The cholinergic drug

The cholinergic drug A cholinergic drug is a drug that acts on the peripheral nervous system, the central nervous system, or both and enhances the effects that are mediated by acetylcholine. It is also known as cholinergic agent, parasympathomimetic drug or cholinergic agonist. [1][2] It can work in two ways; either acting directly by mimicking the effects of acetylcholine at one or more acetylcholine receptors present in the body, or acting indirectly by blocking/inhibiting the enzyme acetylcholine that is responsible for the degradation/ hydrolysis of acetylcholine. [1][2] Depending on the type of receptor to act on, cholinergic drugs are either classified as muscarinic agonists or nicotinic agonists. [6] Anticholinergic drugs: An anticholinergic drug is a drug or an agent that competes with the neurotransmitter acetylcholine for its binding sites at synaptic junctions thereby suppressing or inhibiting its activity and thus preventing the transmission of parasympathetic nerve impulses. [3][4] Depending on the type of receptor to act on, anticholinergic drugs are either classified as muscarinic antagonists or nicotinic antagonists. [6] Pilocarpine: (Chemical formula=C11H16N2O2) Introduction: Pilocarpine is a naturally occurring alkaloid which is extracted from the South American shrub named Pilocarpus jaborandi. It is a non-selective cholinergic parasympathomimetic agonist that binds to muscarinic-M3 receptors and results in contraction of smooth muscles and stimulation of various exocrine glands. [5] The drug is available in the form of eye drops, tablets, suspensions and gel. It has a slow onset of action which is about 10 to 15 minutes but has a longer duration of action of about 6 to 8 hours, and therefore can be given thrice a day. It is inactivated at neuronal synapses and in plasma and is excreted in urine. Pilocarpine can be used in combination with other sympathomimetics, carbonic anhydrase inhibitors, miotics, beta-blockers, or hyperosmotic agents. [8] History: In 1875, Mr. Gerrard discovered pilocarpine from the leaves of Pilocarpus jaborandi. At that time, he believed that there were at least two alkaloids present in this plant. At the same time, M. Hardy isolated pilocarpine. In 1876, the isolated pilocarpine alkaloid was introduced to conventional ophthalmology for the treatment of glaucoma. 1879, Straws, while doing an active research concerning the sudoriferous secretion in cases of facial paralysis, was the first to employ local medication with pilocarpine and published relevant results. Chemical synthesis of pilocarpine: Although pilocarpine looks like a simple molecule but it has a complex chemical synthesis. This is because of the stereospecific construction of the imidazole moiety that is cis to the ethyl group on the butyrolactone ring which makes its synthesis difficult and challenging. The starting reagent for its synthesis is 2-acetylbutyrolactone which undergoes selenenylation by reacting with phenylaelenenyl chloride to produce a seleno lactone 2-acetyl-2-(phenylselenyl) butyrolactone with a yield of 94%. This is then subjected to oxidative elimination of selenoxide in the presence of cyclo-pentadiene and hydrogen peroxide to produce a mixture of endo and exo bicycle ketones in a ratio of 2.3:1. Pyrolysis (flash vacuum thermolysis) of these ketones produces a white solid 3-acetyl-2(5H)-furanone with a yield of 95%. This ketone is then reduced under mild conditions by treating it with an asymmetric reducing agent (+)-?-chlorodiisopinocamphenylborane, which is used particularly for chiral redu ctions, to produce (3R)-3-(1-hydroxyethyl)-2(5H)-furanone in 60% chemical yield and an optical purity of >92% that was determined by NMR analysis. Next, a stereocentre is introduced at C4 of the (3R)-3-(1-hydroxyethyl)-2(5H)-furanone by the Claisen rearrangement at its vinyl ether which produces an exocyclic double bond and the (4R)-acetaldehyde side chain. Both of them are necessary for the formation of the imidazole ring. This will result in a 2:1 mixture of (4R)-(Z)-dehydrohomopilopic aldehyde and (4S)-E-diastereomer in 71% yield. Hydrogenation of (4R)-(Z)-dehydrohomopilopic aldehyde in the presence of pyridine/benzene (1:1) solution at 25?C at 1atm for 1 hour produces (3s,cis)-Homopilopic aldehyde. Finally, when (3s,cis)-Homopilopic aldehyde is reacted with 1,5-disubstituted imidazole under aprotic conditions, it results in the formation of pilocarpine in 61% yield. [9] Structure-activity relationship (SAR): The nitrogen on the imidazole ring is protonated before interacting with the muscarinic receptor. There is a strong ionic interaction between the charged nitrogen atom and an anionic side group of an aspartate residue in the receptor. The methyl substitute