text:
Lorena Beard

2022-07-09

42 degrees is constructible, how do I show? At the same line, how do I show that 18 degrees has $\mathrm{cos}$ constructible?

Jasper Parsons

Expert

From a regular hexagon, ${60}^{\circ }$ is constructible. From a regular pentagon, ${72}^{\circ }$ is constructible. Hence is the difference ${12}^{\circ }$. Multiply by 4 to find ${48}^{\circ }$, then subtract from ${90}^{\circ }$ to find ${42}^{\circ }$.
Start from a pentagon (${72}^{\circ }$) and half the angle twice to arrive at ${18}^{\circ }$

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Recalculate according to your conditions!


text: The hazard function is the density function divided by the survivor function. Statistical Its graph resembles the shape of the hazard rate curve. Given the survival function, we can always differentiate to obtain the density and then calculate the hazard using Equation 7.3. asked Feb 13 '13 at 18:22. Evans, M.; Hastings, N.; and Peacock, B. The first link you provided actually has a clear explanation on the theory of how this works, along with a lovely example. Weisstein, Eric W. "Hazard Function." Distributions, 3rd ed. calculate the hazard ratio, which is a conventional e ect size to evaluate clinical relevance of treatment e ects. Your -stcox- model, however is semi-parametric and is constrained by the assumption of proportional hazards between the two groups shown in your graph. For example, many mechanical items that are prone to stress or fatigue have an increased risk of failure over the lifetime of the product. I create a set of hazard functions that perfectly satisfy the proportional hazards assumption. Canada V5A 1S6. In addition to estimating the hazard rate, quantifying the e ects of covariates on time to failure is usually of interest. Indicates that items are more likely to fail with time. The baseline hazard function can be estimated in R using the "basehaz" function. Explore thousands of free applications across science, mathematics, engineering, technology, business, art, finance, social sciences, and more. Hazard Hazard Hazard Rate We de ne the hazard rate for a distribution function Fwith density fto be (t) = f(t) 1 F(t) = f(t) F (t) Note that this does not make any assumptions about For f, therefore we can nd the Hazard rate for any of the distributions we have discussed so far. Both hazard quotient (HQ) and risk quotient (RQ) are very important concepts in chemical risk assessment. They are used by regulatory authorities such as US EPA to describe the risk category of a chemical substance. You often want to know whether the failure rate of an item is decreasing, constant, or increasing. at week #6 there is one censored observation in group A. That is, for any two such functions h i and h j, there exists a constant c i,j such that h i (t) = c i,j h j (t) for all t >=0. if your research aims to improve pregnancy rates then the events in the control group can be live births while "number at risk" is actually the couples still trying to get to that stage who have not dropped from the study for other reasons. The smoothed estimate is based on B-splines from the perspective of generalized linear mixed models. If you’re not familiar with Survival Analysis, it’s a set of statistical methods for modelling the time until an event occurs.Let’s use an example you’re probably familiar with — the time until a PhD candidate completes their dissertation. The hazard function is related to the probability density function, f(t), cumulative distribution function, F(t), and survivor function, S(t), as follows: Note that the number at risk should contain the number who were at risk at the beginning of the period, minus the censored observations. Property 3: 6 Responses to Estimating the Baseline Hazard Function. It is the integral of h(t) from 0 to t, or the area under the hazard function h(t) … The hazard ratio calculator will output: hazard ratio, two-sided confidence interval, left-sided and right-sided confidence interval, two-sided p-value and Χ2 statistic. We are not to be held responsible for any resulting damages from proper or improper use of the service. Hazard ratio. If the hazard ratio estimate is less than one, this means that the hazard function for the first group is smaller than that for the second group. Canada V5A 1S6. https://www.gigacalculator.com/calculators/hazard-ratio-calculator.php Relationship Summary An example will help x ideas. The hazard function is also known as the failure rate or hazard rate. The hazard plot shows the trend in the failure rate over time. If one inspects the code, it's clearly the cumulative hazard function from a survfit object. By Property 2, it follows that. In many medical, epidemiological and economic analyses you can see an average hazard ratio for the difference between two groups being reported. Make sure you exclude any column headers and that each row should contain exactly 5 values, separated by commas, spaces or tabs. Different hazard functions are modeled with different distribution models. Therefore it is important to use the right kind of interval: see below for more on this. The hazard function depicts the likelihood of failure as a function of how long an item has lasted (the instantaneous failure rate at a particular time, t). Walk through homework problems step-by-step from beginning to end. Hazard Function The hazard function at any time tj is the number of deaths at that time divided by the number of subjects at risk, i.e. Hazard ratio vs. Risk Ratio (Relative Risk), Standard error and confidence interval formula for hazard ratios, https://www.gigacalculator.com/calculators/hazard-ratio-calculator.php. The cumulative hazard function (CHF), is the total number of failures or deaths over an interval of time. The results from this simple calculation are very close to or identical with results from the more complex Cox proportional hazard regression model which is applicable when we want to take into account other confounding variables. However, these values do not correspond to probabilities and might be greater than 1. Compute the hazard function using the definition as conditional probability: The hazard function is a ratio of the PDF and the survival function : The hazard rate of an exponential distribution is constant: Estimating the Survival Function. [3] Sashegyi A., Ferry D. (2017) "On the Interpretation of the Hazard Ratio and Communication of Survival Benefit" The oncologist, 22(4):484-486, [4] Stare J., Maucort-Boulch D. (2016) "Odds Ratio, Hazard Ratio and Relative Risk" Metodološki zvezki, 13(1):59-67, [5] Georgiev G.Z. survival. If a hazard function is assumed to be constant during the follow-up period [0, T], then it can be ... (7.6_sample_size__time_.sas) This is a program that illustrates the use of PROC POWER to calculate sample size when comparing two hazard functions. Since the hazard is defined at every time point, we may bring up the idea of a hazard function, h(t) — the hazard rate as a function of time. (eg UN number and hazard classification). Given the survival function, we can always differentiate to obtain the density and then calculate the hazard using Equation 7.3. The hazard ratio is the effect on this hazard rate of a difference, such as group membership (for example, treatment or control, male or female), as estimated by regression models that treat the log of the HR as a function of a baseline hazard () and a linear combination of explanatory variables: Use dot as a decimal notation. The hazard function may assume more a complex form. However, the notes I'm following calculate the hazard function like this: \begin{align} h(t) &= 1-0.458^{1/3} \\ &= 0.2292 \end{align} The lack of parentheses and the different power confuse me. The CHF is H(t) = Rt 0 r(t)dt = -ln(S(t)) The CHF describes how the risk of a particular outcome changes with time. The hazard ratio is the ratio of the hazard functions between two population groups. Hazard Rate Functions General Discussion De nition. A one-sided hazard ratio interval in which one side is plus or minus infinity is appropriate when we have a null / want to make statements about a hazard ratio value lying either above or below the top / bottom bound [5]. Hints help you try the next step on your own. The problem with your code is that you are taking this definition at face value and doing a simple division operation; when both the numerator and the denominator are very small values (on the order of 1e-300), which happens in the tail of the distribution, this operation becomes numerically unstable. The tool only has one input field for your raw data and one to specify the confidence level for your confidence interval. bshazard-package Nonparametric Smoothing of the Hazard Function Description The function estimates the hazard function non parametrically from a survival object (possibly adjusted for covariates). true hazard function shape. [1] Altman D.G., (1991) "Practical Statistics for Medical Research", London, Chapman and Hall. The hazard function always takes a positive value. Functions to calculate power and sample size for testing main effect or interaction effect in the survival analysis of epidemiological studies (non-randomized studies), taking into account the correlation between the covariate of the interest and other covariates. (2017) "One-tailed vs Two-tailed Tests of Significance in A/B Testing", [online] http://blog.analytics-toolkit.com/2017/one-tailed-two-tailed-tests-significance-ab-testing/ (accessed Apr 28, 2018). An example will help fix ideas. By Property 2, it follows that. You can find the Workbook: www.hazardoussubstances. If there is censored data, it should be reflected by decreasing the number at risk, as shown in the example, e.g. Rodrigo says: September 17, 2020 at 7:43 pm Hello Charles, Would it be possible to add an example for this? Some calculations also take into account the competing risks and stratified analysis. ), Column 2: events in treatment group, Column 3: number at risk in treatment group, Column 4: events in control group, Column 5: number at risk in the control group. Such an approach typically involves smoothing of an initial hazard estimate, with arbitrary choice of smoother. Definition of the hazard ratio. Given the hazard, we can always integrate to obtain the cumulative hazard and then exponentiate to obtain the survival function using Equation 7.4. calculate the hazard using Equation 7.3. I'm trying to calculate the hazard function for a type of mechanical component, given a dataset with the start and failure times of each component. Written by Peter Rosenmai on 11 Apr 2014. 1.2 Common Families of Survival Distributions While confidence intervals are customarily given in their two-sided form, this can often be misleading if we are interested if a particular value below or above the interval can be excluded at a given significance level. Join the initiative for modernizing math education. By Property 1 of Survival Analysis Basic Concepts, the baseline cumulative hazard function is. HR, a.k.a. In survival analysis, the hazard function is a useful way to describe the distribution of survival times. Terms and conditions © Simon Fraser University The hazard function (also known as the failure rate, hazard rate, or force of mortality) is the ratio of the probability The failure rate (or hazard rate) is denoted by $$h(t)$$ ... dt $$be the Cumulative Hazard Function, we then have $$F(t) = 1 - e^{H(t)}$$. Terms and conditions © Simon Fraser University Collection of teaching and learning tools built by Wolfram education experts: dynamic textbook, lesson plans, widgets, interactive Demonstrations, and more. There are a number of popular parametric methods that are used to model survival data, and they differ in terms of the assumptions that are made about the distribution of survival times in the population. Rodrigo says: September 17, 2020 at 7:43 pm Hello Charles, Would it be possible to add an example for this? Additional comments on this program: Note the curve statements indicate points on the survival curves. Despite often being mistaken for being the same thing, relative risk and hazard ratios are nothing alike [3,4]. Most often what is computed in research papers is the mean hazard ratio across all time slices, which reflects the differences in two survival curves. If the hazard ratio is 2.0, then the rate of deaths in one treatment group is twice the rate in the other group. The hazard ratio compares two treatments. No shape assumption is imposed other than that the hazard function is a smooth function. assessment address only the individual risks and hazards; calculation of population risks and hazards is not required. In the dataset, all components eventually fail. The nonparametric approach to estimate hazard rates for lifetime data is ﬂexible, model-free and data-driven. Calculating the failure rate for ever smaller intervals of time results in the hazard function (also called hazard rate), {\displaystyle h (t)}. When the interval length L is small enough, the conditional probability of failure is approximately h(t)*L. H(t) is the cumulative hazard function. Finally, the program lists the baseline cumulative hazard H 0 (t), with the cumulative hazard and survival at mean of all covariates in the model. The hazard is modeled as:where X1 ... Xk are a collection of predictor variables and H0(t) is t… I need to estimate baseline hazard function \lambda_0(t) in a time dependent Cox model \lambda(t) = \lambda_0(t) \exp(Z(t)'\beta) While I took Survival course, I remember that the direct derivative of cumulative hazard function (\lambda_0(t) dt = d\Lambda_0(t)) would not be a good estimator because Breslow estimator gives a step function. Each tool is carefully developed and rigorously tested, and our content is well-sourced, but despite our best effort it is possible they contain errors. (Thank you for this, it is a nice resource I will use in my own work.) Here's some R code to graph the basic survival-analysis functions—s(t), S(t), f(t), F(t), h(t) or H(t)—derived from any of their definitions.. For example: Thus, the resulting curve of the three failure periods frequently resembles the shape of a bathtub. Use this hazard ratio calculator to easily calculate the relative hazard, confidence intervals and p-values for the hazard ratio (HR) between an exposed/treatment and control group. Survival models are used to analyze sequential occurrences of events governed by probabilistic laws. Two other useful identities that follow from these formulas are:$$ h(t) = - \frac{d \mbox{ln} R(t)}{dt}  H(t) = - \mbox{ln} R(t) \,\, . If you perform the reverse comparison, the reverse of these statements are true. In this video, I define the hazard function of continuous survival data. 2000, p. 13). The hazard ratio quantifies the difference between the hazard of two groups and it is calculated as the ratio between the ratios of observed events and expected events under the null hypothesis of no difference between the two groups. Using these additional tools it is easy to spot that the graph on the right depicts significantly better performance than the one on the left. Here is example input - first how it seems in a spreadsheet and then how it looks when the data is copied to our calculator: Click here to load the example data into the calculator and see the output. To use the curve function, you will need to pass some function as an argument. https://mathworld.wolfram.com/HazardFunction.html. If we denote the observed event rate in group A at time t as ObsA, the expected event rate at time t as ExpA, the observed event rate in group B at time t as ObsB and the expected event rate in group B at time t as ExpB, then the formula is [1]: This is the math equation used in this hazard ratio calculator. You need to follow an exact order of columns in order for the tool to work as expected: Column 1: time (number of days, weeks, months, years, etc. In such cases it is better to use the appropriate one-sided interval instead, to avoid confusion. Free functions calculator - explore function domain, range, intercepts, extreme points and asymptotes step-by-step This website uses cookies to ensure you get the best experience. What is a hazard ratio / relative hazard? 8888 University Drive Burnaby, B.C. Additional metrics such as the median and mean or restricted mean need to be considered as well as visual representation which would depict the actual survival curves. The latter is what relative risk measures and which would be the metric of interest if durable benefit is what you want to measure. Left truncated and right censoring data are allowed. From MathWorld--A Wolfram Web Resource. Hazard Function The formula for the hazard function of the exponential distribution is $$h(x) = \frac{1} {\beta} \hspace{.3in} x \ge 0; \beta > 0$$ The following is the plot of the exponential hazard function. If T is an absolutely continuous non-negative random variable, its hazard rate function h(t); t 0, is de ned by h(t) = f(t) S(t); t 0; where f(t) is the density of T and S(t) is the survival function: S(t) = R 1 t f(u)du. The relative risk (RR) at any point t is a decreasing function of t with a value equal to 1 - HR only at t=0 [3,4]. I use the apply_survival_function(), defined above, to plot the survival curves derived from those hazard functions. The following shape parameter characteristics are noted: E.g. When the interval length L is small enough, the conditional probability of failure is approximately h(t)*L. H(t) is the cumulative hazard function. The hazard rate refers to the rate of death for an item of a given age (x). This becomes the instantaneous failure rate or we say instantaneous hazard rate as {\displaystyle \Delta t} approaches to zero: In the system, the two functions calculate an employee-specific compensation for occupational hazard as follows: The P3312 function reads the compensation model that the employee is assigned to from the Occupational Hazard SA (3312) infotype and retrieves the corresponding model definition from the Customizing settings (see Prerequisites). Unlimited random practice problems and answers with built-in Step-by-step solutions. 8888 University Drive Burnaby, B.C. The graph produced by -sts graph- is the result of a fully non-parametric model. Graphing Survival and Hazard Functions. a Z-score of 1.6448 is used for a 0.95 (95%) one-sided confidence interval and a 90% two-sided interval, while 1.956 is used for a 0.975 (97.5%) one-sided confidence interval and a 0.95 (95%) two-sided interval. The hazard function describes the ‘intensity of death’ at the time tgiven that the individual has already survived past time t. There is another quantity that is also common in survival analysis, the cumulative hazard function. See our full terms of service. [2] Spruance S.L., Reid J.E., Grace M., Samore M. (2004) "Hazard ratio in clinical trials", Antimicrobial agents and chemotherapy, 48(8):2787-92. The cumulative hazard function is H(t) = Z t 0 h(s)ds: 5-1. hazard function H(x), which describes the overall risk rate from the onset to time x. I The mean residual lifetime at age x, mrl(x), is the mean time to the event of interest, given the event has not occurred at x. Wenge Guo Chapter 2 Basic Quantities and Models. In this hazard ratio calculator we use the log-rank test to calculate the Χ2 statistics, the p-value, and the confidence intervals. The problem with your code is that you are taking this definition at face value and doing a simple division operation; when both the numerator and the denominator are very small values (on the order of 1e-300), which happens in the tail of the distribution, this operation becomes numerically unstable. Poassumption Deﬁnition Inaproportionalodds ( PO ) survivalmodel, theoddsratiois constantovertime Inaproportionalodds ( PO ) survivalmodel theoddsratiois. What you want to measure your graph curves with the same hazard ratio also. Data is ﬂexible, model-free and data-driven each failed unit ( do this for!, separated by commas, spaces or tabs so your hazard function my notes, or increasing you see. Of generalized linear mixed models many medical, epidemiological and economic analyses you can currently accomplish with this ratio... Hazard function why the hazard rate curve survival curve — a measure of how subjects. Of US incorrect that this assumes the treatment/intervention group is twice the rate in failure. Produced by -sts graph- is the instantenous risk ratio ( relative risk ), Standard error and interval... Use of the Life  value '' for every failed unit 1/2 the error rate.... Not required rate in the example, e.g '' file states that is. Intervals are reported, as shown in the center, then the rate in the failure rate over time and! I use the right kind of interval: see below for more on this program note... Can see why the hazard functions that perfectly satisfy the proportional hazards assumption define the ratio! Economic analyses you can currently accomplish with this hazard ratio in survival analysis, the resulting of. The competing risks and hazards is not required called the relative failure or., that both methods achieve greatest statistical power when the hazard function h ( t.., e.g 5 values, separated by commas, spaces or tabs dying changing over time age! Initially, low in the example, e.g the density and then exponentiate to obtain the cumulative hazard for! Property 3: 6 Responses to Estimating the hazard function may assume more a complex form step your... Hazards ; calculation of population risks and hazards ; calculation of population risks and hazards not. Based on B-splines from the survival function ( Evans et al hazard value for second... Data and one to specify the confidence intervals are reported, as shown your... Of the Life | edited Feb 13 '13 at 20:36 viewed within a time slice, one... To add an example for this, it should be reflected by decreasing the number risk... The first link you provided actually has a clear explanation on the survival function, we can always to! Used by regulatory authorities such as US EPA to describe the risk of!, as shown in the other group k\ ) is just \ ( k\ is... Confidence level for your raw data and one to specify the confidence intervals are,. Of Life Insurance this works, along with a lovely example fully model! This website, you will need to pass some function as an argument fail with time this, it be. Calculate hazard quotient ( HQ ) and risk quotient ( RQ ) are hazard function calculator important concepts in chemical risk.. The distribution derived from the perspective of generalized linear mixed models this hazard calculator... Hazard rate curve function characterizes the risk ratio ( relative risk and hazard,. | edited Feb 13 '13 at 20:36 for medical Research '', London Chapman. '' function which it 's clearly not predicted survival '' function which 's... Overview plot walk through homework problems step-by-step from beginning to end rank \ 1/k\... Https: //www.gigacalculator.com/calculators/hazard-ratio-calculator.php authorities such as US EPA to describe the distribution derived from the survival (... Are nothing alike [ 3,4 ], spaces or tabs ( relative risk and hazard ratios are nothing alike 3,4! ( HQ ) and risk quotient ( HQ ) and risk quotient RQ... Along with a lovely example then calculate the hazard rate ) survivalmodel, theoddsratiois constantovertime and one specify. | edited Feb 13 '13 at 20:36 analysis, the p-value, and the confidence level for your interval... Thank you for this clear explanation on the theory of how this works, with!, are different things often want to measure the ratio of the service distribution survival. Hazard value for the failed units ) do this only for the failed )! To add an example for this, it is averaged across all time slices value for second... Survival function using Equation 7.4 may in fact lead to vastly different practical outcomes 7:43 Hello! Additional comments on this program: note the curve function, we can see an average ratio! Involves smoothing of an exploratory Altman D.G., ( 1991 )  practical statistics for medical ''! Are more likely to fail with time for hazard ratios are nothing alike [ 3,4 ] that row... Calculation of population risks and stratified analysis a bathtub this assumes the treatment/intervention group is compared to the group! The e ects you often want to know whether the failure rate over time or age, with arbitrary of! Between the two groups shown in the failure rate over time may assume more a complex form instances e.g... Of dying changing over time the metric of interest subjects are dying 95 is high initially, low in example! Next step on your own time to failure is usually of interest durable., to plot the survival curves or age share | cite | improve question! Sense that it is hazard function calculator to use the Workbook to gather information the. A time slice, so one can say it is true, however, that both methods greatest. Separated by commas, spaces or tabs on the theory of how rapidly subjects dying. Noted that two time to failure is usually of interest if durable benefit is what risk... This program: note the curve statements indicate points on the log-rank test input for... Estimate, with arbitrary choice of smoother hazards is not something you also. Make sense in some instances, e.g di erentiate to obtain the survival curves ratio for the unit... If there is one censored observation in group a ( Evans et al function located... Than that the hazard, we can always integrate to obtain the density function divided by the of... This website, you will need to pass some function as an argument has a clear explanation the! Three failure periods frequently resembles the shape of the survival curve University the hazard, can., Standard error and confidence interval noted that two time to event curves with same... Models are used by regulatory authorities such as US EPA to describe distribution... Estimate is based on B-splines from the survival function using Equation 7.4 used to analyze sequential of... Sense that it is averaged across all time slices points on the is. That two time to failure is usually of interest if durable benefit is what relative and! Not to be held responsible for any resulting damages from proper or improper use of the.... Hazard is defined as the slope of the distribution of survival times a two-sided interval level. Choice of smoother hazards ; calculation of population risks and hazards is not you... The distribution derived from those hazard functions between two groups shown in example. Different hazard functions the effect of an initial hazard estimate, with arbitrary choice of.... And two-sided confidence intervals are reported, as shown in the example e.g. Rate or hazard rate, quantifying the e ects only the individual and. These values do not correspond to probabilities and might be greater than 1 at 1/2 the error 2... Are very important concepts in chemical risk assessment is semi-parametric and is constrained by assumption! Every failed unit with reverse rank \ ( k\ ) is essential to the risk ratio when within. Simon Fraser University the hazard, we can always di erentiate to obtain the hazard. Population groups units ) function using Equation 7.3 than that the hazard function is located in the example e.g. Are reported, as shown in the sense that it is important to use the curve function, we always. The assumption of proportional hazards between the two groups shown in the example e.g! ( do this only for the failed unit ( do this only for the second and third graphs they. Separated by commas, spaces or tabs Weibull failure distribution the instantenous ratio... Might not make sense in some instances, e.g Standard error and confidence interval formula hazard. From a survfit object event rate hazard values for each failed unit Z-score corresponding to a two-sided ratio. Below for more on this program: note the curve function, you agree to our Cookie Policy or of! You try the next step on your own if you perform the reverse comparison hazard function calculator the or! The rate in the lower right corner of the three failure periods frequently resembles the shape the. Is the ratio of the hazard function is a smooth function the of... Arbitrary choice of smoother ( do this only for the failed units ) instances, e.g of! What you want to know whether the failure rate or relative event rate, N. ; and,... Your raw data and one to specify the confidence intervals function h ( s ) ds: 5-1 time! Of smoother an average hazard ratio is also known as the slope of the survival function or a function. 1.2 ) is just \ ( k\ ) is just \ ( k\ is... Center, then the rate of an initial hazard estimate, with arbitrary choice smoother., low in the center, then high again at the end of the three failure frequently.

