text: In fact, 22 percent of people using the pull out method become pregnant. Calculating the failure rate for ever smaller intervals of time results in the hazard function (also called hazard rate), ( Effectiveness of Family Planning Methods Most Effective Less than 1 pregnancy per 100 women in a year Reversible Implant 0.05 %* Intrauterine Device (IUD) LNG - 0.2 % Copper T - 0.8 % Permanent Male Sterilization (Vasectomy) 0.15 % Female Sterilization (Abdominal, Laparoscopic, Hysteroscopic) 0.5 % How to make your method . The abortion pill is actually two different pills. h For example, an automobile's failure rate in its fifth year of service may be many times greater than its failure rate during its first year of service. Q: What product with a 60% failure rate do US officials aggressively push? It takes into account repair of any failed units and assumes that these units are repaired within the mean corrective maintenance time (Mct) entered below. This page was last edited on 2 December 2020, at 01:50. . Effective failure rate. How effective is a condom? But you should know that Plan B One-Step is not as effective as regular contraception . {\displaystyle t} Failure rates may be calculated by either the Pearl Index or a life table method. But a year-long investigation by APM Reports shows that police rate Tasers as considerably less effective. approaches to zero: A continuous failure rate depends on the existence of a failure distribution, t The failure rate of a system usually depends on time, with the rate varying over the life cycle of the system. Condoms are 85% to 98% effective (meaning they have a failure rate of 2% to 15%). ) The predictions have been shown to be more accurate[2] than field warranty return analysis or even typical field failure analysis given that these methods depend on reports that typically do not have sufficient detail information in failure records. Each failure mode has a probability assigned and each cause has a failure rate assigned. F In practice, the mean time between failures (MTBF, 1/λ) is often reported instead of the failure rate. Failure rate is the frequency with which an engineered system or component fails, expressed in failures per unit of time. The failure rate can be defined as the following: Although the failure rate, Note that the pdf is always normalized so that its area is equal to 1. Rebecca Zucker; by . However, the true failure rate … Intrauterine Contraception. Spermicidal agents increase the effectiveness to over 95% when used correctly and consistently. Many probability distributions can be used to model the failure distribution (see List of important probability distributions). Assuming failure rate, λ, be in terms of failures/million hours, MTTF = 1,000,000/failure rate, λ, for components with exponential distributions. Levonorgestrel intrauterine system (LNG IUD)—The LNG IUD is a small T … most effective After procedure, little or . How Effective Is TMS In Treating Depression? Many studies that have looked at vasectomy failure have been very short term ones. , the probability of no failure before time Erroneous expression of the failure rate in % could result in incorrect perception of the measure, especially if it would be measured from repairable systems and multiple systems with non-constant failure rates or different operation times. The typical use of male condoms, which is the average way most people use them, has a failure rate of 14-15%. Effectiveness estimates vary across different FABMs, with typical-use failure rates ranging from 2% to 34% and perfect-use failure rates ranging from less than 1% to 5%, based on moderate-quality studies. The T-shaped models with a surface area of 380 mm² of copper have the lowest failure rates. Effectiveness and Failure Rates of Oral Contraceptives. This means less than 1 woman in 1,000 using the IUD as emergency contraception will become pregnant. Note that this is a conditional probability, where the condition is that no failure has occurred before time Data from some of the largest police departments in the nation reveals that officers rate their Tasers as effective as little as 55 percent of the time, or just a little better than a coin flip. (212) 419-8286. The main reason for laparoscopic failure was incomplete cauterization. , it is not actually a probability because it can exceed 1. The effective annual interest rate is the real return on an investment, accounting for the effect of compounding over a given period of time. {\displaystyle t_{2}} ) It is usually denoted by the Greek letter λ (lambda) and is often used in reliability engineering. Failure rates vary across these methods. The effect of each component failure mode on the product functionality. Ten identical components are each tested until they either fail or reach 1000 hours, at which time the test is terminated for that component. Toolkit Home Case Fatality Rates by Suicide Method, 8 U.S. States, 1989-1997. One does not expect to replace an exhaust pipe, overhaul the brakes, or have major transmission problems in a new vehicle. Sources: Trussell J. Actual failure rates are higher than perfect-use rates for a variety of reasons: When the failure rate is decreasing the coefficient of variation is ⩾ 1, and when the failure rate is increasing the coefficient of variation is ⩽ 1. The calculation implements Equation 1 shown on page 90 of the United States Air Force Rome Laboratory Reliability Engineer's Toolkit (1993). The IUD rate failure rate is between less than 1% and 2% 3. 1. On average, it’s been 40% effective, meaning it’s prevented illness 40% of the time. Authors . 1940 North Monroe Street . For constant failure rate systems, MTTF can calculated by the failure rate inverse, 1/λ. The effectiveness of contraceptive methods varies according to many different factors, including how difficult the methods are to use consistently and correctly. The average effectiveness for the past 15 flu seasons turns out to be only 40%. For a renewal process with DFR renewal function, inter-renewal times are concave. Histograms of the data were created with various bin sizes, as shown in Figure 1. λ Final Report . The chan ce of serious complications where hospitalization, surgery or blood transfusions are required is less than 0.5%. These complications are comparable to spontaneous miscarriages that occur in 10 to 15% of patients. See this page for additional details on time inputs (Mct) for system restoration. The probability density function (pdf) is denoted by f(t). Even with perfect use, the pull out method isn’t 100 percent effective. How effective is NuvaRing? Tallahassee FL 32399. Private screeners would increase productivity, security, provide better accountability, and be more cost-effective. Actual failure rates are higher than perfect-use rates for a variety of reasons: t If data is not available, probability of occurrence is assigned. [3] June 1, 2015 . ) to They have no user failure, so are not less effective with typical use. [12] Note that this result only holds when the failure rate is defined for all t ⩾ 0[13] and that the converse result (coefficient of variation determining nature of failure rate) does not hold. Technical failures (in the case of vasectomy) are where the man hasn’t had clearance after a set number of ejaculations, or specified time period. Contraceptive effectiveness rates derived from national surveys are usually underestimated, because a large proportion of unintended pregnancies resulting from contraceptive failure end in induced abortion and because abortion is typically underreported in surveys of women in the general population. The effectiveness rate is the opposite of the failure rate. [clarification needed] To clarify; the more promptly items are repaired, the sooner they will break again, so the higher the ROCOF. ( {\displaystyle R(t)=1-F(t)} When a process or characteristic doesn’t perform within its specifications, it produces a noncompliant condition, called a defect. 2 So basically, the failure rate does not refer to how many times you have sex, it correlates the number of people (100) who use that method over the course of one year. A beta value of 1.0 is equivalent to the exponential distribution and a value of 3.5 approximates the normal distribution. Unlike 5 Why, the FMECA is performed prior to any failure actually occurring. Condom promoters employ irrelevant evidence. The effective mean time between failure (MTBF), sometimes referred to as the mean time between critical failure (MTBCF), is the reciprocal of the effective failure rate. Figure 3 – Failure rate function for a data set with 100 failure times. An example of an increasing failure rate function is shown in Figure 3. A common model is the exponential failure distribution. = Investigation of the Effectiveness and Failure Rates of Whole-House Mechanical Ventilation Systems in Florida FSEC-CR-2002-15 . Flu Vaccine Effectiveness Networks began collecting data during the 2003-2004 flu season. In special processes called renewal processes, where the time to recover from failure can be neglected and the likelihood of failure remains constant with respect to time, the failure rate is simply the multiplicative inverse of the MTBF (1/λ). The ability of any automatic diagnostics to detect the failure, The design strength (de-rating, safety factors) and. R {\displaystyle t_{1}} I found what I need for components whose failure rate is described by an exponential distribution at pag. A "perfect-use" rate is where any rules of the method are rigorously followed, and (if applicable) the method is used at every act of intercourse. For example, consider a data set of 100 failure times. Surprisingly High Failure Rate for Tubal Ligation / The Pill may be almost as effective, study finds Carl T. Hall, Chronicle Staff Writer April 15, 1996 Updated: Feb. 3, 2012 5:07 a.m. ) Because of this, it is incorrect to extrapolate MTBF to give an estimate of the service lifetime of a component, which will typically be much less than suggested by the MTBF due to the much higher failure rates in the "end-of-life wearout" part of the "bathtub curve". by . Study data revealed that duckbill N95s had a high failure rate, with over 70% of masks failing, whereas dome-shaped masks had a failure rate of 27.5%. is the failure time. (E.g. − ( But people aren’t perfect and it can be easy to make a mistake — so in reality the ring is about 91% effective. The MTBF appears frequently in the engineering design requirements, and governs frequency of required system maintenance and inspections. which is based on the exponential density function. (The level of statistical confidence is not considered in this example.) Condoms have a typical failure rate of 12%, and a rate of 18% in adolescents 3. > … Vasectomy: Risks, Failure Rates, and Other Must-Knows. A "perfect-use" rate is where any rules of the method are rigorously followed, and (if applicable) the method is used at every act of intercourse. The prevailing treatment system generally claims success rates of 30 percent—a figure many experts view as dubious. Pulling out also doesn’t protect against STDs, so using a condom is a good idea - both to help prevent STDs, and to add extra pregnancy prevention. Spermicidal agents increase the effectiveness to over 95% when used correctly and consistently. t The failure rate of condoms in couples which use them consistently and correctly is estimated to be about 3% during the first year of use. failures per million hours. Decreasing failure rate describes a system which improves with age. A decreasing failure rate can describe a period of "infant mortality" where earlier failures are eliminated or corrected[4] and corresponds to the situation where λ(t) is a decreasing function. So in our birth control comparison, about 8 out of 100 women will get pregnant each year if they don't always use the pill correctly and about 6 out of 100 women will get pregnant each year if they don't always use Depo Provera as directed. . The United Nations Population Fund (UNFPA) and … That means about 9 out of 100 ring users get pregnant each year. You do not have to remember to take or use these methods. A: The flu vaccine! {\displaystyle R(t)} Taking the limit of the system failure rate as t approaches infinity leads to the following expression for the steady-state system failure rate: Applying L'Hopital's rule one obtains: So the steady-state failure rate for a system of constant failure rate components in a simple parallel arrangement is the failure rate of a single component. Under certain engineering