on the nitrogen is positioned in an open region of the binding site. Hydrogen bonding interactions exist between the ester group of pilocarpine and an asparagines residue of the cholinergic receptor. A small hydrophobic pocket exists in the receptor site which can accommodate the methyl group of pilocarpine. The drug has a correct pharmacophore for the muscarinic receptor with a separation between nitrogen and oxygen being 4.4?A. [6] Mechanism of action: Pilocarpine is a direct acting cholinergic agent that resembles acetylcholine and therefore binds to the same muscarinic neuroreceptor and results in its stimulation. In eye, it causes contraction of the iris sphincter muscle and therefore results in miosis (pupil constriction). Clinical uses: Pilocarpine has been used in the treatment of both acute closed-angle and chronic open-angle glaucoma. [8] Glaucoma is a condition when the aqueous contents of the eye cannot be drained. This result in increased intraocular pressure which causes optic nerve damage and can lead to side vision damage (peripheral vision damage) and if not treated, can result in central vision damage and leads to irreversible blindness. [6] Pilocarpine is also used to treat xerostomia which is a condition characterised by dryness of the oral mucosa. The drug acts on cholinergic receptors in the glandular parenchyma thereby increasing the salivary secretion. [7] Pilocarpine hydrochloride (Salagen) tablets are prescribed to the patients suffering from Sjà ¶gren syndrome (SS) in order to treat their symptoms of xerostomia (dry mouth) and xerophthalmia (dry eyes). Sjà ¶gren syndrome (SS) is a chronic, autoimmune, rheumatic disorder in which immune cells attack and destroy the exocrine glands that produce tears and saliva. This in turn makes the individual susceptible to various infections and if untreated may also lead to other complications like bacterial sialadenitis, bacterial conjunctivitis, stomatopyrosis (burning mouth), oral candidiasis, oral ulcers, periodontal disease, accelerated dental caries, corneal ulceration or perforation, malnutrition, weight loss and sleep disruption. [5] Pilocarpine is also used to diagnose cystic fibrosis (CF). [8] Cystic fibrosis is a common hereditary disease which is characterised by scarring (fibrosis) and formation of cyst within the pancreas. The disease is characterised by shortness of breath, frequent chest infections, sinus infections, salty tasting skin, normal appetite but poor growth and poor weight gain, excess mucus production, diarrhea and infertility in males. [14] Sweat test method is used to diagnose of disease in which the drug stimulates sweat glands in order to measure the concentration of chloride and sodium that is excreted in the sweat. Pilocarpine is often used as an antidote for Atropine, Hyoscyamine and Scopolamine poisoning. [8] Adverse effects: Since pilocarpine is a non-selective muscarinic receptor anonist, its use can result in a wide variety of side-effects which can include lacrimation, excessive perspiration, excessive salivation, bronchospasm, increased bronchial mucus secretion, muscle tremors, tachycardia, hypertension, diarrhea, blurred vision and eye pain, browache and miosis when used chronically as an eye drop. When pilocarpine is used in the form systemic injection, it can cross the blood-brain barrier and reach the brain where it can lead to chronic epilepsy. [13] Suggestions for design of new drugs: Pilocarpine has significant delivery problems associated with its low lipophilicity. Its bioavailability in the eye is low, duration of action is fast due to its rapid elimination from the eye and above all, it has serious side effects like miosis and myopia. Based on the knowledge of dependence of drug delivery with physicochemical properties of the drug, a prodrug approach can be used to improve the delivery characteristics of pilocarpine. A prodrug should be designed such that it has a higher lipophilicity than pilocarpine which would enable it to cross the corneal membrane with ease, should have sufficient aqueous solubility so that it could be formulated as eyedrops, should be able to convert back to the active parent drug within the cornea, should have a controlled release and a prolonged duration of action. [10] Curare: Introduction: Curare is a nicotinic antagonist. It is a crude, dried extract from a plant called Chondrodendron tomentosum. [6] It is a mixture of 70 alkaloids. [11] The active principle in curare is tubocurarine (C37H41N2O6). [6]The antidote for curare poisoning is an acetylcholinesterase (AChE) inhibitor (anti-cholinesterase), such as physostigmine or neostigmine. [15] The drug is available in the form of solutions and intravenous injections. It has an onset of action of about 4 to 