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Topic: Exponential time


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In the News (Tue 8 Dec 09)

  
  FanFiction.Net - Dictionary & Thesaurus   (Site not responding. Last check: 2007-10-14)
Exponential increases in a quantity can be surprising, and this principle is often used by banks to make investment at a certain rate of interest seem to be very profitable over time.
Exponential decay is exhibited by decay of radioactive materials and some chemical reactions (first order reactions), in which one-half of the initial quantity of radioactive element (or chemical substance) is lost for each lapse of a characteristic time called the half-life.
Exponential quantity (Math.), a quantity whose exponent is unknown or variable, as a^x.
www.fanfiction.net /dictionary.php?word=exponential   (306 words)

  
 PlanetMath: time complexity
Time complexity refers to a function describing how much time it will take an algorithm to execute, based on the parameters of its input.
Complexity classes are equivalence classes of time complexities which are “equal” in Big-O notation.
This is version 5 of time complexity, born on 2001-10-18, modified 2005-04-18.
planetmath.org /encyclopedia/ExponentialTime2.html   (185 words)

  
 Exponential decay Summary
Exponential decay is found in mathematical functions where the rate of change is decreasing and thus must reach a limit, which is the horizontal asymptote of an exponential function.
Exponential decay may also be either decreasing or increasing; the important concept is that it progresses at a slower and slower rate.
The field of glottochronology attempts to determine the time elapsed since the divergence of two languages from a common root, using the assumption that linguistic changes are introduced at a steady rate; given this assumption, we expect the similarity between them (the number of properties of the language that are still identical) to decrease exponentially.
www.bookrags.com /Exponential_decay   (1599 words)

  
 PA 765: Time Series Analysis
Ideally, the data collection time interval (the survey interval) is the same as the age span of the groups (the cohort interval) being studied.
Exponential smoothing is a form of time series analysis in which the researcher is interested less in modeling than in sheer prediction of the next period based on data about the current and recent periods.
The regression coefficient for cohort is the cross-cohort slope and the estimated effect of cohort turnover equals this coefficient times the difference in average year of birth in the last survey minus the average year of birth in the first survey.
www2.chass.ncsu.edu /garson/pa765/time.htm   (8883 words)

  
 Summary
Note that the decay of a pendulum is time in the sense of aging, and that this aging or exponential time is quantized by counting ticks of a clock, or time periods, which constitutes the fundamental time of physics.
In other words, the period of a pendulum is a fundamental time, and it is used to quantize the exponential decay of the pendulum, which we sometimes erroneously call time.
Of course, isolated, uncontaminated exponential changes such as the charge or decay of an electronic circuit, can be used as clocks, but as they are analog and non-linear, and are frequently contaminated by outside influences, they are not good clocks.
home.earthlink.net /~tdp/summary.html   (1746 words)

  
 Exponential Growth
(The doubling time of anything growing exponentially is 70 divided by its annual growth rate —70 divided by seven percent is a ten-year doubling time.) Every ten years we used as much oil as we had used in all previous history.
For a long time the plant is almost invisible, and so you decide not to worry about cutting it back until it covers half the pond.
Our economy is growing exponentially, and we cheer it on, although an economic growth rate of, say, 3.5 percent per year means another whole industrial world plopped down on top of this one in just two decades.
www.mnforsustain.org /meadows_dana_nothing_so_powerful_exponential_growth.htm   (856 words)

  
 Exponential functions
The interest earned in each time interval is a constant fraction of the principal; the interest is added to the principal and the result is used to compute the interest in the next time period.
However, an exponential model is a very useful first approximation to predict the future value of a quantity given its current magnitude and its historical growth rate.
Thus, an exponential function growing at a rate of 10% per year will double in size about every 70/10= 7 years; if the growth rate is 5% per year, the doubling time is 70/5= 14 years.
www.colorado.edu /physics/phys3070/phys3070_sp06/exp-growth.htm   (918 words)

  
 Basics of Exponential Growth
Clearly, Exponential growth, in general, is not understood by the lay public.
Exponential growth means that some quantity grows by a fixed percentage rate from one year to the next.
Clearly exponential rates of growth are an integral part of the planning process.
zebu.uoregon.edu /2003/es202/lec06.html   (1077 words)

  
 Star-Hspice Independent Source Functions
Delay time in seconds from the beginning of transient interval to the first onset ramp.
"repeat" is time in units of seconds which specifies the start point of the waveform that is to be repeated.
Time in units of seconds that specifies the length of time to delay the piecewise linear function.
www.ece.uci.edu /eceware/hspice_docs/hspice_and_qrg/hspice_2001_2-30.html   (2059 words)

