Sylvia Plath Research Paper Example

Sylvia Plath Research Paper Example Sylvia Plath Paper Sylvia Plath Paper Essay Topic: Anne Sexton Poems Sylvia Plath (October 27, 1932 February 1 1, 1963) was an American poet, novelist and short story writer. Born In Boston, Massachusetts, she studied at Smith College and Newnham College, Cambridge, before receiving acclaim as a professional poet and writer. She married fellow poet Ted Hughes in 1956 and they lived together first in the united States and then England, having two children together, Frieda and Nicholas. Plath suffered from depression for much of her adult and in 1963 she committed suicide. 2] Controversy continues to surround the events of her life and death, as well as her writing and legacy. Plath is credited with advancing the genre of confessional poetry and is best known for her two published collections, The Colossus and Other Poemsand Ariel. In 1982, she won a Pulitzer Prize posthumously, for The Collected Poems. She also wrote The Bell Jar, a semi- autobiographical novel published shortly before her death. Plath was born on October 27, 1932, in the Massachusetts Memorial Hospital, in Bostons Jamaica Plain neighborhood. [4] Her mother, Aurelia Schober Plath (1906- 1994), was a first-generation American of Austrian descent, and her father, Otto Plath (1885-1940b was from Grabow, Germany. ] Plaths father was an entomologist and was professor of biology and German at Boston university; he also authored a book about bumblebees. On April 27, 1935, Plaths brother Warren as born[4] and In 1936 the family moved from 24 Prince Street In Jamaica Plain, Massachusetts, to 92 Johnson Avenue, Winthrop, Massachusetts. [81 Plaths mother, Aurelia, had grown up in Winthrop, and her maternal grandparents, the Schobers, had lived in a section of the town called Point Shirley, a location mentioned in Plaths poetry. While living in Winthrop, eight-year-old Plath published her first poem in the Boston Heralds childrens section. [9] In addition to writing, she showed early promise as an artist, winning an award for her paintings from The Scholastic Art amp; Writing Awards in 1947. 10] Otto Plath died on November 5, 1940, a week and a half after Plaths eighth of complications following the amputation of a foot due to untreated diabetes. Raised as aunltarlan Christian, Plath experienced a loss of faith after her fathers death, and remained ambivalent about religion throughout her Ilfe. He was burled In Winthrop Cemetery; visiting her fathers grave prompted Plath to write the poem Electra on Azalea Path. After his death, Aurelia Plath moved her children and her parents to 26 Elmwood Road, Wellesley, first nine years sealed themselves off like a ship in a bottleÐ ²Ãâ€šÃ¢â‚¬ beautiful inaccessible, bsolete, a fine, white flying College years [edit] Plath attended Bradford Senior High School (now Wellesley High School) in Wellesley, graduating in 1950. [4] Smith College, in Northampton, Massachusetts In 1950, Plath attended Smith College and excelled academically. She wrote to her mother, The world is splitting open at my feet like a ripe, Juicy watermelon. [13] She edited The Smith Review and during the summer after her third year of college Plath was awarded a coveted position as guest editor at Mademoiselle Magazine, during which she spent a month in New York City. 4] The experience was not what she had hoped it would be, and it began a downward spiral. She was furious at not being at a meeting the editor had arranged with Welsh poet Dylan Thomas†a writer whom she loved. She hung around the White Horse bar and the Chelsea Hotel for two days hoping to meet Thomas, but he was already on his way home. Many of the events that took place during that summer were later used as inspiration for her novel The Bell Jar. [1 5] During this time she was refused admission to the Harvard writing seminar. [13] Following electroconvulsive therapy for depression, Plath made her first edically documented suicide attempt in late August 1953 by crawling under her house and taking her mothers sleeping pills. She survived this first suicide attempt after lying unfound in a crawl space for three days, later writing that she blissfully succumbed to the whirling blackness that I honestly believed was eternal oblivion. [4] She spent the next six months in psychiatric care, receiving more electric and insulin shock treatment under the care of Dr. Ruth Beuscher. [4] Her stay at McLean Hospital and her Smith scholarship were paid for by Olive Higgins Prouty, ho had successfully recovered from a mental breakdown herself. Plath seemed to make a good recovery and returned to college. In January 1955, she submitted her thesis The Magic Mirror: A Study of the Double in Two of Dostoyevskys Novels and in June, graduated from Smith with highest honors. [17] She obtained a Fulbright scholarship to Newnham College, Cambridge, in England, where she continued actively writing poetry and publishing her work in the student newspaper Varsity. At Newnham, she studied with Dorothea Krook, whom she held in high regard. [18] She spent her first year winter and spring holidays traveling around Europe. Career and marriage [edit] Plaths stay at McLean Hospital inspired her novel The Bell Jar In a 1961 BBC interview (now held by the British Library Sound Archive),[19] Plath describes how she met Ted Hughes: I happened to be at Cambridge. I was sent there by the [US] government on a government grant. And Id read some of