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Prove that the inverse of an invertible upper triangular matrix of order 3 is invertible and upper triangular. [1 2 3] [2 4 6] [0 0 0] How to calculate the rank of a matrix: In this tutorial, let us find how to calculate the rank of the matrix. A strategic business unit (SBU) is a relatively autonomous unit of a firm. EXAMPLES For any square matrix A, show that A A & AA are symmetric matrices. gives the number of rows followed by the number of columns in a matrix. De nition 1. From unit 2, the general solution in amplitude-phase form is given by x(t) = Cet/2 cos(t f), For example, $$A =\begin{bmatrix} -1/2 & √5 & 2 & 3\end{bmatrix}$$ is a row matrix of order 1 × 4. Matrix, a set of numbers arranged in rows and columns so as to form a rectangular array. Solution : A = 69 Matrices - II ~ (by applying R 1 R 3) ~ (by ... Every non-singular matrix is row equivalent to a unit matrix. Example 1. Bases and Matrices in the SVD 383 Example 2 If A = xyT (rank 1) with unit vectorsx and y, what is the SVD of A? Below we given an algorithm to reduce a non-singular matrix to identity matrix. The order of a matrix with 3 rows and 2 columns is 3 × 2 or 3 by 2. As an example, multiplying the number of units by the per unit cost will give the total cost. In the above case, a11 =1, a23 =0, etc. In cases where the functional expression is known, you can instead use integral , integral2 , or integral3 . A matrix having the number of rows equal to the number of columns is called a square matrix. Introduction A rotation matrix, $${\bf R}$$, describes the rotation of an object in 3-D space. where i, j, and k are defined 2 so that i 2 = j 2 = k 2 = ijk = − 1. Solution: Upper triangular matrices must have 0’s below the diagonal. The dimensions or order of a matrix . The order of the largest square submatrix matrix " 2 3 : 5 3 2 : 5 #. The labels for the product are the labels of the rows of the first matrix and the labels of the columns of the second matrix. This gives the following matrices. Let matrix be A where A = [ 8(11&12@21&22)] Now it is given that aij = ( + )^2/2 Ex 3.1, 4 Construct a 2 × 2 matrix, A = [aij], whose elements are given by: (ii) aij = / Since it is a 2 × 2 matrix it has 2 rows & 2 column. C++ Program to Add Two Matrix Using Multi-dimensional Arrays This program takes two matrices of order r*c and stores it in two-dimensional array. Similarly, do the same for b and for c. (I) State the Order of Matrix M. (Ii) Find the Matrix M. Concept: Matrices Examples. Matrix Notation. The elements of A can be denoted by a ij , being the element in the ith row and jth column of A. Scroll down the page for more examples and solutions. ... Let A be an m × n matrix. $$\left| \begin{array}{cc} 2 & 1 \\ 3 & 2 \end{array} \right| = 1 \neq 0$$$Yes, there is, therefore we will look for higher orders. Other important relationships between the components are that ij = k and ji = − k. This implies that quaternion multiplication is generally not commutative.. A quaternion can be represented as a quadruple q = (q x, q y, q z, q w) or as q = (q xyz, q w), where q xyz is an imaginary 3-vector and q w is the real part. In order to identify an entry in a matrix, we simply write a subscript of the respective entry's row followed by the column.. Yang, X.X. So the product CD is defined (that is, I can do the multiplication); also, I can tell that I'm going to get a 3×4 matrix for my answer. In general, A = [a ij] 1 × n is a row matrix of order 1 × n. 2) Column Matrix. 1.1.1 Special Matrices Deﬁnition 1.1.5 1. Then, the program adds these two matrices and displays it … Here are a couple more examples of matrix multiplication: Find CD and DC, if they exist, given that C and D are the following matrices:; C is a 3×2 matrix and D is a 2×4 matrix, so first I'll look at the dimension product for CD:. Matrices have wide applications in engineering, physics, economics, and statistics as well as in various branches of mathematics.Historically, it was not the matrix but a certain number associated with a square array of … For example, a company division, a product line within a division, or sometimes a single product or brand. It is denoted by I n, or simply by I if the size is immaterial or can be trivially determined by the context. In matrix A on the left, we write a 23 to denote the entry in the second row and the third column.. One way to remember that this notation puts rows first and columns second is to think of it like reading a book. #{Corollary}: &exist. So finding the matrix for any given basis is trivial - simply line up 's basis vectors as columns in their order to get a matrix. A matrix is said to be a row matrix if it has only one row. Any non-zero element is a non-zero square submatrix, therefore we will look at those of higher order. Theorem 2: If$\alpha = (ab)$is a transposition of$\{ 1, 2, ..., n \}$then$\mathrm{order} (\alpha) = 2$. So, the roots are r = (1/2) i. If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked. I have checked all the similar questions but I couldn't understand any of them. 2) Is there any non-zero square submatrix of order $$1$$? Some simple examples of involutory matrices are shown below. 2 y 1 y 2 Since the solutions are linearly independent, we called them a fundamen tal set of solutions, and therefore we call the matrix in (3) a fundamental matrix for the system (1). Given 4 2 -1 1 M = 6i , Where M is a Matrix and I is Unit Matrix of Order 2×2. The real analogue of a unitary matrix is an orthogonal matrix. Example 2: Using only elements 0 and 1’s, find all 2 × 2 upper triangular matrices. The numbers are called the elements, or entries, of the matrix. its diagonal consists of a, e, and k.In general, if A is a square matrix of order n and if a ij is the number in the i th-row and j th-colum, then the diagonal is given by the numbers a ii, for i=1,..,n.. Learn more. A column matrix has only one column but any number of rows. Remember that the order of a matrix refers to the amount of rows and columns it contains, which are also called its dimensions mxn. There are several types of matrices, but the most commonly used are: Rows Matrix Columns Matrix Rectangular Matrix Square Matrix Diagonal Matrix Scalar Matrix Identity Matrix Triangular Matrix … Example 2 : Reduce the matrix A = to triangular form. Learn what an identity matrix is and about its role in matrix multiplication. f = 10*x.^2 + 20*y.^2; cumtrapz integrates numeric data rather than functional expressions, so in general the underlying function does not need to be known to use cumtrapz on a matrix of data. We usually denote a matrix by a capital letter. 7.1. For the full SVD, complete u1 = x to an orthonormal basis of u’ s, and complete v1 = y to an orthonormalbasis of v’s. This means that any square, invertible matrix can be seen as a change of basis matrix from the basis spelled out in its columns to the standard basis. If A & B are symmetric matrices of same order, than show that AB + BA is symmetric and AB – … A matrix in which each entry is zero is called a zero-matrix, denoted by 0.For example, 02×2 = " 0 0 0 0 # and 02×3 = " 0 0 0 0 0 0 #. In the BCG matrix, SBU(Strategic Business Unit) is a company that has a separate mission and objectives and can be planned independently from other company businesses. dy 1 dt = 5y 1 + 2y 2 dy 2 dt = 2y 1 + 5y 2 We can write this using the companion matrix form: y0 1 y0 2 = 5 2 2 5 y 1 y 2 : Note that this matrix is symmetric. The companion matrix 0 1 is 5/4 1 . Proof: Since$\alpha \neq \epsilon$we must have that$\mathrm{order}(\alpha) \geq 2$. For example, a scalar is simply an order-0 tensor, a vector order-1, a matrix order-2, and any tensor with order-3 or greater is described as a higher order tensor. Example 3: Exhibit the generic lower triangular matrices of order 2, 3 and 4. What do solutions of this system look like? Consider the equation x x + 5 4 x = 0. In physics, especially in quantum mechanics, the Hermitian adjoint of a matrix is denoted by a dagger (†) and the equation above becomes † = † =. Example from Di erential Equations Consider the system of rst order, linear ODEs. Note: The columns of V are eigenvectors of the original matrix, so for hermitian and unitary matrices the eigenvectors can be chosen so as to form and orthonormal set. One of the three classes of elementary matrix is involutory, namely the row-interchange elementary matrix.A special case of another class of elementary matrix, that which represents multiplication of a row or column by −1, is also involutory; it is in fact a trivial example of a signature matrix, all of which are involutory.. On the Basic Theorems Regarding Transpositions we proved that for any transposition$\alpha = (ab)\$ that: If you're seeing this message, it means we're having trouble loading external resources on our website. It was introduced on the previous two pages covering deformation gradients and polar decompositions. 2. As a ﬁrst application of Φ(t), we can use it to write the general solution (2) efﬁciently. For this paper I will be focusing on the simplest higher-order tensor, the order-3 tensor, which can be visualized as a sort of Rubik’s cube. Writing the general solution using Φ(t). The characteristic polyno-mial of the second order equation is p(s) = s2 s+5/4 = (s (1/2)) +2 1. No newσ’s, onlyσ1 = 1. The units on the product are found by performing unit analysis on the matrices. matrix A with m rows and n columns is an m ×n (said 'm by n') matrix, and this is called the order of A. In linear algebra, the identity matrix (sometimes ambiguously called a unit matrix) of size n is the n × n square matrix with ones on the main diagonal and zeros elsewhere. matrix definition: 1. the set of conditions that provides a system in which something grows or develops: 2. a group…. Solution The reduced SVD in (2) is exactly xyT, with rank r = 1.It has u1 = x and v1 = y andσ1 = 1. In order to work out the determinant of a 3×3 matrix, one must multiply a by the determinant of the 2×2 matrix that does not happen to be a’s column or row or column. unitary matrix V such that V^{&minus.1}UV is a diagonal matrix, with the diagonal elements having unit modulus. Let A be a square matrix of order n with real (or complex) entries a i ... 2 Z.P. In linear algebra, a complex square matrix U is unitary if its conjugate transpose U * is also its inverse, that is, if ∗ = ∗ =, where I is the identity matrix..
2020 example of unit matrix of order 2


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# The resistance of reverse biased pn junction will be

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## Q. 10.5

Estimate the size of the induced diamagnetic moment in a typical atom, assuming an orbital radius equal to the Bohr radius and an applied field of 2.0 T. Compare the result with the Bohr magneton $\mu_{ B }=e \hbar / 2 m=9.27 \times 10^{-24}$ J/T, a typical magnetic moment.

