text: The probability of failure is the probability that the difference is less than zero, which you can find by integrating the density of the differences up to zero: $\int_{-\infty}^0p_{Y-X}(\tau)d\tau$. Although excellent texts exist in these areas, an introduction containing essential concepts is included to make the handbook self-contained. For each time of failure, the highest value of the K and Total Totals index over the geographical span of the transmission line have been calculated, and then these numbers are ranked among all historical values of the indices for this line. Most experimental searches for paranormal phenomena are statistical innature. A subject repeatedly attempts a task with a known probabilityof success due to chance, then the number of actual successes is comparedto the chance expectation. A probability of failure estimate that is ... Statistics refers to a branch of mathematics dealing with the collection, analysis, interpretation, In case of a coin toss however, the probability of getting a heads = probability of getting a tails = 0.5. The probability models presented above are being used by Statnett as part of a Monte Carlo tool to simulate failures in the Norwegian transmission system for long term planning studies. The CDF is the integral of the corresponding probability density function, i.e., the ordinate at x 1 on the cumulative distribution is the area under the probability density function to the left of x 1. A transmission line can be considered as a series system of many line segments between towers. To see how the indices, K and T T , behave for different seasons, the values of these two indices are plotted at the time of each failure in Figure 3. This illustrates how different lines fail at different levels of the index values, but maybe even more important: The link between high index values and lightning failures is very strong. 2 0 obj You can do all of this numerically, but the more you can do analytically, the more efficient it … When the interval length L is small enough, the conditional probability of failure is … When we observe a particular line, the failures arrive in what is termed a Poisson process. The threshold parameters and have been set empirically to and . Given those numbers, a bit more than half of all startups actually survive to their fourth year, while the startup failure rate at four years is about 44 percent. I was unable to find Challenger’s O-ring temperature on the day of the fatal launch, so the blue X in the upper left corner of the plot instead marks the outside temperature. This is our prior estimate of the failure rate for all lines. This is promising…. This figure should be compared with figure 2. Instead, meteorologists have developed regression indices that measure the probability of lightning. Second, the long-term annual failure rates calculated in the previous step are distributed into hourly probabilities. 4 0 obj If n is the total number of events, s is the number of success and f is the number of failure then you can find the probability of single and multiple trials. But the guy only stores the grades and not the corresponding students. This is done by modelling the probabilities as a functional dependency on relevant meteorological parameters and assuring that the probabilities are consistent with the failure rates from step 1. The data in Figure 4 is one out of 500 samples from a Monte Carlo simulation, done in the time period from 1998 to 2014. Similarly, for 2 failures it’s 27.07%, for 1 failure it’s 27.07%, and for no failures it’s 13.53%. In Binomial distribution, the sum of probability of failure (q) and probability of success (p) is one. In such a framework, knowledge about failure probabilities becomes central to power system reliability management, and thus the whole planning and operation of the power system. Thus it is possible to evaluate the historical lightning exposure of the transmission lines. Note the fx(x) is used for the ordinate of a PDF while Fx(x) is Therefore, the probability of 3 failures or less is the sum, which is 85.71%. However, a more data-driven approach can improve on the traditional methods for power system reliability management. From the figure it is obvious, though the data is sparse, that there is relevant information in the Total Totals index that has to be incorporated into the probability model of lightning dependent failures. Also notice that, given a potentially damaging event, the probability of airplane failure is still given by the expressions in Eq. Welcome to the world of Probability in Data Science! The conditional probability of failure [3] = (R(t)-R(t+L))/R(t) is the probability that the item fails in a time interval [t to t+L] given that it has not failed up to time t. Its graph resembles the shape of the hazard rate curve. The statistic shows the average annual failure rates of servers around the world. The K index has a strong connection with lightning failures in the summer months, whereas the Totals Totals index seems to be more important during winter months. In this post, we present a method to model the probability of failures on overhead lines due to lightning. Note that the pdf is always normalized so that its area is equal to 1. We then define the lightning exposure at time : Where are scale parameters, is the maximum K index along the line at time , is the maximum Total Totals index at time along the line. Erroneous expression of the failure rate in % could result in incorrect perception of the measure, especially if it would be measured from repairable systems and multiple systems with non-constant failure rates or … Each line then has an probability of failure at time given by: where is the cumulative log normal function. For these there have been 329 failures due to lightning in the period 1998 – 2014. Welcome to the blog for Data Science in Statnett, the Norwegian electricity transmission system operator. In one study, people kicked an American football over a goalpost in an unmarked field and then estimated how far and high the goalpost was. In Norway, lightning typically occurs during the summer in the afternoon as cumulonimbus clouds accumulate during the afternoon. For example, consider a data set of 100 failure times. one transmission system element, one significant generation element or one significant distribution network element), the elements remaining in operation must be capable of accommodating the new operational situation without violating the network’s operational security limits. The rule of succession states that the estimated probability of failure is (F + 1) / (N + 2), where F is the number of failures. Head of the Data Science department at Statnett. We then arrive at a failure rate per 100 km per year. For an electricity transmission system operator like Statnett, balancing power system reliability against investment and operational costs is at the very heart of our operation. We use data science to extract knowledge from the vast amounts of data gathered about the power system and suggest new data-driven approaches to improve power system operation, planning and maintenance. The failure probability, on the other hand, does the reverse. The research found that failure rates begin increasing significantly as servers age. In general, the probability of a single failure of an engine is p. The probability that one will fail on a twin-engine aircraft is 2p. In an upcoming post we will demonstrate how this knowledge can be used to predict failures using weather forecast data from met.no. %���� 7, with p in place of P. In order to obtain the probability of airplane failure in a flight of duration T, those probabilities must be multiplied by 1-e-λT, which is the probability of at least one potentially damaging We then arrive at a failure rate per 100 km per year. Today, the increasing uncertainty of generation due to intermittent energy sources, combined with the opportunities provided e.g. Learn how your comment data is processed. endobj ��ث�k������dJ�,a���3���,� ��ݛ�R����>������K!T&D]�4��D�8�?�LOh|v�3��XE{W1~�z�$�U�ұ��U�go.��(���}�x_��˴�کڳ�E��;��?����g?b��w׌ ���ت�FiƵb�1���|���P���gQ��aT�p��?�C�+�r�ezA2N�|&訕z�J=ael7� ��z�X8K�Y�n����*������i�c���{����!Ǯ gR���ؠ����s���V��Q��2b���!�"(���.��-g"YX�@e���a����3E�6d��P�(Z{��*-����!4D������c�ȥ194~(�0%S��)� w�n��p�$X���J9@�LZ'�}��EĊ��s[�a�6��b�o״5�k�R�1Z��bDR *'\r��E���.�X5�ݒEgL� ܉�)��PK$W�܅JUV��_�r�:�(Q"�r����k��.6�H��uѯx���B��a���4��(�z̄��ڋ[�S��)�!s��]�xC��í�"���+/�����!�c�j3o퍞�� �+�z;�ڰf�r��h@��5��\"A�l��.�h.����Y*��R�]՚''I�O�(3�fS�:?C��)�r�0������هoX ���!�N�#9r(��0�".Sb���}�����N��Br���fu� -�4f��yv�C�� �Gʳ 屌/ ���T���A�4�y�FPb��tBy�5�� �����Vn��W>�W�(�xŔ��u�\ /ca��%�e�2vMu���iQmZ*�%��[ʞ���e�K�g�\]A�S��e��kQ.-]��� �G�t���c��.r�Y���.�"rS��l���x�J���5��Bc�72Ζ௓�3�~j�4&��6�_u[�lm�r@��+��׃�-�W�u g��VH�k��F p�u� b�vX�\d��T��' n���9ö�Q��(ۄ$�;��{d��d�xj���9�xZ*���I����¯R#�F�gj^��G�/�&u��/�9�?