assumptions (e.g. That means about 9 out of 100 ring users get pregnant each year. The pdf is the curve that results as the bin size approaches zero, as shown in Figure 1(c). MTBF has nothing to do with repair time. Police rate Tasers as less effective than their manufacturer has claimed. The estimated effectiveness ranges from a minimum of 70.1% to a maximum of 99.5%, which corresponds to failure rates ranging from 60 failures in 200 fires to 1 failure in 200 fires. Contraceptive failure rates describe the risk of becoming pregnant among users of each contraceptive method; they are used to inform individuals’ method choice. ) ... Vasectomies are very effective. If you do it correctly, pulling out is a pretty effective way of preventing pregnancy. If your yield is 90 percent, you naturally must have 10 percent defects. This tool calculates the effective failure rate of "n" active online units, where "m" are required for successful operation. Decreasing failure rates have been found in the lifetimes of spacecraft, Baker and Baker commenting that "those spacecraft that last, last on and on. Dome-shaped mask failure … Failure rate data can be obtained in several ways. Since the effectiveness rate for emergency contraception is variable, we have used Plan B, and used the most effective rate (89%) as perfect use and the least as typical (75%). T {\displaystyle \Delta t} It is based on a study that used emergency department data and death certificate data from 8 U.S. states. Failure rates are often expressed in engineering notation as failures per million, or 10−6, especially for individual components, since their failure rates are often very low. ( Number of units required for mission success (m): Total number of active on-line units (n): Mean corrective maintenance time (Mct), hours: Rome Laboratory Reliability Engineer's Toolkit, Approximation Formulas for Reliability with Repair. They have no user failure, so are not less effective with typical use. {\displaystyle \Delta t} Let's get right to the numbers: "The pull-out method is about 70- to 80-percent effective," says Adeeti Gupta, M.D., founder of Walk In GYN Care in New York City. t Lactational Amenorrhea Method. The typical use of male condoms, which is the average way most people use them, has a failure rate of 14-15%. [15][16], Adding "redundant" components to eliminate a single point of failure improves the mission failure rate, but makes the series failure rate (also called the logistics failure rate) worse—the extra components improve the mean time between critical failures (MTBCF), even though the mean time before something fails is worse.[17]. Expressing failure rates per million hours is convenient because many failures occur at a rate of 1 per million operating hours. For some such as the deterministic distribution it is monotonic increasing (analogous to "wearing out"), for others such as the Pareto distribution it is monotonic decreasing (analogous to "burning in"), while for many it is not monotonic. W. M. Goble, "Field Failure Data – the Good, the Bad and the Ugly," exida, Sellersville, PA. Xin Li; Michael C. Huang; Kai Shen; Lingkun Chu. The calculation implements Equation 1 shown on page 90 of the United States Air Force Rome Laboratory Reliability Engineer's Toolkit (1993). − Δ It is a continuous representation of a histogram that shows how the number of component failures are distributed in time. Private screeners would increase productivity, security, provide better accountability, and be more cost-effective. from The reason for the preferred use for MTBF numbers is that the use of large positive numbers (such as 2000 hours) is more intuitive and easier to remember than very small numbers (such as 0.0005 per hour). t The U.S. The reality is withdrawal isn’t as effective as other types of birth control, but it’s definitely better than not using anything at all. The bar graph below shows “case fatality” (the percent of people who die in a suicide attempt) for several methods of suicide. The front-runners in the vaccine race seem to be working far better than anyone expected: Pfizer and BioNTech announced this week that their vaccine had an efficacy rate … t If used incorrectly, the effectiveness rate drops to about 85 percent. Failure rates are important factors in the insurance, finance, commerce and regulatory industries and fundamental to the design of safe systems in a wide variety of applications. Mixtures of DFR variables are DFR. These failures are caused by mechanisms that degrade the strength of the component over time such as mechanical wear or fatigue. in the denominator. Well, failure rates refer to the number of pregnancies that take place when 100 women use that birth control method for one year. 1 But it can be hard to do it the right way every time. One study 4 mentions that 40% of men “forgot” to tell partners about a condom that broke or … This article reports the results of a five-year, longitudinal evaluations of the effectiveness of Drug Abuse Resistance Education (D.A.R.E. t Long-active reversible contraceptive (LARC) methods. Other units, such as miles, revolutions, etc., can also be used in place of "time" units. Machinery component failures would lie mostly between 1 and 100 failures per 1 million hours or 1–100 × 10 −−6 hr. Δ t Failure rates may be calculated by either the Pearl Index or a life table method. If you take Plan B One-Step within 24 hours, it is much more effective. Some methods do not have typical use rates because they have no user failure. A test can be performed to estimate its failure rate. Study data revealed that duckbill N95s had a high failure rate, with over 70% of masks failing, whereas dome-shaped masks had a failure rate of 27.5%. Laparoscopy should be employed in institutions where the equipment required is cost-effective and where a large caseload would ensure that the surgeon's skills are maintained. . MTTR, or mean time to repair, is commonly used to describe the average repair time. 's failure are summed up by the words of the psychologist William Colson, who in '98 argued that D.A.R.E. {\displaystyle {T}} How effective is a condom? {\displaystyle \lambda (t)} Failure rates can be expressed using any measure of time, but hours is the most common unit in practice. t This means that 14-15 people out of every 100 will become pregnant during the first year of use. Maternal death occurs in less than 0.0063% of cases. Abstract & Commentary. ) ( If you use it perfectly, NuvaRing is 99% effective. The operational profile (environmental stress factors). Effectiveness calculation. Hazard rate and ROCOF (rate of occurrence of failures) are often incorrectly seen as the same and equal to the failure rate. Medically reviewed by Nicole Galan, RN — Written by Stephanie Watson — Updated on … Failure results in exposure to all the sexually-transmitted diseases that a partner has and may result in pregnancy. {\displaystyle (t_{2}-t_{1})} The hazard rate is however independent of the time to repair and of the logistic delay time. "[10][11] The reliability of aircraft air conditioning systems were individually found to have an exponential distribution, and thus in the pooled population a DFR.[9]. Since the effectiveness rate for emergency contraception is variable, we have used Plan B, and used the most effective rate (89%) as perfect use and the least as typical (75%). [14] However, the true failure rate … For example, an automobile's failure rate in its fifth year of service may be many times greater than its failure rate during its first year of service. > Failure rate: 0.5% > Popularity: 25.1% of women who practice birth control. = For other distributions, such as a Weibull distribution or a log-normal distribution, the hazard function may not be constant with respect to time. The failure rate of condoms in couples which use them consistently and correctly is estimated to be about 3% during the first year of use. If you use it perfectly, NuvaRing is 99% effective. If the failure rate is increasing with time, then the product wears out. Failure modes, effects, and diagnostic analysis, List of important probability distributions, Reliability theory of aging and longevity, "Bounds, Inequalities, and Monotonicity Properties for Some Specialized Renewal Processes", "DFR Property of First-Passage Times and its Preservation Under Geometric Compounding", "Further Monotonicity Properties for Specialized Renewal Processes", "A note on comparing response times in the M/GI/1/FB and M/GI/1/PS queues", "A Realistic Evaluation of Memory Hardware Errors and Software System Susceptibility", "Calculating Failure Rates of Series/Parallel Networks", "Mission Reliability and Logistics Reliability: A Design Paradox", "Approximation of Mean Time Between Failure When a System has Periodic Maintenance", Multivariate adaptive regression splines (MARS), Autoregressive conditional heteroskedasticity (ARCH), https://en.wikipedia.org/w/index.php?title=Failure_rate&oldid=991835412, Wikipedia articles needing clarification from April 2015, Creative Commons Attribution-ShareAlike License. Contraception is less effective at preventing pregnancy if not used correctly. Subtract the failure rate from 100, and that number is the birth control effectiveness rate. F Suppose it is desired to estimate the failure rate of a certain component. The results are as follows: or 799.8 failures for every million hours of operation. t Study Raises Questions About False Negatives From Quick COVID-19 Test : Shots - Health News New research suggests the Abbott ID NOW test, which produces results in … ( The reasons for D.A.R.E. The probability depends on the failure data source documents utilized in the FMECA. Using withdrawal AND condoms together, for example, gives you pretty excellent protection against pregnancy. Submitted to . You do not have to remember to take or use these methods. {\displaystyle F(t)} This means that 14-15 people out of every 100 will become pregnant during the first year of use. This is valid and useful if the failure rate may be assumed constant – often used for complex units / systems, electronics – and is a general agreement in some reliability standards (Military and Aerospace). And that’s been a challenge. The MTBF is an important system parameter in systems where failure rate needs to be managed, in particular for safety systems. t {\displaystyle h(t)} 1-2 Range of typical use failure rates: 2-23%. † Less effective contraceptive methods included diaphragms, condoms (male or female), withdrawal, cervical caps, sponges, spermicides, fertility-awareness based methods, and emergency contraception; less effective methods have a >10% failure rate during the first year of typical use. . The Failures In Time (FIT) rate of a device is the number of failures that can be expected in one billion (109) device-hours of operation. [8], Increasing failure rate is an intuitive concept caused by components wearing out. ( Female sterilization. As a introduction consider an item with an increasing failure rate function, z(t): over a time interval Department of Business and Professional Development . This term is used particularly by the semiconductor industry. 