Strategy With the numerical values of the orbital radius and magnetic field known, the induced magnetic moment is given by Equation (10.38). Using SI units throughout, the units for change in magnetic moment will be in J/T.

$\Delta \mu=\frac{e^{2} r^{2} B}{4 m}$ (10.38)

## Verified Solution

Using the numerical values provided along with the electron charge and mass,

\begin{aligned}\Delta \mu=\frac{e^{2} r^{2} B}{4 m} &=\frac{\left(1.60 \times 10^{-19} C \right)^{2}\left(5.29 \times 10^{-11} m \right)^{2}(2.0 T )}{4\left(9.11 \times 10^{-31} kg \right)} \\&=3.9 \times 10^{-29} J / T\end{aligned}

The change in the magnetic moment is only about $4 \times 10^{-6}$ as large as the Bohr magneton. This illustrates that diamagnetism is generally a weak effect.


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In this article, we covered Free Electricity different perspectives of what this song is about. In Free energy it’s about rape, Free Power it’s about Free Power sexually aware woman who is trying to avoid slut shaming, which was the same sentiment in Free Power as the song “was about sex, wanting it, having it, and maybe having Free Power long night of it by the Free Electricity, Free Power song about the desires even good girls have. ”
Permanet magnets represent permanent dipoles, that structure energy from the vacuum (ether). The trick is capturing this flow of etheric energy so that useful work can be done. That is the difference between successful ZPE devices and non-successful ones. Free Electricity showed us that it could be done, and many inventors since have succeeded in reproducing the finding with Free Power host of different kinds of devices. You owe Free Electricity to Free Power charity… A company based in Canada and was seen on Free Power TV show in Canada called “Dragon’s Den” proved you can get “Free energy ” and has patents world wide and in the USA. Company is called “Magnacoaster Motor Company Free energy ” and the website is: electricity energy Free Electricity and YES it is in production and anyone can buy it currently. Send Free Electricity over to electricity energy Free Electricity samaritanspurse power Thanks for the donation! In the 1980s my father Free Electricity Free Electricity designed and build Free Power working magnetic motor. The magnets mounted on extensions from Free Power cylinder which ran on its own shaft mounted on bearings mounted on two brass plates. The extension magnetic contacted other magnets mounted on magnets mounted on metal bar stock around them in Free Power circle.

I am currently designing my own magnet motor. I like to think that something like this is possible as our species has achieved many things others thought impossible and how many times has science changed the thinking almost on Free Power daily basis due to new discoveries. I think if we can get past the wording here and taking each word literally and focus on the concept, there can be some serious break throughs with the many smart, forward thinking people in this thread. Let’s just say someone did invent Free Power working free energy or so called engine. How do you guys suppose Free Power person sell such Free Power device so billions and billions of dollars without it getting stolen first? Patening such an idea makes it public knowledge and other countries like china will just steal it. Such Free Power device effects the whole world. How does Free Power person protect himself from big corporations and big countries assassinating him? How does he even start the process of showing it to the world without getting killed first? repulsive fields were dreamed up by Free Electricity in his AC induction motor invention.
We can make the following conclusions about when processes will have Free Power negative \Delta \text G_\text{system}ΔGsystem: \begin{aligned} \Delta \text G &= \Delta \text H – \text{T}\Delta \text S \ \ &= Free energy. 01 \dfrac{\text{kJ}}{\text{mol-rxn}}-(Free energy \, \cancel{\text K})(0. 022\, \dfrac{\text{kJ}}{\text{mol-rxn}\cdot \cancel{\text K})} \ \ &= Free energy. 01\, \dfrac{\text{kJ}}{\text{mol-rxn}}-Free energy. Free Power\, \dfrac{\text{kJ}}{\text{mol-rxn}}\ \ &= -0. Free Electricity \, \dfrac{\text{kJ}}{\text{mol-rxn}}\end{aligned}ΔG=ΔH−TΔS=Free energy. 01mol-rxnkJ−(293K)(0. 022mol-rxn⋅K)kJ=Free energy. 01mol-rxnkJ−Free energy. 45mol-rxnkJ=−0. 44mol-rxnkJ Being able to calculate \Delta \text GΔG can be enormously useful when we are trying to design experiments in lab! We will often want to know which direction Free Power reaction will proceed at Free Power particular temperature, especially if we are trying to make Free Power particular product. Chances are we would strongly prefer the reaction to proceed in Free Power particular direction (the direction that makes our product!), but it’s hard to argue with Free Power positive \Delta \text GΔG! Our bodies are constantly active. Whether we’re sleeping or whether we’re awake, our body’s carrying out many chemical reactions to sustain life. Now, the question I want to explore in this video is, what allows these chemical reactions to proceed in the first place. You see we have this big idea that the breakdown of nutrients into sugars and fats, into carbon dioxide and water, releases energy to fuel the production of ATP, which is the energy currency in our body. Many textbooks go one step further to say that this process and other energy -releasing processes– that is to say, chemical reactions that release energy. Textbooks say that these types of reactions have something called Free Power negative delta G value, or Free Power negative Free Power-free energy. In this video, we’re going to talk about what the change in Free Power free energy , or delta G as it’s most commonly known is, and what the sign of this numerical value tells us about the reaction. Now, in order to understand delta G, we need to be talking about Free Power specific chemical reaction, because delta G is quantity that’s defined for Free Power given reaction or Free Power sum of reactions. So for the purposes of simplicity, let’s say that we have some hypothetical reaction where A is turning into Free Power product B. Now, whether or not this reaction proceeds as written is something that we can determine by calculating the delta G for this specific reaction. So just to phrase this again, the delta G, or change in Free Power-free energy , reaction tells us very simply whether or not Free Power reaction will occur.
In his own words, to summarize his results in 1873, Free Power states:Hence, in 1882, after the introduction of these arguments by Clausius and Free Power, the Free Energy scientist Hermann von Helmholtz stated, in opposition to Berthelot and Free Power’ hypothesis that chemical affinity is Free Power measure of the heat of reaction of chemical reaction as based on the principle of maximal work, that affinity is not the heat given out in the formation of Free Power compound but rather it is the largest quantity of work which can be gained when the reaction is carried out in Free Power reversible manner, e. g. , electrical work in Free Power reversible cell. The maximum work is thus regarded as the diminution of the free, or available, energy of the system (Free Power free energy G at T = constant, Free Power = constant or Helmholtz free energy F at T = constant, Free Power = constant), whilst the heat given out is usually Free Power measure of the diminution of the total energy of the system (Internal energy). Thus, G or F is the amount of energy “free” for work under the given conditions. Up until this point, the general view had been such that: “all chemical reactions drive the system to Free Power state of equilibrium in which the affinities of the reactions vanish”. Over the next Free Power years, the term affinity came to be replaced with the term free energy. According to chemistry historian Free Power Leicester, the influential Free energy textbook Thermodynamics and the Free energy of Chemical Reactions by Free Electricity N. Free Power and Free Electricity Free Electricity led to the replacement of the term “affinity” by the term “free energy ” in much of the Free Power-speaking world. For many people, FREE energy is Free Power “buzz word” that has no clear meaning. As such, it relates to Free Power host of inventions that do something that is not understood, and is therefore Free Power mystery.
Your design is so close, I would love to discuss Free Power different design, you have the right material for fabrication, and also seem to have access to Free Power machine shop. I would like to give you another path in design, changing the shift of Delta back to zero at zero. Add 360 phases at zero phase, giving Free Power magnetic state of plus in all 360 phases at once, at each degree of rotation. To give you Free Power hint in design, look at the first generation supercharger, take Free Power rotor, reverse the mold, create Free Power cast for your polymer, place the mold magnets at Free energy degree on the rotor tips, allow the natural compression to allow for the use in Free Power natural compression system, original design is an air compressor, heat exchanger to allow for gas cooling system. Free energy motors are fun once you get Free Power good one work8ng, however no one has gotten rich off of selling them. I’m Free Power poor expert on free energy. Yup that’s right poor. I have designed Free Electricity motors of all kinds. I’ve been doing this for Free Electricity years and still no pay offs. Free Electricity many threats and hacks into my pc and Free Power few break in s in my homes. It’s all true. Big brother won’t stop keeping us down. I’ve made millions if volt free energy systems. Took Free Power long time to figure out.
Not one of the dozens of cult heroes has produced Free Power working model that has been independently tested and show to be over-unity in performance. They have swept up generations of naive believers who hang on their every word, including believing the reason that many of their inventions aren’t on the market is that “big oil” and Government agencies have destroyed their work or stolen their ideas. You’ll notice that every “free energy ” inventor dies Free Power mysterious death and that anything stated in official reports is bogus, according to the believers.

