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# Shunsuke Inenaga

According to our database1, Shunsuke Inenaga authored at least 182 papers between 2001 and 2018.

Collaborative distances:
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## Bibliography

2018
Tighter Bounds and Optimal Algorithms for All Maximal α-gapped Repeats and Palindromes - Finding All Maximal α-gapped Repeats and Palindromes in Optimal Worst Case Time on Integer Alphabets.
Theory Comput. Syst., 2018

A hardness result and new algorithm for the longest common palindromic subsequence problem.
Inf. Process. Lett., 2018

Dynamic RLE-Compressed Edit Distance Tables Under General Weighted Cost Functions.
Int. J. Found. Comput. Sci., 2018

Diverse Palindromic Factorization is NP-Complete.
Int. J. Found. Comput. Sci., 2018

Right-to-left online construction of parameterized position heaps.
CoRR, 2018

O(n log n)-time text compression by LZ-style longest first substitution.
CoRR, 2018

Block Palindromes: A New Generalization of Palindromes.
CoRR, 2018

Recovering, Counting and Enumerating Strings from Forward and Backward Suffix Arrays.
Proceedings of the String Processing and Information Retrieval, 2018

Block Palindromes: A New Generalization of Palindromes.
Proceedings of the String Processing and Information Retrieval, 2018

Longest Lyndon Substring After Edit.
Proceedings of the Annual Symposium on Combinatorial Pattern Matching, 2018

Computing longest common square subsequences.
Proceedings of the Annual Symposium on Combinatorial Pattern Matching, 2018

Lyndon Factorization of Grammar Compressed Texts Revisited.
Proceedings of the Annual Symposium on Combinatorial Pattern Matching, 2018

Longest substring palindrome after edit.
Proceedings of the Annual Symposium on Combinatorial Pattern Matching, 2018

Faster Online Elastic Degenerate String Matching.
Proceedings of the Annual Symposium on Combinatorial Pattern Matching, 2018

2017
Inferring strings from Lyndon factorization.
Theor. Comput. Sci., 2017

The "Runs" Theorem.
SIAM J. Comput., 2017

Packed Compact Tries: A Fast and Efficient Data Structure for Online String Processing.
IEICE Transactions, 2017

Efficient Dynamic Dictionary Matching with DAWGs and AC-automata.
CoRR, 2017

Small-space encoding LCE data structure with constant-time queries.
CoRR, 2017

Linear-size CDAWG: new repetition-aware indexing and grammar compression.
CoRR, 2017

Computing Abelian regularities on RLE strings.
CoRR, 2017

Order preserving pattern matching on trees and DAGs.
CoRR, 2017

Faster STR-IC-LCS computation via RLE.
CoRR, 2017

On Two LZ78-style Grammars: Compression Bounds and Compressed-Space Computation.
CoRR, 2017

Efficient Computation of Substring Equivalence Classes with Suffix Arrays.
Algorithmica, 2017

On Reverse Engineering the Lyndon Tree.
Proceedings of the Prague Stringology Conference 2017, 2017

Linear-Size CDAWG: New Repetition-Aware Indexing and Grammar Compression.
Proceedings of the String Processing and Information Retrieval, 2017

Order Preserving Pattern Matching on Trees and DAGs.
Proceedings of the String Processing and Information Retrieval, 2017

On Two LZ78-style Grammars: Compression Bounds and Compressed-Space Computation.
Proceedings of the String Processing and Information Retrieval, 2017

Longest Common Subsequence in at Least k Length Order-Isomorphic Substrings.
Proceedings of the SOFSEM 2017: Theory and Practice of Computer Science, 2017

Computing Longest Single-arm-gapped Palindromes in a String.
Proceedings of the SOFSEM 2017: Theory and Practice of Computer Science, 2017

Small-Space LCE Data Structure with Constant-Time Queries.
Proceedings of the 42nd International Symposium on Mathematical Foundations of Computer Science, 2017

