text:
###### Vecm In R
Basically, a VAR with 2 lags corresponds here to a VECM with 1 lag. jo does not set the rank $$r$$ of the cointegration matrix automatically, it has to be specified. What does the sign of the causality imply w. Transform a VECM to VAR in levels: Phi: Coefficient matrices of the MA represention: No Results! Vignettes of vars. The model uses r_t in New York to model on 2 lags of returns in new york and London (equation 3). It features following models: Univariate models:. Two great resources for finding R packages are rseek and CRAN Task Views. Does exist a matlab code which estimates a VECM - Garch, that is a multivariate cointegration model with Garch effect? Thanks 0 Comments. [email protected] I mean, you can actually understand that. VAR models generalize the univariate autoregressive model ( AR model ) by allowing for more than one evolving variable. 0 draft) Oscar Torres-Reyna [email protected] 2 4 0 7 9 6. , Merton, (1956), "A Contribution to the Theory of Economic Growth", Quarterly Journal of Economics No. #'The arg beta allows to specify constrained cointegrating values, leading to ECT= β^{'}X_{t-1}. 3 7 0 9 8 0. In the Maximum Eigenvalue test, the null hypothesis corresponding to exactly r cointegration vectors is contrasted against the existence of r ± 1 cointegration vectors. Against this background, this paper tries to analyze the major long and short run determinants of tax revenue in the state of Jammu and Kashmir by applying suitable econometric methods such as VECM and by taking a broader set of variables which comprise Economic, Political and demographic sectors. Threshold cointegration in R with package tsDyn Matthieu Stigler Matthieu. Microfit 5 is suitable for short run and long run model. Johansen Cointegration In the Johansen test, the determination of cointegration is seen from the value of trace statistic and max eigen statistic. The $$R$$ function fevd() in package vars allows forecast variance decomposition. Since I seek to apply panel cointegration test suggested by Groen and Kleibergen (2003) I was wondering if you passed by a stata program that apply this method of cointegration to. Exchange rate plays a vital role in a country's level of trade, which is critical to most free market economies in the world. Stigler at gmail. Economist a73f. The Equivalence of Causality Detection in VAR and VECM Modeling with Applications to Exchange Rates T. VAR models generalize the univariate autoregressive model ( AR model ) by allowing for more than one evolving variable. Essentially, it seeks to find stationary linear combinations of the two vectors. However I could not find any option to have following inputs: 1. This instance can be better analysed in the context of a vector-error-correction model (VECM). Macedonia: VECM analysis". It distinguishes between stationary variables with transitory (temporary) effects and nonstationary variables with permanent (persistent) effects. Macedonia has been tested. J ika terbukti ada kointegrasi, maka tahapan VECM dapat dilanjutkan. Threshold cointegration in R with package tsDyn Matthieu Stigler Matthieu. r STAT 8260 Exam 1 - Tuesday, February 26 SHOW ALL WORK 1. View Ita John’s profile on LinkedIn, the world's largest professional community. In Dickey-Fuller tests, the second column specifies three types of models, which are zero mean, single mean, or trend. In both cases Ωand the Γ j's are ﬁxed k ×k matrices, and 1 ≤r It is a unrestricted VAR (not VECM). Visit Stack Exchange. We consider two measures of productivity, namely total factor productivity (TFP) and labor productivity for analysis. Sir, I am trying to test some restrictions in vecm. This functions estimates the matrix of a VECM. Estimation of Cointegrated VAR Models. Johansen Cointegration In the Johansen test, the determination of cointegration is seen from the value of trace statistic and max eigen statistic. 0 = αβ0, where αand βare ﬁxed k ×r matrices with rank r, against TV cointegration of the type Π0 t = αβ 0 t, where αis the same as before but now the β t's are time-varying k×r matrices with constant rank r. Follow 1 view (last 30 days) Monica on 7 Jul 2013. , R, ɛ m, ᴫ (4) Effect of the independent variables like (Y, Ȳ, C, I, ɛ x, R, ɛ m, ᴫ) on trade balance of Ethiopia can be judged by using the following regression model in a linear form especially in the long-run:- T= α +ß 1 Y + ß 2Ȳ + ß 3 C + ß 4 I + ß 5ɛ x + ß 6 R + ß 7ɛ m +ß 8ᴫ + μ t (5). For verified definitions visit AcronymFinder. So the answer to this, is like many things it depends. time series. be decomposed as 1, where PRm r constitutes the rlong-run cointegrating relations and PRm r is a loading matrix of rank r. Using cointegration and error-correction mechanism techniques, this paper investigated the causal relationship between domestic demand, export and economic growth using data pertaining to Bangladesh’s final household consumption and government consumption as a measure of domestic demand, real exports, and real GDP over the period 1971–2011. In this paper we present two procedures to test weak exogeneity in a coin-tegrated system without estimating the cointegration vectors. Essentially, it seeks to find stationary linear combinations of the two vectors. Deﬂning rt as the logarithm of the gross return on stocks during period t, a typical OLS speciﬂcation is as follows, rt!k = µ1dcayt ++ut!k; (5) where rt!k = rt+1 +rt+2 +¢¢¢+rt+k, is the continuously compounded k-period rate of return and  is a constant. Exchange rate plays a vital role in a country's level of trade, which is critical to most free market economies in the world. Estimation of Cointegrated VAR Models. The cointegrating vectors are highlighted in Section 8. July 13, 2015, Using gret l for Principles of Econometrics, 4th Edition No comments. ppt - Free download as Powerpoint Presentation (. Please stop it as much as you can. and Hafer, R. The Engle-Granger approach as described above suffers from a number of weaknesses. The following list gives some of the R packages that are used in this book more frequently: devtools (Wickham and Chang. and are meant to clarify the expression. Intercept and linear. It is a combination of Tong’s TAR model and Engle and Granger’s model of cointegration[30]knownasavectorerror-correctionmodel (VECM). Just how high should R 2 be in regression analysis? I hear this question asked quite frequently. number = NULL) Arguments z An object of class ca. We made use of the statistical Augmented Dickey-Fuller, Phillips-Perron and Phillips-Ouliaris tests for the presence of unit roots and cointegration. Monetary and Fiscal Impacts on Economic Activities in Bangladesh A Note. Introduction. It distinguishes between stationary variables with transitory (temporary) effects and nonstationary variables with permanent (persistent) effects. Beginners with little background in statistics and econometrics often have a hard time understanding the benefits of having programming skills for learning and applying Econometrics. We provide around the clock care by highly trained and compassionate staff. For the two special cases of an intercept and a linear trend there exists a simpler way to declare these terms. Do not run regressions with them in levels, as any result will be spurious. The demand for housing services decreases with the reduction in real rental fee (R), while it increases with household’s (Y) real income. If we select null hypothesis, in case of rejecting null hypothesis there is the same problem. This is consistent with Tswei (2013) findings that earnings exhibit higher volatility because market information is first reflected in the earnings of the current quarter when earnings are announced by quarter. "Measuring Price Discovery Between Nearby and Deferred Contracts in Storable and Non-Storable Commodity Futures Markets. R Tutorial : How to interpret F Statistic in Regression Models. Note:**** The views expressed in this site are those of my own and do not necessarily represent those of my employer. Put your R skills to the test Start Now. 다만 이는∆CPIt에 대한 Time Varying VECM이기 때문에 ∆ert 에 관해서는 다시 외생변수를 설정하여야 할 것이다. As a kind of scarce natural capital, energy makes more and more obvious constraint effects on economic growth. mk ) ABSTRACT In this paper the issue of causality between wages and prices in R. This is not an example of the work produced by our Essay Writing Service. 7 Reject the null r <= 1 40. • In many cases, because the latter explained the former it. Once a model has been estimated, the diagnostic tests as well as the stability anal-ysis, structural analysis and forecasting use the results from the estimation. test showed the existence of three co integrating vectors and the rejection of the null hypothesis of r = 0. Or copy & paste this link into an email or IM:. It distinguishes between stationary variables with transitory (temporary) effects and nonstationary variables with permanent (persistent) effects. Imran Rjn commented> If i am not wrong then you mean to say, residual test which include normality, autocorrelation LM Test, Portmanteau Test and Heteroskedasticity test Sayed Hossain Yes. Still the sign of (also ) is not identi ed. VECM example. Start by testing H 0: r = 0. Unformatted text preview: Lecture 8 VAR, VECM, Granger Econ 324 Ivan Tchinkov 1 Granger Causality (not in the book) • We said you should be cautious about interpreting correlation and regression results as re ecting causality. Terrell The Australian National University, Australia Vector error-correction models (VECM) are increasingly. VECM with 3rd optimal lag or VECM (3). Algorithms. 99) are larger than those of market prices and book value. Section 4 fits a VEC model. In section 4 we outline some potential applications. III A necessary and suﬃcient condition for weak exogeneity in VECM models As it is now well-admitted, the presence or lack of weak exogeneity2 depends crucially on what parameters the focus of attention is, but contrary to what it is often assumed in a cointe-. The advantage of VECM over VAR is that the resulting VAR from VECM representation has more efficient coefficient estimates. "Analysis of Integrated and Cointegrated Time Series with R (2 nd Edition) … offers a rigorous introduction to unit roots and cointegration, along with numerous examples in R to illustrate the various methods. Overview KULKUNYA PRAYARACH, PH. trimming parameter indicating the minimal percentage of observations in each regime. Modeling Long-Run Relationships in Finance II. What does the sign of the causality imply w. Manual for Johanson Cointegration VECM model Posted on January 19, 2015 January 19, 2015 by Noman Arshed Posted in Nomi's Blog Tagged impulse response funtion , johanson juselius model , time series models , Unit Root , variance decomposition , vecm. "Analysis of Integrated and Cointegrated Time Series with R (2 nd Edition) … offers a rigorous introduction to unit roots and cointegration, along with numerous examples in R to illustrate the various methods. Upload your research data, share with select users and make it publicly available and citable. To pass a deterministic term inside the cointegration relation, we can use the exog_coint argument. Vector Identities: Index. Overview KULKUNYA PRAYARACH, PH. Accurate price forecasts can provide investors trading strategies with numerous profits to make appropriate decisions. Vector autoregressive models Vector autoregressive (VAR) models A p-th order vector autoregression, or VAR(p), with exogenous. This video demonstrates the estimation of the VECM on EViews. Unformatted text preview: Lecture 8 VAR, VECM, Granger Econ 324 Ivan Tchinkov 1 Granger Causality (not in the book) • We said you should be cautious about interpreting correlation and regression results as re ecting causality. This study examines the impact of macroeconomic variables on foreign direct investment in Nigeria over the period of 1981 to 2014. Hal ini berarti hipotesis nol yang menyatakan bahwa tidak ada kointegrasi ditolak dan hipotesis alternatif yang menyatakan bahwa ada kointegrasi tidak dapat ditolak. com 8 July 2009 National Institute for Public Finance and Policy, India Agroscope, Federal O ce for Agriculture, Switzerland Matthieu Stigler Matthieu. Based on empirical analysis and econometrics technique, co integration method was adopted to measure the long run relationship between macroeconomic variables (economic growth, exchange rate. Panel vector autoregression (VAR) models have been increasingly used in applied research. The dynamics part of the model describes the SR effects; The CI relation describes the LR relation between the variables. Tables in R (And How to Export Them to Word). Financial deepening indicators are the economic conditions that improve competitive efficiency of the financial market which in turn stimulate the non-financial sectors of an economy; hence, this link between these financial deepening indicators and economic growth has received considerable attention in the developing economy in recent times. chaotic dynamics of non-linear processes in atomic and molecular systems in electromagnetic field and semiconductor and fiber laser devices: new approaches, uniformity and charm of chaos. t VECTOR ERROR CORRECTION MODEL (VECM): Concept Model Short term effects of X on Y Long Term effects of X on Y (long run multiplier) The Speed at which Y returns to equilibrium after deviation has occurred. All gists Back to GitHub. It is important to perform LM diagnostic test after VECM such to use active vec model. I am running VECM and the ECT is negative (correct sign which indicates an equilibrium in the long-run despite short-run shocks) but it is too big (i. July 13, 2015, Using gret l for Principles of Econometrics, 4th Edition No comments. VECM example. Essentially, it seeks to find stationary linear combinations of the two vectors. Penm The Australian National University, Australia R. X and Y are cointegrated. Consequently, there has been a sharp increment of remittance inflow in the recent years. txt) or view presentation slides online. But I noticed it is panal VAR. If it rejects, repeat for H 0: r = 1. Bank Lending Channel in Indonesia's Monetary Policy Transmission Mechanism : A VECM Approach Proceedings of ISER 5th International Conference, Singapore, 5th September 2015, ISBN: 978-93-85465-91-8 29 In some cases Trace and Maximum Eigenvalue. This brings about the problems of the relationships among energy consumption, carbon emissions, and economic growth, which is worthy of long-term attention. is not identi ed from the VECM =) Estimate := ′ instead. com 8 July 2009 National Institute for Public Finance and Policy, India Agroscope, Federal O ce for Agriculture, Switzerland Matthieu Stigler Matthieu. In Section 9 we take stock of the ARCH process. B is an m-by-r cointegration matrix. Good morning Sir My name is Prabhdeep Kaur. Hi, I wanted to estimate a VEC model using vars package and gone through it's ca. Does exist a matlab code which estimates a VECM - Garch, that is a multivariate cointegration model with Garch effect? Thanks 0 Comments. Terrell The Australian National University, Australia Vector error-correction models (VECM) are increasingly. Sorry, I inadvertently omitted the curre. For verified definitions visit AcronymFinder. We consider two measures of productivity, namely total factor productivity (TFP) and labor productivity for analysis. I need to estimate a multivariate VECM-GARCH (or simply VAR-GARCH) in R. The book, now in its second edition, provides an overview of this active area of research in time series econometrics. Although this manual is self-contained, it can be used as a supplementary resource for the “Principles of Econometrics” textbook by Carter Hill, William Griffiths and Guay Lim, 4-th edition (Hill, Griffiths, and Lim 2011). test function uses a constant and trend in the test equation; therefore, the critical. The Equivalence of Causality Detection in VAR and VECM Modeling with Applications to Exchange Rates T. We provide around the clock care by highly trained and compassionate staff. As the results of the above adf and cointegration tests show, the series are both I(1) but they fail the cointegration test (the series are not cointegrated. While programs specifically designed to estimate time-series VAR models are often included as standard. ARDL BOUNDS TESTING APPROACH TO COINTEGRATION: A RE-EXAMINATION OF AUGMENTED FISHER HYPOTHESIS IN AN OPEN ECONOMY R. UNIT ROOT TESTS, COINTEGRATION, ECM, VECM, AND CAUSALITY MODELS Compiled by Phung Thanh Binh1 (SG - 30/11/2013) "EFA is destroying the brains of current generation's researchers in this country. Deterministic terms outside the cointegration relation. 