Wednesday, May 6, 2020

Stopping the Clock An Argument for the End of Age and...

Trash and aging go hand in hand. Take for example a pair of shoes. When a person uses a pair of shoes consistently, the soles will begin to wear down and holes begin to form. A person may repair the sole and patch up the holes, but eventually there comes a time when the well-worn shoe is beyond repair and it is time to chuck them in the trash bin. Trash is made up of things that have aged to the point of uselessness; things that have become undesired and worthless. A person can easily tell when an item is no longer of use to them, but controversy ensues when a person attempts to determine when a human being begins to lose their usefulness. Aging is a fact of life, but how a society deals with this fact varies. In today’s American consumer†¦show more content†¦The fact that he is in a class high enough to allow him to choose when and if he wants to deal with garbage means that he is not forced to have a relationship with trash. Calvino is able to escape being labelled as garbage because he chooses to perform the task of taking it out. He is privileged because he is not forced to deal with trash in the way the group of people that Spelman talks about next in the chapter are forced. The third and final example in Spelman’s chapter, â€Å"On taking Out the Trash†, takes us to India. The section begins with a brief explanation of the caste system in India to help the reader better understand the social context in which the group that has the relationship with trash is situated. The Dalit’s, or the ‘Untouchables’ are a group of people that are quite unlike Calvino. They are a group that is born into their relationship with trash and so they cannot free themselves from the stigmatization that comes with trash. A person that is a Dalit is expected to deal with filth and garbage. They are the designated cleaners, and they themselves can never completely cleanse themselves of this designation. Their stigmatization is obvious because they are labelled untouchables. They are equated with the garbage they handle. Even though they may be in actuality more clean or cleanly than people of another caste, the connection between their job and t heir identity is unbreakable. Spelman makes clear that even â€Å"a clean Dalit remains impure† (20). TheShow MoreRelatedFundamentals of Hrm263904 Words   |  1056 PagesWorkshop 49 Guarding Against Discrimination Practices 65 DID YOU KNOW?: Is a Problem Brewing? 66 Determining Potential Discriminatory Practices 66 The 4/5ths Rule 66 Restricted Policy 66 Geographical Comparisons 67 McDonnell-Douglas Test 67 Responding to an EEO Charge 67 Business Necessity 68 Bona Fide Occupational Qualifications 68 Seniority Systems 68 Selected Relevant Supreme Court Cases 69 Cases Concerning Discrimination 69 Cases Concerning Reverse Discrimination 71 ETHICAL ISSUES IN HRM:Read MoreExploring Corporate Strategy - Case164366 Words   |  658 Pagesbackbone to a programme of study but could sensibly be supplemented by other material. We have provided a mixture of longer and shorter cases to increase the ï ¬â€šexibility for teachers. Combined with the illustrations and the short case examples at the end of each chapter (in both versions of the book) this increases the reader’s and tutor’s choice. For example, when deciding on material for Chapter 2, the case example, Global Forces and the European Brewing Industry, tests a reader’s understanding ofRead MoreDeveloping Management Skills404131 Words   |  1617 Pagesyou to seek out skill practice opportunities in all aspects of your life, including working in assigned teams in this and other courses, planning social events for a campus or communi ty organization, counseling a troubled sibling or friend, managing end-of-semester deadlines, or handling a difficult issue with a boy/girlfriend or spouse. The sooner you begin—and the more you persist in—practicing what you learn in this course, the more you’ll be able to count on these skills as â€Å"automatic responses†Read More_x000C_Introduction to Statistics and Data Analysis355457 Words   |  1422 PagesFit of a Line 221 5.4 Nonlinear Relationships and Transformations 238 5.5 Logistic Regression (Optional) 255 5.6 Interpreting and Communicating the Results of Statistical Analyses 264 Activity 5.1 Exploring Correlation and Regression 267 Activity 5.2 Age and Flexibility 268 Graphing Calculator Explorations 272 6 Probability 279 6.1 Chance Experiments and Events 279 6.2 Deï ¬ nition of Probability 288 ââ€"   Contents ix 6.3 Basic Properties of Probability 295 6.4 Conditional Probability 302

