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Posts by Total # Posts: 678 Why did Germany invade Poland in 1941? =] Why did Japan invade China in 1937? thank you so much =] Why did Japan invade China in 1937? thank you so much =] Describe what can happen to the three-carbon molecules made in the Calvin cycle. A box of mass 1kg is placed on a table and is connected to a hanging mass m by a string strung over a pulley. If the coefficient of kinetic friction between the box and the table is .3 and the box slides at a constant speed of .5m/s what is the weight of the hanging mass? to f... You have just discovered a planetary system consisting of a star (Dagobahr) and its two planets: Rool and Krau. Planet Rool has an average orbital radius 3 times as big as planet Krau. If planet Rool orbits Dagobahr in 2 earth years (1earth year = 365 days). a) how long is the... A box of mass 1kg is placed on a table and is connected to a hanging mass m by a string strung over a pulley. If the coefficient of kinetic friction between the box and the table is .3 and the box slides at a constant speed of .5m/s what is the weight of the hanging mass? Woul... A box of mass 1kg is placed on a table and is connected to a hanging mass m by a string strung over a pulley. If the coefficient of kinetic friction between the box and the table is .3 and the box slides at a constant speed of .5m/s what is the weight of the hanging mass? F_bo... complete the statement: in recoil a)the initial momentum is zero b)the object sticks together after collision c)the total kinetic energy is conserved d)the final speeds of the object are the same b) is wrong. I think it's either c) or d) but i'm going to go with c). a rock is thrown straight up which of the following statemetns concerning the net force acting on the rock at teh top of the path is true? assume air resistance is negligible. a)it's equal to the weight of the rock b) it is instantanwously equal to zero c) it's directi... two objects collide when sliding on a fricitonless horizontal surface. Which quantity is conserved during their collision? a) velocity b) momentum of both objects c)energy d) momentum of each object isn't c) or b) correct? I really think it's c) a rock suspended from a string moves downwards at constant a=g. Which of the following is true concerning the tension in the string? a) the tension is zero b)the tension is equal to the weight of the rock c)the tension is less to the weight of the rock d)the tension is greater... Complete the following statement: The term net force most accurately describes: a) quantity that causes displacement b) quantity that keeps the object moving c) the mass of the object d) the quantity that changes the velocity of an object c) is not the right choice. I believe ... Europa, a moon of Jupiter has an orbital diameter of 1.34x10^9m and a period of 3.55 days. What is the mass of Jupiter? d=1.34x10^9m T=3.55days = 30672s M=? r=71492000m rm=6.7x10^8 r-total= 7414492000m r^3/t^2=GM/4pi^2 741492000^3/306720^2=6.67X10^-11(M)/4pi^2 I got m=2.56x10^2... The mean radius of the Earth is R=6.38x10^6m. At what distance above the Earth's surface will the acceleration of gravity be 4.905m/s^2? F_g=(Gmme)/r^2 4.905=6.67x10^-11(5.98x10^24)/r^2 The mass cancel out so that is how I got the above answer. r=9017663m Is this the corre... A 2.1kg brass ball is transported to the Moon. a)What is the mass of the brass ball on the earth and on the moon? Wouldn't it be 2.1kg for the earth as well as for the moon? b)Determing the weight of thee brass ball on the earth. F_g=(Gm_ballm_earth)/r^2 =20.58N c) the w... "the total angular momentum of an object changes when a net external force acts on the system." This statement is: a)always true b) never true c) sometime true, it depends on the force's direction d) sometime true, it depends on the force's point of applicatio... A lever is 5m long. The distance from fulcrum to the weight to be lifted is 1m. If the worker pushes on the opposite end with 400N, what is the max weight that can be lifted? l=5m h=1m F=400N F_g=? torque=F_gl I first must find torque so that I can plug it into the above equa... Is the answer to this 4? If the filament resistance in an automobile headlamp is 3 ohms, how many amps does it draw when connected to a 12-volt battery? Consider a roller coster car moving along a track from point A to point B to point C. a)if the roller coaster car starts from rest at point A (30m above the bottom of a dip (point b). What would be the speed of the car at the top of the next hill (point C), which is 20 m above... If the net work done on an object is positive then the object's energy is ...? The object's energy would also increase since W= energy right? The object's energy wouldn't increase or decrease. Compared to yesterday you did 3 times the work in one third the time. To so so your power output must have been: a) the same as yesterday's power output b)one third of yesterday's power output c)3 times yesterday's power output d)9 times yesterday's power outpu... A force of 20 N is applied horizontally to a 1 kg mass on a level surface. The coefficient of friction is .2. if the mass is moved a distance of 5m what is the change in KE? W= change in Ke Fd= Change in KE (20)(5)=Change in Ke 200 J =change in Ke But the thing is how would I ... A 1000kg car accelerates from 0 to 25m/s in 8s. What is the average power delivered by the engine? (1hp=746W) P=W/t p=Fd/t P=Fv p=mav =1000(25/8)(25) =78125W which is about 104.725 hp Is this A ball falls from the top of a building . through the air(air resistance is present) to the ground below. How does the KE just before hitting the ground compare to the PE at the top of the building? Isn't KE and PE equal to each other in this situation? Since I believe ene... What work is required to stretch a spring of spring constant 500N/m from x1=.2m to x2=.25m? Assume the unstreched position is at x=0. W=Fd so w=(500)(.25-.2) =500(.05) =25J is this correct? Calculate the work required to compress an initially uncompressed spring with a spring ... If your last electric bill for sept. was $105. If the average price is 6.5 cents per kw, how many kw did your household use in September? 1kw/.065 = x/$105 .065x=105 x=1615.38 kw is this correct? How many Joules is that? I know that 1W =1Joule/second 1kw=1000W so 1615.38kw /10... A 15 N force is needed to move an object with constant velocity of 5 m/s. What power must be delivered to the object by the force? I konw that P=W/t and W=Fd But other than that I am confused . I am not sure how i would solve this problem. A wooden block is moving on a rough level surface. It originally has 25J of kinetic energy. If the friction force acting on it is a constant 1N how far will it slide before comming to a stop? KE=F_f 1/2mv^2=F_n (meu) but the problem i run into is that meu and the mass isn'... A 50kg skier pushes off the top of a hill with an initial speed of 5m/s. Neglect friction. How fast will he be moving after dropping 20m in elevation? I was wondering if i did this problem correct. PE + KE_f = KE_i mgh +1/2mv_f^2 =1/2mv_i^2 50(10)(20) + 1/2 (50)v_f^2 = 1/2(50)... A 50kg skier starts from rest from the top of a 100m slope. What is the speed of hte skier on reaching the bottom of the slope? Neglect friction. would i do this: =PE + KE =mgh +1/2mv^2 =50(10)(100) + 1/2 (50)v^2 =50000 +25v^2 =2000 =v^2 44.7m/s =v Is this correct? Thank in ad... what is cultural blindness HElp me !!!!!!! Malia told Lucia that she had figured out a pattern for computing the number of 3-letter names for any plane if she knew how many letters were named on the plane. For example, if there were four points, there were 4x 3x 2x 1 names possible. lucia said this patt... Algebra 1 In An American Childhood how does Annie Dillard reference life or death through the waterfall scene on page 150 Line L contains the points given in the table below. If the slope of line m is 1/3 the slope of line L what are three points that could be on line m? x 1 2 3 y -7 5 17 A.(1,-2),(2,10),(3,22) B. (1,-7),(2,3),(3,1) C.(1,-7),(2,2),(3,6) D.(1,-7),(2,2),(3,22) : if the quotient 3m^2 +15m / m^2 divided by 30/ m^2 + 5m is simplified to lowest terms, which of the following is the denominator of the resulting expression? the options are 10 30m^2 m^2 +5m or m^2 ( m+5) 10, with the restriction that m cannot be zero. algebra 1 I NEED HELP!! the bottom of a 25-foot ladder is placed 7 feet from a wall. How far will the ladder reach up? Since the ladder, wall, and ground form a right triangle, you can use this formula: A squared + B squared = C squared A = 7 feet C = 25 feet B = distance the ladder will reach 49 + B... You work in the Human Resources department of your organization. You have been charged with recruiting a manager for a department within the Services division. The Vice-President of the Services division stresses to you that "This department hasn t had a good manager... Chemistry- acids and bases Given the following neutralization raction: HCO3^- + OH^- <=> CO2[over]3^- + H2O a. label the conjugate acid-base pairs in this system b. is the forward or reverse reaction favored? Explain. Write net ionic equations that represent the following ractions: a. the ionizat... Okay, so apparently ASA and FeCl3 form a violet complex and FeCl3 forms with phenol groups to make purple. Looking at the structures of ASA and salicylic acid, only salicylic acid has the phenol group. The thing is, salicylic acid is supposed to be an impurity in the synthesiz... culteral diversity The creation of minority group status for Mexican Americans reflected the dynamics of graph y=4 Calculus, antiderivatives A student accelerates from rest at a rate of 3 miles/min^2. How far will the car have traveled at the moment it reaches a velocity of 65 miles/60 min? a(t) = 3 miles/min^2 so v(t) = 3t + k miles/min but when t=0, v=0 so k=0 then v(t)=3t d(t) = 3/2 t^2 + c but when t=0 d, the d... Whilwind, breeze: Downpour is to ?? The answer starts with scr,spr,str,and thr Sprinkle? Spray? Stream? You could try the on-line Rogets Thesaurus, type thesaurus into google. rain, mist, drizzle World History What are some modern examples of cultural blending in art? Consider music, literature, painting etc.. I can't find any info for this topic and I have to write a 1 page report. Possibly one of these artists would make a good topic: Frieda Kahlo http://www.google.com/search?... algebra PLZ HELP!!! y= 9/11x-17 9x-10y=179 You need to use parentheses to tell us what the problem is. Is equation 1, y = 9/(11x-17) or is it y = (9/11)x - 17? y= 9/11x-17 9x-10y=179 Rewrite them as 11 y - 9 x = -187 and -10 y + 9x = 179 Add the last two and you get y = -8 Substitute in any equat... MATH! HELP!!! I am putting < for the square root abbreviation. I don't know how to use it on my comp. 3<99-2<44-6<11=? For Further Reading On a graphing calculator, the carrot symbol is used to show exponents. that s what I used here. Solve your exponents first: 3^99, t... I am putting < for the square root abbreviation. I don't know how to use it on my comp. 3<99-2<44-6<11=? On a graphing calculator, the carrot symbol is used to show exponents. that s what I used here. Solve your exponents first: 3^99, then 2^44, then 6^11 ... PLEASE!!!! HELP!!!! ME!!!! solve the system using substitution {x+2y=11 {3x+2y=13 i just told u this one HELP!!!!!!!! please!!!!! solve the system using substitution {x+2y=11 {3x+2y=13 i just told you how to do the other one; it's the same exact method. solve for x and y. you get: x=-2y+11 and y=(-1/2x)+(11/2). then plug them both back into the original equation (either one, it doesn't matter); y... i really, really, really need help what coordinate point is the solution to the system? {3x+2y=8 {x-y=1 (2,1) please don't think i just made that up, it's correct. you have to use substitution, when you do solve for x and y, you get: x= y+1 and y=x-1, plug in y for 3x+2y=8 and you get: y=1, then plug in... algebra 1 what coordinate point is the solution to the system? {3x+2y=8 {x-y=1 y=x-1 so 3x+2(x-1)=8 3x+2x-2=8 5x-2=8 5x=10 - - 5 5 x=2 Then 2-y=1 -2 -2 -y=-1 y=1 Well, to cut the crap the answer is (2,1) egypt mummification um guys i just wanna know what the plugged eye sockets with What is boil soil :: goat? What is boil soil :: goat? Maths test A store gives a staff discount of one fifth. How much would a member of staff pay for: a) a camera with a retail price of £215? just do 215 divided by 1/5 (0.20) and you'll have the amount in "pounds" (i think that's what that sign stands for)....if you... Inter. Algebra square root sign 2x+3 - square root sign x-2 =2 In my head, I worked it as x=3. I did that because only sqr roots that are rational integers can be subtracted to give a whole number. Now, analytic method. I have no idea, I dont see a simple method in ordinary algebra. how do y... Inter. Algebra Count Iblis how do you simplify 3square root sign with this underneath (3x squared y) to the third power? "3 square root sign" probably means "cube root", in which case [(3 x^2y)^3]^(1/3) = 3 x^2 y The cube root of any quantity x can be written x^(1/3) Inter. Algebra Count Iblis what is the answer to 2 square root sign 18x? The instructions say to simplify or reduce. 2(18x)1/2= 2(92)1/2= 23(2)1/2= 6(2)1/2 If you can leave it in this form, the above is the way to end. If you are to continue to a final answer, then, finish by 61.414 =8... Inter. Algebra Another problem plz help Count Iblis. How do you solve 5/x+2 + 2x/x squared - 4= 3/x-2? 5/x+2 + 2x/x squared - 4= 3/x-2 You write the term: 2x/x squared as 2/x the equation becomes: 5/x+2 + 2/x - 4= 3/x-2 4/x = 0 This equation has no solutions. It is only satisfied in the limi... Inter. Algebra Simplify 2i to the 5th power? (2i)^5 = 2^5 i^4 * i = 32 (-1)^2 * i = 32 i Inter. Algebra what is the answer to 2i to the 5th power? i^2 = -1 --> i^4 = 1 ---> i^5 = i (2i)^5 = 32 i thanks for the info! Inter. Algebra can you simplify 12x squared y cubed? Inter. Algebra what is the answer to 2 square root of 18x? Do you mean 2(18x)1/2? What does it equal. What are we to do with the problem? DrBob222, My problem states 2 square root sign & 18x underneth it. If you could help me with this problem I'd really appreciate it. It must be equal ... Inter. Algebra what is the answer to 12x squared y cubed /2xy squared +6xy y squared +6y+9 /3y cubed +9y squared? You have not written an equation, only an algebraic function, with two variables. You need to add parentheses to clarify the order of operations. There is no "answer"... Inter. Algebra how do you foil 12x squared y cubed? story board??? okay, so what exactly is a story board? I used to assign these. Here were the directions: 1. Divide a page into six sections (like the little frames in a cartoon series in the newspaper). Students usually had two rows or three sections. 2. Decide on the six main actions in a s... World History What was the reason for the downfall of the Han Dynasty and The Roman Empire? Was is partially invasion from barbarians? Han Dynasty: http://www.google.com/search?q=han+dynasty+downfall&ie=utf-8&oe= utf-8&rls=org.mozilla:en-US:official&client=firefox-a Roman Empire: http://www.... social studies person whogives to a business or project hopeing to make a profit investor Financial Management Year Cash Flow(A) Cash Flow (B) 0 -307,206 -27,651 1 14,950 8,726 2 32,391 13,901 3 29,232 9,222 4 390,590 13,140 15% rate of return. what is the payback period for Period A and B. I'm having some troubles with these. Thanks in advance. If a>0 find the minimum value. If a<0 find the maximum value. 1. y=-x²+2x+5 2. y=-2x²-3x+4 These are functions for parabolas, so f(x)=ax²+bx+c when a does not equal 0 In both your examples, the &q... the settlers of jamestown saved their colony by planting? word unscramble louvcarese (2 words) funceelni dearpilshe stiche gametannem thanimoreolans (2 words) ginlapnn At a construction site, a brick fell and hit the ground at 24m/s a) from what height did the brick fall? b) how long was it falling? for a) i got 29.387m and for b) I got 2.448s I got a) by using v^2 =v0^2 +2a(x-x0) for b) I used v=v0+at Did I do this problem correctly? If we u... Can someone please help me with an algebra problem? -\|4-8b\|=12 I really get confused with the absolute value symbols and a negative sign outside of them. Don't worry about it; it does tend to be a bit confusing. I'll explain the difference between inside and outside ne... bay and penninsula What is the difference between a bay and a penninsula? A bay is a body of water -- smaller than a sea or ocean or gulf -- that is not completely surrounded by land. San Francisco Bay is one good example. A peninsula is a land formation that is surrounded on all but one side by... unscrambling word Pages: <<Prev \| 1 \| 2 \| 3 \| 4 \| 5 \| 6 \| 7	{"url":"http://www.jiskha.com/members/profile/posts.cgi?name=Andrea&page=7","timestamp":"2014-04-16T14:32:03Z","content_type":null,"content_length":"28225","record_id":"<urn:uuid:93eb81a8-939a-4434-8d08-52678b38e319>","cc-path":"CC-MAIN-2014-15/segments/1397609523429.20/warc/CC-MAIN-20140416005203-00123-ip-10-147-4-33.ec2.internal.warc.gz"}
Re: st: re: Is there a similar output command as outreg for Summary? [Date Prev][Date Next][Thread Prev][Thread Next][Date Index][Thread Index] Re: st: re: Is there a similar output command as outreg for Summary? From Kit Baum <baum@bc.edu> To statalist@hsphsun2.harvard.edu Subject Re: st: re: Is there a similar output command as outreg for Summary? Date Mon, 16 Mar 2009 09:25:52 -0400 I agree with Roy's concern for brevity. Indeed, to produce an estimation table in -estout-, all you need is eststo clear eststo: reg .... eststo: reg (or whatever) esttab using output.file and the amount of help needed to describe that basic usage is quite minimal. Naturally, just as with the latest revision of -outreg2-, doing something fancier requires some more reading, What I was referring to as very helpful IMHO is the extensive web-based documentation for -estout-, which I find very useful myself when trying to do some of the more complex tasks often required to produce a table 'just so'. PS> Apple have improved in that regard: the current Macintosh line comes with zero manuals! Kit Baum \| Boston College Economics and DIW Berlin \| http://ideas.repec.org/e/pba1.html An Introduction to Stata Programming \| http://www.stata-press.com/books/isp.html An Introduction to Modern Econometrics Using Stata \| http://www.stata-press.com/books/imeus.html On Mar 16, 2009, at 02:33 , Roy wrote: A great thing about John Gallup's original -outreg- is that it does not need extensive documentation to run. Brevity is a virtue in this case. The original Macintosh (computer) once boasted that it came with a single manual. IMHO, the reverse can also be true. SAS is extremely well-documented. I don't know any statistical softwarethat comes with more documentations. All that documentations serves as a post hoc dressing (i.e. bandaid) for the ad hoc syntax (which is understandable, since SAS was one of the earliest to appear). Stata is much better designed with subsequent programming knowhow built into it (plus the benefit of whoever did the writing). As for myself, I would like Stata to keep running like a Stata, which is to say without the need for extensive documentation, and I think many people would agree with me on this one. * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/	{"url":"http://www.stata.com/statalist/archive/2009-03/msg00782.html","timestamp":"2014-04-21T12:55:49Z","content_type":null,"content_length":"7893","record_id":"<urn:uuid:1a1134b5-7702-4707-ac4b-0172336db58c>","cc-path":"CC-MAIN-2014-15/segments/1398223206770.7/warc/CC-MAIN-20140423032006-00011-ip-10-147-4-33.ec2.internal.warc.gz"}
Measurability of essential supremum of function of two variables up vote 4 down vote favorite Let $(X,d)$ be a separable metric space with Borel measure $\mu$. Let $f:X \times X \to \mathbb{R}$ be Borel measurable with respect to the product measure on $X \times X$, and let $g(x)=\ operatorname{ess sup}_{y \in X} f(x,y)$. Is $g(x)$ necessarily measurable? (Is there some argument that can be pieced together using separability of $X$ and Lusin's Theorem, if we assume that $\mu$ is a Radon measure?) Now... the question makes sense in a measure space with no topology. – Gerald Edgar Jun 16 '11 at 14:18 add comment 2 Answers active oldest votes You are right. For each n choose a set of measure less than 1/n on the complement of which f is continuous. Now take the actual sup on each vertical section of this restricted function. up vote 1 This yields a measurable function $f_n$ for each n defined on X. The sup of the increasing sequence of $f_n$ will also be a measurable function F. Except for a null set, F will give the down vote ess sup of the vertical section of f. So modifying F on a null set yields that g is measurable. I have not been able to get this argument to work. The supremum over each vertical section can be expressed as a supremum over countably many points $y$ by continuity and separability, but the countable set on which you take the supremum should be dense in the section and varies across different vertical sections, hence it does not imply that $f_n$ is measurable. Is there a way to fix the argument? – zfzf21 Jun 16 '11 at 20:39 You are right that separabilty is no help here. Instead, use the fact that analytic sets are measurable. Let $F_n$ be the continuous functions defined on a subset of $X\times X$ except for a set of measure $1/n$. Given $t\in \mathbb R$, $f_n^{-1}(t,\infty)$ is equal to the set of all $x\in X$ such that there exists $y\in X$ such that $F_n(x,y)> t$. The single existential quantifier ensures that this set is analytic and, hence, measurable. – Juris Steprans Jun 16 '11 at 22:34 This is very helpful, thank you. There is still one part of the argument I do not understand---why can we take the actual sup on each vertical section, as opposed to the ess sup? We know $f$ is continuous on each vertical section, but the actual sup is not necessarily equal to the ess sup if the section contains a point such that a neighborhood of that point in the section has zero measure. Can we construct our closed set so that almost every section does not contain such points? (If we simply remove all such points from the domain of $F_n$, is the resulting set still Borel measurable?) Thanks – zfzf21 Jun 17 '11 at 4:13 Yes, this has to be taken into account. But, as you suggest, a Cantor Bendixon argument allows you to remove the isolated points and change the domain by only a countable set. This, of course, relies on the fact that X is second countable. – Juris Steprans Jun 17 '11 at 12:05 add comment I am not sure, which one you mean by $\mathrm{ess}\inf$? 1) The essential infimum of the (parametric) function $h_i: x\mapsto f(i,x)$, i.e. the element in $X$, that is the almost-sure greatest lower bound of $h_i$? I think this is the case you tried to prove. I do not know however, how it compares to the second case: up vote 0 down vote 2) Or the essential infimum of the set of functions $\{g_i\}_{i\in X}$ with $g_i: x\mapsto f(x,i)$? I.e. the measureable function from $X$ to $\mathbb{R}$, that is the almost-sure greatest lower bound of the set of functions $\{g_i\}_{i\in X}$? I think in this case, by the definition of the essential infimum of a collection of measurable functions, it is always measureable. add comment Not the answer you're looking for? Browse other questions tagged measure-theory or ask your own question.	{"url":"http://mathoverflow.net/questions/67943/measurability-of-essential-supremum-of-function-of-two-variables","timestamp":"2014-04-21T08:01:25Z","content_type":null,"content_length":"58845","record_id":"<urn:uuid:0a2c2199-7aa1-40c6-b9f4-b642824bc5e6>","cc-path":"CC-MAIN-2014-15/segments/1397609539665.16/warc/CC-MAIN-20140416005219-00436-ip-10-147-4-33.ec2.internal.warc.gz"}
Solve Problems Involving Rates and Unit Analysis 4.17: Solve Problems Involving Rates and Unit Analysis Difficulty Level: Created by: CK-12 Practice Conversion Using Unit Analysis “I would LOVE to climb Mount Everest!” Josh exclaimed at breakfast one morning. “Really?” his Dad said smiling. “Well son, you had better start saving now.” Josh looked up from his oatmeal with a puzzled look on his face. “What makes you say that?” Josh asked. “What makes me say that is that the going rate for one climb on Everest is about $60,000. That’s what makes me say that,” his Dad explained taking a sip of his coffee. “Really? Wow! I had no idea,” Josh said. “Well, I guess I’ll just have to make a lot of money!” Josh said leaving the table. He kept thinking about what his Dad had said all the way to school. Sixty thousand dollars was a lot of money to climb a mountain, but what really amazed Josh was thinking about the numbers of people who had climbed the mountain more than once. When he got to class, he looked up in his book that Apa Sherpa a man from Nepal had successfully climbed Everest 19 times. Now he was often a guide who was paid, but still, Josh couldn’t help thinking about how much money Apa Sherpa would have spent if he had paid to climb Everest 19 times at the rate his father spoke about. How much would it have cost? We can use units, ratios and proportions to solve this problem. By thinking of one trip as a unit, we can look at the proportion and solve for the correct amount of A rate refers to speed or a rate can refer to the amount of money someone makes per hour. When we talk about a unit rate, we look at comparing a rate to 1, or how much it would take for 1 of something. It could be one apple, one mile, one gallon. We are comparing a quantity to one. A key word when working with unit rate is the word “per”. We can use ratios and proportions to solve problems involving rates and unit rates. Jeff makes $150.00 an hour as a consultant. What is his rate per minute? To figure this out, we have to think about the unit rate that Jeff is paid as a consultant. You will see that we have “an hour” written into the problem. This is the unit rate. Also notice that the would "per" is used in the problem. Let’s write the unit rate as a ratio compared to 1. $\frac{\ 150.00}{1}$ Next, we need to think about what the problem is asking for. It is asking for his rate per minute. The given information is in hours, so we need to write a ratio that compares hours to minutes. $\frac{1 \ hour}{60 \ minutes}$ Now we can write an expression combining the two ratios. $\frac{\ 150}{1 \ hour} \cdot \frac{1 \ hour}{60 \ minutes}$ That’s a great question. We don’t compare hours to hours because we aren’t comparing hours. We are comparing money to hours and we need to figure out the rate of money per minute. You always have to think about what is being compared when working with proportions. Next, we can solve. Notice that because 1 hour is diagonal from 1 hour, we can cross cancel the hours. That leaves us with a ratio that compares money to minutes. $\frac{\ 150}{60 \ minutes}$ This also helped us to convert hours to minutes making it easier to figure out the answer to the problem. Now we can divide to figure out our answer. Jeff makes $2.50 per minute. What is unit analysis? Unit analysis is when we look at how to measure individual units in different measurement amounts and it is used to convert units of measurement. When we use unit analysis, we convert different measurement units by comparing the units using ratios and proportions. Unit analysis is very helpful when checking results. Take a look at this dilemma. Juanita worked for 18 hours. She made $116.00 at the end of her shift. Juanita was sure that her manager had made a mistake and that she should have made more money. Juanita makes $9.00 per hour. Did Juanita make the correct amount of money or was there a mistake? To work on this problem, we can use unit analysis. Let’s start by writing a ratio to compare how much Juanita made for the hours worked. $\frac{18 \ hours}{\ 116.00}$ Next, we can use her hourly rate to work with. She makes $9.00 per hour. $\frac{\ 9}{1 \ hour}$ If Juanita makes $9.00 per hour, we can multiply $18 \times 9$ Example A Ten apples cost $3.99. What is the cost for one apple? Solution: .39 Example B Fifteen gallons of gasoline costs $45.00. How much is it per gallon? Solution: $3.00 Example C Two tickets to a ballgame costs $111.50. What is the cost for one ticket? Solution: $55.75 Now let's go back to the dilemma from the beginning of the Concept. Now let’s look at solving this problem. We know that it costs $60,000 for 1 trip up Mount Everest. $\frac{\ 60,000}{1} &= \frac{x}{19}\\x &= \ 1,140,000$ We can also use unit analysis to solve this problem. $60,000 dollars $\left( \frac{19}{x \ dollars}\right)$ $60,000 \times 19 = \ 1,140,000$is the cost of the nineteen trips. This is our solution. a unit that is in relationship with another unit. It could be a pay rate or a rate of speed. It is a unit that is measured. Unit Rate a rate compared to 1. A pay rate would be an amount of money per hour. A gasoline unit rate would be the amount of money for one gallon of gasoline. Unit Analysis is a method of converting different units of measurement by using ratios and proportions to compare and convert the units. Guided Practice Here is one for you to try on your own. Solve and then check using unit analysis. Jesse has a car that holds 14 gallons of gasoline. During the first week of the month, gasoline cost $2.75 per gallon. During the second week of the month, gasoline cost $2.50 per gallon. How much was the total cost for the 28 gallons of gasoline? Let’s start by writing a variable expression to work on this problem. We know that the number of gallons of gasoline does not change. That can be our variable. $x =$ The other parts of the expression include the different prices for the gasoline. This expression will help us to determine how much money Jesse spent on 28 gallons of gasoline. Each full tank is 14 gallons. We can substitute 14 for our variable $x$ $2.75(14)&+ 2.50(14)\\\ 38.50 &+ \ 35.00$ The total amount of money spent was $73.50. We can check our work by using unit analysis. $\frac{2.75}{1 \ gallon} &= \frac{x}{14 \ gallons} = \ 38.50\\\frac{2.50}{1 \ gallon} & = \frac{x}{14 \ gallons} = \ 35.00$ The sum of the money spent was $73.50. Video Review Directions: Use what you have learned to solve each problem. 1. Peter runs at a rate of 10 kilometers per hour. How many kilometers will he cover in 8 hours? 2. A cheetah can run at a speed of 60 miles per hour. What is his distance after 6 hours? 3. What is the distance formula? 4. If a car travels at a rate of 65 miles per hour for 30 minutes, how far will it travel? 5. A train travels at a rate of 50 miles per hour. If it needs to travel 320 miles, how many minutes will it take? 6. A car travels 65 mph for 12 hours. How many miles will it travel? 7. A bus traveled 300 miles at an average speed of 50 miles per hour. How long did this trip take the bus? 8. A car traveled at an average speed of 40 miles per hour through a construction zone. If the car traveled 20 miles at this rate, how many hours did it take to travel the 20 miles? 9. What is velocity? 10. What is the formula for velocity? 11. What is the velocity of an object that travels 500 miles in 2.5 hours? 12. If an object has a velocity of 125 miles per hour, how long will it take to travel 4,375 miles? 13. If an object has a velocity of 7 kilometers per minute, how far will it travel in 2 hours? 14. If an object has a velocity of 4 meters per second, how many kilometers will it travel in 2 days? 15. The formula for density is $D = \frac{m}{v}$$D$$m$$v$ Files can only be attached to the latest version of Modality	{"url":"http://www.ck12.org/book/CK-12-Middle-School-Math-Concepts-Grade-8/r10/section/4.17/","timestamp":"2014-04-16T13:02:51Z","content_type":null,"content_length":"132838","record_id":"<urn:uuid:4018c42b-2988-4d3c-b934-b0b868002fcd>","cc-path":"CC-MAIN-2014-15/segments/1397609523429.20/warc/CC-MAIN-20140416005203-00255-ip-10-147-4-33.ec2.internal.warc.gz"}
Projection Problem May 13th 2010, 08:44 PM #1 Junior Member Apr 2010 Projection Problem Here is a study problem for my final exam tomorrow: Using the basis [1, 2(square root 3)t - (square root 3), 6(square root 5)(t^2 - t + 1/6)] for R3[t] with the L^2[0, 1] inner product, find the projection of the function sin(pie(x)) onto R3[t]. I am given hints as to what some integrals equal to facilitate the problem, but they are too complicated for me to type out on a computer... i'll try my best: integral 0 to 1 of tsin(pie(t))dt = 1/pie and the integral 0 to 1 of t^2sin(pie(t))dt = (pie^2 - 4)/pie^3 thanks in advance for your help! Here is a study problem for my final exam tomorrow: Using the basis [1, 2(square root 3)t - (square root 3), 6(square root 5)(t^2 - t + 1/6)] for R3[t] with the L^2[0, 1] inner product, find the projection of the function sin(pie(x)) onto R3[t]. I am given hints as to what some integrals equal to facilitate the problem, but they are too complicated for me to type out on a computer... i'll try my best: integral 0 to 1 of tsin(pie(t))dt = 1/pie and the integral 0 to 1 of t^2sin(pie(t))dt = (pie^2 - 4)/pie^3 thanks in advance for your help! Use Gram-Schmidt. May 13th 2010, 08:52 PM #2 MHF Contributor Mar 2010	{"url":"http://mathhelpforum.com/advanced-algebra/144668-projection-problem.html","timestamp":"2014-04-16T13:19:14Z","content_type":null,"content_length":"33672","record_id":"<urn:uuid:0dea752b-e6e3-425f-90a2-2a215b4c822a>","cc-path":"CC-MAIN-2014-15/segments/1397609524259.30/warc/CC-MAIN-20140416005204-00215-ip-10-147-4-33.ec2.internal.warc.gz"}
find radius of convergence April 22nd 2007, 06:47 PM find radius of convergence find a power series representation. please help with the radius of convergence. heres the function: f(x) = x^3/(x-3)^2 thanks for helping. April 23rd 2007, 06:41 AM Unless I have done some stupid mistake (as usual :o ). This holds for \|x\|<3, so determine the radius of convergence from the function.	{"url":"http://mathhelpforum.com/calculus/14066-find-radius-convergence-print.html","timestamp":"2014-04-16T08:07:51Z","content_type":null,"content_length":"3749","record_id":"<urn:uuid:1bf40477-ee74-4dfa-859c-f7d2cc960f8f>","cc-path":"CC-MAIN-2014-15/segments/1397609521558.37/warc/CC-MAIN-20140416005201-00175-ip-10-147-4-33.ec2.internal.warc.gz"}
Introduction to the Theory of Thermal Neutron Scattering, third edition. By G. L. Squires. Cambridge University Press, 2012. Pp. 270. Price (paperback) GBP 45.00. ISBN Volume 68 978-1-107-64406-9. Part 5 Page 665 September 2012 Markus Braden^a^* Received 26 April Keywords: book review. Accepted 10 July 2012 Online 15 August 2012 Eighty years after the discovery of the neutron, neutron-scattering techniques have developed into mature methods, yielding unique insights into the static and dynamic properties of solids. The first edition of G. L. Squires' book Introduction to the Theory of Thermal Neutron Scattering was published in 1978, and became one of the most studied textbooks in this field. The new third edition in paperback format is almost unchanged. Therefore it is not suprising that the passing years have rendered parts of this book rather dated, but these are essentially the experimental aspects. Spallation sources, cold neutrons and zero-field polarization are just a few examples of modern instrumentation missing in this book, and the quality of the illustrations is certainly below the standard of today's publications. Furthermore, the reader will not find links to any current scientific topics. However, this introduction aims to explain the quantum-mechanical theory of neutron scattering, and this has not changed since 1978. G. L. Squires deduces the main theoretical concepts for modelling neutron scattering from quantum mechanics in a very elegant, clear and compact manner. The book can be easily and rapidly studied without prior knowledge of scattering experiments, but it is based on the main concepts in quantum mechanics and solid-state physics. Crystals, liquids and magnetic systems are described. The book is addressed more to experimenters wishing to quantitatively analyse their data and less to theorists advancing the models. For example, harmonic lattice dynamics is not explained in this book, but the reader may find the cross section for one-phonon scattering processes. Owing to the clear and compact structure of this book, the important formulae can be found rapidly. The basic properties of the neutron and the definitions in scattering experiments are briefly introduced in the first chapters. Then coherent and incoherent scattering in crystals are described in detail as a method for determining the crystal structure of a material as well as the associated excitations. The more general concept of correlation functions prepares for the treatment of scattering by liquids. The unique magnetic properties of the neutron render it an ideal tool for investigating magnetic structures and magnetic excitations. These magnetic theories are explained in the last third of the book, covering scattering by spin and orbital moments and touching on polarization analysis. At the end of each chapter there are some exercises which can be used for personal Introduction to the Theory of Thermal Neutron Scattering is ideally suited for scientists aiming to quantitatively model neutron-scattering data. Owing to the clear and simple presentation, the proper quantum-mechanical concepts can be quickly learned from Squires' book as a first step into deeper studies with more specialized literature.	{"url":"http://journals.iucr.org/a/issues/2012/05/00/pf0101/pf0101bdy.html","timestamp":"2014-04-20T19:37:42Z","content_type":null,"content_length":"16422","record_id":"<urn:uuid:b9e74bc9-58ce-49a1-8e43-2fc1d535457f>","cc-path":"CC-MAIN-2014-15/segments/1397609539066.13/warc/CC-MAIN-20140416005219-00382-ip-10-147-4-33.ec2.internal.warc.gz"}
Powers of minus one and some bit twiddling Since the start of this year I'm employed as a postdoc on a project for designing a new domain specific language for writing dsp algorithms. The language is called Feldspar and if you want to check it out you can look at the official homepage or download it from hackage. As you can see on these pages Feldspar is a collaboration between Chalmers (where I'm employed), Ericsson and Elte University in Budapest. There are two main goals for the design of Feldspar: first of all it should be possible to program at a very high level, close to how dsp algorithms are normally specified. Secondly, the generated code needs to be very efficient as the kind of applications that Ericsson has for dsp applications are performance critical. I'm involved in various parts of Feldspar but one particular thing on my plate is making sure that the generated code is fast. Recently the language has been used in a pilot project within Ericsson to implement part of the 3gpp standard (a mobile broadband standard, unsurprisingly, given Ericssons involvement). Having people using the language is tremendously useful for us language implementors as we really get a chance to see how well the language works in its intended environment. The Feldspar code that was written in this pilot project was kept very close to the standard and was very similar to the mathematical specification of the algorithms. It's a very nice feature of Feldspar that this is possible, but it poses a challenge for us language implementers. While eyeballing some of the code I notice a little piece of code that I would like to discuss a little: (-1) ^ v30 Just to clarify, in Feldspar this means minus one to the power of v30 and it has nothing to do with xor. v30 is just a variable name. Powers of minus one is a common idiom in mathematics for saying that a value should change sign. If the exponent is even the result will be positive and if the exponent is odd the result is negative. This kind of thing is useful in various places and apparently also in the 3gpp standard. However, actually performing exponentiation would in this case be ridiculously inefficient. But the question is what kind of code we should generate for this? Currently our compiler generates C so the code examples I will show from here on will be written in C. Remember what I wrote above that the result only depends on whether the exponent is even or not. That is very easy to check, it's just the least significant bit! So we might generate the following code (assuming that the exponent is v30 as in the example above): v30 & 1 ? -1 : 1; This is very short and nice and most likely as good as we can hope for, at least for the kind of processors we are targeting. However, I started programming in the 80's and I still instinctively flinch when I see branches in performance critical code. So I got curious to see if I could write the above as straight line code. A straight line code solution which computes the above function would most likely involve some bit twiddling. I spent some time trying to come up with a solution on my own but wasn't very happy with what I managed to produce. I was aiming for a three instruction solution and my solutions were nowhere near that. So I decided to look around, maybe someone else had solved the problem before me. Bit Twiddling Hacks to the rescue! This wonderful list of various bit twiddling tricks doesn't have anything which solves my particular problem but there is one little nugget which is close enough that I could make good use of it: "Conditionally negate a value without branching". The value that we will be negating is 1, we want to negate it depending on the least significant bit of our input value (v30 in our example above). I will not reproduce the code from Bit Twiddling Hacks, you can check it out yourself via the link. Instead I'm just going to present the final result of using that code on my particular problem (using C code): int v; //The exponent int r; //Will contain -1 to the power of int isOdd = v & 1; //Is the exponent odd? r = (1 ^ (-isOdd)) + isOdd; This is a fairly clever piece of code and I'm quite happy with it. However, it will compile to four instructions on typical architectures and I was really hoping for a three instruction solution. Anyone out there who knows of a shorter solution? 5 comments: You can use linear interpolation. p = v & 1 r = -1 * p + 1 * (1-p) r = 1 - 2 * p r = 1 - (p << 1) r = 1 - ((v & 1) << 1) Luke's solution is nice. However, your solution may be fine as well. In math you almost always multiply by (-1)^n, so instead of optimizing (-1)^n optimize (-1)^n * x and apply the bit hack to producing x or -x. r = ((v << 31) >> 31) * 2 + 1 On x86 at least, you can do *2+1 in a single instruction. Possibly slightly shorter and faster on architectures such as x86 with two-address instructions: r = (-(v & 1)) \| 1	{"url":"http://computationalthoughts.blogspot.com/2010/10/powers-of-minus-one-and-some-bit.html?showComment=1285965936163","timestamp":"2014-04-19T22:07:17Z","content_type":null,"content_length":"41888","record_id":"<urn:uuid:b71351cd-0357-41a0-892a-2d93f9c90a28>","cc-path":"CC-MAIN-2014-15/segments/1397609537754.12/warc/CC-MAIN-20140416005217-00059-ip-10-147-4-33.ec2.internal.warc.gz"}
Linear Density Linear density is the number of lattice points or repeat distances per unit length in a particular direction. Since aluminum is FCC, along the [110] direction (face diagonal in the top plane) there are two lattice points (atoms, not counting the starting point) encountered. (see Figure 3-13, page 52). The distance (see packing factor) is The units for this value are lattice points per Angstrom. Changing to nanometers, it becomes 3.49 lattice points per nm.	{"url":"http://web.sunybroome.edu/~biegen_j/matsci/lectures/chap3/lineardensity.htm","timestamp":"2014-04-16T07:23:02Z","content_type":null,"content_length":"1628","record_id":"<urn:uuid:fd8c2d22-d6f3-44b1-9ef0-1fcc8e0299b9>","cc-path":"CC-MAIN-2014-15/segments/1398223202774.3/warc/CC-MAIN-20140423032002-00511-ip-10-147-4-33.ec2.internal.warc.gz"}
Monte Carlo Methods, Second Edition Author(s): Malvin H. Kalos, Paula A. Whitlock Published Online: 13 JUL 2009 Print ISBN: 9783527407606 Online ISBN: 9783527626212 DOI: 10.1002/9783527626212 This introduction to Monte Carlo methods seeks to identify and study the unifying elements that underlie their effective application. Initial chapters provide a short treatment of the probability and statistics needed as background, enabling those without experience in Monte Carlo techniques to apply these ideas to their research. The book focuses on two basic themes: The first is the importance of random walks as they occur both in natural stochastic systems and in their relationship to integral and differential equations. The second theme is that of variance reduction in general and importance sampling in particular as a technique for efficient use of the methods. Random walks are introduced with an elementary example in which the modeling of radiation transport arises directly from a schematic probabilistic description of the interaction of radiation with matter. Building on this example, the relationship between random walks and integral equations is outlined. The applicability of these ideas to other problems is shown by a clear and elementary introduction to the solution of the Schrödinger equation by random walks. The text includes sample problems that readers can solve by themselves to illustrate the content of each chapter. This is the second, completely revised and extended edition of the successful monograph, which brings the treatment up to date and incorporates the many advances in Monte Carlo techniques and their applications, while retaining the original elementary but general approach.	{"url":"http://onlinelibrary.wiley.com/book/10.1002/9783527626212","timestamp":"2014-04-20T11:04:47Z","content_type":null,"content_length":"37245","record_id":"<urn:uuid:63762f8d-53ce-4ddc-a3a8-a5e45766c2b1>","cc-path":"CC-MAIN-2014-15/segments/1398223207046.13/warc/CC-MAIN-20140423032007-00570-ip-10-147-4-33.ec2.internal.warc.gz"}
SProc Categorically - JOURNAL OF PURE AND APPLIED ALGEBRA , 1997 "... The suspension-loop construction is used to define a process in a symmetric monoidal category. The algebra of such processes is that of symmetric monoidal bicategories. Processes in categories with products and in categories with sums are studied in detail, and in both cases the resulting bicate ..." Cited by 42 (14 self) Add to MetaCart The suspension-loop construction is used to define a process in a symmetric monoidal category. The algebra of such processes is that of symmetric monoidal bicategories. Processes in categories with products and in categories with sums are studied in detail, and in both cases the resulting bicategories of processes are equipped with operations called feedback. Appropriate versions of traced monoidal properties are verified for feedback, and a normal form theorem for expressions of processes is proved. Connections with existing theories of circuit design and computation are established via structure preserving homomorphisms. , 1996 "... . We construct a category of circuits: the objects are alphabets and the morphisms are deterministic automata. The construction differs in several respects from the bicategories of circuits appearing previously in the literature: it is parameterized by a monad which allows flexibility in the emergen ..." Cited by 7 (1 self) Add to MetaCart . We construct a category of circuits: the objects are alphabets and the morphisms are deterministic automata. The construction differs in several respects from the bicategories of circuits appearing previously in the literature: it is parameterized by a monad which allows flexibility in the emergent notion of process. We focus on the circuits which arise from a distributive category and the exception monad. These circuits are partial in that they may, based on their state, choose to abort on some inputs. Consequently, certain circuits determine languages, and safety and liveness properties with respect to these languages are captured by circuit equations. Actually, the notions of safety and liveness arise abstractly in any copy category. Extracting the category of circuits which are both safe and live corresponds to the extensive completion of a distributive copy category. Partial circuits coincide with elements of the terminal coalgebra of a specific datatype. The co--induction princ... , 1995 "... The purpose of this paper is to show how one may construct from a synchronous interaction category, such as SProc, a corresponding asynchronous version. Significantly, it is not a simple Kleisli construction, but rather arises due to particular properties of a monad combined with the existence of a ..." Cited by 4 (0 self) Add to MetaCart The purpose of this paper is to show how one may construct from a synchronous interaction category, such as SProc, a corresponding asynchronous version. Significantly, it is not a simple Kleisli construction, but rather arises due to particular properties of a monad combined with the existence of a certain type of distributive law. Following earlier work we consider those synchronous interaction categories which arise from model categories through a quotiented span construction: SProc arises in this way from labelled transition systems. The quotienting is determined by a cover system which expresses bisimulation. Asynchrony is introduced into a model category by a monad which, in the case of transition systems, adds the ability to idle. To form a process category atop this two further ingredients are required: pullbacks in the Kleisli category, and a cover system to express (weak) bisimulation. The technical results of the paper provide necessary and sufficient conditions for a Kleisli... , 1995 "... This is a report on a mathematician's effort to understand some concurrency theory. The starting point is a logical interpretation of Nielsen and Winskel's [30] account of the basic models of concurrency. Upon the obtained logical structures, we build a calculus of relations which yields, when cut d ..." Cited by 4 (3 self) Add to MetaCart This is a report on a mathematician's effort to understand some concurrency theory. The starting point is a logical interpretation of Nielsen and Winskel's [30] account of the basic models of concurrency. Upon the obtained logical structures, we build a calculus of relations which yields, when cut down by bisimulations, Abramsky's interaction category of synchronous processes [2]. It seems that all interaction categories arise in this way. The obtained presentation uncovers some of their logical contents and perhaps sheds some more light on the original idea of processes as relations extended in time. The sequel of this paper will address the issues of asynchrony, preemption, noninterleaving and linear logic in the same setting. 1 Introduction Concurrency in computation is modelled in many different ways. Several attempts at unification have been made. Most recently, Abramsky [1, 2] has proposed the paradigm of relations extended in time as a foundation for theory of processes. His in... - PROCEEDINGS OF THE SIXTH AMAST CONFERENCE, VOLUME 1349 OF LECTURE NOTES IN COMPUTER SCIENCE , 1997 "... The compact closed bicategory Span of spans of reflexive graphs is described and it is interpreted as an algebra for constructing specifications of concurrent systems. We describe a procedure for associating to any Place/Transition system\Omega an expression \Psi\Omega in the algebra Span. The v ..." Cited by 2 (0 self) Add to MetaCart The compact closed bicategory Span of spans of reflexive graphs is described and it is interpreted as an algebra for constructing specifications of concurrent systems. We describe a procedure for associating to any Place/Transition system\Omega an expression \Psi\Omega in the algebra Span. The value of this expression is a system whose behaviours are the same as those of the P/T system. Furthermore, along the lines of Penrose's string diagrams, a geometry is associated to the expression \Psi\Omega which is essentially the same geometry as that usually associated to the net underlying \Omega . , 1996 "... Motivated by a model for syntactic control of interference, we introduce a general categorical concept of bireflectivity. Bireflective subcategories of a category A are subcategories with left and right adjoint equal, subject to a coherence condition. We characterize them in terms of split-idempoten ..." Add to MetaCart Motivated by a model for syntactic control of interference, we introduce a general categorical concept of bireflectivity. Bireflective subcategories of a category A are subcategories with left and right adjoint equal, subject to a coherence condition. We characterize them in terms of split-idempotent natural transformations on id A . In the special case that A is a presheaf category, we characterize them in terms of the domain, and prove that any bireflective subcategory of A is itself a presheaf category. We define diagonal structure on a symmetric monoidal category which is still more general than asking the tensor product to be the categorical product. We then obtain a bireflective subcategory of [C op ; Set] and deduce results relating its finite product structure with the monoidal structure of [C op ; Set] determined by that of C. We also investigate the closed structure. Finally, for completeness, we give results on bireflective subcategories in Rel(A), the category of relati...	{"url":"http://citeseerx.ist.psu.edu/showciting?cid=2101450","timestamp":"2014-04-16T12:07:12Z","content_type":null,"content_length":"26825","record_id":"<urn:uuid:3da55274-b819-4554-81b0-619811abb376>","cc-path":"CC-MAIN-2014-15/segments/1397609523265.25/warc/CC-MAIN-20140416005203-00432-ip-10-147-4-33.ec2.internal.warc.gz"}
Conditions for Vector Space August 23rd 2011, 07:36 AM #1 Conditions for Vector Space Hey guys, After a 3 year hiatus from taking any math courses i'm now taking an intermediate lin alg course and im a bit slow; I say this because I dont want you guys to hurt me for asking something so easy In my text it gives an example of, Let $S =\{ (a_1 , a_2): a_1 , a_2 \in R \}$ For $(a_1 , a_2), (b_1 , b_2) \in S$ and $c \in R$ define, $(a_1 , a_2) + (b_1 , b_2) = (a_1 + b_1, a_2 - b_2)$ and $c(a_1, a_2) = (ca_1, ca_2)$ All is well, and the example goes on to say that the situation described above violates the commutatively of addition and the associativity of addition, which I agree. But it also says it violates VS8 (so it is therefore not a vector space), which is For each pair of elements $a,b$ in $F$ and each element $x$ in $V$, $(a+b)x = ax + bx$ I'm obviously missing something but I do not see how $c(a_1, a_2) = (ca_1, ca_2)$ violates the above condition. It actually makes sense that this is the case to me. If i have a physical vector and I multiply it by a scalar both its points should be multiplied by the scalar (I use a physical vector as an exmaple here I do know that vectors are not just physical). Also, the next example takes the same situation but with the definition of $c(a_1, a_2) = (ca_1, 0)$ And this situation does not violate VS8. But i cannot see why, so clearly I am missing something with the VS8 condition! Thanks guys Re: Conditions for Vector Space In your example $V=S$ and $F=R$. So $x\in S$ means that $x=(x_1, x_2)$. Now, $(a+b)x=(a+b)(x_1, x_2)=((a+b)x_1, (a+b)x_2)=(ax_1 +bx_1, ax_2+bx_2)$ and $ax+bx=a(x_1, x_2)+b(x_1, x_2)=(ax_1,ax_2)+(bx_1,bx_2)=$ $=(ax_1+bx_1, ax_2-bx_2)eq (ax_1 +bx_1, ax_2+bx_2)$. So, $(a+b)x eq ax+bx$ August 23rd 2011, 08:08 AM #2 Junior Member Mar 2011	{"url":"http://mathhelpforum.com/advanced-algebra/186593-conditions-vector-space.html","timestamp":"2014-04-18T15:00:36Z","content_type":null,"content_length":"37682","record_id":"<urn:uuid:c8f70dfd-2a4b-42c9-ad45-62ebc083c17f>","cc-path":"CC-MAIN-2014-15/segments/1397609533689.29/warc/CC-MAIN-20140416005213-00336-ip-10-147-4-33.ec2.internal.warc.gz"}
Fourier Analysis and Synthesis The mathematician Fourier proved that any continuous function could be produced as an infinite sum of sine and cosine waves. His result has far-reaching implications for the reproduction and synthesis of sound. A pure sine wave can be converted into sound by a loudspeaker and will be perceived to be a steady, pure tone of a single pitch. The sounds from orchestral instruments usually consists of a fundamental and a complement of harmonics, which can be considered to be a superposition of sine waves of a fundamental frequency f and integer multiples of that frequency. The process of decomposing a musical instrument sound or any other periodic function into its constituent sine or cosine waves is called Fourier analysis. You can characterize the sound wave in terms of the amplitudes of the constituent sine waves which make it up. This set of numbers tells you the harmonic content of the sound and is sometimes referred to as the harmonic spectrum of the sound. The harmonic content is the most important determiner of the quality or timbre of a sustained musical note. Once you know the harmonic content of a sustained musical sound from Fourier analysis, you have the capability of synthesizing that sound from a series of pure tone generators by properly adjusting their amplitudes and phases and adding them together. This is called Fourier synthesis. One of the important ideas for sound reproduction which arises from Fourier analysis is that it takes a high quality audio reproduction system to reproduce percussive sounds or sounds with fast transients. The sustained sound of a trombone can be reproduced with a limited range of frequencies because most of the sound energy is in the first few harmonics of the fundamental pitch. But if you are going to synthesize the sharp attack of a cymbal, you need a broad range of high frequencies to produce the rapid change. You can visualize the task of adding up a bunch of sine waves to produce a sharp pulse and perhaps you can see that you need large amplitudes of waves with very short rise times (high frequencies) to produce the sharp attack of the cymbal. This insight from Fourier analysis can be generalized to say that any sound with a sharp attack, or a sharp pulse, or rapid changes in the waveform like a square wave will have a lot of high frequency content. As an example of what you learn from a Fourier transform, the transform of a square wave shows that is has only odd harmonics and that the amplitude of those harmonics drops in a geometric fashion, with the nth harmonic having 1/n times the amplitude of the fundamental. │ Fourier analysis of geometric waves │ Fourier series │	{"url":"http://hyperphysics.phy-astr.gsu.edu/hbase/audio/Fourier.html","timestamp":"2014-04-20T01:44:32Z","content_type":null,"content_length":"4471","record_id":"<urn:uuid:34bc4ce9-00ea-43ed-b606-1988a6b0720a>","cc-path":"CC-MAIN-2014-15/segments/1398223206118.10/warc/CC-MAIN-20140423032006-00126-ip-10-147-4-33.ec2.internal.warc.gz"}
March 7th 2010, 08:26 AM hi i have this question set me and i have no idea could someone help me please: Let G be a p-group for some prime p. Assume that G acts on a finite set X and let X^G={x memeber of X \| g.x =g for all g memeber of G} show that order X^G=order X mod p Thanks Rich March 7th 2010, 04:41 PM i fixed the typo you made in the definition of $X^G.$ well, the idea is exactly the same as the one that we use to prove that the center of every finite p-group is non-trivial: consider the partition $\{Gx_1, \cdots , Gx_m \}$ for $X.$ now $x_j \in X^G$ if and only if $\|Gx_j\|=1.$ thus $\|X\|=\sum_{j=1}^m \|Gx_j\|=\|X^G\| + \sum_{x_j otin X^G} \|Gx_j\|.$ but by the orbit-stabilizer theorem we have $\|Gx_j\|=[G:G_{x_j}]$ and since $x_j otin X^G$ implies that $\|Gx_j\| > 1$ and so $[G:G_{x_j}] > 1,$ we'll get $p \mid [G:G_{x_j}]$ for all $x_j otin X^G$ and the result follows.	{"url":"http://mathhelpforum.com/advanced-algebra/132478-groups-print.html","timestamp":"2014-04-16T16:02:55Z","content_type":null,"content_length":"6927","record_id":"<urn:uuid:cb1072f0-2781-4645-ad5f-35f3c4cfdf8d>","cc-path":"CC-MAIN-2014-15/segments/1397609524259.30/warc/CC-MAIN-20140416005204-00522-ip-10-147-4-33.ec2.internal.warc.gz"}
Complexity of Prime Algorithm September 3rd 2006, 01:09 PM #1 Global Moderator Nov 2005 New York City Complexity of Prime Algorithm I am trying to understand something, this is what I was thinking. (Do not dare laugh!) A number is prime if and only if, $\left[ \frac{(n-1)!+1}{n} \right]=\frac{(n-1)!+1}{n}$. If an algorithm is made to run based on this rule, what would be its complexity? I am thinking that since Striling's Forumla shows the factorial behaves like an exponential then its complexity is exponential, right? Now, since its runs in non-deterministic polynomial time there cannot exits a algorithm having complexity in polynomial time. (Because P verses NP). This explains the difficulty of having efficient primality testing. Follow Math Help Forum on Facebook and Google+	{"url":"http://mathhelpforum.com/discrete-math/5317-complexity-prime-algorithm.html","timestamp":"2014-04-18T13:46:17Z","content_type":null,"content_length":"30767","record_id":"<urn:uuid:7287279b-406e-44ee-89f1-eb6cf9ccfd2d>","cc-path":"CC-MAIN-2014-15/segments/1398223201753.19/warc/CC-MAIN-20140423032001-00350-ip-10-147-4-33.ec2.internal.warc.gz"}
Quantum teleportation analysed by mathematical separation tool September 27th, 2011 in Physics / Quantum Physics Scientists from the University of Vienna's Faculty of Physics in Austria recently gave a theoretical description of teleportation phenomena in sub-atomic scale physical systems, in a publication in the European Physical Journal D. For the first time, the Austrian team proved that mathematical tools give us the freedom to choose how to separate out the constituting matter of a complex physical system by selectively analysing its so-called quantum state. That is the state in which the system is found when performing measurement, which can either be entangled or not. The state of entanglement corresponds to a complex physical system in a definite (pure) state, while its parts taken individually are not. This concept of entanglement used in quantum information theory applies when measurement in laboratory A (called Alice) depends on the definite measurement in laboratory B (called Bob), as both measurements are correlated. This phenomenon cannot be observed in larger-scale physical systems. The findings of the Austrian team show that the entanglement or separability of a quantum state whether its sub-states are separable or not; i.e., whether Alice and Bob were able to find independent measurements depends on the perspective used to assess its status. A so-called density matrix is used to mathematically describe a quantum state. To assess this state's status, the matrix can be factorised in different ways, similar to the many ways a cake can be cut. The Vienna physicists have shown that by choosing a particular factorisation, it may lead to entanglement or separability; this can, however, only be done theoretically, as experimentally the factorisation is fixed by experimental conditions. These findings were applied in the paper to model physical systems of quantum information including the theoretical study of teleportation, which consists of the transportation of a single quantum state. Other practical applications include gaining a better understanding of K-meson creation and decay in particle physics, and of the quantum Hall effect, where electric conductivity takes quantisized values. More information: Entanglement or separability: the choice of how to factorize the algebra of a density matrix W. Thirring et al., European Physical Journal D (2011), DOI: 10.1140/epjd/e2011-20452-1 Provided by Springer "Quantum teleportation analysed by mathematical separation tool." September 27th, 2011. http://phys.org/news/2011-09-quantum-teleportation-analysed-mathematical-tool.html	{"url":"http://phys.org/print236338039.html","timestamp":"2014-04-19T05:29:02Z","content_type":null,"content_length":"6695","record_id":"<urn:uuid:aaa24e22-ffa6-4531-83a8-a91a33154338>","cc-path":"CC-MAIN-2014-15/segments/1397609535775.35/warc/CC-MAIN-20140416005215-00341-ip-10-147-4-33.ec2.internal.warc.gz"}
A semianalytical method for the noise emission of finite size ASA 129th Meeting - Washington, DC - 1995 May 30 .. Jun 06 2pAO5. A semianalytical method for the noise emission of finite size objects in shallow water. Hasan N. Oguz Dept. of Mech. Eng., Johns Hopkins Univ., Baltimore, MD 21218 Point sources are commonly used in underwater ambient noise computations to model wave breaking noise. A semianalytical solution to sound emission by a finite size object in shallow water is developed. The coefficients of the normal modes obtained by this technique are compared with the coefficients given by the point source approximation for the case of a hemispherical bubble cloud. The comparison is only good when the size of the bubble cloud is much smaller than the acoustic wavelength. Substantial differences occur when the radiation pattern near the bubble cloud deviates from a circular shape associated with the point dipole emission. Accurate normal modes coefficients given by the current method could be coupled with shallow water propagation models used in ambient noise calculations. [Work supported by the Office of Naval Research.]	{"url":"http://www.auditory.org/asamtgs/asa95wsh/2pAO/2pAO5.html","timestamp":"2014-04-20T23:30:03Z","content_type":null,"content_length":"1527","record_id":"<urn:uuid:fa957c26-9753-4034-975e-d53cfd2955af>","cc-path":"CC-MAIN-2014-15/segments/1397609539337.22/warc/CC-MAIN-20140416005219-00048-ip-10-147-4-33.ec2.internal.warc.gz"}
03-XX Mathematical logic and foundations 03Cxx Model theory 03C05 Equational classes, universal algebra [See also 08Axx, 08Bxx, 18C05] 03C07 Basic properties of first-order languages and structures 03C10 Quantifier elimination, model completeness and related topics 03C13 Finite structures [See also 68Q15, 68Q19] 03C15 Denumerable structures 03C20 Ultraproducts and related constructions 03C25 Model-theoretic forcing 03C30 Other model constructions 03C35 Categoricity and completeness of theories 03C40 Interpolation, preservation, definability 03C45 Classification theory, stability and related concepts [See also 03C48] 03C48 Abstract elementary classes and related topics [See also 03C45] 03C50 Models with special properties (saturated, rigid, etc.) 03C52 Properties of classes of models 03C55 Set-theoretic model theory 03C57 Effective and recursion-theoretic model theory [See also 03D45] 03C60 Model-theoretic algebra [See also 08C10, 12Lxx, 13L05] 03C62 Models of arithmetic and set theory [See also 03Hxx] 03C64 Model theory of ordered structures; o-minimality 03C65 Models of other mathematical theories 03C68 Other classical first-order model theory 03C70 Logic on admissible sets 03C75 Other infinitary logic 03C80 Logic with extra quantifiers and operators [See also 03B42, 03B44, 03B45, 03B48] 03C85 Second- and higher-order model theory 03C90 Nonclassical models (Boolean-valued, sheaf, etc.) 03C95 Abstract model theory 03C98 Applications of model theory [See also 03C60] 03C99 None of the above, but in this section	{"url":"http://www.ams.org/mathscinet/msc/msc2010.html?t=03Cxx&btn=Current","timestamp":"2014-04-24T17:18:19Z","content_type":null,"content_length":"16167","record_id":"<urn:uuid:47c7295a-f424-483b-b9ab-5cae8da725b0>","cc-path":"CC-MAIN-2014-15/segments/1398223206647.11/warc/CC-MAIN-20140423032006-00124-ip-10-147-4-33.ec2.internal.warc.gz"}
Does there exist a non-square number which is the quadratic residue of every prime? MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required. I want to know whether there exist a non-square number $n$ which is the quadratic residue of every prime. I know it is very elementary, and I think those kind of number are not exist, but I don't know how to prove. up vote 9 down vote favorite nt.number-theory quadratic-residues add comment I want to know whether there exist a non-square number $n$ which is the quadratic residue of every prime. I know it is very elementary, and I think those kind of number are not exist, but I don't know how to prove. This is actually an elementary consequence of quadratic reciprocity, generalizing the familiar proof à la Euclid that that are infinitely many primes of the form $4k+3$ (i.e. primes of which $-1$ is not a quadratic residue). We want to show that there exists $p$ such that $(n/p) = -1$. [As stated Paul's question asks only for $(n/p) \neq +1$, but this is trivial (if $n = -1$, take $p=3$; else let $p$ be a factor of $n$), so we'll exclude the finitely many prime factors $p$ of $n$.] By QR there exists a nontrivial homomorphism $\chi: ({\bf Z} / 4n{\bf up vote 14 Z})^* \rightarrow \lbrace 1, -1 \rbrace$ such that $(n/p) = \chi(p)$ for all primes $p \nmid 2n$. Let $a$ be any positive integer coprime to $4n$ such that $\chi(a) = -1$. Then we have a down vote prime factorization $a = \prod_j p_j$, and $\prod_j \chi(p_j) = \chi(a) = -1$. Therefore $\chi(p_j) = -1$ for some $j$, QED. As in Euclid we can iterate this argument to construct infinitely many distinct $p$ for which $(n/p) = -1$. add comment This is actually an elementary consequence of quadratic reciprocity, generalizing the familiar proof à la Euclid that that are infinitely many primes of the form $4k+3$ (i.e. primes of which $-1$ is not a quadratic residue). We want to show that there exists $p$ such that $(n/p) = -1$. [As stated Paul's question asks only for $(n/p) \neq +1$, but this is trivial (if $n = -1$, take $p=3$; else let $p$ be a factor of $n$), so we'll exclude the finitely many prime factors $p$ of $n$.] By QR there exists a nontrivial homomorphism $\chi: ({\bf Z} / 4n{\bf Z})^* \rightarrow \lbrace 1, -1 \ rbrace$ such that $(n/p) = \chi(p)$ for all primes $p \nmid 2n$. Let $a$ be any positive integer coprime to $4n$ such that $\chi(a) = -1$. Then we have a prime factorization $a = \prod_j p_j$, and $\ prod_j \chi(p_j) = \chi(a) = -1$. Therefore $\chi(p_j) = -1$ for some $j$, QED. As in Euclid we can iterate this argument to construct infinitely many distinct $p$ for which $(n/p) = -1$. This follows from the Chebotarev density theorem, or from the earlier and easier Frobenius density theorem. The polynomial $f(x):=x^2-n$ is irreducible in $\mathbb{Q}[x]$, so these density theorems imply that the mod $p$ reduction of $f(x)$ is irreducible for infinitely many primes $p$ (in fact: for half of all primes $p$). up vote 6 down vote It would be interesting to know a proof that didn't rely on these density theorems. add comment This follows from the Chebotarev density theorem, or from the earlier and easier Frobenius density theorem. The polynomial $f(x):=x^2-n$ is irreducible in $\mathbb{Q}[x]$, so these density theorems imply that the mod $p$ reduction of $f(x)$ is irreducible for infinitely many primes $p$ (in fact: for half of all primes $p$). It would be interesting to know a proof that didn't rely on these density theorems. A Chebotarev-free argument is given by our own @Pete L Clark here: up vote 3 down vote http://math.stackexchange.com/questions/6976/proving-that-an-integer-is-the-n-th-power add comment A Chebotarev-free argument is given by our own @Pete L Clark here: Let $a$ be any non-square. Then write $a=p^nm$ for some odd $n$ and prime $p$ which does not divide $m$. By Dirichlet's Theorem on primes in arithmetic progressions and the Chinese Remainder Theorem we can find a prime $q$ which is $1\mod 4$, $(q\|p)=-1$, and $1\mod l$ for each prime $l$ dividing $m$. Then by quadratic reciprocity, $(a\|q)=(p\|q)^n(m\|q)=(q\|p)^n=-1$ up vote 3 (where $(\cdot\|l)$ is the Legendre symbol modulo $l$). down vote add comment Let $a$ be any non-square. Then write $a=p^nm$ for some odd $n$ and prime $p$ which does not divide $m$. By Dirichlet's Theorem on primes in arithmetic progressions and the Chinese Remainder Theorem we can find a prime $q$ which is $1\mod 4$, $(q\|p)=-1$, and $1\mod l$ for each prime $l$ dividing $m$. Then by quadratic reciprocity, $(a\|q)=(p\|q)^n(m\|q)=(q\|p)^n=-1$ (where $(\cdot\|l)$ is the Legendre symbol modulo $l$).	{"url":"http://mathoverflow.net/questions/135820/does-there-exist-a-non-square-number-which-is-the-quadratic-residue-of-every-pri/135821","timestamp":"2014-04-20T11:16:18Z","content_type":null,"content_length":"73377","record_id":"<urn:uuid:fcc28225-56c7-4d93-9183-41218b42e8ac>","cc-path":"CC-MAIN-2014-15/segments/1397609538423.10/warc/CC-MAIN-20140416005218-00348-ip-10-147-4-33.ec2.internal.warc.gz"}
Probability problem. Re: Probability problem. Fourth way by programming, J code: We can shorten that a little: Last edited by gAr (2013-09-26 17:30:02) "Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha? "Data! Data! Data!" he cried impatiently. "I can't make bricks without clay." Re: Probability problem. New problem: A fair coin is tossed 20 times. What is the probability that there will be 5 or more consecutive heads? Last edited by gAr (2013-11-25 01:45:44) "Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha? "Data! Data! Data!" he cried impatiently. "I can't make bricks without clay." Re: Probability problem. Hi gAr; In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. Re: Probability problem. Hi bobbym, "Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha? "Data! Data! Data!" he cried impatiently. "I can't make bricks without clay." Re: Probability problem. Hi gAr; In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. Re: Probability problem. "Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha? "Data! Data! Data!" he cried impatiently. "I can't make bricks without clay." Re: Probability problem. Hi gAr; Trying to convince Agnishom to do some computer math. In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. Re: Probability problem. That's nice, I think he's already doing some. "Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha? "Data! Data! Data!" he cried impatiently. "I can't make bricks without clay." Re: Probability problem. Yes, some of my bad influence rubs off on most people sooner or later. In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. Re: Probability problem. You're not a bad influence. I ask people to stay away from non-free softwares, but most of them are reluctant to learn! "Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha? "Data! Data! Data!" he cried impatiently. "I can't make bricks without clay." Re: Probability problem. Have you been keeping up with geogebra? They are almost done with it. Do you like the 3D? In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. Re: Probability problem. Haven't used the recent releases. Last time when I used 3D, processor was running at 100% even when left idle, don't know now. Any significant changes you observed? "Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha? "Data! Data! Data!" he cried impatiently. "I can't make bricks without clay." Re: Probability problem. I am not a big fan of 3D programs to begin with. I prefer living like a flatlander. I think they have come along alot but still need more work. In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. Re: Probability problem. Me neither. "Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha? "Data! Data! Data!" he cried impatiently. "I can't make bricks without clay." Re: Probability problem. I thought it was a little slow on my machine but it is only a dual core. In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. Re: Probability problem. Even mine is a dual core, but I think it doesn't matter for most of the applications. "Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha? "Data! Data! Data!" he cried impatiently. "I can't make bricks without clay." Re: Probability problem. Also, my graphics card is the low end one. In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. Re: Probability problem. That's fine, CAS wouldn't require a graphics card. Though I think I've read recent mathematica versions make use of it. "Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha? "Data! Data! Data!" he cried impatiently. "I can't make bricks without clay." Re: Probability problem. Yes, they use the Nvidia Cuda card. It speeds up things tremendously, I have a Radeon card. Graphics are important when plotting 3D especially. In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. Re: Probability problem. Yes, that's right. "Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha? "Data! Data! Data!" he cried impatiently. "I can't make bricks without clay." Re: Probability problem. Not that I do alot of 3D work. I do not think there is any CAS that is as good as some other programs are at graphing. In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. Re: Probability problem. I too rarely use 3d, and I recently saw that there's an option to view the plot in stereographic view in sage. But didn't try with the glasses yet. "Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha? "Data! Data! Data!" he cried impatiently. "I can't make bricks without clay." Re: Probability problem. What kind of glasses do you use for it? In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. Re: Probability problem. The red and cyan glasses, like the ones used for viewing 3d films. By the way, is it feasible to create an option to mark the posts containing problems, and then create the links to those posts in one place (e.g. in the beginning of the thread)? That will make the problems more visible. Last edited by gAr (2013-11-21 16:26:04) "Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha? "Data! Data! Data!" he cried impatiently. "I can't make bricks without clay." Re: Probability problem. I am not able to do that. It would have to be done with source code of the forum. In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof.	{"url":"http://www.mathisfunforum.com/viewtopic.php?pid=290601","timestamp":"2014-04-18T21:48:35Z","content_type":null,"content_length":"39101","record_id":"<urn:uuid:703d4c4e-9b16-4ec6-8d69-c7e10a4e11cf>","cc-path":"CC-MAIN-2014-15/segments/1397609535095.9/warc/CC-MAIN-20140416005215-00419-ip-10-147-4-33.ec2.internal.warc.gz"}
Find an Algebra Tutor ...In addition to test prep, I enjoy tutoring biology, math, history, and English. I have experience tutoring at all grade levels and at a collegiate level. My schedule is extremely flexible, and I can tutor during the day, as well as on evenings and weekends. 31 Subjects: including algebra 2, algebra 1, English, dyslexia ...While working on my Molecular Biology BS from Johns Hopkins University, I tutored college students on Math (including Calculus) and Science (including Chemistry). I have worked with individual students and small groups. I like to get feedback from my students often in order to improve their expe... 40 Subjects: including algebra 1, chemistry, algebra 2, calculus ...This material involves motion under constant acceleration and can involve application and manipulation of a set of non-linear equations. In principle, Algebra 1 and some modest extensions are all the math background that is needed for this part of physics. I find however, that some students - e... 13 Subjects: including algebra 1, algebra 2, physics, chemistry ...I offer tutoring sessions for all high school math subjects—from pre-algebra to AP calculus. I have helped to significantly improve students' scores and grades (as much as from an F to an A) in high school math subjects for three years now. I also offer sessions to undergraduate students taking any subject up to differential equations. 15 Subjects: including algebra 2, algebra 1, chemistry, calculus ...My name is Cierra and I am a recent high school graduate, now attending George Mason University. I have a lot of experience as a tutor in both an individualized and group setting. When I was in high school I tutored most Saturday mornings in a program at my high school called BITS (Bulldog Inst... 12 Subjects: including algebra 1, reading, Spanish, writing Nearby Cities With algebra Tutor Annandale, VA algebra Tutors Burke, VA algebra Tutors Centreville, VA algebra Tutors Fairfax Station algebra Tutors Fairfax, VA algebra Tutors Germantown, MD algebra Tutors Great Falls, VA algebra Tutors Herndon, VA algebra Tutors Manassas, VA algebra Tutors Mc Lean, VA algebra Tutors Oak Hill, VA algebra Tutors Oakton algebra Tutors Reston algebra Tutors Sterling, VA algebra Tutors Vienna, VA algebra Tutors	{"url":"http://www.purplemath.com/southern_md_facility_algebra_tutors.php","timestamp":"2014-04-19T10:00:30Z","content_type":null,"content_length":"23881","record_id":"<urn:uuid:74628057-ef1a-4e61-845f-710e5ab5fc38>","cc-path":"CC-MAIN-2014-15/segments/1397609537097.26/warc/CC-MAIN-20140416005217-00389-ip-10-147-4-33.ec2.internal.warc.gz"}
reverse Polish notation (thing) Reverse polish notation is really related to tree traversal algorithms. If you build a and its are the ), you can express any calculation you like. If you read the post order , you get the reverse polish notation equivalent of that. If you use pre order in order , you get polish notation traditional notation , respectively. Building the tree for (3+4)5-2 gives us a tree like this one: (-) - (2) () - (5) (+) - (4) I know it's an awful way to draw a tree... my excuses... Inorder traversal gives us 3+45-2 Preorder traversal is - + 3 4 5 2 Postorder traversal 3 4 + 5 * 2 - Of course, with inorder, you need parenthesis in order to avoid ambiguity, but you don't need them with reverse polish notation. This was also used in the venerable Forth programming language.	{"url":"http://everything2.com/user/koala/writeups/reverse+Polish+notation","timestamp":"2014-04-16T05:29:58Z","content_type":null,"content_length":"21475","record_id":"<urn:uuid:ada8c85f-40ee-427a-86bc-f923c385d750>","cc-path":"CC-MAIN-2014-15/segments/1397609521512.15/warc/CC-MAIN-20140416005201-00272-ip-10-147-4-33.ec2.internal.warc.gz"}