1,2,3 School of Mathematical Sciences, Universiti Sains Malaysia, 11800, Pulau Pinang, Malaysia *Corresponding author: wai_phoong@yahoo. Monetary and Fiscal Impacts on Economic Activities in Bangladesh A Note. ジバンシィ ショートパンツ ハーフパンツ 半ズボン メンズ【Givenchy Vertical Embroidered Logo Swe,ポリス POLICE EVEN イーブン 二つ折り財布 財布 イタリアンレザー PA5502,ダイヤモンドサプライ Diamond Supply Co Dugout Baseball Jersey (black) メンズ | - cccsb. Number of lags to include in each regime. I need to estimate a multivariate VECM-GARCH (or simply VAR-GARCH) in R. This handout illustrates the steps to carry out Unit Root tests, Johansen cointegration test, Granger Causality, variance decomposition and Impulse response functions. In this paper we present two procedures to test weak exogeneity in a coin-tegrated system without estimating the cointegration vectors. Sorry, I inadvertently omitted the curre. Take a look at the tyDyn package. The Engle–Granger approach as described above suffers from a number of weaknesses. This study examines the impact of macroeconomic variables on foreign direct investment in Nigeria over the period of 1981 to 2014. VECM (data, lag, r = 1, include = c ("const", "trend", "none", "both"), beta = NULL, estim = c ("2OLS", "ML"), LRinclude = c ("none", "const", "trend", "both"), exogen = NULL) Arguments data. • In many cases, because the latter explained the former it. Examination administration date confirmed (C. This video demonstrates the estimation of the VECM on EViews. When a test is not rejected, stop testing there, and that value of r is the commonly-used estimate of the number of cointegrating relations. 1 6 1 3 6 9 0. Cite this article. Then I have tested for Granger and I got. If you are good in codes, R is better. Dealing with Structural Breaks ∗ Pierre Perron Boston University This version: April 20, 2005 Abstract This chapter is concerned with methodological issues related to estimation, testing and computation in the context of structural changes in the linear models. Ask Question Asked 5 years, 11 months ago. VEC model equivalent, returned as a vecm model object. A veterinarian is on site at all times. The advantage of VECM over VAR is that the resulting VAR from VECM representation has more efficient coefficient estimates. C2254M (2/11) 3 Description The IM-VECM corner mount adapter is spec ifically designed for use with Sarix ™ IM-E/IM-V Series network dome cameras. Then uses in r-t in London to model on 2 lags of returns in new york and london (equation 4). Once a model has been estimated, the diagnostic tests as well as the stability anal-ysis, structural analysis and forecasting use the results from the estimation. Remarkably this pattern can be observed for single years at least since 1998, though both are assumed to be geometric. In this post, I want to show how to run a vector autoregression (VAR) in R. The model uses r_t in New York to model on 2 lags of returns in new york and London (equation 3). VAR, SVAR and VECM models Christopher F Baum EC 823: Applied Econometrics Boston College, Spring 2013 Christopher F Baum (BC / DIW) VAR, SVAR and VECM models Boston College, Spring 2013 1 / 61. mk ) ABSTRACT In this paper the issue of causality between wages and prices in R. The GSoC might be a good opportunity to introduce VECM-related functionality into statsmodels. Group Work Modeling Long-run Relationship in Finance 1. Keywords: Economic growth, Unemployment, VECM, South Africa 1. #'The arg beta allows to specify constrained cointegrating values, leading to ECT= β^{'}X_{t-1}. Panel vector autoregression (VAR) models have been increasingly used in applied research. Note that since ur. 20, 14195 Berlin, Germany, andreas. number = NULL) Arguments z An object of class ca. 2-d endogenous response variable. Easily share your publications and get them in front of Issuu's. Write equations VAR and VECM equations in R. Further, the R-square value of all three variables are good enough to justify their causality, and p values close to zero also indicates significance. Estimating with unrestricted OLS the level VAR and the VECM will give identical results. I am trying to estimate a VECM model for demand (ln_qt) as dependent variable; and (ln_VKM , lnincome , Lnf ] as three. com 238 Structural Breaks, Cointegration, and Causality by VECM Analysis of. Are these representing the estimates for my loading matrix or also denoted the "alpha" matrix? Thanks in advanced Emil -- View this message in context. "Measuring Price Discovery Between Nearby and Deferred Contracts in Storable and Non-Storable Commodity Futures Markets. Table of Contents Index EViews Help. 3 shows a long serial correlation sequence; therefore, I will let $$R$$ calculate the lag order in the ADF test. VEC model equivalent, returned as a vecm model object. The support for these models in statsmodels leave something t. st: Granger causality test for VECM. We made use of the statistical Augmented Dickey-Fuller, Phillips-Perron and Phillips-Ouliaris tests for the presence of unit roots and cointegration. Can you recommend a good R package for VECM and cointegration? Hi, Cointegration and VECM analysis are given in the link as Screenshots from EVIEWS. In Section 6 we introduce the VECM-lead(CointEq1) Model. Instead of doing that, I have been running R directly off my phone using the terminal. It is fully specified because all parameters have known values. The relationship between carbon dioxide and agriculture in Ghana: a comparison of VECM and ARDL model. Sir, I am trying to test some restrictions in vecm. If the matrix has a full rank (), all components of are. Consequently, there has been a sharp increment of remittance inflow in. Financial deepening indicators are the economic conditions that improve competitive efficiency of the financial market which in turn stimulate the non-financial sectors of an economy; hence, this link between these financial deepening indicators and economic growth has received considerable attention in the developing economy in recent times. Monetary and Fiscal Impacts on Economic Activities in Bangladesh A Note. The $$R$$ function fevd() in package vars allows forecast variance decomposition. given r, the maximum likelihood estimator of β defines the combination of yt−1 that yields the r largest canonical correlations of Δyt with yt−1. If it rejects, repeat for H 0: r = 1. Important note for package binaries: R-Forge provides these binaries only for the most recent version of R, but not for older versions. It is a combination of Tong’s TAR model and Engle and Granger’s model of cointegration[30]knownasavectorerror-correctionmodel (VECM). Are these Granger causality-tests in a VECM context implemented in any standard econometrics software (I am using stata but I could not find any Granger causality-test in a VECM framework)? Thanks to you I can see the problem of a pretest bias when conducting tests in a VECM. Macedonia has been tested. When the rank of the matrix is , there are linear combinations that are nonstationary and r stationary cointegrating relations. [12] Chowdhury, A. Watson (2015). Impulse response analyis. Cointegration - Johansen Test with Stata (Time Series) In the previous discussion we had shown that how we do the cointegration test what we called it as Engle and Granger test. In the VECM you have three dependent variables. Once a model has been estimated, the diagnostic tests as well as the stability anal-ysis, structural analysis and forecasting use the results from the estimation. • In many cases, because the latter explained the former it. In this post, I want to show how to run a vector autoregression (VAR) in R. The Engle–Granger approach as described above suffers from a number of weaknesses. Dealing with Structural Breaks ∗ Pierre Perron Boston University This version: April 20, 2005 Abstract This chapter is concerned with methodological issues related to estimation, testing and computation in the context of structural changes in the linear models. Economist a73f. In section 4 we outline some potential applications. Hello I am also working on Panel VECM in my thesis. If we select null hypothesis, in case of rejecting null hypothesis there is the same problem. pdf), Text File (. The eigenvector is the cointegrating relationship and the weight is their coefficient, if they are used, in for example a VECM. The number of lags used in the vector autoregression is chosen based on the evidence provided by Akaike's Information Criterion (AIC) (see Akaike, 1973). It should be specified as a K \times r matrix. Last active Aug 10, 2019. jo does not set the rank $$r$$ of the cointegration matrix automatically, it has to be specified. I would personally only use a VECM model with a small amount of variables which you are very familiar with and their effects on each other. In the case of a threshold model, it is clear that initial conditions ω t − 1 matter: if the IRF is started in a low or high regime, impacts will be different. Against this background, this paper tries to analyze the major long and short run determinants of tax revenue in the state of Jammu and Kashmir by applying suitable econometric methods such as VECM and by taking a broader set of variables which comprise Economic, Political and demographic sectors. Constraints may be placed on the parameters in the cointegrating equations or on the adjustment terms. 2 4 0 7 9 6. Threshold cointegration in R with package tsDyn Matthieu Stigler Matthieu. I am finding relation between two time series M & M1. VECM with 3rd optimal lag or VECM (3). Consequently, there has been a sharp increment of remittance inflow in. 0 Reject the null. "Analysis of Integrated and Cointegrated Time Series with R (2 nd Edition) … offers a rigorous introduction to unit roots and cointegration, along with numerous examples in R to illustrate the various methods. Namely it is restricted to only a single equation with one variable designated as the dependent variable, explained by another variable that is assumed to be weakly exogeneous for the parameters of interest. cointegration vectors, and then test weak exogeneity. GDP example above was carried out manually in a series of steps in order to familiarize you with the structure of the VEC model and how, at least in principle, they are estimated. If we select null hypothesis, in case of rejecting null hypothesis there is the same problem. , R, ɛ m, ᴫ (4) Effect of the independent variables like (Y, Ȳ, C, I, ɛ x, R, ɛ m, ᴫ) on trade balance of Ethiopia can be judged by using the following regression model in a linear form especially in the long-run:- T= α +ß 1 Y + ß 2Ȳ + ß 3 C + ß 4 I + ß 5ɛ x + ß 6 R + ß 7ɛ m +ß 8ᴫ + μ t (5). For this model, r was identified to be 3. Sign in Sign up Instantly share code, notes, and. Please tell me If I am doing VECM model properly:-lag order selection for VEC/VAR model for variables D. Package tsDyn: Wiki. What does the sign of the causality imply w. The pound sign (#) is a comment charac-ter: Everything to its right is ignored by the R interpreter. Objective Analysis of multivariate time-series data using R: I To obtain parsimonious models for estimation I To extract \useful" information when the dimension is high I To make use of prior information or substantive theory I To consider also multivariate volatility modeling and applications Ruey S. Correlation, Variance and Covariance (Matrices) Description. Further, the R-square value of all three variables are good enough to justify their causality, and p values close to zero also indicates significance. Assume ′ = I r =) Cointegrating space is a Steifel manifold (not the whole r-dimensional linear subspace in RN) 3. In most applications, you will. B is an m-by-r cointegration matrix. In this tutorial we will learn how to interpret another very important measure called F-Statistic which is thrown out to us in the summary of regression model by R. 0 draft) Oscar Torres-Reyna otorres@princeton. Overview KULKUNYA PRAYARACH, PH. For this model, r was identified to be 3. ppt), PDF File (. However I could not find any option to have following inputs: 1. Viewed 736 times 4. Based on empirical analysis and econometrics technique, co integration method was adopted to measure the long run relationship between macroeconomic variables (economic growth, exchange rate. Cointegration - Johansen Test with Stata (Time Series) In the previous discussion we had shown that how we do the cointegration test what we called it as Engle and Granger test. "Analysis of Integrated and Cointegrated Time Series with R (2 nd Edition) … offers a rigorous introduction to unit roots and cointegration, along with numerous examples in R to illustrate the various methods. I am running VECM and the ECT is negative (correct sign which indicates an equilibrium in the long-run despite short-run shocks) but it is too big (i. Assume ′ = I r =) Cointegrating space is a Steifel manifold (not the whole r-dimensional linear subspace in RN) 3. Stigler at gmail. jo does not set the rank $$r$$ of the cointegration matrix automatically, it has to be specified. RUPIAH (KURS) DAN INFLASI DENGAN VECTOR ERROR CORRECTION MODEL (VECM) Universitas Pendidikan Indonesia | repository. Zhepeng Hu, Philip Garcia, Mindy Mallory. multivariate time series (first row being first=oldest value) lag.