Tuesday, May 5, 2020

Englands Greatest Poet And Playwright Was Born At Essay Example For Students

Englands Greatest Poet And Playwright Was Born At Essay Englands greatest poet and playwright was born atStratford-upon-Avon, the son of a tradesman andAlderman of Stratford, John Shakespeare in 1564. William, the eldest son, and third child (of eight) wasbaptised on 26th April 1564 and probably educated atStratford Grammar School, but little isknown of his life up to his eighteenth year. He did notgo to University and his younger contemporary andfellow-dramatist, Ben Johnson, would later speakdisparagingly of his small Latin, and less Greek inthe eulogy prefaced to the Firs Folio. However theGrammar School curriculum would have provided aformidable linguistic, and to some extent literary,education. Although, in 1575 when he was eleven, there was agreat plague in the country and Queen Elizabethjourneyed out of London to avoid its consequences andstayed for several days at Kenilworth Castle nearStratford enjoying festivities arranged by her hostLord Leicester. It is probable these events may havemade a strong impact on the mind of young William. At the age of Eighteen, he married Anne Hathaway, eightyears his senior. Five years later he left for London. William worked at the Globe Theatre and appeared inmany small parts. He first appeared in public as a poetin 1593 with his Venus and Adonis and the followingyear with The Rape of Lucrece. He became jointproprietor of The Globe and also had an interest in theBlackfriars Theatre. The play writing commenced in 1595 and of the 38 playsthat comprise the Shakespeare Cannon, 36 were publishedin the 1st Folio of 1623, of which 18 had beenpublished in his lifetime in what are termed the Quartopublications. Loves Labours Lost and The Comedy of Errors appearto be among the earliest, being followed by The TwoGentlemen of Verona and Romeo and Juliet. Then followedHenry VI, Richard III, Richard II, Titus Andronicus,The Taming of the Shrew, King John, The Merchant ofVenice, A Midsummer Nights Dream, Alls Well that EndsWell, Henry IV, The Merry Wives of Windsor, Henry V,Much Ado about Nothing, As you like it, Twelth Night,Julius Caesar, Hamlet, Troilus and Cressida, Othello,Measure for Measure, Macbeth, King Lear, Timon ofAthens, Pericles, Antony and Cleopatra, Coriolanus,Cymbeline, A Winters Tale, The Tempest, Henry VIII andThe Two Noble Kinsmen. When he retired from writing in 1611, he returned toStratford to live in a house which he had built for hisfamily. His only son, Hamnet died when still a child. He also lost a daughter Judith (twin to Hamnet), buthis third child Susanna married a Stratford Doctor,John Hall and their home Halls Croft is todaypreserved as one of the Shakespeare Properties andadministered by the Shakespeare Birthplace Trust. In 1616 Shakespeare was buried in the Church of theHoly Trinity the same Church where he wasbaptised in 1564. Tradition has it that he died afteran evenings drinking with some of his theatrefriends. His gravestone bears the words:-Good frend for Jesus sake forebeare,to digg the dust encloased heare,Bleste be ye man yt spares thes stones,And curst be he yt moves my bones. In his will Shakespeare left his wife, the former AnneHathaway, his second best bed. We cannot be sure of thereason for this. It may have been the marital