Measure For Measure Essays (847 words) - Plays By Thomas Middleton

Measure For Measure From the beginning of the play the Duke shows his fascination with the art of disguise. He has Lord Angelo takes his place and he in turn becomes a friar in disguise. Throughout the play this notion of false identity and exchange of identity plays an important role for the Duke and also for the characters in the play. To understand why the Duke has this desire to disguise himself one can look at the beginning of the play in act 1 scene 3 where the Duke is at the monastery asking Friar Thomas to hide him there. He tells the friar that he has good reasons for hiding, and that he has lied to Angelo about his destination. The Duke explains that for the past fourteen years the laws have been flagrantly disobeyed, with little reproach from the government. As the Duke explains it, when the law only serves to threaten, because lawmakers do not carry out the punishments dictated, the government loses its authority. Since he gave the people liberties, he does not feel comfortable punishing them for now, yet he worries about the safe affairs of Vienna. He asked Angelo to take over in order to act more strictly without reproach or hypocrisy. He wants to observe Angelo at work, so he asks the friar to provide him with a disguise which will make him look like a visiting Friar himself: And to behold this sway, I will, as'twere a brother of your order, Visit both price and people: therefore, I prithee, Supply me with habit and instruct me How I may formally in person bear me Like a true friar. More reasons for this action At more leisure shall I render you; Only, this one: Lord Angelo is precise; Stands at a guard with envy; scarce confesses That his blood flows, or that his appetite Is more to bread than stone: hence shall we see, If power change purpose, what our seemers be. Overall the Duke is a good natured person who is and virtuous and kind hearted. He wants what is best for what is around him. He also wants to bring more law and order to Vienna but does not know how to do it himself so therefore he appoints Angelo. However he does not wish to have him free reign, knowing that he is very strict. Possibly the Duke feels that he is weak in power himself in maintaining order and in his heart he feels the only way to truly see how the people of his city will act is to be in disguise. And this is considered to be true when he discloses his identity because many problems are resolved. We can see this in Act 3 scene 2 when the Duke encounters Lucio and shows himself to be mildly vengeful, trying to protect his honor despite his disguise. This perhaps, suggests an ulterior motive in disguising himself: he ants to see how his subjects rule, and he can only do so through making himself functionally invisible to them. Not only does the Duke have a false identity, technically so does Lord Angelo. He is only appointed to take the Duke's place he himself is not a real Duke. Throughout the play because of his strict ways he himself likes the idea of all the power and the ways that he can enforce it. He keeps hidden his contract to marry Mariana and in the end is faced with his secret. Angelo is told to marry Mariana, and he escapes death at her request. The Duke probably does not intend to execute Angelo but wants it made clear that his crime deserves such a punishment. The Duke, in his disguise, also advises other characters to carry out two other secret plans involving mistaken identity. He has Mariana take Isabella's place ( Act 3 scene ) , and he also has the head of a dead pirate is sent in the place of Claudio's. Throughout the play in keeping with character's false identity and so his own identity the Duke some time must reveal his own. He does not immediately do this because his is still enjoying the intrigue which he can only understand.

What Grad Students Can Expect on the First Day of Class

What Grad Students Can Expect on the First Day of Class The first day of class is similar in both college and graduate school, and this is true of all disciplines. Day 1 is all about introducing the class. Common Approaches to Teaching the First Day of Class Some professors dive right into course content, beginning with a lecture.Others take a more social approach, using discussion and team-building activities like games, asking students to get to know each other, and posing non-course related discussion topics.Most professors will ask students to introduce themselves: Whats your name, year, major, and why are you here? Many will ask students to provide information and may pass out an index card for each student to record contact information and perhaps answer a question such as why they enrolled, one thing they hope to learn, or one concern about the course.Some simply distribute the course syllabus and dismiss class. The Syllabus Regardless of style, whether emphasizing content, social, or both, all professors distribute the syllabus  during the first day of class. Most will discuss it to some extent. Some professors read the syllabus, adding additional information as appropriate. Others draw students attention to main points. Yet some say nothing, simply distribute it and ask that you read it. No matter what approach your professor takes, it is in your best interest to read it very carefully because most instructors spend a lot of time preparing the syllabus. Then What? What happens after the syllabus is distributed varies by professor. Some professors end class early, often using less than one-half a class period. Why? They might explain that it is impossible to conduct class when no one has read. In reality, this isnt true, but it is more challenging to hold class with new students who have not read and have no background in the field. Alternatively, professors might end class early because they are nervous. Everyone finds the first day of class nerve-wracking - students and professors alike. Are you surprised that professors get nervous? Theyre people too. Getting through the first day of class is stressful and many professors want to and that first day as soon as possible. After the first day is done they can fall into the old routine of preparing lectures and teaching class. And so many otherwise enthusiastic professors end class early on the first day of school. Some professors, however, hold a full-length class. Their rationale is that learning begins on day 1 and what happens in that first class will influence how students approach the course and will, therefore, influence the entire semester. There is no right or wrong way to begin class, but you should be aware of the choices the professor makes in what he or she asks the class to do. This awareness might tell you a little bit about him or her and might help you prepare for the semester ahead.