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×

# Integrable?

$\large{\displaystyle \int ^{\frac{\pi}{2}}_{0} \arccos (\tan \left(\frac{x}{2}\right)) dx}$

Note by Tanishq Varshney
1 year, 5 months ago

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What makes you think it has a closed form? · 1 year, 5 months ago

Actually while solving one of the question , my mistake yielded this, so I checked it on wolfram alpha and it gave me an answer. · 1 year, 5 months ago

You didn't answer my question: is there a closed form? · 1 year, 5 months ago

I couldn't find it , probability of finding its closed form is 1/2 ;). · 1 year, 5 months ago

Can you at least tell where/how you form this integral? · 1 year, 5 months ago

The simplest form I can find is $$\displaystyle 2 \sum_{n=0}^\infty \dfrac{ (-1)^n (2n)!!}{(2n+1)(2n+1)!!}$$. · 1 year, 5 months ago

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## Basic College Mathematics (10th Edition)

$\frac{4}{3}$ $\frac{8}{7}$ $\frac{1}{5}$ $\frac{19}{12}$
The reciprocal of $\frac{3}{4}$ is $\frac{4}{3}$. The reciprocal of $\frac{7}{8}$ is $\frac{8}{7}$. The reciprocal of 5 is $\frac{1}{5}$. The reciprocal of $\frac{12}{19}$ is $\frac{19}{12}$.


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Drake
Drake C++ Documentation
drake_throw.h File Reference

Detailed Description

Provides a convenient wrapper to throw an exception when a condition is unmet.

This is similar to an assertion, but uses exceptions instead of ::abort(), and cannot be disabled.

#include <type_traits>
#include "drake/common/drake_assert.h"
Include dependency graph for drake_throw.h:
This graph shows which files directly or indirectly include this file:

drake

Macros

#define DRAKE_THROW_UNLESS(condition)
Evaluates condition and iff the value is false will throw an exception with a message showing at least the condition text, function name, file, and line. More...

◆ DRAKE_THROW_UNLESS

 #define DRAKE_THROW_UNLESS ( condition )
Value:
do { \
typedef ::drake::assert::ConditionTraits< \
typename std::remove_cv_t<decltype(condition)>> Trait; \
static_assert(Trait::is_valid, "Condition should be bool-convertible."); \
static_assert( \
!std::is_pointer_v<decltype(condition)>, \
"When using DRAKE_THROW_UNLESS on a raw pointer, always write out " \
"DRAKE_THROW_UNLESS(foo != nullptr), do not write DRAKE_THROW_UNLESS" \
"(foo) and rely on implicit pointer-to-bool conversion."); \
if (!Trait::Evaluate(condition)) { \
::drake::internal::Throw(#condition, __func__, __FILE__, __LINE__); \
} \
} while (0)
std::enable_if_t< std::is_same_v< typename Derived::Scalar, Expression >, MatrixLikewise< double, Derived > > Evaluate(const Eigen::MatrixBase< Derived > &m, const Environment &env=Environment{}, RandomGenerator *random_generator=nullptr)
Evaluates a symbolic matrix m using env and random_generator.
Definition: expression.h:1454

Evaluates condition and iff the value is false will throw an exception with a message showing at least the condition text, function name, file, and line.

The condition must not be a pointer, where we'd implicitly rely on its nullness. Instead, always write out "!= nullptr" to be precise.

Correct: DRAKE_THROW_UNLESS(foo != nullptr); Incorrect: DRAKE_THROW_UNLESS(foo);

Because this macro is intended to provide a useful exception message to users, we should err on the side of extra detail about the failure. The meaning of "foo" isolated within error message text does not make it clear that a null pointer is the proximate cause of the problem.


text:
Elementary Geometry for College Students (5th Edition)

$a\approx10.9$ ft $b\approx11.7$ ft
$\sin47^{\circ}=\frac{b}{16}$ $b=16\times\sin47^{\circ}$ $b\approx11.7$ Using Pythagorean Theorem to find $a$. $a=\sqrt {16^{2}-b^{2}}$ $a\approx\sqrt{16^{2}-11.7^{2}}$ $a\approx10.9$


text:
# Reading Merkulov: Differential geometry for an algebraist (4 in a series)

Published: Mon 24 April 2006

Suppose we have a presheaf $$\mathcal F$$ of abelian groups over $$M$$ and pick a point $$x$$. On the collection of all abelian groups defined over some neighbourhood of $$x$$ (disjoint union) we put an equivalence relation which identifies $$f\in\mathcal F(U)$$ and $$g\in\mathcal F(V)$$ precisely if there is some open $$W$$ in the intersection where $$f$$ and $$g$$ coincide. (or more precisely, their restrictions coincide). The set of equivalence classes turns out to be an Abelian group $$\mathcal F_x$$ called the stalk of the presheaf $$\mathcal F$$ at $$x$$.

So, with more fluff introduced, the stalk is all the elements in the presheaf that are defined above any neighbourhood of the point, and counted as the same if they seem to be.

For an open set $$U$$ and a point $$x\in U$$ there is a canonical group morphism $$\rho_x:\mathcal F(U)\to\mathcal F_x$$ which sends an element $$f\in\mathcal F(U)$$ to its equivalence class. This image is the germ of $$f$$ at $$x$$.

## Example

Let $$\mathcal O$$ be the presheaf of holomorphic function on $$\mathbb C$$. Then $$\mathcal O_{z_0}$$ is precisely the set of all convergent power series of the form $$\sum_{n=0}^\infty c_n(z-z_0)^n$$ for complex $$c_n$$. The germ of some $$f$$ defined on a neighbourhood of $$z_0$$ is precisely the Taylor series around that point.

## Example

Take $$\mathbb Z$$ the constant presheaf where over each open set, the additive group of all integers hovers. Then we have for the construction of the stalk a disjoint union of copies of $$\mathbb Z$$ indiced by all the neighbourhoods of the point. Since all the neighbourhoods contain $$x$$ they all have a non-empty intersection, on which elements agree if they have the same value. So $$\mathcal F_x=\mathbb Z$$ for any point $$x$$. The germ of $$i\in\mathbb Z=\mathcal F(U)$$ at $$x$$ is $$i\in\mathbb Z=\mathcal F_x$$.

We define exact sequences by looking at the induced maps of the stalks. A sequence of sheave morphisms is exact if for every point on the underlying space, the corresponding induced stalk map sequences are exact.

## Example

We can construct a morphism of sheaves of abelian groups from $$\mathbb C$$ to $$\mathcal O$$ by sending $$c\in\mathbb C(U)$$ to the function $$f(z)=c$$ in $$\mathcal O(U)$$. For some point $$z_0$$, this induces a stalk map that takes $$c$$ in $$\mathbb C_{z_0}$$ and sends it to the function defined by the convergent power series $$c(z-z_0)^0=c$$. Regardless of $$z_0$$, this map is obviously an injection, and so this map is a monomorphism.