bed thebest bed being reserved for guests. It may suggest thatthey had a not altogether happy marriage whichnevertheless produced three children, Susanna, born onMay 26th 1583 and twins , Hamnet and Judith, born onFebruary 2nd 1585. These entries appear in the HolyTrinity Register. .u27e1ff1596631c77763aff06e9d0e22c , .u27e1ff1596631c77763aff06e9d0e22c .postImageUrl , .u27e1ff1596631c77763aff06e9d0e22c .centered-text-area { min-height: 80px; position: relative; } .u27e1ff1596631c77763aff06e9d0e22c , .u27e1ff1596631c77763aff06e9d0e22c:hover , .u27e1ff1596631c77763aff06e9d0e22c:visited , .u27e1ff1596631c77763aff06e9d0e22c:active { border:0!important; } .u27e1ff1596631c77763aff06e9d0e22c .clearfix:after { content: ""; display: table; clear: both; } .u27e1ff1596631c77763aff06e9d0e22c { display: block; transition: background-color 250ms; webkit-transition: background-color 250ms; width: 100%; opacity: 1; transition: opacity 250ms; webkit-transition: opacity 250ms; background-color: #95A5A6; } .u27e1ff1596631c77763aff06e9d0e22c:active , .u27e1ff1596631c77763aff06e9d0e22c:hover { opacity: 1; transition: opacity 250ms; webkit-transition: opacity 250ms; background-color: #2C3E50; } .u27e1ff1596631c77763aff06e9d0e22c .centered-text-area { width: 100%; position: relative ; } .u27e1ff1596631c77763aff06e9d0e22c .ctaText { border-bottom: 0 solid #fff; color: #2980B9; font-size: 16px; font-weight: bold; margin: 0; padding: 0; text-decoration: underline; } .u27e1ff1596631c77763aff06e9d0e22c .postTitle { color: #FFFFFF; font-size: 16px; font-weight: 600; margin: 0; padding: 0; width: 100%; } .u27e1ff1596631c77763aff06e9d0e22c .ctaButton { background-color: #7F8C8D!important; color: #2980B9; border: none; border-radius: 3px; box-shadow: none; font-size: 14px; font-weight: bold; line-height: 26px; moz-border-radius: 3px; text-align: center; text-decoration: none; text-shadow: none; width: 80px; min-height: 80px; background: url(; position: absolute; right: 0; top: 0; } .u27e1ff1596631c77763aff06e9d0e22c:hover .ctaButton { background-color: #34495E!important; } .u27e1ff1596631c77763aff06e9d0e22c .centered-text { display: table; height: 80px; padding-left : 18px; top: 0; } .u27e1ff1596631c77763aff06e9d0e22c .u27e1ff1596631c77763aff06e9d0e22c-content { display: table-cell; margin: 0; padding: 0; padding-right: 108px; position: relative; vertical-align: middle; width: 100%; } .u27e1ff1596631c77763aff06e9d0e22c:after { content: ""; display: block; clear: both; } READ: I Do or Please Don't: Hawaii's Same Sex Marriages EssayThere is no direct evidence of the marriage of WilliamShakespeare to Anne Hathaway although most historiansaccept that an entry in the Bishops Register atWorcester in November 1582 regarding the issue of amarriage licence to William Shaxpere and Anne Whateleyof Temple Grafton does not refer to the famous bard. However the following day a guarantee of ?40 wasundertaken in Stratford by two yeomen of the townagainst the prevention of the legal marriage of WilliamShagspere and Anne Hathway on only one reading of thebanns. In 1582 , ?40 was a considerable sum of moneyand one cannot believe that the simple fact of Annesbeing three months pregnant would warrant it. Nomarriage of an Anne Whatelely has ever been traced,neither has the marriage of Anne Hathway, but lack ofrecord does not mean that it did not happen.