Teds poems in this magazine and I was very impressed and I wanted to meet him. I went to this little celebration and thats actually where we met Then we saw a great deal of each other. Ted came back to Cambridge and suddenly we found ourselves getting married a few months later We kept writing poems to each other. Then it Just grew out of that, I guess, a feeling that we both were writing so much and having such a fine time doing it, we decided and world-wanderer with a voice like the thunder of The couple married on June 16, 1956, at St George the Martyr Holborn in the London Borough of Camden with Plaths mother in attendance. Plath returned to Newnham in October to begin her second year. In early 1957, Plath and Hughes moved to the United States and from September 1957 Plath taught at Smith College. In the middle of 1958, the couple moved to Boston. Plath took a Job as a receptionist in the psychiatric unit of Massachusetts General Hospital and in the evening took creative writing seminars given by poet Robert Lowell (also attended by the writers Anne Sexton and George Starbuck). Plath and Hughes first met the poet W. S. Merwin, who admired their work and was to remain a lifelong friend. Plath resumed psychoanalytic treatment in December, working with Ruth Beuscher. [4] Chalcot Square, near Primrose Hill in London, Plath and Hughes home from 1959 Plath and Hughes travelled across Canada and the United States, staying at he Yaddo artist colony in New York State in late 1959. The couple moved back to the United Kingdom in December 1959 and[22] lived in London at 3 Chalcot Square, near the Primrose Hill area of Regents Park. Their daughter Frieda was born on 1 April 1960 and in October, Plath published her first collection of poetry, The Colossus.

Car Costs and New Technologies Essay Example | Topics and Well Written Essays - 1250 words

Car Costs and New Technologies - Essay Example Therefore, it does not look at the welfare of the people and the nation as a whole. On the other hand is the socialist economy. Most of the economists believe that government intervention and holdings are less efficient as they do not answer to the price changes or the change in the demand of the consumers. This is because the government relies on the tax collection for its revenues and less worried about the demand situation (US Department of State, 2010). Â  But still, most of the countries adopt some form of the mixed economy in allocating resources because they believe that both the private and the public sector play an important role. A mixed economy is a blend of free market and socialism. It is an economy that has a lot of freedoms but at the same regulations from the government keep a constant check. Â  The economists of these nations believe that some of the industries are better under the control of the government while others are better off under the supervision of the private entrepreneurs. For example, The development of the infrastructure; road, rail, air, and port, administration of justice, defense of the nation and education is under the control of the government. At the same time, there are certain institutions where the government intervenes in the market to settle out the price levels such as utilities, agriculture, and water. In this way, it regulates these likely monopolies (US Department of State, 2010). For example, Water and Power Development Authority keep a check on the charge of electricity in Pakistan keeping the best interests of the economy at heart. At the same time, the government regulates the private sector by creating standards and policies to guard the consumer interests and increase the welfare of the people.

Quantifying systemic risk in the European banking sector. A Research Paper

Quantifying systemic risk in the European banking sector. A multidimensional approach - Research Paper Example Systemic risk is the ultimate threat, its sources are varied and the propagation mechanisms involve major imbalances. The financial banking domain supports the present research, a choice motivated by the imperative of identifying potential risk-carrying factors in order to deeply analyse their impact and raise mechanisms for an efficient calibration of financial exposure levels. A major breakup within the banking sector, initially designed to serve the real economy generates severe imbalances with long-term implications for the whole financial industry and potential destructive nature for the economic environment. The preference for this topic is justified by its actuality and utmost importance for the European banking, financial community and the entire economic arena. Banks’ policies and strategies, new products, technologies and services, competition policies and the competitive environment provide space for risk’s rise. In addition, the increased level of financial integration and the globalization ties facilitate the appearance of new contagion channels, as previous banking experiences and worldwide tensions show. Mapping the current needs of the global economy means to identify risks and quantify their effects. A major challenge is to restore and strengthen the financial and economic stability and the prerequisite for achieving this goal is the understanding of systemic risk nature, its sources in terms of structures and sizes. The rich existing academic literature focused on theoretical models and empirical evidences around the systemic risk notion and the effects on the entire financial-banking