### Space étalé and sheafifications

Given a presheaf $$\mathcal F$$, we construct the set $$|\mathcal F|$$ as the disjoint union of all stalks $$\mathcal F_x$$. There's an natural projection $$\pi:f_x\mapsto x$$ down to the underlying topological space. We can introduce a topology on $$|\mathcal F|$$ by constructing, for each open set $$U\subseteq M$$ and each element $$f\in\mathcal F(U)$$, the set $$[U,f]=\{\rho_x(f)\mid x\inU\}\subseteq|\mathcal F|$$ and take these sets to be a basis of our topology. So an open set is given from the $$[U,f]$$ by a sequence of (possibly infinite) unions and finite intersections.

This turns out to be a covering of $$\mathcal F$$, i.e. each $$e\in|\mathcal F|$$ has an open neighbourhood which is homeomorphic to its image under the projection $$\pi$$. We call the topological space $$|\mathcal F|$$ with this topology the space étalé of the presheaf $$\mathcal F$$.

Using the space étalé, then, we can construct a canonical sheaf. A continuous section of a covering space $$\pi\colon\mathcal F\to M$$ over a subset $$U\subseteq M$$ is a continuous map $$\sigma\colon U\to|\mathcal F|$$ such that $$\pi\circ\sigma=\mathbb 1$$.

## Example

$$\mathbb R$$ is a covering space of the circle (viewed as the interval [0,1] with 0 identified with 1) with the projection $$x\mapsto x\pmod1$$. A continuous section of the upper open halfcircle is a map $$\sigma_n\colon x\mapsto x+n$$. Indeed, $$\pi\circ\sigma_n$$ takes some point $$x$$ to $$x+n$$ and then to $$x+n\pmod1$$

Now, let $$\Gamma(U,|\mathcal F|)$$ denote the set of all continuous sections of $$|\mathcal F|$$ over $$U$$. This ends up in the same category that $$\mathcal F$$ goes to. From this, we then define a sheaf $$\hat{\mathcal F}$$ by setting $$\hat{\mathcal F}(U)=\Gamma(U,|\mathcal F|)$$, and letting restriction be the usual restriction of maps. This gives us a functor from presheaves to sheaves called sheafification.

## Example

We already saw that $$\mathbb Z_{\text{const}}$$ assigning the group $$\mathbb Z$$ to each open subset $$U$$ of a manifold $$M$$ and with all restrictions being identity morphisms is not a sheaf. What happens if we sheafify? First, we need to construct our space étalé. This is the disjoint union of all stalks. A stalk over a point $$x$$ is the quotient of the disjoint union of all $$\mathbb Z_{\text{const}}(U)$$ for $$x\in U$$ with the equivalence relation that identifies $$(n,U)\equiv(m,V)$$ if there is some $$W\subset U\cap V$$ such that $$n|_W=m|_W$$. Now, all neighbourhoods of $$x$$ intersect in some open subset, and since all restrictions are identities, we identify $$(n,U)$$ with $$(n,V)$$ for all pairs of open neighbourhoods $$U$$,$$V$$; so in end-effect all stalks are isomorphic, as groups, to $$\mathbb Z$$.

The space étalé is thus the disjoint union for all points $$x\in M$$ of copies of $$\mathbb Z$$; i.e. the set of ordered pairs on the form $$(x,n)$$ for $$x\in M$$ and $$n\in\mathbb Z$$. Finally, our sheafified sheaf assigns to each open subset $$U\subseteq M$$ the group of sections $$\Gamma(U,|\mathbb Z_{\text{const}}|)$$, thus a point there is a function $$U\to U\times\mathbb Z$$ such that $$x\mapsto n_x$$ for some $$n_x\in\mathbb Z$$. Since this map has to be continuous, the map is constant on neighbourhoods. And thus we recover the sheaf of locally constant maps for the constant sheaf; just as exhibited earlier.

### Kernels and quotients

Let $$\tau:\mathcal A\to\mathcal B$$ be a map of sheaves. For any open $$U\subseteq M$$, we define $$\mathcal K(U)=\ker\tau_U\colon\mathcal A(U)\to\mathcal B(U)$$. The sheaf $$\mathcal K$$ formed by these groups together with the induced morphisms from is called the kernel of the sheaf map.

The quotient of a sheaf map is formed almost the same way - pointwise components are formed as expected, but the presheaf thus formed need not be a sheaf. So we sheafify it.


text:
A polynomial function where the highest exponent is 2 is called a quadratic function. The graph of a quadratic function is called a parabola. It looks either like a happy smile, or a sad frown. You can see different parabolas below.

Theory

The quadratic function looks like this:

 $f\left(x\right)=a{x}^{2}+bx+c,$

where $a$, $b$ and $c$ are constants. The constants $a$ and $b$ are called coefficients. The term $a{x}^{2}$ is called a second-degree term or quadratic term, the term $bx$ is called a first-degree term or linear term, and $c$ is called the constant term.

Below you see a picture of the graphs of four different quadratic functions. Note that all have either a maximum or minimum.

Rule

### Parabola(MaximumandMinimum)

• When : The graph is smiling, and the function has a minimum (vertex).

• When : The graph is sad, and the function has a maximum (vertex).

Example 1

 $f\left(x\right)=\text{}0.5\text{}{x}^{2}˘x˘3$

Determine if the parabola has a maximum or a minimum.

You see that the coefficient in front of ${x}^{2}$ is a positive number ($a>0$). Therefore, the graph smiles and have a minimum.

Example 2

 $f\left(x\right)=-{x}^{2}˘x+12$

Determine if the parabola has a maximum or a minimum.

In this case, the coefficient in front of ${x}^{2}$ is a negative number ($a<0$). Therefore, the graph will face downwards and have a maximum, as in the figure below:

There are several methods to use to find the maximum or minimum. You can use the derivative, a sign chart, or the method that follows here:

Rule

### FindingtheMaximumorMinimumofaParabola

When you have the quadratic function

 $f\left(x\right)=a{x}^{2}+bx+c,$

you can find the $x$-values and $y$-values of the vertex like this:

The $x$-value of the maximum or minimum point:

 $x=-\frac{b}{2a}$

$y$-value of the maximum or minimum point:

 $y=f\phantom{\rule{-0.17em}{0ex}}\left(-\frac{b}{2a}\right)$

Example 3

Determine if the graph of $f\left(x\right)={x}^{2}-4x+4$ has a maximum or a minimum, and find this point

The function $f\left(x\right)$ has $a=1$, $b=-4$ and $c=4$. Since $a=1>0$ in the expression, you know that the graph is smiling and you have a minimum.

First, find the $x$-value, and then the $y$-value, of this minimum:

$\begin{array}{llll}\hfill x& =\frac{-\left(-4\right)}{2\cdot 1}=\frac{4}{2}=2\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill y& =f\left(2\right)\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & ={2}^{2}-\left(4\cdot 2\right)+4\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & =4-8+4\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & =0\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\end{array}$

$\begin{array}{llll}\hfill x& =\frac{-\left(-4\right)}{2\cdot 1}=\frac{4}{2}=2\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill y& =f\left(2\right)={2}^{2}-4\cdot 2+4=4-8+4=0\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\end{array}$

The minimum is then $\left(2,0\right)$.

Upon inspection of $f\left(x\right)={x}^{2}-4x+4$, you can see that this is a square and therefore has only one zero. In this case, the zero and the minimum are the same point.


text:
# Weakening democracy lol

#### JohnG

##### Senior Member
I think woke is the revolution eating its own children. Woke is the tail end of the rise of feminism and civil rights. The easy pickings have been plucked. If we want further equality we are going to have to do things that are not easy to identify, nor guaranteed to work. Woke is the frustration of the lack of progress, instead of pointing the guns outward towards shared enemies, the guns are pointed inward and the progressives start attacking themselves. The woke ethical standards are now so high that nobody qualifies. Certainly not the people claiming to be woke.

I consider myself progressive and I did not hear about woke through conservative channels. I heard it about it in progressive circles. People who identified as woke.

I have no doubt that it fits nicely into the conservative narrative and it makes perfect sense that they took it and ran with it. It doesn't make it wrong. Sometimes even the evil people say something true.

That all seems pretty vague. I can give you a very specific example of a fabrication of wokeness and it's effectiveness as a political tool by the right.

4 days ago a Virginia Rebublican won his election for governor. Surveys indicate he won that race, fueled by women, who voted based on education issues, specifically CRT in schools.

He focused on that issue during his campaign and it worked.

Only thing is there is zero CRT being taught in Virginia schools. It was just another fear tactic that the "Woke" progressives are going to ruin their lives. I know this is anecdotal, but it's very typical.

There are some very serious culture undercurrents going on in the USA. I don't think wokeness is one of them. I think the issue you are confusing it with is online echo chambers. They exist for every kind of nut imaginable.

It's not mutually exclusive. Conservatives can use dog whistles, taken out of context, to garner support while the same term inside the liberal camp can mean something different.

