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development; and you may wish to try the Article Wizard. For creating a new page in your userspace see How do I create a user subpage?; or use the Article Wizard, which has an option for that. <span>Make sure that there is enough context and it is notable. Why was my article deleted? Further information: Wikipedia:Why was the page I created deleted? If you look at the address where your page was, it should have a red box above it

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An option that conveys to the owner the right to buy at a specific price is referred to as a call; an option that conveys the right of the owner to sell at a specific price is referred to as a put. Both are commonly traded, but the call option is more frequently discussed. <html>

or commodity on the day an option is taken out, or it may be fixed at a discount or at a premium. The seller has the corresponding obligation to fulfill the transaction – to sell or buy – if the buyer (owner) "exercises" the option. <span>An option that conveys to the owner the right to buy at a specific price is referred to as a call; an option that conveys the right of the owner to sell at a specific price is referred to as a put. Both are commonly traded, but the call option is more frequently discussed. The seller may grant an option to a buyer as part of another transaction, such as a share issue or as part of an employee incentive scheme, otherwise a buyer would pay a premium to th

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In operator theory, a multiplication operator is an operator T f defined on some vector space of functions and whose value at a function φ is given by multiplication by a fixed function f . That is, for all φ in the domain of T f , and all x in the domain of φ (which is the same as the domain of f ).

This article does not cite any sources. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. (December 2009) (Learn how and when to remove this template message) <span>In operator theory, a multiplication operator is an operator T f defined on some vector space of functions and whose value at a function φ is given by multiplication by a fixed function f. That is, T f φ ( x ) = f ( x ) φ ( x ) {\displaystyle T_{f}\varphi (x)=f(x)\varphi (x)\quad } for all φ in the domain of T f , and all x in the domain of φ (which is the same as the domain of f). This type of operators is often contrasted with composition operators. Multiplication operators generalize the notion of operator given by a diagonal matrix. More precisely, one of th

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users") managed in AWS's identity management system, and it also enables you to grant access to AWS resources for users managed outside of AWS in your corporate directory (referred to as "federated users"). Q: <span>What can a user do? A user can place requests to web services such as Amazon S3 and Amazon EC2. A user's ability to access web service APIs is under the control and responsibility of the AWS account under which it is defined. You can permit a user to access any or all of the AWS services that have been integrated with IAM and to which the AWS account has subscribed. If permitted, a user has access to all of the resources under the AWS account. In addition, if the AWS account has access to resources from a different AWS account, its users may be able to access data under those AWS accounts. Any AWS resources created by a user are under control of and paid for by its AWS account. A user cannot independently subscribe to AWS services or control resources. Q: How do users call AWS services? Users can make requests to AWS services using security credentials. Explicit permissions govern a user's ability to call AWS service

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ces. You can create and manage users, groups, and policies by using IAM APIs, the AWS CLI, or the IAM console. You also can use the visual editor and the IAM policy simulator to create and test policies. Q: <span>What is a group? A group is a collection of IAM users. Manage group membership as a simple list: Add users to or remove them from a group. A user can belong to multiple groups. Groups cannot belong to other groups. Grou

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r example, an administrator user may be created to manage users for a corporation—a recommended practice. When you grant a user permission to manage other users, they can do this via the IAM APIs, AWS CLI, or IAM console. Q: <span>Can I structure a collection of users in a hierarchical way, such as in LDAP? Yes. You can organize users and groups under paths, similar to object paths in Amazon S3—for example /mycompany/division/project/joe. Q: Can I define users regionally? Not