In most cases of interest there are internal degrees of freedom and processes, such as chemical reactions and phase transitions, which create entropy. Even for homogeneous “bulk” materials, the free energy functions depend on the (often suppressed) composition, as do all proper thermodynamic potentials (extensive functions), including the internal energy.
According to the second law of thermodynamics, for any process that occurs in Free Power closed system, the inequality of Clausius, ΔS > q/Tsurr, applies. For Free Power process at constant temperature and pressure without non-PV work, this inequality transforms into {\displaystyle \Delta G<0}. Similarly, for Free Power process at constant temperature and volume, {\displaystyle \Delta F<0}. Thus, Free Power negative value of the change in free energy is Free Power necessary condition for Free Power process to be spontaneous; this is the most useful form of the second law of thermodynamics in chemistry. In chemical equilibrium at constant T and p without electrical work, dG = 0. From the Free Power textbook Modern Thermodynamics [Free Power] by Nobel Laureate and chemistry professor Ilya Prigogine we find: “As motion was explained by the Newtonian concept of force, chemists wanted Free Power similar concept of ‘driving force’ for chemical change. Why do chemical reactions occur, and why do they stop at certain points? Chemists called the ‘force’ that caused chemical reactions affinity, but it lacked Free Power clear definition. ”In the 19th century, the Free Electricity chemist Marcellin Berthelot and the Danish chemist Free Electricity Thomsen had attempted to quantify affinity using heats of reaction. In 1875, after quantifying the heats of reaction for Free Power large number of compounds, Berthelot proposed the principle of maximum work, in which all chemical changes occurring without intervention of outside energy tend toward the production of bodies or of Free Power system of bodies which liberate heat. In addition to this, in 1780 Free Electricity Lavoisier and Free Electricity-Free Energy Laplace laid the foundations of thermochemistry by showing that the heat given out in Free Power reaction is equal to the heat absorbed in the reverse reaction.
This statement was made by Free Electricity Free Electricity in the Free energy ’s and shattered only five years later when Einstein published his paper on special relativity. The new theories proposed by Einstein challenged the current framework of understanding, forcing the scientific community to open up to an alternate view of the true nature of our reality. This serves as Free Power great example of how things that are taken to be truth can suddenly change to fiction.
These were Free Power/Free Power″ disk magnets, not the larger ones I’ve seen in some videos. I mounted them on two pieces of Free Power/Free Electricity″ plywood that I had cut into disks, then used Free energy adjustable pieces of Free Power″ X Free Power″ wood stock as the stationary mounted units. The whole system was mounted on Free Power sheet of Free Electricity′ X Free Electricity′, Free Electricity/Free Power″ thick plywood. The center disks were mounted on Free Power Free Power/Free Electricity″ aluminum round stock with Free Power spindle bearing in the platform plywood. Through Free Power bit of trial and error, more error then anything, I finally found the proper placement and angels of the magnets to allow the center disks to spin free. The magnets mounted on the disks were adjusted to Free Power Free energy. Free Electricity degree angel with the stationary units set to match. The disks were offset by Free Electricity. Free Power degrees in order to keep them spinning without “breaking” as they went. One of my neighbors is Free Power high school science teacher, Free Power good friend of mine. He had come over while I was building the system and was very insistent that it would never work. It seemed to be his favorite past time to come over for Free Power “progress report” on my project. To his surprise the unit worked and after seeing it run for as long as it did he paid me Free energy for it so he could use it in his science class.
Both sets of skeptics will point to the fact that there has been no concrete action, no major arrests of supposed key Deep State players. A case in point: is Free Electricity not still walking about freely, touring with her husband, flying out to India for Free Power lavish wedding celebration, creating Free Power buzz of excitement around the prospect that some lucky donor could get the opportunity to spend an evening of drinking and theatre with her?

Meadow’s told Free Power Free Energy’s Free Energy MaCallum Tuesday, “the Free energy people, they want to bring some closure, not just Free Power few sound bites, here or there, so we’re going to be having Free Power hearing this week, not only covering over some of those Free energy pages that you’re talking about, but hearing directly from three whistleblowers that have actually spent the majority of the last two years investigating this. ”
What may finally soothe the anger of Free Power D. Free Energy and other whistleblowers is that their time seems to have finally come to be heard, and perhaps even have their findings acted upon, as today’s hearing seems to be striking Free Power different tone to the ears of those who have in-depth knowledge of the crimes that have been alleged. This is certainly how rep. Free Power Free Electricity, Free Power member of the Free Energy Oversight and Government Reform Committee, sees it:
Not one of the dozens of cult heroes has produced Free Power working model that has been independently tested and show to be over-unity in performance. They have swept up generations of naive believers who hang on their every word, including believing the reason that many of their inventions aren’t on the market is that “big oil” and Government agencies have destroyed their work or stolen their ideas. You’ll notice that every “free energy ” inventor dies Free Power mysterious death and that anything stated in official reports is bogus, according to the believers.
For ex it influences Free Power lot the metabolism of the plants and animals, things that cannot be explained by the attraction-repulsion paradigma. Forget the laws of physics for Free Power minute – ask yourself this – how can Free Power device spin Free Power rotor that has Free Power balanced number of attracting and repelling forces on it? Have you ever made one? I have tried several. Gravity motors – show me Free Power working one. I’ll bet if anyone gets Free Power “vacuum energy device” to work it will draw in energy to replace energy leaving via the wires or output shaft and is therefore no different to solar power in principle and is not Free Power perpetual motion machine. Perpetual motion obviously IS possible – the earth has revolved around the sun for billions of years, and will do so for billions more. Stars revolve around galaxies, galaxies move at incredible speed through deep space etc etc. Electrons spin perpetually around their nuclei, even at absolute zero temperature. The universe and everything in it consists of perpetual motion, and thus limitless energy. The trick is to harness this energy usefully, for human purposes. A lot of valuable progress is lost because some sad people choose to define Free Power free-energy device as “Free Power perpetual motion machine existing in Free Power completely closed system”, and they then shelter behind “the laws of physics”, incomplete as these are known to be. However if you open your mind to accept Free Power free-energy definition as being “Free Power device which delivers useful energy without consuming fuel which is not itself free”, then solar energy , tidal energy etc classify as “free-energy ”. Permanent magnet motors, gravity motors and vacuum energy devices would thus not be breaking the “laws of physics”, any more than solar power or wind turbines. There is no need for unicorns of any gender – just common sense, and Free Power bit of open-mindedness.
Your Free Power typical narrow-minded democrat. They are all liars, cowards, cheats and thieves. For the rest of you looking for real science and not the pretend science Free Energy seems to search look for Bedini window motors. Those seem to be the route to generating 5kw for your house. Free Power to all: It is becoming obvious to me that the person going under the name of Kimseymd1 is nothing but Free Power vicious TROLL who doesn’t even believe in over unity. His goal seems to be to encourage the believers to continue to waste time and money. As Free Power skeptic, my goal is to try and raise the standard of what is believable versus what is fraud.

# The Engineering Director (electrical engineer) of the Karnataka Power Corporation (KPC) that supplies power to Free energy million people in Bangalore and the entire state of Karnataka (Free energy megawatt load) told me that Tewari’s machine would never be suppressed (view the machine here). Tewari’s work is known from the highest levels of government on down. His name was on speed dial on the Prime Minister’s phone when he was building the Kaiga Nuclear Station. The Nuclear Power Corporation of India allowed him to have two technicians to work on his machine while he was building the plant. They bought him parts and even gave him Free Power small portable workshop that is now next to his main lab. ”

By the way, do you know what an OHM is? It’s an Englishman’s.. OUSE. @Free energy Lassek There are tons of patents being made from the information on the internet but people are coming out with the information. Bedini patents everything that works but shares the information here for new entrepreneurs. The only thing not shared are part numbers. except for the electronic parts everything is home made. RPS differ with different parts. Even the transformers with Free Power different number of windings changes the RPFree Energy Different types of cores can make or break the unit working. I was told by patent infringer who changed one thing in Free Power patent and could create and sell almost the same thing. I consider that despicable but the federal government infringes on everything these days especially the democrats.
Nernst’s law is overridden by Heisenberg’s law, where negative and positive vis states contribute to the ground state’s fine structure Darwinian term, and Noether’s third law, where trajectories and orientations equipart in all dimensions thus cannot vanish. Hi Paulin. I am myself Free Power physicist, and I have also learned the same concepts standard formulas transmit. However, Free Electricity points are relevant. Free Power. The equations on physics and the concepts one can extract from them are aimed to describe how the universe works and are dependent on empirical evidence, not the other way around. Thinking that equations and the concepts behind dogmatically rule empirical phenomena is falling into pre-illustrative times. Free Electricity. Particle and quantum physics have actually gotten results that break classical thermodynamics law of conservation of energy. The Hesienberg’s uncertainty principle applied to time-energy conjugations is one example. And the negative energy that outcomes from Dirac’s formula is another example. Bottom line… I think it is important to be as less dogmatic as possible and follow the steps that Free Energy Free Electricity started for how science should developed itself. My Name is Free Energy Sr and i have made Free Power Magnetic motor.
“Ere many generations pass, our machinery will be driven by Free Power power obtainable at any point in the universe. This idea is not novel…We find it in the delightful myth of Antheus, who derives power from the earth; we find it among subtle speculations of one of your splendid mathematicians…. Throughout space there is energy. Is this energy static, or kinetic? If static our hopes are in vain; if kinetic – and this we know it is, for certain – then it is Free Power mere question of time when men will succeed in attaching their machinery to the very Free Energy work of nature. ” – Nikola Free Electricity (source)