6 minutes and duration of action of about 80 to 120 minutes. It is eliminated through kidney and liver. History of curare: During the sixteenth century, the South American indigenous people used curare as a paralyzing poison where they killed the prey by dipping the arrows or blowgun darts in curare. [16]The prey is killed due to asphyxia in which the respiratory muscles fail to contract. [16] In 1780, Abbe Felix Fontana studied the effects of curare on heart, voluntary muscles and nerves and found that it affects the voluntary muscles of the body as compared to the other two. [15] In 1800, Alexander von Humboldt reported the method used by the Orinoco River natives to prepare the curare toxin from its plant source.[16] During 1811-1812 Benjamin Collins Brodie (1783-1862), a leading English surgeon, experimented with curare. [16]He found that curare paralysed the respiratory muscles but the heart continued to beat for a while. [16]He was the first to show that if the animals respiration is maintained artificially, recovery is complete. [16] In 1850, George Harley found that tetanus or strychnine poisoning can be cured by using curare. [15] From 1887 the Burroughs Wellcome catalogue listed under its Tabloids brand name, tablets of curare at 1/12 grain (price 8 shillings) for use in preparing a solution for hypodermic injection. [15] In 1939, Henry Hallett Dale reported the antagonistic effect of curare on acetylcholine. [15] Mechanism of action: Curare is a non-depolarizing muscle relaxant that blocks the nicotinic acetylcholine receptor. The main toxin of curare, d-tubocurarine, is a competitive antagonist of acetylcholine and so occupies the same position on the receptor as the neurotransmitter but does not switch it on. The overall effect on the body is the same as it would be in the absence of acetylcholine. [15] History of tubocurarine: In 1935, Harold King of London was experimenting on a sample of curare in Sir Henry Dales laboratory and was not only able to isolate tubocurarine in its pure form from the crude drug but also discovered its chemical structure. [16] In 1912, tubocurarine was used for the first time in medicine. [15] In 1942, tubocurarine was used along with anaesthetics in surgical procedures to relax muscles. [15] Structure-activity relationship: The structure of tubocurarine is shown in fig. Although the molecule does not have an ester group to bind to the nicotinic receptor, but it has two positively charged nitrogen atoms, one of which is a tertiary nitrogen atom while the other is a quaternary nitrogen. One of them binds to the anionic binding region of the nicotinic receptor while the other binds to a nearby cysteine residue that is 0.9-1.2nm away. Such an intreraction is so strong that it makes up for the lack of the ester binding interaction. Also, the distance between the two positive centres is 1.15nm which is also important for the activity of the drug. [6] Indication Curare is used in the diagnosis of myasthenia gravis, [17]which is an autoimmune disease in which antibodies are produced against acetylcholine nicotinic post synaptic receptors at the neuro-muscular junction. [18] Curare is also used in surgical procedures in association with general anesthesia in order to facilitate in the relaxation of abdominal muscles when it is not possible with inhalation anesthesia. [12] Adverse effects: Curare has undesirable side-effects, the most common of which include hypotension (by ganglion-block and histamine release), bronchoconstriction (by histamine release), skeletal muscles paralysis and asphyxia (impaired breathing). [15] Suggestions for design of new drugs: Tubocurarine has undesirable side effects because it also acts as an antagonist at the nicotinic receptors of the autonomic nervous system. Also, its deactivation depends on metabolic mechanisms involving enzymatic deactivation and/or excretion, the efficiency of which varies from patient to patient and is particularly poor for patients with low levels of plasma esterases or kidney failure. Therefore, a self-destruct mechanism can be introduced into the design of a new drug for its sufficiently rapid breakdown. If a good electron withdrawing group is introduced on to a carbon that is beta to the quaternary nitrogen centre, Hofmann elimination is possible under the slightly alkaline pH of blood (pH = 7.4) and body temperature. The electron-withdrawing groups will function to increase the acidity of the hydrogen on the beta-carbon such that it is easily lost. Thus by introducing such a group, the drug is inactivated and is unable to bind to its receptor due to the loss of the positive charge on the quaternary centre and is split into two molecules. Thus deactivation occurs at a constant rate between patients. [6]