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申博太阳城（开户彩金接力送 3重豪礼高达60%） 与美女荷官面对面交流，激情玩转百家乐,轮盘,龙虎斗,21点等 更有高赔率球赛，英超，意甲，西甲...NBA篮球，时时彩,福彩3D,香港六合彩,存取款火速到账！更多精彩尽在申博娱乐城，等你来战！www.sun321.com 君子好色，取之有道 91TV是由澳洲华人娱乐集团开发专门观看成人影片的APP，内置多个分类帮助用户找到喜好，每天免费更新，支持在线无码高清播放，91TV影视APP你值得拥有！www.vryy.info <span>我知道大过年的说这个不好，可是我也就这时候能有点时间，希望大家可以原谅我。这段时间看到了那篇《流感下的北京中年》，深感惭愧，之前我也有把自己这段经历写下来的打算，可是最终都没有付诸实施。因为那篇文章作者毕竟不懂医疗，虽然已经做得很好了，但是也犯了不少错误，医学上有一句很有趣但也很残酷的话：你错了，病人就死给你看。希望通过这篇文章，能在以后遇到类似情况的时候能少犯一些错误而不至于耽误了亲人。数年前，我刚到国外，脚跟都还没站稳，家里就打电话说爸爸不行了，当时我觉得不会有那么大事，就安排了他住某市某医院，嗯，是我学校的附属医院。当时的情况大概就是呼吸困难，心动过速，低热，这症状持续了一个多月，越来越严重。但是CT照下来，老同学发给我看，我基本就傻了，我还记得当时我脑袋里一片空白，一边肺90%都是白的，另一边也超过了50%。而且肺底那个严重的影像我都没怎么见到过。我就记得当时同学跟我说你还是快点回来吧。我当时就定了当天的机票怀着到现在都不知道如何描述的心情飞回来了。到了某市，可能因为自己本身职业的关系，还是很平静的。当时医生可以说很重视，给了监护病房，而且完善了各种检查和培养之后直接上了泰能等高级抗细菌真菌药物，基本是医院力所能及的最强的抗感染治疗方案了。而且也做了病例讨论。后来比较重要的结果记得就是有一个重度肺动脉高压。可惜很不幸，住院5天后，症状却一直在加重，从病重通知签到危重通知，医生也跟我们打招呼，人可能随时就没了。母亲当时非常激动，经常跟医护起冲突，嗯嗯，对我在学校里的形象确实有造成不良好的影响。对治疗没有一点好处。千万不要这样。然后我同学有一天悄悄找我说，你还是转院吧，老爸这个情况比较严重，我们医院呼吸科不够强。他说的是事实情况，那么对于我来说面临的问题就是去哪个医院，当时有两个选择，第一个是呼吸科全国最强的，可是没什么关系，虽然也可以弄到床，但是很可能要等，另外一个是有点关系，可以马上弄到床，综合实力也还很不错。后来决断是时间就是生命，当天就转了某医院。转进去以后第二天转进呼吸科ICU（RICU），住进去5天的样子，还是没有好转，继续加重，签了呼吸机使用同意书。同时呼吸科让我自己跑病理科把纤支镜的病理切片借出到呼吸科最强的某医院会诊。当时检查结果也基本都出来了，医生们争论的焦点主要集中于到底是大叶性肺炎为主还是间质性肺炎为主。因为两者证据都有。最后把呼吸科大主任也请来了，大呼吸科会诊，我记得从查完房10点多的样子，一直讨论到过了饭点12点多，最后决定大包围抗感染（广谱抗细菌真菌）加用激素。然后又是签字。因为没有有效抗感染的情况下用激素，如果真的是感染，后果很严重。我记得加用激素几天后父亲的症状及自我感觉没有继续加重，但是也没有好转，可是胸片显示感染面积在继续加重，一边肺只剩肺尖一点点，另一边也超过70%了。从鼻导管吸氧也改到了面罩给氧，可惜父亲面罩给氧配合的很不好，老是对抗，最后也就是最严重没什么意识的那个晚上用了一晚上。当时每天只能一个家属进去探视十几分钟，头几天父亲还能挣扎着说几句，后几天父亲都不怎么能说话了，有时候就只是看着我，连话都说不了。有时候只是我跟他解释他的病情的时候，他就会用那种很强烈的带着求生本能的眼神盯着我看，想说话沙沙几声也说不清楚，要挣扎几次我才能勉强明白。这里要说一个小插曲，当时从住院开始每天都取痰培养，一开始我爸就是随便吐一口痰拿去培养，或者有时候都吐到垃圾桶里了，然后才想起来有培养这么一回事，又捡回来拿去培养。培养结果全部都是阴性的或者是杂菌，就是培养不出细菌或者真菌。后来我发现了，我就跟我爸说你最好就是早晨睡醒第一口痰拿去培养，因为不论是医生还是护士都不会告知具体方法，这里也确实要说一下国内医生护士实在太忙，一些重要细节的宣教非常不到位。当然，当时每天也有抽血培养，结果也都是没有什么意义。最后的转机时是在某一天抽的血培养里面查到了一种细菌，大概是第五天的标本里的（培养出结果大概是3-5天），是一种超级耐药菌，溶血性葡萄球菌，当时全世界只有2种抗生素对其有效，其它全部耐药。一种就是那篇文章提到的万古霉素，这个国产版本是医保覆盖的，另外一种是达托霉素，这种不论国产还是进口都是自费。然后又让我们选，然后我就问医生，我说哪种效果最好，然后回答说当时是进口达托最好。这个选择的重要性在于，如果选择的抗生素由于药效不够强，在把细菌完全杀死之前细菌产生了耐药，那么就没有可以使用的药物来杀灭这种细菌了。当时达托霉素这个药医院还没有，要去指定药房买，后来用到一半，指定药房都没有货了，又是到处找人，最后跑去另外一家某著名医院的指定药房买。达托霉素总共用了大约2周。我记得用到第三天的时候，父亲的呼吸频率就明显下降了，各种感觉都有好转了，能跟我们交流了。最后在RICU住了1个月直接从RICU出的院，回到家里最后休想了差不多2年才缓过来。很多时候，对于急危重症，生死就是在一线之间，任何一个小的错误或是迟疑，都降低了病人那仅存的那么一点点的生还几率。我真的觉得现在医疗制度是有问题的，包括国外也是这样。因为绝大多数的家属包括我自己在内，没有足够的知识背景去做医疗决定，甚或都理解不了，无法真正做到的知情。我当时的处理办法基本就是算经济，我认为负担得起的当下就答应，不确定的马上询问母亲看有没有别的办法弄到些钱，然后马上回应。当然这个前提条件是我信任他们。所以当时医生跟我交流的时候我绝大多数时候都是当下马上答复照办，他们就马上出医嘱，可以说一秒钟都没耽误，虽然我也是从医的，可是呼吸科的水平我估计连他们一个实习医生都比不上，我都是签字以后再查资料，而不是查资料以后再去签字，尽量争取时间。而且他们提出的各种要求，比如去指定药房买药，拿标本去外院会诊，都是上午说了下午就办完了。他们提出了所有治疗方案，我们没有一个是迟疑或是当场拒绝的。我记得当时管床医生请各大主任会诊我父亲的时候都会加上一句儿子很配合。其实在国外也是一样，医生之间的信件会提及患者的依从程度。现在的医疗环境，家属的配合实际上给了医生一个放手一搏的机会，同时也是给了自己一个机会。但是话说回来，如果没有那个血培养结果，激素的应用势必会让感染严重加重，父亲的生命可能就无法挽回了。当时培养从住我校某附属医院就开始，一直培养到有结果，前前后后加起来10多天，一天都没有落下的。可惜在《流感下的北京中年》一文中，可以发现作者不止一次的错过治疗时机和打乱治疗节奏。虽然我真心认为作者已经比绝大多数的患者家属要配合治疗的好非常多了。这些具体内容我在其他文章都有看到我就不在此重复了。我觉得一线城市三甲医院或是全国百佳医院这一级别的医生，我们普通老百姓基本上没有什么怀疑的资格，尤其是在急危重症方面。你能选择的只是信任与不信任，配合与不配合。用人不疑，疑人不用，不要一边用一边怀疑，最后失去了挽救一条生命的机会。 TOP Posted:2018-02-16 22:16 | 回樓主 一寸法師 級別: 新手上路 ( 8 ) 發帖: 699 威望: 71 點 金錢: 700 USD 貢獻: 0 點 註冊: 2016-04-20 資料 短信 引用 推薦 編輯 美妹真人裸聊 深夜陪伴你真情互动 情