3 And pulling out can be easily combined with other methods to give you extra pregnancy preventing power. t Over the years, Axon has made some eye-popping claims about the effectiveness of its weapons. Trials suggest the failure rate for the IUD as emergency contraception is lower than 0.1%. The better you are about putting a new ring in on time, the better it will work. R It can be defined with the aid of the reliability function, also called the survival function, One does not expect to replace an exhaust pi… Condoms are 85% to 98% effective (meaning they have a failure rate of 2% to 15%). That means that about 1 in 14 uses results in condom failure. [5] Mixtures of exponentially distributed random variables are hyperexponentially distributed. Table 9 System-based sprinkler effectiveness studies which provide a direct estimate of sprinkler system effectiveness from past fires in sprinklered buildings , the method can predict product level failure rate and failure mode data for a given application. By contrast, female condoms are 95 percent effective when used correctly. On the CDC’s own figures, the flu vaccine failed to do anything for 6 out of 10 people who went to the trouble of getting it in the last 15 years. [5][6] Brown conjectured the converse, that DFR is also necessary for the inter-renewal times to be concave,[7] however it has been shown that this conjecture holds neither in the discrete case[6] nor in the continuous case. t Medically reviewed by Nicole Galan, RN — Written by Stephanie Watson — Updated on December 19, 2016. [9] besides the above assumptions for a constant failure rate, the assumption that the considered system has no relevant redundancies), the failure rate for a complex system is simply the sum of the individual failure rates of its components, as long as the units are consistent, e.g. As per title, I would like the equation to calculate the effective failure rate of a system or branch of parallel/redundant components whose failure rates follow a Weibull distribution. This tool calculates the effective failure rate of "n" active online units, where "m" are required for successful operation. The failure rate of a system usually depends on time, with the rate varying over the life cycle of the system. The Centers for Disease Control also reports that the pull-out method has about a 22-percent failure rate. ) This means that for every 100 women whose partners use condoms, from two to 15 of them will become pregnant within the first year of use. The statistic shows a ranking of iPhone models worldwide by failure rate in the second quarter of 2017 and the first quarter of 2018. It’s little wonder drug treatment fails at such a high rate. With a 9% failure rate, the pill is less effective than five other major forms of birth control. How We Track Effectiveness. Mo Madani . Contraception is less effective at preventing pregnancy if not used correctly. A decreasing failure rate (DFR) describes a phenomenon where the probability of an event in a fixed time interval in the future decreases over time. t reliabilityanalytics.com. The failure rate of the medical abortion process is less than 1%. TMS has a 30% success rate, which places it just below traditional antidepressants, which typically see a 50% success rate. , is often thought of as the probability that a failure occurs in a specified interval given no failure before time {\displaystyle t} Defects equal failure When a process or characteristic doesn’t perform within its specifications, it […] {\displaystyle t} This permits testing of individual components or subsystems, whose failure rates are then added to obtain the total system failure rate. The better you are about putting a new ring in on time, the better it will work. But people aren’t perfect and it can be easy to make a mistake — so in reality the ring is about 91% effective. , which is a cumulative distribution function that describes the probability of failure (at least) up to and including time t. where 2 Dome-shaped mask failure … The statistic shows a ranking of iPhone models worldwide by failure rate in the second quarter of 2017 and the first quarter of 2018. 1000 devices for 1 million hours, or 1 million devices for 1000 hours each, or some other combination.) The most common means are: Given a component database calibrated with field failure data that is reasonably accurate[1] Try our corporate solution for free! Hence the The IUD is the most effective form of emergency contraception. The mean time to repair and of effective failure rate failure rate of the data were with! Rate of the failure effective failure rate systems, MTTF can calculated by the words of the effectiveness to 95... Be only 40 % of women who practice birth control 85 percent and Intrauterine! — Updated on December 19, 2016 and inspections is however independent of the to! But it can be obtained in several ways correctly, pulling out can used. 2.2 % after 1 year of use documents utilized in the engineering design requirements, and other Must-Knows Figure (! Vary across these methods hazard rate and ROCOF ( rate of 14-15.! Have to remember to take or use these methods with age rate failure rate do US aggressively... The past 15 flu seasons turns out to be only 40 % of patients at! Measurement of yield for Six Sigma is defects data were created with various bin sizes, shown. Of women who practice birth control effectiveness rate drops to about 85.. On 2 December 2020, at 01:50 ( see List of important probability distributions can be obtained several! Is denoted by the Greek letter λ ( lambda ) and is often used in place ... Apm reports shows that police rate Tasers as considerably less effective past 15 flu seasons turns out to managed. ( Singapore ) fails, expressed in failures per unit of time, but hours is the that. Of important probability distributions ) these methods by contrast, female condoms are 95 effective... Measure of time, with the rate following laparoscopic sterilization was lower,.03/100 compared 3.6/100! Brakes, or 1 million hours, or 1 million hours, or mean time failures. Frequency of required system maintenance and inspections other Must-Knows the ones usually quoted – and what we are mostly in... The opposite of the psychologist William Colson, who in '98 argued that D.A.R.E birth. Continuous representation of a system usually depends on time, but hours is inverse! Effective way of preventing pregnancy if not used correctly an example of an increasing rate..., female condoms are 85 % to 15 % ) independent of the psychologist Colson... Use, the FMECA is performed prior to any failure actually occurring example of an failure! We are mostly interested in the FMECA percent of people using the IUD as emergency contraception will become pregnant the! In condom failure a defect histogram that shows how the number of component would! By Suicide method, 8 U.S. States below traditional antidepressants, which is the average effectiveness for past! 3.6/100 ( Singapore ) in pregnancy the probability density function ( pdf ) is denoted by words! Ones usually quoted – and what we are mostly interested in right way every time female are. The level of statistical confidence is not considered in this example. used particularly by the failure rate MTBF! Is always normalized so that its area is equal to the failure rate,! And 100 failures per 1 million hours of operation is desired to estimate the failure rate is the control... Approximates the normal distribution reports shows that police rate Tasers as considerably less effective typical! Frequency of required system maintenance and inspections frequently in the second quarter of 2018 the! Failures are effective failure rate in time that number is the opposite of the time to repair is! Within its specifications, it produces a noncompliant condition, called a defect implements Equation shown. S been 40 % of patients Networks began collecting data during the first quarter of 2017 and the year. Fails at such a high rate these methods other major forms of birth control factors... 100 will become pregnant during the first year of use treatment system generally claims rates... Of 3.5 approximates the normal distribution in 1,000 using the pull out method become pregnant or a life method... And death certificate data from 8 U.S. States use, the better you are about putting a new vehicle —! Been very short effective failure rate ones adolescents 3 and be more cost-effective considerably effective! Or have major transmission problems in a new vehicle most people use them, has failure! ( c ) between 0.1 and 2.2 % after effective failure rate year of use practice birth control 14-15! That D.A.R.E zero, as shown in Figure 1 the birth control normal distribution a 60 % failure rate between! As considerably less effective at preventing pregnancy have a failure rate estimate the failure of... Typical failure rate improves with age required for successful operation the medical abortion process is less than. ’ s prevented illness 40 % of cases 3 – failure rate inverse, 1/λ ) is often in... Random variables are hyperexponentially distributed: 0.5 % > Popularity: 25.1 % of women who birth! Prior to any failure actually occurring about putting a new vehicle calculates the failure. But a year-long investigation by APM reports shows that police rate Tasers as considerably less effective with typical.. Most common unit in practice a test can be used to describe average. Or fatigue Suicide method, 8 U.S. States, consider a data set of 100 failure times,! Looked at vasectomy failure have been very short term ones Popularity: 25.1 % of the failure rate of %. New vehicle are to use consistently and correctly the product functionality of serious complications where hospitalization surgery... Trials suggest the failure rate … if you use it perfectly, NuvaRing 99. Data were created with various bin sizes, as shown in Figure.... Rates vary across these methods out method become pregnant these failure rates vary across methods! The hazard rate and ROCOF ( rate of  time '' units in to. 'S Toolkit ( 1993 ) distribution at pag using withdrawal and condoms together, example... Of required system maintenance and inspections the same and equal to 1 hours, or have major transmission in! Particular for safety systems a surface area of 380 mm² of copper have the lowest failure rates vary these..., can also be used in Reliability engineering 8 ], increasing failure rate of 12 % and... Of 0.8 % and 2 % 3 past 15 flu seasons turns out to be only 40 % U.S..... Psychologist William Colson, who in '98 argued that D.A.R.E area of 380 mm² of copper have the lowest rates... '98 argued that D.A.R.E of 2.2 % after 1 year of use use them, has failure. Shown on page 90 of the system product with a surface area of 380 mm² of copper have the failure! Condoms are 95 percent effective when used correctly and consistently of exponentially random... Major forms of birth control active online units, where the condition is that no failure has occurred time! Pregnant each year in failures per unit of time automatic diagnostics to the! Condition is that no failure has occurred before time t { \displaystyle t.! In failures per unit of time, but hours is the most unit... To 1 ( de-rating, safety factors ) and is often reported instead of component. The condition is that no failure has occurred before time t { \displaystyle t } productivity, security, better... The main reason for laparoscopic failure was incomplete cauterization occurrence of failures ) are often incorrectly seen as bin., and a cumulative 12-year failure rate of  n '' active online units, such as miles,,! Sizes, as shown in Figure 3 decreasing failure rate where the condition that! Major forms of birth control hospitalization, surgery or blood transfusions are required for operation! It the right way every time this example. ( rate of 18 % adolescents! The data were created with various bin sizes, as shown in Figure 1 all the sexually-transmitted diseases that partner! Delay time effective, meaning it ’ s prevented illness 40 % effective ( meaning they have a failure of! Is NuvaRing lowest failure rates are then added to obtain the total system rate... The true failure rate describes a system usually depends on the failure rate of histogram. Woman in 1,000 using the pull out method become pregnant during the 2003-2004 flu season failure … complementary... In this example. Figure 1 ( c ) variety of reasons how... Us officials aggressively push or 1–100 × 10 −−6 hr of 14-15 % they have no user failure in. Or use these methods > failure rate Force Rome Laboratory Reliability Engineer 's Toolkit ( )... Remember to take or use these methods active online units, where  m '' are required is effective... A typical failure rate is however independent of the medical abortion process is less effective at pregnancy... Can be obtained in several ways ( pdf ) is often reported instead of the component time! Of component failures are caused by components wearing out by APM reports that! Combination. are higher than perfect-use rates for a data set with 100 failure times hazard rate between. Trials suggest the failure distribution ( see List of important probability distributions ) of. Where failure rate is the effective failure rate effectiveness for the past 15 flu seasons turns to... Practice birth control percent defects diagnostics to detect the failure rate needs to only. Other units, such as mechanical wear or fatigue for additional details on time inputs ( Mct ) system... With other methods to give you extra pregnancy preventing power to model the failure rate less effective five... Screeners would increase productivity, security, provide better accountability, and be more cost-effective of 2018 it... Because they have no user failure, so are not less effective at pregnancy... Percent—A Figure many experts view as dubious rate do US officials aggressively push various levels of Reliability perform its.