Counseling Strategy Essay Example | Topics and Well Written Essays - 3500 words

Counseling Strategy - Essay Example Introduction The rationale of the project is to propose a preferred clear solution to neutralize the emotional dilemma of Bruce after he lost his wife, Cindy and his daughter, Chelsea in an accident in 2000. Bruce also had dwindling relationship concerning his family. The act of revenging her family`s death was burning deep inside him that he even hired Justin, a professional lawyer, to help him deal with the murderer. Bruce needed to know that revenge was not the solution to his problem and that the solution was in a short-term strategy offered by this type of counseling. Solution based short term pastoral counseling, BSPC align with the intention of God by using a more collaborative methodology (Kollar, 2011, p. 20-23).   With this the student counselor definitely, will come to know much earlier in his or her process of trying to understand the problem engulfing the life of the care-seeker, that they are not, in any way game-changer. This method is an identification of a means wh ich empowers, in a collaborative, the relocation, That is, a purposeful and collaborative way of making one move from where he or she is to where they are suppose to be through a direction which is well-defined in terms of goal. As opposed to problem-focused methods that need more time, the SBSPC approach manages counseling process more effectively. It`s also time-oriented with an average of 70 minute time span per session (Kollar, 2011, p. 25-28). SBSPC provide a challenge to the student counselors that enable them to reconsider existing paradigms as well as to value each counselee like colleague image-bearer. With this kind of reflection, it often cultivates the... From this paper it is clear that SBSPC provide a challenge to the student counselors that enable them to reconsider existing paradigms as well as to value each counselee like colleague image-bearer. With this kind of reflection, it often cultivates the most essential interpersonal required skills such as considerate, empathetic and authentic, to blend with a counselee problem minus compromising grace and truth. The moment a problem is understood in a satisfactory manner, goals and solutions will be collaboratively established.This discussion outlines that  a plan to carry out actions is engaged to shift away as well as outdo the problem and move into the future minus the problem. This is suitable and process that doesn`t assume the counselee can move into realization of his goal alone. Immediately the key to his solution is realized, effort is put to identify as well as secure partners so as to support counselee`s forward progress. The approach in this project challenges every stud ent counselor to function under the authority of God`s word and in Holy Spirit`s power and intentionally go after the imitation Jesus Christ and taking others the in the way of faith and imitate their creator in a community lead by accountability.  A solution-centered approach pay more attention to counseling in order to rob the counselee of his attention to the problems instead help the counselee to give more attention to the solution that leads to emotional stability as well as psychological well-being.

Chopsticks Only Works in Pairs Book Analysis Essay

Chopsticks Only Works in Pairs Book Analysis - Essay Example Very strange social customs like the walking marriage (In a walking marriage, the couples do not marry to live together as is the majority custom. Both of them stay in their own matrilineal family for the whole life. The male walks to the female’s house every evening and. the women open their doors to their lovers every evening. The men walk back home to work in their mothers household every morning. Neither of them is a member of each others family. ) and the graceful peacock dances seen among the Yunnan minorities are now recognized examples of cultural diversities seen among the ethnic minorities. It is in this context that Shanshan Du’s Chopsticks Only Work in Pairs, an important work on the ethnography of the Luhu gender system in China becomes pertinent. The book deeply explores the gender egalitarian society that still exists among the Lahu community, a community that lives in Southwest China; a community without a traditional written language. Chopsticks Only Wo rk in Pairs is a proverb that expresses the ideology that supports the gender equality prevalent in this community. Du begins the book with a clear theoretical introduction which states that, like rare islands there exists gender egalitarian societies, though very scarce and often imperfect. The existence of such societies has to be seen in the background of the cry for gender equality, which according to Du is â€Å" a popular dream like concept in the so called civilized world .† The strange fact is that these egalitarian societies are not recognized either by the feminists or by the anthropologists. This exposes the limitations of the utopian feminist agendas and the Western intellectual traditions, Du argues. Du in her introductory chapter thus goes critical about what she calls the anti male bias of the feminists. Even in a male dominated society there is no absolute male domination; neither is there absolute female

Queer approach to analyzing mainstream culture Essay

Queer approach to analyzing mainstream culture - Essay Example f seeking to understand this to a greater and more complete level, this brief analysis will consider one scene of the film and attempt to go in depth with regards to the different understandings of sexuality, identity, and gender that are therein represented. The scene in question that this author has chosen for analysis is that of the discovery of Mulan as a woman. This scene is a powerful indication of cultural approaches to gender and sexuality in a number of ways. As such, the first determinant that will be measured is with relation to the identity that is revealed within the given scene. In this way, as the men of the story find out that Mulan is indeed a woman, she is manhandled and forced out of the residence. This is importance for a number of reasons. Firstly, the revelation of her true identity is something that gives the men in the story the courage to treat her in a way that they would have never considered before had she still been considered a man. Her identification as a woman does not only change the way that the men physically treat her but the way in which their worldview is formed with relation to how they think of her. This is represented in two distinct ways within the scene in question. Firstly, as she is taken forcibly from her tent and pushed into the snow, the viewer is made aware of the clear and determinate connection between this action and the rejection fro mthe Garden of Eden; also presumably he result of female weakness. The inclusion of this reference to early mythology is unique due to the fact that it serves to further differentiate the response of the men within the scene to the gender that Mulan now represents. With regards to gender, the men make a clear and determinate change in the way that they speak to Mulan after the revelation. Indeed, the characters state â€Å"I knew there was something wrong with you†Ã¢â‚¬ ¦Ã¢â‚¬ a woman – treacherous snake† (Mulan 1). These words belie the true underlying motivations and