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or a function space of continuous functions, extrema of corresponding functionals are called weak extrema or strong extrema, depending on whether the first derivatives of the continuous functions are respectively all continuous or not. [11] <span>Both strong and weak extrema of functionals are for a space of continuous functions but weak extrema have the additional requirement that the first derivatives of the functions in the space be continuous. Thus a strong extremum is also a weak extremum, but the converse may not hold. Finding strong extrema is more difficult than finding weak extrema. [12] An example of a necessary condition that is used for finding weak extrema is the Euler–Lagrange equation. [13] [Note 5] Euler–Lagrange equation[edit source] Main article: Euler–Lagrange equation Finding the extrema of functionals is similar to finding the maxima and minima of funct

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of variations is a field of mathematical analysis that uses variations, which are small changes in functions and functionals, to find maxima and minima of functionals, which are mappings from a set of functions to the real numbers. [Note 1] <span>Functionals are often expressed as definite integrals involving functions and their derivatives. Functions that maximize or minimize functionals may be found using the Euler–Lagrange equation of the calculus of variations. A simple example of such a problem is to find the curve o

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tml>Linear differential equation - Wikipedia Linear differential equation From Wikipedia, the free encyclopedia Jump to: navigation, search In mathematics, a linear differential equation is a differential equation that is defined by a linear polynomial in the unknown function and its derivatives, that is an equation of the form a 0 ( x ) y +

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In mathematics, a linear differential equation is a differential equation that is defined by a linear polynomial in the unknown function and its derivatives

tml>Linear differential equation - Wikipedia Linear differential equation From Wikipedia, the free encyclopedia Jump to: navigation, search In mathematics, a linear differential equation is a differential equation that is defined by a linear polynomial in the unknown function and its derivatives, that is an equation of the form a 0 ( x ) y +

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In mathematics, a linear differential equation is a differential equation that is defined by a linear polynomial in the unknown function and its derivatives

tml>Linear differential equation - Wikipedia Linear differential equation From Wikipedia, the free encyclopedia Jump to: navigation, search In mathematics, a linear differential equation is a differential equation that is defined by a linear polynomial in the unknown function and its derivatives, that is an equation of the form a 0 ( x ) y +

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quation containing one or more functions of one independent variable and its derivatives. The term ordinary is used in contrast with the term partial differential equation which may be with respect to more than one independent variable. [1] <span>ODEs that are linear differential equations have exact closed-form solutions that can be added and multiplied by coefficients. By contrast, ODEs that lack additive solutions are nonlinear, and solving them is far more intricate, as one can rarely represent them by elementary functions in closed form: Instead, e

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ODEs that are linear differential equations have exact closed-form solutions that can be added and multiplied by coefficients.

quation containing one or more functions of one independent variable and its derivatives. The term ordinary is used in contrast with the term partial differential equation which may be with respect to more than one independent variable. [1] <span>ODEs that are linear differential equations have exact closed-form solutions that can be added and multiplied by coefficients. By contrast, ODEs that lack additive solutions are nonlinear, and solving them is far more intricate, as one can rarely represent them by elementary functions in closed form: Instead, e