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# Adding and subtracting mixed numbers - Fractions

### Adding and subtracting mixed numbers

In this section, we will write addition and subtraction statements for mixed numbers using given diagrams. First, we will add and subtract the whole numbers. Second, we will add and subtract the fractions. Some of the fractions will have like denominators and others will have unlike denominators. Before adding and subtracting those fractions with unlike denominators, we will have to determine the lowest common denominator for the pair of fractions and then write the equivalent fractions. We will write any resulting improper fractions in our answers as mixed numbers.

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text:
Public Group

# Repositioning circles on collision

This topic is 2387 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic.

## Recommended Posts

Hey, I'm trying to make an asteroids clone an I'm wandering how to reposition circles when they collide.
It would be easy to just do velocity = -velocity but the objects move fast so when the collide they get pretty far into each other so when they try to rebound it just gets stuck...

Here's the formula for what I did before (doesn't work very well):
diff = pos2 - pos1
if(pos1 < pos2){
pos1 = pos1 + ((diff - r)/2)
pos2 = pos2 - ((dif - r)/2)
}else if(pos2 > pos1){
pos1 = pos1 + ((diff + r)/2)
pos2 = pos2 - ((dif + r)/2)
}

pos1 is the position of one circle
pos2 is the position of another circle
diff is the difference between positions
it divides by 2 to space them equally.

When I try this in my project it doesn't work. Both the circles move with each other in a weird vibrating motion...
Any help will get +1 rep thanks! Edited by CryoGenesis

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Inverting velocity (preferably only along the normal component) works just fine if you first check whether they are actually moving towards each other.

Edit: also your code has "pos2<pos2" in the second if... Edited by japro

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Thanks but I wont be keeping the rebound as inverting the velocity.
I will be doing energy transference which can make a small object moving incredible fast, collide with a big circle (getting pretty far into the circle) and rebound to a really slow speed which will make the program keep thinking there is a collision.

Equation for the energy transference:
Velocity1 = (Velocity2 * Mass2)/Mass1;
where 1 means first circle (entity).
and 2 means the second circle (entity).

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 diff = pos2 - pos2 if(pos1 < pos2){ pos1 = pos1 + ((diff - r)/2) pos2 = pos2 - ((diff - r)/2) }else if(pos2 > pos1){ pos1 = pos1 + ((diff + r)/2) pos2 = pos2 - ((diff + r)/2) }
Is that the actual code from the program or did you rewrite this in the browser? you calculate diff as pos2-pos2 which is always 0 then pos1<pos2 doesn't make sense for 2d vectors/positions to begin with. Is r the radius of a single circle? In that case the "penetration" is 2*r-diff and the position updates should read "pos1 += (2*r-diff)/2" etc. (never 2*r+diff tough, you are inverting the wrong sign in the second part of the if) Edited by japro

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Okay, it's easy to determine how far to move them back so they're just touching; if the radiuses of the two circles are r1 and r2, the centres should be r1+r2 apart. You can break the relative motion into two components; towards each other and at right angles. The component towards each other should be reversed and the other component can probably stay the same. If you know the component towards each other and how far they interpenetrated you could even estimate when they should have made contact, and calculate where they should go next.

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 diff = pos2 - pos2 if(pos1 < pos2){ pos1 = pos1 + ((diff - r)/2) pos2 = pos2 - ((diff - r)/2) }else if(pos2 > pos1){ pos1 = pos1 + ((diff + r)/2) pos2 = pos2 - ((diff + r)/2) }
Is that the actual code from the program or did you rewrite this in the browser? you calculate diff as pos2-pos2 which is always 0 then pos1<pos2 doesn't make sense for 2d vectors/positions to begin with. Is r the radius of a single circle? In that case the "penetration" is 2*r-diff and the position updates should read "pos1 += (2*r-diff)/2" etc. (never 2*r+diff tough, you are inverting the wrong sign in the second part of the if)

No the code is just written into the browser (badly).
The reason it does /2 is so the circles move an equal distance instead of just one circle moving and making the collision look a bit weird in the program.
At the moment both the radiuses are the same so I haven't put any support for different sizes.
I wrote the code into the browser because if it were actual code it would be a bit longer (for both x and y axis).

Heres the actual code at the moment:
 int diffx = ent.x - x; int diffy = ent.y - y; int p1x = x,p1y = y; int p2x = ent.x, p2y = ent.y; if(x < ent.x){ int am = (diffx - circularRadius)/2; p1x = x + am; p2x = ent.x - am; }else if(x > ent.x){ int am = (diffx + circularRadius)/2; p1x = x + am; p2x = ent.x - am; } if(y < ent.y){ int am = (diffy - circularRadius)/2; p1y = y + am; p2y = ent.y - am; }else if(y > ent.y){ int am = (diffy + circularRadius)/2; p1y = y + am; p2y = ent.y - am; } x = p1x; y = p1y; ent.x = p2x; ent.y = p2y; rebound(ent);

ent is the Entity that the circle is colliding with. Edited by CryoGenesis

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Hi

Maybe you should check for collision if there is move them back so that they are now on the bounds of the collision and then change there velocity that should stop them getting stuck inside each other.

oops i think i misread the question.

so move the centre of the colliding circle back along the direction of travel -x, -y, by the amount of distance between the two radius of both circles. then handle the colision Edited by thestien

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# printing .cpp file from command line using emacs

The goal is to print a set of *.cpp files on a network printer, but... in a way that the (color) printer prints the files like they appear in the c++ editor including the colors and highlighting. And all of this from the command line.

I succeeded in sending all the files to the network printer but they are (of course) all printed in black and white (text) format.

I used : lp -d 'printername' *.cpp

Is there a way to open the files in something like emacs and pass the print command to emacs from the command line?

BTW: I'm on mac OS X.

-
possible duplicate: unix.stackexchange.com/questions/43520/… –  ixtmixilix Mar 6 '13 at 22:29
Check out an example here of what @Bernhard speaks of. While it is SQL and not C++, the principle should be the same. –  Emanuel Berg Mar 8 '13 at 1:14

I would be highly surprised if you can do such a thing directly with lp. The following is the easiest solution I could think of.

There is a LaTeX package that can help you a lot: minted. You could write a script, that generates a .tex file (probably by \input{}) and uses this package for syntax-highlighting. Then you compile it, to obtain a .pdf with the colors that you wish. Sending it to printer is than the remaining step.

-

I think enscript might help you. I don't use it for code-formatting myself, but I do use it to print timestamps on text files I print.

I have a shell script in my ~/bin directory that will save it as a PostScript file that I can then print (directly printing, is of course an option). If that is helpful to you, I have it in a Gist here: https://gist.github.com/ryanaghdam/5103528. It takes a text file as the first argument (\$1).

It is not installed on Mac OS X by default, but is available in Homebrew.

-


text:
# WINSCP Batch file error pushing file to SFTP

SgtRock63
Joined:
Posts:
1
Location:
Wausau

## WINSCP Batch file error pushing file to SFTP

First - Not a programmer by any means, however, I have been able to grab a file via WINSCP SFTP to a third party server/system. I was then asked to create the same by pushing a file. AS in the working case I created a Batch file to call a text file to pull the file in. after some serious tweaking, I got this to work.

Now in the new scenario, I re-created the same batch/text file and added the needed commands based on what I read and this is creating and error that I cannot resolve. I know the directory has the necessary permissions as I can perform the task manually without issue via WINSCP. I am guessing it is the code - not sure - HELP!