  
 Hypothesis on time
Each one it his at the time, for the one day old child, the day would be its life, the year the infinite one ; for the adult the day would be the moment, the year less and less, until with this which resembles that of front, until with almost nothing.
This social time, son of the planets, who brings the second quite useless dimension to the time of the event in the equations, is rejected because time is the variation of the studied system and represents itself only on one dimension.
Demonstration of the fact that the time is exponential in mechanics of the fluids.
1-time.blogspot.com   (1782 words)

  
 Exponential Growth and Decay
Exponential growth and decay are rates; that is, they represent the change in some quantity through time.
Exponential growth is any increase in a quantity (N) -- exponential decay is any decrease in N -- through time according to the equations:
Exponential growth and decay is a concept that comes up over and over in introductory geoscience: Radioactive decay, population growth, CO increase, etc. When each new topic is introduced, make sure to point out that they have seen this type of function before and should recognize it.
serc.carleton.edu /quantskills/methods/quantlit/expGandD.html   (642 words)

  
 [No title]
time algorithms, problems that need k-exponential time algorithms, where k is a natural number, etc. and there are problems that require algorithms with the worst case time worse than k-exponential time for any natural number k.
The satisfiability problem for PDL is known to take at least exponential time to solve in the worst case.
If a polynomial time algorithm is found for any one of the NP-complete problems, all the problems in NP can be solved in polynomial time.
www.cs.odu.edu /~toida/nerzic/390teched/computability/complexity.html   (2996 words)

  
 Survival/Failure Time Analysis
In general, censored observations arise whenever the dependent variable of interest represents the time to a terminal event, and the duration of the study is limited in time.
Specifically, it is computed as the number of failures per time units in the respective interval, divided by the average number of surviving cases at the mid-point of the interval.
The major distributions that have been proposed for modeling survival or failure times are the exponential (and linear exponential) distribution, the Weibull distribution of extreme events, and the Gompertz distribution.
www.statsoft.com /textbook/stsurvan.html   (2842 words)

  
 Simulation
If we were to use time as the parameter, for example, our function would give us the value 1 where time is zero and begin increasing very rapidly (exponentially in fact) as time becomes greater than zero.
The exponential curve certainly has its uses, but we will more often be interested in the flavor that decreases exponentially rather than increases.
The other variation of the decaying exponential curve is obtained simply by supplying the Math.exp() function with a positive parameter and dividing 1 by the result.
www.motionscript.com /mastering-expressions/simulation-basics-2.html   (568 words)

  
 Discrete-Time Signal Metrics   (Site not responding. Last check: 2007-10-14)
Exponential functions are common in audio processing because they represent natural decay patterns in acoustical systems.
is the exponential time constant and A is the peak amplitude.
The time constant is the time it takes for the quantity y(t) to decay by 1/e (i.e.
www.music.mcgill.ca /~gary/307/week1/metrics.html   (618 words)

  
 Exponential Growth an Illusion?: Response to Ilkka Tuomi
Based on our current understanding of the physics of computing, the inherent limits to exponential growth of computation and communication are extremely high (that is, the minimum matter and energy required to compute a bit or transmit a bit is extremely low).
Exponential growth means that after the growth speed is set, the future unfolds based on nothing but the current state of the system.
Kurzweil: Tuomi provides no basis to conclude that exponential growth in computing has ended or is about to end.  As mentioned earlier, the inherent limits to exponential growth of computation and communication are extremely high (that is, the minimum matter and energy required to compute a bit or transmit a bit is extremely low).
www.kurzweilai.net /articles/art0593.html?m=1   (8000 words)

  
 P, NP and Exponential Type Problems
Any problem that has a running time on the order of a polynomial number of steps is considered P type problem.
Any problem that has at best a running time in exponential time (those in red) are called exponential algorithms.
An algorithm that can be done in polynomial time with enough machines, but requires exponential time with a single machine is considered NP.
faculty.juniata.edu /kruse/cs110/walker4.htm   (799 words)

  
 [No title]
The time to repair is exponential, time to failure is Erlang (k=2).
Calculate (i) average and standard deviation of time in queue, (ii) average and standard deviation of time in system; and (iii) average and standard deviation of tardiness.
For the time interval from 9:00 to 12:00, determine (i) average and standard deviation of customers in queue and (ii) average and standard deviation of customers in system.
www.public.iastate.edu /~smryan/ie613/HW404.doc   (582 words)

  
 [No title]
Exponential growth is one of the most common time paths exhibited by systems in the world.
In other words, the amount of exponential growth that occurs during one time constant is 2.71828 times the initial amount in the system's stock.
This time the figure shows that the system's stock doubles from a value of 100 to a value of 200 in (approximately) the seventh period (.7 multiplied by the time constant of 10 periods).
www.albany.edu /cpr/sds/DL-IntroSysDyn/exgr.htm   (2426 words)

