay After the carnage of World War I, however, Freud felt it necessary to add another instinct, or source of energy to the id. So, he proposed Thanatos, the death instinct. Thanatos accounts for the instinctual violent urges of humankind. Obviously the rest of the personality would have somehow to deal with these two instincts. It is interesting to note how Hollywood has capitalised on the id; box office success is highly correlated with movies that stress sex, violence, or both. We can come nearer to the id with images, and call it chaos, a cauldron of  seething excitement. We suppose that it is somewhere in direct contact  with somatic processes, takes over from their instinctual needs and gives  them mental representation. These instincts fill it with energy, but it has  no organisation and no unified will, only an impulsion to obtain satisfaction  for the instinctual needs, in accordance with the pleasure principle. (Hinsie Campbell, 1970 cited in Berger 1995 p. 106) The id is a source of energy and should not be retained too much, but at the same time we must contain it, otherwise its force and desire for pleasure shall dominate our lives, inhibiting our life progress; our lives would be dominated by impulses. The id knows no values, no good or evil, no morality. The quantitative factor, which is so closely bound up with the pleasure principle, dominates all its processes. We view the id as containing instinctual cathexes seeking discharge. According to Freud, the id constitutes the total psychic apparatus of the newborn; the psychic later splits into three parts adding an ego and superego. Although this view that the psyche is all id at birth has been criticised, what is generally held is that the id precedes the development of the ego and the superego. The ego is thought to start functioning early in life, around the age of five or six months old and is concerned with the environment. This is because the ego is involved in making sure that the id secures its gratifications. (Berger 1995 p.106) After researching the ego, I, as I think many, found its concepts much more complicated than the id. I will try to simplify the central ideas of the ego, as often it helps to make a more precise and understandable picture in ones own mind. A primary function of the ego is to mediate between the id and the superego, trying to keep them in balance. The ego is the part of the psychic apparatus which is the mediator between the person and reality, (Hinsie Campbell 1970 cited in Berger 1995 p.107) not only this but it functions to perceive and adapt to reality. Tasks of the ego include such things as perception, motor control and the use of the reality principle. The ego seeks to influence the id and its tendencies by the external world. It also tries to substitute the reality principle for the pleasure principle, which rules unrestrictedly in the id. Ego represents the common sense and reason whilst the id contains passion. The functional importance of the ego to the id is well captured in an analogy used by Joan Riviere (1962), where it is like a man on horse back, who has to hold in check the superior strength of the horse, with the difference being that the rider tries to do so with his own strength, whilst the ego uses borrowed forces. The ego is in the habit of transforming the ids will into action as if it were its own. (Rieviere 1962 p.15) Speaking broadly, perceptions may have the same significance for the ego as instincts have for the id. At the same time the ego is subject to the influence of the instincts too. As shown by Freud in Civilisation and its discontents there are two classes of instincts; one is the sexual instincts known as Eros, and the second is the instinct of death. The death instinct would thus seem to express itself as an instinct of destruction directed against the external world and other organisms. Sadism and masochism are both manifestations of the destructive instinct. Masochism is a union between destructiveness directed inward and sexuality (Freud 1957). It is in sadism, where the death instinct twists the erotic aim in its own sense and at the same time satisfies the erotic urge. The instinct of destruction, moderated and and tamed, inhibited in its aim, must, when it is directed toward objects, provide the ego with the satisfaction of its vital needs and with control over nature. (Freud 19 57) The transformation of erotic libido into ego-libido of course involves an abandonment of sexual aims. This highlights an important function of the ego in its relation to Eros. Riviere (1962) explains that by getting hold of the libido from the object cathexes, setting itself up as a sole love-object, and