mm-4049 === Subject: Re: Are you smarter than your calculator? Yvahk: op bonfr=16 gura whfg glcr gur ahzoref va. -- Lau === Subject: Re: Are you smarter than your calculator? [Followups set to rec.puzzles] minehub@gmail.com said: I preferred 4300. -- Richard Heathfield Usenet is a strange place - dmr 29/7/1999 http://www.cpax.org.uk email: rjh at the above domain, - www. === Subject: Game of Life ! ... Game of Life is a study in deterministic chaos. A rectangular array of cells is populated or vacated in subsequent generations according to the current generation and the rules in the start screen. Choose the initial density of the random population, and from several screen hence program resolutions. Program keeps time and notes the point of inevitable stability. http://www.wizardscripts.com/details_res.php?sbres_id=158 === Subject: Re: desired function That is one but you don't need the root. 1 - 1/(x+1) is simpler. Remove del for email === Subject: Re: desired function Just curious: How did you find those functions? It took me like 5 minutes to come up with 1 - 1 / root(x+1), and I was only able to find that by picturing what the graph would look like and then finding a function that resembled that behaviour (i.e. square root function). === Subject: trig question how do I solve for x, where y and a are given? y = sin(ax) This seems like a simple and common problem but I can't find the answer... === Subject: Re: trig question x = 1/a arcsin(y) === Subject: Probability Question Can anyone confirm for me how often you would lose 4 in a row in a roulette game, betting either red or black? By my calculation it would be on average once every 52 spins on double zero roulette. For a straight 50/50 game like flipping a coin it would be on average once every 64 flips. === Subject: Re: Probability Question 25.49 spins. 29.8 flips. No wonder you're losing. === Subject: Re: Probability Question How did you come up with those figures? === Subject: Integration I've been learning about different methods of integration in my university calculus class, and I understand the importance of integration in mathematics and in solving physical problems, but I was just wondering if there are any jobs or fields of study that regularly require solutions to integrals that have never been solved before. It seems to me (based on what I've learned) that integration is so fundamental and so widely known that virtually every possible useful integral must have been solved (or proved to be unsolvable) already. Is there anyone that actually needs to USE the techniques of integration for practical applications? === Subject: Re: Integration No, for practical applications you only need a hammer and nails. === Subject: Re: A Multidimensional On-the-Wall Question because then I'd be shaving my feet === Subject: Re: A Multidimensional On-the-Wall Question They don't. They reverse front to back. Remove del for email === Subject: Re: A Multidimensional On-the-Wall Question You've had various answers, but here's what seems to me the essential point. A mirror reverses front and back, not left and right. You've no experience of such a reversal within physical space, so your mind misinterprets what you see. If you're facing north, the image appears to be someone like you facing south. In physical space the only way for you to reach such a position is to turn through 180 degrees about a vertical axis; so from long habit your mind interprets the image as if you'd done that. The apparent reversal of left and right is entirely due to that non-existent turn in your imagination. HTH. (If you wanted, I could explain it using 3 x 3 matrices.) Ken Pledger. === Subject: Re: A Multidimensional On-the-Wall Question I think the confusion comes from the overloading of the terms left and right, which come from inherent symmetries of the human body. Mirrors do reverse left/right parity. What they do not reverse is left/right direction. Somebody knows that the mirror reverses left and right parity, so they incorrectly conclude that left and right direction are reversed (lay on your side to disprove this), and then they wonder by the apparent symmetry of the mirror why other directions are not also reversed. === Subject: Re: A Multidimensional On-the-Wall Question The orientation of the line between your eyes defines the direction of the apparent reversal ..... === Subject: Re: A Multidimensional On-the-Wall Question Not really. Lying on your side will not produce an apparent reversal of up and down. On Tue, 01 May 2007 18:30:56 -0400, Steve Giannoni Remove del for email === Subject: then New Zealand daylight time will run for 28wks??? Cc: mcdonewt@yahoo.co.nz Progmme Stds Mgr Mr D Edm... tvnz, I consulted dept of Internal Affairs and suggested that, should 24th September be a Sunday before Leap Year, then New Zealand daylight time