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The picture above is taken from here.Mathematical rigour. Mathematical links. Presentation. etc.Now, it is not about how complicated the math you are getting involved into, or how fancy or advanced the topic you choose for your exploration, it’s a matter of how well presented is your paper.Before I go on forth, I will have to describe a bit of my paper because it will be referenced from time to time in my argument below. I received a 17/20 when marked by my teacher (I know this after getting my diploma) but as I was chosen for moderation by the IBO, they marked me up by 3 points and deemed my IA to be 20/20 (thank you, IBO). So the marks that I have obtained has shown that my IA is certified by the IBO with reduced bias - that is, it is marked and moderated by IBO certified examiners.My IA is about something very simple; rotation of a spoon, to cool down coffee. But instead of a person doing it, the sets of equations that are developed are so that a robot can be programmed to do it for you. To reach such equations, I have used, complex numbers and differential equations (even though the DE part is not even transparently shown in the paper due to the page constraint). That’s it.Now, I will go through each criterion to highlight which part is crucial and is left out by most students.N.B. I will not go through every single detail within a criterion. I will only highlight crucial parts per criterion that I found many people are missing in their IAs. For general suggested details required by the IBO, you can find so in one of the previous answers to this question.Criterion A: Communication.Unless your paper is a pure math paper, doing intense proofs (which I doubt as it is hard to find something original and new at the IB level), do you use software to aid you?In my IA, I used Tables,Graphs using GeoGebra and Adobe Photoshop,computed logarithmic regressions using TI-Nspire CXand computed errors by generating hundreds of data using Excel.And I used all of this software not solely to fulfil this criterion. Instead, I was forced to use them because each and every single one of them is crucial to arrive at my conclusion. This is what helped me secure the criteria in this one. Question yourself when tackling a problem, is technology necessary? Or a better question would be, would it help me to reach a better solution by using technology?Criterion B: Mathematical presentation.Do you use a proper mathematical editor when writing your equations? Are the variables italicised? Are the non-variables non-italicised? Are the parentheses aligned with your giant fractions? Do you define variables properly? Small things like this, if not done properly, would definitely hurt the eyes, and brains of the person reading your paper (if not yet obvious: your marker). Presentation is a key tool in scoring this criterion.Criterion C: Personal engagement.This criterion is quite hard to score to be honest. One of the many things that pushed my IA to a full score in this criterion is because I have managed to unify the Euler’s number, [math]e[/math] and [math]\pi[/math] in one single equation and realising that fact took me months.This is part of the personal engagement that they want. A pure demonstration of you appreciating the beauty of maths. That simplifying something into these two important mathematical constants are considered needed to do. I mean, look at the following example.Let [math]r[/math] be the radius, and [math]C[/math] be the circumference, both of the same circle. Then take a fraction of the two, [math]r/C[/math]. On first sight, you might think, well that's pretty nice already. But on a closer inspection, we realise something magnificent (which seemed almost trivial at first):[math]C = 2 \pi r[/math]Which implies,[math]\dfrac{r}{C} = \dfrac{r}{2 \pi r} = \dfrac{1}{2 \pi}[/math]See? You can simplify something that might look pretty simplified already at first to a better version of it.Such intuition is what IB wants from you. Thus, you need to demonstrate this level of intuition to ensure you score a full mark in this criterion.Criterion D: Reflection.This criterion is easy for you to score a 2/3, but not a 3/3. To score a full mark, the keywords that you must be aware of are critical analysis and further research. You must evaluate your findings properly. If you want to find a newer method or a better equation than the current one you have, Why? If you want to modify something, or assume something in your model, ask yourself, Why? These are important questions that will aid you to assess your own judgements critically.Furthermore, recognize whether your research can have some continuation in it (which it must if it is a good one). Identify what is lacking in your research such as the limitations of your model. For example, the model you currently build is perfect on sunny days, but not applicable during rainy ones. Or perhaps, your equation can be used only for something of a fixed radius, a better one would be of varying radius, hence this can be continued in a new research paper, etc.Criterion E: Use of Mathematics.This is considered to be the hardest criterion to score of them all. Before submitting