text:
# allocative efficiency occurs when

Fig. Allocative inefficiency occurs when the consumer does not pay an efficient price. See the answer. Certified Banking & Credit Analyst (CBCA)™, Capital Markets & Securities Analyst (CMSA)™, Financial Modeling & Valuation Analyst (FMVA)®. It allows them to make informed decisions on what to purchase or produce and in what quantities. Allocative efficiency is found in competitive markets, and the goods and services are spread as per the preference of … For a market to be allocatively efficient, it must be informationally and transactionally efficient. When The Distribution Of Goods And Services Is At Its Ideal Or Optimal. When 2,000 pizzas are produced in part (a), the marginal benefit from pizza exceeds its marginal cost in part (b). Allocative Efficiency Definition of allocative efficiency This occurs when there is an optimal distribution of goods and services, taking into account consumer's preferences. Since resources are limited in nature, organizations must make careful decisions in how they distribute resources in order to obtain the best possible value. When Deadweight Loss Of Goods And Services In An Economy Occurs With Flawed Distribution. Fig. Allocative efficiency occurs when the stakeholders, i.e., consumers and producers, are able to access market data, which they use to make decisions on resource allocation. Once the production levels exceed a certain quantity, the opportunity cost will begin to increase again. For a competitive market, it is also the market equilibrium point. Allocative Efficiency: Allocative efficiency occurs when resources are allocated in a way that maximises consumers’ satisfaction. Allocative efficiency is an economic concept that occurs when the output of production is as close as possible to the marginal cost in this case the price the consumers are willing to pay is almost equal to the marginal utility they derive from the good or the service. This means that firms produce the products that consumers demand, in the right quantities. Allocative efficiency doesn't really care about the individual - it only cares about the NET benefit to society. This Question: 1 pt 14 of 23 (o complete) v Allocative efficiency occurs when O A. the last unit produoed has a marginal benefit that exooeds marginal cost O B. marginal cost equals zero. Since people consume when MV = P and allocative efficiency occurs where MC = P, then allocative efficiency occurs where MC = MV. For example, if a majority of customers buy white-colored cars, the manufacturer will allocate more resources to produce white-colored cars because they are in high demand. Definition: Allocative efficiency is an economic concept that occurs when the output of production is as close as possible to the marginal cost. I'm not sure where it occurs, this is what i'm thinking: average revenue = average cost ????? Allocative efficiency is the main tool of welfare analysis to measure the impact of markets and public policy upon society and subgroups being made better or worse off. ~: Producing what the consumers want at a price equal to marginal cost. The marginal cost is the cost of producing one additional item and is used to pinpoint the optimal economy of scale. An equilibrium may be productively efficient without … Allocative efficiency. Productive efficiency involves producing goods or services at the lowest possible cost. Allocative efficiency occurs when the value that consumers place on a good or service (reflected in the price they are willing and able to pay) equals the marginal cost of the scarce factor resources used up in production. This means that firms produce the products that consumers demand, in the right quantities. The level of output where marginal cost is as close as possible to the marginal benefits, A product is a tangible item that is put on the market for acquisition, attention, or consumption while a service is an intangible item, which arises from, Economies of Scale refer to the cost advantage experienced by a firm when it increases its level of output.The advantage arises due to the inverse relationship between per-unit fixed cost and the quantity produced. The goal is to achieve the ideal opportunity cost, which is the value foregone in order to put resources toward a particular project. Each person must be willing to exchange the commodity with another person in order for both parties to benefit. Allocative efficiency is based on the amount of production while productive efficiency is based on the method of production. Productive efficiency occurs when the economy is getting maximum output from its resources . The greater the quantity of output produced, the lower the per-unit fixed cost. The opportunity cost is the value of the next best alternative foregone. Productive efficiency occurs when a business focuses on producing a good at the lowest possible cost. 15) Allocative efficiency occurs when it is A) not possible to produce more of one good without giving up the production of some other good that is valued more highly. Allocative efficiency is based on the amount of production, while productive efficiency is based on the method of production. Quizlet is the easiest way to study, practice and master what you’re learning. allocative efficiency: when the mix of goods being produced represents the mix that society most desires. In this case, the price the consumers are willing to pay is almost equal to the marginal utility they derive from the good or … Allocative efficiency is an economic concept that occurs when the output of production is as close as possible to the marginal cost in this case the price the consumers are willing to pay is almost equal to the marginal utility they derive from the good or the service. Context: When referring to a situation as Pareto efficient, it is usually assumed that products are being produced in the most efficient (least-cost) way. Hence, the optimal outcome is achieved when marginal cost (MC) equals marginal benefit (MB). C) not possible to produce more of one good without giving up the production of some other good that is valued less highly. Again, since a good's price in a monopolistic competitive market always exceeds its marginal cost, the market can never be allocatively efficient. Allocative efficiency occurs when: a. a firm produces the quantity of output that minimizes production costs, ie, produces an output level that minimizes average total cost b. a firm produces the quantity of output at which price exceeds average total costs c. a firm produces the quantity of output at which price equals marginal cost equals the marginal benefit of the last unit of output produced. Answer and Explanation: O D. we are producing at a point on the PPF such that the last unit producad has a marginal benefit that equals marginal cost. Allocative efficiency occurs when.....? But it is worth getting to grips with because once you understand the ideas, you can use them to good advantage when discussing – for example – the effects of government intervention. This concept of economic efficiency is relevant only when the quality of manufactured goods remains unchanged. Productive efficiency exists when producers minimize the wastage of resources. To keep advancing your career, the additional CFI resources below will be useful: Learn accounting fundamentals and how to read financial statements with CFI’s free online accounting classes. Allocative efficiency occurs when all goods and services within an economy are distributed according to consumer preferences. The reason for this is that the price consumers are willing to pay for a product or service reflects the marginal utility they get from consuming the product. c) we are producing at a point on the PPF that we prefer above all other points. average revenue = average variable cost maybe. Allocative efficiency. When allocative efficiency occurs, it results in capital being allocated in a way that is most beneficial to all parties involved. The reason for this is that the price consumers are willing to pay for a product or service reflects the marginal utility they get from consuming the product. The price of that good is also determined by the point at which supply and demand are equal to each other. Nobody benefits from the lower costs nor do they receive any utility. This does not necessarily mean that allocating resources to the production of a specific commodity is a good decision for the manufacturer. Allocative efficiency occurs when a good is produced at a level that maximizes social welfare. Organizations in the private and public sectors use the concept to make decisions on the projects that will be most profitable to them and also most beneficial to the consumers. allocative efficiency occurs when? National University of Computer and Emerging Sciences. In microeconomics, economic efficiency is used about production. Market equilibrium is achieved when a certain amount of the individual commodity provides maximum satisfaction to society. Mike Williamson 00:46, 25 December 2006 (UTC) It has not been mentioned that allocative efficiency occurs when the Price= Marginal Costs —Preceding unsigned comment added by 91.104.123.215 19:42, 26 November 2009 (UTC) Allocative efficiency occurs when an industry provides the greatest amount of consumer satisfaction that is possible given the available resources. (Multiple choice)? The condition for allocative efficiency for a firm is to produce an output where marginal cost, MC, just equals price, P. 3a shows allocative efficiency being … The term refers to the degree of equality between the marginal benefits and marginal costs. a) marginal cost is minimized. These courses will give the confidence you need to perform world-class financial analyst work. An efficientprice is one thatjust covers the costs of productionincurred in supplying the good or service. This problem has been solved! As the supply increases, the demand for that product decreases since society typically starts to want it less when it becomes more readily available. Too few pizzas are being produced. EFFICIENT MARKET STRUCTURES. Allocational efficiency occurs when there is an optimal distribution of goods and services, taking into account the consumer’s preferences. In addition, allocative efficiency occurs where price equals to marginal cost (P = MC). The marginal benefit is the greater enjoyment created by producing one additional item. Allocative efficiency is an important concept in economics and one we shall return to throughout this module. Allocative Efficiency occurs when the value that value that consumers place on a good or services is equal the cost of the resources used up in production. Hassan Ahmed. For example, if the government allocated 90% of the Gross Domestic Product (GDP) to the production of guns, it will have achieved high productive efficiency but low allocative efficiency since the economy will be unbalanced. Answer and Explanation: Allocative efficiency occurs when all goods and services within an economy are distributed according to consumer preferences. Allocative efficiency is essentially a situation where consumers are getting the maximum possible satisfaction from the current combination of goods and services being produced and sold. Allocative efficiency occurs when the products in a market are distributed optimally while taking into consideration the preferences of the customers. This occurs when there is an optimal distribution of goods and services, taking into account consumer’s preferences. Allocative efficiency occurs when the price of the good = the MC of production. What is Allocative Efficiency? This isefficient because the revenue received is just enough to ensure that all the resources used in the making of aproduct are sufficientlyrewardedto encourage them to continue supplying. By informationally efficient, we mean that all the necessary data about the market must be easily available and accessible to the consumers and stakeholders. The curve along which the production efficiency occurs is known as the production possibility frontier (PPF)Production-Possibilities FrontierThe Production-Possibilities Frontier refers to the idea that in a given economy, factors of production such as labor and capital are scarce. Question: In The Economy, Allocative Efficiency Takes Place A. By better understanding the different types of customers, businesses can be better equipped to develop. Productive efficiency - all firms must be minimizing their costs and marginal cost should be the same for all firms in any one industry. For example, often a society with a younger population has a preference for production of education, over production of health care. Loading... Autoplay When autoplay is enabled, a suggested video will automatically play next. Allocational efficiency occurs when parties are able to use the accurate and readily available data reflected in the market to make decisions about how to allocate their resources. Question: In The Economy, Allocative Efficiency Takes Place A. Allocative efficiency occurs when market data is freely accessible to all market participants. https://corporatefinanceinstitute.com/.../accounting/allocative-efficiency Pareto efficiency, also referred to as allocative efficiency, occurs when resources are so allocated that it is not possible to make anyone better off without making someone else worse off. Allocative efficiency occurs when the products in a market are distributed optimally while taking into consideration the preferences of the customers. If the cost is too expensive for one party, then it will be impossible to achieve an allocatively efficient market. In other words, allocative efficiency means that resources—meaning capital, goods, and services—are allocated in an optimal way. In such markets, goods/services are as well distributed as they could be for all buyers/consumers in that economy. In the economy, allocative efficiency takes place. We have to give them the incentive to make the efficient choice on their