System for Attenuating Noise in an Input Signal Patent application title: System for Attenuating Noise in an Input Signal Sign up to receive free email alerts when patent applications with chosen keywords are published SIGN UP A noise attenuation system attenuates noise in an input signal. The system may estimate a power of the input signal, and determine a noise power value based on the input power estimate. The noise power value corresponds to an estimate of a noise power within the input signal. The system may determine an attenuation factor based on the noise power value, and attenuate the input signal by using the attenuation factor. A method for attenuating noise in an input signal, comprising:receiving the input signal;estimating a power level of the input signal to obtain an input power estimate;determining a noise power value based on the input power estimate, the noise power value corresponding to an estimate of a noise power within the input signal;determining an attenuation factor based on the noise power value; andattenuating the input signal using the attenuation factor. The method according to claim 1, where determining the noise power value comprises determining whether the input power estimate at a given time is larger than the noise power value at a previous The method according to claim 1, where determining the noise power value comprises increasing the noise power value at a given time if the input power estimate at the given time is larger than the noise power value at a previous time. The method according to claim 1, where determining the noise power value comprises determining the noise power value at a given time based on the noise power value determined at a previous time and multiplied by an adjustment factor. The method according to claim 1, where determining the noise power value comprises bounding the noise power value below by a predetermined lower noise limit. The method according to claim 1, where over a predetermined period determining the noise power value is performed based on the input power estimate smoothed by a filter. The method according to claim 1, where determining the attenuation factor is based on the input power estimate. The method according to claim 1, where determining the attenuation factor comprises determining an indicator value indicating the presence of a wanted signal component in the input signal at a given The method according to claim 8, where the indicator value is increased if the input power estimate at the given time is larger than the product of the noise power value at the given time and a predetermined sensitivity factor. The method according to claim 9, where the indicator value is decreased if the input power estimate at the given time is smaller than the product of the noise power value at the given time and a predetermined sensitivity factor. The method according to claim 8, where the indicator value is decreased if the input power estimate at the given time is smaller than the product of the noise power value at the given time and a predetermined sensitivity factor. The method according to claim 8, where the indicator value is bounded above by a predetermined indicator maximum value, bounded below by a predetermined indicator minimum value, or both. The method according to one of claim 8, where the attenuation factor is based on a quotient of the indicator value and the input power estimate. The method according to one of claim 13, where the attenuation factor is time dependent. The method according to claim 1, where the acts of estimating the power of the input signal, determining the noise power value, determining the attenuation factor, and attenuating the input signal are repeated at successive points in time. The method according to claim 1, where the input signal comprises an acoustic wanted signal component. The method according to claim 1, where the attenuation factor is bounded by a predetermined attenuation minimum value, a predetermined attenuation maximum value, or both. The method according to claim 1, where attenuating the input signal comprises attenuating the input signal at a noise attenuator that comprises circuitry, a computer-readable storage medium with computer-executable instructions embodied thereon, or both. A computer program product comprising one or more computer-readable storage media having computer-executable instructions embodied thereon and programmed to:receive the input signal;estimate a power of the input signal to obtain an input power estimate;determine a noise power value based on the input power estimate, the noise power value corresponding to an estimate of a noise power within the input signal;determine an attenuation factor based on the noise power value; andattenuate the input signal using the attenuation factor. An apparatus for attenuating noise, comprising:means for receiving an input signal;means for estimating a power of the input signal to obtain an input power estimate;means for determining a noise power value based on the input power estimate, the noise power value corresponding to an estimate of a noise power within the input signal;means for determining an attenuation factor based on the noise power value; andmeans for attenuating the input signal using the attenuation factor. A computer program product comprising one or more computer-readable storage media having computer-executable instructions embodied thereon for:estimating a power level of an input signal to obtain an input power estimate;determining a noise power value based on the input power estimate, the noise power value corresponding to an estimate of a noise power within the input signal;adjusting the noise power value over time based on a comparison between the input power estimate and the noise power value;determining an indicator value indicating the presence of a wanted signal component in the input signal;adjusting the indicator value over time based on a comparison between the input power estimate and a product of the noise power value and a sensitivity factor;determining an attenuation factor based on the indicator value and the input power estimate; andattenuating the input signal using the attenuation factor. The computer program product of claim 21, where adjusting the noise power value comprises:comparing the input power estimate for a first portion of the input signal with the noise power value for a preceding portion of the input signal;decreasing the noise power value for the first portion of the input signal when the input power estimate for the first portion of the input signal is less than the noise power value for the preceding portion of the input signal; andincreasing the noise power value for the first portion of the input signal when the input power estimate for the first portion of the input signal is greater than the noise power value for the preceding portion of the input signal. The computer program product of claim 21, where adjusting the indicator value comprises:comparing the input power estimate and the product of the noise power value and the sensitivity factor; increasing the indicator value when the input power estimate is less than the product of the noise power value and the sensitivity factor; anddecreasing the indicator value when the input power estimate is greater than the product of the noise power value and the sensitivity factor. The computer program product of claim 21, where determining the attenuation factor comprises:calculating an attenuation factor candidate based on a quotient of the indicator value and the input power estimate; andsetting the attenuation factor to the attenuation factor candidate when the attenuation factor candidate falls between an attenuation factor minimum and an attenuation factor maximum. BACKGROUND [0001] 1. Priority Claim This application claims the benefit of priority from European Patent Application No. 09004056.9, filed Mar. 20, 2009, which is incorporated by reference. 2. Technical Field This application relates to signal processing and, more particularly, to attenuating noise in an input signal. 3. Related Art In a variety of situations, signals may be used to transmit information between two communication partners. Many different types of signals may be used to transmit information, including electric signals, radio signals, light signals, and sound signals. A signal may include both wanted signal components and noise components. The wanted signal components carry the information to be transmitted between communication partners, while the noise components may reduce signal quality or otherwise interfere with the intelligibility of the wanted signal components. In a telephone system, a sound signal from a user maybe transformed at the sender side into an electric signal. The electric signal may be forwarded via electronic components of a telephone network to a receiver. At the receiver, the electric signal may be transformed back by electronic components into a wanted sound signal. If noise is present in the electric signal received at the receiver side, then artifacts may be audible in the resulting sound signal. Various electronic components in a telephone network, such as network access devices (NADs) or network access modules (NAMs), may add noise to the electric signal. The electronic components may generate noise even when no wanted signal component is present. The noise may be noticeable as artifacts to the receiving party, particularly during pauses of the wanted signal. Some systems use noise gates, squelch functions, or Wiener-type filters to suppress noise. A noise gate may have the property of suppressing all input signals that have levels below a certain threshold, as shown in FIG. 10 . In FIG. 10 , an input signal with an intensity level below a gate threshold with an absolute value of 0.4 results in an output of level of zero (i.e., no output at all), while an input signal with an intensity level above the gate threshold may pass with unchanged intensity. Some noise suppression approaches may have a negative impact on the wanted signal components of an input signal. Therefore, a need exists for an improved noise attenuation system, which may have less of a negative impact on the wanted signal components of an input signal. SUMMARY [0009] A noise attenuation system attenuates noise in an input signal. The system may estimate a power of the input signal, and determine a noise power value based on the input power estimate. The noise power value corresponds to an estimate of a noise power within the input signal. The system may determine an attenuation factor based on the noise power value, and attenuate the input signal by using the attenuation factor. Other systems, methods, features, and advantages will be, or will become, apparent to one with skill in the art upon examination of the following figures and detailed description. It is intended that all such additional systems, methods, features and advantages be included within this description, be within the scope of the invention, and be protected by the following claims. BRIEF DESCRIPTION OF THE DRAWINGS [0011] The system may be better understood with reference to the following drawings and description. The components in the figures are not necessarily to scale, emphasis instead being placed upon illustrating the principles of the invention. Moreover, in the figures, like referenced numerals designate corresponding parts throughout the different views. FIG. 1 illustrates an input signal. FIG. 2 illustrates a first representation of noise in the input signal of FIG. 1. FIG. 3 illustrates a second representation of noise in the input signal of FIG. 1. [0015]FIG. 4 illustrates a noise attenuation system attenuating noise in an input signal. FIG. 5 is a method of determining a noise power value. FIG. 6 is a method of determining an indicator value. [0018]FIG. 7 is a method of determining an attenuation factor. FIG. 8 illustrates a noise power value and an input power estimate plotted over time during a noise attenuation process. [0020]FIG. 9 illustrates an input signal, an input power estimate, a noise power value, an indicator value, an attenuation factor, and an output signal plotted over time during a noise attenuation process. [0021]FIG. 10 illustrates one implementation of a noise gate. FIG. 11 is a noise attenuation system. [0023]FIG. 12 is a noise attenuation system in a vehicle. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS [0024] A noise attenuation system may attenuate undesirable noise in a signal. FIG. 1 illustrates a signal 102 with both wanted signal components 104 and noise components. The signal 102 may be transmitted from an electronic circuit that provides access to a network, such as a network access device (NAD). FIG. 1 shows the intensity of the signal 102 over time. While a wanted signal component 104 starts shortly before the 4 second, no signal seems to be present at earlier times in FIG. 1. However, if the scale for the intensity value is enlarged, which is shown in FIG. 2, a noise component 202 may be recognized at times between second 1 and second 3.5 where no wanted signal component is present. FIG. 3 illustrates a time-frequency analysis of the noise component 202 of FIG. 2 over the first few seconds. A user receiving the signal 102 as an electric input signal to its telephone system or another sound reproducing system may hear the sound of the noise component 202 during an initial period before the wanted signal component 104 is received from the remote partner. [0025]FIG. 4 illustrates the operation of a noise attenuation system. The noise attenuation system may receive the signal 102 of FIGS. 1-3 as the input signal. If the noise attenuation system receives the signal 102, the system may attenuate at least a portion of the noise component 202. The noise attenuation system may estimate a power of an input signal and derive an estimate of the power of a noise component in the input signal from the power of the input signal. The system may use the noise power estimate to determine an attenuation factor dynamically in dependence on the estimated power of the noise component. In this way, the noise attenuation system may be more effective in adapting its attenuation behavior to the presence of noise. In particular, the noise attenuation system may attenuate noise during pauses of a wanted signal component in the input signal, particularly in low noise conditions, with less deterioration of the wanted signal component, as it may more clearly discern between noise and a wanted signal component with low power. The noise attenuation system of FIG. 4 may be a part of a device that processes acoustic signals, such as a communication device. FIG. 11 illustrates a noise attenuation system within a communication device 1102. The noise attenuation system may include a processor 1104, a memory 1106, and a driver/output 1108, such as a transmitter, speaker, or device driver. The communication device may be a network access module, a mobile or landline telephone, a hands-free system, a portable or stationary radio system, a system for controlling devices via voice control, or another sound processing device. Alternatively, the input signal may be received from a network access module, such as a network access module of a telephone network, or a radio network. The noise attenuation system and/or the communication device may be installed in the cabin of a vehicle. Alternatively, the input signal may be received from a system that is physically or wirelessly linked to the cabin of a vehicle. FIG. 12 illustrates a noise attenuation system installed in a vehicle 1202, such as in the cabin of the vehicle. The input signal may include an acoustic signal from a microphone, from a device for reproducing recorded sound, such as a CD or a DVD player or a radio, or from a device giving spoken instructions to a user, such as an electronic navigation device or a system issuing speech prompts. The input signal may be received from a hands-free system. FIG. 4 , an input signal is received at act 402. The input signal may include a noise component and a wanted signal component. In some applications, the noise component may have been added by an electronic component. When a wanted signal is processed by an electronic component, such as during transport through a network, the electronic component may add an electronic noise component to the wanted signal component. Electronic components generating noise may be devices that process and/or amplify acoustic or non-acoustic signals. In particular, such electronic components may be network access The input signal received at act 402 may be a digital signal or an analog signal. If the received input signal is a digital signal, the received input signal may be represented by a time-ordered sequence of samples or of blocks of samples. Alternatively, if the received input signal is an analog signal, act 402 may include digitizing the received input signal. To digitize an analog signal, a parameter of the analog signal may be determined. In one implementation, the parameter may be the amplitude or the power of the input signal. The parameter of the signal may be determined at a plurality of successive times by a sampling process. In other words, the input signal may be sampled to obtain signal samples or samples. The successive times may be separated by substantially equal periods of time. Each sample may have a sample value corresponding to the respective signal parameter value (e.g., the respective amplitude or the power of the signal). The time at which a sample has been obtained is called the sample time. Samples may be ordered in time according to their sample times. A sequence of time-ordered samples may be called a digital signal. The digital or digitized input signal may be a time-ordered sequence of samples with sample values x(k), where k is the index of the respective sample in the sequence of samples representing the input signal. The index k corresponds to the sample time where the sample value x(k) has been determined. A time-ordered sequence of samples may be divided into blocks of samples. A block may include a fixed number of samples or a variable number of samples. In one implementation, a block may include only one sample. In other implementations, a block may include more than one sample. The input signal may be represented by a sequence of blocks which has been built from the sequence of samples. The corresponding sequence of blocks representing the signal may be ordered in time. A block of samples may be assigned a block value representing the sample values in the block. The block value may be the average, or a weighted average, of the sample values of all or a part of the samples in the block, or may be the value of a selected sample from the block. Each block of samples may be assigned a block time representing the sample times of the samples in the block. The block time may be the sample time of one of the samples in the block (e.g., the first or the last one). The block time may be an average of the sample times of the samples in the block. Subsequent processing of the input signal may be determined for a sample or for a block of samples, such as at the sample time of the sample or the block time of the block. In one implementation, various signal processing quantities, such as an input power estimate, a noise power value, or an attenuation factor may be determined for a sample or for a block of samples. The samples may be divided into consecutive blocks of N successive samples. The blocks may be numbered by an index according to their order. In a first step, the average x ,cur(n) of the sample values of the samples in the n-th block (i.e., the block with index n) may be determined and assigned to the n-th block as the block value: x p , cur ( n ) = 1 N block m = 0 N block - 1 x ( nN block - m ) . ( 1 ) ##EQU00001## At act 404, the noise attenuation system obtains an input power estimate for the input signal. The power of the input signal may be the modulus or the absolute value of the signal strength. Alternatively, the power of the input signal may be the square of the modulus of the signal strength of the input signal. In other implementations, the noise attenuation system may use another way of estimating the power of the input signal. In one implementation, the sequence of sample values or block values representing the digital or digitized input signal may be smoothed in order to obtain the input power estimate. One sample or block of the smoothed sequence may correspond to one sample or block of the unsmoothed sequence. The corresponding samples or blocks may have the same sample time. For the smoothing, a first order Infinite Impulse Response (IIR) filter may be used. In this way, abrupt changes in the input signal may be removed before further processing of the input signal takes place. The sequence of the block values x ,cur(n) may be smoothed using a first order Infinite Impulse Response (IIR) filter characterized by the parameters β between 0 and 1 for increasing input signal power and β between 0 and 1 for declining input signal power, thus obtaining the input power estimate x (n) as: x P ( n ) = { β p , r x p ( n - 1 ) + ( 1 - β p , r ) x p , cur ( n ) , for x p , cur ( n ) > x p ( n - 1 ) , β p , f x p ( n - 1 ) + ( 1 - β p , f ) x p , cur ( n ) , for x p , cur ( n ) ≦ x p ( n - 1 ) . ( 2 ) ##EQU00002## At act 406, the noise attenuation system determines a noise power value. The noise power value is represented as x (n). The noise power value may be the modulus or the absolute value of the signal strength of a noise component. Alternatively, the noise power value may be the square of the modulus of the signal strength of a noise component. In other implementations, the noise attenuation system may use another way of estimating the power of a noise component. As will be described below, FIG. 5 illustrates further details of one implementation of a noise attenuation system that calculates a noise power value for an input signal. At act 408, the noise attenuation system determines an attenuation factor. The attenuation factor is represented as g (n). The attenuation factor may be based on the input power estimate. So, it becomes possible to react more flexibly to different input power levels. The attenuation factor may also be determined based on an indicator value that indicates the presence of a wanted signal component in the input signal at a given time. The indicator value may be based on the noise power value. The indicator value and/or the attenuation factor may be dependent on the input power estimate. As will be described below, FIG. 6 illustrates further details of one implementation of a noise attenuation system that calculates an indicator value for an input signal, and FIG. 7 illustrates further details of one implementation of a noise attenuation system that calculates an attenuation factor for the input signal. At act 410, the noise attenuation system attenuates the input signal based on the attenuation factor. The system may include a noise attenuator that includes circuitry, a computer-readable storage medium with computer-executable instructions embodied thereon, or both. In one implementation, the noise attenuator may multiply the input signal by the attenuation factor to attenuate at least some noise in the input signal. Multiplying the input signal may comprise multiplying each of the samples of the digital or digitized input signal with the attenuation factor. The attenuation factor may be applied to a single sample or to all or a part of the samples in one or more blocks of samples. At act 412, the noise attenuation system outputs a noise reduced version of the input signal. The output signal is represented as y(k). The noise attenuation system of FIG. 4 may be used to attenuate noise components during periods when the input power estimate of the input signal does not exceed the noise power value multiplied by a predetermined factor. The noise attenuation system may be applied to identify pauses in a wanted signal component of an input signal. The noise may be strongly reduced during pauses, while at times where a wanted signal component is present, the attenuation may be adapted to avoid deteriorating the wanted signal component. Particularly, the wanted signal component may be a speech signal component. During a noise attenuation process, one or more of the acts 402-412 may be repeated multiple times. The acts 402-412 may be performed for one sample or block. In other words, the acts 402-412 may be performed at the same sample time or block time. In particular, if the input signal is represented by a sequence of samples or blocks of samples, the acts 402-412 may be performed for each sample or block of samples in the sequence. FIG. 5 illustrates a method of determining a noise power value of an input signal. The noise power value may correspond to an estimate of the noise power component in the input signal. The system may derive the noise power value x (n) from an input power estimate. In one implementation, the noise power value may be determined based on the input power estimate smoothed by a filter. The filter may be an Infinite Impulse Response (IIR) filter. The IIR filter may be of first order, or of a higher order. In particular, the noise power value may be equal to the input power estimate. Determining the noise power estimate based on the input power estimate smoothed by a filter may be performed for a single sample or block of samples having a sample time or a block time at a given time. The noise power estimate may be performed for a predetermined amount of samples or blocks of samples. The predetermined amount of samples or blocks may be the samples or blocks obtained directly after the method has been started. Alternatively or in addition, determining the noise power estimate based on the input power estimate smoothed by a filter may be performed for a fraction of the samples or blocks for which the method is performed. The fraction of samples may be distributed regularly or irregularly over all the samples for which the method is performed. In one implementation, the noise power value x (n) may be determined according to the following equation: x N ( n ) = { β n x n ( n - 1 ) + ( 1 - β n ) x p ( n ) , for n < n init max { κ dec , f x n ( n - 1 ) , x n , min } , for n ≧ n init , x n ( n - 1 ) > x p ( n ) , τ dec > τ dec , th max { κ dec , s x n ( n - 1 ) , x n , min } , for n ≧ n init , x n ( n - 1 ) > x p ( n ) , τ dec ≦ τ dec , th max { κ inc , f x n ( n - 1 ) , x n , min } , for n ≧ n init , x n ( n - 1 ) ≦ x p ( n ) , τ inc > τ inc , th max { κ inc , s x n ( n - 1 ) , x n , min } , for n ≧ n init , x n ( n - 1 ) ≦ x p ( n ) , τ inc ≦ τ inc , th . ( 3 ) ##EQU00003## It can be seen from equation (3) that, during a predetermined initialization period n<n with an n >0, i.e. dealing with blocks with an index n<n , the noise power value is based on the input power estimate, but smoothed by a first order Infinite Impulse Response (IIR) filter characterized by the parameter β . At act 502 of FIG. 5, the noise attenuation system determines whether the attenuation process is within an initialization period. The initialization period may last for a predetermined time, number of samples, or number of blocks. If the attenuation process is still within the initialization period, then the system determines the noise power value based on the input power estimate smoothed by a first order Infinite Impulse Response filter at act 504, such as according to equation (3). Alternatively, if the predetermined initialization period has past, then act 502 proceeds to act 506. At act 506, the attenuation system compares the current input power estimate to a preceding noise power value. In one implementation, act 506 may include determining whether the input power estimate at a given time is larger than the noise power value at a previous time. In addition or instead, act 506 may include determining whether the input power estimate at a given time is smaller than or equal to the noise power value determined at a previous time. The input power estimate may be determined for a sample or block of samples where the sample time or the block time is the given time. The noise power value may be determined for a sample or block of samples preceding the sample or block of samples whose sample time or block time is the given time. The preceding sample or block of samples may be directly preceding or may be separated by a predetermined number of samples or blocks. The time interval between the given time and previous time may comprise sample times or block times of a fixed or variable number of samples or blocks. The noise attenuation system may increase the noise power value at a given time if the input power estimate at the given time is larger than the noise power value at a previous time. In addition or instead, the noise power value at the given time may be increased if the input power estimate at the given time is equal to the noise power value at the previous time. The noise attenuation system may also decrease the noise power value at a given time if the input power estimate at the given time is smaller than the noise power value at a previous time. In one implementation, the noise power value at a given time may be determined, based on the noise power value determined at a previous time, multiplied by an adjustment factor. The noise power value determined at a previous time may be determined for a sample or block of samples preceding the sample or block of samples whose sample time or block time is the given time. The preceding sample or block of samples may be directly preceding or may be separated by a predetermined number of samples or blocks. The time interval between the given time and the previous time may comprise sample or block times of a fixed or variable number of blocks of samples. The adjustment factor may be a constant, or may be time dependent. To permit adaptation of the method to a varying signal, the difference between the given time and the previous time may vary with time. At act 506, the noise attenuation system determines whether to increase the noise power value or decrease the noise power value. As discussed above, the noise power value may be decreased if the input power estimate for a given time is less than the noise power value at a preceding time. The decrease of the noise power value may be performed at acts 508, 510, and/or 512. As discussed above, the noise power value may be increased if the input power estimate for a given time is greater than or equal to the noise power value at a preceding time. The increase of the noise power value may be performed at acts 514, 516, and/or 518. After the predetermined initialization period, the input power value may be limited by the lower limit x ,min. Similarly, the noise power value may be bounded below by a predetermined lower noise limit. The predetermined lower noise limit may be constant or time-dependent. At a block index n where the input power estimate is smaller than the noise power value at the preceding block with index n-1, the noise power value may be reduced by a positive factor κ ,f<1 or κ ,s<1 depending on the number of preceding decreases τ being more than a given threshold value τ ,th, or not. The parameter κ ,s realizes a slow decrease, while κ ,f, which is effective after a number τ ,th of slow decreases, has the effect of a fast decrease so as to follow larger changes in the input power estimate quickly. In the case that the input power estimate at a block index n is equal or larger than the noise power value at the preceding block with index n-1, the noise power value may show a corresponding behavior, e.g., the noise power value may be increased by a positive factor κ.sub.inc,s>1 to cause a small increase when the number of consecutive increases is less or equal than τ.sub.inc,th, and the noise power value may be increased by the positive factor κ.sub.inc,f>1 for a steeper increase after the number of consecutive increases exceeds τ.sub.inc,th. In the process of FIG. 5, the noise attenuation system determines whether the number of preceding noise power value decreases is less than a threshold at act 508. If the number of decreases is less than the threshold, then the system sets the noise power value based on a slow decrease from the preceding noise power value at act 510. If the number of decreases is above the threshold, then the system sets the noise power value based on a fast decrease from the preceding noise power value at act 512. When the system is set to increase the noise power value, the noise attenuation system determines whether the number of preceding noise power value increases is less than a threshold at act 514. If the number of increases is less than the threshold, then the system sets the noise power value based on a slow increase from the preceding noise power value at act 516. If the number of increases is above the threshold, then the system sets the noise power value based on a fast increase from the preceding noise power value at act 518. FIG. 6 illustrates a method of determining an indicator value. The indicator value may indicate the presence of a wanted signal component in the input signal at a given time. The indicator value may be based on the noise power value and/or the input power estimate. The noise attenuation system may adjust the indicator value over time to indicate whether various portions of the input signal are likely to contain wanted signal components. In one implementation, the indicator value is adjusted based on a comparison between the input power estimate and a product of the noise power value and a sensitivity factor. The sensitivity factor may be a predetermined constant, or may vary with time. The sensitivity factor may be dependent on the maximum and/or the minimum value of the input power estimate and/or of the noise power value in a period of time. In one implementation, the indicator value may be used to discern between periods where the input power estimate of the input signal is higher than the noise power value, multiplied by a sensitivity factor α>0, e.g., where the wanted signal component is predominant, and periods where this is not the case. In this context, the sensitivity factor α may be defined and the criterion may be established that a frame n is assumed to comprise a wanted signal component if the quotient between the input power estimate and the noise power value is greater than the sensitivity factor. Based on this criterion, the indicator value x (n) may be defined as follows: x gate ( n ) = { max { x gate , min , β gate , f x gate ( n - 1 ) } , for x p ( n ) > α x n ( n ) min { x gate , max , β gate , r x gate ( n - 1 ) } , otherwise . ( 4 ) ##EQU00004## From equation (4), it can be seen that x (n) decreases to a minimum value as long as the above criterion is met (e.g., as long as the input power estimate exceeds the product of the noise power value and the sensitivity factor). In this case, the indicator value may be decreased by the positive factor β ,f<1 for each consecutive block n until it reaches a minimum value x ,min as long as the criterion for the presence of a wanted signal is met by consecutive blocks of samples. If the above criterion is not satisfied, then the indicator value may be increased by the positive factor β ,r>1 for each consecutive block n until an upper limit of x ,max is reached. Values for x ,max and x ,min may be chosen to optimize the behavior of the attenuation factor. The value for the upper limit x ,max may be chosen such that no noise is audible in periods where the input signal does not comprise any wanted signal component, while x ,min may be selected such that the wanted signal component is not degraded in periods where a wanted signal component is present, even if a small amount of noise may still be audible. In the process of FIG. 6, the noise attenuation system may determine whether to increase the indicator value or decrease the indicator value at act 602. If the input power estimate is less than the product of the noise power value and a sensitivity factor, then act 602 proceeds to act 604 and the indicator value is increased. Increasing the indicator value may include multiplying the indicator value determined at a previous time by a predetermined positive factor greater than one. The previous time may be the block time or the sample time of a block or sample which precedes the given time. The indicator value may also be increased if the input power estimate at the given time is equal to the product of the noise power value at the given time and the sensitivity factor. If the input power estimate is greater than the product of the noise power value and a sensitivity factor, then act 602 proceeds to act 612 and the noise power value is decreased. Decreasing the indicator value may include multiplying the indicator value determined at a previous time by a predetermined positive factor smaller than one. The previous time may be the block time or the sample time of a block or sample which precedes the given time. The indicator value may also be decreased if the input power estimate at the given time is equal to the product of the noise power value at the given time and the sensitivity factor. The indicator value may be bounded above by a predetermined indicator maximum value and/or may be bounded below by a predetermined indicator minimum value. The indicator maximum value and/or the indicator minimum value may be a predetermined constant or may be a predetermined function of the time. The indicator maximum value and/or the indicator minimum value may be a predetermined function of the input power estimate and/or of the noise power estimate. If the signal power estimate is below the product of the noise power value and a sensitivity factor at a given time, the indicator value determined at a previous time may be increased and compared to the indicator maximum value. At act 606, the noise attenuation system compares the increased indicator value with an indicator value maximum. If the increased indicator value is less than the indicator value maximum, then the noise attenuation system uses the increased indicator value at act 608 to calculate an attenuation factor. If the increased indicator value is greater than the indicator value maximum, then the noise attenuation system uses the indicator value maximum at act 610 to calculate the attenuation factor. FIG. 7 illustrates further details of one implementation of a noise attenuation system that calculates an attenuation factor for the input signal. If the signal power estimate is above and/or equal to the product of the noise power value and the sensitivity factor at a given time, the indicator value determined at a previous time may be decreased and compared to the indicator minimum value. At act 614, the noise attenuation system compares the decreased indicator value with an indicator value minimum. If the decreased indicator value is greater than the indicator value minimum, then the noise attenuation system uses the decreased indicator value at act 616 to calculate an attenuation factor. If the decreased indicator value is less than the indicator value minimum, then the noise attenuation system uses the indicator value minimum at act 618 to calculate the attenuation factor. [0061]FIG. 7 illustrates a method of determining an attenuation factor. The attenuation factor may be based on the quotient of the indicator value and the input signal estimate. The attenuation factor may be time dependent. The attenuation factor may be based on the quotient of the squared moduli of the indicator value and the input signal estimate. In this way, a more abrupt distinction between the presence and the absence of a wanted signal component may be obtained. The attenuation factor may be equal to the squared moduli of the indicator value and the input signal estimate. The attenuation factor may be bounded below by a predetermined attenuation minimum value and bounded above by a predetermined attenuation maximum value. The attenuation maximum and minimum values may be constant, or at least one of them may be time dependent. The attenuation maximum and minimum values may depend on the source for the input signal. Hence, it becomes possible to adapt the method more closely to the characteristics of the signal source. The attenuation factor may be time dependent. The attenuation factor may depend directly on the time, and/or the attenuation factor may depend on quantities which are time dependent. The attenuation factor may also be dependent on the input power estimate. Changes of the attenuation factor caused by changes of the indicator value may decrease with increasing input power estimate. With the help of the indicator value, the attenuation factor g (n) may be: g NS ( n ) = max { g NS , min , min { g NS , max , 1 - x gate ( n ) x p ( n ) } } . ( 5 ) ##EQU00005## From equation (5), it can be seen that the behavior of the attenuation factor is similar to that of the indicator value, but with an inverted trend. If a wanted signal component is present in the input signal, then the indicator value falls to low values while the input power estimate increases, and the term 1 - x gate ( n ) x p ( n ) gets ##EQU00006## close to 1 with the consequence that { g NS , max , 1 - x gate ( n ) x p ( n ) } ##EQU00007## and hence , the attenuation factor get to the upper limit of g ,max, if the limits g are chosen correspondingly. In the absence of a wanted signal component in the input signal, the term 1 - x gate ( n ) x p ( n ) ##EQU00008## will be close to zero and thus , the attenuation factor tends towards the lower limit of g ,min. In addition, it can be seen that when the input power estimate x (n) is small, changes of the indicator value x (n) have a stronger effect on the attenuation factor g (n). At times where the input power estimate is high in comparison to the indicator value, changes of the indicator value cause small changes of the attenuation factor. In other words, changes in the indicator value have a stronger effect on the attenuation factor at times with low input power estimate. The attenuation factor described by equation (5) is well suited for attenuating noise at times where there is only a weak input signal or no input signal at all. In the method of FIG. 7 , the noise attenuation system may determine a quotient of the indicator value and the input signal estimate at act 702. For example, the system may divide the indicator value by the input power estimate to obtain the quotient. At act 704, the noise attenuation system may subtract the quotient from 1 to obtain an attenuation factor candidate. At act 706, the system compares the attenuation factor candidate to an attenuation factor maximum. If the attenuation factor candidate is above the maximum, then the system uses the attenuation factor maximum as the attenuation factor at act 708. If the attenuation factor candidate is below the maximum, then act 706 proceeds to act 710. At act 710, the system compares the attenuation factor candidate to an attenuation factor minimum. If the attenuation factor candidate is above the minimum, then the system uses the attenuation factor candidate as the attenuation factor at act 712. If the attenuation factor candidate is below the minimum, then the system uses the attenuation factor minimum as the attenuation factor at act 714. Having determined the attenuation factor, the input signal may be attenuated by using the attenuation factor. The input signal may be attenuated by multiplying the k-th sample value x(k) with the attenuation factor which may be derived from the data block n to which the data sample belongs. In this way, an output signal sample value y(k) is obtained as: ( k ) = g NS ( k N block ) x ( k ) . ( 6 ) ##EQU00009## In equation (6), the operator .left brkt-top. .right brkt-bot. denotes the next integer number greater or equal to its argument. In this way, the attenuation factor may be applied to the samples of the input signal using the original rate of samples, even if the attenuation factor is derived from blocks of samples of the size N The effect of the attenuation factor g on the input signal x(k) is similar to a scalar version of a Wiener filter. So, in another implementation, squared values may be used in the attenuation factor, such that g (n) comprises the quotient x gate ( n ) 2 x p ( n ) 2 or x gate 2 ( n ) x p 2 ( n ) . ##EQU00010## However, the attenuation factor according to equation (6) provides a more gentle suppression characteristic. FIGS. 8 and 9 illustrate one implementation of the behavior of an input signal, an input power estimate, a noise power value, an indicator value, an attenuation factor, and an output signal plotted over time during a noise attenuation process. In FIG. 9a, the amplitude of an input signal is shown. Four intervals of speech are recorded, and the level of remote noise has been set to zeroes until about 14.5 seconds. The noise level increases to about -47 db in a time interval between about 14.5 and 24 seconds. The solid line in FIGS. 8 and 9b shows the input power estimate according to equation (2). The dashed line represents the noise power value determined according to equation (3). It can be seen that the noise power value approximates a lower limit of the input power estimate. At a time of about 17.5 seconds, one can observe that the rate with which the noise power value is increased switches from the smaller κ.sub.inc,s to the larger k.sub.inc,f and thus leads to a much steeper incline which continues until a time is reached where the noise power value becomes larger than the input power FIG. 9c shows the progress of the indicator value according to equation (4) as derived from the values for the input power estimate and the noise power value illustrated in FIG. 9b. It can be seen that the indicator value is at or near its upper limit x ,max over periods where no speech component is present in the input signal or where the power estimate for the input signal is clearly above the noise power value. At times where the input power estimate for the input signal is close to the noise power value or is even below it, the indicator value quickly falls to its lower limit of x ,min. The indicator value, multiplied by 20, is also depicted as a dashed line in FIG. 9a, showing that it has a high value during periods where the input signal has a low amplitude. FIG. 9d illustrates the progress of the attenuation factor as described by equation (5). Over periods where the input power estimate is low, the attenuation factor behaves about inversely to the indicator value, e.g., it rises when the indicator value falls, and it falls when the indicator value rises, and it is at a high value when the indicator value is at a low value, and vice versa. Most of time, the attenuation factor is either at its lower limit g ,min or at its upper limit g However, at the times where the input power estimate is at a high level over an extended period of time, there is a time interval where the indicator value changes to high values, but the attenuation factor does not react to the change by a corresponding decline. This behavior is due to the fact that, according to the presence of x (n) in the nominator of the expression for g (n) in equation (5), changes in the indicator value have a smaller effect when the value of x (n) is high. Hence, the implementation illustrated in FIG. 9 is adapted to attenuating noise where the input power estimate is low. Such a situation may be present if noise is attenuated during pauses of a speech signal. This may happen if the input signal is the speech of a speaker over a telephone line, where the noise of the telephone system is attenuated during speech pauses. Another situation to which the noise attenuation system may be applied is attenuating noise in the reproduction of sound by a high quality amplifier, such as the amplifier of a car stereo system. In this case, noise may be mainly attenuated during passages with low sound level or between two pieces of music. In FIG. 9e, the output signal corresponding to the input signal of FIG. 9a and generated by the noise attenuation system discussed above is shown. It can be seen that the noise has been dampened or removed from the speech pauses in the periods where the signal level has been low, e.g., in about the first 14 seconds and at times later than about 24 seconds. Each of the processes described may be encoded in a computer-readable medium such as a memory, programmed within a device such as one or more circuits, one or more processors or may be processed by a controller or a computer. If the processes are performed by software, the software may reside in a memory resident to or interfaced to a storage device, a communication interface, or non-volatile or volatile memory in communication with a transmitter. The memory may include an ordered listing of executable instructions for implementing logic. Logic or any system element described may be implemented through optic circuitry, digital circuitry, through source code, through analog circuitry, or through an analog source, such as through an electrical, audio, or video signal. The software may be embodied in any computer-readable or signal-bearing medium, for use by, or in connection with an instruction executable system, apparatus, or device. Such a system may include a computer-based system, a processor-containing system, or another system that may selectively fetch instructions from an instruction executable system, apparatus, or device that may also execute instructions. A "computer-readable storage medium," "machine-readable medium," "propagated-signal" medium, and/or "signal-bearing medium" may comprise a medium (e.g., a non-transitory medium) that stores, communicates, propagates, or transports software or data for use by or in connection with an instruction executable system, apparatus, or device. The machine-readable medium may selectively be, but not limited to, an electronic, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, device, or propagation medium. A non-exhaustive list of examples of a machine-readable medium would include: an electrical connection having one or more wires, a portable magnetic or optical disk, a volatile memory, such as a Random Access Memory (RAM), a Read-Only Memory (ROM), an Erasable Programmable Read-Only Memory (EPROM or Flash memory), or an optical fiber. A machine-readable medium may also include a tangible medium, as the software may be electronically stored as an image or in another format (e.g., through an optical scan), then compiled, and/or interpreted or otherwise processed. The processed medium may then be stored in a computer and/or machine memory. While various embodiments of the invention have been described, it will be apparent to those of ordinary skill in the art that many more embodiments and implementations are possible within the scope of the invention. Accordingly, the invention is not to be restricted except in light of the attached claims and their equivalents. Patent applications by Bernd Iser, Ulm DE Patent applications by Gerhard Schmidt, Ulm DE Patent applications by Harman Becker Automotive Systems GmbH Patent applications in class Spectral adjustment Patent applications in all subclasses Spectral adjustment User Contributions: Comment about this patent or add new information about this topic:	{"url":"http://www.faqs.org/patents/app/20100239104","timestamp":"2014-04-25T06:20:51Z","content_type":null,"content_length":"85403","record_id":"<urn:uuid:0005378f-5394-496b-99be-34044a32eb2a>","cc-path":"CC-MAIN-2014-15/segments/1398223210034.18/warc/CC-MAIN-20140423032010-00514-ip-10-147-4-33.ec2.internal.warc.gz"}
Summary: I/O-efficient Point Location using Persistent B-Trees Lars Arge, Andrew Danner, and Sha-Mayn Teh Department of Computer Science, Duke University We present an external planar point location data structure that is I/O-efficient both in theory and practice. The developed structure uses linear space and answers a query in optimal O(logB N) I/Os, where B is the disk block size. It is based on a persistent B-tree, and all previously developed such structures assume a total order on the elements in the structure. As a theoretical result of independent interest, we show how to remove this assumption. Most previous theoretical I/O-efficient planar point location structures are relatively compli- cated and have not been implemented. Based on a bucket approach, Vahrenhold and Hinrichs therefore developed a simple and practical, but theoretically non-optimal, heuristic structure. We present an extensive experimental evaluation that shows that, on a range of real-world Geographic Information Systems (GIS) data, our structure uses fewer I/Os than the structure of Vahrenhold and Hinrichs to answer a query. On a synthetically generated worst-case dataset, our structure uses significantly fewer I/Os. The planar point location problem is the problem of storing a planar subdivision defined by N line segments such that the region containing a query point p can be computed efficiently. Planar point location has many applications in, e.g., Ge-	{"url":"http://www.osti.gov/eprints/topicpages/documents/record/914/1453063.html","timestamp":"2014-04-19T12:49:15Z","content_type":null,"content_length":"8592","record_id":"<urn:uuid:8affe6b6-3e10-406d-ab4f-68bd4f08777d>","cc-path":"CC-MAIN-2014-15/segments/1398223204388.12/warc/CC-MAIN-20140423032004-00103-ip-10-147-4-33.ec2.internal.warc.gz"}
[SOLVED] Re-writing ODE August 7th 2009, 11:41 PM #1 Junior Member Feb 2006 Victoria, Australia [SOLVED] Re-writing ODE im stuck on a problem. Show that the ODE $dy/dx=\frac{2x+e^y}{1+x^2}<br />$, can be written in the form $(1+2xe^{-y})dx-(1+x^2)e^{-y}dy=0$ Im stuck and i cant figure out what to do or what method to use. A nudge in the right direction would be good EDIT: sorry about that, i fixed it up. Sorry fixed the typo.. :S Last edited by sterps; August 7th 2009 at 11:54 PM. Please put parenthesis... Is it $\frac{2x+e^y}{1+x}$ ? Is it $2x+\frac{e^y}{1+x}$ ? In either case are you sure there's not a typo somewhere ? Because I really can't see where 1+x² comes from :s That's better $\frac{dy}{dx}=\frac{2x+e^y}{1+x^2} \Rightarrow (1+x^2) dy=(2x+e^y) dx$ Do you agree ? (that's just cross multiplying) Then you may ask... "How did they get there ?" Notice that there are $e^{-y}$ and where there was $e^y$, there's 1. So what you have to think is "I may have to divide the whole equation by $e^y$" See what this gives : $\frac{1+x^2}{e^y} \cdot dy=\frac{2x+e^y}{e^y} \cdot dx$ (1/e^y = e^(-y)) $e^{-y} (1+x^2) dy=(2xe^{-y}+1) dx$ Looks better to you ? wow thanks a tonne! yea i did the whole cross multiplying thing already, i just got confused when i saw ${e^-y}$ and that 1. thanks for that ill take it from there, ill let you know how i go! yea thats the nudge i needed. thanks again, i didnt have to really do anything after that, aside from from minus one side to the other. thanks again! August 7th 2009, 11:49 PM #2 August 8th 2009, 12:04 AM #3 Junior Member Feb 2006 Victoria, Australia August 8th 2009, 12:14 AM #4 August 8th 2009, 12:21 AM #5 Junior Member Feb 2006 Victoria, Australia August 8th 2009, 12:31 AM #6 Junior Member Feb 2006 Victoria, Australia	{"url":"http://mathhelpforum.com/differential-equations/97326-solved-re-writing-ode.html","timestamp":"2014-04-18T08:52:35Z","content_type":null,"content_length":"46277","record_id":"<urn:uuid:e293131b-f2a5-4742-8d74-c428502d182d>","cc-path":"CC-MAIN-2014-15/segments/1397609533121.28/warc/CC-MAIN-20140416005213-00517-ip-10-147-4-33.ec2.internal.warc.gz"}
Algebra Archive \| June 27, 2008 \| Chegg.com i need help with these problem rewrite as a single expression: csc x - cos x cot x i have: (1/sin x) - (cos x/1)(cos x/sin x) so then i combine so i have (1 - cos ^2 x)/ sin x but it doesn't apply to any pythagoream identities. and it doesn't suit the answer options.. Perform addition. Simplify the result using fundamentalidentities: Perform addition. Simplify the result using fundamentalidentities: Rewrite so it's not a fraction: 9. rewrite so it's not a fraction 1. simplify to basic trig function: • Show less	{"url":"http://www.chegg.com/homework-help/questions-and-answers/algebra-archive-2008-june-27","timestamp":"2014-04-18T13:24:40Z","content_type":null,"content_length":"34289","record_id":"<urn:uuid:6c7cace8-b963-4973-a1b1-9c6007258038>","cc-path":"CC-MAIN-2014-15/segments/1397609533689.29/warc/CC-MAIN-20140416005213-00638-ip-10-147-4-33.ec2.internal.warc.gz"}
Northern California, CA Palo Alto, CA 94301 Experienced, credentialed math tutor (Stanford/M.I.T. grad) ...Please do make sure that you are either within my 10 mile travel radius or are willing to work with me online. I have loved tutoring/teaching math (pre-algebra, algebra 1 , geometry, algebra 2, precalculus, calculus) for over 17 years. I am a credentialed classroom... Offering 10 subjects including algebra 1	{"url":"http://www.wyzant.com/Northern_California_algebra_1_tutors.aspx","timestamp":"2014-04-20T21:23:06Z","content_type":null,"content_length":"57623","record_id":"<urn:uuid:707b3379-f97a-43b3-b859-85677efe89de>","cc-path":"CC-MAIN-2014-15/segments/1397609539230.18/warc/CC-MAIN-20140416005219-00013-ip-10-147-4-33.ec2.internal.warc.gz"}
Zone of instability May 26, 2010 By Matt Asher I woke up from my afternoon nap feeling a bit off-kilter, so I decided to go for another random walk. In particular, I wanted a journey that avoided the center, but didn’t just run for an exit either. After playing around for a while I came up with this: # Take a wacky walk, return the final "track" steps wackyWalk <- function(iters, track=iters) { locations = c() mean2use = 0 sd2use = 1 for (i in 1:iters) { mean2use = rnorm(1,mean2use,sd2use) # The farther from the center, the smaller the variance sd2use = abs(1/mean2use) if(track > (iters - i) ) { locations = c(locations, mean2use) # How many steps to take iters = 300 track = 300 locations = wackyWalk(iters,track) # Start us off with a plot for (i in 1:track) { # To create a pseudo animation, take a break between plotting points Basically, during each iteration the program samples from a normal distribution centered at the same location as the previous iteration, with standard deviation equal to the inverse of the previous location. So if the sequence is at 5, the next number will be sampled from the $Normal(5, (frac{1}5)^2)$ distribution. Run it a few times and you’ll see how the blue dot bounces around for a bit near 0, then shoots off to one side or the other, where it will most likely hang out for the rest of its life. There are a number of interesting questions about this sequence which, sadly, will remain unanswered. Among these are: For a given number of iterations, how many times is this sequence expected to cross zero? What is the maximum (or minimum) value the sequence is expected to obtain over a fixed number of iterations? Will the sequence ever diverge to some flavor of infinity? My hunch for this last question is to say no, since the normal distribution is thin-tailed, and the standard deviation is set to converge to 0 (slowly) as the value of the sequence gets larger and larger. At the same time, I suspect that the higher the number of iterations, the larger (in absolute terms) the final number in the sequence. This makes general sense, as the farther you get from 0, the harder it is to return to 0. During testing, I saw a lot of plots that wiggled back and forth, getting closer to the edges of the plot with each wiggle. Since I’m never content to just have a thought without actually testing it out, I plotted the final value in the sequence after $2^x$ iterations, where x went from 1 to 20. Here’s the result: Sure enough, as a general trend, the more iterations you run, the farther you are from zero. It would have been interesting to see how the 8th trial ended up north of 300, but I only tracked the final result for these. I suspect that it made up most of the ground in a single leap while sampling from a Normal with extremely high variance (ie when the previous number was very close to 0). Here’s the extra bit of code for comparing final location to number of iterations: # How does the number of steps compare with distance from center meta = c() for (j in 1:20) { iters = 2^j track = 1 meta = c(meta, wackyWalk(iters,track)) plot(1:20, abs(meta), pch=20, col="blue",xlab="2^x",ylab="abs value of final number in sequence") These results, I should note, provide very little evidence that the sequence, if extended out to infinite length, will have to converge or diverge. Weird things happen when you start to consider random walks of infinite length, and the one sure limitation of Monte Carlo testing is that no matter how long let a computer simulation run, your PC will crash well before it performs an infinite number of calculations, and most likely before you finish your coffee. daily e-mail updates news and on topics such as: visualization ( ), programming ( Web Scraping ) statistics ( time series ) and more... If you got this far, why not subscribe for updates from the site? Choose your flavor: , or	{"url":"http://www.r-bloggers.com/zone-of-instability/","timestamp":"2014-04-16T19:17:40Z","content_type":null,"content_length":"45318","record_id":"<urn:uuid:af146e86-c2b4-4e52-bbad-6e0af84b392d>","cc-path":"CC-MAIN-2014-15/segments/1397609524644.38/warc/CC-MAIN-20140416005204-00384-ip-10-147-4-33.ec2.internal.warc.gz"}
Java BigInteger prime numbers up vote 8 down vote favorite I a m trying to generate a random prime number of type BigInteger, that is between an min and max value which I supply. I am aware of the BigInteger.probablePrime(int bitlength, random), but I am not sure how or even if the bitlength translates into a max/min value of the outputted prime. Thanks, Steven1350 java primes biginteger add comment 2 Answers active oldest votes BigInteger.probablePrime(bitLength, random) is going to return a (probable) prime of the specified bit length. That translates into a maximum value of 2^bitlength - 1 and a minimum of 2^(bitlength - 1). As much as I hate it as an answer, it's probably your best bet unless you want to start delving into number theory. up vote 2 down vote accepted What you would have to do is figure out the bit lengths that your range calls for, then pass them to probablePrime() until you get back a prime that's in the right range. Interesting. From the Doc, "the probability that the returned BI is composite is < 2^-100", pretty unlikely indeed! Would you know by chance the complexity of this method? – ring0 Feb 18 '11 at 17:20 Instead of invoking probalePrime with a bitlength the range calls for one could create a random big integer in the range and invoke nextProbablePrime on it. This will generate the prime number faster as invoking problePrime multiple times. Of cours you will have to tackle the situation where the reult is bigger than the max value of your range. – Markus Kreusch Sep 22 '12 at 11:03 add comment jprete's answer is fine if your ratio max/min is not close to 1. If you have a narrow range, your best bet is probably just to do something like the following: // this is pseudocode: // round min down to multiple of 6, max up to multiple of 6 min6 = floor(min/6); max6 = ceil(max/6); maybePrimeModuli = [1,5]; b = generateRandom(maybePrimeModuli.length); // generate a random offset modulo 6 which could be prime x = 6(min6 + generateRandom(max6-min6)) + b; // generate a random number which is congruent to b modulo 6 up vote 3 // from 6min6 to 6*max6-1 down vote // (of the form 6k+1 or 6k+5) // the other choices 6k, 6k+2, 6k+3, 6k+4 are composite } while not isProbablePrime(x); The density of primes is fairly high overall, it's basically 1 in log(x), so you shouldn't have to repeat too many times to find a prime number. (just as an example: for numbers around 10 ^23, one in every 52 integers on average is a prime number. The above code only bothers with 2 out of every 6 numbers, so you'd end up looping an average of 17 times for numbers around 10 Just make sure you have a good primality test, and the Java BigInteger has one. As an exercise for the reader, extend the above function so it filters out more composite numbers ahead of time by using 30k + x (modulo 30, there are 22 moduli that are always composite, only 8 remaining that could be prime), or 210k + x. edit: see also US patent #7149763 (OMFG!!!) 1 Do you need to add min2 to x? – jprete Nov 26 '09 at 2:07 thanks, i forgot about that – Jason S Nov 26 '09 at 2:15 Er...you probably want to flip the while-loop termination too...missed that one before. Other than that I think you're clear. – jprete Nov 26 '09 at 2:31 doh, i'm having a bad day :-) – Jason S Nov 26 '09 at 2:35 the math is willing, but the fleshing out is weak – Jason S Nov 26 '09 at 2:37 add comment Not the answer you're looking for? Browse other questions tagged java primes biginteger or ask your own question.	{"url":"http://stackoverflow.com/questions/1801003/java-biginteger-prime-numbers","timestamp":"2014-04-20T17:00:49Z","content_type":null,"content_length":"76834","record_id":"<urn:uuid:3c91be63-019d-4de8-bd2e-ee649412cc31>","cc-path":"CC-MAIN-2014-15/segments/1397609538824.34/warc/CC-MAIN-20140416005218-00543-ip-10-147-4-33.ec2.internal.warc.gz"}
Truncated Cube JGV Example: A Truncated Cube The JGV instance above shows a truncated cube. The eight white faces are equilateral triangles; the other six faces are regular octagons. Click here to see where the corners of the original cube were removed. I made this page by substituting my own data in a Geometry Center webpage. Prof. Joel Roberts School of Mathematics University of Minnesota Minneapolis, MN 55455 Office: 351 Vincent Hall Phone: (612) 625-1076 Dept. FAX: (612) 626-2017 e-mail: roberts@math.umn.edu TT>	{"url":"http://www.math.umn.edu/~roberts/java.dir/JGV/trunc_cube1.html","timestamp":"2014-04-20T05:42:46Z","content_type":null,"content_length":"7800","record_id":"<urn:uuid:d67a1318-fd48-4328-b213-57fd9f82e5f5>","cc-path":"CC-MAIN-2014-15/segments/1397609538022.19/warc/CC-MAIN-20140416005218-00255-ip-10-147-4-33.ec2.internal.warc.gz"}
Frederick, CO Math Tutor Find a Frederick, CO Math Tutor ...I taught the Biology section of the MCAT for a national test prep agency for over 1 year. I had 30+ hours of training to prepare me for my Biology MCAT classes. In order to teach for this agency I had to score at least a 13 on the Biology section, which I did. 26 Subjects: including precalculus, SAT math, ACT Math, trigonometry ...I have two years of experience tutoring general chemistry for majors and non-majors at DTCC and have worked as a general biology teaching assistant at CU Boulder that included tutoring hours, running review sessions, and in class assistance. I have conducted industrial pharmaceutical organic che... 39 Subjects: including algebra 2, public speaking, elementary (k-6th), elementary math ...I've worked with high school and college students, priding myself on being able to explain any concept to anyone. I worked as a tutor and instructional assistant at American River College in Sacramento, CA for 15 years. I also attended UC Berkeley as an Engineering major.I took this class at American River College in Sacramento, CA. 11 Subjects: including algebra 1, algebra 2, calculus, geometry ...Precalculus is the vital stepping stone toward beginning of understanding the work around us via trigonometry, geometry, and algebra. I have tutored high school students whilst a graduate student in preparation for calculus at college. I have many years of formal training (I have a PhD in experimental particle physics) and the years of experience as a teacher. 47 Subjects: including SAT math, discrete math, electrical engineering, MATLAB ...I believe that once a person that struggles with mathematics sees that in action, mathematics becomes much more manageable. I teach mathematics for understanding, so that the skills learned by doing mathematics translate into useful skills applicable to the real world. I have worked with studen... 13 Subjects: including geometry, prealgebra, trigonometry, statistics Related Frederick, CO Tutors Frederick, CO Accounting Tutors Frederick, CO ACT Tutors Frederick, CO Algebra Tutors Frederick, CO Algebra 2 Tutors Frederick, CO Calculus Tutors Frederick, CO Geometry Tutors Frederick, CO Math Tutors Frederick, CO Prealgebra Tutors Frederick, CO Precalculus Tutors Frederick, CO SAT Tutors Frederick, CO SAT Math Tutors Frederick, CO Science Tutors Frederick, CO Statistics Tutors Frederick, CO Trigonometry Tutors Nearby Cities With Math Tutor Brighton, CO Math Tutors Dacono Math Tutors East Lake, CO Math Tutors Eastlake, CO Math Tutors Erie, CO Math Tutors Evergreen, CO Math Tutors Firestone Math Tutors Fort Lupton Math Tutors Johnstown, CO Math Tutors Lafayette, CO Math Tutors Longmont Math Tutors Louisville, CO Math Tutors Mead, CO Math Tutors Platteville, CO Math Tutors Superior, CO Math Tutors	{"url":"http://www.purplemath.com/frederick_co_math_tutors.php","timestamp":"2014-04-16T10:37:33Z","content_type":null,"content_length":"24014","record_id":"<urn:uuid:b7ae9d25-7b74-4efb-af56-a35a6d45b603>","cc-path":"CC-MAIN-2014-15/segments/1397609523265.25/warc/CC-MAIN-20140416005203-00113-ip-10-147-4-33.ec2.internal.warc.gz"}
How do matrices work? As I said, one of the most common (and important) uses is that you can use matrixes to solve systems of lineair equations (by, for example, using gaussian elimination or Cramer's rule for square To fully understand minors/cofactors, you'll need to know what determinants are, do you?	{"url":"http://www.physicsforums.com/showthread.php?t=89926","timestamp":"2014-04-21T02:13:41Z","content_type":null,"content_length":"46348","record_id":"<urn:uuid:4f67f8ca-27bb-469c-bc62-176eaf3301bd>","cc-path":"CC-MAIN-2014-15/segments/1397609539447.23/warc/CC-MAIN-20140416005219-00600-ip-10-147-4-33.ec2.internal.warc.gz"}
[Baypiggies] Baypiggies snippets Alex Martelli aleax at google.com Thu Mar 22 18:15:38 CET 2007 On 3/22/07, Stephen McInerney <spmcinerney at hotmail.com> wrote: > Monte, about this nested compare "a <= x <= b" > Q1: Since what version has it been in? I never knew about it! I was there in 1.5 when I got started with Python; I believe it's quite old. Q2: Can anyone comment on the efficiency of > "a <= x <= b" vs "x in xrange(a,b)" (obviously the latter is worse, and > only > good for integer a,b) > In particular, is Python smart enough to binary-search the xrange object? > Just curious. Type 'xrange' does not even define a __contains__ method. I wonder how a patch implementing one would be seen by python-dev; I'm pretty sure it would be rejected if it tried to use binary search, though (why take O(log N) time if you're going to the trouble of implementing __contains__ when it obviously can be done in O(1) time?). Q3: C++ people would balk at the idiom "a <= x <= b" > since it does not evaluate right-to-left. (The two <= subexpressions > cannot be separately evaluated from the other. So it has to be > parsed and evaluated all in one) ??? comparison chaining short-circuits, so OF COURSE a and b ARE "separately evaluated"! E.g: >>> 23 < 15 < (7/0) the 7/0 is NOT attempted (it would raise if it were) -- no need, because the 23 < 15 check has already failed. In C++, a && b && c would similarly be evaluated left-to-right, with short-circuiting, so I don't see what objections there could be. Short-circuiting operators (&& and \|\| in C and C++, and, or and comparison chaining in Python) always go left-to-right. Q4: are the idioms "a == x == b", "a != x != b" and "a is x is b" legal? Yep, chaining applies to all comparison operators, including ==, !=, is, and is not. -------------- next part -------------- An HTML attachment was scrubbed... URL: http://mail.python.org/pipermail/baypiggies/attachments/20070322/86f7bb1f/attachment.htm More information about the Baypiggies mailing list	{"url":"https://mail.python.org/pipermail/baypiggies/2007-March/002013.html","timestamp":"2014-04-18T01:52:23Z","content_type":null,"content_length":"4858","record_id":"<urn:uuid:36624b1d-3850-4675-8fe0-131df2dac5b9>","cc-path":"CC-MAIN-2014-15/segments/1397609532374.24/warc/CC-MAIN-20140416005212-00630-ip-10-147-4-33.ec2.internal.warc.gz"}
Irregularity Strength of Regular Graphs Let $G$ be a simple graph with no isolated edges and at most one isolated vertex. For a positive integer $w$, a $w$-weighting of $G$ is a map $f:E(G)\rightarrow \{1,2,\ldots,w\}$. An irregularity strength of $G$, $s(G)$, is the smallest $w$ such that there is a $w$-weighting of $G$ for which $\sum_{e:u\in e}f(e)\neq\sum_{e:v\in e}f(e)$ for all pairs of different vertices $u,v\in V(G)$. A conjecture by Faudree and Lehel says that there is a constant $c$ such that $s(G)\le{n\over d}+c$ for each $d$-regular graph $G$, $d\ge 2$. We show that $s(G) < 16{n\over d}+6$. Consequently, we improve the results by Frieze, Gould, Karoński and Pfender (in some cases by a $\log n$ factor) in this area, as well as the recent result by Cuckler and Lazebnik. Full Text:	{"url":"http://www.combinatorics.org/ojs/index.php/eljc/article/view/v15i1r82","timestamp":"2014-04-20T01:06:13Z","content_type":null,"content_length":"14623","record_id":"<urn:uuid:41ccf006-52d3-49bc-82dd-908da924664e>","cc-path":"CC-MAIN-2014-15/segments/1397609537804.4/warc/CC-MAIN-20140416005217-00626-ip-10-147-4-33.ec2.internal.warc.gz"}
"Transient" of the discrete-time Riccati equation up vote 3 down vote favorite It is a well-known result that, if the pair $(A,Q^{1/2})$ is stabilizable and the pair $(A, C)$ is detectable, the solution to the discrete-time Riccati recursion $P(t+1) = A P(t) A^T - A P(t) C^T\ (CP(t)C^T + R)^{-1}\ CP(t) A^T + Q$ converges to the unique stabilizing solution of the Algebraic Riccati Equation $P = A P A^T - A P C^T(CPC^T + R)^{-1}CP A^T + Q$ from any initial positive semidefinite matrix $P(0)=P_0$. Do you know any result on the behavior of $P(t)$ during the transient, or more generally for all $t \geq 0$? More precisely, I need some result that ensures that $P(t)$ is stabilizing for all $t \geq 0$, under fair conditions on $A$, $C$, $Q$, $R$, and for arbitrary $P_0$. Thank you very much in advance, EDIT. Some background: We consider a discrete-time, linear, time invariant system of the form $x(t+1) = Ax(t) + v(t)$ $y(t) = Cx(t) + w(t)$ where $x(t) \in R^n$, $A\in R^{n\times n}$, $y(t)\in R^p$, $C\in R^{p\times n}$, and $v$ and $w$ are zero-mean, uncorrelated white noises (say, Gaussian) with appropriate dimensions, with variances $Q$ and $R$ respectively. The predictor $\hat{x}(t+1\|t)$, that is, the best linear estimator of $x(t+1)$ given $y(0), \cdots, y(t)$, is given by the Kalman filter. It can be expressed recursively substituting the equations of the Kalman filter into each other. The variance $P(t+1)$ of the corresponding prediction error $\tilde{x}(t+1\|t) = \hat{x}(t+1\|t)-x(t+1)$ is then given (recursively) by the Riccati equation. The "dual" of the linear estimation problem above is the "linear quadratic regulator" problem of optimal control, and the Riccati equation is fundamental also in this context. Given matrices $A\in R^{n\times n}$ and $B \in R^{n\times m}$ with $m\leq n$, to say that the pair $(A, B)$ is reachable means that the matrix $[B\ AB\ \cdots\ A^{n-1}B]$ has full rank ($=n$). The pair $(A, B)$ is stabilizable if with a suitable "change of base" $(A,B)\mapsto(T^{-1} A T, T^{-1}B)$ it can be put in the form $\left(\left[\begin{matrix} A_{11} & A_{12} \\\\ 0 & A_{22} \\\\ \end{matrix}\right], \left[\begin{matrix} B_1 \\\\ 0 \\\\ \end{matrix}\right]\right)$ where $(A_{11}, B_1)$ is reachable and $A_{22}$ is Hurwitz (all eigenvalues in the interior of the unit disk). Dually, given matrices $A\in R^{n\times n}$ and $C \in R^{p\times n}$ with $p\leq n$, to say that the pair $(A, C)$ is observable means that the matrix $\left[\begin{matrix} C \\\\ CA \\\\ \vdots \\\\ CA^{n-1} \end{matrix}\right]$ has full rank. The pair $(A, C)$ is detectable if with a suitable "change of base" $(A,C)\mapsto(T^{-1} A T, CT)$ it can be put in the form $\left(\left[\begin{matrix} A_{11} & 0 \\\\ A_{21} & A_{22} \\\\ \end{matrix}\right], \left[\begin{matrix} C_1 & 0 \end{matrix}\right]\right)$ where $(A_{11}, C_1)$ is observable and $A_{22}$ is Hurwitz. Finally, the matrix $P=P^T\geq 0$ is stabilizing if the "closed loop" matrix $A - KC$ is Hurwitz, where $K = A P C^T(CPC^T + R)^{-1}$. For more details, see for example the Wikipedia pages on Kalman filter, controllability, observability, and Kalman decomposition. For a full reference, see e.g. A. H. Jazwinski, Stochastic Processes and Filtering Theory. linear-algebra oc.optimization-control 2 Federico -- you'll need to add some more background, I think. You don't seem to have said what sort of objects A, Q and C are, although perhaps to an expert it's obvious from "stabilizable" and "detectable". – Scott Morrison♦ Dec 11 '09 at 21:20 add comment 1 Answer active oldest votes The following paper: up vote 1 provides a geometric positive answer to your question. (The paper discusses the private case where the measurement noise is of unit variance, but this isn't really a shortcoming, because down vote the covariance matrix of the measurement noise can be diagonalized and then all the measurement equation scaled). The answer is based on the fact that geometrically the time evolution of the Riccati equation is a flow on a Grassmann manifold. In the paper, it is proved that this flow preserves the positivity and of P, and that the time evolution matrix of the estimated state vector X is decaying. add comment Not the answer you're looking for? Browse other questions tagged linear-algebra oc.optimization-control or ask your own question.	{"url":"http://mathoverflow.net/questions/8557/transient-of-the-discrete-time-riccati-equation","timestamp":"2014-04-20T16:14:05Z","content_type":null,"content_length":"54876","record_id":"<urn:uuid:563287c3-c3c7-4af9-955a-4b1f91afd27d>","cc-path":"CC-MAIN-2014-15/segments/1397609538824.34/warc/CC-MAIN-20140416005218-00356-ip-10-147-4-33.ec2.internal.warc.gz"}
Got Homework? Connect with other students for help. It's a free community. • across MIT Grad Student Online now • laura* Helped 1,000 students Online now • Hero College Math Guru Online now Here's the question you clicked on: The base of a cone has a radius of 6 cm. The height of the cone is 15 cm. What is the slant height of the cone? A. 4.58 B. 16.16 C. 19.21 D. 5.26 • one year ago • one year ago Your question is ready. Sign up for free to start getting answers. is replying to Can someone tell me what button the professor is hitting... • Teamwork 19 Teammate • Problem Solving 19 Hero • Engagement 19 Mad Hatter • You have blocked this person. • ✔ You're a fan Checking fan status... Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy. This is the testimonial you wrote. You haven't written a testimonial for Owlfred.	{"url":"http://openstudy.com/updates/509acd6de4b085b3a90e346e","timestamp":"2014-04-20T13:43:21Z","content_type":null,"content_length":"37272","record_id":"<urn:uuid:cbd8a7f8-8d0a-4630-8973-a1e347ed491a>","cc-path":"CC-MAIN-2014-15/segments/1398223206647.11/warc/CC-MAIN-20140423032006-00149-ip-10-147-4-33.ec2.internal.warc.gz"}
62 CHAPTER 4 Did We Meet or Exceed Our Goal? To run the statistical test using a confidence interval, set the confidence to 80% for a one-sided alpha of 0.1. The critical value of t for 80% confidence and 5 degrees of freedom is 1.476. The stan- dard error of the mean, as shown in the previous equation, is 0.111. The critical difference for the confidence interval, therefore, is 1.476 (0.111), or about 0.164, so the confidence interval of the log values ranges from 0.861 to 1.189. Using the EXP function to convert these natural log values back to times in minutes, the confidence interval ranges from 2.4 to 3.3 minutes. The upper bound of the confidence limit exceeds the criterion of 3 minutes, so the results do not support the claim that most callers would complete the task in less than 3 minutes. The confidence interval does suggest that, given the data in hand, most callers would complete the task in less than 3.5 minutes. References Agresti, A., Franklin, C.A., 2007. Statistics: The Art and Science of Learning from Data. Pearson, New York. Armitage, P., Berry, G., Matthews, J.N.S., 2002. Statistical Methods in Medical Research, 4th ed. Blackwell Science, Oxford, UK. Bangor, A., Kortum, P.T., Miller, J.T., 2008. An empirical evaluation of the system usability scale. Int. J. Hum. Comput. Interact. 6, 574594. Chapanis, A., 1988. Some generalizations about generalization. Hum. Fact. 30, 253267.	{"url":"http://my.safaribooksonline.com/book/-/9780123849687/4-did-we-meet-or-exceed-our-goal/62","timestamp":"2014-04-20T04:51:30Z","content_type":null,"content_length":"70431","record_id":"<urn:uuid:835b6bd0-e223-4702-8d0a-25706ab1b55f>","cc-path":"CC-MAIN-2014-15/segments/1397609537864.21/warc/CC-MAIN-20140416005217-00039-ip-10-147-4-33.ec2.internal.warc.gz"}
Geometry and the imagination You are currently browsing the tag archive for the ‘amenability’ tag. Geometric group theory is not a coherent and unified field of enquiry so much as a collection of overlapping methods, examples, and contexts. The most important examples of groups are those that arise in nature: free groups and fundamental groups of surfaces, the automorphism groups of the same, lattices, Coxeter and Artin groups, and so on; whereas the most important properties of groups are those that lend themselves to applications or can be used in certain proof templates: linearity, hyperbolicity, orderability, property (T), coherence, amenability, etc. It is natural to confront examples arising in one context with properties that arise in the other, and this is the source of a wealth of (usually very difficult) problems; e.g. do mapping class groups have property (T)? (no, by Andersen) or: is every lattice in $\text{PSL}(2,\mathbb{C})$ virtually orderable? As remarked above, it is natural to formulate these questions, but not necessarily productive. Gromov, in his essay Spaces and Questions remarks that often the mirage of naturality lures us into featureless desert with no clear perspective where the solution, even if found, does not quench our thirst for structural mathematics . . . Another approach . . . has a better chance for a successful outcome with questions following (rather than preceding) construction of new objects. A famous question of the kind Gromov warns against is the following: Question: Is Thompson’s group $F$ amenable? Recall that Thompson’s group is the group of (orientation-preserving) PL homeomorphisms of the unit interval with breakpoints at dyadic rationals (i.e. rational numbers of the form $p/2^q$ for integers $p,q$) and derivatives all powers of $2$. This group is a rich source of examples/counterexamples in geometric group theory: it is finitely presented (in fact $FP_\infty$) but “looks like” a transformation group; it contains no nonabelian free group (by Brin-Squier), but obeys no law. It is not elementary amenable (i.e. it cannot be built up from finite or abelian groups by elementary operations — subgroups, quotients, extensions, directed unions), so it is “natural” to wonder whether it is amenable at all, or whether it is one of the rare examples of nonamenable groups without nonabelian free subgroups (see this post for a discussion of amenability versus the existence of free subgroups, and von Neumann’s conjecture). This question has attracted a great deal of attention, possibly because of its long historical pedigree, rather than because of the potential applications of a positive (or negative) answer. Recently, two papers were posted on the arXiv, promising competing resolutions of the question. In February, Azer Akhmedov posted a preprint claiming to show that the group $F$ is not amenable. This preprint was revised, withdrawn, then revised again, and as of the end of April, Akhmedov continues to press his claim. Akhmedov’s argument depends on a new geometric criterion for nonamenability, roughly speaking, the existence of a $2$-generator subgroup and a subadditive non-negative function on the group whose values grow at a definite rate on words in the subgroup whose exponents satisfy suitable parity conditions and inequalities. The non-negative function (Akhmedov calls it a “height function”) certifies the existence of a sufficiently “bushy” subset of the group to violate Folner’s criterion for amenability. Akhmedov’s paper reads like a “conventional” paper in geometric group theory, using methods from coarse geometry, careful combinatorial and counting arguments to establish the existence of a geometric object with certain large-scale properties, and an appeal to a standard geometric criterion to obtain the desired result. Akhmedov’s paper is part of a series, relating (non)amenability to certain other interesting geometric properties, some related to the so-called “traveling salesman” property, introduced earlier by Akhmedov. On the other hand, in May, E. Shavgulidze posted a preprint claiming to show that the group $F$ is amenable. Interestingly enough, Shavgulidze’s argument does not apply to the slightly more general class of Stein-Thompson groups in which slopes and denominators of break points can be divisible by an arbitrary (but prescribed) finite set of prime numbers. Moreover, his methods are very unlike any that one would expect to find in the typical geometric group theory paper. The argument depends on the construction, going back (in some sense) to a paper of Shavgulidze from 1978, of a measure on the space $C(I)$ of continuous functions on the interval which is quasi-invariant under the natural action of the group of diffeomorphisms of the interval of regularity at least $C^3$. In more detail, let $D^n$ denote the group of diffeomorphisms of the interval of regularity at least $C^n$ for each $n$, and let $C$ denote the Banach space of continuous functions on the interval that vanish at the origin. Define $A:D^1 \to C$ by the formula $A(f)(t) = \log(f'(t)) - \log(f'(0))$. The space $C$ can be equipped with a natural measure — the Wiener measure $w_\sigma$ of variance $\ sigma$, and this measure can be pulled back to $D^1$ by $A$, which is thought of as a topological space with the $C^1$ topology. Shavgulidze shows that the left action of $D^3$ on $D^1$ quasi-preserves this measure. Here the Wiener measure on $C$ is the probability measure associated to Brownian motion (with given variance). A “sample” trajectory $W_t$ from $C$ is characterized by three properties: that it starts at the origin (i.e. $W_0=0$), that is it continuous almost surely (this is already implicit in the fact that the measure is supported on the space $C$ and not some more general space), and that increments are independent, with the distribution of $W_t - W_s$ equal to a Gaussian with mean zero and variance $(t-s)\sigma$. Shavgulidze’s argument depends first on an argument of Ghys-Sergiescu that shows Thompson’s group is conjugate (by a homeomorphism) to a discrete subgroup of the group of $C^\infty$ diffeomorphisms of the interval. A bounded function $f$ on $F$ determines a continuous bounded function $\pi_\delta(f)$ on $D^{1+\delta}$ (for $\delta<1/2$) by a certain convolution trick, using both the group structure of $F$, and its discreteness in $D^ 3$. Roughly, given an element $g \in D^{1+\delta}$, the set of elements of $F$ whose (group) composition with $g$ is uniformly bounded in the $C^{1+\delta}$ norm is finite; so the value of $\pi_\ delta(f)$ is obtained by taking a suitable average of the value of $f$ on this finite subset of $F$. This reduces the problem of the amenability of $F$ to the existence of a suitable functional on the space of bounded continuous functions on $D^{1+\delta}$, which is constructed via the pulled back Wiener measure as above. There are several distinctive features of Shavgulidze’s preprint. One of the most striking is that it depends on very delicate analytic features of the Wiener measure, and the way it transforms under the action of $D^3$ on $D^1$ — a transformation law involving the Schwartzian derivative — and suggesting that certain parts of the argument could be clarified (at least from the point of view of a topologist?) by using projective geometry and Sturm-Liouville theory. Another is that the crucial analytic quality — namely differentiability of class $C^{1+1/2}$ — is also crucial for many other natural problems in $1$-dimensional analysis and geometry, from regularity estimates in the thin obstacle problem, to Navas’ work on actions of property (T) groups on the circle. At least one of the preprints by Akhmedov and Shavgulidze must be in error (in fact, a real skeptic’s skeptic such as Michael Aschbacher is not even willing to concede that much . . .) but even if wrong, it is possible that they contain things more valuable than a resolution of the question that prompted them. Update (7/6): Azer Akhmedov sent me a construction of a (nonabelian) free subgroup of $D^1$ that is discrete in the $C^1$ topology. This is not quite enough regularity to intersect with Shavgulidze’s program, but it is interesting, and worth explaining. This is my (minor) modification of Azer’s construction (any errors are due to me): Proposition: The group $D^1$ contains a discrete nonabelian free subgroup. Sketch of Proof: First, decompose the interval $[0,1]$ into countably many disjoint subintervals accumulating only at the endpoints. Choose a free action on two generators by doing something generic on each subinterval, in such a way that the derivative is equal to $1$ at the endpoints. This can certainly be accomplished; for concreteness, choose the action so that for each subinterval $I_i$ there is a point $x_i$ in the interior of $I_i$ whose stabilizer is trivial. Second, for each pair of distinct words in the generators, choose a subinterval and modify the action there so that the derivatives of those words in that subinterval differ by at least some definite constant $C$ at some point. In more detail: enumerate the pairs of words somehow $p_1, p_2, p_3$ where each $p_i$ is a pair of words $(w_{i1}, w_{i2})$ in the generators, and modify the action on the subinterval $I_i$ so the words in $p_i$ differ by at least $C$ in the $C^1$ norm on the interval $I_i$. Since we are modifying the generators infinitely many times, but in such a way that the support of the modification exits any compact subset of the interior, we just need to check that the modifications are $C^1$. Since there are only finitely many pairs of words, both of which are of bounded length (for any given bound), when $i$ is sufficiently big, one of the words $w_{i1}$, $w_{i2}$ has length at least $n(i)$ where $n(i)$ goes to infinity as $i$ goes to infinity. Without loss of generality, we can order the pairs so that $w_{i1}$ is the “long” word. Now this is how we modify the action in $I_i$. Recall that the point $x_i$ has trivial stabilizer, so the translates $y_{ij}$ of $x_i$ under the suffixes of $w_{i1}$ are distinct. Take disjoint intervals about the $y_{ij}$ and observe that each $y_{ij}$ is taken to $y_{ij+1}$ by one of the generators. Modify this generator inside this disjoint neighborhood so that $y_{ij}$ is still taken to $y_{ij+1}$, but the derivative at that point is multiplied by $1+ C/n(i)$, and the derivative at nearby points is not multiplied by more than $1+C/n(i)$. Since the neighborhoods of the $y_{ij}$ are disjoint, these modifications are all compatible, and the derivative of the generators does not change by more than $1+C/n(i)$ at any point. Since $n(i)$ goes to infinity as $i$ goes to infinity, we can perform such modifications for each $i$, and the resulting action is still $C^1$. But now the derivative of $w_{i1}$ at $x_i$ has been multiplied by $1+C$, so $w_{i1}$ and $w_{i2}$ differ by at least $C$ in the $C^1$ norm. qed. It is interesting to observe that this construction, while $C^1$, is not $C^{1+\epsilon}$ for any $\epsilon>0$. For big $i$, we have $n(i) \sim \log(i)$ whereas $\|I_i\| = o(1/i)$. Introducing a “bump” which modifies the derivative by $1/\log(i)$ in a subinterval of size $o(1/i)$ will blow up every Holder norm. (Update 8/10): Mark Sapir has created a webpage to discuss Shavgulidze’s paper here. Also, Matt Brin has posted notes on Shavgulidze’s paper here. The notes are very nice, and go into great detail, as far as they go. Matt promises to update the notes periodically. (Update 11/18): Matt Brin has let me know by email that a significant gap has emerged in Shavgulidze’s argument. He writes: Lemma 5 is still unproven. It claims a property about the distributions $u_n$ on the simplexes $D_n$ that is needed for the second part of the paper. The main result does not need the particular distributions $u_n$ given in the paper, but does need distributions on the $D_n$ that satisfy the properties claimed by Lemmas 5, 6 and that cooperate with Lemma 9. Ufe Haagerup claims an argument that the $u_n$ in the paper does not satisfy the conclusion of Lemma 5. Another distribution was said to be suggested by Shavgulidze, but at last report, it did not seem to be working In light of this, it would seem to be reasonable to consider the question of whether $F$ is amenable as wide open. (Update 9/21/2012): Justin Moore has posted a preprint on the arXiv claiming to prove amenability of $F$. It is too early to suggest that there is expert consensus on the correctness of the proof, but certainly everything I have heard is promising. I have not had time to look carefully at the argument yet, but hope to get a chance to do so before too long. (Update 10/2/2012): Justin has withdrawn his claim of a proof. A gap was found by Akhmedov. Recent Comments Ian Agol on Cube complexes, Reidemeister 3… Danny Calegari on kleinian, a tool for visualizi… Quod est Absurdum \|… on kleinian, a tool for visualizi… dipankar on kleinian, a tool for visualizi… Ludwig Bach on Liouville illiouminated	{"url":"http://lamington.wordpress.com/tag/amenability/","timestamp":"2014-04-16T13:22:02Z","content_type":null,"content_length":"61525","record_id":"<urn:uuid:97f0b8e2-2f18-4004-89be-0d24d4d3777c>","cc-path":"CC-MAIN-2014-15/segments/1397609523429.20/warc/CC-MAIN-20140416005203-00168-ip-10-147-4-33.ec2.internal.warc.gz"}