Sunday, April 19, 2020

My Last Duchess Essays (462 words) - My Last Duchess,

My Last Duchess A dramatic monologue is defined as a poem in which a single character is speaking to a person or persons- usually about an important topic. The purpose of most dramatic monologues is to provide the reader with an overall or intimate view of the character's personality. A great poet can use punctuation and rhythm to make the poem appear as if it were an actual conversation. Robert Browning, known as the father of the dramatic monologue, does this in his poem, "My Last Duchess." The Duke of Ferrara, the speaker in "My Last Duchess," is portrayed as a jealous, arrogant man who is very controlling over his wife. The Duke of Ferrara was made jealous by everything the duchess did, no matter how unimportant it was. He was especially jealous of Fra Pandolf, the man who painted the duchess in the poem. A woman should be pleased only by her husband, as was not the case with the duchess and Fra Pandolf. She was "too easily impressed" by the painter (line 23). Fra Pandolf was not the only man that made the duke jealous. Everyone who passed the duchess received "much the same smile" as the duke (line 44). The duke expected to be the only man to receive a smile from his wife. Another aspect of the duke's character addressed in the poem is his condescending attitude. Two times in the poem the duke needlessly told the names of the artists who created the masterpieces that he owned (lines 3 & 56). He felt superiority over the emissary he was speaking to by dropping these names. The duke addressed the emissary as a"never read stranger" (line 6). Not only was it patronizing for the duke to call him a stranger, but he called him unintelligent too. The third character trait of the duke is his controlling behavior. In lines nine and ten he told the emissary that no one "puts by the curtain" that he had drawn for him but the duke himself. He felt the need to control who ever looked at the painting of the duchess. The main evidence of his dominating behavior is in line 46. The line reads, "...then all smiles stopped together." The line is ambiguous, but the most likely interpretation is that the duke had his wife killed. The poem can be interpreted in several different ways, but in all cases the duke is a very controlling man. Although "My Last Duchess" was set centuries in the past, lessons can be learned from it and used in today's society. No single moral lies beneath the poem but if one had to be found, it would be the golden rule. Do unto others as you would like them to do unto you. One would surely agree that the duke gained nothing by being the way he was. Nothing but kindness gets a person ahead, no matter what society that person is from.