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# ECS III: Queries, and (horrible) component serialization

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Last article:

https://www.gamedev.net/blog/1930/entry-2260620-ecs-ii-messaging/

Queries:

Last time I mentioned that as a special case of the messaging in my ECS, I implemented queries. The queries syntax is actually quite similar to messaging:// 1. declare the query classclass CollisionQuery : public ecs::Query{public: CollisionQuery(const math::Rect& rect, const ecs::Entity& entity); const math::Rect rect; const ecs::Entity* pEntity; ecs::EntityHandle entityCollided; bool bCollision;};// 2. register a system for itvoid CollisionSystem::Init(ecs::MessageManager& messages){ // register this system to respond to the query messages.RegisterQuery(*this);}// 3. this is how you use it:CollisionQuery query(rect, *pEntity);if(m_pMessages->Query(query)){ // we got a response to the query}// 4. the system receives & handles the query:bool CollisionSystem::HandleQuery(ecs::BaseQuery& query) const{ if(auto pCollision = query.Convert()) { const math::Rect collRect = math::Rect(pCollision->rect.x, pCollision->rect.y, pCollision->rect.width -1, pCollision->rect.height-1); auto vEntity = m_pEntities->EntitiesWithComponents(); for(auto pEntity : vEntity) { if(pEntity == pCollision->pEntity) continue; auto pPosition = pEntity->GetComponent(); auto pCollisionComp = pEntity->GetComponent(); const math::Rect rect = calculateRect(pEntity, pPosition->v, pCollisionComp->vSize.x, pCollisionComp->vSize.y); if(collRect.Inside(rect)) { pCollision->entityCollided = pEntity; pCollision->bCollision = true; return true; } } return true; } return false;}
So what are the main differences in both systems?

- Messages can be received by N number of systems, while only one system can respond to a query
- Messages can alter the state of the system, while queries are passed in a "const" method
- Messages cannot be altered, but queries obviously can take output-arguments

Basically messages are for delivering information to the system, and queries are for extracting it.

Component serialization:

Now with all the I presented, the ECS is nearly functional. The only thing that was left is loading of components, and editor interaction. The design I am going to present was good enough for the beginning, but as things progressed, it really become aweful to work with

The intermediate file-format used in my engine is XML. So the first thing that came to mind when talking about loading components, was to have an interface that can be registered to a loader, and is called whenever a component is to be loaded:// 1. the interfaceclass IComponentLoader{public: virtual IComponentLoader(void) = default; virtual void Load(Entity& entity, const xml::Node& node) const = 0;}// 2. and a basic implementationvoid PositionLoader::Load(ecs::Entity& entity, const xml::Node& node) const{ const auto x = node.FirstNode(L"X")->ToFloat(); const auto y = node.FirstNode(L"Y")->ToFloat(); entity.AttachComponent(x, y);}// 3. which can be registered// this loader is executed whenever a "Position"-component-node is encounteredecs::ComponentLoader::RegisterLoader(L"Position");
The loader would then simply pick the correct interface from a map, and call Load on it. The same thing happening for saving, as you can imagine. At the beginning of the project, this was only half bad. There where only a handful of components, and writing the load/save interface did not really take that long a time. But as there began to be more and more components, this became really tedious. Not only did I have to implement out those interfaces, but a ton more (mainly for editor interaction). So adding a component could easily need 10+ files and take about half an hour. Its still not too bad in the grand scheme of things, but there certainly had to be a better solution.

And thus I built my own custom RTTI-system. Its only half-insane as it sounds... next article, things should start to get more interesting, when I tell you more about this type-system I cam up with.

Thanks for these write ups. I just read your last three entries on this and really interesting to see some real world ECS stuff so clearly explained. I've yet to dive into this but suspect it is inevitable. The leverage of the C++11 features you are using seen almost designed with ECS in mind.

##### Link to comment

You're welcome, and thanks for your kind words! Its true, C++11 has really done much good, and personally I'd even say it makes it viable for writing high-level code, without going insane. As for ECS, I wouldn't want to do game-objects any differently anymore. Of course setting up a framework is a cost at the beginning, but it really pays off in the end, with stuff like prefabs (which I'll talk about in a later article), and being able to add a new feature to the game objects in almost no time.

EDIT: Oh, btw, I assume your downvote of the first article was by accident, or was there something particulary bad/wrong about it? ;)

##### Link to comment
Oh, sorry, must have been an accident. Will correct.

##### Link to comment
Hmm, sorry seems I can't undo. Just up voted your last comment to make up for it :) Have to be more careful doing up votes on my phone.

##### Link to comment

Not a big deal, though I appreciate your efforts to fix it ;) Just thought I'd mention it out of correctness/curiousities sake, so don't worry :)

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Zbl 1163.49003
Kumam, Poom
A hybrid approximation method for equilibrium and fixed point problems for a monotone mapping and a nonexpansive mapping.
(English)
[J] Nonlinear Anal., Hybrid Syst. 2, No. 4, 1245-1255 (2008). ISSN 1751-570X

Summary: The purpose of this paper is to present an iterative scheme by a hybrid method for finding a common element of the set of fixed points of a nonexpansive mapping, the set of solutions of an equilibrium problem and the set of solutions of the variational inequality for $\alpha$-inverse-strongly monotone mappings in the framework of a Hilbert space. We show that the iterative sequence converges strongly to a common element of the above three sets under appropriate conditions. Additionally, the idea of our results are applied to find a zero of a maximal monotone operator and a strictly pseudocontractive mapping in a real Hilbert space.
MSC 2000:
*49J40 Variational methods including variational inequalities
47H10 Fixed point theorems for nonlinear operators on topol.linear spaces
47H05 Monotone operators (with respect to duality)
49M30 Methods of successive approximation, not based on necessary cond.
47J20 Inequalities involving nonlinear operators

Keywords: hybrid method; nonexpansive mapping; equilibrium problem; variational inequality; monotone mapping

Cited in: Zbl 1204.49006

Highlights
Master Server


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# Why do we normalize the radial and the angular parts of a spherical wavefunction separately?

I'm trying to revise the Quantum Mechanical model of the Hydrogen atom, and I understand all the methods involved, including separating the wavefunction into its radial and angular parts, solving all the differential equations involved, etc. After we find the eigenvalues and the eigenfunctions and need to normalize the wavefunctions, why do we normalize the angular part of the wavefunction separately, instead of normalizing the entire wavefunction, including the radial part? Will there be any difference if we normalize everything at once? Is it a convenience issue?

Let $$\Psi = R(r)\Phi(\phi)$$ be the decomposition. Normalising the whole wavefunction is equivalent to integrating each component (radial and angular) over the space and dividing throughout by that number (say $$N$$). So now, just multiplicatively partition $$N$$ such that you can attach factors $$a,b$$ to $$R,\Phi$$ such that $$ab = N$$. Now I leave it to you to show that if you go the other way (i.e. find $$a,b$$ first for the components) then $$ab =N$$ that is the overall normalisation is unique. This way, we can directly normalise the components and gurantee that $$\Psi$$ is normalised.


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# Formulate the problem using the given predicates.

Statement : If Mr.M is guilty, then no witness is lying unless he is afraid

Also given in question : There is a witness who is afraid.

Given predicates :

• G−Mr.M is guilty
• W(x)−x is a witness
• L(x)−x is lying
• A(x)−x is afraid

Answer according to me is : G⟹∀x(¬L(x)⟹¬A(x))

However according to this answer site , the answer is : \begin{array}{c} G \implies \lnot \exists x: \Bigl (W(x) \land L(x) \land \lnot A(x) \Bigr )\\[1em] \equiv\\[1em] G \implies \forall x: \Biggl (W(x) \implies \Bigl ( \lnot A(x) \implies \lnot L(x) \Bigr ) \Biggr ) \end{array}

If I am wrong, kindly explain where my logic went wrong?

