Friday, July 30, 2010

To what extent is Victor Frankenstein a victim?

One way in which we could consider Victor a victim occurs after he destroys the female mate which would be a companion for his original creature.  When he makes his first creature, his physical neglect of that creature is pretty apparent, as is his failure to properly consider and care for the creature's emotional well-being.  However, Victor tries to avoid making similar mistakes in creating a mate.  He cannot predict the personality, wants, or capabilities of this second creature any more than he could predict those aspects of the first.  He realizes that the female "might refuse to comply" with the agreement made between Victor and her mate, that the monsters "might even hate each other," or that they could procreate and make "a race of devils" who would destroy the earth.  His conscience feels burdened, and so he tries to make the right and most responsible decision.  After this, the creature kills Victor's best friend, Henry Clerval, and later his new bride, Elizabeth.  These tragedies then lead to the death of Victor's father.  The monster wounds Victor again and again, attempting to make Victor as miserable as the monster feels himself to be, all because Victor has tried to make the right decision.  Even if he did not make the best choice the first time, he's trying to do so now, and he is victimized for it.

Do seismic waves travel fastest through rock? Why?

Seismic waves, which travel in the same way as sound waves, travel fastest through denser objects than objects with lower density. 


The Newton-Laplace equation can be used to find the speed of sound through a gas:


`c=sqrt(K/rho)`


It can also be used on any other material. This includes steel, rock, magma, and even the upper atmosphere around space. In this formula, c is referring to the speed of sound in the medium, K is the bulk modulus of the material, and `rho` is the density of the medium. The bulk modulus of a material describes how the material responds to compression, and is the ratio of how much a material compresses under uniform pressure.


Rock has a much higher bulk modulus than air. Think about how much air can be compressed into a cylinder versus rock. You would struggle to compress rock at all, whereas air yields easily to pressure.


The sound itself is a wave in the particles themselves, traveling through with motion. Particles in rock are closer together than those in the air, and can easily be pushed by those around them. This is why seismic waves travel better in rock.

Wednesday, July 28, 2010

Obtain the line integral

Given `f=x^2z ds`


`x=cost, y=2t, z=sint `   for `0<=t<=\pi`


We have to find the line integral i.e.


`\int_{c} f(x,y,z)ds=\int_{c} x^2z ds`


                 = `\int_{c} f(x(t),y(t),z(t)). ||r'(t)|| dt`


where ,


`||r'(t)||=\sqrt{(\frac{dx}{dt})^2+(\frac{dy}{dt})^2+(\frac{dz}{dt})^2}`


          = `\sqrt{sin^2t+2^2+cos^2t}`


          = `\sqrt{1+4}`


          = `sqrt{5}`



Therefore we have,


`\int_{c}f(x,y,z)ds=\int_{0}^{\pi}cos^2tsint . \sqrt{5} dt`


                 = `\sqrt{5}\int_{0}^{\pi}cos^2tsint dt`


Take , `cost=u`, so `cos^2t=u^2`


Therefore,  `-sint dt=du`


When t=0, then u=1 and when 


         t= `\pi`, then u=-1


Hence we have,


`\int_{c}f(x,y,z)ds=\sqrt{5}\int_{1}^{-1}-u^2 du`


                 `= \sqrt{5}\int_{-1}^{1}u^2du`


                  = `\sqrt{5}[\frac{u^3}{3}]_{-1}^{1}`


                  = `\frac{2\sqrt{5}}{3}`





(b)  Now we have the curve  `16y=x^4` `f(x,y)=16y-x^4` parameterized by  the curves 


  `x=2t, y=t^4 `  for `0<=t<=1`


We have to find the line integral :


`\int_{c} f(x,y) ds=\int_{c} xy ds`


               `=\int_{c} f(x(t),y(t))||r'(t)|| dt`


 where,


`||r'(t)||=\sqrt{(\frac{dx}{dt})^2+(\frac{dy}{dt})^2}`


          `=\sqrt{2^2+(4t^3)^2}`


           = `\sqrt{4+16t^6}`


           = `2\sqrt{1+4t^6}`



Therefore we have,


`\int_{c} f(x,y) ds=\int_{0}^{1}2t^5. 2\sqrt{1+4t^6} dt`


               `=4\int_{0}^{1}t^5\sqrt{1+4t^6} dt`


Now take,


`\sqrt{1+4t^6}=u`


Therefore,


`\frac{1}{2\sqrt{1+4t^6}}.24t^5 dt=du`


i.e. `12t^5 dt=udu`


i.e. `t^5dt=\frac{u}{12} du`


When t=0, then u=1 and when


         t=1, then u= `\sqrt{5}`


Therefore we have,


`\int_{c} f(x,y)ds=4\int_{1}^{\sqrt{5}}\frac{u^2}{12} du`


               `=\int_{1}^{\sqrt{5}}\frac{u^2}{3} du`


                `=[\frac{u^3}{9}]_{1}^{\sqrt{5}}`


                 = `\frac{5\sqrt{5}-1}{9}` 


                 = 1.131             

What are the main incidents of Gulliver's Travels?