your paper, please make sure that all mathematics involved is correct. Check it for the nth time. If not, you will only get a maximum of 2/6 for this criterion.Some relevant mathematics is used. The mathematics explored is partially correct. Some knowledge and understanding are demonstrated. - for achievement level of 2The above is quoted from the IBO website[1] itself.Now to score a full mark you must fully understand every single point of what the IB wants.Relevant mathematics commensurate with the level of the course is used. The mathematics explored is precise and reflects the sophistication and rigour expected. Thorough knowledge and understanding are demonstrated. - for achievement level of 6Again, another quote from IBO.The keywords are bold. The first key point, your work must commensurate with HL maths. In layman terms, this just means do not use middle school algebra as your core tool in your research. Use HL maths.Rigour. This is the most important of all.Every single math IA I have read in my entire life lack this. You can simply google for the meaning of mathematical rigour and get a very formal definition of it. But the simplest way of me explaining this in terms of an IB math IA is that you must tackle your equations with care. That is, you must present the math (or your equations) in such a way that it is strongly and logically valid. A very simple (but not very strong example) I can think and give of is:Suppose we have an equation defined by [math]z(t) = t + \ln(t)[/math] with [math]t[/math] being a variable. While it seems obvious that [math]t > 0[/math] as [math]\ln(t)[/math] is undefined in the reals when [math]t \leq 0[/math], you must state and show this fact. This is because, say you do some 'intricate' substitution with the equation, let [math]t = 1/ \cos(x) = \sec(x)[/math] with the domain [math]\{x \in \R: x \neq \pi/2 + \pi n[/math] where [math]n \in \Z \}[/math] (pronounced ‘the set x in the real domain, such that, [math]x \neq \pi/2 + \pi n[/math] where n is an integer’) . You may or may not have realised that while [math]\cos(x) \neq 0,[/math][math]t = \sec(x) > 0[/math] as [math]t > 0[/math]whereas generally this wouldn’t be true as the range/codomain/image of [math]y = \sec(x)[/math] is the set:[math]\{y \in \R\ : y \leq -1[/math] or [math]y \geq 1\} \quad (*)[/math](pronounced ‘the set y in the real domain, such that, [math]y \leq -1[/math] or [math]y \geq 1[/math]’)Note: [math](*)[/math] is pronounced as star.Now we have [math]t = \sec(x) > 0[/math], but notice [math]t = \sec(x)[/math] cannot take the values [math]t \in (0,1).[/math] We know this from [math](*)[/math]. And thus, we can make the following deduction,[math]t \geq 1 > 0[/math]which satisfies our first constraint (that [math]t > 0[/math]) and second constraint (which is [math](*)[/math] that is [math]t \geq 1[/math]).Hence, we know the new domain for [math]z(t)[/math] is indeed [math]t \geq 1[/math] if we make this substitution in [math]z(t) = t + \ln(t)[/math] instead of the obvious [math]t > 0[/math].This example might seem trivial as this ‘intricate’ substitution I’ve used in the example above is actually simple. But in reality, a substitution may get as messy as it can, and you might do it several times, say to solve a system using integration by parts. So please state such conditions as lucid as possible.This idea of being rigorous is expected of you from the IBO if you really want to score a 20/20 IA.And the last part, “thorough knowledge and understanding are demonstrated”.This is why I’ve mentioned earlier in this post that the fanciness of your topic does not matter at all. You do not have to pick some complicated topic like Stochastic analysis or the Chinese remainder theorem as suggested on some Math HL IA websites.With the (lack of) mathematical knowledge you possess during IB, you can’t demonstrate a strong understanding in these topics. Stochastic analysis is something you take in 2nd/3rd year of a Math degree to understand it properly; while the Chinese remainder theorem, to understand it properly (despite the idea itself is fairly simple), you have to take some basic abstract algebra classes to learn some ring theory (as the ones you’ve learn in the IB Discrete Mathematics Option topic is insufficient).Don’t get me wrong, I’m not against you wanting to use it. I’m against you wanting to use it but unable to show a pure grasp of the topic on paper, let alone, verbally. Even if you choose to study these topics, it will cost you too much time as remember that you have tons of other work to do like your other 5 IAs, your EE, your TOK essay, the TOK presentation and even your CAS reports.You can pick a simple topic say, vectors, and do some clever manipulations in it as long as you can demonstrate that you have a thorough understanding of it. What is this example of manipulations that can demonstrate your understanding in a topic you asked?Well, an example would be:Given two vectors [math]\mathbf{a}[/math] and [math]\mathbf{b}[/math]. Then what is the component of [math]\mathbf{a}[/math] in the direction of [math]\mathbf{b}[/math]? Well, we know that:[math]\mathbf{a} \cdot \mathbf{b} = | \mathbf{a} | | \mathbf{b} | \cos(\theta)[/math]through