Also, conservatives are bound to misunderstand the nuances of a liberal concept. I'm convinced that those republicans had replaced CRT with "white man bad". Not entirely wrong. But misses nearly everything CRT is about. And that's fine. We shouldn't dumb down our internal language just because there are idiots on the other side who won't get it. Everybody is made smarter by using clear unambiguous language. If somebody is hellbent on misunderstanding you, there's nothing you can do to fix that.
RW political messaging is hampering the US moving forward. They are going to forever pay $200 for a vial of insulin because they can't stomach the idea of paying into a universal health care system that might help someone they don't "approve of". In Canada, our national radio station has been pretty good (not perfect) at educating people about the downsides of letting stigmatized minorities wither from lesser opportunities, and the human and economic costs of doing that. The basic concepts of what is happening (and why) aren't hard to grasp - it's the solutions that are complicated. Many people do a great job laying it out. However, there is a great interest in using it as a political divisive tool and the social and economic concepts are being countered with a narrative of victimization. Fox News is the most watched news feed and Tucker Carlson has the most watched program among adults aged 25 to 54. Its hard to cut through their relentless griping about how vulnerable groups are causing all America's problems. Now that it's a proven successful business model, it doesn't get any easier. #### Swammerdami ##### Squadron Leader Staff member I just noticed this thread and was slightly surprised to see I'd not posted. Briefly: OP is wrong, very very wrong. 100% wrong. He has it backwards. There is definitely such a thing as too much reductionism! Sometimes I wish I'd memorized the names of the major fallacies of reasoning; then I could just post a 2-word response, probably in Latin. Instead I will explain Fallacy #5 with examples. @ OP, do you find the following reasonable? "I stubbed my toe and that didn't hurt much, so go ahead and chop off my arm. Same-same." "A year ago my local newspaper published a letter from some moron or liar. So go ahead and bombard every American household with bullshit, some of it carefully constructed by the Kremlin. Same-same. Sure, millions of voters are stupid enough to be duped, but that's their fault, not mine." These caricatures do not form a long well-reasoned essay. But I've posted essays and links to essays on this topic before. Google knows where they are. Horse, water, drink? #### DrZoidberg ##### Contributor I think woke is the revolution eating its own children. Woke is the tail end of the rise of feminism and civil rights. The easy pickings have been plucked. If we want further equality we are going to have to do things that are not easy to identify, nor guaranteed to work. Woke is the frustration of the lack of progress, instead of pointing the guns outward towards shared enemies, the guns are pointed inward and the progressives start attacking themselves. The woke ethical standards are now so high that nobody qualifies. Certainly not the people claiming to be woke. I consider myself progressive and I did not hear about woke through conservative channels. I heard it about it in progressive circles. People who identified as woke. I have no doubt that it fits nicely into the conservative narrative and it makes perfect sense that they took it and ran with it. It doesn't make it wrong. Sometimes even the evil people say something true. That all seems pretty vague. I can give you a very specific example of a fabrication of wokeness and it's effectiveness as a political tool by the right. 4 days ago a Virginia Rebublican won his election for governor. Surveys indicate he won that race, fueled by women, who voted based on education issues, specifically CRT in schools. He focused on that issue during his campaign and it worked. Only thing is there is zero CRT being taught in Virginia schools. It was just another fear tactic that the "Woke" progressives are going to ruin their lives. I know this is anecdotal, but it's very typical. There are some very serious culture undercurrents going on in the USA. I don't think wokeness is one of them. I think the issue you are confusing it with is online echo chambers. They exist for every kind of nut imaginable. It's not mutually exclusive. Conservatives can use dog whistles, taken out of context, to garner support while the same term inside the liberal camp can mean something different. Also, conservatives are bound to misunderstand the nuances of a liberal concept. I'm convinced that those republicans had replaced CRT with "white man bad". Not entirely wrong. But misses nearly everything CRT is about. And that's fine. We shouldn't dumb down our internal language just because there are idiots on the other side who won't get it. Everybody is made smarter by using clear unambiguous language. If somebody is hellbent on misunderstanding you, there's nothing you can do to fix that. RW political messaging is hampering the US moving forward. They are going to forever pay$200 for a vial of insulin because they can't stomach the idea of paying into a universal health care system that might help someone they don't "approve of".

In Canada, our national radio station has been pretty good (not perfect) at educating people about the downsides of letting stigmatized minorities wither from lesser opportunities, and the human and economic costs of doing that.

The basic concepts of what is happening (and why) aren't hard to grasp - it's the solutions that are complicated. Many people do a great job laying it out. However, there is a great interest in using it as a political divisive tool and the social and economic concepts are being countered with a narrative of victimization.

Fox News is the most watched news feed and Tucker Carlson has the most watched program among adults aged 25 to 54. Its hard to cut through their relentless griping about how vulnerable groups are causing all America's problems. Now that it's a proven successful business model, it doesn't get any easier.
"hampering the US moving forward."

The measure of success for democracy isn't the degree of socialism in a society. If a majority of the people would vote for the Nazi party and the Nazis as such got into power that isn't a failure of democracy. That's exactly how democracy should work.

If progressives fail to convince voters to vote for them, then perhaps we should work on our arguments?

The degree of democracy of a society also isn't based on the amount of boring-as-fuck media people are willing to suffer through. If the progressive message isn't fun to listen to, we'll just have to work on our delivery. Seriousness and humorlessness is NOT the same thing. This is something us progressives can learn a thing or two from the conservatives.

#### Swammerdami

Staff member
The measure of success for democracy isn't the degree of socialism in a society. If a majority of the people would vote for the Nazi party and the Nazis as such got into power that isn't a failure of democracy. That's exactly how democracy should work.

Just to make sure I'm following you, there is a well-known historical instance when a majority of the people DID vote for the Nazi party and the Nazis (as such) DID get into power. It happened in Germany in 1932. Is this exactly how democracy "should" work?

(If you nit-pick that the Nazi coalition won only 44% of the vote and had to mount a "Stop the Steal" campaign to obtain complete control, you lose.)

#### fromderinside

##### Mazzie Daius
The measure of success for democracy isn't the degree of socialism in a society. If a majority of the people would vote for the Nazi party and the Nazis as such got into power that isn't a failure of democracy. That's exactly how democracy should work.

Just to make sure I'm following you, there is a well-known historical instance when a majority of the people DID vote for the Nazi party and the Nazis (as such) DID get into power. It happened in Germany in 1932. Is this exactly how democracy "should" work?

(If you nit-pick that the Nazi coalition won only 44% of the vote and had to mount a "Stop the Steal" campaign to obtain complete control, you lose.)
The Nazi Party only garnered 43.7% of the vote. As you wrote They managed to win a majority of seats by joining with another party to form a government.

#### fromderinside

##### Mazzie Daius
The measure of success for democracy isn't the degree of socialism in a society. If a majority of the people would vote for the Nazi party and the Nazis as such got into power that isn't a failure of democracy. That's exactly how democracy should work.

Just to make sure I'm following you, there is a well-known historical instance when a majority of the people DID vote for the Nazi party and the Nazis (as such) DID get into power. It happened in Germany in 1932. Is this exactly how democracy "should" work?

(If you nit-pick that the Nazi coalition won only 44% of the vote and had to mount a "Stop the Steal" campaign to obtain complete control, you lose.)

### Adolf Hitler's rise to power

(Summarized from above) The Nazi Party only garnered 43.7% of the vote. As you wrote They managed to win a majority of seats by joining with another party to form a government. Even then it is only because President von Hindenburg of Germany feared anarchy if he didn't acknowledge this coalition as winners they never would have won power.

#### DrZoidberg

##### Contributor
The measure of success for democracy isn't the degree of socialism in a society. If a majority of the people would vote for the Nazi party and the Nazis as such got into power that isn't a failure of democracy. That's exactly how democracy should work.

Just to make sure I'm following you, there is a well-known historical instance when a majority of the people DID vote for the Nazi party and the Nazis (as such) DID get into power. It happened in Germany in 1932. Is this exactly how democracy "should" work?

(If you nit-pick that the Nazi coalition won only 44% of the vote and had to mount a "Stop the Steal" campaign to obtain complete control, you lose.)

I was not referring to that particular historical event. Hitler grabbed power in a coup. Which is the opposite of democracy.

I only posed a hypothetical. But fascists have historically gotten into power lawfully.

In the 2012 Egyptian election Mohammed Morsi won on a openly anti-democratic Islamist Muslim Brotherhood ticket. He got 40% of the vote and created a coalition together with Al-Nour (30% of the vote) an even more bonkers anti-democratic Islamist party. Together they got 70% of the vote on the promise to make a one party islamist state. That was a free and fair election. The will of the people had spoken.

In 2010 Fidesz took power in Hungary in a free and fair election. They won again in 2014. A free and fair election. At this point they voted for constitutional changes to game the parliament in favour of Fidesz. This could only have succeeded if Fidesz won the 2018 election. The people cast their vote, Fidesz won and free and fair elections were history. Next Hungarian elections are next year. Who wants to bet against Fidesz winning?

The take away from this is that people do sometimes value things other than democracy as a greater good.

#### Swammerdami

Staff member
The measure of success for democracy isn't the degree of socialism in a society. If a majority of the people would vote for the Nazi party and the Nazis as such got into power that isn't a failure of democracy. That's exactly how democracy should work.
Just to make sure I'm following you, there is a well-known historical instance when a majority of the people DID vote for the Nazi party and the Nazis (as such) DID get into power. It happened in Germany in 1932. Is this exactly how democracy "should" work?

(If you nit-pick that the Nazi coalition won only 44% of the vote and had to mount a "Stop the Steal" campaign to obtain complete control, you lose.)
I was not referring to that particular historical event. Hitler grabbed power in a coup. Which is the opposite of democracy.
You didn't refer to that particular historical event. I did.

But I'm curious why you state that Hitler grabbed power in a coup. Before we proceed I think we'll need clarification of why some fascist takeovers are coups and some are not. . In accordance with German law, President Paul von Hindenburg appointed Mr. Hitler to be Chancellor and later issued the Verordnung des Reichspräsidenten zum Schutz von Volk und Staat.

Is your insight that 44% is less than 50%? What about the 2016 U.S. election where Trump prevailed with 46% to Clinton's 48%? Anyway, Hitler's coalition got 52% in the 1933 elections.

52% is more than 50%. Where's the coup? Are you the arbiter of whether or not a particular election is "exactly how democracy should work"?

#### lpetrich

##### Contributor
It is a problem with democracy -- if one votes to shut it down, then restoring it can be difficult.

As to Fidesz, it was hard to predict that Fidesz would try to tweak the electoral system so that it would be hard to defeat. Likewise with Nazism. There was no hint that it would end up outlawing all political parties but it itself, even its coalition partners.

That reminds me of a monarchist objecting to some ex-monarchy republics having provisions in their constitutions that forbid the re-establishment of monarchy. It would be hard to undo such a re-establishment.

#### DrZoidberg

##### Contributor
The measure of success for democracy isn't the degree of socialism in a society. If a majority of the people would vote for the Nazi party and the Nazis as such got into power that isn't a failure of democracy. That's exactly how democracy should work.
Just to make sure I'm following you, there is a well-known historical instance when a majority of the people DID vote for the Nazi party and the Nazis (as such) DID get into power. It happened in Germany in 1932. Is this exactly how democracy "should" work?

(If you nit-pick that the Nazi coalition won only 44% of the vote and had to mount a "Stop the Steal" campaign to obtain complete control, you lose.)
I was not referring to that particular historical event. Hitler grabbed power in a coup. Which is the opposite of democracy.
You didn't refer to that particular historical event. I did.

But I'm curious why you state that Hitler grabbed power in a coup. Before we proceed I think we'll need clarification of why some fascist takeovers are coups and some are not. . In accordance with German law, President Paul von Hindenburg appointed Mr. Hitler to be Chancellor and later issued the Verordnung des Reichspräsidenten zum Schutz von Volk und Staat.

Is your insight that 44% is less than 50%? What about the 2016 U.S. election where Trump prevailed with 46% to Clinton's 48%? Anyway, Hitler's coalition got 52% in the 1933 elections.

52% is more than 50%. Where's the coup? Are you the arbiter of whether or not a particular election is "exactly how democracy should work"?

I think what makes a democracy is the populations general attitude towards politics. In authoritarian regimes people don't talk about politics. It's not safe to. And their opinion doesn't matter anyway. In authoritarian regimes political discussions among the citizens is reduced to poking fun at their leaders in various ways.

The Pro-Trump Capital Hill riot does prove one thing. Americans feel empowered. They feel that their voice matters. And that's the primary hallmark of a well functioning democracy. I was in Egypt during the revolution. The Egyptians on Tahir square who rose up to topple Mubarak were prepared to die. Maybe not all of them. But they were warriors going to battle. They didn't wear war paint and dressed in a parody of native American dress. They didn't have humorous t-shirts.

A lot of people in well functioning well run democratic societies don't care about politics and can't be bothered to vote. In democracies people only get engaged in politics when they feel something is not developing in the right direction. So apathy and cynicism isn't necessarily a sign of a democracy not working.