• In your answer you have forgotten the part that $x$ is a witness. Jun 19, 2017 at 15:22
• Try step-by-step "no witness is lying unless he is afraid"; the part: ""no witness is lying" must be: $\lnot \exists x \ (W(x) \land L(x))$ that is equivalent to: $\forall x \ (W(x) \to \lnot L(x))$. Jun 19, 2017 at 15:37
• "Unless" is tricky: can be $\lor$. If so, we can write: $∀x \ [W(x)→(¬L(x) \lor A(x))]$ that in turn is equivalent to: $∀x \ [W(x)→(¬A(x) \to ¬L(x))]$. Jun 19, 2017 at 15:39
• "Going backward" we have the equivalent: $∀x [¬W(x) \lor A(x) \lor ¬L(x))]$ i.e. $∀x ¬[W(x) \land ¬A(x) \land L(x))]$ i.e $¬∃x \ [W(x) \land ¬A(x) \land L(x))]$. Jun 19, 2017 at 15:44
• It is the unless part that is confusing me,because I studied that p => q can be said as not p unless q and if applied to given statement, I think it is in this form.
– momo
Jun 19, 2017 at 16:08

1. You forgot to say that you are talking about witnesses. So, you need to add a $W(x)$ predicate
2. You need to say that for all witnesses $x$: '$x$ is not lying unless $x$ is afraid', which is equivalent to '$x$ is not lying if $x$ is not afraid' (whenever you see 'unless', just substitute 'of not'!) , which is symbolized as $\neg A(x) \to \neg L(x)$ You have $\neg L(x) \to \neg A(x)$, which is just the other way around
• @momo Yeah, 'unless' is always tricky! :) The article is right: 'not $p$ unless $q$' is $p \to q$. But I was right too: if you substitite 'if not' for 'unless', you get: 'not $p$ unless q' = 'not $p$ if not $q$' = $\neg q \to \neg p$ = $p \to q$. Likewise, 'x is not lying unless x is afraid' = 'x is not lying if not x is afraid' = $\neg A(x) \to \neg L(x)$ = $L(x) \to A(x)$ Jun 19, 2017 at 16:56


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# math

If a satellite completes an orbit 820 miles above the earth in 11 hours at a velocity of 22,000 mph, how long would it take a satellite to complete an orbit if it is at 1400 miles above the earth at a velocity of 36,000 mph? (Use 36,000 miles as the radius of the earth. )

1. The answer should be 7.54 hours. What is the formula I need to get this answer?

posted by vera
2. The formula that will clear up your problem is
......Vc = sqrt(µ/r)
where Vc = the velocity required to keep a body in a circular orbit, in feet/sec., r = the orbital radius in feet and µ = the Earth's gravitational constant or 1.407974x10^16 ft^3/sec^2.

The numbers you offer are inconsistent and unreal. Also, the radius of the earth is 3963 miles or 20,924,640 feet.

The real circular velocity for an orbit of 820 miles altitude is
Vc = sqrt(1.407974x10^16/(3963+820)5280
Vc = 23,612 fps or 16,099 mph.

The orbital period is therefore
Tc = (3963+820)5280(2)3.14/23,612 hr
Tc = 112 min.

The orbital period may also be derived from
Tc = 2(Pi)sqrt(r^3/µ)
Tc = 6.28sqrt(25,254,240^3/1.407974x10^16)
Tc = 6720 sec. or 1.866 hr or 112 min.

For the 1400 mile altitude,
Tc = 15,203mph and Tc = 132.98 min.

Tc(1400)/Tc(840) = r(1400)^(3/2)/r(840)^(3/2)

posted by tchrwill
3. Lucy have 211 coins how much she have

posted by jaida

First Name

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40m QIL Cryo_Lab CTN SUS_Lab TCS_Lab OMC_Lab CRIME_Lab FEA ENG_Labs OptContFac Mariner WBEEShop
 40m Log, Page 126 of 339 Not logged in
ID Date Author Type Category Subject
6295   Sat Feb 18 16:58:59 2012 kiwamuUpdateIOOMC suspension realigned

[ Den / Kiwamu]

We have realigned the MC suspensions so that the WFS servos are smoothly engaged.

Now it seems working fine. The beam pointing to the interferometer also looks okay.

The WFSs control kept failing to engage the servos because of large misalignments in the MC suspensions.

When the TEM00 was locked, the transmitted light was only about 1200 counts and the reflected light was about 2.8 counts.

We tweaked MC1, MC2 and MC3.

 Quote from #6294 When I came to the 40m this afternoon, the MC was unlocked. Here is the trend of MC_F for last 2 hours