Computing Abelian String Regularities Based on RLE.
Proceedings of the Combinatorial Algorithms - 28th International Workshop, 2017

Shortest Unique Palindromic Substring Queries in Optimal Time.
Proceedings of the Combinatorial Algorithms - 28th International Workshop, 2017

Almost Linear Time Computation of Maximal Repetitions in Run Length Encoded Strings.
Proceedings of the 28th International Symposium on Algorithms and Computation, 2017

Tight Bounds on the Maximum Number of Shortest Unique Substrings.
Proceedings of the 28th Annual Symposium on Combinatorial Pattern Matching, 2017

Faster STR-IC-LCS Computation via RLE.
Proceedings of the 28th Annual Symposium on Combinatorial Pattern Matching, 2017

Computing All Distinct Squares in Linear Time for Integer Alphabets.
Proceedings of the 28th Annual Symposium on Combinatorial Pattern Matching, 2017

2016
Generalized pattern matching and periodicity under substring consistent equivalence relations.
Theor. Comput. Sci., 2016

Faster Lyndon factorization algorithms for SLP and LZ78 compressed text.
Theor. Comput. Sci., 2016

Closed factorization.
Discrete Applied Mathematics, 2016

Longest Common Subsequence in at Least k Length Order-isomorphic Substrings.
CoRR, 2016

Deterministic sub-linear space LCE data structures with efficient construction.
CoRR, 2016

Packed Compact Tries: A Fast and Efficient Data Structure for Online String Processing.
CoRR, 2016

Dynamic index and LZ factorization in compressed space.
CoRR, 2016

Fully dynamic data structure for LCE queries in compressed space.
CoRR, 2016

Computing longest single-arm-gapped palindromes in a string.
CoRR, 2016

Shortest unique palindromic substring queries in optimal time.
CoRR, 2016

Tight bound on the maximum number of shortest unique substrings.
CoRR, 2016

A hardness result and new algorithm for the longest common palindromic subsequence problem.
CoRR, 2016

Computing All Distinct Squares in Linear Time for Integer Alphabets.
CoRR, 2016

Dynamic Index and LZ Factorization in Compressed Space.
Proceedings of the Prague Stringology Conference 2016, 2016

Computing Smallest and Largest Repetition Factorizations in O(n log n) Time.
Proceedings of the Prague Stringology Conference 2016, 2016

Efficiently Finding All Maximal alpha-gapped Repeats.
Proceedings of the 33rd Symposium on Theoretical Aspects of Computer Science, 2016

Compacting a Dynamic Edit Distance Table by RLE Compression.
Proceedings of the SOFSEM 2016: Theory and Practice of Computer Science, 2016

Fully Dynamic Data Structure for LCE Queries in Compressed Space.
Proceedings of the 41st International Symposium on Mathematical Foundations of Computer Science, 2016

Shortest Unique Substring Queries on Run-Length Encoded Strings.
Proceedings of the 41st International Symposium on Mathematical Foundations of Computer Science, 2016

Computing DAWGs and Minimal Absent Words in Linear Time for Integer Alphabets.
Proceedings of the 41st International Symposium on Mathematical Foundations of Computer Science, 2016

Packed Compact Tries: A Fast and Efficient Data Structure for Online String Processing.
Proceedings of the Combinatorial Algorithms - 27th International Workshop, 2016

Finding Gapped Palindromes Online.
Proceedings of the Combinatorial Algorithms - 27th International Workshop, 2016

Deterministic Sub-Linear Space LCE Data Structures With Efficient Construction.
Proceedings of the 27th Annual Symposium on Combinatorial Pattern Matching, 2016

Fully-online Construction of Suffix Trees for Multiple Texts.
Proceedings of the 27th Annual Symposium on Combinatorial Pattern Matching, 2016