Saturday, March 14, 2020

20 Biographical Essay Topics What to Include in a Who-Am-I Essay

20 Biographical Essay Topics What to Include in a Who-Am-I Essay In the previous guide, we learned about 10 facts on a â€Å"who am I† biographical essay, which we hope you found interesting and intellectually stimulating. If you haven’t had the chance to read that guide, we highly recommend you go through the first one before reading through this one. In this second guide, we share 20 topics for a â€Å"who am I† biographical essay. This guide is perfect to give you a head start in writing a great biographical essay. Many students are stuck trying to find out the perfect topic for themselves, which is why we’ve written this guide for you. In the end of this guide, we’ve also written a â€Å"who am I† essay example on one of the 20 topics we are going to discuss. This will give you a better idea of how a biographical essay is written. Without further ado, here are 20 topics for a â€Å"who am I† biographical essay: How Identity Issues Can Affect Your Mental Health The Signature Effect: Self-Identity and Uniqueness Motives Stages of Self-Awareness How a Sense of Connectivity can Affect Our Lives Positively The Correlation between Self-Identity, Nature and the Environment Relationship between Environmental Self-Identity, Preferences, Intentions and Behavior Why Does a Child Feel Embarrassed in Front of a Mirror? How Does a Person Become Self-Aware of Himself/Herself? What is Self-Awareness? Is it Found in the Animal Kingdom Too? The Definition of â€Å"Flow† Moments and its Effect on our Lives Why a Heightened Sense of Self Awareness Makes You More Insecure and Nervous Aggressive Consciousness: How it Affects the Person’s Identity Reasons Why Deep Self-Awareness is Rarely Found in Our Society Elaborating the Difference between Self-Awareness and Intelligence Correlation between Life, Nature and Identity How Social Media Plays a Vital Role in Shaping our Identities Can we Perceive Self-Awareness in our Dreams too? Relationship between Self-Awareness, Personality and Intellectual Development Emotional Intelligence: Is it Related to Self-Identity? The Supernatural Monitoring Hypothesis and its Effect on Our Identities We highly recommend you choose a topic which truly appeals to your intellect and one which you can easily work with. To make things even easier, here is a â€Å"who am I† essay sample: Sample Biographical Essay: The Supernatural Monitoring Hypothesis and its Effect on our Identities Many believers think that God is a strategic social agent who’s able to perceive thoughts and actions of human beings. How does it affect our identities and what does science have to say about this phenomenon known as The Supernatural Monitoring Hypothesis? In this essay, we discuss the life of Jonathan Gale, who’s a believer in God, so we can be certain about the effects an omnipotence entity like God can have on our lives. Gale was born in 1897, in Demopolis, Alabama. He was the first son in a Roman catholic family. Soon after he was born, Gale was baptized by a father who served at the St. Leo Catholic Church of Alabama. It was the first time he was first introduced to a supernatural identity and its intentions. When Gale grew to be a young man, he was influenced by his religion and the presence of an omnipotence being, watching his actions, intentions, thoughts and everything else. This paved the way for Gale to becoming a pious person, prohibiting himself from bad actions which, according to him, would lead to brutal punishment. Gale gained saint-like attributes and lived his whole life believing that God is perceiving his every move. His influence on society was remarkable. He was able to astonish people through his deeds and crystal clear intentions – without the typically shady looks we usually get from others in similar circumstances. Just like any young man with ambitions, Gale graduated and became an orthopedist. He believed that helping others would please God and so he played his part by treating patients whose bones were badly injured through accidents or other calamities. Gale married Lorraine Watson, a beautiful and religious dentist who shared similar traits. Gale met her when he went for a dental checkup, which was performed by Watson herself. Soon after marriage, Gale had twin babies, both boys. He raised his children while teaching them about God and that he perceives everything we do. Psychologically speaking, Gale had a heightened level of public-awareness; the same you might observe when a person is under video surveillance. Will M. Gervais and Ara Norenzayan found that believers show familiar symptoms of a person who is aware that he’s under camera surveillance. But since God is believed to be everywhere and can anticipate every step of a human being, there are multiple awareness levels that are exercised by this omnipotent entity. Believers like Gale are influenced by God through public, private and environmental awareness – which means that God is able to watch wherever we are at any given point in time. Since studies have proven that people under surveillance are more polite, honest and fair because they desire to have a good sense of social responsibility, it proves why believers of God have such saint-like attributes. The supernatural monitoring hypothesis is a phenomenon that has always been neglected by psychologists since it is so complex and related to religion. But if psychologists can investigate this matter, I personally believe that we could learn a great deal about becoming a better person, without getting ourselves involved in religion. That’s wraps up our sample essay. Let’s move on to our final guide on how to write a â€Å"who am I† biographical essay so you can write a perfect, clear, concise and interesting assignment. We are certain that you will receive very positive feedback from your professor, once you’ve read and followed all of our guides. References: Escalas, J., White, K., Townsend, C., Ward, M. K., Chan, C., Kettle, K. L., Broniarczyk, S. M. (2013). Self-Identity and Consumer Behavior Dissociative versus Associative Responses to Social Identity Threat: The Role of Consumer Self-Construal Self-Affirmation through the Choice of Highly Aesthetic Products Its Not Me, Its You: How Gift Giving Creates Giver Identity Threat as a Function of Social Closeness Identifiable but Not Identical: Combining Social Identity and Uniqueness Motives in Choice The Signature Effect: Signing Influences Consumption-Related Behavior by Priming Self-Identity An . Journal of consumer research, 39(5), xv-xviii. Tyler, T. R., Kramer, R. M., John, O. P. (2014). The psychology of the social self. Psychology Press. Olivos, P., Clayton, S. (2017). Self, Nature and Well-Being: Sense of Connectedness and Environmental Identity for Quality of Life. In Handbook of Environmental Psychology and Quality of Life Research (pp. 107-126). Springer International Publishing. Papacharissi, Z. (2013). 12 A Networked Self Identity Performance and Sociability on Social Network Sites. Frontiers in new media research, 207. Van der Werff, E., Steg, L., Keizer, K. (2013). The value of environmental self-identity: The relationship between biospheric values, environmental self-identity and environmental preferences, intentions and behaviour. Journal of Environmental Psychology, 34, 55-63. Dan Jones, (2011) God as a Cosmic CCTV – The Philosopher in the Mirror Will M. Gervais, Ara Norenzayan, (2011) Like a camera in the sky? Thinking about God increases public self-awareness and socially desirable responding – Journal of Experimental Social Psychology, Elsevier Inc.