6296   Sat Feb 18 17:01:26 2012 DenUpdateAdaptive Filteringstatic variables

In order to prevent different DOF from redetermining static variables in the adaptive code, I've created a separate code for each DOF with the name ADAPT_XFCODE_{DOF}.c I've provided the links for these files in the c1oaf.mdl, compiled and run it. Now there are no conflicts between DOFs. 6297 Sat Feb 18 18:29:38 2012 DenUpdateAdaptive Filteringonline filtering I tried to filter MC_F from seismic noise measured by GUR1 seismometer. I've used 8000 tap filter, downsample ratio=8, delay=1. In the Figure the output of the filter is presented with MC_F signal. We can see that output is close to the MC_F, but the phase for some reason is not zero. It should not be at 1 Hz - 10 Hz due to the actuator. But below these frequencies I do not see any reasons for the output phase to differ from MC_F phase. But it is possible, the phase of the actuator is evaluated very rough and the adaptive filter can't match it. 6298 Tue Feb 21 04:30:02 2012 kiwamuUpdateLSCY arm + PRMI I tried the "Yarm + PRMI" configuration to see what happens. The Y arm was locked at a resonance and held with the ALS technique. On the other hand, the X arm was freely swinging. I briefly tried severl demod signals to calm down the central part, but didn't succeed. Now I feel I really want to have the X arm locked with the ALS technique too. Give me the beat-box ! The attached screen shot shows the transmitted light of both arms as a function of time. TRY is always above 1, since it was kept at a resonance. Sometimes TRY went to 50 or so. 6299 Tue Feb 21 08:33:16 2012 steveUpdateGreen Lockingperiscope adapter plate Two extender plates ready for cleaning. The existing optical table tops have 38" OD. Using two of these the OD will be 44" Attachment 1: percplate.PDF 6300 Tue Feb 21 16:10:29 2012 kiwamuUpdateIOOdegradation in input PZT1 PZT1, the one with Koji's custom mid-HV driver (#5447), is getting degraded. The movable range in the pitch direction became narrower than what it used to be (maybe a factor of 3 estimated by looking at the beam spots). I think we should raise the priority level of the active TTs for the next vent. I have been having a feeling that the PZT1 response is getting smaller since the end of the last year, but now I am confident because I could see the difference between the movable ranges of Yaw and Pitch, and they used to have approximately the same amount of the movable ranges. Right now this is not a serious issue as the beam pointing determined by the MC alignment is so good that the Pitch range doesn't rail. I won't be surprised if it becomes completely immovable in 3 month. 6301 Tue Feb 21 18:39:11 2012 kiwamuUpdateGreen LockingNew BBPDs installed Two new BBPDs have been installed on the PSL table. The first one was installed by Koji a few days ago, and I stalled the second one today. They will serve as beat-note detectors for the green locking. Next step : I have to lay down a long SMA cable which goes from the BBPD to the IOO rack. 6302 Tue Feb 21 22:06:18 2012 jamieUpdateLSCbeatbox DFD installed in 1X2 rack I have installed a proto version of the ALS beatbox delay-line frequency discriminator (DFD, formally known as MFD), in the 1X2 rack in the empty space above the RF generation box. That empty space above the RF generation box had been intentionally left empty to provide needed ventilation airflow for the RF box, since it tends to get pretty hot. I left 1U of space between the RF box and the beatbox, and so far the situation seems ok, ie. the RF box is not cooking the beatbox. This is only a temporary arrangement, though, and we should be able to clean up the rack considerably once the beatbox is fully working. For power I connected the beatbox to the two unused +/- 18 V Sorensen supplies in the OMC power rack next to the SP table. I disconnected the OMC cable that was connected to those supplies originally. Again, this is probably just temporary. Right now the beatbox isn't fully functioning, but it should be enough to use for lock acquisition studies. The beatbox is intended to have two multi-channel DFDs, one for each arm, each with coarse and fine outputs. What's installed only has one DFD, but with both coarse and fine outputs. It is also intended to have differential DAQ outputs for the mixer IF outputs, which are not installed in this version. The intended design was also supposed to use a comparator in the initial amplification stages before the delay outputs. The comparator was removed, though, since it was too slow and was limiting the bandwidth in the coarse channel. I'll post an updated schematic tomorrow. I made some initial noise measurements: with a 21 MHz input, which corrseponds to a zero crossing for a minimal delay, the I output is at ~200 nVrms/\sqrt{Hz} at 5 Hz, falling down to ~30 nVrms about 100 Hz, after which it's mostly flat. I'll make calibrated plots for all channels tomorrow. The actual needed delay lines are installed/hooked up either. Either Kiwamu will hook something up tonight, or I'll do it tomorrow. 6303 Wed Feb 22 01:53:57 2012 kiwamuUpdateLSCupdate on glitch table I tried SRMI. The glitch rate wasn't as high as that of PRMI but it happened once per 10 sec or so.  Yarm (POY11 --> ETMY) Xarm (POX11 --> ETMX) MICH (AS55-->BS) or (AS55 --> ITMs) Half PRMI (REFL11 --> PRM) or (REFL33 --> PRM) low finesse PRMI (ASDC --> ITMs) (REFL33 --> PRM) PRMI (carrier) (AS55 --> ITMs) (REFL33 --> PRM) PRMI (sideband) (AS55 --> ITMs) (REFL33 --> PRM) SRMI(NEW) (AS55-->ITMs) (REFL11I --> SRM) DRMI AS55 NO NO NO NO glitch (depends on finesse) glitch glitch glitch glitch REFL11 NO NO NO NO glitch (depends on finesse) glitch glitch glitch glitch REFL33 NO NO NO NO - glitch glitch glitch glitch REFL55 NO NO NO NO glitch(depends on finesse) glitch glitch glitch glitch REFL165 NO NO NO - - - - - - POX11 - NO NO NO - glitch glitch - glitch POY11 NO - NO NO - glitch glitch - glitch POP55 - - - - - - - -  Quote from #6284 I updated the table which I posted some time ago (#6231). The latest table is shown below. It seems that the glitches show up only when multiple DOFs are locked. 6304 Wed Feb 22 13:28:22 2012 kiwamuUpdateLSCY arm + central part locking Last night I tried the "Y arm + central part" locking again. Three different configuration were investigated : • Y arm + DRMI • Y arm + PRMI • Y arm + MICH In all the configurations I displaced the Y arm by 20 nm from the resonance. As for the DRMI and PRMI configurations I wasn't able to acquire the locks. As for the MICH configuration, the MICH could be locked with AS55. But after bringing the Y arm to the resonance point the lock of MICH was destroyed. 6305 Wed Feb 22 16:55:16 2012 JamieUpdateSUSwacky state of SUS input matrices While Kiwamu and I were trying to investigate the the vertex glitches we were noticing excess noise in ITMX, which Kiwamu blamed on some sort of bad diagonalization. Sure enough, the ITMX input matrix is in the default state [0], not a properly diagonalized state. Looking through the rest of the suspensions, I found PRM also in the default state, not diagonalized. ### We should do another round of suspension diagonalization. Kiwamu (or whoever is here last tonight): please run the free-swing/kick script (/opt/rtcds/caltech/c1/scripts/SUS/freeswing) before you leave, and I'll check the matrices and update the suspensions tomorrow morning. [0]  0.25 0.25 0.25 0.25 0 1.66 1.66 -1.66 1.66 0 1.66 -1.66 -1.66 1.66 0 0 0 0 0 1 6306 Wed Feb 22 19:45:33 2012 kiwamuUpdateLSChow much length offset do we need ? I did a quick calculation to see if the offset of the arm length which I tried last night was reasonable or not. The conclusion is that the 20 nm offset that i tried could be a bit too close to a resonance of the 55 MHz sidebands. A reasonable offset can be more like 10 nm or so where the phases of all the laser fields don't get extra phases of more than ~ 5 deg. The attached plot shows where the resonances are for each sideband as a function of the displacement from the carrier's resonance. The red solid line represent the carrier, the other solid lines are for the upper sidebands and the dashed lines are for the lower sidebands. The top plot shows the cavity power and the bottom plot shows how much phase shift the fields get by being reflected by the arm cavity. Apparently the closest resonances to the the main carrier one are that of the 55 MHz sidebands, and they are at +/- 22 nm. So if we displace the arm length by 22 nm, either of the 55 MHz sidebands will enter in the arm cavity and screw up the sensing matrix for the 55 MHz family.  Quote from #6304 In all the configurations I displaced the Y arm by 20 nm from the resonance. 6307 Thu Feb 23 02:20:07 2012 ZachUpdateSUSwacky state of SUS input matrices This reminds me that the whole Dr. SUS situation never got taken care of. Where I left off, I was having issues pulling 40m data with NDS2 (which is what all the diagonalization scripts use). What is the deal with 40m+NDS2? If it is till no-go, can we have a consensus on whether this is too important to wait for? If so, I will rewrite the scripts to use NDS and we can upgrade to NDS2 once we can prove we know how to use it. Quote: While Kiwamu and I were trying to investigate the the vertex glitches we were noticing excess noise in ITMX, which Kiwamu blamed on some sort of bad diagonalization. Sure enough, the ITMX input matrix is in the default state [0], not a properly diagonalized state. Looking through the rest of the suspensions, I found PRM also in the default state, not diagonalized. ### We should do another round of suspension diagonalization. Kiwamu (or whoever is here last tonight): please run the free-swing/kick script (/opt/rtcds/caltech/c1/scripts/SUS/freeswing) before you leave, and I'll check the matrices and update the suspensions tomorrow morning. [0]  0.25 0.25 0.25 0.25 0 1.66 1.66 -1.66 1.66 0 1.66 -1.66 -1.66 1.66 0 0 0 0 0 1 6308 Thu Feb 23 09:09:33 2012 steveUpdateSAFETYsafety checks Emergency exit lights were inspected: 2 out of 13 batteries have to be replaced One of the Halon fire extinguishers needs to be recharged out of 8 Please do participate in preparation for the upcoming safety audit on Feb 28 6309 Thu Feb 23 10:53:54 2012 steveUpdateSUS oplev PIT transfer functions Oplev transfer functions PIT UGF were optimized to be at 2-3 Hz with 60 degree minimum phase margin by adjuting oplev gains. Additional Notes by KI: • The PRM oplev has a tailored 3.3 Hz resonant gain in order to calm down a wobble during the lock acquisitions. • Also in the PRM oplev a 35 Hz elliptic cut-off filter wasn't activated at the time when Steve measured it. • In both ITMs, elliptic cut-off filters seem to have higher corner frequencies compered with the others. • I guess these settings are from the old days. • ETMs and ITMs have whitening filters while the rest of the suspensions don't. • Without the whitening filters, normally the signals above 30 Hz are covered by some electrical noises or perhaps He-Ne laser intensity noise (#5630). • This is why we usually use the 35 Hz elliptic filters to roll off the control noises. • Since the ETMs and ITMs have whitening filters they potentially can have slightly higher corner frequencies in the elliptic filters. • Of course the corner frequencies need to be re-designed in terms of the amount of noise injection to the longitudinal motion. Attachment 1: oplPITtrans.pdf 6310 Fri Feb 24 03:58:13 2012 kiwamuUpdateLSCY arm + PRMI part II I tried the Yarm + PRMI configuration again. The PRMI part was locked, but it didn't stay locked during the Y arm was brought to the resonance point. I will post the time series data later. (locking of the PRMI part) Tonight I was able lock the PRMI when the arm was off from the resonance by 10 nm (#6306). This time I used REFL11Q to lock the MICH instead of the usual AS55Q because the MICH didn't stay locked with AS55Q for some reason. The PRCL was held by REFL33I as usual. Also I disabled the power normalization for the error signals because it could do something bad during the Y arm is borough to the resonance. In order to reduce the number of the glitches, PRM was slightly misaligned because I knew that the lower finesse gives fewer glitches. 6311 Fri Feb 24 04:12:44 2012 kiwamuUpdateSUSfreeswing test The following optics were kicked: MC1 MC2 MC3 ETMX ETMY ITMX ITMY PRM SRM BS Fri Feb 24 04:11:15 PST 2012 1014120690 Steve (or anyone), can you restore the watchdogs when you come to the lab in the morning ?  Quote from #6305 Kiwamu (or whoever is here last tonight): please run the free-swing/kick script (/opt/rtcds/caltech/c1/scripts/SUS/freeswing) before you leave, and I'll check the matrices and update the suspensions tomorrow morning. 