Factorizing a String into Squares in Linear Time.
Proceedings of the 27th Annual Symposium on Combinatorial Pattern Matching, 2016

2015
Compressed automata for dictionary matching.
Theor. Comput. Sci., 2015

Dynamic edit distance table under a general weighted cost function.
J. Discrete Algorithms, 2015

Constructing LZ78 tries and position heaps in linear time for large alphabets.
Inf. Process. Lett., 2015

Detecting regularities on grammar-compressed strings.
Inf. Comput., 2015

Fully-online construction of suffix trees and DAWGs for multiple texts.
CoRR, 2015

Dynamic index, LZ factorization, and LCE queries in compressed space.
CoRR, 2015

Constructing LZ78 Tries and Position Heaps in Linear Time for Large Alphabets.
CoRR, 2015

Efficiently Finding All Maximal $α$-gapped Repeats.
CoRR, 2015

Diverse Palindromic Factorization is NP-Complete.
CoRR, 2015

Computing Left-Right Maximal Generic Words.
Proceedings of the Prague Stringology Conference 2015, 2015

A Faster Longest Common Extension Algorithm on Compressed Strings and its Applications.
Proceedings of the Prague Stringology Conference 2015, 2015

A Faster Algorithm for Computing Maximal \alpha -gapped Repeats in a String.
Proceedings of the String Processing and Information Retrieval, 2015

Efficient Algorithms for Longest Closed Factor Array.
Proceedings of the String Processing and Information Retrieval, 2015

A new characterization of maximal repetitions by Lyndon trees.
Proceedings of the Twenty-Sixth Annual ACM-SIAM Symposium on Discrete Algorithms, 2015

Inferring Strings from Full Abelian Periods.
Proceedings of the Algorithms and Computation - 26th International Symposium, 2015

Diverse Palindromic Factorization Is NP-complete.
Proceedings of the Developments in Language Theory - 19th International Conference, 2015

Semi-dynamic Compact Index for Short Patterns and Succinct van Emde Boas Tree.
Proceedings of the Combinatorial Pattern Matching - 26th Annual Symposium, 2015

LZD Factorization: Simple and Practical Online Grammar Compression with Variable-to-Fixed Encoding.
Proceedings of the Combinatorial Pattern Matching - 26th Annual Symposium, 2015

An Opportunistic Text Indexing Structure Based on Run Length Encoding.
Proceedings of the Algorithms and Complexity - 9th International Conference, 2015

2014
Inferring strings from suffix trees and links on a binary alphabet.
Discrete Applied Mathematics, 2014

A new characterization of maximal repetitions by Lyndon trees.
CoRR, 2014

Computing Abelian Covers and Abelian Runs.
Proceedings of the Prague Stringology Conference 2014, Prague, Czech Republic, 2014

Closed Factorization.
Proceedings of the Prague Stringology Conference 2014, Prague, Czech Republic, 2014

Faster Compact On-Line Lempel-Ziv Factorization.
Proceedings of the 31st International Symposium on Theoretical Aspects of Computer Science (STACS 2014), 2014

Shortest Unique Substrings Queries in Optimal Time.
Proceedings of the SOFSEM 2014: Theory and Practice of Computer Science, 2014

Inferring Strings from Lyndon Factorization.
Proceedings of the Mathematical Foundations of Computer Science 2014, 2014

Computing Palindromic Factorizations and Palindromic Covers On-line.
Proceedings of the Combinatorial Pattern Matching - 25th Annual Symposium, 2014

2013
Palindrome pattern matching.
Theor. Comput. Sci., 2013

Fast q-gram mining on SLP compressed strings.
J. Discrete Algorithms, 2013

Foreword.
Int. J. Comput. Math., 2013

Faster Compact On-Line Lempel-Ziv Factorization
CoRR, 2013

Detecting regularities on grammar-compressed strings
CoRR, 2013

Efficient Lyndon factorization of grammar compressed text
CoRR, 2013

Computing convolution on grammar-compressed text
CoRR, 2013

Compressed Automata for Dictionary Matching.
Proceedings of the Implementation and Application of Automata, 2013

Computing Reversed Lempel-Ziv Factorization Online.
Proceedings of the Prague Stringology Conference 2013, Prague, Czech Republic, 2013

Faster Lyndon Factorization Algorithms for SLP and LZ78 Compressed Text.
Proceedings of the String Processing and Information Retrieval, 2013

Permuted Pattern Matching on Multi-track Strings.
Proceedings of the SOFSEM 2013: Theory and Practice of Computer Science, 2013

Detecting Regularities on Grammar-Compressed Strings.
Proceedings of the Mathematical Foundations of Computer Science 2013, 2013

Computing Convolution on Grammar-Compressed Text.
Proceedings of the 2013 Data Compression Conference, 2013

From Run Length Encoding to LZ78 and Back Again.
Proceedings of the 2013 Data Compression Conference, 2013

Efficient Lyndon Factorization of Grammar Compressed Text.
Proceedings of the Combinatorial Pattern Matching, 24th Annual Symposium, 2013

Converting SLP to LZ78 in almost Linear Time.
Proceedings of the Combinatorial Pattern Matching, 24th Annual Symposium, 2013

2012
An efficient algorithm to test square-freeness of strings compressed by straight-line programs.
Inf. Process. Lett., 2012

Finding Characteristic Substrings from Compressed Texts.
Int. J. Found. Comput. Sci., 2012

Efficient LZ78 factorization of grammar compressed text
CoRR, 2012

Time and Space Efficient Lempel-Ziv Factorization based on Run Length Encoding
CoRR, 2012

Speeding-up $q$-gram mining on grammar-based compressed texts
CoRR, 2012

The Position Heap of a Trie.
Proceedings of the String Processing and Information Retrieval, 2012

Efficient LZ78 Factorization of Grammar Compressed Text.
Proceedings of the String Processing and Information Retrieval, 2012

Computing q-Gram Non-overlapping Frequencies on SLP Compressed Texts.
Proceedings of the SOFSEM 2012: Theory and Practice of Computer Science, 2012

Speeding Up q-Gram Mining on Grammar-Based Compressed Texts.
Proceedings of the Combinatorial Pattern Matching - 23rd Annual Symposium, 2012

2011
Verifying and enumerating parameterized border arrays.
Theor. Comput. Sci., 2011

Password Based Anonymous Authentication with Private Information Retrieval.
JDIM, 2011

Missing pattern discovery.
J. Discrete Algorithms, 2011

Computing q-gram Non-overlapping Frequencies on SLP Compressed Texts
CoRR, 2011

Computing q-gram Frequencies on Collage Systems
CoRR, 2011

Restructuring Compressed Texts without Explicit Decompression
CoRR, 2011

Fast $q$-gram Mining on SLP Compressed Strings
CoRR, 2011

Computing Longest Common Substring/Subsequence of Non-linear Texts.
Proceedings of the Prague Stringology Conference 2011, 2011

Inferring Strings from Suffix Trees and Links on a Binary Alphabet.
Proceedings of the Prague Stringology Conference 2011, 2011

Fast q-gram Mining on SLP Compressed Strings.
Proceedings of the String Processing and Information Retrieval, 2011

Faster Subsequence and Don't-Care Pattern Matching on Compressed Texts.
Proceedings of the Combinatorial Pattern Matching - 22nd Annual Symposium, 2011

Palindrome Pattern Matching.
Proceedings of the Combinatorial Pattern Matching - 22nd Annual Symposium, 2011

An Anonymous Authentication Protocol with Single-database PIR.
Proceedings of the Ninth Australasian Information Security Conference, 2011

2010
An Efficient Algorithm to Test Square-Freeness of Strings Compressed by Balanced Straight Line Programs.
Chicago J. Theor. Comput. Sci., 2010