How will you work out the details of your solution to your problem? How will you refine your solution so that it can withstand other people s criticism? Weegy: Yes of course.. it is very important. [ [ Through multiple iterations, a subset of solutions is selected from the population of solutions, and variation operators are applied to the subset of solutions so that a new population of solutions is initialized and then mapped. If a predetermined number of iterations has been reached, that is if the precision coefficient has been satisfied, the substantially optimum solution is selected from ...	{"url":"http://www.weegy.com/?ConversationId=1E18900D","timestamp":"2014-04-16T04:28:36Z","content_type":null,"content_length":"33614","record_id":"<urn:uuid:9afa003b-1989-400d-af4b-f0ae8fde440b>","cc-path":"CC-MAIN-2014-15/segments/1398223205375.6/warc/CC-MAIN-20140423032005-00353-ip-10-147-4-33.ec2.internal.warc.gz"}
Sunday FunctionSunday Function Let’s do two functions today. As sometimes happens, in this case we’re not so interested in the functions themselves as the fact that these functions happen to be part of a general class of functions. Just as we can classify the real numbers as even, odd, or neither (numbers like pi, 1/2, and the rest of the non-integers are neither), we can classify functions as odd, even, or neither. This is a random even function and its graph: What makes this function even? A function is even if it’s symmetric about the y-axis. In other words an even function will have the same value at at x = 1 as it does at x = -1, and correspondingly for all other values of x. To say the same thing symbolically, a function is even if and only if Not so bad. Odd functions are similar, and here’s an example: Odd functions are antisymmetric about the y axis. Along the lines of even functions, symbolically you can say that a function is odd if and only if: Odd and even function tend to follow similar though not identical patterns to odd and even numbers. An even function times an even function is an even function. Odd times odd is even. Odd times even is odd. For instance, if you take our even and our odd functions above and multiply them, you’ll get an odd function with a graph like this: All this is vaguely interesting, but really why bother with it? Mathematically there’s a number of reasons. Understanding the properties of even and odd functions can help simplify a lot of problems. For instance, that last odd function integrated from minus infinity to infinity is zero because the area below the curve on the right is exactly balanced by the area above the curve on the left. We know that without actually having to do the integral by hand. There’s a number of other important properties along those lines that can make your life easier. But from a physics standpoint these symmetry and antisymmetry properties are even more important. The symmetric or antisymmetric character of a wavefunction under exchange of particles is the fundamental difference between bosons and fermions, leading to such important phenomena as the Pauli exclusion principle. We’re going to go into some detail about that soon, which is why we’re laying the groundwork now. Until then, enjoy the weekend! 1. #1 rdbhcx May 10, 2009 ooo! good topic! can’t wait for the next post. 2. #2 Uncle Al May 10, 2009 Is gravitation even-function? Newton’s r^2 and Green’s paired squares, Einstein’s ten equations. Obviously even. A parity Eotvos experiment tests for odd-function gravitation. Oppose chemically identical opposite parity atomic mass distributions as enantiomorphic space groups P3(1)21 versus P3(2)21 or P3(1) versus P3(2). The former contains quartz, berlinite and analogues, cinnabar, tellurium, selenium, benzil. Quartz is densely packed, 12.557 A^3/atom. In P3(1) / P3(2), the gamma-polymorph of glycine is more densely packed, 7.869 A^3/atom. Quantized gravitations require supplementing Einstein-Hilbert action with a parity-violating Chern-Simons term providing mass to the gauge field. Einstein alone won’t quantize – why would that be? Somebody should look. 3. #3 Jesse June 2, 2009 Great post! What software/program are you using to draw those graphs? It looks pretty neat! 4. #4 Matt Springer June 2, 2009 I’m using the new Mathematica. The older versions graphed a not-very-pretty B/W image, but the newer one does great visual work and is very customizable.	{"url":"http://scienceblogs.com/builtonfacts/2009/05/10/sunday-function-31/","timestamp":"2014-04-17T04:37:46Z","content_type":null,"content_length":"49802","record_id":"<urn:uuid:17d01e76-3545-426f-8980-eccfb107e7bb>","cc-path":"CC-MAIN-2014-15/segments/1398223206672.15/warc/CC-MAIN-20140423032006-00610-ip-10-147-4-33.ec2.internal.warc.gz"}
Positive Bias: Look Into the Dark - Less Wrong Comments (48) Sort By: Old I think something else is going on with the 2 4 6 experiment, as described. Many of the students are making the assumption about the set of potential rules. Specifically, the assumption is that most pairs of rules in this set have the following mutual relationship: most of the instances allowed by one rule, are disallowed by the other rule. This being the case, then the quickest way to test any hypothetical rule is to produce a variety of instances which conform with that rule, to see whether they conform with the hidden rule. I'll give you an example. Suppose that we are considering a family of rules, "the third number is an integer polynomial of the first two numbers". The quickest way to disconfirm a hypothetical rule is to produce instances in accordance with it and test them. If the rule is wrong, then the chances are good that an instance will quickly be discovered that does not match the hidden rule. It is much less efficient to proceed by producing instances not in accordance with it. I'll give a specific example. Suppose the hidden rule is c = a + b, and the hypothesized rule being tested is c = a - b. Now pick just one random instance in accordance with the hypothesized rule. I will suppose a = 4, b = 6, so c = -2. So the instance is 4 6 -2. That instance does not match the hidden rule, so the hypothesized rule is immediately disconfirmed. Now try the following: instead of picking a random instance in accordance with the hypothesized rule, pick one not in accordance with it. I'll pick 4 6 8. This also fails to match the hidden rule, so it fails to tell us whether our hypothesized rule is correct. We see that it was quicker to test an instance that agrees with the hypothetical rule. Thus we can see that in a certain class of situations, the most efficient way to test a hypothesis is to come up with instances that conform with the hypothesis. Now you can fault people on having made this assumption. But if you do, then it is still a different error from the one describe. If the assumption about the kind of problem faced had been correct, then the approach (testing instances that agree with the hypothesis) would have been a good one. The error, if any, lies not in the approach per se but in the assumption. Finally, I do not think one can rightly fault people for making that assumption. For, it is inevitable that very large and completely untested assumptions must be made in order to come to a conclusion at all. For, infinitely many rules are consistent with the evidence no matter how many instances you test. The only way ever to whittle this infinity of rules consistent with all the evidence down to one concluded rule is to make very large assumptions. The assumption that I have described may simply be the assumption which they made (and they had to make some assumption). Furthermore, it doesn't matter what assumptions people make (and they must make some, because of the nature of the problem), a clever scientist can learn what assumptions people tend to make and then violate those assumptions. So no matter what people do, someone can come along, construct an experiment in which those assumptions are violated, and then say, "gotcha" when the majority of his test subjects come to the wrong conclusions (because of the assumptions they were making which were violated by the experiment). In the situation you described, it would be necessary to test values that did and didn't match the hypothesis, which ends up working an awful lot like adjusting away from an anchor. Is there a way of solving the 2 4 6 problem without coming up with a hypothesis too early? In the situation you described, it would be necessary to test values that did and didn't match the hypothesis, which ends up working an awful lot like adjusting away from an anchor. Is there a way of solving the 2 4 6 problem without coming up with a hypothesis too early? Sooo many double posts! This new interface is buggy as @#$! Come up with several hypotheses in parallel, perhaps? The problem is not that they come up with a hypothesis too early, it's that they stop too early without testing examples that are not supposed to work. In most cases people are given as many opportunities to test as they'd like, yet they are confident in their answer after only testing one or two cases (all of which came up positive). The trick is that you should come up with one or more hypotheses as soon as you can (maybe without announcing them), but test both cases which do and don't confirm it, and be prepared to change your hypothesis if you are proven wrong. Following what Constant has pointed out, I am wondering if there is, in fact, a way to solve the 2 4 6 problem without first guessing, and then adjusting your guess. Following what Constant has pointed out, I am wondering if there is, in fact, a way to solve the 2 4 6 problem without first guessing, and then adjusting your guess. The problem is not that they are trying examples which confirm their hypothesis it's that they are trying only those examples which test their hypothesis. The article focuses on testing examples which don't work because people don't do this enough. Searching for positive examples is (as you argue) a neccessary part of testing a hypothesis, and people seem to have no problem applying this. What people fail to do is to search for the negative as well. Both positive and negative examples are, I'd say, equally important, but people's focus is completely imbalanced. I meant that first comment to be more speculative than definite. I was speculating about an alternative explanation of the observed behavior, which locates the fault elsewhere. Building on the previous commenter: Through playing various games of this sort, people develop a prior on the space of rules which has a lot of mass around rules of the type "X,X+2,X+4" or "X,2X,3X". Why is it that I suspect Constant didn't guess the rule properly? Isn't it the entire point of the post that confirmation bias is the tendency NOT TO CHECK ASSUMPTIONS? Are you searching for positive examples of positive bias right now, or sparing a fraction of your search on what positive bias should lead you to not see? Did you look toward light or darkness? Your hypothesis is that positive biases are generally bad. It is thus my duty to try and disprove your idea, and see what emerges from the result. Let's take your example, but now the sequences are ten numbers long and the initial sequence is 2-4-6-10-12-14-16-18-20-22 (the rule is still the same). Picking a sequence at random from a given set of numbers, we have only one chance in 10! = 3628800 of coming up with one that obeys the rule. Someone following the approach you recommended would probably fist try one instance of "x,x+2,x+4..." or "x,2x,3x,...", then start checking a few random sequences (getting "No" on each one, with near certainty). In this instance, disregarding positive bias doesn't help (unless you do a really brutal amount of testing). This is not just an artifact of "long" sequences - had we stuck with the sequence of three numbers, but the rule was "all in ascending order, or one number above ten trillion", then finding the right rule would be just as hard. What gives? Even worse, suppose you started with two assumptions: 1) the sequence is x,2x,3x,4x,5x,... 10x 2) the sequence is x, x+2, x+4,... x+18 You do one or two (positive) tests of 1). They comes up "yes". You then remember to try and disprove the hypothesis, try a hundred random sequences, coming up with "no" every time. You then accept However, had you just tried to do some positive testing of 1) and 2), you would very quickly have found out that something was wrong. Analysis: Testing is indeed about trying to disprove a hypothesis, and gaining confidence when you fail. But your hypothesis covers uncountably many different cases, and you can test (positively or negatively) only a very few. Unless you have some grounds to assume that this is enough (such as the uniform time and space assumptions of modern science, or some sort of nice ordering or measure on the space of hypotheses or of observations), then neither positive nor negative testing are giving you much information. However, if you have two competing hypothesis about the world, then a little testing is enough to tell which one is correct. This is the easiest way of making progress, and should always be Verdict: Awareness of positive bias causes us to think "I may be wrong, I should check". The correct attitude in front of these sorts of problems is the subtly different "there may be other explanations for what I see, I should find them". The two sentiments feel similar, but lead to very different ways of tackling the problem. I think the Wason selection task with cards is an even more direct demonstration of the tendency to seek confirmatory, but not disconfirmatory, tests of a hypothesis. Stuart, you do have a "nice ordering measure" - simpler hypotheses ("all ascending") have a higher prior probability than complex ones ("all ascending OR one over ten trillion" or randomness). Positive testing of contradictory, high-prior-probability hypotheses is still negative testing of your original hypothesis, no? This experiment isn't up to the usual standards of an economics experiment. When economists do such an information experiment, we give subjects some indication of the distribution that the hidden truth will be drawn from, and then we actually draw from that distribution. You can always make subjects look like fools if you give them an example that is rare given their prior expectations. Robin, I observe that Nature also fails to live up to the usual standards of an economics experiment. Stuart and Constant, in AI/machine learning we have a formal notion of "strictly more general concepts" as those with a strictly greater set of positive examples, and symmetrically for strictly more specific concepts. (This is not usually what I mean when I say "concept" but this is the term of art in machine learning.) Positive bias implies that people look at a set of examples and a starting concept, and try to envision a strictly more specific concept: for example, "ascending by 2 but all numbers positive". We seem to focus less on finding a strictly more general concept, such as "separated by equal intervals" or "in ascending order" or "any sequence not ending in 2". Why do we only look in the more-specific direction and see only half the universe of concepts? Instinct, one might simply say, and be done with it it. One might try a Bayesian argument that any more general concept would concentrate its probability mass less, and do a poorer job of explaining the positive examples found - for it seems that 10-12-14 is an unlikely thing to see, if the generator is "any sequence" than "any sequence separated by intervals of 2". But this is an invalid argument if you are the one generating the examples! As for the initial example being misleadingly specific, heck, people read nonexistent coincidences into Nature all the time. It may not be fair of the experimenter but it is certainly realistic as a test of a rationalist's skill. If you are testing examples in an oracle, "positive" and "negative" are symmetrical labels. This point alone should make it very clear that, from the standpoint of probability theory, we are dealing strictly with a bizarre quirk of human psychology. Flynn, you write, "Isn't it the entire point of the post that confirmation bias is the tendency NOT TO CHECK ASSUMPTIONS?" You simply can't check all your assumptions in finite time in this task, which is a problem, because you must complete the task in a finite time. That is not your fault - that is intrinsic in the challenge. Therefore some of your assumptions will necessarily go untested - and they will necessarily be enormous assumptions. The reason for this is that the set of possible rules is too large - it's infinite - and remains infinite no matter how much testing you do. See also Stuart's comment and Robin's comment. I think they express major points I was trying to make, more clearly than I did. Eliezer, yes sometimes nature includes rare events, but only rarely. We should evaluate human inference abilities on average across the kinds of cases humans face, and not just for rare surprising The plethora of incorrect hypothesis compared to the relatively few correct (so far) theories seem to speak against this. I'm not sure I buy the whole 'subverbal' thing -- it seems to me that misleading phrasing is a big part of the problem. If asked to find the "rule" which "governs" a sequence of three numbers, I'd (incorrectly ...) assume that the questioner was thinking of some simple rule that can be used to generate all of the valid sequences. Given the examples, I'd guess it was something like 'x x+2 x+4' or '2x 2(x+1) 2(x+2).' Now, after I started typing this I realized that you could map all ascending 3 integer sequences to the whole numbers, so there is a "rule" that could be used to generate the solution, but nobody would look at the solution in these terms naturally -- instead, we think of the solution as the set of sequences with the "property" of being in ascending order. If the questioner said that he was thinking of "a property which sequences of 3 numbers either have or lack," rather than a "rule" which "governs" the sequences, I suspect more folks would discover the correct solution. Robin, I suspect that Eliezer has a different perspective on that, given his line of work. Availability bias on which biases to overcome? The creation of a seed AI is an event so rare that is has never happened (so far as we can tell), but failure to get it right on the first try could eliminate all life in the solar system. There is perhaps room for discussing average and better inference abilities with respect to common and rare events, although we would do well to be clear on exactly what we are arguing. Constant made an important point: infinitely many rules are consistent with the evidence no matter how many instances you test. Therefore any guess you make must be influenced by prior expectations. And like lusispedro said, based on experience students probably put a lot more weight on rules based on simple equations than rules based on inequalities. I'm sure I could get the percentage of people who guess correctly down to 0% by simply choosing the perfectly valid rule: "sequences (a,b,c) such that EITHER a less than b less than c OR b is a multiple of 73." Why? Because rules of that sort are given low weight in subjects' priors. It seems very normal to expect that the rule will be more restrictive or arithmetic in nature. But if I am supposed to be sure of the rule, then I need to test more than just a few possibilities. Priors are definitely involved here. Part of the problem is that we are trained like Monkeys to make decisions on underspecified problems of this form all the time. I've hardly ever seen a "guess the next [number\|letter\|item] in the sequence problem that didn't have multiple answers. But most of them have at least one answer that feels "right" in the sense of being simplest, most elegant or most obvious or within typical bounds given basic assumptions about problems of that type. I'm the sort of accuracy-minded prick who would keep testing until he was very close to certain what the rule was, and would probably take forever. An interesting version of this phenomenon is the game: "Bang! Who's dead". one person starts the game, says "Bang!", and some number of people are metaphorically dead, based on a rule that the other participants are supposed to figure out (which is, AFAIK, the same every time, but I'm not saying it here). The only information that the starter will give is who is dead each time. Took me forever to solve this, because I tend to have a much weaker version of the bias you consider here. But realistically, most of my mates solved this game much faster than I did. I suspect that this "jump to conclusions" bias is useful in many situations. After seeing the four examples (including one that didn't fit) given, it didn't even occur to me that someone could think the first one indicated a X-2X-3X pattern. It's hard to tell what will confirm and what will disconfirm in such a broad space of possibilities. A bit off topic but after numerous incidents of mocking Eliezer, Mencius Moldbug has launched a full-scale assault on Bayesianism. He hasn't shown any inclination to post his critiques here, but perhaps some of the luminaries here could show him the error of his ways. That is a good link, Ambitwistor. The last paragraph refers to an interesting psychological hypothesis, which I'd like to expand on in an example related to the "Look Into the Dark" post. Let's rephrase EY's proposition to give it more of a social "plot". "You're a smuggler in a strange foreign land, where they only allow exports of goods in certain combinations of quantities, so as to keep their domestic lobby groups happy. [Yes, it's a convulated example, but governments can be convoluted.] Trouble is, everyone knows the rule except you and your gang of smugglers, and if you ask, you become a suspect. Furthermore, you don't actually know what you're smuggling, since your fence always seals them in the standard export containers, which are numbered ordinally "First", "Second", and "Third". Since you're an amoral smuggler boss, in charge of a lot of obedient "mule" underlings, you can send as many people through customs as you want and no matter how many get arrested, you won't be a suspect. Also, you have an infinite number of empty export containers with the usual "First", "Second" or "Third" labels. If your mule gets arrested with an empty container, he'll be released immediately. So basically, you can test the rule all you want, since you'll witness any arrest that happens. Just as you and your team of criminals arrives at the customs checkpoint, a man goes into customs with 2 "First" boxes, 4 "Second" boxes, and 6 "Third" boxes. You can start making a tidy profit as soon you determine what the rule is. What is your next move?" Granted, it is a convoluted example and I'm worried that in its current form it would just confuse too many test subjects. Perhaps someone would think of a more straightforward equivalent. The point, though, is to make the test sound less like the sort of rule we are familiar with from math class. As several posters have alluded, usually a rule in math class is much stricter and requires some arithmetic. A bureaucratic rule, convoluted though it may be, will often be mathematically simpler. E.g., "The extremely powerful pineapple lobby has pushed through a law requiring that no other fruit (papaya or mango) be exported in greater numbers than pineapples. Exports from the politically weak mango industry must not exceed papaya exports. Pineapples are labelled Third; papayas labelled Second; mangos labelled First." My hypothesis is that people will come up with this rule faster than they would when faced with the phrasing from the original post. (Of course, the "domestic lobby groups happy" phrasing is sort of a giveaway ... maybe it should be replaced with a more neutral explanation, or none at all.) We're playing a game in which you, the player, start with a number sequence. There is a rule governing which number comes next, and whoever determines the rule will recieve $10. Any one can play, but I tagged the people who i think will be most interested. If you guess a number, I will tell you if it is correct, and if so, I will add it to the existing sequence. Please only guess one number each day. Please only guess one number at a time, dont try and fill in a section of the sequence. If you guess the rule, I will tell you if you are correct or incorrect. If correct, you win $10. If incorrect, you may not guess the rule again for 3 days. Original sequence: 2, 4, 6 The sequence so far is: 2, 4, 6, 10, 18, 30, 50, 82, 134, 218, 354, 622, 623, 630 47 comments Updated about a month ago Craig Fleischman (Indiana) wrote at 7:44pm on July 13th, 2007 10? Message - Delete Dan Margolis (Japan) wrote at 8:31pm on July 13th, 2007 7 Message - Delete Jeff Borack wrote at 1:03am on July 14th, 2007 10 yes, 7 no Delete Dan Margolis (Japan) wrote at 9:52am on July 14th, 2007 Its like fibonacci sequence except starting at 2. The next digit is the sum of the two previous digits. So it would be 2, 4, 6, 10, 16, 26, 42, 68, 110... So... X0 = 2, X1 = 4, Xn = (Xn-1 + Xn-2) Message - Delete Jeff Borack wrote at 12:16pm on July 14th, 2007 Incorrect Delete Dan Margolis (Japan) wrote at 12:38pm on July 14th, 2007 Worth a shot...I can't deduce much from so few numbers... Message - Delete Elliot Alyeshmerni wrote at 7:06pm on July 14th, 2007 im gonna go with 18 Message - Delete Jeff Borack wrote at 8:24pm on July 14th, 2007 a job well done Delete Yvette Monachino wrote at 8:08pm on July 15th, 2007 30 Message - Delete Jeff Borack wrote at 10:47am on July 16th, 2007 30 works Delete Yvette Monachino wrote at 11:06am on July 16th, 2007 50 Message - Delete Jeff Borack wrote at 11:35am on July 16th, 2007 good Delete Elliot Alyeshmerni wrote at 2:25pm on July 16th, 2007 82, still havent gotten the sequence down so this is a bit of a guess Message - Delete Jeff Borack wrote at 2:33pm on July 16th, 2007 good Delete Elliot Alyeshmerni wrote at 3:19pm on July 16th, 2007 i think we all got this sequence now.. Message - Delete Jeff Borack wrote at 3:36pm on July 16th, 2007 i dont think anyone has it. but i welcome you to guess. If your right, $10. If your wrong, at least you'll save yvette! Good luck. Delete Peter Dahlke wrote at 7:31pm on July 16th, 2007 134 next? Message - Delete Jeff Borack wrote at 8:07pm on July 16th, 2007 yup Delete Elliot Alyeshmerni wrote at 10:49pm on July 16th, 2007 218 Message - Delete Jeff Borack wrote at 11:15pm on July 16th, 2007 218 Delete Victor Baranowski wrote at 10:16am on July 17th, 2007 IDK where it started, but assuming we started with 2, 4, 6 the sequence is: Xn = X (n-1) + [(X(n-1) - X(n-2)) + (X(n-2)-X(n-3))] or something like that... Message - Delete Jeff Borack wrote at 10:26am on July 17th, 2007 Interesting guess, I thought people were gonna say Xn = X(n-1)+X(n-2)+2, but both are wrong. Sorry Vic. The more interesting question is: why did it take so long for someone to guess? Is the reward for guessing the correct answer to low or is the penalty to high? Delete Jeff Borack wrote at 10:45am on July 17th, 2007 I'm changing the rule of 1 rule guess/week. You can now guess once every three days. Numbers are still once a day even though elliot broke that rule and i accepted the number. Delete Elliot Alyeshmerni wrote at 11:43am on July 17th, 2007 this a answer works for every number except 6 and 18, but i'll put it down anyway X(n)=2X(n-1)-X(n-3) Message - Delete Victor Baranowski wrote at 12:22pm on July 17th, 2007 Ya, that was similar to mine. Why the sequence goes from 10 to 18 is the tricky part of this whole thing, which makes me think the equation is going to be pretty ugly or wierd... maybe jeff made a mistake :P Message - Delete Victor Baranowski wrote at 12:23pm on July 17th, 2007 Oh, and I might as well guess 354... Message - Delete Jeff Borack wrote at 2:19pm on July 17th, 2007 a) the solution is beutiful b) i didn't make any mistakes yet c) 354 is good Delete Victor Baranowski wrote at 2:46pm on July 17th, 2007 Can I cite a) in response to your b) ? Message - Delete Jeff Borack wrote at 8:20pm on July 17th, 2007 Hmmmm, I'm not sure. It depends on when you think the mistake was made. Technically it did come before b), but i could also argue that the mistake what made when i clicked the "Add your comment" button. a) the solution is... very nice and good b) i didn't make any mistakes in the number sequence yet. c) web browsers and AIM should have spell checkers. this isn't the 20th century anymore. Delete Tait Kowalski wrote at 3:48pm on July 18th, 2007 Sequence goes x(n) = x(n-1)+2x(n-3) so the next number = 354 + 2134 = 622 next number is 622 Message - Delete Jeff Borack wrote at 4:41pm on July 18th, 2007 Welcome Tait! That is the wrong rule, but ill accept your guess at the next number. Delete Elliot Alyeshmerni wrote at 6:28pm on July 19th, 2007 the next number is fuck you jeff, just give us the answer lol Message - Delete Jeff Borack wrote at 6:47pm on July 19th, 2007 Sorry elliot, want me to call the Whaaaaaaaaaaaaaaaambulance? Delete Victor Baranowski wrote at 4:29pm on July 22nd, 2007 is the next number 620? Message - Delete Jeff Borack wrote at 7:23pm on July 22nd, 2007 hmm strange guess. 620 is not a number Delete Victor Baranowski wrote at 8:46am on July 23rd, 2007 howabout 623? Message - Delete Jeff Borack wrote at 12:40pm on July 23rd, 2007 : ) 623 is the next number Delete Craig Fleischman (Indiana) wrote at 12:55pm on July 23rd, 2007 630? Message - Delete Jeff Borack wrote at 12:59pm on July 23rd, 2007 630 is good Delete Victor Baranowski wrote at 1:51pm on July 23rd, 2007 Solution: the next number is whatever number is guessed, as long as it is higher than the previously guessed number. Message - Delete Jeff Borack wrote at 2:28pm on July 23rd, 2007 hahaha, yup. it took a lot of time but not a lot of guesses. i expected the guessing to to into the hundreds of thousands. do you accept paypal? Delete Victor Baranowski wrote at 2:35pm on July 23rd, 2007 no, i accept shots and beers the next time we hang out. Message - Delete Yvette Monachino wrote at 4:10pm on July 27th, 2007 that is the dumbest sequence i have ever heard of Message - Delete Jeff Borack wrote at 5:08pm on July 27th, 2007 It's about thinking outside the box, yvette, something i wouldnt expect most MATH majors to understand! : p Victory for the engineers!!! Delete Yvette Monachino wrote at 2:08pm on July 30th, 2007 aw thats a cute remark, knowing that you don't actually know what real math is i won't take that as an insult, and the only victory you accomplished is adding yourself to the long list of pompous engineers, so congrats :) Message - Delete Jeff Borack wrote at 2:52pm on July 30th, 2007 While I might be pompous, I unfortunately can't be considered much of an engineer. I did bioengineering, which certainly doesnt count, and i've never actually engineered anything. Neither has vic, hes in law school. It is true that i don't know what real math is (although i would love for you to teach me). However, I would imagine that real math does involve thinking outside the box on occasion. In this particular example, it required you to test a number you thought was not part of the sequence. If you believed you had found the sequence, and contintued to test numbers that fit that sequence, you would never derive the answer. By simply testing a number that does not appear to fall into the sequence, such as 2 million, it's easy to find the solution. Does this sound like any 'real' math problems you have ever encountered? I just want to summarize what I learned in this thread in order to ensure that I understand it. As I understand, the steps for determining the rule should be something like this: 1. See sequence. 2. What relations do the elements share? All are numbers, integers, even, differ by two, and are in ascending order. The rule is likelier to contain each (but not all) of these as a clause than not to. 3. If any relation you thought of belongs to a larger class, add that class. 4. Try to disconfirm each relation by creating sequences that violate only this relation (as well as its descendents, necessarily). Test general attributes first, since if they fail, the descendents can be considered impossible. 5. Create a candidate rule which consists of all relations that were not disconfirmed. 6. Offer the rule to the examiner. Quite a bit more laborious than blurting out "n[i] = n[i-1]+2", I have to admit. But then n[i]=n[i-1]+2 is wrong, so... You need to do a lot more to demonstrate irrationality than this. Obviously, as other commenters have pointed out, there are an infinite number of rules that agree with any given finite sequence of experimental results so obviously you can never conclusively demonstrate that your rule is indeed the correct one. Moreover, you can't even be 'bias free' in the sense of assigning all possible rules the same probability unless you want to assign each rule probability 0. Now you might be tempted to just give up at this point but this is exactly the same problem we face when doing science. We have an infinite number of possible rules that extend the results we have seen so far and we need to guess which is most likely. Amazingly we do it pretty well but justifying it seems impossible, it's the classical philosophical problem of induction. In short it's not clear anyone is 'wrong'. Maybe they have a good initial probability distribution for what sorts of rules people normally pick. Heck it's not even clear what it means to be 'wrong' in this sense, i.e., having an implausible a priori probability distribution I have two observations, one personal and one general: Once, I tried to apply artificial neural nets on the task to evaluate positional situations in the game of Go. I did a very basic error, which was to train the net only on positive examples. The net quickly learned to give high scores for these, but then I tested on bad situations it still reported high scores. Maybe a little naive mistake, but you have to learn sometimes. A very common example is testing of software. Usually, people pay much attention on testing the positive cases, and verifying that they work as they should. Less time is spent on testing things that should not work, sometimes resulting in programs that generates answers when it should not. The problem here is that testing the positive cases usually consists of a limited set, while the negative cases are almost infinite. Anyone who finds the game described at the top of the article interesting, check out Zendo, a game based upon a similar idea. I've found Zendo handy when explaining the concept in the OP and the various other ideas of experimental design and inductive investigation. Plus, it's lots of fun. :-) Zendo is my go-to exercise for explaining just about any idea in inductive investigation. (But it's even more useful as a tool for reminding myself to do better. After years, the number of Zendo games I lose due to positive bias is still far higher than I'd like... even when I think I've taken steps to avoid that.) As my group's usual Zendo Master, I have a lot of players fall into this trap. I like to train new players with one easy property like "A Koan Has The Buddah Nature If (and only if) it contains a red piece." Once they understand the rules, I jump to something like "A Koan Has The Buddah Nature Unless It contains exactly two pieces." Switching from a positively-marked property (there is a simple feature which all these things have) to a negatively-marked property (there is a simple feature which all these things lack) can be pretty eye-opening. I showed Zendo to a math professor once who fell smack into the 2-4-6 trap and tried to build as many white-marked koans as possible. He even asked why the game didn't punish people for just making the same koan over and over again, since it would be guaranteed to "follow the rule." I eventually managed to convey that the object of the game is to be able to tell me, in words, what you think the rule is. Since then I've been more explicit that "part of the game involves literally just saying, out loud, what you think defines the property." People always seem to think that the zendo is a sort of a silent lecture, when really it's more of a laboratory class. He even asked why the game didn't punish people for just making the same koan over and over again, since it would be guaranteed to "follow the rule." I eventually managed to convey that the object of the game is to be able to tell me, in words, what you think the rule is. Maybe this provides some insight into the nature of positive bias. In the game, the only goal is to find the rule; there is no punishment for asking a wrong sequence. But I guess the real life is not like this. In real life, especially in the ancient environment, making a wrong guess is costly; and our cognitive algorithms were optimized for that. For example, imagine that the rule is some taboo, punishable by death. It is better to avoid the punishment, than to find the boundaries precisely. Avoiding a superset of the taboo also has some cost, but that cost is probably cheaper than being stoned to death. If you know that the sequence "2-4-6" does not get you killed (unlike some other sequences, not explicitly known which ones), it may be wise to guess "2-4-6" over and over again. One thing that helped me really get this one is testing software upgrades. It's insanely tedious. Most stuff just keeps working. But if you don't test, you're just asking for something to come back and bite you in the backside. e.g. recent work example: upgrading Tomcat 6.0.16 to 6.0.29. Minor point release from the Apache Software Foundation, computer scientists famous for their dedication to engineering stability. I so didn't want to bother testing this at all - days and days of tedium. Then this bit us - someone decided the letter of the spec beat mountains of real-world code in a stable branch maintenance release . And it's in mountains of real-world code because of this. My opinion of Apache slipped somewhat. But my systems stayed up. I still hate lining up testing, but a few of these and you start to expand your map of chances large enough to mess you up. Sysadmins know that computers are evil and out to get them, and that the only way around this is not to give them the opportunity. A friend of mine has a similar story involving why he never allows code-changes after code freeze dates, even if X, even if Y, even if Z. His story, however, involves avatars in a video game sorting their layers in strange ways on obscure video cards to cause breastplates to unexpectedly sort below breasts, which is why I still remember it. It's like backups or freedom 0. Approximately no-one gets it until they've been bitten in real life. (I am particularly bad at learning without direct application of forehead to concrete, but am attempting to think more clearly.) Funny, "three numbers in ascending order" was the first hypothesis that popped in my mind. I think most people would come up with the correct answer 'with extension'. Such as 'increasing by 2 in ascending order' where the correct answer 'ascending order' is the basis that they have then specified further. In my eyes they have then given a partially correct answer and should not strive so hard to 'avoid this mistake' in the future. My reasoning is that you might then 'dismiss out of hand' a partially correct answer and by default do the same to the 'fully correct answer'. It is better then, to make a habit out of breaking down a hypotheses before dismissing it. Or you could just use up all your energy on convincing yourself that nothing should be believed, ever. Since belief means to know without proof. Hey there! Welcome to Less Wrong! I'd say you should read the Sequences, but that's clearly what you're doing :D. I'd suggest going ahead and introducing yourself over here. I agree with you that some people might come up with the rule, but with unnecessary additions. The point of looking into the dark is that people may tend to add on to those extensions, when they should really be shaving them down to their core. And they can only do so (Or at least do so more effectively.) by looking into the dark. Also, that's not exactly the commonly accepted definition of "Belief" around here. For what most would think of when you refer to "belief" check out here, here, and the related The Simple Truth article, and really the entire Map and Territory sequence Again, welcome! Thought experiment. Suppose you have two oracles, and your task is to find out whether or not they have the same rule. If each oracle is considered as "A lookup table produced by a coin flip for each possible input, except that there's a 50% chance that the second is just a copy of the first" then of course any input is as likely as any other to exhibit a difference, and you can easily compute the probability of no difference after n tests fail to exhibit one. But if you have an assumption that simpler rules are more likely (eg. your prior is 2^-complexity) then what's your optimal A plausible strategy is to follow the same strategy as you would if you had to find the rule of a single oracle; you always send the input that gives you the most bits about Oracle A's rule. That way, you maximise the probability of exhibiting a difference given that one exists. So if you can generate an input which, under your current model of the space of A's possible rules (and the probability of each), has exactly a 50% chance of matching A, then it also has a 50% chance of matching B; moreover these probabilities are independent, so you have 25%+25%=50% chance of exhibiting a difference. If instead you picked an input with a 30% chance of matching A, your chance of exhibiting a difference is 21%+21%=42%. It seems much of our cognitive architecture was developed in the context of social situations. Indeed, the standard experiments on checking modus ponens and modus tollens understanding show sharp increases in ability when they are presented as social rules (e.g. http://en.wikipedia.org/wiki/Wason_selection_task checking whether someone is violating the "minor drinking alcohol" rules, rather than cards gives much higher performance). Testing whether you understand a social rule by deliberately violating your current understanding can be a very, very expensive test. It seems plausible that this cost has led to the human default ways for testing implicit rules to avoid seeking out these negatives, even when the cost would be low. We're good at reasoning with social situations, and bad with more abstract situations. As such, we can't be doing them the same way. Something that helps in social situations is unlikely to cause a bias in more abstract situations. In other words, our current architecture was developed in the context of social situations, and the fact that we do significantly better in those situations shows that it's the only time we use it. Otherwise, we use different, lousy architecture that won't exhibit the same biases. Are you searching for positive examples of positive bias right now, or sparing a fraction of your search on what positive bias should lead you to not see? Isn't what positive bias should lead you to not see a positive example of positive bias? Or am I explaining the joke? I intuitively wanted to see if the combination 8-6-4 or 6-4-2 would be acceptable, without actually making a guess at the rule. I looked at the two acceptable answers and the one unacceptable answer and thought, okay, but that doesn't prove a rule. The rule the experiment wants you to think about is a pattern like 2-4-6-8-10, so let's see if something disproves that pattern. Would 6-4-2 be acceptable? Obviously, it wouldn't. If I wasn't under the influence of hindsight bias I might continue on to try and see if different intervals were not acceptable I.e. 2-2-2 until I could differentiate between ascending order and the intervals, but knowing me and the likelihood of anyone actually guessing the rule I would put that as a very low probability. Still, this strikes me as the kind of thing where it's best to avoid bringing up a solution-- get more information, and study and discuss the information, and then try to solve it. If people did this perhaps they would come closer to getting it right? Haha... And before I read this blog I thought I was irrational. Probably still am. I wonder why noone cares to mention Ockham's Razor in this situation. As already a couple of times mentioned, there are infinite rules possible to describe a finite set of numbers. thereby we can only start at the least restricting rule possible and work our way farther in until we get to a point where we are not able to find a set of numbers working for our rule, but not for the rule to find within a certain interval of time. thereby i start by saying its all numbers. obviously ill find a couple of pairs not matching the correct rule. ill then start trying whole numbers. after that i might try ascending numbers or at least a>b or b>c... the only important thing to do here is to find the simplest solution still possible. So i actually wouldnt try finding anything thats not fitting my assumptions, since there would be way more sets not fitting my assumption and not fitting the solution. If I was advising an AI on how to solve this question, I might recommend guessing many sets of three random numbers, and just looking at the ratio of 'yes' to 'no'. A result of 1/6 yes, could then be matched against various rules and there ratios. This would greatly reduce the solution set, and ordering would likely jump to the front as a likely possibility. If I were answering the question for myself, I would likely try to break it, by that I mean get you to either add a new rule, or to say 'I don't know'. { e, i, pi }	{"url":"http://lesswrong.com/lw/iw/positive_bias_look_into_the_dark/","timestamp":"2014-04-20T13:33:32Z","content_type":null,"content_length":"207537","record_id":"<urn:uuid:3d66079a-de7c-4816-a283-504f99e7f2e8>","cc-path":"CC-MAIN-2014-15/segments/1398223202457.0/warc/CC-MAIN-20140423032002-00006-ip-10-147-4-33.ec2.internal.warc.gz"}
Patent US7093137 - Database management apparatus and encrypting/decrypting system 1. Field of the Invention The present invention relates to an encryption/decryption system used in a system for performing encrypted data communications, and to a database management apparatus for encrypting and managing a 2. Description of the Related Art In an information system such as a computer and a network used by a large number of general users, there is a serious problem that some malicious users illegally access and amend information. Therefore, the encryption technology has been widely adopted as an effective countermeasure. A well-known encryption technology is disclosed in detail by the following document. ‘Communications of the ACM Vol. 21, No.2 (1978) P120. A Method for Obtaining Digital Signatures and Public Key Crypto systems: R. L. Rivest, A. Shamir, and L. Adleman, MIT Laboratory for Computer Science and Department of Mathematics’ The encrypting method published in this document is generally accepted as a considerably reliable method, and is referred to as an RSA (Rivest-Sharmir-Adleman) method. A system derived from this RSA method has been developed as an authentication system for a signature used in an electronic trading system, and has been put to practical use. The RSA method is a public key (asymmetric) encryption system based on the difficulty in factorization in prime numbers, and obtains as ciphertext a remainder obtained by dividing a result of raised data by a large integer. The feature of the RSA method is that it is difficult to find two original primes (p and q) from the product of the two original primes. Even if the product of the two primes can be detected, it is very difficult to detect the p and the q, or estimate the decoding operation. The above mentioned RSA method is practical in a sense, and highly reliable when the bit length of data as an encryption key is long enough. To guarantee the reliability, it is normal to use encryption key data of 256 bits in length. However, it is not long enough in some cases, and the necessity of an encryption key of 512 or 1024 bits in data length is actually discussed. However, since the data length is practically limited by the operation precision and operation speed of a computer, it is not efficient to have a long bit. That is, there has been the problem with the RSA method and the encrypting method derived from the RSA method that the reliability of these methods is limited by the performance of a computer. There also is the problem that the methods require a considerable change in the reliability test, etc. of the authentication system based on the change in bit length of an encryption key. In addition, since the database management apparatus has to encrypt and store the database which is managed therein to guarantee the security of the database. To improve the security, a more complicated encrypting process can be performed, but it also requires a long time to perform operations. A database contains a large volume of data. In a data retrieving process, data relating to a specific item and matching given conditions is selected from the large volume of data, and a record (row data) containing an item data matching the condition is output. Therefore, in a data retrieval system for processing a large volume of data, a prolonged operation time lowers the performance of the As described above, a database containing a confidential data is required to guarantee security, and an encrypting process to improve the security has the problem that the process can lower the availability of the database. Conventionally, when a database is encrypted, it is normal that the entire target file is encrypted using a fixed encryption key generated by, for example, a password, etc. However, as described above, since an encrypting process has been performed using a fixed encryption key according to the conventional system, the security level of each data item is averaged. In addition, when there are a plurality of items containing the same data, the same encryption results are output, thereby causing the possibility that the encryption key can be decrypted. The present invention aims at providing an encryption/decryption apparatus capable of performing an encrypting process without a precision operation result and realizing a general purpose encrypting/ decrypting process which is highly reliable and easily adds and changes an application. Another object of the present invention is to provide a database management apparatus capable of guaranteeing the security of a database, and quickly retrieving data. A further object of the present invention is to provide a database management apparatus capable of encrypting a specific data item in a database with the security improved more than that of another data item. That is, the database management apparatus according to the present invention encrypts data of a column item used in a retrieving process using a column key commonly used for the column item, and encrypts data of other column items using a row key specific to each row. The encryption device according to the present invention includes: a plaintext data obtaining unit for obtaining plaintext data to be encrypted; a vector generation unit for sequentially generating vectors defined in a closed area of an n(n≧1)-dimensional space; and a logical operation unit for generating encrypted data with a logical operation performed on the plaintext data obtained by the plaintext data obtaining unit and the vector element generated by the vector generation unit in bit units. On the other hand, a decryption device according to the present invention also includes the vector generation unit; and an inverse logical operation unit for decoding the plaintext data by an inverse operation of the logical operation using the ciphertext data. The database management apparatus uses the encryption device according to the present invention in a data encrypting process, and uses the decryption device according to the present invention when ciphertext data is decrypted into plaintext data. The encryption system according to the present invention includes: a vector generation unit for generating a vector r[j ]using each element of a vector defined in a closed area of the n(n≧1) -dimensional space, and an angle Ω[n ]determined by a parameter set P in such a way that each of the vectors r[j](j≧0) sequentially generated using a non-linear function containing at least the n-dimensional rotation matrix R[n](Ω[n]) for rotation of the vector cannot match each other in the n-dimensional space; and a binary operation unit for generating encrypted data using a binary operation of plaintext data and the element of the vector r[j ]generated by the vector generation unit. The decryption system according to the present invention includes: a vector generation unit for generating a vector r[j ]using each element of a vector defined in a closed area of the n(n≧1) -dimensional space, and an angle Ω[n ]determined by a parameter set P in such a way that each of the vectors r[j](j≧0) sequentially generated using a non-linear function containing at least the n-dimensional rotation matrix R[n](Ω[n]) for rotation of the vector cannot match each other in the n-dimensional space; and an inverse binary operation unit for receiving encrypted data generated in a binary operation of plaintext data and the element of a vector r[j ]generated in a method similar to that of the vector generation unit, and decrypting the plaintext data in an inverse binary operation corresponding to an inverse operation of the binary operation using the vector r[j ]generated by the vector generation unit and the encrypted data. With the above mentioned configuration, the vectors defined in the closed area of the n(n≧1)-dimensional space are sequentially generated, and ciphertext data is generated in a logical operation of plaintext data to be encrypted and the element of the vector. Thus, by encrypting plaintext data using elements of multidimensional vector, an encrypting process can be performed without a precision operation such as the RSA method, etc., and a reliable general-purpose encrypting/decrypting process capable of easily adding and changing an application can be realized. The database management apparatus according to the present invention includes: an encryption unit for encrypting data of a predetermined column item of a database using a column key common among the column items, and encrypting data of other column items using a column key specific to each row; and a storage unit for storing a database encrypted by the encryption unit. With the configuration, the security can be improved by assigning a different key to each row when a database is encrypted. When a retrieving process is performed, a high-speed retrieving process can be realized by encrypting data input for retrieval using a column key common among the predetermined column items, and comparing the item data of the encrypted retrieving data and the item data of the encrypted database. In addition, the security can be furthermore reinforced by encrypting the data of the column items other than the column item used in the retrieving process using the combination of the row key specific to each row and the column key common among the column items. Furthermore, a database can be stored in a separate place to generate a database system so that a request for a retrieving process can be issued from a separate information terminal through a network. In this case, the data of a predetermined column item (column item used in a retrieving process) is encrypted using a column key common among the column items, and the data of other column items is encrypted using a row key specific to each row. When a request to retrieve a database is issued from another information terminal, the retrieving data is encrypted using a column key common among the column items, and the encrypted retrieving data is transmitted through a network. By receiving the retrieving data, the process of retrieving the encrypted database can be performed, and the encrypted data obtained as a retrieval result is returned to the information terminal through the network. Therefore, since data is transmitted constantly in an encrypted state, the database security can be guaranteed. When a database is encrypted, the database management apparatus according to the present invention encrypts the data of the column items used in a retrieving process using a column key common among the column items, encrypts the data of other column items requiring high security using a row key specific to each row with the row key further encrypted using another key common among the rows. Practically, the database management apparatus according to the present invention includes: a first encryption unit for encrypting data of predetermined column items of a database using a column key common among the column items, and encrypting data of other column items using a row key specific to each row; a second encryption unit for encrypting the row key used in encrypting the data of other column items in the database encrypted by the first encryption unit using another key common among the rows; and a storage unit for storing the database encrypted by the first encryption unit together with the row key encrypted by the second encryption unit. With the configuration, when a database is encrypted, the data of the column items other than a predetermined column item used in a retrieving process can be encrypted using a different key for each row so that different values can be obtained as encryption results of the data having the same values in the column items. Furthermore, higher security can be realized by complicating the decryption of the key by re-encrypting the key (row key), which is used in encrypting the column items, using another key. In addition, when the row key is generated using a row number assigned to each row of the database and a random number, which makes the encryption of the key furthermore difficult, the security can be successfully reinforced. Furthermore, a database system can be configured by a first terminal device for managing a database, and a second terminal device for searching the database independent of the first terminal device. In the database, the first terminal device encrypts the database, stores the encrypted database in a storage medium and distributes the storage medium, and the second terminal device retrieves data in the stored encrypted database stored in the distributed storage medium, decrypts the data obtained as the retrieval result, and displays the resultant data. In this case, the data of the predetermined column item of the database is encrypted using a column key common among the column items, the data of other column items is encrypted using a row key specific to each row, and the row key is encrypted using another key common among the rows, thereby storing the database in a storage medium and distributing the storage medium with the security successfully guaranteed. FIG. 1 shows the configuration of the database management apparatus according to the first embodiment of the present invention; FIG. 2 is a flowchart of the operations of the database encrypting process performed by the database management apparatus; FIGS. 3A and 3B are flowcharts of the operations of the database searching process performed by the database management apparatus; FIGS. 4A and 4B are flowcharts of the practical operations of the retrieving process in step H13 shown in FIG. 18A; FIG. 5 shows the configuration of the database according to the first embodiment of the database management apparatus of the present invention; FIG. 5( a) shows the state before encryption; FIG. 5( b ) shows the state after encryption; and FIG. 5( c) shows the state after decryption; FIG. 6 shows the configuration of the column key and the row key according to the first embodiment of the database management apparatus; FIG. 7 shows the configuration of the database according to the second embodiment of the database management apparatus; FIG. 7( a) shows the state before encryption; FIG. 7( b) shows the state after encryption of the present invention; and FIG. 7( c) shows the state after decryption; FIG. 8 shows the configuration of the composite key according to the second embodiment of the database management apparatus of the present invention; FIG. 9 is a block diagram of the configuration of the database system according to the third embodiment of the database management apparatus of the present invention; FIG. 10 shows the database management apparatus according to the fourth embodiment of the present invention; FIG. 11 is a block diagram of the configuration of the functions of the database management apparatus; FIG. 12 shows the configuration of the dialog for setting a basic key in the database management apparatus; FIG. 13 shows an example of a basic key parameter table in the database management apparatus; FIG. 14 shows the configuration of the dialog for setting a key specification in the database management apparatus; FIG. 15 shows an example of an entry in the key specification table in the database management apparatus; FIG. 16 shows the data flow when the database is encrypted and decrypted in the database management apparatus; FIGS. 17A and 17B are flowcharts of the operations of the database encrypting process performed by the database management apparatus; FIGS. 18A and 18B are flowcharts of the operations of the database searching process performed by the database management apparatus; FIGS. 19A and 19B are flowcharts of the practical operations of the retrieving process in step P13 shown in FIG. 18A; FIG. 20 shows the configuration of the database in the database management apparatus; FIG. 20( a) shows the state before encryption; FIG. 20( b) shows the state after encryption of the present invention; and FIG. 20( c) shows the state after decryption; FIG. 21 is a block diagram of the configuration of the database according to the fifth embodiment of the database management apparatus of the present invention; FIG. 22 shows the contents of the data of the storage medium used in the database system; FIG. 23 shows the configuration of the system for performing encrypted data communications according to an embodiment of the present invention; FIG. 24 is a block diagram of the configuration of the circuit of the PC the security device used in the system; FIG. 25 shows the configuration of the database of the security device; FIG. 26 is a flowchart of the operations of the process of the PC and the security device when a user entry is made in the embodiment; FIG. 27 is a flowchart of the operations of the process of the PC and the security when data is encrypted in the embodiment; FIGS. 28A and 28B are flowcharts of the operations of the encrypting and decrypting processes in the embodiment; FIG. 29 shows the method of encryption operations using multidimensional vectors according to the present invention; FIG. 30 shows the configuration of the system showing the principle of the encryption/decryption system according to the present invention; FIG. 31 shows an example of the internal functions of devices 110 and 112 shown in FIG. 8; FIG. 32 is a flowchart of the process of generating a multidimensional vector; FIG. 33 is a flowchart of the encryption/decryption system using the process of generating a multidimensional vector; FIG. 34 is a flowchart of the decrypting process according to an embodiment of the present invention; FIG. 35 is a flowchart of the process of generating a three-dimensional vector r[j ]according to an embodiment of the present invention; FIG. 36 is a flowchart of the process of generating an n-dimensional rotation matrix R[n](Ω[n]) according to an embodiment of the present invention; and FIGS. 37A through 37C show the rotating operation of the three-dimensional vector according to an embodiment of the present invention. An embodiment of the present invention is described by referring to the attached drawings. FIG. 1 shows the configuration of the database management apparatus according to the present invention. The apparatus includes a database in a matrix form in rows and columns, and has the functions of encrypting and managing the database, encrypting input retrieving data, and searching the database according to the encrypted retrieving data. It reads a program stored in a storage medium such as a magnetic disk, etc., and is realized by a computer whose operation is controlled by the program. As shown in FIG. 1, the apparatus comprises a CPU 311, a display device 312, an input device 313, a program storage device 314, a key storage device 315, and a data storage device 316. The CPU 311 controls the entire apparatus, reads the program stored in the program storage device 314, and performs various processes according to the program. According to the present embodiment, the CPU 311 performs a database encrypting process as shown in FIG. 2, and a database searching process as shown in FIGS. 3A through 4B. The display device 312 is a device for displaying data. For example, an LCD (liquid crystal display), a CRT (cathode-ray tube), etc. are used. The input device 313 is a device for inputting data, and can be, for example, a keyboard, a mouse, etc. The program storage device 314 comprises, for example, ROM, RAM, etc. and stores a necessary program for the apparatus. The apparatus requires a program such as a database management program, an encryption program, etc. The program storage device 314 can comprise, in addition to semiconductor memory, a magnetic and an optical storage medium. The storage medium includes a portable medium such as CD-ROM, etc. and a fixed medium such as a hard disk, etc. All or a part of the program stored in the storage medium can be received from a transmission control unit of a server and a client through a transmission medium such as a network circuit, etc. The storage medium can be a storage medium of a server provided in a network. Furthermore, the program can be designed to be installed in the appliances of a server and a client after being transmitted to the server and the client through a transmission medium such as a network circuit, etc. The key storage device 315 comprises, for example, RAM, etc. and stores a key (a row key and a column key) used when a database is encrypted. The data storage device 316 is a device for storing various data necessary for the apparatus, and comprises, for example, RAM or an external storage device such as a magnetic disk device, etc. The data storage device 316 is provided with a database storage area 316 a for storing a database, an encryption setting information storage area 316 b for storing information (an item to be retrieved, a non-encrypted item, etc.) set by an operator when a database is stored, a retrieval setting information storage area 316 c for storing information (a target column item, a retrieval character string, etc.) set by an operator when a database is searched, a comparison character string storage area 316 d for storing a comparison character string when a database is searched, etc. Before describing the operations of the apparatus, the database encrypting method used by the apparatus is first described below. If a different key is used for each row (record) when a database is encrypted, it becomes more difficult to decrypt a key, thereby improving the security. However, since the encrypted data has to be decrypted using a key for each row or the input retrieving data (keyword) has to be encrypted using a key for each row when a database is searched, it takes a long time to obtain a retrieval result. On the other hand, if a database is encrypted using a different key for each column, retrieving data is encrypted using only a key corresponding to a column item to be retrieved, thereby searching a database at a high speed. However, when there are the same data in the same column, the same encryption results are output, which may allow the key to be decrypted. The feature of the present invention resides in that the data of a column item frequently used in a retrieving process is encrypted using a common column key, and the data of other column items is encrypted by assigning a different key to each row when a database is encrypted. That is, the security can be improved by using a different key for each row, and a high-speed retrieving process can be realized by encrypting the data input to a retrieving item using a column key, and comparing the encryption result with the encrypted data in the database. FIG. 5 shows the configuration of the database according to the first embodiment of the database management apparatus of the present invention; FIG. 5( a) shows the state before encryption; FIG. 5( b ) shows the state after encryption; and FIG. 5( c) shows the state after decryption. FIG. 6 shows the configuration of the column key and the row key according to the first embodiment of the database management apparatus. As shown in FIG. 5( a), the apparatus has a matrix in rows and columns. FIG. 5( a) shows personal data as a database. The database has a record comprising the items of: ‘number’, ‘name’, ‘weight’, ‘height’, ‘age’, and ‘phone’. The database is encrypted using a column key and a row key. That is, when a column item frequently used in a retrieving process comprises ‘name’, ‘state’, and ‘age’, the data of each row of the column item is encrypted using a column key common among column items such as the ‘apple’, ‘orange’, ‘lemon’, etc. as shown in FIG. 6, and the data of each row of other column items ‘weight’, ‘height’, and ‘phone’ is encrypted using a key specific to each row. It is assumed that the row of the ‘number’ is not encrypted. As a row key, ‘tiger’, ‘dog’, ‘cat’, ‘mouse’, ‘elephant’, ‘cow’, ‘pig’, ‘rabbit’, ‘lion’, etc. are used. These column keys and row keys determine a predetermined nonlinear function, and an encrypting (decrypting) process is performed by a binary operation (inverse binary operation) of the function and the vector mathematically generated using the function. In this case, the encryption/decryption system according to the present invention can be used as described below. FIG. 5( b) shows the result of encrypting the database shown in FIG. 5( a) using the column key and the row key. The database storage area 316 a of the data storage device 316 stores the database in the state as shown in FIG. 5( b). When the database is searched, the retrieving data is encrypted using a column key corresponding to the column item used in the retrieval, and then a retrieving process is performed. For example, when the data such as ‘Florida’ in the ‘State’ is to be retrieved, the ‘Florida’ input as a retrieving data is encrypted using the column key ‘apple’ of the ‘state’, thereby obtaining ‘h/fDD’. The data such as the ‘h/fDD’ is retrieved from each row of the column of the ‘state’. Thus, it is determined that the data corresponding to the ‘number2’ and ‘number8’ exist. In addition, when the encrypted database is restored to the original state, the column key and the row key used in the encrypting process are used. When the data is decrypted using the column key and the row key used in the database encrypting process as shown in FIG. 5( b), the original data can be obtained as shown in FIG. 5( c). Described below are the operations of the apparatus. The process (a) of encrypting a database, and the process (b) of retrieving a database are separately described below. The program for realizing each function shown in the flowchart in FIGS. 2 through 4 is stored in a storage medium of the program storage device 314 in program code readable by the CPU. The program can also be transmitted through a transmission medium such as a network (a) When a database is encrypted: FIG. 2 is a flowchart of the operations of the database encrypting process performed in the apparatus. FIG. 5( a) shows the state of the non-encrypted database stored in the database storage area 316 a of the data storage device 316. First, on the database encryption setting screen, a database to be encrypted is specified (step G11). Then, in the column items provided in the database, a column item used in a retrieving process and a column item not to be encrypted are set (step G12). In the example shown in FIG. 20( a), the column items used in a retrieving process are ‘name’, ‘state’, and ‘age’, and the column item not to be encrypted is ‘number’. The set information is stored in the encryption setting information storage area 316 b of the data storage device 316. Then, the row key and the column key used when the database is encrypted are determined (step G13). The information about the determined row key and column key is stored in the key storage device 315 When the column items in the database are sequentially specified after the above mentioned setting operations (step G14), the encryption system for the column item is determined according to the setting information (step G15). In this case, since the column item of the ‘number’ in the database is set as a non-encrypted item, no process is performed. That is, the item of the ‘number’ is unchanged as the original data. When the specified column item is set as a column item to be used in a retrieving process, a common column key for the column item stored in the key storage device 315 is read (steps G15 and G16), and the data in each row of the column item is encrypted using the column key (step G17). That is, the data of each row of each item of the ‘name’, ‘state’, and ‘age’ of the database is encrypted using a key specific to each column such as ‘apple’, ‘orange’, ‘lemon’, etc. as shown in FIG. 6. If the specified column item is not set as a column item for use in a retrieving process, that is, the other column items, then a row key corresponding to each row stored in the key storage device 315 is read (steps G15 through G18), and the data of each row of the column item is encrypted using a specific row key (steps G19 and G20). That is, as for the data of each item of the ‘state’, ‘weight’, and ‘height’ of the database, the data in row 1, 2, 3, 4, 5, 6, 7, 8, and 9 is encrypted respectively using the corresponding row keys ‘tiger’, ‘dog’, ‘cat’, ‘mouse’, ‘elephant’, ‘cow’, ‘pig’, ‘rabbit’, and ‘lion’ as shown in FIG. 6. Thus, the encrypting process is repeatedly performed for each column item of the database. When the data encrypting process is completed on each row of all column items, the encrypted database is overwritten in the database storage area 316 a of the data storage device 316 (step G22). FIG. 5( b) shows this state. (b) When a database is retrieved: FIGS. 3A and 3B are flowcharts of the operations of the database retrieving process performed by the apparatus. Assume that a database is encrypted in the encrypting process described above in (a) above, and stored in the data storage device 316. First, as shown in the flowchart shown in FIG. 3A, the database retrieval setting screen, retrieval information is input (step H11). Inputting retrieval information refers to inputting an item category title (hereinafter referred to as “column item”) to be retrieved (that is, an item category title referring to a category of items to be retrieved), and a retrieving character string (keyword). The input information is stored in the retrieval setting information storage area 316 c of the data storage device 316. When the retrieval information is input through the input device 313 , a pre-retrieval process is performed (step H12). In this pre-retrieval process, as shown in the flowchart shown in FIG. 3B, it is determined whether or not the column item input to be retrieved is a pre-retrieval process column item (step I11). If yes (YES in step I11), then the retrieving character string is encrypted using a common column key for the column item (step I12). A predetermined column item refers to an item to be retrieved (item used in a retrieving process) set when the database is encrypted, and practically corresponds to each of the items ‘name’, ‘state’, and ‘age’. The information relating to the item to be retrieved is stored in the encryption setting information storage area 316 b of the data storage device 316. Therefore, in step I11, it is determined whether or not an input column item is a predetermined column item by referring to the encryption setting information storage area 316 b. A common column key item to the column items is stored in the key storage device 315. Therefore, in step I12, a column key corresponding to the column item is read from the key storage device 315, and a retrieving character string is encrypted. For example, if the specified item is ‘state’, then a retrieving character string can be encrypted using the column key such as ‘orange’, etc. If an input column item to be retrieved is not a predetermined column item (NO in step I11), then the retrieving character string is not encrypted. After the above mentioned pre-retrieval process, the database is searched (refer to FIG. 4A)(step H13), and the data obtained as a retrieval result is displayed on the display device 312 (step H14). FIGS. 4A and 4B show a database searching process. FIGS. 4A and 4B are flowcharts of the practical operations of the retrieving process in step H13. First, as shown in the flowchart shown in FIG. 4A, a retrieving character string is set in the comparison character string storage area 316 d of the data storage device 316 as a character string to be compared with the database (step J11). In this case, as described above, if a column item input to be retrieved is a predetermined column item ‘name’, ‘state’, and ‘age’), then the retrieving character string is encrypted using the column key corresponding to the column item, and set in the comparison character string storage area 316 d in the pre-retrieval process. If the input item is not a predetermined column item, it is not encrypted, remains unchanged, and set in the comparison character string storage area 316 d. Then, the encryption system is determined by a column number of the encrypted database stored in the database storage area 316 a of the data storage device 316 (step J12). Thus, when an item to be retrieved is a predetermined column item encrypted using a column key, the data in each row of the target column is sequentially scanned (steps J12 and J13), and the character string of the data of the target item contained in the specified row is compared with the retrieving character string (encrypted character string) set in the comparison character string storage area 316 d (step J14). In the comparing process, as shown in the flowchart shown in FIG. 4B, the encrypted character string of the data of a target item retrieved from the database is compared with the encrypted character string for use in a retrieving process, and it is determines whether or not they match each other (step K11). When they match each other (YES in step K11), the record data containing the matching items is extracted as a database search result (step K12). The process is repeated until the end of the encrypted database, the corresponding data is sequentially extracted (step J15), and the extracted data is output as a retrieval result (step J20). Practically, in the example of the encrypted database shown in FIG. 5( b), for example, if the data such as ‘Florida’ in the item ‘state’, etc. is specified for retrieval, then the ‘Florida’ input as retrieving data is encrypted using the column key ‘apple’ of the ‘state’, thereby obtaining ‘h/fDD’. The data such as the ‘h/fDD’, etc. is retrieved from the column of the ‘state’. Thus, it is determined that the data corresponding to both ‘number 2’ and ‘number 8’ exists. On the other hand, when an item to be retrieved corresponds to one of other column items encrypted using a row key, the data in each row of the target column is sequentially scanned (steps J12 through J16), the data of a target item contained in a specified row is decrypted using a row key specific to each row (step J17), and then the result is compared with the retrieving character string (non-encrypted character string) set in the comparison character string storage area 316 d (step J18). In the comparing process, as shown in the flowchart shown in FIG. 4B, it is determined whether or not the decrypted character string of the data in a target column retrieved from the database matches the non-encrypted character string for use in a retrieving process (step K11). If they match each other (YES in step K11), then the record data containing the matching item is extracted as a database retrieval result (step K12). The process is repeated to the end of the encrypted database, the corresponding data is sequentially extracted (step J19), and the extracted data is output as a retrieval result (step J20). Practically, in the example of an encrypted database shown in FIG. 5( b), for example, when the data such as ‘163’ in the item ‘eight’ is specified to be retrieved, the data in row 1 of the ‘weight’ is decrypted using a row key such as the ‘tiger’, etc. Similarly, the data in rows 2, 3, 4, 5, 6, 7, 8, and 9 is decrypted respectively using the corresponding row keys ‘tiger’, ‘dog’, ‘cat’, ‘mouse’, ‘elephant’, ‘cow’, ‘pig’, ‘rabbit’, and ‘lion’ as shown in FIG. 6. Then, based on the ‘163’ input as retrieving data, the column of the ‘state’ or the corresponding data is retrieved. Thus, it is determined that the data corresponding to the ‘number 3’ and ‘number 9’ exists. Thus, when a database is encrypted, a predetermined column item used in a retrieving process is encrypted using a common column key. In a retrieving process, retrieving data is encrypted using the common column key, and compared with the encrypted data in the database, thereby realizing high-speed retrieval. In addition, a column item other than the predetermined column item is assigned a different key for each row and encrypted to improve the security. In this case, when a retrieving process is performed, the decryption using a key for each row is required. Therefore, it takes a longer time than in the retrieving process on the predetermined column item, which, however, is not a problem because the item is not frequently used in the retrieving process. According to the first embodiment, the data of the column items other than a predetermined column item is encrypted using a specific row key for each row. However, according to the second embodiment, a specific row key for each row and a common column key for a corresponding column item are used in combination in an encrypting process to furthermore improve the security. FIG. 7 shows the