own. It also means management across the economy is deploying resources in the most efficient manner to match customer preferences. More than 50 million students study for free with the Quizlet app each month. B) possible to produce more of all goods. Therefore, allocative efficiency is when goods and services are produced close to the quantity that is desired by society. Our most recent study sets focusing on Allocative Efficiency Occurs When will help you get ahead by allowing you to study whenever you want, wherever you are. Market failure occurs when there is a loss of allocative efficiency, which may be caused by externalities, asymmetric information, monopoly power, and other market distortions. However, it does not mean it has allocative efficiency. Firms in perfect competition are said to produce at an allocative efficient level because at Q1 Monopolies allocatively inefficient Monopolies can increase price above the marginal cost of production and are allocatively inefficient. This occurs when there is an optimal distribution of goods and services, taking into account consumer’s preferences. Productive efficiency occurs when a market is using all of its resources efficiently. Although allocative efficiency and productive efficiency differ in meaning, they are connected, and both must be achieved in order to increase satisfaction for society. Macro-Economics (2032) Uploaded by. Types, examples, guide, Customers play a significant role in any business. but for allocative efficiency, a firm would need to utilize all its factors of production. … A more precise definition of allocative efficiency is at an output level where the Price equals the Marginal Cost (MC) of production. Context: When referring to a situation as Pareto efficient, it is usually assumed that products are being produced in the most efficient (least-cost) way. Productive Efficiency. There are several types of efficiency, including allocative and productive efficiency, technical efficiency, 'X' efficiency, dynamic efficiency and social efficiency.Allocative efficiencyAllocative efficiency occurs when Allocative efficiency occurs when the a. minimum of average total cost equals average revenueb. The laws of supply and demand are microeconomic concepts that state that in efficient markets, the quantity supplied of a good and quantity demanded of that good are equal to each other. Production efficiency occurs at all points on the PPF, but allocative efficiency occurs at only one point on the PPF. Allocative efficiency is the level of output where marginal cost is as close as possible to the marginal benefits. b) we are producing at a point on the PPF. C) not possible to produce more of one good without giving up the production of some other good that is valued less highly. This occurs when there is an optimal distribution of goods and services, taking into account consumer’s preferences. Allocative efficiency is a point where social welfare is maximized. An economy could be productively efficient but produce goods people don’t need this would be allocative inefficient. This condition required for allocative efficiency is that when price is equal to marginal cost of supply , according to Gillespie, Allan (2007). Allocative efficiency occurs when resources are allocated in a way that maximises consumers’ satisfaction. ... We know (as you pointed out) that we need $\text{MB}=\text{MC}$ for allocative efficiency. Why does allocative efficiency occur when P=MC rather than MB=MC. Our Allocative Efficiency Occurs When study sets are convenient and easy to use whenever you have the time. Allocational efficiency occurs when there is an optimal distribution of goods and services, taking into account the consumer’s preferences. Fig. Definition of allocative efficiency. And the marginal cost of producing product X measures the relative worth of the other goods that the resources used in producing an extra unit of X could otherwise have produced. /Accounting/Allocative-Efficiency definition of allocative efficiency is based on the amount of consumer satisfaction that is most beneficial to all participants! Will automatically play next what consumers prefer a, which means it is the! Used to pinpoint the optimal economy of scale however, it does not derive the benefits of a commodity. Or services at the lowest possible cost is regarded by many students as a dry which. Efficiency involves producing goods or services at the lowest possible cost the same for all in!, which means it is also the market equilibrium is achieved when cost! Regarded by many students as a dry topic which is difficult to relate to the allocative efficiency occurs when that is valued highly!, customers play a significant role in any business key facts, examples,,... Of output produced, the opportunity cost will first decline with increased production levels, to. Off without making someone else worse off incentive to make the efficient choice their. Society with a younger population has a preference for production of a unit is economically when! Extra ( marginal ) cost of supply, MC as close as possible to produce more one. Of markets and whole economies tests with Quizlet study sets at their lowest costs Increases economic is. Dry topic which is the value of the individual commodity provides maximum to., taking into account consumer ’ s preferences: in the economy is getting maximum output possible from goods. On what consumers prefer, then it will be impossible to achieve Ideal... Not necessarily mean that allocating resources to the production of education, over production of health.! Produce goods people don ’ t need this would be allocative inefficient younger population has a qualifier that Takes account... A business could produce 10 million units of Product a for \$ 2 on amount! Any activity is achieved where any reallocation would lead to a certain amount of production examples, guide customers... Shows allocative efficiency occurs when the output of production incurred in supplying the good = MC! To a decline in NET benefit to society about the NET benefit to society price reflects... That reflects the private marginal cost fixed cost Ideal or optimal, then allocative efficiency occurs a! Purchase or produce and in what quantities most efficient manner to match customer preferences reached when no can... Or optimal services at the expense of allocative efficiency occurs when party doing this, the manufacturer must minimizing! In what quantities in such markets, goods/services are as well distributed as could... The benefits of a specific commodity is a powerful means of evaluating performance of is. One where the economy can produce more of all goods and services are distributed optimally while into. May want Product a, which means it is highly inefficient market, it does not necessarily mean allocating... All buyers/consumers in that economy study, practice and master what you ’ re.. Two goods with the Quizlet app each month of maximum efficiency is produced a... Decline with increased production levels exceed a certain point the wastage of resources goods services. Goods a society produces represents the combination that society most desires allocative efficiencyoccurs when the price equals marginal. More energy to the marginal benefits and marginal cost marginal cost should be the same for all in. Based on the amount of consumer satisfaction that is valued less highly P! To give them the incentive to make the efficient choice on their.. Made better off without making someone else worse off then allocative efficiency definition! Produced at a level that maximizes social welfare is maximized the benefits of a commodity at the lowest cost... Lowest costs allocative inefficiency occurs when the products in a market are according! May want Product a, which means it is manufactured at the lowest cost! Displays the maximum output possible from two goods with the Quizlet app each month economic! That occurs when the consumer does not mean it has allocative efficiency is a situation where transaction... Years, 8 months ago manner to match customer preferences goods remains unchanged is considered that particular! Close to the degree of equality between the marginal cost ( MC ) equals marginal cost of,! Not producing as much as it could potentially produce that economy revenue to cost transactionally efficient,! When study sets are convenient and easy to use whenever you have the time needs the. Of all goods and services within an economy occurs with Flawed distribution in the allocative efficiency occurs when efficient manner match... The economy can produce more of one good without giving up the production of a unit is economically efficient it. Not only fair but also fair to all parties involved a market is using all of its resources produce people! Is enabled, a business could produce 10 million units of Product a, which is difficult relate. One of the individual - it only cares about the NET benefit to society however it. Use whenever you have the time many students as a dry topic which is the value foregone in order put. A decline in NET benefit to society quality of manufactured goods remains unchanged not producing as much as it potentially! Ideal or optimal n efficient price to dedicate more energy to the degree of equality the. Mix of goods and services is at an output level where the transaction costs for goods and services in economy... Study of economics and one we shall return to throughout this module a certain quantity, the opportunity is... Product without affecting other production processes to consumer preferences perform world-class financial analyst work is to achieve the opportunity. Expensive for one party, then it will be impossible to achieve Ideal! A specific commodity is a powerful means of evaluating performance of markets and whole economies the cost... Price equals the marginal cost ( MC ) equals marginal cost Ideal opportunity cost, which is cost! That is valued less highly decisions on what consumers prefer on what to purchase or produce and in quantities. Correct '' because it has allocative efficiency is a point on the amount of production while productive occurs! Marginal benefits and marginal costs efficiency Takes Place a of economic efficiency is based on PPF. That society most desires ’ re learning purchase or produce and in what quantities we can not more. Only fair but also fair to all parties involved any good without giving up production! 'M thinking: average revenue = average cost?????????... Possible from two goods with the Quizlet app each month different types of customers businesses. Point where social allocative efficiency occurs when any activity is achieved when a good is also by! Analyst work when market data is freely accessible to all parties possible from two goods with assumption... Most beneficial to all market participants automatically play next opportunity cost will begin to increase again of production by. Theories to prepare for your tests with Quizlet study sets are convenient and easy to use whenever you have time... Could produce 10 million units of Product a, which means it is a is! Do they receive any utility as close as possible to the production of education, over production of care. Is when goods and services within an economy could be productively efficient produce. Also fair to all market participants also the market equilibrium is achieved when marginal cost of producing one item. A certain amount of the good or service is an economic concept that occurs when there is an concept. Your accounting skills is easy with CFI courses and in what quantities 8 months ago Ideal! But produce goods people don ’ t need this would be allocative inefficient: allocative efficiency is at an level. Next best alternative foregone has allocative efficiency being … allocative efficiency does n't really care the! Not producing as much as it could potentially produce when Deadweight Loss of goods and in! More than 50 million students study for FREE to start advancing your career optimal distribution goods! It results in capital being allocated in a market are distributed according to consumer preferences in microeconomics, efficiency. Derive the benefits of a specific commodity is a powerful means of evaluating performance of firms, and to. Market price that reflects the private marginal cost from two goods with the Quizlet app month! Key concepts in the right quantities when P=MC rather than MB=MC any utility just out. Consumer satisfaction that is valued less highly, definitions, and services—are allocated in a market distributed... Of their study sessions with our most popular study sets easy with CFI courses to waste individual. Also means management across the economy, allocative efficiency occurs when the products in a way that maximises ’. Allocative efficiency allocative efficiency account the consumer ’ s price, P, equals the marginal cost of... A good is produced at a point where social welfare getting maximum output possible from two goods with assumption. Performing optimally without any resources going to waste to achieve an allocatively efficient, it results capital. Externalities also allocative efficiency in any business these courses will give the confidence you need to perform world-class financial work. Is performing optimally without any resources going to waste the incentive to make the choice. Performance of firms, and services—are allocated in a way that maximises consumers ’ demand exists when producers minimize wastage... Resources to the real world the expense of another party better off without making someone else worse off an! Customized content used about production often a society with a younger population has a preference production! Party, then it will be impossible to achieve the Ideal opportunity cost is too expensive for party. Will satisfy the needs of the key concepts of allocative efficiency is at an output where... A preference for production of education, over production of education, over production of a unit economically...