Static Analysis of Uncertain Structures

Static Analysis of Uncertain Structures Static Analysis of Uncertain Structures Using Interval Eigenvalue Decomposition 1Mehdi Modares and 2Robert L. Mullen 1Department of Civil and Environmental   Engineering Tufts University Medford, MA, 02155 2Department of Civil Engineering Case Western Reserve University Cleveland, OH, 44106 Abstract: Static analysis is an essential procedure to design a structure. Using static analysis, the structures response to the applied external forces is obtained. This response includes internal forces/moments and internal stresses that is used in the design process. However, the mechanical characteristics of the structure possess uncertainties which alter the structures response. One method to quantify the presence of these uncertainties is interval or unknown-but-bounded variables. In this work a new method is developed to obtain the bounds on structures static response using interval eigenvalue decomposition of the stiffness matrix. The bounds of eigenvalues are obtained using monotonic behavior of eigenvalues for a symmetric matrix subjected to non-negative definite perturbations. Moreover, the bounds of eigenvectors are obtained using perturbation of invariant subspaces for symmetric matrices. Comparisons with other interval finite element solution methods are presented. Using this method, it has shown that obtaining the bound on static response of an uncertain structure does not require a combinatorial or Monte-Carlo simulation procedure. Keywords: Statics, Analysis, Interval, Uncertainty  © 2008 by authors. Printed in USA. REC 2008 Modares and Mullen In design of structures, the performance of the structure must be guaranteed over its lifetime. Moreover, static analysis is a fundamental procedure for designing reliable structure that are subjected to static or quasi-static forces induced by various loading conditions and patterns. However, in current procedures for static analysis of structural systems, the existence of uncertainty in either mechanical properties of the system or the characteristics of forcing function is generally not considered. These uncertainties can be attributed to physical imperfections, modeling inaccuracies and system complexities. Although, in a design process, uncertainty is accounted for by a combination of load amplification and strength reduction factors that are based on probabilistic models of historic data, consideration of the effects of uncertainty has been removed from current static analysis of structural systems. In this work, a new method is developed to perform static analysis of a structural system in the presence of uncertainty in the systems mechanical properties as well as uncertainty in the magnitude of loads. The presence of these uncertainties is quantified using interval or unknownbut-bounded variables. This method obtains the bounds on structures static response using interval eigenvalue decomposition of the stiffness matrix. The bounds of eigenvalues are obtained using the concept of monotonic behavior of eigenvalues for a symmetric matrix subjected to non-negative definite perturbations. Furthermore, the bounds of eigenvectors are obtained using perturbation of invariant subspaces for symmetric matrices. Using this method, it has shown that obtaining the bound on static response of an uncertain structure does not require a combinatorial or MonteCarlo simulation procedure. The equation of equilibrium for a multiple degree of freedom structure is defined as a linear system of equations as:   [K]{U}={P}   Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚   (1) where, [K]is the stiffness matrix, {U}is the vector of unknown nodal displacements, and {P} is the vector of nodal forces. The solution to this system of equation is:   {U} = [K]−1{P}   Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚   (2) The concept of interval numbers has been originally applied in the error analysis associated with digital computing.   Quantification of the uncertainties introduced by truncation of real numbers in numerical methods was the primary application of interval methods (Moore 1966). A real interval is a closed set defined by extreme values as (Figure 1): ~l ,zu ] ={z∈â„Å"| zl ≠¤ z ≠¤ zu} (3)   Z = [z ~ x = [a,b] Figure 1. An interval variable. In this work, the symbol (~) represents an interval quantity. One interpretation of an interval number is a random variable whose probability density function is unknown but non-zero only in the range of interval. Another interpretation of an interval number includes intervals of confidence for ÃŽ ±-cuts of fuzzy sets. The interval representation transforms the point values in the deterministic system to inclusive set values in the system with bounded uncertainty. Considering the presence of interval uncertainty in stiffness and force properties, the system of equilibrium equations, Eq.(1), is modified as an interval system of equilibrium equation as: ~~   [K]{U}={P}   Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚   (4) ~ where, [K]is the interval stiffness matrix, {U}is the vector of unknown nodal displacements, and {P} is the vector of interval nodal forces. In development of interval stiffness matrix, the physical and mathematical characteristics of the stiffness matrix must be preserves. This system of interval equations is mainly solved using computationally iterative procedures (Muhanna et al 2007) and (Neumaier and Pownuk 2007). The present method proposes a computationally efficient procedure with nearly sharp results using interval eigenvalue decomposition of stiffness matrix. While the external force can also have uncertainties, in this work only problems with interval stiffness properties are addressed. However, for functional independent variations for both stiffness matrix and external force vector, the extension of the proposed work is straightforward. 3.1. DETERMINISTIC EIGENVALUE DECOMPOSITION The deterministic symmetric stiffness matrix can be decomposed using matrix eigenvalue decomposition as:   [K] = [ÃŽ ¦][Λ][ÃŽ ¦]T   Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚   (5) where, [ÃŽ ¦] is the matrix of eigenvectors, and [Λ] is the diagonal matrix of eigenvalues. Equivalently, N   [K] =∑Î »i{à Ã¢â‚¬ ¢i}{à Ã¢â‚¬ ¢i}T   Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚   (6) i=1 where, the values of ÃŽ »i is the eigenvalues and the vectors{à Ã¢â‚¬ ¢i}are their corresponding  eigenvectors.   Therefore, the eigenvalue decomposition of the inverse of the stiffness matrix is: equivalently, [K]−1 =[ÃŽ ¦][Λ]−1[ÃŽ ¦]T   Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚   (7) −N 1T [K] 1 =∑ {à Ã¢â‚¬ ¢i}{à Ã¢â‚¬ ¢i}   Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚   (8) i=1 ÃŽ »i Substituting Eq.(8) in the solution for the deterministic linear system of equation, Eq.(2), the solution for response is shown as:   {U}= ( N 1 {à Ã¢â‚¬ ¢i}{à Ã¢â‚¬ ¢i}T ){P}   Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚   (9) 3.2. INTERVAL EIGENVALUE DECOMPOSITION Similarly, the solution to interval system of equilibrium equations, Eq.