our understanding (of the definition) of the dot product.where [math]\theta[/math] is the angle between the two vectors and [math]| \mathbf{a} |[/math] is the norm/magnitude of the vector [math]\mathbf{a}[/math] and similarly [math]| \mathbf{b} |[/math] for the vector [math]\mathbf{b}[/math].Then we can rearrange to have in terms of [math]\mathbf{b}[/math]. That is we have,[math]| \mathbf{a} | \cos(\theta) = \dfrac{\mathbf{a} \cdot \mathbf{b}}{| \mathbf{b} |}[/math].And thus this is the component of [math]\mathbf{a}[/math] in the direction of [math]\mathbf{b}[/math]. The clever manipulation part is just when you realised that you can just divide both sides by [math]| \mathbf{b} |[/math] to get the desired result.Well now you’re asking me, ‘What is the application of what I have just shown in the example above. Some manipulations, yeah, but why would we do that?Well it turns out. If we let Force [math]= \mathbf{F}[/math] and Displacement [math]= \mathbf{s}[/math]. And substitute [math]\mathbf{a} \rightarrow \mathbf{F}[/math] and [math]\mathbf{b} \rightarrow \mathbf{s}[/math]. We have that,[math]| \mathbf{F} | \cos(\theta) = \dfrac{\mathbf{F} \cdot \mathbf{s}}{| \mathbf{s} |}[/math].We have not just found an equation to represent Force in terms of Displacement, but better, we found a representation of the component of Force in the direction of the Displacement of which the force is applied! Now is that not useful?!If you can do this multiple times in your paper, you have clearly demonstrated that you indeed understand the tool/topic you are using and you are capable of manipulating it in such a way that it becomes useful for you that you can draw a meaningful conclusion (if not many conclusions) from it.On top of all that, remember THE MOST IMPORTANT aspect of the Math IA!The exploration should be accessible to fellow students.I did not say this. The IBO said this in their FAQ[2]. It is a very important aspect that your IA must satisfy. What you can do is give your completed IA to your peers who are equally mathematically driven as you are to read and evaluate it. Ask them if they can understand every step of it. Ask them where are the holes that got them lost.Congratulations for reading up to this point, it shows that you are determined and have the drive and motivation to write a good IA. Or maybe you are just desperate? At this point, it doesn’t matter. Just go and try to write the best IA you can with this guide in hand. Even if you are not able to demonstrate with the precision as described in this guide, you would still be getting a mark within the 15+ range if you follow it as close as possible.If some of you feel that this is too much and want to just score a 14/20. My two cents would be to just read the IBO website[3] and the Internal Assessment section under the Mathematics HL guide (this is SO important to read!).I really hope this helps all of you readers. Do give an upvote if you feel this is helpful and please share it with your friends. Best of luck everyone!Some topics that I see as very useful and feasible for the average IB Math HL student:Pure MathematicsAnything that falls under this is quite hard. Do a pure mathematics IA only if you are crazily confident in your mathematical knowledge and skill.Proofs (by contradiction & induction) - weak induction is sufficient. Note that a lot of mathematical proofs are by contradiction. You must learn it and see many examples of the proofs.Prime numbers (Option 10)Linear diophantine equations (Option 10)Modular arithmetic and hence, Fermat’s Little Theorem (Option 10)Group theory (from Option 8)Lagrange’s theorem (from Option 8)Homomorphisms and isomorphism (from Option 8)Harder but more rewarding Pure MathematicsAnything that falls under here is super hard. But the journey of understanding things is very rewarding. Do this if and only if you have a suitable and sufficient math background beforehand. It is DEFINITELY not for everyone.Bounds on trigonometric functions or logarithms (this is super useful for mathematicians in general e.g. [math]|\sin x| \leq x[/math] for all [math]x[/math] real.)First Isomorphism TheoremThe First and Second Supplementary Laws to Quadratic Reciprocity (or even the Quadratic Reciprocity Law itself)Rational Root TheoremAlgebraic and transcendental numbersApplied MathematicsRudimentary topics are as below:Precalculus (Differentiation & integration) - obviously?Vectors (Dot product, cross product, triple scalar product)Trigonometry (clear applications, sine and cosines are everywhere)Probability & statistics (also everywhere)These are considered rudimentary because they form most of the tools used in more ‘advanced’ mathematics. Here are some of the more advanced (but still in syllabus) ones:Power series (very, very, very helpful but you have to understand it first! - from Option 9, anyone can do it)Matrices! (everyone can learn it, so many applications such as Linear maps)Linear ordinary differential equations (Linear ODEs - if you do Option 9)Inverse trigonometryGraph theory (if you do Option 10)Mean Value Theorem (MVT - Option 9 anyone can do it)Hypothesis testing & confidence intervals (if you do Option 7)Type I, type II error (if you do Option 7)etc.N.B. I