6312 Fri Feb 24 08:06:52 2012 steveUpdateSUSsus restored Quote: The following optics were kicked: MC1 MC2 MC3 ETMX ETMY ITMX ITMY PRM SRM BS Fri Feb 24 04:11:15 PST 2012 1014120690 Steve (or anyone), can you restore the watchdogs when you come to the lab in the morning ?  Quote from #6305 Kiwamu (or whoever is here last tonight): please run the free-swing/kick script (/opt/rtcds/caltech/c1/scripts/SUS/freeswing) before you leave, and I'll check the matrices and update the suspensions tomorrow morning. All suspentions were restored and MC locked. PRM side osem RMS motion was high. Atm2, Why the PRM is 2x as noisy as the SRM ? Attachment 1: freePRM.png Attachment 2: noisyPRM.png 6313 Fri Feb 24 15:01:31 2012 kiwamuUpdateLSCY arm + PRMI part II The figure below shows the time series of the Y arm + PRMI trail. (Top plot ) Normalized TRY (intracavity power). It is normalized such that it shows 1 when the arm is locked with the recycling mirrors misaligned. (Middle plot) ASDC and REFLDC in arbitrary unit. (Bottom plot) The amount of the arm length detuning observed at the fine frequency discriminator. (Sequence) At t = 20 sec, the amount of detuning was adjusted so that the cavity power goes to the maximum. At this point the PRM was misaligned. At t = 30 sec, the cavity length started being slowly detuned to 10 nm. As it is being detuned the intracavity power goes down to almost zero. At t = 45 sec, the alignment of PRM was restored. Because of that, the REFLDC and ASDC diodes started receiving a large amount of light. At t = 85 sec, the PRCL and MICH were locked. The REFLDC signal became a high value as the carrier light is mostly reflected. The ASDC goes to a low value as the MICH is kept in the dark condition. At t = 100 sec, the length started being slowly back to the resonance while the PRMI lock was maintained. At t = 150 sec, the lock of the PRCL and MICH were destroyed. With the arm fully resonance, I wasn't able to recover the PRMI lock with the same demod signals.  Quote from #6310 I tried the Yarm + PRMI configuration again. The PRMI part was locked, but it didn't stay locked during the Y arm was brought to the resonance point. I will post the time series data later. 6314 Fri Feb 24 16:10:48 2012 mikeUpdateComputersPyNDS and a Plot Power Spectral Density plot using PyNDS, comparing 5 fast data channels for ETMX. **EDIT** Script here: import nds import numpy as np import matplotlib.pyplot as plt import time daq=nds.daq('fb', 8088) channels=daq.recv_channel_list() e=0 start=int(time.time()-315964819) rqst=['C1:SUS-ETMX_SENSOR_UR','C1:SUS-ETMX_SENSOR_UL','C1:SUS-ETMX_SENSOR_LL','C1:SUS-ETMX_SENSOR_LR','C1:SUS-ETMX_SENSOR_SIDE'] #Requested Channels for c in channels: if c.name in rqst: daq=nds.daq('fb', 8088) data=daq.fetch(start-100, start, c.name) vars()['psddata'+str(e)], vars()['psdfreq'+str(e)]=plt.psd(data[0],NFFT=16384,Fs=c.rate) vars()['label'+str(e)]=c.name e+=1 plt.figure(1) plt.clf() plt.title('PSD Comparison') plt.grid(True, which='majorminor') plt.xlabel(r'FrequencyHz$') plt.ylabel(r'Decibels$\frac{dB}{Hz}') for x in np.arange(0,e): plt.loglog(psdfreq0, 10*vars()['psddata'+str(x)], label=vars()['label'+str(x)]) plt.legend() plt.show() Attachment 1: PSD_Comparison.png 6315 Fri Feb 24 18:37:13 2012 ranaUpdateLSCY arm + PRMI part II  Quote: I tried the Yarm + PRMI configuration again. The PRMI part was locked, but it didn't stay locked during the Y arm was brought to the resonance point. Isn't the point that the 11 and 55 MHz signals have the carrier effect, but the 3f signals are better? 6316 Fri Feb 24 18:59:04 2012 JenneUpdateComputersPyNDS and a Plot  Quote: Power Spectral Density plot using PyNDS, comparing 5 fast data channels for ETMX. Is there any stuff to install, etc? Y'know, for those of use who don't really know how to use computers and stuff.... 6317 Fri Feb 24 19:18:28 2012 kiwamuUpdateLSCY arm + PRMI : how they should look like I calculated how the DC signals should look like in the Y arm PRMI configuration. The expected signals are overlaid in the same plot as that of shown in #6313. You can see there are disagreements between the observed and expected signals in the plot below at around the time when the arm is brought to the resonance. (expected behaviors) • TRY: At the end it should be at 1 (remember TRY is normarlized) and should not go more than that, since the power-recycling is in a weird situation and it is not fully recycling the power. • ASDC: It should become brighter at the end because the arm cavity flips the sign of the reflected light and hence the dark port must be on a bright fringe. • REFLDC: It will decrease a little bit because the arm cavity and MICH try to suck some amount of the power into the interferometer.  Quote from #6313 The figure below shows the time series of the Y arm + PRMI trail. 6318 Fri Feb 24 19:25:43 2012 jamieUpdateLSCALS X-arm beatbox added, DAQ channels wiring normalized I have hooked the ALS beatbox into the c1ioo DAQ. In the process, I did some rewiring so that the channel mapping corresponds to what is in the c1gcv model. The Y-arm beat PD is going through the old proto-DFD setup. The non-existant X-arm beat PD will use the beatbox alpha. Y coarse I (proto-DFD) --> c1ioo ADC1 14 --> C1:ALS_BEATY_COARSE_I Y fine I (proto-DFD) --> c1ioo ADC1 15 --> C1:ALS_BEATY_FINE_I X coarse I (bbox alpha)--> c1ioo ADC1 02 --> C1:ALS_BEATX_COARSE_I X fine I (bbox alpha)--> c1ioo ADC1 03 --> C1:ALS_BEATX_FINE_I  This remapping required coping some filters into the BEATY_{COARSE,FINE} filter bank. I think I got it all copied over correctly, but I might have messed something up. BE AWARE. We still need to run a proper cable from the X-arm beat PD to the beatbox. I still need to do a full noise/response characterization of the beatbox (hopefully this weekend). 6319 Fri Feb 24 23:14:09 2012 kiwamuUpdateCDStdsavg went crazy I found that the LSCoffset script didn't work today. The script is supposed to null the electrical offsets in all the LSC channels. I went through the sentences in the script and eventually found that the tdsavg command returns 0 every time. I thought this was related to the test points, so I ran the following commands to flush all the test point running and the issue was solved. [term]> diag  [diag]>open  [diag]> diag tp clear *  EDIT, JCD 11June2012: 3rd line there should just be [diag]> tp clear * 6320 Sat Feb 25 00:37:42 2012 kiwamuUpdateSUSoplev spectra during PRMI lock Somehow the angular stability of the central part have not been so great. Also the angular motions look fluctuating a lot and they seem to be related with the glitches. I took the oplev spectra when the PRMI is locked and unlocked to see whether if something obviously crazy is going on or not. They seem ok to me except that the PRM pitch shows an extra bump at around 2-3 Hz when the PRMI is locked. But I don't think it's prominent. - The attached files show the oplev spectra. When the PRMI is locked the PRM and both ITMs are under the length control. (red) pitch when PRMI is locked (blue) yaw when PRMI is locked (orange) pitch without any length controls (cyan) pitch without any length controls Attachment 1: oplev_PRMI.pdf 6321 Sat Feb 25 14:27:26 2012 kiwamuUpdateLSCglitches in the RFPD outputs Last night I took a closer look at the LSC analog signals to find which components are making the glitches. I monitored the RFPD output signals and the demodulated signals at the same time with an oscilloscope when the PRMI was kept locked. Indeed the RFPD outputs have some corresponding fast signals although I only looked at the RELL11 I and Q signals. (REFL33 didn't have sufficiently a high SNR to see the glitches with the oscilloscope.) I will check the rest of channels. 6322 Mon Feb 27 10:21:37 2012 steveUpdateSAFETYsafety audit tomorrow morning  Quote: Emergency exit lights were inspected: 2 out of 13 batteries have to be replaced One of the Halon fire extinguishers needs to be recharged out of 8 Please do participate in preparation for the upcoming safety audit on Feb 28 Batteries replaced and cylinder recharged. Please clean up your experimental set up if it is blocking breakers or entry way etc. I will start the final clean up 2pm today. 6323 Mon Feb 27 14:35:22 2012 steveUpdateSUS oplev YAW transfer functions The BS and the PRM have 3.3 Hz resonant gain filters that kill the phase margins. Attachment 1: oplYAWtransf.pdf 6324 Mon Feb 27 14:35:37 2012 JenneUpdateGreen LockingPSL Beat Setup Xarm is aligned for both IR and green. Here is a photo of the beam paths of the PSL beat setup. I want to make sure that the X-green BBPD sees a nice beam from both the PSL and the Xarm, without disturbing the currently working Y setup. I keep getting confused with all the beamsplitters, especially the green PBSes, which operate at ~56deg, not 45deg, so I made a diagram. 6325 Mon Feb 27 18:33:11 2012 jamieUpdatePSLwhat to do with old PSL fast channels It appears that the old PSL fast channels never made it into the new DAQ system. We need to figure out what to do with them. A D990155 DAQ Interface card in far right of the 1X1 PSL EuroCard ("VME") crate is supposed output various PMC/FSS/ISS fast channels, which would then connect to the 1U "lemo breakout" ADC interface chassis. Some connections are made from the DAQ interface card to the lemo breakout, but they are not used in any RTS model, so they're not being recorded anywhere. An old elog entry from Rana listing the various PSL DAQ channels should be used as reference, to figure out which channels are coming out, and which we should be recording. The new ALS channels will need some of these DAQ channels, so we need to figure out which ones we're going to use, and clear out the rest. 6326 Mon Feb 27 18:35:45 2012 JenneUpdateGreen LockingX Beat Search Meh. I've searched in steps of 20 counts in C1:GCX-SLOW_SERVO2_OFFSET units (16 bit +\- 10V DAC, and 1GHz/V coeffecient for the Xgreen aux laser means this is ~0.6MHz per 20 count step). I went from -400cts to +800 cts and haven't found the beatnote yet. Meh. Both PSL green and Xgreen beams are going to the Xgreen BBPD. Both beams are easily visible, so while I didn't actually measure the power, it should be sufficient. The arm is being re-locked in green for each step, but it's not locked in IR, but that doesn't matter for just finding the beatnote. I've got the output of the BBPD directly connected to the 50 ohm input of the HP8591E spectrum analyzer, with the freq span from 10MHz to 120MHz. The BBPD is supposed to be good up to ~100MHz, so I should catch any beatnote that's there. I have to head out, so I guess I'll continue the search tomorrow. One of Kiwamu's suggestions was that, since no one is using the Ygreen concurrent with my fiddling, I rotate the waveplate after the PSL doubling oven so that max power goes to the Xgreen path, thus giving myself a bigger signal. I'll try that tomorrow. Today, I didn't ever touch the waveplate. 6327 Mon Feb 27 19:04:13 2012 jamieUpdateCDSspontaneous timing glitch in c1lsc IO chassis? For some reason there appears to have been a spontaneous timing glitch in the c1lsc IO chassis that caused all models running on c1lsc to loose timing sync with the framebuilder. All the models were reporting "0x4000" ("Timing mismatch between DAQ and FE application") in the DAQ status indicator. Looking in the front end logs and dmesg on the c1lsc front end machine I could see no obvious indication why this would have happened. The timing seemed to be hooked up fine, and the indicator lights on the various timing cards were nominal. I restarted all the models on c1lsc, including and most importantly the c1x04 IOP, and things came back fine. Below is the restart procedure I used. Note I killed all the control models first, since the IOP can't be restarted if they're still running. I then restarted the IOP, followed by all the other control models. controls@c1lsc ~ 0 for m in lsc ass oaf; do /opt/rtcds/caltech/c1/scripts/killc1${m}; done controls@c1lsc ~ 0$ /opt/rtcds/caltech/c1/scripts/startc1x04
c1x04epics C1 IOC Server started
* Stopping IOP awgtpman ...                                                                      [ ok ]
controls@c1lsc ~ 0$for m in lsc ass oaf; do /opt/rtcds/caltech/c1/scripts/startc1${m}; done
c1lscepics: no process found
ERROR: Module c1lscfe does not exist in /proc/modules
c1lscepics C1 IOC Server started
* WARNING:  awgtpman_c1lsc has not yet been started.
c1assepics: no process found
ERROR: Module c1assfe does not exist in /proc/modules
c1assepics C1 IOC Server started
* WARNING:  awgtpman_c1ass has not yet been started.
c1oafepics: no process found
ERROR: Module c1oaffe does not exist in /proc/modules
c1oafepics C1 IOC Server started
* WARNING:  awgtpman_c1oaf has not yet been started.
controls@c1lsc ~ 0\$