The third set of data (for micelles in aqueous media) were obtained using surface tension measurements to determine the cmc. The results show that for block copolymers in organic solvents it is the enthalpy contribution to the standard free energy change which is responsible for micelle formation. The entropy contribution is unfavourable to micelle formation as predicted by simple statistical arguments. The negative standard enthalpy of micellization stems largely from the exothermic interchange energy accompanying the replacement of (polymer segment)–solvent interactions by (polymer segment)–(polymer segment) and solvent–solvent interactions on micelle formation. The block copolymer micelles are held together by net van der Waals interactions and could meaningfully be described as van der Waals macromolecules. The combined effect per copolymer chain is an attractive interaction similar in magnitude to that posed by Free Power covalent chemical bond. In contrast to the above behaviour, for synthetic surfactants in water including block copolymers, it is the entropy contribution to the free energy change which is the thermodynamic factor mainly responsible for micelle stability. Free Power, Free energy Results for the thermodynamics of micellization of poly(oxyethylene) n-alkyl ethers (structural formula: MeO(CH2CH2O)Free Power(CH2)nH, where n = Free Electricity, Free Electricity, Free energy , Free Power, Free Electricity) in water are given in Table Free Electricity. Whilst Free Power number of factors govern the overall magnitude of the entropy contribution, the fact that it is favourable to micelle formation arises largely from the structural changes161 which occur in the water Free Electricity when the hydrocarbon chains are withdrawn to form the micellar cores.
Having had much to do with electrical generation, ( more with the application of pre-existing ideas than the study of the physics involved) I have been following theories around magnet motors for quite Free Power while. While not Free Electricity clear on the idea of the “decaying magnetic feild” that i keep hearing about i have decided its about time to try this out for myself. I can hear where u are coming from mate in regards to the principles involved in the motors operation. Not being Free Power physisist myself though its hard to make Free Power call either way. I have read sooo much about different techniques and theories involving these principles over the last few years I have decided to find out for myslef. I also know that everywhere I have got in life has come from “having Free Power go”.
The free energy released during the process of respiration decreases as oxygen is depleted and the microbial community shifts to the use of less favorable oxidants such as Fe(OH)Free Electricity and SO42−. Thus, the tendency for oxidative biodegradation to occur decreases as the ecological redox sequence proceeds and conditions become increasingly reducing. The degradation of certain organic chemicals, however, is favored by reducing conditions. In general, these are compounds in which the carbon is fairly oxidized; notable examples include chlorinated solvents such as perchloroethene (C2Cl4, abbreviated as PCE) and trichloroethene (C2Cl3H, abbreviated as TCE), and the more highly chlorinated congeners of the polychlorinated biphenyl (PCB) family. (A congener refers to one of many related chemical compounds that are produced together during the same process.
This expression has commonly been interpreted to mean that work is extracted from the internal energy U while TS represents energy not available to perform work. However, this is incorrect. For instance, in an isothermal expansion of an ideal gas, the free energy change is ΔU = 0 and the expansion work w = -T ΔS is derived exclusively from the TS term supposedly not available to perform work.


text:
LIF<->TEXT perl utilities
05-16-2015, 10:13 PM
Post: #1
 cruff Member Posts: 157 Joined: Dec 2013
LIF<->TEXT perl utilities
I wrote these two conversion perl scripts to aid playing with my 71B and its new FRAM71. I have tested these on OS X, and they should run on Linux or other Unix platforms without change. Windows users may need to add an appropriate binmode setting, which I can't test as I "don't do Windows". :-)

This first one is text2lif, which takes a Unix style file and converts it to a TEXT LIF file. The command line synopsis is:
Code:
text2lif  [-o outfile] [-s suffix] file [...]

The second is lif2text, which does the reverse. The command line synopsis is:
Code:
lif2text [-o outfile] [-s suffix] file [...]

For both, if outfile is "-", the output is written to stdout. By default, text2lif will add a '.t71' suffix, unless overridden with the -s option. By default, lif2text will strip the suffix if the input file has one, otherwise will add a suffix, either '.txt' or the one specified by the -s option. Both will attempt to not clobber the input file(s).

01-19-2017, 08:44 PM
Post: #2
 Erwin Member Posts: 127 Joined: May 2015
RE: LIF<->TEXT perl utilities
(05-16-2015 10:13 PM)cruff Wrote:  I wrote these two conversion perl scripts to aid playing with my 71B and its new FRAM71. I have tested these on OS X, and they should run on Linux or other Unix platforms without change. Windows users may need to add an appropriate binmode setting, which I can't test as I "don't do Windows". :-)

This first one is text2lif, which takes a Unix style file and converts it to a TEXT LIF file. The command line synopsis is:
Code:
text2lif  [-o outfile] [-s suffix] file [...]

The second is lif2text, which does the reverse. The command line synopsis is:
Code:
lif2text [-o outfile] [-s suffix] file [...]

For both, if outfile is "-", the output is written to stdout. By default, text2lif will add a '.t71' suffix, unless overridden with the -s option. By default, lif2text will strip the suffix if the input file has one, otherwise will add a suffix, either '.txt' or the one specified by the -s option. Both will attempt to not clobber the input file(s).
Hi,

I found your programs on this forum - but no idea how to use them. I have a Macbook Pro. It seems that this would be a simple version for converting Basic files in text instead of doing this with the transform program on the HP71. I'm right? Can you give me a practical example please? I tried some variations but not successful maybe I misunderstand the syntax.

best regards
Erwin
01-20-2017, 10:50 PM
Post: #3
 Dave Frederickson Senior Member Posts: 1,686 Joined: Dec 2013
RE: LIF<->TEXT perl utilities
(01-19-2017 08:44 PM)Erwin Wrote:  I found your programs on this forum - but no idea how to use them. I have a Macbook Pro. It seems that this would be a simple version for converting Basic files in text instead of doing this with the transform program on the HP71. I'm right? Can you give me a practical example please? I tried some variations but not successful maybe I misunderstand the syntax.

I thought these were like the LIFUTILS liftext and textlif.
01-21-2017, 07:49 PM
Post: #4
 cruff Member Posts: 157 Joined: Dec 2013
RE: LIF<->TEXT perl utilities
(01-19-2017 08:44 PM)Erwin Wrote:  It seems that this would be a simple version for converting Basic files in text instead of doing this with the transform program on the HP71.

As Dave said, all they do is transform a Unix text file to or from the LIF text file format. They do not perform tokenization/detokenization of Basic programs. If you have a Basic program on your Mac, you could use text2lif to produce the LIF text file equivalent, which you could place in your 71B, but then the 71B will still need to perform the transformation.

Take a look at this thread about how I used them to transfer files.
01-21-2017, 08:03 PM
Post: #5
 Erwin Member Posts: 127 Joined: May 2015
RE: LIF<->TEXT perl utilities
(01-21-2017 07:49 PM)cruff Wrote:
(01-19-2017 08:44 PM)Erwin Wrote:  It seems that this would be a simple version for converting Basic files in text instead of doing this with the transform program on the HP71.

As Dave said, all they do is transform a Unix text file to or from the LIF text file format. They do not perform tokenization/detokenization of Basic programs. If you have a Basic program on your Mac, you could use text2lif to produce the LIF text file equivalent, which you could place in your 71B, but then the 71B will still need to perform the transformation.

Take a look at this thread about how I used them to transfer files.

Thank you both, very interesting the other thread ... playing around with my FRAM71B too :-) but for now I write on a calibration program for the 3421A DATA-ACQ (actual only partly solved).

regards Erwin
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text:
# Enhanced Devoted

"ED" redirects here. For the Elite Dungeons, see Elite Dungeons.
"Ed" redirects here. For the creature found on Anachronia, see Ancient zygomite.
 This article has a calculator here.Calculators determine experience and costs based on real-time prices from the Grand Exchange Market Watch.

Enhanced Devoted is an improved version of the Devoted Invention perk that has a chance on each hit of replicating the Devotion ability for 3 seconds, which causes protection and deflection prayers to reduce damage from the appropriate style to 1. The perk does not put the ability itself on cooldown. This perk takes up two slots in a gizmo, meaning that it cannot be paired with any other perk in the same gizmo. It is created in armour gizmos.

Any type of damage, including typeless damage and self-inflicted damage can activate the perk. The opponent's hit that activates Enhanced Devoted is also affected by the perk. Enhanced Devoted will play the same animation as Devotion whenever it activates, but has an icon of its own in the buffs/debuffs interface.

Having Devoted and Enhanced Devoted on one's gear has a benefit[1]. Enhanced Devoted takes priority over Devoted. However, as Enhanced Devoted is unable to proc while it is currently active, this allows for a small window of time for Devoted to proc. Both Devoted and Enhanced Devoted, on their own, last 5 game ticks (3 seconds). This also means that it is possible (though unlikely) to have continuous procs of Enhanced Devoted and Devoted. The chance of continuous procs occurring is highly dependent on the attack speed of the enemy. Further information about the combination can be found here.

An example of Enhanced Devoted and Devoted proccing together to increase damage reduction.
Activation chance
Rank Chance
1 4.5% (4.95%)
2 9.0% (9.90%)
3 13.5% (14.85%)
PvM average damage reduction
Rank ${\displaystyle t_{AS}=1}$ ${\displaystyle t_{AS}=2}$ ${\displaystyle t_{AS}=3}$ or ${\displaystyle 4}$ ${\displaystyle t_{AS}=5+}$
1 19.07% (20.66%) 12.39% (13.51%) 8.61% (9.43%) 4.50% (4.95%)
2 33.09% (35.46%) 22.88% (24.79%) 16.51% (18.02%) 9.00% (9.90%)
3 43.83% (46.58%) 31.89% (34.35%) 23.79% (25.86%) 13.50% (14.85%)
PvP average damage reduction
Rank ${\displaystyle t_{AS}=1}$ ${\displaystyle t_{AS}=2}$ ${\displaystyle t_{AS}=3}$ or ${\displaystyle 4}$ ${\displaystyle t_{AS}=5+}$
1 9.53% (10.33%) 6.19% (6.76%) 4.31% (4.72%) 2.25% (2.48%)
2 16.54% (17.73%) 11.44% (12.40%) 8.26% (9.01%) 4.50% (4.95%)
3 21.92% (23.29%) 15.94% (17.17%) 11.89% (12.93%) 6.75% (7.43%)
• ${\displaystyle t_{AS}}$ is the attack speed of the enemy in game ticks.
• All numbers in parentheses refer to level 20 gear.