Resistance to Organizational Change in Business Essay -- Business Deve

By any objective measure, the amount of important, frequently distressing, change in organizations has grown enormously over the last two decades (Kotter, 1996). Jeffrey M. Hiatt, CEO of Prosci Inc., (as cited by Gibson, Ivancevich, Donnelly & Konopaske, 2009, p. 481) explained, â€Å"thirty years ago, a fortune 100 probably had one or two enterprise wide change initiatives going on; today that number is probably between 20 and 25.† The speed of global, economic, and technological development makes change an inevitable element of organizational life. Change is a pervasive, persistent, and permanent condition for all organizations (Gibson, et al., 2009). Organizational change means different things, and strategic renewal comes in different forms. Organizational change includes such concepts as first-order; incremental, continuous change and second-order, transformational/revolutionary, discontinuous change: †¢ First-order, incremental change, which may include modifications in systems, processes, or structures; however, it does not involve basic change in strategy, core values, or corporate identity. First-order changes preserve and develop the organization: they are changes created, almost contradictory, to sustain organizational continuity and order. †¢ Second-order, discontinuous change is transformational, extreme, and substantially alters the organization at its core. Second-order change does not involve developing change, rather it entails transforming the makeup of the organization (Palmer, Dunford, & Akin, 2009). In addition, Nadler and Tushman (as cited in Palmer, et. al, 2011) develop this distinction involving incremental and discontinuous change, explaining th... ...telnikov, V. (2001). Strategic management. Retrieved from Company Vision: http://www.1000ventures.com/business_guide/crosscuttings/vision_creating.html Kotter, J. P. (1996). Leading change. Boston, MA.: Harvard Bsuiness Review Press. Logan, B. C. (2007). A framework for mixed stakeholders and mixed methods. Ejbrm.com , http://www.ejbrm.com/vol6/v6-i1/CrumpAndLogan.pdf. Palmer, I., Dunford, ,. R., & Akin, ,. G. (2009). Managing organizational change (2n ed.). New York, NY.: McGraw-Hill Irwin. Preziosi, R. C. (1996). Organizational diagnosis questioinnaire (ODQ). Spector, B. (2010). Implementing organizational chang: Theory into practice (2nd ed.). Upper Saddle River: Pearson Prentice Hall. Vecchio, R. P. (2008). Leadership understanding the dynamics of power and Influence in Organizations,(2nd ed.). Notre Dame, Indiana: university of Notre Dame Press.