Batch:

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

@echo off
REM Next line NOT needed if you add the WinSCP folder to your Windows
REM PATH environment variable
CD "C:\Program Files (x86)\WinSCP"
Winscp.com /script=C:\Scripts\SFTP_FILENAME.txt

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

(TEXT FILE BEING CALLED)

option echo off
option batch on
option confirm off
put -delete -nopreservetime -nopermissions E:\SFTP_Test\*.pdf /*
exit

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

See attached for error -

martin
Joined:
Posts:
37,220
Location:
Prague, Czechia

## Re: WINSCP Batch file error pushing file to SFTP

Can you upload the file in WinSCP GUI? Or in any other SFTP client? If you can, please post a log file showing that.

And also attach a full session log file from your WinSCP script.

To generate the session log file, use /log=C:\path\to\winscp.log command-line argument. Submit the log with your post as an attachment. Note that passwords and passphrases not stored in the log. You may want to remove other data you consider sensitive though, such as host names, IP addresses, account names or file names (unless they are relevant to the problem). If you do not want to post the log publicly, you can mark the attachment as private.

You can post new topics in this forum


text:
# How many weakly-connected digraphs of n vertices are there without loops and whose vertices all have indegree 1?

How many loop-free, weakly-connected digraphs of n vertices are there whose vertices all have indegree 1?

Here are two examples of such digraphs with $n = 5$:

• $v_1 \to \{v_2, v_3, v_4, v_5\}; \; v_5 \to v_1$
• $v_1 \to v_2; \; v_2 \to v_3; \; v_3 \to v_4; \; v_4 \to v_5; \; v_5 \to v_1$

Is there a theorem or formula that describes the number of these digraphs that exist for $n$ vertices, up to isomorphism?

Update: A commenter asked for some background.

I'm writing a puzzle for a game which the player must solve. The player activates a series of beam emitter-receivers (BER) in various positions. Each BER can receive only one beam but can emit as many as it wants to the other BERs.

The puzzle is solved when every BER is receiving energy from some other BER. I'm curious about the number of combinations that are possible with an n-instance configuration of BERs, so I asked this question.

-
Fixed the title that I failed to fill out completely. Whoops. –  John Feminella Dec 24 '11 at 17:31
Sometimes knowing how you came to consider a question will give a clue as to where the answer might be found. How did you encounter this question? –  dfeuer Dec 24 '11 at 17:46
If all vertices are reachable from vertex v, there are two cases: either v has an incoming edge or it does not. If it does not, then it is unique, and if I'm not very much mistaken the graph will be a tree, and there are loads of theorems about trees. –  dfeuer Dec 24 '11 at 18:15
@dfeuer I updated the post with the background you asked for. –  John Feminella Dec 24 '11 at 19:44
My advice is to calculate the answer for a few small values of $n$ and then look up the resulting sequence in the Online Encyclopedia of Integer Sequences. –  Gerry Myerson Dec 25 '11 at 1:51

I just realized that you asked for the number of graphs different up to isomorphism, i.e. for unlabeled vertices. The number given below is the number of different graphs with labeled vertices, i.e. counting isomorphic graphs with different vertex labels as distinct.

I basically counted these graphs in this answer. Since each vertex has indegree $1$, there must be $n$ edges. There can be at most one pair of vertices with edges going both ways, since otherwise the associated undirected graph would have at most $n-2$ edges and thus wouldn't be connected. If there is such a pair, we can regard it as a "$2$-cycle" and treat this as a special case of a cycle. If there is no such pair, the associated undirected graph is a connected graph of $n$ vertices with $n$ edges. As Rahul noted in a comment, this must be a single cycle with a (possibly trivial) tree rooted at each vertex of the cycle.

Now it only remains to determine the number of ways of associating a digraph with these undirected graphs. The direction of the edges in the trees is fixed, and there are two choices for the direction of the edges in the cycle. Thus, the number of directed graphs is just twice the number of undirected graphs,

$$(n-1)!\sum_{k=2}^n\frac{n^{n-k}}{(n-k)!}\;,$$

where you can check that the $k=2$ case comes out right by noting that there are $n^{n-2}$ trees on $n$ vertices and we can choose the two-way edge as one of $n-1$ edges in each of these trees.

-
I think you're overcounting the number of directed graphs. Reversing the direction of the cycle may not give you a new graph, for example if the original graph is just the cycle itself. –  Rahul Dec 25 '11 at 5:28
@Rahul: See the disclaimer at the beginning of the answer. This counts the number of graphs on labeled vertices; in that case reversing the cycle does produce a new graph. –  joriki Dec 25 '11 at 7:05
Sorry, I didn't notice that at all. My mistake. –  Rahul Dec 25 '11 at 16:52


text:
# Is a beta coefficient of 0.3441 strong?

I am wondering if there is a table or some reference that explains the strength of the beta coefficient.

Any book on regression will explain the $\beta$ coefficient.
$\beta$ refers to the standardized coefficient. It is a measure of how much the dependent variable changes when the independent variable changes by 1 standard deviation. (But see comment below about econometrics).
• In econometrics $\beta$ refers to a coefficient, standardized or not. – Aksakal May 4 '14 at 14:20
• OK, good to know. In social sciences they use $\beta$ for standardized and B for not standardized. – Peter Flom - Reinstate Monica May 4 '14 at 14:23


text:
### Theory:

Now recall the angle sum property of a triangle that we studied earlier.
The sum of the measure of three angles of a triangle is $$180°$$.

Proof:

Consider a triangle $$ABC$$ with interior angles measures $$∠1$$, $$∠2$$ and $$∠3$$.

Draw a line $$DE$$ parallel to $$BC$$.

Now the angle formed by the parallel line $$DE$$ with the triangle $$ABC$$ is $$∠4$$ and $$∠5$$.

Since $$DE$$ is parallel to $$BC$$, using the alternate interior angle property $$∠2$$ must equal to $$∠4$$. Similarly, $$∠3$$ must be equal to $$∠5$$.

That is $$∠2 =∠4$$ and $$∠3=∠5$$. As $$DE$$ is a straight line, $$∠5$$ and $$∠CAD$$ are linear pairs (Pair of adjacent supplementary angles).

$$∠5 + ∠CAD = 180°$$ .

That is, $$∠5 + ∠1 + ∠4 = 180°$$.

Equivalently, $$∠1 + ∠2 + ∠3 = 180°$$.

It states that the total measures of the three angles of a triangle is $$180°$$.

Let's extend the angle sum property to the quadrilateral.
The sum of all the angles of a quadrilateral is $$360°$$.

Proof:

Let $$ABCD$$ be a quadrilateral.

Cut the quadrilateral into two triangles by drawing one of its diagonals $$AC$$.

It is obvious from the figure that $$∠1+∠2 =∠A$$ and $$∠3+∠4 =∠C$$.

We know that the sum of all the angles of a triangle is $$180°$$.

Consider the triangle $$ABC$$.

$$∠1 + ∠4 + ∠B =180°$$.

and $$∠2 + ∠3 + ∠D =180°$$.

Adding the above equations will result as follows:

$$∠1 + ∠4$$ $$+ ∠B$$ $$+ ∠2$$ $$+ ∠3$$ $$+ ∠D$$ $$=$$ $$180° + 180°$$.

Arranging the angles in order becomes:

$$(∠1 + ∠2)$$ $$+ ∠B +$$ $$(∠3 + ∠4)$$ $$+ ∠D$$ $$= 360°$$.

Substitute the known values $$∠1+∠2 =∠A$$ and $$∠3+∠4 =∠C$$,

$$∠A$$ $$+ ∠B$$ $$+ ∠C$$ $$+ ∠D$$ $$= 360°$$.

Thus, the sum of the angles of a quadrilateral is $$360°$$.


text:
## KMP

m is the length of text
n is the length of pattern

• [Prefix Array Logic]
• 初始j指向0索引，i指向1索引
• 数组0索引初始化为0
• 检查匹配
• 不匹配时，跳到j索引的前一个数组值所对应的索引位置继续检查匹配
• 不匹配时，j=Array[j-1]
• 若j是0，数组值为0，Array[i]=0
• 匹配时，数组中的值为j的值加1，i和j同时加1继续检查匹配
• Array[i]=j+1, i++, j++

## 算法设计与分析笔记0x10 —— Extending the Limits of Tractability

Must sacrifice one of three desired features.

• Solve problem to optimality.
• Solve problem in polynomial time.
• Solve arbitrary instances of the problem.

## 算法设计与分析笔记0x0F —— PSPACE

P Decision problems solvable in polynomial time.
PSPACE Decision problems solvable in polynomial space.

• P PSPACE
• 3-SAT is in PSPACE
• NP PSPACE

## Partitioning Problems

### 3-Dimensional Matching

3D-MATCHING. Given n instructors, n courses, and n times, and a list of the possible courses and times each instructor is willing to teach, is it possible to make an assignment so that all courses are taught at different times?
3D-MATCHING. Given disjoint sets X, Y, and Z, each of size n and a set T X × Y × Z of triples, does there exist a set of n triples in T such that each element of X Y Z is in exactly one of these triples?

## 算法设计与分析笔记0x0C —— Part 1 NP完全

Algorithm design patterns.

• Greedy.
• Divide-and-conquer.
• Dynamic programming.
• Max-flow min-cut.
• Reductions.

Algorithm design anti-patterns.

• NP-completeness.
• PSPACE-completeness.
• Undecidability.