industry support the importance of the addressed subject. The new global realities and the features of the regulatory and supervisory activities underline the need for a more powerful, solid crises management and European solutions for managing systemic risk. I. Literature review The first theoretical approaches on systemic risk can be traced back t o the period 1929-1933, during the Great Depression; as a distinctive figure, history invokes John Maynard Keynes1, who describes the economy marked by a shock in the financial system - a sequence of events generically called contagion. Broadly speaking, systemic risk is related to complex negative events simultaneously affecting institutions, markets and networks. In a narrow sense, the core element of the term is the contagion from one market structure to another. Explaining the notion of systemic risk requires a clarification of concepts proceeding and succeeding its rise: the systemic event, and respectively, the systemic crisis. A systemic event occurs when negative information about an institution spreads in the system and adversely impacts the participants. Allen and Gale (2000) and Freixas, Parigi and Rochet (2000) examine the risk of contagion in the shape of a domino effect, as an essential element of the systemic risk architecture. High-impact systemic events (for example , a bank collapse result of an initial shock) translate into contagion; if the shock doesn’t lead to failure, the event can be narrowed. A systemic event has two components: the shocks (idiosyncratic, systematic) and the propagation mechanisms. If idiosyncratic shocks affect individual financial institutions, systematic shocks spread across the whole economy and imbalance all financial structures in the same time. Systematic shocks are reflected in

Management of Amlodipine Influenced Gingival Overgrowth

Management of Amlodipine Influenced Gingival Overgrowth Surgical Management of Amlodipine influenced gingival overgrowth in Hypertensive patient. Abstract: Drug-influenced gingival overgrowth (DIGO) is a serious concern both for the patient and the clinician. A number of local and systemic factors such as plaque, hormonal changes, drug ingestion, heredity can cause or influence gingival overgrowth. Certain anticonvulsants, immuno-suppressive drugs and a number of calcium channel blockers have been shown to produce similar gingival overgrowths in certain susceptible patients. Amlodipine is a comparatively new calcium channel blocker may induce gingival overgrowth in case of underlying inflammatory component. A 38-year-old hypertensive female patient on amlodipine (10 mg/day, single dose orally) since eight months, sought dental attention because of the resultant gingival overgrowth. Clinical examination, Medical history and histological assessment further helped to formulate a diagnosis of DIGO. Six weeks after phase-I therapy and drug substitution, undisplaced flap surgery was performed. The patient’s gingiva seemed to be normal at six month follow-up visit, with no signs of recurrence. Key words: Gingival overgrowth, Hypertension, Amlodipine, Undisplaced flap surgery. Drug influenced gingival overgrowth. Introduction: There are many factors (causal or modifying) involved in gingival overgrowth. Plaque accumulation on teeth causes gingival inflammation and may lead to inflammatory enlargement. Gingival overgrowth can be seen in patients with familial hereditary gingival fibromatosis, pregnancy, and leukemia. DIGO is a well-documented side effect of some pharmacologic agents, including, but not limited to, calcium channel blockers (CCBs), phenytoin, and cyclosporine[1,2 ]. It can be a serious concern for patients due to the concomitant unesthetic appearance and the formation of new niches for the periopathogenic bacteria [3]. Despite the relatively high prevalence of nifedipine-influenced gingival overgrowth, [4 ] amlodipine has less frequently been reported as the potential etiologic cause of gingival overgrowth[5] .Amlodipine is a comparatively new long acting dihydropyridine calcium channel blocker that is used in the management of both hypertension and angina. Unwanted effects associated with ch ronic usage of amlodipine are few and are mainly related to vasodilation. The pharmacological effects of these drugs are specific but the clinical and histological features of the enlargement caused by the different drugs are similar. The clinical appearance of DIGO is usually characteristic, although variants are seen depending on the location of lesions, the irritants involved and the extent of inflammation. As the condition progresses, the marginal and papillary gingival overgrowth and may interfere with speech, mastication and aesthetics. In the patients with preexisting periodontitis and DIGO the deepening of periodontal pockets and associated subgingival microbiota may increase periodontal attachment and bone loss. The surgical treatment is a definitive therapy for DIGO, in absence of spontaneous regression following drug substitution and phase-I Therapy. The common surgical technique is the simple excision of the excessive gingival tissue with– external bevel gingivectomy (EBG) or internal (reverse) bevel gingivectomy (IBG). The surgical approach of undisplaced full thickness flap, in this context, is more suitable to eliminate periodontal pockets (Pocket wall) in presence of adequate attached gingiva and to improve the alveolar bone morphology. In the present report, a