configuration of the database according to the second embodiment; FIG. 7( a) shows the state before encryption; FIG. 7( b) shows the state after encryption; and FIG. 7( c) shows the state after decryption. FIG. 8 shows the configuration of the composite key according to the second embodiment. As shown in FIG. 7( a), the apparatus has a matrix in rows and columns. Here shows personal data as a database. The database has a record comprising the items of: ‘number’, ‘name’, ‘weight’, ‘height’, ‘age’, and ‘phone’. The database is encrypted using a composite key. That is, when a column item frequently used in a retrieving process comprises ‘name’, ‘state’, and ‘age’, the data of each row of the column item is encrypted using a column key common among column items such as the ‘apple’, ‘orange’, ‘lemon’, etc. as shown in FIG. 8, and the data of each row of other column items ‘weight’, ‘height’, and ‘phone’ is encrypted using a composite key of a column key and a row key such as ‘banana+a row key’, ‘lychee+a row key’, ‘apricot+a row key’, etc. It is assumed that the row of the ‘number’ is not encrypted. As a row key, ‘tiger’, ‘dog’, ‘cat’, ‘mouse’, ‘elephant’, ‘cow’, ‘pig’, ‘rabbit’, ‘lion’, etc. are used. These column keys and row keys determine a predetermined nonlinear function, and an encrypting (decrypting) process is performed by a binary operation (inverse binary operation) of the function and the vector mathematically generated using the function. In this case, the encryption/decryption system according to the present invention can be used as described below. FIG. 7( b) shows the result of encrypting the database shown in FIG. 7( a) using a composite key. The database storage area 316 a of the data storage device 316 stores the database in the state as shown in FIG. 7( b). When the database is searched, as in the above mentioned first embodiment, the retrieving data is encrypted using a common column key corresponding to the column item used in the retrieval, and then a retrieving process is performed. For example, when the data such as ‘Florida’ in the ‘State’ is to be retrieved, the ‘Florida’ input as a retrieving data is encrypted using the column key ‘apple’ of the ‘state’, thereby obtaining ‘h/fDD’. The data such as the ‘h/fDD’ is retrieved from each row of the column of the ‘state’. Thus, it is determined that the data corresponding to the ‘number2’ and ‘number8’ exist. In addition, when the encrypted database is restored to the original state, the composite key used in the encrypting process is used. When the data is decrypted using the composite key used in the database encrypting process as shown in FIG. 7( b), the original data can be obtained as shown in FIG. 7( c). Since the processes performed when a database is encrypted or when an encrypted database is searched are the same as those of the above mentioned first embodiment (FIGS. 2 through 4B) except the data of each row of the column items other than a predetermined column item is encrypted using a combination of a column key and a row key, the explanation of the processes are omitted here. Thus, the column items frequently used in a retrieving process are encrypted using a column key common among the column items, thereby realizing high speed retrieval as in the above mentioned first embodiment. Other column items are encrypted using a column key and a row key as a composite key, thereby furthermore reinforcing the security. According to the first and second embodiments, the present invention is designed as a single apparatus, but can also be designed as a database system for requesting a retrieving process from another information terminal through a network with the database stored in separate places. Described below is the above mentioned database system. FIG. 9 is a block diagram of the configuration of the database system according to the third embodiment of the present invention. The system comprises a first terminal device 320 and a second terminal device 330. The first terminal device 320 is connected to the second terminal device 330 through a network 340. The first terminal device 320 is used as a server computer for providing a database service, and comprises a retrieval device 321 for searching a database, and a data storage device 322 for storing a database. The second terminal device 330 requests the first terminal device 320 to search a database, receives the result from the first terminal device 320 as a client computer, and comprises a retrieval request device 331 and a decryption device 332. With the database system, the first terminal device 320 encrypts the data of each row of a predetermined column item of a database using a column item common among corresponding column items as described above by referring to FIG. 2, encrypts the data of each row of other column items using a row key specific to each row, and stores the result in the data storage device 322. When the second terminal device 330 requests the first terminal device 320 to search a database, the second terminal device 330 performs the processes up to the pre-retrieval process shown in FIG. 3A. That is, the retrieval request device 331 of the second terminal device 330 determines whether or not a column item input to be retrieved is a predetermined column item, and encrypts a retrieving character string (keyword) using a column key common among corresponding column items when the input column item is a predetermined column item. When the input column item is not the predetermined column item, the encrypting process is not required. After the pre-retrieval process, the second terminal device 330 transmits a retrieving character string to the first terminal device 320 through the network 340. The first terminal device 320 performs the retrieving process as described above by referring to FIGS. 4A and 4B by receiving the retrieving character string. That is, the retrieval device 321 of the first terminal device 320 determines whether or not a column item to be retrieved is a predetermined column item, compares the retrieving character string (encrypted character string) obtained from the second terminal device 330 with the data of each row of the corresponding column item in the encrypted database in the data storage device 322 if the column item is a predetermined column item, and extracts the corresponding data. In addition, if a column item to be retrieved is an item other than the predetermined, then the data of the corresponding column item of the encrypted database in the data storage device 322 is decrypted using a key for each row, the retrieving character string (non-encrypted character string) obtained from the second terminal device 330 is compared with the decrypted data of each row, and the corresponding data is extracted. When a retrieval result can be obtained, the first terminal device 320 returns the data obtained as the retrieval result as encrypted data to the second terminal device 330 through the network 340. The second terminal device 330 shares an encryption key with the first terminal device 320. Therefore, when the second terminal device 330 receives a retrieval result from the first terminal device 320, the decryption device 332 can decrypt the data using the encryption key. In this case, since encrypted data is communicated between the first terminal device 320 and the second terminal device 330, the security of the database can be guaranteed. Thus, even in a database system having a database on the first terminal device 320 to search the database by access from the second terminal device 330, the data of a column item frequently used in a retrieving process is encrypted using a column key common among the corresponding column items, and the data of other column items are encrypted using a row key specific to each row, thereby improving the security and realizing high-speed retrieval. The data of the column items other than the predetermined column item can be encrypted using a composite key of a row key specific to each row and a column key common among the corresponding column items as in the above mentioned second embodiment, thereby furthermore improving the security. Described below is a further embodiment of the database management apparatus according to the present invention. FIG. 10 shows the configuration of the database management apparatus according to the fourth embodiment of the present invention. The apparatus encrypts and manages a database arranged as a matrix in rows and columns, and searches the encrypted database. It can be realized by a computer for reading a program which is stored in a storage medium such as a magnetic disk, etc., and controls the operations of the computer. As shown in FIG. 10, the apparatus comprises a CPU 411, a display device 412, an input device 413, a program storage device 414, a key generation device 415, a data storage device 416, and a database I/F 417. The CPU 411 controls the entire apparatus, reads a program stored in the program storage device 414, and performs various processes according to the program. According to the present embodiment, the CPU 411 performs an encrypting process for a database as shown in FIGS. 17A and 17B, and a retrieving process for the database as shown in FIGS. 18A through 19. The display device 412 is a device for displaying data, and can be, for example, an LCD (liquid crystal display), a CRT (cathode-ray tube), etc. The input device 413 is a device for inputting data, and can be, for example, a keyboard, mouse, etc. The program storage device 414 comprises for example, ROM or RAM, etc., and stores a program required by the apparatus. A program required by the apparatus can be, a database encryption program, a database search program, etc. The program storage device 414 can be, in addition to semiconductor memory, magnetic and optical storage media. The storage medium includes a portable medium such as CD-ROM, etc. and a fixed medium such as a hard disk, etc. A program stored in the storage medium can be designed such that a part or all of the program can be transmitted from a server or a client to a transmission control unit through a transmission medium such as a network circuit, etc. Furthermore, the storage medium can be that of a server provided in a network. Furthermore, the program can be transmitted to a server or a client through a transmission medium such as a network circuit, etc. The key generation device 415 is a device for generating an encryption key used in encrypting a database, and comprises, in this embodiment, a basic key generation unit 415 a, a row key generation unit 415 b, and a column key generation unit 415 c for generating three encryption keys, that is, a basic key, a row key, and a column key respectively. The data storage device 416 stores various data and tables required for the apparatus, and comprises RAM, or an external storage device such as a magnetic disk device, etc. The data storage device 416 comprises a basic key parameter table 416 a, a basic key storage unit 416 b, a key specification table 416 c, an encrypted data storage unit 416 d, and a retrieval character string storage unit 416 e. The basic key parameter table 416 a is a table in which a parameter value of a basic key is entered (refer to FIG. 13). The basic key storage unit 416 b stores a parameter value of a basic key obtained in a specifying operation by an operator. The key specification table 416 c is a table storing the types (non-encryption, a row key, a column key) of encryption system defined for each column (field) of a database (refer to FIG. 15). The encrypted data storage unit 416 d stores an encrypted database. The retrieval character string storage unit 416 e stores a retrieving character string specified by an operator when a database is searched. The database I/F 417 is an interface for transmitting and receiving data to and from an external database storage device 418 provided independent of the apparatus. The external database storage device 418 contains a plurality of database files (original data), and these database files are designed to be selectively read by access from the apparatus. Described below is the method of applying the above mentioned encryption system to a database in the apparatus. When a database is encrypted, it is difficult to decrypt a key if a different key is used for each row (record), thereby improving the security. However, since the encrypted data has to be decrypted using a key for each row or the input retrieving data (keyword) has to be encrypted using a key for each row when a database is searched, it takes a long time to obtain a retrieval result if a different key is used for any row. On the other hand, if a database is encrypted using a different key for each row (field), retrieving data is encrypted using only a key corresponding to a column item to be retrieved, thereby searching a database at a high speed. However, when there are the same data in the same column, the same encryption results are output, which may allow the key to be The feature of the present invention resides in that the data of a column item frequently used in a retrieving process is encrypted using a common key (column key), the data of other column items is encrypted using a different key (row key) for each row, and the key (row key) different for each row is encrypted using another common key (basic key) among the rows. The encrypting process (decrypting process) using a basic key can determine a predetermined nonlinear function, and an encrypting (decrypting) process is performed by a binary operation (inverse binary operation) of the function and the vector mathematically generated using the function. In this case, the encryption/decryption system according to the present invention can be used as described below. FIG. 20 shows a practical example. FIG. 20 shows the configuration of the database of the apparatus according to the present invention; FIG. 20( a) shows the state before encryption; FIG. 20( b) shows the state after encryption of the present invention; and FIG. 20( c) shows the state after decryption. As shown in FIG. 20( a), the apparatus encrypts a database arranged in a matrix in rows and columns. In this example, personal data is processed as a database. The database contains column items (fields) of ‘code’, ‘name’, ‘state’, ‘age’, and ‘phone’. The database is encrypted using a column key and a row key. That is, when a column item frequently used in a retrieving process comprises ‘state’ and ‘age’, the data (record) of each row of the column item is encrypted using a column key common among column items, and the data of each row (record) of other column items ‘name’ and ‘phone’ is encrypted using a specific row key for each row. Thus, the results are stored in a record file. At this time, a row key used when the corresponding column item is encrypted is encrypted using a basic key, and the encrypted row key is added to each record, and the result is stored. The data of the column item ‘code’ is not encrypted. FIG. 20( b) shows the result of encrypting the database shown in FIG. 20( a) using the column key and the row key. In this case, the column item such as ‘line key’ is added, and row keys (9658, 9143, 8278, . . . ) are added to the column item. The encrypted data storage unit 416 d of the data storage device 416 shown in FIG. 10 stores a database in the state shown in FIG. 20( b). When the database is searched, the retrieving data is encrypted using a column key corresponding to the column item used in the retrieval, and then a retrieving process is performed. For example, when the data such as ‘Florida’ in the ‘State’ is to be retrieved, the ‘Florida’ input as a retrieving data is encrypted using the column key of the ‘state’, thereby obtaining ‘h/fDD’. The data such as the ‘h/fDD’ is retrieved from each row of the column of the ‘state’. Thus, it is determined that the data corresponding to the ‘code 1002’ and ‘code 1008’ exist. In addition, when the encrypted database is restored to the original state, the column key, the row key, and the basic key used in the encrypting process are used. When the data is decrypted using the column key, the row key, and the basic key used in the database encrypting process as shown in FIG. 20(b), the original data can be obtained as shown in FIG. 20( c). Described below is the practical configuration for encrypting/decrypting a database. FIG. 11 is a block diagram of the configuration of the functions of the apparatus according to the present invention. The input process system of the apparatus comprises a basic key specification unit 421, a basic key setting unit 422, a key specification input unit 423, and a key specification setting unit 424. The encryption process system of the apparatus comprises a data read unit 425, a record input memory 426, an encrypting unit 427, an encrypted record write memory 428, and a data write unit 429. The encryption process system of the apparatus comprises an encrypted record read memory 430, a decrypting unit 431, a record output memory 432, and a data output unit 433. In addition, the above mentioned basic key parameter table 416 a, the basic key storage unit 416 b, the key specification table 416 c, and the encrypted data storage unit 416 d are used. The basic key parameter table 416 a is used for the basic key setting unit 422. The basic key storage unit 416 b, the key specification table 416 c, and the encrypted data storage unit 416 d are used for both encrypting unit 427 and decrypting unit 431. Various types of memory 426, 428, 430, and 432 shown in FIG. 11 is a group of registers, and provided in a predetermined area of the data storage device 416. When a database is encrypted with the configuration, a basic key is specified in an operation of an operator through the basic key specification unit 421. The basic key setting unit 422 reads the parameter value of the basic key specified by the basic key specification unit 421 from the basic key parameter table 416 a, and sets it in the basic key storage unit 416 b. Practically, the basic key is specified through the basic key setting dialog as shown in FIG. 12. The basic key setting dialog is a screen for optional specification of a basic key by an operator. On the screen, a basic key specification button unit 441, an OK button 442, and a cancel button 443 are provided. The basic key specification button unit 441 comprises a plurality of buttons. When an operator presses an optional button among these buttons, a parameter value of the basic key is determined depending on the position of the pressed button. The OK button 442 is used to guarantee the specification of a basic key, and the cancel button 443 is used to cancel the specification of the basic button. For example, assume that 16 buttons 1 through 16 are arranged on the basic key specification button unit 441 sequentially from left to right. As shown in FIG. 13, the parameter value of the basic key is defined corresponding to the positions of these buttons on the basic key parameter table 416 a. When an operator presses the button 1 on the basic key specification button unit 441, the parameter value of 5 of the basic key is determined according to the basic key parameter table 416 a. Similarly, when the button 2 on the basic key specification button unit 441 is pressed, the parameter value of 7 of the basic key is determined. Then, the external database storage device 418 is accessed, and the database to be encrypted is specified from among various databases stored in the external database storage device 418. After specifying the database, the operator specifies a key specification for each data item of the database through the key specification input unit 423. The key specification setting unit 424 enters the key specification information in the key specification table 416 c in the specifying operation of the key specification by the key specification input unit 423. Practically, the key specification is entered through the key specification setting dialog as shown in FIG. 14. The key specification setting dialog is a screen on which an encryption system (type of key used in encryption) is optionally specified by an operator for each array item (field) of the database. On the screen an encryption system specification column 451, an OK button 452, and a cancel button 453 are provided. As an encryption system, a key (row key) can be used for each row, or a key (row key) common among the columns can be used. In this example, a value can be input as an encryption system for each column item of a database to the encryption system specification column 451. The value can be 0 (non-encryption), 1 (a row key), or 2 (a column key). The OK button 452 is used to set the key specification. The cancel button 453 is used to cancel the setting of the key specification. When the encryption system is specified in the key specification setting dialog, the contents of the specification are entered in the key specification table 416 c as the key specification information for each column item. FIG. 15 shows an example of an entry in the key specification table 416 c. In this example, non-encryption is set as the item of the column number 1 of the database, a row key is set as the item of the column number 2, a column key is set as the item of the column number 3, a column key is set as the item of the column number 4, and a column key is set as the item of the column number 5. The item having the column number of 1 is ‘code’. The item having the column number of 2 is ‘name’. The item having the column number of 3 is ‘state’, the column having the column number of 4 is ‘age’, and the item having the column number of 5 is ‘phone’. When a basic key is set in the basic key storage unit 416 b, and when key specification information for each column item is set in the key specification table 416 c, the database is encrypted in the following procedure according to the setting information That is, as shown in FIG. 11, a database specified from the external database storage device 418 is read in row units (record units) by the data read unit 425, and sequentially stored in the record input memory 426. The encrypting unit 427 encrypts a record stored in the record input memory 426 using the basic key parameter table 416 a and the basic key storage unit 416 b. The encrypting process is described below in detail by referring to FIG. 16. After a record is encrypted by the encrypting unit 427 and stored in the encrypted record write memory 428, it is written to the encrypted data storage unit 416 d through the data write unit 429. Thus, the encrypted database is generated in the encrypted data storage unit 416 d. The database is decrypted in the inverse procedure. That is, first, the encrypted database stored in the encrypted data storage unit 416 d is read in row units (record units), and sequentially stored in the encrypted record read memory 430. The decrypting unit 431 decrypts the encrypted record stored in the encrypted record read memory 430 using the key specification table 416 c and the basic key storage unit 416 b. The decrypting process is described below in detail by referring to FIG. 16. The record decrypted by the decrypting unit 431 is stored in the record output memory 432, and is then output to a data file 434 through the data output unit 433. Thus, a decrypted database is generated in the data file 434. The data file 434 is provided in a predetermined area of the data storage device 416 shown in FIG. 10. FIG. 16 shows a practical example. FIG. 16 shows the flow of data when a database is encrypted and decrypted in the apparatus according to the present invention. Assume that the record in row 1 of the database specified to be encrypted is read by the data read unit 425, and stored in the record input memory 426. In this case, using the database shown in FIG. 20( a) as an example, the data having 5 items, that is, ‘1001’, ‘John’, ‘New York’, ‘22’, ‘407-228-6611’ in row 1 of the database is sequentially stored in the record input memory 426. The encrypting unit 427 encrypts the 5-item record for each item by referring to the key specification table 416 c. For example, when the contents set in the key specification table 416 c are as shown in FIG. 15, the first item (‘code’) data of the record corresponding to the column number 1 is not encrypted, and is written as is to the encrypted record write memory 428. In addition, the second item (‘name’) data of the record corresponding to the column number 2 is encrypted using a row key, and is written to the encrypted record write memory 428. A row key is generated at random using the row number and random numbers, and a different value is used for each row. The data of the third item (‘state’) of the record corresponding to the column number 3 is encrypted using a column key. The column key has a value common among the columns. Similarly, the data of the fourth item (‘age’) of the record corresponding to the column number 4 is encrypted using a column key, and the data of the fifth item (‘phone’) of the record corresponding to the column number 5 is encrypted using a row key. Then, they are written to the encrypted record write memory 428. Thus, a 1-row encrypted data of ‘100i’, ‘wjls’, ‘noevjolc’, ‘jh’, and ‘jgdltytfhDSk’ is generated in the encrypted record write memory 428. Furthermore, the encrypting unit 427 encrypts a row key used when the record is encrypted using the parameter value set in the basic key storage unit 416 b and a basic key common among the rows, and then the row key after the encryption is added to the encrypted record write memory 428. In the example shown in FIG. 16, the data ‘9568’ is a row key after the encryption. The above mentioned process is repeatedly performed on each row of the database, and the encrypted database is stored in the encrypted data storage unit 416 d. FIG. 20( b) shows this state. When an decrypting process is performed, the process inverse to the encrypting process is performed. That is, the encrypted database stored in the encrypted data storage unit 416 d is read in a record unit to the encrypted record read memory 430. Assuming that the encrypted record in row 1 is read to the encrypted record read memory 430, in the above mentioned example, a 6-item encrypted data of ‘1001’, ‘wjls’, ‘noevjolc’, ‘jgdltytfhDSk’, and ‘9568’ containing a row key is sequentially stored in the encrypted record read memory 430. The decrypting unit 431 decrypts the 6-item data record corresponding to each item by referring to the key specification table 416 c. In the example shown in FIG. 15, the data of the first item (‘code’) corresponding to the column number 1 is non-encrypted, the data is written as is to the record output memory 432. The data of the second item (‘name’) corresponding to the column number 2 is decrypted using a row key, and the result is written to the record output memory 432. Since the row key is encrypted in the encrypting process using a basic key, the row key is decrypted using the basic key to restore it to the original data. In addition, the data of the second item (‘name’) corresponding to the column number 3 is decrypted using a column key and written to the record output memory 432. Similarly, the data of the fourth item (‘age’) corresponding to the column number 4 is decrypted using a column key, and the data of the fifth item ‘phone’) corresponding to the column number 5 is decrypted using a row key. The results are written to the record output memory 432. Thus, 1-row decrypted data (original data), that is, ‘1001’, ‘John’, ‘New York’, ‘22’, ‘407-228-6611’ is generated in the record output memory 432. The above mentioned process is repeatedly performed on each row of the encrypted database, and the decrypted database is stored in the data file 434. FIG. 20( c) shows this state. The operations of the apparatus according to the present invention are described below by referring to the flowchart. In this example, the process (a) performed when a database is encrypted, and the process (b) performed when a database is searched are separately described below. The program for realizing each function in the flowchart is stored as CPU-readable program code in the storage medium of the program storage device 414. The program can be transmitted as program code through a transmission medium such as a network circuit. (a) When a database is encrypted: FIGS. 17A and 17B are flowcharts of the operations of the database encrypting process performed by the apparatus according to the present invention. Assume that a non-encrypted database is stored in the external database storage device 418. FIG. 17A shows this state. When a database is encrypted, a basic key is first set as shown in the flowchart in FIG. 17A (step N11). The basic key is set through the basic key setting dialog as described above. That is, as shown in the flowchart in FIG. 17B, the basic key setting dialog shown in FIG. 12 is displayed on the display device 412 when a database is encrypted (step O11). The basic key setting dialog is provided with the basic key specification button unit 441, and the operator specifies a basic key by pressing an optional button in a plurality of buttons arranged on the basic key specification button unit 441. If the operator pressed the OK button 452 to specify a basic key after the operator presses an optional button in the basic key specification button unit 441 (step O12), then the parameter value of the basic key corresponding to the position of the button is read from the basic key parameter table 416 a shown in FIG. 13, and is set in the basic key storage unit 416 b (step O13). Then, a database to be encrypted is specified (step N12). According to the present invention, the external database storage device 418 independent of the present apparatus stores various databases (original data). Therefore, when an encrypting process is performed, the external database storage device 418 is accessed through the database I/F 417, and a database is to be encrypted should be After a database to be encrypted is specified, a column item for use in a retrieving process in the database and a column item not to be encrypted are set (step N13), and an encryption key (a row key and a column key) for each column item is determined (step N14). The setting process is performed through the key specification setting dialog as shown in FIG. 14. The key specification setting dialog is a screen on which an encryption system (type of key used in encryption) is optionally specified by an operator for each column item (field) of the database. The screen is displayed on the display device 412 when a database to be encrypted is specified. In this example, a value can be input as an encryption system for each column item of a database to the encryption system specification column 451 provided in the key specification setting dialog shown in FIG. 31. The value can be 0 (non-encryption), 1 (a row key), or 2 (a column key). In this case, in the database shown in FIG. 20( a), the column items used in a retrieving process are ‘state ’ in column 3, and ‘age’ in column 4. A column key is specified for these column items, and a row key is specified for other items ‘name’ in column 2 and ‘phone’ in column 5. A column item not to be encrypted is ‘code’ in column 1. The encryption key set in this example is entered in the key specification table 416 c as key specification information as shown in FIG. 15. After the setting operation, the database is encrypted as follows. That is, the data in each row of the database is sequentially read from the first row to the record input memory 426 shown in FIG. 11 (step N15). At this time, a row key is generated at random based on a line number assigned to each row by the row key generation unit 415 b of the key generation device 415 and a random number, and is stored in a predetermined area of the data storage device 416 (step N16). Each column item of the row data read to the record input memory 426 is sequentially specified from the first column (step N17), and the encryption system for the specified column item is determined according to the key specification information stored in the key specification table 416 c (step N18), and is encrypted using a row key or a column key (steps N19 through N22). Practically, since the item ‘code’ in the first column of the database is set as a non-encryption item as shown on the key specification table 416 c shown in FIG. 15, no action is taken (steps N18 through N23). That is, the item ‘code’ remains original data. Since a row key is set for the item ‘name’ in the second row, the row key (specific to each row) corresponding to the row number generated in step N16 is read from a predetermined area of the data storage device 416 (steps N18 through N21), and the data in the second column is encrypted using the row key (step N22). In addition, since a column key is set for the item ‘state’ in the third column, the column key (key common among the columns) corresponding to the column number is generated by the column key generation unit 415 c of the key generation device 415 (steps N18 and N19), and the data in the third column is encrypted using the column key (step N20). Similarly, the item ‘age’ in the fourth column is encrypted using a column key, and the item ‘phone’ in the fifth column is encrypted using a row key. The encrypted data of each column item is stored in the encrypted record write memory 428 shown in FIG. 11. When the last item is encrypted, the row key used in encrypting the second and third columns of the data of the line is encrypted using the basic key, and added to the encrypted record write memory 428 (step N25). The basic key is generated by the basic key generation unit 415 a of the key generation device 415. The basic key generation unit 415 a reads the parameter value set by the operator in the basic key setting dialog shown in FIG. 12 from the basic key storage unit 416 b , and generates a basic key based on the parameter value. When 1-row encrypted data and data obtained by encrypting a row key using a basic key are stored in the encrypted record write memory 428, the data is stored in the encrypted data storage unit 416 d (step N25). The above mentioned encrypting process is repeatedly performed on each row (steps N26 through N15). When the data in all rows are encrypted, the final state of the encrypted database is shown in FIG. 20( b). In this encrypted database, the row key is encrypted using a basic key, and is added to the last item of each row. (b) When a database is searched: The process of searching an encrypted database is described below. FIGS. 18A and 18B are flowcharts of the operation of the database searching process performed in the present apparatus. Assume that a database is encrypted in the encrypting process shown in (a) above and stored in the basic key storage unit 416 b. First, as shown in the flowchart in FIG. 18A, the retrieval information is input on the database search setting screen not shown in FIG. 18A (step P11). An input of the retrieval information refers to inputting a column item to be retrieved and a retrieving character string (keyword). The input information is stored in a predetermined area of the data storage device 416. When the retrieval information is input through the input device 413, the pre-retrieval process is performed (step P12). In this pre-retrieval process, as shown in the flowchart in FIG. 18B, it is determined whether or not the column item input to be retrieved is a predetermined column item (step Q11). When it is determined that the input item is a predetermined column item (YES in step Q11), the retrieving character string is encrypted using a column key common among the column items (step Q12). A predetermined column item refers to an item to be retrieved which is set when the database is encrypted. Practically, it refers to each of the items ‘state’ and ‘age’. A column key is set for an item to be retrieved. Therefore, it is determined in step Q11 whether or not an input item is a predetermined column item depending on the type of key set for the corresponding column item by referring to the key specification table 416 c. If it is a predetermined column item, then a column key corresponding to the column item is generated by the column key generation unit 415 c of the key generation device 415, and the retrieving character string is encrypted using the column key. If the input column item input to be retrieved is not a predetermined column item (NO in step Q11), then the retrieving character string is not encrypted as described above. After the above mentioned pre-retrieval process, the database is searched (refer to FIGS. 19A and 19B) (step P13), and the data obtained as a retrieval result is displayed on the display device 412 (step P14). FIGS. 19A and 19B shows the process of searching a database. FIGS. 19A and 19B are flowcharts of practical operations of the searching process in step P13. First, as shown in the flowchart in FIG. 19A, a retrieving character string is set as a character string to be compared with the database in the retrieval character string storage unit 416 e of the data storage device 416 (step R11). In this case, if the input item is a column item to be retrieved (‘state’, ‘age’), then the retrieving character string is encrypted using a column key corresponding to the column item in the pre-retrieval process, and the result is set in the retrieval character string storage unit 416 e. If the input item is not the column item to be retrieved, then it is not encrypted, but is set as is in the retrieval character string storage unit 416 e. Then, the encryption system of the encrypted database stored in the basic key parameter table 416 a of the data storage device 416 is determined based on the column number (step R12). If an item to be retrieved is a predetermined column item encrypted using a column key, then each row data in a target column is sequentially scanned (steps R12 and R13), and an encrypted character string in the row is compared with a retrieving character string (encrypted character string) set in the retrieval character string storage unit 416 e (step R14). In this comparing process, the encrypted character string in the row, which is retrieved from the database, is compared with the retrieving encrypted character string as shown in the flowchart in FIG. 19B, and it is determined whether or not they match each other (step S11). If they match each other (YES in step S11), then the record data including the matching item is extracted as a database retrieval result (step S12). The process is repeated up to the end of the encrypted database, the corresponding data is sequentially extracted (step R15), and the extracted data is output as a retrieval result (step R21). Practically, in the example of the encrypted database shown in FIG. 20( b), when the data ‘Florida’ in the item ‘state’ is specified to be retrieved, the ‘Florida’ input as retrieving data is encrypted using the column key in row 3 of ‘state’, thereby obtaining ‘h/fDD’. The data ‘h/fDD’ is retrieved from the column of ‘state’. Thus, the data corresponding to the code numbers of 1001 and 1008 exists. When an item to be retrieved is a column item encrypted using a row key, row data of the target column is sequentially scanned (steps R12 through R16). Since each row key used when each piece of row data is encrypted is encrypted using a basic key, it is necessary to decrypt each row key using a basic key (step R17). When each row key is decrypted using a basic key, an encrypted character string in each row is decrypted using a row key (step R18), and the decrypted character string is compared with the retrieving character string (non-encrypted character string) set in the retrieval character string storage unit 416 e (step R19). In this comparing process, the encrypted character string in the row, which is retrieved from the database, is compared with the retrieving encrypted character string as shown in the flowchart in FIG. 19B, and it is determined whether or not they match each other (step S11). If they match each other (YES in step S11), then the record data including the matching item is extracted as a database retrieval result (step S12). The process is repeated up to the end of the encrypted database, the corresponding data is sequentially extracted (step R20), and the extracted data is output as a retrieval result (step R21). Practically, in the example of the encrypted database shown in FIG. 20( b), when the data ‘Jhon’ in the item ‘name’ is specified to be retrieved, the row key ‘9654’ (encrypted data) corresponding to the row 1 of the ‘name’ is decrypted using a basic key, and then ‘wJIS’ in row 1 is decrypted using the row key, thereby obtaining the data such as ‘Jhon’. Similarly, after a row key (encrypted data) corresponding to each row is decrypted using a basic key, the original data is obtained by decrypting the data of each row using the row key. As shown in FIG. 20( c), after the data of each row of the item ‘name’ is decrypted using each row key, data matching ‘Jhon’ input as retrieving data is retrieved from the decrypted data. Thus, it is determined that the data corresponding to the code number of ‘1001’ exists. Thus, when a database is encrypted, a predetermined column item used in a retrieving process is encrypted using a common column key so that the retrieving data can be encrypted using the common column key in the retrieving process, and compared with the encrypted data in the database, thereby realizing a high-speed retrieving process. Furthermore, a column item other than the predetermined column item is encrypted using a key specific to each row, and the row key is encrypted using a basic key, thereby complicating the decryption of the keys and realizing high security. According to the fourth embodiment, the present invention is designed in device units, but a database system can be designed in terminal units by dividing the terminals into those for database management and those for database search. Described below is a database system according to the fifth embodiment of the present invention. FIG. 21 is a block diagram of the configuration of the database system according to the fifth embodiment. The present system comprises a server device 1100 and a plurality of (thee terminals in this example) portable terminals 1200 a, 1200 b, 1200 c, . . . The server device 1100 communicates online with each of the portable terminals 1200 a, 1200 b, 1200 c, . . . , and they communicate data through storage media 1400 a, 1400 b, 1400 c, . . . The server device 1100 is used as a server computer for providing database services, and comprises a distribution data collection device 1101 for collecting data to be distributed to each terminal, an encryption device 1102 for encrypting a database, a AP software storage unit 1103 for storing various application software (AP), and a database storage unit 1104 for storing various databases. The AP software storage unit 1103 and the database storage unit 1104 can be, for example, a data storage device such as a magnetic disk device, etc. In addition, the server device 1100 can also comprise a display device, an input device, etc. normally provided for a general-purpose computer not shown in the attached drawings. On the other hand, the portable terminals 1200 a, 1200 b, 1200 c, . . . are used as a client computer for receiving a database from a server device. The portable terminal 1200 a comprises a decryption device 1201 a for decrypting an encrypted database, and a database search device 1202 a for searching a database. The portable terminals 1200 b and 1200 c have the similar configuration, and respectively comprise decryption devices 1201 b and 1201 c, and database search devices 1202 b and 1202 c. The portable terminals 1200 a, 1200 b, 1200 c, . . . are provided with a medium read device in addition to a display device, an input device, etc. although they are not shown in the attached drawings. These portable terminals 1200 a, 1200 b, 1200 c , . . . are not provided with a browsing function for viewing data online, and are designed to communicate data with the server device 1100 through the storage media 1400 a, 1400 b, 1400 c, . . . The storage media 1400 a, 1400 b, 1400 c, . . . are portable storage media containing, for example, CF cards (compact flash memory cards). A card reader/writer 1300 is a device for writing and reading data to and from the storage media 1400 a, 1400 b, 1400 c, . . . , and is connected to the server device 1100. With the configuration, the server device 1100 reads a database specified by an operator from among various databases in the database storage unit 1104, and encrypts it through the encryption device 1102. In this case, the encryption device 1102 encrypts the database in the method similar to that used in the fourth embodiment. That is, a predetermined column item used in a retrieving process is encrypted using a common column key while column items other than the predetermined column item are encrypted using a different key for each row, and the row key is encrypted using a basic key. The database encrypted by the encryption device 1102 is stored in a file, and the encrypted data file is stored in the storage media 1400 a, 1400 b, 1400 c, . . . such as a CF card, etc. using the card reader/writer 1300. In this case, when an encrypted data file is stored in the storage media 1400 a, 1400 b, 1400 c, . . . , a key specification table 1403, a basic key parameter table 1404, and a application program 1401 are stored in addition to an encrypted data file 1402 as shown in FIG. 22. The key specification table 1403 is a table storing the type (non-encryption, a row key, a column key) of encryption system defined for each column (field) of a database, and has the configuration similar to that of the key specification table 416 c according to the fourth embodiment (refer to FIG. 15). The basic key parameter table 1404 is a table in which a parameter value of a basic key is entered, and has the configuration similar to that of the basic key parameter table 416 a according to the fourth embodiment (refer to FIG. 13). The key specification table 1403 and the basic key parameter table 1404 are stored in the encryption device 1102. The application program 1401 is used when a database is searched, and is stored in the AP software storage unit 1103. The storage media 1400 a, 1400 b, 1400 c, . . . are respectively distributed to the portable terminals 1200 a, 1200 b, 1200 c, . . . Each user can retrieve data by inserting the distributed storage media 1400 a, 1400 b, 1400 c, . . . in his or her own terminal. That is, for example, the portable terminal 1200 a inserts the distributed storage medium 1400 a, and reads the key specification table 1403 and the basic key parameter table 1404 in addition to the application program 1401 and the encrypted data file 1402 stored in the storage medium 1400 a for the data retrieving process. Then, the application program 1401 for a data retrieving process is activated, a predetermined column item is specified, the encrypted data file 1402 is retrieved, and the data obtained as a result of the retrieval is decrypted and displayed. A data retrieving process is performed by the database search device 1202 a provided in the portable terminal 1200 a. The database search device 1202 a is operated according to the application program 1401, and is similar to the database search device according to the fourth embodiment. Data is decrypted by the decryption device 1201 a. The decryption device 1201 a performs a database decrypting process as in the fourth embodiment by referring to the key specification table 1403 and the basic key parameter table 1404. Thus, if a database system is designed with a database management terminal independent of a database retrieval terminal, then a customer managing database can be encrypted and stored in a storage medium, and then distributed to a sales person. Thus, the sales person can use another terminal to retrieve data. In this case, since the database stored in the storage medium is encrypted in the above mentioned method, the security of the data can be guaranteed. The storage medium stores not only an encrypted data file, but also a data retrieving application program. Therefore, it is not necessary for a portable terminal to be provided with a data retrieving application program, and the system can be realized with a simple portable terminal. According to the database management apparatus, the data of a column item other than a predetermined column item used when a retrieving process is performed is encrypted using a different key for each row, and the key used when the column item is encrypted is encrypted using another key, thereby complicating the decryption of a key and realizing high security. Described below is the encryption/decryption system used in the database management apparatus. FIG. 23 shows the concept of the configuration of an encrypted data communications system. In FIG. 23, 11 a and 11 b are personal computers (hereinafter referred to as PCs), and 12 a and 12 b are security devices. In this example, data communications are established between the PC 11 a of a user A and the PC 11 b of a user B. The PCs 11 a and 11 b are general-purpose computers, and they can be respectively connected to the security devices 12 a and 12 b. The security devices 12 a and 12 b comprises IC cards. Information is written to the security devices 12 a and 12 b when they are delivered from their factory. The information includes the production number of an IC card, the user ID of each member of a group, and an encryption key (private key P1, P2). The information is common among the members of a group, and is not public. FIG. 24 is a block diagram of the configuration of the circuit of the PC 11 a and the security device 12 a. The PC 11 b and the security device 12 b have the same configurations as the PC 11 a and the security device 12 a. The PC 11 a is a general-purpose computer comprising a CPU 21, and processes data by invoking a primary program. To the CPU 21, a storage device 22, RAM 23, a keyboard 24, a display unit 25, and a card I/F (interface) 26 are connected through a system bus. The storage device 22 comprises, for example, a hard disk device, a floppy device, a CD-ROM device, etc., and stores various data, programs, etc. In this example, it stores plaintext data to be encrypted, an authentication file described later, etc. In addition, a program stored in a storage medium (a disk, etc.) is installed in the storage device 22. The CPU 21 reads a program installed in the storage device 22, and performs a process according to the program. The RAM 23 functions as the primary memory of the apparatus according to the present invention, and stores various data required to perform the process for the apparatus. The keyboard 24 is an input device for inputting data and issuing an instruction of various functions. The display unit 25 comprises, for example, a CRT (cathode ray tube), an LCD (liquid crystal display), etc., and is a display device for displaying data. The card I/F 26 is connected to the security device 12 a through a connector 27, and controls input and output of data to and from the security device 12 a. The security device 12 a comprises an IC card and a CPU 31, and processes data by invoking a secondary program. ROM 32, RAM 33, and flash memory 36 are connected to the CPU 31 through a system bus. The ROM 32 stores a secondary program for realizing the function as the security device 12 a. The RAM 33 stores various data required for a process performed by the security device 12 a. In this example, it comprises an input buffer 34 for temporarily storing data transmitted from the PC 11 a, and an output buffer 35 for temporarily storing data to be transmitted to the PC 11 a. Flash memory 36 is used as a storage device for storing a database 41 shown in FIG. 25. As shown in FIG. 25, the database 41 comprises information (non-public information) common among the members and information (public information) specific to each member. The information (non-public information) common among the members includes a production number, the user ID of each member of the group, and encryption key data (private key P1, P2). The information (public information) specific to each member includes encryption key data (public key P3, P4), and a password. The password is used as a part of the public key. A connector 37 is used to electrically connect the security device 12 a to the PC 11 a. Briefly described below are the operations performed when encrypted data communications are set in the system shown in FIG. 23. First, the security devices 12 a and 12 b used as IC cards are transmitted to each member of a group. The security devices 12 a and 12 b are provided with the database 41 in which a production number, the user ID of each member of a group, and the encryption key data (private key P1, P2) are entered in advance. Each member writes the encryption key (public key P3, P4) and a password to the security devices 12 a and 12 b. The written information is stored in the public portion of the database 41. When encrypted data is transmitted from the PC 11 a to the PC 11 b, each member (users A and B) inserts the security devices 12 a and 12 b respectively to the PCs 11 a and 11 b to perform an encrypting process. In this case, according to the present invention, the encryption algorithm is based on the generation of a vector described later. At this time, the parameter (hereinafter also referred to as a ‘constant’) for determination of a nonlinear function for generation of the vector is determined by an encryption key (private and public keys). The encrypted document is transmitted together with a public key to a correspondent. On the reception side, using the received public key and the receiver's private key, the encrypted document is decrypted using a vector generated using the same nonlinear function. Described below is the operation according to the embodiment. In this embodiment, by referring to the PC 11 a and the security device 12 a shown in FIG. 23, the operations of the processes are described in each of the two modes of (a) user entry, and (b) data encryption. (a) User Entry First, a user makes a user entry when the usee established encrypted data communications using the security device 12 a. That is, a member assigned the security device 12 a (IC card) enters information about the public portion shown in FIG. 25 in his or her own PC 11 a. FIGS. 26( a) and 26(b) are flowcharts of the operations of the processes of the PC 11 a and the security device 12 a performed when a user entry is made. A user inputs user authentication data in the PC 11 a through the primary program on the PC 11 a (step A11). In this case, the user authentication data refers to a user ID. The primary program transfers the input user ID to the input buffer 34 of the security device 12 a (step A12). Then, it passes control to the secondary program on the security device 12 a. On the security device 12 a side, when the secondary program confirms that the data is stored in the input buffer 34, it reads the data (step B11). Then, the secondary program accesses the flash memory 36 of the security device 12 a, and checks whether or not the user ID input as the user authentication data has been entered in the database 41 stored in the flash memory 36. As a result, if the user ID has not been entered in the database 41 (NO in step B12), then it is determined that the user is not a member of the group, and the process terminates (step B13). If the user ID has been entered in the database 41 (YES in step B12), then it is determined that the user is a member of the group, and the user is requested through the PC 11 a to enter his or her password and encryption key (public key)(step B14). In response to the request, the user inputs his or her password and encryption key (public key) (step A13). The primary program on the PC 11 a transfers the input password and the encryption key (public key) to the input buffer 34 of the security device 12 a (step A14). The password is used as a part of a public key. When the password and encryption key (public key) are input from the user authenticated as a group member, the secondary program of the security device 12 a reads the input information, encrypts it as necessary, and writes the result to the public portion of the database 41 stored in the flash memory 36 (step B15). At this time, the nonlinear function used by a user in an encrypting process is determined. A plurality of constants used in the function are fixed by a key. According to an embodiment of the present invention, a multidimensional vector generation function is used as a nonlinear function, which is described later in detail. After processing the information, the secondary program generates a report of the database 41 (step B16), stores it in the output buffer 35 of the security device 12 a, and passes control to the primary program (step B17). To the above mentioned report, the encrypted data to be used by the primary program when a user authenticating process is performed is written. On the PC 11 a side, the primary program confirms that data is stored in the output buffer 35 of the security device 12 a, reads the data, and writes it as file data to the storage device 22 (step A15). The written file data is processed as an authentication file, and is used for a user authentication check when encrypted data communications are hereinafter established (step A16). (b) Data Encryption Data encryption refers to actually encrypting and transmitting a document. FIGS. 27( a) and 27(b) are flowcharts of the operations of the processes performed by the PC 11 a and the security device 12 a when data is encrypted. A user inputs his own user ID and password with the security device 12 a (IC card) inserted in the PC 11 a. By inputting the user ID and password, the primary program of the PC 11 a refers to the authentication file, and authenticates the user (step C12). If the user is not a registered user (NO in step C121) as a result of the authentication check (step C121), then the primary program enters a termination procedure (step C16). If the user is a registered user (YES in step C121), then the primary program transmits the input user ID and password to the security device 12 a (step C13). On the security device 12 a, the secondary program reads the user ID and password (step D11). Then, the secondary program compares the information with the contents of the database 41 in the flash memory 36, and authenticates the user (step D12). As a result of the user authentication check, the secondary program generates an authentication report indicating whether or not the user has been registered in the security system, transfers the authentication report to the security device 12 a, and passes it to the primary program of the PC 11 a (step D13). On the PC 11 a side, the primary program reads the authentication report transmitted from the security device 12 a, and confirms that the user has been authenticated on the security device 12 a side (step C14). If the user is rejected in the user authentication check, that is, if the authentication report indicates that the user is not a registered user (NO in step C15), then the primary program of the PC 11 a notifies the user of it, and terminates the process (step C16). If the user is confirmed as a registered user in the user authentication check, that is, if the authentication report indicates that the user is a registered user (YES in step C15), then the primary program of the PC 11 a performs the following encrypted data communications. That is, the primary program reads the plaintext data (generated document) to be encrypted from the storage device 22, transfers it with the authentication report added to it to the input buffer 34 of the security device 12 a, and passes control to the secondary program of the security device 12 a (step C17). A authentication report is added to the plaintext data to allow the security device 12 a to confirm that the document has been received from the registered user authenticated by the security device 12 a. On the security device 12 a side, the secondary program reads the plaintext data transmitted from the PC 11 a (step D14). If no authentication report is added to the plaintext data (NO in step D15), then it is determined that the document is not received from a registered user, thereby terminating the process (step D16). On the other hand, if an authentication report is added to the plaintext data (YES in step D15), then it is determined that the document is received from a registered user, and the secondary program encrypts the plaintext data by the encryption system using a multidimensional vector described later (step D17). Then, the secondary program stores a decryption key (public key) and encrypted data (encrypted document) in the output buffer 35 of the security device 12 a, and transmits them to the PC 11 a (step D18). The primary program of the PC 11 a receives the decryption key and the encrypted data (encrypted document) (step C18), outputs them as a file in the storage device 22 of the PC 11 a, or passes control to the communications software such as electronic mail, etc., and transmits them externally (to the PC 11 b shown in FIG. 1)(step C19). Described below are the operations of the encrypting process performed by the security device 12 a. FIG. 28A is a flowchart of the operations of an encrypting process. The plaintext data (message data) to be encrypted is defined as M (step E11). The data M is binary data. The secondary program of the security device 12 a first applies a scramble 1 in bit units to the data M (step E12). The obtained data is defined as M′ (step E13). The secondary program XORs (obtains an exclusive logical sum) by adding the data M′ to the random numbers generated mathematically and sequentially, and then performs an encrypting process (step E14 ). At this time, a generation function of a multidimensional vector r is used as a random number generation function. In this case, the function for generation of the multidimensional vector r, or a constant used for the function is determined by an encryption key (private and public keys). That is, the secondary program reads a private key (P1, P2) and a public key (P3, P4) from the database 41 when an encrypting process is performed, generates a multidimensional vector r according to the function using the encryption keys as a parameter constant, and performs a logical operation such as M′ XOR r, thereby performing an encrypting process. Thus, the obtained encrypted data is defined as C (step E15). Practically, assume that, as shown in FIG. 29, r is a three-dimensional vector (x, y, z) and the computation precision of the vector components x, y, and z is 16 bit. According to the equation (1) described later, the three-dimensional vectors r (x, y, z) are sequentially generated as r0, r1, r2, r3, When the data M is given as m0 m1 m2 m3 m4 m5 m6 . . . as a sequence of 8-bit data (a character string having 8 bits for each character), M is decomposed in two-element (8 bits) units based on the computation precision (16 bits). If the three-dimensional vector is r0, then the data M and r0 (x0, y0, z0) are XORed (obtained as an exclusive logical sum), thereby performing computation by (x XOR m0 m1)(y XOR m2 m3)(z XOR m4 m5) . . . , etc. As a result of the computation, the encrypted data C such as C0 C1 C2 C3 C4 C5 etc. can be obtained. The secondary program furthermore applies a scramble 2 in bit units to the data C obtained as described above (step E16). The obtained data is defined as C′, and output as the final encrypted data (step E17). In the above mentioned process, the unreadableness level of illegal deciphering can be raised by repeatedly performing the similar encrypting process with the C′ defined as M′. If the form of the function for generation of the multidimensional vector r is changed, the unreadableness level can be furthermore raised. Described below is the operation of the decrypting process performed by the security device 12 a. FIG. 28B is a flowchart of the operation of the decrypting process. The decrypting process can be performed simply by inversely performing the encrypting process. That is, assuming that the encrypted data is defined as C′ (step F11), the secondary program of the security device 12 a first applies an inverse scramble 2 which is inverse to the scramble 2 applied in the encrypting process in bit units onto the data C (step F12). Thus, the data C can be obtained as the data before applying the scramble 2 (step F13). Then, the secondary program decrypts the data C by performing a computing process such as C XOR r, etc. (step F14), thereby obtaining the data M′ before performing an encrypting process (step F15). The secondary program applies an inverse scramble 1 which is inverse to the scramble 1 applied in the encrypting process in bit units onto the data M1 (step F12). Thus, the data can be obtained as the data before applying the scramble 1, that is the plaintext data M can be obtained (step F17). If the process of repeating an encrypting process with the C′ defined as the M′, changing the form of a function for generation of a multidimensional vector r, etc. has been added in the encrypting process, then a decrypting process is performed corresponding to the added process. According to the present invention, a set P of parameters (constants) determining the function for a multidimensional vector r in the encrypting process performed using a multidimensional vector r is divided into two portions, and expressed as follows. P={Ps, Pp} where Ps is a private parameter, and corresponds to the encryption key (private key P1, P2) stored in the non-public portion of the database 41, and Pp is a public parameter, and corresponds to the encryption key (public key P3, P4) stored in the public portion of the database 41. Ps together with Ps is used in authenticating a user, and encrypting and decrypting data. According to the present embodiment, there are two Ps and two Pp, but it is obvious that the number of parameters is not limited to this application. Described below is the encryption system according to an embodiment of the present invention. Assume that the vector in the n(n≧1)-dimensional space is r, and the matrix sequentially generating new vectors r[j](j=0, 1, 2, 3, . . . ) from the initial value r[0 ]is R. At this time, the vector r [j ]is expressed by a nonlinear function of the following quation (1). r [j] =a·R(P,r [j−1])r [j−1] +c(1) where a is an appropriate constant coefficient, P is a set of constants used in the matrix, and an encryption key (private key P1, P2) stored in a non-public portion of the database 41 and an encryption key (public key P3, P4) stored in a public portion of the database 41 are used. c is a constant vector for spatial translation of a vector. In equation (1) above, the coefficient a sets a condition for each vector to be in the closed space area of a multidimensional space when an appropriate restriction (for example, \|R\|≦1) is placed on the matrix R. The constant vector c guarantees that the vector r[j ]will not converge into a trivial point (for example, an insignificant point having r=0) (c=0 is obviously allowed). In the n-dimensional space, the vector r has n components (r=(x1, x2, . . . , xn)). In computation, a numeral data is generally represented by the precision of bit length (m) (for example, 8 bytes or 64 bytes) as defined by a compiler. Therefore, if the vector r cannot be regenerated with data precision of n×m at a moment in the sequential vector generation method, the subsequent vector r cannot be correctly regenerated (or the matrix R is so defined). This holds true with the initial value r[0 ]of the vector r. That is, only when the initial value r[0 ]can be regenerated with data precision of n×m, the subsequent vectors r[1], r[2], r[3], . . . can be guaranteed. In the encrypting process according to an embodiment of the present invention, one or more components, depending on the defined data length, of the vector r obtained in the equation (1) above are arranged, and are XORed (processed in an exclusive logical operation) on each bit with the character string (normally 8 bits per character) corresponding to the total bit length. This is referred to as the first encrypting process which has been described above by referring to FIG. 29. The procedure can be performed in a duplex process as a countermeasure against decryption. In this case, the matrix R of the equation (1) above can be changed again to generate a new vector so that another encrypting process can be performed in the same method as the first encrypting process. This is referred to as the second encrypting process. In a practical example, n equals 2 (n=2). First, R is defined as an operation in which r[j−1 ]rotates by θ round the normal set on the plane. The R is a matrix of 2×2, and can be represented as $R ⁡ ( θ ) = ( cos ⁢ ⁢ θ - sin ⁢ ⁢ θ sin ⁢ ⁢ θ cos ⁢ ⁢ θ ) ( 2 )$ In this case, θ is a kind of parameter. That is, the parameter is given as a function of r[i−1 ]and can be represented by the following equation. At this time, the transformation represented by the equation (2) above can be formally represented by the equation (1) above. In this case, the nonlinearity complicates the vector generating process. In the equation (3) above, P is defined as a set of constants used in the nonlinear function f, and the encryption key (private key P1, P2) stored in the non-public portion of the database 41 and the encryption key (public key P3, P4) stored in the public portion of the database 41 are used. Thus, by using the vectors r sequentially generated in a multidimensional space in an encrypting process, the encrypting process can be performed independent of the precision or performance of a computer as compared with such an encrypting process as the RSA. In addition, an application can be easily added and amended. Furthermore, the present embodiment disables a decrypting process to be successfully performed because of the constant coefficient a, the constant P (private and public keys), the constant vector c, and the initial value r[0 ]of the vector all of which should be completely obtained in a decrypting process. For example, assuming that the P contains five constants with a three-dimensional vector, the number of values to be given as the initial value r[0 ]can be obtained by the following equation. If each of the values is a 8-digit real number, then all vectors can be regenerated at the probability of 10^−96. The probability nearly equals 0, thereby hardly permitting successful decryption. Furthermore, in the method according to the present invention, it is necessary to explicitly indicate the function f for determining E of the rotation matrix R (θ), thereby furthermore complicating illegal decryption. Additionally, according to the above mentioned embodiment, a vector is generated using a function determined by defining a private key and a public key, but a vector can also be generated using a function determined by defining at least a public key. Furthermore, each constant (a, P, c) for determination of a function used to generate a vector is fixed when it is used, and the function is also fixed. However, a constant for determination of a function can be dependent on a password (an encryption key to be used as a part of a public key) as described below. It is possible to allow each constant for determination of a function to be dependent on a password in an encrypting process in which the function can be determined such that vectors sequentially generated in a closed area of the n(n≧1)-dimensional space cannot match each other. The password is used as a part of a public key. The function should be fixed. That is, in the equation (1) above, where a is a constant coefficient, P is a set of constants (private and public keys) to be used in a matrix, c is a constant vector for spatial translation of a vector, and K is a password. The password K is input by a user, and is stored in the public portion of the database 41. The secondary program reads the password K from the database 41, and determines each constant (a, P, c) of the equation (1) above based on the password K. Then, using the function based on the constants, a multidimensional vector is generated, and data is encrypted. Thus, by making each constant for determination of a function dependent on a password, the security of the encryption can be improved as compared with the case where each constant is fixed. It is also possible in an encrypting process where vectors defined in the closed area of a n(n≧1)-dimensional space are sequentially generated, and a function is set such that generated vectors cannot match each other, each constant for determination of the function can be dependent on a password and a real time. A password is used as a part of a public key. The function is fixed. That is, in the equation (1) above, where a is a constant coefficient, P is a set of constants (private and public keys) to be used in a matrix, c is a constant vector for spatial translation of a vector, K is a password, and t is a real time. The password K is input by a user, and is stored in the public portion of the database 41. The secondary program reads the password K from the database 41, and determines each constant (a, P, c) of the equation (1) above based on the password K, and the real time t. Then, using the function based on the constants, a multidimensional vector is generated, and data is encrypted. Thus, by making each constant for determination of a function dependent on a password, and additionally making each constant depending on a real time, each constant depends not only on a password, but also on a real time, thereby furthermore improving the security of the encryption. It is also possible in an encrypting process where vectors defined in the closed area of a n(n≧1)-dimensional space are sequentially generated, and a function is set such that generated vectors cannot match each other, each constant for determination of the function can be dependent on a password and a real time, and additionally the selection of function matrix can be dependent on a password. A password is used as a part of a public key. That is, in the equation (1) above, R→R [K ] where a is a constant coefficient, P is a set of constants (private and public keys) to be used in a matrix, c is a constant vector for concurrent movement with a vector, K is a password, t is a real time, and R is a matrix. The password K is input by a user, and is stored in the public portion of the database 41. The secondary program reads the password K from the database 41, and determines each constant (a, P, c) of the equation (1) above based on the password K, and the real time t. The secondary program selects the matrix R using these constants depending on the password K. Based on the selected matrix R, a multidimensional vector is generated, and data is encrypted. Thus, by making each constant for determination of a function dependent on a password, additionally making each constant depending on a real time, and by selecting a matrix depending on a password, each constant depends not only on a password, but also on a real time, and the function using the constants are also selected depending on a password, thereby furthermore improving the security of the encryption. It is also possible in an encrypting process where vector defined in the closed area of a n(n≧1)-dimensional space are sequentially generated, and a function is set such that generated vectors cannot match each other, each constant for determination of the function can be dependent on a password and a real time. A password is used as a part of a public key. A function type is selected depending on a password and a real time. That is, in the equation (1) above, R→R [K,t ] where a is a constant coefficient, P is a set of constants (private and public keys) to be used in a matrix, c is a constant vector for spatial translation of a vector, K is a password, t is a real time, and R is a matrix. The password K is input by a user, and is stored in the public portion of the database 41. The secondary program reads the password K from the database 41, and determines each constant (a, P, c) of the equation (1) above based on the password K, and the real time t. The secondary program selects the matrix R using these constants depending on the password K and the real time t. Based on the selected matrix R, a multidimensional vector is generated, and data is Thus, by making each constant for determination of a function dependent on a password, additionally making each constant depending on a real time, and by selecting a matrix depending on a password, each constant depends not only on a password, but also on a real time, and the function using the constants are also selected depending on a password and a real time, thereby furthermore improving the security of the encryption. It is also possible in an encrypting process where vectors defined in the closed area of a n(n≧1)-dimensional space are sequentially generated, and a new function is generated by linearly combining a plurality of functions such that the generated vectors cannot match each other, a constant for determination of the function can be dependent on a password and a real time. A password is used as a part of a public key. A function type is selected depending on a password and a real time. Furthermore, a linear combination coefficient is dependent on a password and a real time. That is, assuming that a matrix generating a new vector r[j](j=0, 1, 2, 3, . . . ) from the initial value r[0 ]of the vector r in a n(n≧1)-dimensional space is R[d ](d=0, 1, 2, 3, . . . ), a new vector can be generated by the following equation. $r j = ∑ d ⁢ W d ⁡ ( K , t ) ⁢ { a d ⁡ ( K , t ) ⁢ R d , K , t ⁡ ( P j ⁡ ( K , t ) , r j - 1 ) + c j } ( 4 )$ In the equation (1) above, a is a constant coefficient, P is a set of constants (private and public keys) to be used in a matrix, c is a constant vector for spatial translation of a vector, K is a password, t is a real time, R is a matrix, and W is a linear combination coefficient. The password K is input by a user, and is stored in the public portion of the database 41. The secondary program reads the password K from the database 41, and determines each constant (a, P, c) of the equation (4) above based on the password K, and the real time t. The secondary program selects a matrix R obtained by linearly combining a plurality of matrices. The linear combination coefficient W[d ]used in the matrix R is determined by the password K and the real time t. Depending on the selected nonlinear function (4), a multidimensional vector is generated to encrypt data. Thus, using a new matrix obtained by linearly combining a plurality of matrices, a constant determining each matrix is made to be dependent on a password and a real time, matrix selection is made to be dependent on a password and a real time, and a linear combination coefficient is made to be dependent on a password and a real time, thereby furthermore improving the security of encrypted data. Furthermore, in an encrypting process in which the function can be determined such that vectors sequentially generated in a closed area of the n(n≧1)-dimensional space cannot match each other, the type of function can be optionally defined by a user, and can be dynamically combined with others when it is applied to the main encryption algorithm. That is, a user-defined function is compiled to a compiled basic encryption program to sequentially generating multidimensional vectors, and the compilation result is used through dynamic linking when the entire program is executed. Thus, a malicious user such as a hacker, etc. can be rejected almost completely. As described above, vectors defined in a closed area of an n(n≧1)-dimensional space can be sequentially generated, and encrypted data can be generated in a logical operation using plaintext data to be encrypted and the components of the vectors. Therefore, an encrypting process can be performed without high precision or performance required in the RSA method, etc. Furthermore the encrypting process can be performed with high reliability, and with an application easily added or amended. Thus, by applying various keys to a parameter set P in the equation (1), an optional encrypted data communications system can be defined. Therefore, it is sufficient only to describe the encryption/decryption algorithm using a common key (private key). Described below in detail is the encryption/ decryption system according to an embodiment of the present invention. FIG. 30 shows the principle of the encryption/decryption system according to an embodiment of the present invention. In FIG. 30, the security devices in devices 110 and 112 respectively on the transmission and reception sides, that is, encryption/decryption engines store common keys (private keys). When encrypted data communications are established from one device 110 to another device 112, the primary program of the device 110 passes control to the secondary program of the security device of exclusive The security device for performing an encrypting process on the transmission side uses a nonlinear function variable according to a parameter corresponding to a common key. That is, vectors are generated chaotically and sequentially using a nonlinear function for translation and rotation of n-dimensional vectors defined in a closed area of an n-dimensional space, and encrypted data is generated by performing a logical operation in bit units between plaintext data and the generated vectors. The security device for performing a decrypting process on the reception side generates the vectors as on the transmission side, performs an inverse operation on the generated vectors, and easily decrypts the received encrypted data into the plaintext data. In the encryption/decryption system according to the present invention, a parameter for determination of a nonlinear function used to generate the above mentioned multidimensional vector is secret to the third party. Therefore, according to the present invention, the generation of the n-dimensional vector is determined by defining at least a common key (private key), thereby sequentially generating the n-dimensional vectors using a nonlinear function capable of generating chaos such that each of the generated n-dimensional vectors cannot match each other. That is, the present invention comprises: a vector generation unit for generating a vector r[j ]using each component of a vector defined in a closed area of the n(n≧1)-dimensional space, and an angle Ω[n ]determined by a parameter set P in such a way that each of the vectors sequentially generated using a non-linear function (corresponding to equation (1)) containing at least the n-dimensional rotation matrix R[n](Ω[n]) (corresponding to R in equation (1)) for rotation of the vector cannot match each other in the n-dimensional space; in an encrypting process, a binary operation unit for generating encrypted data using a binary operation of plaintext data and the component of the vector generated by the vector generation unit; and, in a decrypting process, an inverse binary operation unit for generating the plaintext data in an inverse binary operation corresponding to an inverse operation of the binary operation using the vector r[j ]generated by the vector generation unit and the encrypted data. Especially, the present invention comprises: a rotation matrix generation unit for generating the n-dimensional rotation matrix R[n](Ω[n]) for rotation of the vector using the (n−1)-dimensional rotation matrix R[n−1 ](Ω[n−1]) as an (n−1)-dimensional small matrix by using each component of a vector defined in a closed area of the n(n≧1)-dimensional space, and an angle Ω[n ]determined by a parameter set P; a vector generation unit for generating vectors r[j ]such that each of the vectors r[j](j≧0) sequentially generated using a nonlinear function containing at least the rotation matrix R[n](Ω[n]) cannot match each other in the n-dimensional space; and a binary operation unit for generating encrypted data using a binary operation of plaintext data and the component of the vector generated by the vector generation unit. The encryption/decryption system according to the present invention relates to an encrypting/decrypting process performed when a transmitter and receiver of data establish data communications using a common security device (encryption device). According to the present encryption system, a data transmitter (encryption side) generates ciphertext by performing a predetermined logical operation (normally, an exclusive logical sum operation) in bit units using a key sequence with which a plaintext data message has been generated based on a predetermined common key. A data receiver (decryption side) obtains an original plaintext by performing a predetermined logical operation (same operation as on the encryption side) in bit units using the same key sequence as on the encryption side based on a predetermined common key. In this encryption system, a multidimensional vector generation device is used as a random number generation device for generating the above mentioned key sequence. In this case, various parameters and initial state for determination of a vector generation function of the multidimensional vector generation device are provided as common keys FIG. 30 shows an example of the configuration of the encryption system to which the present invention is applied. The encryption device 110 comprises a multidimensional vector generation function unit 101 and a logical operation process function unit 102. Similarly, the decryption device 112 comprises a multidimensional vector generation function unit 121 and a logical operation process function unit 122. In FIG. 30, between the encryption device 110 on the encryption side and the decryption device 112 on the decryption side, for example, a common key is distributed using an IC card, etc. in a security state, and the common key is shared. The encryption device 110 on the encryption side generates a multidimensional vector based on the function determined by a