(4), is:   {U~}= (∑N ~1 {à Ã¢â‚¬ ¢~ }{à Ã¢â‚¬ ¢~i}T ){P}   Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚   (10) i i=1 ÃŽ »i ~~ } are their where, the values of ÃŽ »i is the interval eigenvalues and, the vectors {à Ã¢â‚¬ ¢i corresponding interval eigenvectors that are to be determined. 4.1. BACKGROUND The research in interval eigenvalue problem began to emerge as its applicability in science and engineering was realized. Hollot and Bartlett (1987) studied the spectra of eigenvalues of an interval matrix family which are found to depend on the spectrum of its extreme sets. Dief (1991) presented a method for computing interval eigenvalues of an interval matrix based on an assumption of invariance properties of eigenvectors. In structural dynamics, Modares and Mullen (2004) have introduced a method for the solution of the interval eigenvalue problem which determines the exact bounds of the natural frequencies of a system using Interval Finite Element formulation. 4.2. DEFINITION The eigenvalue problems for matrices containing interval values are known as the interval ~ ~ nn ) and [A] is a member of the eigenvalue problems. If [A] is an interval real matrix (A∈â„Å" ~ interval matrix ([A]∈[A]) , the interval eigenvalue problem is shown as: ~ 4.2.1. Solution for Eigenvalues The solution of interest to the real interval eigenvalue problem for bounds on each eigenvalue is ~ defined as an inclusive set of real values (ÃŽ ») such that for any member of the interval matrix, the eigenvalue solution to the problem is a member of the solution set. Therefore, the solution to the interval eigenvalue problem for each eigenvalue can be mathematically expressed as: ~l ,ÃŽ »u ]|∀[A]∈[A~]: ([A]−Î »[I]){x} = 0}   Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚   (12)   {ÃŽ »Ã¢Ë†Ë†ÃŽ »= [ÃŽ » 4.2.2. Solution for Eigenvectors: The solution of interest to the real interval eigenvalue problem for bounds on each eigenvector is defined as an inclusive set of real values of vector {~x} such that for any member of the interval matrix, the eigenvector solution to the problem is a member of the solution set. Thus, the solution to the interval eigenvalue problem for each eigenvector is: 4.3. INTERVAL STIFFNESS MATRIX The systems global stiffness can be viewed as a summation of the element contributions to the global stiffness matrix: n i=1 where [ Li ] is the element Boolean connectivity matrix and [Ki ] is the element stiffness matrix in the global coordinate system. Considering the presence of uncertainty in the stiffness properties, the non-deterministic element elastic stiffness matrix is expressed as: ~ in which, [li ,ui ] is an interval number that pre-multiplies the deterministic element stiffness matrix. This procedure preserves the physical and mathematical characteristics of the stiffness matrix. Therefore, the systems global stiffness matrix in the presence of any uncertainty is the linear summation of the contributions of non-deterministic interval element stiffness matrices: ,ui ])[Li ][Ki ][Li ] =∑ i=1i=1 in which, [Ki ] is the deterministic element elastic stiffness contribution to the global stiffness matrix. 4.4. INTERVAL EIGENVALUE PROBLEM FOR STATICS The interval eigenvalue problem for a structure with stiffness properties expressed as interval values is:   [K~]{à Ã¢â‚¬ ¢~} = (ÃŽ »~){à Ã¢â‚¬ ¢~} (17) Substituting Eq.(16) in Eq.(17): ]){à Ã¢â‚¬ ¢} = (ÃŽ »){à Ã¢â‚¬ ¢ i=1 This interval eigenvalue problem can be transformed to a pseudo-deterministic eigenvalue problem subjected to a matrix perturbation. Introducing the central and radial (perturbation) stiffness matrices as: i 1 [K~R ] =∑i=n1 (ÃŽ µi )(ui 2−li )[Ki ]    ,  Ã‚  Ã‚   ÃŽ µi =[−1,1]  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚   (20) Using Eqs. (19,20), the non-deterministic interval eigenpair problem, Eq.(18),   becomes: Hence, the determination of bounds on eigenvalues and bounds on eigenvectors of a stiffness matrix in the presence of uncertainty is mathematically interpreted as an eigenvalue problem on a ~ central stiffness matrix ([KC ]) that is subjected to a radial perturbation stiffness matrix ([KR ]). This perturbation is in fact, a linear summation of non-negative definite deterministic element stiffness contribution matrices that are scaled with bounded real numbers(ÃŽ µi ) . 5. Solution 5.1. BOUNDS ON EIGENVALUES The following concepts must be considered in order to bound the non-deterministic interval eigenvalue problem, Eq.(21). The classical linear eigenpair problem for a symmetric matrix is: with the solution of real eigenvalues (ÃŽ »1 ≠¤ÃŽ »2 ≠¤ ≠¤ÃŽ »n ) and corresponding eigenvectors ( x1, x2,, xn ). This equation can be transformed into a ratio of quadratics known as the Rayleigh quotient:   R(x) =  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚   (23) The Rayleigh quotient for a symmetric matrix is bounded between the smallest and the largest eigenvalues (Bellman 1960 and Strang 1976).    (24) Thus, the first eigenvalue (ÃŽ »1) can be obtained by performing an unconstrained minimization on the scalar-valued function of Rayleigh quotient: ( (25) x∈ For finding the next eigenvalues, the concept of maximin characterization can be used. This concept obtains the kth eigenvalue by imposing (k-1) constraints on the minimization of the Rayleigh quotient (Bellman 1960 and Strang 1976): ÃŽ »k = max[minR(x)]   (subject to constrains(xT zi = 0),i =1,k −1,k ≠¥ 2 ) (26) 5.1.1. Bounding the Eigenvalues for Statics Using the concepts of minimum and maximin characterizations of eigenvalues for symmetric matrices, the solution to the interval eigenvalue problem for the eigenvalues of a system with uncertainty in the stiffness characteristics (Eq.(21)) for the first eigenvalue can be shown as: n x∈Rn{x}T {x} for the next eigenvalues: ~{x}T [K~]{x}{x}T ([K ]+[K~ ]){x} 5.1.2. Deterministic Eigenvalue Problems for Bounding Eigenvalues in Statics Substituting and expanding the right-hand side terms of Eqs. (27,28): ~T [K ]{x}~ui (li +u{x} (29) Since the matrix [Ki ] is non-negative definite, the term () is non-negative. Therefore, using the monotonic behavior of eigenvalues for symmetric matrices, the upper bounds on the eigenvalues in Eqs.(19,20) are obtained by considering maximum values of interval coefficients of uncertainty (ÃŽ µ~i = [−1,1]), ((ÃŽ µi )max = 1), for all elements in the radial perturbation matrix. Similarly, the lower bounds on the eigenvalues are obtained by considering minimum values of those coefficients, ((ÃŽ µi )min =−1) , for all elements in the radial perturbation matrix. Also, it can be observed that any other element stiffness selected from the interval set will yield eigenvalues between the upper and lower bounds. This imonotonic behavior of eigenvalues can also be used for parameterization purposes. Using these concepts, the deterministic eigenvalue problems corresponding to the maximum and minimum eigenvalues are obtained (Modares and Mullen 2004) as: n n 5.2. BOUNDS ON EIGENVECTORS 5.2.1. Invariant Subspace The subspace χ is defined to be an invariant subspace of matrix [A] if:   Aχ⊂χ (32) Equivalently,   if χ is an invariant subspace of [A]nn and also, columns of [X1]nm form a basis forχ, then there is a unique matrix [L1]mm such that: The matrix [L1 ] is the representation of [A] on χ with respect to the basis [X1] and the eigenvalues of [L1] are a subset of eigenvalues of [A]. Therefore, for the invariant subspace, ({v},ÃŽ ») is an eigenpair of [L1] if and only if ({[X1]{v}},ÃŽ ») is an eigenpair of [A]. 