Data Protection Essay

Introduction In this report I am going to explain data protection, talk about the data protection acts, rights and principles. I’m going to talk about a data controller and a data processor and what their responsibilities are. What personal and sensitive data are. What a data receiver is and what his rights are, what is involved in direct marketing and I will mention an example of abuse or corruption that occurred in Ireland. Data protection acts Data protection is legal control over and access to use of data stored in computers. The office of the data protection commissioner is responsible for upholding the privacy rights of individuals in relation to the processing of their personal data. The acts state the information must be accurate, only those who should have access to it do and it is only to be used for specified purposes. You have the right to access your own information and correct wrong data or even erase it. Moran (2014) states that â€Å"you can have data without information, but you cannot have information without data†. Rights and principles There are 8 principles of data protection 1. It must be collected and fairly used 2. It must only be held and used for the reasons given to the information commissioner 3. It can only be used for registered purposes and showed to those mentioned in the register entry 4. You must only have the details you need for the job you are doing 5. It must be accurate and kept up to date 6. Cannot be kept longer than necessary for the registered purpose 7. Information must be kept safe and secure, must be backed up and kept away from unauthorised access 8. Files must not be transferred outside of the EU. Unless the country it is being sent to has a suitable data protection law. Data controller Data controller is a person who controls the contents and use of personal data. â€Å"Those who, either alone or with others control the contents and use of personal data. Data controllers can be either legal entities such as  companies, Government departments or voluntary organisations, or they can be individuals such as G.P’s, pharmacists or sole traders† (the office of the data protection commissioner (2014). The responsibilities of a data controller 1. Obtain and process the information fairly 2. Keep it only for one or more specified and lawful purposes 3. Process it only in ways compatible with the purposes for which it was given to you initially 4. Keep it safe and secure 5 .Keep it accurate and up-to-date 6. Ensure that it is adequate, relevant and not excessive 7. Retain it no longer than is necessary for the specified purpose or purposes 8. Give a copy of his/her personal data to any individual, on request Data processor Data processor is a person who processes personal data on behalf of a data controller but does not include an employee of a data controller who processes such data in the course of his employment. The office of the data protection commissioner (2014) states that â€Å" the data processor is distinct from the data controller for whom they are processing the personal data†¦someone who is contracted to provide a particular data processing service (e.g. a tax advisor) would be a data processor†. Personal data The office of the data protection commissioner (2014) states that â€Å"†personal data† means data relating to a living individual who is or can be identified either from the data or from the data in conjunction with other information that is in, or is likely to come into, the possession of the data controller†. Sensitive data Sensitive data is someone private information which may be related to their gender, age, race, marital status or sexual preference etc. The office of the data protection commissioner states that â€Å"relates to specific categories of data which are defined as data relating to a person’s racial origin; political opinions or religious or other beliefs; physical or mental health; sexual life; criminal convictions or the alleged commission of an offence; trade union membership. You have additional rights in relation to the  processing of any such data†. Data receiver (controller) The data receiver is the data controller he/she is the person who receives the data Direct Marketing Direct marketing is giving individuals information about products and services, is it completely legal providing it respects the individual’s right to privacy. The office of the data protection commissioner states that â€Å"The basic rule that applies to direct marketing is that you need the consent of the individual to use their personal data for direct marketing purposes. As a minimum, an individual must be given a right to refuse such use of their personal data both at the time the data is collected (an â€Å"opt-out†) and, in the case of direct marketing by electronic means, on every subsequent marketing message. The â€Å"opt-out† right must be free of charge†. Abuse and Corruption in Ireland May 2010: Captain Evan Cullen versus Michael O’Leary: Ryanair CEO Michael O’Leary apologised for wrongly describing a trade union official as a â€Å"failed Aer Lingus pilot† during RTE’s Prime Time in September 2006. The apology formed part of a settlement of a High Court action against him by Irish Air Line Pilots Association (IALPA) president, Captain Evan Cullen. Mr O’Leary also agreed to make a contribution to two charities by Mr Cullen as part of the settlement. In taking his defamation case Mr Cullen claimed the â€Å"failed pilot† had caused damage to his reputation both in his community and among his work colleagues. Mr Cullen said the remarks had caused â€Å"considerable upset to both himself and his family†, but that he was pleased his â€Å"good name and reputation as a pilot† has been fully vindicated. Conclusion In this report I have explained data protection, talked about the data protection acts, rights and principles. I’ve talked about a data controller and a data processor and what their responsibilities are, What personal and sensitive data are. What a data receiver is and what his rights are, what is involved in direct marketing and I have mentioned an example of abuse or corruption that occurred in Ireland. Reference list Kosta, E. (2013) Consent in European Data Law, Leiden: Nijhoff. Moran, D. (2014) â€Å"Brainy Quotes† [Online], available: http://www.brainyquote.com/quotes/keywords/data.html [accessed 28th November 2014] Office of the data protection commissioner (2014) â€Å"A guide for data Controllers† [Online], available: http://www.dataprotection.ie/docs/A-Guide-for-Data-Contollers/696.htm [accessed 28th November 2014] Defamation Ireland (2014) â€Å"Defamation cases in Ireland† [Online], available:http://www.defamationireland.com/defamation-cases-in-ireland/ [accessed 28th November 2014]