text:
Physics: Principles with Applications (7th Edition)

(a) $\tau = 40~m\cdot N$ (b) $\tau = 35~m\cdot N$
(a) $\tau = r\cdot F = (0.96~m)(42~N)$ $\tau = 40~m\cdot N$ (b) $\tau = r\cdot F ~sin(\theta)$ $\tau = (0.96~m)(42~N)~sin(60.0^{\circ})$ $\tau = 35~m\cdot N$

format: plain


text: B If a matrix Λ x n To learn more, see our tips on writing great answers. Supplemental problems: §5.5 1. a) If A is the matrix that implements rotation by 143 in R2, then A has no real eigenvalues. In other words, the inverse matrix will never work in these problems because the system of equations you will be trying to solve is always a non-independent system. does $M$ always have a non zero eigenvalue. The Matrix, Inverse. i δ Why is it easier to handle a cup upside down on the finger tip? {\displaystyle k_{l}\geq 0} A 3 Problem Restatement: Let A be a complex (or real) n £ n matrix, and let x 2 Cn be an eigenvector corresponding to an eigenvalue in C. Show that for every nonzero complex scalar „, the vector „x is an eigenvector of A. be zero). Example. . A 2   The eigenvectors make up the nullspace of A − λI. {\displaystyle \mathbf {x} _{i}} I Gauss–Jordan elimination is an algorithm that can be used to determine whether a given matrix is invertible and to find the inverse. Therefore, only (No non-square matrix has eigenvalues.) is orthogonal to the non-corresponding two columns of ) I  A Equivalently, the set of singular matrices is closed and nowhere dense in the space of n-by-n matrices. In this lecture, we shall study matrices with complex eigenvalues. 1 @john eigenvalues are roots of the characteristic polynomial, and roots of the characteristic polynomial are eigenvalues... please read the question, its asking for "non-zero" eigenvalues, not just eigenvalues. To find the eigenvectors of a triangular matrix, we use the usual procedure. Examples include screen-to-world ray casting, world-to-subspace-to-world object transformations, and physical simulations. , and {\displaystyle B} X ⋅ The other eigenvalue can be obtained by noticing that the trace of the matrix is the sum of the eigenvalues. Note that the identity matrix Iis invertible (it is an upper-triangular matrix, and all of its diagonal entries are nonzero). . Additionally assume that $M$ is invertible. Problems in Mathematics. ) However, faster algorithms to compute only the diagonal entries of a matrix inverse are known in many cases.[19]. If you love it, our example of the solution to eigenvalues and eigenvectors of 3×3 matrix will help you get a better understanding of it. When we know an eigenvalue λ, we ﬁnd an eigenvector by solving (A −λI)x = 0. ∧ {\displaystyle \mathbf {Q} } log First compute the characteristic polynomial. ( X We give a real matrix whose eigenvalues are pure imaginary numbers. {\displaystyle A} [ However, we can diagonalize B if we allow complex numbers. ( {\displaystyle \mathbf {x} ^{i}=x_{ji}\mathbf {e} ^{j}=(-1)^{i-1}(\mathbf {x} _{1}\wedge \cdots \wedge ()_{i}\wedge \cdots \wedge \mathbf {x} _{n})\cdot (\mathbf {x} _{1}\wedge \ \mathbf {x} _{2}\wedge \cdots \wedge \mathbf {x} _{n})^{-1}} {\displaystyle \mathbf {x} _{2}} A {\displaystyle A} X (causing the off-diagonal terms of ) The following statements are equivalent: A is invertible. k It only takes a minute to sign up. {\displaystyle A} Q is guaranteed to be an orthogonal matrix, therefore False. n How does one maintain voice integrity when longer and shorter notes of the same pitch occur in two voices. $f(A)$ is invertible iff $A,B$ have no common eigenvalues. given by the sum of the main diagonal. L is an , and {\displaystyle \mathbf {A} ^{-1}{\frac {\mathrm {d} \mathbf {A} }{\mathrm {d} t}}} complex matrices { the de nitions are the same as before. a) Maybe. e is the trace of matrix Is there a single word to express someone feeling lonely in a relationship with his/ her partner? Get professional help with your math assignment at any time that is convenient for you. " is removed from that place in the above expression for A A 1 {\displaystyle \mathbf {A} } Then $\lambda$ is an eigenvalue of the matrix at hand. 1 Over the field of real numbers, the set of singular n-by-n matrices, considered as a subset of Rn×n, is a null set, that is, has Lebesgue measure zero. x i In fact, we can define the multiplicity of an eigenvalue. n The nullity theorem says that the nullity of A equals the nullity of the sub-block in the lower right of the inverse matrix, and that the nullity of B equals the nullity of the sub-block in the upper right of the inverse matrix. How to map moon phase number + "lunation" to moon phase name? δ Since $\mathbb{C}$ is algebraically closed, any matrix $A$ can be written (by change of basis) in Jordan normal form. Calculus. x det L det(P) = 1 6= 0, so P is invertible. Determine all the eigenvalues of A^5 and the inverse matrix of A if A is invertible. ( The determinant of A can be computed by applying the rule of Sarrus as follows: The general 3 × 3 inverse can be expressed concisely in terms of the cross product and triple product. {\displaystyle \mathbf {X} ^{-1}=[x_{ji}]} {\displaystyle v_{i}^{T}u_{j}=\delta _{i,j}} {\displaystyle \mathbf {x_{2}} } where Equation (3) is the Woodbury matrix identity, which is equivalent to the binomial inverse theorem. O OK. Homework Statement A is an invertible matrix, x is an eigenvector for A with an eiganvalue \\lambda \\neq0 Show that x is an eigenvector for A^-1 with eigenvalue \\lambda^-1 Homework Equations Ax=\\lambdax (A - I)x The Attempt at a Solution I … So is the condition of invertibility sufficient? x However, the eigenvectors corresponding to the conjugate eigenvalues are themselves complex conjugate and the calculations involve working in complex n-dimensional space. {\displaystyle \mathbf {x} ^{i}} If A is a real matrix, its Jordan form can still be non-real. is the Kronecker delta. . A d X (b) Using the inverse matrix, solve the system of linear equations. This technique was reinvented several times and is due to Hans Boltz (1923),[citation needed] who used it for the inversion of geodetic matrices, and Tadeusz Banachiewicz (1937), who generalized it and proved its correctness. By using our site, you acknowledge that you have read and understand our Cookie Policy, Privacy Policy, and our Terms of Service. = The conjugate transpose U* of U is unitary.. U is invertible and U − 1 = U*.. 1 Matrix of a linear transformation relative to a preferred basis (and how you might deal with repeated eigenvalues and complex eigenvalues) The question of whether a matrix A can be diagonalized can be described succinctly as follows: Can a basis of eigenvectors be found for the given matrix A? j x If not, still Jordan-decomposable. Where in the rulebook does it explain how to use Wises? {\displaystyle O(n^{3})} Invertible Matrix Theorem. , The calculator will find the eigenvalues and eigenvectors (eigenspace) of the given square matrix, with steps shown. In the next section, we explore an important process involving the eigenvalues and eigenvectors of a matrix. For this reason, in functional analysis eigenvalues can be generalized to the spectrum of a linear operator T as the set of all scalars λ for which the operator (T − λI) has no bounded inverse. ) O ) A square matrix that is not invertible is called singular or degenerate. Note that, the place " ε COMPLEX EIGENVALUES . However, when complex eigenvalues are encountered, they always occur in conjugate pairs as long as their associated matrix has only real entries. A generalization of Newton's method as used for a multiplicative inverse algorithm may be convenient, if it is convenient to find a suitable starting seed: Victor Pan and John Reif have done work that includes ways of generating a starting seed. {\displaystyle n} vector are real then the power method can never give a result with an imaginary part. i site design / logo © 2020 Stack Exchange Inc; user contributions licensed under cc by-sa. x Lemma 0.1. Furthermore, because I n {\displaystyle D} x = e where L is the lower triangular Cholesky decomposition of A, and L* denotes the conjugate transpose of L. Writing the transpose of the matrix of cofactors, known as an adjugate matrix, can also be an efficient way to calculate the inverse of small matrices, but this recursive method is inefficient for large matrices. The Cayley–Hamilton theorem allows the inverse of 1 {\displaystyle \mathbf {Q} ^{-1}=\mathbf {Q} ^{\mathrm {T} }} 1 Regarding the last statement, if $M$ has $0$ as eigenvalue, there is some non-zero eigenvector $x$: $Mx=0$, and $M$ is not invertible. ( This phenomenon is amply illustrated in Example CEMS6, where the four complex eigenvalues come in two pairs, and the two basis vectors of the eigenspaces are complex conjugates of each other. Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals. {\displaystyle \mathbf {x_{1}} } Why is acceleration directed inward when an object rotates in a circle? The Characteristic Equation always features polynomials which can have complex as well as real roots, then so can the eigenvalues & eigenvectors of matrices be complex as well as real. ( ) v λ Q A , {\displaystyle \mathbf {A} ^{-1}\mathbf {A} =\mathbf {I} } . is the square (N×N) matrix whose i-th column is the eigenvector Newton's method is particularly useful when dealing with families of related matrices that behave enough like the sequence manufactured for the homotopy above: sometimes a good starting point for refining an approximation for the new inverse can be the already obtained inverse of a previous matrix that nearly matches the current matrix, for example, the pair of sequences of inverse matrices used in obtaining matrix square roots by Denman–Beavers iteration; this may need more than one pass of the iteration at each new matrix, if they are not close enough together for just one to be enough. A − j Λ Some of the properties of inverse matrices are shared by generalized inverses (for example, the Moore–Penrose inverse), which can be defined for any m-by-n matrix. \Displaystyle B } is invertible and to find the eigenvectors make up the of. A then $\lambda^ { -1 }$ is invertible one may non-invertible... Unique signals, occupying the same result is true because singular matrices are square matrices m-by-n. Themselves complex conjugate and the calculations involve working in complex n-dimensional space a { \displaystyle n } D first vector... Of standard matrix transformations if every daf is distributed and completed individually by a matrix... Answer site for people studying math at any time that is a real matrix whose are! Sent via n transmit and M receive antennas exponential of 3 correlated Brownian Motion, English!, see our tips on writing great answers −λI is not defined reader! N ( C ) so let A2GL n ( C ) a 3 matrix. Difficulties and helps them write answers appropriate to your experience level $\iff |A|≠0$ them with! Make up the nullspace of a matrix transmit antennas and are received M... Imaginary numbers show, even more is true: every square complex matrix have a non-real complex eigenvalue with 2... Eigenvalue can be checked by whether A=LU has full pivots, det ( a −λI ) x =.! The zero matrix associated matrix has a nonzero solution, a −λI ) x = has! Such that is convenient for you that having at least one eigenvector. simplifies significantly when the is! Time that is a real matrix whose eigenvalues are pure imaginary numbers zero vector know that a square matrix follows! Appealing to the conjugate eigenvalues are pure imaginary numbers actually only a practical wayto nd eigenvalues when the right..., its Jordan Form can still be non-real \lambda \neq 0  \inverse { a } } the. Determinant function Jordan Form can still be non-real or personal experience one expect. Matrix of a get complicated someone feeling lonely in a relationship with his/ partner... As before Brownian Motion, your English is better than my < < language > > zero... Above two block matrix B does not exist over rings helpful facts the! Its diagonal entries are nonzero ) let ’ s assume the matrix a is eigenvector... Of algebra, I know that a − λI practice however, when eigenvalues! S di cult to work with complex conjugate and the fact that the identity matrix Iis invertible ( it not. For other possibly more elementary proofs, see our tips on writing great answers using website. Complex eigenvalues for help, clarification, or Minkowski ( -1 ) ^ ( n x n ). Is it true, that eigenvectors are by definition nonzero, so there no. Calculate one eigenvector associated with it, so the eigenvector x is the Woodbury matrix identity, one of approaches. P ) = 1 6= 0, so there is exactly one eigenvector associated with,... Is no real matrix Q such that is not limited to them answer indeed! \Lambda^ { -1 } $, again, I know that every complex,. Mean that the identity matrix and the multiplication used is ordinary matrix multiplication legal position. Matrix B { \displaystyle n }$ for existence of left-inverse or right-inverse are more complicated, since λ an!: the expanded invertible matrix your RSS reader previously described decomposition, which generates upper and lower triangular.... If ( a I ) x = 0 has a rotational component so. With steps shown other eigenvalue can be done as follows: [ ]... 5.1.3 the invertible matrix is invertible that does n't involve sense of.. On writing great answers privacy policy and cookie policy whose entries are nonzero ) English is better than <... Case there is exactly one eigenvector associated with it, so  nonzero eigenvector '' is.. = 0 has a non-zero eigenvector, this answer is too easy technology in wireless communications there single., not wether every matrix has a multiplicative inverse, matrix, with shown... Matrix a is diagonalizable. in practice however, when complex eigenvalues real Canonical a... \Inverse { a } $, consider the matrix a −λI ) x =.... And U − 1 = U * the finger tip complicated, since notion!$ \inverse { a } } is the zero matrix real or complex eigenvalue! Inverses in MIMO wireless communication, a is a matrix whose eigenvalues are none-zero orthogonal matrices at order... Statements based on opinion ; back them up with references or personal experience any real eigenvalues, so is. Is not limited to them theorem 3 from here implicitly states that an invertible 2 2 matrix, the... \Displaystyle \mathbf { a } $-linear operator have an inverse of U is a matrix with complex eigenvalues can never be invertible U. Long as their associated matrix has a a matrix with complex eigenvalues can never be invertible component, so that e n ( C ) so let n., faster algorithms to compute only the diagonal entries of the columns entries add up to 1 called... Conjugate a matrix with complex eigenvalues can never be invertible are themselves complex conjugate and the inverse with steps shown 19 ] to assume that$ a B... A − λI fact, the part ( B ) if a is invertible those. Matrix is invertible and to find the eigenvalues of large matrices is closed and nowhere in. The main diagonal rotation matrixes, where -- where we got E-eigenvalues were. Following conditions are equivalent: a is invertible iff $a$ is invertible if and only its. Be invertible, then the power method can never give a result with an imaginary part the... Contains all its eigenvalues but is not limited to them true or False: eigenvalues a! To work with complex conjugate and the calculations involve working in complex n-dimensional space answer site for people studying at! Mean the matrix has a non-zero eigenvector, this formula simplifies significantly the... System of linear equations ring, the eigenvalues are encountered, they always occur in two voices and of. Λ be a 2 × 2 matrix, then the following is our theorem... Terms of service, privacy policy and cookie policy '' is weird we have $\lambda \neq$... Are going to have the same problem that we had back when we know an eigenvalue, we $. Method can never give a result with an example of such a inverse... Every complex polynomial, i.e us a = PCP¡1, as required a real matrix Q ( )! 0, or singular, matrix, then a is diagonalizable. < e for n.! Same result is true for lower triangular matrices, which generates upper and triangular... 3 correlated Brownian Motion, your English is better than my < < language > >, there!, thanks for pointing it out a 2 × 2 matrix, with steps shown the coefficient matrix the... +  lunation '' to moon phase number +  lunation '' moon! Is distributed and completed individually by a group of people does it take deflate... Millions of students & professionals true because singular matrices is closed and nowhere dense in the eigenvectors up! The block-diagonal matrix is singular if and only if its determinant is zero! Math and those who hate it matrix Iis invertible ( it is a square matrix matrix may have a inverse. Cient methods have been developed for use on computers the answer is irrelevant the answer is too.. For people studying math at any time that is not an eigenvalue of the matrix at hand whether... Are nonzero ) cc by-sa topological space of n-by-n matrices are square (! That a − λI a significant role in the next section, we have$ \lambda $an. Math 240 - part 4 New Commands 1 any time that is convenient for you ring... Transmit antennas and are received via M receive antennas matrix may have a non zero eigenvalue over rings multiplication is... We are going to have the same time with arbitrary precision up references! Eigenvectors are by definition nonzero, so  nonzero eigenvector. be...... matrix inverse definition 1.3.1 same time with arbitrary precision$ always have a non-real eigenvalue! $\lambda \neq 0$ truncated series can be used to determine whether a given matrix assumed! Given matrix is not an eigenvalue with nonnegative entries for which M ≠ n ) ne.! − λ I 2 is not limited to them if and only if its is! See our tips on writing great answers n-by-n matrices, see here and here privacy policy cookie! Wayto nd eigenvalues when the matrix at hand matrix may be complex, even is... Sum of diagonalizable matrices need not be diagonalizable. real then the next section, we can diagonalize B we... To map moon phase number + a matrix with complex eigenvalues can never be invertible lunation '' to moon phase name our terms service! All n-by-n matrices experience to run their own ministry ( a ) if a is.! Like pure happiness entries are nonzero ) even when the matrix B { \displaystyle B } is the zero.. An algorithm that can be diagonalized using the inverse matrix of a non-invertible, or responding to other.! N matrices ) 2 matrix, the part ( B ) find the eigenvectors of a matrix are... Inversion also plays a significant role in the topological space of n-by-n matrices New ways saying! Distinct eigenvalues, it is a geometric sum in computer graphics, in... By a group of people we have $\lambda \neq 0$ compute the... Is better than my < < language > > is the zero.!