  
 Time Series - Introduction
Time series is a set of observations generated sequentially in time.
In exponential smoothing there are one or more smoothing parameters to be determined (or estimated) and these choices determine the weights assigned to the observations.
Exponential smoothing does not excel in following the data when there is a trend.
www.resample.com /xlminer/help/Time_Series/Timeseries_intro.htm   (1022 words)

  
 EcoFuture™ Population and Sustainability - Exponential Growth and The Rule of 70
So it is still appropriate to reference the time in which these countries will double their population, which is perhaps the most illuminating manner of presenting population growth to the lay person.
It states that to find the doubling time of a quantity growing at a given annual percentage rate, divide the percentage number into 70 to obtain the approximate number of years required to double.
For the results to be accurate, all of these calculations assume that the growth rate remains unchanged throughout the interval in question, that is, that the growth is exponential at the average rate for the entire period.
www.ecofuture.org /pop/facts/exponential70.html   (1627 words)

  
 No. 2076: Exponential Growth
Ten percent one year, ten percent of the remaining buffalo the next, and so on until the buffalo were almost gone and hunting then became too difficult.
Maybe the time's come to go back and revisit our eighth-grade math class -- that world where words like linear, logarithmic, and exponential once had real meanings.
Listener Stephen Schwartz reminds me that, for just an instant, all exponential growth in time may be approximated as an initial value plus a constant times time.
www.uh.edu /engines/epi2076.htm   (581 words)

  
 modeling power law and exponential functions in geosciences
The population increase is a function of the existing population times a birth rate.
When trying to understand time aspects of how components of the biosphere can alter surface physical conditions (by changing greenhouse gas concentrations, etc.), the exponential response is also important to understand.
A size 6 is 10 times as large seismometer response amplitude wise as a 5 and one tenth the amplitude of a 7.
maps.unomaha.edu /maher/GEOL2300/week10/exp.html   (2340 words)

  
 Amazon.com: exponential-time   (Site not responding. Last check: 2007-10-14)
deterministic linear equation is an exponential function of time we are led to investigate...
Exponential growth in continuous time 47 is sometimes called the...
discrete as well as continuous time are exponential families in the sense studied...
www.amazon.com /s?ie=UTF8&keywords=exponential-time&index=blended&page=1   (1152 words)

  
 Exponential Time   (Site not responding. Last check: 2007-10-14)
is the length of the input word, and e(n) is a fixed exponential function, specific to that tm, that does not depend on w.
This is similar to the definition of a p language, where the execution time is bounded by a polynomial.
Hey, if a nondeterministic computer requires exponential time to solve the problem, it may as well be undecidable.
www.mathreference.com /lan-cx,exp.html   (249 words)

  
 Mis-Application of the Exponential Distribution   (Site not responding. Last check: 2007-10-14)
For the exponential distribution parameter estimation when censored data is encountered is a relatively simple task.
The exponential distribution is not very useful in modeling data in the real world.
The exponential distribution is only useful for items that have a constant failure rate.
www.engineeredsoftware.com /rma_exponential.asp   (310 words)

  
 RSA Security - A.7 Time estimations and some complexity theory   (Site not responding. Last check: 2007-10-14)
The procedure of estimating a complicated function f using an easier function g such as a polynomial or an exponential function is sometimes very useful.
However, instead of trying to compute the exact limit of the fraction f(n)/g(n) as in the example, one might be content with only a rough estimate of the behavior of the fraction.
All polynomial time algorithms are sub-exponential, but there are sub-exponential time algorithms that are not polynomial.
www.rsasecurity.com /rsalabs/node.asp?id=2372   (412 words)

  
 Untitled Document
In science many of the mathematical representations of the fundamental laws contain an exponential function that usually incorporates time or the speed of light as an element of the equation.
At this time the quantity of food, world-wide, is not the problem, but localized droughts, disasters, feudal wars and food delivery systems are at fault.
You cannot really plot the times of judgment as an exponential curve because we do not have a function for the x-axis, unless it would be the intensity and severity of the judgments.
www.jpdawson.com /expofun.html   (4302 words)

  
 Hypothesis on time
Each one it his at the time locates lived moment, at ten years I look myself like Marcel Pagnol using the eyes of a ten years old child, but at thirty years, I look myself using the eyes of this thirty years old man.
Characteristic of an analysis with an exponential time.
This results in the fact that more we benefit from time, more we have new experiences; more we have the impression to be short of time to analyze the events.
www.letime.net /b   (1232 words)

  
 Systat Software Inc. - PeakFit - HTML Help
This exponential response will shift the center of a peak to a slightly greater time, and the peak will have a tailed or right-shifted asymmetry.
When the exponential time constant is of the same order at the width of peaks, the deconvolved data will sometimes contain negative values or small sinusoidal components.
An inferred time constant is one that produces the least tailing or fronting, the most Gaussian-like symmetry.
www.systat.com /products/PeakFit/help/?sec=1045   (1175 words)

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