Why is the element stiffness matrix singular in a finite element formulation? 1. So that it can accomodate rigid element dis- placements without introducing spurious nodal 2 Because we made a mistake in the formula- tion the stiffness matrix should not be sin- g 3. Because we havent enforced any displace ment boundary conditions(it's a variational approach after all) Statement(1)

Lead-in The news that a sheep in Scotland has been successfully cloned 1) got me wondering What good would it be to clone humans? What would I do with a clone of myself? Then 2) it hit me that I could have my clone go into work for me while went out hiking, biking, sking,etc.! really could be in two places at once

Symbolism and Ritual It's a huge topic, it could cover a whole course 1. Two examples: a. Mariage ritual from the Kuna called\the dragging' i. Bride and groom would not choose each other, but their parents would arrange the marriage secretly. The groom's friends would traditionally surprise him and drag him down the street. (Now a days, they don't fight back so hard and they know ahead of time)

Social welfare function W: Rn-R gives social utility W(u1, u2,. un ). W is strictly increasing is socially optimal if it solves max Wu(a1), u2(a2),., un(n) st>Tis>w Proposition 1.29. If is SO, it is PO. I Proposition 1. 30. Suppose that preferences are continuous, strictly monotonic, and strictly convex. Then, for any PO allocation x* with >>0,v i, there exist ai

20.1 The magnetic field and its application 1. The magnetic field and its features Gravitational field FG=mg -gravitational force caused by mass Electric field =gE -electric force caused by electric charge Magnetic field--? While the magnetic field has similarities to the other fields, it also has some unique features that distinguish it from the others

三种基本形式 If had a bike.I would lend it to you(f从句用过去时,主句用 should/ would/ could/ mighti不定式) If he had been here he would have helped you(从句过去完成时,主句 should would/ could/ might+不定式完成时) I would do it some other wa(从句用 should/ were to3主句用 should/woud could /might+不定式)

Sorting: There is a series of data in random order, we sort them depending a certain key word. Datalist: an finity set of data waiting to be sorted. Key: data object has many attribute areas, namely there are many data element, one of all these elements can be used to distinguish object, we use it as sorting key. we also call it sorting code

A. Based on the information in the story, we can safely come to a lesson that everybody needs a happy life, and this happiness can play an important role in keeping our life active and meaningful. As a matter of fact, it should become our goal of life to be happy. Without happiness, many people will feel that life is empty and worthless.  B. If we read this story carefully, it is not hard for us to arrive at a lesson that everybody needs a happy life, and this happiness can play an important role in keeping our life active and meaningful. …

Intensive Study There's a Lot More to Life than a Job Para.1 It has often been remarked that the saddest thing about youth is that it is wasted on the young. Para. 2 Reading a survey report on first-year college students, I recalled the regret, \If only knew then what know now

Dyspnea is defined as an awareness of difficulty in breathing It is therefore a symptom, usually described by the patient as \shortness of breath,\whether the sensation is due to actual difficulty in breathing or is essentially an awareness of hyperventilation. If the symptom becomes striking, it always companies with dilatation of nares, cyanosis, use of accessory muscles of respiration and abnormalities of respiratory rate, depth or rhythm