Thursday, February 27, 2020

Marketing Mix Stimuli Essay Example | Topics and Well Written Essays - 3000 words - 1

Marketing Mix Stimuli - Essay Example The researcher states that product portfolio of Ariel brand can be explained in the following manner. Ariel Excel Gel The product is designed for low-temperature cleaning. A unique design of the bottle and innovative gel formulae of the product give a user the opportunity to wash clothes with high precision. The gel gets dissolve very easily in water hence solvency rate increases. The detergent is able to remove various types of stains such as tomato sauce, dirt, chocolate etc from cloths. Ariel Powder Ariel Powder is designed to give brilliant cleaning in every wash. The detergent can wash colored garments without causing harm to fabrics of a garment. The detergent should be dosed directly on the cloth by taking water as the surfactant. Ariel Excel Liquitabs Ariel Excel Liquitabs is able to remove stains such as oil, tar, grease etc. The product should be dosed in the lower drawer of Washing Machine. Ariel Tablets Ariel Tablets provides the convenience of using to users. The product has been developed in order to get a brilliant wash from the smallest possible dose. The study will be incomplete if it misses the opportunity to explain the role of consumer behavior in purchasing a detergent product. A psychoanalytical theory proposed by Sigmund Freud states that human personality depends on different variables such as id (biological need driven gratification), ego (conflict between the hedonistic requirement of id and ethical constraint of superego) and superego (behavior backed by social responsibility). Many consumers show boycotts of non-eco-friendly products in order to show their environmental concern. These customers prefer â€Å"ethical consumption† in order to maintain environmental sustainability. Foxall et al. have divided motivation into six components such as social needs, physiological needs, cognitive needs, symbolic needs, experiential needs and hedonic needs in order to explain customer demand. Customers purchase Ariel detergent in order t o satisfy their daily household needs hence purchase behavior is more driven by id aspect in contrast to other elements of psychoanalytic theory. Detergent purchase behavior of a customer can be briefed in the following manner.   People purchase detergent as daily household item hence they do not spend much time on the pre-purchase decision. Self-consciousness plays the very small role in purchasing decision. Brand conscious customers purchase Ariel due to the brand name of Procter & Gamble. Many customers purchase Ariel with an intention to satisfy self-esteem. Psychographics VALS or â€Å"Value and Lifestyle† framework has divided consumers into four segments such as â€Å"Actulizers† (Customers spending large sum of money on purchasing in order to show taste and attitude), Fulfilled (Customers purchasing product after doing rigorous background research), Believers (purchasing product in order to satisfy traditional family value) and Strivers (Customers purchasing low priced but stylish products). A study shows that believers play the significant role in purchasing detergent. Believers prefer well-known brands hence they choose Ariel over unknown local brands. Involvement Detergent is a low involvement product because customers do not require huge financial resources to purchase it.

Tuesday, February 11, 2020

Public Health Report Essay Example | Topics and Well Written Essays - 250 words

Public Health Report - Essay Example A meeting held later only informed them of the advantages of the project, but Lopez, and others resisted. The authorities had used Senate Bill 2 of 2007 to designate the location of the homeless shelter as â€Å"by right† hence eliminating pressure from residents and the NIMBYs. Although NIMBY remained in Santa Ana, the targeted warehouse had a capacity of 200 beds. The opposition was mostly due to lack of consultation from the neighbors resulting to undermined civil rights, and distraction from the homeless people including breaking into laundry rooms, leaving needles and feces behind, and taking showers using hosepipes. Despite the validity of these arguments, no supervisor attended. With SB2 in place, the residents of Santa Ana have a tough journey ahead since the council has no authority to stop the shelter in a city-approved zone. In the end, it appears that residents will have to learn how to live with the