put an anyone can do it wherever I feel that someone can just understand it by directly reading that particular topic and an if you do wherever I think you have to learn it step by step before diving into that particular topic. Say Hypothesis testing, you have to learn some new definitions first like the null and alternative hypotheses, significance level, critical region, which takes time to understand. However, such process sometimes can be quick depending on a person.Power series is put first and bolded because it gives so much new insight to the user when tackling a problem. The fact that I didn’t know how to understand it during my IB years (because I didn’t take the Calculus option) upsets me as it could have helped me to further my research a lot. An example of a power series is:[math]e^x = 1 + x + \dfrac{x^2}{2!} + \dfrac{x^3}{3!} + ... \,= \displaystyle \sum_{n=0}^{\infty} \dfrac{x^n}{n!}[/math]Very advanced:Multivariable calculus (Partial differentiation without integration as integration is harder). Use only when you truly need more than one variable to solve your problem.This falls under very advanced not because it is hard, but because it is out of the IB syllabus, which I am strongly against. However, there are certain conditions where you truly need to address your system in terms of two variables (or more), and such attempt would require the usage of multivariable calculus (also known as vector calculus).I hope this additional section would give some new insights on what topics you should focus on. However, note that I am in no position to discourage you from doing any other topics. This is just a suggestion by me in which, I think, is sufficient and feasible for any IB math HL IA student to take their time to learn, adapt despite their other IAs, EEs, TOKs and everything and apply in solving their problem in their respective IAs.Good luck again!EDIT:I’ve updated the example under Rigour to make it look more rigorous to give a better idea on what it really means for an IB level research paper.Added pictures of tools used to support Criterion A.Updated on how to read the set notation of the domain and codomain under the Rigour example.Added a (nice) application to the example under demonstrating thorough understanding.Added suggestions of topics that are feasible for a math IA for the average IB student.Remove a sentence regarding the norm as it is convention in the IB to write the norm as it is written up there.Added the MOST IMPORTANT ASPECT sectionMade small fixes, added more suggestions to feasible topics (25/5/2020). Thank you for 125 votes!Footnotes[1] Mathematics SL and HL teacher support material[2] Mathematics SL and HL teacher support material[3] Mathematics SL and HL teacher support material

A research analyst is a like an Journalist covering political, finance, technical & every thing related to oil & gas including new emerging technologies, new petroleum products & its techno-commercial feasibility, keep tracking the process licensors & its costs, …etc..Find below some subject jargon used by various organizations for their position for Business Research Analyst.As a Research Analyst, you will be responsible for collecting, analyzing and synthesizing information on key issues. You will develop client-ready industry overviews, case materials, financial analyses and other knowledge products in support of consultant teams. You will be responsible for working with consultants to scope and prioritize their research needs, identifying the key issues through discussions with requestors and, on that basis, to determine the most appropriate, cost-effective and timely research solutions. Gathering the necessary raw information from a broad spectrum of sources, you will analyze and synthesize your findings into targeted, McKinsey-formatted end products. These end products may be in the form of single exhibits, written summaries, basic fact packs, and spreadsheetsYou are encouraged to build a solid knowledge base, developing an appropriately broad understanding of the relevant structure, players, and trends in your topic area(s). To help build your expertise you will be leveraging internal and external networks, including leading industry sources and proprietary tools and models.At Frost & Sullivan, the role will evolve into a profile where you will be required to play a significant role understanding client’s business issues, challenges and aspirations. We believe that your ability to deliver solutions to clients’ problems will depend more on your talent, skills and real life business experience than just your degree, bring experienced marketing, market research and consulting experts who have significant exposure to, and a comprehensive understanding of, the Oil & Gas Upstream equipment and services markets in South Asia and Middle East, working on a variety of custom research and consulting projects. The ideal candidate brings a mix of strong domain knowledge, market experience and functional skills relating to market research and growth consulting.Track the developments in the Upstream Oil & Gas market regularly (technology developments, new projects, new opportunities, policies, supply chain)Work on a variety of syndicated