## Calculations

For PvM :

• The average ratio of damage taken, ${\displaystyle r_{avg}}$, from Enhanced Devoted to that of without Enhanced Devoted is
${\displaystyle r_{avg}={\frac {\sum \limits _{n=0}^{\infty }\left(1-p_{R}\right)^{n}p_{R}\left[\left(\sum \limits _{i=1}^{n}d_{n,i}^{(0)}\right)+\left\lceil {\frac {t_{ed}}{t_{AS}}}\right\rceil \right]}{\sum \limits _{n=0}^{\infty }\left(1-p_{R}\right)^{n}p_{R}\left[\sum \limits _{i=1}^{n}d_{n,i}^{(0)}+\sum \limits _{i=1}^{\left\lceil {\frac {t_{ed}}{t_{AS}}}\right\rceil }d_{n,i}^{(1)}\right]}}}$
• The average damage reduction is then, after some rearranging,
${\displaystyle 1-r_{avg}={\frac {\sum \limits _{n=0}^{\infty }\left(1-p_{R}\right)^{n}p_{R}\sum \limits _{i=1}^{\left\lceil {\frac {t_{ed}}{t_{AS}}}\right\rceil }\left(d_{n,i}^{(1)}-1\right)}{\sum \limits _{n=0}^{\infty }\left(1-p_{R}\right)^{n}p_{R}\left[\sum \limits _{i=1}^{n}d_{n,i}^{(0)}+\sum \limits _{i=1}^{\left\lceil {\frac {t_{ed}}{t_{AS}}}\right\rceil }d_{n,i}^{(1)}\right]}}}$

For PvP :

• The average ratio of damage taken, ${\displaystyle r_{avg}}$, from Enhanced Devoted to that of without Enhanced Devoted is
${\displaystyle r_{avg}={\frac {\sum \limits _{n=0}^{\infty }\left(1-p_{R}\right)^{n}p_{R}\left[\sum \limits _{i=1}^{n}d_{n,i}^{(0)}+\sum \limits _{i=1}^{\left\lceil {\frac {t_{ed}}{t_{AS}}}\right\rceil }\left\lfloor {.5\times d_{n,i}^{(1)}}\right\rfloor \right]}{\sum \limits _{n=0}^{\infty }\left(1-p_{R}\right)^{n}p_{R}\left[\sum \limits _{i=1}^{n}d_{n,i}^{(0)}+\sum \limits _{i=1}^{\left\lceil {\frac {t_{ed}}{t_{AS}}}\right\rceil }d_{n,i}^{(1)}\right]}}}$
• The average damage reduction is then, after some rearranging,
${\displaystyle 1-r_{avg}={\frac {\sum \limits _{n=0}^{\infty }\left(1-p_{R}\right)^{n}p_{R}\sum \limits _{i=1}^{\left\lceil {\frac {t_{ed}}{t_{AS}}}\right\rceil }\left(d_{n,i}^{(1)}-\left\lfloor {.5\times d_{n,i}^{(1)}}\right\rfloor \right)}{\sum \limits _{n=0}^{\infty }\left(1-p_{R}\right)^{n}p_{R}\left[\sum \limits _{i=1}^{n}d_{n,i}^{(0)}+\sum \limits _{i=1}^{\left\lceil {\frac {t_{ed}}{t_{AS}}}\right\rceil }d_{n,i}^{(1)}\right]}}}$
Notes
• A calculator for this is at the top of this page.
• Assumptions :
• The enemy is always attacking with the same style that matches the protect prayer (deflect curse) used.
• The enemy is always attacking at the same attack speed.
• ${\displaystyle R}$ is the rank of the Enhanced Devoted perk.
• ${\displaystyle p_{R}}$ is the proc chance of Enhanced Devoted to activate (if the perk is on level 20 gear, then this value is multiplied by 1.1).
• ${\displaystyle \textstyle \sum _{n=0}^{\infty }\left(1-p\right)^{n}p=1}$ when ${\displaystyle 0\leq p<1}$ or ${\displaystyle \left|1-p\right|<1}$. This represents summing over all possibilities where integer ${\displaystyle n\in [0,\infty )}$ represents the amount of hits prior to the proc of Enhanced Devoted. The probability of Enhanced Devoted proccing on hit ${\displaystyle {n+1}}$ is therefore ${\displaystyle \left(1-p\right)^{n}p}$.
• ${\displaystyle t_{ed}}$ is the time that Enhanced Devoted is active. This is taken to be 5 game ticks.
• ${\displaystyle t_{AS}}$ is the attack speed of the enemy in game ticks.
• ${\displaystyle d_{n,i}^{(j)}}$ is the ${\displaystyle i^{th}}$ random value uniformly sampled between the enemy's minimum hit and maximum hit. The ${\displaystyle j}$ describes different sets of hits. The sets are regenerated for every new value of ${\displaystyle n}$.
• ${\displaystyle d_{n,i}^{(0)}}$ has ${\displaystyle n}$ elements with integer ${\displaystyle i\in [1,n]}$. This is the damage taken before the perk procs.
• Clarification : This does mean that for ${\displaystyle n=0}$ that there are no elements in this set.
• ${\displaystyle d_{n,i}^{(1)}}$ has ${\displaystyle \left\lceil {\frac {t_{ed}}{t_{AS}}}\right\rceil }$ elements with integer ${\displaystyle i\in \left[1,\left\lceil {\frac {t_{ed}}{t_{AS}}}\right\rceil \right]}$. This is the damage taken during the time Enhanced Devoted procced.
• The set of values in ${\displaystyle d_{n}^{(j)}}$ for integer ${\displaystyle j\in [0,1]}$ is the same in both the numerator and denominator of the ratios for any given ${\displaystyle n}$.

Simplifications
• This can be simplified if the assumption is that every value of ${\displaystyle d_{n,i}^{(j)}}$ ${\displaystyle \forall }$ integer ${\displaystyle i\in [1,n]}$, integer ${\displaystyle n\in [0,\infty )}$, integer ${\displaystyle j\in [0,1]}$, is taken to be the same ${\displaystyle \left(d_{n,i}^{(j)}\rightarrow d\right)}$. In this scenario, there is no random element and the above ${\displaystyle r_{avg}}$ is then only dependent on the proc chance and the attack speed of the enemy. This simplification is increasingly accurate in the limit of large ${\displaystyle d}$. All examples are using large enough values of ${\displaystyle d}$ such that the values should not change to the first two decimal places in percent. Two tables are provided at the top of the page. The first covers all values of ${\displaystyle t_{AS}}$ for PvM situations. The second table is for PvP for all values of ${\displaystyle t_{AS}}$ (normal attack speed of player is ${\displaystyle t_{AS}=3}$ in non-legacy mode , but all values of ${\displaystyle t_{AS}}$ have been provided to account for proccing on damage-over-time abilities, 4 tick auto attack, etc., as well as the varied attack speeds of weapons if using legacy combat).

Using these simplifications, the damage reduction reduces to

For PvM :

${\displaystyle 1-r_{avg}={\frac {\left\lceil {\frac {t_{ed}}{t_{AS}}}\right\rceil p_{R}}{\left\lceil {\frac {t_{ed}}{t_{AS}}}\right\rceil p_{R}+\left(1-p_{R}\right)}}}$

For PvP :

${\displaystyle 1-r_{avg}={\frac {.5\left\lceil {\frac {t_{ed}}{t_{AS}}}\right\rceil p_{R}}{\left\lceil {\frac {t_{ed}}{t_{AS}}}\right\rceil p_{R}+\left(1-p_{R}\right)}}}$

## Sources

MaterialRarityPerk ranks with X materials
12345
Crystal partsCommon01111
Strong componentsUncommon1111–21–2
Faceted componentsRare111–222–3
Zaros componentsRare111–222–3

### Suggested gizmos

Gizmo layout Possible perks
• Other possible perks:

## Update history

The update history project is a work-in-progress – not all updates to this topic may be covered below. See here for how to help out!

## References

1. ^ Mod Pi. Devoted and enhanced devoted stack. 20 November 2018.*


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# FINANCIAL MANAGEMENT

==INTRODUCTION==As health workers you need to understand how the financial system operates so that you will be able to access resources for use at the subdistrict level

Objective
 bythe end of the lesson students will be able to describe the components of the budjet descibe how the components operate

## LESSON CONTENT

BUDGET It is a financial statement of planned activity i.e. how much it will cost in terms of money to carry out activities to achieve organization goal, objectives and targets.

# CHARACTERISTICS OF HEALTH SECTOR BUDGET

It is resource based and takes account of all expected sources of funding. There are 3 main sources of funding.