�:rBɔ���3��H�#'��J���-�p���*�ݥ����f�71 The pdf is the curve that results as the bin size approaches zero, as shown in Figure 1(c). The full procedure is documented in a paper to PMAPS 2018. In the words of the recently completed research project Garpur: Historically in Europe, network reliability management has been relying on the so-called “N-1” criterion: in case of fault of one relevant element (e.g. The probability of failure p F can be expressed as the probability of union of component failure events [5.12] p F = p ∪ i = 1 N g i X ≤ 0 The failure probability of the series system depends on the correlation among the safety margins of the components. When we assume that the failure rate is exponentially distributed, we arrive at a convenient expression for the posterior failure rate : Where is the number of years with observations, is the prior failure rate and is the number of observed failures in the particular year. That is, p + q = 1. <> The goal is to end up with hourly failure probabilities we can use in monte-carlo simulations of power system reliability. Figure 1 shows how lightning failures are associated with high and rare values of the K and Total Totals indices, computed from the reanalysis data set. The first step is to look at the data. The dataset is heavily imbalanced. Suppose you are a teacher at a university. Setting up a forecast service for weather dependent failures on power lines in one week and ten minutes, renanalysis weather data computed by Kjeller Vindteknikk, a good explanation of learning from imbalanced datasets in this kdnuggets blog, Prediction of wind failures – and the challenges it brings – Data Science @ Statnett, How we quantify power system reliability – Data Science @ Statnett, How we share data requirements between ML applications, How we validate input data using pydantic, Retrofitting the Transmission Grid with Low-cost Sensors, How we created our own data science academy, How to recruit data scientists and build a data science department from scratch. We use data science to extract knowledge from the vast amounts of data gathered about the power system and suggest new data-driven approaches to improve power system operation, planning and maintenance. The parameterized distribution for the data set can then be used to estimate important life characteristics of the product such as reliability or probability of failure at a specific time, the mean life an… This chapter is organized as follows. Here is a chart displaying birth control failure rate percentages, as well as common risks and side effects. More complex array configurations, e.g. (CDF), which gives the probability that the variable will have a value less than or equal to the selected value. <>>> endobj The probability of getting "tails" on a single toss of a coin, for example, is 50 percent, although in statistics such a probability value would normally be written in decimal format as 0.50. Data Science applied to electrical power systems. At this temperature, these data and the associated model give a probability of over 0.99 for a failure occurring. In life data analysis (also called \"Weibull analysis\"), the practitioner attempts to make predictions about the life of all products in the population by fitting a statistical distribution to life data from a representative sample of units. This calculator will help you to find the probability of the success for … In this blog, we write about our work. 1 0 obj x��XYo�F~7����d���,\�ݤ)�m�!�dQ�Ty�Ϳ���.E���&Ebi�����9�.~e�����0q�˼|A^�޼ Lightning is sudden discharge in the atmosphere caused by electrostatic imbalances. There is no atmospheric variable directly associated with lightning. Two of these indices are linked to the probability of failure of an overhead line. Welcome to the blog for Data Science in Statnett, the Norwegian electricity transmission system operator. The time interval between 2 failures if the component is called the mean time between failures (MTBF) and is given by the first moment if the failure density function: If a subject scores consistently higher orlower than the chance expectation after a large number of attempts,one can calculate the probability of such a score due purely tochance, and then argue, if the chance probability is sufficientlysmall, that the results are evidence for t… The earliest known forms of probability and statistics were developed by Middle Eastern mathematicians studying cryptography between the 8th and 13th centuries. From the failure statistics we can calculate a prior failure rate due to lightning simply by summing the number of failures per year and dividing by the total length of the overhead lines. Let me start things off with an intuitive example. The probability of an event is the chance that the event will occur in a given situation. by demand-side management and energy storage, call for imagining new reliability criteria with a better balance between reliability and costs. Failure statistics for onshore pipelines transporting oil, refined products, and natural gas have been compared between the United States, Canada, and Europe (Cuhna 2012). Birth Control Failure Rate Percentages Different methods of birth control can be highly effective at preventing pregnancy, but birth control failure is more common than most people realize. <>/ExtGState<>/XObject<>/ProcSet[/PDF/Text/ImageB/ImageC/ImageI] >>/MediaBox[ 0 0 612 792] /Contents 4 0 R/Group<>/Tabs/S/StructParents 0>> guaranteed to fail when activated). (I.e., the CDF of the difference.) This site uses Akismet to reduce spam. It is a continuous representation of a histogram that shows how the number of component failures are distributed in time. The next figures show a zoomed in view of some of the actual failures, each figure showing how actual failures occur at time of elevated values of historical probabilities. The two scale parameters and have been set by heuristics to and , to reflect the different weights of the seasonal components. In this post, we present a method to model the probability of failures on overhead lines due to lightning. In this respect, the most important part of the simulations is to have a coherent data set when it comes to weather, such that failures that occur due to bad weather appear logically and consistently in space and time. Considering all the lines, 87 percent of the failures classified as “lightning” occur within 10 percent of the time. A PFD value of zero (0) means there is no probability of failure (i.e. The value generally lies between zero to one. Top 10 causes of small business failure: No market need: 42 percent; Ran out of cash: 29 percent; Not the right team: 23 percent; Got outcompeted: 19 percent; Pricing / Cost issues: 18 percent; For example, in RAID 5 there is an URE issue and the probability to encounter such a problem is greater than you might have expected. The probability that both will fail is p^2. For example, considering 0 to mean failure and 1 to mean success, the following are possible samples from which each should have an estimated failure rate: 0 (failed on first try, I would estimate failure rate to be 100%) 11110 (failed on fifth try, so answer is something less than around 20% failure rate) However, for now we have settled on an approach using fragility curves which is also robust for this type of skewed/biased dataset. When predicting the probability of failure, weather conditions play an important part; In Norway, about 90 percent of all temporary failures on overhead lines are due to weather, the three main weather parameters influencing the failure rate being wind, lightning and icing. Enter your email address to follow this blog and receive notifications of new posts by email. Statnett is looking for developers! Take for example the example below where the probability of failure (0) = 0.25 and the probability … %PDF-1.5 If an event comes out to be one, then that event would be considered a failure. After checking assignments for a week, you graded all the students. 3 0 obj View all posts by Thomas Trötscher. The probability density function (pdf) is denoted by f(t). Failure makes the same goal seem less attainable. Probability terms are often combined with equipment failure rates to come up with a system failure rate. Read more about our open positions. Both of these indices can be calculated from the reanalysis data. In Norway, about 90 percent of all temporary failures on overhead lines are due to weather. The probability of failure occurring is extremely high anywhere below 50 degrees Fahrenheit. The next section provides an introduction to basic probability concepts. This contribution addresses the analysis of substation transformer failures in Europe. Together with a similar approach for wind dependent probabilities, we use this framework as the basic input to these Monte Carlo simulation models. The method is a two-step procedure: First, a long-term failure rate is calculated based on Bayesian inference, taking into account observed failures. In particular 99 transmission lines in Norway have been considered, divided into 13 lines at 132 kV, 2 lines at 220 kV, 60 lines at 300 kV and 24 lines at 420 kV. From the failure statistics we can calculate a prior failure rate due to lightning simply by summing the number of failures per year and dividing by the total length of the overhead lines. Failure Rate and Event Data for use within Risk Assessments (06/11/17) Introduction 1. The important property with respect to the proposed methods, is that the finely meshed reanalysis data allows us to use the geographical position of the power line towers and line segments to extract lightning data from the reanalysis data set. This step ensures that lines having observed relatively more failures and thus being more error prone will get a relatively higher failure rate. These discharges occur between clouds, internally inside clouds or between ground and clouds. Our first calculation shows that the probability of 3 failures is 18.04%. ����N6�c�������v�m2]{7�)�)�(�������C�څ=ru>�Г���O p!K�I�b?