case of amlodipine-influenced gingival overgrowth (AIGO) has been presented wherein the AIGO was treated in the following phases: (1) substitution of the drug , (2) thorough Phase-1 therapy, (3) surgical excision of the residual gingival overgrowth and (4) maintenance and supportive therapy. Case Description: A 38-year-old female patient was referred to us with complaint of swollen and bleeding gums in the upper and lower jaw. Past medical history revealed hypertension for which the patient received amlodipine (10 mg/day, single dose orally) for the last eight months. The patient had noted a gradual and painless enlargement of the gingiva for first 4 months and then she noticed bleeding gums. A generalized fibrous gingival enlargement with edematous marginal gingiva, owing to superimposed inflammatory component, was found throughout the maxillary and mandibular gingiva (Fig. 1A,B,C,D). Presence of generalized periodontal pockets (≠¥7-8mm) and clinical attachment loss (≠¥5-6mm) was a prominent feature of gingival overgrowth indicating a vertical enlargement of gingiva. Purulent discharge and bleeding on probing were detected which were in accordance with the inflammation. Treatment: On request, patient’s physician substituted amlodipine with Beta Adrenergic blocker (Atenolol), after which, patient was recalled for through scaling and root planing. Oral hygiene instructions, chlorhexidine mouthwash 0.2% of 10ml twice a day was prescribed. At follow-up after six weeks, residual inflammatory component of the enlargement resolved(Fig-2) but the gingival overgrowth needed definitive surgical treatment. Under adequate local anesthesia (xylocaine 2%), the pocket depth was marked, (Fig-3) an internal bevel incision was taken up to the alveolar crest. (Fig-4) Crevicular and interdental incision along the base of the pocket wall was released and full thickness mucoperiosteal flap was reflected. (Fig-5) The excised mass was stored in formalin for further histopathologic investigation. Scaling, root planning and curettage were completed. Osseous resective surgery, using carbide burs, along with copious saline irrigation was done to recontour thickened bony plates, le dges and deep interdental craters. (Fig-6) Flaps were trimmed and approximated using interrupted silk sutures. Routine post surgical instructions, a course of antibiotics and analgesics (Cap. Amoxycillin 500mg three times a day for five days and Ibufrofen 400 mg three times a day for three days) and 0.2% chlorhexidine was prescribed twice a day for fifteen days. Microscopic inspection of the gingival biopsy specimens demonstrated a connective tissue hyperplasia, acanthosis of overlying epithelium and elongated rete ridges together with inflammatory cells. Sutures were removed after 1 week. Healing was uneventful and the patient’s appearance and overall function improved considerably at six month follow up. (Fig-7) Oral hygiene instructions were given from first visit and reinforced in all subsequent visits. Discussion: Amlodipine is a second-generation dihydropyridine CCB that can cause gingival overgrowth. The prevalence of amlodipine-influenced gingival overgrowth has been shown to be between 1.7% and 3.3%[6,7]. Lafziet al.(2006) had reported rapidly developing gingival hyperplasia in patient receiving 10 mg/day of amlodipine within 2 month of onset. [8] The incidence of gingival overgrowth with nifedipine therapy has been reported to be as high as 20%, [9] and a study by Prisant (2002) [10] reported that the prevalence with the use of CCBs might be as high as 38%.Gingival overgrowth considered to be 3.3 times more common in men than in women [10] .The most common form is bacterial plaque–influenced gingival disease, which presents as gingivitis. Use of phenytoin, cyclosporine, and CCBs, as well as vitamin C deficiency, can also predispose to development of gingival overgrowth, as can hormonal shifts during pregnancy. The reason for these adverse events is not absolutely known, but mechani sms involving inflammatory and non inflammatory pathways have been suggested [11]. For example, individual sensitivity to a drug’s metabolic pathway might be a trigger [11]. Untreated gingival overgrowth might lead to bleeding, infection, abscess, ulceration, cosmetic deficiency and/or functional difficulty (eg, chewing, talking) [10]. Treatment of drug-influenced gingival overgrowth includes cessation/replacement of the drug and decreasing other risk factors with meticulous mechanical and chemical plaque control. Replacing the affecting drug with another agent is also recommended when possible[12]. In present case of DIGO patient was under treatment for hypertension since last 8 months and was prescribed tablet Amlodipin 10mg/day by her physician. Thorough SRP and replacing the Amlodipin with Atenolol was done. Drug substitution and thorough SRP did not result into regression of the enlargement. The surgical treatment is a definitive therapy for DIGO, in absence of spontaneous regression following drug substitution and phase-I Therapy. Classic gingival surgery primarily deals with the treatment of pockets – i.e., gingival sulci that are deepened due to a proliferation or an increase in bulk of gingival tissue in a coronal direction, with or without apical migration of the epithelial attachment. External bevel gingivectomy (EBG) and internal bevel gingivectomy (IBG) should be reserved for cases not responding to non surgical methods or severe cases that affect