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ODEs that are linear differential equations have exact closed-form solutions that can be added and multiplied by coefficients.

quation containing one or more functions of one independent variable and its derivatives. The term ordinary is used in contrast with the term partial differential equation which may be with respect to more than one independent variable. [1] <span>ODEs that are linear differential equations have exact closed-form solutions that can be added and multiplied by coefficients. By contrast, ODEs that lack additive solutions are nonlinear, and solving them is far more intricate, as one can rarely represent them by elementary functions in closed form: Instead, e

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olutions that can be added and multiplied by coefficients. By contrast, ODEs that lack additive solutions are nonlinear, and solving them is far more intricate, as one can rarely represent them by elementary functions in closed form: Instead, <span>exact and analytic solutions of ODEs are in series or integral form. Graphical and numerical methods, applied by hand or by computer, may approximate solutions of ODEs and perhaps yield useful information, often sufficing in the absence of exact, analyti

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exact and analytic solutions of nonlinear ODEs are usually in series or integral form.

olutions that can be added and multiplied by coefficients. By contrast, ODEs that lack additive solutions are nonlinear, and solving them is far more intricate, as one can rarely represent them by elementary functions in closed form: Instead, <span>exact and analytic solutions of ODEs are in series or integral form. Graphical and numerical methods, applied by hand or by computer, may approximate solutions of ODEs and perhaps yield useful information, often sufficing in the absence of exact, analyti

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analysis Population dynamics Chaos Multistability Bifurcation Coupled map lattices Game theory[show] Prisoner's dilemma Rational choice theory Bounded rationality Irrational behaviour Evolutionary game theory v t e <span>A complex system is a system composed of many components which may interact with each other. In many cases it is useful to represent such a system as a network where the nodes represent the components and the links their interactions. Examples of complex systems are Earth's glo

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A complex system is a system composed of many components which may interact with each other.

analysis Population dynamics Chaos Multistability Bifurcation Coupled map lattices Game theory[show] Prisoner's dilemma Rational choice theory Bounded rationality Irrational behaviour Evolutionary game theory v t e <span>A complex system is a system composed of many components which may interact with each other. In many cases it is useful to represent such a system as a network where the nodes represent the components and the links their interactions. Examples of complex systems are Earth's glo

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l Line integral Surface integral Volume integral Jacobian Hessian matrix Specialized[show] Fractional Malliavin Stochastic Variations Glossary of calculus[show] Glossary of calculus v t e <span>In mathematics, a Taylor series is a representation of a function as an infinite sum of terms that are calculated from the values of the function's derivatives at a single point. The concept of a Taylor series was formulated by the Scottish mathematician James Gregory and formally introduced by the English mathematician Brook Taylor in 1715. If the Taylor seri

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In mathematics, a Taylor series is a representation of a function as an infinite sum of terms that are calculated from the values of the function's derivatives at a single point.

l Line integral Surface integral Volume integral Jacobian Hessian matrix Specialized[show] Fractional Malliavin Stochastic Variations Glossary of calculus[show] Glossary of calculus v t e <span>In mathematics, a Taylor series is a representation of a function as an infinite sum of terms that are calculated from the values of the function's derivatives at a single point. The concept of a Taylor series was formulated by the Scottish mathematician James Gregory and formally introduced by the English mathematician Brook Taylor in 1715. If the Taylor seri

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In mathematics, a field is a set on which addition, subtraction, multiplication, and division are defined, and behave as when they are applied to rational and real numbers.

Module-like[show] Module Group with operators Vector space Linear algebra Algebra-like[show] Algebra Associative Non-associative Composition algebra Lie algebra Graded Bialgebra v t e <span>In mathematics, a field is a set on which addition, subtraction, multiplication, and division are defined, and behave as when they are applied to rational and real numbers. A field is thus a fundamental algebraic structure, which is widely used in algebra, number theory and many other areas of mathematics. The best known fields are the field of rational

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mple above reduces to this one if the arrows are represented by the pair of Cartesian coordinates of their end points. Definition[edit source] In this article, vectors are represented in boldface to distinguish them from scalars. [nb 1] <span>A vector space over a field F is a set V together with two operations that satisfy the eight axioms listed below. The first operation, called vector addition or simply addition + : V × V → V, takes any two vectors v and w and assigns to them a third vector which is commonly written

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ors 2 Continuous dual space 2.1 Examples 2.2 Transpose of a continuous linear map 2.3 Annihilators 2.4 Further properties 2.5 Topologies on the dual 2.6 Double dual 3 See also 4 Notes 5 References Algebraic dual space[edit source] <span>Given any vector space V over a field F, the (algebraic) dual space V ∗ (alternatively denoted by V ∨ {\displaystyle V^{\vee }} or V ′ {\displaystyle V'} ) [1] is defined as the set of all linear maps φ: V → F (linear functionals). Since linear maps are vector space homomorphisms, the dual space is also sometimes denoted by Hom(V, F). The dual space V ∗ itself becomes a vector space over F w