converting the libido of the id, the ego is working in opposition to the purposes of Eros and placing itself at the service of the opposing instinctual impulses. It has to participate in some of the other object-cathexes of the id, so to speak. This implies an importance of the theory of narcissism. At the beginning, all of the libido is collected in the id. The id sends part of this libido out into erotic object-cathexes, where the ego, once grown stronger, tries to gain this object-libido and to force itself on the id as a love object. The narcissism of the ego is thus a secondary one, which has been withdrawn from objects. Usually, when one is able to trace instinctual impulses back, we find them to be derivatives of Eros. Some creatures die in the act, or after, copulation because after Eros has been eliminated through the process of satisfaction, the death instinct has a free hand for accomplishing its purposes. (Riviere 1960 p.37) Freud (1963) sees civilisation as based upon individuals learning to control their sexual urges and finding other ways of getting gratification.  But because sexual impulses are powerful, there is always a tension between them and the institutions in society. Civilisation, as Freud points out in Civilisation and its Discontents (1957), is the cause of many of our miseries: it forces us to give up uninhibited instinctual gratifications (in particular, genital satisfactions and aggressiveness), and it creates guilt. Life consists of the struggle of mankind between Eros and death, betw een instinct of life and instinct of destruction; this presents the meaning of the evolution of civilisation. Now we turn to explore the third structure, the superego. According to Freud, the superego is the agency in our psychs involved with conscience, morality and ideal aspirations. The superego consists of two parts, the conscience and the ego-ideal. The conscience is the familiar metaphor of angel and devil on each shoulder. The conscience decides what course of action one should take, what is right and what is wrong, and forces the ego to inhibit the id in pursuit of morally acceptable, not pleasurable or even realistic, goals. The ego ideal is an idealised view of ones self. Comparisons are made between the ego-ideal and ones actual behaviour. Both parts of the superego develop with experience with others or through social interactions. According to Freud, a strong superego serves to inhibit the biological instincts of the id, while a weak one gives into the ids urgings. The superego is part of a trio that controls our urges and desires. The id being the urge at its raw form, the ego filtering the urge (in a very complicated manner!) and the superego is the decider of whether or not the urge can be satisfied immediately or must be put aside for later. The superego is not created when we are born, rather we are born with the superego and it develops over the course of our life as new rules and regulations are brought to light. The superego is known as the seat of morality, part conscious and part unconscious. It is the part of us that induces guilt. In Civilisation and its Discontents, this question is posed, what means does civilisation employ in order to inhibit the aggressiveness which opposes it? To this, Freud explains that ones aggressiveness is internalised, it is sent back to where it came from, and it is directed toward ones own ego. There its taken over by a portion of  the ego, which sets itself over against the rest of the ego as superego, and which now, in the form of conscience, is ready to put into action against the ego the same harsh aggressiveness that the ego would have liked to satisfy upon other, extraneous individuals. The tension between the harsh superego and the ego is called the sense of guilt. Civilisation controls ones desire for aggression by setting up an agency (the superego) within a person to watch over it and control it. We can compare the superego to a personal watchdog, keeping us in line with the rules of society, sometimes these rules are broken and the superego lets us know by inducing in us a sense of guilt. When we do well, our superego makes us swell with pride and joy. Our superegos are shaped primarily by the superegos of our grandparents, as they shape our parents superegos, who then socialise us and give us our moral sensibilities. The severity of our superegos is not tied to how strict our parents were when raising us, but the way they have dealt with their Oedipus complexes and our  internalization of this process. Too complex to fully expand on now, I shall just say that the superego develops, according to psychoanalytic theory, out of our need to deny hostile