Hitler exploited a legal loophole to topple the very institution his main job was to protect. That's a coup. Just because something is legal, doesn't make it morally right, or even in the spirit of what the law was intended to do. The entire point of laws is to direct people into constructive endevours that act to make the world a better place. I think few people think Hitler managed to do that.

#### DrZoidberg

##### Contributor
It is a problem with democracy -- if one votes to shut it down, then restoring it can be difficult.

As to Fidesz, it was hard to predict that Fidesz would try to tweak the electoral system so that it would be hard to defeat. Likewise with Nazism. There was no hint that it would end up outlawing all political parties but it itself, even its coalition partners.

My Hungarian ex-wife explained it to me. People think in dichotomies. In Hungarian politics the divide is between socialists and the conservatives. In 2006 this guy won the election for the socialists.

https://en.wikipedia.org/wiki/Ferenc_Gyurcsány

It turned out that he was a Putin puppet, sold out his nation, cooked the books and was generally, the worst possible prime minister a country can have. It all exploded in his face in a public manner. In the 2010 election the voters swung heavily to the right, just because they hated this guy so much. Fidesz was the leader of the conservative block, so managed to nab power. And that's the whole story. All they need to be is NOT massive traitors to their nation, and they will always look better than the socialists preceding them. It's not a hard competition to win.

That reminds me of a monarchist objecting to some ex-monarchy republics having provisions in their constitutions that forbid the re-establishment of monarchy. It would be hard to undo such a re-establishment.

But constitutions can be changed. If there's enough popular support for something it will happen. What matters ultimately in a democracy is the will of the people. Actually, that's also what ultimately matters in a dictatorship. If people's basic needs aren't met no ruler is safe.

#### Swammerdami

Staff member
The measure of success for democracy isn't the degree of socialism in a society. If a majority of the people would vote for the Nazi party and the Nazis as such got into power that isn't a failure of democracy. That's exactly how democracy should work.
Just to make sure I'm following you, there is a well-known historical instance when a majority of the people DID vote for the Nazi party and the Nazis (as such) DID get into power. It happened in Germany in 1932. Is this exactly how democracy "should" work?
I was not referring to that particular historical event. Hitler grabbed power in a coup. Which is the opposite of democracy.
You didn't refer to that particular historical event. I did.

But I'm curious why you state that Hitler grabbed power in a coup. Before we proceed I think we'll need clarification of why some fascist takeovers are coups and some are not. . In accordance with German law, President Paul von Hindenburg appointed Mr. Hitler to be Chancellor and later issued the Verordnung des Reichspräsidenten zum Schutz von Volk und Staat.

Hitler exploited a legal loophole to topple the very institution his main job was to protect. That's a coup. Just because something is legal, doesn't make it morally right, or even in the spirit of what the law was intended to do. The entire point of laws is to direct people into constructive endevours that act to make the world a better place. I think few people think Hitler managed to do that.

Can you be more specific? As I say, Hitler's Party won the Parliament; Hitler was appointed Chancellor in accordance with their constitutional processes. What "loophole" are you talking about? And anyway, is a "loophole" a "coup"?

Many or most democracies have idiosyncrasies. U.S. has the peculiar Electoral College which leads to R's becoming President despite the D winning the popular vote. Does this mean Trump won in 2016 via a loophole? Or via a coup? Google thinks "coup" is "a sudden, violent, and illegal seizure of power from a government." Do you have a different definition? (You do seem to have a Humpty-Dumptyish approach to definitions. What do you think a "Jewish temple" is again?

I'm trying to understand your "That's exactly how democracy should work." Was Trump's election "exactly how democracy should work"? Why wasn't Hitler's?

#### lpetrich

##### Contributor
has the numbers in its table "NSDAP federal election results (1924–1933)"

DateFractionRankSeatsNotes
1924 May6.5%632 / 472H in prison
1924 Dec3.0%814 / 493H released
1928 May2.6%912 / 491
1930 Sep18.3%2107 / 577After financial crisis
1932 Jul37.3%1230 / 608H Presidency cand
1932 Nov33.1%1196 / 584
1933 Mar43.9%1288 / 647H Chancellor

Adolf Hitler was *not* directly elected leader, and his party did *not* win a majority of votes in any election where it had competition. Instead, it got into power by making a deal with the German National People's Party (DNVP), a nationalist-conservative party: - "National conservatism is a nationalist variant of conservatism that concentrates on upholding national and cultural identity. National conservatives usually combine this patriotism with conservative stances promoting traditional cultural values, opposition to immigration, and family values."

In the middle of 1933, the Nazis outlawed all political parties but theirs. That included the DNVP, and the DNVP meekly shut itself down.

#### Swammerdami

Staff member
The topic was NOT Hitler's rise to power; it was Dr. Z's definition of "coup" and how to determine "exactly how democracy should work." There is reason to believe that GOP voter suppression has affected many elections in "red" states, and quite possibly even the 2016 Presidential Election. But the suppression measures were passed under the authority of "democratically elected" bodies. Is that exactly how democracy SHOULD work?

#### lpetrich

##### Contributor
So it's not a real coup if it's done from within? There is a name for that sort of coup: (translation of Spanish autogolpe). It's when a democratically elected leader makes himself dictator, and the article listed Adolf Hitler as an example, and Donald Trump as an attempted example.

#### DrZoidberg

##### Contributor
The measure of success for democracy isn't the degree of socialism in a society. If a majority of the people would vote for the Nazi party and the Nazis as such got into power that isn't a failure of democracy. That's exactly how democracy should work.
Just to make sure I'm following you, there is a well-known historical instance when a majority of the people DID vote for the Nazi party and the Nazis (as such) DID get into power. It happened in Germany in 1932. Is this exactly how democracy "should" work?
I was not referring to that particular historical event. Hitler grabbed power in a coup. Which is the opposite of democracy.
You didn't refer to that particular historical event. I did.

But I'm curious why you state that Hitler grabbed power in a coup. Before we proceed I think we'll need clarification of why some fascist takeovers are coups and some are not. . In accordance with German law, President Paul von Hindenburg appointed Mr. Hitler to be Chancellor and later issued the Verordnung des Reichspräsidenten zum Schutz von Volk und Staat.

Hitler exploited a legal loophole to topple the very institution his main job was to protect. That's a coup. Just because something is legal, doesn't make it morally right, or even in the spirit of what the law was intended to do. The entire point of laws is to direct people into constructive endevours that act to make the world a better place. I think few people think Hitler managed to do that.

Can you be more specific? As I say, Hitler's Party won the Parliament; Hitler was appointed Chancellor in accordance with their constitutional processes. What "loophole" are you talking about? And anyway, is a "loophole" a "coup"?

Many or most democracies have idiosyncrasies. U.S. has the peculiar Electoral College which leads to R's becoming President despite the D winning the popular vote. Does this mean Trump won in 2016 via a loophole? Or via a coup? Google thinks "coup" is "a sudden, violent, and illegal seizure of power from a government." Do you have a different definition? (You do seem to have a Humpty-Dumptyish approach to definitions. What do you think a "Jewish temple" is again?

I'm trying to understand your "That's exactly how democracy should work." Was Trump's election "exactly how democracy should work"? Why wasn't Hitler's?
No democratic country on Earth is perfect. They're all riddled with exploitable loopholes and exploits. They're also all different, can into existence in different historical contexts, have different economies and different cultures and ethnic compositions.

The ones that are stable have found a recipe that works. The ones that aren't haven't. I can't be more specific than that.

USA is an extremely well functioning democracy. It has problems, yes. But they all do.

USA has gamed the voter power and given more weight to less populace States. If they didn't US politics would be California, Texas and New York and the opinions of the rest of the country would be irrelevant. This would be bad. That's why Trump won in spite of only getting 46%.

In EU the voting power of small states is disproportionaly high. This is necessary, or no small state would join the EU.

So many people are rigidly hung up on democratic principles so that they forget about pragmatism. Nobody should give a shit about what should work. They should care about what actually works.

#### Swammerdami

Staff member
The ones that are stable have found a recipe that works. The ones that aren't haven't. I can't be more specific than that.
Is it a yes-no thing? Or is there a gradation between perfect democracy (if you think there is such a thing) and severely flawed democracy? If the latter is your opinion, then you have a nuanced view not dissimilar from my own.

Where you confuse me and make your message ambiguous is with phrases like "exactly how democracy should work." Trump and his QOPAnon allies use immoral trickery or non-democratic means to obtain electoral victory, and so did Adolf Hitler. Is it your position that one of these rises to power was EXACTLY how democracy SHOULD work and the other was exactly how democracy should NOT work?

If you DO perceive NUANCE, do you see that your diction misleads?

Had you posted what you did but without the word "exactly", I would have skimmed your post, agreed to disagree, and moved on. Perhaps I'm too pedantic but that adverb struck me as so absurd I felt I had no choice but to respond! If, on reflection, you now realize that that adverb was a bad rhetorical flourish that detracted from more nuanced thought, then you can recant and we can move on. (But I won't hold my breath!)

USA has gamed the voter power and given more weight to less populace States. If they didn't US politics would be California, Texas and New York and the opinions of the rest of the country would be irrelevant. This would be bad. That's why Trump won in spite of only getting 46%.

Two points:

(1) If the U.S. had a popular vote for President, as many would find preferable, do you see that this would NOT give New York and California special power? Each vote in California would have the EXACT same weight as each vote in Rhode Island.

(2) Portugal has different culture and traditions from Spain. It makes some sense that Portugal has its own voice in the EU, rather than being lumped in with Spain. Do you think North and South Dakota have sufficiently diverse cultures so that each needs its own electoral advantage? Is there a good reason why Rhode Island gets 2 Senators and the similar region of Southeastern Massachusetts does not? Almost 4 centuries ago, Rhode Island was started as a refuge from the authoritarian Puritanism of Massachusetts. Rhode Island's founder embraced Baptism. Do you think religious schism still separates Rhode Island from its Bristol County neighbors? (Spoiler alert! Rhode Island is now the most CATHOLIC of all the 50 states! )

If you want to argue that Yes, North Dakota and South Dakota have different cultures and so somehow merit the extra political power, all I can do is laugh. And point out there is more cultural variation just in Northern California than in the entirety of Flyover Land put together!

#### DrZoidberg

##### Contributor
The ones that are stable have found a recipe that works. The ones that aren't haven't. I can't be more specific than that.
Is it a yes-no thing? Or is there a gradation between perfect democracy (if you think there is such a thing) and severely flawed democracy? If the latter is your opinion, then you have a nuanced view not dissimilar from my own.

Where you confuse me and make your message ambiguous is with phrases like "exactly how democracy should work." Trump and his QOPAnon allies use immoral trickery or non-democratic means to obtain electoral victory, and so did Adolf Hitler. Is it your position that one of these rises to power was EXACTLY how democracy SHOULD work and the other was exactly how democracy should NOT work?

If you DO perceive NUANCE, do you see that your diction misleads?

Had you posted what you did but without the word "exactly", I would have skimmed your post, agreed to disagree, and moved on. Perhaps I'm too pedantic but that adverb struck me as so absurd I felt I had no choice but to respond! If, on reflection, you now realize that that adverb was a bad rhetorical flourish that detracted from more nuanced thought, then you can recant and we can move on. (But I won't hold my breath!)