oral hygiene or functionality, or can be performed for cosmetic reasons. IBG approach has the benefit of limiting the large denuded connective tissue wound that results from the external gingivectomy, thereby minimizing postoperative pain and bleeding. It is accepted that gingival surgery (both EBG and IBG) is essentially limited to the treatment of pseudopockets. But if true pockets associated with bone defects are present then undisplaced flap surgery can be the treatment modality for the massive enlargement. The advantages of this technique are removal of pocket wall and osseous contouring simultaneously eliminating the gingival overgrowth and pocket in presence of adequate attached gingiva. In this case report undispalced flap surgery was performed for eliminating pocket and osseous contouring in presence of adequate attached gingiva. However regardless of the treatment option employed, regular maintenance and recall follow up are mandatory to achieve the long term success. Conclusion Gingival overgrowth is an overlooked but potentially harmful side effect of treatment with amlodipine and other calcium channel blockers and every physician should be aware of this, particularly if adverse oral symptoms arise during drug use. The amlodipine influenced gingival overgrowth in this case completely resolved when the patient was switched to Beta Adrenergic blocker (Atenolol) followed by surgical excision of the overgrowth. Another factor contributing to the excellent response to the therapy is the patient compliance in maintaining the oral hygiene. Lastly the patients’ documented data should be shared with the physician to gain his confidence and respect for the dental community. In addition, he will be motivated to refer patients with complains of gum swelling at a much earlier stage or in fact, advice dental consultation for improvement of oral hygiene before prescribing the list of drugs that may influence gingival overgrowth in presence of preexisting gingival inflammation. References 1

Ap Biology Lab 1 Questions

AP Biology Lab 1 Ross Lordo Introduction Questions 1. The solute potential would be -2. 48. If the concentration inside the cell is . 15 M, then would diffusion out of the cell and into the solution of . 1 M. This is due to water potential and the tendency for water to move from areas of high water potential to low water potential. 2. The turgor pressure must be equal to the water potential if there is no net diffusion.The cell and environment have reached equilibrium and the movement of water is equal on both sides. Getting Started 1. Kinetic energy is the energy an object possesses due to its motion. The difference between kinetic energy and potential energy is the kinetic energy is the energy of an object that is already in motion and potential energy is the energy possessed by an object at rest. Potential energy is stored energy, while kinetic energy is energy being exerted. 2.Temperature can affect the rate of diffusion. If the temperature is colder, the rate of diffusion is muc h slower as a result of all particles becoming closer together. If the temperature is warmer, there is much more energy present and therefore allows for the diffusion to take place at a fast rate. The distance a molecule needs to travel across the membrane can also affect the rate of diffusion. If the distance across the membrane is large, then the rate of diffusion will be much slower and vise versa. 3.A high temperature can speed up the diffusion process by providing more energy for the molecules and also for eliminating in double bonds in the phospholipid membrane. A low temperature will decline the rate of diffusion, as the particles will have less energy. The distance travelled will also affect diffusion rates. The longer the distance, the slower the diffusion is going to take place. The shorter the distance, the quicker the rate of diffusion 4. Gradients offer a pathway for molecules to go in and out of the cell.Many molecules are to big to fit through the semipermeable phosph olipid membrane and these gradients allow these large molecules to be able to cross through the cell. 5. Most cells are small because diffusion can take place at a quicker rate. The convolutions allow for more space to be able to be used in order to get molecules across the membrane. These small cells allow for materials to quickly be able to reach the cell membrane and get in or out of the cell, without having to make a long journey from an inside part of the cell. . Water will move out of the cell. The high water potential means there is little solute in the cell and more in the outside environment. In order to balance these concentrations, water moves out of the cell and creates equilibrium with the environment. 7. If saltwater is applied to a plant, the plant would shrivel up and die. This is a result of the water moving out of the cells in order to try to balance the concentration of solute compared to inside the cell.The water movement out of the cell would cause the cell to s hrink and the lack of water would eventually cause the plant to die. 8. A plant can control its turgor pressure through its central vacuole and cell wall. If a great amount of water is inside the cell, the central vacuole will take in some of the water to take some of the pressure of the cell wall. The cell wall can also eliminate water from making its way into the cell. The would cause the cell to keep expanding, but slowly eliminate its excess water.