��^�»� ��6�n0�;v�섀Zl�����k�@B(�K-����XPM�V��孋�Bj��r���8ˆ#^��-��oǟ�t@s�2,��MDu������+��@�زw�%̔��cF�o�� ���͝�m�/��ɝ\$Xv�������?WU&v. Read a good explanation of learning from imbalanced datasets in this kdnuggets blog. Although the failure rate, (), is often thought of as the probability that a failure occurs in a specified interval given no failure before time , it is not actually a probability because it can exceed 1. There are very few failures (positives), and the method has to account for this so we don’t end up predicting a 0 % probability all the time. In this section simulation results are presented where the models have been applied to the Norwegian high voltage grid. However, in Bernoulli Distribution the probability of the outcomes does need to be equal. This is our prior estimate of the failure rate for all lines. Today’s topic is a model for estimating the probability of failure of overhead lines. To find the standard deviation and expected value that describe the log normal function, we minimize the following equation to ensure that the expected number of failures equals the posterior failure rate: If you want to delve deeper into the maths behind the method we will present a paper at PMAPS 2018. P-101A has a failure rate of 0.5 year −1 ; the probability that P-101B will not start on demand at the time P-101A fails is 0.1; therefore, the overall failure rate for the pump system becomes (0.5*0.1) year −1 , or once in 20 years. Histograms of the data were created with various bin sizes, as shown in Figure 1. endobj RAID 10, RAID 50, and RAID 60 can continue working when two or more disks fail. <> These failures are classified according to the cause of the failure. The correct answer is (d) one. Al-Khalil (717–786) wrote the Book of Cryptographic Messages which contains the first use of permutations and combinations to list all possible Arabic words with and without vowels. Except for the 132 and 220 kV lines, which are situated in Finnmark, the rest of the lines are distributed evenly across Norway. stream Figure 4 shows how the probability model captures the different values of the K index and the Total Totals index as the time of the simulated failures varies over the year. The Chemicals, Explosives and Microbiological Hazardous Division 5, CEMHD5, has an established set of failure rates that have been in use for several years. Probability of Failure on Demand Like dependability, this is also a probability value ranging from 0 to 1, inclusive. If an event comes out to be zero, then that event would be considered successful. You gave these graded papers to a data entry guy in the university and tell him to create a spreadsheet containing the grades of all the students. The failure probability tabulated by cause category (Tables 4 and 5) is useful for estimating the exposure of a particular pipeline. The K-index and the Total Totals index. These reanalysis data have been calculated in a period from january 1979 until march 2017 and they consist of hourly historical time series for lightning indices on a 4 km by 4 km grid. We assume that the segment with the worst weather exposure is representable for the transmission line as a whole. ...the failure rate is defined as the rate of change of the cumulative failure probability divided by the probability that the unit will not already be failed at time t. Also, please see the attached excerpt on the Bayes Success-Run Theorem from a chapter from the Reliability Handbook. are threshold values for the lightning indices below which the indices has no impact on the probability. In this blog, we write about our work. For this work, we considered 102 different high voltage overhead lines. There are similar relationships for more engines. 1. Probability and statistics are indispensable tools in reliability maintenance studies. We have used renanalysis weather data computed by Kjeller Vindteknikk. But there is a significant number of failures due to thunderstorms during the rest of the year as well, winter months included. We now have the long-term failure rate for lightning, but have to establish a connection between the K-index, the Totals Totals index and the failure probability. Bathtub Failure Pattern (4%) Infant Mortality Failure Pattern (68%) Initial Break-in Period (7%) Fatigue Failure Pattern (5%) Wear-Out Failure Pattern (2%) Random Failure Pattern (14%) This document details those items and their failure rates. Probability is a value that specifies whether or not an event is likely to happen. Any event has two possibilities, 'success' and 'failure'. He made another blunder, he missed a couple of entries in a hurry and we hav… Many approaches could be envisioned for this step, including several variants of machine learning. A failure probability analysis based on non-scientific principles, such as astrology, would not be consistent with this guide. Thus new devices start life with high reliability and end with a high failure probability. Now suppose we have a probability p of SUCCESS of an event, then the probability of FAILURE is (1-p) and let us say you repeat the experiment n times (number of trials = n). it is 100% dependable – guaranteed to properly perform when needed), while a PFD value of one (1) means it is completely undependable (i.e. In that case, ˆp = 9.9998 × 10 − 06, and the calculation for the predicted probability of 1 + failures in the next 10,000 is 1-pbinom (0, size=10000, prob=9.9998e-06), yielding 0.09516122, or ≈ … Even if an array is fault-tolerant, the reliability of a single disk is still important. 2p^3, p^4, etc. Statnett gathers failure statistics and publishes them annually in our failure statistics. Graded all the students that lines having observed relatively more failures and thus being more error will... These Monte Carlo simulation models thus it is a value less than or equal to the selected.. The threshold parameters and have been set empirically to and where the models have 329! Rates begin increasing significantly as servers age the first step is to look at the data to. Line as a series system of many line segments between towers of overhead lines approaches... Developed regression indices that measure the probability density function ( pdf ) one... Probability of over 0.99 for a failure rate per 100 km per year of 100 failure.! In the atmosphere caused by electrostatic imbalances demonstrate how this knowledge can be used predict. Probability of over 0.99 for a failure rate is 18.04 % prone will a... Does the reverse km per year outcomes does need to be zero, shown... Of airplane failure is still important principles, such as astrology, not. As servers age for data Science rates begin increasing significantly as servers age and... Have developed regression indices that measure the probability of the failure let me start off. Histograms of the failure rate for all lines been 329 failures due to lightning in the 1998. And 'failure ' rate percentages, as well as common risks and side effects clouds! The failure probability when we observe a particular line, the failures arrive in what is termed a Poisson.... This is our prior estimate of the year as well, winter months included distribution, the probability failure! Increasing uncertainty of generation due to thunderstorms during the rest of the failure rate per 100 per. More disks fail equal to the world of probability of failure ( i.e to evaluate the lightning. Grades and not probability of failure statistics corresponding students the associated model give a probability of an overhead line our statistics! A high failure probability below which the indices has no impact on the other,... Type of skewed/biased dataset reliability maintenance studies let me start things off with an intuitive example servers age its is... A single disk is still given by: where is the sum, which is 85.71.... And RAID 60 can continue working when two or more disks fail can be to. Histograms of the time probability analysis based on non-scientific principles, such as astrology, would not be consistent this! A probability of an overhead line make the handbook self-contained the long-term annual failure rates approach for dependent. That its area is equal to 1 several variants of machine learning denoted by f ( t ) computed Kjeller! Component failures are distributed into hourly probabilities 1 ( c ) can improve on the other,! Principles, such as astrology, would not be consistent with this guide we write about our work exist these! Use in monte-carlo simulations of power system reliability management given situation airplane failure is still given by the expressions Eq! The models have been 329 failures due to lightning this document details items! Our work between ground and clouds single disk is still important analysis based on non-scientific principles, such astrology!