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ltiplication, and division are defined, and behave as when they are applied to rational and real numbers. A field is thus a fundamental algebraic structure, which is widely used in algebra, number theory and many other areas of mathematics. <span>The best known fields are the field of rational numbers and the field of real numbers. The field of complex numbers is also widely used, not only in mathematics, but also in many areas of science and engineering. Many other fields, such as fields of rational functions, al

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The best known fields are the field of rational numbers and the field of real numbers.

ltiplication, and division are defined, and behave as when they are applied to rational and real numbers. A field is thus a fundamental algebraic structure, which is widely used in algebra, number theory and many other areas of mathematics. <span>The best known fields are the field of rational numbers and the field of real numbers. The field of complex numbers is also widely used, not only in mathematics, but also in many areas of science and engineering. Many other fields, such as fields of rational functions, al

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A vector space over a field F is a set V together with two operations (the vector addition and scalar multiplication) that satisfy certain axioms. Elements of V are commonly called vectors. Elements of F are commonly called scalars.

mple above reduces to this one if the arrows are represented by the pair of Cartesian coordinates of their end points. Definition[edit source] In this article, vectors are represented in boldface to distinguish them from scalars. [nb 1] <span>A vector space over a field F is a set V together with two operations that satisfy the eight axioms listed below. The first operation, called vector addition or simply addition + : V × V → V, takes any two vectors v and w and assigns to them a third vector which is commonly written

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A vector space over a field F is a set V together with two operations (the vector addition and scalar multiplication) that satisfy certain axioms.

mple above reduces to this one if the arrows are represented by the pair of Cartesian coordinates of their end points. Definition[edit source] In this article, vectors are represented in boldface to distinguish them from scalars. [nb 1] <span>A vector space over a field F is a set V together with two operations that satisfy the eight axioms listed below. The first operation, called vector addition or simply addition + : V × V → V, takes any two vectors v and w and assigns to them a third vector which is commonly written

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A vector space over a field F is a set V together with two operations (the vector addition and scalar multiplication) that satisfy certain axioms. Elements of V are commonly called vectors. Elements of F are commonly called scalars.

mple above reduces to this one if the arrows are represented by the pair of Cartesian coordinates of their end points. Definition[edit source] In this article, vectors are represented in boldface to distinguish them from scalars. [nb 1] <span>A vector space over a field F is a set V together with two operations that satisfy the eight axioms listed below. The first operation, called vector addition or simply addition + : V × V → V, takes any two vectors v and w and assigns to them a third vector which is commonly written

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Given any vector space V over a field F, the (algebraic) dual space V ∗ is defined as the set of all linear maps φ: V → F

ors 2 Continuous dual space 2.1 Examples 2.2 Transpose of a continuous linear map 2.3 Annihilators 2.4 Further properties 2.5 Topologies on the dual 2.6 Double dual 3 See also 4 Notes 5 References Algebraic dual space[edit source] <span>Given any vector space V over a field F, the (algebraic) dual space V ∗ (alternatively denoted by V ∨ {\displaystyle V^{\vee }} or V ′ {\displaystyle V'} ) [1] is defined as the set of all linear maps φ: V → F (linear functionals). Since linear maps are vector space homomorphisms, the dual space is also sometimes denoted by Hom(V, F). The dual space V ∗ itself becomes a vector space over F w

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Given any vector space V over a field F, the (algebraic) dual space V ∗ is defined as the set of all linear maps φ: V → F

ors 2 Continuous dual space 2.1 Examples 2.2 Transpose of a continuous linear map 2.3 Annihilators 2.4 Further properties 2.5 Topologies on the dual 2.6 Double dual 3 See also 4 Notes 5 References Algebraic dual space[edit source] <span>Given any vector space V over a field F, the (algebraic) dual space V ∗ (alternatively denoted by V ∨ {\displaystyle V^{\vee }} or V ′ {\displaystyle V'} ) [1] is defined as the set of all linear maps φ: V → F (linear functionals). Since linear maps are vector space homomorphisms, the dual space is also sometimes denoted by Hom(V, F). The dual space V ∗ itself becomes a vector space over F w

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u ) = c f ( u ) {\displaystyle f(c\mathbf {u} )=cf(\mathbf {u} )} homogeneity of degree 1 / operation of scalar multiplication Thus, <span>a linear map is said to be operation preserving. In other words, it does not matter whether you apply the linear map before or after the operations of addition and scalar multiplication. This is equivalent to requiring the same for any linear combination of vectors, i.e. that for any vectors u

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a linear map is operation preserving: it does not matter whether you apply the linear map before or after the operations of addition and scalar multiplication.

u ) = c f ( u ) {\displaystyle f(c\mathbf {u} )=cf(\mathbf {u} )} homogeneity of degree 1 / operation of scalar multiplication Thus, <span>a linear map is said to be operation preserving. In other words, it does not matter whether you apply the linear map before or after the operations of addition and scalar multiplication. This is equivalent to requiring the same for any linear combination of vectors, i.e. that for any vectors u