Lacsap’s Fractions

Lacsap’s Fractions IB Math 20 Portfolio By: Lorenzo Ravani Lacsap’s Fractions Lacsap is backward for Pascal. If we use Pascal’s triangle we can identify patterns in Lacsap’s fractions. The goal of this portfolio is to ? nd an equation that describes the pattern presented in Lacsap’s fraction. This equation must determine the numerator and the denominator for every row possible. Numerator Elements of the Pascal’s triangle form multiple horizontal rows (n) and diagonal rows (r). The elements of the ? rst diagonal row (r = 1) are a linear function of the row number n. For every other row, each element is a parabolic function of n.Where r represents the element number and n represents the row number. The row numbers that represents the same sets of numbers as the numerators in Lacsap’s triangle, are the second row (r = 2) and the seventh row (r = 7). These rows are respectively the third element in the triangle, and equal to each other bec ause the triangle is symmetrical. In this portfolio we will formulate an equation for only these two rows to ? nd Lacsap’s pattern. The equation for the numerator of the second and seventh row can be represented by the equation: (1/2)n * (n+1) = Nn (r) When n represents the row number.And Nn(r) represents the numerator Therefore the numerator of the sixth row is Nn(r) = (1/2)n * (n+1) Nn(r) = (1/2)6 * (6+1) Nn(r) = (3) * (7) Nn(r) = 21 Figure 2: Lacsap’s fractions. The numbers that are underlined are the numerators. Which are the same as the elements in the second and seventh row of Pascal’s triangle. Figure 1: Pascal’s triangle. The circled sets of numbers are the same as the numerators in Lacsap’s fractions. Graphical Representation The plot of the pattern represents the relationship between numerator and row number. The graph goes up to the ninth row.The rows are represented on the x-axis, and the numerator on the y-axis. The plot forms a parabo lic curve, representing an exponential increase of the numerator compared to the row number. Let Nn be the numerator of the interior fraction of the nth row. The graph takes the shape of a parabola. The graph is parabolical and the equation is in the form: Nn = an2 + bn + c The parabola passes through the points (0,0) (1,1) and (5,15) At (0,0): 0 = 0 + 0 + c ! ! At (1,1): 1 = a + b ! ! ! At (5,15): 15 = 25a + 5b ! ! ! 15 = 25a + 5(1 – a) ! 15 = 25a + 5 – 5a ! 15 = 20a + 5 ! 10 = 20a! ! ! ! ! ! ! therefore c = 0 therefore b = 1 – a Check with other row numbers At (2,3): 3 = (1/2)n * (n+1) ! (1/2)(2) * (2+1) ! (1) * (3) ! N3 = (3) therefore a = (1/2) Hence b = (1/2) as well The equation for this graph therefore is Nn = (1/2)n2 + (1/2)n ! which simpli? es into ! Nn = (1/2)n * (n+1) Denominator The difference between the numerator and the denominator of the same fraction will be the difference between the denominator of the current fraction and the previous fraction . Ex. If you take (6/4) the difference is 2. Therefore the difference between the previous denominator of (3/2) and (6/4) is 2. ! Figure 3: Lacsap’s fractions showing differences between denominators Therefore the general statement for ? nding the denominator of the (r+1)th element in the nth row is: Dn (r) = (1/2)n * (n+1) – r ( n – r ) Where n represents the row number, r represents the the element number and Dn (r) represents the denominator. Let us use the formula we have obtained to ?nd the interior fractions in the 6th row. Finding the 6th row – First denominator ! ! ! ! ! ! ! ! ! ! ! ! – Second denominator ! ! ! ! ! ! ! ! ! ! ! ! ! denominator = 6 ( 6/2 + 1/2 ) – 1 ( 6 – 1 ) ! = 6 ( 3. 5 ) – 1 ( 5 ) ! 21 – 5 = 16 denominator = 6 ( 6/2 + 1/2 ) – 2 ( 6 – 2 ) ! = 6 ( 3. 5 ) – 2 ( 4 ) ! = 21 – 8 = 13 ! ! -Third denominator ! ! ! ! ! ! ! ! ! ! ! ! – Fourth denominator ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! – Fifth denominator ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! denominator = 6 ( 6/2 + 1/2 ) – 3 ( 6 – 3 ) ! = 6 ( 3. 