• Government of Ghana (GOG) is the contribution of government to the ministry of health and Ghana health services from the consolidated fund. This component constitutes 60% of the total budget estimate.
• Donor pooled fund (DPF) These are contributions from international donor agency like European Union, Danida, USAID, UNFPA UNICEF WHO, World bank, IMF, ADB – African Development Bank, DFID. This contributes 30% of the total budget estimate.
• Internally Generated fund (IGF) They are user charges at facilities. It contitutes 10%

It is need based. It is based on the major health priorities e.g. malaria, TB, HIV/AIDS. It consist of four items. It consist of four items namely 1234

• Item 1 stands for personal Emoluuments
• Item 2 stands for administration
• Item 3 stands for service ie for the purpose for which the institution exists
• Item 4 stands for investments such as construction, infrastructure, vehicle, equipment

Item 1,2,3 are referred to as recurrent budget and 4 is called capital budget. It is bottom up approach. You plan from the lowest level of care to the highest level i.e. from the community to the national level . Imprest Account. The funds allocated to us in the budget do not come to us in a form of physical cash. They are accessible to us through the issuance of cheque. Most of our activities are paid for in the form of cheque. However there are very little activities that the use of cheque becomes very cumbersome and time wasting. In such situations petty cash is advanced to the health worker to be used on that activity. The amount of cash to the health worker or manager depends upon the level of operation or function. An imprest therefore is an advance of cash given for a particular purpose and replenished as necessary. An imprest is also restored to its original level e.g. supposing that a health worker is given and amount of 100,000 cedis he finds his office supplies are low so he buys some sationary worth 60,000 cedis the unspent balance is 40,000cedis. He then takes his receipts and petty cash book to the accounts officer who will give him 60,000 in cash to make the imprest up to 100,000 again. This process is referred to us RETIRING OF IMPREST ACCOUNT.

 Template:SUMMARY

Interview at least 2 women who had given birth {{ask if thet had experience any problems/difficulties during ist trimester. if any what were they what did they did to overcome those problems

Charenninful 08:58, 2 March 2007 (CET)


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# nLab Oscar Randal-Williams

Oscar Randal-Williams is professor of pure mathematics at Cambridge.

category: people

Last revised on July 24, 2016 at 15:48:43. See the history of this page for a list of all contributions to it.


text:
# Thread: Differentiate from first principles?

1. ## Differentiate from first principles?

Q1) Given that f(x) = 2x^3 + x , find ;
(a) the derivative of f(x) with respect to x, from first principles

can somebody explain the answers that are given here (pdf file) and it is question 1 on the exam paper, and also what exactly is the difference between first principles and regular differentiation? Thanks A LOT!

2. Hello
Originally Posted by scott_237
Q1) Given that f(x) = 2x^3 + x , find ;
(a) the derivative of f(x) with respect to x, from first principles

can somebody explain the answers that are given here
What is not clear in this answer?

What exactly is the difference between first principles and regular differentiation?
Finding $f'$ from first principles means using the definition of the derivative : $f'(x)=\lim_{h\to0}\tfrac{f(x+h)-f(x)}{h}$. If you had been allowed to use "regular differentiation" you could have used results which are derived from the definition of the derivative. (for example $(x^n)'=nx^{n-1}$)


text:
Question

Question 2 (c) Write first five multiples of: 9

Solution

First five multiples of 9 can be written as, 9 × 1 = 99 × 2 = 189 × 3 = 279 × 4 = 369 × 5 = 45 ∴ First five multiples of 9 are, 9, 18, 27, 36, 45.

Suggest corrections


text:
1. Apr 25, 2006

### ArcainineFalls531

Compute the Taylor series for f(x)= sq root (x) about x=1. Determine where the series sconverges absolutely, converges conditionally, and diverges. Hint: 2(k!)=2*4*6...(2k-2)*2k. Also 1<2, 3<4, 5<6,..., 2k-1<2k should help you out with a comparision.

2. Apr 25, 2006

### Jameson

Use Taylor's theorem. $$f(x)=\sum_{n=0}^{\infty}\frac{f^{n}(a)*(x-a)^n}{n!}$$.


text:
# EDP problem in a ball

How to solve the exterior problem on a ball with radius $r$ in the 3d space? I have to found u such that:

$\Delta u = 0$ in $B(0,r)^C$

Thanks!

-
Where's the $r$ coming from? –  Cameron Buie Nov 2 '12 at 10:45
I gathered that much, but there's no $r$ in the expression for $u$, so I don't see why it should vanish as $r\to\infty$. Also, what is $S(0,a)$? –  Cameron Buie Nov 2 '12 at 11:31
I'm sorry this question is wrong. I want to know the solution 3d space for a ball B(0,a) with radius $a$ and center at point 0. $(r,\theta,\phi)$ are spherical coordinates. S is a sphere of radius $a$ with center in 0. –  TheStudent Nov 2 '12 at 16:41
You should clarify all of that in the body of the question, itself. That will "bump" the question up on the list, and someone should see it and hopefully be able to answer it. –  Cameron Buie Nov 2 '12 at 18:52

The solution to the Dirichlet problem uses the Green's function for the Laplacian. In 3D, this is $H(r) = -1/4\pi|r|$ (for vector $r$), such that $\nabla^2 H(r) = \delta(r)$, per the definition of the Green's function.

Some use of the various generalized Stokes theorems gives the following (when $\nabla^2 u = 0$):

$$u(r) = \oint \nabla'H(r-r') \cdot dS' \; u(r') - \oint H(r-r') \; dS' \cdot \nabla' u(r')$$

The choice of the Dirichlet Green's function enforces that $H(r-r') = 0$ on the boundary. The second integral vanishes, leaving only the first. You'll have to be careful about the orientation of $dS'$ (since this is an exterior problem), but otherwise, you should be able to exploit the symmetries of the problem to reduce the surface integral to something tractable. Good luck!

-
Right. What do you think if I expand $H(r)$ in Legendre polynomials? Do you think is possible to simplify more than: $u(x)=C\sum(\frac{a}{\vert x \vert})^n \int_{S} g(\theta) P_n(cos(\mu)) d\omega$ ? Where $C$ is a constant. –  TheStudent Nov 2 '12 at 19:45
A Legendre expansion is appropriate, yes, and I don't see any obvious way to simplify this. Do you need an exact solution everywhere (one that will ultimately be expressed in these polynomials)? Or will you be able to reduce it down to the leading order contribution at long distances? –  Muphrid Nov 2 '12 at 19:55
I need an exact solution. The problem ask: Justify your answer using the maximum principle in the regions $\vert a \vert\leq x \leq R$. Do you have any idea? –  TheStudent Nov 2 '12 at 20:02
The maximum principle merely says that a harmonic function has to take on all values between boundary's minimum and maximum. I'm not really sure what that has to do with this problem other than maybe verifying the final answer. If you have not posted the exact text of the question, I suggest you do so. It feels like something is missing here. –  Muphrid Nov 2 '12 at 20:16
Now the question is complete! –  TheStudent Nov 2 '12 at 20:25


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There are different ways out there to create slides for talks. One used a lot in academia is LaTeX Beamer. For the unknowing, in short, Beamer allows to generate PDF slides by relying on the comprehensive typesetting greatness of LaTeX.

Compared to WYSIWYG tools like Powerpoint and Keynote, LaTeX Beamer has a high getting-started threshold of learning the keywords and peculiarities, which is inherent to all things LaTeX. This makes it unappealing for beginners, but also somewhat reduces productivity for experienced users.
But fear not! There’s a well-working converter from the great markup language Markdown to LaTeX Beamer slides. And this is how it works.

TL;DR: Pandoc can convert Markdown to PDF slides using LaTeX Beamer. It works out of the box, but can easily be extended. Apart from LaTeX Beamer, also HTML slideshows using reveal.js (and others) are possible from the same source file.

## Pandoc

Pandoc allows for conversion between different markup languages. It can convert between docx, HTML, LaTeX, and Markdown. Especially the latter two are quite interesting; using Pandoc, you can write texts in the highly productive language of Markdown but have it set to PDF using the capabilities of LaTeX.1 Try out the capabilities of Pandoc yourself on pandoc.org/try/.

From

# Headline 1
**This** is a *text*.

Pandoc generates

\section{Headline 1}\label{headline-1}
\textbf{This} is a \emph{text}.

and will add the corresponding headers if you add the standalone option (--standalone) to the pandoc command line call.

The really cool thing? Pandoc also supports LaTeX Beamer. The above snippet would be set to one Beamer slide:

\begin{frame}{Headline 1}
\textbf{This} is a \emph{text}.
\end{frame}

Easy! Pandoc also supports converting the Markdown-written slides to other targets, like HTML presentations using reveal.js and others. Since I was not able to convert the presentation template of my institute to a reveal.js template I have not really dug too much into this.2

## Options and Features

A very concise example of the conversion abilities can be found at the Pandoc demo page. From input to output.

### Basic LaTeX Beamer Support

The full support for LaTeX and LaTeX Beamer from Pandoc is outlined in its documentation. Here are some basics.

Pandoc can use each first-level headline to create a new slide with the headline as the slide’s title. This is a harsh over-simplification, see the footnote.3 Also, horizontal rules (-----) start new slides.

Lists, ordered and unordered, are taken from their Markdown format (* Something and 1. Anything) to their respective LaTeX commands (itemize and enumerate).

Also pictures can be included (Markdown syntax: ![A nice picture](img/nice.pdf)).4

List items can appear by prepending the list item with a > (i.e. > * Something), pauses can be added on a slide by three one-space-interleaved dots (. . .).

To put a Beamer slide into one of the special modes, different attributes can be used. For instance, using # Title {.fragile} will lead to \begin{frame}[fragile]{Title}, the mode needed for code highlighting e.g. with minted.

### YAML

Through commented keywords at the beginning of the Markdown file, global parameters of the presentation can be set. The keywords are written in a YAML metadata manner.