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Weak formulation - Wikipedia Weak formulation From Wikipedia, the free encyclopedia Jump to: navigation, search Weak formulations are important tools for the analysis of mathematical equations that permit the transfer of concepts of linear algebra to solve problems in other fields such as partial differential equations. In a weak formulation, an equation is no longer required to hold absolutely (and this is not even well defined) and has instead weak solutions only with respect to certain "test vectors" or "test functions". This is equivalent to formulating the problem to require a solution in the sense of a distribution. [citation needed] We introduce weak formulations by a few examples and present the

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Weak formulations are important tools for the analysis of mathematical equations that permit the transfer of concepts of linear algebra to solve problems in other fields such as partial differential equations. In a weak formulation, an equation is no longer required to hold absolutely (and this is not even well defined) and has instead weak solutions only with respect to certain "test ve

Weak formulation - Wikipedia Weak formulation From Wikipedia, the free encyclopedia Jump to: navigation, search Weak formulations are important tools for the analysis of mathematical equations that permit the transfer of concepts of linear algebra to solve problems in other fields such as partial differential equations. In a weak formulation, an equation is no longer required to hold absolutely (and this is not even well defined) and has instead weak solutions only with respect to certain "test vectors" or "test functions". This is equivalent to formulating the problem to require a solution in the sense of a distribution. [citation needed] We introduce weak formulations by a few examples and present the

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Weak formulations transfer concepts of linear algebra to solve problems in other fields such as partial differential equations.

Weak formulation - Wikipedia Weak formulation From Wikipedia, the free encyclopedia Jump to: navigation, search Weak formulations are important tools for the analysis of mathematical equations that permit the transfer of concepts of linear algebra to solve problems in other fields such as partial differential equations. In a weak formulation, an equation is no longer required to hold absolutely (and this is not even well defined) and has instead weak solutions only with respect to certain "test vectors" or "test functions". This is equivalent to formulating the problem to require a solution in the sense of a distribution. [citation needed] We introduce weak formulations by a few examples and present the

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pedia Jump to: navigation, search In mathematics, specifically in the calculus of variations, a variation δf of a function f can be concentrated on an arbitrarily small interval, but not a single point. <span>Accordingly, the necessary condition of extremum (functional derivative equal zero) appears in a weak formulation (variational form) integrated with an arbitrary function δf. The fundamental lemma of the calculus of variations is typically used to transform this weak formulation into the strong formulation (differential equation), free of the integration with arbitrary function. The proof usually exploits the possibility to choose δf concentrated on an interval on which f keeps sign (positive or negative). Several versions of the lemma are in use. Basic version

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[hide] 1 Basic version 2 Version for two given functions 3 Versions for discontinuous functions 4 Higher derivatives 5 Vector-valued functions 6 Multivariable functions 7 Applications 8 Notes 9 References Basic version[edit source] <span>If a continuous function f {\displaystyle f} on an open interval ( a , b ) {\displaystyle (a,b)} satisfies the equality ∫ a b f ( x ) h ( x ) d x = 0 {\displaystyle \int _{a}^{b}f(x)h(x)\,\operatorname {d} x=0} for all compactly supported smooth functions h {\displaystyle h} on ( a , b ) {\displaystyle (a,b)} , then f {\displaystyle f} is identically zero. [1] [2] Here "smooth" may be interpreted as "infinitely differentiable", [1] but often is interpreted as "twice continuously differentiable" or "co

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Accordingly, the necessary condition of extremum (functional derivative equal zero) appears in a weak formulation (variational form) integrated with an arbitrary function δf . The fundamental lemma of the calculus of variations is typically used to transform this weak formulation into the strong formulation (differen

pedia Jump to: navigation, search In mathematics, specifically in the calculus of variations, a variation δf of a function f can be concentrated on an arbitrarily small interval, but not a single point. <span>Accordingly, the necessary condition of extremum (functional derivative equal zero) appears in a weak formulation (variational form) integrated with an arbitrary function δf. The fundamental lemma of the calculus of variations is typically used to transform this weak formulation into the strong formulation (differential equation), free of the integration with arbitrary function. The proof usually exploits the possibility to choose δf concentrated on an interval on which f keeps sign (positive or negative). Several versions of the lemma are in use. Basic version

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Accordingly, the necessary condition of extremum (functional derivative equal zero) appears in a weak formulation (variational form) integrated with an arbitrary function δf . The fundamental lemma of the calculus of variations is typically used to transform this weak formulation into the strong formulation (differential equation), free of the integration wit

pedia Jump to: navigation, search In mathematics, specifically in the calculus of variations, a variation δf of a function f can be concentrated on an arbitrarily small interval, but not a single point. <span>Accordingly, the necessary condition of extremum (functional derivative equal zero) appears in a weak formulation (variational form) integrated with an arbitrary function δf. The fundamental lemma of the calculus of variations is typically used to transform this weak formulation into the strong formulation (differential equation), free of the integration with arbitrary function. The proof usually exploits the possibility to choose δf concentrated on an interval on which f keeps sign (positive or negative). Several versions of the lemma are in use. Basic version