wishes we have,  incestuous in nature, which may simply be described as our Oedipus complexes. I believe the words of David Stevenson (1966) give a clear and concise insight into the superego. While the ego may temporarily repress certain urges of the id in fear of  punishment, eventually these external sources of punishment are internalised,  and the child will not steal a chocolate, even unwatched, because he has taken  punishment, right, and wrong into himself. The superego uses guilt and self-reproach  as its primary means of enforcement for these rules. But if a person has done  something which is acceptable, he experiences pride and self-satisfaction. I have discussed the structural relationship within the mental personality, and although very complex, Freuds work on the ego, superego and id has continued to be greatly studied, respected and used to expend our fields of knowledge.

Inverse Matrix Condition Number

Inverse Matrix Condition Number Inverse Matrix and Condition No. Saswati Rakshit Contents (Jump to) Aim Scope/Applications Introduction/Basics Objective System Flow Mathematics Figure/Descriptions Future Works References Aim: Consider 2 random matrices B and C of size 8Ãâ€"8 and write a cpgm / matlab to find A to satisfy the bellow condition: If AÃâ€"B = C Prove A = CÃâ€"B-1 And repeat the pgm for matrix of size 32Ãâ€"32 and 128Ãâ€"128. Scope/Application: In many applications we require inversion of matrix. In Linear Algebra, if AÃâ€"B=C, and from B and C we can compute A where A=CÃâ€"B-1. Stimulus-Response Computations In this framework, a system is provided with an input, called a  stimulus, and the resulting response of the system is measured. Some typical examples of stimuli are visual scenes i.e. if we increase incident light’s intensity then scene’s brightness will increase. The general goal is to find a  function  that accurately describes the relation between stimulus and response. Many systems can be modeled as a linear combination of equations, and thus written as a matrix equation: [Interactions]{response}= {stimuli} The system response can thus be found using the matrix inverse. Sometimes in image processing application if we have noisy image matrix and if we know what the noise matrix was added we can find the clear image by multiplying noisy image matrix with inverted noise matrix. Intro/Basics: We have considered two 8Ãâ€"8 matrices B and C. We suppose AÃâ€"B = C. Now by performing matrix multiplication on A and B we get C. Now we have to compute A from B and C. So AÃâ€"B = C and we have to proof A = CÃâ€"B-1. It is conceptually easy to compute AÃâ€"B = C and to find A = CB-1 for 2 dimensional matrices. But for large dimensional matrices it is not possible to easily compute because there is some round off errors in A which is the result of B-1 related to B’s condition number. Thecondition numberof a function with respect to an argument measures how much the output value of the function can change for a small change in the input argument. The condition number of a regular (square) matrix is the product of the norm of the matrix and the norm of its inverse and hence depends on the kind of matrix-norm. Condition number of a square nonsingular (invertible) matrix A is defined by: cond () = |||| ·|||| where the || ·|| above could be any of the norms defined for matrices. The numerical value of the condition number of an nÃâ€"n matrix depends on the particular norm used .The norm of a square matrix A is a non-negative real number denoted by ||A||. These matrix norms have the following properties: 1. ||A|| à ¯Ã¢â€š ¬Ã‚ ¾Ãƒ ¯Ã¢â€š ¬Ã‚  Ãƒ ¯Ã¢â€š ¬Ã‚ ° if A ≠  0 2. ||à ¯Ã‚ Ã‚ §A|| à ¯Ã¢â€š ¬Ã‚ ½Ãƒ ¯Ã‚ Ã‚ ¼Ãƒ ¯Ã‚ Ã‚ §Ãƒ ¯Ã‚ Ã‚ ¼Ã‚ ·Ãƒ ¯Ã‚ Ã‚ ¼Ãƒ ¯Ã‚ Ã‚ ¼A|| for any scalar value à ¯Ã‚ Ã‚ §Ãƒ ¯Ã¢â€š ¬Ã‚  Ãƒ ¯Ã¢â€š ¬Ã‚   à ¯Ã¢â€š ¬Ã‚ ³Ãƒ ¯Ã¢â€š ¬Ã‚ ®Ãƒ ¯Ã¢â€š ¬Ã‚  Ãƒ ¯Ã‚ Ã‚ ¼Ãƒ ¯Ã‚ Ã‚ ¼A|| à ¯Ã¢â€š ¬Ã‚ «Ãƒ ¯Ã¢â€š ¬Ã‚  Ãƒ ¯Ã‚ Ã‚ ¼Ãƒ ¯Ã‚ Ã‚ ¼B|| ≠¤ à ¯Ã¢â€š ¬Ã‚  Ãƒ ¯Ã‚ Ã‚ ¼Ãƒ ¯Ã‚ Ã‚ ¼A|| à ¯Ã¢â€š ¬Ã‚ «Ãƒ ¯Ã¢â€š ¬Ã‚  Ãƒ ¯Ã‚ Ã‚ ¼Ãƒ ¯Ã‚ Ã‚ ¼B||à ¯Ã¢â€š ¬Ã‚  Ãƒ ¯Ã¢â€š ¬Ã‚   à ¯Ã¢â€š ¬Ã‚ ´Ãƒ ¯Ã¢â€š ¬Ã‚ ®Ãƒ ¯Ã¢â€š ¬Ã‚  Ãƒ ¯Ã‚ Ã‚ ¼Ãƒ ¯Ã‚ Ã‚ ¼AB|| ≠¤ à ¯Ã¢â€š ¬Ã‚  Ãƒ ¯Ã‚ Ã‚ ¼Ãƒ ¯Ã‚ Ã‚ ¼A|| ·Ãƒ ¯Ã‚ Ã‚ ¼Ãƒ ¯Ã‚ Ã‚ ¼B||à ¯Ã¢â€š ¬Ã‚  Ãƒ ¯Ã¢â€š ¬Ã‚   à ¯Ã¢â€š ¬Ã‚ µÃƒ ¯Ã¢â€š ¬Ã‚ ®Ãƒ ¯Ã¢â€š ¬Ã‚  Ãƒ ¯Ã‚ Ã‚ ¼Ãƒ ¯Ã‚ Ã‚ ¼Ax|| ≠¤ à ¯Ã¢â€š ¬Ã‚  Ãƒ ¯Ã‚ Ã‚ ¼Ãƒ ¯Ã‚ Ã‚ ¼A|| ·Ãƒ ¯Ã‚ Ã‚ ¼Ãƒ ¯Ã‚ Ã‚ ¼||à ¯Ã¢â€š ¬Ã‚  Ãƒ ¯Ã¢â€š ¬Ã‚  for any vector The norm of a matrix is a measure of how large its elements are. It is a way of determining the â€Å"size† of a matrix that is not necessarily related to how many rows or columns the matrix has. Three commonly used norms are: 1. The 1-norm: = This is the maximum absolute column sum where simply we sum the absolute values down each column and then take the biggest answer. 