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Topic: Interval Research

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Interval (mathematics) - Wikipedia, the free encyclopedia Interval arithmetic, also called interval mathematics, interval analysis, and interval computation, was introduced by mathematicians in the 1950s and 1960s as an approach to putting bounds on rounding errors in mathematical computation. Interval notation is the notation in which permitted values for a variable are expressed as ranging over a a certain interval; "5 < x < 9" is an example of the application of interval notation. Intervals of type (1), (5), (7), (9) and (11) are called open intervals (because they are open sets) and intervals (2), (6), (8), (9), (10) and (11) closed intervals (because they are closed sets). en.wikipedia.org /wiki/Interval_(mathematics)

Interval scale On interval measurement scales, one unit on the scale represents the same magnitude on the trait or characteristic being measured across the whole range of the scale. For example, if anxiety were measured on an interval scale, then a difference between a score of 10 and a score of 11 would represent the same difference in anxiety as would a difference between a score of 50 and a score of 51. Interval scales do not have a "true" zero point, however, and therefore it is not possible to make statements about how many times higher one score is than another. davidmlane.com /hyperstat/A30751.html

Interval Intervals are a useful concept in the discussion of the degrees of a scale, the notes within triads and chords, for transposition and for harmony analysis. A major interval appears in the major scale of which the bottom note of the two is the key-note. Note that a minor interval does not necessarily appear in the minor scale of which the bottom note of the two is the key-note. ourworld.compuserve.com /homepages/neil_hawes/theory45.htm

Interval The inversion of an augmented interval is diminished and of a diminished interval is augmented. This unique interval, which cannot be spelled as a major, minor, or perfect interval, is considered unusually dissonant and unstable (tending to want to resolve to another interval) in Western Music. To find the interval, count the lines or spaces that the two notes are on as well as all the lines or spaces in between. cnx.rice.edu /content/m10867/latest

PlanetMath: interval This is version 4 of interval, born on 2003-07-14, modified 2005-01-21. Loosely speaking, an interval is a part of the real numbers that start at one number and stops at another number. In [1,2], an open interval is always called a segment, and a closed interval is called simply an interval. planetmath.org /encyclopedia/Interval.html

Intervals Intervals that are perfect have a certain sound that is variously described by musicians as "pure", "hollow" or "bare". Historically, the tritone was known as the "interval of the devil"; its position between the perfect 4th and perfect 5th made it quite difficult to sing in tune. But looking at those four intervals, if you ask yourself the question, "Is the top note in the major scale of the bottom note?", the only interval for which the answer is "yes" would be the one with the 'A' on top. www.musictheory.halifax.ns.ca /10intervals.html

Confidence Interval If the researcher were to take 100 random samples with a 95% confidence interval for each sample, then he or she expects that for 95 of the 100 samples (95%), the range of values produced by the confidence interval procedure will include the true mean of the population. Although the researcher in practice only has a single sample, the researcher is confident that their interval contains the true mean due to the process used to calculate the confidence interval. An alpha of.01 is a 99% Confidence Interval (note the larger red lines), which means only 1 line should not intersect in 5 runs (100%-1%=99%), and an alpha of.1 is a 90% Confidence Interval (note the smaller red lines), which means 10 lines should not intersect in 5 runs (100%-10%=90%). www.cvgs.k12.va.us /DIGSTATS/main/descriptv/d_confidence.htm

Interval Training Interval Training is a way to improve your aerobic capacity, the ability of the body to remove oxygen from the air and transfer it through the lungs and blood to the working muscles. By timing your intervals, or even picking a visual goal, say "I'll run to the third telephone pole on the right", you'll find that the workout will fly by. Simply put, Interval Training means varying the intensity within a workout. www.bodytrends.com /articles/cardio/interval.htm

aerobic interval training The accumulated oxygen deficit for bouts with rest intervals is the difference between the theoretical oxygen demand of the bouts and the actual oxygen used during both the bouts and the rest periods. Interval training is about setting a demanding intensity level and working at that level for the prescribed work/rest ratios until you cannot continue. Because interval training is intense, it is a great method for improving both aerobic and anaerobic fitness. www.pponline.co.uk /encyc/0145.htm

1.3.5.2. Confidence Limits for the Mean Interval estimates are often desirable because the estimate of the mean varies from sample to sample. For example, for a 95% confidence interval, we go to the row identified by 95.000 in the first column and extract an interval of (9.25824, 9.26468) from the last two columns. Instead of a single estimate for the mean, a confidence interval generates a lower and upper limit for the mean. www.itl.nist.gov /div898/handbook/eda/section3/eda352.htm