predetermined common key, obtains an exclusive logical sum using a plaintext and the component data of the vector as a random number sequence to transform the plaintext message into ciphertext, and transmits the ciphertext to the decryption device 112. The decryption device 112 which has received the ciphertext generates a vector from the ciphertext through the logical operation process function unit 122 having the same function as the multidimensional vector generation function unit 101 provided in the encryption device 110, obtains an exclusive logical sum of the vector and the generated random number sequence, and restores the original plaintext message. In addition, since the processes performed by the encryption device 110 and the decryption device 112 are practically the same as each other, the processing devices such as a computer, etc. can have the functions of both encryption device 110 and decryption device 112. FIG. 31 shows the configuration of the encrypting and decrypting programs of the encryption device 110 and the decryption device 112. A primary program 131 manages input and output of data, determines whether or not the data is to be encrypted or decrypted, and manages the entire encrypting and decrypting processes. A parameter list generation library 132 stores a common key distributed using an IC card, etc. An encryption/decryption engine 133 receives a common key as a parameter from the parameter list generation library 132, generates a rotation vector based on a matrix determined by a multidimensional vector rotation function generation library 134, and encrypts plaintext or decrypts ciphertext using a component of the vector. Described below in detail is the generation of a multidimensional vector. Considering the rotation for the vector r[j−1 ]defined in a multidimensional (n-dimensional) space, a generalized rotation angle is represented by Ω[n], and the operation corresponding to the rotation is represented by R[n](Ω[n]) as a matrix of n×n. That is, R[n](Ω[n]) acts on r[j−1], and rotates the vector. The equation (1) is rewritten into the following equation (5), that is, a general equation of a rotation vector, thereby defining a new vector r[j]. r [j] =aR [n](Ω[n])r [j−1] +c(5) where a is a constant satisfying \|a\|≦1. c is a n-dimensional constant vector. The equation above indicates that a new vector r[j ]is generated from the vector r[j−1 ]through rotation and spatial According to the present invention, nonlinear sequence can be generated such that the sequence of generated r vectors cannot be chaotic, that is, the original sequence in a closed space by setting the rotation angle Ω[n ]dependent on r. That is, Ω[n ]can be formally represented by a function of a parameter P and a vector r as shown in the following equation (6) (corresponding to equation (3)). Ω[n]=Ω[n](P,r [j−1])(6) where P indicates a set of any number of parameters used in the function for Ω[n]. P={p [i] \|i=1, 2, 3, . . . }(7) For example, in a two-dimensional vector, a two-dimensional rotation angle Ω[n ]is represented by the components x and y of the two-dimensional vector r=(x, y) as follows. Ω[2] =p [1] x+p [2] y+p [3 ] where the parameters p[1], p[2], and p[3 ]are optionally given. The practical operations performed when the above mentioned two-dimensional vector is processed by the encryption devices 110 and 112 used in the system shown in FIG. 30 is described by referring to the flowchart shown in FIG. 32. The two-dimensional vector r is represented by r=(x, y) using the components x and y of an orthogonal coordinate system. The rotating operation of the angle Ω[n]=θ for the vector is represented by a two-dimensional matrix as follows. $R 2 ⁡ ( θ ) = ( cos ⁢ ⁢ θ - sin ⁢ ⁢ θ sin ⁢ ⁢ θ cos ⁢ ⁢ θ ) ( 8 )$ Assuming that the function for a rotating operation of a vector using a function θ=p[1]x+p[2]y+p[3 ]and an obtained rotation angle is stored in the multidimensional vector rotation function generation library 134 (refer to FIG. 31), and the initial value x[0], y[0 ]of r[0 ]and the value of P, that is, p[1=1], p[2=1], p[3]=1, are stored in the parameter list generation library 132 in advance (refer to FIG. 31) as common keys, an example is described below by referring to FIG. 32. To generate a two-dimensional vector, the initial value r[0 ](including component data x[0], y[0]) and the parameter p[1], p[2], p[3 ]of the function defining a rotation angle θ are read from the parameter list generation library 132 (refer to FIG. 31), and stored in the work area of the memory of the devices (110, 112) (step 21). Based on the value x[0], y[0 ]of r[0], the angle θ=p[1]x[j−1] +p[2]y[l−1]+p[3](θ=p[1]x[0]p[2]y[0]+p[3]) is computed, and the computation result is stored as the value θ (step 22). Then, to determine the value of the element od the rotation matrix R, cos θ and sin θ are obtained, and are stored as cos_t and sin_t respectively (step 23). Next, a new vector r[j ]is computed by the equation r[j]=aR[2](Ω[2])r[j−1]+c (step 24). That is, the following computation is performed to generate a new vector r[j](component x[j], y[j]). x [j] =a(“cos [—] t”x [j−1]−“sin[—] t”y [j−1])+c [—] x; y [j] =a(“sin [—] t”x [j−1]−“cos[—] t”y [j−1])+c [—] y; Then, the subsequent rotation angle E is obtained based on the components of the vector r[j](step 22), and the above mentioned steps 23 and 24 are repeated, thereby sequentially generating vectors. In the encryption/decryption system according to the present invention, since a trigonometric function is introduced using the rotation, and a product of the trigonometric functions are used, the nonlinearity is improved more than a normal chaos function, thereby furthermore complicating the decryption. Described below is the process of encrypting data by generating a multidimensional vector. As shown in FIG. 33, an n-dimensional rotation matrix R[n](Ω[n]) is first generated in the encrypting process (step 41). The method of generating the matrix is described later in detail. Then, a vector is generated using a nonlinear function containing the n-dimensional rotation matrix R[n](Ω[n]) (step 42). The vectors r[j ]are sequentially generated such that they cannot match each other in the n-dimensional space. A binary operation is performed using the plaintext data and the components of the vectors generated by the vector generation unit, thereby generating encrypted data (step 43). Then, the encrypted data is transmitted to the reception device of the receiver (step 44). Described below is a binary operation in step 43. Assume that each of the sequentially generated vectors r is represented by N bits. For example, when a two-dimensional vector is expressed by components x and y, each of the data values of the x and y is represented by 16 bits, the data of x and y is arranged in N bits (for example, 32 bits). The vector string r[j](j=1, 2, 3, . . . ) obtained in the procedure and the data string M[j ](j=1, 2, 3, . . . ) represented in N bit units by dividing plaintext data M to be encrypted are used as binary operators to obtain an exclusive logical sum (XOR), and the result C[j ](j=1, 2, 3, . . . ) is obtained as encrypted data. That is, the following computation is performed. C [j] =r [j ] op M [j](9) The above mentioned binary operator op is normally an exclusive logical sum for each. However, since an exclusive logical sum is reversible, it is not desired to use it as an operator for encryption. To compensate for this demerit of the exclusive logical sum, it is recommended to introduce an operation of scrambling an exclusive logical sum with the bits of M[j ]as binary operators. In this case, the following equation exists. where S indicates a scrambling operation for scrambling the bits of M[j], and XOR indicates the definition as an operation of the subsequent exclusive logical sum. Then, encrypted data is obtained by C[j]=r[j ]op M[j]. The decrypting process is described below by referring to FIG. 33. In the decrypting process, as in the encrypting process, a rotation matrix R[n](Ω[n]) for rotation of a vector defined in a closed area of an Ω[n ]dimensional process is first generated (step 45). Vectors r[j ]are sequentially generated such that each of the vectors generated using a nonlinear function containing the rotation matrix R[n](Ω[n]) matches each other in the n-dimensional space (step 46). Then, decrypted data is generated by performing an inverse binary operation corresponding to the inverse operation of the binary operation performed in step 43 using the received encrypted data and the components of the vector r[j ]generated in the vector generating step 46 (steps 47 and 48). In this decrypting process, the received encrypted character strings C[j ](j=1, 2, 3, . . . ) are sequentially retrieved to perform a decrypting operation while generating a vector corresponding to C [j]. This process is described below by referring to the flowchart shown in FIG. 34. The decrypting process starts with j=0 (step 51), the encrypted data C[j ]is retrieved (step 52), an n-dimensional rotation matrix R[n](Ω[n]) is generated (step 53), and a vector r[j ]is generated (step 54). Then, an operation is performed by M[j]=r[j ]op^−1 C[j ]to yield decrypted data (plaintext M[j]) (step 55). If the encrypted data C has not been completely processed, then the next encrypted data is retrieved with j=j+1 (steps 56 and 57) to generate R[n](Ω[n]), and repeat the process of generating the subsequent vector r[j]. The process of repeating steps 52 through 56 is performed until the encrypted data C[j ]is completely processed. Then, the above mentioned first encrypting and decrypting embodiment is extended into a more practical procedure of encrypting data, and is described below as the second embodiment. First, the following equation is performed. C [0] =r [0 ] op M [0](11) Then, a check sum Σ[0 ]for C[0 ]is computed. Furthermore, the equation (9) above is rewritten into the following equation for j where j≧1. C [j]=(r [j ] op Σ [j−1]) op M [j](12) The check sum is represented by, for example, the number of is contained in the computed value of C as a binary indicating the number of bits equal to the number of bits of r[j]. In the equation, Σ[0 ]is obtained from the value of encrypted data C[0], E[1 ]is obtained from C[1], and E[2 ]is obtained from C[2 ]in the following computation order. That is, the transmitter obtains C[0 ]by C[0]=r[0 ]op M[0 ]for the encrypted data C[0 ]for M[0], thereby obtaining the check sum Σ[0 ]of C[0]. For the encrypted data C[1 ]for M[1], C[1 ]is computed by C[1]=(r[1 ]op Σ[j−1]) op M[1], thereby obtaining the check sum E[1 ]of C[1]. The subsequent data M[j ]is encrypted by C[j]=(r[j ]op Σ[j−1]) op M[1 ]with Σ[j−1 ]obtained by the previous data taken into account. r[j ]and Σ[j−1 ]are computed with the same data width (number of bits). The receiver for decrypting the data receives C[0], C[1], C[2], . . . , and computes M[0]=r[0 ]op^−1C[0], and has to obtain the check sum Σ[0 ]from the received C[0]. Using this, M[1 ]is computed for C[1 ]by the following equation. M [1]=(r [1 ] op Σ [0]) op^−1 C [1](13) The subsequent data M[j ]is decrypted by the following equation using the check sum Σ[j−1 ]obtained for the received C[j−1]. M [j]=(r [j ] op Σ [j−1]) op^−1 C [j](14) The encrypted data obtained in the above mentioned procedure has been processed by different keys, it is assumed that the data is durable against an attempt to decrypt the data using an assumed key. If the number of dimensions becomes large in a multidimensional space rotation system, the number of elements of a rotation matrix R also becomes large, thereby causing the problem that an operation load is large in an encrypting/decrypting process. To solve the problem, a method of computing a multidimensional space rotation matrix in an encryption system using a multidimensional space rotation system from a pseudo space rotation matrix having a smaller number of dimensions. Described below is deriving a rotation matrix R[n](Ω[n]) for the multidimensional space rotation. The first method is to generate an n-dimensional rotation matrix R[n](Ω[n]) from the (n−1)-dimensional rotation matrix R[n−1 ](Ω^n−1). Since a method for a multidimensional space rotation is complicated, a two-dimensional space rotation is described below for simple explanation. A two-dimensional vector r is represented by the following equation using the components x and y of an orthogonal coordinate system. The rotating operation of the angle Ω[n]=θ for the vector is represented as a two-dimensional matrix as follows. $R 2 ⁡ ( θ ) = ( cos ⁢ ⁢ θ - sin ⁢ ⁢ θ sin ⁢ ⁢ θ cos ⁢ ⁢ θ ) ( 16 )$ where the subscript of 2 on the left side indicates that the operation is defined in a two-dimensional space. The operation satisfies the conditions of the following equations. \|R [2](θ)\|=1(17) R [2](−θ)=R [2](θ)^−1(18) The equation (17) guarantees that the size of the vector of the rotation in the rotating operation remains constant, and the equation (18) indicates that there is an rotating operation to restore the vector of the rotation to the original state. For extension to a three-dimensional rotation, the description on the right side of the equation (16) is simplified and formally represented as follows. $R 2 ⁡ ( θ ) = ( α 11 α 12 α 21 α 22 ) ( 19 )$ where α[11]=α[22]=cosθ and α[21]=−α[12]=sinθ. In the case of a three-dimensional rotation, it is reasonable to start with the rotation using each of the three orthogonal axes as a rotation axis. It can be represented by any of the following three matrices. $R 3 , 1 ⁡ ( θ ) = ( 1 0 0 0 α 11 α 12 0 α 21 α 22 ) ( 20 ⁢ - ⁢ 1 ) R 3 , 2 ⁡ ( θ ) = ( α 11 0 α 12 0 1 0 α 21 0 α 22 ) ( 20 ⁢ - ⁢ 2 ) R 3 , 3 ⁡ ( θ ) = ( α 11 α 12 0 α 21 α 22 0 0 0 1 ) ( 20 ⁢ - ⁢ 3 Note that they can be obtained by adding 1 as a diagonal element in the two-dimensional space rotating operation provided by the equation (19). In addition, it is obvious that the rotation of the three-dimensional vector in the operation is shown in FIGS. 37A through 37C. The above mentioned matrices (20-1), (20-2), and (20-3) are three-dimensional matrices including two-dimensional matrices indicating the rotating operation in a two-dimensional space. A generalized three-dimensional rotation is obtained by retrieving three matrices (which can be duplicate) from the above mentioned matrices, and sequentially multiplying one by each other. A generalized rotation angle in a three-dimensional space can be represented by the following equation. where the rotating operation R[3](Ω[3]) for a three-dimensional vector is represented by the following equation. R [3](Ω[3])=R [3,i](θ[i])R [3,j](θ[j])R [3,k](θ[k])(21) where i, j, and k can be any of 1, 2, and 3, and can be normally duplicate on condition that the operation does not continue on the same axis. For example, i, j, and k can be 1, 2, and 1. If an ‘inverse rotation angle’ is represented by −Ω[3]=(−θ[1], −θ[2], −θ[3]), then the inverse rotating operation of the rotating operation represented by the equation (21) can be represented by the following equation with the significance taken into account. R[3](−Ω[3])=R [3,k](−θ[k])R [3,j](−θ[j])R [3,i](−θ[i])(22) The rotating operation defined by the equation (21) normally takes the following form. $R 3 ⁡ ( Ω 3 ) = ( β 11 β 12 β 13 β 21 β 22 β 23 β 31 β 32 β 33 ) ( 23 )$ where matrix element is uniquely determined from the equations (16), (19), (20-1) through (20-3), and (21). For R[3](Ω[3]), the following two features are satisfied. \|R [3](Ω[3])\|=1(24) R [3](−Ω[3])=R [3](Ω[3])^−1(25) Described below is the generation of a vector in an actual three-dimensional space. In a three-dimensional space, a vector r[j ]can be generated by storing the order of multiplication of rotation matrices. If a rotation angle is represented by x[j−1]=x, y[j−1]=y, z[j−1]=z for simple explanation of three-dimensional rotation, the following equations exist. θ[1] =p [11] x+p [12] y+p [13] z+p [14 ] θ[2] =p [21] x+p [22] y+p [23] z+p [24 ] θ[3] =p [31] x+p [32] y+p [33] z+p [34 ] The three-dimensional rotating operation R[3](Ω[3]) is represented by the multiplication of the following three rotation matrixes as shown by the equation (21) above in the method described later, that is, R [3](Ω[3])=R [3,i](θ[i])R [3,j](θ[j])R [3,k](θ[k]) where integers i, j, and k are any of 1, 2, and 3, and normally can be duplicate. That is, there are 3×2×2 (=12) methods of multiplication of R[3,1](θ[1]), R[3,2](θ[2]), R[3,3](θ[3]), and the order of the multiplication depends on the parameter of the transmitter. In this encrypting process, the flow of the vector r[j ]generating process in the three-dimensional space is shown in FIG. 35. That is, R[3](Ω[3]) is prepared based on the order of multiplication specified by the parameter of the transmitter (step 61). Then, the initial value r[0 ]of the vector, and the parameters p[11 ] through p[34 ]of the function for computation of the rotation angles θ[1], θ[2 ]and θ[3 ]are stored (step 62). Then, using the components (x, y, z) of r[0](r[j−1]), the following operations are performed (step 63). θ[1] =p [11] x+p [12] y+p [13] z+p [14 ] θ[2] =p [21] x+p [22] y+p [23] z+p [24 ] θ[3] =p [31] x+p [32] y+p [33] z+p [34 ] Then, R[3](Ω[3]) is computed, and a new vector r[j ]is generated by the equation (5). At this time, the order of multiplication is specified depending on the parameter of a transmitter as described above, for example, on the employee number, etc. of the transmitter. As for the rotation matrix R[3](Ω[3]), the transmitter (and the receiver) does not compute the rotation matrix R[3](Ω[3]) based on the order specified each time data is transmitted, but 12 functions are stored in advance, and any of the functions can be specified. Described below is the method of applying the procedure of extending the above mentioned two-dimensional rotation to the three-dimensional rotation, and the three-dimensional rotation to the four-dimensional rotation. In this case, four two-dimensional matrices, that is, R[4,i](Ω[3]) (i=1, 2, 3, 4,), are obtained by adding 1 to the equation (23) as a diagonal element. That is, the following equations are obtained. $R 4 , 1 ⁡ ( Ω 3 ) = ( 1 0 0 0 0 β 11 β 12 β 13 0 β 21 β 22 β 23 0 β 31 β 32 β 33 ) ( 26 ⁢ - ⁢ 1 ) R 4 , 2 ⁡ ( Ω 3 ) = ( β 11 0 β 12 β 13 0 1 0 0 β 21 0 β 22 β 23 β 31 0 β 32 β 33 ) ( 26 ⁢ - ⁢ 2 ) R 4 , 3 ⁡ ( Ω 3 ) = ( β 11 β 12 0 β 13 β 21 β 22 0 β 23 0 0 1 0 β 31 β 32 0 β 33 ) ( 26 ⁢ - ⁢ 3 ) R 4 , 4 ⁡ ( Ω 3 ) = ( β 11 β 12 β 13 0 β 21 β 22 β 23 0 β 31 β 32 β 33 0 0 0 0 1 ) ( 26 ⁢ - ⁢ 4 )$ Furthermore, the rotating operation for the rotation angle Ω[4 ]in a four-dimensional space is defined by the following equation. R [4](Ω[4])=R [4,i](Ω[3,i])R [4,j](Ω[3,j])R [4,k](Ω[3,k])R [4,l](Ω[3,l])(27) Ω[3,i](i=1, 2, 3, 4) is another three-dimensional rotation angle Ω[3 ]different from the angle defined above. By repeating the definition, the rotating operation R[n](Ω[n]) for the rotation angle Ω[n ]in the n-dimensional space can be normally represented by the following equation. $R n ⁡ ( Ω n ) = ∏ i = 1 n ⁢ ⁢ R n , i ⁡ ( Ω n - 1 , i ) ( 28 )$ It is easily confirmed that the obtained rotating operation satisfies the features of the equations (29) and (30) by taking the order of the product on the right side of the equation (28) into \|R [n](Ω[n])\|=1(29) R [n](−Ω[n])=R [n](Ω[n])^−1(30) The n-dimensional rotation matrix R[n](Ω[n]) can be generated by performing the processes according to the flowchart in FIG. 36. That is, k=2 is first set (step 30), and the 2-dimensional rotation matrix R[2](Ω[2]) is generated (step 31). Then, it is determined whether or not the value of k is smaller than n (step 32). If yes, the value of k is incremented by 1 (step 33), and the k-dimensional rotation matrix R[k](Ω[k]) is generated such that it can include the (k−1)-dimensional rotation matrix R[k−1](Ω[k−1]) as a (k−1) -dimensional small matrix (step 34). Then, a product of the k generated k-dimensional rotation matrix R[kj1](Ω[j1]), R[kj2](Ω[j2]), . . . , R[kjk](Ω[jk]) is obtained to obtain a rotation matrix R[k](Ω[k]) (step 35). Then, by repeating the steps 34 and 35 from k=2 to k=n, the n-dimensional rotation matrix R[n](Ω[n]) can be generated. In the second method described below, a pseudo-rotation matrix is obtained by arranging a plurality of rotation matrices of smaller number of dimensions as diagonal blocks with remaining elements set to zero. The second method is described below in detail. For example, the elements of the rotation matrix R in a six-dimensional space are as shown by the following equation (37) indicating a large volume of computation. $R = ( R 1 , 1 R 1 , 2 R 1 , 3 R 1 , 4 R 1 , 5 R 1 , 6 R 2 , 1 R 2 , 2 R 2 , 3 R 2 , 4 R 2 , 5 R 2 , 6 R 3 , 1 R 3 , 2 R 3 , 3 R 3 , 4 R 3 , 5 R 3 , 6 R 4 , 1 R 4 , 2 R 4 , 3 R 4 , 4 R 4 , 5 R 4 , 6 R 5 , 1 R 5 , 2 R 5 , 3 R 5 , 4 R 5 , 5 R 5 , 6 R 6 , 1 R 6 , 2 R 6 , 3 R 6 , 4 R 6 , 5 R 6 , 6 ) ( 37 )$ Then, the rotation matrix R is computed by replacing it with a pseudo-rotation matrix. The pseudo-rotation matrix Q is obtained by arranging a plurality of spatial rotation matrices of smaller number of dimensions as diagonal blocks with remaining elements set to zero. For example, in a six-dimensional space, a pseudo-rotation matrix Q as represented by the following equation (38) is used. $Q = ( A 0 0 B ) = ( A 1 , 1 A 1 , 2 A 1 , 3 0 0 0 A 2 , 1 A 2 , 2 A 2 , 3 0 0 0 A 3 , 1 A 3 , 2 A 3 , 3 0 0 0 0 0 0 B 1 , 1 B 1 , 2 B 1 , 3 0 0 0 B 2 , 1 B 2 , 2 B 2 , 3 0 0 0 B 3 , 1 B 3 , 2 B 3 , 3 ) ( 38 )$ where A and B are three-dimensional rotation matrices. When the elements of the pseudo-rotation matrix Q are compared with the elements of the rotation matrix R, the Q contains more zero elements, thereby requiring smaller volume of computation. In addition, its encrypting function sufficiently works. Normally, a multidimensional spatial rotation matrix Q can be set as represented by the following equation (39). $Q = ( A 1 0 ⋯ 0 0 A 2 ⋯ 0 ⋮ ⋮ ⋮ ⋮ 0 0 ⋯ A i ) ( 39 )$ where A1, A2, . . . , Ai are multidimensional spatial rotation matrices. Thus, the volume of computation can be considerably reduced and an encrypting process or a decrypting process can be quickly performed by replacing a rotation matrix in a multidimensional spatial rotation system with a pseudo-rotation matrix obtained by arranging a plurality of rotation matrices with smaller number of dimensions set as diagonal blocks with remaining elements set to zero. In a further method, the value of P obtained in a similar transformation represented by the following equation (40) can be used as a new pseudo-spatial rotation matrix. p=SQ*S ^T(40) In the equation (40), q is the above mentioned pseudo-rotation matrix, and S is a permutation matrix. As shown in the following equation (41), it is a square matrix with each row and column containing a 1 as an element. $S = ( 0 0 1 0 0 1 0 0 0 0 0 1 1 0 0 0 ) ( 41 )$ For example, when the pseudo-rotation matrix Q is represented by the equation (38) above (in a six-dimensional space), the pseudo-spatial rotation matrix P is represented by the following equation $P = ( A 1 , 1 0 A 1 , 2 0 A 1 , 3 0 0 B 1 , 1 0 B 1 , 2 0 B 1 , 3 A 2 , 1 0 A 2 , 2 0 A 2 , 3 0 0 B 2 , 1 0 B 2 , 2 0 B 2 , 3 A 3 , 1 0 A 3 , 2 0 A 3 , 3 0 0 B 3 , 1 0 B 3 , 2 0 B 3 , 3 ) ( 42 )$ A practical example is represented by the following equation (43). $S = ( 1 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 1 ) ( 43 )$ Thus, by replacing a rotation matrix in a multidimensional spatial rotation system with a pseudo-rotation matrix obtained by combining permutation matrices having a plurality of rotation matrices with smaller number of dimensions set as diagonal blocks with remaining elements set to zero, the computation process can be complicated, thereby making furthermore difficult decryption. The feature of the present encryption system is that with an increasing number of spatial dimensions, encrypted data can be decrypted with the more difficulty, that a software process can be quickly performed, thereby requiring no special hardware for encrypting and decrypting processes, and that the privilege (authority) for hierarchy and decryption for personal use, group use, etc. can be minutely prescribed. Therefore, the application of the present invention includes management of personal and private data, management of confidential mail, management of broadcast communications data, etc., and various other fields. In addition, since the present invention can improve the security of the data in the server of an Internet environment, a system administrator and an Internet service provider can make the most of the present invention. Furthermore, according to the present invention, the parameter P and the constant vector c can be time dependent, and the P can be represented by the following equation. P(t)={p [i](t)¦i=1, 2, 3 . . . }(31) where the c can be set to c(t). Additionally, the initial value r[0](t) can also be time dependent. In an actual encrypting process, the initial value r[0 ]of the vector is substituted for r[j−1](j=1) on the right side. The obtained new vector r[1 ]is substituted for the r[j−1 ]on the right side of the equation (5). By repeating the process, new vectors are sequentially generated. The time dependence represented by the equation (31) indicates that the same encrypted data cannot be obtained even if the same original data is encrypted at different times. If a parameter set and functions are carefully set in the equation (6), the vectors r[j ]sequentially generated by the equation (5) can be prevented from converging into a balanced solution. It is said to be difficult to decrypt data encrypted in a chaos or random system if the key is secret. The encryption system according to the present invention inherits the above mentioned features. The feature of the present encryption system is, in addition to the desired features of the above mentioned conventional encryption system, to be able to freely amend (customize) the encrypting procedure for the following grounds. 1. The representation of the rotation matrix R[n](Ω[n]) according to the equation can be optionally determined. 2. The function Ω[n](P, r[j−1]) on the right side of the equation (6) and the parameter P can be optionally set on condition that the function value is not dispersed. 3. Various ‘initial values’ can be optionally set. 4. The vector r[j ]obtained by optionally repeating the operation of the equation (5) starting with the initial value of an optional vector can be set again as an initial value of the vector used in an encrypting/decrypting process. 5. When an operation with a floating point is performed, an operation result depends on a numeral operation processor and a compiler. Therefore, a decrypting process requires a decryption environment which is the same as an encryption environment. The procedure according to the present embodiment can be performed using integers. In this case, a multidimensional space can be sectioned by a grid, and a vector indicated by coordinates of a discrete grid point changes by rotation and spatial translation. The encrypting procedure in the multidimensional rotation vector system of the present encryption system includes a number of options. For example, a multidimensional vector rotating operation cannot be simply set, and a person trying to decrypt encrypted data (system) has to regenerate the system of a rotation generation unit, identify the function system prescribing a generalized multidimensional vector rotation angle, and correctly detect the parameter (key). According to the present invention, there is the lowest possibility that the vector r[j ]can be regenerated because there is a very large number of ways of setting nonlinear functions for obtaining a rotation angle Ω[n ]from the state of a rotation vector r[j−1 ]with a parameter P as a key, and determining the configuration of rotation matrices. Since the present encryption system generates an n-dimensional rotation matrix from a rotation matrix having a dimension smaller than the n-dimensional rotation matrix, it applies to a sequential process. Furthermore, since a nonlinear function for sequential or chaotic generation of vectors through spatial translation and rotation of a n-dimensional vector defined in a closed area of an n-dimensional space using the n-dimensional rotation matrix is defined by a real number according to the present invention, an encrypting/decrypting process can be performed for optionally and digitally represented data. Therefore, the present invention can be utilized in various applications. Described below is the application of the encryption/decryption system of the present invention to the above mentioned embodiments of the database management apparatus. According to the present invention, a multidimensional spatial rotation system (multidimensional spatial vector system) is used as an encryption algorithm of a database. In the multidimensional spatial rotation system, sequential vectors are generated in a multidimensional space based on a predetermined function, and the components of the vectors are key streams for encryption. In the multidimensional spatial rotation system, computation can be performed by an information processing device even with low performance. Therefore, the system can be applied to a portable terminal. That is, in an environment in which a database according to the present invention is externally accessed, the encryption system is desired to process data with the security of the data successfully guaranteed. At this time, to encrypt the database according to the present embodiment, column keys are different from row keys. Therefore, the parameter of the predetermined function is determined using at least one of the column keys and the row keys, thereby generating a key stream for encryption. Thus, a key stream unique to each row and column can be generated. As described above in detail, according to the database management apparatus of the present invention, data of column items used in a retrieving process is encrypted using a column key common among the column items while data of other column items is encrypted using a row key unique to each row when a database is encrypted. Therefore, the security can be improved by using different keys for respective rows. When a retrieving process is performed, the data input for retrieval is encrypted using a column key common among predetermined column items, and the encrypted retrieving data is compared with the encrypted database, thereby realizing a high-speed retrieving process.	{"url":"http://www.google.com/patents/US7093137?dq=artistshare","timestamp":"2014-04-18T04:42:40Z","content_type":null,"content_length":"298638","record_id":"<urn:uuid:21122f91-484e-401f-9e08-41af1f683380>","cc-path":"CC-MAIN-2014-15/segments/1397609532480.36/warc/CC-MAIN-20140416005212-00154-ip-10-147-4-33.ec2.internal.warc.gz"}
RE: st: Replace missing values by 0 Notice: On March 31, it was announced that Statalist is moving from an email list to a forum. The old list will shut down at the end of May, and its replacement, statalist.org is already up and [Date Prev][Date Next][Thread Prev][Thread Next][Date Index][Thread Index] RE: st: Replace missing values by 0 From "Nick Cox" <n.j.cox@durham.ac.uk> To <statalist@hsphsun2.harvard.edu> Subject RE: st: Replace missing values by 0 Date Mon, 9 Aug 2010 16:20:13 +0100 Should be replace `x' = 0 if missing(`x') -----Original Message----- From: Nick Cox I have one specific and one general comment here. Specifically, Martin is correct to underline that . is not the only missing value, but the loop in question is easily fixed by foreach x of varlist prean pa_kurn{ replace `x' = 0 if missing(x) Generally, a minimal -search missing- points to several resources. One of the very first entries, to [I] missing values, answers this question comprehensively, so it is difficult to see why it was felt necessary to send it to Statalist. Martin Weiss Stata even forgives the missing blank after -if-! Amazing! inp prean pa_kurn . 5 . 3 . . foreach x of varlist prean pa_kurn{ replace `x' = 0 if(`x' == .) One problem with this "first-principles" approach is that you have to compare explicitly with all missing values, i.e. also the extended ones. -recode- can help avoid this problem. Neil Shephard foreach x of varlist prean pa_kurn{ replace `x' = 0 if(`x' == .) ...is one way to skin this cat. Martin Weiss input myvar recode myvar (mis = 0) Tirthankar Chakravarty Tobias Friedli > I have two variabled called "prean" and "pa_kum" that contain missing values. > These missing values i would like to replace by 0 (zero). What command can i > use to do this? * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/	{"url":"http://www.stata.com/statalist/archive/2010-08/msg00409.html","timestamp":"2014-04-20T18:33:00Z","content_type":null,"content_length":"9595","record_id":"<urn:uuid:7ea4b08e-b86f-456d-9ac1-780745277c3f>","cc-path":"CC-MAIN-2014-15/segments/1398223205137.4/warc/CC-MAIN-20140423032005-00182-ip-10-147-4-33.ec2.internal.warc.gz"}
Limit of Trig Function Without knowing L'Hopital's Rule, one can show this is the case using the Squeeze Theorem. You can find a proof here. For simplicity sinx can be expanded as $x -\frac{x^3}{3!} + \frac{x^5}{5!} - \frac{x^7}{7!}........$ So the Limit now becomes $<br /> Lim_{x->0} \frac{x -\frac{x^3}{3!} + \frac{x^5}{5!} - \frac{x^7} {7!}........}{x}<br /> <br />$ $<br /> = Lim_{x->0} {1 -\frac{x^3}{x3!} + \frac{x^5}{x5!} - \frac{x^7}{x*7!}........}<br /> <br />$ $<br /> = 1<br />$ Its better if you follow Chris Last edited by Krizalid; February 9th 2009 at 01:49 AM. Thank you but I am still a little lost here. magentarita's not ready to diggest ADARSH's post since he/she's covering limits. But, follow Chris L T521's link, which provides a geometric proof. Or you can use the definition of the derivative : $\lim_{x \to 0} \frac{f(a+x)-f(a)}{x}=f'(a)$ let f be the sine function, and a=0, remember that the derivative of the sine function is cosine, and observe I guess this method suits the most what you're currently doing...	{"url":"http://mathhelpforum.com/calculus/72585-limit-trig-function.html","timestamp":"2014-04-20T16:23:32Z","content_type":null,"content_length":"54634","record_id":"<urn:uuid:30716fc8-1dd0-4eb9-a443-cc35b1195612>","cc-path":"CC-MAIN-2014-15/segments/1397609538824.34/warc/CC-MAIN-20140416005218-00488-ip-10-147-4-33.ec2.internal.warc.gz"}
Need to find the net force and the average force..... Mmmm... I have just tried to solve this problem using the equation of kinematics I gave and the work-kinetic energy theorem and both gave me that the average force is 32000 N. Do you know what is the correct answer (from the textbook, if you took the problem from one)? About using momentum, you must have a function that describes how it changes over time, in order to derivate it and find force. Then, you will need to integrate the force and divide it by the time interval. Unfortunately, I see no way of doing this for this kind of exercise.	{"url":"http://www.physicsforums.com/showthread.php?t=558379","timestamp":"2014-04-21T04:45:10Z","content_type":null,"content_length":"45928","record_id":"<urn:uuid:ebf7f6a9-99d0-438a-a99e-4d85bfc2522b>","cc-path":"CC-MAIN-2014-15/segments/1397609539493.17/warc/CC-MAIN-20140416005219-00537-ip-10-147-4-33.ec2.internal.warc.gz"}
How does altitude affect power output? A couple of years ago I took a vacation to Colorado and spent a week bicycling in the mountains. I had my SRM equipped road bike along. I can personally attest, there is a noticeable loss of power at At first I felt like I had no power at all. It seemed like any effort anywhere near FTP left me gasping for air. After a few days' acclimation the riding got better - power came up to respectable levels and I re-calibrated my own sense of what exertion level would send me into the red zone. When I returned home I did some research about loss of power in the mountains. I wanted to know what happened to functional threshold power at altitude. Obviously it went down. But I wanted to understand whether there was a mathematical relationship between my wattage at different altitudes. What I found is there are a handful of studies where exercise physiologists have tried to quantify power loss as a function of altitude. The results of the studies were all within a few percentage points of each other. Because I'm an engineer and not a scientist, I figured I'd just average them all together. After all, how exact does it need to be? Here is the table I created from the data I found. It shows approximately what kind of wattage you should be able to produce at any given altitude. Feet Meters % FTP 0 0 100% 1000 300 99% 2000 610 98% 3000 910 96% 4000 1220 95% 5000 1520 93% 6000 1830 92% 7000 2130 90% 8000 2440 88% 9000 2740 86% 10,000 3050 83% 11,000 3350 81% 12,000 3660 78% 13,000 3960 75% 14,000 4270 72% You can use this table to figure out what wattage you can produce, or what your FTP will be, for whatever altitude you're headed for. Just divide your current FTP wattage by the %FTP percentage corresponding to the altitude you live at. Then multiply that number by the %FTP percentage for the altitude you'll be riding at. An example Suppose you live at 3000ft. and you'll be riding at 10,000ft. Your FTP is 300watts. To get your equivalent FTP for your ride at altitude, the first thing you do is divide FTP by the %FTP for 3000ft.: 300 / 96% = 312.5 Now multiply this number by the %FTP for 10,000ft.: 312.5 * 83% = 259watts Your power output at altitude will roughly correspond to an FTP equivalent of 259 watts.	{"url":"http://www.twowheelblogs.com/how-altitude-affects-power-output","timestamp":"2014-04-19T17:37:20Z","content_type":null,"content_length":"14500","record_id":"<urn:uuid:326e523f-a57a-46e4-8955-c52ff3c4f2ce>","cc-path":"CC-MAIN-2014-15/segments/1398223206147.1/warc/CC-MAIN-20140423032006-00116-ip-10-147-4-33.ec2.internal.warc.gz"}
Mrs. Fields Trivia is HERE – Win FREE COOKIES! Mrs. Fields Trivia – December 15th 2011 Here’s your chance again to win another amazing gift of FREE cookies from Mrs. Field Enter the contest by leaving a comment on our blog. If we pick you as our winner, we will contact you via the email you’ve provided. We will draw 1 name from the correct answers given and that person will receive a FREE Mrs. Fields Holiday Memories Tin ($44.00 Value, with shipping). Answers will be accepted until midnight (December 15^th, 2011). Limited to one win per month per entrant. Winner will be notified via email. Prize Details: The prize from now and for the next week is our NEW Holiday Memories Tin – item #11W423, a $44.00 value, including shipping. It contains 60 Nibblers® bite-sized cookies. Perfection! Question: How many neighbors could you deliver smiles to with just one case pack of our Silver Polka Dot Best Bites Box? Share this on Facebook and Twitter – The more entries we have the more prizes we’ll give away! 199 responses to “Mrs. Fields Trivia is HERE – Win FREE COOKIES!” 1. 24 neighbors. 2. 24! Unless I’m greedy.. then JUST ME!! 3. I could deliver to 24 neighbors 5. 30 neighbors 2 nibblers each 7. Twenty if my kids don’t eat them all! 8. 24 very happy neighbors. 9. 12, I dont want to give them just one each 10. You can make 24 neighbors happy! Or if you really wanna be nice 576! Hope I win some cookies! 12. A ton! 13. It doesn’t matter how many are in the case….each neighbor has more than one occupant….so each gift is multiplied into many smiles! 14. You can give a pack to 12 different neighbors 15. I would deliver them to my mom’s senior complex so she could make all her friends happy! 16. 24 neighbors!! 17. I think you could make lots of neighbors happy..like 24ish! 18. 12 or 24 depending on what size you buy 19. WITH 4 KIDS THEY’LL NEVER MAKE IT TO THE NEIGHBORS HOUSE!!!!!!!!!!!!!!!!!! 21. if i gave two to every person in my family i could feed thirty people….and they would all have smiles on their faces…. 24. We always loved these cookies my dad always bought them what a treat for all 5 of us! 26. The case has 12 boxes but there are 48 cookies in a box. So technically you could make 576 people if you gave them each a cookie:) MMM cookies 27. The case has 12 boxes but there are 48 cookies in a box. So technically you could make 576 people if you gave them each a cookie:) MMM cookies. So the answer is 12 or 576 depending on how generous we are:) 28. 12, my neighbors LOVE cookies! 29. Depends on portion size, I’d go with 576 if I want to cover everyone 30. 2 they get 10 cookies each,you don’t want to be to greedy. But the rest to the family because you cannot keep your hands off them!!!! 31. Well, I could give one cookie each to 576 neighbors. Hmmm, do I have that many neighbors? OK, I could give one box each to 24 neighbors. That seems more reasonable. But that’s a lot of houses to visit. How about I pick four neighbors and them each three boxes? Those four neighbors would definitely be smiling! And me too! I’m sure they would invite me in to have some tea and cookies! 32. I could deliver smiles to 10 neighbors because they are “packaged in half dozens in a special wrapper to preserve freshness.” However, I need to make sure they do not have nut allergies because the products do come in contact with nuts or nut oils. 34. well i guess it would be 24 neighbors..unless i have got a gallon of milk..then i guess it would be two people.my haleybug and myself..just saying… 35. I could give cookies to 30 neighbors!! Two a piece of course. You can’t eat just one 36. 24 Very Lucky Neighbors! 37. 24 neighbors and /or friends and more if I only give them one cookie each. 39. 24! 40. It all depends on how many neighbors you want to share them with, lol. I’m a good neighbor so I would say I have 24 very lucky neighbors! 41. for holliday miss field i give 9000 of our cook to my neighbors becors so sweet and thiy disve in our mouth like cotte cand it sece to give and love in peiss homme and to see the smill on the face when thiy take the frist baert of thos cook praisle ……. 42. That would make for 24 very good neighbors 43. I trilateral love your cookies my all time favorite!!! 44. I would be able to share with 10 very lucky neighbors! 45. 24 neighbors! I promise to do so, if I win! 48. 576 if each neighbor gets just one little cookie. Or 24 if each neighbor gets one box. Just depends on how they are distributed! 50. 24 if I shared with each a box!! 51. Everyone! 53. 60 neighbors, 1 nibbler each…and since I live in an apartment building I have said amount. 54. 576 of my neighbors would smile. 56. 24 I imagine, but ideally as many neighbors as I can fit into one house…and CERTAINLY A LOT MORE NEIGHBORS THAN FAMOUS AMOS CAN SATISFY!!! 57. It would be enough to deliver smiles and to say “Thank You” to 24 neighbors 58. You can’t just give one cookie, so 24 of my neighbors would receive a package of cookies, then they can share with their family! 60. 24 Neighbors! 61. 24. 62. You can give to 24 neighbors-that’s alot! 63. 12 verrry happy, smiling neighbors 65. 12 neighbors! 66. 10 neighbors 67. Well the answer would be 24, but in all honesty…It would be 23..Cause of course I need a snack to 68. I’m going to say 24 because: “Now Mrs. Fields® can be your perfect handout gift! We are offering HUGE savings when you buy a case of 12 or 24.” 69. The Best Bites Box case holds 24. Assuming there is just 1 person in each home at the time, I would be able to deliver 24! 70. just one I only would she is always nice to me 71. I would share with 24 my neighbors, who would be so happy. 72. 24 people! 73. 12 neighbors 78. 24 very happy neighbors! 79. 24 neighbors! 80. 60 neighbors 1 each 81. 24 happy neighbors 84. I could deliver a numerous amount of these to quiet a few people. I really think I would have to go to the shelter here locally and hand them out to the people who dont get cookies or even food for that matter. Thanks for doing great giveaway 85. 24 neighbors…allegedly. But on the way, um….let’s just say ‘munch,munch, munch”. 87. 24 OR AS MANY AS IS LEFT OVER AFTER I EAT SOME!!!! LOL 88. I could deliver smiles to 24 neighbors. 89. 23.. lol id so have to keep one for my niece… <3 90. 24 neighbors with one box. 576 neighbors with all 24 box’s! Just depends on how many neighbors you have. lol 91. 24 neighbors!!! 92. This is a time for giving so probably 18 93. 576 if I were to give everyone just one cookie. 95. I would have say 24 neighbors would be kinder to you! 98. 12…how excited and happy they would be 99. 576 neighbors would be very happy with a cookie…or 12 neighbors can get a box of cookies… 101. 24 neighbors. 102. 24 if I had that many neighbors in lonely in a small town in Maine 103. 24 neighbors! 104. 23 neighbors, cause I have no idea where that last yummy, delicious box went! 105. 24 of them! 106. 24 neighbors, although I do enjoy having the occasional cookie with a glass of milk, so the number might have decreased. can’t blame the cookie lover 109. 24 neighbors could have them. 111. 24 people as we all share in a little joy together 112. I want to be my own neighbor!!! lol… I would feed as many as I can actually I would like to win this and donate it to a small homeless community here so they can share your wonderful cookies and the great xmas cheer they bring when you eat them. Thank you Mrs.Fields I love your cookies!! Good Luck to everyone. Merry Christmas 113. 24 neighbors, if I can get them out of the house. 114. 25 neighbors would be really happy 116. You can place a smile on 48 of your neighbor’s faces. 117. I would share with all of the cute neighborhood children, my grandchildren, and nieces & nephews. 118. 24 Sweet neighbors! 119. I would give a box of these to every single person I know and then everyone I came in contact with just to see someone smile. I love seeing people smile! Merry Christmas to everyone! 120. 24 neighbors but I would take it up to the VA hospital and give it to the soldiers. 121. That is easy..576 neighbors if they got one cookie each. Or 12 family’s could get a tin of 36 cookies each. They are a family of 4 each person in the family would get 9 each. How ever in my family there is 5 adults so they would get 7.2 cookies 123. i would deliver i tin to each neighbor,so they can share with family and friends that drop by.because you know they will be ordering some .once they take that first bite,their hooked.so 24 i each.and i will have the one i win so i don’t need 1.thanks □ Our lucky winner of this weeks Mrs. Fields trivia question is Barbara S…. CONGRATULATIONS!! One of our Mrs. Fields representatives will be contacting you shortly. Thank you to all those who participated. Visit us next week for your chance to win FREE COOKIES!!! 125. I would be able to give 44 neighbors 1 cookie! 126. 24 happy neighbors if you give them one each. THank you so much for the giveaway! 127. 24. But I’m pretty sure that is not enough. 128. Give each neighbor 2 tins, so they can give 1 to someone. Pay it forward 129. 23 lucky neighbors and 1 for me! 130. 24 that’s my lucky number 131. 24 neighbors! most are family lol 132. 24 very happy neighbors!! 133. Doesn’t matter how many as long as my neighbors are happy 134. SINCE EACH COOKIE CONTAINS A SMILE … YOU COULD DELIVER 576 SMILES WITH THE SILVER POLKA DOT BEST BITE BOX ! 135. 24 with one box. 576 with a case 137. 24 neighbors unless my kids saw them first then they wouldn’t make it out of my house! 138. 24? 139. 24 Neighbors :D!<3 142. 24 of my sons neighbors which would be alot of very happy college kids!!! 143. 23 but I would make my neighbors that get taken for grant smile …care givers,police department ,firedepartment, animal shelter, etc… 146. I love to share with family and friends… as many as possible. 148. 24 very happy little kids 149. 24 I meant ! 151. 24 neighbors with a box of 24 cookies each, of course. Giving out 576 cookies to the same amount of neighbors would be tedious. (And since I live in a rural area, quite impossible!) 152. 24 Neighbors, each one will get one box so they can share with their friends and family. 153. 24 very lucky neighbors! 154. #60 one for each neighbor 155. 1 for me and 23 for my neighbors!! 156. 24 neighbors, unless I ate some first 157. 24 neighbors would be very happy! 159. I would be able to share them with 24 neighbors, which in return I’ll receive smiles upon their faces. In return will make me smile as well. So 24 neighbors! 160. I could feed my entire neighborhood and two other neighborhoods. Thank you for the contest! 161. 24 happy neighbors 162. I love Mrs. Fields cookies..My favorite cookie is the chocolate chip cookie!! Happy Holidays!!!! 163. 24 unless my sister finds them 164. 60 is what i should have said 165. Probably should share with 24 neighbors, but I don’t guarantee there would be any left once it got into my home! 167. 24 one of my favorite numbers 168. 576 neighbors with one cookie each or one box to 24 neighbors 169. I’d make 24 of my neighbors smile. 170. I would take those 24 boxes to our local food bank to cheer up those in need this holiday season 171. 23 neighbors + myself we’d all have big smiles 172. well, 12 boxes come in one case, so 12 boxes for twelve nieghbors, OR 12 times 48 cookies in each box = 576 cookies, if you have a party, but then again you cant tell them how many cookies to im going with 12, one box for each nieghbor!!!!!!!!!!!!!!!!!!!!!!!!!!!!! 173. Well, 24 boxes in a case…but if everyone gets one cookie, that’s a lot of smiles 174. 24 Happy Neighbors. 178. 24…well actuall 23 neighbors plus 1 for me! 179. 12 neighbors. After having the first cookie, you just got to have another one. 181. 576 neighbors would be very happy with a cookie…or 12 neighbors can get a box of cookies… 184. 24 smiles 185. the smiles are endless so every neighbors. 186. 12 happy neighbors. 187. 24 smiles 188. aw* my neighbors would be my best friend if they received this! The answer is 24! (but if my sweet tooth gets the best of me, 23 haha) 190. 576 neighbors would get one cookie 24 neighbors with a case pack. 191. 20, I have to keep 4 for me & my roommates 192. A lot of neighbors! I’ll have to say about 576! 193. 24 neighbors! Then I would buy more to spread the job! 194. None! I would attack them before I left the house :/ 195. None. For over 15 years I am yet to arrive home with any cookies left from my purchase. In fact they wouldn’t even make it out of the shopping centre! YUM 196. 12 very happy neighbors! 197. 24 YUMMY!!!!! 198. 12! But I would buy 2 cases because I have a LOT of neighbors. You must be logged in to post a comment. Posted by in facebook, Giveaways, twitter Tags: facebook giveaway, facebook trivia contest, Giveaways, mrs. fields giveaways	{"url":"http://www.mrsfields.com/blogs/blog/2011/12/mrs-fields-trivia-is-here-win-free-cookies-24/","timestamp":"2014-04-19T01:56:38Z","content_type":null,"content_length":"267266","record_id":"<urn:uuid:09eb49e8-7d9c-4f6d-a4c7-0376e9fadc8f>","cc-path":"CC-MAIN-2014-15/segments/1397609535745.0/warc/CC-MAIN-20140416005215-00469-ip-10-147-4-33.ec2.internal.warc.gz"}
Somerdale, NJ Algebra 2 Tutor Find a Somerdale, NJ Algebra 2 Tutor Students and families,Only in my third year of teaching, I have developed extensive knowledge around elementary mathematics. I have taught students in grades 2-12 in a variety of settings - urban classrooms, after-school programs, summer enrichment, and summer schools. I work with students to develop strong conceptual understanding and high math fluency through creative math games. 9 Subjects: including algebra 2, geometry, ESL/ESOL, algebra 1 I have been a part time college instructor for over 10 years at a local university. While I have mostly taught all levels of calculus and statistics, I can also teach college algebra and pre-calculus as well as contemporary math. My background is in engineering and business, so I use an applied math approach to teaching. 13 Subjects: including algebra 2, calculus, geometry, statistics ...During my high school years, I had the chance to tutor younger students in topics with which they were having trouble. I have tutored mathematics from algebra I up through precalculus. More recently, I have had the opportunity to unofficially tutor my fellow classmates in higher level subjects, such as college-level physics, chemistry, and some of calculus I, II, and III. 7 Subjects: including algebra 2, chemistry, physics, calculus ...I have been tutoring for pay for over five years, as well as volunteering for countless years previous. Although most of the students I tutor are at a level between prealgebra and precalculus, I am very well versed in higher mathematics. I am friendly and considerate of all learning styles and abilities. 11 Subjects: including algebra 2, calculus, geometry, algebra 1 ...Patterns and algebra; 4. Data analysis, probability and discrete mathematics; 5. Mathematical processes; I am a provider of experienced, professional one-on-one attention. 22 Subjects: including algebra 2, statistics, ASVAB, geometry	{"url":"http://www.purplemath.com/Somerdale_NJ_algebra_2_tutors.php","timestamp":"2014-04-18T00:30:42Z","content_type":null,"content_length":"24369","record_id":"<urn:uuid:375ae377-667e-4673-87f9-6f3b08e67911>","cc-path":"CC-MAIN-2014-15/segments/1397609532374.24/warc/CC-MAIN-20140416005212-00179-ip-10-147-4-33.ec2.internal.warc.gz"}
Multiplication cancellation proof December 4th 2007, 06:14 AM Multiplication cancellation proof I need help with this proof also x = y <=> xz = yz use only addition and multiplication for proof x, y and z are natural numbers December 4th 2007, 10:24 AM I do not see a problem here, you just want to go from the right to the left and then from the left to the right. Only basic algebraic manipulation is required. Let $x,y,z \in \mathbb{N}$ Suppose $x = y$. Multiplying both sides by $z$ we obtain: $xz = yz$ Thus we have $x = y \implies xz = yz$ For the converse, suppose $xz = yz$. Subtracting $yz$ from both sides, we obtain: $z(x - y) = 0$. Now $z e 0$, since $z \in \mathbb{N}$, thus we must have $x - y = 0$. But this means $x = y$. Thus we have $xz = yz \implies x = y$. Therefore, if $x,y,z \in \mathbb{N}$, $x = y \Longleftrightarrow xz = yz$. December 4th 2007, 06:53 PM If anyone else can show this proof using only multiplication and addition, that would be helpful...thanks.	{"url":"http://mathhelpforum.com/number-theory/24130-multiplication-cancellation-proof-print.html","timestamp":"2014-04-20T08:23:31Z","content_type":null,"content_length":"7680","record_id":"<urn:uuid:af273aa5-90f9-453c-9478-9d4e8a3b8409>","cc-path":"CC-MAIN-2014-15/segments/1397609538110.1/warc/CC-MAIN-20140416005218-00020-ip-10-147-4-33.ec2.internal.warc.gz"}
Every Deterministic Nonclairvoyant Scheduler has a Suboptimal Load Threshold when quoting this document, please refer to the following URN: urn:nbn:de:0030-drops-25447 URL: http://drops.dagstuhl.de/opus/volltexte/2010/2544/ Edmonds, Jeff Every Deterministic Nonclairvoyant Scheduler has a Suboptimal Load Threshold The goal is to prove a surprising lower bound for resource augmented nonclairvoyant algorithms for scheduling jobs with sublinear nondecreasing speed-up curves on multiple processors with the objective of average response time. Edmonds and Pruhs in SODA09 prove that for every $\e > 0$, there is an algorithm $\alg_{\e}$ that is $(1\!+\!\epsilon)$-speed $O({1 \over \e2})$-competitive. A problem, however, is that this algorithm $\alg_{\e}$ depends on $\e$. The goal is to prove that every fixed deterministic nonclairvoyant algorithm has a suboptimal speed threshold, namely for every (graceful) algorithm $\alg$, there is a threshold $1\!+\!\beta_{\alg}$ that is $\beta_{\alg} > 0$ away from being optimal such that the algorithm is $\Omega({1 \over \e \beta_{\alg}})$ competitive with speed $(1 \!+\! \beta_{\alg}) \!+\! \e$ and is $\omega(1)$ competitive with speed $1 \!+\! \beta_{\alg}$. I have worked very hard on it and have felt that I was close. The proof technique is to use Brouwer's fixed point theorem to break the cycle of needing to know which input will be given before one can know what the algorithm will do and needing to know what the algorithm will do before one can know which input to give. Every thing I have can be found at BibTeX - Entry author = {Jeff Edmonds}, title = {Every Deterministic Nonclairvoyant Scheduler has a Suboptimal Load Threshold}, booktitle = {Scheduling}, year = {2010}, editor = {Susanne Albers and Sanjoy K. Baruah and Rolf H. M{\"o}hring and Kirk Pruhs}, number = {10071}, series = {Dagstuhl Seminar Proceedings}, ISSN = {1862-4405}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, Germany}, address = {Dagstuhl, Germany}, URL = {http://drops.dagstuhl.de/opus/volltexte/2010/2544}, annote = {Keywords: Scheduling} Keywords: Scheduling Seminar: 10071 - Scheduling Issue date: 2010 Date of publication: 03.05.2010 DROPS-Home \| Fulltext Search \| Imprint	{"url":"http://drops.dagstuhl.de/opus/volltexte/2010/2544/","timestamp":"2014-04-17T06:45:59Z","content_type":null,"content_length":"7706","record_id":"<urn:uuid:c8f90357-eeac-4994-956e-a5605a1e25e6>","cc-path":"CC-MAIN-2014-15/segments/1397609526311.33/warc/CC-MAIN-20140416005206-00529-ip-10-147-4-33.ec2.internal.warc.gz"}
Frax - Explore the Infinite What are Fractals? By Tom Watch Frax in action The natural world around us is defined by irregular surfaces and shapes with uneven edges and rough corners. However, since Euclid classical geometry has only described the smooth ideal shapes - the circle, sphere, square, cube… - rarely, if ever, found in nature. Fractals are the geometry of the natural world, they describe the texture of reality! This insight was introduced by the Polish born French/American mathematician, Benoit Mandelbrot. In 1975 he coined the word ‘fractal’ as a way to describe shapes that are detailed at all levels of scale. What started as an investigation into an obscure area of mathematics culminated in Mandelbrot defining the new field of fractal geometry. “Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line…” as described by Mandelbrot in his introduction to The Fractal Geometry of Nature. Fractal geometry is an extension to classical geometry, which with the aid of computers, can model and describe structures from sea-shells to galaxies! Benoit Mandelbrot • Wikipedia The most striking characteristic of fractals is their self-similarity, the way the whole resembles smaller parts of itself at different scales. This property reveals natural fractal structures all around us - the way a branch with small twigs can look like a larger branch, which looks similar to the entire tree. How the jagged surface of a rock can look similar to an entire mountain, or how a river network resembles the smaller streams and tributaries that feed it. Once you are aware of fractal patterns you will start seeing them everywhere! Fancy a fractal sight-seeing tour? Here are some Google Earth locations to get you started! Fractal Dimension Another key characteristic of a fractal is its dimension. We are all familiar with topological dimension; the single dimension of a straight line, the two dimensions of a shape or the three dimensions of objects and the space around us. However, things aren't so straight forward with shapes more complicated than the normal Euclidean forms. It was Felix Hausdorff who proposed a different way of looking at the measure of dimension by introducing the notion of a fractional, or fractal dimension (also called the Hausdorff dimension). This allows the intriguing notion of one-and-a-half-dimensional objects, i.e. fractals! To properly understand fractional dimensions we first need a general concept of measuring dimension with more complicated objects. A cube, which has three dimensions, can be cut into eight (2^3) half-sized cubes. This is generalised as an n-dimensional shape being composed of m^n copies of itself that are scaled to 1/m size. Divide each side by 2 (scale 1/2) 1D line 2 copies m^n = 2^1 = 1 2D square 4 copies m^n = 2^2 = 4 3D cube 8 copies m^n = 2^3 = 8 Divide each side by 3 (scale 1/3) 1D line 3 copies m^n = 3^1 = 1 2D square 9 copies m^n = 3^2 = 9 3D cube 27 copies m^n = 3^3 = 27 Now if we can count the number of copies that an object contains of itself, and we know how they were scaled, we can determine its dimension using: dimension = log(no. copies) / -log(scale) So for the cube split into 8 copies each at 1/2 scale gives a dimension result of 3, which of course we already knew… however, let's see how this applies to a fractal shape. The classic example of a self-similar shape with a fractional dimension is the Koch Curve. Devised by Helge von Koch in 1904, this snowflake curve is part of a family of shapes affectionately referred to by mathematicians as a ‘pathological’ - it is defined as being infinitely long and yet contained within a finite area! Step 1 (base shape) Step 2 Step 3 Step 4 For every step each line segment is replaced with the base shape from step one. This effectively adds four copies of the previous shape at a third of the scale. Plugging this into our formula gives the resulting dimension: log(4) / -log(1/3) ≈ 1.26 A comparison of dimensions for many other fractals can be seen in this list. How Long is a Coastline? It was when Mandelbrot was scouring through obscure and forgotten journals like an 18th century naturalist, that he came across an eccentric and unremembered mathematician called, Lewis Fry Richardson. Richardson's paper, "How long is the coastline of Britain?", caught Mandelbrot's attention because such a seemingly simple question of geography actually exposes essential features of fractal geometry. The measured length of the coastline actually depends on the size of your measuring stick. Using a map you could estimate a rough distance. Driving around the coast you would record a more accurate, and longer result. If you were then to walk around measuring every nook and cranny your answer would be greater still. Ultimately as the measurements of the coastline become more and more accurate the resulting length approaches infinity! Obviously the practicalities of such a measurement make it infeasible, so a technique called box counting is often used to to estimate fractal dimension. Mandelbrot's paper that discussed the Hausdorrf dimension in relation to this so-called coastline paradox was a turning point that set his thinking along a fractal path. Incidentally, the fractal dimension of Britain's coastline is about the same as the Koch curve above, ≈ 1.26 The First Fractal Explorations The discovery of the first mathematical fractal is attributed to, Karl Weierstrauss, in 1861. He found a continuous function that is nowhere differentiable, i.e. a curve made entirely of corners that is impossible to determine its rate of change at any point. Weierstrauss's function was a shock to mathematicians at the time and it was deemed to be an aberration resembling nothing found in nature. In his pursuit to bring a new rigour to the field of logical calculus, pioneered by Augustin-Louis Cauchy, Weierstrauss is now known as the father of modern analysis where precise notions of number and continuity are sought. Soon after Weierstrauss, Georg Cantor (the inventor of set theory), was on a quest to understand continuity and infinity. This led him, in 1883, to the fractal now known as the Cantor set (an unfortunate misattribution as it was actually discovered by, Henry Smith, in 1875). Starting with a line, remove the middle third, leaving two equal lines. Then remove the middle third from each of these and so on ad infinitum, and you are left with the Cantor set: At the time, Cantor, wouldn't have referred to this as a fractal, he used it as an example of a "nowhere dense" set that has "zero measure". Paradoxically a randomly thrown dart would have an infinitesimally small chance to hit it as every part consists almost entirely of holes! Complex Numbers Complex numbers are the building blocks of mathematical fractals, but to understand them we should first clarify the different groups (sets) of numbers: Naturals: 1, 2, 3 etc… Integers: 0 and negative whole numbers Rationals: all numbers that can be written as a fraction of two integers Irrationals: numbers such as π, φ, √2 that can't be written as a fraction Reals: all of the above and represent all points on an infinitely long number line. Finally we get to complex numbers, which encompass all real numbers as well as combinations that use the square root of negative numbers! Complex numbers were originally conceived as tools for solving cubic equations but are now used in many scientific and engineering fields. Leonhard Euler denoted the symbol i, to mean the square root of -1 and called it the imaginary unit. Complex numbers are made up of two parts, real and imaginary, and are usually expressed in the z = x + yi where x & y are real numbers and i = √-1 In 1685, John Wallis, realised that complex numbers could be represented in a diagram. The horizontal x axis is the real number line with the vertical y axis for the imaginary numbers. This representation helps lead to an intuitive understanding of complex arithmetic. Incidentally, Wallis also introduced the symbol ∞ for infinity. To dig deeper we highly recommend A Visual, Intuitive Guide to Imaginary Numbers. Julia and Fatou Our flyby through the field of fractals now brings us to two French mathematicians, Gaston Julia, and, Pierre Fatou. Around the time of the First World War they were both independently studying transformations in the complex plane. A transformation is a rule that for any given point on a plane provides another point. It can be thought of acting simultaneously on the entire plane, picking it up, moving, spinning, stretching, folding, twisting then laying it back down in a new configuration. Julia and Fatou were both particularly interested in the process of iteration - that is using the result of one transformation as the input for the next transformation. This was of course at a time before modern computer graphics, so their calculations were carried out by hand and sketched manually. Even so they found attractors, points in space that pulled in the surrounding points towards them, and repellors that pushed the points away. This can be seen below when iteratively squaring a complex number - depending on the starting location the result will either orbit around an attractor spiralling down to a point, or the orbit will 'escape to infinity' as the point gets pushed further and further away. Julia and Fatou realised that the boundary between the areas of attraction and repulsion was very complicated, but without computers to automate the calculating process they were never to see the beauty and detail of their ideas. The area defined by this boundary is now known as the Julia set. Self-Squared Dragons The work of Julia and Fatou remained largely unrecognised by mathematicians until Mandelbrot shone new light on it in the late 1970s. At the time, Mandelbrot, was working at IBM but it was as a visiting professor at Harvard University that he began to study Julia sets. Mandelbrot started with the simplest possible transformation: z → z^2 + c z and c are complex numbers where c is a constant and z starts as the coordinates of a point on the complex plane. The result of the equation then becomes the new value of z and the process is repeated for a set number of iterations. For every point in the complex plane, Mandelbrot, plotted a black dot for the points that were captured (attracted to a point) and left blank those where the magnitude of z grew very large, 'escaped to infinity'. Below are Julia set fractals plotted for different values of c: Mandelbrot was astonished by their complexity and called them "self-squared dragons"! A Map of Julia Sets - The Mandelbrot Map! Looking at the example Julia set fractals above you will notice that some are single connected shapes while others are disconnected, almost dust-like. For a while, Mandelbrot, wondered what the relationship between the connected and disconnected forms was, then he stuck on the idea of making a map of the behaviour. This time, Mandelbrot, created Julia sets for each coordinate on the complex plane and plotted a point for those that were connected. He realised the disconnected Julia sets were those where the orbit of the starting point grew to infinity, which greatly simplified the generation of the map. Using the same formula as before, but with an initial value of z as [0, 0] (the origin) and c as the coordinate of the point on the plane, z is calculated iteratively until its magnitude exceeds a 'bailout' threshold. If this threshold is reached, the point is considered disconnected and outside the Mandelbrot set. If, after a fixed number of iterations, the magnitude of the point is still under the threshold then it is within the Mandelbrot set (marked in orange below): The Mandelbrot Map fractal showing the locations of a few Julia set fractals. However, the truly amazing aspect of this seemingly trivial quadratic formula, z^2 + c, is that as you zoom into the boundary more and more detail is resolved - in fact in mathematical terms it is infinitely detailed! Dressing the Fractal In their naked black and white skeletal forms, the Mandelbrot and Julia set fractals have intriguing structures, but we can elevate these to a level of real beauty. In the fractal world there are hundreds of different schemes that have been devised to add interesting color and form to the raw fractal shape. They all work as a by-product of the iteration process. The simplest is iteration based coloring - the iteration number, at which the magnitude of z exceeds the bailout threshold, is used as an index to choose a color from a lookup table. In Frax, if you use the spread gesture in Lights mode to flatten the 3D height, the result is an extended form of this iteration based coloring. Of course we don't stop there as we add 3D height, two independent light sources, surface marbling, two procedural texture layers that can twist, ripple and swirl, and combine together in unique ways to add an additional surface profile… Further Reading This has been a very top-level introduction to the world of fractals and we hope it has aided your understanding of this fascinating subject. The field is itself almost fractal in nature, with many different orbits and branches to follow! These are some good books and websites worth investigating if you want to dig deeper:	{"url":"http://www.fract.al/background","timestamp":"2014-04-20T05:46:54Z","content_type":null,"content_length":"39030","record_id":"<urn:uuid:7eb19576-560e-4fb7-a5a4-b99a0e211f23>","cc-path":"CC-MAIN-2014-15/segments/1397609538022.19/warc/CC-MAIN-20140416005218-00434-ip-10-147-4-33.ec2.internal.warc.gz"}
[Numpy-discussion] randint for long type (permutations) Will Woods will.woods@ynic.york.ac... Thu Jun 14 07:37:54 CDT 2007 I want to choose a subset of all possible permutations of a sequence of length N, with each element of the subset unique. This is then going to be scattered across multiple machines using mpi. Since there is a one-to-one mapping between the integers in the range 0 <= x < N! and the possible permutations, one solution would be to choose M < N! integers randomly, check for uniqueness, and then scatter only the integers so that individual nodes can construct the permutations. However the integers need to be of type long, and randint doesn't work for numbers which cannot be converted to int. Any suggestions? More information about the Numpy-discussion mailing list	{"url":"http://mail.scipy.org/pipermail/numpy-discussion/2007-June/028183.html","timestamp":"2014-04-20T01:48:58Z","content_type":null,"content_length":"3284","record_id":"<urn:uuid:80ccbb2c-dfb8-4a26-a3ee-7512ba7d3397>","cc-path":"CC-MAIN-2014-15/segments/1397609539705.42/warc/CC-MAIN-20140416005219-00382-ip-10-147-4-33.ec2.internal.warc.gz"}
The Millennium Problems: The Seven Greatest Unsolved Mathematical Puzzles of Our Time In May 2000, the Clay Mathematics Institute elevated seven long-standing open problems in mathematics to the status of "Millennium Prize Problems," endowing each with a million-dollar prize. The seven particular problems were chosen in part because of their difficulty, but even more so because of their central importance to modern mathematics. The problems and the corresponding general areas of mathematics are as follows. 1 The Riemann Hypothesis Number Theory 2 Yang-Mills Existence and Mass Gap Mathematical Physics 3 The P versus NP problem Computer Science 4 Navier-Stokes Existence and Smoothness Mathematical Physics 5 The Poincaré Conjecture Topology 6 The Birch and Swinnerton-Dyer Conjecture Number Theory 7 The Hodge Conjecture Algebraic Geometry The Navier-Stokes equations were first written down in the early 1820's, Riemann made his hypothesis in an 1859 paper, and the Poincaré conjecture dates from 1904. The remaining problems arose in the period 1950-1971. In The Millennium Problems, Keith Devlin aims to communicate the essence of these seven problems to a broad readership. It is, of course, a very ambitious goal. The preface makes it clear what Devlin's ground rules are. First he assumes only "a good high school knowledge of mathematics." Second, he is writing "not for those who want to tackle one of the problems, but for readers — mathematician and non-mathematician alike — who are curious about the current state at the frontiers of humankind's oldest body of scientific knowledge." He is clear that the readership drives the level of the book, so that precise statements of the problems will not always be given. Rather the goal is "to provide the background to each problem, to describe how it arose, explain what makes it particularly difficult, and give... some sense of why mathematicians regard it as important." After the short preface, the book has an interesting Chapter 0, and then one chapter for each problem in the above order. These seven chapters are constructed similarly. Most have a long historical component, generally including biographical information about the person or persons after whom the conjecture is named. Each has substantial background mathematical information, with topics ranging from complex numbers in Chapter 1 and group theory in Chapter 2 to congruences in Chapter 6 and algebraic varieties in Chapter 7. Applications are emphasized when possible. A nice theme in Chapters 2 and 4 is that mathematicians are behind physicists and engineers and just trying to catch up. Each chapter concludes with a discussion of the millennium problem itself. Chapter 5 illustrates how Devlin ties the various units of a chapter into a coherent narrative. It begins with four pages about the life and work of Henri Poincaré. It moves on to introduce "rubber sheet geometry" in terms of how subway maps and refrigerator wiring diagrams are not geometrically faithful to the physical objects they represent, but nonetheless clearly capture all relevant information. This unit is important as it will make readers feel that topology is natural, rather than weird. Chapter 5 next introduces the concepts of vertices, edges, faces and finally Euler characteristic in terms of the Königsberg bridge problem. It introduces non-orientable surfaces and makes the introduction of an ambient four-space seem natural, since it is necessary for an embedding of the Klein bottle. It topologically classifies closed surfaces first crudely in terms of their orientability, and then completely in terms of networks drawn upon them and the Euler characteristic of these networks. It gives a very attractive example of two seemingly linked rings that in fact can be pulled apart. This example shows the reader that not everything is geometrically obvious, and thus underscores the utility of algebraic invariants that can rigorously confirm that two objects are topologically different. It discusses how the ordinary two-sphere is characterized among all closed surfaces by having the property that any loop on it can be shrunk continuously to a point. Finally, by way of this two-dimensional analogy, it discusses the actual three-dimensional Poincaré conjecture. The strain imposed by the challenge of communicating all seven millennium problems to a broad readership naturally shows at times. In the Navier-Stokes chapter, for example, the background mathematical information presented is calculus and specifically differentiation. Readers are instructed that "dy/dx" is to be read "dee-wye by dee-ex." Some seven pages later, the Navier-Stokes equations themselves are presented. They are four coupled non-linear partial differential equations in four independent variables. The exposition is gentle, but readers new to calculus will only understand at a superficial level. The strain is felt somewhat more in Chapter 6 and particularly so in Chapter 7. But these various strains are unavoidable, and I think in general Devlin has done a very good job giving general readers a feel for the seven millennium problems. The Millennium Problems concentrates on the past and present of the problems, but it's also natural to wonder about their future! Can we expect to see some prizes handed out within our lifetimes? Devlin raises this question at the end of the various chapters, but always in a noncommittal way. His mention of the "twenty-fifth century" in the preface may incline some readers to be pessimistic. My personal feeling is that there are good reasons for optimism. I'll take this opportunity to put down my guess that the torrid pace of mathematical progress in the 21st century will include the solution of at least two of the millennium problems before 2020 and at least five before the end of the century. When solutions to the millennium problems do come, it would be nice if the general public recognized them for the monumental achievements that they will be. Books such as Keith Devlin's The Millennium Problems will help a great deal. Part of the interesting Chapter 0 appears in slightly reworked form in the November 2002 installment of Devlins's angle, The inaccessibility of modern mathematics. More information on the millennium problems, including official statements of the problems, is available at the Clay Mathematics Institute. Devlin in his preface refers also to a forthcoming official CMI book, to which he will be a contributor. There are several shorter introductions to the seven millennium problems at a somewhat more advanced level than Devlin's book. One is by Barry Cipra in a volume reviewed by MAA Online. While Devlin's book is generally free from errors, and Cipra's book has been especially well edited, both make the same error with respect to the now proved higher-dimensional Poincaré conjecture. In dimensions four and greater, a simply-connected compact manifold can still exhibit great topological complexity. Only after one assumes that homology groups are also trivial in degrees one through the dimension minus one is such a manifold guaranteed to be homeomorphic to a sphere. David Roberts is an assistant professor of mathematics at the University of Minnesota, Morris.	{"url":"http://www.maa.org/publications/maa-reviews/the-millennium-problems-the-seven-greatest-unsolved-mathematical-puzzles-of-our-time?device=desktop","timestamp":"2014-04-20T20:12:52Z","content_type":null,"content_length":"102211","record_id":"<urn:uuid:f7b59842-3dac-40c9-848d-0fdb4d7be631>","cc-path":"CC-MAIN-2014-15/segments/1397609539066.13/warc/CC-MAIN-20140416005219-00470-ip-10-147-4-33.ec2.internal.warc.gz"}
Help With Limits! May 26th 2009, 06:55 PM #1 Junior Member May 2009 Help With Limits! Question#1.Determine the Values for c and N so that: $<br /> \frac {10x^5-15x^3+2}{cx^n-6x^2+18}<br />$ And the above equation equals ( I suck at this latex stuff) $<br /> \frac {10}{7}<br />$ Which equals:1.42857142857143 Solve for C and N Let f(x)=9x^8-12x^3+3 and g(x)=c·x^n-6x^2+18 with c cant be 0. Then : $<br /> \frac {fx}{gx}<br />$ Equals to 0 This Implies that N is either less than, equal to, or more than ______? I know my latex is pretty bad so if anything looks confusing, let me know and I'll try to fix it. I think I know the first one. I believe the value for C must be 7 and N must be 4 since there is a horizontal assymtote. Correct? On the right path? I am lost on the second one. Last edited by mvho; May 26th 2009 at 08:01 PM. The solution should be 10/7, it's constant, therefor n must be equal to 5 => n = 5 Then we have $<br /> \frac {10x^5-15x^3+2}{cx^5-6x^2+18}<br />$ This is equal to $<br /> \frac {10x^5}{cx^5-6x^2+18}-\frac{15x^3}{cx^5-6x^2+18}+\frac{2}{cx^5-6x^2+18}<br />$ Now consider $lim_{x \to \infty} \ [ \frac {10x^5}{cx^5-6x^2+18}-\frac{15x^3}{cx^5-6x^2+18}+\frac{2}{cx^5-6x^2+18} ]$ = $lim_{x \to \infty} \ \frac {10x^5}{cx^5-6x^2+18}-lim_{x \to \infty} \ \frac{15x^3}{cx^5-6x^2+18}$ $+ lim_{x \to \infty} \ \frac{2}{cx^5-6x^2+18} ]$ = $lim_{x \to \infty} \ \frac {10x^5}{cx^5-6x^2+18} - 0 + 0$ In this case you only have to consider the x-terms with the biggest exponent (here it is x^5, this will tell you the limes) Therefor the same problem is = $lim_{x \to \infty} \ \frac {10x^5}{cx^5-6x^2+18}$ = $lim_{x \to \infty} \ \frac {10x^5}{c*x^5}$ and the solution should be 10/7, I guess you will be able to find c = 7 In these cases it is only important to check on the x-term with the highest exponents, for f it is 8 for g it is n. Let's determine three cases if n=8: f/g -> const; x to infty if n < 8 f/ g -> infty, x to infty if n > 8 f/g -> 0; x to infty because you have something like this $\frac{12x^8}{0.5x^9} = \frac{12}{0.5x} \to \infty, \ x\to \infty$ Did you understand? Thanks Man, Looks like I made a mistake and N should be 5 instead of 4. I never really understood the logic since I just know the short cut that for Horizontal assymtotes, you will divide the coefficient in front of the numerator by the denonminator if the degree is greater on the top. If the degrees are the same, then it will just approach You're welcome. Not sure, what you are talking about. If the degree of of the numerator f(x) is greater than the degree of the denominator g(x), then $\lim_{x \to \infty} \frac{f(x)}{g(x)} = \infty$ If the degree of of the numerator f(x) is smaller than the degree of the denominator g(x), then $\lim_{x \to \infty} \frac{f(x)}{g(x)} = 0$ No, probably not. It approaches a constant in $\mathbb{R}$ In general, with a rational function, $\frac{a_n x^n + a_{n-1} x^{n-1} + \cdot \cdot \cdot + a_1 x + a_0}{b_m x^m + b_{m-1} x^{m-1} + \cdot \cdot \cdot + b_1 x+ b_0}$, as x goes to infinity, you can divide both numerator and denominator by $x^m$ and get $\frac{a_nx^{n-m}+ a_{n-1}x^{n-m-1}+ \cdot\cdot\cdot+ a_1x^{1-m}+ a_0x^{-m}}{b_m+ b_{m-1}x^{-1}+ \cdot\cdot\cdot+ b_1x^{1-m}+ b_2x^{-m}} Now, as x goes to infinity, all negative powers of x go to 0 so the denominator goes to b_m. What happens in the numerator depends on the relation between m and n. If n> m, $x^{n-m}$ is still a positive power so the numerator goes to infinity and, since the denominator is going to a finite, non-zero power, the entire fraction goes to infinity. If n< m, then every power of x in the numerator is negative so the numerator goes to 0. Since the denominator goes to a finite, non-zero number, the fraction goes to 0. Finally, if n= m, all terms in the numerator except the first have negative power and go to 0 so the numerator goes to $a_n$ and the fraction goes to $\frac{a_n}{b_m}= \frac{a_n}{b_n}$ since n= m. Last edited by mr fantastic; May 27th 2009 at 05:32 AM. Reason: Fixed latex Thanks everyone, question solved! May 26th 2009, 09:15 PM #2 Senior Member Nov 2008 May 26th 2009, 09:20 PM #3 Senior Member Nov 2008 May 26th 2009, 10:33 PM #4 Junior Member May 2009 May 26th 2009, 11:34 PM #5 Senior Member Nov 2008 May 27th 2009, 05:29 AM #6 MHF Contributor Apr 2005 May 27th 2009, 03:35 PM #7 Junior Member May 2009	{"url":"http://mathhelpforum.com/pre-calculus/90644-help-limits.html","timestamp":"2014-04-16T06:10:04Z","content_type":null,"content_length":"56245","record_id":"<urn:uuid:98bb609b-9182-4942-8885-57ee7cc5ae5c>","cc-path":"CC-MAIN-2014-15/segments/1397609521512.15/warc/CC-MAIN-20140416005201-00537-ip-10-147-4-33.ec2.internal.warc.gz"}
How to Convert Milliliters (Ml) to Grams Method 1 of 3: Understand Prefixes and Standard Units 1. 1 Read the following definitions and examples. □ Grams is a unit of mass. The gram is a unit of mass in the metric system and the International System of Units. Grams were originally defined as the mass of one cubed centimeter (cm³) of 4°C water ^[1]. Grams is abbreviated g. □ Milliliter is a unit of volume. Mls is an abbreviation for milliliters. Milla (m) is the metric prefix denoting to the power of one thousandth, which is to the 0.001 power. Liter (L) is the unit of volume equal to one cubic decimeter or 1,000 cubic centimeters (cm³).^[2] Therefore, a milliliter (ml) is one thousandth the volume of a liter, or equal to one cubed centimeter (cm³). Method 2 of 3: How to Convert Milliliters to Grams if Measuring Pure Water If you are trying to convert the units on pure water from mls to grams, your job couldn't be easier. 1. 1 Do nothing. A milliliter is equal to one cubed centimeter (cm³). The mass of one cubed centimeter (cm³) of 4°C water by definition is one gram. Therefore, X mls of 4°C water equals X grams of □ For example: 1 ml of water equals 1 gram of water. 1,000 mls of water equals 1,000 grams of water. Method 3 of 3: How to Convert Milliliters to Grams if Measuring Anything Else If you are measuring a substance other than pure water, you have to account for the substance's density. See below. 1. 1 Determine the substance's density. Density is mass per unit volume. Therefore, density measures the compactness of a substance ^[3]. Often your question will provide you with the density. Other times you may need to look up the density on a chart or table. Make sure your density units are in g/ml. If not convert them. □ The density of water is 1 g/ml. Therefore if your substance's density is higher than 1 g/ml then your substance is more dense than water. If your substance's density is less than 1 g/ml, then your substance's density is less than water. □ For example, if I was trying to convert 10 mls of ethanol to grams. I would look up the density of ethanol, and find it is 789.00 kg/m³. I would then need to convert kg/m³ to g/ml. I know that kg/m³ = 1,000g/100x100x100cm³ = 0.001g/cm³ = .0001g/ml. Knowing this, I would multiply 789.00 kg/m³ by 0.001g/ml and get 0.789 g/ml, as the density of ethanol. 2. 2 Multiply mls by density. Multiply the mls of your substance by its density in g/ml. The ml units will cancel, and you will be left with grams and your answer. □ For example if I was trying to convert 10 mls of ethanol to grams. I would multiply 10 mls by 0.789 g/ml, and get 7.89 grams. I now know that 10 mls of ethanol weighs 7.89 grams. □ Note that ethanol weighs less than the same volume of water. Remember, 10 mls of water is equal to 10 grams of water. But here we found that 10 mls of ethanol only weighs 7.89 grams. This is because ethanol is less dense than water. □ Conversely, if your substance was more dense than water, its density was greater than 1, your substance would weigh more than the same volume of pure water. Article Info Thanks to all authors for creating a page that has been read 141,755 times. Was this article accurate?	{"url":"http://www.wikihow.com/Convert-Milliliters-(Ml)-to-Grams","timestamp":"2014-04-19T09:59:29Z","content_type":null,"content_length":"67517","record_id":"<urn:uuid:5cd06301-83a5-4c49-96f0-589419649ecd>","cc-path":"CC-MAIN-2014-15/segments/1397609537097.26/warc/CC-MAIN-20140416005217-00110-ip-10-147-4-33.ec2.internal.warc.gz"}