will run for 28 weeks, not 27 weeks as announced by Min Internal Affairs Rick Barker. WOls.. (D.I.A.) replied my analysis is good and this may occur from Sunday 24.9.2023 to 7.4.2024, in about 16 years from 2007. It should repeat x number of times per 400 years Gregorian calendar. E.g. Oct Nov Dec Jan Feb March = 31+30+31+31+28+31 + leap day = 6*4weeks + 3+2+3+3+0+3 + leap day= 24*7 +14 + leap day. = 26weeks (+leap day.) To this may be added up 6 days of September + leap day + 7 days of April, bringing the total to 28 weeks exactly. The order in council is too hasty, being mainly inspired-precipitated by global warming in United States and flashing around the world. And PM helen clark ban vicious dog breeds. And European tv viewers Rugby World Cup was definitely mentioned. The tides will be thrown out of Bung by the sudden change in the calendar. I trust in the Pope Mathematicians to work these things out better. Eight leap years per 33 years would give a calendar of 365.242424 days which is far better than 365.2425 (Pope Gregory XIII.) Tropical year applies 365.2422 days. By similar clock arithmetic 100 years = 3*33 +1. Add centuries cc. to years yy. The remainder is 0 4 8 12 16 20 24 28 (leap years) then space gap 5 years. SPRINGING FORWARD ONE WEEK EARLIER It is no guarantee of a better summer, but sunlovers will be basking in three more weeks of longer evenings come September. http://www.stuff.co.nz/hlc/1,,76866~4043530a6000~,00.html tvnz 6 pm ONE 30.4.2007 Monday said end of September 30th.9.2007. This is the wrong formula. Complaint ACCURACY. SHOULD be the LAST SUNDAY in September. i look forward to your report. please === Subject: How many unique chess matches exist? Given all possible moves in all possible combinations, how many unique, non-stalemate games of chess exist? I couldn't tell you why this question has been on my mind, but it's bugging the crap out of me and I can't seem to come up with a way to calculate it. Any Ideas? === Subject: Re: How many unique chess matches exist? Go to Wikipedia and look up Shannon Number. === Subject: Re: How I Can Do Some Algorithm To finding all possible combinations of M different symbols? .be I prefer notation all possible combinations of N different symbols of length M. Then the product (a + b + ... + n)^M gives all possible N^M strings of the given kunzmilan === Subject: Re: How I Can Do Some Algorithm To finding all possible combinations of M different symbols? Those aren't different combinations. They are different permutations if that is what you meant but you are going to have to be more specific. Remove del for email === Subject: Matrix (Neumann) Convergence Originator: israel@math.ubc.ca (Robert Israel) I trying to prove the following Neumann Series (I + ST + (ST)^2 + (ST)^3 + ... ) = (I - ST)^(-1) where I is the n X n identify matrix, S is a n X n diagonal matrix, and T is a n X n complex symmetric matrix. Note that (ST)^2 = (ST) (ST), (ST)^3 = (ST)(ST)(ST), etc. and (I - ST)^(-1) is the inverse of (I-ST). Let s_k denote the kth diagonal element of S. We know that magnitude of sum_1^n s_k is less than or equal to 1 (|sum_(k=1)^n s_k| <=1). Further, the magnitude of s_k is less than 1. We also know that the diagonal elements of T are zero and that magnitude of each of the off-diagonal elements is 1. The series converges if the spectral radius of ST is less than one or if a matrix norm of ST is less than 1. Let N_m(ST) denote the the column norm of ST of the mth column. Then N_m(ST) = {sum_(k=1)^n | s_k| } - s_m. If the column norm N_m(ST) is less than |sum_(k=1)^n s_k| < 1 for m, then the converges. I can't prove this statement. Any suggestions on how I could prove if the Neunmann series converges based on the restrictions on S and T? Please send a copy of your response to my e-mail address (bergers@aol.com). Scott === Subject: Postdoc need in Systems Engineer in Enterprise Knowledge-Based Systems Originator: israel@math.ubc.ca (Robert Israel) I'm recruiting for a Systems Engineer in Enterprise Knowledge-Based Systems Brad Parish, PHR Program Manager, ORNL Postdoctorial Recruitment bradley.parish@orau.org phone: 865-576-2311 fax: 865-576-0287 U.S. Department of Energy Oak Ridge National Laboratory P.O. Box 2008 Building 5100, MS-6173 Oak Ridge, Tennessee 37831-6173 Systems Engineer in Enterprise Knowledge-Based Systems Engineering Science and Technology Division Oak Ridge National Laboratory Oak Ridge, Tennessee Project Description: The Decision Engineering Group in the Engineering Science and Technology Division (ESTD) at the Oak Ridge National Laboratory (ORNL) is seeking identify post doctoral and post master candidates. The Decision Engineering Group's focus is on research and development associated with building, maintaining and development of enterprise knowledge-based systems- integrating advances in