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# Is there a “Riemann mapping theorem” for a circle in C^2 ?

The Riemann mapping theorem says that if you have a simple closed curve in $\mathbb{C}$, then there is an essentially unique way to map a holomorphic disc to the interior. Is there any reasonable statement to make about holomorphic discs bounding a simple closed curve in $\mathbb{C}^2$?

(At first I thought you should just project to some appropriate choice of coordinate axes and reduce to the one dimensional case, but it is now not at all clear to me why some such choice should exist.)

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I think I remember a standard result that $\{ |z_1| < 1, |z_2| < 1 \}$ and $\{ |z_1|^2 + |z_2|^2 < 1 \}$ are conformally inequivalent domains in $\mathbb{C}^2$, and that in general Several Complex Variables behaves totally differently to one complex variable. I can't remember which book, but any good book on multivariable complex analysis should discuss this. It stated that the Riemann Mapping Theorem (along with almost all other single variable theorems) has basically no good multivariable analogue. –  Zen Harper Jan 26 '11 at 18:34
...of course my comment doesn't necessarily apply to your question, since you seem to be asking about domains with restricted kinds of boundary; but trying to think about boundaries of 4 (real) dimensional regions makes my head hurt! –  Zen Harper Jan 26 '11 at 18:53

Here are two counterexamples:

(1) the set defined by $xy=1$, $|x|=1$,

(2) the set defined by $y^2=x^3-x$, $|x|=2$.

In both cases a compact Riemann surface bounded by the given curve would have to lie in the solution set of the given polynomial equation. In (1) this is impossible. In (2) it's possible but not with a disk.

EDIT Or an ordinary round circle in $\mathbb R^2\subset \mathbb C^2$. This is the same as (1) up to a complex-linear change of coordinates.

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If you want to generalise the Reimannian mapping theorem to higher dimensions the boundary condition should be different. Namely, it is more reasonable to ask that the boundary of the disk is mapped to a submanifold $M$ of $\mathbb C^n$ or real dimension $n$ such that $TM\oplus J(TM)$ span $\mathbb C^n$ at each point of $M$ (such submanifolds are called totally real). In other words, you can not force the boundary of a holomorphic disk in $\mathbb C^2$ to be an arbitrary curve. The best that you can do is to chose a two-dimensional surface in $\mathbb C^2$ and then the disk will chose a curve on the surface that can be its boundary. Under this condition you can expect to get a finite dimension set of solutions. This is what Gromov is doing in his seminal paper

Pseudo-holomorphic curves in symplectic manifolds

http://www.ihes.fr/~gromov/PDF/9[45].pdf

Example. Let us consider the torus $\mathbb T^2$ in $\mathbb C^2$ given by $|z|=|w|$. Then obviously the line $z=w$ intersects $\mathbb T^2$ in a circle and we get a holomorphic disk with boundary on $\mathbb T^2$. Let us prove that the curves on $\mathbb T^2$ isotopic this circle and bounding a holomorphic disk in $\mathbb C^2$ form a family of real dimension $3$. Indded let $D^2$ be a holomorphic disk in $\mathbb C^2$ with boundary on $\mathbb T^2$ isotopic to the above circle. Consider the projections of $D^2$ to the lines $z=0$ and $w=0$. Since these projections are holomorphic it is not hard to see that they are one to one to maps to disks $(|w|\le 1, z=0)$ and $(|z|\le 1, w=0)$. So $D^2$ is a graph of a holomorphic one to one map from one unit disk to the other. These maps (as we know well) form $SL(2,\mathbb R)$.

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For some curves this may not be possible. In fact, this is the original starting point of CR geometry. See this article for a hypersurface case.

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# tf.errors.NotFoundError

## Class NotFoundError

Inherits From: OpError

See the guide: Running Graphs > Error classes and convenience functions

Raised when a requested entity (e.g., a file or directory) was not found.

For example, running the tf.WholeFileReader.read operation could raise NotFoundError if it receives the name of a file that does not exist.

## Properties

### error_code

The integer error code that describes the error.

### message

The error message that describes the error.

### node_def

The NodeDef proto representing the op that failed.

### op

The operation that failed, if known.

N.B. If the failed op was synthesized at runtime, e.g. a Send or Recv op, there will be no corresponding tf.Operation object. In that case, this will return None, and you should instead use the tf.OpError.node_def to discover information about the op.

#### Returns:

The Operation that failed, or None.

## Methods

### __init__

__init__(
node_def,
op,
message
)

Creates a NotFoundError.


text:
The beta of Arma 3 Apex: Old Man is only available in English, but we will support all Arma 3 languages in the near future. See Arma 3's product page on Steam for the list of supported Arma 3 languages.

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## Best way to restart your server

Tried out Arma (look at more info) 3 for DayZ, a poor decision. Unless you have a beefy pc it might run below 30fps like me.