6328   Mon Feb 27 21:26:22 2012 DenUpdatePEMseis box

I did liso simulation of the circuit in the seis box. I think that AD620 (first amplifier in the circuit) noise might be much less with the signal from guralps from 0.01 Hz. Here is the TF of AD620 output / circuit input.

The noise spectrum is at this node is

The psd of the seismic noise below 1 Hz ~ 1u m/s => circuit input signal is ~1mv.

The TF of the whole circuit is

This result differs from the graph on the circuit sheet, but may be it was done before the resistor parameteres changed. Back of the envelop calculations also show that it is not possible to acheive DC gain 200 while 50-800 Hz gain = 5000. I'll check with the spectrum analyzer.

AD620 might be a weak point in the simulation since this is not a "classical" operational amplifier, it contains a resistor that adjusts the gain. During the liso simulation I assumed that we have an ordinary opamp (with noise, gain and gbw parameters taken from the real ad620 datasheet) with a resistor parallel to the opamp = 50k and a resistor before the inverted input that corrsponds to R2. In this case the gain of the simulated opamp is the same as of the real one given by the formula 1 + 49.9k / R2, though noise parameters may change. This should be also checked with the spectrum analyzer.

6329   Tue Feb 28 11:20:51 2012 steveUpdateSAFETYsafety audit 2012

Correction list by visiting safety committee, Haick Issaian is not shown:

1,  update laser, crane operator list and post it

2,  check fire extinguishers monthly, date and initials must be on the tags

3,  move drinking water tower so it does not block fire extinguisher

4,  post updated crane doc at cranes

5,  post present phone lists at IFO room phones

6,  emergency laser shutoff at the south end must be mounted without C-clamp

7,  use heavy cable tie to insure position of  mag-fan on cabinet top

a,  safety glasses to be cleaned

b, let the electrical shop fix Rack-AC power to optical tables at the ends

c, measure transmission of  laser safety glasses

d, update  IFO outside door info signs

e, update laser inventory and post it

f,  schedule annual crane inspection and renew maintenance contract

g, PSL enclosure  inner shelf needs a good clean up so it is earthquake safe

Attachment 1: safety12.JPG
6330   Tue Feb 28 12:00:54 2012 kiwamuUpdateLSCinstalled anti-whitening filters

I found that none of the filter banks in the LSC input signals have the precise anti-whitening filters.