In politics everyone thinks their side is rational and that the other side is swindled by demagogues. The truth is of course that it's a bit of both on both sides.

What sets liberals and conservatives apart is basic values.

I can recommend The Righteous Mind by Jonathan Haidt. He interviewed liberals and conservatives and asked them about their basic values. This book spells it out.

Fundamentally it comes down to how "fairness" is defined.

I'm a big believer in systems design and implicit nudging.

Either a system is self correcting and people acting within it makes it more stable over time. Or it becomes less stable over time.

It's also important to stay humble. Its entirely possible that the secret sauce that makes democracy so successful in the modern age, has eluded us all. The real reason democracies work might be something so subtle and left field that nobody has thought about it yet.

There's no shortage of democratic experiments that failed. In hindsight we're guessing what the problems were. But we don't really know. Not really.

USA has gamed the voter power and given more weight to less populace States. If they didn't US politics would be California, Texas and New York and the opinions of the rest of the country would be irrelevant. This would be bad. That's why Trump won in spite of only getting 46%.

Two points:

(1) If the U.S. had a popular vote for President, as many would find preferable, do you see that this would NOT give New York and California special power? Each vote in California would have the EXACT same weight as each vote in Rhode Island.

(2) Portugal has different culture and traditions from Spain. It makes some sense that Portugal has its own voice in the EU, rather than being lumped in with Spain. Do you think North and South Dakota have sufficiently diverse cultures so that each needs its own electoral advantage? Is there a good reason why Rhode Island gets 2 Senators and the similar region of Southeastern Massachusetts does not? Almost 4 centuries ago, Rhode Island was started as a refuge from the authoritarian Puritanism of Massachusetts. Rhode Island's founder embraced Baptism. Do you think religious schism still separates Rhode Island from its Bristol County neighbors? (Spoiler alert! Rhode Island is now the most CATHOLIC of all the 50 states! )

If you want to argue that Yes, North Dakota and South Dakota have different cultures and so somehow merit the extra political power, all I can do is laugh. And point out there is more cultural variation just in Northern California than in the entirety of Flyover Land put together!
1) the current US electoral system is the result of the civil war. Maybe don't fuck with until after the next civil war. Obviously things have changed since then. What was sensible and fair then, isn't now. But how are you going to change it now, without starting that civil war we're trying to avoid?

2) cultures shift gradually across Europe. I argue that borders between European nations can be drawn anywhere in Europe. Its all arbitrary.

The reason why we don't lump Portugal and Spain together in the EU is because its easier not to. There's no other reason. Its just practical this way


text:
Using the Context Panel - Maple Help

Using the Context Panel with DynamicSystems

Description

 • The DynamicSystems context-sensitive options in the Context Panel give you the ability to access almost all of the commands in the DynamicSystems package with the click of a mouse.
 • The DynamicSystems menu in the Context Panel consists of four submenus: System Creation, Conversion, Manipulation, and Plotting. Using these submenus, you can create DynamicSystems System Objects, convert between different DynamicSystems equation and matrix representations, analyze the dynamics of a system, and obtain plots of the frequency, impulse, and system response characteristics to a wide variety of inputs.

Accessing the Context-Sensitive Options

 • You can access the context-sensitive options for any of the following four inputs: continuous and discrete differential equations, state-space Matrices, continuous and discrete transfer functions, and zero-pole-gain Matrices. The inputs must be defined in the following manner to access the context-sensitive options:
 – Differential Equations: list of equation(s)
 – State Space Matrices: sequence of 4 Matrices
 – Transfer Functions: Matrix of one or several rational polynomials
 – Zero-Pole-Gain Matrices: sequence of 3 Matrices
 • From the Context Panel for one of these items, select Dynamic Systems. There are four submenus.

System Creation

 • Use the System Creation submenu to create DynamicSystems System Objects from the different DynamicSystems representations. After the System Objects are created, they can be used with any of the commands found within the DynamicSystems package.

 • Use the Conversions submenu to convert between the four DynamicSystems representations mentioned above, namely Differential Equation, State Space Matrices, Transfer Function, and Zero-Pole-Gain Matrices.

 • Use the Manipulations submenu to conduct analysis operations on all the DynamicSystems representations.
 • The following analysis operations are available from the Context Panel:

 Characteristic Polynomial Controllability Matrix Controllable Grammians Gain Margin Phase Margin Observability Matrix Observable

Note: The majority of these commands are only available for State Space inputs.

 • Use the Plots submenu to explore the underlying system dynamics using different plotting commands.
 • The plotting operations available through the context-sensitive options are listed below:

 Bode Plot Impulse Response Plot Magnitude Plot Phase Plot Nichols Plot Nyquist Plot Response Plot Root Contour Plot Root Locus Plot Zero Pole Plot

 • When creating a Response Plot, you can select from the following input signals:

 Chirp Ramp Sine Square Step Triangle

Examples

Conversion Example

1. Enter $\frac{1}{s+1}$.

 > $\frac{1}{s+1}$
 $\frac{{1}}{{s}{+}{1}}$ (1)

2. Select the expression. From the Context Panel, select Dynamic Systems>Conversions>Transfer Function to Differential Equation. The result will be:

$\left[\frac{ⅆ}{ⅆt}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}\mathrm{x1}\left(t\right)=-\mathrm{x1}\left(t\right)-\mathrm{u1}\left(t\right),\mathrm{y1}\left(t\right)=-\mathrm{x1}\left(t\right)\right]$

Plotting Example

3. Enter $\frac{1}{s+1}$.

 > $\frac{1}{s+1}$
 $\frac{{1}}{{s}{+}{1}}$ (2)

4. Select $\frac{1}{s+1}$, and from the Context Panel, select Dynamic Systems>Plots>Phase Plot.


text:
# Aspect-oriented vs explicit style in Python [closed]

Readability counts, but is very subjective. The following snippets are equivalent in functionality and turn a generator iterator into a chunked HTTP response in Flask. Which of those two patterns is more Pythonic, readable and convenient?

A) Aspect style with function decorators that change the return value:

@app.route('/')
@optional_streaming_decorator
@progress_log_decorator
def index() -> Iterator:
"""Index page, optionally HTTP chunk-streamed and formatted."""
return Foo.get_instance().are_changes_locked()

or

B) explicit decorators within the function body

@app.route('/')
"""Index page, optionally HTTP chunk-streamed and formatted."""
response = Foo.get_instance().are_changes_locked()

• Around here, we generally don't like brevity. – Stephen Rauch Jul 1 '19 at 2:20
• I added docstrings. The code above is now exactly as it is in my project, except from the Foo class, which is irrelevant for this example. – Hubert Grzeskowiak Jul 1 '19 at 3:19
• You say yourself that it is subjective, that IMHO means its not a good fit for the kind of "objective" QA-style system here. In addition, you did not provide a lot of code to judge the code/differences in a greater context, which makes this question tend even more to the off-topic side of things. – AlexV Jul 1 '19 at 6:11
• I don't see how this question could possibly be off-topic. It is matched by the first point of on-topic examples: "If you have a working piece of code from your project and are looking for open-ended feedback in the following areas: Application of best practices and design pattern usage (...)". This question is about the usage of decorators for transforming the return value of a Flask view function and I provided a real piece of code I am using in production. – Hubert Grzeskowiak Jul 1 '19 at 6:57

are all subjective and open to debate, even though "Pythonic" is less so than the others. That said, a simplified version may be illustrative. Comparing

@foo
@bar
def baz(value: T) -> T:
return value

to

def baz(value: T) -> FooT:
return foo(bar(value))

there are two issues with the former:

1. The final return type is now hidden in foo.
2. It is easy to confuse the layering - is baz(value) equivalent to foo(bar(baz(value))) or bar(foo(baz(value))) (or even baz(foo(bar(value))) in case of a novice)? Nested decorators come up so rarely that I would have to look at the documentation to be absolutely sure whether they were in the right sequence.

There seems to be two situations where multi-level decorators would be fine:

1. If they pass through the return value unchanged. A logger would be a typical example.
2. If the decorators are commutative, that is, their order doesn't matter for the outcome.


text:
# How to solve an absolute value

Please, can someone help me to solve this:
|x - 2| = 1/e
I really don't know the way in which I could solve an absolute value.

-
Either $x-2={1\over e}$ or $-(x-2)={1\over e}$. Can you take it from here? –  David Mitra Dec 14 '11 at 12:13
So, I have to join the values of the two cases (if it's positive, or if it's negative) and take the solution of the join? –  Overflowh Dec 14 '11 at 12:18
You would solve each separately. The original equation will have two solutions. So, yes "join" makes sense. The solution set of the original equation is the union (join) of the solution sets of the equations from the two cases. –  David Mitra Dec 14 '11 at 12:23
It might also help you if you draw a graph: wolframalpha.com/input/?i=plot+%7B%7Cx-2%7C%2C+1%2Fe%7D –  Martin Sleziak Dec 14 '11 at 12:27
For the intuition, it is useful to know that $|x-2|$ is the distance between $x$ and $2$. This distance is $1/e$ precisely when $x=2+1/e$ and when $x=2-1/e$, that is, $1/e$ to the right and $1/e$ to the left of $2$. (I am assuming that by $e$ you mean the base for the natural logarithms.) –  André Nicolas Dec 14 '11 at 17:23
From the definition of absolute value, $x$ is a solution of $$\tag{1}|x-2|={1\over e}$$ if and only if $$\tag{2}x-2={1\over e}$$ or $$\tag{3}-(x-2)={1\over e}.$$ (Since $|x-2|$ is either $x-2$ or $-(x-2)\,$.)
For emphasis: if $a$ is a solution of either equation (2) or equation (3), it must be a solution of equation (1). On the other hand, if $a$ is a solution of equation (1), it must be a solution of one of equations (2) or (3).


text:
# Show that the equation of a straight line meeting the circle$x^2+y^2=a^2$in two points at equal distances$'d'$from a point$(x_1,y_1)$

Show that the equation of a straight line meeting the circle$$x^2+y^2=a^2$$in two points at equal distances$$'d'$$from a point$$(x_1,y_1)$$on its circumference is $$xx_1+yy_1–a^2+d^2/2=0$$. I tried to solve this problem by taking the centre origin and their making the line as chord of contact from the point given and making it another circle but could not solve it.