2. The inifinity-norm: = This is the maximum absolute row sum where simply we sum the absolute values along each row and then take the biggest answer. 3. The Euclidean norm: = This is the square root of the sum of all the squares. However, regardless of the norm, this condition number is always greater or equal to 1. If it is close to one, the matrix is well conditioned which means its inverse can be computed with good accuracy. If the condition number is large, then the matrix is said to be ill-conditioned. Practically, such a matrix is almost singular (not invertible), and the computation of its inverse or solution of a linear system of equations is prone to large numerical errors. A matrix that is not invertible has the condition number equal to infinity. Mathematically, if the condition number is less than ∞, the matrix is invertible. Numerically, there are roundoff errors which occur. A high condition number means that the matrix is almost non-invertible. The higher the condition number, the greater is the error in the calculation. This condition number helps to estimate how difficult a matrix will be to numerically invert. This condition number has certain properties: 1. For any matrix A, cond (A) ≠¥Ãƒ ¯Ã¢â€š ¬Ã‚  1 2. For identity matrix, cond (I) = 1 3. For any matrix A and scalar à ¯Ã‚ Ã‚ §, cond à ¯Ã¢â€š ¬Ã‚ ¨Ãƒ ¯Ã‚ Ã‚ §Ãƒ ¯Ã¢â€š ¬Ã‚  A) = cond (A) 4. For any diagonal matrix D = Diag(di), cond (D) = (max |di|)/(min|di|) A matrix A is ill-conditioned if relatively small changes in the input (in the matrix A) can cause large change in the output (the solution of Ax = b), i.e. the solution is not very accurate if input is rounded. Otherwise it is well-conditioned. If a matrix is ill-conditioned, then a small roundoff error can have a drastic effect on the output. However, if the matrix is well-conditioned, then the computerized solution is quite accurate. Thus the accuracy of the solution depends on the conditioning number of the matrix. Objective: To know how to determine the matrix inverse in an efficient manner. If AÃâ€"B=C and we have to prove A=CÃâ€"B-1 where A, B and C are nÃâ€"n matrices (n = 8, 32, 128) and find out the condition number of matrix using norms and finding accuracy. System flow: Steps performed: 1. Taking two matrices B and C of order 8Ãâ€"8. 2. Performing Matrix multiplication and result is stored in matrix A (performed using C Code) 3. Now calculate B-1 (performed using C Code) 4. Now again multiplying C and B-1. We get result matrix which is not accurate. 5. We need to calculate norms and condition number of a matrix (B) so we need to find norms of B and B-1. We can calculate norms in different way. Here we have used most popularly used 3 types of norms to calculate condition number of that matrix (B) which we need to get in inverse form. The norms are: 1-norm = Infinity-norm = iii) Euclidean norm = 6. Now we use norms to find condition number of matrix B by using formula cond (B) = |||| ·|||| Flow Diagram yes no Math For 22 Matrix First we consider a 22 matrix such that A= B= So by multiplying A and B we ge a 22 matrix C = Now We need to prove A=CB-1 So we need to find B-1 B-1 = 0.800 -0.200 -0.600 0.400 So now by doing CxB-1 = =A (proved) Before finding B-1 we can calculate condition number of B for the correctness of above proof, As we know cond (B) = |||| ·|||| Condition number using the 1-norm and inifinity-norm: Formula used Row Sum taking absolute values B = 2 13 3 47 Column sum 5 5 (taking absolute values) (max) Row sum B-1 = 0.800 -0.200 1.000 -0.600 0.400 1.000 Col Sum 1.4 .6 Applying 1-Norm = = maximum absolute column sum = 5, 1 = 1.4, So, cond1 (B) =  ·1 = 5Ãâ€"1.4= 7 Applying infinity-norm = = max absolute row sum = 7, ∞ = 1 So, cond∞ (B) =  ·Ã¢Ë†Å¾ = 7 Like this way we have also found condition number using the Euclidean norm which is = =5.47 = 1.095 CondE (B) =  ·E = 5.82 Here cond(B) is low in all cases.so we successfully get A =C. Because of low condition number of B,the inverse of B is acceptable. For 88 Matrix A = 1 2 3 4 1 2 2 1 2 3 1 4 3 4 2 1 4 1 3 2 3 3 1 2 2 2 1 4 2 2 2 1 3 2 1 4 3 1 2 1 1 1 2 3 1 2 2 1 1 2 1 2 1 2 1 2 2 2 3 3 2 1 2 2 B= 4 1 3 2 3 3 1 2 2 3 1 4 3 4 2 1 2 2 1 4 2 2 2 1 1 1 2 3 1 2 2 1 2 2 3 3 2 1 2 2 1 2 3 4 1 2 2 1 1 2 1 2 1 2 1 2 3 3 1 3 2 3 1 1 C=AÃâ€"B=27 30 28 52 27 37 28 20 35 38 42 64 35 46 35 27 42 35 41 59 37 43 31 27 29 29 32 49 28 37 27 22 34 30 35 50 32 39 28 25 22 24 24 41 21 29 22 17 23 25 22 39 22 30 20 15 34 33 30 53 32 40 28 23 B-1= -0.016 -0.429 0.063 0.524 0.063 -0.397 -0.222 0.587 -0.365 0.143 -0.540 0.048 0.460 -0.127 -0.111 0.508 0.095 0.071 -0.381 -0.143 0.119 