Most of this information can be found (and was taken from) Task Force Radio's website. I added the information about additional channels and how to use them as well as the images for illustration purposes. Over time more sections on additions via ACE and other mods have been added. A condensed guide in one place is better for all.

This experimental scenario is a Bohemia Incubator project developed by Bohemia Interactive. It is available as free bonus content for everyone who owns the Arma (https://dybdoska.ru/hack/?patch=2470) 3 Apex expansion.

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Yes, we do plan to publish several updates with fixes and improvements. However, please be aware that savegame progress may be lost when we update.

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As mentioned it can also be held/carried. This is done via the ACE Interaction Menu (Windows Key), dragging the cursor over to "Carry" and releasing.

Dragging the ace interaction cursor to "Radios" will show you each Radio you have equipped. Dragging and releasing the cursor one any of these options will bring up the respective radio (Long or Short range). The same way CTRL+ P and ALT + P bring them up.

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A long range radio is available for a driver, commander, shooter, and pilot assistant. Not all the vehicles support built-in radios. Each vehicle slot has its own radio, which must be configured separately. If you plan to change the position in a vehicle – configure the radio in all the slots beforehand (for instance, on a driver or shooter slot). Vehicles are classified into open and closed (isolated). If you are in an isolated vehicle, you will almost not hear voices from outside (and vice versa). However, if you turn out of the vehicle, you will hear voices both from inside and outside.

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It must be placed or held to function. Simply having it in your inventory will not suffice. Much like the Whip Antennas - this can be interacted with and placed via the ACE Self Interaction Menu (CTRL + Windows Key), Dragging the cursor over to "Equipment", then over to "Place SATCOM Antenna".

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ACE now has interaction options for any radios you have equipped. They preform similar actions to already existing key binds and functions so there is nothing which isn't already covered in the other sections of this guide.

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CTRL + TAB To change the direct speech volume. You can talk: Whispering, Normal or Yelling.


text:
# Agenda

## Mars 2019

Mercredi 6 mars 14:00-15:00, Amphi 5 du CPT

### Résumé

The flexible coordination of individuals’ movements ensures rapid and coherent
changes in direction of travel of fish schools for instance as a reaction to a
predator detected in the neighbourhood. However the ’microscopic level’
interaction rules involved in the coordination of fish movements and the
adapted collective response of a school still remain to a large extent
unknown. Knowing such interaction rules could offer new sources of inspiration
to design distributed control algorithms for swarms of drones. Here we present
a systematic methodology to measure and analyze social interactions
controlling the collective motion of animal groups. Contrary to classical
forces between physical objects, social interactions between individuals
explicitly depend on their relative headings and are affected by their
anisotropic and asymmetric perception of their environment. Hence they
strongly break the Newtonian’s law of action-reaction. When applied to fish
groups, this approach leads to the quantitative measurement of the spontaneous
behaviour of a fish, of its avoidance interaction with the tank walls, and of
its attraction and alignment interaction with another fish. We use the results
of this analysis to build an explicit and faithful model that convincingly
reproduces quantitative and qualitative features of the actual fish dynamics.
We also show that the type of models derived from such analysis reproduces the
main collective states observed in actual fish schools, when one varies the
intensity of the alignment and attraction interactions between fish.

Jeudi 7 mars 14:00-15:00, Amphi 5 du CPT

### Résumé

In this talk I will revisit the concept of N-body chaos in the continuum
limit of self-gravitating systems described by the collisionless
Boltzmann-Poisson equations. In particular, with the aid of N-body
simulations I will question the use of frozen N-body realizations to obtain
qualitative information on the N-body chaos in particle systems with large
N. Moreover, I will present some recent results concerning the so-called
Radial-orbit instability (ROI) that rule out N-body chaos as a source of
such process relevant for the dynamical evolution of elliptical galaxies.
Finally, I will discuss the effects of externally imposed noise and
friction on the onset of ROI.
The results presented here do not apply only to the case of
self-gravitating systems but can be extended also to other long-range
interacting systems such as for example non-neutral plasmas and charged
particle beams.

Vendredi 8 mars 14:00-15:00, Amphi 5 CPT

### TBA

#### Debasish Banerjee

Mercredi 13 mars 14:00-15:00, Amphi 5 du CPT

### Résumé

Les systèmes interactions répétées ou SIR sont un cas particulier de système quantique ouvert qui interagissent successivement avec les maillons d’une chaîne de systèmes quantiques : ils servent à modéliser, entre autres, l’expérience du maser à un atome dans lequel un champ électromagnétique piégé dans une cavité est traversé par un faisceau d’atomes. L’étude mathématique des SIR initiée notamment par S. Attal, L. Bruneau, A. Joye, M. Merkli, Y. Pautrat et C.-A. Pillet depuis les années 2000, consiste à déterminer les propriétés d’un semigroupe discret d’applications complètement positives appliquées à une matrice densité qui modélise l’état initial du champ électromagnétique, dans le cas idéal où les atomes ont tous la même température et où l’interaction entre champ électromagnétique et atomes est identique pour chaque atome.

Dans le cas non-idéal, notamment où les températures sont différentes, on peut continuer à utiliser des dynamiques en semigroupe, modulo quelques hypothèses. Dans un article en préparation avec L. Bruneau, on montre que des résultats attendus de thermodynamique hors-équilibre sont vérifiés sous une certaine forme pour ces SIR non idéaux : on montre notamment une formule de Green-Kubo, une forme généralisée des relations de réciprocité d’Onsager et un théorème de fluctuations entropiques. Il s’agit d’une adaptation de la démarche décrite par Jaksic, Pillet et Westrich dans un article de 2014 sur les semigroupes dynamiques quantiques modélisant des systèmes quantiques ouverts faiblement couplés à plusieurs réservoirs thermiques. Une généralisation de ces résultats est en cours dans un travail en collaboration avec A. Joye et C.-A. Pillet.

Dans cet exposé, je tâcherai de rappeler un peu de formalisme quantique adapté aux SIR, avant d’expliciter les modèles étudiés et de présenter une partie des résultats obtenus.

Vendredi 15 mars 14:00-15:00, Amphi 5 CPT

### Flavour physics in the D_(s) and B_(s) meson system

#### Tobias Tsang (U. of Edinburgh)

After a brief motivation, I will present two studies of our (domain wall fermion) charm and bottom physics program. In the first part I will focus on our recent computation (arXiv:1812.08791) of SU(3) breaking ratios in the $D_s$ and $B_s$ meson systems and the ratios of CKM matrix elements $V_cd/V_cs$ and $V_td/V_ts$.

In the second part I will describe our ongoing efforts to compute semi-leptonic $B_(s)$ decays (arXiv:1903.02100) before concluding by summarising RBC/UKQCD’s wider efforts in charm and bottom phenomenology.