Data Types in SQL Statements The length of an INTERVAL is the same as the number of characters required to represent it as a string and is determined by the interval precision, leading precision and the seconds precision (where it applies). When an INTERVAL value is multiplied by a numeric value, the scale of the result is equal to that of the INTERVAL and the precision of the result is the leading precision of the INTERVAL increased by 1. The interval precision of the result is the combined interval precision of the two operands, e.g. developer.mimer.se /documentation/Mimer_SQL_Reference_Manual/Syntax_Rules4.html

INTLAB - INTerval LABoratory Version 5 Given a complex interval midrad(a,r) by midpoint "a" and radius "r", current implementation of f(midrad(a,r)) calculates the midpoint of the result interval to be f(a), and calculates the radius of the result interval by formulas developed by N. Boersken (see INTLAB documentation). Interval vector and matrix operations are very fast in INTLAB; however, nonlinear computations and loops may slow down the system significantly due to interpretation overhead and extensive use of the operator concept. Therefore, for given input interval X and some x in X it is not necessarily f(x) in f(X), where f(x) follows the usual definition of the main part of the function. www.ti3.tu-harburg.de /~rump/intlab

Development Tools Feature Stories The width of an interval is a natural measure of the accuracy of an interval approximation. Fortunately, intervals and arithmetic on intervals can be implemented in existing computers using a pair of floating-point numbers--one for the lower bound, and one for the upper bound. An interval is a range of numbers, for example, the interval between 2 and 3 contains all the numbers between and including 2 and 3. wwws.sun.com /software/sundev/news/features/intervals.html

Interval International.com Timeshares Interval Timeshare Interval International has been at the forefront of the industry in maintaining the highest standards of quality and excellence since 1976. Interval provides its members - vacation owners from around the world - with a variety of exchange services and other exciting benefits to enhance their vacation experiences. Interval International is second in Timeshare exchange services to only RCI.com (Resort Condominiums International, LLC) in popularity throughout the world. www.vacationtimesharerentals.com /interval-international.asp

Publications Related to Early Interval Work of R. E. Moore Under Moore's direction and influence, general purpose interval arithmetic became available for use on early computers (see [1]); and a program for bounding the solution of ordinary differential equations was produced (see [3], [10], [13], [14]). Reference [6] discusses interval valued functions, interval contractions, a metric topology for interval numbers, interval integrals, and contains an extensive discussion of Moore's use of interval analysis to bound the solution of ordinary differential equations. In [9], Moore states that he conceived of interval arithmetic and some of its ramifications in the spring of 1958. interval.louisiana.edu /Moores_early_papers/bibliography.html

Sample Size Calculator For example, if you use a confidence interval of 4 and 47% percent of your sample picks an answer you can be "sure" that if you had asked the question of the entire relevant population between 43% (47-4) and 51% (47+4) would have picked that answer. When you put the confidence level and the confidence interval together, you can say that you are 95% sure that the true percentage of the population is between 43% and 51%. The wider the confidence interval you are willing to accept, the more certain you can be that the whole population answers would be within that range. www.surveysystem.com /sscalc.htm

Statistics Glossary - Confidence Intervals These intervals may be calculated by, for example, a producer who wishes to estimate the difference in mean daily output from two machines; a medical researcher who wishes to estimate the difference in mean response by patients who are receiving two different drugs; etc. A confidence interval for the difference between two means specifies a range of values within which the difference between the means of the two populations may lie. A confidence interval gives an estimated range of values which is likely to include an unknown population parameter, the estimated range being calculated from a given set of sample data. www.cas.lancs.ac.uk /glossary_v1.1/confint.html

Interval House Interval House is a non-profit organization that provides free and confidential support services to victims of domestic violence regardless of race, ethnicity, sexual orientation or gender. Interval House is dedicated to providing services to prevent and break the cycle of family and intimate partner abuse. We help victims end the violence in their lives through advocacy, support groups, shelter and other services. www.intervalhousect.org

CSC378: Interval Trees The interval C is also stored in the leaf node to the right of 1843 because this node also satisfies conditions (1) and (2). An internal node is said to ``span'' the union of the elementary intervals in its subtree. Suppose we have a set of composers and their lifespans; each lifespan is an interval of years between the composer's birth and death. www.dgp.toronto.edu /people/JamesStewart/378notes/22intervals

Boost Interval Arithmetic Library Another common reason to use interval arithmetic is when the computer doesn't produce exact results: by using intervals, it is possible to quantify the propagation of rounding errors. They use the checking policy to produce empty intervals when the input interval is strictly outside of the domain of the function. Whenever possible, the interval result should be the smallest one able to satisfy the property (it is not really useful if the new functions always answer [-∞,+∞]). www.boost.org /libs/numeric/interval/doc/interval.htm