0.381 -0.167 -0.024 0.270 -0.214 0.921 -0.905 -0.579 0.746 0.278 -0.484 0.206 0.571 0.175 -0.810 0.175 0.159 -0.111 -0.635 0.079 0.143 -0.317 0.381 -0.317 -0.016 0.111 0.063 -0.571 0.071 -0.714 1.857 0.786 -1.286 -0.500 0.643 0.159 -0.214 0.365 -0.238 -0.135 -0.032 0.722 -0.373 A=CÃâ€"B-1 =0.995 1.983 3.029 3.987 1.029 1.984 2.006 0.979 1.992 2.975 1.035 3.983 3.035 3.980 2.005 0.972 3.989 0.971 3.029 1.984 3.029 2.981 1.006 1.970 1.993 1.980 1.027 3.987 2.027 1.984 2.004 0.977 2.991 1.976 1.027 3.986 3.027 0.983 2.004 0.974 0.996 0.986 2.022 2.990 1.022 1.987 2.004 0.983 0.994 1.986 1.021 1.991 1.021 1.988 1.005 1.982 1.992 1.979 3.028 2.987 2.028 0.983 2.007 1.975 Relative Error for A11=(1-.995)=.005,A12= 0.017 and so on When we perform CÃâ€" B-1, we do not get original value of A because of B-1. If B-1 is not accurate we will not get accurate A. To get accuracy of A-1 we need to find condition number of B. As we know cond (B) = |||| ·|||| Condition number using the 1-norm and inifinity-norm: Formula used Row Sum taking absolute values B = 4 1 3 2 3 3 1 2 19 2 3 1 4 3 4 2 1 20 (max) 2 2 1 4 2 2 2 1 16 1 1 2 3 1 2 2 1 13 2 2 3 3 2 1 2 2 18 1 2 3 4 1 2 2 1 16 1 2 1 2 1 2 1 2 12 3 3 1 3 2 3 1 1 17 Column sum 16 16 15 25 16 19 13 11 (taking absolute values) (max) B-1 = For B-1, Row sum (max) taking absolute values = 6.428 (7th row) and column sum(max) taking absolute values = 4.906 (4th column) Applying 1-Norm = = maximum absolute column sum = 25, 1 = 4.906, So, cond1 (B) =  ·1 = 25Ãâ€"4.906 = 122.65 Applying infinity-norm = = max absolute row sum = 20, ∞ = 6.428 So, cond∞ (B) =  ·Ã¢Ë†Å¾ = 20Ãâ€"6.428 = 128.56. Like this way we have also found condition number using the Euclidean norm which is = 17.83. So here we can say that as the condition number of matrix B is high for all three cases, therefore the inverse of this matrix is showing numerical roundoff errors. Concept of Relative Error and Condition Number assume A is nonsingular and Ax = b if we change b to b + à ¢Ã‹â€ Ã¢â‚¬  b, the new solution is x + à ¢Ã‹â€ Ã¢â‚¬  x with A(x + à ¢Ã‹â€ Ã¢â‚¬  x) = b + à ¢Ã‹â€ Ã¢â‚¬  b the change in x is à ¢Ã‹â€ Ã¢â‚¬  x = A-1à ¢Ã‹â€ Ã¢â‚¬  b ‘condition’ of the solution †¢ the equations are well-conditioned if small à ¢Ã‹â€ Ã¢â‚¬  b results in small à ¢Ã‹â€ Ã¢â‚¬  x †¢ the equations are ill-conditioned if small à ¢Ã‹â€ Ã¢â‚¬  b can result in large à ¢Ã‹â€ Ã¢â‚¬  x [Singular matrix:A square matrix is called singular matrix if it’s determinant is zero.i.e. a singular matrix is not invertible] Example: Consider the linear system Ax = b with So = So here we easily find x= Now ,we change a small in b.let change in b is à ¢Ã‹â€ Ã¢â‚¬  b= So changed value= and solving the system A = we get =A= where x= changed to = due to small change in b. Now to calculate least condition number of the system we need to find Relative Error in the output and relative error in the input. Here we have relative error in the input/relative residual. = 0.01 Relative Error in the output =1 As we know, If condition number is closed to 1 then relative error and relative residual will be close. The condition number is defined by: Relative error in the output =Condition number Ãâ€" Relative error in the input. So,condition number= 1/.01=100 A matrix has high condition number is related to the fact that A is close to the singular matrix B= The following result shows that 1/cond(A) indicates how close A is to a singular matrix.Here cond(A) is 100 so, 1/cond(A)=.01 which is close enough. Description: The condition number associated with the  linear equation  Ax=bgives a bound on how inaccurate the solutionxwill be after approximation. This is before the effects of  round-off error  are taken into account; conditioning is a property of the matrix. Weshould think of the condition number as being the rate at which the solution,x, will change with respect to a change inb. Thus, if the condition number is large, even a small error inbmay cause a large error inx. On the other hand, if the condition number is small then the error inxwill not be much bigger than the error inb. The condition number may also be infinite, but this implies that the problem does not possess a unique, well-defined solution for each choice of data that is, the matrix is not invertible, and no algorithm can be expected to reliably find a solution. For large dimensional matrix such as for 3232 and 128128, the condition number is high and so inverse of that large dimensional matrix will give much error in output. Codes and Output Matrix multiplication int main() { int m, n, p, q, c, d, k, sum = 0; int A[10][10], B[10][10], C[10][10]; printf(Enter rows and columns of An); scanf(%d%d, m, n); printf(Enter the