operations research, mathematics, statistics, decision analysis, software engineering, database, data mining, expert system, and Geographic Information System to systematically analyze, model, solve, and visualize problems in the areas of energy, national and global security, and environment. Individual will conduct research and development in the areas of transportation security and transportation system planning and assessments - will help design, develop, and implement enterprise decision support systems. The individual will work with researchers in the Decision Engineering Group, Engineering Science and Technology Division, and across ORNL. Qualifications: Applicants cannot have received the most recent degree more than five years prior to the date of application and must complete all degree requirements before starting their appointment. Expected duration of these appointments is one year with the possibility of an extension. We are especially seeking individuals with strong background in the fields of operations research/system analysis, visualization of modeling and simulation results with special focus on network modeling and decision analysis and decision support. a MS/PhD in operations research, systems engineering, engineering management, decision sciences, modeling and simulation, and computer science - or an equivalent combination of education and experience. a Proficiency in CPLEX, Arena, and Matlab is a plus. a Strong programming skills (.Net, C++, MS SQL Database tools, user interface development). Willingness to build expertise in enterprise IT issues a Excellent communications skills and the ability to organize and work in an interdisciplinary research teams are required. a Creativity and innovative thinking in developing solutions to complex problems. a The candidate must have excellent writing skills for a The candidate must be a self-starter who knows how to learn and is interested in broadening his/her knowledge. The nature of the work on national security programs requires that the candidate be a United States citizen. Frequent travel may be required. For additional information on the Engineering Science and Technology Division click on the following URL: http://www.ornl.gov/sci/engineering_science_technology/ For additional information on the Decision Engineering Group click on the following URL: http://cta.ornl.gov/cta/. The Decision Engineering Group is located at the National Transportation Research Center (a joint research facility of ORNL and the University of Tennessee) in Knoxville, TN. How to Apply: Qualified applicants may apply online at https://www2.orau.gov/ORNL_POST/. All applicants will need to register before they can begin the online application. For complete instructions, on how to apply, please see the instructions at http://www.orau.gov/orise/edu/ornl/ornl-pdpm/application.htm. When applying for this position, please reference the position title and number (ORNL07-28-ESTD). This appointment is offered through the ORNL Postdoctoral Research Associates Program and is administered by Oak Ridge Associated Universities (ORAU). This appointment is open to all qualified U.S. citizens who currently work in the U.S and are available for interview, without regard to race, color, age, religion, sex, national origin, physical or mental disability, or status as a Vietnam-era veteran or disabled veteran. === Subject: Origin of some concepts and symbols Originator: israel@math.ubc.ca (Robert Israel) I'd like to know about the first use of the big union and intersection signs for the union/intersection of a family of sets, the power set notation, the unique existence quantifier (with exclamation mark), the notation {x | property}, the double arrow for equivalence, the negation of various relations by overlaying a slash, the subset-equal sign, and the notion of a subset in the modern sense (for Cantor, a subset was a proper subset). As far as I could see, these are not available in http://members.aol.com/jeff570/mathsym.html Earliest Uses of Various Mathematical Symbols which is otherwise very useful. Any hints are appreciated. Arnold Neumaier === Subject: Re: Origin of some concepts and symbols Content-Length: 1029 Originator: rusin@vesuvius Florian Cajori's A History of Mathematical Notations has a section on logic where symbols like our union and intersection signs are attributed to Peano (Formulaire des Mathematiques). He also quotes extensively from Russel and Whitehead's Principia. I'd start there. KP . === Subject: algebraic integers - logarithmic expression Originator: israel@math.ubc.ca (Robert Israel) let P(d) be the set of all irreducible monic polynomials with integer coefficients, such that all roots are of modulus less than d. consider L(delta), the supremum over all p in P(d) of the quantity L(p,delta) = deg(p)^(-1) sum_{|z|