Friday, January 31, 2020

Using Tight-Binding Model Essay Example for Free

Using Tight-Binding Model Essay Abstract— In this study, using tight binding model a simple analytical approach has been proposed to investigate the energy dispersion of graphene under the conditions of different planner strain distribution. Here the change in the angle between the primitive unit vectors due to application of external strain has been taken into consideration to propose the approach. From our proposed model it is found that graphene under relaxed or symmetrical strain distribution is a zero bandgap semiconductor. However a band gap is opened as the asymmetrical strain is applied to it. It is seen that upto a certain level of strain (i.e. 12.2 % parallel to carbon-carbon bond and 7.3% perpendicular to carbon-carbon bond) the band gap of graphene increases and then begin to fall . So, four different assumptions have been made for angular change of primitive unit vectors for four different regions of applied strain (i.e. before and after the strain of 12.2 % parallel to carbon-carbon bond before and after the strain of 7.3% perpendicular to carbon-carbon bond). The result obtained in the present study are compared and found an excellent agreement, with more or less 96% accuracy with that of determined from first principle technique. Keywords—Graphene, planner strain, tight binding model, energy dispersion, band-gap. I. INTRODUCTION Graphene, a strictly two-dimensional material having unusual and interesting properties [1] is a rapidly rising star on the horizon of material science and condensed matter physics. It is a material of interest in semiconductor industry because of its exceptionally high crystal and electronic quality, excellent transport properties (i.e. high electron mobility [2] and high thermal conductivity), and as it is planner, it is capable of extreme device scaling comparing with silicon technology. However these excellent properties are associated with a major drawback; graphene is a zero bandgap semiconductor or semimetal [3]-[4]. For large scale manufacturing, the absence of bandgap is the most difficult engineering issue to solve. The zero bandgap revels that it is impossible to switch graphene based device from the conductive to the nonconductive state. So it can not be used in the logic circuit. As the zero bandgap property of graphene limits its application in practical fields, scientists are working to find out the methods to open the bandgap in graphene. To solve this problem several methods have been proposed, such as graphene nanoribbin using quantum confinement effect in its transverse direction [5]-[8], bilayer graphene introducing symmetry breaking between two carbon layers via an external electric field [9],[10] , by the process of doping [11]-[13] and by the process of external strain [14],[15]. To investigate the bandgap opening by the above methods, several techniques have been applied for calculating the band structure of graphene such as first principal calculation, tight binding modeling, k.p method etc. All of them are performed earlier using the software simulation or numerical techniques, which require a huge computational complexity and time consuming and need high capacity super computer. In our study we have proposed a simple analytical approach to investigate the energy dispersion of graphene under different planner strain condition. Using the proposed method the bandgap opening is calculated under the application of asymmetrical strain parallel and perpendicular to the carbon-carbon bond in graphene. The results obtained from the proposed method is compared with the result published by the first principle method and found to be in good agreement with more or less 96 % accuracy. II. METHOD Graphene is a honeycomb lattice of regular hexagonal structure. But it loses its regular hexagonal structural symmetry under uniaxial/shear strain. When planar stress is applied to graphene, the position of carbon atoms shift relative to each other. As a result the vector position of lattice point changes. To explain this, the angle between a1 and a2 is considered here as ÃŽ ¸ instead of assuming 60o which is true for ideal or relaxed graphene structure. The eï ¬â‚¬ect in the tight-binding Hamiltonian is that the parameters of tight-binding scales changes accordingly. The strained lattice structure of graphene is shown in Fig.1. We have used the simple nearest Neighbor tight binding model. Here each Carbon atom is ÏÆ' bonded with three of its nearest neighbor Carbon atoms. Fig.1 : The direct lattice structure of graphene under strained condition The primitive unit vectors can be represented by where The separation of the carbon atoms (A and B) can be represented by three vectors R1, R2, R3 From Tight-binding energy dispersion model the formula of energy dispersion is given by [13] (1) Where Here is a fitting parameter which is often called the nearest neighbor overlap energy or hopping integral. The value of varies from 2.7eV to 3.3eV. (2) This is the generalized equation for the energy dispersion of graphene. Here is the angle between the primitive unit vectors. For the unstrained or relaxed condition, the value of the angle = 60o. In this case the Ï€ bands overlap at direct point or K point of the two dimensional brillouin zone. (a) (b) Fig.2(a) energy dispersion of relaxed graphene and (b) the corresponding brillouin zone. We have investigated the electronic structure of graphene under different planar strain distributions by the tight-binding (TB) approach. The graphene has been strained in three different ways [12]. These are : (i) symmetrical strain distribution (keeping the hexagonal symmetry unchanged) as shown in fig. 3.1(a) , (ii) asymmetrical strain distribution parallel to C-C bonds as shown in Fig. 3.1(b) , (iii) asymmetrical distribution perpendicular to C-C bonds as shown in Fig.3.1(c). Fig 