6 Fabulous Hints to Become a Successful Writing Major

6 Fabulous Hints to Become a Successful Writing Major 6 Fabulous Hints to Become a Successful Writing Major There are several skills one must improve to be a truly great writer. Here we are going to name six key skills for excellent writing, as well as tips on how to acquire and improve these traits. 1. Knowledge of Grammar, Spelling, and Punctuation You can have creative ideas and excellent writing abilities, but without proper spelling, grammar, and punctuation, you cannot communicate your ideas effectively. People do not want to read writings that are full of errors, and you lose credibility when you cannot spell or punctuate properly. The best way to improve your language is to read. Read books, newspapers, favorite blogs - read anything. The more you read, the more spelling and grammar become second nature to you. Another way to improve your grammar is to search the Internet any time you are uncertain about how to punctuate a sentence or which verb tense to use. There are many excellent grammar websites devoted to consult you. 2. Understanding Your Purpose There are different types of writing for different purposes: narrative, persuasive, literary analysis, etc. To write effectively, first you must understand the purpose of the paper you are dealing with. Are you analyzing literature? Are you telling an entertaining story? Are you persuading the reader to agree with your opinion? When you are writing a college paper, look through the restrictions carefully. If your professor provides you with the demands, read them a couple of times to make sure you have fully understood your task. If you thoroughly understand the purpose of each piece you handle, you will be on your way to a writing master’s degree! 3. Imagination Excellent writers have perfect imagination. It is a skill you cannot be taught of, but you can develop it. Go to different places, observe people, try something new. Write down your observations in a notebook. If you have a dream, you can record it in your journal as well. Open your imagination even further by reading novels that take place in fantasy lands, or by watching movies that explore unique topics. Imagination comes from exploration and experience, so cultivate your imagination by being open to different places, people, and adventures. 4. Discipline A guaranteed way to improve any skill is to practice, so the best way to become a better writer is to write. Even if you are not in the vein to do this, or you feel like you have a writer’s block, simply take the pen or start typing. Write something every day, even if it is a short entry about what you have experienced and thought that day. The more you write, the more you will improve. You even won’t notice how you have became a writing MFA. 5. Research Skills When it comes to academic writing, being a good researcher is a must. Who is a good researcher? Someone who can find convincing, valid evidence to support the claim in his/her writing. One way to improve your research skills is to evaluate the sources you have chosen. While choosing a source to use in your paper, ask yourself the following questions: Was this source recently updated, or it is outdated? Who wrote this information? Would this person or organization be involved to this topic? Is it a trustworthy source with credible information? Is this information relevant to my topic? Make sure you are getting your research from the sources that are credible, current and relevant. The most important item for an excellent research is to know which sources to use. You also should be able to synthesize researches from several different sources, instead of using only one and simply paraphrasing its information. 6. Ability to Take Constructive Criticism We are our own biggest critics, so we must criticize our writings. Take yourself through multiple drafts instead of deciding that the very first one you have written is the best. Focus on your spelling, grammar, word choice, and organization. Do you stay on topic? Do you use strong vocabulary? Moreover, you can ask others for feedback, and do not take their criticism personally. The only way to get better is to continue learning and improving your writing skills. No writer is perfect, so continue striving for constant improvement. If you follow these tips, you will be amazed how much your writing skills have improved!

Understanding the Definition of Symmetric Difference

Understanding the Definition of Symmetric Difference Set theory uses a number of different operations to construct new sets from old ones. There are a variety of ways to select certain elements from given sets while excluding others. The result is typically a set that differs from the original ones. It is important to have well-defined ways to construct these new sets, and examples of these include the union, intersection, and difference of two sets. A set operation that is perhaps less well-known is called the symmetric difference. Symmetric Difference Definition To understand the definition of the symmetric difference, we must first understand the word or. Although small, the word or has two different uses in the English language. It can be exclusive or inclusive (and it was just used exclusively in this sentence). If we are told that we may choose from A or B, and the sense is exclusive, then we may only have one of the two options. If the sense is inclusive, then we may have A, we may have B, or we may have both A and B. Typically the context guides us when we run up against the word or and we don’t even need to think about which way it’s being used. If we are asked if we would like cream or sugar in our coffee, it’s clearly implied that we may have both of these. In mathematics, we want to eliminate ambiguity. So the word or in mathematics has an inclusive sense. The word or is thus employed in the inclusive sense in the definition of the union. The union of the sets A and B is the set of elements in either A or B (including those elements that are in both sets). But it becomes worthwhile to have a set operation that constructs the set containing elements in A or B, where or is used in the exclusive sense. This is what we call the symmetric difference. The symmetric difference of the sets A and B are those elements in A or B, but not in both A and B. While notation varies for the symmetric difference, we will write this as A ∆ B For an example of the symmetric difference, we will consider the sets A {1,2,3,4,5} and B {2,4,6}. The symmetric difference between these sets is {1,3,5,6}. In Terms of Other Set Operations Other set operations can be used to define the symmetric difference. From the above definition, it is clear that we may express the symmetric difference of A and B as the difference of the union of A and B and the intersection of A and B. In symbols we write: A ∆ B (A ∠ª B) – (A ∠© B). An equivalent expression, using some different set operations, helps to explain the name symmetric difference. Rather than use the above formulation, we may write the symmetric difference as follows: (A – B ) ∠ª (B – A). Here we see again that the symmetric difference is the set of elements in A but not B, or in B but not A. Thus we have excluded those elements in the intersection of A and B. It is possible to prove mathematically that these two formulas are equivalent and refer to the same set.​ The Name Symmetric Difference The name symmetric difference suggests a connection with the difference of two sets. This set difference is evident in both formulas above. In each of them, a difference of two sets was computed. What sets the symmetric difference apart from the difference is its symmetry. By construction, the roles of A and B can be changed. This is not true for the difference between two sets. To stress this point, with just a little work we will see the symmetry of the symmetric difference since we see A ∆ B (A – B ) ∠ª (B – A) (B – A) ∠ª (A – B ) B ∆ A.