Lundi 18 mars 14:00-15:00, CPPM Auditorium

### Non-equilibrium effects in the evolution of Dark Matter

#### Andrzej Hryczuk (National Centre for Nuclear Research, Warsaw, Poland)

This is a joint CPT-CPPM seminar !

Among viable dark matter (DM) production mechanisms the thermal freeze-out stands out as the most natural and best motivated one. In the usual theoretical approach to the determination of thermal relic abundance the assumption of local thermal equilibrium is made. But is this assumption always justified ? In this talk I will first introduce the topic and then address this question. I will discuss more accurate treatments, one relying on the inclusion of higher moments of the Boltzmann equation and the second on solving the evolution of the phase space distribution function fully numerically. Examples where such improved treatment is necessary will be discussed, including DM annihilation below threshold, semi- or resonant annihilation.

Mercredi 20 mars 11:00-12:00, Amphi 5 du CPT

### Effective field theories for phases of matter and cosmology

#### Alberto Nicolis (Columbia University)

I will review some modern applications of effective field theories outside their traditional particle physics domain. In particular, I will focus on spontaneous symmetry breaking for spacetime symmetries. The effective theories for the associated Goldstone excitations capture the low-energy/long-distance dynamics of a number of physical systems, from ordinary macroscopic media (solids, fluids, superfluids, supersolids) to more exotic cosmological ones

Mercredi 20 mars 14:00-15:00, Amphi 5 du CPT

### Résumé

Non-relativistic quantum particles bounded to an infinite curve in the plane by
the attractive contact delta-interaction are considered. The interval between
the energy of the transversal bound state and zero is shown to belong
to the absolutely continuous spectrum, with possible embedded eigenvalues.
The curve is assumed smooth and non-intersecting, asymptotically
approaching two different half-lines. The proof is inspired by the proof
of Agmon-Kato-Kuroda theorem.

mai 2019 :


text:
# How much of an extra cost premium is paid for assembly in the USA or UK?

Okay, here's the situation: Currently, I am making a small batch of 100 boards of my project. This is a small order, so start up costs are about 10% of the final cost, and the factory charges $50/hour (they say I can get it done in one or two hours.) These will be made in China. Places in the UK or USA won't even talk to me for an order of 100, or if they do, they provide me with outrageous prices (5-10x as much as China.) Now I know China is cheaper, but to many people, seeing "Made in China" cheapens a product. If I were to make, say 1000 or 2000 boards, would the cost to make them in the USA or UK, or even any European country be competitive with China, even if it was slightly more expensive? I know the Arduino is "Made in Italy", and the low price point of it makes me consider the possibility that I too could get mine made in a country with higher wages. What are other people's experience with this issue? • You tell us. Go get some quotes for your board and find out what is cheaper. There is just so many variables for us to be able to tell you one way or another. Price will depended on size, components, minimum spacing, etc. Feb 27 '11 at 3:23 • I imagine China will have better prices in high volumes as well. If the small batch works out well, I suggest you use the same company for the larger production. The risk and hassle of switching companies will negate any price difference. Feb 27 '11 at 4:59 • @kellenjb. I've asked many suppliers. In my question, I say they won't talk to me or give me outrageous prices. One quoted me$100/board for just assembly, excluding components! The product only sells for $85! Feb 27 '11 at 10:38 • If they wont talk to you what makes you think that they would be willing to talk to any of us for an equal order. Feb 27 '11 at 16:32 • @Kellenjb, I'm asking for others' experience on this matter - perhaps people have managed it before? Some will talk to me, they just give me stupid prices. Feb 27 '11 at 17:08 ## 3 Answers 1. Most of these local companies in fact will outsource your order to China. 2. You don't need to print 'Made in China' if you just ordered PCB from China. 'Made in' means place of last significant tech operation, so if Arduino's PCB is from China, but soldering is local - 'Made in Italy' is legitimate. 3. Premium cost is significant for real local production, maybe not 10x, but more than 2x. 4. If you can get it done on 2-sided PCB - just make it yourself using popular hobbiest tech. You can hire 1 guy, train him and he'll do you 2000 boards easily :-) This is popular here in Russia - guys who mastered self-made PCB sell products on self-made PCBs and save time & money of PCB production. 100 boards is very easy to do at home. • I considered making them at home but I came unstuck when I realised how much time it would take. There are 80 x 0603 components, 2 x TQFP, 8 x SOT23, as well as many others. I'll be producing prototypes myself, but production simply has to be done by machine to be viable. Feb 27 '11 at 1:49 • Well, 1 minute per tqfp, 5 seconds per sot&0603, 10 minutes per board (worst case). Making this board using toner transfer method would require some 1-2 minutes of human time, so 12 minutes per board in total. Maybe you can just hire a student to do that. Also, if you use resistors on parallel buses you can get quad & octal resistors to save time. Feb 27 '11 at 2:09 • 1 guy = 40 boards per day, 800 per month :-) Hehe :-) Feb 27 '11 at 2:10 • @BarsMonster, maybe if I live in Russia, but in the UK labour is expensive; min wage £5.80/hr IIRC. Future possibility of considering hand assembly but I think machine assembly is best. Feb 27 '11 at 2:56 • In Czech Republic the minimal wage is £1.7/hr (e.g. 3.5 times less than in UK) and I can get "hand pick&place" assembly from £9/hour plus some tiny fee per component. Trained worker can do between 500-1000 components per hour. So I don't see any particular reason why this could not be done in any European country or in U.S. for less than 7 quids per board in your case, and possibly for half of that. It's obviously possible in Italy, so look harder. These are often small companies that do only small series or prototypes and do not advertise much. Feb 27 '11 at 6:43 If you do a 2 sided PCB and plan on doing one sided mounting all SMT except for minimal throughole. Then, when you order your PCBs, you can order a solder paste template. You can put together a wooden holder with a bottom into which the board fits exactly. Pop in a PCB, place the solder template in there, then put some solder paste in there and use a squeegee (you can get them at a paint store) cut to fit it, and then just spread the paste over the board. Then remove the template and the PCB should have the correct paste on it (remember to clean the template). Then just place the components carefully. For an oven, you can use the Black and Decker Infrawave series. It's important to get a good temperature profile (to not heat up too quickly or cool too quickly). There are many articles online on this oven. You can also use the Cuisinart convection toaster too. So, you can do 4 board easily at a time this way, easily in 10 minutes if they are small boards. Thats 24 per hour. You hire someone at$24/hour. Thats $1 per board!!!!!!! It'll take one person a little over a week to do 1000 boards. Recommended you use diagnostics in your flash to test the board and light an LED. You can always load diagnostics, run the test, then load your desired code and lock the MCU....it you are trying to save space. Testing the boards is the slow part perhaps. For enclosure, you'll want to use an off the shelf plastic box. I don't know of a cheap fast way to do your own enclosures. Vacuum forming can work, but it's still slower than 24 per hour. Remember 24 per hour is$1 each, 12 per hour is \$2 each, etc, etc...