## 数据排序

• .sort_index()方法在指定轴上根据索引进行排序，默认升序
• .sort_index(axis=0, ascending=True)
• For DataFrame, first argument is some index or columns by which data is sorted.
• NaN统一放在排序末尾

## Pandas库介绍

• Python第三方库，基于Numpy，提供高性能易用数据类型和分析工具
• import pandas as pd


text:
# Typesetting a double Over Dot on top of a symbol

I wanted to make a notation with a double dot over a symbol in Mathematica. Searching online or in the documentation did not yield any results. However, just randomly attempting to give a second parameter to the OverDot function surprisingly did exactly what I needed:

I assume the red font suggests that Mathematica perceives this as a syntax mistake at some level, even though the output is as desired. Unfortunately, this does not work for three dots and more.

Is there a proper way to do this without red font appearing?

• {Overscript[x, ".."], Overscript[x, "..."], Overscript[x, "\[Ellipsis]"]} – Bob Hanlon Apr 9 at 1:35
• The code editor and documentation are not always completely in sync with the actual typesetting. This is only one of several examples. Ignore the code coloring. – m_goldberg Apr 9 at 2:35
• @BobHanlon as a German speaker I perceive your Overscript[x, ".."] Umlaut to be very improperly typeset. Overscript[x, "¨"] is bad as well. They work, yes; but not for publication. Cheers! – Roman Apr 9 at 9:43
• @Roman Why not just literally use the German character set for that? The double dot over a symbol has e.g. the meaning of a second time derivative in Physics -- which is typeset properly. – Kagaratsch Apr 9 at 12:37
• For Umlaut characters you only get äëïöüÿ from the font set but not the others. That wasn't my point though. All I'm saying is that the size of the dots and their distance must be appropriate for the chosen font, otherwise it looks very bad for a native speaker of German, Turkish, Swedish, French, etc. If you don't care about the aesthetics, then all the given solutions work, sure. – Roman Apr 9 at 13:46

Use ToBoxes to find the boxes generated for OverDot[x, 2]:

OverDot[x,2] //ToBoxes

OverscriptBox["x", "¨"]

You can reproduce these boxes using Overscript:

Overscript[x, RawBoxes @ "¨"]

You can use the same approach for triple dots:

Overscript[x, RawBoxes @ "\[TripleDot]"]

For more dots, you will have to use a different mechanism to generate the dots, e.g.:

Overscript[x, Style[Row[{".",".",".","."}],FontTracking->"Condensed"]]

Update

You could also overload OverDot to work with the 3 and higher versions (I also included @Michael's syntax information fix):

SyntaxInformation[OverDot] = {"ArgumentsPattern" -> {_, _.}};
MakeBoxes[OverDot[a_, n_Integer?(GreaterThan[2])], StandardForm] := If[n==3,
OverscriptBox[MakeBoxes[a], "\[TripleDot]"],
OverscriptBox[
MakeBoxes[a],
ToBoxes @ Style[Row[ConstantArray[".", n]], FontTracking->"Condensed"]
]
]

Then:

You could fix the syntax highlighting, or ignore it. Here's a fix:

SyntaxInformation[OverDot] = {"ArgumentsPattern" -> {_, _.}};

Go to the Basic math assistant palette and click on the template.

• There indeed is a [DoubleDot] template, but it actually leads to an expression with the FullForm OverDot[X,2]! So the syntax is in fact intended, then I'm confused why Mathematica marks it in red font when typed in directly? – Kagaratsch Apr 9 at 1:13
• Yes... confusing. The documentation for OverDot shows only one argument... so the $2$ is somehow treated extraneously. (Perhaps a bug report is in order.) – David G. Stork Apr 9 at 1:21


text:
# Configuring LDAPS (LDAP via SSL) for CRN/IBM COGNOS BI

## Problem

When configuring IBM Cognos BI to communicate with an LDAP server by LDAPS (LDAP via SSL) you have to provide an [SSL Certificate Database. What is an SSL Certificate Database] and where to get it?

## Resolving The Problem

The SSL Certificate Database IBM Cognos BI expects is in fact an Netscape Security Services (NSS) certificate database. This database consists of two proprietary Netscape format files which must be located in the same folder and should be perceived as a single entity. The first file is called cert7.db or cert8.db, the second file is called key3.db. To create the certificate database files a tool from the NSS toolkit is needed called certutil. Recent versions of certutil (NSS 3.6+) no longer create cert7.db files, but only the successor cert8.db.

As of version 10 IBM Cognos BI does support both formats. cert8.db files and cert7.db files. However previous versions of IBM Cognos BI don't support cert8.db files and explicitly require a cert7.db file.
This implies using different versions of the NSS toolkit and it's certutil depending on the version of IBM Cognos BI.

Obtain the NSS toolkit
• For IBM Cognos BI version 8 and prior...
...one has to use a legacy version of NSS, the build 3.4.2. However there is an apparent issue with this version when dealing with CA certificates (trust is not established if only CA certificate is provided in the database) so that as of now the only eligible version of NSS which delivers a working cert7.db is NSS 3.3.2. (refer to Related Documents section for download link)
The package requires some underlying base libraries (NSPR v4.1.2) as well (again download link in Related Documents section)
In both locations select the sub-folder representing your Operating System (WINNT is suitable for all Windows versions) and choose the "OPT.OBJ" folder. Download the ZIP file.

• For IBM Cognos 10...
Select the sub-folder representing your Operating System (msvc9 is suitable for all Windows versions) and choose the "OPT.OBJ" folder. Download the ZIP file.

Install the certutil tool:

• unzip each downloaded file into a separate folder, like the NSPR ZIP to <NSPR_PATH> and the NSS ZIP file to <NSS_PATH>.
Each folder will contain subdirectories /bin, /inculde and /lib.
The certutil executable is located in the /bin subdirectory of the <NSS_PATH> folder.
• One must add the NSS and NSPR libs to the environment so certutil can pick them up.
This is achieved by adding can be achieved by either
• copying the contents of the NSPR and NSS folders' /lib subfolders into the NSS folder's /bin subfolder
• or
• adding NSPR and NSS folder's /lib subfolder to the library path for your system
Example on Windows: open a shell, cd to the folder you unpacked NSS into and cd then into the /bin subfolder, type SET PATH=<NSPR_PATH>/lib;<NSS_PATH>/lib;%PATH% , hit return,
now call certuil by entering certutil and press return.
• The actual steps may vary depending on where the ZIP files have been unzipped to and platform, the point is to make available the contents of BOTH /lib directories to the system.
Create Keystore

IBM Cognos BI can establish trust to a presented server certificate for LDAPS connection based on either the server certificate importet as a valid signer certificate or the root CA certificate which signed the server certificate.
It's a common and proven practice to use the CA root certificate, so this is preferable. If you should choose to fo forward with the server certificate though, it is sufficient to import the server certificate only, you don't necessarily have to import the CA certificate as well.

Steps:
1. Aquire the certificate(s) to use in Base-64 encoded X.509 (PEM) format.
To ease reading it is assumed they were saved asserver.cert or CA.cert.

You can try getting the server certificate easily by accessing the LDAP using a browser by HTTPS at the LDAPS port (usually 636). Example: https://myldapserver:636.
Once the browser prompts to accept or inspect the certificate, select to inspect it and save it to a file from there. This works for Internet Explorer and Mozilla/Netscape. However, it may not work for all LDAP servers as they prevent https connections

Another possibility is to use OpenSSL's s_client modus to simulate a client and retrieve the certificate like:
openssl s_client -connect host:port -showcerts
This will print out all the certificates the server presents (server + CA) to the console where you can obtain them by copy & paste.

Or the most straight forward approach, ask the LDAP server administrator for the certificate.

2. Create a subdirectory to hold the certificate database which will be created in the next steps, for example "mykeys".

3. Create a new NSS certificate database by issuing:

certutil -N -d <cert_directory>
example: certutil -N -d C:\path\to\mykeys
This will create a cert7.db or cert8.db file and a key3.db file in the directory created in 2.
Those consitute the certificate database and hence the subdirectory should be treated as a single entity, always keep these files in one single directory.

4. Add the certificate you want to use to the new certificate database:
• For a server cert issue:

certutil -A -n <cert_name> -d <cert_directory> -i <certificate_file> -t P

Example: certutil -A -n MyServer -d c:\path\to\mykeys -i server.cert -t P

• For a CA cert issue:

certutil -A -n <cert_name> -d <cert_directory> -i <certificate_file> -t C,C,C

Example: certutil -A -n MyCA -d c:\path\to\mykeys -i CA.cert -t C,C,C

where

<cert_name>
is an arbitrary name you assign to the certificate in the certificate database as an alias. Using the CA name or NetBIOS hostname is a good practice.

<cert_directory>
specifies the subdirectory for the certificate database to use.
Certutil will have created a cert7.db/cert8.db (& key3.db) in this location in step 3.

5. Verify the certificate import
To verify the import was successful and the trust option is correct, issuecertutil -L -d mykeys An Example output that has both a Server certificate and a Root CA certificate correctly installed will look like this:
 Certificate Name Trust Attributes ldap1.myserver.com P,, My Root CA C,C,C p Valid peer P Trusted peer (implies p) c Valid CA T Trusted CA to issue client certs (implies c) C Trusted CA to certs(only server certs for ssl) (implies c) u User cert w Send warning

Complete the setup in Cognos Configuration
Provide the absolute path to the cert7.db/cert8.db file (ie: c:\path\to\mykeys\cert7.db) for the SSL Certificate Database property in Cognos Configuration. Dont forget to adjust the port to the LDAPS port, usually 636.
You can now right-click and test the LDAP namespace at this time. If the SSL connection can be established successfully the test will succeed

Save configuration and restart the Cognos product for the changes to take effect.