Got Homework? Connect with other students for help. It's a free community. • across MIT Grad Student Online now • laura* Helped 1,000 students Online now • Hero College Math Guru Online now Here's the question you clicked on: PLS HELP ME IN LAB 10????? • one year ago • one year ago Your question is ready. Sign up for free to start getting answers. is replying to Can someone tell me what button the professor is hitting... • Teamwork 19 Teammate • Problem Solving 19 Hero • Engagement 19 Mad Hatter • You have blocked this person. • ✔ You're a fan Checking fan status... Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy. This is the testimonial you wrote. You haven't written a testimonial for Owlfred.	{"url":"http://openstudy.com/updates/50991874e4b02ec0829c97a4","timestamp":"2014-04-19T22:43:02Z","content_type":null,"content_length":"49992","record_id":"<urn:uuid:c01523f5-d8d2-45d4-9980-79f665ab3a6d>","cc-path":"CC-MAIN-2014-15/segments/1398223211700.16/warc/CC-MAIN-20140423032011-00396-ip-10-147-4-33.ec2.internal.warc.gz"}
[FOM] re harvey re my "effective number theorists" (II) Gabriel Stolzenberg gstolzen at math.bu.edu Sat Apr 15 23:33:05 EDT 2006 This is part II of my reply to Harvey's reply to my message, "effective number theorists." Again, it begins with a quote from my message, followed by Harvey's question about it and then my answer to his question. > > However, it remains to be checked whether number theorists mean > >the same thing by these words that Harvey does. They are, after > > all, classical mathematicians and "effective algorithm" is a term > > used by classical mathematicians not constructivists. > I don't know what you have in mind for a possible difference between > how I use the relevant words and how number theorists use the relevant > words. I would like to hear. Sorry, I was trying to be tactful and ended up being misleading. They may indeed use words like 'algorithm' a different way, e.g., as in classical recursion theory (although I think this is unlikely). But the main difference I have in mind is that you call something a construction (say, a bound or algorithm) only if it is one and you say that there is none only if there is none---whereas I would need to know more before I could be confident that number theorists do too. My reason is that number theorists are classical mathematicians and classical math is rich in cases where algorithms are said to have been defined when not only have they not been but cannot be. And it also is rich in false claims of the form, "We've proved that it exists but there is no construction." I'll mention just a few cases. In an elementary analysis text, the authors define "an algorithm" for adding infinite decimals. But there isn't any such algorithm. (Because there isn't any for deciding, for all infinite decimals, p and q, whether p + q < 2, in which case, the whole number part of its expansion is 1, or not < 2, in which case, it's 2.) In a calculus book, Peter Lax gave what he said was an algorithm (informal computer program) for getting intermediate values under the assumption of the IVT. But there is no such algorithm. He included a "step" that cannot in general be carried out. In a preprint I once received, a prominent philosopher wrote, "As long as we accept the correctness of Newton's Law of Gravity, for example, we are committed to the statement that the evolution of an N-body system will be in accordance with the solutions to the appropriate system of differential equations; and it is to this day quite unknown whether the solutions to these equations are recursively calculable even when N = 3." The view he expresses here had been folklore since the beginning of the last century and, for all I know, still is. However, I wrote back explaining that he was talking here about a 1st order ODE that, sufficiently close to the initial conditions (close enough to stay away from collisions and then some), satisfies a Lipshitz condition. Hence, we're talking about Picard's method, which is a construction par excellance. (In this case, the solutions are even analytic.) The philosopher then removed the statement from his paper. With best regards, More information about the FOM mailing list	{"url":"http://www.cs.nyu.edu/pipermail/fom/2006-April/010420.html","timestamp":"2014-04-20T18:44:43Z","content_type":null,"content_length":"5799","record_id":"<urn:uuid:7899d10c-8e32-4b79-a187-ffeafbddb0d4>","cc-path":"CC-MAIN-2014-15/segments/1398223205137.4/warc/CC-MAIN-20140423032005-00550-ip-10-147-4-33.ec2.internal.warc.gz"}
RealTime Data Compression Following the previous post on Binary Arithmetic Coder , we left with a simple-to-ask but difficult-to-answer question : how to update the probability that the next value will be a 0 or a 1 ? Indeed. Presuming that we can update P0 (probability that next value will be a zero) suppose that we accept a simple idea : the past is a strong indicator for the future. This may not always be true, but for compression it appears to work relatively well. At this stage, we can outline the strong relationship between compression and : compression ratio will only be as good as the algorithm can predict the future (the next bit in this case). Trying to predict the future is not limited to compression, and massive amount of investment have been and are currently spent around this applied concept. In this post however, we'll keep our mind focused on compression, considering other fields only if they can help this objective. A first simple way to evaluate P0 is to count the number of 0 and 1 previously seen. Then, simply set : P0 = N0 / (N0+N1). It works, and is a simple way to achieve convergence towards optimal stationary statistics. But, in fact, no source is really static. They constantly evolve (otherwise, compression would be trivial). The probability should therefore adapt to the source, and consequently, more weight should be given to the most recent bits. A very simple way to achieve this property is by giving to new bits a fixed share of the updated probability. For example 20%. This is an easy method to gradually and smoothly "reduce" the weight of older records. And we get : newP0 = oldP0 x (1-share) + NewBitIsZero x share This works too, although we start to wonder what should be such "share" ? 20% ? 10% ? It is very tempting to believe that the optimal adaptation share can be found as a unique value. And indeed, through brute force testings (such as Genetic Algorithms ) an optimal value can be found. [Edit : an excellent example of "optimal adaptation share" is provided by Shelwien here : However, the optimal value will be true only for a given file, number of contexts and precision level. Change any parameter, and the optimal value will change too.. Could such optimal adaptation share be guessed beforehand, through calculation, rather than sheer experimentation ? Well, unfortunately no. It depends too much on the source, although some basic rules of thumb do apply : if the file is small, the share will be higher. If it is large, the share will be lower. This points towards something retrospectively obvious : at the beginning of the file, when statistics are still scarce, the adaptation must be faster. Then, the more we accumulate statistics, the more accurate they should become, so the adaptation share must become lower. It does not answer to the question "how much", but hints towards a moving value, becoming lower as we progress into the source file. In order to get closer to the "how much" answer, I've collected some statistics, that we'll see and comment in a later post...	{"url":"http://fastcompression.blogspot.fr/2012_01_08_archive.html","timestamp":"2014-04-20T09:05:53Z","content_type":null,"content_length":"81089","record_id":"<urn:uuid:24ee21d1-9ec0-4106-b9a0-f26cb46f8742>","cc-path":"CC-MAIN-2014-15/segments/1398223206147.1/warc/CC-MAIN-20140423032006-00194-ip-10-147-4-33.ec2.internal.warc.gz"}
Andover, MA Trigonometry Tutor Find an Andover, MA Trigonometry Tutor ...I tutor all secondary level math subjects, and always seem to have one or two that are in Algebra 1. Algebra 2 is one of the subjects I've been tutoring in this year, twice a week since October. There are some areas that students tend to find difficult, such as matrices, where this may be their first exposure. 44 Subjects: including trigonometry, chemistry, writing, calculus ...I am patient in explaining. I also ask simple questions to ensure your full understanding of a particular subject. After all, it is my duty and joy to know that you have gained confidence in 12 Subjects: including trigonometry, chemistry, geometry, algebra 1 ...I taught full time High school and College Physics, Math and Electrical Engineering (College), most in Greater Boston area. My ten years Industry experience as a Physicist (MS) and Electrical Engineer (MS), provided a unique insight in problem solving and gave me a “project and results oriented ... 6 Subjects: including trigonometry, physics, algebra 1, precalculus I absolutely love math and love helping students to overcome their fear of math and to excel in it. I have been teaching and tutoring for over 25 years. I have had much success over the years with a lot of repeat and referral business. 19 Subjects: including trigonometry, geometry, GRE, algebra 1 ...However, my preferences are nearby places such as Lawrence, Andover, Lowell, North Reading, Malden, Danvers, Salem, Methuen and Peabody. If you think you need some help in math and physics, do not hesitate to contact me. I look forward to hearing from you soon. 10 Subjects: including trigonometry, calculus, geometry, algebra 1	{"url":"http://www.purplemath.com/Andover_MA_Trigonometry_tutors.php","timestamp":"2014-04-16T10:17:24Z","content_type":null,"content_length":"24057","record_id":"<urn:uuid:88debe79-e8b8-42e7-b71f-031181891f8a>","cc-path":"CC-MAIN-2014-15/segments/1397609523265.25/warc/CC-MAIN-20140416005203-00456-ip-10-147-4-33.ec2.internal.warc.gz"}
[SciPy-Dev] Periodic Boundary Conditions and kd-trees Patrick Varilly patvarilly@gmail.... Thu Mar 1 14:03:53 CST 2012 Hi Emanuele, Thanks for your comments, I will definitely look into cover trees and ball trees, since these are new to me. As an aside, though, "distance to the minimum image" satisfies the triangle inequality, since its the natural metric for points on tori (easiest to see for 2D periodic boundary conditions). What breaks down is the idea that if you have three points with x-coordinates x1 < x2 < x3, then d(2,3) < d(1,3) [but d(1,3) <= d(1,2) + d(2,3) remains true]. This is what might cause trouble with kd-trees, but my thinking was that if I could phrase all kd-tree operations in terms of answering the question "what is the minimum distance between x and region Y of space", then the only difference between PBCs and open boundary conditions is how you answer that question. On Thu, Mar 1, 2012 at 4:45 PM, Emanuele Olivetti > ** > Hi Patrick, > The general kd-tree algorithm works for distance functions that are metric > (e.g. triangle inequality holds). As far as I know the current SciPy > implementation > of kd-tree works for Euclidean distance only. There is another similar > algorithms, > the BallTree, which is implemented in scikits-learn [0] and it is very > fast (Cython) > but again for Euclidean distance only. > Recently Jake VanderPlas, the author of scikits-learn BallTree started to > extend it to other distances and set up a templated code for inserting the > distance > you like [0]. This might be of interest to you but pay attention to your > periodic/modulo > distance because it might not be metric. > Recently I started to extend a pure-Python implementation of the cover-tree > algorithm which is another very efficient data structure for fast nearest > neighbor [1]. > The implementation is slow in building the cover-tree - at the moment - > and very fast during queries but the good thing is that it works for > general > metrics. You might be interested in this as well. Unfortunately I am > swamped in > other activites so my improvements are very very slow now. It should be > usable though. > Best, > Emanuele > [0]: https://github.com/jakevdp/pyDistances > [1]: https://github.com/emanuele/PyCoverTree > On 03/01/2012 03:31 PM, Patrick Varilly wrote: > Hi, > I am writing to ask for some guidance / advice with modifying SciPy's > kd-tree code. I'm writing a Python code with SciPy that deals with a set > of points in 3D. For each one of them, I need to list which other points > are within a distance r. The trouble is that the points are in a periodic > box, so "distance between x and y" means "distance between x and closest > image of y". Currently, I'm using code that does a dumb O(N^2) brute force > search, and was about to code up a cell list to replace it (cell lists are > commonly used for this in molecular dynamics codes). However, KD-trees > seem like a much more generally useful structure for this, and SciPy > already implements kd-trees for open boundary conditions. Since periodic > boundary conditions (PBCs) are quite common in most molecular simulation > and analysis codes, having PBC-aware kd-trees would be useful to a large > number of users. > I am thinking of modifying scipy.spatial.kdtree to adapt it to periodic > boundary conditions, and would like to ask if anyone else has done this or > something similar to it already. If not, is there any advice that can be > had on potential problems that can come up that I should know about before > embarking on this modification? My goal would be to contribute this change > back to SciPy, so any advice on what the most SciPythonic way of exposing > PBCs in the kd-tree interface would also be welcome. > Thanks, > Patrick > _______________________________________________ > SciPy-Dev mailing listSciPy-Dev@scipy.orghttp://mail.scipy.org/mailman/listinfo/scipy-dev > _______________________________________________ > SciPy-Dev mailing list > SciPy-Dev@scipy.org > http://mail.scipy.org/mailman/listinfo/scipy-dev -------------- next part -------------- An HTML attachment was scrubbed... URL: http://mail.scipy.org/pipermail/scipy-dev/attachments/20120301/2baf5ff9/attachment.html More information about the SciPy-Dev mailing list	{"url":"http://mail.scipy.org/pipermail/scipy-dev/2012-March/017176.html","timestamp":"2014-04-19T15:50:37Z","content_type":null,"content_length":"8085","record_id":"<urn:uuid:c8713eab-ddc0-479d-a937-b103d76b757b>","cc-path":"CC-MAIN-2014-15/segments/1398223202774.3/warc/CC-MAIN-20140423032002-00627-ip-10-147-4-33.ec2.internal.warc.gz"}
Results 1 - 10 of 57 - ARTIFICIAL INTELLIGENCE , 1997 "... In the feature subset selection problem, a learning algorithm is faced with the problem of selecting a relevant subset of features upon which to focus its attention, while ignoring the rest. To achieve the best possible performance with a particular learning algorithm on a particular training set, a ..." Cited by 1023 (3 self) Add to MetaCart In the feature subset selection problem, a learning algorithm is faced with the problem of selecting a relevant subset of features upon which to focus its attention, while ignoring the rest. To achieve the best possible performance with a particular learning algorithm on a particular training set, a feature subset selection method should consider how the algorithm and the training set interact. We explore the relation between optimal feature subset selection and relevance. Our wrapper method searches for an optimal feature subset tailored to a particular algorithm and a domain. We study the strengths and weaknesses of the wrapper approach and show a series of improved designs. We compare the wrapper approach to induction without feature subset selection and to Relief, a filter approach to feature subset selection. Significant improvement in accuracy is achieved for some datasets for the two families of induction algorithms used: decision trees and - Machine Learning , 1997 "... . We discuss algorithms for learning and revising user profiles that can determine which World Wide Web sites on a given topic would be interesting to a user. We describe the use of a naive Bayesian classifier for this task, and demonstrate that it can incrementally learn profiles from user feedback ..." Cited by 288 (14 self) Add to MetaCart . We discuss algorithms for learning and revising user profiles that can determine which World Wide Web sites on a given topic would be interesting to a user. We describe the use of a naive Bayesian classifier for this task, and demonstrate that it can incrementally learn profiles from user feedback on the interestingness of Web sites. Furthermore, the Bayesian classifier may easily be extended to revise user provided profiles. In an experimental evaluation we compare the Bayesian classifier to computationally more intensive alternatives, and show that it performs at least as well as these approaches throughout a range of different domains. In addition, we empirically analyze the effects of providing the classifier with background knowledge in form of user defined profiles and examine the use of lexical knowledge for feature selection. We find that both approaches can substantially increase the prediction accuracy. Keywords: Information filtering, intelligent agents, multistrategy - CONFERENCE ON UNCERTAINTY IN ARTIFICIAL INTELLIGENCE , 1994 "... In this paper, we examine previous work on the naive Bayesian classifier and review its limitations, which include a sensitivity to correlated features. We respond to this problem by embedding the naive Bayesian induction scheme within an algorithm that carries out a greedy search through the space ..." Cited by 208 (7 self) Add to MetaCart In this paper, we examine previous work on the naive Bayesian classifier and review its limitations, which include a sensitivity to correlated features. We respond to this problem by embedding the naive Bayesian induction scheme within an algorithm that carries out a greedy search through the space of features. We hypothesize that this approach will improve asymptotic accuracy in domains that involve correlated features without reducing the rate of learning in ones that do not. We report experimental results on six natural domains, including comparisons with decision-tree induction, that support these hypotheses. In closing, we discuss other approaches to extending naive Bayesian classifiers and outline some directions for future research. - Data Mining and Knowledge Discovery , 1997 "... . One method for detecting fraud is to check for suspicious changes in user behavior. This paper describes the automatic design of user profiling methods for the purpose of fraud detection, using a series of data mining techniques. Specifically, we use a rule-learning program to uncover indicators o ..." Cited by 164 (20 self) Add to MetaCart . One method for detecting fraud is to check for suspicious changes in user behavior. This paper describes the automatic design of user profiling methods for the purpose of fraud detection, using a series of data mining techniques. Specifically, we use a rule-learning program to uncover indicators of fraudulent behavior from a large database of customer transactions. Then the indicators are used to create a set of monitors, which profile legitimate customer behavior and indicate anomalies. Finally, the outputs of the monitors are used as features in a system that learns to combine evidence to generate high-confidence alarms. The system has been applied to the problem of detecting cellular cloning fraud based on a database of call records. Experiments indicate that this automatic approach performs better than hand-crafted methods for detecting fraud. Furthermore, this approach can adapt to the changing conditions typical of fraud detection environments. Keywords: fraud detection, rule l... , 1992 "... Multivariate decision trees overcome a representational limitation of univariate decision trees: univariate decision trees are restricted to splits of the instance space that are orthogonal to the feature's axis. This paper discusses the following issues for constructing multivariate decision trees: ..." Cited by 119 (6 self) Add to MetaCart Multivariate decision trees overcome a representational limitation of univariate decision trees: univariate decision trees are restricted to splits of the instance space that are orthogonal to the feature's axis. This paper discusses the following issues for constructing multivariate decision trees: representing a multivariate test, including symbolic and numeric features, learning the coefficients of a multivariate test, selecting the features to include in a test, and pruning of multivariate decision trees. We present some new and review some well-known methods for forming multivariate decision trees. The methods are compared across a variety of learning tasks to assess each method's ability to find concise, accurate decision trees. The results demonstrate that some multivariate methods are more effective than others. In addition, the experiments confirm that allowing multivariate tests improves the accuracy of the resulting decision tree over univariate trees. Contents 1 Introduc... , 1995 "... In this doctoral dissertation, we study three basic problems in machine learning and two new hypothesis spaces with corresponding learning algorithms. The problems we investigate are: accuracy estimation, feature subset selection, and parameter tuning. The latter two problems are related and are stu ..." Cited by 107 (8 self) Add to MetaCart In this doctoral dissertation, we study three basic problems in machine learning and two new hypothesis spaces with corresponding learning algorithms. The problems we investigate are: accuracy estimation, feature subset selection, and parameter tuning. The latter two problems are related and are studied under the wrapper approach. The hypothesis spaces we investigate are: decision tables with a default majority rule (DTMs) and oblivious read-once decision graphs (OODGs). , 1996 "... Naive Bayesian classifiers which make independence assumptions perform remarkably well on some data sets but poorly on others. We explore ways to improve the Bayesian classifier by searching for dependencies among attributes. We propose and evaluate two algorithms for detecting dependencies among at ..." Cited by 69 (5 self) Add to MetaCart Naive Bayesian classifiers which make independence assumptions perform remarkably well on some data sets but poorly on others. We explore ways to improve the Bayesian classifier by searching for dependencies among attributes. We propose and evaluate two algorithms for detecting dependencies among attributes and show that the backward sequential elimination and joining algorithm provides the most improvement over the naive Bayesian classifier. The domains on which the most improvement occurs are those domains on which the naive Bayesian classifier is significantly less accurate than a decision tree learner. This suggests that the attributes used in some common databases are not independent conditioned on the class and that the violations of the independence assumption that affect the accuracy of the classifier can be detected from training data. 23.1 Introduction The Bayesian classifier (Duda - Journal of Machine Learning Research , 2003 "... We describe a methodology for performing variable ranking and selection using support vector machines (SVMs). The method constructs a series of sparse linear SVMs to generate linear models that can generalize well, and uses a subset of nonzero weighted variables found by the linear models to prod ..." Cited by 67 (13 self) Add to MetaCart We describe a methodology for performing variable ranking and selection using support vector machines (SVMs). The method constructs a series of sparse linear SVMs to generate linear models that can generalize well, and uses a subset of nonzero weighted variables found by the linear models to produce a final nonlinear model. The method exploits the fact that a linear SVM (no kernels) with # 1 -norm regularization inherently performs variable selection as a side-e#ect of minimizing capacity of the SVM model. The distribution of the linear model weights provides a mechanism for ranking and interpreting the e#ects of variables. , 1993 "... The results of empirical comparisons of existing learning algorithms illustrate that each algorithm has a selective superiority; it is best for some but not all tasks. Given a data set, it is often not clear beforehand which algorithm will yield the best performance. In such cases one must search th ..." Cited by 63 (2 self) Add to MetaCart The results of empirical comparisons of existing learning algorithms illustrate that each algorithm has a selective superiority; it is best for some but not all tasks. Given a data set, it is often not clear beforehand which algorithm will yield the best performance. In such cases one must search the space of available algorithms to find the one that produces the best classifier. In this paper we present an approach that applies knowledge about the representational biases of a set of learning algorithms to conduct this search automatically. In addition, the approach permits the available algorithms' model classes to be mixed in a recursive tree-structured hybrid. We describe an implementation of the approach, MCS, that performs a heuristic bestfirst search for the best hybrid classifier for a set of data. An empirical comparison of MCS to each of its primitive learning algorithms, and to the computationally intensive method of cross-validation, illustrates that automatic selection of l... - Proceedings of ACM SIGIR-90 , 1990 "... Term clustering and syntactic phrase formation are methods for transforming natural language text. Both have had only mixed success as strategies for improving the quality of text representations for document retrieval. Since the strengths of these methods are complementary, we have explored combini ..." Cited by 63 (6 self) Add to MetaCart Term clustering and syntactic phrase formation are methods for transforming natural language text. Both have had only mixed success as strategies for improving the quality of text representations for document retrieval. Since the strengths of these methods are complementary, we have explored combining them to produce superior representations. In this paper we discuss our implementation of a syntactic phrase generator, as well as our preliminary experiments with producing phrase clusters. These experiments show small improvements in retrieval effectiveness resulting from the use of phrase clusters, but it is clear that corpora much larger than standard information retrieval test collections will be required to thoroughly evaluate the use of this technique.	{"url":"http://citeseerx.ist.psu.edu/showciting?cid=70404","timestamp":"2014-04-17T20:14:24Z","content_type":null,"content_length":"38717","record_id":"<urn:uuid:b9620fbb-0271-41a2-88c8-47acf30ec747>","cc-path":"CC-MAIN-2014-15/segments/1397609530895.48/warc/CC-MAIN-20140416005210-00544-ip-10-147-4-33.ec2.internal.warc.gz"}
East Palo Alto, CA Geometry Tutor Find an East Palo Alto, CA Geometry Tutor ...I think I have more appreciation now for the beauty and power of calculus than I did when I first learned it! It's so rewarding to explain these concepts to students, and watch their excitement when things all start to make sense. Calculus is so much easier for students when they understand the... 10 Subjects: including geometry, calculus, algebra 1, algebra 2 ...This helps us get to know each other and establish a good relationship. I also greatly appreciate feedback so I can continually improve as a tutor. I have a somewhat busy schedule, though I will be as flexible as possible with time. 27 Subjects: including geometry, chemistry, calculus, physics ...I love teaching math, English, and Psychology. I enjoy encouraging students to accept and enjoy math and understand its many benefits. I'm very skilled at making difficult information seem very clear and simple. 18 Subjects: including geometry, English, reading, writing Hi. My name is Susyn. I have been a tutor for over 20 years. 52 Subjects: including geometry, English, chemistry, accounting I am a Naperville North High School and University of Illinois Urbana-Champaign graduate with a degree in Mathematics. I have extensive problem-solving experience including winning 1st place at the ICTM State Math Contest in 2007 and placing in the top 500 in the national Putnam competition. My tu... 17 Subjects: including geometry, chemistry, algebra 2, calculus Related East Palo Alto, CA Tutors East Palo Alto, CA Accounting Tutors East Palo Alto, CA ACT Tutors East Palo Alto, CA Algebra Tutors East Palo Alto, CA Algebra 2 Tutors East Palo Alto, CA Calculus Tutors East Palo Alto, CA Geometry Tutors East Palo Alto, CA Math Tutors East Palo Alto, CA Prealgebra Tutors East Palo Alto, CA Precalculus Tutors East Palo Alto, CA SAT Tutors East Palo Alto, CA SAT Math Tutors East Palo Alto, CA Science Tutors East Palo Alto, CA Statistics Tutors East Palo Alto, CA Trigonometry Tutors	{"url":"http://www.purplemath.com/East_Palo_Alto_CA_Geometry_tutors.php","timestamp":"2014-04-18T05:38:51Z","content_type":null,"content_length":"24005","record_id":"<urn:uuid:6443db1f-482c-431d-85f1-bc98b58ea2da>","cc-path":"CC-MAIN-2014-15/segments/1397609532573.41/warc/CC-MAIN-20140416005212-00227-ip-10-147-4-33.ec2.internal.warc.gz"}
CGTalk - Muscle system - Siggraph Paper please!!! 06-16-2003, 03:36 AM Hello everybody. I heard somewhere that on 1997 someone presented a paper at SIGGRAPH that discussed a way to create a muscle system. I need to get my hands on the "theory" of muscles ASAP because I will develop a college project based on that math theory. The thing is that I've been searching everywhere and I haven't had any luck. Do you happen to know where can I find it?	{"url":"http://forums.cgsociety.org/archive/index.php/t-69782.html","timestamp":"2014-04-21T12:11:23Z","content_type":null,"content_length":"7908","record_id":"<urn:uuid:4dd0300e-44f5-484a-ab66-e52254f1abe6>","cc-path":"CC-MAIN-2014-15/segments/1397609539776.45/warc/CC-MAIN-20140416005219-00572-ip-10-147-4-33.ec2.internal.warc.gz"}
Math Forum Discussions Math Forum Ask Dr. Math Internet Newsletter Teacher Exchange Search All of the Math Forum: Views expressed in these public forums are not endorsed by Drexel University or The Math Forum. Topic: Can someone help solve this geometry problem (on triangle)? thanks. Replies: 1 Last Post: Dec 6, 2012 8:33 AM Messages: [ Previous \| Next ] mark Re: Can someone help solve this geometry problem (on triangle)? thanks. Posted: Dec 6, 2012 8:33 AM Posts: 204 Registered: 12/6/04 Yes. Date Subject Author 11/28/12 Can someone help solve this geometry problem (on triangle)? thanks. Viet 12/6/12 Re: Can someone help solve this geometry problem (on triangle)? thanks. mark	{"url":"http://mathforum.org/kb/message.jspa?messageID=7933144","timestamp":"2014-04-17T16:16:34Z","content_type":null,"content_length":"17034","record_id":"<urn:uuid:88df22db-1588-4a47-826a-aa026d6af429>","cc-path":"CC-MAIN-2014-15/segments/1397609530136.5/warc/CC-MAIN-20140416005210-00597-ip-10-147-4-33.ec2.internal.warc.gz"}
Whatâs The Difference Between Watts And Volt-Amperes? Both watts (W) and volt-amperes (VA) are units of measurement for electrical power. Watts refer to “real power,” while volt-amperes refer to “apparent power.” Usually, electronic products show one or both of these values to provide information about how much energy they will consume or how much current they will draw. Each of these values can be used for various purposes. Table Of Contents What Are Watts? The real power in watts is the power that performs work or generates heat. Power in watts is the rate at which energy is consumed (or generated). One watt is one joule (energy) per second (1 W = 1 J/ s). You pay your utility company for watts expressed as energy, which is power consumed for a time period, typically shown by your utility company in kilowatt-hours. For example, a 100-W light bulb left on for 10 hours consumes 1 kW-hour of energy (100 W x 10 hours = 1000 W-hours = 1 kW-hour). How Are Watts Calculated? Real power for dc circuits is simply the voltage (V[dc]) times the current (I[dc]): W = V[dc] x I[dc] (1) The concept for calculating the real power for ac circuits is straightforward, though performing the calculation is much more difficult. To get the power in watts, you need to know the instantaneous voltage with time, v(t), and the instantaneous current with time, i(t). When you multiply these together, you get the instantaneous power with time, p(t). Since this instantaneous power is changing over time, we need to get an average value, so we integrate the power over a period of time and divide by the time period to get the average. That gives us the watts dissipated by the device in a circuit with voltage v(t) across it and current i(t) through it for the period of time evaluated. Assuming that the voltage and current are both periodic waveforms of period T, the strict mathematical way to express the power calculation for a periodic waveform of period T is: So while this may be easy to visualize, it is not easy to calculate. Even the measurement of real power in watts for ac circuits requires specialized equipment (a wattmeter) because the voltage and current waveforms must be measured over a precise period of time, the measurements must be simultaneous, and the average must be calculated over the measurement time period. A standard multimeter can’t make this type of power measurement. What Are Watts Used For? These ratings are useful if you have to get rid of the heat generated by the device consuming the watts or if you want to know how much you will pay your utility company to use your device since you pay for kilowatt-hours (power used for a period of time). To combine the real power of multiple dc or ac devices, you can just add up the individual power ratings in watts of each device to get the total power (watts add linearly). What Are Volt-Amperes? The apparent power in VA is used to simplify power ratings, making it easier to calculate current draw. Since VA = RMS volts x RMS amps, you can divide the VA rating by your RMS voltage to get the RMS current the device will draw. Knowing the RMS current helps you properly size wires and circuit breakers or fuses that supply current to your device. How Are Volt-Amperes Calculated? The apparent power for dc circuits is simply the voltage (V[dc]) times the current (I[dc]): VA = V[dc] x I[dc] (3) The apparent power for dc circuits is the same as real power for dc circuits (for dc, VA = W). For ac circuits, VA are the product of the RMS voltage (V[RMS]) times the RMS current (I[RMS]): VA = V[RMS] x I[RMS] (4) You can calculate the apparent power in volt-amperes for ac circuits by multiplying the measured RMS voltage times the measured RMS current. A standard multimeter usually can make both of these RMS What Are Volt-Amperes Used For? Volt-amperes provide insight into the amount of current drawn by a product or circuit, assuming you know the voltage. For example, the standard residential voltage in the United States is 120 V[RMS]. If a product is rated for 300 VA (the rating implies this is the maximum VA the product will draw) and is powered from a 120-V[RMS] ac line voltage, you can calculate the expected maximum current as 300 VA/120 V[RMS] = 2.5 A[RMS] maximum (see the figure). Thus, you would want to ensure that the wires and associated circuitry supplying this product accommodate at least 2.5 A[RMS]. To combine the apparent power of multiple dc devices, volt-amperes add linearly. However, to combine the apparent power (or current) of multiple ac devices, there is no straightforward way to get an exact total because the currents for each device are not necessarily in phase with each other, so they don’t add linearly. But if you do simply add the individual VA ratings (or currents) together, the total will be a conservative estimate to use since the actual total will always be less than or equal to this value. Another term that is useful in this discussion is power factor (PF). The power factor is defined as the ratio of W to VA: Power factor = PF = W/VA (5) Power factor is always a number between zero and one because the watts drawn by a device are always less than or equal to the volt-amperes. Note that it is possible for a circuit to have a large voltage across it and to draw substantial current, but consume no energy (dissipate zero watts). While this seems counterintuitive, it is true if the circuit is purely reactive (a pure capacitor or pure inductor). The circuit will do no work and produce no heat, so it is drawing (and dissipating) zero watts. Yet it can draw substantial current, resulting in substantial VA. In this case, the power factor is zero. This is possible because the phase relationship between the voltage and current waveforms is such that the circuit is alternately absorbing real power and giving that real power back, so the net real power consumption is zero. W and VA are both units of measurement for power, but that’s where the similarity ends. Watts do work or generate heat, while volt-amperes simply provide you with information you need to size wires, fuses, or circuit breakers. Watts add linearly, while volt-amperes doe not. And to measure W, you need a special wattmeter. You can calculate VA by using a standard multimeter to measure V[RMS] and I [RMS] and finding the product (see the table). For more articles focused on ac and dc power-related topics, visit Agilent Technologies’ power blog, “Watt’s Up?” at Discuss this Article 15 I have visited to this site multiple times and everytime I find beneficial jobs for me so I would suggest please come to this site and take the chance from here sepatu futsal nike tiempo sepatu adidas adizero f50 • Login or register to post comments First visit to this site. I'm interested in developing enbedded software & robotics • Login or register to post comments The idea for determining the real energy for ac tour is uncomplicated, though executing the computation is much more difficult. To get the energy in h, you need to know the immediate volts eventually, and the immediate present eventually.data mining business • Login or register to post comments A nice clear exposition. • Login or register to post comments This is a great article, Thanks for giving me this information. Keep posting Furniture Jepara : Mebel Jati : Kursi Tamu Minimalis : Mebel Jepara Minimalis : Mebel Jepara : • Login or register to post comments There is a common misconception about watts and volt-amperes. People misunderstands both the same. But there is a whole different way of calculating the both. Thanks for posting a detailed explanation on the topic. install windows explorer 8 • Login or register to post comments I have long been on this website. Read article useful for my own. Today I want to share the news of my writing this article on my blog. You can see the latest information you can see on my homepage Kata Mutiara Bijak Terbaru - Dicoba - Lagu Terbaru • Login or register to post comments This is a wonderful article, Given so much info in it, These type of articles keeps the users interest in the website, and keep on sharing more ... good luck • Login or register to post comments Very good post! We are linking to this particularly great content on our website. Keep up the good writing. • Login or register to post comments Very nice blog to read and to get inform i like it very much and impressed from it you know that you are so beautiful about your work so keep it up Jual furniture jepara Toko furniture jepara • Login or register to post comments This article is very informative and useful. Thanks for sharing.. Toys and Games \| Koleks • Login or register to post comments To merge the actual energy of several dc or ac gadgets, you can just add up the individual energy scores in h of each system to get the complete energy.A conventional multi meter cannot make this type of energy statistic.utah seo • Login or register to post comments Great article For all those who included questionable links: please get a life! Because here nobody will click on your malware links! • Login or register to post comments You Get it Right! I have confusions between the two power measurement., now that you posted this articles you send the answer to my mind...Thanks for the great Blog! keep it up. • Login or register to post comments Very interesting article! • Login or register to post comments	{"url":"http://electronicdesign.com/energy/what-s-difference-between-watts-and-volt-amperes","timestamp":"2014-04-18T10:44:03Z","content_type":null,"content_length":"133253","record_id":"<urn:uuid:8e250c96-7d1e-49ed-9e6d-4fe910b8073a>","cc-path":"CC-MAIN-2014-15/segments/1398223206147.1/warc/CC-MAIN-20140423032006-00261-ip-10-147-4-33.ec2.internal.warc.gz"}
If the probabilistic consensus algorithm is used it is possible to give the expected number of errors in a particular consensus sequence. This is produced by simply summing the error rates at each Each confidence value has a known error rate determined by the formula 10^(-confidence / 10.0). We also know the frequency that each confidence value occurs in the consensus sequence and hence know the expected number of errors for each confidence value. Working on the assumption that we are likely to check and fix the consensus bases with the lowest confidence values first, this allows us to give information on the cumulative number of errors that we would fix by checking every consensus base with a confidence value less than a particular threshold. The List Confidence option, in the View menu, provides this ability. The dialogue simply allows selection of one or more contigs. Pressing OK then produces a table similar to the following: Sequence length = 164068 bases. Expected errors = 168.80 bases (1/971 error rate). Value Frequencies Expected Cumulative Cumulative Cumulative errors frequencies errors error rate 0 0 0.00 0 0.00 1/971 1 1 0.79 1 0.79 1/976 2 0 0.00 1 0.79 1/976 3 3 1.50 4 2.30 1/985 4 30 11.94 34 14.24 1/1061 5 2 0.63 36 14.87 1/1065 6 263 66.06 299 80.94 1/1867 7 151 30.13 450 111.06 1/2841 8 164 25.99 614 137.06 1/5168 9 96 12.09 710 149.14 1/8344 10 80 8.00 790 157.14 1/14069 The above table tells us that we have 164068 bases in our consensus sequences with an expected 169 errors (giving us an average error rate of one in 971). Next it lists each confidence value along with the frequency of this value and the expected number of errors. For any particular confidence value the cumulative columns tell us how many bases in the sequence have the same or lower confidences and how many errors are expected in those bases. From this we know that if all these bases were checked and all the errors fixed we would have a new expected error rate. In the above table we see that there are 790 bases with confidence values of 10 or less. We expect there to be 157 errors in those 790 bases. As we expect there to be about 169 errors in total that implies that manually checking those 790 bases would leave only 12 undetected errors. Given that the sequence length is 164068 bases this means an average error rate of 1 in 14069. Note that this error rate could be achieved by checking only .48% of the total number of consensus bases. In this particular example, editing the same sequence with a 100% consensus cutoff using the either of the frequency bases consensus methods would require checking 25165 bases (15.34%), although the overall error rate would be better. This page is maintained by James Bonfield. Last generated on 2 Febuary 1999. URL: http://www.mrc-lmb.cam.ac.uk/pubseq/manual/gap4_122.html	{"url":"http://cmmg.biosci.wayne.edu/staden/gap4_122.html","timestamp":"2014-04-18T18:23:36Z","content_type":null,"content_length":"5134","record_id":"<urn:uuid:c1e33a14-7b1d-43db-988f-051d1ed6105c>","cc-path":"CC-MAIN-2014-15/segments/1397609535095.7/warc/CC-MAIN-20140416005215-00132-ip-10-147-4-33.ec2.internal.warc.gz"}
Responding to "Eleven Equations" Comments, Math Notation, and More Wow that was quite an experience, I have been looking at sites like Hacker News, Reddit and DZone for years but to see my own post go to #1 on Hacker News and rise high on Reddit and DZone was quite a thrill, with over 70K hits at the time of this writing. It has completely changed my life the phone is ringing off the hook with endorsement offers, it looks like I will only be wearing Nike for the next year. The best part was the over 200 comments on my Blog, Hacker News, and Reddit, it spawned some spirited discussion on all three locations and many people added their own equations some that I was unfamiliar with and I learned a few new things, excellent! The various discussions for the most part were great and very enjoyable and I’d like to thank everyone who contributed. In the post I commented that I wondered how I would feel about the list in a year and I already think I would change the list by one equation. I was tempted to respond to the comments on all of the forums, I know I should at least respond on my own blog, I just figured I’d do it as a post that way I could hit a number of topics. One thing that people objected to was the title, which induced some inferences in the tone of the title. One redditer summed it up as: Someone presuming, yet again, to know what "every" Computer Scientist should know? A title like "my favourite computer science equations" might be better. This list contains a lot of ideas which are only relevant in very narrow domains. Yes, probably on the title comment, but the title was an intentional "spoof" if you will of a title of an article on Wired, and if you read my post you would have gotten that. Actually I confess that you might even accuse me of "Hacker News Post Popularity Hacking" as I saw the Wired post rise up and figured that there was a high probability that a similar CS related post could achieve a similar placement, actually I think it exceeded my expectations and went even higher, it shot to #1 in under two hours of my submitting it and it stayed on the front page for almost a day. I felt the tone I was setting, by using the term "rip off" and the Spinal tap joke (This one goes to eleven) that I don’t think anyone got, was subtly light hearted, perhaps it was too subtle. I recall reading that the title is key to getting people to read posts, and clearly this title was somewhat controversial which probably helped it, actually most of my titles are fairly boring or references that make them less popular, but I generally title things the way want not for popularity, well with this one exception. Another thing that people took umbrage with was the use of the equations, as I just explained since I had set my title accordingly my format was now set. One commenter, in two different comments on a thread on Hacker News added: I think this is a pretty silly post, to be honest. CS covers so much, and everytime I see a list of "things you should know", I have to resist the urge to roll my eyes and ignore it. But then I read it, and inevitably roll my eyes anyway. I disagree. Programming is math. Highly advanced math, in fact. It's just a different type of math. And the 11 equations in the OP's article just barely touches on what CS is about. There is far more to it than that. I mostly agree with this commenter. I admit that the sentiment that this not really about the equations but the general domain knowledge is implied, again perhaps too subtle. At one point someone mentions memorizing these equations which again means you are missing the point. It’s about knowing what these equations mean and how to use them. I feel that the math domain knowledge for our field is growing and becoming more important. Do I use any of this for my day job? Well no, but I hope to one day. As to the broad domain I actually have a post "Math For Programmer TNG" that covers a very broad domain of math that I think is potentially relevant. Also not all areas of math are going to be used in every math related job. As to the narrowness insinuated by the two comments above, the post touched on the following domains: Combinatorics, Logic, Boolean Algebra, Set Theory, Lattice Theory, Probability Theory, Statistics , Category Theory, Number Theory including Complex Numbers, Relational Algebra, Abstract Algebra, Linear Algebra, Shannon Information Theory, Algorithmic Information Theory, Kolmogorov complexity, Graph Theory, Formal Language Theory, Automata Theory, Combinatory Logic, Lambda Calculus, Machine Learning, Data Mining, Encryption, Limits, Topology, Fourier Analysis and The Simpsons. Not exactly narrow, or am I missing something here? In fact the list was picked in part for diversity. The Pumping Lemma turned out to be fairly controversial, I do admit that the Pumping Lemma was perhaps a bit "contrived" as an Equation and as one person put it: "that's the most hideous formulation of the pumping lemma I have ever seen". That formulation came from Wikipedia. As I mentioned I really did want something from Formal Language Theory or Automata Theory and it’s not so much about determining which language is regular but knowing the difference between a Regular Language and a Context Free Language so that you are not the cargo cult coder who tries to parse html with regular expressions because you understand these distinctions. I think the following exchange summed up what I was going for: (except the Pumping Lemma, WTF?) Reply:"Seriously, you never learnt theoretical computer science? As in, theory of computation? Automata theory? Complexity theory? Nothing like that?" There were a number of comments about the use of mathematical notation including the following: "Shannon's Information Theory, Eigenvector, DeMorgan's Laws, etc. None of those names are meaningful or descriptive. And then the greek letters and made up symbols. Math could learn something from Computer Science: This commenter seemed to have an issue with the actual names of things in math. I found this to be very narrow minded. Math is many things including being a domain of knowledge, that’s like complaining about the names: Ytterbium in Chemistry, Bose–Einstein Condensate in Physics, Borneo in world Geography, or Impressionism in art. Really!?! Now the complaints about the notation are more understandable but still unreasonable in my opinion, math in some respects is a language, perhaps somewhere between a natural language and programming language, it has a notation and to really be able to understand it you need to learn this notation (language). Someone remarked that symbols were "unfriendly". Well I find Chinese, Arabic^1, etc. to consist of unfriendly symbols, but that’s because I don’t know them. Also like natural languages you have inconsistencies, and multiple meanings for symbols. One person complained about my notation for the Set version of De Morgan's laws, this may be a nonstandard notation, I saw it in some course notes on probability and set theory and I liked it and I just used it without thinking about it. I do think it’s more elegant. This makes a good point about math. If you learn it and read from diverse sources you will encounter notational differences. This has been my experience, in fact if you look on the Wikipedia page for De Morgan's laws you will find the following example from Modal Logic: I am used to the notation used in Hughes and Cresswell: That’s just how things work. You can get hung up on it and complain or you can accept it and move on. Don’t get me wrong it would be nice if there was a notational standard that every one followed for all math. Like natural languages Math has its equivalences of "Homographs", for example the following symbols can have multiple context dependent meanings: \|b\| can mean absolute value of b if it is a number or cardinality of b if it is a set or length of b if it is string, ∂ can mean Partial Derivative or Topological Boundary, and as we saw ∧ and ∨ can mean meet and join or "logical and" and "logical or". Just as Math has "Homographs", as in natural languages it also has its equivalences of "Polysemes", meaning that there are multiple ways to express the same ideas. For example set difference can be expressed as (S – T) or (S \ T), the Powerset notation can be either 2^S or P(S), and meet and join can be expressed as the either of the following sets of symbols: The list of both math "Homographs" and "Polysemes" is much longer. For De Morgan's laws, someone added the following generalization using the Existential and Universal Quantifiers, which is really interesting and also illustrates the duality: It's not much of a generalization, but I prefer the predicate version of De Morgan's: ~∀x p(x) ≡∃x ~p(x) ~∃x p(x) ≡∀x ~p(x) If you read the Wikipedia Article it includes this generalization as well: The above equations do generalize De Morgan's laws within Logic and Set Theory respectively but my point was to further generalize them in terms of Lattices which is a different concept all together and gets at the deeper intuition about the interrelation of Logic and Set Theory, quoting from Combinatorics the Rota way: by Rota and Kung, an amazing book I am trying to read, emphasis on the word "As John Von Neumann put it, the theory of Boolean Algebras is "pointless" set theory. This set version would be written using the complement exponentiation notation as follows: I really do prefer this notation, I originally encountered it in "Introduction to Probability Theory" by By Ali Ghodsi and Cosmin Arad, lecture 1(pdf). This notation is also used in Combinatorics the Rota way. So this notation is now the official notation of my blog, get used to it or hit the road. ;) A commenter (who was also the demorgans notation complainer) responded with the following: For the rest, they seem more likely to be used by someone doing something related to machine learning/AI/information theory than you run of the mill I-spend-all-day-parsing-user-input programmer. Thank you for making me feel like I'm not a 'true' computer scientist. Next would you like to tell me about how I'm not a 'man' because I don't like to work on cars? Well I hate to break it to you, but if this list makes you feel that way then chances are you are like me: a software developer with a CS Degree and that does not make you or me a Computer Scientist. This is from Wikipedia: "The general public sometimes confuses computer scientists with other computer professionals having careers in information technology, or think that computer science relates to their own experience with computers, ... Oh, and yes you are not a man if you do not at least know how to change your oil, including the filter. ;) Also a number of people remarked that I did not explain the equations in enough detail and I did not provide code examples. It was meant as high level post, if I were to explain all of these equations the post would have been excessively long, maybe even a whole book. As to the code examples again it would be too long, if you want code examples that relate to math, I have posts for that, I recommend the following posts on my blog, some were linked in the original post: "O(log(n))", "Triangles, Triangular Numbers, and the Adjacency Matrix", "The Combinatorial and Other Math of the Java Collections API", "Math You Can Use : Refactoring If Statements with De Morgan's Laws", and "Monoid for the Masses". Regrettably some people responded with the sentiment of: I’m not good at math or that math is too hard, I don’t think I can get a CS degree. Fortunately there were a number of comments of encouragement to counter these sentiments, my favorite was this one: Don't let this be intimidating to you - instead of asking yourself "how come I don't know this?" ask yourself "how can I learn more about this?". This might sound cheesy and simplified but it's as simple as "nobody was born knowing this". I'm 31 and I wish I had the money to go back in education and learn all of this with the official way but for now I'm just picking resources on the web and who knows? It just might happen... I have a post planned to talk about my experiences and thoughts about learning math, I will say if you are a programmer you are doing math in a sense. You just need to formalize your understanding of the underlying concepts. If it is any consolation I find Math to be very hard at times, I pretty much suck at it in the traditional sense, but it is so beautiful and when you grok a concept, at least for me, it is an incredible buzz. Every new concept that you learn changes how you see everything, I see so much math in programming and the world now it’s scary, I just wish I could figure out how to express it. Everything is math. Over the last few years my ability to understand things has greatly increased and continues to do so. Yes it’s hard but it is so worth it. A number of commenters added their own equations to the discussion, and this was the best part, which included a few new things for me. In general my list was mostly directed at more pure math oriented equations that I felt were fairly central to a specific discipline and encapsulated certain principles. Here are a few recommendations and thoughts: One person pointed out the absence of P=NP or P ≠ NP, to which I would respond "D’oh!" If I was doing this over I might even replace the Pumping Lemma with P=NP. One poster recommended triangular numbers: Here's a real simple and practical equation: 1+2+3+4 . . . N = N(N+1)/2 This equation represents the number ofedges on a complete graph with N+1 vertices or the number of possible pairings given N+1 objects. Useful whenestimating O(N) for certain algorithms that involve comparing an item to everyother item in a set. I love Triangular Numbers and this is a great equation, I wrote a whole post "Triangles, Triangular Numbers, and the Adjacency Matrix" on exactly what he is mentioning, and considered that equation but rejected it because triangular numbers are sort of a special case of the Binomial Coefficient equation: Here are some of the other equations and theorems that were suggested, I wouldn’t really consider these because they didn’t fit my theme and criteria but that doesn’t mean they aren’t interesting: One commenter accused me of shoehorning in Euler’s Identity. This is partially true. He also accused me of "Name Dropping". That’s not true. A defender supplied the following course notes: Analytic Combinatorics: A Primer I followed up on that and found that you can download a copy of Analytic Combinatorics: by Flajolet and Sedgewick. Warning: pretty advanced stuff. As the popularity of my post was waning on Hacker News a math oriented post called "Fuzzy string search" was making its way up the ranks. It’s an interesting post and I think it helps illustrate a couple of points I have been making here, first of all it uses mathematical notation, which is not uncommon when writing about these types of topics. Additionally the post includes the equation for the Triangle Inequality: An equation that crossed my mind when writing my equations post. It is not the equation itself, but the concept, if you become familiar with the idea of a Metric or Metric Spaces, you instantly recognize this equation concept without having to read the associated text, not that you shouldn’t read the associated text. Knowing these ideas gives you the ability to better understand more complex ideas that are based on these concepts. I think this is the case in all knowledge domains. Also I noticed that there was not one comment on that post complaining about math notation. A lot of what went on is part of an ongoing conversation, I blogged about it in "The Math Debate" which links to other famous blogs of the same ilk. Ultimately the equations probably don’t apply to most programming jobs, the title contained as some commenters pointed out "Computer Science Geeks" not "Corporate Software Developers". A few people castigated the commenters who seemed to be advocating positions of ignorance, thanks, BTW. I personally find it tragic, the following comment sums this up: "Someone with a CS degree who knows nothing of De Morgan's law should have their credit removed and be demoted to making websites or performing tech support tasks. Reply: "There goes 98% of your CS graduates then. I wish I was joking, but alas.." Of course it’s a bit I ironic that as I am wrapping this up, "A co-Relational Model of Data for Large Shared Data Banks" by Erik Meijer, Gavin Bierman just popped up on Hacker News, the relevant quote is: Every programmer is familiar with the two dual forms of De Morgan’s laws The writing quality of the post was criticized. I don't know what people will think of this post, I feel like I just wrote a clip show. I admit that previous post was not my best effort, while it was fun putting it together it was not easy, I had hoped to learn all of the equations in more detail, I did to some degree, I confess I still don’t fully get the Y-Combinator, but I will. I finally decided to just push it out and move on. This post, while being relevant to my mission of blogging about math was something of a social experiment in popularity, it was interesting but I will be returning to the true mission of my blog which is my journey through math and the pursuit of a real Software Engineering discipline. Ultimately I am interested in the readers, like a young colleague of mine who was too busy to comment because he was following the links to learn new things he didn't know, not the complainers and naysayers. There were many positive comments and again, thanks. I did feel a needed to refute some of the negative comments. The bottom line is if you want to read about math, you need to get used to the notation, it probably won't help you to build CRUD Web apps but it will hopefully help you take your career to the next level. ^1Actually this is not true I find them to be quite beautiful, especially Arabic.	{"url":"http://www.elegantcoding.com/2011/12/responding-to-eleven-equations-comments.html","timestamp":"2014-04-16T04:12:13Z","content_type":null,"content_length":"122383","record_id":"<urn:uuid:cdc38fbc-a6fd-4bda-bba9-0d5feb821dd5>","cc-path":"CC-MAIN-2014-15/segments/1397609521512.15/warc/CC-MAIN-20140416005201-00262-ip-10-147-4-33.ec2.internal.warc.gz"}
Can we have a finite cyclic group of rational numbers (under multiplication)? up vote 0 down vote favorite I am a PDE guy, who works in imaging. We are trying to exploit the inherent group structure of an image, i.e. we consider a representation of the similitude group ($SIM(2)=\mathbb{R}^2\ltimes(SO(2)\ times\mathbb{R}^{+})$) (group of scaling, translation and rotation) on the space $\mathbb{L}_{2}(\mathbb{R}^2)$, which is the space of images. We work with a generalization of the wavelet transform on the $SIM(2)$ group. We have been trying to discretize the group of scalings or dilations, $a\in\mathbb{R}^{+}$. Now in our context we wish to stay away from "a=0" (for numerical as well as theoretical purposes) and have a maximum scaling value ($a<\infty$, practical purposes). So we are trying to come up with a discrete group over $\mathbb {R}^{+}$ or $\mathbb{R}$ (where we substitute $\tau=log(a)$). We were thinking along the lines of either a cyclic multiplicative modulo group of rationals (between say $\frac{1}{d}$ and $b$) or a cyclic additive modulo group of reals (between say $-d$ and $b$) respectively where $d,b$ are predefined integers or real numbers. Though the whole construction of substituting a infinite group with a a finite group (with a different operation) may seem dubious, it allows us to justify the numerics in best possible (mathematical) way. So my question is such a construction of a finite cyclic group possible. It might be the case that due to my lack of knowledge in the field of groups this question may have an obvious answer. Nevertheless I would be grateful if someone could guide me in the right finite-groups gr.group-theory 4 The only finite subgroup of the additive group $\mathbf{R}$ is the trivial group, and the only finite subgroups of the multiplicative group $\mathbf{R}^\times$ are the trivial group and the order-$2$ group generated by $-1$. – Chandan Singh Dalawat May 30 '12 at 8:00 add comment closed as off topic by Dan Petersen, Chandan Singh Dalawat, Chris Godsil, Felipe Voloch, Andreas Blass May 30 '12 at 13:27 Questions on MathOverflow are expected to relate to research level mathematics within the scope defined by the community. Consider editing the question or leaving comments for improvement if you believe the question can be reworded to fit within the scope. Read more about reopening questions here.If this question can be reworded to fit the rules in the help center, please edit the question. 1 Answer active oldest votes Since you want a multiplicative group of rationals bounded between $\frac{1}{d}$ and $b$, you can prove its non-existence in an easy way: assume your group exists and is non-trivial and let $g\neq1$ be one of its elements. Consider $g^n$. If $0 < g < 1$, then $g^n\to0$; if $g>1$, then $g^n\to\infty$. On the other hand, $g^n$ must belong to your group for all $n$, showing that up vote 2 such bounds you want cannot exist. Analogue procedure shows that a bounded additive group of real numbers cannot exist. down vote add comment Not the answer you're looking for? Browse other questions tagged finite-groups gr.group-theory or ask your own question.	{"url":"http://mathoverflow.net/questions/98336/can-we-have-a-finite-cyclic-group-of-rational-numbers-under-multiplication","timestamp":"2014-04-16T22:03:31Z","content_type":null,"content_length":"47154","record_id":"<urn:uuid:8698267e-3596-4daf-bf94-164932e778ef>","cc-path":"CC-MAIN-2014-15/segments/1397609525991.2/warc/CC-MAIN-20140416005205-00577-ip-10-147-4-33.ec2.internal.warc.gz"}
MathGroup Archive: January 1996 [00356] [Date Index] [Thread Index] [Author Index] Re: Complex Default • Subject: [mg3057] Re: Complex Default • From: withoff (David Withoff) • Date: 30 Jan 1996 05:17:46 -0600 • Approved: usenet@wri.com • Distribution: local • Newsgroups: wri.mathgroup • Organization: Wolfram Research, Inc. • Sender: daemon at wri.com The recent exchange about assuming that symbols are real (or specifying other mathematical properties of expressions) has turned out to be more interesting than I had thought, given that this is such a common suggestion and such a well-travelled corner of computer algebra. All of the comments that have been made so far are essentially correct, and some of them have even been new (at least to me). It is important to make a distinction between the visible interface to this functionality and the underlying implementation. All of the suggested interfaces (attributes, options, global variables, etc.) seem fine, and will probably all play a role if and when the functionality that you want is implemented. If there isn't an algorithm that can do anything useful with the extra assumptions, though, then it doesn't much matter how you specify them. This is a common problem. The modifications needed to do something useful with the extra information are rarely simple. Sometimes, completely new algorithms are needed. Sometimes algorithms aren't available, or are prohibitively slow. Even when algorithms are available, implementing them can be a formidable task. Suppose, for example, that one function calls another, and that the first function is told that all of the symbols are real. The first function might introduce intermediate variables that are allowed to be complex (even in the most down-to-earth calculations, it is common to make temporary excursions into the complex plane), which it then passes along to the second function. The second function could be something like Solve, which may then be faced with the task of solving a system of complicated equations amidst a forest of assumptions about various symbols. It might need to know whether some combination of those symbols is real, or positive, or has some other property. Sometimes, it won't have enough information. What should it do then? Give up? Suppose that the algorithm for determining the properties of a particular combination of symbols is very time consuming. How hard should the program work to come up with a solution? It may be that a very tiny subset of this functionality will do many of the things that people want to do. It is easy to see that the general problem is close to impossible to solve, but maybe we don't need to solve the general problem. A first attempt at solving part of the problem can be found in the RealOnly.m package, which is available on MathSource. That package is a good example to illustrate what can and cannot be done without a terrific amount of work. It would be useful to have some examples of specific things that you wish Mathematica could do, and where it is actually possible to do them, including not just the interface, but also the underying algorithm, and where the extra functionality is worth the inevitable speed degradation. Finally, it might be useful to keep in mind that there are two types of solutions to this problem, which might be called the "hackery" approach and the "purist" approach. With the "hackery" approach, you add clever rules to Power, Solve, Integrate, and so forth, until the system processes most of the assumptions that you give it. That is a lot of work, and such systems always have embarassing cracks. Systems that use that approach seem to be acceptable for lots of people, though, as long as you don't push them too hard. The "purist" approach is to have the algorithms abandon the problem unless they can verify the required assumptions. For example, if the only available integration algorithm assumes that all of the symbols are generic complex numbers, then an input like Integrate[expr, x, RealSymbols -> True] would generate a warning message about the lack of an algorthm and give up. Dave Withoff Research and Development Wolfram Research	{"url":"http://forums.wolfram.com/mathgroup/archive/1996/Jan/msg00356.html","timestamp":"2014-04-18T21:10:04Z","content_type":null,"content_length":"38078","record_id":"<urn:uuid:85531dc2-6926-43e2-9678-c103cacbe595>","cc-path":"CC-MAIN-2014-15/segments/1398223207046.13/warc/CC-MAIN-20140423032007-00372-ip-10-147-4-33.ec2.internal.warc.gz"}
Zentralblatt MATH Publications of (and about) Paul Erdös Zbl.No: 417.10039 Autor: Erdös, Paul; Katai, I. Title: On the growth of some additive functions on small intervals. (In English) Source: Acta Math. Acad. Sci. Hung. 33, 345-359 (1979). Review: Let g: N > R denote a non-negative strongly additive function, and let f[k](n) = max{g(n+j): j = 1,...,k}. The authors give conditions which imply that for every \epsilon > 0 and every k[0] the inequality f[k](n) < (1+\epsilon)f[k](0) holds for k \geq k[0] and all but \delta(\epsilon,k[0])x integers n in [1,x], \delta(\epsilon,k[0]) > 0 for k[0] > oo. Some questions concerning the necessity of the conditions remain open. The main part of the paper is devoted to the special case g = \omega, where \omega(n) denotes the number of distinct prime factors of n in N. Let 0[k](n) = max{\omega(n+j): j = 1,...,k},o[k](n) = max{\omega(n+j): j = 1,...,k}. The authors prove, by use of Brun's sieve, that for every \epsilon > 0 the inequalities ( log[2] = log log) 0[k](n) \geq (1-\epsilon)\rho(\frac{log k}{log[2]n}) log[2]n, o[k](n) \leq (\overline{\rho}(\frac{log k}{log[2]n})+\epsilon) log[2]n hold for every k \geq 1 apart from a set of n's having zero density. Here \rho, \overline{\rho} are defined as the inverse functions of \Psi with \Psi(r) = r log ^r/[e] +1 for r \geq 1 resp. 0 < r \ leq 1, \overline{\rho}(u) = 0 for u \geq 1. This result corresponds to similar upper resp. lower bounds obtained by I.Kátai [Publ. Math., Debrecen 18, 171-175 (1971; Zbl 261.10029)]. Reviewer: L.Lucht Classif.: * 11N35 Sieves 11N05 Distribution of primes 11N37 Asymptotic results on arithmetic functions Keywords: sieve methods; additive functions; growth; strongly additive function; number of distinct prime factors Citations: Zbl.261.10029 © European Mathematical Society & FIZ Karlsruhe & Springer-Verlag │Books │Problems │Set Theory │Combinatorics │Extremal Probl/Ramsey Th. │ │Graph Theory │Add.Number Theory│Mult.Number Theory│Analysis │Geometry │ │Probabability│Personalia │About Paul Erdös │Publication Year│Home Page │	{"url":"http://www.emis.de/classics/Erdos/cit/41710039.htm","timestamp":"2014-04-16T19:02:10Z","content_type":null,"content_length":"5633","record_id":"<urn:uuid:925541d7-3b18-492d-9b13-de2e5527ef8f>","cc-path":"CC-MAIN-2014-15/segments/1398223211700.16/warc/CC-MAIN-20140423032011-00481-ip-10-147-4-33.ec2.internal.warc.gz"}