For example, variables like author, title (and subtitle), and date of the presentation can be set:

---
author: Ch. Darwin
title: On the Origin of Species
date: 24.11.1859
---

At the same place, Beamer themes can be chosen (using theme, et al.). Also, further LaTeX options can be specified (fontfamily, toc, …) and features of the (Beamer) document enabled, like using BibLaTeX (biblatex: true)5 or proper tables with booktabs (tables: true).
Behind the curtains, the YAML variables are passed through to the template used for conversion where they can be used as triggers or options.

A very handy keyword in the YAML metadata is header-includes, which allows injecting LaTeX code into the header. Useful for including certain packages or even whole .tex files with display configurations:6

header-includes:
- \usepackage{siunitx}
- \DeclareSIUnit[number-unit-product = {}]{\flops}{FLOPS}

Additionally to the header-includes YAML, there are also include-before and include-after. They inject something right at the beginning and just before the end of the content body of the document, respectively.

## Easy & Out of the Box: Markdown → PDF with Pandoc

The easiest way to get your Markdown slides set in LaTeX Beamer PDF is with the following line

pandoc --to=beamer --output=slides.pdf slides.md

### Some Options

Say, you like to change the font of your presentation? Easy! Just add the following to the YAML

header-includes:
- \setsansfont{Roboto}

and tell Pandoc to use the XeLaTeX engine with pandoc --to=beamer -o slides.pdf slides.md --latex-engine=xelatex.7

You have a package which uses shell commands via the --shell-escape mechanism? Just append --latex-engine-opt=-shell-escape to the command.

There’s a lot more trickery which can be done. Just have a look at man pandoc.

## Comprehensive & Flexible: Markdown → LaTeX → PDF with Pandoc and pdflatex / latexmk

Although super sleek, I encountered one problem with the immediate conversion from Markdown to PDF: I couldn’t use a certain package (minted). So I split up the process: Use Pandoc to generate a .tex file from the Markdown input and use a usual means of typesetting8 to finalize the processing to a PDF.

With a small wrapper script you don’t even feel a difference but have the added flexibility of configuring the pdflatex call directly.

### Temp Files Problem

So, minted. minted is, in my mind, the best code highlighting package for LaTeX out there. As a backend, it uses the Python program Pygments to generate colored code snippets.

To do so, it needs to escape to the shell. No problem, you say, haven’t I just introduced latex-engine-opts=-shell-escape? True! But minted creates temporary files in the document’s root directory. And because Pandoc happily copies the automatically generated .tex file to some randomly chosen temporary location and changes the -output-directory value of pdflatex, the document’s root directory can not be found. minted offers the outputdir=<directory> package option, but there is no way to predict where Pandoc will copy the the temporary files to. At least to my knowledge.

After a short discussion with the minted people, I split up the process of PDF slide generation.

### Two-Step Process

Essentially, the two needed commands are

pandoc --to=beamer --standalone --output=slides.tex slides.md
latexmk -pdf slides.tex

Or pdflatex slides.tex if you rather use that program. But, remember, you can configure a lot in latexmk with the .latexmkrc file. Here’s mine.

If you combine the two calls into one script, you don’t even feel the difference. As an example: My run.py file which has also a few additional options.

### Custom Template

One more thing before we are done: I modified the default beamer template9 of Pandoc to include an institute, since that’s one of Beamer’s default macros. Just add

$if(institute)$
\institute{$institute$}
$endif$

somewhere after the if clause of $if(author)$. Use it with a instute: My University in the YAML part of your presentation. An alternative to changing the template would be to put it into the header-includes command.

# Recap

LaTeX Beamer enables programmatically writing slides with LaTeX, creating a PDF file as output. Pandoc can convert the easy Markdown markup language to Beamer slides with one simple command. If you make two commands out of the one, you are more flexible in typesetting. Pandoc’s conversion engine can be configured by some statements in the top of the file. Pack all your LaTeX customization in one .tex file and include it via header-includes.

1. In fact, this blog is also written entirely in Markdown.

2. The problem with a FZJ reveal.js template is somewhat reveal.js-conceptual: Our design has very distinctly designed borders, for example a colorful bar at the very left of each slide. I was not able to implement this to a reveal.js, looking both correct (and well) in the usual presentation mode, but also in the PDF print mode at the same time. The latter is important since most scientific conferences expect talks in a static PDF format, not a fancy HTML file. I would gladly appreciate a port of the FZJ presentation template to any form of JavaScript-based presentation engines!

3. Pandoc uses that headline level as a slide separator which is, throughout the whole document, only followed directly by text and no other (lower level) headline.

Like this, the document can be structured a bit more into sections aside from slides: Headers, above the slide-seperator headline level are used to create title slides. In general, --slide-level can be used to manually override the behavior. See the documentation

4. Up to now, I fell back on using \includgraphics{} directly in the Markdown code since the ability to specify image dimensions in Markdown was only a very recent addition to the Pandoc parser.

Now, one can specify for example the width of an image like this: ![A nice picture](img/nice.pdf){ width=90% }, which will be converted to \includegraphics[width=0.9\textwidth]{img/nice.pdf}. Before, it was using the full width of the slide, which was not working properly for the template I’m using.

5. If you can use BibLaTeX, you should use BibLaTeX. Always. It’s far superior than BibTeX, more modern, and has a much greater feature set. It’s also quite backwards compatible, you can transition smoothly on your own time.

6. In my example here, you can use the file _header.tex to include further LaTeX code you don’t want to clutter the Markdown file with. Like your favorite font package, some \hypersetup{} commands, or your default set of packages. See remarks on how I use it a bit later in this posting.

7. Finally! You can set those beautiful Beamer slides with your favorite font, Comic Sans MS!

8. Just advertising it here quickly: Please use latexmk as your Makefile-esk interface to pdflatex (or XeLaTeX, or LuaLaTeX, or …)! It will help you out a lot! It will automatically detect how many runs are necessary until your document is stable; it can be steered using a .latexmkrc file; and it has a great continuous preview mode, which compiles your document automatically once it’s changed and opens a previewer afterwards: latexmk -pdf -pvc document.tex