5 ) – 3 ( 3 ) ! = 21 – 9 = 12 denominator = 6 ( 6/2 + 1/2 ) – 2 ( 6 – 2 ) ! = 6 ( 3. 5 ) – 2 ( 4 ) ! = 21 – 8 = 13 denominator = 6 ( 6/2 + 1/2 ) – 1 ( 6 – 1 ) ! = 6 ( 3. 5 ) – 1 ( 5 ) ! = 21 – 5 = 16 ! ! We already know from the previous investigation that the numerator is 21 for all interior fractions of the sixth row.Using these patterns, the elements of the 6th row are 1! (21/16)! (21/13)! (21/12)! (21/13)! (21/16)! 1 Finding the 7th row – First denominator ! ! ! ! ! ! ! ! ! ! ! ! – Second denominator ! ! ! ! ! ! ! ! ! ! ! ! – Third denominator ! ! ! ! ! ! ! ! ! ! ! ! – Fourth denominator ! ! ! ! ! ! ! ! ! ! ! ! ! ! denominator = 7 ( 7/2 + 1/2 ) – 1 ( 7 – 1 ) ! =7(4)–1(6) ! = 28 – 6 = 22 denominator = 7 ( 7/2 + 1/2 ) – 2 ( 7 – 2 ) ! =7(4)–2(5) ! = 28 – 10 = 18 denominator = 7 ( 7/2 + 1/2 ) – 3 ( 7 – 3 ) ! =7(4)–3(4) ! = 28 – 12 = 16 denominator = 7 ( 7/2 + 1/2 ) – 4 ( 7 – 3 ) ! =7(4)–3(4) ! = 28 – 12 = 16 ! ! ! ! ! ! Fifth denominator ! ! ! ! ! ! ! ! ! ! ! ! – Sixth denominator ! ! ! ! ! ! ! ! ! ! ! ! denominator = 7 ( 7/2 + 1/2 ) – 2 ( 7 – 2 ) ! ! =7(4)–2(5) ! ! = 28 – 10 = 18 ! ! denominator = 7 ( 7/2 + 1/2 ) – 1 ( 7 – 1 ) ! =7(4)–1(6) ! = 28 – 6 = 22 We already know from the previous investigation that the numerator is 28 for all interior fractions of the seventh row. Using these patterns, the elements of the 7th row are 1 (28/22) (28/18) (28/16) (28/16) (28/18) (28/22) 1 General Statement To ? nd a general statement we combined the two equations needed to ? nd the numerator and to ? nd the denominator. Which are (1/2)n * (n+1) to ? d the numerator and (1/2)n * (n+1) – n( r – n) to ? nd the denominator. By letting En(r) be the ( r + 1 )th element in the nth row, the general statement is: En(r) = {[ (1/2)n * (n+1) ] / [ (1/2)n * (n+1) – r( n – r) ]} Where n represents the row number and r represents the the element number. Limitations The ‘1’ at the beginning and end of each row is taken out before making calculations. Therefore the second element in each equation is now regarded as the ? rst element. Secondly, the r in the general statement should be greater than 0. Thirdly the very ? rst row of the given pattern is counted as the 1st row.Lacsap’s triangle is symmetrical like Pascal’s, therefore the elements on the left side of the line of symmetry are the same as the elements on the right side of the line of symmetry, as shown in Figure 4. Fourthly, we only formulated equations based on the second and the seventh rows in Pascal’s triangle. These rows are the only ones that have the same pattern as Lacsap’s fractions. Every other row creates either a linear equation or a different parabolic equation which doesn’t match Lacsap’s pattern. Lastly, all fractions should be kept when reduced; provided that no fractions common to the numerator and the denominator are to be cancelled. ex. 6/4 cannot be reduced to 3/2 ) Figure 4: The triangle has the same fractions on both sides. The only fractions that occur only once are the ones crossed by this line of symmetry. 1 Validity With this statement you can ? nd any fraction is Lacsap’s pattern and to prove this I will use this equation to ? nd the elements of the 9th row. The subscript represents the 9th row, and the number in parentheses represents the element number. – E9(1)!! ! – First element! ! ! ! ! ! ! ! ! ! ! ! ! – E9(2)!! ! – Second element! ! ! ! ! ! ! ! ! ! ! ! ! – E9(3)!! ! – Third element! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! {[ n( n/2 + 1/2 ) ] / [ n( n/2 + 1/2 ) – r( n – r) ]} {[ 9( 9/2 + 1/2 ) ] / [ 9( 9/2 + 1/2 ) – 1( 9 – 1) ]} {[ 9( 5 ) ] / [ 9( 5 ) – 1( 8 ) ]} {[ 45 ] / [ 45 – 8 ]} {[ 45 ] / [ 37 ]} 45/37 {[ n( n/2 + 1/2 ) ] / [ n( n/2 + 1/2 ) – r( n – r) ]} {[ 9( 9/2 + 1/2 ) ] / [ 9( 9/2 + 1/2 ) – 2( 9 – 2) ]} {[ 9( 5 ) ] / [ 9( 5 ) – 2 ( 7 ) ]} {[ 45 ] / [ 45 – 14 ]} {[ 45 ] / [ 31 ]} 45/31 {[ n( n/2 + 1/2 ) ] / [ n( n/2 + 1/2 ) – r( n – r) ]} {[ 9( 9/2 + 1/2 ) ] / [ 9( 9/2 + 1/2 ) – 3 ( 9 – 3) ]} {[ 9( 5 ) ] / [ 9( 5 ) – 3( 6 ) ]} {[ 45 ] / [ 45 – 18 ]} {[ 45 ] / [ 27 ]} 45/27 E9(4)!! ! – Fourth element! ! ! ! ! ! ! ! ! ! ! ! ! – E9(4)!! ! – Fifth element! ! ! ! ! ! ! ! ! ! ! ! ! – E9(3)!! ! – Sixth element! ! ! ! ! ! ! ! ! ! ! ! ! – E9(2)!! ! – Seventh element! ! ! ! ! ! ! ! ! ! ! ! ! â₠¬â€œ E9(1)!! ! – Eighth element! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! [ n( n/2 + 1/2 ) ] / [ n( n/2 + 1/2 ) – r( n – r) ]} {[ 9( 9/2 + 1/2 ) ] / [ 9( 9/2 + 1/2 ) – 4( 9 – 4) ]} {[ 9( 5 ) ] / [ 9( 5 ) – 4( 5 ) ]} {[ 45 ] / [ 45 – 20 ]} {[ 45 ] / [ 25 ]} 45/25 {[ n( n/2 + 1/2 ) ] / [ n( n/2 + 1/2 ) – r( n – r) ]} {[ 9( 9/2 + 1/2 ) ] / [ 9( 9/2 + 1/2 ) – 4( 9 – 4) ]} {[ 9( 5 ) ] / [ 9( 5 ) – 4( 5 ) ]} {[ 45 ] / [ 45 – 20 ]} {[ 45 ] / [ 25 ]} 45/25 {[ n( n/2 + 1/2 ) ] / [ n( n/2 + 1/2 ) – r( n – r) ]} {[ 9( 9/2 + 1/2 ) ] / [ 9( 9/2 + 1/2 ) – 3 ( 9 – 3) ]} {[ 9( 5 ) ] / [ 9( 5 ) – 3( 6 ) ]} {[ 45 ] / [ 45 – 18 ]} {[ 45 ] / [ 27 ]} 45/27 {[ n( n/2 + 1/2 ) ] / [ n( n/2 + 1/2 ) – r( n – r) ]} {[ 9( 9/2 + 1/2 ) ] / [ 9( 9/2 + 1/2 ) – 2( 9 – 2) ]} {[ 9( 5 ) ] / [ 9( 5 ) – 2 ( 7 ) ] } {[ 45 ] / [ 45 – 14 ]} {[ 45 ] / [ 31 ]} 45/31 {[ n( n/2 + 1/2 ) ] / [ n( n/2 + 1/2 ) – r( n – r) ]} {[ 9( 9/2 + 1/2 ) ] / [ 9( 9/2 + 1/2 ) – 1( 9 – 1) ]} {[ 9( 5 ) ] / [ 9( 5 ) – 1( 8 ) ]} {[ 45 ] / [ 45 – 8 ]} {[ 45 ] / [ 37 ]} 45/37 From these calculations, derived from the general statement the 9th row is 1 (45/37)! ! (45/31)! ! (45/27)! (45/25)! (45/25)! (45/27) (45/31)! (45/37)! ! 1 Using the general statement we have obtained from Pascal’s triangle, and following the limitations stated, we will be able to produce the elements of any given row in Lacsap’s pattern. This equation determines the numerator and the denominator for every row possible.

Subliminal Advertising and Modern Day Brainwashing

The advertising industry, a prominent andpowerful industry, engages in deceptive subliminal advertising which most us are unaware of. By bypassing our unconscious mind using subliminal techniques, advertisers tap into the vulnerabilities surrounding our unconscious mind, manipulating and controlling us in many ways. Since the 1940 s subliminal advertising blossomed until now, when you can find subliminals in every major advertisement and magazine cover. Legislation against the advertisers has had no effect in curbing the use of subliminals. In this Information Age, it seems people are no longer in control of the people. The ones in control are the ones with knowledge (as usual). In this case, the advertisers have it; you don t. Until†¦show more content†¦Despite the lack of conventional scientific evidence, I believe there exists a consciousness that lies outside of our normal awareness. Although I will later provide evidence, the paper assumes the existence of such a phenom enon. Introduction What is your favorite ad on TV or in a magazine? Why do you like it? Is it the dry humor? Or the dramatic irony? Advertisers use subliminal techniques to put hidden messages into their ads. By now, your subconscious mind has a full load of them, each expertly targeted by the advertisers. Although the exact consequences are unknown, one can guess it is like being brainwashed every time you see an ad. Heaving Breasts Do advertisers really put subliminal messages on their ads? Let s explore this topic. Go to the vending machine and buy a can of Diet Cokeâ„ ¢. The can looks pretty ordinary--script letters on white bubbles floating on a silver can. Turn your attention now to the passion red glass on the lower left and hold the can arm s-length away from you. Do you see them now? Almost everyone I have shown the can to readily perceived the sexual image. 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