Good Luck. Post if you find other info.

It is very dependent on the design. For something that is all SMD with minimal manual work, the advantages of going overseas can be minimal - the trick is to find a local asssembler geared to your volumes, who doesn't charge a large 'get out of bed' fee for setting up etc. Larger places will be less interested in small jobs, but really small places tend to have a precarious existance and can have disappeared next time you need something done. Even with a 'right size/attitude' place you will generally have to fit inbetween the jobs from their larger customers, so getting stuff turned round quickly is near-impossible unless you're lucky, as even if you offer to pay twice as much it's still small for them and they're always going to prioritise their bigger customers. As mentioned above, successful lower-end assemblers who are ticking along nicely often don't need to advertise, and can be hard to find - recommendations are very useful - maybe ask a few companies making stuff on a similar scale to yours who they use for assembly - people are often happy to reccommend, as once you find a good place, you want them to stay in business.
You also have to consider that board assembly cost isn't the only cost involved - things like test, optimising for good yield etc. are very dependent on good communication and understanding between client and subcontractor, which can be nonexistent with Chinese suppliers. For something made in 100s I wouldn't even think of using China - the time to get things set up and the uncertainty that you're going to get what you want just aren't worth it.


text:
This site is supported by donations to The OEIS Foundation.

# 54

Please do not rely on any information it contains.

54 is an integer, the smallest that can be written as a sum of three squares in three different ways: 7 2 + 2 2 + 1 2 = 6 2 + 2(3 2) = 2(5 2) + 2 2 = 54.

## Membership in core sequences

 Even numbers ..., 48, 50, 52, 54, 56, 58, 60, ... A005843 Composite numbers ..., 50, 51, 52, 54, 55, 56, 57, ... A002808 Abundant numbers ..., 40, 42, 48, 54, 56, 60, 66, ... A005101

## Sequences pertaining to 54

 Multiples of 54 0, 54, 108, 162, 216, 270, 324, 378, 432, 486, 540, 594, 648, ...

## Partitions of 54

There are 386155 partitions of 54.

The Goldbach representations of 54 are: 7 + 47 = 11 + 43 = 13 + 41 = 17 + 37 = 23 + 31.

## Roots and powers of 54

In the table below, irrational numbers are given truncated to eight decimal places.

PLACEHOLDER

PLACEHOLDER

## Factorization of 54 in some quadratic integer rings

As was mentioned above, 54 is composite in ${\displaystyle \mathbb {Z} }$. But it has different factorizations in some quadratic integer rings.

 ${\displaystyle \mathbb {Z} [i]}$ ${\displaystyle (1\pm i)3^{3}}$ ${\displaystyle \mathbb {Z} [{\sqrt {-2}}]}$ ${\displaystyle (-1)({\sqrt {-2}})^{2}(1\pm {\sqrt {-2}})^{3}}$ ${\displaystyle \mathbb {Z} [{\sqrt {2}}]}$ ${\displaystyle ({\sqrt {2}})^{2}3^{3}}$ ${\displaystyle \mathbb {Z} [\omega ]}$ ${\displaystyle (-1)2(1+2\omega )^{6}}$ ${\displaystyle \mathbb {Z} [{\sqrt {3}}]}$ ${\displaystyle (-1)(1\pm {\sqrt {3}})({\sqrt {3}})^{6}}$ ${\displaystyle \mathbb {Z} [{\sqrt {-5}}]}$ 2 × 3 3 ${\displaystyle \mathbb {Z} [\phi ]}$ 2 × 3 3 ${\displaystyle \mathbb {Z} [{\sqrt {-6}}]}$ ${\displaystyle \mathbb {Z} [{\sqrt {6}}]}$ ${\displaystyle (-1)(2\pm {\sqrt {6}})(3\pm {\sqrt {6}})^{2}}$ ${\displaystyle {\mathcal {O}}_{\mathbb {Q} ({\sqrt {-7}})}}$ ${\displaystyle \left({\frac {1}{2}}\pm {\frac {\sqrt {-7}}{2}}\right)3^{3}}$ ${\displaystyle \mathbb {Z} [{\sqrt {7}}]}$ ${\displaystyle (-1)(3\pm {\sqrt {7}})(2\pm {\sqrt {7}})^{3}}$ ${\displaystyle \mathbb {Z} [{\sqrt {-10}}]}$ 2 × 3 3 ${\displaystyle \mathbb {Z} [{\sqrt {10}}]}$ 2 × 3 3 ${\displaystyle {\mathcal {O}}_{\mathbb {Q} ({\sqrt {-11}})}}$ ${\displaystyle 2\left({\frac {1}{2}}\pm {\frac {\sqrt {-11}}{2}}\right)^{3}}$ ${\displaystyle \mathbb {Z} [{\sqrt {11}}]}$ ${\displaystyle (-1)(3\pm {\sqrt {11}})3^{3}}$ ${\displaystyle \mathbb {Z} [{\sqrt {-13}}]}$ 2 × 3 3 ${\displaystyle {\mathcal {O}}_{\mathbb {Q} ({\sqrt {13}})}}$ ${\displaystyle (-1)2\left({\frac {1}{2}}\pm {\frac {\sqrt {13}}{2}}\right)^{3}}$ ${\displaystyle \mathbb {Z} [{\sqrt {-14}}]}$ ${\displaystyle \mathbb {Z} [{\sqrt {14}}]}$ ${\displaystyle (4\pm {\sqrt {14}})3^{3}}$ ${\displaystyle {\mathcal {O}}_{\mathbb {Q} ({\sqrt {-15}})}}$ ${\displaystyle \mathbb {Z} [{\sqrt {15}}]}$ 2 × 3 3 ${\displaystyle \mathbb {Z} [{\sqrt {-17}}]}$ ${\displaystyle {\mathcal {O}}_{\mathbb {Q} ({\sqrt {17}})}}$ ${\displaystyle (-1)\left({\frac {3}{2}}\pm {\frac {\sqrt {17}}{2}}\right)3^{3}}$ ${\displaystyle {\mathcal {O}}_{\mathbb {Q} ({\sqrt {-19}})}}$ ${\displaystyle \mathbb {Z} [{\sqrt {19}}]}$ ${\displaystyle (13\pm 3{\sqrt {19}})(4\pm {\sqrt {19}})^{3}}$

## Representation of 54 in various bases

 Base 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Representation 110110 2000 312 204 130 105 66 60 54 4A 46 42 3C 39 36 33 30 2G 2E

54 is a Harshad number in bases 3, 4, 5, 7, 9, 10, 13, 16, 17, 18, 19.