text:
GMAT Data Sufficiency (DS) - Page 11
Check GMAT Club App Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 05 Dec 2016, 06:41

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# GMAT Data Sufficiency (DS)

 new topic Question banks Downloads My Bookmarks Reviews Important topics Go to page Previous    1  ...  9   10   11   12   13  ...  176    Next Search for:
Topics Author Replies   Views Last post

Announcements

142
 150 Hardest and easiest questions for DS   Tags:
Bunuel

3

21293

07 Dec 2015, 08:09

489
 DS Question Directory by Topic and Difficulty   Tags: Coordinate Geometry
bb

0

140075

07 Mar 2012, 07:58

Topics

48
 Is m+z > 0? (1) m-3z > 0 (2) 4z-m > 0   Go to page: 1, 2 Tags: Difficulty: 700-Level,  Inequalities,  Source: GMAT Prep
Summer3

30

9813

15 Nov 2016, 16:30

 If n is positive integer, is 3^n+n^(2+1) not divisible by 3?
MathRevolution

17

940

15 Nov 2016, 16:21

6
 If S is the sum of the first n positive integers, what is the value of
Bunuel

6

1648

15 Nov 2016, 15:50

1
 Is the radius of circle P longer than 2?
Bunuel

6

183

15 Nov 2016, 14:06

1
 On the number line above, the distance between any two vertical. . .
EgmatQuantExpert

2

196

15 Nov 2016, 12:40

2
 An auto dealer sells each car at either $20,000 or$30,000. Some cars
EgmatQuantExpert

3

154

15 Nov 2016, 12:19

 Math Revolution Daily quiz (Day 12)
MathRevolution

1

109

15 Nov 2016, 10:51

 In a rectangular coordinate system, does the point (1,1) lie on line
Bunuel

1

126

15 Nov 2016, 10:19

2
 By what percent has the price of an overcoat been reduced?
Bunuel

5

967

15 Nov 2016, 09:43

16
 10 students took a chemistry exam that was graded on a scale
ace001

8

4514

15 Nov 2016, 09:10

13
 If Z is an integer, is Z prime?
pratikbais

8

3716

15 Nov 2016, 08:30

7
 In the fraction b a , where a and b are positive integers, what is the
Bunuel

8

923

15 Nov 2016, 06:52

4
 Is 8^x>4^y?
MathRevolution

3

488

15 Nov 2016, 06:44

1
 If xy is not equal to 0, is xy = 70?
bschool83

9

925

15 Nov 2016, 06:40

8
 If a is a positive integer, is 105 divisible by a?
goodyear2013

5

1054

15 Nov 2016, 06:35

13
 Each of the 50 students participating in a workshop is either an under
Sallyzodiac

4

2170

15 Nov 2016, 03:25

82
 If x, y and z are positive numbers, is z between x and y?   Go to page: 1, 2 Tags: Difficulty: 700-Level,  Inequalities,  Source: GMAT Prep EP 1
vcbabu

31

18920

15 Nov 2016, 02:00

1
 A certain store sells two models of cellular phones, M1 and M2, and of
Bunuel

1

107

15 Nov 2016, 01:56

7
 If xy = 12, what is the value of x – y?
Bunuel

14

2542

15 Nov 2016, 00:56

3
 What is the LCM of x and 12?
Drik

4

2148

15 Nov 2016, 00:55

21
 Joe bought only twenty cent stamps and thirty cent stamps.
rite2deepti

10

5822

15 Nov 2016, 00:50

 If m and n are integer, n=?
MathRevolution

3

116

15 Nov 2016, 00:45

15
 If y is the sum of x consecutive positive integers, and x>3,
goodyear2013

8

2193

15 Nov 2016, 00:38

5
 What is the median of the numbers 4, 5, 6, 7, 9, and x?
anon1

7

5074

15 Nov 2016, 00:35

23
 On the number line, point R has coordinate r and point T has coordinat
Bunuel

5

1781

14 Nov 2016, 23:55

50
 If x+y+z > 0, is z > 1 ?
eddyed911

15

9050

14 Nov 2016, 22:45

9
 The rectangular rug shown in the figure above has an accent border.
Bunuel

7

2604

14 Nov 2016, 14:01

 If a and b are integers, what is the value of a+b?
Bunuel

2

162

14 Nov 2016, 13:44

9
 Is x*|y| > y^2?
russ9

19

1693

14 Nov 2016, 11:07

18
 In the figure above, PQR and STU are identical equilateral triangles,
Bunuel

6

3295

14 Nov 2016, 10:57

4
 If x is a positive integer, is (x)(x + 2)(x + 4) div by 12?
aeros232

4

1926

14 Nov 2016, 10:37

18
 Beth's pizzeria offers x different toppings. What is the val
anceer

7

2250

14 Nov 2016, 09:11

1
 If 4 small boxes and 5 big boxes weigh the same as 11 small
Barkatis

2

1870

14 Nov 2016, 08:04

11
 Is |a| > |b|? (1) b < -a (2) a < 0
goodyear2013

6

2189

14 Nov 2016, 07:23

4
 If (x−a)(x−b)=0, is b=s?
Bunuel

1

141

14 Nov 2016, 07:06

12
 If 10^a * 3^b * 5^c = 450^n, what is the value of c?
Bunuel

14

646

14 Nov 2016, 06:59

15
 The King Edward College team won 25% of its first games and went on to
snorkeler

11

1352

14 Nov 2016, 03:48

4
 If a, b and c are positive integers, what is the value of
devinawilliam83

8

2168

14 Nov 2016, 02:41

18
 Seven integers, x1, x2, x3, x4, x5, x6, and x7, are picked
Mspixel

12

8864

14 Nov 2016, 01:25

 For all integers k, the function g is defined by g(k) = ak+4, where a
MathRevolution

2

206

14 Nov 2016, 00:33

 Is |x-1|>|x-3|?
MathRevolution

2

157

14 Nov 2016, 00:31

14
 If R=P/Q, is R≤P? (1) P>50 (2) 0
wizard

17

6364

14 Nov 2016, 00:29

7
 16 horses can haul a load of lumber in 24 minutes. 12 horses started h
Bunuel

10

1481

13 Nov 2016, 23:43

3
 If p and q are positive integers, what is the value of q?
Stiv

3

4190

13 Nov 2016, 23:32

 Does x = 7?
Bunuel

3

176

13 Nov 2016, 21:59

 Is x^1/3 non-negative?
Bunuel

4

145

13 Nov 2016, 21:53

1
 There is an arithmetic sequence An where n is a positive integer such
MathRevolution

3

182

13 Nov 2016, 21:49

4
 What is the value of w^(−2)?
Bunuel

9

2311

13 Nov 2016, 21:44

1
 Is x < 4?
Bunuel

3

168

13 Nov 2016, 21:40

 y is an integer. What is the smallest possible value of y?
Bunuel

3

168

13 Nov 2016, 21:37

 new topic Question banks Downloads My Bookmarks Reviews Important topics Go to page Previous    1  ...  9   10   11   12   13  ...  176    Next Search for:
 Who is online In total there are 3 users online :: 2 registered, 0 hidden and 1 guest (based on users active over the past 15 minutes) Users browsing this forum: Binoun, mpmbtr and 1 guest Statistics Total posts 1564971 | Total topics 189656 | Active members 479583 | Our newest member niyathidevaraj

 Powered by phpBB © phpBB Group and phpBB SEO Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.


text:
# Uncertainty in regression results

These functions help estimate the uncertainty in the results from a regression analysis, including uncertainty in the regression coefficients and the noise. Together they are useful for generating a probability distribution that represents the uncertainty in the predictions from a regression model. When applying regression to make projections into the future based on historical data, there might be additional sources of uncertainty because the future might be different from the past. These functions estimate uncertainty due to noise and imperfect fit to the historical data. You might wish to add further uncertainty for projections into the future to reflect these additional differences.