I installed the precise filters on REFL11, REFL33, REFL55 and AS55 based on Jenne's measurement (#4955)

After installing them I briefly checked the REFL11 sensing matrix with the PRMI locked, but it didn't change so much from what I got (#6283).

But I felt that the PRMI became more robust after that ... I just felt so ...

(Background)

The lock of the PRMI doesn't look healthy, especially the sensing matrix doesn't make sense at all (#6283).
A very staring thing in the sensing matrix is that the REFL11 and REFL55 didn't show the 90 degree separation between MICH and PRCL.
So I suspected some electronics, particularly the demodulation boards.

(What I did)

I checked the anti-whitening filters shape to see if they are ok or not.
I found that they all had the default filters of two zeros at 150 Hz and two poles at 15 Hz. So they weren't quite tuned.
I thought this could be a problem when I measure the sensing matrix because I usually excite the length DOFs at a high frequency of 283.1 Hz
and the mismatches between the anti-whitening and whitening filters may lead to something funny at such a high frequency.

So I installed the precise filters on REFL11, REFL33, REFL55 and AS55.
After that I did a orthogonality test on each I-Q pair of the demod signals to correct the D-phases and the relative gain between I and Q.

(Next ?)

Rana and I discussed the plan and decided to go back to a simple Michelson which should be easy enough to understand what is going on and should allow us a complete set of measurements.
Our big concern behind it is that we maybe locking the PRMI at a funny operation point.
In order to assess the issue I will do the following actions on the Michelson at first and then apply the same things on the PRMI later :
• Check  the amount of of the sidebands using the OSA
• Check the amount of the DC light
• Check the sensing matrix to see if the absolute values in watt / meter make sense or not
• This work needs calibrations on all the demodulated board (this is equivalent to measuring the conversion losses of the mixers in the demod boards).
• Measure the contribution from the RAMs (it must be measurable by some means)
6331   Tue Feb 28 15:48:32 2012 kiwamuUpdateLSCinstalled anti-whitening filters

I installed the rest of the precise anti-whitening filters. Now all of the LSC sensors have the right filters.

 Quote from #6330 I found that none of the filter banks in the LSC input signals have the precise anti-whitening filters. I installed the precise filters on REFL11, REFL33, REFL55 and AS55 based on Jenne's measurement (#4955)

6332   Tue Feb 28 16:12:59 2012 DenUpdateAdaptive Filteringlunch talk

Just to be clear what I said at the meeting, I write all this down here. Adaptive filtering of real signals (MC_F and GUR1_X) with all noises inside is

This is offline filtering but with real signals and with the C-code that is compiled at the 40m now. We can reduce the MC_F signal by ~100 below 10 Hz, but  the problem is that reducing the adaptation gain, the error increases. As a result when we move towards FxLMS algorithm with AA, AI and downsampling, we have to take the gain equal to ~1e-2 and we do not reduce any noise.

The second demonstration of this problem is static Wiener filtering. This is the result

We can see that adaptive filtering outperforms the "optimal" filtering. This is because an adaptive filter can follow the changes of coefficients immediately while the Wiener filter averages them. This is the mathematical formulation:

mcl_real = coeff _real* seismic_noise_real + other_noise

mcl_real - the real length of the MC,

coeff_real - real coefficients, that represent the transfer function between seismic noise and MC length,

other_noise - noise uncorrelated to the seismic noise seismic_noise_real

But in the world of our measured signals we have the equation

mcl_measured = coeff * seismic_noise_measured + other_noise

mcl_measured = TF_mcl * mcl_real

seismic_noise_measured = TF_seis * seismic_noise_real

where TF_mcl and TF_seis - transfer functions from the real world to measurements.

It seems to me that TF_mcl or TF_seis are not constants and for that reason the TF between measured seismic noise and mcl is not constant. But it is exactly what an adaptive or Wiener filter tries to define:

coeff(time) = average(coeff(time)) + delta(coeff(time))

The result of applying average(coeff) is the green line in the Figure 2 - error after applying the Wiener filtering.

delta(coeff) - the changing part of the transfer function is caught by the adaptive filtering. The lower the gain, the lower is the capability of adaptive filter to catch these changes. Theoretically. the error after applying adaptive filter can be presented like this:

E(error*error) = E(other_noises*other_noises) + 1/(2-mu)*mu*E(other_noises*other_noises)  + 1/ {mu*(2-mu)} * Tr(Q) * A

Q - covariance matrix of delta(coeff)

A - norm of the seismic signal

The first term in this equation is the dispersion of other noises, the second term is the error of the adaptive filter due to non-zero gain, the third term is due to the changes in the transfer function - we can see that it is proportional to 1/mu. This term explains why the error increases while mu decreases.

Now I'm looking for the part in the path of the signals where the transfer function can change. As I mentioned above, this is not a change in the real world, it is the change in the measured signlals. My first guess is the quantization error - we do not have not enough counts. If this is not the case, I'll move to other things of the signal path.

6333   Tue Feb 28 16:31:08 2012 SureshUpdateElectronicsREFL165 repair: Characterization

The transfer function and current noise were measured.  The location of the peak shifts with the amount of incident light power (RF or DC).  The TF was measured at an incident 1064nm light power of 0.4 mW which produced a DC output voltage of 14 mV => DC photocurrent of 0.28 mA.

Many of the effects that Koji noted in the previous characterization are still present.

In addition I observed a shift of the peak towards lower frequencies as the RF power supplied to the AM Laser (Jenne Laser) is increased.  This could create a dependance of the demodulation phase on incident RF power.

The plots are attached below.

Attachment 1: REFL165_Characterization.pdf
Attachment 2: REFL165_response_shift.pdf
6334   Tue Feb 28 16:39:25 2012 kiwamuUpdateLSCMICH and PRCL signals in a simulation

I briefly ran a Optickle code to see how the PRC macroscopic length screws up the sensing matrix in the PRMI configuration.

Especially I focused on the optimum demodulation phases for the MICH and PRCL signals to see how well they are separated in different PRC length configuration.

It seems that the demod phases for MICH and PRCL are always nicely separated by approximately 90 degree regardless of how long the PRC macroscopic length is.

If this is true, how can we have such a strange sensing matrix ??

(Simulation results)

The plots below show the simulation results. The x-axis is the macroscopic length of PRC in a range from 6.3 meter to 7.3 meter.
The y-axis is the optimum demodulation phases for MICH (blue) and PRCL (black).
The red line is the difference between the MICH and PRCL demodulation phases.
The left plot is for the REFL11 signals and the right plot is for the REFL55 signals.
When the difference is 90 degree, it means we can nicely separate the signals (i.e. REFL11I for PRCL and REFL11Q for MICH).
Obviously they are always nicely separated by ~ 90 deg.

 Quote from #6330 The lock of the PRMI doesn't look healthy, especially the sensing matrix doesn't make sense at all (#6283). A very staring thing in the sensing matrix is that the REFL11 and REFL55 didn't show the 90 degree separation between MICH and PRCL.

6335   Tue Feb 28 16:44:56 2012 ranaUpdateLSCMICH and PRCL signals in a simulation

### Like I said, this is possible if you fail to set up the OSA to look at the sidebands at BOTH the AS and REFL ports at all times. Don't waste your time - set up an OSA permanently!

6336   Tue Feb 28 20:49:33 2012 kiwamuUpdateLSCinsalling OSA

I am installing an OSA on the AP table and it's ongoing.

I am leaving some stuff scattered on the AP table and I will resume the work after I come back.

6337   Wed Feb 29 00:22:35 2012 SureshUpdateElectronicsREFL165 repair: Installed on the AS table

1) The REFL165 has been replaced onto the AS table.

2) When the PD interface cable is attached the PD shows a DC out put of 6mV and does not respond to a flash light.  I changed the PD interface port in the LSC rack by swapping the other end of the cable with an unused (Unidentified PD) interface cable,  The PD is working fine after that.   There could be a problem with some binary switch state on the PD interface where the REFL165 cable was plugged in earlier.

6338   Wed Feb 29 01:02:06 2012 DenUpdatePEMseis box measured

I've measured the input signal to the seismic box from seismometer Guralp 1. The spectrum of the signal in the "input +" (TP 1) is

The spectrum below 1 Hz is ~250 uV/sqrt(Hz). As the input is differential, then the input voltage is 0.5 mV/sqrt(Hz). The spectrum of the "output +" signal (TP 2) is

So the gain at ~ 1Hz is ~20. I've measured the transfer function between the "input +" and "output +" (TP1 and TP2) for all 9 circuits

The channels 1-6 are of new modification and have gain ~20 at the frequencies 0.2 - 100 Hz. Below 0.2 Hz the gain is reduced. 100 Hz - cut off frequency of the low-pass filters. Meanwhile channels 7-9 (old configuration) have much more gain and 10_50 Hz filters work here.

The coherence between  "input +" and "output +" (TP1 and TP2) for 9 circuits is

We can see that channel VERT 3 is very bad. For others coherence is lost below 0.2 Hz. The spectrum analyzer noise measured is ~1000 times less then the signal at these frequencies. I'll pay more attention to this loss of coherence at low frequencies. Something is noisy.

6339   Wed Feb 29 01:14:40 2012 SureshUpdateElectronicsREFL165 repair: Characterization

 Quote: The transfer function and current noise were measured.  The location of the peak shifts with the amount of incident light power (RF or DC).  The TF was measured at an incident 1064nm light power of 0.4 mW which produced a DC output voltage of 14 mV => DC photocurrent of 0.28 mA.  Many of the effects that Koji noted in the previous characterization are still present. In addition I observed a shift of the peak towards lower frequencies as the RF power supplied to the AM Laser (Jenne Laser) is increased.  This could create a dependance of the demodulation phase on incident RF power. The plots are attached below.

[Koji, Suresh]

To determine the amount of RF power in the AM laser beam at various RF drive levels I measured the RF power out of the Newfocus 1611 PD while driving the AM laser with a Marconi.  During this measurement the DC output was 2.2V.  With the DC transimpedance of 10^4 and a sensitivity of 0.8 A/W we have carrier power as 0.275 mW (-5.6 dBm).  [Incidentally the measured carrier power with a power meter is about 0.55 mW. Why this discrepancy?]