market studies, custom research and consulting engagementsActively contribute in research and market analysis to execute bespoke consulting engagements in the Oil & Gas industryDevelop strategic content on specific industries and markets; contribute to print media, etc.Interact with analysts at different level in an empathetic manner with single minded focus on timely and successful completion of projectsResearch and Strategic Evaluation - Develop market intellectual property and powerful, actionable strategic recommendations based on a comprehensive understanding of the Client's markets/industrySupport Business Development – Assist the business development team in conducting detailed business needs analysis and demonstrate expert industry knowledge. Assist in creation of project proposals and ensure that a client's strategic intent translates into a Frost & Sullivan consulting solutionDomain Expertise - Act as a subject matter expert and provide advisory to the internal teamsThis is an exceptional opportunity focused on research and analysis into the Oil and Gas industry for a world leading consultancy.Working closely with consultants and clients you will be heavily involved in research and analytics into the industry, providing thought-provoking information and insight. Working on a variety of project areas including:- Regulatory affairs- Pricing- Logistics- Costs- Brands and branding- Commercial information- Company benchmarking (potential M&A's)Analysts to have extensive expertise across the entire energy value chain, and provide fact-based research and analysis on best practices and the use of information technology to assist energy companies to improve performance and maximize technology investments.

It's difficult to find an accurate and meaningful Australian map.Most internet images are out of date, inaccurate or based on projections and promises. I've included a copy of the "Broadband and Availability Quality and Summary Report" made in December 2013 for NBN Co. since this information is up to date.Here's a link to a commercial site that has aggregated the major telco's analyses. Interactive maps show the complex state of broadband coverage in Australia:Coverage Maps - Mobile and Broadband Coverage, Telstra, Optus, Vodafone Networks & MoreMost broadband in Australia relies on xDSL with speeds of 3 - 20Mb/sec. A few areas have received fibre optic NBN during the Labor Government's tenure and achieve up to 110Mb/sec. Those of us who live where cable TV is available, receive 40Mb/sec over the cable network. Many people rely on the 3G and 4G mobile networks for any broadband access.Broadband Availability and Quality: Summary Report23 December 2013Summary ReportThe Australian Government has indicated that it is determined that the many Australians without adequate fixed line broadband today will be prioritised in the rollout of the National Broadband Network (NBN). To assist with the prioritisation of the NBN rollout, the Government asked that the Department of Communications undertake an analysis of broadband quality and availability in all areas of Australia. This Summary Report is the first release of material from that analysis.Broadband services are delivered using a range of technologies across the country to homes and businesses, principally via digital subscriber line (xDSL) technology over the copper access network, 3G and 4G mobile networks, the hybrid fibre coaxial (HFC) networks, fibre-to-the-node (FTTN) networks and fibre-to-the-premises (FTTP) networks. In addition to terrestrial networks allAustralian premises are covered by satellite broadband networks.The findings are based on a spatial analysis of the coverage of broadband customer access networks, along with an estimate of their likely performance based on known constraints. This analysis used available information and measured broadband availability as a description of the infrastructure currently in place and used the possible speeds achievable over that infrastructure as the measure of quality. The methodology used in this analysis was determined after reference to international examples.Overall the analysis found that there are areas of inadequate access to infrastructure across the country and that approximately 1.4 million premises (13 per cent) are in areas where less than 40 per cent of premises can access a fixed broadband service. The premises in this group are located in regional or remote areas of Australia or distributed as small pockets of poor service in metropolitan and outer metropolitan areas.NBN Co’s recommended deployment scenario is included in the Strategic Review that was undertaken by the company between October and December 2013. The Strategic Review included estimated costs to allow for areas with poorer current broadband service to be prioritised. NBN Co will prioritise the areas of greatest need where this is logistically and commercially feasible.The key findings of this analysis of Australian broadband availability and quality are that approximately:Availability [1]9.9 million premises (91 per cent) have access to fixed line broadband services delivered via xDSL technology.3.1 million premises (28 per cent) have access to a high speed broadband