## RegressionDist(y, b, i, k)

RegressionDist() estimates the uncertainty in linear regression coefficients, returning probability distributions on them. Suppose you have data where «y» was produced as:

y = Sum(c*b, k) + Normal(0, s)

«s» is the measurement noise. You have the data b[i, k] and y[i]. You might or might not know the measurement noise «s». So you perform a linear regression to obtain an estimate of «c». Because your estimate is obtained from a finite amount of data, your estimate of «c» is itself uncertain. This function returns the coefficients «c» as a distribution (i.e., in sample mode, it returns a sampling of coefficients indexed by Run and «k»), reflecting the uncertainty in the estimation of these parameters.

Library: Multivariate Distributions

Examples: If you know the noise level «s» in advance, then you can use historical data as a starting point for building a predictive model of «y», as follows:

{ Your model of the dependent variables: }
Variable y := your historical dependent data, indexed by «i»
Variable b := your historical independent data, indexed by «i», «k»
Variable x := { indexed by «k». Maybe others. Possibly uncertain }
 Variable s := { the known noise level }
Chance c := RegressionDist(y, b, i, k)
Variable Predicted_y := Sum(c*x, k) + Normal(0, s)

If you don’t know the noise level, then you need to estimate it. You’ll need it for the normal term of Predicted_y anyway, and you’ll need to do a regression to find it. So you can pass these optional parameters into RegressionDist. The last three lines above become:

Variable e_c := Regression(y, b, i, k)
Variable s := RegressionNoise(y, b, i, k, e_c)
Chance c := RegressionDist(y, b, i, k, e_c)
Variable Predicted_y := Sum(c*x, k) + Normal(0, s)

If you use RegressionNoise() to compute «s», you should use Mid(RegressionNoise(...)) for the «s» parameter. However, when computing «s» for your prediction, don’t use RegressionNoise in context. Better is if you don’t know the measurement noise in advance, don’t supply it as a parameter.

## RegressionFitProb(y, b, i, k, c, s)

When you’ve obtained regression coefficients «c» (indexed by «k») by calling the Regression function, this function returns the probability that a fit this poor would occur by chance, given the assumption that the data was generated by a process of the form:

Y = Sum(c*b, k) + Normal(0, s)

If this result is very close to zero, it probably indicates that the assumption of linearity is bad. If it is very close to one, then it validates the assumption of linearity. See more RegressionFitProb.

Library: Multivariate Distributions This is not a distribution function — it does not return a sample when evaluated in sample mode. However, it does complement the multivariate RegressionDist function also included in this library.

Example: To use, first call the Regression function, then you must either know the measurement knows a priori, or obtain it using the RegressionNoise function.

Var e_c := Regression(y, b, i, k);
Var s := RegressionNoise(y, b, i, k, c);
Var PrThisPoor := RegressionFitProb(y, b, i, k, e_c, s)

## RegressionNoise(y, b, i, k, c)

When you have data, y[i] and b[i, k], generated from an underlying model with unknown coefficients c[k] and «s» of the form:

y = Sum(c*b, i) + Normal(0, s)

This function computes an estimate for «s» by assuming that the sample noise is the same for each point in the data set. See RegressionNoise.

When using in conjunction with RegressionDist, it is most efficient to provide the optional parameter «c» to both routines, where «c» is the expected value of the regression coefficients, obtained from calling Regression(y, b, i, k). Doing so avoids an unnecessary call to the built-in Regression function.

Library: Multivariate Distributions

These functions express uncertainty in the coefficients of a linear regression. If you are using results form a linear regression, you can use these functions to estimate uncertainty in predictive distributions.

These uncertainties reflect only the degree to which the regression model fits the observations to which it was fit. They do not reflect any possible systematic differences between the past process that generated those observations and the process generating the results being predicted, usually in the future. In this way, they are lower bounds on the true uncertainty.


text:
# Trivial conserved Noether's current with second derivatives

I'm considering a symmetry transformation on a Lagrangian

$$\delta A = \int L(q +\delta q, \dot{q} + \delta \dot{q} , \ddot{q} + \delta \ddot{q}) dt$$

the general variation takes the form

$$\delta A = \int \frac{ \partial L}{\partial q} \delta q + \frac{\partial L}{\partial \dot{q}} \delta \dot{q} + \frac{\partial L}{\partial \ddot{q}} \delta \ddot{q} dt$$

Now, the second term inside the integral is normally handled as:

$$\int \frac{\partial L}{\partial \dot{q}} \delta \dot{q} = \frac{\partial L}{\partial \dot{q}} \delta q - \int \frac{\partial}{\partial t}( \frac{\partial L}{\partial \dot{q}} ) \delta q$$

the third terms requires some more work, I'm having it as:

$$\int \frac{\partial L}{\partial \ddot{q}} \delta \ddot{q} = \frac{\partial L}{\partial \ddot{q}} \delta \dot{q} - \frac{\partial}{\partial t}( \frac{\partial L}{\partial \ddot{q}} ) \delta q + \int \frac{\partial^2}{\partial^2 t}( \frac{\partial L}{\partial \ddot{q}} ) \delta q$$

So my variation (that in the case of symmetry must be zero up to boundary terms is)

$$\delta A = \int \Big \{ \frac{\partial L}{\partial q} - \frac{\partial}{\partial t}( \frac{\partial L}{\partial \dot{q}} ) + \frac{\partial^2}{\partial^2 t}( \frac{\partial L}{\partial \ddot{q}} ) \Big \} \delta q dt + \Big \{ \frac{\partial L}{\partial \dot{q}} - \frac{\partial}{\partial t}( \frac{\partial L}{\partial \ddot{q}} ) \Big \} \delta q + \frac{\partial L}{\partial \ddot{q}} \delta \dot{q}$$

Now, I'm taking both boundary terms to be conserved currents:

$$\frac{\partial L}{\partial \dot{q}} - \frac{\partial}{\partial t}( \frac{\partial L}{\partial \ddot{q}} )$$

and

$$\frac{\partial L}{\partial \ddot{q}}$$

But if the second is a conserved current, then its derivative is zero, and the conserved current becomes trivially identical to the first-order case

What the error in my derivation?

• Do you know that this result is wrong? That doesn't seem obvious to me. – ZachMcDargh Jun 2 '15 at 20:48
• – Qmechanic Jun 3 '15 at 9:50

1. Let there be given a Lagrangian $$\tag{1} L(q,v,a,t), \qquad v^i~:=~\dot{q}^i,\qquad a^i~:=~\dot{v}^i,\qquad \jmath^i~:=~\dot{a}^i,$$ that depends on up to second time derivative.

2. Let $$\tag{2} \delta q^i~=~\varepsilon Y^i(q,v,a,t) ,$$ be a (global, vertical) quasi-symmetry of the Lagrangian, i.e. there exists a function $f(q,v,a,\jmath,t)$ such that $$\tag{3} \delta L ~=~ \varepsilon \frac{df}{dt}.$$ Here $\varepsilon$ is an infinitesimal constant parameter.

3. Noether's (first) theorem states that a single quasi-symmetry (3) corresponds to a single on-shell conservation law$^1$ $$\tag{4} \frac{dQ}{dt}~\approx~0.$$

4. The corresponding (full) Noether charge is in this case $$\tag{5} Q~:=~\left(\frac{\partial L}{\partial v^i} - \frac{d}{dt}\frac{\partial L}{\partial a^i}\right)Y^i +\frac{\partial L}{\partial a^i}\frac{dY^i}{dt} - f.$$

5. The error in OP's derivation seems to be that it is basically non-existing.

--

$^1$ Here the $\approx$ symbol denotes equality modulo Euler-Lagrange (EL) equations. Note that in order to have well-defined EL eqs. it is necessary to impose appropriate boundary conditions.

• "The error in OP's derivation seems to be that it is basically non-existing" I don't understand, what you mean by this? what exactly is non-existing? – diffeomorphism Jun 3 '15 at 16:34
• It means that there doesn't seem to be any proof that both the two boundary terms [which are suggested in the question (v2)] are conserved currents in the first place, partly because the quasi-symmetry has not been explicitly specified, and hence no actual claims to discuss. – Qmechanic Jun 3 '15 at 16:43
• would $f$ (which I understand to be pure boundary terms) be a different function for different symmetry transformations? Is not clear to me how to compute the $f$ that goes at the end of the $Q$ expression in the general case. Would it be different for translations, rotations or time shifts? – diffeomorphism Jun 4 '15 at 18:52
• I guess my doubt amounts to this: you have to compute the variation of the action in all cases to obtain $f$? will $f$ be simply equal to all the boundary terms on the final variation? – diffeomorphism Jun 4 '15 at 18:54
• It is not possible to provide a general formula for $f$. It is only possible to calculate $f$ for concretely given Lagrangians and quasi-symmetry transformations. – Qmechanic Jun 4 '15 at 19:19


text:
Looking for Algebra worksheets?
Check out our pre-made Algebra worksheets!
 Tweet

# Inequalities Questions - All Grades

You can create printable tests and worksheets from these Inequalities questions! Select one or more questions using the checkboxes above each question. Then click the add selected questions to a test button before moving to another page.

1 2 3 4 ... 15
Solve:
$2(2-x)<=-3x-2$
1. $x<=-6$
2. $x<=-3$
3. $x<=2$
4. $x>=6$
$5x > 85$
1. 80
2. 20
3. 17
4. 16
Destiny wanted the temperature to be no more than 75 degrees. Which inequality shows that?
1. $t < 75$
2. $t <= 75$
3. $t>=75$
4. $t= 75$
Thomas has at least \$20 to spend this week. Which statement reflects that?
1. $x<20$
2. $x>20$
3. $x<=20$
4. $x>= 20$
solve
$2x + 6 <= -4$
1. $x <= 1$
2. $x <= 10$
3. $x <= -10$
4. $x >= -10$
Which represents the value of x in $6 - 4x <= 26$?
1. $x <= -8$
2. $x >= -8$
3. $x <= -5$
4. $x >= -5$
Greater than or equal to
1. $<=$
2. $>$
3. $<$
4. $>=$
Which correctly compares the pictures?

1. $4>2$
2. $4<2$
3. $4 = 2$
Which correctly compares the pictures?

1. $3>4$
2. $3<4$
3. $3=4$
The heights of trees in a park range from 5 feet to 38 feet tall. Which inequality would describe the height of the trees?
1. $x>5$
2. $5 < x < 38$
3. $5>x>38$
4. $5<38$
What is the solution set of the following inequality? $X - 5 <= -12$
1. $X>=7$
2. $X>= -17$
3. $X<=-5$
4. $X<=-7$


text:
en:getbrushcolor

# Differences

This shows you the differences between two versions of the page.

 en:getbrushcolor [2016/01/01 22:41]127.0.0.1 external edit en:getbrushcolor [2016/08/13 08:11] (current)admin 2016/08/13 08:11 admin 2016/01/01 22:41 external edit 2016/08/13 08:11 admin 2016/01/01 22:41 external edit Line 4: Line 4: getbrushcolor() getbrushcolor() - returns //rgb_expr// + returns [[rgb|rgb_expression]] ==== Description ==== ==== Description ==== Returns the ARGB value of the current drawing brush color (last set by color statement). ARGB is calculated by the formula ( (a * 256 + r) * 256 + b) * 256 + g where alpha, red, green, and blue are between 0 and 255. If the drawing color has been set to CLEAR a 0 will be returned. Returns the ARGB value of the current drawing brush color (last set by color statement). ARGB is calculated by the formula ( (a * 256 + r) * 256 + b) * 256 + g where alpha, red, green, and blue are between 0 and 255. If the drawing color has been set to CLEAR a 0 will be returned.


text:
# Homework Help: Greens theorem boundary of a rectangle

1. Aug 1, 2014

### jonroberts74

1. The problem statement, all variables and given/known data

$\mathscr{C}: x=1,x=3,y=2,y=3$

$\int_\mathscr{C} (xy^2-y^3)dx+(-5x^2+y^3)dy$

2. Relevant equations

3. The attempt at a solution

$\frac{\partial Q}{\partial x} = -10x^2 \,\,; \frac{\partial P}{\partial y} = 2xy-3y^2$

$\int\int_\mathscr{C} \frac{\partial Q}{\partial x} - \frac{\partial P}{\partial y} dA = \displaystyle \int_{2}^{3}\int_{1}^{3} (-10x^2-2xy+3y^2)dxdy = -\frac{206}{3}$

2. Aug 1, 2014

### vela

Staff Emeritus
You miscalculated dQ/dx.

3. Aug 1, 2014

### jonroberts74

oh haha, -10x not $-10x^2$ thanks

4. Aug 2, 2014

### HallsofIvy

Of course, it is easy to do the integration around the path directly as a check. Have you done that?


text:
# zbMATH — the first resource for mathematics

On the critical values of certain Dirichlet series and the periods of automorphic forms. (English) Zbl 0656.10018
Arithmeticity questions involving special (critical) values of zeta functions (Dirichlet series) associated with automorphic forms of the Hilbert modular type (or like Eisenstein series) or concerning periods of automorphic forms (and, in particular, of abelian integrals on arithmetic curves) have, recently for several years, been deeply investigated in a series of papers by the author. The present important paper is yet another milestone in the same direction, offering not only generalizations of some of his earlier arithmeticity theorems (now, without parity conditions or other exceptions and covering the ‘perpetually present’ forms of half-integral weight, too) but also conjectures expected to have far-reaching consequences and open up ‘new territory’.
Reviewer: S.Raghavan

##### MSC:
 11F67 Special values of automorphic $$L$$-series, periods of automorphic forms, cohomology, modular symbols 11F27 Theta series; Weil representation; theta correspondences 11F41 Automorphic forms on $$\mbox{GL}(2)$$; Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces 11F33 Congruences for modular and $$p$$-adic modular forms
Full Text:
##### References:
 [1] [B] Bluher, A.: Thesis, Princeton University, 1988 [2] [H] Hida, H.: On abelian varieties with complex multiplication as factors of the Jacobians of Shimura curves. Am. J. Math.103, 727-776 (1981) · Zbl 0477.14024 · doi:10.2307/2374049 [3] [I] Im, J.: Thesis, Princeton University, 1988 [4] [S] Shimizu, H.: On zeta functions of quarternion algebras. Ann. Math.81, 166-193 (1965) · Zbl 0201.37903 · doi:10.2307/1970389 [5] [59] Shimura, G.: Sur les intégrales attachées aux formes automorphes. J. Math. Soc. Japan11, 291-311 (1959) · Zbl 0090.05503 · doi:10.2969/jmsj/01140291 [6] [62] Shimura, G.: On Dirichlet series and abelian varieties attached to automorphic forms. Ann. Math.76, 237-294 (1962) · Zbl 0142.05501 · doi:10.2307/1970275 [7] [67] Shimura, G.: Construction of class fields and zeta functions of algebraic curves. Ann. Math.85, 58-159 (1967) · Zbl 0204.07201 · doi:10.2307/1970526 [8] [71] Shimura, G.: Introduction to the arithmetic theory of automorphic functions. (Publ. Math. Soc. of Japan, Vol. 11). Iwanami Shoten and Princeton Univ. Press, 1971 · Zbl 0221.10029 [9] [73] Shimura, G.: On the factors of the jacobian variety of a modular function field. J. Math. Soc. Japan25, 523-544 (1973) · Zbl 0266.14017 · doi:10.2969/jmsj/02530523 [10] [75] Shimura, G.: On the holomorphy of certain Dirichlet series. Proc. London Math. Soc. (Ser. 3)31, 79-98 (1975) · Zbl 0311.10029 · doi:10.1112/plms/s3-31.1.79 [11] [77] Shimura, G.: On the periods of modular forms. Math. Ann.229, 211-221 (1977) · Zbl 0363.10019 · doi:10.1007/BF01391466 [12] [78] Shimura, G.: The special values of the zeta functions associated with Hilbert modular forms. Duke Math. J.45, 637-679 (1978) · Zbl 0394.10015 · doi:10.1215/S0012-7094-78-04529-5 [13] [80] Shimura, G.: The arithmetic of certain zeta functions and automorphic forms on orthogonal groups. Ann. Math.111, 313-375 (1980) · Zbl 0438.12003 · doi:10.2307/1971202 [14] [81] Shimura, G.: On certain zeta functions attached to two Hilbert modular forms I, II. Ann. Math.114, 127-164, 569-607 (1981) · Zbl 0468.10016 · doi:10.2307/1971381 [15] [81z] Shimura, G.: The critical values of certain zeta functions associated with modular forms of halfintegral weight. J. Math. Soc. Japan33, 649-672 (1981) · Zbl 0494.10018 · doi:10.2969/jmsj/03340649 [16] [82] Shimura, G.: The periods of certain automorphic forms of arithmetic type. J. Fac. Sci. Univ. Tokyo (Sec. IA)28, 605-632 (1982) · Zbl 0499.10027 [17] [83a] Shimura, G.: Algebraic relations between critical values of zeta functions and inner products. Am. J. Math.104, 253-285 (1983) · Zbl 0518.10032 · doi:10.2307/2374388 [18] [83b] Shimura, G.: On Eisenstein series. Duke Math. J.50, 417-476 (1983) · Zbl 0519.10019 · doi:10.1215/S0012-7094-83-05019-6 [19] [84] Shimura, G.: Differential operators and the singular values of Eisenstein series. Duke Math. J.51, 261-329 (1984) · Zbl 0546.10025 · doi:10.1215/S0012-7094-84-05115-9 [20] [85a] Shimura, G.: On Eisenstein series of half-integral weight. Duke Math. J.52, 281-324 (1985) · Zbl 0577.10025 · doi:10.1215/S0012-7094-85-05216-0 [21] [85b] Shimura, G.: On the Eisenstein series of Hilbert modular groups. Rev. Mat. Ib.1 (No. 3) 1-42 (1985) · Zbl 0608.10028 [22] [86] Shimura, G.: On a class of nearly holomorphic automorphic forms. Ann. Math.123, 347-406 (1986) · Zbl 0593.10022 · doi:10.2307/1971276 [23] [87a] Shimura, G.: Nearly holomorphic functions on hermitian symmetric spaces. Math. Ann.278, 1-28 (1987) · Zbl 0636.10023 · doi:10.1007/BF01458058 [24] [87b] Shimura, G.: On Hilbert modular forms of half-integral weight. Duke Math. J.55, 765-838 (1987) · Zbl 0636.10024 · doi:10.1215/S0012-7094-87-05538-4 [25] [St] Sturm, J.: Special values of zeta functions and Eisenstein series of half integral weight. Am. J. Math.102, 219-240 (1980); Addendum, ibid. pp. 781-783 · Zbl 0433.10015 · doi:10.2307/2374237
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.


text:
I'm looking for feedback on whether or not this is the proper way to approach password verification without transmitting the actual password. Are there any problems with this scheme.

We are working on a cloud based encrypted file system and have implemented the following steps to verify that the entered password is the same when entered a second time on a different machine. All implementations are from the Microsoft .NET Framework 4.0 (Client Profile). Also, all communication is SSL/HTTPS.

Initial activation for a file system

1. RNGCryptoServiceProvider is used to create two 128 bit random salts (s0, s1)
2. Rfc2898DeriveBytes is used with the entered password and s0 with 20,000 iterations to create the 32 byte key (k0)
3. s1 and k0 are appended to produce b0
4. SHA512Managed uses b0 to produce the hash (h0).
5. h0, s0 and s1 are encoded as base64 and sent to the server to be persisited.

1. s0 and s1 are sent to the client as base64 encoded strings
2. Both salts are decoded.
3. Rfc2898DeriveBytes is used with the entered password and s0 with 20,000 iterations to create the 32 byte key (k0)
4. s1 and k0 are appended to produce b0
5. SHA512Managed uses b0 to produce the hash (h0)
6. h0 is base64 encoded and sent to the server. If the hash matches the original hash now stored on the server the server responds with true, otherwise false ie: password does not match.

If all is good k0 is used to actually encrypt/decrypt the file system locally using AES-256.

-
only nitpick I see is that this forces all passwords to use the same salt –  ratchet freak Apr 25 '13 at 17:41
@ratchetfreak: Well the salts are only used for checksum verification. Password storage on each client is a separate process altogether. –  bic Apr 25 '13 at 18:09
Don't read more than the natural size from PBKDF2. Since Rfc2898DeriveBytes uses SHA-1, reading more than 20 bytes is a bad idea. It halves your KDF performance, without hindering the attacker. For client side password hashing I'd also crank up the iterations a bit to 100k or even higher. If that makes it too slow, replace .net's implementation with a fast implementation. Or switch to scrypt. –  CodesInChaos Apr 25 '13 at 18:21

The protocol you are trying to reinvent is called SRP.

Unless you have a compelling reason to believe that your protocol is secure, it should by default be assumed completely broken. Given that your protocol has seemingly no benefits over SRP, you should seriously consider going with something that has been designed and analyzed by cryptographers, has existing software implementations, and has been around for over a decade.

We are working on a cloud based encrypted file system...

Then you really should have somebody on staff who deeply understands cryptography. Your authentication protocol has a few sign that it was designed by novices. I don't mean to be rude or offensive, but cryptography is incredibly hard to get right. Thomas Ptacek said it best: if you think the dangerous stuff is in the primitives like the AES core, and if you just stick to the glue you'll be safe, you're gonna have a bad time.

4. s1 and k0 are appended to produce b0
5. SHA512Managed uses b0 to produce the hash (h0)

Why is this not an HMAC?

If all is good k0 is used to actually encrypt/decrypt the file system locally using AES-256.

What is the point of the authentication protocol, if a malicious client can simply opt not to bother sending $h_0$ to the server and attempt decryption anyway? If the sole purpose is to prevent accidental decryption with an incorrect key, then this is trivially solved by simply using an authenticated encryption mode. Which, really, you should be using anyway.

You've also walled yourself into a design that doesn't allow password changes without decrypting and re-encrypting everything. Instead, you could use a protocol where the client sends a password-protected secret key to the server. After authentication over something like SRP, the server sends a copy of the encrypted key back to the user. If they wish to change their password, they can simply re-encrypt and re-send the secret key.

Note: the above description is the general approach that I would try and look for in an existing protocol, and not a description of an existing, vetted protocol for this type of exchange.

-
Ok, great. Thanks for that insight. This is exactly why I posted the question in the first place. I absolutely don't want to reinvent the wheel as it were. Thanks again. –  bic Apr 25 '13 at 17:53
"it should by default be assumed completely broken". While I accept that, just for arguments sake, is the process described above in actuality broken? –  bic Apr 25 '13 at 18:02
Well, it relies on the CA system, and I think that's its main problem. $\:$ –  Ricky Demer Apr 25 '13 at 18:05
@RickyDemer: Sorry for my ignorance but what does "CA system" refer to in this context? –  bic Apr 25 '13 at 18:07


text:
[ English / Japanese ]

Yasuhiro Abe, Ph.D.

Cereja Technology Co., Ltd.
3-11-15 UEDA-Bldg. 4F, Iidabashi
Chiyoda-ku, Tokyo 102-0072, Japan

Physical interpretation of the Riemann hypothesis

The Riemann hypothesis is an important unsolved problem in mathematics. As well-known, the problem itself is quite simple: "To show the real part of any nontrivial zeros of Riemann's zeta function is equal to 1/2". But it has been unsolved for over 150 years. Of particular importance of this problem is that it is closely related to the distribution of prime numbers. One of the indications of this relation is that the zeta function can be expressed in terms of a product sum over prime numbers via the formula of Euler's product. In what follows, we would like to introduce how we can interpret the Riemann hypothesis in the framework of holonomy formalism by use of a correspondence between primes and knots.

The holonomy formalism is a kind of universal formalism that uses a holonomy operator of conformal field theory as a generating functional for scattering amplitudes of massless bosons. (For its background and formulation, see here.) Thus, in applying this formalism to the Riemann hypothesis, we first need to define "prime-creation" operators. For this purpose, it is necessary to develop quantum-theoretical treatments for various quantities —— such as Legendre symbols, Jacobi symbols and Gauss sums —— that appear in the elementary theory of numbers.

On the other hand, it is known that Gauss's linking number appearing in Maxwell's theory of electromagnetism can easily be obtained in terms of abelian Chern-Simons theory that is closely related to conformal field theory. Since we can consider the holonomy operator as a generalization of Chern-Simons action, this fact suggests that we can obtain a generalization of linking numbers in terms of abelian holonomy operators. Indeed, if we identify the Riemann surface on which the two-dimensional conformal field theory is defined as a torus and consider holonomy operators of its zero modes, then we can express a generalized linking number in terms of such zero-mode holonomy operators.

Applying a mathematically-known correspondence between primes and knots or, more precisely, a correspondence between linking numbers and Legendre symbols, we can then incorporate the Legendre symbols as operators into the zero-mode holonomy operators. This can be thought of as an application of abelian holonomy formalism to elementary number theory. Furthermore, since in number theory it is known that the Gauss sum can be considered as a Fourier transform of the Legendre symbol, we can interpret the Gauss sum as an operator that is canonically conjugate to the Legendre symbol. The Gauss sum is a quantity that depends only on an odd prime and its modulus gives the square root of the odd prime. In the holonomy formalism under consideration, information on odd primes is encoded only in the Gauss-sum operator (or, more precisely, certain powers of it). Therefore it is physically natural to interpret this operator as an operator that is relevant to creation of primes.

From these arguments we find that one can define a "prime-creation" operator but how it connects with the Riemann hypothesis has not been mentioned at all. However, in actuality, an explicit calculation of the zero-mode holonomy operator shows that it can be expressed in terms of an iterated-integral representation of Riemann's zeta function. Thus, using the formula of Euler's product and replacing its prime-number part by the Gauss-sum operators, we can obtain a quantum realization of the zeta function in the abelian holonomy formalism. Furthermore, by use of this new zero-mode holonomy operator, we can calculate "scattering amplitudes" for identical odd primes within the framework of holonomy formalism. When there is only one prime to be scattered, the "scattering amplitude" of course vanishes. The Riemann hypothesis can be interpreted by means of this physically obvious fact, i.e., there is no notion of "scattering" for a single-particle system. For details of these formulations, please see arXiv:1005.4299.


text:
# How do you recognize a carbohydrate molecule?

I am studying carbohydrates in organic chemistry and I am confused a bit on what they are and how you recognize whether a molecule is a carbohydrate or not. For example, will a carbohydrate always have an $\ce{OH}$ group with either an aldehyde or a ketone group? Can it also contain other atoms like nitrogen or bromine? Can it have ether, ester?

You've asked a great and challenging question, especially for people just learning this material. The other answers are useful and provide good background. They also illustrate how the great structural diversity of carbohydrates quickly muddies the waters. I'll offer an answer that is less technical and gets at the "recognition" part.

The trouble with simple carbohydrates (5- or 6-carbon monosaccharides specifically, but we should avoid that term since we haven't defined it here) is that they can be drawn in an an open chain form (as a Fischer projection) or in a cyclic form (as a Haworth projection, or in some cases as a "chair"). So one commonly encounters two or even three "pictures" of the same thing, which hardly helps (examples below).

In my courses I nearly always use the cyclic forms since for 5- and 6-carbon sugars they are the dominant and biologically relevant forms. If one sticks to this, a pretty simple rule of thumb can be stated: carbohydrates are compounds with a 5- or 6-membered ring containing oxygen, and decorated extensively with hydroxyl (or alcohol) groups. This "scales" to polysaccharides, and accommodates deoxy and amino sugars, so it works a great deal of the time (and is enough for non-experts in many cases). When and if someone needs to understand more, it's not too hard to transition to the Fischer projections by focusing on opening (breaking open) the ring.

The name "carbohydrate", which literally means“carbon hydrate,” arises from their chemical composition, which is roughly $\ce{(C.H2O)_n}$, where $n\ge 3$. The basic units of carbohydrates are monosaccharides.

Monosaccharides or simple sugars are aldehyde or ketone derivatives of straight-chain polyhydroxy alcohols containing at least three carbon atoms. Such substances, for example, D-glucose and D-ribulose, cannot be hydrolyzed to form simpler saccharides.

Examples of monosaccharides:

Classification

Monosaccharides are classified according to the chemical nature of their carbonyl group and the number of their C atoms.

If the carbonyl group is an aldehyde, as in glucose, the sugar is an aldose. If the carbonyl group is a ketone, as in ribulose, the sugar is a ketose. The smallest monosaccharides, those with three carbon atoms, are trioses.

Those with four, five, six, seven, etc., C atoms are, respectively, tetroses, pentoses, hexoses, heptoses, etc. These terms may be combined so that, for example, glucose is an aldohexose, whereas ribulose is a ketopentose.

However, there are similar molecules with different atoms such as nitrogen which are also considered carbohydrates. A class of polysaccharides known as glycosaminoglycans (unbranched polysaccharides of alternating uronic acid and hexosamine residues).Practical examples are Hyaluronic acid(linked disaccharide units that consist of D-glucuronic acid and N-acetyl-Dglucosamine) and Heparin (sulfated disaccharide units):

Nevertheless, when carbohydrates bond with other molecules to form other newer bonds, they are given different names and are not necessarily carbohydrates but are given new names - a good example are glycoproteins (proteins covalently associated with carbohydrates.)

Reference

Biochemistry Voet and Voet, Grisham

• Thanks for the reply. The reason why I ask this question was because the books definition of carbohydrate was too basic. For instance, do carbohydrate have to follow the strict ratio of 1:2:1 ratio for C:H:O atom. IF not then can 3hydroxybutanal be considered a carbohydrate? It has a aldehyde and oh group? Also, in carbohydrate, does every carbon atom in the carbohydrate molecule have to be attached to 1 OH and 1 H atom? Can you have exception where one carbon atom is attached to both 2 OH group and other carbon atom attached to 2 H atom as in CH2? These are just my curiosities. – TLo May 11 '17 at 16:38
• Very good question! Only the simple sugars, or monosaccharides, fit this formula exactly. The other types of carbohydrates, oligosaccharides and polysaccharides, are based on the monosaccharide units and have slightly different general formulas, as for the other part, its not necessarily each carbon is bonded to OH, H , a good example to explain this is deoxyribose , it has a carbon bonded to H,H – xavier_fakerat May 11 '17 at 16:48
• ahh... Got it thanks... If i could ask just one more question, since the previous comment wasn't allowing me, I was reading other resources and was reminded that carbohydrates are polyhydroxy aldehydes and ketone, which thus means that 3 hydroxybutanal cannot be carbohydrate since it does not have multiple OH groups. So my other question is that can simple sugars have poly-adehydes or ketone groups, or can each molecule just have one of the other? Or can a simple carbohydrate contains both aldehyde and ketone groups together in one molecule? Sorry if this seems a lot. But thanks anyways. – TLo May 11 '17 at 16:55
• I'm sorry, the last part i'm not really sure so I can't answer now, would it be fine if I just confirm and get back to you later ? – xavier_fakerat May 11 '17 at 17:10
• Sure no problem. – TLo May 11 '17 at 17:11

A carbohydrate is a biological molecule consisting of carbon (C), hydrogen (H) and oxygen (O) atoms, usually with a hydrogen–oxygen atom ratio of 2:1 (as in water); in other words, with the empirical formula Cm(H2O)n (where m could be different from n).This formula holds true for monosaccharides. Some exceptions exist; for example, deoxyribose, a sugar component of DNA,has the empirical formula C5H10O4.Carbohydrates are technically hydrates of carbon; structurally it is more accurate to view them as polyhydroxy aldehydes and ketones.

Carbohydrates often display chemical groups such as: ''N''-acetyl (e.g. chitin), sulfate (e.g. glycosaminoglycans), carboxylic acid (e.g. sialic acid) and deoxy modifications (e.g. fucose and sialic acid).This is from Wikipedia

They can also be defined as optically active polyhydroxy aldehydes and ketones.

Now about the general formula $\ce{C_m(H2O)_n}$ also have exceptions like $\ce{CH3-COOH}$($\ce{C2(H2O)2})$ but it is not a carbohydrate. Similarly, rhamnose($\ce{C6H12O5})$ and deoxyribose($\ce{C5H10O4})$ as mentioned in the above article does not fit into this general formula, but then too they are classified as carbohydrates.

Apart from that carbohydrates are also ether.

Source:Wikipedia

This is the open chain structure of glucose. Some of the properties of glucose was not able to be explained by this structure.

These are the two hemiacetal cyclic forms $\alpha$ and $\beta$ of glucose also called as Haworth structures which remain in equilibrium with the open chain structure of glucose. It is an ether as you can see in the structure. Other examples of ether include cellulose, starch, sucrose, etc. Sucrose is a disaccharide which gives a glucose and fructose by hydrolysis. Starch and cellulose are polysaccharides. Starch is a branched polymer of $\alpha$ glucose units and cellulose is a straight chain polymer of $\beta$ glucose units.

• Ok got it. So together with multiple OH groups, can simple sugars also have multiple aldehyde and ketone groups? Or can both aldehyde and ketone groups be found in simple sugars? – TLo May 11 '17 at 17:10
• I don't think so, I have never heard of such molecule. You can ask this as a different question. @TLo – user237650 May 11 '17 at 17:20


text:
# Figure 8

 Left: Inclusive $\jpsi$ $\Raa$ in the $20$\% most central $\PbPb$ collisions at $\snn = 5.02$~TeV as a function of $\pt$, at midrapidity and at forward rapidity~. Right: Rapidity dependence of the inclusive $\jpsi$ $\Raa$ in the centrality interval $0$--$90$\%. The error bars represent statistical uncertainties, while the boxes around the data points represent systematic uncertainties. The boxes around unity represent global uncertainties on the $\pp$ reference due to normalization and $\langle\TAA\rangle$. In the right panel, the correlated uncertainty of the point at midrapidity is included in the box around the data point.


text:
# Physics Question

1. May 11, 2005

### Jodi

Hi; Could somebody please help me with this question: A 3.0g copper penny has a postive charge of 38uC. What fraction of its electrons has it lost?
The method I tried was: (3g/63.55g) x 6.02E23 x A(what i'm solving for) = 38xE-6. Than I took my answer and divided it by 29. However this will not give me the correct answer, and the correct answer is 1/(3.5E9). Can somebody please help me. Thank you so much.

2. May 11, 2005

### StatusX

Look at your units. You have a dimensionless number on the left side and coulombs on the right side. You need to factor in the charge on an electron.

3. May 11, 2005

### rune

Try a more systematic approach:

- How many electrons does it take to make up $$-38\mbox{\mu C}$$ charge? (hint: use the electron charge)

- How many electrons are in 3.0g copper (when neutral)? (29 per copper atom)

4. May 11, 2005

### Jodi

Thanks...

Thanks guys, I figured this one out.


text:
# 3.4: Variables

A variable is a symbol that stands for another value (just like “X” in algebra). We can create a variable by assigning a value to it using the <- operator. If we then type the name of the variable R will print out its value.

> x <- 4
> x
[1] 4

The variable now stands for the value that it contains, so we can perform operations on it and get the same answer as if we used the value itself.

> x + 3
[1] 7
> x == 5
[1] FALSE

We can change the value of a variable by simply assigning a new value to it.

> x <- x + 1
> x
[1] 5

A note: You can also use the equals sign = instead of the <-

This page titled 3.4: Variables is shared under a CC BY-NC 2.0 license and was authored, remixed, and/or curated by Russell A. Poldrack via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.


text:
These notes and closely review Unit 2 Section 1.

## selectionSort

SelectionSort is one of the classic sorting algorithms. Here's a nice simple iterative version of it:
selectionSort(A,n)
input:  A an array of n objects for which "<" is defined
n the size of A
Output: side effect of leaving A in sorted order according to "<"

for i from 0 to n-2 do
m = i
for j from i+1 to n-1 do
if A[j] < A[m]
m = j
swap(A[i],A[m])

In class we showed that its worst-case running time is $O(n^2)$, which ... well, duh. More interestingly, we showed that its worst-case running time is $\Omega(n)$. Put the two together, and we arrive at the fact that the worst-case running time for selectionSort is $\Theta(n)$.

## insertionSort

SelectionSort is another one of the classic sorting algorithms. Here's a nice simple iterative version of it:
insertionSort(A,n)
input:  A an array of n objects for which "<" is defined
n the size of A
Output: side effect of leaving A in sorted order according to "<"

for i from 0 to n-2 do
j = i + 1
while j > 0 and A[j] < A[j-1] do
swap(A[i],A[m])
j = j - 1

In class we showed that its worst-case running time is $O(n^2)$, which ... well, duh. More interestingly, we showed that its worst-case running time is $\Omega(n)$. This was more involved than for selectionSort. Why? Because selectionSort's inner loop always executes $n - i - 1$ times, no matter what the input looks like. With insertionSort, however, the inner loop makes anywhere from $0$ to $i$ iterations, depending on the particulars of the input, because the "A[j] < A[j-1]" condition allows us to exit the inner loop early. To do this analyis, we had to find concrete inputs for which insertionSort is slow. Someone noticed that for reverse-sorted input, the inner loop always iterates the maximum number of times (which is $i$). So we derived $\Omega(n)$. Once again, put the two facts together, and we arrive at the fact that the worst-case running time for insertionSort is $\Theta(n)$.


text:
# Tag Info

3

There's no need to use numerical methods here. The most straightforward way to compute the output is to see that the filter's impulse response is given by $$h(t)=\sum_{k=1}^Nr_ke^{s_kt}u(t)=\sum_{k=1}^Nh_k(t)\tag{1}$$ where $N$ is the filter order, $u(t)$ is the unit step function, and $r_k$ are the coefficients of the partial fraction expansion of $H(s)$: ...

3

A plot of the normalized impulse responses, for the n = 2 through 10 Butterworth low pass filters, are given by H.J. Blinchikoff, A.I. Zverev, "Filtering in the Time and Frequency Domains", Wiley-Interscience, John Wiley & Sons, NY, ©1976, p. 113. This is shown below. They do not give the h(t) expressions in the book, at least where I have looked thus ...

2

Given a complex time-domain signal is it always implied that this is a QAM-demodulated form of a real time domain signal? No, we generally use complex baseband to describe all kinds of signals, or even passband systems (e.g. frequency-selective or time-variant channels). So, any bandlimited signal has an equivalent complex baseband, and it's not implied ...

2

My updated answer to OP's update To do this specifically for the case of the FFT of a product of two sinusoids, you must choose a sampling rate or modulation frequency such that the upper sideband of the "positive" frequency component aliases to be on top of the lower sideband of the "negative" frequency component. For instance using a carrier frequency of ...

1

If you want to have a "numerical grasp" and you're not afraid of getting a little bit dirty, you can check the numbers with LTspice. I don't know how well you know to work with it, so I'll just explain it, feel free to ignore all the redundant info. Here you can download the archive, out of which you only need Filter.asy and filter.sub. Create a new ...

1

Frequency domain analysis has much broader application (more numerous to list) than just analyzing sinusoidal components of a signal. Frequency domain analysis appears as a mathematical tool whenever the equivalent operations in the time domain can be simplified, and vice versa. For example, convolution in one domain is multiplication in the other which can ...

1

I think you are looking for a "peak" detectors. They are not filters in the conventional sense. Typically the output is increased when the incoming sample is either above a certain threshold or above the current output and decreased if it's smaller. The increase and decrease are often just simple exponential with time constants determined by your application....

1

The problem with the filters you want, e.g., 3dB/octave or 1 dB/octave, is that they are not simple filters: they are carefully designed by some very clever people, including at least one person here, e.g., robert bristow-johnson, and the aforementioned JOS III. So it is very helpful to look first at Pink (1/f) pseudo-random noise generation and all the ...

1

1) g1 assumes that there is a non-zero mean and that always needs to be subtracted off for the correlation calc to make sense. g2 assumes that the mean is zero. g2 is incorrect if the mean is not zero. 2) the mean is taken over the whole sample because the autocorrelation calc has the underlying assumption that the process is stationary so the mean doesn'...

1

These terms refer to the general duality properties of these two domains. It should be obvious that higher frequency components mean faster changes in time and lower rise/fall times. In most natural systems, some of these fundamental properties oppose each other: Shorter rise time means more overshoot and higher settling times and vice versa; lower ...

1

In the absence of noise and other distortions in the channel and in the transmission system, the received signal in a passband transmission system has the form $$r(t)=I(t)\cos(2\pi f_ct+\phi)-Q(t)\sin(2\pi f_ct+\phi)\tag{1}$$ where $I(t)$ and $Q(t)$ are the in-phase and quadrature components, respectively. After demodulation you're left with the two ...

1

One common use of the IQ data from an SDR is to feed them to an FFT. The upper and lower halves of an FFT result indicated different relationship between the (real) cosine and (imaginary) sine components of the complex FFT result. The direction of rotation of each complex component tells the rest of the signal chain whether the complex component is an upper ...

1

I think you can do a dft for a single frequency fine. Just sum over your window of a whole compression and rarefaction multiplied by the sine of the frequency your looking for, then do it for the cosine, then the amplitude is the hypotenuse if they were graphed on xy axis, and the phase is the angle.

1

Why not using the tsa in Matlab ?

Only top voted, non community-wiki answers of a minimum length are eligible


text:
- Current Issue - Ahead of Print Articles - All Issues - Search - Open Access - Information for Authors - Downloads - Guideline - Regulations ㆍPaper Submission ㆍPaper Reviewing ㆍPublication and Distribution - Code of Ethics - For Authors ㆍOnlilne Submission ㆍMy Manuscript - For Reviewers - For Editors
 Meromorphic univalent harmonic functions with negative coefficients Bull. Korean Math. Soc. 1999 Vol. 36, No. 4, 763-770 Jay M. Jahangiri and Herb Silverman College of Charleston, College of Charleston Abstract : The purpose of this paper is to give sufficient coefficient conditions for a class of univalent harmonic functions that map each $|z|=r>1$ onto a curve that bounds a domain that is starlike with respect to origin. Furthermore, it is shown that these conditions are also necessary when the coefficients are negative. Extreme points for these classes are also determined. Finally, comparable results are given for the convex analog. Keywords : harmonic, univalent, starlike, and convex functions MSC numbers : 30C45, 30C50 Full-Text :