Interval Algebra: A review Interval algebra provides a good compromise between these, since it is non-quantitative and abstract - yet it is complete in the sign algebra of (-,0,+). Given two intervals A = [a1,a2] and B = [b1,b2], though there are 3^4 = 81 relations between the four points, only 13 of these valid for ordered non-zero intervals. It is also possible to extend interval algebra to provide some degree of description for relative size, symmetry and relative orientation. www.cse.iitk.ac.in /~amit/interval/interval.html

New Confidence Interval Applet ( 7-Aug-1996) Pick an alpha for which a large number of confidence intervals are to be calculated by sliding the arrow along the alpha scale. Each interval is based on a sample of size 5 taken from a standard normal distribution (mean=0 and variance=1). The first line of text allows you to see what intervals cover the true mean of 0 for the current set of 50 intervals as you change alpha. www.stat.sc.edu /~west/javahtml/ConfidenceInterval.html

ACA 2003 T6: Interval Computation Interval arithmetic provides both an algorithm and verification for the global optimization problem of problem 4; intervals are also useful for problem 2, as a way to control the exposure to excessive rounding error. A second one is the adaptation of the interval Newton algorithm to this arithmetic. The bounds produced by an interval method can be used, for example, to prove a theorem, to ensure that critical calculations are reliable, or to verify the accuracy of a floating-point computation. www.cas.mcmaster.ca /~nedialk/aca2003

Font Size Intervals In the HTML font size interval system as implemented in mainstream browsers, if the user's medium has 16 pixels per em, then size 1 is 60%, or 10 pixels; however, if the user's medium has 12 pixels per em, then size 1 is 75%, or 9 pixels. Even when legibility per se is not impaired, arbitrary or ill-conceived font size interval differences often interfere unacceptably with the accessibility, logical clarity, or aesthetics of documents. Neither the problem nor the solution are new: Netscape included it in its original implementation of size attributes on the now-deprecated FONT element, and the HTML heading sizes 1-6 have adapted to the user's base size since Mosaic. style.cleverchimp.com /font_size_intervals/altintervals.html

Effects of cisapride on QTc interval in neonates -- Bernardini et al. 77 (3): 241 -- Archives of Disease in Childhood - Fetal and Neonatal Edition QTc interval increase (0.550) was revealed as a result of syncope. Similarly, we recently observed a neonate with a prolongation in QTc interval induced by cisapride. The QTc interval prolongation was confirmed by two successive ECGs performed on days 32 (0.489) and 36 (0.500). fn.bmjjournals.com /cgi/content/full/77/3/F241

Interval Arithmetic Notes The natural interval extension of any function that is monotonic (always increasing or decreasing) returns the interval whose endpoints are the function applied to the input enpoints. The operations are expected to return an interval that contains the image of the input intervals under the operation, but the resulting interval need not be the smallest interval that contains the results of the operations. The natural interval extension of any differentiable function is found by the extrema of the functions results. graphics.cs.uiuc.edu /~jch/cpts330/ia.html

fat loss and fitness: interval training The bottom line is that short-term intense interval work is not designed to train the body to become an efficient fat burner as is required for long-distance endurance activities. Remember too, interval training is very stressful on the body and joints and should not be done more than two times a week. An easy method of determining maximum exercise heart rate for interval work is to subtract your age from 220 and then use 90-95 percent of that figure. www.cbass.com /INTERVAL.HTM

Interval Form The purpose of this entry form is to collect interval information from popular song (pop, rock, jazz) to place in a database, which will later be drawn from to individualize a students' recognition of certain intervals completely based on works, or at the least genre, from which they are familiar. Below are three interval entry forms, with one, two, and three entry forms in each respectively. If you do have more than three to submit, simply click the "return to interval form" on the next page to add more entries. theory.music.indiana.edu /t109/study/interval_form.htm

Interval International With Interval International, you can vacation at different resorts at different times of the year through a variety of exchange options. Interval International's present inventory now includes more than 2,500 resort locations in 60 countries on six continents. In addition to worldwide exchange opportunities, your Interval International membership also provides you with an array of travel benefits, including discounts on air fare, car rentals, cruises and travel packages. www.flagshipclub.com /files/interval.htm

Interval FAQ from Site Entry Page These questions and answers are extracted from the interval computations listserv (reliable_computing@interval.louisiana.edu), personal communications, and other sources. The best single Web source of interval information is Vladik Kreinovich's Interval Computation web site and sites pointed to from there. Examples of interval arithmetic, 30 Oct 2000 Is [A] - [A] = 0? www.mscs.mu.edu /~georgec/IFAQ

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