In Jonathan Swift's Gulliver's Travels, the narrative's main incidents can be found in the book's four voyages. In the first voyage, Gulliver is stranded on Lilliput, an island of small people wracked by petty disputes, such as a disagreement regarding the proper way to crack open an egg. Then, on the second voyage, Gulliver finds himself in Brobdingnag, a region of gigantic individuals, where he is put on display like some kind of freak or pet. In the third voyage, Gulliver travels to multiple locations, including Laputa and Balnibarbi, whose inhabitants are obsessed with absurd, abstract ideas. Finally, in his last voyage, Gulliver meets the Houyhnhms, a race of intelligent horses who enslave the barbaric, human-like Yahoos. Throughout his voyages, Gulliver is exposed to a variety of differing perspectives, and one of the main points of the novel's many incidents is to reveal how, by changing one's perspective, it's possible to observe life's often ridiculous nature.  

What is the moral of the story "An Astrologer's Day" by R.K. Narayan?

The astrologer is portrayed as a man who has always had to live by his own wits and on his luck. He pretends to be a learned astrologer, but



He was as much a stranger to the stars as were his innocent customers.



The moral of "An Astrologer's Day" seems to relate to the fact that the protagonist does not rely on the hocus-pocus of the pseudo-science of astrology with its useless paraphernalia, but on his own perception, intuition, and practical experience. If he knew more about astrology, he would be handicapped. When he runs into Guru Nayak, he talks a lot about the messages he supposedly reads in the stars, but he is only using the stars to befuddle his nemesis. The reader can see quite clearly that the astrologer is talking about the stars but really using his own practical knowledge to get himself out of a tight spot with a man who would kill him if he recognized him as the man he was searching for.


The best expression of the moral of the story may be the principle expressed by Laurence Sterne, author of the classic novel Tristram Shandy. 



An ounce of a man's own wit is worth a ton of other people's.



In the story "An Astrologer's Day," the protagonist's nemesis Guru Nayak is not relying on his "own wit." He is going from one astrologer to another, believing one of them will be able to answer his question, "Where can he find the man who tried to kill him in his village years ago?" Guru Nayak's quest is futile. How could anyone read the answer to that question in the stars? One after another, the astrologers send him on wild goose chases until, just by accident, Guru Nayak runs into the very man he has been looking for, although he doesn't recognize him.


The astrologer is versatile and adaptable. He has had to learn by experience. That is perhaps the main advantage of relying on your own perception, intuition, experience, and "street smarts."

Tuesday, July 27, 2010

Why does the ghost feel humbled?

In this comic reversal on the classic ghost story, this ghost feels humbled because he is unable to frighten the Otis family. Although he tries everything in his arsenal of "ghost haunting an ancestral English home" tricks, he scares nobody. The practical, down-to-earth American Otises refuse to see him as anything but a nuisance who puts bloodstains on their library floor and clanks around in old armor. The Otis twins, young boys, rather than fearing him, enjoy playing practical jokes on him and tormenting him. The parents use a modern stain remover to rub out his blood. The ghost, who takes his job seriously, is in despair. Finally, he is humbled in a more profound way by the willingness of the compassionate young Otis daughter to pray for him and help him to go to his final rest. 

Monday, July 26, 2010

Critically consider historical and modern management theories and propose your own model of management.

Since historical and modern theories of management are based on scientific research, findings and theorizing, I would propose a management model built around the scientific findings on the female brain and the male brain. The model would capitalize, for example, on women's exceptionally developed brain centers for communication and hearing. The model would also capitalize, for example, on men's exceptionally developed brain centers for analytical approaches to problem solving and tolerance for conflict.

Neuropsychiatrist Louann Brizendine, M.D., author of The Female Brain and The Male Brain, identifies and explains the hardwired areas of exceptionally well developed brain competencies in females and males. My perception is that the lack of influence of women's brain competencies in management and management theory is detrimental to the ethical, humanistic and profitable function of business (and government). My model of management would incorporate the strengths and competencies of each of these two brain types and map out contingency approaches that utilize and capitalize on each of these types in business situations and crises.

For instance, since a male brain tolerates conflict because of its well developed recognition of aggression, business environments that are dynamic (rapidly and frequently changing) mesh with aggression/conflict competencies. Since a female brain is well developed in communication and hearing, business situations that depend upon resolution management or vision sharing mesh with hearing the expression of problems and with communicating higher ideals and overarching objectives.

Management and leadership teams in my proposed management model would have an equal or near equal number of female brains and male brains in each; would have authority allocated horizontally without rank or hierarchy; would have a fluid structure so that sub-groups could emerge and realign as situational needs arose. This management and leadership team structure would have the advantage of key components of the underpinnings of management theory built into its functionality: motivation, intrinsic reward, career development, efficiency and effectiveness and human relations. Management and leadership teams would work through brain competency strengths to ethically and humanistically secure the outcomes and outputs needed to maximize profit.


[Dr. Yasin Olum, "Modern Management Theories and Practices." Makerere University, Uganda (2004).]

find square roots of -1+2i

We have to find the square root of `-1+2i` i.e. `\sqrt{-1+2i}` We will find the square roots of the complex number of the form x+yi , where ...