Discuss the theme of appearance and reality in Macbeth Essay

Discuss the theme of appearance and reality in Macbeth - Essay Example He is one who King Duncan trusts, and he has the favor of all his countrymen, but he betrays this trust and, for a while, everyone is deceived into believing that he mourns the death of Duncan as he seems to, that he killed the two guards out of his love for Duncan, and that will be a good ruler because he will think of the interests of the people, and not himself. The Thane of Cawdor was also a man who Duncan trusted, as he says in Act 1, Scene 4, â€Å"He was a gentleman on whom I built/An absolute trust†, but he, too, betrays that trust. Lady Macbeth is not suspected for her part in Duncan’s death, till she starts walking and talking in her sleeps, and ironically, Macduff wants to save her from hearing about it (2.3.85-88). Macduff himself is not trusted by his wife and Malcolm, because both believe him to be a traitor to the country, whereas, he is one who is willing to sacrifice all for his country, and it is he who later kills Macbeth. The sons who are suspected o f killing their fathers (Malcolm and Donalbain, and Fleance) also show how seeming truths are not always true. Images presented through language also play an important role in presenting the theme of appearances and reality. Numerous images conveying the idea of concealment occur in the speech of almost all the characters. Sometimes the concealment is in the form of clothes, where clothes supposedly hide what a person truly is. Thus Macbeth chides Ross for â€Å"dress[ing]† him â€Å"[i]n borrowed robes† (1.3.108-109) when Ross calls him the Thane of Cawdor. This is because he does not know that the Thane of Cawdor that was, no longer owns the title. Similarly, Macbeth talks of â€Å"put[ting] on manly readiness† (2.3.135), when the people are not really ready at all. Other forms of disguise also occur, such as masks: Macbeth tells the murderers he has hired, that he is â€Å"Masking the business from the common eye/For sundry weighty reasons† (3.1.125-126). Later, he

THE LAW OF TORT Essay Example | Topics and Well Written Essays - 500 words

THE LAW OF TORT - Essay Example Simon had a dizzy neck after his car accident and had gone to see the doctor who diagnosed him of whiplash. After hearing that he has a vital presentation to present before the final of the programme, he advised Simon to return to the gym and work out through the pain. This was a wrong advice on the part of the Company doctor. After listening to his advice, he worked through the pain, and as a consequence, Simon passed out during the presentation and was taken to hospital where he was diagnosed with trapped nerves in his neck and as a consequence, was unable to appear in the finale. Applying the rule of law laid down in the Boman Case, the Company doctor is liable for Simon passing out in the presentation and the subsequent diagnosis in the hospital. Simon would not have gone and worked out if he was not advised by his doctor to do so. Therefore, applying the tort of professional negligence, we come to the conclusion that the Company doctor is liable for the injuries which happened subsequent to training after getting diagnosed of whiplash. Looking at the remedy available to Simon, the doctor is liable to pay for the damages which occurred after he worked out at the gym, which includes the cost of treatment for getting diagnosed at the hospital, but not the losses incurred due the failure of Simon to attend the finale.These costs must be paid by the doctor to Simon as damages for the tort he committed,. He was negligent in his services and deserves to pay a price for such inefficient and nonprofessional advice. In the second issue, the case is whether Simon has a defence against the claim of the pedestrian for the damage to her laptop, her loss of book and her illness. The answer to this problem is yes Simon does have absolute defence against the claim of the pedestrian. The pedestrian was not remotely anywhere close to Simon’s responsibility of duty of care while the accident occurred. Simon does not owe her any duty of care in the first