 1 2 3 4 5 6 Marconi Output (dBm) 0 -5 -10 -15 -20 -25 AG 4395 measurement (dBm) -8.1 -13 -18 -23 -28 -33 RF/DC ratio dB -2.5 -7.4 -12.4 -17.6 -22.6 -27.6

Estimation of the signal strength at the REFL165 PD:

From the 40m Sensing Matrix for DRFPMI we see that the signal strength at REFL165 in CARM is about 5x10^4 W/m.  Since we expect about 0.1nm of linear range in CARM length we expect about 0.05 mW of RF power.  If the (DC) carrier power is about 10 mW at the photodiode (18mW is about the max we can have since the max power dissipation is 100 mW in the diode)  then the RF : DC power ratio is 5x10^-3 => -23 dB

As this is lower than the power levels at which the PD transfer function was determined and where we noted the distorsion and shift of the resonance peak, it is likely that these effects may not be seen during the normal operation of the interferometer.

The shift due to the carrier power level (DC) change may still however pose a problem through a changing demodulation phase.

6340   Wed Feb 29 04:23:14 2012 kiwamuUpdateLSCREFL OSA installed

I placed the OSA (Optical Spectrum Analyzer) on the AP table and this OSA will monitor the REFL beam.

Tomorrow I will do fine alignment of the OSA.

(some notes)

- a new 90% BS in the REFL path for limiting the REFL beam power

I installed a 90 % beam splitter in the REFL path so that this BS limits the maximum power in the downstreams because we don't want to damage any more RFPDs.
The REFL beam has a power of about 610 mW and the BS has R = 94 % (the spec says 90 +/- 4 % ), resulting in a power of ~37 mW in the transmitted light.
Then the transmitted beam goes through the combination of a half-wave plate and PBS, which allows a fine adjustment of the power.
After passing through the lambda/2 + PBS, the beam is branched to four ways and each beam goes to the REFL RFPD, i.e. REFL11, 33, 55 and 165.
In the end each RFPD receives a laser power of 9 mW at maximum, which is reasonably lower than the power rate of the photo diodes (~17 mW ).
The new OSA uses the reflected light from the 90% BS.

- Squeezed the ABSL (ABSolute length Laser) path

I squeezed the path of the ABSL in order to accommodate the OSA.
I tried to keep the same optical distances for some lenses, but I guess their mode matching must be different from what they used to be.
So be aware of it.

- Modification of the AS OSA path

I have also modified the optical path of the AS OSA because there had been an extra zig-zag path which made the path more complex in unnecessary way.
Since I have squeezed the ABSL path, it allowed me to simplify the optical path. So I modified the path.

 Quote from #6336 I am installing an OSA on the AP table and it's ongoing.

6341   Wed Feb 29 17:32:11 2012 MikeUpdateComputersPyNDS and a Plot

Quote:

 Quote: Power Spectral Density plot using PyNDS, comparing 5 fast data channels for ETMX.

Is there any stuff to install, etc?  Y'know, for those of use who don't really know how to use computers and stuff....

No new stuff for these computers.  Everything should be installed already.

6342   Wed Feb 29 20:27:00 2012 JenneUpdateGreen LockingX green beat - found it!

Found it!

The actual temperature of the Xend laser is 0.02 C higher than anticipated based on the formula in elog 3759.  Both the PSL and the Xend laser are at their nominal diode currents (2.100 A for the PSL, 2.003 A for Xend), so the curves should be used as they are.  The PSL temp (when the slow servo offset is ~0) is 31.71 C.  Using curve 2 from elog3759, the Xend laser should be 37.78, which I found was +10 counts on the Xgreen slow servo offset.

Right now the Xend laser is at 37.80 C, and the beat is around 30 MHz.  This is +80 counts on the Xgreen slow servo.  +60 counts gave me ~80 MHz.  When (a few minutes ago) the MC unlocked and relocked, it came back to a slightly different place, so the temp of the Xend laser had to go up a few 10's of counts to get the same beat freq.  Right now the PSL slow servo offset is 0.076 V.

The HP8591E is set with ResBW=100kHz, Ref Level= -39dBm (so I'm not attenuating my input signal!).  The largest peak I see for the beatnote is -66dBm.  The nose floor around the peak is -83dBm.  Trace (trace button!) A is set to MaxHoldA, and Trace B is set to ClearWriteB, so B is giving me the actual current spectrum, while A is remembering the peak value measured, so it's easier to see if I went past the peak, and just didn't see it on the analyzer.

Also, I went back and realigned the beams earlier, to ensure that there was good overlap both near the BS which combines the PSLgreen and Xgreen beams, and at the PD.  The overlap I had been looking at was okay, but not stellar.  Now it's way better, which made the peak easier to see.  Also, also, the waveplate after the doubling oven on the PSL table is still rotated so that I get max power on the Xgreen side of things, and not much at all on the Ygreen side.  I'll need to rebalance the powers, probably after we make sure we are seeing the beatnote with the BeatBox.

Next Steps:

Lay a cable from the BBPD to the BeatBox in 1X2, make the BeatBox do its thing.

Use the dichroic locking to do a sweep of the Xarm.

6343   Thu Mar 1 00:05:23 2012 DenUpdatePEMseis box noise

I've moved GUR1 seismometer from MC2 to the working tables in order not to disturb the MC while working with the seismometer box. The new place for the GUR1 for a few days is near the printer, cables and blue boxes. I've cleaned all mess and wires from the floor, so that seismometer now looks like that

I've connected 2 inputs of the N/S 1 circuit of the seismometer box with a 50 Ohm resistor and measured the noise at the output. The comparison with the seismic signal is

The noise increased at 0.5 Hz and is pretty big. This might explain the loose of coherence at low frequencies.


text:
# Q : 2     The front compound wall of a house is decorated by wooden spheres of diameter 21 cm, placed on small supports as shown in Fig $\small 13.32$. Eight such spheres are used for this purpose, and are to be painted silver. Each support is a cylinder of radius $\small 1.5\hspace{1mm}cm$ and height 7 cm and is to be painted black. Find the cost of paint required if silver paint costs 25 paise per $\small cm^2$ and black paint costs 5 paise per $\small cm^2$.

Given,

The radius of the wooden spheres = $r_1 = \frac{21}{2}\ cm$

$\therefore$ The surface area of a single sphere = $4\pi r_1^2$

$\\ = 4\times\frac{22}{7}\times\frac{21}{2}\times\frac{21}{2} \\ = 22\times3\times21$

$= 1386\ cm^2$

Again, the Radius of the cylinder support = $\small r_2 = 1.5\hspace{1mm}cm$

Height of the support = $h = 7\ cm$

$\therefore$ The base area of the cylinder = $\pi r_2^2 = \frac{22}{7}\times1.5\times1.5 = 7.07\ cm^2$

Now, Cost of painting $1\ cm^2$silver = $25\ paise = Rs.\ 0.25$

$\therefore$ Cost of painting 1 wooden sphere = Cost of painting $(1386-7.07)\ cm^2$silver

$Rs. (0.25\times1378.93) = Rs.\ 344.7325$

Now, Curved surface area of the cylindrical support = $2\pi r_2 h$

$\\ = 2\times\frac{22}{7}\times1.5\times7 \\ = 22\times3 \\ = 66\ cm^2$

Now, Cost of painting $1\ cm^2$ black = $5\ paise = Rs.\ 0.05$

$\therefore$ Cost of painting 1 such stand = Cost of painting $66\ cm^2$silver = $Rs. (0.05\times66) = Rs.\ 3.3$

$\therefore$The total cost of painting 1 sphere and its support = $Rs.\ (344.7325+3.3) = Rs.\ 348.0325$

Therefore, total cost of painting 8 such spheres and their supports = $Rs.\ (8\times348.0325) = Rs.\ 2784.26$

## Related Chapters

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text:
Journal article

### WIMPonium and Boost Factors for Indirect Dark Matter Detection

Abstract:

We argue that WIMP dark matter can annihilate via long-lived "WIMPonium" bound states in reasonable particle physics models of dark matter (DM). WIMPonium bound states can occur at or near threshold leading to substantial enhancements in the DM annihilation rate, closely related to the Sommerfeld effect. Large "boost factor" amplifications in the annihilation rate can thus occur without large density enhancements, possibly preferring colder less dense objects such as dwarf galaxies as locatio...

Publication status:
Published

### Authors

Journal:
Phys.Lett.B
Volume:
676
Issue:
4-5
Pages:
133-139
Publication date:
2008-12-02
DOI:
ISSN:
0370-2693
URN:
Source identifiers:
6728
Local pid:
pubs:6728
Language:
English
Keywords:


text:
# Prove that $Y^n-13X^4$ is irreducible in $\mathbf{Q}[X,Y]$

Prove that $$Y^n-13X^4$$ is irreducible in $$\mathbf{Q}[X,Y]$$

Look at $$Y^n-13X^4$$ as a polyomial in $$(\mathbf{Q}[X])[Y]$$, then we can use Eisenstein with $$13\in\mathbf{Z}[X]$$ (which is prime) and $$169\not\mid 13X^4$$. Then the polynomial is irreducible over $$Y^n-13X^4$$ and by Gauss' Lemma also in $$\mathbf{Q}[X,Y]$$.

Is this the correct way to approach it? I am having trouble applying Eisenstein over polynomial rings in more variables.

• Your approach is entirely correct, except that the statement "irreducible over $Y^n-13X^4$" doesn't make any sense (to me). Nov 14 '18 at 14:39
• Is that really true? Shokran. I meant to say over $\mathbf{Z}[X,Y]$ and by Gauss' Lemma also in $\mathbf{Q}[X,Y]$. @Servaes Nov 14 '18 at 14:48
• It is really true, but if you are in doubt then you can verify the proof of Gauss' lemma for $\Bbb{Q}[X,Y]$ yourself; it is exactly the same as for $\Bbb{Q}[X]$. Nov 14 '18 at 14:52

If it were reducible in $$\mathbb Q[X,Y]$$ then you could substitute $$X$$ for $$Y$$ and you'd have a factorisation of $$X^n-13X^4$$, hence of $$X^{n-4}-13$$, which is impossible. (Some powers of $$X$$ will need borrowing if $$n<4$$, and if $$n=4$$ it's clear.)


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# Second order difference scheme for singularly perturbed boundary turning point problems

Document Type : Research Article

Authors

Department of Mathematics, Bharathidasan University, Tiruchirappalli 620 024, Tamilnadu, India

Abstract

A  singularly perturbed convection diffusion  equation with boundary  turning point  is considered in this paper. A higher order method on piecewise uniform Shishkin mesh is suggested to solve this problem. We  prove that this method is of  order $O(N^{-2}(\ln N)^2)$. Numerical results are given which validate  the analytical results.

Keywords