elements of An); for (c = 0; c for (d = 0; d scanf(%d, A[c][d]); printf(Enter rows and columns of Bn); scanf(%d%d, p, q); printf(Enter the elements of Bn); for (c = 0; c for (d = 0; d scanf(%d, B[c][d]); for (c = 0; c for (d = 0; d for (k = 0; k sum = sum + A[c][k]*B[k][d]; } C[c][d] = sum; sum = 0; } } for (c = 0; c for (d = 0; d printf(%dt, C[c][d]); printf(n); } getch(); } Matrix inverse #include #include int main() { float a[10][10],b[10][10],tem=0,temp=0,temp1=0,temp2=0,temp4=0,temp5=0; int n=0,m=0,i=0,j=0,p=0,q=0; printf(Enter size of 2d array(Square matrix) : ); scanf(%d,n); for(i=0;i { for(j=0;j { printf(Enter element no. %d %d :,i,j); scanf(%f,a[i][j]); if(i==j) b[i][j]=1; else b[i][j]=0; } } for(i=0;i { temp=a[i][i]; if(temp temp=temp*(-1); p=i; for(j=i+1;j { if(a[j][i] tem=a[j][i]*(-1); else tem=a[j][i]; if(temp temp=temp*(-1); if(tem>temp) { p=j; temp=a[j][i]; } } //row exchange in both the matrix for(j=0;j { temp1=a[i][j]; a[i][j]=a[p][j]; a[p][j]=temp1; temp2=b[i][j]; b[i][j]=b[p][j]; b[p][j]=temp2; } //dividing the row by a[i][i] temp4=a[i][i]; for(j=0;j { a[i][j]=(float)a[i][j]/temp4; b[i][j]=(float)b[i][j]/temp4; } //making other elements 0 in order to make the matrix a[][] an indentity matrix and obtaining a inverse b[][] matrix for(q=0;q { if(q==i) continue; temp5=a[q][i]; for(j=0;j { a[q][j]=a[q][j]-(temp5*a[i][j]); b[q][j]=b[q][j]-(temp5*b[i][j]); } } } printf(nnn); printf(Inverse of the matrix using Guass jordan elimination method:nn); for(i=0;i { for(j=0;j { printf(%.3f,b[i][j]); } printf(n); } getch(); } Matrix Condition Number #include #include int main() { int i,j,n,p,x=0,m=0,q,z=0,i1,j1; float Cond_A,poo,a[5][5],b[5],c[5],A[50][50],B[50][50],k[50],l[50]; printf(n n); printf(Program to find condition number of a matrix using infinity-norm); printf(n nn); printf(Enter rows and columns of An); scanf(%d%d, m, n); printf(Enter the elements of An); for (i = 0; i for (j = 0; j scanf(%f, A[i][j]); for(i=0;i { b[x]=0;c[x]=0; for(j=0;j { b[x]=b[x]+A[i][j]; } ++x; } for(i=0;i //FINDING LARGEST { if(b[i]>m) m=b[i]; } printf(largest row sum is %d,m); printf(nnEnter rows and columns of inv[A]n); scanf(%d%d, p, q); printf(Enter the elements of [A]n); for (i1 = 0; i1 for (j1 = 0; j1 scanf(%f, B[i1][j1]); for(i1=0;i1 { k[z]=0;l[z]=0; for(j1=0;j1 { k[z]=k[z]+B[i1][j1]; } ++z; } poo = k[0]; for(i1=1;i1 //FINDING LARGEST { if(k[i1]>poo) poo=k[i1]; } printf(largest row sum is %f,poo); Cond_A=m*poo; printf(nnCondition number of A is %f,Cond_A); //return 0; getch(); } Future works: If we work with a foggy image matrix(C) and we know the fog matrix(B) added to that image and the relation AÃâ€"B = C exist we will know whether it is possible to get the clear image matrix(A) by doing CÃâ€"B-1 calculating condition number of matrix B. If the condition number of matrix B is high then it is not possible to get accurate A from CÃâ€"B-1 as roundoff errors will increase. References: Matrix Inverse and Condition, Berlin Chen, Department of Computer Science Information Engineering, National Taiwan Normal University. Inversion error, condition number, and approximate inverses of uncertain matrices,  Laurent El Ghaoui, Department of Electrical Engineering and Computer Science,  University of California at Berkeley, Berkeley, CA 94720, USA. faculty.nps.edu/rgera/MA3042/2009/ch7.4.pdf www.rejonesconsulting.com/CS210_lect07.pdf http://teal.gmu.edu/ececourses/ece699/notes/note4.html Weisstein, Eric W. Matrix Norm. From MathWorldA Wolfram Web Resource. http://mathworld.wolfram.com/MatrixNorm.html

Capital Punishment is an Effective Deterrent :: Argumentative Persuasive Essays

Capital Punishment is an Effective Deterrent Throughout history, statistics have proven that Capital Punishment has been an effective deterrent of major crime. Capital Punishment is the lawful infliction of death among criminals and has been used to punish a wide variety of offenses for many years all over the world (Bedau 16). When the death penalty is enforced, it shows society that committing a capital crime has deadly consequences. In early times, many methods of Capital Punishment were used to deter a variety of crimes. For over a century, the uniform method for executing persons in America was hanging, although starvation was very common also. There were exceptions which included spies, traitors, and deserters who would face a firing squad. Then in 1888, New York directed the construction of an "electric chair" (Flanders 11). It was believed that the new harnessed power of electricity would prove to be a more scientific and humane means of execution. The first electrocution took place in New York in 1890. In the past, capital crimes were much different than they are now. Robbery and the selling of alcohol to underage customers was a serious capital crime (McCuen and Baumgart 21). Rape was also a crime where the criminal was sentenced to death. In America, only thirty-seven states authorize the death penalty. In most of those thirty-seven states, murder is the only capital crime. The Supreme Court requires that two conditions must be met in order for a specific murder to warrant the death penalty (Nardo 32). The first condition is that it must be first degree murder, which is the deliberate and premeditated taking of life. The second is that one or more aggravating circumstances must be present. Aggravating Circumstances refer to those aspects of a crime that increase its severity. An example of an aggravating circumstance would be torture in conjunction with a murder. ("Capital Punishment" 32). Every society has faced the problem of what to do with its most troublesome criminals. Many people in the past have argued whether or not Capital Punishment is justified and necessary. Most societies now believe that a criminal should receive punishment proportional to the crime committed. Most societies believe that such a severe punishment was necessary to install fear in others. While more social structures developed, the crimes developed into public and private offenses. Public offenses such as witchcraft and blasphemy, were punished by the state; while private offenses still were answered by acts of personal retribution. The enforcement of Capital Punishment in the early twentieth century declined drastically because of all of the controversy.

English Essay on the Short Story “The Island”

English essay on the short story† The Island† We all know the word Freedom, but do we truly know what it means? It’s a good word which explains: No commitments, no chains, no concerns and no insecurity. The Scottish short story ‘The Island’ is an expression for this freedom and to indulge you to something bigger than yourself. It could be God or in this case, it is the beautiful nature. This short story is published in 1992 and the author is unknown. The main character is Doris (last name unknown), she has a son, named John who is married with Annette, and is Doris’ daughter-in-law.We can estimate Doris to be 50-60 years old, if we figure her son, John’s age and his status as a married man. Doris’ relationship with the young couple is difficult, because she is an outsider, she is old, and they are young, both John and his wife Annette. â€Å"When Doris visited, Annette never found her jobs, or asked favours. If there were children , it might be different, but in her heart Doris doubted it. †(p. 1, ll. 11-12). According to this line, we easily get to know what Doris experience is with Annette. And we get to know that Doris want to involve herself more in the young couple’s life. She had half hoped that John, at least, would say he really wanted her to come. But no. Certainly her daughter-in-law did not need her. â€Å"(p. 1, ll. 8-9). And it comes to express, that Doris also not want to be alone, not needed. John and Annette, mostly Annette, tread Doris like a child. â€Å"They saw several more beaches that Doris wanted to explore on foot, but she was imprisoned in the back seat. †(p. 1, ll. 34-35). And they, John and Annette keep saying that Doris needs to relax and take it easy. The Island we are on is called Tiree. Tiree is an island off the west coast of Scotland.As long as Doris stays on the island, she becomes freer. First of all, she meets an elderly man, carrying fish in a basket o n the beach. They small-talk, and she looks at the nature around her and the man. † Standing here she felt that her house in the busy Anchusa Road belonged in another world. †(p. 2, ll. 48-49). I can imagine this feeling Doris feels, because I had stood in a directly situation like her. The busy world is far from you, and you are flying. You have no concerns about anything, you’re not bound to anything and you’re feeling like you’re flying.It is an inexpressible moment. And it gives you the taste of freedom. That’s why we, in the end of this short story, hear that Doris want to live on the island. And after this boost of freedom, she sees an otter. †She breathes a sigh of pleasure. †(p. 2, l. 53). After this experience John and Annette observe, that Doris becomes very obstinate. In the short story it sounds like, John and Annette are forced to live with Doris, because else where they can’t get her house, after she dies of co urse. The nature has a big role in this short story. Feature Article –  The Plane of the Sleeping Beauty AnalysisBecause it helps Doris to see the freedom, and to be free. We can see in different