7th International Conference on Multiphase Flow ICMF 2010, Tampa, FL USA, May 30-June 4, 2010 Augmentation of Airlift Pump Performance in Step Geometry A. Karimi, P. Hanafizadeh, S. Ghanbarzadeh and M. H. Saidi Multiphase Flow Research Group, Centre of Excellence in Energy Conversion, School of Mechanical Engineering, Sharif University of Technology, Tehran, Iran, P O. Box: 11155-9567 E-mail: saman@tsharif.edu Keywords: step upriser pipe, airlift pump, two phase flow pattern, flow regime Airlift pumps are devices which are widely used in industrial applications. Parameters such as diameter of the pipe, tapering angle of the upriser pipe, submergence ratio (which is defined by the ratio of immersed length to the total length of the upriser), the gas flow rate, bubble diameter, and inlet gas pressure affect the performance of these pumps. In the previous work (Hanafizadeh et al. 2009) the effect of tapering angle and bubble diameter were considered. In this research, the performance of airlift pump with a vertical riser length of 914 mm and initial diameters of 6 and 8 mm and various height for steps namely: 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8 and 0.9 m in submergence ratio of 0.6 is investigated numerically. This paper reports the improvement in performance of step airlift pump in comparison with ordinary type. Also in the present study effect of height of steps and secondary pipe diameter were considered. The result shows that in constant gas flow rate exist special height and secondary diameter for step which the performance of the pump can be optimized. The numerical results were compared with the experimental data of White (2001) showing a reasonable agreement. The results have indicated that step airlift pump has higher efficiency than the pump with constant pipe diameter. Two phase lifting pumps are simple devices for rising liquids and mixtures of liquids and solid particles. Its operation is based on the use of buoyancy force to pump the liquid and solid particles through a partially submerged vertical upriser pipe in the fluid which should be pumped. A gas phase is injected at the bottom of the pipe to produce an upward flow in the riser pipe (Figure 1). Separator tank -Do~H - - f Air injector i 1 Main tank Figure 1: Schematic of Airlift pump. 1. Overhead collecting tank, 2. Upriser tube, 3. Compressor, 4. Air injector, 5. Water reservoir. The gas liquid two phase mixture is lighter than the liquid and rises to the free surface. Injected gas decreases the hydrostatic weight of the flow column. This type of pumping has low efficiency, but great advantages in utilization of them over mechanical pumps are lower initial and maintenance costs, easy installation, small space requirements, simplistic design and construction, ease of flow rate regulation. These advantages accompanied by the absence of moving mechanical parts cause that two phase lifting pump can be used for pumping of different fluids which are corrosive, abrasive or slurries, explosive, toxic, sandy or salty (Giot 1982). These pumps are used for, pumping of viscous liquids like hydrocarbons in oil field industry Kato et al. 1975, underground well drilling (Giot 1982), under sea mining (Gibson 1961 and Mero 1968, bioreactors (Chisti 1992 and Trystam and Pigache 1992) Besides, they are used to prevent icing on some high altitude (Abed 1977). Fundamentally the flow in air lift pump can be modeled by two phase flow in vertical tube. Therefore, different two phase flow patterns such as bubbly, slug, chum and annular flow are used to describe the flow in these pumps. White and Beardmore (1962) and Zukoski (1966) realized that the effects of surface tension on the dynamics of vertical slug flow are very important when the tube diameter is decreased below 20 mm. Lately, Kouremenos and Staicos (1985) preformed their investigations on small diameter air lift pumps down to 12 mm diameters and low length upriser in the range of 1 to 3 m, with submergence ratios between 0.55 and 0.7. More recently, a wide range of investigating the application of two phase pumps in moving liquids at 7th International Conference on Multiphase Flow ICMF 2010, Tampa, FL USA, May 30-June 4, 2010 nuclear fuel reprocessing plants has been realized, such as de Cachard and Delhaye (1996). These studies have been mostly concerned in the accuracy of the air lift pump rather than the efficiency. Previous laboratory experiments (Geest et al. 2001 and Guet et al. 2002) with water and air showed that the increasing the size of the injected bubbles can improve the efficiency. Most of the work that has been done on air lift pumps involves the usage of an upriser pipe with constant diameter (Darbandi et al. 2007, Hanafizadeh and Saidi 2008 and Kassab et al. 2009). Therefore not much information is available on effect of step geometry for upriser pipes on airlift pump performance. In this research, the performance of two phase pump is investigated numerically for different submergence ratios and different diameter. In order to verify, the numerical results are compared with the experimental data (White 2001). The comparison shows the numerical results are in good agreement with the experimental data. Also the performance of two phase pump is shown for different tapered angles of the upriser pipe and different bubble diameter (10-2 to 1 nmm). g gravity H depth of water K interphase momentum exchange coefficient k turbulent kinetic energy upriser tube length liter per minute secondary phase Governing equations The numerical simulations presented here are based on the two-fluid, Eulerian-Eulerian model (Simonin 1990, Mudde et al. 1997, Lehr et al. 2002, Dhotre and Joshi 2007, Dhotre et al. 2007). The Eulerian modeling system is based on ensemble-averaged mass and momentum transport equations for each phase. In the present work, the liquid phase behaves as the continuum and the gaseous phase (bubbles) as the dispersed phase. The continuity equation for phase q is S(Pqaq) + V. (PqaqVq) = (mlpq rhqp) + Sq (1) where, o(q, Vq and pq are the void fraction, velocity and density of phase q, respectively. rhpq characterizes the mass transfer from the pth to qth phase, and rhqp characterizes the mass transfer from phase q to phase p. It is supposed that mass transfer between two phases is zero (rilpq = rilqp = 0). The momentum conservation for multiphase flow is described by the volume averaged momentum equation as - (qpqVq) + V. (aqpq;qVq) = -oqVp + V. Tq + qpqg + aqpq(Fq + Flift,q + Fvm,q) + (Kpq(p q)+ ilpqVpq) Ti mass flow rate source term here g is the acceleration due to gravity, Tq is the phase stress-strain tensor, Fq is an external body force, lift,q is a lift force, Fvm,q is a virtual mass force, p is the pressure shared by all phases, and Kpq is the interphase momentum exchange coefficient. Vpq is the interphase velocity (If rilpq > 0 Vpq = Vp ; if rilqp > 0 Vqp = Vq ). It is assumed that interphase conversion does not occur in this case, so interphase velocity is set to be zero. void fraction Tq = a"q[q(VVq + VVq) + q (Aq bulk viscosity shear viscosity stress-strain tensor turbulent dissipation 3 Iq) V. q here itq and Aq are the shear and bulk viscosities of phase q, respectively. Lift forces mainly act on a particle due to velocity gradients in the primary phase flow field. The lift force is computed from the following equation. Flift = -0.5pqp(Vq Vp) X (V X Vq) primary phase The lift force will be more important for larger particles. Therefore, the inclusion of lift forces is not appropriate for closely packed particles or very small particles. For multiphase flows, virtual mass occurs when a secondary phase accelerates relative to the primary phase. F =oq(dV dpV, Fvm = 0.5aqpq ( dt dt where, the term denotes the phase material time derivative of the form dq (4) 0(4) dt = at + (Yq V) (6) The virtual mass effect is significant when the secondary phase density is much smaller than the primary phase density e.g., for a transient bubble column, however the virtual mass effect in this study is negligible. Turbulence model Turbulence is taken into consideration for the continuous phase. The dispersed gas phase is modelled as laminar flow, but the influence of the dispersed phase on the turbulence of the continuous phase is taken into account with Sato's additional term (Sato and Sekoguchi 1975). The well-known single-phase turbulence models are usually used to model turbulence of the liquid phase in Eulerian-Eulerian multiphase simulations. In the present case the standard k model is used (Launder and Spalding 1972). The governing equations for the turbulent kinetic energy k and turbulent dissipation e are: - (Xqpqkq) + V. (aqpqUqkq) =V. tq Vk) + (OqGk,q OqpqEq) + Kpq(Cpqk- Cqpkq) p=1 (7) Kpq (Up Uq). t'p Vat Yp1p a p + Kpq (Up q). It'q VXq (QqPqEq) + V. (aqpqiqEq) = v.(a Utqq/) + C[lQLqGkq C21ZtqPqEq + C3, Kq(Cpqkp Cqpkq) (8) - Kpq (Up + Kpq (Up Up Up Uq). LVq Ct (T 4 / 7th International Conference on Multiphase Flow ICMF 2010, Tampa, FL USA, May 30-June 4, 2010 the terms Cpq and Cqp canbe approximated as Cpq = 2, Cqp = 2 1 + pq pq- (' +p [lpJ where, r1pq is available in (Csanady 1963). Geometry and grid mesh specification In this research, the domain of solution is selected in a manner that boundaries are conformed on cylindrical coordinate system, also, the mesh lines divide the geometry span to control volume forming the hexahedral sector. Figure 2 shows the air lift pump geometry with applied meshing. The airlift pump geometry consists of a vertical pipe having a length of L (upriser pipe) within a liquid reservoir. Air is injecting in lower part of the vertical pipe. In this model, the reservoir has a cylindrical shape, the riser tube with 914 mm long, 6 mm initial diameter, different tapered angles. Air injector pipe diameter is 3.175 mm. Figure 2: Air lift pump with step geometry showing the applied mesh To make certain grid independency of the results from nodes number, four meshes (5000, 7000, 9000, and 11000 nodes) have been tested and pressure at axial of upriser have been compared. Figure 3 shows that the pressure at 9000 nodes is least nodes number which the results are finally independent of them. Table 1 shows the characteristics of grid mesh that have been applied for numerical modeling. 0 0.2 0.4 0.6 0.8 1 Position (m) Figure 3: Validation of mesh independency Table 1 Specification of grid mesh Cells 8340 Faces 17246 Nodes 8905 minimum volume 5.09 maximum volume 715e- Numerical solution In this study computational method of CFD packaged which is used for discretizing the governing equation, is based on the control volume frame work which is proposed by Patankar (1980). A collocated grid is used to all variables are stored at the centre of control volume. The governing equations are solved using the SIMPLE algorithm. The details of discretization are found in Fogt and Peric (1994). The time dependent equations are solved to increase the stability of the numerical solution. For any iteration the system of two continuity and two momentum equations with the transport equations of turbulent energy and dissipation are solved. Turbulent variables and velocity near the wall of the control volume are estimated from the wall laws. Velocities of both phases are calculated from the respective momentum equations. After determination of velocity, pressure computed from the liquid continuity equation. Volume fraction is calculated from the continuity equation of the gas phase. Results and discussion The present study deals with various step height and inlet and outlet diameter tube size of an airlift pump. The effect of step geometry is compared with ordinary type of airlift pumps. Also, various step positions and diameters are considered in operation of airlift pumps. 7th International Conference on Multiphase Flow ICMF 2010, Tampa, FL USA, May 30-June 4, 2010 For verification, which is depicted in Figure 4, the obtained results at submergence ratio of 0.4 and pipe diameter of 10 mm are compared with experimental data (White 2001). The comparison showed the predictions were in reasonable agreement with experimental data and can predicted the overall behaviour of it. The difference justification with experimental results can be attributed to the bubble size estimation, isotherm and incompressible flow assumption, relinquishment of surface adhesion influences, and approximations employed on numerical modelling. (H/L=0.4, D =10mm) S Experimental [17] - Present work S 0 0.25 0.5 0.75 1 1.25 1.5 Air Flow Rate (LPM) Figure 4 Comparison between experimental results and present work Comparison between step and ordinary airlift Figure 5 shows the comparison between ordinary and step airlift pump. In this case the step is mounted at the height of 0.2 m with inlet and outlet diameters of 6 and 12 mm, respectively. It is clearly shown that the SALP has more outlet liquid mass flow rate than the OALP in the same inlet air flow rate. So it is obvious in Fig. 5-b that SALP will have more efficient than OALP Comparisons between present work and experimental results S0 004 - 1 S0 003 0 0.2 0.4 Air Flow Rate (LPM) 0.6 0.8 a) comparison of exit liquid mass flow rate in terms of injected air mass flow rate for airlift with and without 0 0.2 0.4 Air Flow Rate (LPM) b) comparison of efficiency in terms of injected air mass flow rate for airlift with and without step Fig. 5 comparison of airlift pump with and without step; for submergence ratio of 0.6, height of step 0.2 m, inlet diameter - -OALP - - SALP 7th International Conference on Multiphase Flow ICMF 2010, Tampa, FL USA, May 30-June 4, 2010 6mm and outlet diameter 12mm In Figure 6, the flow pattern map of Taitel et al. (1980) is marked with the Solid line and the flow pattern map of Hewitt-Roberts (1969) is marked with the Round Dot line. It is demonstrated that the SALP is located in the slug region but the OALP incline to the chum region. It is mentioned before by other researchers (Kassab et al. 2007) the best flow regime for operating of airlift systems is slug flow. So as it is expected the efficiency of SALP is higher than OALP. 10 Bubbly Slug Bubble Wispy .. Annular -- SALP - - OALP 0.01 0.1 1 10 100 Air Superficial Velocity (m/s) Figure 6 Comparison two flow pattern maps for SALP and OALP Figure 7 shows the variation of water flow rate with air flow rate for SALP with various heights of steps. The submergence ratio is 0.6 and the inlet and outlet diameter m 0006 - 0002 0 0.5 1 Air Flow Rate (LPM) of step are 6 and 12 mm, respectively. Figure 8 shows the variation of outlet water flow rate with injected air flow rate for various steps heights in submergence ratio of 0.6 and inlet and outlet step diameters of 8 and 12 mm, respectively. The variation of water mass flow rate with step height is illustrated in Fig. 9 in constant submergence ratio of 0.6. Two air flow rate namely 0.5 and 0.8 LPM correspond to Fig. 9-a, b, respectively. It is realized that for a particular air flow rate always exist a specific height for step which maximize the outlet water flow rate. Comparison between Figs. 9-a and b shows that the optimum height of step is decreased when the injected air flow rate increases. It can be described by regards to the fact that increase in air flow rate advance the transition of slug flow regime to chur flow. Increase in pipe area section can postpone the flow pattern transition and hence the slug flow can be abided in the upriser pipe. It can be concluded that setting the step in the optimum height can improve the efficiency of the pump. Figure 10 shows the variation of water mass flow rate with step height in submergence ratio of 0.6. In this case the inlet and outlet diameters are 8 and 12 mm which are illustrated in Figs. 10-a and b, respectively. The comparison between Figs. 9 and 10 shows that increase in inlet diameter increases the optimum height of step. Increase in pipe diameter in constant air flow rate postpones the transition of slug flow regime to chum. It means that this transition happens in higher height of upriser so the optimum height of step must be increase when the initial diameter of the pipe is increased. _,0 007 * 0006 o 003 Z 0002 1.5 2 0 0.5 1 1.5 Air Flow Rate (LPM) Figure 7 Variation of water mass flow rate with air mass flow rates for different SALP in submergence ratio of 0.6, inlet diameter of 6mm and outlet diameter of 12mm ............. step=0.4(m) - - step=0.2(m) - - step-0.5(m) 7th International Conference on Multiphase Flow ICMF 2010, Tampa, FL USA, May 30-June 4, 2010 to 0016 0 012.. 0 008 step ........*** .. step c 0 004 - - ste S-- step 0 ----- i ---- i ---- i 0 0.5 1 1.5 Air Flow Rate (LPM) S 0016 - 0 004 s -- step 0.5(m) S-- step=0.4(m) -............. step=0.3(m) 0 0.5 1 1.5 2 Air Flow Rate (LPM) Figure 8 Variation of water mass flow rate with air mass flow rates for different SALP in submergence ratio of 0.6, inlet diameter of 8mm and outlet diameter of 12mm "0 0044 " 00043 0 0.2 0.4 0.6 0.8 1 Step Height (m) 0 0.2 0.4 0.6 0.8 1 Step Height (m) a b Figure 9 Variation of water mass flow rate with step height in submergence ratio of 0.6, inlet diameter of 6mm and outlet diameter of 12mm; a: for injected air of 0.5 LPM, b: for injected air of 0.8 LPM .Z 0 0044 0 0.2 0.4 0.6 0.8 1 Step High (m) n 0 0088 .- 0 0076 0 0.2 0.4 0.6 0.8 1 Step High (m) a b Figure 10 Variation of water mass flow rate with step height in submergence ratio of 0.6, inlet diameter of 8mm and outlet diameter of 12mm; a: for injected air of 0.5 LPM, b: for injected air of 0.8 LPM Effect of Step Height on the Efficiency of the Moreover, in this study the influence of step height on the airlift pump performance has been investigated. The Efficiency of air lift pump is defined by Niklin (1963) as below : Qppg(L H) - QqPaLf() QqPaLn( ) where, Qp is liquid mass flow rate, Qq is air flow rate, p is the liquid density, Po and Pa are injection and atmospheric pressures, respectively. Figures 11 and 12 present the results of the efficiency as a function of air flow rate at various step heights in constant submergence ratio. Figure 11 is depicted for inlet diameter of 6 mm in submergence ratio of 0.6 but Fig. 12 is depicted for 8 mm inlet diameter. Moreover, these figures clearly reveal that the maximum 1.5 2 Air Flow Rate (LPM) 7th International Conference on Multiphase Flow ICMF 2010, Tampa, FL USA, May 30-June 4, 2010 efficiency occur at the specific step height. Besides, as it shows from Figure 11 and Figure 12, the maximum efficiency occurs in higher step height when the diameter of the pipe is increased. So it seems that increase in pipe diameter can postpone the transition of slug flow pattern to chum flow and increase the efficiency of the pump. 0.5 1 1.5 Air Flow Rate (LPM) Figure 11 Variation of efficiency with air flow rates for different SALP in submergence ratio of 0.6, inlet diameter of 6 mm and outlet diameter of 12 mm 0.5 1 1.5 Air Flow Rate (LPM) 1.5 2 Air Flow Rate (LPM) Figure 12 Variation of efficiency with air flow rates for different SALP in submergence ratio of 0.6, inlet diameter of 8 mm and outlet diameter of 12 mm The liquid flow rate versus air flow rate is illustrated in Fig. 13-a. Also, the efficiency of SALP is depicted in Fig. 13-b. these figures clearly show that there is an optimum outer diameter for SALP which the efficiency of the pump is maximized in it. It is obvious that the very large outer diameter can destroy the slugs and therefore reduce the efficiency of the pump. Figure 13-b reveals that very large outer diameter not only improve the efficiency of airlift pump but also deteriorate the operation of the pump. The liquid mass flow rate versus pipe outer diameter is shown in Fig. 14. It seems that there is a specific outer diameter which can optimize the operation of the pump. This cross section can stable the slug flow regime and therefore the efficiency of the pump improve in this - - step=0.2(m) .. --- step=0.3(m) ._ -............. step=0.4(m) S .. . .. step=0.5(m) . ... "!- -P -0-5 - step-0.2(m) ... - step=0.6(m) - -- step0.7(m) - step 0.8(m) ........... step=0.9(m) 7th International Conference on Multiphase Flow ICMF 2010, Tampa, FL USA, May 30-June 4, 2010 0 0.1 0.2 0.3 0.4 0.5 0.6 Air flow rate(kg/s) 0 0.002 0.004 0.006 Air flow rate (LPM) a b Figure 13 comparison of effect of outer diameter in SALP with 6 mm inlet diameter; a: liquid flow rate versus air flow rate, b: efficiency versus air flow rate Outer diameter (mm) Figure 14 variation of liquid mass flow rate with outer diameter of the pipe a 0 0086 . 00081 1 1.5 2 2.5 3 1 1.2 1.4 1.6 1.8 2 2.2 a b Figure 15 variation of liquid mass flow rate with diameter ratio, a: inlet diameter of 6mm; b: inlet diameter of 8 mm The variation of water mass flow rate versus of diameter ratio, which is defined by ratio of outlet to inlet diameter, is demonstrated in Figs. 15-a and b for inlet diameters of 6 and 8 mm, respectively. These figures show that the maximum liquid mass flow rates, moreover the diameter ratio, depends on the other parameters such as inlet diameter. Generally, the dimensionless parameter of diameter ratio cannot be introduced as the only effective parameter in performance of SALP. In Fig. 17 the operation of two SALPs with outer diameters of 8 and 10 mm is demonstrated on the flow pattern map of Hewitt and Roberts (1969) and Teital et al. (1980). As it is clear the SALP with outer diameter of 10 is located in the slug flow region and consequently has a higher efficiency. g 0.002 0 * D out= 8 mm - - D out= 10 mm - - D out= 21.94 mm " 0.0061 \| 0.006 1 0.0058 - 0.0057 0.1 1 Figure 16 Comparison of flow pattern maps for two SALP with outer diameters of 8 and 10 mm In this paper, the performance of airlift pump with step geometry is investigated numerically. It was seen that in SALP there is an optimum height for step position which the efficiency of the pump can be maximized in that position. The outlet diameter of upriser pipe in step geometry is the other important parameter which can affect the performance of the pump. The best position of step is where the transition of flow regime from slug flow to churn flow occurs in the pipe. Maximum amount of liquid is lifted if the pump operates in the slug regimes so the best efficiency for this type of pumps is always occurred in this flow regime. Increase in cross sectional area along the upriser pipe due to step geometry can increases the efficiency of the pump. The results showed that the outer diameter of step also has an optimum value which can retain the flow pattern in slug regime. This research was funded by Iran Supplying Petrochemical Industries Parts, Equipment and Chemical Design Corporation (SPEC) as a joint research project with Sharif University of Technology (project no. KPR-8628077). The contribution is greatly appreciated. Abed, K., A. Theoretical study on the performance of airlift pumps. The Inst. of Engineers, MC, Vol. 77: 202 (1977). Chisti, Y Assure bioreactor sterility, Chem. Eng. Prog. Vol. 88(9): 80 (1992). Csanady, G. T. Turbulent diffusion of heavy particles in the atmosphere. J. Atmos. Science Vol. 20: 201-208 (1963). Darbandi M., Saidi M. H., Hanafizadeh P, A numerical approach to simulate two-phase flow in airlift pumps, Int. Conf. on Comp. Meth. ICMM2007, Japan (2007). De Cachard F., Delhaye J. M., A slug-chur model for small-diameter airlift pumps. Int. J. Multiphase Flow, 22 (4): 627-649 (1996). Dhotre, M., T. and Joshi, J., B. Design of a gas distributor: three-dimensional CFD simulation of a coupled system consisting of a gas chamber and a bubble column. Chem. Eng. Journal Vol. 125: 149-163 (2007). Dhotre, M., T., Niceno, B., N., Smith, B., L. Large eddy simulation of a bubble column using dynamic sub-grid scale model. Chem. Eng. J., doi:10.1016/j.cej.2007.04.016. Fogt, H., and Peric, M. Numerical calculation of gas_ liquid flow using a two- fluid finite volume method. Num. Method in Multiphase Flows, Vol. 185: 73-80 (1994). 7th International Conference on Multiphase Flow ICMF 2010, Tampa, FL USA, May 30-June 4, 2010 Geest S. van., Ellepola J. H., Oliemans, R.VA. Comparison of different air injection methods to improve gas-lift performance. Proc. the 10t Con. Multiphase, France (2001). Gibson, A., H. Hydraulics and its applications. 5th Edition, Constable, London (1961). Giot, M. 1982. Three phase flow, Handbook of multiphase systems, edited by G. Hetsroni, Hemisphere, McGraw Hill. Guet, S., Ooms, G. and Oliemans, R. V A. Influence of bubble size on the transition from low-re bubbly flow to slug flow in a vertical pipe. Exp. Th. Fluid Sc., Vol. 26 (6): 635-641 (2002). Hanafizadeh, P. and Saidi, M. H., Integral solution for gravity driven gas-liquid two phase flow, Proc. of 11th Fluid Dyn. Conf. FD2008 1211, Iran (2008). Hanafizadeh P, Saidi M. H., Zamiri A., Karimi A., Effect of Bubble Size and Angle of Tapered Upriser Pipe on the Effectiveness of a Two Phase Lifting Pump, FEDSM2009-78214, Proc. FEDSM2009, ASME (2009). Hewitt, G.F., Roberts, D.N., Studies of two-phase flow patterns by simultaneous X-ray and flash photography. UKAEA Report AERE-M2159 (1969). Kassab, S. Z., Kandil, H. A., Warda, H. A., and Ahmed, W. H., Air-lift pumps characteristics under two-phase flow conditions. Int. J. Heat and Fluid Flow, 30: 88-98 (2009). Kato, H., Miyazawa, T, Timaya, S., and Iwasaki, T; A study of an airlift pump for solid particles. Bull. JSME 18: 286-294 (1975). Kouremenos, D. A. and Staicos, J. Performance of a small air-lift pump. Int. J. Heat Fluid Flow 6: 217-222 (1985). Launder, B., E., Spalding, D., B. Mathematical models of turbulence, GB: Academic Press, London (1972). Lehr, F., Millies, M., and Mewes, D. Bubble-size distributions and flow fields in bubble columns. A.I.Ch.E. J. Vol. 48 (11): 2426-2443 (2002). Mero, J. L. Seafloor minerals, A Chemical Engineering Challenge. Chem. Eng. J. Vol. 43 (2): 73 (1968). Mudde, R. F, Lee, D. J., Reese, J., and Fan, L. S. Role of coherent structures on Reynolds stresses in a 2-d bubble column. A.I.Ch.E. Journal, Vol. 43: 913-926 (1997). Nicklin, D.J. The airlift pump theory and optimization, Trans. Inst. Chem. Eng., J. 41: 29-39 (1963). Patankar, S. V Numerical heat transfer and fluid flow, McGraw-Hill, New York (1980). Sato Y, Sekoguchi, K., Liquid velocity distribution in two-phase bubbly flow, Int. J. Multiphase Flow Vol. 2: 79-95 (1975). Simonin O., Eulerian formulation for particle dispersion in turbulent two-phase flows, Proceedings of the 5th Workshop on Two-Phase Flow Predictions, Germany (1990). Taitel, Y, Barea, D., and Dukler, A.E. Modeling flow pattern transitions for steady upward gas-liquid flow in vertical tubes. AIChE J. 26: 345-354 (1980). Trystam, G. and Pigache, S. Modeling and simulation of a large scale air lift fermenter. Proc. Eur. Symp. Comp.-Aid. Proc. Eng.-2: 5171-5176 (1992). White, E. T., and Beardmore, R. H., The velocity of rise of single cylindrical air bubbles through liquids contained in vertical tubes. Chem. Eng. Sci. Vol. 17: 351-361 (1962). White, S., J. Bubble pump design and performance. MSc Thesis Georgia Institute of Technology (2001). Zukoski, E. E. Influence of viscosity, surface tension, and inclination angle on motion of long bubbles in closed tubes. J. Fluid Mech. 20: 821-832 (1966).	{"url":"http://ufdc.ufl.edu/UF00102023/00441","timestamp":"2014-04-18T21:17:26Z","content_type":null,"content_length":"52334","record_id":"<urn:uuid:8008f2d2-4e6f-4ef3-ba5b-0045697ae43a>","cc-path":"CC-MAIN-2014-15/segments/1397609535095.9/warc/CC-MAIN-20140416005215-00450-ip-10-147-4-33.ec2.internal.warc.gz"}
When limit superior diverges March 29th 2011, 03:28 PM When limit superior diverges Prove that $\lim\sup x_n=\infty\iff \forall M>0,\forall n\in\mathbb N,\exists k_0\ge n$ so that $x_k>M.$ I think is an easy problem, but I'm confused, the statement establishes that $x_k$ is bounded below, but not above. How to prove this? March 29th 2011, 05:41 PM Which part are you having trouble with? Try firstly the only if statement. Then, you want to prove that $\limsup x_n=\infty$ but evidently by assumption you have that $\displaystyle \sup_{n\ geqslant N}x_n\geqslant M$ for every $M\in\mathbb{R}^+$ so that $\displaystyle \limsup x_n=\lim_{N\to\infty}\sup_{n\geqslant N}x_n\geqslant M$ from where the conclusion follows since $M$ were arbitrary (intuitively you can take the limit as $M\to\infty$ of both sides of this last expression, but the left side is 'unaffected' by the limit since there is no $M$)	{"url":"http://mathhelpforum.com/differential-geometry/176228-when-limit-superior-diverges-print.html","timestamp":"2014-04-20T22:25:12Z","content_type":null,"content_length":"7220","record_id":"<urn:uuid:009c15c7-22c4-487b-a303-0b5046d6fc60>","cc-path":"CC-MAIN-2014-15/segments/1397609539230.18/warc/CC-MAIN-20140416005219-00582-ip-10-147-4-33.ec2.internal.warc.gz"}
Domain Theory in HOL - IN POPL , 2010 "... Building semantic models that account for various kinds of indirect reference has traditionally been a difficult problem. Indirect reference can appear in many guises, such as heap pointers, higher-order functions, object references, and shared-memory mutexes. We give a general method to construct m ..." Cited by 16 (9 self) Add to MetaCart Building semantic models that account for various kinds of indirect reference has traditionally been a difficult problem. Indirect reference can appear in many guises, such as heap pointers, higher-order functions, object references, and shared-memory mutexes. We give a general method to construct models containing indirect reference by presenting a “theory of indirection”. Our method can be applied in a wide variety of settings and uses only simple, elementary mathematics. In addition to various forms of indirect reference, the resulting models support powerful features such as impredicative quantification and equirecursion; moreover they are compatible with the kind of powerful substructural accounting required to model (higher-order) separation logic. In contrast to previous work, our model is easy to apply to new settings and has a simple axiomatization, which is complete in the sense that all models of it are isomorphic. Our proofs are machine-checked in Coq. - The Computer Journal , 1994 "... The LCF system provides a logic of fixed point theory and is useful to reason about nontermination, recursive definitions and infinite-valued types such as lazy lists. Because of continual presence of bottom elements, it is clumsy for reasoning about finite-valued types and strict functions. The ..." Cited by 12 (4 self) Add to MetaCart The LCF system provides a logic of fixed point theory and is useful to reason about nontermination, recursive definitions and infinite-valued types such as lazy lists. Because of continual presence of bottom elements, it is clumsy for reasoning about finite-valued types and strict functions. The HOL system provides set theory and supports reasoning about finite-valued types and total functions well. In this paper a number of examples are used to demonstrate that an extension of HOL with domain theory combines the benefits of both systems. The examples illustrate reasoning about infinite values and nonterminating functions and show how domain and set theoretic reasoning can be mixed to advantage. An example presents a proof of correctness of a recursive unification algorithm using well-founded induction. , 2009 "... Abstract. We present a Coq formalization of constructive ω-cpos (extending earlier work by Paulin-Mohring) up to and including the inverselimit construction of solutions to mixed-variance recursive domain equations, and the existence of invariant relations on those solutions. We then define operatio ..." Cited by 12 (4 self) Add to MetaCart Abstract. We present a Coq formalization of constructive ω-cpos (extending earlier work by Paulin-Mohring) up to and including the inverselimit construction of solutions to mixed-variance recursive domain equations, and the existence of invariant relations on those solutions. We then define operational and denotational semantics for both a simplytyped CBV language with recursion and an untyped CBV language, and establish soundness and adequacy results in each case. 1 , 1994 "... Most new theorem provers implement strong and complicated type theories which eliminate some of the limitations of simple type theories such as the HOL logic. A more accessible alternative might be to use a combination of set theory and simple type theory as in HOL-ST which is a version of the HOL s ..." Cited by 3 (0 self) Add to MetaCart Most new theorem provers implement strong and complicated type theories which eliminate some of the limitations of simple type theories such as the HOL logic. A more accessible alternative might be to use a combination of set theory and simple type theory as in HOL-ST which is a version of the HOL system supporting a ZF-like set theory in addition to higher order logic. This paper presents a case study on the use of HOL-ST to build a model of the -calculus by formalising the inverse limit construction of domain theory. This construction is not possible in the HOL system itself, or in simple type theories in general. 1 Introduction The HOL system [GM93] supports a simple and accessible yet very powerful logic, called higher order logic or simple type theory. This is probably a main reason why it has one of the largest user communities of any theorem prover today. However, it is heard every now and then that users cannot quite do what they would like to do, e.g. due to restrictions in t... - Proceedings of the 8th International Workshop on Higher Order Logic Theorem Proving and Its Applications (LNCS 971 , 1995 "... This paper presents an approach to the problem of introducing non-primitive recursive function definitions in higher order logic. A recursive specification is translated into a domain theory version, where the recursive calls are treated as potentially non-terminating. Once we have proved termin ..." Cited by 2 (0 self) Add to MetaCart This paper presents an approach to the problem of introducing non-primitive recursive function definitions in higher order logic. A recursive specification is translated into a domain theory version, where the recursive calls are treated as potentially non-terminating. Once we have proved termination, the original specification can be derived easily. "... Abstract. The goal of this lecture is to show how modern theorem provers—in this case, the Coq proof assistant—can be used to mechanize the specification of programming languages and their semantics, and to reason over individual programs and over generic program transformations, as typically found ..." Cited by 1 (0 self) Add to MetaCart Abstract. The goal of this lecture is to show how modern theorem provers—in this case, the Coq proof assistant—can be used to mechanize the specification of programming languages and their semantics, and to reason over individual programs and over generic program transformations, as typically found in compilers. The topics covered include: operational semantics (small-step, big-step, definitional interpreters); a simple form of denotational semantics; axiomatic semantics and Hoare logic; generation of verification conditions, with application to program proof; compilation to virtual machine code and its proof of correctness; an example of an optimizing program transformation (dead code elimination) and its proof of correctness. , 1993 "... s from the Third Workshop Flemming Nielson (editor) October 1993 1 Introduction The third DART workshop took place on Thursday August l9th and Friday August 20th at the Department of Computer Science (DIKU) at the University of Copenhagen; it was organized by Mads Rosendahl and others at DIKU, and ..." Add to MetaCart s from the Third Workshop Flemming Nielson (editor) October 1993 1 Introduction The third DART workshop took place on Thursday August l9th and Friday August 20th at the Department of Computer Science (DIKU) at the University of Copenhagen; it was organized by Mads Rosendahl and others at DIKU, and Torben Amtoft and Susanne Brønberg helped producing this report. The first day comprised survey presentations whereas the second contained more research oriented talks. The primary aim of the workshop was to increase the awareness of DART participants for each other's work, to stimulate collaboration between the di#erent groups, and to inform Danish industry about the skills possessed by the groups. The DART project started in March 1991 (prematurely terminating a smaller project on Formal Implementation, Transformation and Analysis of Programs) and is funded by the Danish Research Councils as part of the Danish Research Programme on Informatics. To date it has received about 8 million Danis...	{"url":"http://citeseerx.ist.psu.edu/showciting?cid=1606726","timestamp":"2014-04-25T05:08:42Z","content_type":null,"content_length":"30374","record_id":"<urn:uuid:630df435-485d-439b-a8e5-65db189bd63b>","cc-path":"CC-MAIN-2014-15/segments/1398223210034.18/warc/CC-MAIN-20140423032010-00145-ip-10-147-4-33.ec2.internal.warc.gz"}
Media, PA Trigonometry Tutor Find a Media, PA Trigonometry Tutor ...I teach reading music in both treble and bass clefs, time and key signatures. I also teach Solfege (Do, Re Mi..) and intervals to help with correct pitch. I use IPA to teach correct pronunciation of foreign language lyrics (particularly Latin). I have a portable keyboard to bring to lessons and music if the student doesn't have their own selections that they wish to learn. 58 Subjects: including trigonometry, reading, chemistry, calculus ...I am a graduate from the University of Pittsburgh with a B.S degree in Pre-Med and a minor in Chemistry which requires knowledge of advanced math. I had a 3.4 GPA. I have tutored math and sciences in many volunteer and job opportunities. 13 Subjects: including trigonometry, chemistry, geometry, biology ...On the other hand, if you have chosen one of the other talented tutors, keep on learning! "An expert problem solver must be endowed with two incomparable qualities: a restless imagination and a patient pertinacity." - Howard W. Eves, American MathematicianMy expertise is in the field of analyti... 9 Subjects: including trigonometry, chemistry, algebra 2, geometry ...I find that many students are in Algebra II with inadequate basic skills and become lost. My approach is to first assess basic skills, and bring the student up to competence for Algebra II. I have private notes, past exams, for study and practice. 35 Subjects: including trigonometry, chemistry, English, geometry ...I can come to your home, or we can meet at a mutually convenient location. I am currently on a leave of absence from a high-school math position in southern Maryland while my wife finishes her master's degree, so my available hours are very flexible! I firmly believe that anyone can succeed in mathematics, and love helping individuals realize their potential. 8 Subjects: including trigonometry, calculus, geometry, algebra 1 Related Media, PA Tutors Media, PA Accounting Tutors Media, PA ACT Tutors Media, PA Algebra Tutors Media, PA Algebra 2 Tutors Media, PA Calculus Tutors Media, PA Geometry Tutors Media, PA Math Tutors Media, PA Prealgebra Tutors Media, PA Precalculus Tutors Media, PA SAT Tutors Media, PA SAT Math Tutors Media, PA Science Tutors Media, PA Statistics Tutors Media, PA Trigonometry Tutors	{"url":"http://www.purplemath.com/Media_PA_Trigonometry_tutors.php","timestamp":"2014-04-20T23:53:28Z","content_type":null,"content_length":"24220","record_id":"<urn:uuid:4df60ef6-8928-4abc-b7ca-1371a573f8c5>","cc-path":"CC-MAIN-2014-15/segments/1398223205137.4/warc/CC-MAIN-20140423032005-00356-ip-10-147-4-33.ec2.internal.warc.gz"}
Is Imagining the Tenth Dimension accurate? Welcome to PF; Does this book accurately represent what is known about the higher dimensions? No. "What is known about higher dimensions" can probably be summed up as "not much" or "almost nothing" ... but you'd need to define "higher" and "dimension" (and, for that matter, "accurate") to be sure. You got a link to those youtube things? If not, could you suggest a better one for someone with only a cursory knowledge of such things? I can be more definite that that - you will not find any book that will accurately cover many-dimensional physical models for someone with only cursory knowledge. You just have to learn the math.	{"url":"http://www.physicsforums.com/showthread.php?p=4272076","timestamp":"2014-04-19T02:15:07Z","content_type":null,"content_length":"24068","record_id":"<urn:uuid:c4fd0361-1dd2-4abc-8ebc-50a76b26fa15>","cc-path":"CC-MAIN-2014-15/segments/1397609535745.0/warc/CC-MAIN-20140416005215-00214-ip-10-147-4-33.ec2.internal.warc.gz"}
[R] Time series, least squares line Daniel Malter daniel at umd.edu Wed Aug 6 00:08:07 CEST 2008 For the first part: Create a two-column data frame of which one contains your data (Y) and the other the time index (time). Then do: plot(Y~time,type="l") ##lower case L if you want a least-squares line, run a linear regression of Y on time and add that line together with lines for the confidence bands using the abline() command. Are you sure you want an LS-line though? cuncta stricte discussurus -----Ursprüngliche Nachricht----- Von: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org] Im Auftrag von Gareth Campbell Gesendet: Tuesday, August 05, 2008 5:48 PM An: R Help Betreff: [R] Time series, least squares line I have a time-series of standards measured for Refractive index. They are daily standards, however, I didn't run one everyday so some days have no data. I can plot the values, but the x-axis does not represent the correct time series (i.e. it's just an evenly spaced 1,2,3 type axis). I want to plot the points with some form of representitive date line on the x-axis. I don't think the ts() function will work in this instance as I have missing Once I have that data, I want to plot a least squares line with 95% confidence interval bands. Can anyone help with this?? Thanks in advance. Gareth Campbell PhD Candidate The University of Auckland P +649 815 3670 M +6421 256 3511 E gareth.campbell at esr.cri.nz gcam032 at gmail.com [[alternative HTML version deleted]] R-help at r-project.org mailing list PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code. More information about the R-help mailing list	{"url":"https://stat.ethz.ch/pipermail/r-help/2008-August/170083.html","timestamp":"2014-04-16T10:17:08Z","content_type":null,"content_length":"4693","record_id":"<urn:uuid:5d6c5c3b-c4e9-4b34-891d-619209fb9992>","cc-path":"CC-MAIN-2014-15/segments/1397609523265.25/warc/CC-MAIN-20140416005203-00067-ip-10-147-4-33.ec2.internal.warc.gz"}
How do you go about implementing a interpreter(in Haskell) for a simple programming language which is an imperative-style language up vote 2 down vote favorite I have been given with the language semantics and everything i should know.It'd only support few operations and there wouldn't be any concept of Data Types. So i can store anything in a variable and operate on them. I'd have loops and conditions and function calls and that is it. I am looking for a start, an example not a theory book. Has anyone ever implemented such a basic language interpreter in Haskell? I am looking for pointers and references. Thanks ! 2 Is this homework? – augustss Apr 27 '12 at 7:08 add comment 3 Answers active oldest votes I'm working on one right now as a practice project. It's a dynamically-typed language, so variables don't have to be declared, but each value has an associated type. I implemented that using an algebraic data type in Haskell: data Value = BoolValue Bool -- ^ A Boolean value. \| NumberValue Double -- ^ A numeric value. \| StringValue String -- ^ A string value. -- (several others omitted for simplicity) For execution of programs, I'm using the StateT and ErrorT monad transformers on top of IO: -- \| A monad representing a step in an RPL program. -- This type is an instance of 'MonadState', so each action is a function that -- takes an 'RPLContext' as input and produces a (potentially different) -- 'RPLContext' as its result. It is also an instance of 'MonadError', so an -- action may fail (with 'throwRPLError'). And it is built on the 'IO' monad, -- so 'RPL' computations can interact with the outside world. type RPL = StateT RPLContext (ErrorT RPLError IO) -- \| Executes an 'RPL' computation. -- The monadic result value (of type @a@) is discarded, leaving only the final -- 'RPLContext'. runRPL :: RPL a -- ^ The computation to run -> RPLContext -- ^ The computation's initial context -> IO (Either RPLError RPLContext) -- ^ An 'IO' action that performs the operation, producing either -- a modified context if it succeeds, or an error if it fails. runRPL a = runErrorT . (execStateT a) The "context" is a combination of a data stack (it's a stack-based language) and an "environment" that holds all the variables that are currently in scope: -- \| The monadic state held by an 'RPL' computation. data RPLContext = RPLContext { contextStack :: Stack, -- ^ The context's data stack. up vote 5 down vote contextEnv :: Env -- ^ The context's environment. accepted } (Note that Stack is just an alias for [Value].) On top of that foundation, I have a variety of helper functions to do things like manipulate the stack in the current context (held by the StateT part of the RPL monad). For example, here are the functions involved in pushing a value onto the stack: -- \| Pushes a value onto the stack. pushValue :: Value -> RPL () pushValue x = modifyStack (x:) -- \| Transforms the current stack by a function. modifyStack :: (Stack -> Stack) -> RPL () modifyStack f = do stack <- getStack putStack $ f stack -- \| Returns the entire current stack. getStack :: RPL Stack getStack = fmap contextStack get -- \| Replaces the entire current stack with a new one. putStack :: Stack -> RPL () putStack stack = do context <- get put $ context { contextStack = stack } getStack, putStack, and modifyStack are modeled after MonadState's get, put, and modify functions, but they operate on just one field of the RPLContext record. All the language's built-in commands are just actions in the RPL monad, which build on top of tools like pushValue. For parsing code in my language, I'm using Parsec. It's pretty nice. On a separate track, unrelated to my RPL interpreter, you might find "Write Yourself a Scheme in 48 Hours" helpful. add comment I would first encode the entire program in an EDSL. That EDSL would itself be a monad and resemble IO. A GADT makes this very easy to encode: {-# LANGUAGE GADTs, KindSignatures #-} module Interp where import SomeStuff data Expr :: * -> * where -- Commands Print :: String -> Expr () GetLine :: Expr String -- Variables (created on demand) GetVar :: Name -> Expr Value SetVar :: Name -> Value -> Expr () -- Loop constructs While :: Expr Bool -> Expr a -> Expr () For :: Expr a -> Expr Bool -> Expr b -> Expr c -> Expr () -- Expr is a monad up vote 5 down Return :: a -> Expr a vote Bind :: Expr a -> (a -> Expr b) -> Expr b instance Monad Expr where return = Return (>>=) = Bind runExpr :: Expr a -> StateT Variables IO a runExpr (Print str) = liftIO (putStrLn str) runExpr GetLine = liftIO getLine runExpr (While p x) = fix $ \again -> do b <- runExpr p when b (runExpr x >> again) runExpr ... For simple languages you can even do something as simple as this without a dedicated EDSL: parseProgram :: Parser (StateT Variables IO ()) parseProgram = ... It's often forgotten that Haskell takes the notion of functional programming to its conclusion. Let the parser return the program itself. Then you just need to runStateT it with a suitable starting state. add comment One way would be to have your interpreter run in a StateT monad, using a Map to emulate mutable variables. Simple example: import Control.Monad.State import Data.Map (Map) import qualified Data.Map as Map type VarName = String data Value = VInt Int \| VString String type InterpreterState = Map VarName Value type InterpretM = StateT InterpreterState IO up vote 3 down vote putVar :: VarName -> Value -> InterpretM () putVar varname value = modify (Map.insert varname value) getVar :: VarName -> InterpretM Value getVar varname = do m <- gets (Map.lookup varname) case m of Just x -> return x Nothing -> error $ "Variable " ++ varname ++ " is undefined" The interpreter would then run in the InterpretM monad. The above accessors give it access to mutable variables (with no support for goodness like closures and lexical scope). add comment Not the answer you're looking for? Browse other questions tagged haskell or ask your own question.	{"url":"http://stackoverflow.com/questions/10345058/how-do-you-go-about-implementing-a-interpreterin-haskell-for-a-simple-programm","timestamp":"2014-04-16T15:20:35Z","content_type":null,"content_length":"74547","record_id":"<urn:uuid:a49fd633-89da-49f0-a4cd-bf07eaf1b6ee>","cc-path":"CC-MAIN-2014-15/segments/1397609523429.20/warc/CC-MAIN-20140416005203-00385-ip-10-147-4-33.ec2.internal.warc.gz"}
Sieve Diagram Sieve Diagram¶ Plots a sieve diagram for a pair of attributes. Examples (ExampleTable) Input data set. A sieve diagram is a graphical method for visualizing the frequencies in a two-way contingency table and comparing them to the expected frequencies under assumtion of independence. The sieve diagram was proposed by Riedwyl and Schüpbach in a technical report in 1983 and later called a parquet diagram ([Riedwy1994]). In this display the area of each rectangle is proportional to expected frequency and observed frequency is shown by the number of squares in each rectangle. The difference between observed and expected frequency (proportional to standard Pearson residual) appears as the density of shading, using color to indicate whether the deviation from independence is positive (blue) or negative (red). The snapshot below shows a sieve diagram for Titanic data set and attributes sex and survived (the later is actually a class attribute in this data set). The plot shows that the two variables are highly associated, as there are substantial differences between observed and expected frequencies in all of the four quadrants. For example and as highlighted in a balloon, the chance for not surviving the accident was for female passengers much lower than expected (0.05 vs. 0.14). Orange can help to identify pairs of attributes with interesting associations. Such attribute pairs are upon request (Calculate Chi Squares) listed in Interesting attribute pair. As it turns out, the most interesting attribute pair in Titanic data set is indeed the one we show in the above snapshot. For a contrast, the sieve diagram of the least interesting pair (age vs. survival) is shown below. [Riedwy1994] Riedwyl, H., and Schüpbach, M. (1994). Parquet diagram to plot contingency tables. In Softstat ‘93: Advances in Statistical Software, F. Faulbaum (Ed.). New York: Gustav Fischer, For documentation suggestions or questions please use our	{"url":"http://orange.biolab.si/docs/latest/widgets/rst/visualize/sievediagram/","timestamp":"2014-04-16T13:16:36Z","content_type":null,"content_length":"11000","record_id":"<urn:uuid:41c18912-6060-4294-9725-41b3d630392e>","cc-path":"CC-MAIN-2014-15/segments/1398223206672.15/warc/CC-MAIN-20140423032006-00520-ip-10-147-4-33.ec2.internal.warc.gz"}
[SciPy-user] Numpy/Scipy float precision vs Python list float issue Ruben Salvador rsalvador.wk@gmail.... Mon Apr 20 08:58:01 CDT 2009 Hi everybody! First of all I should say I am a newbie with Python/Scipy. Have been searching a little bit (google and lists) and haven't found a helpful answer...so I'm posting. (sorry for double posting, since I also just posted this in numpy-discussion...just in case some of you are in both lists....but I didn't figure out which only list should I post this to) I'm using Scipy/Numpy to do image wavelet transforms via the lifting scheme. I grabbed some code implementing the transforms with Python lists (float type). This code works perfectly, but slow for my needs (I'll be doing some genetic algorithms to evolve coefficients of the filters and the forward and inverse transform will be done many times). It's just implemented by looping in the lists and making computations this way. Reconstructed image after doing a forward and inverse transform is perfect, this is, original and reconstructed images difference is 0. With Scipy/Numpy float arrays slicing this code is much faster as you know. But the reconstructed image is not perfect. The image difference maximum and minimum values returns: maximum difference => 3.5527136788e-15 minimum difference => -3.5527136788e-15 Is this behavior expected? Because it seems sooo weird to me. If expected, anyway to override it? I include some test code for you to reproduce. It's part of a transform over a 8x8 2D signal (for simplicity). It's not complete (again for simplicity), but enough to reproduce. It does part of a forward and inverse transform both with lists and arrays, printing the differences (there is commented code showing some plots with the results as I used when transforming real images, but for the purpose, is enough with the return results I think). Code is simple (maybe long but it's always the same). Instead of using the faster array slicing as commented above, I am using here array looping, so that the math code is exactly the same as in the case list. This happens in the next three system/platforms. * System 1 (laptop): 64 bit processor running Kubuntu 8.04 32 bits Python 2.5.2 (r252:60911, Jul 31 2008, 17:28:52 Numpy version: 1:1.0.4-6ubuntu3 Scipy version: 0.6.0-8ubuntu1 * System 2 (PC): Windows Xp on 64 bit processor Enthought Python distribution (EPD Py25 v4.1.30101). This is a Python 2.5.2 with Numpy 1.1.1 and Scipy 0.6.0 * System 3 (same PC as 2): Debian Lenny 64 bit on 64 bit processor Not sure about versions here, but doesn't mind because behavior is prety much the same in the 3 systems Thanks everybody in advance for the help! Ruben Salvador PhD Student Industrial Electronics Center Universidad Politecnica de Madrid -------------- next part -------------- An HTML attachment was scrubbed... URL: http://mail.scipy.org/pipermail/scipy-user/attachments/20090420/3bb95849/attachment.html -------------- next part -------------- A non-text attachment was scrubbed... Name: floattest.py Type: text/x-python Size: 7160 bytes Desc: not available Url : http://mail.scipy.org/pipermail/scipy-user/attachments/20090420/3bb95849/attachment.py More information about the SciPy-user mailing list	{"url":"http://mail.scipy.org/pipermail/scipy-user/2009-April/020755.html","timestamp":"2014-04-19T21:20:08Z","content_type":null,"content_length":"5987","record_id":"<urn:uuid:ed577b6a-4c8b-402d-833d-e2e781841d6e>","cc-path":"CC-MAIN-2014-15/segments/1397609537376.43/warc/CC-MAIN-20140416005217-00369-ip-10-147-4-33.ec2.internal.warc.gz"}
Got Homework? Connect with other students for help. It's a free community. • across MIT Grad Student Online now • laura* Helped 1,000 students Online now • Hero College Math Guru Online now Here's the question you clicked on: For the new compound ICl2F+2: Calculate the maximum wavelength of electromagnetic radiation that is capable of breaking the weakest bond. Express your answer in meters. Bond energies (kJ/mol) are: I-I (150) F-F (160) Cl-Cl (240) • one year ago • one year ago Your question is ready. Sign up for free to start getting answers. is replying to Can someone tell me what button the professor is hitting... • Teamwork 19 Teammate • Problem Solving 19 Hero • Engagement 19 Mad Hatter • You have blocked this person. • ✔ You're a fan Checking fan status... Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy. This is the testimonial you wrote. You haven't written a testimonial for Owlfred.	{"url":"http://openstudy.com/updates/50a96964e4b0129a3c90534a","timestamp":"2014-04-16T13:10:03Z","content_type":null,"content_length":"39754","record_id":"<urn:uuid:b6e54472-8857-473a-b7af-fb5a96f8fcae>","cc-path":"CC-MAIN-2014-15/segments/1397609523429.20/warc/CC-MAIN-20140416005203-00175-ip-10-147-4-33.ec2.internal.warc.gz"}
Math Forum Discussions Math Forum Ask Dr. Math Internet Newsletter Teacher Exchange Search All of the Math Forum: Views expressed in these public forums are not endorsed by Drexel University or The Math Forum. Topic: How to Plot 3 dimensional data in Matlab Replies: 3 Last Post: May 5, 2013 8:10 AM Messages: [ Previous \| Next ] Re: How to Plot 3 dimensional data in Matlab Posted: May 5, 2013 7:56 AM I didn't understand exactly what are you trying to do here. If your new to matlab i don't think you should start by plotting data using matrices with more then 2 dimensions. I can't help you if you insist on using matrices with 3 dimensions because i'm not familiar with the method. However, if you can use 2d matrices, which has a correspond matrix for each dimension i can help you. This is an easy code that do not help to understand how to plot 3d plot but it useful to get you started: x = linspace(-10,10,50); y = linspace(-10,10,50); [x3d_grid,y3d_grid] = meshgrid(x,y); z3d_grid = sin(x3d_grid) - cos(y3d_grid); Date Subject Author 5/5/13 How to Plot 3 dimensional data in Matlab Pavan 5/5/13 Re: How to Plot 3 dimensional data in Matlab Nasser Abbasi 5/5/13 Re: How to Plot 3 dimensional data in Matlab Yehonatan 5/5/13 Re: How to Plot 3 dimensional data in Matlab Bruno Luong	{"url":"http://mathforum.org/kb/message.jspa?messageID=8912061","timestamp":"2014-04-18T21:43:27Z","content_type":null,"content_length":"20089","record_id":"<urn:uuid:dbcfc607-7b15-4271-841e-ae92c02aeca2>","cc-path":"CC-MAIN-2014-15/segments/1397609535095.9/warc/CC-MAIN-20140416005215-00607-ip-10-147-4-33.ec2.internal.warc.gz"}
An Oracle Restored Some observations on a remarkable discovery One of the principal reasons for the 'Mt.Sinai encounter', recorded in Exodus 25-31, was to instruct Moses as to the precise details of construction of the portable sanctuary that would function as God's dwelling place on earth - the tabernacle - together with its furnishings, and manner of use. Concerning the high-priestly vestments, we read particularly of the oracle - the Urim and Thummim (Ex.28:30) - provided for the guidance of the people in difficult and uncertain times. Details are lacking of the nature and use of these items^(1), but we are informed that they were held in a pouch - called the breastplate (or, in some translations, breastpiece) - attached to the front of the ephod - the outmost garment of the high priest. This breastplate was formed from a single piece of highly-embroidered linen cloth one cubit long and half a cubit wide, folded over in two to form a square, half a cubit by half a cubit (about 9in.x 9in). It was adorned with twelve precious stones on which were engraved the names of the tribes - ie those of the sons and grandsons of Jacob arranged according to their order of birth. These were set out in four rows of three stones each (Ex.28:15-30) [Appendix 1]. [Link to a Web site on the Tabernacle] In Ian Mallett's paper The Breastplate of Judgment^(2), attention is drawn to the many interesting features attending the matrix of integers formed from the characteristic values (hereafter "CVs") [Appendix 2] of the breastplate names: 2. The contiguous multiples of 37 The following attributes, predicated upon 37^(3) and its multiples, may be readily ascertained: 1. The value of the matrix (i.e. the sum of its components) is 3700, or 10^2x37^(4) 2. Of these, the 6 occupying 'odd' positions total 1850, or 50x37, and the 6 occupying 'even' positions, the same 3. The first 9 form a square; they total 2812, or 76x37 4. The remainder - forming the final row of 3 - total 888, or 24x37 5. The first value is 259, or 7x37 6. The remaining values in the square may be grouped into 4 connected pairs - each representing a multiple of 37, thus: At (a), we have the breastplate matrix and observe that it may be divided into 6 regions, here designated I, II, III, IV, V and VI - as at (b) - such that the sum of the name CVs within each region is a multiple of the uniquely-symmetrical number 37 - as represented at (c) - the corresponding multipliers of 37 being depicted at (d). Remarkably, the 6 segments of the breastplate, defined above - each a multiple of 37 - may be combined to generate the first nine multiples of the interesting number 296 (= 8.37). The details are presented in the following set of miniatures: This fact is highly significant because of the associations 296 has with earlier discoveries in the biblical text: it is the characteristic value of the 7th and final Hebrew word of Gen.1:1 (meaning 'the earth'), and is a factor of the Greek form of both 'Jesus' (= 888, or 3.296) and 'Christ' (= 1480, or 5.296). Further, it represents the difference between the cubes of 6 and 8, and is a factor of 1184 - one of a unique pair of 'friendly' numbers. A computer simulation reveals that only 1% of random sets of 6 multiples of 37, over the same range, will be found to possess this feature. We read in John's Gospel, "He was in the world, and the world was made by him, and the world knew him not." (ch.1, v.10). Remarkably, the breastplate is imprinted with our Creator's 'signature' - the bottom row (value 888) conveying the encoded name, 'Jesus', and the connected block above (value 1480), the title, 'Christ', thus: And we further observe powerful symbolism in the fact that the ratio, name:title, represented numerically by 888:1480, or 3:5, is identical with that of the sides of the mercy seat (Ex.25:17-22) - central element in tabernacle worship! [Details concerning the derivation of the characteristic values of the Creator's name and title are given in Appendix 3.] The foregoing facts lead directly to a pythagorean view of the breastplate - one in which the Lord's Name plays an essential role. As we have just seen, the breastplate matrix (value 100x37) may be divided into two blocks, thus: Here, it may be observed that the square roots of the multipliers of 37, {6,8,10} form a pythagorean triple that is a simple multiple of the classic case, {3,4,5}! Four such triangles are generated when a square of side 10 units is rotated by 36.87° (nearly 37°!) within a centred square of side 14 units, thus: The sum of these squares is 296 - a number that has already been shown to be an essential feature of the breastplate. It has already been observed that the sum of the odd-numbered names is precisely one half of the total, and therefore equal to the sum of the even numbered names. However, as revealed below, there is another arrangement which halves the structure numerically, and two which divide it in the ratio 1/4:3/4, thus: Further, in 925, we have the value of the Creator's name and title, as derived from the English analogue of the Hebrew alphabetic numbering scheme^(5). A computer simulation reveals that about 5% of equivalent random sets exhibit these combined properties. We observe that 7 of the 12 integers in the array exhibit interesting relationships of the form, Multiple (M) / Divisor (D) = Quotient (Q) 259 (the 1st) / 7 (the 6th) = 37 570 (the 5th) / 30 (the 3rd) = 19 162 (the 10th) / 54 (the 4th) = 3 570 (the 5th) / 95 (the 9th) = 6 The order of appearance of these elements in the matrix is as follows: i.e. M D D M D D M and we observe symmetry in the types represented, and between types, thus: Further, an examination of the four quotients (Q) - 19, 3, 37, and 6 - reveals them to be significant and related figurate ^(6) numbers, thus: There are a number of points of contact between the numerical features of the breastplate, as outlined above, and those of the Hebrew Bible's first verse: • both reveal 37 to be the dominant factor (a feature heralded by their totals: Gen.1:1 = 2701 = 37 x 73; breastplate matrix = 3700 = 37 x 100; • the total of Gen.1:1 divides thus: 2701 = 999 + 999 + (999 - 296); the breastplate total may be written, 3700 = 999 + 999 + 999 + (999 - 296), or 2701 + 999; indeed, as the following figure reveals, this combination is actually present (as are the many multiples of 296, as we have already seen): • the factors of 2701, viz 37 and 73, and of 703 (i.e. 999 - 296), viz 19 and 37, are richly figurate; the same structures are implied by the breastplate data as Figure 8 reveals (observe that 6 x 6-as-triangle symmetrically disposed about 37-as-hexagon yields a hexagram of 73); • the multipliers of 37 in both Gen.1:1 and Creator's name (ie 73 and 64, respectively) are themselves related to 37: 73, by digit reversal, and 64, by the cube suggested by the hexagonal form of Clearly, they are the work of one supreme author! As has been demonstrated in an earlier paper ^(8), 2368 and 2701 - symbols of the Creator and Creation, respectively - are also objects of considerable significance per se in the field of numerical geometry^(9). Both exhibit compound symmetries which take the form of two-dimensional arrangements of uniform three-dimensional elements^(10) Here we observe 37 cubes - each of 64 units^(11) - set out as a regular hexagram. Remarkably, the figure is harmonised by the fact that these cubes are represented in two-dimensions by numerical hexagons - each of 37 units^(3)! The total represented is 37x64, or 2368 - the characteristic value (CV) of the Lord (Appendix 3). In the next diagram, 2701, or 37x73 - the CV of Gen.1:1 - is depicted as a hexagram of 73 gnomons - each of 37 units^(3). Figure 10 may now be centred and superimposed on Figure 11, thus: The 'halo' of 36 visible gnomons (blue) embodies 36x37, or 1332 units, and the total represented by the whole is thus 1332+2368, or 3700 units - the sum of the 12 breastplate names! However, it should not go unnoticed that the components of the total are to be found in a principal division of the breastplate matrix [Figure 2], and therefore participate in the pythagorean connection noted in Section 2! Further, the 24 gnomon elements underlying the outline of the central hexagram represent 24x37, or 888 units - the CV of 'Jesus' and bottom row of the matrix! Alternatively, the last diagram may be perceived as the augmentation of Figure 11 by a hexagram of 37 smaller cubes - each of value 27 (i.e. 3^3). Clearly, the value represented by this hexagram would be 27x37, or 999. We observe that both 999 and 2701 are present in the breastplate - and form a significant division of it [Figure 9]. The fact that these constructions are hybrid - incorporating both two- and three-dimensional elements - is itself symbolic: it mirrors the dual nature of Jesus who was both perfect man and God! Referring again to Figure 2 we observe that the division of the figure into two groups of 5 and 7 tiles, respectively, establishes further links with the Gen.1:1 phenomena. Thus we find that 37 is the arithmetic mean of 25 (= 5^2) and 49 (= 7^2) and, again, the centroid element^(12) of the 73rd numerical triangle (an alternative representation of Gen.1:1^(8)) is found to occupy the 25th position in the 49th row! The phrase, I am Alpha and Omega..., occurs three times in the text of the Bible's last book (Rev.1:8, 21:6, 22:13) - its final appearance being followed by the words, ...the beginning and the end, the first and the last. It is the Lord Jesus Christ who is making the amazing claim that all things are from him and for him!^(13) In the original Greek this significant phrase is rather peculiarly expressed each time it appears, thus: whereas the first letter of the alphabet, Alpha, is given by name ('^(14) The matter appears to have been designed to attract the attention of the careful reader. But to what purpose? Consulting Appendix 3, we observe the following numerical implications of this arrangement: The more obvious expressions of the phrase would have involved either the names, or the symbols, of both letters, with the following numerical implications: CV(A) = 1; CV( and the final possibility of symbol followed by name: CV(A) = 1; CV( Clearly, the only arrangement to yield a multiple of 37 is precisely that found in the text! - and we observe that the particular multiple, 1332 - representing 'Alpha and Omega' - is that which not only accompanies 2368 ('The Lord') in the breastplate matrix [Figure 2] but also functions as the outline hexagram ('the halo') in the representation of 'The Lord of Creation' [Figure 11(c)]!! Again, in the context of the first verse of the Bible (Gen.1:1) - that 'treasure-trove' of numerical geometry ^(7)^(8) - we find a similar association: the central Hebrew word is formed from the first and the last letters of the alphabet; immediately preceding it is 'Elohim', meaning 'God' - the Creator! It seems abundantly obvious, therefore, that He who created all things and designed the breastplate is also the One who inspired the writing of the Book of Revelation! Behind the original jewels of the breastplate lay the Urim and Thummim - those mysterious instruments ordained by God for the guidance of his people. They, along with the breastplate and ephod were lost during the Babylonian captivity. However, in essence, they live on in the miracle of the breastplate matrix! Here, indeed, is an oracle for today! Here is tangible and compelling evidence of God's Being and Sovereignty, and a guarantee of biblical truth! Those whose beliefs and actions are guided by reason now have an opportunity to grasp these fundamental realities, recognising that in these days God is drawing our attention to hitherto-unnoticed designs which authenticate scripture beyond reasonable doubt. To quote the writer of The Breastplate of Judgment: "What mind could conceive such an amazing array of mathematical phenomena save the Creator himself, the Wonderful Numberer, Jesus Christ, who is the Messiah of Israel and the Saviour of the world?" email: vernon.jenkins@virgin.net Link to Double Indemnity This page was last modified 2006-03-11. (1) The Urim and Thummim were clearly more than the equivalent of a pair of dice (as some have contended) for God did not always provide an answer (1Sam.14:36-37, 28:6). The response came either by a voice from heaven or by an impulse upon the mind of the high priest. This oracle was of great use to Israel (e.g. Nu.27:21, 1Sam.23:6-12). (2) Obtainable from PALMONI RESEARCH, 4 Tynesdale, Whitby, Ellesmere Port, CH65 6RB, U.K. (3) As an integer, thirty-seven has unique geometrical properties: 37 uniform squares or circles (as appropriate) can be arranged to fill any one of three symmetrical frames - octagon, hexagon, or hexagram; in hexagon form, it represents a typical 2D view of a cube of dimension 4, i.e. a stack of 64 unit cubes; it is also the difference between the cubes of 4 and 3. These features are illustrated in the following diagrams: Clearly, 37 is associated with 16 axes of symmetry, and in this sense it is the most symmetrical of all numbers. But, in addition, as a denary object, it provides a basis for many interesting mathematical recreations (see The Ultimate Assertion: Evidence of Supernatural Design in the Divine Prologue, CEN Tech.J., vol.7(2), 1993, Appendix, pp.192-196). (4) This appears significant since the breastplate was itself a square, and 10 is a highly significant number: a prominent feature of human anatomy, principal radix of man's number systems from the beginning, and collective unit in the now near universal principles of decimalisation and metrication. (5) In Appendix 2, an outline is provided of the historically-attested Hebrew alphabetic numbering scheme. If the Roman alphabet is superimposed on this, and the values 500, 600, 700, and 800, assigned to the extra four letters W, X, Y, and Z, we then have a modern equivalent of this ancient scheme. Under this regime, the name 'JESUS' would assume the value 515 (i.e. 10+5+100+300+100), and the title 'CHRIST', 410 (i.e. 3+8+90+9+100+200); 'JESUS CHRIST' would therefore become 925, or 5^2x37. (6) In the context of this page a figurate number is one which, when represented as a set of uniform circular or spherical counters, completely fills a polygonal or polyhedral frame. Examples are illustrated above. (7) Such data are presented in the The Beginning of Wonders and in a number of printed documents, including The Ultimate Assertion: Evidence of Supernatural Design in the Divine Prologue. Please email the author for details. (8) See for example The Arbiters of Truth (9) Numerical geometry describes the study of those two- and three-dimensional structures that involve both number and form, i.e. the figurate numbers. These lie close to the heart of mathematics, and the symmetries represented are absolute in the sense that they are independent of radix, of time, and of place. (10) Here, the 4th solid gnomon (= 37, difference between the 4th and the 3rd cubes) and the 4th cube (= 64 units) are symbolically represented by (11) The 'units' referred to in this account are the unit cubes which function as counters in the construction of the diagrams. (12) One in every three numerical triangles is built around a single counter which then functions as the centroid element - i.e. that which is equidistant from each of the three sides. Such a triangle is the 73rd. (13) See also Colossians 1:16 (14) The writer is indebted to Captain Richard Prendergast for drawing his attention to this interesting anomaly. Jacob fathered 12 sons by four women: his wives, Leah and Rachel; and his concubines - maidservants of Leah and Rachel - and surrogate mothers, Zilpah and Bilhah (Gen.29:31-35; 30:1-24; 35:16-18). The following table lists the names of the sons, in order of birth, with their respective mothers. 1. REUBEN Leah 2. SIMEON Leah 3. LEVI Leah 4. JUDAH Leah 5. DAN Rachel/Bilhah 6. NAPHTALI Rachel/Bilhah 7. GAD Leah/Zilpah 8. ASHER Leah/Zilpah 9. ISSACHAR Leah 10. ZEBULUN Leah 11. JOSEPH Rachel 12. BENJAMIN Rachel Jacob's favorite son, Joseph, sold into slavery through the treachery of his elder brothers, ultimately became Pharaoh's 'right-hand man', married an Egyptian, and fathered two sons, MANASSEH and EPHRAIM (Gen.41:50-52). These two particular grandsons of Jacob were destined to become proxies for their father in the above list. The tribes - now numbering 13, and each identified by the name of its progenitor - remained in Egypt for some 400 years. Following the Exodus, and before entering the 'promised land', a significant event took place: at God's command, the sons of Levi were set apart and dedicated to His service; in due course, they would therefore not feature in the apportionment of the land between the tribes (Deut.10:8-9). Accordingly, we deduce that the name of Levi would not appear on the breastplate, for the high priest who bore it would himself have been of that tribe; again, as we have seen, Joseph would have been represented by his two sons. A reading of Nu.1 confirms these facts. Many centuries after these events occurred, it became the practice to use Hebrew letters as numerals. All written words and names have since become fairly interpretable as numbers. Details of the Hebrew alphabetic numbering scheme are given in Appendix 2. The names of the tribes of Israel (assuming it is these that were engraved on the jewels of the breastplate), in progenitor birth order, and with their full numerical interpretations, are listed in the table below along with their Strong's reference number bracketed. [Note: to verify these Hebrew spellings you may access www.blueletterbible.org using the relevant reference number.] * In contrast to the other 11, the Hebrew rendering of the name Zebulun occurs in different ways - as detailed below: Observe that the column headed 'Freq(uency)' records the number of times each variation occurs in the Old Testament text; and that headed 'CV', the numerical values to be associated with these. For the purposes of the current exercise, it is clear that latter may be read either as 101 or 95. However, the latter is preferred here because, (a) it relates to the most frequent of the variations, (b) it is this value that raises the total of the 'Tribes of Israel' to a significant multiple of 37, and the one which establishes many of the internal breastplate characteristics. It is worth noting that this layout corresponds with the engravings on the two onyx stones mounted on the shoulderpieces of the ephod (Ex.28:9-12). The following diagrams present a summary of the matters discussed above. The breastplate is here represented as a tiled rectangle - the tiles being numbered from right to left, in the Hebrew manner - with the omitted names, Levi and Joseph, shown in their proper positions, by order of birth. Here, finally, is the breastplate prepared for analysis as a 4 x 3 matrix of name CVs: Appendix 2 - The Hebrew Alphabetic Numbering Scheme The Hebrew alphabet has 22 letters - five with 'end forms', i.e. variants used only when words end with one or other of these letters. From circa 200 BC, as the following table reveals, each letter was made to function as a numeral - thus copying the earlier Greek model (c 600 BC). The practice that existed then was to record numbers on an additive basis, i.e. the value represented by a string of letters was simply the sum of the tabular values assigned to each. The characteristic value (CV) of a conventional Hebrew word, name, or phrase, is obtained in this manner. As an illustration of the procedure, the characteristic value of the name SIMEON is derived below. We observe that all Hebrew reading proceeds from right to left. Thus, CV (SIMEON) = 50 + 6 + 70 + 40 + 300 = 466 Appendix 3 - The numerical interpretation of Greek words The Greek alphabet is an ordered set of 24 upper/lowercase pairs of characters. The position and numerical value of each letter of each of these pairs is detailed below: This scheme was introduced circa 600 BC for the purpose of recording numbers on an additive basis, the missing values, 6 and 90, being represented by non-alphabetic symbols. Thus, every string of letters was potentially a number - interpreted by summing the tabular values of the letters. As a unique example of this procedure, the characteristic values (CVs) of the Lord's Name and Title are evaluated below: Observe that the letter values appear above and their respective sums below.	{"url":"http://homepage.virgin.net/vernon.jenkins/oracle.htm","timestamp":"2014-04-18T11:02:58Z","content_type":null,"content_length":"45162","record_id":"<urn:uuid:ce3113d1-b430-4f83-b647-0b74474c28b2>","cc-path":"CC-MAIN-2014-15/segments/1398223205375.6/warc/CC-MAIN-20140423032005-00586-ip-10-147-4-33.ec2.internal.warc.gz"}
Wiretap Channel in the Presence of Action-Dependent States and Noiseless Feedback Journal of Applied Mathematics Volume 2013 (2013), Article ID 423619, 17 pages Research Article Wiretap Channel in the Presence of Action-Dependent States and Noiseless Feedback ^1School of Information Science and Technology, Southwest JiaoTong University, Chengdu 610031, China ^2Institute for Experimental Mathematics, Duisburg-Essen University, Ellernstraße 29, 45326 Essen, Germany ^3Computer Science and Engineering Department, Shanghai Jiao Tong University, Shanghai 200240, China Received 29 November 2012; Accepted 3 January 2013 Academic Editor: Jin Liang Copyright © 2013 Bin Dai et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. We investigate the wiretap channel in the presence of action-dependent states and noiseless feedback. Given the message to be communicated, the transmitter chooses an action sequence that affects the formation of the channel states and then generates the channel input sequence based on the state sequence, the message, and the noiseless feedback, where the noiseless feedback is from the output of the main channel to the channel encoder. The main channel and the wiretap channel are two discrete memoryless channels (DMCs), and they are connected with the legitimate receiver and the wiretapper, respectively. The transition probability distribution of the main channel depends on the channel state. Measuring wiretapper’s uncertainty about the message by equivocation, the capacity equivocation regions are provided both for the case where the channel inputs are allowed to depend noncausally on the state sequence and the case where they are restricted to causal dependence. Furthermore, the secrecy capacities for both cases are formulated, which provide the best transmission rate with perfect secrecy. The result is further explained via a binary example. 1. Introduction Equivocation was first introduced into channel coding by Wyner in his study of wiretap channel [1], see Figure 1. It is a kind of degraded broadcast channels. The object is to transmit messages to the legitimate receiver, while keeping the wiretapper as ignorant of the messages as possible. After the publication of Wyner’s work, Csiszár and Körner [2] investigated a more general situation: the broadcast channels with confidential messages, see Figure 2. The model of [2] is to transmit confidential messages to receiver 1 at rate and common messages to both receivers at rate , while keeping receiver 2 as ignorant of the confidential messages as possible. Measuring ignorance by equivocation, a single-letter characterization of all the achievable triples was provided in [2], where is the second receiver’s equivocation to the confidential messages. Note that the model of [2] is also a generalization of [3], where no confidentiality condition is imposed. In addition, Merhav [4] studied a specified wiretap channel and obtained the capacity region, where both the legitimate receiver and the wiretapper have access to some leaked symbols from the source, but the channels for the wiretapper are more noisy than the legitimate receiver, which shares a secret key with the In communication systems there is often a feedback link from the receiver to the transmitter, for example, the two-way channels for telephone connections. It is well known that feedback does not increase the capacity of discrete memoryless channel (DMC). However, does the feedback increase the capacity region of the wiretap channel? In order to solve this problem, Ahlswede and Cai studied the general wiretap channel (the wiretap channel does not need to be degraded) with noiseless feedback from the legitimate receiver to the channel encoder [5] (see Figure 3), and both upper and lower bounds of the secrecy capacity were provided. Specifically, for the degraded case, they showed that the secrecy capacity is larger than that of Wyner’s wiretap channel (without feedback). In the achievability proof, Ahlswede and Cai [5] used the noiseless feedback as a secret key shared by the transmitter and the legitimate receiver, while the wiretapper had no additional knowledge about the key except his own received symbols. Based on the work of [5], Dai et al. [6] studied a special case of the general wiretap channel with noiseless feedback and found that the noiseless feedback enhances the secrecy capacity of the nondegraded wiretap channel. Besides Ahlswede and Cai’s work, the wiretap channel with noisy feedback was studied in [7], and the wiretap channel with secure rate-limited feedback was studied in [8], and both of them focused on bounds of the secrecy capacity. Since the feedback in the model of wiretap channel is often used as a shared secret key, the techniques used in the secret sharing scheme play an important role in the construction of the practical secure communication systems, see [9–11]. Communication through state-dependent channels, with states known at the transmitter, was first investigated by Shannon [12] in 1958. In [12], the capacity of the discrete memoryless channel with causal (past and current) channel state information at the encoder was totally determined. After that, in order to solve the problem of coding for a computer memory with defective cells, Kuznecov and Cybakov [13] considered a channel in the presence of noncausal channel state information at the transmitter. They provided some coding techniques without the determination of the capacity. The capacity was found in 1980 by Gel’efand and Pinsker [14]. Furthermore, Costa [15] investigated a power-constrained additive noise channel, where part of the noise is known at the transmitter as side information. This channel is also called dirty paper channel. The assumption in these seminar papers, as well as in the work on communication with state-dependent channels that followed, is that the channel states are generated by nature and cannot be affected or controlled by the communication system. In 2010, Weissman [16] revisited the above problem setting for the case where the transmitter can take actions that affect the formation of the states, see Figure 4. Specifically, Weissman considered a communication system where encoding is in two parts: given the message, an action sequence is created. The actions affect the formation of the channel states, which are accessible to the transmitter when producing the channel input sequence. The capacity of this model is totally determined both for the case where the channel inputs are allowed to depend noncausally on the state sequence and the case where they are restricted to causal dependence. Meanwhile, Weissman [16] found that the feedback from the channel output to the channel encoder cannot increase the channel capacity. This framework captures various new channel coding scenarios that may arise naturally in recording for magnetic storage devices or coding for computer memories with defects. Inspired by the above works, Mitrpant et al. [17] studied the transmission of confidential messages through the channels with channel state information (CSI). In [17], an inner bound on the capacity-equivocation region was provided for the Gaussian wiretap channel with CSI. Furthermore, Chen and Vinck [18] investigated the discrete memoryless wiretap channel with noncausal CSI (see Figure 5) and also provided an inner bound on the capacity-equivocation region. Note that the coding scheme of [18] is a combination of those in [1, 14]. Based on the work of [18], Dai and Luo [19] provided an outer bound on the wiretap channel with noncausal CSI and determined the capacity-equivocation region for the memoryless case. In this paper, we study the wiretap channel in the presence of action-dependent states and noiseless feedback, see Figure 6. This work is inspired by the wiretap channel with CSI [18], the channel with action-dependent CSI [16], and the wiretap channel with noiseless feedback [5]. The motivation of this work is to investigate the transmission of confidential messages through the channel with action-dependent CSI and noiseless feedback. More concretely, in Figure 6, the transmitted message is encoded as an action sequence , and is the input of a discrete memoryless channel (DMC). The output of this DMC is the channel state sequence . The main channel is a DMC with inputs and and output . The wiretap channel is also a DMC with input and output . Moreover, there exists a noiseless feedback from the output of the main channel to the channel encoder; that is, the inputs of the channel encoder are the transmitted message , the state sequence , and the noiseless feedback, while the output is . Since the action-dependent state captures various new coding scenarios for channels with a rewrite option that may arise naturally in storage for computer memories with defects or in magnetic recording, it is natural to ask the following two questions.(i)How about the security of these channel models in the presence of a wiretapper?(ii)What can the noiseless feedback do in the model of wiretap channel with action-dependent Measuring wiretapper’s uncertainty about the transmitted message by equivocation, the capacity-equivocation regions of the model of Figure 6 are provided both for the case where the channel input is allowed to depend noncausally on the state sequence and the case where it is restricted to causal dependence. The contribution of this paper is as follows.(i)Compared with the existing model of wiretap channel with side information [18] (see Figure 5), the channel state information in [18] is a special case of that in our new model; that is, the model of [18] is included in the model of Figure 6. Therefore, our result generalizes the result of [18].(ii)Our new model also extends the model of Figure 4 by considering an additional secrecy constraint, and therefore our result also generalizes the result of [16]. In this paper, random variab1es, sample values, and alphabets are denoted by capital letters, lowercase, letters and calligraphic letters, respectively. A similar convention is applied to the random vectors and their sample values. For example, denotes a random -vector , and is a specific vector value in , that is the, th Cartesian power of . denotes a random -vector , and is a specific vector value in . Let denote the probability mass function . Throughout the paper, the logarithmic function is taken to the base 2. The remainder of this paper is organized as follows. In Section 2, we present the basic definitions and the main result on the capacity-equivocation region of wiretap channel with action-dependent channel state information and noiseless feedback. In Section 3, we provide a binary example of the model of Figure 6. Final conclusions are presented in Section 4. 2. Notations, Definitions, and the Main Results In this section, the model of Figure 6 is considered into two parts. The model of Figure 6 with noncausal channel state information is described in Section 2.1, and the causal case is described in Section 2.2, see the following. 2.1. The Model of Figure 6 with Noncausal Channel State Information In this section, a description of the wiretap channel with noncausal action-dependent channel state information is given by Definition 1 to Definition 5. The capacity-equivocation region composed of all achievable pairs is given in Theorem 6, where the achievable pair is defined in Definition 5. Definition 1 (action encoder). The message takes values in , and it is uniformly distributed over its range. The action encoder is a deterministic mapping: The input of the action encoder is , while the output is . The channel state sequence is generated by a DMC with input and output . The transition probability distribution is given by Note that the components of the state sequence may not be i.i.d. random variables, and this is due to the fact that is not i.i.d. generated. The transmission rate of the message is . Definition 2 (channel encoder and the main channel). The main channel is a DMC with finite input alphabet , finite output alphabet , and transition probability , where . . The inputs of the main channel are and , while the output is . There is a noiseless feedback from the output of the main channel to the channel encoder. At the th time, the feedback (where and takes values in ) is the previous time output of the main channel. Since the channel encoder knows the state sequence in a noncausal manner, at the th time, the inputs of the channel encoder are , , and , while the output is ; that is, the th time channel encoder is a conditional probability that the message , the feedback , and the channel state sequence are encoded as the th time channel input . Definition 3 (wiretap channel). The wiretap channel is also a DMC with finite input alphabet , finite output alphabet , and transition probability , where . The input and output of the wiretap channel are and , respectively. The equivocation to the wiretapper is defined as The cascade of the main channel and the wiretap channel is another DMC with transition probability: Note that is a Markov chain in the model of Figure 6. Definition 4 (decoder). The decoder for the legitimate receiver is a mapping , with input and output . Let be the error probability of the receiver, and it is defined as . Definition 5 (achievable pair in the model of Figure 6). A pair (where ) is called achievable if, for any (where is an arbitrary small positive real number and ), there exist channel encoders decoders such that The capacity-equivocation region is a set composed of all achievable pairs, and it is characterized by the following Theorem 6. The proof of Theorem 6 is in Appendices A and B. Theorem 6. A single-letter characterization of the region is as follows: where , which implies that . Remark 7. There are some notes on Theorem 6, see the following. (i) The region is convex, and the proof is directly obtained by introducing a time-sharing random variable into Theorem 6, and, therefore, we omit the proof here.(ii) The range of the random variable satisfies The proof is in Appendix C.(iii) Without the equivocation parameter, the capacity of the main channel with feedback is given by The formula (8) is proved by Weissman [16], and it is omitted here.(iv) Secrecy capacity:the points in for which are of considerable interest, which imply the perfect secrecy . Definition 8 (the secrecy capacity ). The secrecy capacity of the model of Figure 6 with noncausal channel state information is denoted by Clearly, we can easily determine the secrecy capacity of the model of Figure 6 with noncausal channel state information by Proof of (10). Substituting into the region in Theorem 6, we have Therefore, the secrecy capacity . Thus the proof is completed. 2.2. The Model of Figure 6 with Causal Channel State Information The model of Figure 6 with causal channel state information is similar to the model with noncausal channel state information in Section 2.1, except that the state sequence in Definition 1 is known to the channel encoder in a causal manner, that is, at the th time (), the output of the encoder , where and is the probability that the message , the feedback , and the state are encoded as the channel input at time . The capacity-equivocation region for the model of Figure 6 with causal channel state information is characterized by the following Theorem 9, and it is proved in Appendices D and E. Theorem 9. A single-letter characterization of the region is as follows: where , which implies that . Remark 10. There are some notes on Theorem 9, see the following. (i) The region is convex.(ii) The range of the random variable satisfies The proof is similar to that in Theorem 6, and it is omitted here.(iii) Without the equivocation parameter, the capacity of the main channel with feedback is given by The formula (14) is proved by Weissman [16], and it is omitted here.(iv) Secrecy capacity :the points in for which are of considerable interest, which imply the perfect secrecy . Definition 11 (the secrecy capacity ). The secrecy capacity of the model of Figure 6 with causal channel state information is denoted by Clearly, we can easily determine the secrecy capacity of the model of Figure 6 with causal channel state information by Proof of (16). Substituting into the region in Theorem 9, we have Therefore, the secrecy capacity . Thus the proof is completed. 3. A Binary Example for the Model of Figure 6 with Causal Channel State Information In this section, we calculate the secrecy capacity of a special case of the model of Figure 6 with causal channel state information. Suppose that the channel state information is available at the channel encoder in a casual manner. Meanwhile, the random variables , , , , , and take values in , and the transition probability of the main channel is defined as follows. When , When , Note that here . The wiretap channel is a (binary symmetric channel) BSC with crossover probability , that is, The channel for generating the state sequence is a BSC with crossover probability (), that is, From Remark 10 we know that the secrecy capacity for the causal case is given by Note that , , and are achieved if is a function of and is a function of and , and this is similar to the argument in [ 16]. Define and , then (22) can be written as and this is because the joint probability distribution can be calculated by Since is a function of , we have Then, it is easy to see that Now it remains to calculate the characters , , and ; see the remaining of this section. Let take values in . The probability of is defined as follows: and . In addition, there are 16 kinds of and 4 kinds of . Define the following: The character depends on the joint probability mass functions , and we have The character depends on the joint probability mass functions , and we have The character depends on the joint probability mass functions , and we have where is from . By choosing the above , , and , we find that where . Moreover, is achieved when , and . On the other hand, and “=” is achieved if , and . Moreover, and “=” is achieved if , and . Therefore, the secrecy capacity for the causal case is given by Figures 7, 8, and 9 give the secrecy capacity of the model of Figure 6 with causal channel state information for several values of . It is easy to see that the secrecy capacity is increasing while is getting larger. 4. Conclusion In this paper, we study the model of the wiretap channel with action-dependent channel state information and noiseless feedback. The capacity-equivocation regions are provided both for the case where the channel inputs are allowed to depend noncausally on the state sequence and the case where they are restricted to causal dependence. Furthermore, the secrecy capacities for both cases are formulated, which provide the best transmission rate with perfect secrecy. The result is further explained via a binary example. The contribution of this paper is as follows.(i)Compared with the existing model of wiretap channel with side information [18] (see Figure 5), the channel state information in [18] is a special case of that in our new model; that is, the model of [18] is included in the model of Figure 6. Therefore, our result generalizes the result of [18].(ii)Our new model also extends the model of Figure 4 by considering an additional secrecy constraint, and therefore our result also generalizes the result of [16]. A. Proof of the Direct Part of Theorem 6 In this section, we will show that any pair is achievable. Gel’efand-Pinsker’s binning, block Markov coding, and Ahlswede-Cai’s secret key on the feedback system are used in the construction of the code book. Now the remainder of this section is organized as follows. The code construction is in AppendixA.1. The proof of achievability is given in Appendix A.2. A.1. Code Construction Since , and , it is sufficient to show that the pair is achievable, and note that this implies that . The construction of the code and the proof of achievability are considered into two cases.(i)Case1:.(ii)Case2:. We use the block Markov coding method. The random vectors , , , , , and consist of blocks of length . The message for blocks is , where () are i.i.d. random variables uniformly distributed over . Note that in the first block, there is no . Let () be the output of the wiretap channel for block , , . Similarly, , and () is the output of the main channel for block . The specific values of the above random vectors are denoted by lowercase (i) Code Construction for Case1. Given a pair , choose a joint probability mass function such that The message set satisfies the following condition: where is a fixed positive real numbers and Note that is from and (A.2). Let . Code-book generation: (a) Construction of and . In the first block, generate a i.i.d. sequence according to the probability mass function , and choose it as the output of the action encoder. Let be the state sequence generated in response to the chosen action sequence . For the th block (), generate i.i.d. sequences , according to the probability mass function . Index each sequence by . For a given message (), choose a corresponding as the output of the action encoder. Let be the state sequence generated in response to the action sequence . (b) Construction of the Secret Key. For the th block (), firstly we generate a mapping (note that ). Define a random variable (), which is uniformly distributed over , and is independent of. Reveal the mapping to both receivers and the transmitter. Then, when the transmitter receives the output of the -1th block, he computes as the secret key used in the th block. (c) Construction of . In the first block, for the transmitted action sequence and the corresponding state sequence , generate a i.i.d. sequence according to the probability mass function . Choose as a realization of for the first block. For the th block (), given the transmitted action sequence and the corresponding state sequence , generate ( as ) i.i.d. sequences , according to the probability mass function . Distribute these sequences at random into bins such that each bin contains sequences. Index each bin by . For a given , , , and a secret key , the transmitter chooses a sequence from the bin (where is the modulo addition over ) such that . If such multiple sequences in bin exist, choose the one with the smallest index in the bin. If no such sequence exists, declare an encoding error. (d) Construction of . For each block, the is generated according to a new discrete memoryless channel (DMC) with inputs , , and output . The transition probability of this new DMC is , which is obtained from the joint probability mass function . The probability is calculated as follows: Decoding. For the th block (), given a vector and a secret key ( is known by the receiver), try to find a sequence such that . If there exist sequences with the same , by using the secret key , put out the corresponding . Otherwise, that is, if no such sequence exists or multiple sequences have different message indices, declare a decoding error. (ii) Code Construction for Case2. Given a pair , choose a joint probability mass function such that The message set satisfies the following condition: Let . Code-book generation: (a) Construction of and .In the first block, generate a i.i.d. sequence according to the probability mass function , and choose it as the output of the action encoder. Let be the state sequence generated in response to the chosen action sequence . For the th block (), generate i.i.d. sequences , according to the probability mass function . Index each sequence by . For a given message (), choose a corresponding as the output of the action encoder. Let be the state sequence generated in response to the action sequence . (b) Construction of the Secret Key. For the th block (), firstly we generate a mapping (note that ). Define a random variable (),which is uniformly distributed over , and is independent of. Reveal the mapping to both receivers and the transmitter. Then, when the transmitter receives the output of the -1th block, he computes as the secret key used in the th block. (c) Construction of . In the first block, for the transmitted action sequence and the corresponding state sequence , generate a i.i.d. sequence according to the probability mass function . Choose as a realization of for the first block. For the th block (), given the transmitted action sequence and the corresponding state sequence , generate ( as ) i.i.d. sequences , according to the probability mass function . Distribute these sequences at random into bins such that each bin contains sequences. Index each bin by . For a given , , , and a secret key , the transmitter chooses a sequence from the bin (where is the modulo addition over ) such that . If such multiple sequences in bin exist, choose the one with the smallest index in the bin. If no such sequence exists, declare an encoding error. (d) Construction of . The is generated the same as that for the case 1, and it is omitted here. Decoding. For the th block (), given a vector and a secret key ( is known by the receiver), try to find a sequence such that . If there exist sequences with the same , by using the secret key , put out the corresponding . Otherwise, that is, if no such sequence exists or multiple sequences have different message indices, declare a decoding error. A.2. Proof of Achievability The rate of the message is defined as and it satisfies In addition, note that the encoding and decoding scheme for Theorem 6 is exactly the same as that in [16], except that the transmitted message for the legitimate receiver is . Since the legitimate receiver knows , the decoding scheme for Theorem 6 is in fact the same as that in [16]. Hence, we omit the proof of here. It remains to show that , see the following. Since the message is encrypted by , the equivocation about is equivalent to the equivocation about the secret key . There are two ways for the wiretapper to obtain the secret key . One way is that he tries to guess the from its alphabet . The other way is that he tries to guess the feedback ( is the output of the main channel for the previous block, and ) from the conditional typical set , and this is because for a given and sufficiently large , . Note that there are sequences when and . Therefore, the equivocation about is , and note that and , and then is obtained. The details about the proof are as follows. First, we will show that is independent of and , and this is used in the proof of . Since is independent of (), and all of them are uniformly distributed over , the fact that is independent of and is proved by the following (A.9): Then, for both cases is proved by the following ( A.10): where is from that is a Markov chain, is from that is a Markov chain, follows from the fact that is independent of and , and is from the fact that the wiretapper can guess the specific vector (corresponding to the key ) from the conditional typical set , and is uniformly distributed over ( is the key used in block ). On the other hand, where (1) is from the fact that , () is the state sequence for block , and is a function of , (2) is from and that are i.i.d. generated random vectors, and the channels are discrete memoryless. Therefore, it is easy to see that, for the case 1, is proved by (A.10) and (A.11). For the case 2, is proved by the formula (A.10). Thus, for both cases is proved. The proof of Theorem 6 is completed. B. Proof of the Converse Part of Theorem 6 In this section, we prove the converse part of Theorem 6: all the achievable pairs are contained in the set . Suppose that is achievable; that is, for any given , there exists a channel encoder-decoder such that Then we will show the existence of random variables such that Since is uniformly distributed over , we have . The formulas (B.3), (B.4), and (B.5) are proved by LemmaB.1; see the following. LemmaB.1. The random vectors and and the random variables , , , , , , and of Theorem 6 satisfy where . Note that . Substituting and (5) into (B.6), (B.7), and (B.8) and using the fact that , the formulas (B.3), (B.4), and (B.5) are obtained. The formula (B.2) is from It remains to prove LemmaB.1; see the Proof of LemmaB.1.The formula (B.6) follows from (B.10), (B.13), and (B.21). The formula (B.7) is from (B.11), (B.17) and (B.22). The formula (B.8) is proved by (B.12), (B.18), and (B.23). Part(i). We begin with the left parts of the inequalities (B.6), (B.7), and (B.8); see the following. Since is a Markov chain, for the message , we have For the equivocation to the wiretapper, we have Note that and follow from Fano’s inequality, and (B.12) is from the fact that is a deterministic function of . Part (ii). By using chain rule, the character in formulas (B.10) and (B.11) can be bounded as follows: where formula (1) follows from that , and formula (2) follows from that and formula (3) follows from that . Proof of (B.14).The left part of (B.14) can be rewritten as where (1) is from the fact that is a deterministic function of . The right part of (B.14) can be rewritten as where (2) is from the fact that is a deterministic function of . The formula (B.14) is proved by (B.15) and (B.16). The proof is completed. Part(iii). The character in formula (B.11) can be rewritten as follows: Part (iv). The character in formula (B.12) can be rewritten as follows: Part (v) (single letter). To complete the proof, we introduce a random variable , which is independent of , , , , and . Furthermore, is uniformly distributed over . Define Part (vi). Then (B.13) can be rewritten as Analogously, (B.17) is rewritten as follows: Similarly, (B.18) can be rewritten as follows: Substituting (B.21), (B.22), (B.23) into (B.10), (B.11), and (B.12), LemmaB.1 is proved. The proof of Theorem 6 is completed. C. Size Constraint of the Auxiliary Random Variable in Theorem 6 By using the support lemma (see [20, page 310]), it suffices to show that the random variable can be replaced by new one, preserving the Markovity and the mutual information , , , and furthermore, the range of the new satisfies, . The proof is in the reminder of this section. Let Define the following continuous scalar functions of : Since there are functions of , the total number of the continuous scalar functions of is . Let . With these distributions , we have According to the support lemma ([20, page 310]), the random variable can be replaced by new ones such that the new takes at most different values and the expressions (C.3), (C.4), and (C.5) are D. Proof of the Direct Part of Theorem 9 In this section, we will show that any pair is achievable. Block Markov coding and Ahlswede-Cai’s secret key on the feedback system are used in the construction of the code-book. Now the remainder of this section is organized as follows. The code construction is in Appendix D.1. The proof of achievability is given in Appendix D.2. D.1. Code Construction Since , , and , it is sufficient to show that the pair is achievable, and note that this implies that . We use the block Markov coding method. The random vectors , , , , , and consist of blocks of length . The message for blocks is , where () are i.i.d. random variables uniformly distributed over . Note that, in the first block, there is no . Let () be the output of the wiretap channel for block , , . Similarly, and () are the output of the main channel for block . The specific values of the above random vectors are denoted by lowercase Given a pair , choose a joint probability mass function such that The message set satisfies the following condition: where is a fixed positive real numbers. Code-book generation: (i) Construction of and .In the first block, generate a i.i.d. sequence according to the probability mass function , and choose it as the output of the action encoder. Let be the state sequence generated in response to the chosen action sequence . For the th block (), generate i.i.d. sequences , according to the probability mass function . Index each sequence by . For a given message (), choose a corresponding as the output of the action encoder. Let be the state sequence generated in response to the action sequence . (ii) Construction of the Secret Key. For the th block (), firstly we generate a mapping (note that ). Define a random variable (	{"url":"http://www.hindawi.com/journals/jam/2013/423619/","timestamp":"2014-04-16T19:34:18Z","content_type":null,"content_length":"1045456","record_id":"<urn:uuid:8a9211e0-cc0f-45b8-9105-6a0e8c6c3324>","cc-path":"CC-MAIN-2014-15/segments/1398223206120.9/warc/CC-MAIN-20140423032006-00627-ip-10-147-4-33.ec2.internal.warc.gz"}