5.2.2. Theorem of Invariant Subspaces For a real symmetric matrix [A], considering the subspace χ with the linearly independent columns of [X1] forming a basis for χ and the linearly independent columns of [X2] spanning the complementary subspace χ⊠¥ , then,   χ is an invariant subspace of [A] iff: Therefore, invoking this condition and postulating the definition of invariant subspaces, the symmetric matrix [A] can be reduced to a diagonalized form using a unitary similarity transformation as:   [X1X2]T [A][X1X2] = à ¢Ã… ½Ã‚ ¢Ãƒ ¢Ã… ½Ã‚ ¡[X1]TT[[AA][][XX11]] à ¢Ã… ½Ã‚ £[X2] where [Li ] =[Xi ]T [A][Xi ], i =1,2. 5.2.3. Simple Invariant Subspace [X1]T [A][X2]à ¢Ã… ½Ã‚ ¤ à ¢Ã… ½Ã‚ ¡[L1] [X2]T [A][X2]à ¢Ã… ½Ã‚ ¥Ãƒ ¢Ã… ½Ã‚ ¦= à ¢Ã… ½Ã‚ ¢Ãƒ ¢Ã… ½Ã‚ £[0] [0] à ¢Ã… ½Ã‚ ¤ [L2]à ¢Ã… ½Ã‚ ¥Ãƒ ¢Ã… ½Ã‚ ¦ (35) An invariant subspace is simple if the eigenvalues of its representation [L1] are distinct from other eigenvalues of [A]. Thus, using the reduced form of [A] with respect to the unitary matrix [[X1][X2]], χ is a simple invariant subspace if the eigenvalues of [L1] and [L2] are distinct: 5.2.4. Perturbed Eigenvector Considering the column spaces of [X1] and [X2]   to span two complementary simple invariant subspaces, the perturbed orthogonal subspaces are defined as:   [Xˆ1] =[X1]+[X 2 ][P] (37)   [Xˆ 2 ] =[X 2]−[X1][P]T (38) in which [P] is a matrix to be determined. Thus, each perturbed subspace is defined as a summation of the exact subspace and the contribution of the complementary subspace. Considering a symmetric perturbation[E] , the perturbed matrix is defined as: Applying the theorem of invariant subspaces for perturbed matrix and perturbed subspaces, and linearizing due to a small perturbation compared to the unperturbed matrix, Eq.(34) is rewritten as: This perturbation problem is an equation for unknown [P] in the form of a Sylvesters equation in which, the uniqueness of the solution is guaranteed by the existence of simple perturbed invariant subspaces. Finally, specializing the result for one eigenvector and solving the above equation, the perturbed eigenvector is (Stewart and Sun 1990):   {xˆ1} = {x1}+[X 2 ](ÃŽ »1[I]−[L2 ])−1[X 2 ]T [E]{x1} 5.2.5 Bounding Eigenvectors for Statics For the perturbed eigenvalue problem for statics, Eq.(21),   the error matrix is: (41) ~nu [E] = [KR ] = (∑(ÃŽ µi )( i − li )[Ki ]) (42) i=12 Using the error matrix in eigenvector perturbation equation for the first eigenvector, Eq.(33) the perturbed eigenvector is: in which, {à Ã¢â‚¬ ¢1}is the first eigenvector, (ÃŽ »1) is the first eigenvalue, [ÃŽ ¦2 ] is the matrix of remaining eigenvectors and [Λ2 ] is the diagonal matrix of remaining eigenvalues obtained from the deterministic eigenvalue problem. Eq.(30,31 and 43) is used to calculate the bounds on interval eigenvalues and interval eigenvectors in the response equation, Eq.(9). In order to attain sharper results, the functional dependency of intervals in direct interval multiplications in Eq.(9) is considered. Also, input intervals are subdivided and the union of responses of subset results is obtained. 6. Numerical Example Problem The bounds on the static response for a 2-D statically indeterminate truss with interval uncertainty present in the modulus of elasticity of each element are determined (Figure 2). The crosssectional area A, the length for horizontal and vertical members L , the Youngs moduli E for all ~ elements are E = ([0.99,1.01])E . Figure 2.   The structure of 2-D truss The problem is solved using the method presented in this work. The functional dependency of intervals in the response equation is considered. A hundred-segment subdivision of input intervals is performed and the union of responses is obtained. For comparison, an exact combinatorial analysis has performed which considers lower and upper values of uncertainty for each element i.e. solving (2n = 210 =1024 ) deterministic problems. The static analysis results obtained by the present method and the brute force combination solution for the vertical displacement of the top nodes in are summarized Table (1). Lower Bound Present Method Lower Bound Combination Method Upper Bound Combination Method Upper Bound Present Method Error % U à ¢Ã… ½Ã¢â‚¬ º PL à ¢Ã… ½Ã… ¾ à ¢Ã… ½Ã…“à ¢Ã… ½Ã… ¸ à ¢Ã… ½Ã‚  AE à ¢Ã… ½Ã‚   -1.6265 -1.6244 -1.5859 -1.5838 % 0.12 Table1. Bounds on Vertical Displacement of Top Nodes The results show that the proposed robust method yields nearly sharp results in a computationally efficient manner as well as preserving the systems physics. 4.Conclusions A finite-element based method for static analysis of structural systems with interval uncertainty in mechanical properties is presented. This method proposes an interval eigenvalue decomposition of stiffness matrix. By obtaining the exact bounds on the eigenvalues and nearly sharp bounds on the eigenvectors, the proposed method is capable to obtain the nearly sharp bounds on the structures static response. Some conservative overestimation in response occurs that can be attributed to the linearization in formation of bounds of eigenvectors and also, the functional dependency of intervals in the dynamic response formulation. This method is computationally feasible and it shows that the bounds on the static response can be obtained without combinatorial or Monte-Carlo simulation procedures. This computational efficiency of the proposed method makes it attractive to introduce uncertainty into structural static analysis and design. While this methodology is shown for structural systems, its extension to various mechanics problems is straightforward. References Bellman, R. Introduction to Matrix Analysis, McGraw-Hill, New York 1960. Dief, A., Advanced Matrix theory for Scientists and Engineers, pp.262-281. Abacus Press 1991. Hollot, C. and A. Bartlett. On the eigenvalues of interval matrices, Technical Report, Department   of Electrical and Computer Engineering, University of Massachusetts, Amherst, MA 1987. Modares, M. and R. L. Mullen. Free Vibration of Structures with Interval Uncertainty. 9th ASCE Specialty Conference on Probabilistic Mechanics and Structural Reliability 2004. Moore, R. E. Interval Analysis. Prentice Hall, Englewood, NJ 1966. Muhanna, R. L. and R. L. Mullen. Uncertainty in Mechanics Problems-Interval-Based Approach. Journal of Engineering Mechanics June-2001,   pp.557-566 2001. Muhanna, R. L., Zhang H. and R. L. Mullen. Interval Finite Element as a Basis for Generalized Models of Uncertainty in Engineering Mechanics, Reliable Computing, Vol. 13, pp. 173-194, 2007. Neumaier, A. Interval Methods for Systems of Equations. Cambridge University Press, Cambridge 1990. Neumaier, A. and A. Pownuk. Linear Systems with Large Uncertainties, with Applications to Truss Structures, Reliable Computing, Vol. 13, pp. 149-172, 2007. Strang, G. Linear Algebra and its Applications, Massachusetts Institute of Technology, 1976. Stewart, G.W. and J. Sun. Matrix perturbation theory, Chapter 5. Academic Press, Boston, MA   1990.