• You should really try to come up with a better title than a fragment of the first sentence of your question. – amd Oct 19 '18 at 21:38

If $$(h,k),(p,q)$$ the two intersections $$h^2+k^2=p^2+q^2=a^2$$

$$d^2=(h-x_1)^2+(k-y_1)^2=h^2+k^2+x_1^2+y_1^2-2(hx_1+ky_1)$$

$$\iff2(hx_1+ky_1)+d^2-2a^2=0$$

Similarly, $$2(px_1+qy_1)+d^2-2a^2=0$$

So, the locus of the two intersections will be $$2(xx_1+yy_1)+d^2-2a^2=0$$

• Why did you do $h^2+k^2=p^2+q^2$?? – priyanka kumari Oct 19 '18 at 11:21
• @priyanka, Both $(h,k);(p,q)$ lie on the same given circle – lab bhattacharjee Oct 19 '18 at 11:37
• Yes!! I realised it now thank you. – priyanka kumari Oct 19 '18 at 11:38


text:
$$\renewcommand\AA{\unicode{x212B}}$$

# Mantid Workbench Changes¶

## New Features¶

• Subsampling of data on surface plots is now only performed if the number of rows or columns is greater than 100 (instead of 50)

• Sample shapes can now be plotted by right-clicking the workspace and selecting Show Sample Shape. This will plot all Sample, Container and Component shapes attached to the workspace, add a black arrow for the beam direction and colored arrows for the lattice vectors. For more details see 3D Mesh Plots for Sample Shapes.

• Mantid Workbench is now compatible with matplotlib v3.6

• Scripts generated by the Algorithm History Interface now include an import of mantid.simpleapi.

• Qt has been upgraded to version 5.15.

• Mouse cursor now changes to a horizontal double arrow when hovering over peak and range markers in the fitting tool, indicating they can be dragged left and right.

• Added button to figure tool bar which hides the figure (unhidden using the plots tab).

• In the error reporter, a label showing the maximum character limit of the additional context text has been added.

• Drop support for ICAT v3

• Normalisation (by maximum value) is available in Superplot

## Bugfixes¶

• In the fitting widget, if a tie is edited to an invalid value Workbench will display an error and revert the tie to its previous value.

• Fixed bug in the Mean algorithm where an invalid input workspace name would cause Mantid to crash.

• Fixed a bug where the user could drag the width handles of an unselected peak in the fit browser.

• Fixed a bug where property values were shortened in history

• Fixed a bug where data from workspaces (i.e the fit parameters) accessed from the Fit Browser could not be copied.

• The sensitivity of vertial and horizontal lines on plots, including the peak picker and range selector tools, has been increased.

• When plotting with exported script, the “Show Minor Gridlines” checkbox in the Axes tab will be ticked and fixed toggle grid lines button affecting minor lines.

• Fixed a bug where the user couldn’t reselect a peak in the fitting tool after adding another

• The tooltips of properties in an algorithm dialog will now provide the full description of a property.

• Fixed a bug where collapsing plots using a splitter handle could result in a crash.

• Fixed bug where marker labels became unattached when zooming and panning.

• Saving script from history dialog in Linux will be saved with .py extension

• Fixed a bug that prevented arrays from displaying properly in sample logs

• Fixed bug where Load and Rebin showed up twice (upper and lower case) in the algorithms tab search.

• Fixed bug with AddSampleLogMultiple where including log types and keeping the parser box ticked would crash Mantid.

• Fixed a bug where waterfall plots were updated unconditionally during ADS updates

• When a file with mantid algorithms is loaded, and the user accepts workbench adding the mantid API import line, the new import is always added to the top of the file

• Fixed a bug where the superplot plot area shrunk on some data

• Fixed a bug where spectra plots with error bars could not have normalisation turned off.

• Fix inconsistent text size when opening multiple script editor tabs on macOS

• Fixed bug where Delta and Elastic function peaks were not connected to the fitting window GUI.

• Grid lines will not turn on unexpectedly when changing axis format in a 3-D plot.

## InstrumentViewer¶

### New features¶

• Control points on the shapes drawn using the Pick or Draw tab now give cursor feedback.

• Added the ‘Keep original workspace’ rebin option on the ‘Pick’ tab. This will ensure the originally loaded data is rebinned when ticked and not the previously rebinned data.

• Add option to Instrument Viewer display settings to highlight detectors with zero counts

### Bugfixes¶

• The sensitivity of resizing a masked shape using its corners has been increased for screens with larger resolutions.

• Fixed a bug where Y histogram data was not being summed correctly when plotting ALF data on the Pick tab in units of Out of Plane angle.

## SliceViewer¶

### New features¶

• add HKL values to the image info table in the slice viewer when viewing a workspace with HKL coordinates

• Users can now double click on the SliceViewer plot axis to edit their limits more accurately.

• Added ‘Concise View’ check box to the Slice Viewer Peak View to show a reduced number of columns in the peak table view.

• Enable the cut viewer tool in non-orthogonal view

### Bugfixes¶

• Slice viewer now displays ‘-’ instead of -DBL_MAX in some energy transfer readings.

• Fix bug causing cut representation to be re-drawn on the sliceviewer colorfill plot on changing viewing axes when non-axis aligned cutting tool was not enabled.

• Fix bug in sliceviewer where the line plots produced by the ROI tool were not updated if the cursor was released outside the axes.

• Fixed a bug in sliceviewer where a matplotlib deprecation warning appears when toggling on the nonorthogonal axes.

• Fixed bug where the SliceViewer plot would would resize by small amounts as the cursor info changed.

Release 6.6.0


text:
# Tetragonal disphenoid honeycomb

Tetragonal disphenoid tetrahedral honeycomb
Type convex uniform honeycomb dual
Coxeter-Dynkin diagram
Cell type
Tetragonal disphenoid
Face types isosceles triangle {3}
Vertex figure
tetrakis hexahedron
Space group Im3m (229)
Symmetry [[4,3,4]]
Coxeter group ${\displaystyle {\tilde {C}}_{3}}$, [4,3,4]
Dual Bitruncated cubic honeycomb
Properties cell-transitive, face-transitive, vertex-transitive

The tetragonal disphenoid tetrahedral honeycomb is a space-filling tessellation (or honeycomb) in Euclidean 3-space made up of identical tetragonal disphenoidal cells. Cells are face-transitive with 4 identical isosceles triangle faces. John Horton Conway calls it an oblate tetrahedrille or shortened to obtetrahedrille.[1]

A cell can be seen as 1/12 of a translational cube, with its vertices centered on two faces and two edges. Four edges have 6 cells, and 2 edges have 4 cells.

The tetrahedral disphenoid honeycomb is the dual of the uniform bitruncated cubic honeycomb.

Its vertices form the A*
3
/ D*
3
lattice, which is also known as the Body-Centered Cubic lattice.

## Geometry

This honeycomb's vertex figure is a tetrakis cube: 24 disphenoids meet at each vertex. The union of these 24 disphenoids forms a rhombic dodecahedron. Each edge of the tessellation is surrounded by either four or six disphenoids, according to whether it forms the base or one of the sides of its adjacent isosceles triangle faces respectively. When an edge forms the base of its adjacent isosceles triangles, and is surrounded by four disphenoids, they form an irregular octahedron. When an edge forms one of the two equal sides of its adjacent isosceles triangle faces, the six disphenoids surrounding the edge form a special type of parallelepiped called a trigonal trapezohedron.

An orientation of the tetragonal disphenoid honeycomb can be obtained by starting with a cubic honeycomb, subdividing it at the planes ${\displaystyle x=y}$, ${\displaystyle x=z}$, and ${\displaystyle y=z}$ (i.e. subdividing each cube into path-tetrahedra), then squashing it along the main diagonal until the distance between the points (0, 0, 0) and (1, 1, 1) becomes the same as the distance between the points (0, 0, 0) and (0, 0, 1).

## Hexakis cubic honeycomb

Hexakis cubic honeycomb
Pyramidille[2]
Type Dual uniform honeycomb
Coxeter–Dynkin diagrams
Cell Isosceles square pyramid
Faces Triangle
square
Space group
Fibrifold notation
Pm3m (221)
4:2
Coxeter group ${\displaystyle {\tilde {C}}_{3}}$, [4,3,4]
vertex figures
,
Dual Truncated cubic honeycomb
Properties Cell-transitive

The hexakis cubic honeycomb is a uniform space-filling tessellation (or honeycomb) in Euclidean 3-space. It can be seen as a cubic honeycomb with each cube subdivided by a center point into 6 elongated square pyramid cells. John Horton Conway calls it a pyramidille.[3]

Cells can be seen in a translational cube, using 4 vertices on one face, and the cube center. Edges and colored by how many cells are around each of them.

There are two types of planes of faces: one as a square tiling, and flattened triangular tiling with half of the triangles removed as holes.

Tiling Symmetry plane p4m, [4,4] (*442) pmm, [∞,2,∞] (*2222)

### Related honeycombs

It is dual to the truncated cubic honeycomb with octahedral and truncated cubic cells:

If the square pyramids of the pyramidille are joined on their bases, another honeycomb is created with identical vertices and edges, called a square bipyramidal honeycomb, or the dual of the rectified cubic honeycomb.

It is analogous to the 2-dimensional tetrakis square tiling:

## Square bipyramidal honeycomb

Square bipyramidal honeycomb
Oblate octahedrille[4]
Type Dual uniform honeycomb
Coxeter–Dynkin diagrams
Cell Square bipyramid
Faces Triangles
Space group
Fibrifold notation
Pm3m (221)
4:2
Coxeter group ${\displaystyle {\tilde {C}}_{3}}$, [4,3,4]
vertex figures
,
Dual Rectified cubic honeycomb
Properties Cell-transitive, Face-transitive

The square bipyramidal honeycomb is a uniform space-filling tessellation (or honeycomb) in Euclidean 3-space. John Horton Conway calls it a oblate octahedrille or shortened to oboctahedrille.[5]

A cell can be seen positioned within a translational cube, with 4 vertices mid-edge and 2 vertices in opposite faces. Edges are colored and labeled by the number of cells around the edge.

It can be seen as a cubic honeycomb with each cube subdivided by a center point into 6 elongated square pyramid cells. The original cubic honeycomb walls are removed, joining pairs of square pyramids into elongated square bipyramids (octahedron). Its vertex and edge framework is identical to the hexakis cubic honeycomb.

There is one type of plane with faces: a flattended triangular tiling with half of the triangles as holes. These cut face-diagonally through the original cubes. There are also square tiling plane that exist as nonface holes passing through the centers of the octahedral cells.

Tiling Symmetry plane Square tiling "holes" flattened triangular tiling p4m, [4,4] (*442) pmm, [∞,2,∞] (*2222)

### Related honeycombs

It is dual to the rectified cubic honeycomb with octahedral and cuboctahedral cells:

## Phyllic disphenoidal honeycomb

Phyllic disphenoidal honeycomb
Eighth pyramidille[6]
(No image)
Type Dual uniform honeycomb
Coxeter-Dynkin diagrams
Cell
Phyllic disphenoid
Faces Rhombus
Triangle
Space group
Fibrifold notation
Coxeter notation
Im3m (229)
8o:2
[[4,3,4]]
Coxeter group [4,3,4], ${\displaystyle {\tilde {C}}_{3}}$
vertex figures
,
Dual Omnitruncated cubic honeycomb
Properties Cell-transitive, face-transitive

The phyllic disphenoidal honeycomb is a uniform space-filling tessellation (or honeycomb) in Euclidean 3-space. John Horton Conway calls this a Eighth pyramidille.[7]

A cell can be see as 1/48 of a translational cube with vertices positioned: one corner, one edge center, one face center, and the cube center. The edge colors and labels specify how many cells exist around the edge.

### Related honeycombs

It is dual to the omnitruncated cubic honeycomb: