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 White Rose Maths - Year 4 - Block 4 - Divide by 10 (Problem Solving and Reasoning)Subject: Mathematics Age range: 7-11 Resource type: Worksheet/Activity  Last updated 30 November 2018 - Share through email
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A set of reasoning and problem solving worksheets to use alongside the White Rose Maths scheme. The questions have been differentiated 3 ways, each with an individual sheet of questions for that level. Answers are also included. This set of worksheets is for Year 4, Autumn Block 4 (Multiplication and Division), focusing on the third small step of dividing by 10. Details of how it has been differentiated can be found below: • 1 Star sheet (Working Towards Expected Level): Be able to solve problems by dividing 2 digit numbers by 10. • 2 Star sheet (Expected Level): Be able to solve problems by dividing 3 digit numbers by 10. • 3 Star sheet (Working at greater depth): Be able to solve problems by dividing 4 digit numbers by 10. Each worksheet contains a total of 8 questions. These questions could be used as a whole, or cut up into strips of 4 questions for a shorter task. They could also be used for partner work, depending on the ability of the children. If you have any questions, please feel free to ask. Likewise, I am still developing these resources, so any helpful comments would also be appreciated. Tes paid licence How can I reuse this? Get this resource as part of a bundle and save up to 38%A bundle is a package of resources grouped together to teach a particular topic, or a series of lessons, in one place. White Rose Maths - Year 4 - Block 4 - Multiplication and Division (Varied Fluency and Problem Solving and Reasoning Bundle)A set of varied fluency and a set of problem solving and reasoning worksheets to use alongside the White Rose Maths scheme. Both sets of questions have been differentiated 3 ways, each with an individual sheet of questions for that level. Answers are also included. These sets of worksheets are for Year 4, Autumn Block 4 (Multiplication and Division), with a set of worksheets focusing on each small step for varied fluency and problem solving and reasoning. Details of how they have been differentiated can be found below: Multiply by 10: • 1 Star sheet (Working Towards Expected Level): Be able to multiply 1 digit numbers, using place value counters where needed to help. • 2 Star sheet (Expected Level): Be able to multiply 2 digit numbers, using place value counters where needed to help. • 3 Star sheet (Working at greater depth): Be able to multiply 3 digit numbers, using place value counters where needed to help. Multiply by 100: • 1 Star sheet (Working Towards Expected Level): Be able to multiply 1 digit numbers by 100. • 2 Star sheet (Expected Level): Be able to multiply 2 digit numbers by 100. • 3 Star sheet (Working at greater depth): Be able to multiply 3 digit numbers by 100. Divide by 10: • 1 Star sheet (Working Towards Expected Level): Be able to divide 2-digit numbers by 10. • 2 Star sheet (Expected Level): Be able to divide 3-digit numbers by 10. • 3 Star sheet (Working at greater depth): Be able to divide 4-digit numbers by 10. Divide by 100: • 1 Star sheet (Working Towards Expected Level): Be able to divide 3 digit numbers by 100. • 2 Star sheet (Expected Level): Be able to divide 4 digit numbers by 100. • 3 Star sheet (Working at greater depth): Be able to divide 5 digit numbers by 100. Multiply and Divide by 1 and 0: • 1 Star sheet (Working Towards Expected Level): Be able to multiply and divide 1 digit numbers by 1 and 0. • 2 Star sheet (Expected Level): Be able to multiply and divide 2 digit numbers by 1 and 0. • 3 Star sheet (Working at greater depth): Be able to multiply and divide 3 digit numbers by 1 and 0. Multiply and Divide by 6: • 1 Star sheet (Working Towards Expected Level): Be able to multiply and divide by 6 up to and including 5x6. • 2 Star sheet (Expected Level): Be able to multiply and divide by 6 up to and including 12 x 6. • 3 Star sheet (Working at greater depth): Be able to use 6 times table facts to solve bigger multiplications past 12 x 6. Multiply and Divide by 9: • 1 Star sheet (Working Towards Expected Level): Be able to multiply and divide by 9, up to and including 5x9. • 2 Star sheet (Expected Level): Be able to multiply and divide by 9, up to and including 12x9. • 3 Star sheet (Working at greater depth): Be able to use 9 times table facts to solve bigger multiplications past 12x9. Multiply and Divide by 7: • 1 Star sheet (Working Towards Expected Level): Be able to multiply and divide by 7, up to and including 5x7. • 2 Star sheet (Expected Level): Be able to multiply and divide by 7, up to and including 12x7. • 3 Star sheet (Working at greater depth): Be able to use 7 times table facts to solve bigger multiplications past 12x7. The varied fluency worksheets contain a total of 8 questions, some broken down into parts (a, b, c etc.) with 2 examples of each question type. This provides children with the varied fluency that White Rose aim for. These questions can be used as a quick starter and cut up so that only the first 4 questions are used, or given as more of a main activity with all 8 questions. They could also be used for partner work, depending on the ability of the children. The problem solving and reasoning worksheets contain a total of either 6 or 8 questions. These questions could be used as a whole, or cut up into strips of 3 or 4 questions for a shorter task. They could also be used for partner work, depending on the ability of the children. If you have any questions, please feel free to ask. Likewise, I am still developing these resources, so any helpful comments would also be appreciated.  White Rose Maths - Year 4 - Block 4 - Multiplication and Division (Problem Solving and Reasoning practice)A set of reasoning and problem solving worksheets to use alongside the White Rose Maths scheme. The questions have been differentiated 3 ways, each with an individual sheet of questions for that level. Answers are also included. These sets of worksheets are for Year 4, Autumn Block 4 (Multiplication and Division), focusing on all the small steps. Details of how it has been differentiated can be found below: Multiply by 10: • 1 Star sheet (Working Towards Expected Level): Be able to multiply 1 digit numbers, using place value counters where needed to help. • 2 Star sheet (Expected Level): Be able to multiply 2 digit numbers, using place value counters where needed to help. • 3 Star sheet (Working at greater depth): Be able to multiply 3 digit numbers, using place value counters where needed to help. Multiply by 100: • 1 Star sheet (Working Towards Expected Level): Be able to multiply 1 digit numbers by 100. • 2 Star sheet (Expected Level): Be able to multiply 2 digit numbers by 100. • 3 Star sheet (Working at greater depth): Be able to multiply 3 digit numbers by 100. Divide by 10: • 1 Star sheet (Working Towards Expected Level): Be able to divide 2-digit numbers by 10. • 2 Star sheet (Expected Level): Be able to divide 3-digit numbers by 10. • 3 Star sheet (Working at greater depth): Be able to divide 4-digit numbers by 10. Divide by 100: • 1 Star sheet (Working Towards Expected Level): Be able to divide 3 digit numbers by 100. • 2 Star sheet (Expected Level): Be able to divide 4 digit numbers by 100. • 3 Star sheet (Working at greater depth): Be able to divide 5 digit numbers by 100. Multiply and Divide by 1 and 0: • 1 Star sheet (Working Towards Expected Level): Be able to multiply and divide 1 digit numbers by 1 and 0. • 2 Star sheet (Expected Level): Be able to multiply and divide 2 digit numbers by 1 and 0. • 3 Star sheet (Working at greater depth): Be able to multiply and divide 3 digit numbers by 1 and 0. Multiply and Divide by 6: • 1 Star sheet (Working Towards Expected Level): Be able to multiply and divide by 6 up to and including 5x6. • 2 Star sheet (Expected Level): Be able to multiply and divide by 6 up to and including 12 x 6. • 3 Star sheet (Working at greater depth): Be able to use 6 times table facts to solve bigger multiplications past 12 x 6. Multiply and Divide by 9: • 1 Star sheet (Working Towards Expected Level): Be able to multiply and divide by 9, up to and including 5x9. • 2 Star sheet (Expected Level): Be able to multiply and divide by 9, up to and including 12x9. • 3 Star sheet (Working at greater depth): Be able to use 9 times table facts to solve bigger multiplications past 12x9. Multiply and Divide by 7: • 1 Star sheet (Working Towards Expected Level): Be able to multiply and divide by 7, up to and including 5x7. • 2 Star sheet (Expected Level): Be able to multiply and divide by 7, up to and including 12x7. • 3 Star sheet (Working at greater depth): Be able to use 7 times table facts to solve bigger multiplications past 12x7. Each worksheet contains a total of either 6 or 8 questions. These questions could be used as a whole, or cut up into strips of 3 or 4 questions for a shorter task. They could also be used for partner work, depending on the ability of the children. If you have any questions, please feel free to ask. Likewise, I am still developing these resources, so any helpful comments would also be appreciated. White Rose Maths - Year 4 - Block 4 - Divide by 10 (Varied Fluency and Problem Solving)A set of varied fluency and a set of problem solving and reasoning worksheets to use alongside the White Rose Maths scheme. Both sets of questions have been differentiated 3 ways, each with an individual sheet of questions for that level. Answers are also included. This set of worksheets is for Year 4, Autumn Block 4 (Multiplication and Division), focusing on the third small step of dividing by 10. Details of how it has been differentiated can be found below: • 1 Star sheet (Working Towards Expected Level): Be able to divide 2-digit numbers by 10. • 2 Star sheet (Expected Level): Be able to divide 3-digit numbers by 10. • 3 Star sheet (Working at greater depth): Be able to divide 4-digit numbers by 10. The varied fluency worksheets contain a total of 8 questions, some broken down into parts (a, b, c etc.) with 2 examples of each question type. This provides children with the varied fluency that White Rose aim for. These questions can be used as a quick starter and cut up so that only the first 4 questions are used, or given as more of a main activity with all 8 questions. They could also be used for partner work, depending on the ability of the children. The problem solving and reasoning worksheets contain a total of 8 questions. These questions could be used as a whole, or cut up into strips of 4 questions for a shorter task. They could also be used for partner work, depending on the ability of the children. If you have any questions, please feel free to ask. Likewise, I am still developing these resources, so any helpful comments would also be appreciated. Your rating is required to reflect your happiness. It's good to leave some feedback. Something went wrong, please try again later. This resource hasn't been reviewed yet To ensure quality for our reviews, only customers who have purchased this resource can review it Report this resource to let us know if it violates our terms and conditions. Our customer service team will review your report and will be in touch. Not quite what you were looking for? 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 Use our online Division Calculator to effortlessly find the quotient of two numbers. Simply input the dividend and divisor, then hit the '=' button to see the division outcome. The Division Calculator is an online tool crafted meticulously to assist users in performing division tasks with utmost precision. Core Functionality: This digital marvel effortlessly divides any two numbers, whether they're whole numbers, fractions, or decimals, presenting results in a clear, easy-to-understand format. Key Features: - Instant Results: Say goodbye to tedious manual calculations.
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The Division Calculator isn't just a tool—it's a bridge to understanding, designed to make division a simpler, more approachable concept for all. Whether for academic, professional, or personal use, it stands ready to serve. Our Division Calculator is designed to swiftly and accurately perform division operations. Whether you're dividing large numbers, fractions, or decimals, this tool provides the answer instantly, saving you time and ensuring accuracy. - Antilog calculator
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Division CalculatorDivision is one of the four basic operations of arithmetic, the others being addition, divideion, and multiplication. The division of two natural numbers is the process of calculating the number of times one number is contained within the other. Division can also be thought of as the process of evaluating a fraction, and fractional notation (a ⁄ b) is commonly used to represent division. Everyday CalculationFree calculators and unit converters for general and everyday use. Calculators » Math » Long division with steps Long Division CalculatorOur online tools will provide quick answers to your calculation and conversion needs. On this page, you can divide two numbers using long division method with step by step instruction. Numbers may be whole numbers, integers, or decimals Sample: 205 divided by 2 using long division Divide each digit of the dividend with the divisor starting from left to right. Bring down the next digit after each step as shown below: Divide 2 by 2. Write the remainder after subtracting the bottom number from the top number. Bring down next digit 0. Divide 0 by 2. Write the remainder after subtracting the bottom number from the top number. Bring down next digit 5. Divide 05 by 2. Write the remainder after subtracting the bottom number from the top number. 4. Put the decimal point. Remember: A decimal number, say, 3 can be written as 3.0, 3.00 and so on. Bring down next digit 0. Divide 10 by 2. Write the remainder after subtracting the bottom number from the top number. End of long division (Remainder is 0 and next digit after decimal is 0). 205 ÷ 2 = 102.5 More Math Calculators- Square root with division
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Solving Boolean Satisfiability Problems With The Quantum Approximate Optimization AlgorithmSami boulebnane and ashley montanaro, prx quantum 5 , 030348 – published 10 september 2024. Supplemental Material- INTRODUCTION
- DEFINITIONS AND PRELIMINARIES
- ACKNOWLEDGMENTS
One of the most prominent application areas for quantum computers is solving hard constraint satisfaction and optimization problems. However, detailed analyses of the complexity of standard quantum algorithms have suggested that outperforming classical methods for these problems would require extremely large and powerful quantum computers. The quantum approximate optimization algorithm (QAOA) is designed for near-term quantum computers, yet previous work has shown strong limitations on the ability of QAOA to outperform classical algorithms for optimization problems. Here we instead apply QAOA to hard constraint satisfaction problems, where both classical and quantum algorithms are expected to require exponential time. We analytically characterize the average success probability of QAOA on a constraint satisfaction problem commonly studied using statistical physics methods: random k -SAT at the threshold for satisfiability, as the number of variables n goes to infinity. We complement these theoretical results with numerical experiments on the performance of QAOA for small n , which match the limiting theoretical bounds closely. We then compare QAOA with leading classical solvers. For random 8-SAT, we find that for more than 14 quantum circuit layers, QAOA achieves more efficient scaling than the highest-performance classical solver we tested, WalkSATlm. Our results suggest that near-term quantum algorithms for solving constraint satisfaction problems may outperform their classical counterparts.  - Received 19 September 2023
- Revised 28 July 2024
- Accepted 5 August 2024
DOI: https://doi.org/10.1103/PRXQuantum.5.030348  Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Published by the American Physical Society Physics Subject Headings (PhySH)Authors & Affiliations- Phasecraft Ltd. , Bristol, United Kingdom
- * Contact author: [email protected]
- † Also at University College London.
- ‡ Also at University of Bristol.
Popular SummaryCombinatorial optimization—optimizing a function over a discrete domain—is considered a promising application of quantum computers. The quantum approximate optimization algorithm (QAOA) is the best-known near-term quantum algorithm for this task. The algorithm nonetheless poses several challenges. On the theoretical side, the techniques for predicting the algorithm's performance remain limited. On the practical side, QAOA depends on a set of hyperparameters to be tuned; this task could potentially be a difficult optimization problem of its own. In this work, we address these issues for a specific combinatorial optimization problem: k -SAT, one of the most fundamental and well-studied problems in computer science. When applying QAOA to this constraint satisfaction problem, we aim at producing an exact solution (satisfying all constraints) rather than maximizing the quality of the solution, as is usually done in the literature. Also, we use common QAOA hyperparameters for all k -SAT instances rather than training them on an instance-by-instance basis. In this setting, we develop analytic methods to estimate the probability of QAOA outputting an exact solution to k -SAT as the instance size goes to infinity. These results are validated and complemented by a set of numerical experiments, pointing to a potential advantage of QAOA over best-known classical algorithms for k -SAT. A natural next step in this line of research is to determine the ultimate extent of the acceleration over classical algorithms and to shed light on the problem structures QAOA leverages to achieve speedup.  Article TextVol. 5, Iss. 3 — September - November 2024  Authorization RequiredOther options. - Buy Article »
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Download & ShareComparison of numerical results to limiting theoretical predictions. Top: points are empirical averages. Solid lines are fits to empirical averages, dashed lines are scaling predicted by theory (assuming unknown constant factor is 1). Error bars are too small to be seen. Bottom: points are relative differences in excess scaling exponents between numerical and theoretical results, solid lines are added to guide the eye. (a) k = 8 , varying p ; (b) p = 1 , varying k . Scaling behavior of QAOA on random k -SAT. Top: analytic scaling exponents c in terms of p , such that success probability is predicted to be 2 − c n up to lower-order terms. Fit to a power law for each k . Fits are c ≈ 0.13 p − 1.12 ( k = 2 ), c ≈ 0.57 p − 0.51 ( k = 4 ), c ≈ 0.69 p − 0.32 ( k = 8 ). Bottom: median running time (solid line) compared with running time estimated from average success probability for random 8-SAT instances (dashed line). Lines are linear fits. Error bars are too small to be seen. Scaling behavior of median running times of selected classical and quantum algorithms for 8-SAT. WalkSAT QAOA uses p = 60 . Running times of QAOA compared with WalkSATlm for random 8-SAT. Top: scaling exponent α in running time approximately 2 α n for QAOA estimated by inverting analytic ( p ≤ 10 ) and numerical ( p ≤ 60 ) results on average probabilities, and from numerical results on median running times for n ∈ { 12 , … , 20 } . Horizontal line is experimentally estimated WalkSATlm median running time scaling exponent. Other lines are fits. Blue dashed line is fitting based on all p , blue solid line is using p ≤ 10 . Error bars are too small to be seen. Bottom: histogram of ratios of running times of QAOA ( p = 60 ) and WalkSAT for n = 20 instances. QAOA optimization landscape at p = 1 and for k = 2 . By periodicity (following from the integrality of the cost function), β and γ can be, respectively, restricted to [ − π , π ] and [ − 2 π , 2 π ] . In case the represented function is negligible except on a small part of this domain, we choose to enlarge the rectangle while keeping centered at 0 ; for instance, when enlarging by a factor of 2 , the represented domain is [ − ( π / 2 ) , ( π / 2 ) ] × [ π , π ] . The central symmetry is a general feature of QAOA, applying to all cost functions and diagonal unitaries. (a) Logarithmic success probability. (b) Exponential fit. (c) Correlation coefficient. QAOA optimization landscape at p = 1 and for k = 4 (enlargement: 2 × ). (a) Logarithmic success probability. (b) Exponential fit. (c) Correlation coefficient. QAOA optimization landscape at p = 1 and for k = 8 (enlargement: 2 × ). (a) Logarithmic success probability. (b) Exponential fit. (c) Correlation coefficient. QAOA optimization landscape at p = 1 and for k = 16 (enlargement: 4 × ). (a) Logarithmic success probability. (b) Exponential fit. (c) Correlation coefficient. Relative variation of scaling exponent and optimized angles after reoptimization from analytic method. The relative error for the exponent is defined as the ratio between the new and old value, minus 1. For angles, the distance between the old angles ( β (i) , γ (i) ) and the new ones ( β (f) , γ (f) ) is calculated by considering the representative of ( β (f) , γ (f) ) closest to the ( β (i) , γ (i) ) in order to account for 2 π periodicity in the β j and 4 π periodicity in the γ j . The β components of the difference vector ( β (f) − β (i) , γ (f) − γ (i) ) are then rescaled by ( 1 / ( π 2 p ) ) , and the γ components by ( 1 / ( 2 π 2 p ) ) , mapping the 2 -norm of the resulting vector into [ 0 , 1 ] . (a) Exponent. (b) Angles. Sign up to receive regular email alerts from PRX Quantum Reuse & PermissionsIt is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures. - Forgot your username/password?
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 | | x^{\msquare} | \log_{\msquare} | \sqrt{\square} | \nthroot[\msquare]{\square} | \le | \ge | \frac{\msquare}{\msquare} | \cdot | \div | x^{\circ} | \pi | | \left(\square\right)^{'} | \frac{d}{dx} | \frac{\partial}{\partial x} | \int | \int_{\msquare}^{\msquare} | \lim | \sum | \infty | \theta | (f\:\circ\:g) | f(x) | | | ▭\:\longdivision{▭} | \times \twostack{▭}{▭} | + \twostack{▭}{▭} | - \twostack{▭}{▭} | \left( | \right) | \times | \square\frac{\square}{\square} | - Pre Algebra Order of Operations Factors & Primes Fractions Long Arithmetic Decimals Exponents & Radicals Ratios & Proportions Percent Modulo Number Line Expanded Form Mean, Median & Mode
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| | x^{\msquare} | \log_{\msquare} | \sqrt{\square} | \nthroot[\msquare]{\square} | \le | \ge | \frac{\msquare}{\msquare} | \cdot | \div | x^{\circ} | \pi | | \left(\square\right)^{'} | \frac{d}{dx} | \frac{\partial}{\partial x} | \int | \int_{\msquare}^{\msquare} | \lim | \sum | \infty | \theta | (f\:\circ\:g) | f(x) | | | - \twostack{▭}{▭} | \lt | 7 | 8 | 9 | \div | AC | | + \twostack{▭}{▭} | \gt | 4 | 5 | 6 | \times | \square\frac{\square}{\square} | | \times \twostack{▭}{▭} | \left( | 1 | 2 | 3 | - | x | | ▭\:\longdivision{▭} | \right) | . | 0 | = | + | y | - long\:division\:\frac{121}{19}
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We want your feedbackPlease add a message. Message received. Thanks for the feedback. Microsoft will start charging for Windows 10 updates next year. Here's how much As Windows 10 begins its final year of official support, Microsoft is executing a familiar game plan for its business customers. Also: What is a TPM, and why does Windows 11 require one? Last April, in separate posts on the Windows IT Pro Blog and on the Microsoft Education Blog , the company revealed its price list for commercial and education customers who want to continue receiving security updates for Windows 10 after the end-of-support deadline arrives on October 14, 2025. The company has previously confirmed that it plans to offer a version of this program for consumers, but those details still a complete mystery. Here's what we know so far. How much will Windows 10 updates cost?Business customers will need to pay dearly to stick with Windows 10. A license for the Extended Security Updates (ESU) program is sold as a subscription. For the first year, the cost is $61. For year two, the price doubles, and it doubles again for year three. That Microsoft blog post doesn't do the math on those, probably because the total is uncomfortably high. A three-year ESU subscription will cost $61 + $122 + $244, for a total of $427 per PC. Also: How to upgrade your 'incompatible' Windows 10 PC to Windows 11 The program closely resembles what Microsoft offered for Windows 7's end-of-support date in 2020, although the Windows 10 price is 22% higher than the $350 total cost of that program, which started at $50 for year one. Don't think you can game the system by jumping into the program after sitting out for a year or two. "ESUs are cumulative," Microsoft said, and you can't buy year two unless you've already paid for year one. Education customers are getting off much easier. The rules are the same, but the price for the first year is $1. It doubles to $2 in the second year and doubles again to $4 in the third and final year, for a grand total of ... $7 per PC. Also: Yes, you can upgrade that old PC to Windows 11, even if Microsoft says no. These readers proved it Administrators who want to get a head start can sign up for the first year of an ESU license as early as October 2024, one year before the actual end-of-support date. As was the case with Windows 7, Redmond really wants business customers to upgrade to Windows 11, which explains the high price tag. Microsoft's April announcements talk just as much about what you don't get with an ESU license as they do about the updates themselves. Extended Security Updates are not intended to be a long-term solution but rather a temporary bridge. ESUs do not include new features, non-security fixes, or design change requests. The ESU program does not extend technical support for Windows 10. Technical support is limited to the activation of the ESU licenses, installation of ESU monthly updates, and addressing issues that may have been caused due to an update itself. What discounts are available?Businesses that use one of Microsoft's official cloud-based update management services, like Microsoft Intune and Windows AutoPatch, get a discount that takes the first year cost down to $45, but Microsoft doesn't specify what happens in the second and third years. Those solutions are mainly applicable to very large organizations that pay for Windows Enterprise edition licenses and manage them in the cloud, and it's worth noting that the option applies only to devices that are owned by an organization; personal (BYOD) devices aren't eligible. There's also an option for businesses that sign up for Windows 365. Subscribers who access a Windows 11 Cloud PC on Windows 365 from a physical device running Windows 10 automatically get an ESU license for their Windows 10 PC. Similar discounts are available for devices running Azure Virtual Desktop. Also: The best Windows laptop you can buy Microsoft also says it plans to offer discounts to nonprofit organizations, but details aren't available on that yet either. What about consumers and small businesses?On the page that announced details of the ESU program for commercial customers, a Microsoft spokesperson wrote that details and prices for consumers "will be shared at a later date" on the company's consumer end-of-support page . Five months later, those details are still missing. "Final pricing and enrollment conditions will be made available closer to the October 2025 date for end of support" is the official word on that page. Also: Still have a Windows 10 PC? You have 5 options before support ends next year In the meantime, the tens or hundreds of millions of consumers and small businesses stuck on Windows 10 -- because their hardware isn't supported on Windows 11 -- are still waiting for word on what they're supposed to do. Microsoft's recommendation, naturally, is "Buy a new PC." But asking customers to throw away a perfectly good PC seems like a strange ask from a company that touts its sustainability efforts. The Windows 7 ESU program was messy. It was not exactly friendly to small businesses and there was no option at all for consumers. The difference, of course, is that those customers had a straightforward option to upgrade to the successor OS, Windows 10. It's possible that Microsoft will be more prepared this time around. It better be, because a frightfully large number of PCs will need support when October 2025 rolls around. Note: This post was originally published in April 2024. The most recent update was on September 10, 2024. Still have a Windows 10 PC? You have 5 options before support ends next yearMicrosoft has a big windows 10 problem, and only one year to solve it, windows 11 finally outscores windows 10 among pc gamers. An Adaptive Differential Evolution Algorithm Based on Data Preprocessing Method and a New Mutation Strategy to Solve Dynamic Economic Dispatch Considering Generator Constraints- Published: 08 September 2024
Cite this article - Ruxin Zhao ORCID: orcid.org/0000-0002-6810-2631 1 ,
- Wei Wang 1 ,
- Tingting Zhang 1 ,
- Chang Liu 2 ,
- Lixiang Fu 1 ,
- Jiajie Kang 1 ,
- Hongtan Zhang 1 ,
- Yang Shi 1 &
- Chao Jiang 1
Differential evolution (DE) algorithm is a classical natural-inspired optimization algorithm which has a good. However, with the deepening of research, some researchers found that the quality of the candidate solution of the population in the differential evolution algorithm is poor and its global search ability is not enough when solving the global optimization problem. Therefore, in order to solve the above problems, we proposed an adaptive differential evolution algorithm based on the data processing method and a new mutation strategy (ADEDPMS). In this paper, the data preprocessing method is implemented by k -means clustering algorithm, which is used to divide the initial population into multiple clusters according to the average value of fitness, and select candidate solutions in each cluster according to different proportions. This method improves the quality of candidate solutions of the population to a certain extent. In addition, in order to solve the problem of insufficient global search ability in differential evolution algorithm, we also proposed a new mutation strategy, which is called “DE/current-to- \({p}_{1}\) best& \({p}_{2}\) best”. This strategy guides the search direction of the differential evolution algorithm by selecting individuals with good fitness, so that its search range is in the most promising candidate solution region, and indirectly increases the population diversity of the algorithm. We also proposed an adaptive parameter control method, which can effectively balance the relationship between the exploration process and the exploitation process to achieve the best performance. In order to verify the effectiveness of the proposed algorithm, the ADEDPMS is compared with five optimization algorithms of the same type in the past three years, which are AAGSA, DFPSO, HGASSO, HHO and VAGWO. In the simulation experiment, 6 benchmark test functions and 4 engineering example problems are used, and the convergence accuracy, convergence speed and stability are fully compared. We used ADEDPMS to solve the dynamic economic dispatch (ED) problem with generator constraints. It is compared with the optimization algorithms used to solve the ED problem in the last three years which are AEFA, AVOA, OOA, SCA and TLBO. The experimental results show that compared with the five latest optimization algorithms proposed in the past three years to solve benchmark functions, engineering example problems and the ED problem, the proposed algorithm has strong competitiveness in each test index. This is a preview of subscription content, log in via an institution to check access. Access this articleSubscribe and save. - Get 10 units per month
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Price includes VAT (Russian Federation) Instant access to the full article PDF. Rent this article via DeepDyve Institutional subscriptions  Similar content being viewed by others Optimization of economic dispatch using updated differential evolution algorithmDynamic economic dispatch based on improved differential evolution algorithm.  Automated Differential Evolution for Solving Dynamic Economic Dispatch ProblemsExplore related subjects. Data availabilityThe materials and associated data will be made available on rational request. Al-Betar, M. A., Awadallah, M. A., Zitar, R. A., & Assaleh, K. (2023). Economic load dispatch using memetic sine cosine algorithm. Journal of Ambient Intelligence and Humanized Computing, 14 (9), 11685–11713. Article Google Scholar Andrei, N. (2008). An unconstrained optimization test functions collection. Advanced Modeling Optimization, 10 (1), 147–161. Google Scholar Anita, Yadav, A., & Kumar, N. (2021). 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Author informationAuthors and affiliations. School of Information Engineering, Yangzhou University, Yangzhou, 225127, Jiangsu, China Ruxin Zhao, Wei Wang, Tingting Zhang, Lixiang Fu, Jiajie Kang, Hongtan Zhang, Yang Shi & Chao Jiang School of Intelligent Manufacturing, Yangzhou Polytechnic Institute, Yangzhou, 225127, Jiangsu, China You can also search for this author in PubMed Google Scholar ContributionsRuxin Zhao, Wei Wang and Tingting Zhang wrote the main manuscript text. Chang Liu, Jiajie Kang and Lixiang Fu prepared figures and tables. Hongtan Zhang, Shi Yang and Chao Jiang were responsible for editing. All authors reviewed the manuscript. Corresponding authorCorrespondence to Ruxin Zhao . Ethics declarationsConflict of interest. The authors declared that they have no conflicts of interest to this work. Informed consentFor all the above contents and statements, all authors in this manuscript have informed consent. Additional informationPublisher's note. Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Rights and permissionsSpringer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Reprints and permissions About this articleZhao, R., Wang, W., Zhang, T. et al. An Adaptive Differential Evolution Algorithm Based on Data Preprocessing Method and a New Mutation Strategy to Solve Dynamic Economic Dispatch Considering Generator Constraints. Comput Econ (2024). https://doi.org/10.1007/s10614-024-10705-2 Download citation Accepted : 20 August 2024 Published : 08 September 2024 DOI : https://doi.org/10.1007/s10614-024-10705-2 Share this articleAnyone you share the following link with will be able to read this content: Sorry, a shareable link is not currently available for this article. Provided by the Springer Nature SharedIt content-sharing initiative - Differential evolution algorithm
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Differential evolution (DE) algorithm is a classical natural-inspired optimization algorithm which has a good. However, with the deepening of research, some researchers found that the quality of the candidate solution of the population in the differential evolution algorithm is poor and its global search ability is not enough when solving the global optimization problem. Therefore, in order to ...