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the necessary condition of extremum is functional derivative equal zero. the weak formulation of the necessary condition of extremum is an integral with an arbitrary function δf .

pedia Jump to: navigation, search In mathematics, specifically in the calculus of variations, a variation δf of a function f can be concentrated on an arbitrarily small interval, but not a single point. <span>Accordingly, the necessary condition of extremum (functional derivative equal zero) appears in a weak formulation (variational form) integrated with an arbitrary function δf. The fundamental lemma of the calculus of variations is typically used to transform this weak formulation into the strong formulation (differential equation), free of the integration with arbitrary function. The proof usually exploits the possibility to choose δf concentrated on an interval on which f keeps sign (positive or negative). Several versions of the lemma are in use. Basic version

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the necessary condition of extremum is functional derivative equal zero. the weak formulation of the necessary condition of extremum is an integral with an arbitrary function δf .

pedia Jump to: navigation, search In mathematics, specifically in the calculus of variations, a variation δf of a function f can be concentrated on an arbitrarily small interval, but not a single point. <span>Accordingly, the necessary condition of extremum (functional derivative equal zero) appears in a weak formulation (variational form) integrated with an arbitrary function δf. The fundamental lemma of the calculus of variations is typically used to transform this weak formulation into the strong formulation (differential equation), free of the integration with arbitrary function. The proof usually exploits the possibility to choose δf concentrated on an interval on which f keeps sign (positive or negative). Several versions of the lemma are in use. Basic version

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the weak formulation of the necessary condition of extremum is an integral with an arbitrary function δf .

pedia Jump to: navigation, search In mathematics, specifically in the calculus of variations, a variation δf of a function f can be concentrated on an arbitrarily small interval, but not a single point. <span>Accordingly, the necessary condition of extremum (functional derivative equal zero) appears in a weak formulation (variational form) integrated with an arbitrary function δf. The fundamental lemma of the calculus of variations is typically used to transform this weak formulation into the strong formulation (differential equation), free of the integration with arbitrary function. The proof usually exploits the possibility to choose δf concentrated on an interval on which f keeps sign (positive or negative). Several versions of the lemma are in use. Basic version

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the weak formulation of the necessary condition of extremum is an integral with an arbitrary function δf .

pedia Jump to: navigation, search In mathematics, specifically in the calculus of variations, a variation δf of a function f can be concentrated on an arbitrarily small interval, but not a single point. <span>Accordingly, the necessary condition of extremum (functional derivative equal zero) appears in a weak formulation (variational form) integrated with an arbitrary function δf. The fundamental lemma of the calculus of variations is typically used to transform this weak formulation into the strong formulation (differential equation), free of the integration with arbitrary function. The proof usually exploits the possibility to choose δf concentrated on an interval on which f keeps sign (positive or negative). Several versions of the lemma are in use. Basic version

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remum (functional derivative equal zero) appears in a weak formulation (variational form) integrated with an arbitrary function δf . The fundamental lemma of the calculus of variations is typically used to transform this weak formulation into <span>the strong formulation (differential equation), free of the integration with arbitrary function. <span><body><html>

pedia Jump to: navigation, search In mathematics, specifically in the calculus of variations, a variation δf of a function f can be concentrated on an arbitrarily small interval, but not a single point. <span>Accordingly, the necessary condition of extremum (functional derivative equal zero) appears in a weak formulation (variational form) integrated with an arbitrary function δf. The fundamental lemma of the calculus of variations is typically used to transform this weak formulation into the strong formulation (differential equation), free of the integration with arbitrary function. The proof usually exploits the possibility to choose δf concentrated on an interval on which f keeps sign (positive or negative). Several versions of the lemma are in use. Basic version

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Accordingly, the necessary condition of extremum (functional derivative equal zero) appears in a weak formulation (variational form) integrated with an arbitrary function δf . The fundamental lemma of the calculus of variations is typically used to transform this weak formulation into the strong formulation (differential equation), free of the integration with arbitrary function.

pedia Jump to: navigation, search In mathematics, specifically in the calculus of variations, a variation δf of a function f can be concentrated on an arbitrarily small interval, but not a single point. <span>Accordingly, the necessary condition of extremum (functional derivative equal zero) appears in a weak formulation (variational form) integrated with an arbitrary function δf. The fundamental lemma of the calculus of variations is typically used to transform this weak formulation into the strong formulation (differential equation), free of the integration with arbitrary function. The proof usually exploits the possibility to choose δf concentrated on an interval on which f keeps sign (positive or negative). Several versions of the lemma are in use. Basic version

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The fundamental lemma of the calculus of variations transforms this weak formulation of the necessary condition of extremum into the strong formulation, free of the integration with arbitrary function.

pedia Jump to: navigation, search In mathematics, specifically in the calculus of variations, a variation δf of a function f can be concentrated on an arbitrarily small interval, but not a single point. <span>Accordingly, the necessary condition of extremum (functional derivative equal zero) appears in a weak formulation (variational form) integrated with an arbitrary function δf. The fundamental lemma of the calculus of variations is typically used to transform this weak formulation into the strong formulation (differential equation), free of the integration with arbitrary function. The proof usually exploits the possibility to choose δf concentrated on an interval on which f keeps sign (positive or negative). Several versions of the lemma are in use. Basic version

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The fundamental lemma of the calculus of variations transforms this weak formulation of the necessary condition of extremum into the strong formulation, free of the integration with arbitrary function.

pedia Jump to: navigation, search In mathematics, specifically in the calculus of variations, a variation δf of a function f can be concentrated on an arbitrarily small interval, but not a single point. <span>Accordingly, the necessary condition of extremum (functional derivative equal zero) appears in a weak formulation (variational form) integrated with an arbitrary function δf. The fundamental lemma of the calculus of variations is typically used to transform this weak formulation into the strong formulation (differential equation), free of the integration with arbitrary function. The proof usually exploits the possibility to choose δf concentrated on an interval on which f keeps sign (positive or negative). Several versions of the lemma are in use. Basic version

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If a continuous function on an open interval satisfies the equality for all compactly supported smooth functions on , then is identically zero.

[hide] 1 Basic version 2 Version for two given functions 3 Versions for discontinuous functions 4 Higher derivatives 5 Vector-valued functions 6 Multivariable functions 7 Applications 8 Notes 9 References Basic version[edit source] <span>If a continuous function f {\displaystyle f} on an open interval ( a , b ) {\displaystyle (a,b)} satisfies the equality ∫ a b f ( x ) h ( x ) d x = 0 {\displaystyle \int _{a}^{b}f(x)h(x)\,\operatorname {d} x=0} for all compactly supported smooth functions h {\displaystyle h} on ( a , b ) {\displaystyle (a,b)} , then f {\displaystyle f} is identically zero. [1] [2] Here "smooth" may be interpreted as "infinitely differentiable", [1] but often is interpreted as "twice continuously differentiable" or "co

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any other way. If they both happened to be identically structured, both would have the same impact on the balance sheet and the income statement. Structurally and practically, the two instruments are identical. Where the similarities stop <span>The primary difference between notes payable and bonds stems from securities laws. Bonds are always considered and regulated as securities, while notes payable are not necessarily considered securities. For example, securities law explicitly defines mortgage notes, co

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t maturity. The $3 difference represents the interest return on the security. Treasury Notes and Bonds Treasury notes and bonds, on the other hand, are securities that have stated interest rates that are paid semi-annually until maturity. <span>What makes notes and bonds different are the terms to maturity. Notes are issued in one-, three-, five-, seven- and 10-year terms. Conversely, bonds are long-term investments with terms of more than 10 years. To learn more about T-bills and other

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the security. Treasury Notes and Bonds Treasury notes and bonds, on the other hand, are securities that have stated interest rates that are paid semi-annually until maturity. What makes notes and bonds different are the terms to maturity. <span>Notes are issued in one-, three-, five-, seven- and 10-year terms. Conversely, bonds are long-term investments with terms of more than 10 years. To learn more about T-bills and other money market instruments, read An Introduction to Treasury Securities, The Basics of the T-Bill, and our Money Market Tutorial. For further readi

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t the U.S. government sells in order to pay off maturing debt and to raise the cash needed to run the federal government. When you buy one of these securities, you are lending your money to the government of the U.S. Understanding T-bills <span>T-bills are short-term obligations issued with a term of one year or less, and because they are sold at a discount from face value, they do not pay interest before maturity. The interest is the difference between the purchase price and the price paid either at maturity (face value) or the price of the bill if sold prior to maturity. For example, an invest

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What is a 'Certificate Of Deposit - CD' <span>A certificate of deposit (CD) is a savings certificate with a fixed maturity date, specified fixed interest rate and can be issued in any denomination aside from minimum investment requirements. A CD restricts access to the funds until the maturity date of the investment. CDs are generally issued by commercial banks and are insured by the FDIC up to $250,000 per individual. BREAKING DOWN 'Certificate Of Deposit - CD'

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to the funds until the maturity date of the investment. CDs are generally issued by commercial banks and are insured by the FDIC up to $250,000 per individual. BREAKING DOWN 'Certificate Of Deposit - CD' <span>A certificate of deposit is a promissory note issued by a bank. It is a time deposit that restricts holders from withdrawing funds on demand. A CD is typically issued electronically and may automatically renew upon the maturity of the original CD. When the CD matures, the entire amount of principal,as well as interest earned,

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What is 'Commercial Paper' <span>Commercial paper is an unsecured, short-term debt instrument issued by a corporation, typically for the financing of accounts receivable, inventories and meeting short-term liabilities. Maturities on commercial paper rarely range any longer than 270 days. Commercial paper is usually issued at a discount from face value and reflects prevailing market interest rates. BREAKING DOWN 'Commercial Paper' Commercial paper is not usually backed by any form of collateral, making it a form of unsecured debt. As a resu

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