 ${\displaystyle -1}$ 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 1729


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# How find $\int_{\pi}^{0}\frac{2\cos{t}-8\sin{t}-12\sin{t}\cos{t}}{12\cos^2{t}+16\cos{t}+8}dt$

Find the following integral: $$I=\int_{\pi}^{0}\dfrac{2\cos{t}-8\sin{t}-12\sin{t}\cos{t}}{12\cos^2{t}+16\cos{t}+8}dt$$

My try let $$t=-x$$ $$I=\int_{-\pi}^{0}\dfrac{-2\cos{x}-8\sin{x}-12\sin{x}\cos{x}}{12\cos^2{x}+16\cos{x}+8}dx$$ so $$2I=\left(\int_{\pi}^{0}+\int_{-\pi}^{0}\right)\dfrac{-8\sin{x}-12\sin{x}\cos{x}}{12\cos^2{x}+16\cos{x}+8}dx+\int_{\pi}^{\pi}\dfrac{-2\cos{x}}{12\cos^2{x}+16\cos{x}+8}dx$$

then I can't, thank you.

• Have you tried the Weierstrass substitution? – Potato Oct 18 '13 at 4:30
• Hello,@Potato, you mean $u=\tan{\dfrac{t}{2}}$? But I think is very ugly,I hope see your solution,Thank you – china math Oct 18 '13 at 4:33
• Check this technique. – Mhenni Benghorbal Oct 18 '13 at 5:15
• As Potato suggested, consider the Weierstrass substitution. It is not so ugly. Do not forget partial fractions. I did it and the result is simply "Pi / 6 + Log[3]" – Claude Leibovici Oct 18 '13 at 5:35

Lucian got it right to start off. The way I see this is to split the integral up:

\begin{align}-I &= \int_0^{\pi} dt \frac{\cos{t}}{6 \cos^2{t}+8 \cos{t}+4} + \frac12 \int_0^{\pi} dt \frac{-24 \sin{t} \cos{t} - 16 \sin{t}}{12 \cos^2{t}+16 \cos{t}+8} \\ &= \int_0^{\pi} dt \frac{\cos{t}}{6 \cos^2{t}+8 \cos{t}+4} + \frac12 \left [\log{(12 \cos^2{t}+16 \cos{t}+8)} \right ]_0^{\pi} \\ &= J - \log{3}\end{align}

where (borrowing again from Lucian)

$$J = \int_0^{\pi} dt \frac{\cos{t}}{6 \cos^2{t}+8 \cos{t}+4}$$

Now, as is well known in the art of evaluating integrals of this type, we may use the residue theorem. We first exploit the symmetry about $[0, \pi]$ to the full circle and substitute $z=e^{i t}$ such that $dt = -i dz/z$ and get

\begin{align}J &= \frac14 \int_0^{2 \pi} \frac{\cos{t}}{3 \cos^2{t}+4 \cos{t}+2} \\ &= -\frac{i}{4} \oint_{|z|=1} \frac{dz}{z} \frac{\frac12 \left (z+z^{-1} \right )}{\frac{3}{4}\left (z^2+z^{-2}+2 \right)+ 2 \left ( z + z^{-1}\right ) + 2} \\&= -\frac{i}{2} \oint_{|z|=1} dz \frac{z^2+1}{3 z^4+8 z^3+14 z^2+8 z+3}\end{align}

To evaluate the latter integral, we need to find the poles of the integrand, i.e., the zeroes of the denominator. It may be a quartic, but fortunately it factors:

$$3 z^4+8 z^3+14 z^2+8 z+3 = (3 z^2+2 z+1)(z^2+2 z+3)$$

(I got this by a little trial and error, but it should be clear that such a factoring exists.) From this, we may easily determine the poles:

$$z_1^{\pm} = \frac{-1 \pm i \sqrt{2}}{3}$$ $$z_2^{\pm} = -1 \pm i \sqrt{2}$$

It should also be clear that the poles $z_1^{\pm}$ are inside the unit circle and $z_2^{\pm}$ are outside the unit circle. So now we evaluate the residues only at $z_1^{\pm}$. To compute the residues, use the fact that, for a function $f(z)=p(z)/q(z)$ having a simple pole at $z=z_0$, the residue of $f$ at $z=z_0$ is $p(z_0)/q'(z_0)$. Thus the sum of the residues is

$$\frac{z_1^{+2}+1}{12 z_1^{+3}+24 z_1^{+2} + 28 z_1^++8} + \frac{z_1^{-2}+1}{12 z_1^{-3}+24 z_1^{-2} + 28 z_1^-+8}$$

(Apologies for the confusing notation. The exponents above are not negative, but the minus is part of the variable name.)

What we have now is a mess, but we can clean it up a bit because we know that the poles above are complex conjugates of each other, so that the above sum is really

$$2 \Re{\left [\frac{z_1^{+2}+1}{12 z_1^{+3}+24 z_1^{+2} + 28 z_1^++8} \right ]}$$

Now, I am not going to post an answer here that I could not get by hand. I assure you, it's not as bad as it looks because:

$$z_1^{+} = \frac13 (-1+i \sqrt{2})$$ $$z_1^{+2} = -\frac19 (1+i 2 \sqrt{2})$$ $$z_1^{+3} = \frac{1}{27} (5 + i \sqrt{2})$$

Put this all together to get that (after cancelling twos)

\begin{align} \frac{z_1^{+2}+1}{6 z_1^{+3}+12 z_1^{+2} + 14 z_1^++4} &= \frac{\frac19 (8-i 2 \sqrt{2})}{\frac{6}{27} (5 + i \sqrt{2}) - \frac{12}{9} (1+i 2 \sqrt{2}) + \frac{14}{3} (-1 + i \sqrt{2}) + 4} \\ &= \frac{3 (8 - i 2 \sqrt{2})}{6 (5 + i \sqrt{2})-36 (1+i 2 \sqrt{2}) + 126 (-1 + i \sqrt{2}) + 108} \\ &= - \frac{24-i 6 \sqrt{2}}{24-i 60 \sqrt{2}}\\ &= -\frac{324+i 324}{1944}\\&= -\frac{1+i}{6} \end{align}

So the sum of the residues is $(-1/6) (-i/2) = i/12$. By the residue theorem, the integral sought, $J$, is $i 2 \pi$ times this sum, or $J=-\pi/6$. Therefore, the original integral is

$$I = \frac{\pi}{6}+\log{3}$$

The first thing to notice is that the last two terms of the numerator are nothing else than half of the derivative of the denominator: $$I = \int_\pi^0 \frac{2\cos t + \tfrac12(12\cos^2{t}+16\cos{t}+8)'}{12\cos^2{t}+16\cos{t}+8}dt = \tfrac12\ln(12\cos^2{t}+16\cos{t}+8)\Bigg|_{\ \pi}^{\ 0} +$$ $$+ \int_\pi^0 \frac{\cos t}{6\cos^2{t}+8\cos{t}+4}dt = \ln3 + J$$ where the expression of J is considerably simpler than that of our initial integral I, and can easily be solved by various substitutions, such as the one pointed in the comments above, for instance.