Counting and Verifying Maximal Palindromes.
Proceedings of the String Processing and Information Retrieval, 2010

Dynamic Edit Distance Table under a General Weighted Cost Function.
Proceedings of the SOFSEM 2010: Theory and Practice of Computer Science, 2010

An Identifiable Yet Unlinkable Authentication System with Smart Cards for Multiple Services.
Proceedings of the Computational Science and Its Applications, 2010

Verifying a Parameterized Border Array in O(n1.5) Time.
Proceedings of the Combinatorial Pattern Matching, 21st Annual Symposium, 2010

2009
Efficient algorithms to compute compressed longest common substrings and compressed palindromes.
Theor. Comput. Sci., 2009

Linear-Time Text Compression by Longest-First Substitution.
Algorithms, 2009

Finding Characteristic Substrings from Compressed Texts.
Proceedings of the Prague Stringology Conference 2009, Prague, Czech Republic, August 31, 2009

Modeling Costs of Access Control with Various Key Management Systems.
Proceedings of the International Conference on Parallel and Distributed Processing Techniques and Applications, 2009

Towards Modeling Stored-value Electronic Money Systems.
Proceedings of the World Congress on Nature & Biologically Inspired Computing, 2009

Counting Parameterized Border Arrays for a Binary Alphabet.
Proceedings of the Language and Automata Theory and Applications, 2009

Lightweight Parameterized Suffix Array Construction.
Proceedings of the Combinatorial Algorithms, 20th International Workshop, 2009

Testing Square-Freeness of Strings Compressed by Balanced Straight Line Program.
Proceedings of the Theory of Computing 2009, 2009

2008
Reachability on Suffix Tree Graphs.
Int. J. Found. Comput. Sci., 2008

Parameterized Suffix Arrays for Binary Strings.
Proceedings of the Prague Stringology Conference 2008, Prague, Czech Republic, 2008

Computing Longest Common Substring and All Palindromes from Compressed Strings.
Proceedings of the SOFSEM 2008: Theory and Practice of Computer Science, 2008

String Kernels Based on Variable-Length-Don't-Care Patterns.
Proceedings of the Discovery Science, 11th International Conference, 2008

An Efficient Algorithm to Test Square-Freeness of Strings Compressed by Balanced Straight Line Program.
Proceedings of the Structure-Based Compression of Complex Massive Data, 22.06., 2008

2007
Simple Linear-Time Off-Line Text Compression by Longest-First Substitution.
Proceedings of the 2007 Data Compression Conference (DCC 2007), 2007

Efficient Computation of Substring Equivalence Classes with Suffix Arrays.
Proceedings of the Combinatorial Pattern Matching, 18th Annual Symposium, 2007

2006
Sparse compact directed acyclic word graphs.
Proceedings of the Prague Stringology Conference, 2006

Reachability on suffix tree graphs.
Proceedings of the Prague Stringology Conference, 2006

Sparse Directed Acyclic Word Graphs.
Proceedings of the String Processing and Information Retrieval, 2006

A New Family of String Classifiers Based on Local Relatedness.
Proceedings of the Discovery Science, 9th International Conference, 2006

On-Line Linear-Time Construction of Word Suffix Trees.
Proceedings of the Combinatorial Pattern Matching, 17th Annual Symposium, 2006

2005
A fully compressed pattern matching algorithm for simple collage systems.
Int. J. Found. Comput. Sci., 2005

On-line construction of compact directed acyclic word graphs.
Discrete Applied Mathematics, 2005

Composite Pattern Discovery for PCR Application.
Proceedings of the String Processing and Information Retrieval, 2005

Fully Incremental LCS Computation.
Proceedings of the Fundamentals of Computation Theory, 15th International Symposium, 2005

Practical Algorithms for Pattern Based Linear Regression.
Proceedings of the Discovery Science, 8th International Conference, 2005

2004
Ternary directed acyclic word graphs.
Theor. Comput. Sci., 2004

Compact directed acyclic word graphs for a sliding window.
J. Discrete Algorithms, 2004

Efficiently Finding Regulatory Elements Using Correlation with Gene Expression.
J. Bioinformatics and Computational Biology, 2004

Finding Missing Patterns.
Proceedings of the Algorithms in Bioinformatics, 4th International Workshop, 2004

A Fully Compressed Pattern Matching Algorithm for Simple Collage Systems.
Proceedings of the Prague Stringology Conference 2004, Prague, Czech Republic, August 30, 2004

An Efficient Pattern Matching Algorithm on a Subclass of Context Free Grammars.
Proceedings of the Developments in Language Theory, 2004

Finding Optimal Pairs of Cooperative and Competing Patterns with Bounded Distance.
Proceedings of the Discovery Science, 7th International Conference, 2004

2003
Bidirectional Construction of Suffix Trees.
Nord. J. Comput., 2003

A Note on Randomized Algorithm for String Matching with Mismatches.
Nord. J. Comput., 2003

Ternary Directed Acyclic Word Graphs.
Proceedings of the Implementation and Application of Automata, 2003

Linear-Time Off-Line Text Compression by Longest-First Substitution.
Proceedings of the String Processing and Information Retrieval, 2003

Inferring Strings from Graphs and Arrays.
Proceedings of the Mathematical Foundations of Computer Science 2003, 2003

Discovering Most Classificatory Patterns for Very Expressive Pattern Classes.
Proceedings of the Discovery Science, 6th International Conference, 2003

2002
Bidirectional Construction of Suffix Trees.
Proceedings of the Prague Stringology Conference 2002, Prague, Czech Republic, 2002

A Note on Randomized Algorithm for String Matching with Mismatches.
Proceedings of the Prague Stringology Conference 2002, Prague, Czech Republic, 2002

Compact Directed Acyclic Word Graphs for a Sliding Window.
Proceedings of the String Processing and Information Retrieval, 2002

Space-Economical Construction of Index Structures for All Suffixes of a String.
Proceedings of the Mathematical Foundations of Computer Science 2002, 2002

Finding Best Patterns Practically.
Proceedings of the Progress in Discovery Science, 2002

Discovering Best Variable-Length-Don't-Care Patterns.
Proceedings of the Discovery Science, 5th International Conference, 2002

The Minimum DAWG for All Suffixes of a String and Its Applications.
Proceedings of the Combinatorial Pattern Matching, 13th Annual Symposium, 2002

2001
Construction of the CDAWG for a Trie.
Proceedings of the Prague Stringology Conference 2001, Prague, Czech Republic, 2001

On-Line Construction of Symmetric Compact Directed Acyclic Word Graphs.
Proceedings of the Eighth International Symposium on String Processing and Information Retrieval, 2001

A Practical Algorithm to Find the Best Episode Patterns.
Proceedings of the Discovery Science, 4th International Conference, DS 2001, Washington, 2001

On-Line Construction of Compact Directed Acyclic Word Graphs.
Proceedings of the Combinatorial Pattern Matching, 12th Annual Symposium, 2001


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First, the generalized power function rule. When you compute df /dt for f(t)=Cekt, you get Ckekt because C and k are constants. Jump to: navigation, search. Chain rule. If the derivatives a' and b' are continuous, then F' is continuous, given the continuity of f and f' 1. 2.1 Applications; Statement. These rules are also known as Partial Derivative rules. The chain rule will allow us to create these âuniversal â relationships between the derivatives of different coordinate systems. Hot Network Questions Reversed DIP Switch Why does DOS ask for the current date and time upon booting? 0. Finding relationship using the triple product rule for partial derivatives. These three âhigher-order chain rulesâ are alternatives to the classical Fa`a di Bruno formula. The inner function is the one inside the parentheses: x 2-3.The outer function is â(x). 1 Statement. #4 Report 5 years ago #4 (Original post by swagadon) df(x-ct) /dt doesnt equal -cdf(x-ct) / dt though? you are probably on a mobile phone). Tree diagrams are useful for deriving formulas for the chain rule for functions of more than one variable, where each independent variable also depends on â¦ I have to calculate partial du/dt and partial du/dx . Note that a function of three variables does not have a graph. 11 Partial derivatives and multivariable chain rule 11.1 Basic deï¬ntions and the Increment Theorem One thing I would like to point out is that youâve been taking partial derivatives all your calculus-life. Contents. âx ây Since, ultimately, w is a function of u and v we can also compute the partial derivatives âw âw and . Using the chain rule and the derivatives of sin(x) and x², we can then find the derivative of sin(x²). Clip: Total Differentials and Chain Rule > Download from iTunes U (MP4 - 111MB) > Download from Internet Archive (MP4 - 111MB) > Download English-US caption (SRT) The following images show the chalkboard contents from these video excerpts. To find its partial derivative with respect to x we treat y as a constant (imagine y is a number like 7 or something): fâ x = 2x + 0 = 2x. If z is a function of y and y is a function of x, then the derivative of z with respect to x can be written \frac{dz}{dx} = \frac{dz}{dy}\frac{dy}{dx}. The chain rule states that the derivative of f(g(x)) is f'(g(x))âg'(x). atsruser Badges: 11. Nov 7, 2020 #29 haruspex. Notes Practice Problems Assignment Problems. Due to the nature of the mathematics on this site it is best views in landscape mode. Let's return to the very first principle definition of derivative. Thus the chain rule implies the expression for F'(t) in the result. The counterpart of the chain rule in integration is the substitution rule. The chain rule for functions of more than one variable involves the partial derivatives with respect to all the independent variables. Partial differentiation - chain rule. Use the new quotient rule to take the partial derivatives of the following function: Not-so-basic rules of partial differentiation. \ \end{equation*} 14. But this right here has a name, this is the multivariable chain rule. Given that f is continuous, both of these partial derivatives are continuous, so by a previous result G is differentiable. chain rule x-ct=u du/dt=-c df(x-ct) /dt = df(u)/du * du/dt = df(u)/du *-c , not -cdf(x-ct) / dt ive tried a new change of variables x+ct=y x-ct=s this gave me Vxx - Vtt/c^2 = 4Vys and I think Vys is zero since V= g(y) + f(s) 0. reply. Let z = z(u,v) u = x2y v = 3x+2y 1. The method of solution involves an application of the chain rule. âu âv âw âw âx âw ây = + âu âx âu ây âu âw âw âx âw ây = + . The following chain rule examples show you how to differentiate (find the derivative of) many functions that have an âinner functionâ and an âouter function.âFor an example, take the function y = â (x 2 â 3). Introduction to the multivariable chain rule. Examples. Partial Derivative Solver Learn more about partial derivatives chain rule 0. Click each image to enlarge. Prev. From Calculus. Just as in the previous univariate section, we have two specialized rules that we now can apply to our multivariate case. Show Mobile Notice Show All Notes Hide All Notes. Find â2z ây2. Section. The triple product rule, known variously as the cyclic chain rule, cyclic relation, cyclical rule or Euler's chain rule, is a formula which relates partial derivatives of three interdependent variables. The basic concepts are illustrated through a simple example. Chain Rule for Second Order Partial Derivatives To ï¬nd second order partials, we can use the same techniques as ï¬rst order partials, but with more care and patience! Insights Author. Be aware that the notation for second derivative is produced by including a 2nd prime. The notation df /dt tells you that t is the variables and everything else you see is a constant. Mobile Notice. Quite simply, you want to recognize what derivative rule applies, then apply it. Science Advisor. 