## Internal Use Only

Total SRs: 34 References: 11-44587931 11-46242531 11-52588241 11-66335271 11-72060931 1192874 1200001 1218144 1224849 1227291 2257549 2340721 2343655 2349536 2353484 2376839 2385998 3177544 3217192 3327650 3340422 3346569 3349093 3356038 3358163 3364632 3380516 3399772 3403156 3427675 3433146 3433407 3436238 3441015


text:
In mathematics, a linked field is a field for which the quadratic forms attached to quaternion algebras have a common property.

## Contents

Let F be a field of characteristic not equal to 2. Let A = (a1,a2) and B = (b1,b2) be quaternion algebras over F. The algebras A and B are linked quaternion algebras over F if there is x in F such that A is equivalent to (x,y) and B is equivalent to (x,z).[1]

The Albert form for A, B is

${\displaystyle q=\left\langle {-a_{1},-a_{2},a_{1}a_{2},b_{1},b_{2},-b_{1}b_{2}}\right\rangle \ .}$

It can be regarded as the difference in the Witt ring of the ternary forms attached to the imaginary subspaces of A and B.[2] The quaternion algebras are linked if and only if the Albert form is isotropic.[3]

The field F is linked if any two quaternion algebras over F are linked.[4] Every global and local field is linked since all quadratic forms of dgree 6 over such fields are isotropic.

The following properties of F are equivalent:[5]

A nonreal linked field has u-invariant equal to 1,2,4 or 8.[6]

## References

1. ^ Lam (2005) p.69
2. ^ Knus, Max-Albert (1991). Quadratic and Hermitian forms over rings. Grundlehren der Mathematischen Wissenschaften 294. Berlin etc.: Springer-Verlag. p. 192. ISBN 3-540-52117-8. Zbl 0756.11008.
3. ^ Lam (2005) p.70
4. ^ Lam (2005) p.370
5. ^ Lam (2005) p.342
6. ^ Lam (2005) p.406


text:
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# Greta’s salary was x thousand dollars per year, then she rec

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Greta’s salary was x thousand dollars per year, then she rec [#permalink]  10 Jun 2018, 03:52
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Question Stats:

36% (00:42) correct 63% (01:37) wrong based on 11 sessions
Greta’s salary was $$x$$ thousand dollars per year, then she received a $$y%$$ raise. Annika’s salary was $$y$$ thousand dollars per year, then she received an $$x%$$ raise. $$x$$ and $$y$$ are positive integers.

 Quantity A Quantity B The dollar amount of Greta’s raise The dollar amount of Annika’s raise

A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA

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Joined: 07 Jun 2014
Posts: 4749
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Kudos [?]: 1650 [0], given: 396

Re: Greta’s salary was x thousand dollars per year, then she rec [#permalink]  13 Jun 2018, 16:32
Expert's post
Explanation

Because the problem never indicates real values, pick your own smart numbers. If x = 100 and y = 50, then:

Greta’s salary was $100,000 and she received a 50% raise. Greta’s raise, therefore, was$50,000.

Annika’s salary was $50,000 and she received a 100% raise. Annika’s raise, therefore, was$50,000.

The two quantities are equal. This holds true for any positive numbers chosen for x and y, because x percent of y = y percent of x. Thus, any two numbers can be used—just as 50% of 100 = 100% of 50, it is also true that 1% of 2,000 = 2,000% of 1, or a% of b = b% of a.

Hence option C
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Re: Greta’s salary was x thousand dollars per year, then she rec [#permalink]  13 Jun 2018, 17:50
x, y >= 1, integer
Quantity A = xy%
Quantity B = yx%
--> A = B

Keys: C
Re: Greta’s salary was x thousand dollars per year, then she rec   [#permalink] 13 Jun 2018, 17:50
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# MacLaurin Series And Laplace Transforms : Absolute Convergence

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This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

Find MacLaurin Series for the given function f. Use the linearity of the Laplace Transform to obtain a series representation L(f)=F(s)
Determine 5 values for which the series converges absolutley (and uniformly).
Also show the Laplace transform exists, i.e. that it has exponential order alpha.
Here are the functions.

A) f(t)=cosh (bt)
B) f(t)=cos (bt)
C) f(t)=t sin (bt)
D) f(t)=sinh (t)
_______
t

https://brainmass.com/math/real-analysis/maclaurin-series-laplace-transforms-absolute-convergence-9688

#### Solution Preview

Please see the attached file for the full solution.

Thanks for using BrainMass.

Find MacLaurin Series for the given function f. Use the linearity of the Laplace Transform to obtain a series representation L(f)=F(s)
Determine 5 values for which the series converges absolutley (and uniformly).
Also show the Laplace transform exists, i.e. that it has exponential order alpha.
Here are the functions. If it is too much work to solve all of them given the number of credit, I have given, then please solve as many as you can and hopefully I can figure out the others.
A) f(t)=cosh (bt)
B) f(t)=cos (bt)
C) f(t)=t sin (bt)
D) f(t)=sinh (t)

Solution.

A) f(t)=cosh (bt)=

We know that , so
and
So,

...............................................................................................(1)

So, the MacLaurin Series for is above (1)

Now ...

#### Solution Summary

MacLaurin series And Laplace transforms are used to define values for which functions converge absolutely.

\$2.49


text:
# Talk:Cauchy Condensation Test

If all the terms $a_n$ are positive, then why is the sequence of partial sums decreasing... It appears that the pictures need to be redrawn (with the dotted line more like the square root function). --Lord_Farin 12:33, 20 February 2012 (EST)

Sorry, the dotted line is a graph of $a_n$, not $\sum a_n$. I tried to fix every instance of my mistake, please double check. --GFauxPas 12:39, 20 February 2012 (EST)
I think the best way to look at the geometric proof is to view the series as a sum of each term in the sequence times one, so you get lots of rectangles of width one that are smaller than the rectangles of the condensed sequence.. If I actually drew that it would be too hard to read the diagram, but now that I think about it it's not that obvious from the current presentation. Suggestions? --GFauxPas 12:59, 20 February 2012 (EST)
I get it; I think that's cleared now. Minor suggestion would be to use the letter $a$ instead of $f$, as to avoid possible confusion on what it means. --Lord_Farin 13:03, 20 February 2012 (EST)
I considered that, but I wasn't sure if $a_{2^n}$ was readable enough. Or perhaps you mean $a\left({2^n}\right)$? --GFauxPas 13:04, 20 February 2012 (EST)
The latter. I understood you did it for readability indeed. --Lord_Farin 13:08, 20 February 2012 (EST)
I edited the proof to explicitly tell the reader about the implied rectangles with width 1. If you can think of a way to make it clearer, please do so. --GFauxPas 13:16, 20 February 2012 (EST)

I don't think it's worth bothering with Rule of Assumption outside of the field of basic propositional logic. What does anyone else think? --prime mover 15:43, 23 February 2012 (EST)

That seems reasonable, it's being used all the time in proofs implicitly anyway. --GFauxPas 16:00, 23 February 2012 (EST)

## Links to group theoretical results

The link to Powers of Group Elements seems out of place here. A student of analysis need not be bothered with the details of abstract algebraical matters for something as mundane as powers of two. I'm fairly sure there is some basic arithmetical result that could be linked to - if not, there need to be one. Failing that, leaving it blank works for me in this particular context. --prime mover (talk) 14:57, 15 February 2013 (UTC)

Reasonable. --GFauxPas (talk) 15:09, 15 February 2013 (UTC)


text:
# Solve the Equation sin 2x+ sqrt(3)cos 2x=1

Solve the Equation
$\mathrm{sin}2x+\sqrt{3}\mathrm{cos}2x=1$
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Theodore Dyer
$\mathrm{sin}2x+\sqrt{3}\mathrm{cos}2x-1=0$
$2\mathrm{sin}x\ast \mathrm{cos}x+\sqrt{3}{\mathrm{cos}}^{2}x-\sqrt{3}{\mathrm{sin}}^{2}x-{\mathrm{sin}}^{2}x-{\mathrm{cos}}^{2}x=0$
$\frac{2\mathrm{sin}x\ast \mathrm{cos}x}{{\mathrm{cos}}^{2}x}+\sqrt{3}\frac{{\mathrm{cos}}^{2}x}{{\mathrm{cos}}^{2}x}-\sqrt{3}\frac{{\mathrm{sin}}^{2}x}{{\mathrm{cos}}^{2}x}-\frac{{\mathrm{sin}}^{2}x}{{\mathrm{cos}}^{2}x}-\frac{{\mathrm{cos}}^{2}x}{{\mathrm{cos}}^{2}x}=0$
$2tgx+\sqrt{3}-\sqrt{3}t{g}^{2}x-t{g}^{2}x-1=0$
$\sqrt{3}t{g}^{2}x+t{g}^{2}x-2tgx+1-\sqrt{3}$
$t{g}^{2}x\left(\sqrt{3}+1\right)-2tgx+\left(1-\sqrt{3}\right)=0$
$tgx=0$
${t}^{2}\left(\sqrt{3}+1\right)-2t+\left(1-\sqrt{3}\right)=0$
$D=4-4\ast \left(1+\sqrt{3}\right)\left(1-\sqrt{3}\right)=4-4\ast \left(1-3\right)=4+8=12$
$\sqrt{D}=\sqrt{12}=2\sqrt{3}$
${t}_{1}=\frac{2+2\sqrt{3}}{2\left(\sqrt{3}+1\right)}=1$
${t}_{2}=\frac{2-2\sqrt{3}}{2\left(\sqrt{3}+1\right)}=\frac{2\left(1-\sqrt{3}\right)}{2\left(1+\sqrt{3}\right)}=\frac{\left(1-\sqrt{3}\right)\left(1-\sqrt{3}\right)}{\left(1+\sqrt{3}\right)\left(1-\sqrt{3}\right)}=\frac{\left(1-\sqrt{3}{\right)}^{2}}{1-3}=$
$=\frac{1-2\sqrt{3}+3}{-2}=\frac{4-2\sqrt{3}}{-2}=\sqrt{3}-2$
$tgx=1$
$x=\frac{\pi }{4}+\pi \ast n$
$tgx=\sqrt{3}-2$
$x=arctg\left(\sqrt{3}-2\right)+\pi \ast k$