3(a) Graphene system with symmetrical strain distribution, (b) asymmetrical strain distribution perpendicular to C-C bonds, and (c) asymmetrical strain distribution parallel to C-C bonds. Corresponding primitive cells in black, reciprocal lattices in green dashed and Brillouin zones in green grey are illustrated below the deformed lattices. Γ, K, M, R and S are the high symmetrical points. Lx and Ly are the half of the diagonal lengths of the primitive cells in parallel and perpendicular direction of the carbon-carbon bond. As the strain is applied to the graphene, it causes the deformation of the regular hexagonal structure of it . It also causes the deformation in the primitive unit cell. If the strain is symmetric then the band property of the system does not change but for asymmetrical strain , the band property of the system changes due to symmetry breaking. When an asymmetrical strain parallel to C-C bond is applied, it causes a deformation in the primitive unit cell. This deformation is taken as a change in angle between the primitive unit vectors. Here the strain is applied upto 12.2 % and it is seen that with the increase in strain the angle between the primitive unit vectors is reduced by following a 3 degree polynomial with respect to Lx and Ly(where Lx and Ly are in nanometer). The equation of is (3) This value of is then put in equation (2) to calculate the band gap under different strain distribution . It is seen that up to Ly =0.2396 nm band gap of graphene increases then the bandgap begin to fall . For this region the assumption of is different and it is, (4) In case asymmetrical applied strain perpendicular to C-C bond , up to 7.3 % strain the angle between the primitive unit vectors is increased by following a 2 degree polynomial with respect Lx and Ly. The equation of is, (5) Now up to Lx = 0.1323 nm band gap of graphene increases and then the bandgap begins to fall. For this region the assumption of is, (6) III.RESULT Asymmetrical strain distribution results in the opening of the bandgap between the maximum of the valance band and the minimum of the conduction band in graphene. When an asymmetrical strain parallel to carbon-carbon bond is applied, Ly increases. Then for the system in order to come back to its lowest energy, Lx decreases during the structural relaxation. Due to change of Lx and Ly, the angle between the primitive unit vectors decreases and causes the symmetry breaking. This angular change is taken as the parameter of deformed primitive cell to calculate the electronic structure of graphene. For example, for Ly = 0.2196, 0.2236, 0.2396, and 0.2436 nm the corresponding optimized values of Lx are Lx= 0.1228, 0.1224, 0.1217 and 0.1216 nm. Then from our proposed model the corresponding angle between the primitive unit vectors are =59.47o, 58.91o, 54.79o and 57.75o. The corresponding electronic structure or band diagrams are shown in fig.4 with the extended view at K point (a) (b) (c) (d) Fig.4 Extended view of bandgap opening for (a) Ly=0.2196 nm and Lx=0.1228 nm (b) Ly=0.2236 nm and Lx=0.1224 nm (c) Ly=0.2396 nm and Lx=0.1217 nm (d) Ly=0.2436 nm and Lx=0.1216 nm. Similar behavior is obtained in the graphene system, when asymmetrical strain perpendicular to carbon-carbon bond is applied. In this case for example for Lx =0.1268, 0.1292, 0.1353 nm the corresponding optimized Ly are Ly=0.2126, 0.2120 and 0.2105 nm and the corresponding deformed angle are = 60.52o, 61.05oand 60.38o. The opening of bandgap corresponding to these deformed angle are shown in fig.5 (a) (b) (c) FIG.4 EXTENDED VIEW OF BANDGAP OPENING FOR (A) LX=0.1268 NM AND LY= 0.2126 NM (B) LX= 0.1292 NM AND LY=0.2120 NM (C) LY=0.1353 NM AND LX= 0.2105 NM . These results revels that the zero bandgap or semi-metallic behavior of graphene sheet gets modified or a bandgap is opened when asymmetrical strain is applied to it. Now the question is what is the reason behind this? We know that planner graphene consists of strong bonds and delocalized pz electrons. Here orbitals are formed by overlapping the pz orbitals of the carbon atoms in the hexagonal lattice. These and bands touches each other at the K point causing zero bandgap. When the strain is applied the carbon-carbon bonds of graphene get elongated. Due to this elongation of carbon-carbon bonds, the electron clouds get localized on the corresponding carbon atoms. Therefore a restriction is imposed on movement of the electrons which causes the opening the bandgap at the K point. In this way, under strained condition, graphene loses its semimetal characteristics and turns into a direct bandgap semiconductor. IV.COMPARISON WITH ESTABLISHED METHOD: In this study, we have calculated the band gap of graphene under the application of asymmetrical strain by an analytical approach. The calculated value is found to be in great agreement with the measured value obtained by first principle calculation [14]. It is found that in case of asymmetrical strain distribution parallel and perpendicular to C-C bond, the percentage of error is more or less 4 % for most of the data which is shown In this study an analytical model has been proposed for investigating the energy dispersion of strained graphene under the distribution of the planner strain in parallel and perpendicular to carbon-carbon bond. Using the proposed model the energy dispersion for different planner strain has been calculated. From our study it is seen that for relaxed or symmetrically strained graphene, the band gap of the system is zero. When asymmetrical strain parallel or perpendicular to carbon-carbon bond is applied then a finite bandgap is opened. And it is also seen that tuning the percentage strain, the band gap can also be tuned. Here it is also seen that comparing the perpendicular strain, parallel strain parallel to the carbon -carbon bond more induces more bandgap. 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