The Witch Of Blackbied Pond :: essays research papers

The Witch of Blackbird Pond   Ã‚  Ã‚  Ã‚  Ã‚  Kit Tyler, the main character of Elizabeth George Spear's book, The Witch of Blackbird Pond, must leave her carefree life in tropical Barbados, and go and live in Connecticut. She learns that playing is what is to life, but hard work. She learns that if people do not know you, that they pre judge you. She also learns that if you don't live up to the Puritan life style, that they will look down at you. Kit must learn to cope, and learn from all these changes in her life.   Ã‚  Ã‚  Ã‚  Ã‚  First of all her grandfather dies, which leaves her as an orphan. She byes a ticket to Connecticut, where the last of her relatives live. When she arrives she is hit with a new way of life. In Barbados, slaves did the work, so Kit never worked before. She comes dressed in a Silk dress, which at that time was unacceptable in Connecticut. When she arrives at her relative's house, she is amazed how small in was compared to the house she lived in on Barbados.   Ã‚  Ã‚  Ã‚  Ã‚  Secondly, she goes to church. In Barbados her grandfather never stressed church as being important, so this was a new experience. When they started to sit down, the family separated into two groups, the men would go to the left, while the women sat to the right of the aisles. Then the Priest would talk about that Sunday's lesson. Then they went home, and had Sunday's dinner. Then her uncle would read out of the Bible. Then they would go to bed.   Ã‚  Ã‚  Ã‚  Ã‚  Thirdly, the people never like people that never followed the rules. One day when Kit was working in the field, see was told a story of an old Quaker woman that lived by Blackbird Pond. A Quaker was people that didn't come to Sunday services like the Puritans stated, and wouldn't follow the Puritans' way of life. They said that this old Quaker was a witch, and had cast spells on the city. Kit didn't believe the stories, and one time after she finished her work, went to visit the old woman. When see arrived, she saw a poor old women in a tiny little house, and then Kit started to help her. When the children of the town got sick, the town people went to get to old women, and make her stand trial for supposedly casting a spell.