platform including fibre-to-the-premises, fibre-to-the-node, hybrid fibre coaxial networks and fixed wireless networks.8.8 million premises (81 per cent) have access to 3G mobile broadband services and 6.4 million premises (59 per cent) have access to 4G services.All Australian premises are covered by satellite broadband, although there is a limit to the capacity of these services and therefore not all premises can access a service.Quality3.1 million premises (28 per cent) have access to peak download speeds of between 25 megabits per second (Mbps) to 110 Mbps download.7.1 million premises (65 per cent) are in areas that have access to peak median download speeds of less than 24 megabits per second over the copper network.0.7 million (6 per cent) premises are unable to get access to a fixed broadband service.Of the premises with access to xDSL broadband services over copper, 3.7 million of these are located in areas with an estimated peak median download speed of less than 9 Mbps, and 920,000 have an estimated peak median download speed of less than 4.8 Mbps.In summary (Figure 1), whilst there is a section of the Australian community who only have limited access to a broadband service, the more significant national issue is the quality of broadband services.xDSL QualityThe findings of this, and many other studies, note that the most common form of fixed broadband connection is provided by xDSL technologies, which reflects the widespread availability of this access technology. Figure 2 provides information on the percentage of premises with access to a xDSL service that are likely to receive particular xDSL median peak download speeds.Figure 2. Percentage of premises in each band of modeled median peak download speedsBroadband services are generally more available, and of higher quality, in metropolitan areas as compared to regional and remote areas. Although premises within regional and remote towns that are located close to the exchange do have access to higher quality xDSL services, premises located further away from the exchange and on the outskirts of towns do not. The analysis has also identified many small urban areas that have limited availability to fixed broadband services and a large number of premises that can access a basic service at speeds that are less than 9 Mbps.It is important to note that broadband availability and quality is affected by multiple factors. Key elements are considered in this analysis but there is a range of other factors that impact individual circumstances. There will be premises whose individual circumstances don’t accord with the high or low rating for broadband availability and quality that their local area has received in this analysis.Data InputsThis analysis was based on the following data inputs:current carrier network coverage data from all major telecommunications carriers, and a number of smaller players with customer access networks,reports from the Telstra Wholesale website,empirical xDSL usage data comprised of 20,000 real world xDSL download sync speeds and the associated cable loss and the location and number of small, medium and large pair gains, andthe locations and counts of premises was based on the Geocoded National Address File (G NAF).All data sources are current as at July to October 2013, with the exception of Telstra’s spatial representation of its mobile coverage (current as at January 2013). It is noted that telecommunications carriers continue to invest in infrastructure and broadband availability and quality is therefore dynamic. [2]This analysis represents a snapshot of broadband access as at December 2013.Next StepsThis Summary Report is the first release of material from the broadband availability and quality analysis and provides a national snapshot. The Department is refining the granular detail of the analysis and compiling maps which will be published along with the methodology used. There will be an opportunity to provide feedback on the methodology and the results.Further information on this analysis will also be available via a website that will allow end users to access the results for their local community and provide feedback on their individual experience.If you have any questions about this material please email [email protected].[1] The total of this section exceeds 100 per cent because the majority of premises have access to multiple broadband technologies.[2] Investment in the mobile market is resulting in expanding networks particularly in 4G coverage. Telstra announced on 18 December 2013 its 4G network coverage had expanded to reach 85 per cent of the Australian population. Optus has dual 4G networks and aims to expand its 4G coverage to over 70 per cent of the population in metropolitan areas by April 2014.Note: The government site from which I extracted this report promised up-to-date maps "soon", in December 2013. As of May, 2014, these maps are yet to appear. When they do, they should be an accurate source of information.Sources:1. Coverage Maps - Mobile and Broadband Coverage, Telstra, Optus, Vodafone Networks & More2. Page on google.com.au (Broadband Availability and Coverage: Summary Report, December 2013. Department of Communications, Australia. [PDF])