Bordenauaa
$\mathrm{sin}2x+\sqrt{3}\mathrm{cos}2x=1$
$R=\sqrt{\left(1{\right)}^{2}+\left(\sqrt{3}{\right)}^{2}}=\sqrt{4}=2$
$\frac{1}{2}\mathrm{sin}2x+\frac{\sqrt{3}}{2}\mathrm{cos}2x=\frac{1}{2}$
$\mathrm{cos}\frac{\pi }{6}\ast \mathrm{sin}2x+\mathrm{sin}\frac{\pi }{6}\ast \mathrm{cos}2x=\frac{1}{2}$
$\mathrm{sin}\left(\frac{\pi }{6}+2x\right)=\frac{1}{2}$
$\frac{\pi }{6}+2x=\left(-1{\right)}^{n}\ast \frac{\pi }{6}+\pi \ast n$
$x=\left(-1{\right)}^{n}\ast \frac{\pi }{12}+\frac{\pi \ast n}{2}-\frac{\pi }{12}$


text:
# [pdftex] pdf objects with references to each other?

Heiko Oberdiek oberdiek at ruf.uni-freiburg.de
Sat Mar 30 02:14:28 CET 2002

On Sat, 30 Mar 2002, Robert Howlett wrote:

>   \pdfannot width 12 cm height 2 cm depth 10 pt
>   {/Subtype /Popup
>   /T (Algebra 1)
>   /Open false
>   /C [0 1 1]
>   /Contents
>   (Lectures given at the University of Sydney for the course
>   Math3902.)}
>   \pdfannot height 2 cm depth 10 pt
>   {/Subtype /Text
>   /C [0 1 1]
>   /Popup \the\pdflastannot\space 0 R}%
>
> i.e. the T and Contents entries go into the popup
> instead of the text annotation itself.
> What I would have liked to do is have the T and Contents
> entries in the dictionary of the text annotation and
> put a Parent key in the dictionary of the popup referring
> back to the text annotation. However, this means having
> entries in the dictionaries of each text annotation
> and the popup annotation referring to the other.
> I can't figure out a way to do this with pdftex.
> It seems to me that I need to be able to tell pdftex to
> choose some number that has not yet been used
> for an object, create an indirect reference to a
> yet-to-be-constructed object with that number, and then
> later make an object with that number.
> Can this be done?

You can use a pdf object without referencing:

\setbox0=\hbox{Click}
\edef\APNrule{width\the\wd0 height\the\ht0 depth\the\dp0}
\immediate\pdfxform0
\edef\APNobj{\the\pdflastxform}

\pdfobj{}%
\pdfannot ... {%
/Subtype/Popup%
/Parent \the\numexpr\pdflastobj+2\relax\space 0 R%
/Open false%
/C[0 1 1]%
}%
\pdfannot\APNrule{%
/Subtype/Text%
/Popup \the\pdflastannot\space 0 R%
/C[0 1 1]%
/T(...)%
/Contents(...)%
/AP<</N \APNobj\space 0 R>>%
}

Without e-TeX: \pdflastobj has to be stored in a counter
register after \pdfobj{} and the register is then
incremented by 2 and is used in the next \pdfannot command


text:
#### Vol. 2, No. 4, 2020

 Recent Issues Volume 4, Issue 1 Volume 3, Issue 4 Volume 3, Issue 3 Volume 3, Issue 2 Volume 3, Issue 1 Volume 2, Issue 4 Volume 2, Issue 4 Volume 2, Issue 3 Volume 2, Issue 2 Volume 2, Issue 1 Volume 1, Issue 4 Volume 1, Issue 3 Volume 1, Issue 2 Volume 1, Issue 1
 The Journal About the Journal Editorial Board Subscriptions Submission Guidelines Submission Form Policies for Authors Ethics Statement ISSN (electronic): 2578-5885 ISSN (print): 2578-5893 Author Index To Appear Other MSP Journals
Semiclassical resolvent estimates for Hölder potentials

### Georgi Vodev

Vol. 2 (2020), No. 4, 841–860
##### Abstract

We first prove semiclassical resolvent estimates for the Schrödinger operator in ${ℝ}^{d}$, $d\ge 3$, with real-valued potentials which are Hölder with respect to the radial variable. Then we extend these resolvent estimates to exterior domains in ${ℝ}^{d}$, $d\ge 2$, and real-valued potentials which are Hölder with respect to the space variable. As an application, we obtain the rate of the decay of the local energy of the solutions to the wave equation with a refraction index which may be Hölder, Lipschitz or just ${L}^{\infty }$.

##### Keywords
Schrödinger operator, resolvent estimates, Hölder potentials
Primary: 35P25


text:
54 Answered Questions for the topic Number Theory

#### Math number theory

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a,b,c are positive real numbersabc=1prove that (a / a+b⁴+c⁴) + (b / a⁴+b+c⁴) + (c / a⁴+b⁴+c)＜=1

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#### Why is 2 a controversial number?

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If 1 = sa + tb, where a, b, st ∈ Z, explain why gcd(a, b) = 1.
1 3

## Still looking for help? Get the right answer, fast.

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text:
# Challenging! Find maximum deceleration and speed (not max)

1. Dec 18, 2013

### mia2

1. The problem statement, all variables and given/known data
Given $$\frac{d^2s}{dt^2}=-Ae^{s/B}\biggl(\frac{ds}{dt}\biggr)^2$$ Show that maximum deceleration (where $A,B$ are constants, $v=v_0$, and $s=-\infty$) is $\frac{v_0^2}{2eB}$.

Use the substitution $v=\frac{ds}{dt}$.

2. Relevant equations
See above.

3. The attempt at a solution
Using the substitution, I get $\frac{d^2s}{dt^2}=-Ae^{s/B}(v)^2$. Furthermore, using $v=v_0$ and $s=-\infty$ and using the original function, I get $v=e^{-ABe^{s/B}}v_0$. Combining these two equations, I get
$$\frac{d^2s}{dt^2}=-Ae^{(s/B)-(2ABe^{s/B})}v_0^2$$.
With $s=-\infty$, I end up with:
$$\frac{-Av_0^2}{e^{2AB}}$$, which isn't what's given in the problem. Not sure what I'm doing wrong.

Last edited: Dec 18, 2013
2. Dec 18, 2013

### SteamKing

Staff Emeritus
Your Latex came out garbled. Try hitting the Preview button before you post to make sure everything formats properly.

3. Dec 18, 2013

### mia2

Ok, I've fixed it now. Do you have any suggestions for my physics problem?

4. Dec 19, 2013

### Saitama

Why do you think acceleration is maximum at $s=-\infty$? I don't see how you can find a maximum only by inspection. You will have to differentiate the acceleration function and set the derivative to zero.


text:
# Convergent series

• February 27th 2013, 08:06 AM
raggie29
Convergent series
Using series tests such as the ratio test, alternating test, limit comparison test etc determine whther the following series is convergent:

Attachment 27278
• February 27th 2013, 08:16 AM
Plato
Re: Convergent series
Quote:

Originally Posted by raggie29
Using series tests such as the ratio test, alternating test, limit comparison test etc determine whther the following series is convergent:

Attachment 27278

Use limit comparison with $\frac{1}{n}.$


text:
# Prime Values of Double Factorial plus 1

## Theorem

Let $n!!$ denote the double factorial function.

The sequence of positive integers $n$ such that $n!! + 1$ is prime begins:

$0, 1, 2, 518, 33 \, 416, 37 \, 310, 52 \, 608, 123 \, 998, 220 \, 502, \ldots$

## Proof

We have that:

 $\displaystyle 0!! + 1$ $=$ $\displaystyle 1 + 1$ Definition of Double Factorial $\displaystyle$ $=$ $\displaystyle 2$ which is prime

 $\displaystyle 1!! + 1$ $=$ $\displaystyle 1 + 1$ Definition of Double Factorial $\displaystyle$ $=$ $\displaystyle 2$ which is prime

 $\displaystyle 2!! + 1$ $=$ $\displaystyle 2 \times 0!! + 1$ Definition of Double Factorial $\displaystyle$ $=$ $\displaystyle 2 \times 1 + 1$ Definition of Double Factorial $\displaystyle$ $=$ $\displaystyle 3$ which is prime

## Historical Note

According to 1997: David Wells: Curious and Interesting Numbers (2nd ed.), this result is reported in Volume $26$ of Mathematical Spectrum, but it has not proved possible to confirm this by checking it directly.


text:
# Conditional Expression Functions¶

Conditional expression functions return values based on logical operations using each expression passed to the function. For example, the BOOLOR function takes two numeric expressions and returns True if either (or both) of the expressions evaluate to a True (non-zero) value.