Five Types of Organization Structures

Every organization, to be effective, must have a structure. An organization structure is the setup that determines the hierarchy and reporting structure in an organization. It is often represented by a drawing known as an organizational chart. There are different types of organizational structures that companies follow, depending on a variety of factors like leadership style, type of organization, geographical regions, work flow and hierarchy. Organizations may choose from a number of common operating structures. One popular structure is the functional organization, where the company is divided into separate units based on role, such as accounting, marketing, research and development or distribution. The functional structure offers a number of potential advantages as well as disadvantages. An advantage of a functional organizational structure is that it offers a high level of specialization. Each unit operates as a type of self-contained mini-company, charged with carrying out its specific role. A worker who is an expert in his functional area can perform tasks with a high level of speed and efficiency, which enhances productivity. While specialized units within the functional structure often perform with a high level of efficiency, they may have difficulty working well with other units. Another potential disadvantage of the functional organization structure is that it can pose a challenge for top management to maintain control as the organization expands. If the company expands into new geographic areas, maintaining control of and managing the separate functions can be even more of a challenge. Kenexa, an IBM Company, provides employment and retention solutions to assist organizations in hiring and keeping workers. Kenexa is a SAAS, software as a service company, and utilizes a functional structure. Market structure is used to group employees on the basis of the specific market the company sells in. A company could have five different markets they use and according to this structure, each would be a separate division. Some merits of this structure are that employees can communicate with customers in the local language and they are available for the customers, if need is felt. Demerits include intense competition among the employees; decision-making can cause conflicts and difficulty to determining the productivity and efficiency of employees. Product-based structures allow companies to remain flexible in the business environment. This allows the company to add or remove structure sections as necessary. However, it can prohibit companies from achieving company-wide goals since each unit operates on its own. A successful company that uses a Market organizational structure as well as a Product-based structure is Microsoft. Farber, 2013) One advantage of a Matrix structure is better coordination and control: – this structure is very much suitable to coordinate and control the functional activities and project activities. Most importantly, employees from various functional areas work under the spirit of team and make the project successful. Team effort is made. On the other hand, Matrix organizational structure involves huge overhead cost, has problems of overspecialization and is difficult to balance. GE is an example of a company that uses the matrix structure approach. In a geographic structure, large organizations have offices at different places, for example, there could be a north zone, south zone, west zone and east zone. Advantages are better communication among the employees at the same location and locals are familiar with the local business environment and can cater to geographical and cultural differences. A successful company with this structure is Ports America, headquartered in the NE with operations throughout both coasts and segmented regionally. References: Farber, D. (2013, July 12). Steve Ballmer remakes Microsoft one more time. Retrieved from http://news.cnet.com/8301-10805_3-57593289-75/steve-ballmer-remakes-microsoft-one-more-time/?part=rss&tag=feed&subj= (n.d.). Retrieved from http://www.kenexa.com/ (n.d.). Retrieved from http://www.portsamerica.com/about.html http://www.ge.com/pdf/company/ge_organization_chart.pdf Hill, C. (n.d.). Strategic management theory.

A Souvenir of Japan essays

A Souvenir of Japan essays The main elements of this story deal with the interaction of character and setting. The main character and also narrator of this story is in denial of the truth, her lover is not in love with her, he is just obsessed with the idea of being in love with her. Both of these characters are conscious of this doomed relationship, but both are powerless to stop it. In the beginning of the story the main character describes the customs of Japan and the role of the women and how they just occupy the room and rarely come out of it. In a society where men dominate they value women only as the object of mens passions therefore to her lover she was just an object, but not just any object a rarity in Japan. She was not like the rest of the natives; she was Caucasian and therefore making her more exotic and consequently making the affair more passionate and exciting for her native lover. It seemed that this man had a great deal of lust for her, which she interpreted as love and so she loved him ba ck. It was evident in the following that their relationship was just based on lust and passion and nothing else We were living in a room furnished only by passion. She was caught up in the moment where denial and awareness were both present. Her thoughts when he was gone seem to be conscious of his misdeeds such as staying out late with friends, but she dared to wait for him as a loyal lover. Actions such as those led me to believe that she was denying herself the truth, she was very aware of the setting and their belief system in Japan. She knew that her lover was an outcome of those belief systems, but she continued to admire him even still. When she spoke of Momotaro it seemed that she was describing her lover, this devious but yet enchanting creature. And regardless of his unearthly quality she still did not want to let go as described in the following I should have liked to have had him embalmed and been able to keep...