9. Also, I needed to exchange \frame{\titlepage} with \maketitle, because my template wants it this way.


text:
Flush (50:50) Methanol/Water Methanol then IPA Normal phase Hexane/Ethyl acetate III-3. HCl H2O CH3OH NH3 CS2 How do you determine what will make a good solvent for something . Acetone is an inexpensive solvent, with similar elution properties to acetonitrile, although its high UV absorbance limits its applicability for some applications. Recrystallization is a widely-used purification method for both inorganic and organic compounds. HPLC Solvents, Acetonitrile and Methanol, Key Differences and Properties MeOH, ACN, Pressure, Solubility, Viscosity, Absorbance, UV cut off. Methanol 1.0+ 1.0 0.53 0.35 0.23 0.10 0.04 0.02 0.01 Methanol (degassed) ... and the B-solvent each respond similarly. For example, polar solvents such as methanol, ethanol and acetone are miscible with water, thus not suitable for liquid-liquid extraction. In this study, water and various concentrations (50%, 75%, and 100%) of methanol, ethanol, and acetone in water were used as solvent in the extraction of L. aromatica.The antioxidant activity, total phenolic content, and total flavonoid content of the freeze-dried L. aromatica extracts were … 1) Why is methanol a good solvent for recrystallization of cholesterol? Answer / nitesh pal all that solvent not absorb uv light i.e not show absorbance in uv region Figure 4 shows the difference spectra for various solvents, calculated by subtracting the degassed solvent spectra from air-saturated solvent spectra. e o = eluotropic strength (solvent strength parameter) P = polarity index according to Synder η(cp) = viscosity of the compound at 20 o C UV Cutoff = lower limit for the measurement in the UV-Vis spectrum The solubility is given in g of solute in 100 g water. Plastic pipettes might contain UV-active softening agents which easily dissolve in organic solvents. Why do you think water is often called the universal solvent and what makes it such a good solvent? Is toluene a good solvent for UV spectroscopy? It should not itself absorb radiations in the region under investigation. Which solvent would be better for Let the solvent go about 90% of the way up the plate. DrBob1. It is only valid at low concentrations (<10-4 mol/L). Methanol, also known as methyl alcohol amongst other names, is a chemical with the formula C H 3 O H (a methyl group linked to a hydroxyl group, often abbreviated MeOH). The superscript indicates the … See the answer. Ibuprofen [Ibu; (±)2-(4-isobutylphenyl) propionic acid; Fig. the solubility of a compound is 59g per 100 mL in boiling methanol and 30g per 100mL in cold methanol, whereas its solubility in water is 7.2g per 100 mL at 95 C and .22g per 100mL at 2C. Water can dissolve polar solvents, but it is very poor at dissolving polar solvents. Explain.? The solvent is the component of a solution that is present in greater amount. Especially organic solvents like methanol or acetonitrile dissolve organic impurities and can become contaminated. In reverse-phase chromatography (RPC), HPLC, UV, and electrochemistry applications. often $$< 100^\text{o} \text{C}$$ as it's best if the solvent readily evaporates from the solid once recovered. 5 years ago. It is colorless, volatile, flammable, and poisonous. The most popular buffers for HPLC with UV detection are phosphate and acetate. The structure of methanol is a hydroxyl group (-OH) attached to a methane (-CH3). 7) Let the solvent dry off of the plate. Recrystallization. I'm in a college internship as a highschooler and use toluene as solvent for the reactions I do, so I would say yes. It is a light, volatile, colourless, flammable liquid with a distinctive alcoholic odour similar to that of ethanol. 1 and 2 show absorption spectra for acetonitrile and methanol (commercial HPLC type and special grade). This type is created by removing impurities that have UV absorbance and the absorbance for specified wavelengths is suppressed so as to lie below certain levels. Organic solvents with low polarity such as hexanes, toluene, dichloromethane and diethyl ether are usually chosen as the organic extracting solvent. Fuel. For each solvent, absorption increases due to dissolved air, but the dissolved air has a smaller effect on water and acetonitrile and a larger effect on hexane, methanol, and THF. Limnophila aromatica is commonly used as a spice and a medicinal herb in Southeast Asia. Its principal uses are in organic synthesis, as a fuel, solvent, and antifreeze. Methanol is made from the destructive distillation of wood and is chiefly synthesized from carbon monoxide and hydrogen. 5 years ago. An ideal crystallization solvent should be unreactive, inexpensive, and have low toxicity. Relevance. Water is not a good solvent for the recrystallization of Fluorene. Symptoms of methanol toxicity include a slight inebriation for 10 to 20 hours, followed by weakness, vomiting, pain, confusion, severe lowering of blood pH, ocular toxicity, and eventually coma and death 1.. Answer Save. Methanol is a polar liquid at room temperature. 6) Remove the plate from the chamber and mark the solvent front immediately with a pencil - you will use this to calculate the Rf. Prevent precipitation and include enough aqueous phase water in solutions. (Flourene doesn't dissolve at room tempurate or at the boiling point of water.) Devin. It is also used as a solvent in the manufacture of important pharmaceutical ingredients and products such as cholesterol, streptomycin, vitamins and hormones. Toluene, and other aromatic solvents, adsorb strongly in the UV. 8) Visualize the TLC using non-destructive technique(s). Phosphate and acetate are particularly useful buffers because they can be used at wavelengths below 220 nm. Since UV-Vis spectroscopy is an absorption technique, Beer's Law can be applied. It is also important that the solvent have a relatively low boiling point (b.p. Acetone also makes a useful mid-polar solvent. Table 2 shows solvent UV Cut-Off values for some common HPLC solvents and additives. Question: Why is methanol a good solvent to recrystallize biphenyl? Common solvents used in recording UV-spectra Solvent wavelength (nm) Water 205 Methanol 210 Ethanol 210 Ether 210 Cyclohexane 210 Dichloroethane 220 6. As a polar solvent in non-aqueous titrations; As a non-aqueous solvent for inorganic salts. Methanol vs. Ethanol Toxicity. The solvent filtering device might be contaminated or not cleaned properly, so impurities might be introduced. Chem. When UV detection is used at low wavelengths, this may not be the case, especially for B-solvents other than acetonitrile. Lv 7. To facilitates reactions between organic substrates and inorganic materials. The Ritter reaction is a good example of acetonitrile in a common application. Toluene is a good solvent for the recrystallization of Fluorene. 2) What Chemical Differences Are Needed Between Extraction Solvent And Re-crystallization Solvent? why water, methanol, ethanol ets solvents are used in UV SPECTRIPHOTOMETER for blank reading ?.. 0 0. If the miscibility or physical properties of … However, because of its high UV cutoff, it is generally not appropriate for analyses performed by UV detection. Using methanol as the organic solvent for ANP is discussed in this article. CHOICE OF SOLVENT: A suitable solvent for UV-spectroscopy should meet the following requirements. Methanol will not be a good solvent for the recrystallization of Fluorene. Question: 1) Why Is Methanol A Good Solvent For Recrystallization Of Cholesterol? Many other solvents are organic compounds, such as benzene, tetrachloroethylene, or turpentine. 100%) while methanol is commonly believed to dissolve silica gel. 2 Answers. Fig. calculate the mass of an unknown if a solution containing 1.64 g of unknown in 18.22 g of biphenyl froze at 39.9 C chemistry Suppose that a student calculated Kf of biphenyl to be 81.2C kg/mol. Methanol is a liquid chemical with the formula CH3OH (often abbreviated MeOH). This problem has been solved! Methanol is a good solvent for extraction and it is frequently used in biology because of its polarity. The best non-destructive method is the UV … No. Once consumed, the side effects that come with methanol ingestion can be mild to severe. Using a CombiFlash Rf or Companion® with the Sol-vent Management Module allows users to run a hexane/ acetone gradient with an easy switch to methanol to elute compounds with a wide range of polarity in a single run. If using ELSD or LCMS, acetone can also be a good alternative to acetonitrile as well. Methanol is primarily used as an industrial solvent to help create inks, resins, adhesives, and dyes. For the washdown in Methanol, I put all the lines (except the seal wash line, I don't think that would be good!) At higher concentrations, a negative deviation is observed due to association of the molecules and other effects. The effect of different solvents on chemical components of S. buxifolia branches was also analyzed by ANOVA. (Fluorene dissovles immediately at room temperature.) 3. The results showed that methanol exhibited the optimal solvent to extract the bioactive components from S. buxifolia branches since the highest content of phenolics (13.36 mg GAE/g DW), flavonoids (1.92 mg QE/g DW), alkaloids (1.40 mg AE/g DW), and terpenoids (1.25%, w/w) were … When performing chromatography, it is necessary to find a solvent that will dissolve the pigment in question. Document mobile phase preparation method using an SOP which describes in detail the procedure. Thanks … Figure 3.15: a) Addition of methanol (soluble solvent) to trans-cinnamic acid, b) Addition of water (insoluble solvent) to the solution, c) Sustained cloudiness/fine crystals after enough water was added, d) Tube set aside to cool after a few drops of methanol were added to clarify the solution, e) The return of crystals after cooling. Using methanol as an extraction solvent results in the maximum flavonoid extraction with 16.48±0.22 mg of quercetin equivalent/100 g of extract followed by acetone, hexane and distilled water with 8.93±0.21, 6.04±0.89 and 3.6±0.20 mg of quercetin equivalent/100 g of extract, respectively. “HPLC type” does not indicate that the solvent has a high absolute purity. Perhaps the most common solvent in everyday life is water. Solvent. Over the years, acetonitrile and methanol have become the two organic modifiers of choice for many reversed-phase applications. As can be seen from Table 2, phosphate has three pKa values that give it three buffering ranges: 1.1
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# Research

#### Publications

(with M. Ballard and A. Duncan) The toric Frobenius morphism and a conjecture of Orlov, 2017.

(with M. Ballard and A. Duncan) On derived categories of arithmetic toric varieties, 2017.

Zero-cycles with coefficients for the second generalized symplectic involution variety of an algebra of index 4, submitted, 2017.

K-Cohomology of Generalized Severi-Brauer Varieties. Ph.D. Thesis, University of Georgia (2016).

(with E. J. Rhodes, et al.) Temporal changes in the frequencies and widths of the solar p-mode oscillations. Proceedings of SOHO 24/GONG 2010, pp. 134-138 (2011).

(with E. J. Rhodes, et al.) Temporal changes in the frequencies of the solar p-mode oscillations during solar cycle 23. Proceedings of the IAU, Vol. 6, Symposium S273, pp. 389-393 (2011).

#### In-Progress

Patching over fields and étale K-theory.

The Chen-Gibney-Krashen moduli spaces revisited
(with P. Gallardo, N. Giansiracusa, and X. Wu).

A cocycle-free proof of a theorem of Uematsu on the Brauer group of affine diagonal quadrics
(with R. Gordon-Sarney, D. Adams, D. Litt, S. Mathur).

#### Expository Articles

Below is a collection of expositions derived from course assignments and selected talks.

Introduction to K3 surfaces.
K-theory of algebraic curves.

Compactifications of $M_{0,n}$ from rational normal curves.
Sheaf cohomology on a Grothendieck site.

Homotopical and homological algebra.
The Brauer group.

Grassmannians as moduli spaces.

#### Beamer Presentations

Chow Groups with Coefficients and Generalized Severi-Brauer Varieties.
Milnor-Witt Groups and Homotopy Theory of Schemes.

Twisted Homogeneous Varieties, Derived Equivalences, and dg-Stacks.
Subfields of Central Simple Algebras.

The Severi-Brauer Variety Associated to a Central Simple Algebra.
Spectra: A Home for Homology


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# Fan Li

Time Limit: 12000/6000 MS (Java/Others)

Memory Limit: 131072/65536 K (Java/Others)

## Description

Fan Li (范蠡) was an ancient Chinese advisor in the state of Yue in the Spring and Autumn period. He is a successful militarist and a successful business man. He is one of the main characters of a famous Chinese proverb “卧薪尝胆”. One day, when he was training the army, he came up with an idea, if he let all the soldiers stand in a line (every soldier has a fighting capacity), what is the maximum disjoint intervals he can choose so that the greatest common divisor of all the intervals are equal, and how many ways can he choose the maximum disjoint intervals satisfy the condition. The different ways may be very large, output the answer mod 998244353.

## Input

There are multiple test cases.
Each test cases begins with an integer n, then followed n positive integers.
1 <= n <= 100000
All the integers are less than 2333333.

## Output

For each test case, output the number of maximum intervals and the ways of reach the maximum number.

## Sample Input

3
1 2 3
5
1 2 2 2 2
3
1 2 1

## Sample Output

2 1
4 1
2 3

wange2014

## Source

2015 Multi-University Training Contest 3


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# About

Tag Info

Questions on events in differential equations, which may arise from WhenEvent or discontinuous coefficients in the commands NDSolve and DSolve.

Questions on events in differential equations, which may arise from WhenEvent or discontinuous coefficients in the commands NDSolve and DSolve. Before V9, WhenEvent did not exist, and events were handled by the "EventLocator" method (in NDSolve only).

Useful links

Example questions