sections that the nature has an effect at Doris: The next morning it was raining but Doris went out all the same. A mist had come in from the sea and every blade of grass was hung with silver droplets. It was, to Doris, even more beautiful than the day before. She found a patch with creamy mushrooms. She picked one, peeled off the delicate skin and ate it. †(p. 2, ll. 65- 68). According to these lines, we can tell, that the nature has a big influence on Doris. I think she never tried to eat a mushroom, uncooked.And we can tell, because she lives in the city, she had too much influence from it, and that shows us, people like Annette and John. And that’s why they flip out in the end of the short story, because they hear Doris wild idea to sell the house in Anchusa Road, and move to the island:† †You’ll do no such thing. † Annette was startled into open bad manners. †(p. 3, l. 116). This clearly shows us, what kind of people they are too, compared to Doris, especially Annette. We can conclude the short story ‘The Island’ as a released giving story to people without freedom and to those people who is still in chains, and can’t get out.The short story shows a lot of things, we can categorize as the themes of this short story. Freedom, relationships in the family and identity, but the most important of these themes is freedom. Over and over again, we can reed trough the lines, that Doris doesn’t has it, and wants it, and the only thing, in her case, who can give it to her, is the nature. Therefore the nature plays a big role in this short story, and we know it from our own lives. The nature gives and shows us, the humans, freedom.

Fall of Icarus Poems

After reading Landscape With The Fall of Icarus by William Carlos Williams and Musee Des Beaux Arts by W. H. Auden, a clear idea is present. Both authors seem to minimize the importance of Icarus’s death, but with what intent? In both poems, self-concern outweighs any intentions to help Icarus. It is clear to me what the authors were trying to express by implying that people simply had their own things to do, too used to disaster to even care about anyone besides themselves.In the Landscape With The Fall Of Icarus, Williams makes it clear that people are too concerned with themselves to notice anything happening around them. That idea started to become present when Williams wrote â€Å"the edge of the sea concerned with itself†. This quote demonstrates how everyone only cared about what they were doing. The message was very clear to me when the poem said â€Å"insignificantly off the coast there was a splash quite unnoticed this was Icarus drowning†.The way Willi ams used the word â€Å"insignificantly† while describing Icarus’s fall made me think that he wanted to give the impression that Icarus’s fall was not important to anyone and it was just another daily tragedy. In the Musee des Beaux Arts by W. H. Auden, the message Auden was trying to give seems to jump out of the page. For example, a quote from the poem says â€Å"how everything turns away Quite leisurely from the disaster; the ploughman may Have heard the Splash, the forsaken cry, But for him it was not an important failure†.This quote clearly shows how people can so easily turn from disaster without a second thought. And even though someone may have heard the splash and the cry, it was not an â€Å"important failure† to them because he was not affected. I think Auden meant the reason for people’s selfishness, when it comes to disaster, to be from how used they were to tragedy. If disaster is an often occurrence, it’s harder to be a s affected from it. The first lines of Musee de Beaux Arts are â€Å"About suffering they were never wrong, The old Masters: how well they understood Its human position: how it takes place†.This beginning to the poem demonstrates that same idea: that people are accepting of suffering. People understood its human position; they understood how it takes place. This is why I think Auden made Icarus’s death seem unimportant, simply because people were so used to it. Also, the last lines of Auden’s poem were â€Å"the expensive delicate ship that must have seen Something amazing, a boy falling out of the sky, Had somewhere to get to and sailed calmly on. This quote from the text seems to give a clear answer to why Icarus’s death seemed so unimportant; it was simply because people were too caught up in their own business to care for each other’s. As you can see, Icarus’s death in the poems Landscape With The Fall Of Icarus and Musee des Beaux Arts seemed very unimportant. By reading the poems carefully, you can see the two author’s meaning behind this, which was that people were too concerned with themselves to care.