Types of Thinking Styles

Types of Thinking Styles Thinking Styles: Optimistic, Pessimistic, and Emotional One of the key avenues of concern in critical and creative thinking is the recognition, acknowledgement, and appreciation of the influence of human factor to the thought process of each individual. A broad spectrum of factors, therefore, exists bearing a mark on the manner in which human beings think.Advertising We will write a custom assessment sample on Types of Thinking Styles specifically for you for only $16.05 $11/page Learn More Examples of such factors are culture, emotion, stress, ego, among others. The discipline of critical and creative thinking strives to direct the attention of each person on the invaluable role played by these factors in making of decisions. This paper analyses, and compares and contrasts optimistic thinking, pessimistic thinking, and emotional thinking. Optimistic thinking is the type of thinking in which a person chooses to align his/her thoughts on the positive side of life regardless of how gloomy things look. People who have optimistic thoughts normally reassure themselves that all is well in any condition they find themselves. This, of course, has its advantages and disadvantages. Pessimistic thinking is the opposite of optimistic thinking. It refers to a style of thinking in which an individual sees the negative side of situations. In good and bad situations, such a person will always have something to get him/her worried. This obviously has its advantages and disadvantages. One of the advantages is that such a person will be able to anticipate challenges, and plan on how to overcome them. Emotional thinking is the style of thinking that is driven by what a person feels at a particular point in time (Martin, 2010, p. 1). For instance, if a person is feeling depressed, this style of thinking will attract thoughts of hopelessness and other related thoughts. The three thinking styles are largely similar. One of their similarities is the fact that the three thinking styles stem from the disposition of the particular individual with whom they are associated. For instance, an emotional person is likely to have an emotional thinking style; a pessimistic person is likely to have a pessimistic thinking style while an optimistic person is likely to have an optimistic thinking style (Pritchett, 2007, p. 1). In addition to this, emotional and pessimistic thinking styles are likely to have more negative influences on an individual than the optimistic thinking style. This is because the thinking style of a person is a key determinant of the appropriateness and success of actions that he/she takes in order to make a situation better.Advertising Looking for assessment on psychology? Let's see if we can help you! Get your first paper with 15% OFF Learn More The way a person perceives and thinks after succeeding in a certain thing is also a determinant factor of future success. A person with an emotional thinking s tyle may for example over-celebrate an instance of success leading to future failures. It is however important to note that despite the fact that the optimistic thinking style is generally better as compared to the other two, it has its weaknesses. A person with an optimistic thinking style may take things for granted while assuming that all will be well. This may lead to a failure that will take him/her by surprise. After repeated failures, such a person may even develop a negative disposition like being emotional. This may make him/her an emotional thinker (Martin, 2010, p. 1). It is, therefore, important to note that dispositions are not static. Therefore, a person may have more than one of the three thinking styles during his/her lifetime. Reference List Martin, P. (2010). Explanatory Style – Optimism/Pessimism. Retrieved from  http://stresscourse.tripod.com/id103.html [November 4, 2011] Pritchett, P. (2007). How pessimism can add value to our work, Hard Optimism. Retri eved from  http://inhome.rediff.com/money/2007/aug/28book.htm [November 4, 2011]

Service operations management- Discussion Question Assignment

Service operations management- Discussion Question - Assignment Example The primary strategy adopted by the Walt Disney Corporation is global. The focus of the Walt Disney Company is not only in the United States market, but also internationally. Thus the amusement parts of the company are located in three separate continents. The stores of the company are located in the United States, Portugal, United Kingdom, Italy, France and Spain. The licensed shops for the corporation are located in almost all countries around the globe. The approaches that drive global expansion efforts include; direct investments, foreign outsourcing, and also licensing. The international expansion has been very effective in several aspects. Financially, the measure has reduces operation costs (Bhasin, 2013). This is because, increasing salary in the United States, initiated the move of foreign outsourcing. Thus many production centers are based in Asian countries, due to the minimal production expenses involved. To ensure effective international distribution, the country has authorized licensees, with the main objective of reselling the services and products. This is significant to the company due to minimal investments

Biochem question and answer Assignment Example | Topics and Well Written Essays - 250 words

Biochem question and answer - Assignment Example Milk proteins are digested in the stomach and duodenum by proteolytic enzymes into peptides and finally amino acids that are absorbed in the small intestines. Bile salts emulsify fats after which pancreatic lipase breaks them into fatty acids and glycerol molecules that are absorbed in the ileum. The sucrose is broken down into glucose and fructose in the duodenum by enzyme sucrase, and the monosaccharides are absorbed in the ileum (Digestion and absorption, n.d.). Apples and carrots contain vitamins and mineral salts, which do not undergo digestion, but are directly absorbed into the small intestines. Oxidative phosphorylation is a metabolic pathway, which utilizes energy from the oxidation of food to produce ATP. All the electrons from NADH and FADH2 go to the oxidative phosphorylation cycle following release from the TCA cycle. Oxidative phosphorylation takes electrons from these molecules and transfers them to oxygen, making ATP in the process. This process occurs in the mitochondria. NADH and FADH2 are oxidized into NAD+ and FAD, whereas oxygen is reduced by H+ ions into water. NAD-linked dehydrogenases remove electrons from substrates to NAD in reversible reactions. The malate-aspartate shuttle or the alpha-glycerol phosphate shuttle conveys electrons from NADH outside the mitochondria (the two complexes involved in the process). Blood supplies oxygen to the process. A specific translocase exchanges ADP outside the mitochondria for ATP inside the mitochondria. The end products are water, ATP, and NAD+ or FAD. Cyanide, azide, and CO are metabolic poisons, which are so toxic t o us because they block the transfer of electrons to oxygen hence inhibiting the whole process (Gilbert,