ot the Navigation Panel: Go backward to This is Not the Fallacy Go up to All People in Canada are the Same Age Go forward to This is Not the Fallacy Switch to graphical version (better pictures & formulas) Go to University of Toronto Mathematics Network Home Page This step is not the source of the fallacy. This statement is correctly appealing to the induction assumption. Remember, in order to prove a statement of the form "if A, then B", what you do is assume A and derive B from it. In our case, A is the statement S(k): "in any group of k people, everyone has the same age", and B is the statement S(k+1): "in any group of k+1 people, everyone has the same age." Step 4 says that all we have to do to complete the proof is assume A is true and try to derive B from it. Therefore, it is legitimate to use A and treat it as true in the process of proving B. That's exactly what we're doing here. At this stage in the proof, we have two things are disposal: 1. we are assuming that, in every group of k people, everyone has the same age, and 2. we now have a particular group G of k+1 people, and are trying to use the above assumption to prove that everyone in G has the same age. Within G, there happens to be a group of k people (namely, the group of everyone in G except for the one person P). Since we are operating under the assumption that, in every group of k people, everyone has the same age, it follows that everyone in this smaller group within G has the same age. And, it is perfectly legitimate to use this knowledge about this smaller group within G to try to show something about G itself, which is what the subsequent steps in the proof attempt to do. Why don't you go back to the list of steps in the proof and see if you can identify which one is wrong, now that you know it isn't this one? This page last updated: May 26, 1998 Original Web Site Creator / Mathematical Content Developer: Philip Spencer Current Network Coordinator and Contact Person: Joel Chan - mathnet@math.toronto.edu Navigation Panel: Previous \| Up \| Forward \| Graphical Version \| U of T Math Network Home	{"url":"http://www.math.toronto.edu/mathnet/plain/falseProofs/guess25.html","timestamp":"2014-04-17T06:41:01Z","content_type":null,"content_length":"3191","record_id":"<urn:uuid:06e1d4c6-2ef3-4db9-9bd3-0f67c8cd2bef>","cc-path":"CC-MAIN-2014-15/segments/1397609526311.33/warc/CC-MAIN-20140416005206-00567-ip-10-147-4-33.ec2.internal.warc.gz"}
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3rd Grade Math Lessons \| 3rd Grade Math \| Math Games \| Math Worksheets 3rd Grade Math Lessons In 3rd grade math lessons you will get all types of examples and practice problems on different topics along with the solutions. Third grade math lessons are arranged in such a way that students can learn math while playing the third grade math games. Keeping in mind the mental level of child in 3rd grade, every efforts has been made to introduce new concepts in a simple language, so that the child understands them easily. The difficulty level of the problems has been reduced and mathematical concepts have been explained in the simplest possible way. Each topic contains a large number of examples to understand the applications of concepts. In 3rd grade math we will mainly learn about Four-Digit Numbers, Comparison of Numbers, Addition, Subtraction, Multiplication, Division, Geometrical Shapes and Figures, Measurement of Length, Measurement of Mass, Measurement of Capacity, Measurement of Time, Money, Fractional Numbers, Pictographs, Mental Arithmetic, Patterns, etc….. If student follow math-only-math they can improve their knowledge by practicing third grade math worksheets which will help you to score in 3rd grade math test. Formation of Four-Digit Numbers: Finding smallest and largest 4-digit numbers; showing 4-digit numbers on the abacus; place value of 4-digit numbers; writing 4-digit numbers in numerals, in words and in the expanded form. Four Digit Numbers: Learn what are the numbers comes under 4-digit numbers; representing 4-digit numbers on the abacus. Four-digit Numbers in Numerals and Words: Learn how to write the 4-digit numbers in numerals using commas; writing 4-digit numbers in words and expanded form of a 4-digit numbers. International and Roman Numerals: We know how to write English or International numbers of one, two, three and four digits upto 9999. Under this section we cover expressing numbers in Roman and in English numerals. Conversion of Numbers to Roman Numerals: Learn how to express numbers to Roman numerals. Conversion of Roman Numerals to Numbers: Learn how to express Roman numerals to English numerals. Comparison of Numbers: Compare one-digit numbers; arrange one-digit numbers; compare two-digit numbers; arrange two-digit numbers; compare three-digit numbers; arrange three-digit numbers; compare four-digit numbers; arrange four-digit numbers; Comparison of One-digit Numbers: Learn how to compare (using symbols greater than: >, less than: <, equal to: =) and arrange 1-digit numbers. Comparison of Two-digit Numbers: Learn how to compare (using signs greater than: >, less than: <, equal to: =) and arrange 2-digit numbers in ascending and descending order. Comparison of Three-digit Numbers: Learn how to compare the numbers (using symbols or signs greater than: >, less than: <, equal to: =) and arrange 3-digit numbers in ascending and descending order. Comparison of Four-digit Numbers: Learn how to compare any 4-digit numbers (using symbols or signs greater than: >, less than: <, equal to: =) and arrange the 4-digit numbers in ascending and descending order. Compare Two Numbers: Learn how to compare the numbers using symbols to find the greater number and the smaller number. Face value and place value: Learn how each digit in a number has a face value and a place value and their difference. Finding and Writing the Place Value: Learn the process to identify, find and write the place value of the digits in the number. Numbers with Digits: Learn how to form the greatest number and the smallest number with the given digits. Circle the Smallest Number: Practice the worksheet in finding the smallest number in each question. Circle the Greatest Number: Practice the worksheet in finding the largest number in each question. Geometrical shapes and figures: Basic Shapes: Learn the basic geometrical three dimensional (3-D) figures or shapes. Surfaces of The Solids: Learn what are the two types of surfaces of the solids or 3-D figures. Common Solid Figures: Learn about the geometric common 3-D shapes such as cube, cuboid, cylinder, cone and sphere. The explanation will help to identify each shapes, number of surfaces, number of plane surfaces, number of curved surfaces, number of edges and about their number of vertices. Points, Lines and Shapes: Learn the definition of point & definition of lines. Line-Segment, Ray and Line: Learn the distinction between the line-segment, ray and line along with the symbol. Types of Lines: Learn the difference between the straight lines and curved lines. Geometrical Design and Models: Learn how to do designs and models along with the basic geometrical shapes using square, rectangle, triangle and circle to follow the patterns. Measurement of Length: Standard Unit of Length: Learn the three main standard units of length, i.e., kilometer (km), meter (m) and centimeter (cm). Conversion of Standard Unit of Length: Learn how to convert the different units of length i.e. meter, centimeters, decimeters and kilometers. Addition of Length: Learn to add the units of length with conversion and without conversion. Subtraction of Length: Learn to subtract the units of length with conversion and without conversion. Measurement of Mass: What is Mass?: Learn the standard units of mass, i.e., kilogram (kg) and gram (g). Conversion of Standard Unit of Mass: Learn how to convert the different units of mass i.e. kilogram and gram. Addition of Mass: Learn to add the units of mass with conversion and without conversion. Subtraction of Mass: Learn to subtract the units of mass with conversion and without conversion. Measurement of Capacity: Standard Unit of Capacity: Learn the standard units of capacity, i.e., liter (l) and milliliter (ml). Conversion of Standard Unit of Capacity: Learn how to convert the different units of capacity i.e. liter and milliliter, the relationship between different capacities. Addition of Capacity: Learn to add the units of capacity with conversion and without conversion, word problems. Subtraction of Capacity: Learn to subtract the units of capacity with conversion and without conversion, word problems. Measurement of Time: Different Ways of Reading Time: Learn the easiest way to tell time by observing the hour – hand and minute – hand. Telling Time: Learn how to understand the position of hour – hand and minute – hand indicate to tell the time shown on the specific clock. Introduction of Indian Money (Rupees and Paise): Money: Indian money available in two forms: coins and currency notes Writing Money in Words and Figure: Learn to write the amounts of money in words and write the amounts of money in figures. Conversion of Money: Convert the amount of money from rupees to paisa and to convert the amount of money from paisa to rupees. Addition of Money: Learn to add the amounts of money with conversion and add the amounts of money without conversion Subtraction of Money: Learn to subtract the amounts of money with conversion and subtract the amounts of money without conversion Multiplication of Money: Learn to multiply the amounts of money by a number. Division of Money: Learn to divide the amounts of money by a number. Fractional Numbers: Learn the basic concept of fractional numbers step-by-step with help of different types of pictures. Fraction as a Part of a Whole: Learn how the fraction represents an object as the part of a whole. Fraction as a Part of Collection: Learn how the fraction is the part of a collection of objects. Greater or Smaller Fraction: Learn how to find a fraction is greater or smaller between the pairs of fractions and arranging the fractions in ascending order & descending order. Convert a Fraction to an Equivalent Fraction: Learn how to find the equivalent fractions of the given fraction. Verify Equivalent Fractions: Learn how to check the given pairs of fractions are equivalent. Proper Fraction and Improper Fraction: Learn the difference and identify to separate the proper and improper fractions. Data Handling: Learn some of the basic ideas how the pictures can be easily recognizable as representing the objects. Pictorial Representation: Introduction of pictograph. Examples of Pictographs: Some pictograph samples are shared to understand how the information presented through the pictures of different objects is used to answer the questions. Problems on Pictographs: The solved problems will help us to understand how on the basis of the pictograph we can easily get more information by observing this picture-graph. Mental Arithmetic and Patterns: Learn some important tricks and skills which are used to solve mental arithmetic questions of addition and subtraction easily and conveniently. Mental Math Addition: Learn to add numbers by using tricks and skills in an easy method. Mental Math Subtraction: Learn to subtract numbers by using tricks and skills in an easy method. From 3rd Grade Math Lessons to HOME PAGE Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need. New! Comments Have your say about what you just read! Leave me a comment in the box below. 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188 helpers are online right now 75% of questions are answered within 5 minutes. is replying to Can someone tell me what button the professor is hitting... • Teamwork 19 Teammate • Problem Solving 19 Hero • Engagement 19 Mad Hatter • You have blocked this person. • ✔ You're a fan Checking fan status... Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy. This is the testimonial you wrote. You haven't written a testimonial for Owlfred.	{"url":"http://openstudy.com/users/ezhyl_marie/answered","timestamp":"2014-04-20T18:34:00Z","content_type":null,"content_length":"105596","record_id":"<urn:uuid:69a3328f-f04b-4388-ace1-8d925bc47c3a>","cc-path":"CC-MAIN-2014-15/segments/1397609539066.13/warc/CC-MAIN-20140416005219-00048-ip-10-147-4-33.ec2.internal.warc.gz"}
Placement Test Study Guides and Test Preparation - Placement Testing Center Getting Ready for the Placement Tests Studying for the placement tests will lead to a better performance and more class options. By obtaining a better score, you may be able to skip one or more basic math and English classes and get a head start towards your academic goals. Before taking the test, review these helpful online resources. Tips for Taking the Placement Tests • Take the placement test seriously. Your Placement Test results will determine into which classes you are eligible to enroll. Retesting is limited, so do your best the first time. • Study and review the subjects you are testing. Study and review may help improve your placement results, particularly for math and chemistry, subjects for which you may not have recently • Familiarize yourself with the type of test questions that are found on the tests. Sample test questions are available on the links above. Knowing the format of the test questions can help you relax and concentrate during the test. • Get a good night’s sleep and have a light meal or snack before arriving to the test session. The English and Math test will take approximately 2 hours. Being tired and/or hungry could hurt your performance in any test session. There are morning, afternoon and early evening test sessions. Take the test at a time when you are usually most alert. • During the English and Math tests, work carefully. The English and Math tests are computerized and are not timed. Read and re-read the questions carefully, and check each answer before submitting it. This will result in the highest possible course placement. • Students will receive their English, Math, and ESL test results before leaving the Center. For Chemistry, results are available the following day online in the student’s Web Advisor account, under Test Summary. English Study Resources The English placement test has two parts: Sentence Skills and Reading Comprehension. Each part consists of 20 questions each and the test is not timed, but may take approximately one hour. The Sentence Skills test measures your ability to correct sentences by substituting a word or phrase underlined in the sentence. It will also ask you to specifically rewrite sentences without changing the meaning. Reading Comprehension measures your analytical and comprehensive reading skills and your ability to apply what you have read. Math Study Resources Depending on your background in math, you will start with either the Arithmetic or the Elementary Algebra test. If you do well in either of these tests, you will automatically proceed to the next higher math test. The test is not timed, but may take approximately 1.5 hours. The Arithmetic Test measures your ability to perform basic operations and solve problems that involve fundamental arithmetic concepts. Elementary Algebra The Elementary Algebra Test measures your ability to perform basic algebraic operations and to solve problems that involve elementary algebraic concepts. Depending on your progress in the Elementary Algebra Test, you may be required to complete the College Level Math Test. This test measures your ability to perform college-level algebraic operations and to solve problems that involve college-level algebraic concepts. ESL Study Resources The ESL Placement Test includes an essay on an assigned topic, a listening comprehension test, and a reading and grammar test. Students will have one hour to write the essay. The essays are evaluated based on students’ ability to focus on the topic, organize and support their ideas, and the effectiveness and correctness their language. The computerized reading and listening tests are not timed, but may take approximately two hours. Test results will be available when students meet with a counselor at the end of the test. Chemistry Study Resources The Chemistry Placement Test consists of 44-multiply choice questions and students have 45 minutes to complete it. A periodic table of the elements is provided. This test clears a prerequisite only for Chemistry 101A. In order to enroll in Chemistry 101A, students must complete two course prerequisites: Chemistry 102 and Math 152. For students interested in other Chemistry classes, please refer the Ohlone College Catalog for perquisites specific to those classes. The majority of the test deals with topics such as elements and their properties, chemical formulas, concentrations of solutions, gases, oxidation numbers, redox reactions and the concepts of acids and bases. The best preparation for the test is to review high school algebra and chemistry. Those who wish to prepare for the test and do not have a chemistry text may find helpful one of the test-preparation books for standardized achievement tests in chemistry. These can be obtained in most bookstores. For clearing the Math 152 prerequisite, refer to the Math Study Resources. Skip plugin info. or other browser plug-in/add-on for opening PDF documents is required to open files on this page marked "PDF".	{"url":"http://www.ohlone.edu/org/placement/studyguides.html","timestamp":"2014-04-19T01:49:49Z","content_type":null,"content_length":"22913","record_id":"<urn:uuid:6355378c-fb8d-4a52-9da3-173c25639708>","cc-path":"CC-MAIN-2014-15/segments/1398223203235.2/warc/CC-MAIN-20140423032003-00130-ip-10-147-4-33.ec2.internal.warc.gz"}
statistics; very basic December 8th 2007, 10:00 AM statistics; very basic Suppose that you have a fair coin, and you label the head side 1 and the tail side 0. Now, fake flipping the coin 2 times and write down the sampling distribution of the sample means. Repeat flipping the coin 4 times and 10 times. What is it asking? The result in the book is n=2 p=0.5 x P(X=x) 0 0.25 1 0.50 2 0.25 What does that mean? Thanks a lot. December 8th 2007, 10:09 AM Suppose that you have a fair coin, and you label the head side 1 and the tail side 0. Now, fake flipping the coin 2 times and write down the sampling distribution of the sample means. Repeat flipping the coin 4 times and 10 times. What is it asking? The result in the book is n=2 p=0.5 x P(X=x) 0 0.25 1 0.50 2 0.25 What does that mean? Thanks a lot. Flipping the coin twice gives you only one possibility of getting a 0 and 0. Flipping the coin twice gives you two possibilities of getting a 0 and 1: (0 and 1) and (1 and 0) Flipping the coin twice gives you only one possibility of getting a 1 and a 1. So there are 4 possible results, thus the probability of getting two 0's is 1/4, the probability of getting a 0 and a 1 is 2/4, and the probability of getting two 1's is 1/4. Now what are all the possible results for flipping the coin 4 times? etc. December 8th 2007, 10:27 AM Shall I use like combinations? How can I know how many combinations of 1s I can find? And what-in the previous post- then it means x=0,1,2 with written next 0.25, 0.5, 0.25 Like 2 means 0,1 and 1,0 ? I am sorry. I am not able to understand all this stuff. Thank you for helping.	{"url":"http://mathhelpforum.com/statistics/24452-statistics-very-basic-print.html","timestamp":"2014-04-21T09:41:45Z","content_type":null,"content_length":"5637","record_id":"<urn:uuid:3e9b6c5a-8b90-4b3b-83cb-a3895ccea317>","cc-path":"CC-MAIN-2014-15/segments/1397609539705.42/warc/CC-MAIN-20140416005219-00093-ip-10-147-4-33.ec2.internal.warc.gz"}
Model of a fixed-bed reactor In our project we plan to construct a fixed bed flocculation filtration tank, where immobilized laccases degrade synthetic estrogen and other harmful substances. As a small selection we plan to characterize our different laccases for three estrogens, three analgesics, four PAHs, one insecticide and three possible redox mediators. If we could model the degradation of one substrate by one laccase, we could easily replace the specific K[cat] K[M]^-1 quotient of other laccases and the amounts of the other substrates. We ignore the possible cofactors ABTS, syringaldazine and viuloric acid, because on the one hand using these cofactors would increase the costs, and on the other hand they are harmful substances. As shown by Team Substrate Analytic TVEL0 degrades ethinyl estradiol without a redox mediator. So the reaction should follow the Michaelis Menten kinetics. The reaction The normal Michaelis Menten kinetics (1) can be adapted for low substrate concentrations. In order to do this formula (2) replaces [ES] in formula (3). The result is formula (4). The velocity of this reaction describes the change of the substrate concentration over time (5). Formula (6) and (7) solve the integral. Equation (8) is the resulting formula to determine the time dependent substrate concentration by a given start concentration A. This transformation of the Michaelis Menten kinetic can be found in "Stryer biochemie". The resulting formula is suitable for very low substrate concentrations. In this case we can estimate degradation of initial substrate concentrations below 0.1 µg L^-1. Because there isn't any information about the K[cat] K[M]^-1 quotient for the degradation of estradiol in the enzyme database Brenda the K[cat] K[M]^-1 quotients were used for modeling the oxidation of ABTS, a redox mediator of the laccase. ABTS is used in this case only as placeholder, until suitable data for the substrates are available. In the following picture a few possible reactions of our laccase are shown. We use K[cat] K[M]^-1 values from 11 to 643500 that result in degradation time points from 0.07s to 1500s. Furthermore we try to integrate different temperatures to our model. In a span from 10°C to 30°C and a K[cat] K[M]^-1 value of 1, the degradation differs from 40 s to 100s. Extend the model with sewage plant data The sewage plant in Schloss Holte provided information about the discharge water, particularly water temperature, pH value and flow rate. The temperature and pH value have a direct influence on the enzymatic activity. Dependent on the enzymatic activity we want to calculate the time our fixed-bed reactor will need to degrade 80 % of the substrates. This will be the dwell time. Combined with the actual flow rate we can determine the reactor size. To estimate the feasibility we want to know how much enzyme has to be produced for a sewage plant. A model of the required enzyme amount dependent of K[cat] K[M]^-1 values and flow rate. The next step will be, to add more substrates and different laccases to our model. Hence we will need more data about laccases. K[cat] K[M]^-1 values have to be determined as well as the specifity of the laccases. We have the opportunity to work with a lab-scale water treatment system. So we plan to test our model in defined conditions.	{"url":"http://2012.igem.org/Team:Bielefeld-Germany/Modell","timestamp":"2014-04-18T22:15:41Z","content_type":null,"content_length":"32901","record_id":"<urn:uuid:37c5ac1a-9d6a-4dde-bb4f-d5cc62970c94>","cc-path":"CC-MAIN-2014-15/segments/1397609535095.9/warc/CC-MAIN-20140416005215-00566-ip-10-147-4-33.ec2.internal.warc.gz"}
What should a teacher do if a student asks a question that he or she cannot answer? As a teacher your student ask you... - Homework Help - eNotes.com What should a teacher do if a student asks a question that he or she cannot answer? As a teacher your student ask you a question "In math or languages". And you don't know the answer BUT this student knows the answer, what will you do!!? O_o!!! This question for teachers,,,, especially teachers of the French language ... ^_^ Since students are naturally curious, they are going to ask questions I can't answer. I usually ask the student to make a guess or inference, but I am also honest. I help the student find the answer. I always tell students to ask any question. If I don't know the answer, I'll find out what it is! I think it is a good thing when a teacher does not know an answer to a question and admits that. Certainly, none of us knows everything, and it would be dishonest to pretend otherwise. But, what is even more important to me is that when I don't know and say so, I am modeling something for my students, that their teacher is a learner, too. Sometimes we look things up on the spot, thanks to technology today, sometimes I do research and report back to the class, and sometimes I treat it as a voluntary homework assignment for the entire class and give a few extra points for intellectual curiosity and work. The above posters make excellent points. Put the ball back into the student's court by asking him or her to make and inference or draw a conclusion. Frequently, the teacher and the class will arrive at an answer together. In addition, let the teacher should let the student know that he or she does not know but is willing to find out. The teacher should encourage the students to find the answer first. If the information is factual, content oriented information that the teacher should know, then the teacher would need to work harder at strengthening his or her foundational knowledge. The worst thing a teacher can do is pretend to know the answer, because it's been my experience that students are pretty adept at spotting someone who doesn't know what they are talking about. Beyond that, I agree with the above answers. Teachers are rightly encouraged to model the behaviors and skills they wish to see from their students. What better way is there to do this than by demonstrating curiosity and a desire to be a lifetime learner? In fact, I would suggest that the fact that students are asking tough questions is a dead giveaway that the teacher is creating an atmosphere of curiosity and rigorous intellectual give-and-take. That said, a teacher should obviously strive to learn as much as possible about the subject they teach. I always have a "we're all learning together" motto in my classroom. When a student has a question that I cannot answer, I can use that as a real 'life-long learning moment' to show the students how to find the answer, possibly on a search engine or database, definitely illustrating the point that regardless of diploma, you never stop having to learn, teach yourself, or fact find. Since most students all have smart phones now, it definitely wouldn't be wise to try to bluff your way out of the situation with a made-up answer! It is far too easy for students to look up the facts for themselves--which on my 'open technology campus' is exactly what I might challenge the students to do-- "Okay, class, I admit that I have no idea what the answer to the question is, so everyone pull out their phones. First one to find the correct answer is the winner!" Often, my students ask questions that can't be answered by anyone, such as "How was the universe created?" We have a wall outside our classroom where these questions are posted. I have found that students enjoy contributing to the Great Wall of Questions as well as reading what others have asked. It's a way to spark intellectual curiosity and to display the depth of thinking that led to asking the question in the first place. When parents and guests come to visit the school, they often linger at the wall, sometimes asking questions of their own. If I suspect the student can get to the answer, sometimes I'll ask questions of my own to help them along in their reasoning, or I'll load up an image from the internet to guide them. Teachers are obviously not infallible, nor can any teacher be expected to answer all questions knowledgeably. I am always quick to admit if I don't have the answer to a specific question, but then I usually tell the student(s) that I will try to look it up and have an answer the next day. I can often find the answer with a minute or two of Googling (if it is a question in which a definitive answer can be provided), and that also shows the student that a little extra work on their part could have provided the answer to their own question. The above posts really tell you all you need to know if a student asks a question you don't know the answer to despite your knowledge of the subject. I, too, had the "we're in this together" attitude developed in class, so the idea that I had to look for the answer also helped students admit when they didn't get something. I found it a very useful tool to show students that learning is lifelong, and no one can know everything. Again, students could see that it was ok to ask questions to try to stump the teacher, especially in an honors class, which I then turned around to them and asked which ways they would use to find the answer. I love the idea of the questions in the hallway! What intellectual curiosity on display! s/he should tell the student"that u ve raised a good issue and tell him that i will tell it tommorrow" well thats what most of my teachers do If they don't know the answer they should say 1 of these 3 things: 1) Tell the child they don't know the answer and that they will find the answer for tomorrow. 2) Tell the child to research the question and tell them for tomorrow. 3) Tell the child to ask their parents. I agree ths students will totally be able to tell if you do not know the answer and are trying to act like you do. Then you lose credibility and trust, which are so important for a comfortable classroom environment. I know a teacher that gives her students extra credit if they can come up with a question that she cannot answer. This motivates students to think critically. Then she has them find the answer and share it with the class. I love this idea and will begin trying it myself. Just tell the student that you do not know about it and then appreciate his curiosity and tell him that you will search about it and then search and tell him You can tell the student to look it up themselves because it provides a great learning opportunity for them. It will also help with their research skills. Then while they try to find the answer, you can look it up yourself and provide further background on whatever they found. So it will seem like you knew the answer all along. Join to answer this question Join a community of thousands of dedicated teachers and students. Join eNotes	{"url":"http://www.enotes.com/homework-help/what-do-you-do-student-asks-question-you-cant-408247","timestamp":"2014-04-18T14:07:58Z","content_type":null,"content_length":"56638","record_id":"<urn:uuid:a6e7976e-c2d9-495a-b164-09e8cf2635b0>","cc-path":"CC-MAIN-2014-15/segments/1397609533689.29/warc/CC-MAIN-20140416005213-00548-ip-10-147-4-33.ec2.internal.warc.gz"}
Workshop on Theories of Types and Proofs Workshop on Theories of Types and Proofs Preliminary Program and Second Call for Contributed Papers (The deadline for Contributed Papers: July 7th) Workshop on Theories of Types and Proofs Satellite Workshop of TACS'97 September 8 - 19, 1997 Tokyo Institute of Technology Tokyo, Japan The aim of this two-week workshop is to exchange ideas and research results in the area of Theories of Types and Proofs. Researchers interested in this area are welcome to participate and make contributions to the workshop. The workshop will consist of a series of lectures, contributed talks, and discussion hours. The workshop solicits for contributed papers in the field of theories of types and proofs and related topics. On-going research works and already published contributions are also welcome. If you want to give a talk, please fill in the form below and send us with an extended abstract (2 - 10 pages, in ps file) by e-mail to <ttp@is.titech.ac.jp> by July 7. The authors who submit a paper will be notified of the acceptance/rejection by July 25. If you want just participate the workshop, please fill the first three lines of the form below and send it by August 15, 1997. For more information, please send an e-mail to <ttp@is.titech.ac.jp>. The workshop period is just before the TACS'97 conference at Sendai, Japan (September 23 - 27). See the Web at http://tacs97.ito.ecei.tohoku.ac.jp /tacs97.html for the information on TACS'97. Our Web page is at The following lectures will be given (the scheduling will be announced Henk Barendregt (Catholic University Nijmegen): 1. The methodology of proof-checking. 2. Systems for formmalizing proofs. 3. The technology of proof-checking. Stefano Berardi (University of Torino): 1. Yet Another Constructivization of Classical Logic (part I) 2. Yet Another Constructivization of Classical Logic (part II) Mariangiola Dezani (University of Torino, Tokyo Inst. of Technology) Trees and Types Ryu Hasegawa (University of Tokyo) 1. Applications of analytic functors to theoretical computer science (part I) 2. Applications of analytic functors to theoretical computer science (part II) 3. Applications of analytic functors to theoretical computer science (part III) Susumu Hayashi (Kobe University) 1. Comparing constructive programming with practical formal methods - Constructive programming is possible but not indispensable - 2. Towards Proof Animation from Constructive Programming Sachio Hirokawa (Kyushu University) 1. Principal types of lambda-terms and their application to the analysis of proofs 2. What is a lambda-caluclus for classical logic? Mitsu Okada (Keio University) 1. A semantic framework for computation models based on classical linear logic and classical linear type theory. 2. Inductive type theory + algebraic rewriting Luke Ong (Oxford University) Continuation semantics for call-by-value lambda mu Masahiko Sato (Kyoto University) Classical Brouwer-Heyting-Kolmogorov interpretation Masako Takahashi (Tokyo Institute of Technology) Lambda-representable functions over free structures revisited Hirofumi Yokouchi (Gunma University) Syntax and semantics of type assignment systems The workshop is expecting to be sponsored by the Mathematical Society of Japan as a part of the regional workshop program of the society. Upon the formal approval, a lecture note (including lectures and original papers selected from contributed talks) will be published as a volume in a new lecture note series of the Mathematical Society of Japan. Workshop Organizers: Mariangiola Dezani (University of Torino, Tokyo Inst. of Technology) Mitsu Okada (Keio University) Masako Takahashi (Tokyo Institute of Technology, chair) Program committee: Henk Barendregt (Catholic University Nijmegen) Mariangiola Dezani (University of Torino, Tokyo Inst. of Technology) Ryu Hasegawa (University of Tokyo) Mitsu Okada (Keio University) Masako Takahashi (Tokyo Institute of Technology, chair) Hirofumi Yokouchi (Gunma University) Local Arrangement: Yohji Akama (University of Tokyo) Toshihiko Kurata (Tokyo Institute of Technology) Important dates: Submission of extended abstract Monday July 7, 1997 Notification of acceptance Friday July 25, 1997 registration for participants August 15, 1997 workshop September 8 - 19, 1997 Do you participate the whole period? If not, specify the dates of your stay. Title of Your Talk:	{"url":"http://www.seas.upenn.edu/~sweirich/types/archive/1997-98/msg00137.html","timestamp":"2014-04-21T04:38:38Z","content_type":null,"content_length":"7095","record_id":"<urn:uuid:c74734c4-020c-4973-a50b-e1039d7bfe32>","cc-path":"CC-MAIN-2014-15/segments/1398223207046.13/warc/CC-MAIN-20140423032007-00037-ip-10-147-4-33.ec2.internal.warc.gz"}
Certifying lexbfs recognition algorithms for proper interval graphs and proper interval bigraphs Results 1 - 10 of 13 "... A rigid interval graph is an interval graph which has only one clique tree. In 2009, Panda and Das show that all connected unit interval graphs are rigid interval graphs. Generalizing the two classic graph search algorithms, Lexicographic Breadth-First Search (LBFS) and Maximum Cardinality Search (M ..." Cited by 56 (4 self) Add to MetaCart A rigid interval graph is an interval graph which has only one clique tree. In 2009, Panda and Das show that all connected unit interval graphs are rigid interval graphs. Generalizing the two classic graph search algorithms, Lexicographic Breadth-First Search (LBFS) and Maximum Cardinality Search (MCS), Corneil and Krueger propose in 2008 the so-called Maximal Neighborhood Search (MNS) and show that one sweep of MNS is enough to recognize chordal graphs. We develop the MNS properties of rigid interval graphs and characterize this graph class in several different ways. This allows us obtain several linear time multi-sweep MNS algorithms for recognizing rigid interval graphs and unit interval graphs, generalizing a corresponding 3-sweep LBFS algorithm for unit interval graph recognition designed by Corneil in 2004. For unit interval graphs, we even present a new linear time 2-sweep MNS certifying recognition algorithm. Submitted: - J. Graph Theory "... Abstract We prove that the complements of interval bigraphs are precisely those circular arc graphs of clique covering number two which admit a representation without two arcs covering the whole circle. We give another characterization of interval bigraphs, in terms of a vertex ordering, that we hop ..." Cited by 19 (5 self) Add to MetaCart Abstract We prove that the complements of interval bigraphs are precisely those circular arc graphs of clique covering number two which admit a representation without two arcs covering the whole circle. We give another characterization of interval bigraphs, in terms of a vertex ordering, that we hope may prove helpful in finding a more efficient recognition algorithm than presently known. We use these results to show equality, amongst bipartite graphs, of several classes of structured graphs (proper interval bigraphs, complements of proper circular arc graphs, asteroidal-triple-free graphs, permutation graphs, and co-comparability graphs). Our results verify a conjecture of Lundgren and disprove a conjecture of M"uller. 1 Background A graph H is an interval graph if it is the intersection graph of a family of intervals Iv, v 2 V (H). (Two vertices v; v 0 are adjacent in H if and only if Iv and Iv0 intersect.) If the - European J. Combin , 2007 "... For graphs G and H, a mapping f: V (G)→V (H) is a homomorphism of G to H if uv ∈ E(G) implies f(u)f(v) ∈ E(H). If, moreover, each vertex u ∈ V (G) is associated with costs ci(u), i ∈ V (H), then the cost of the homomorphism f is � u∈V (G) cf(u)(u). For each fixed graph H, we have the minimum cost h ..." Cited by 14 (6 self) Add to MetaCart For graphs G and H, a mapping f: V (G)→V (H) is a homomorphism of G to H if uv ∈ E(G) implies f(u)f(v) ∈ E(H). If, moreover, each vertex u ∈ V (G) is associated with costs ci(u), i ∈ V (H), then the cost of the homomorphism f is � u∈V (G) cf(u)(u). For each fixed graph H, we have the minimum cost homomorphism problem, written as MinHOM(H). The problem is to decide, for an input graph G with costs ci(u), u ∈ V (G), i ∈ V (H), whether there exists a homomorphism of G to H and, if one exists, to find one of minimum cost. Minimum cost homomorphism problems encompass (or are related to) many well studied optimization problems. We prove a dichotomy of the minimum cost homomorphism problems for graphs H, with loops allowed. When each connected component of H is either a reflexive proper interval graph or an irreflexive proper interval bigraph, the problem MinHOM(H) is polynomial time solvable. In all other cases the problem MinHOM(H) is NP-hard. This solves an open problem from an earlier paper. 1 , 2010 "... A certifying algorithm is an algorithm that produces, with each output, a certificate or witness (easy-to-verify proof) that the particular output has not been compromised by a bug. A user of a certifying algorithm inputs x, receives the output y and the certificate w, and then checks, either manual ..." Cited by 10 (2 self) Add to MetaCart A certifying algorithm is an algorithm that produces, with each output, a certificate or witness (easy-to-verify proof) that the particular output has not been compromised by a bug. A user of a certifying algorithm inputs x, receives the output y and the certificate w, and then checks, either manually or by use of a program, that w proves that y is a correct output for input x. In this way, he/she can be sure of the correctness of the output without having to trust the algorithm. We put forward the thesis that certifying algorithms are much superior to non-certifying algorithms, and that for complex algorithmic tasks, only certifying algorithms are satisfactory. Acceptance of this thesis would lead to a change of how algorithms are taught and how algorithms are researched. The widespread use of certifying algorithms would greatly enhance the reliability of algorithmic software. We survey the state of the art in certifying algorithms and add to it. In particular, we start a - DISCRETE APPLIED MATHEMATICS , 2003 "... ..." - Proceedings of the 32nd International Workshop on Graph-Theoretic Concepts in Computer Science (WG 2006), Lecture Notes in Computer Science , 2006 "... Abstract. We give two new algorithms for recognizing proper circulararc graphs and unit circular-arc graphs. The algorithms either provide a model for the input graph, or a certificate that proves that such a model does not exist and can be authenticated in O(n) time. 1 ..." Cited by 9 (0 self) Add to MetaCart Abstract. We give two new algorithms for recognizing proper circulararc graphs and unit circular-arc graphs. The algorithms either provide a model for the input graph, or a certificate that proves that such a model does not exist and can be authenticated in O(n) time. 1 "... For digraphs D and H, a mapping f: V (D)→V (H) is a homomorphism of D to H if uv ∈ A(D) implies f(u)f(v) ∈ A(H). For a fixed digraph H, the homomorphism problem is to decide whether an input digraph D admits a homomorphism to H or not, and is denoted as HOM(H). An optimization version of the homomo ..." Cited by 7 (2 self) Add to MetaCart For digraphs D and H, a mapping f: V (D)→V (H) is a homomorphism of D to H if uv ∈ A(D) implies f(u)f(v) ∈ A(H). For a fixed digraph H, the homomorphism problem is to decide whether an input digraph D admits a homomorphism to H or not, and is denoted as HOM(H). An optimization version of the homomorphism problem was motivated by a realworld problem in defence logistics and was introduced in [13]. If each vertex u ∈ V (D) is associated with costs ci(u), i ∈ V (H), then the cost of the homomorphism f is u∈V (D) c f(u)(u). For each fixed digraph H, we have the minimum cost homomorphism problem for H and denote it as MinHOM(H). The problem is to decide, for an input graph D with costs ci(u), u ∈ V (D), i ∈ V (H), whether there exists a homomorphism of D to H and, if one exists, to find one of minimum cost. Although a complete dichotomy classification of the complexity of MinHOM(H) for a digraph H remains an unsolved problem, complete dichotomy classifications for MinHOM(H) were proved when H is a semicomplete digraph [10], and a semicomplete multipartite digraph [12, 11]. In these studies, it is assumed that the digraph H is loopless. In this paper, we present a full dichotomy classification for semicomplete digraphs with possible loops, which solves a problem in [9]. "... For graphs G and H, a mapping f: V (G)→V (H) is a homomorphism of G to H if uv ∈ E(G) implies f(u)f(v) ∈ E(H). If, moreover, each vertex u ∈ V (G) is associated with costs ci(u), i ∈ V (H), then the cost of the homomorphism f is ∑ u∈V (G) cf(u)(u). For each fixed graph H, we have the minimum cost h ..." Cited by 5 (4 self) Add to MetaCart For graphs G and H, a mapping f: V (G)→V (H) is a homomorphism of G to H if uv ∈ E(G) implies f(u)f(v) ∈ E(H). If, moreover, each vertex u ∈ V (G) is associated with costs ci(u), i ∈ V (H), then the cost of the homomorphism f is ∑ u∈V (G) cf(u)(u). For each fixed graph H, we have the minimum cost homomorphism problem, written as MinHOM(H). The problem is to decide, for an input graph G with costs ci(u), u ∈ V (G), i ∈ V (H), whether there exists a homomorphism of G to H and, if one exists, to find one of minimum cost. Minimum cost homomorphism problems encompass (or are related to) many well studied optimization problems. We describe a dichotomy of the minimum cost homomorphism problems for graphs H, with loops allowed. When each connected component of H is either a reflexive proper interval graph or an irreflexive proper interval bigraph, the problem MinHOM(H) is polynomial time solvable. In all other cases the problem MinHOM(H) is NP-hard. This solves an open problem from an earlier paper. Along the way, we prove a new characterization of the class of proper interval bigraphs. 1 "... This is not a survey article. Rather it is a personal statement written for a lifelong friend and collaborator. Still it is an ambition of this article to trace some of the key moments of our development in the past 40 years. In doing so perhaps some evidence has arisen which otherwise seems to be o ..." Add to MetaCart This is not a survey article. Rather it is a personal statement written for a lifelong friend and collaborator. Still it is an ambition of this article to trace some of the key moments of our development in the past 40 years. In doing so perhaps some evidence has arisen which otherwise seems to be obscured by the hectic day-to-day academic life. Thus the title.	{"url":"http://citeseerx.ist.psu.edu/showciting?cid=610231","timestamp":"2014-04-19T15:37:42Z","content_type":null,"content_length":"36393","record_id":"<urn:uuid:c054a66a-bc42-47f1-88e2-2dbd8d593898>","cc-path":"CC-MAIN-2014-15/segments/1397609537271.8/warc/CC-MAIN-20140416005217-00306-ip-10-147-4-33.ec2.internal.warc.gz"}
Eragon: The books, the movie Re: Eragon: The books, the movie There is no proof that that is the official cover. It could be fan art. I also found it on a fan art website. Real Member Re: Eragon: The books, the movie No offence but for a series which is so popular and has sold so many copies, the covers seem quite amateurish. Re: Eragon: The books, the movie Maybe so, but the covers still have a lot of originality. You don't usually get a trilogy with a single dragon on the front of each book. Re: Eragon: The books, the movie I think the author let an amigo do the cover art. Not a proffessional artist. i dunno... and frankly I don't care. The story rocks and thats what matters. A logarithm is just a misspelled algorithm. Re: Eragon: The books, the movie If anyone is interested, I have found a close-up picture of Glaedr, high-quality. I'll post it soon. Re: Eragon: The books, the movie A logarithm is just a misspelled algorithm. Re: Eragon: The books, the movie Not very good, but still something. Re: Eragon: The books, the movie OOoh NICE! Muahaha.. why do all these dragon pictures look like mug shots? A logarithm is just a misspelled algorithm. Re: Eragon: The books, the movie Just noticed something. Glaedr bears a similar resemblance to the Green Dragon... Re: Eragon: The books, the movie Hey you're right! That green dragon probably is just a modified pic. :-( At any rate. I just saw the Eragon movie and I'm sad to say its a total disaster. :-( The producer choose to squeeze a book the length of The Lord of the Rings into a mere 1 hour and 40 minutes. The plot is rushed and unexplained, key scenes in the story are missing and a good deal of the plot is rearranged and the movie ends before it ever begins. The entire story is so abbreviated that all the originality is stifled and what remains is perhaps the cheesiest, most stereotypical, worst film adaptation of a book I have ever seen. This movie will most likely scare away people who otherwise would have enjoyed the book. The books are marvelous, but the movie? Two thumbs way down! And now I'm angry because Fox still owns the rights so someone who actually wants to make a good movie about it, can't. Last edited by mikau (2006-12-18 14:32:50) A logarithm is just a misspelled algorithm. Re: Eragon: The books, the movie That's a shame. And I was going to see that. Real Member Re: Eragon: The books, the movie You know that part where the Shade is giving a pep talk to his army? That looks almost identical to when Saruman gives a pep talk to his army in Isengard. lol Re: Eragon: The books, the movie It did, come to think of it! But just to illustrate just how bad, and rushed, and badly rushed it was... in the book saphira starts small but gets big by growing naturally, and gradually learns to communicate with eragon through mental telepethy. In the movie, she flies into the air while still quite small, in the air she suddenly and magically grows in a series of odd explosions. She returns to the ground just moments later, fully grown and able to speak. She tells Eragon her name instead of being named by him. When I saw that I wanted to scream! Really really a horrible distortion of the story. :-( A logarithm is just a misspelled algorithm. Re: Eragon: The books, the movie Oh, man, that must really, really drag. That sounds like a bunch of math math. Re: Eragon: The books, the movie Yeah it was mathin' pieace of math! I mean what the math is that about? But yeah, what bugs me most is if someone came along who actually wanted to do the movie justice, the rights are gone. It looks like some cheap amatuer walked in and made a half hearted attempt to cash in on the success of the series. Now they'll probably throw it into a closet and walk away. :-( I guess our only hope is they learn the extreme mistake they made and if they make a move of eldest, they make it really long. A logarithm is just a misspelled algorithm. Re: Eragon: The books, the movie On a scale of 1 to 10, how would you rate the movie? Re: Eragon: The books, the movie hmm... well it wasn't like it was horrifying to the point where people were leaving the theater. If 7 is average, probably a 5. But generally I'd have to agree with most reviews I read, which I initially thought were rather harsh. A lot of them gave it 2 or 2.5 stars pit of 5, a C rating seems to be the average. The special effects are great but thats reallly all there is. Is it worth the price of a ticket? I'm afraid I have to say no. However, if you walk into the movie thinking its going to be total garbage, you may not be as dissapointed. A logarithm is just a misspelled algorithm. Re: Eragon: The books, the movie Well, I'm in luck. I will go and see it, however. Re: Eragon: The books, the movie hey devante, just curious, did you see the movie? What did you think of it? A logarithm is just a misspelled algorithm. Re: Eragon: The books, the movie Just testing something here, don't mind me. A logarithm is just a misspelled algorithm. Re: Eragon: The books, the movie Nope, not yet.	{"url":"http://www.mathisfunforum.com/viewtopic.php?pid=53109","timestamp":"2014-04-17T12:56:53Z","content_type":null,"content_length":"28602","record_id":"<urn:uuid:66ad9a0a-1e4d-449b-95b9-3316fe5fa180>","cc-path":"CC-MAIN-2014-15/segments/1397609530131.27/warc/CC-MAIN-20140416005210-00207-ip-10-147-4-33.ec2.internal.warc.gz"}
Courses in Physics Courses in Physics PHY 1010: Introduction to Physics I (4) Pre- or corequisite: MTH 1010 or 1210 An introductory level college physics course using mathematics through algebra and trigonometry. Topics covered include kinematics and Newton’s laws with vectors, energy and momentum conservation, retational motion, harmonic motion, and thermodynamics. Four lecture hours per week. PHY 1020: Introduction to Physics II (4) Prerequisite: PHY 1010 A continuation of Principles of Physics 1. Topics include electrostatics, circuits, electric and magnetic fields, geometric optic, quantum mechanics, atomic structure and nuclear physics. Four lecture hours per week. PHY 2010: General Physics Lab I (1) Pre- or corequisite: PHY 1010 or PHY 3010; An introductory laboratory course in physics. Experiments are intended to support lecture material in PHY 1010 and PHY 3010. Includes general laboratory procedures and methods of data analysis. Three hours of laboratory work per week. PHY 2020: General Physics Lab II (1) Prerequisite: PHY 2010; pre- or corequisite: PHY 1020 or PHY 3020 A continuation of General Physics Lab 1. Experiments are intended to support lecture material in PHY 1020 and PHY 3020. Three hours of laboratory work per week. PHY 3010: College Physics I (4) Pre- or corequisite: MTH 2040 An introductory level, calculus-based physics course. Topics covered include kinematics, Newton’s laws, energy and momentum conservation, rotational motion, gravity, thermodynamics, and fluid dynamics. Four lecture hours per week. PHY 3020: College Physics II (4) Prerequisite: PHY 3010; Pre- or corequisite: MTH 2050 A continuation of College Physics 1. Topics covered include electrostatics, circuits, electric and magnetic fields, electromagnetic waves, geometric optics, diffraction and interference, and special relativity. Four lecture hours per week. PHY 3030: Electronics (4) Prerequisites/Co-requisites: MTH 2040 and PHY 1020 or PHY 3020 Analog and digital electronics for scientific applications. Topics include Thevenin’s Theorem, capacitors and inductors, high/low pass filters, semiconductors, transistors, operational amplifiers, Boolean logic, logic gates, logic circuits, and analog to digital conversion. Three lecture hours and three laboratory hours per week. PHY 3040: Modern Physics (3) Prerequisite: PHY 3020 Twentieth century developments in physics. Topics include special relativity, introductory quantum theory, the particle theory of light, the wave nature of electrons, and atomic structure. Three lecture hours per week. PHY 3041: Experimental Modern Physics (1) Prerequisite: PHY 3020; pre- or corequisite: PHY 3040 A laboratory class with experiments relating to important 20th century developments in physics. Lab experiments may include measuring the speed of light; measuring Plank’s constant using a photoelectric effect device; measuring critical properties of superconductors; performing experiments observing EMR (electron spin resonance) and NMR (nuclear spin resonance); and detecting alpha, beta and gamma particles resulting from nuclear decay. Three laboratory hours. PHY 4010: Quantum Physics (3) Prerequisite: PHY 3040 Non-relativistic quantum mechanics. Topics include an introduction to wave mechanics; mathematical tools of quantum mechanics; and the application of quantum mechanics to spin 1/2 systems, the one- dimensional harmonic oscillator and the hydrogen atom. PHY 4950, 4951: Special Topics in Physics (1-3, 1-3) Prerequisite: Permission of instructor Pursuit of some subject which is not normally covered in a regularly scheduled class. May be taken once or twice for one, two, or three semester hours of credit per semester. PHY 4970: Independent Study (1-3)	{"url":"http://www.wise.virginia.edu/science/courses/physics?page=0%2C0%2C0%2C0%2C0%2C0%2C0%2C0%2C1","timestamp":"2014-04-17T00:52:50Z","content_type":null,"content_length":"21523","record_id":"<urn:uuid:4157296c-144a-45be-8d46-2c4a7858fe2b>","cc-path":"CC-MAIN-2014-15/segments/1398223210034.18/warc/CC-MAIN-20140423032010-00085-ip-10-147-4-33.ec2.internal.warc.gz"}
Newest 'flag-varieties lie-algebras' Questions I've recently read the following line in an interesting paper: It is well-known that the cohomology ring of a flag variety $G/B$ is isomorphic to the quotient ring of the ring of polynomial ... Let $G$ be a real semisimple Lie group and $\mathfrak{g}$ be its complexified Lie algebra. We have the flag variety $\mathcal{B}$ of $\mathfrak{g}$ which is the set of all Borel subalgebras of ...	{"url":"http://mathoverflow.net/questions/tagged/flag-varieties+lie-algebras","timestamp":"2014-04-20T03:12:35Z","content_type":null,"content_length":"35103","record_id":"<urn:uuid:da211c15-73df-47b2-82b9-f2221e6a5012>","cc-path":"CC-MAIN-2014-15/segments/1398223210034.18/warc/CC-MAIN-20140423032010-00458-ip-10-147-4-33.ec2.internal.warc.gz"}
A Generic Open-address Hash Table Implementation with an STL-like Interface Hash tables are very common data structures. They provide efficient key based operations to insert and search for data in containers. Like many other things in Computer Science, there are trade offs associated to the use of hash tables. They are not good choices when there is a need for sort and select operations. There are two main issues regarding the implementation of hash based containers: the hash function and the collision resolution mechanism. The hash function is responsible for the arithmetic operation that transforms a particular key into a particular table address. The collision resolution mechanism is responsible for dealing with keys that hash to the same address. Although the C++ STL (Standard Template Library) does not support hash based containers, most compilers like GCC or Visual C++ have their own implementation - it is worth noting that TR1 (Technical Report 1) already offers unordered map and set structures. Also, a good alternative is STLport [1], which provides the following class templates: • hash_set • hash_map • hash_multiset • hash_multimap Interfaces of hash table implementations from different compilers may vary. Besides, not all of them support TR1. Integrating STLport into your code might not be that easy (unless you are already using it, of course). Finally, most of these hash based containers use separate chaining as the collision resolution mechanism, which is a straightforward method, but not the only one. Open addressing is a method for handling collisions through sequential probes in the hash table. It can be very useful when there is enough contiguous memory and knowledge of the approximate number of elements in the table is available. Two well known open addressing strategies are linear probing and double hashing, which I briefly discuss in the next section. In this article, I present a generic standalone STL-like implementation of a hash table that uses either linear probing or double hashing as the collision resolution mechanism. It serves as the underlying implementation of the four class templates mentioned above, and it is constructed with many C++ techniques applied in STLport. The code follows very closely to the STL and extended SGI concepts. Precisely, only one operation is not implemented (the reason is explained later). In addition, the code also works as an interesting introduction to generic programming. This is a brief article, and I do not provide neither theoretical discussion about hash tables nor all the implementation details. I am more interested in providing the source code so others can inspect, give suggestions, and hopefully benefit from it. Hash Table Parameterization The following class template is the underlying implementation of hash_set, hash_map, hash_multiset, and hash_multimap. template < class key_t, class value_t, class hash_fcn_t, class increment_t, class equal_key_t, class get_key_t, class alloc_t> class hash_table__ Most of the template parameters above have meaningful names and a straightforward role. The first one, key_t, is the type of the hash table key. The second, value_t, is the type of the value. (In a set, the value is the actual the key; in a map, the value is a pair containing the key and value.) The hash function is represented by the third parameter. Skipping the fourth parameter, which I will explain in the next paragraph, the fifth parameter, equal_key_t, is a binary predicate used to determine whether two keys are equal. The parameter get_key_t has an interesting responsibility: it is a unary function used to obtain the key of a value stored in the hash table. This parameter must be set in accordance to the type of the value. The last template parameter is the allocator type. There is only one significant difference between linear probing and double hashing. With linear probing, when a collision is detected, the algorithm looks for the position right next to the current table address to check if it is available. It keeps doing that until it finds an empty spot (once it reaches the end of the table, it starts over). Naturally, it is important that the table is not full. (This implementation assumes a maximum load factor of 5/10.) With double hashing, a second hash function is used as the increment from the current table address to the other positions the algorithm looks for. In this particular case, there is an extra concern of writing a second hash function that will not lead to an infinite loop. A good usual choice is an increment that is prime to the size of the table. I already provide two template specializations (for integral types) to use as the argument for the parameter increment_t. //For linear probing. template <class key_t> struct unit_increment std::size_t operator()(const key_t&){ return 1; } //For double hashing. template <class key_t> struct hash_increment{}; //Specialization for integral types are just like this one. template <> struct hash_increment<short> std::size_t operator()(short x){return (x % 97) + 1;} The behaviours of linear probing and double hashing are very similar. However, double hashing is less subjected to the formation of clusters, since keys that hash to the same address are likely to be spread throughout the table. On the other hand, implementation of linear probing might be a little bit simpler because of issues related to the erase operation. See [2] for more details. As I mentioned before, hash_table__ is the underlying implementation of the map and set class templates. This is done through composition as shown in the code below for the case of hash_map. template < class key_t, class value_t, class hash_fcn_t = hash<key_t>, class increment_t = unit_increment<key_t>, class equal_key_t = std::equal_to<key_t>, class alloc_t = std::allocator<std::pair<key_t, value_t> > > class hash_multimap typedef std::pair<key_t, value_t> Map_pair; typedef hash_table__< alloc_t> HT; HT underlying_; Under the hood, the hash table is implemented with std::vector. Therefore, implementation of an iterator is relatively simple. Basically, it is necessary to have a pointer to the vector, an integral type to indicate the current position (or index), and some intelligence for the iteration process. There is, though, one point that is worth talking about. When an iterator is dereferenced, a reference to an instance is provided. However, when a const_iterator is dereferenced, a constant reference is provided. Since this is just a mater of type difference, instead of writing two implementations for the iterators, we could use an auxiliary traits class template to do the job. One of the template parameters of the iterator implementation is the hash table type. The other is the traits type. For the definition of the type iterator, the class template non_const_traits is used. For the definition of the type const_iterator, the class template const_traits is used. The following code shows the idea: template <class value_t> struct const_traits typedef const value_t* pointer; typedef const value_t& reference; template <class value_t> struct non_const_traits typedef value_t* pointer; typedef value_t& reference; //Iterator implementation. template < class hash_container_t, class constness_traits_t> struct hash_table_iterator__ typedef typename constness_traits_t::pointer pointer; typedef typename constness_traits_t::reference reference; reference operator()const {return (this->container_)[this->current_].value_;} pointer operator->()const {return &(operator*());} A final issue is that conversion between an iterator and a const_iterator should be handled properly. Please refer to the source code for examples. Using the Code The usage of the code is just like for any STL container. Here is an example: #include "hash_map.h" #include <iostream> int main() using namespace hashcol; typedef hash_map<int,double> Map; typedef Map::value_type value_type; typedef Map::iterator iterator; Map map; map.insert(value_type(8, 8.888)); map.insert(value_type(1, 1.111)); map.insert(value_type(12, 12.12)); map.insert(value_type(3, 3.3)); map.insert(value_type(122, 122.122)); std::cout << "\nSize is: " << map.size(); std::cout << "\nElements are:"; for (iterator it = map.begin(); it != map.end(); ++it) std::cout << "\n\tKey = " << it->first << " Value = " << it->second; return 0; • [1] STLport - http://www.stlport.org/ • [2] Sedgewick R. Algorithms in C++ - Fundamentals, Data Structures, Sorting and Searching (3^rd edn). Addison-Wesley, 1998	{"url":"http://www.codeproject.com/Articles/23085/A-generic-open-address-hash-table-implementation-w?fid=985032&df=90&mpp=10&sort=Position&spc=None&tid=3825808","timestamp":"2014-04-17T13:32:43Z","content_type":null,"content_length":"82435","record_id":"<urn:uuid:e082dee7-d183-4c68-9331-d367aec691c7>","cc-path":"CC-MAIN-2014-15/segments/1397609530131.27/warc/CC-MAIN-20140416005210-00509-ip-10-147-4-33.ec2.internal.warc.gz"}
Add 99 more and post it forever. Re: Add 99 more and post it forever. Re: Add 99 more and post it forever. In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. Re: Add 99 more and post it forever. Re: Add 99 more and post it forever. 88^2 + 89^2 + 93^2 + 98^2 = 33918 In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. Re: Add 99 more and post it forever. Did you delete it? We were in the 33,000's a long time already! Re: Add 99 more and post it forever. Yes, I cleaned it all up and put us back in synch. 95^2 + 96^2 + 97^2 + 112^2 = 40194 In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. Re: Add 99 more and post it forever. Re: Add 99 more and post it forever. 90^2 + 94^2 + 100^2 + 116^2 = 40392 In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. Re: Add 99 more and post it forever. Re: Add 99 more and post it forever. 94^2 + 97^2 + 99^2 + 112^2 = 40590 In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. Real Member Re: Add 99 more and post it forever. 163^2 + 118^2 + 14^2 = 40689 'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.' 'God exists because Mathematics is consistent, and the devil exists because we cannot prove it' 'Who are you to judge everything?' -Alokananda Re: Add 99 more and post it forever. 2 x 93^2 + 99^2 + 117^2 = 40788 In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. Real Member Re: Add 99 more and post it forever. Now, I can also do it 169^2 + 111^2 + 2^2 +1^2 'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.' 'God exists because Mathematics is consistent, and the devil exists because we cannot prove it' 'Who are you to judge everything?' -Alokananda Re: Add 99 more and post it forever. Yes, you can! 95^2 + 96^2 + 101^2 + 112^2 = 40986 In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. Re: Add 99 more and post it forever. Re: Add 99 more and post it forever. 84^2 + 88^2 + 100^2 + 128^2 = 41184 In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. Re: Add 99 more and post it forever. Re: Add 99 more and post it forever. 95^2 + 97^2 + 102^2 + 112^2 = 41382 In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. Re: Add 99 more and post it forever. 200^2 + 39^2 + 6^2 + 1^2 + 1^2 + 1^2 Re: Add 99 more and post it forever. 84^2 + 85^2 + 87^2 + 91^2 + 107^2 = 41580 In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. Re: Add 99 more and post it forever. Re: Add 99 more and post it forever. 2 x 98^2 + 99^2 + 113^2 = 41778 In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. Re: Add 99 more and post it forever. Re: Add 99 more and post it forever. In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. Re: Add 99 more and post it forever.	{"url":"http://www.mathisfunforum.com/viewtopic.php?id=18558&p=17","timestamp":"2014-04-16T13:04:26Z","content_type":null,"content_length":"35618","record_id":"<urn:uuid:0222fe36-7486-4851-a0e5-3ea2ad639e53>","cc-path":"CC-MAIN-2014-15/segments/1397609523429.20/warc/CC-MAIN-20140416005203-00183-ip-10-147-4-33.ec2.internal.warc.gz"}
Crystal Lake, IL Statistics Tutor Find a Crystal Lake, IL Statistics Tutor ...I also have experience working as both a GED and ESL tutor.Microsoft Access is a relational database management program, which allows users to create and manage their own databases. This database can then be used to create reports and track ongoing trends. I am highly versed in multiple versions of Microsoft Access, including the most recent version of the software. 39 Subjects: including statistics, reading, English, calculus ...Many students who hated math started liking it after my tutoring. That is my specialty. I provide guidance based on their attitude interest and ability. 12 Subjects: including statistics, calculus, geometry, algebra 1 ...I taught trigonometry and algebra 2 to high school juniors in the far north suburbs of Chicago for the past two years. I am currently attending DePaul University to pursue my master's degree in applied statistics. I have tutored students of varying levels and ages for more than six years. 19 Subjects: including statistics, calculus, geometry, algebra 1 ...Since then, I have continued reviewing pre-calculus material and I expect to do so for a long time - it is a subject I enjoy a great deal. I am now working on learning how to use the graphing calculator (TI-84) for pre-calculus problems. I prefer that students send me copies of the problems that they are having difficulty with before we meet, so that their time and money is not 13 Subjects: including statistics, geometry, algebra 2, algebra 1 ...I did not "magically" become smarter; I understood concepts, identified concepts, and practiced. I can guide any student to success using this regime. Given my credentials and experience, please do not hesitate to contact me for further information. 16 Subjects: including statistics, chemistry, calculus, algebra 2 Related Crystal Lake, IL Tutors Crystal Lake, IL Accounting Tutors Crystal Lake, IL ACT Tutors Crystal Lake, IL Algebra Tutors Crystal Lake, IL Algebra 2 Tutors Crystal Lake, IL Calculus Tutors Crystal Lake, IL Geometry Tutors Crystal Lake, IL Math Tutors Crystal Lake, IL Prealgebra Tutors Crystal Lake, IL Precalculus Tutors Crystal Lake, IL SAT Tutors Crystal Lake, IL SAT Math Tutors Crystal Lake, IL Science Tutors Crystal Lake, IL Statistics Tutors Crystal Lake, IL Trigonometry Tutors Nearby Cities With statistics Tutor Algonquin statistics Tutors Barrington Hills, IL statistics Tutors Bull Valley, IL statistics Tutors Carpentersville statistics Tutors Cary, IL statistics Tutors Huntley, IL statistics Tutors Inverness, IL statistics Tutors Lake In The Hills statistics Tutors Lakemoor, IL statistics Tutors Lakewood, IL statistics Tutors Mchenry, IL statistics Tutors Oakwood Hills, IL statistics Tutors Port Barrington, IL statistics Tutors Prairie Grove, IL statistics Tutors Volo, IL statistics Tutors	{"url":"http://www.purplemath.com/Crystal_Lake_IL_Statistics_tutors.php","timestamp":"2014-04-18T15:49:39Z","content_type":null,"content_length":"24462","record_id":"<urn:uuid:2d35240c-1745-4488-8396-c59d119bba5a>","cc-path":"CC-MAIN-2014-15/segments/1397609533957.14/warc/CC-MAIN-20140416005213-00654-ip-10-147-4-33.ec2.internal.warc.gz"}
The Muslim Observer By Syed Aslam Mohammad Abdus Salam, was born in 1926 in the state of Punjab, India. Salam family had a passion for education and learning. At the age of fourteen he scored the highest marks ever recorded in high school examination in Punjab university. After completing his MA in mathematics from Punjab University he went to England and received his PhD degree in Theoretical Physics in the year 1951 from University of Cambridge .His doctoral thesis contained comprehensive and fundamental work in Quantum Electrodynamics. By the time it was published , it had already gained him an international reputation. In 1957 he was invited to take a chair at Imperial College, London, as Professor of Theoretical Physics. It is remarkable that the simple peasant boy, who went on to become the youngest professor in the history of Imperial College, at the age of thirty .While at Imperial College, he had the privilege of interacting with great minds, such as Bertrand Russell, Einstein, Oppenheimer, and Wolfgang Pauli to name a few. Dr. Salam and Paul Matthews created a lively theoretical physics group here at Imperial College. During the early 1960 he moved back to Pakistan, where played a very significant role in establishing the Pakistan Atomic Energy Commission and Pakistan Space and Upper Atmosphere Research Commission. In 1974 he left Pakistan and moved to Oxford, England where he died on 21st November 1996 at the age of 70 after a prolonged illness. His body was brought to Pakistan and buried in Rabwah, Punjab. Mohammad Abdus Salam was the first Pakistani to win the Nobel laureate in Physics for his work in Electro-Weak Theory. He did the research on the physics of elementary particles. In 1968 he introduced a theory of weak neutral currents, to explain the behavior and properties of elementary particles. He proposed that the electromagnetic force and the weak force are not distinct and separate, but two manifestations of the same fundamental force, which he called the “electroweak” force. By the mid-1970s other scientists’ work had confirmed his theory, and in 1979 he won the Nobel Prize in Physics for the proposed theory. Salam made a major contribution in Quantum Field Theory and advancement of Mathematics at the Imperial College. With his student, Riazuddin, Salam made important contributions to the modern theory on neutrinos, neutron stars and black holes, as well as the work on modernizing the quantum mechanics and quantum field theory. As a teacher and science promoter, Salam is remembered as a founder and scientific father of mathematical and theoretical physics in Pakistan. Even until his death, he continued to contribute in physics and tirelessly advocated for the development of science in third world countries. Dr Salam is one of the most honored physicists. He was awarded the Hopkins and Adam prizes in 1958. He was the first recipient of the Maxwell Medal. In 1971, he was awarded the Oppenheimer Medal and prize. In 1976 the London Institute of Physics awarded him the Gutherie Medal and prize. In 1979, UNESCO bestowed on him the Einstein Medal. In 1983 he was awarded the Lomonsove Gold Medal by the USSR Academy of Sciences.	{"url":"http://muslimmedianetwork.com/mmn/?tag=elementary-particles","timestamp":"2014-04-19T00:31:17Z","content_type":null,"content_length":"32786","record_id":"<urn:uuid:11d52e22-72d5-4023-8b7c-8f6d16fdcd9c>","cc-path":"CC-MAIN-2014-15/segments/1398223201753.19/warc/CC-MAIN-20140423032001-00249-ip-10-147-4-33.ec2.internal.warc.gz"}