1.1 Statement for function of two variables composed with two functions of one variable; 1.2 Conceptual statement for a two-step composition; 1.3 Statement with symbols for a two-step composition; 2 Related facts. Rep:? Apply the chain rule to find the partial derivatives \begin{equation*} \frac{\partial T}{\partial\rho}, \frac{\partial T}{\partial\phi}, \ \mbox{and} \ \frac{\partial T}{\partial\theta}. Example. Chain rule for partial differentiation. Chain rule: partial derivative Discuss and solve an example where we calculate partial derivative. Differentiation of algebraic and trigonometric expressions can be used for calculating rates of change, stationary points and their nature, or the gradient and equation of a tangent to a curve. â¢ The formulas for calculating such derivatives are dz dt = @f @x dx dt + @f @y dy dt and @z @t = @f @x @x @t + @f @y @y @t â¢ To calculate a partial derivative of a variable with respect to another requires im-plicit diâµerentiation @z @x = Fx Fz, @z @y = Fy Fz Summary of Ideas: Chain Rule and Implicit Diâµerentiation 134 of 146 Just like ordinary derivatives, partial derivatives follows some rule like product rule, quotient rule, chain rule etc. Use the Chain Rule to find the indicated partial derivatives. For example, @w=@x means diï¬erentiate with respect to x holding both y and z constant and so, for this example, @w=@x = sin(y + 3z). Hi there, I am given that u = F(x - ct), where F() is ANY function. Home / Calculus III / Partial Derivatives / Chain Rule. Homework Helper. Before using the chain rule, letâs obtain $$(\partial f/\partial x)_y$$ and $$(\partial f/\partial y)_x$$ by re-writing the function in terms of $$x$$ and $$y$$. For example, sin(x²) is a composite function because it can be constructed as f(g(x)) for f(x)=sin(x) and g(x)=x². Partial derivatives are computed similarly to the two variable case. If you are going to follow the above Second Partial Derivative chain rule then thereâs no question in the books which is going to worry you. If â¦ And it's important enough, I'll just write it out all on it's own here. Boas' "Mathematical Methods in the Physical Sciences" is less than helpful. $u = xe^{ty}$, $x = \alpha^2 \beta$, $y = \beta^2 \gamma$, $t = \gamma^2 \alpha$; $\dfrac{\partial u}{\partial \alpha}$, $\dfrac{\partial u}{\partial \beta}$, $\dfrac{\partial u}{\partial \gamma}$ when $\alpha = -1$, $\beta = 2$, $\gamma = 1$ JS Joseph S. Numerade Educator 01:56. In other words, it helps us differentiate *composite functions*. Partial Derivatives Chain Rule. Problem in understanding Chain rule for partial derivatives. = 3x2e(x3+y2) using the chain rule â2z âx2 = â(3x2) âx e(x3+y2) +3x2 â(e (x3+y2)) âx using the product rule â2z âx2 = 6xe(x3+y2) +3x2(3x2e(x3+y2)) = (9x4 +6x)e(x3+y2) Section 3: Higher Order Partial Derivatives 10 In addition to both â2z âx2 and â2z ây2, when there are two variables there is also the possibility of a mixed second order derivative. Since w is a function of x and y it has partial derivatives and . But what about a function of two variables (x and y): f(x,y) = x 2 + y 3. In calculus, the chain rule is a formula for determining the derivative of a composite function. You appear to be on a device with a "narrow" screen width (i.e. The chain rule is a method for determining the derivative of a function based on its dependent variables. The chain rule relates these derivatives by the following formulas. Partial Derivative Rules. The chain rule for functions of more than one variable involves the partial derivatives with respect to all the independent variables. Solution: We will ï¬rst ï¬nd â2z ây2. Tree diagrams are useful for deriving formulas for the chain rule for functions of more than one variable, where each independent variable also depends on other variables. This rule is called the chain rule for the partial derivatives of functions of functions. and partial du/dx = . And its derivative (using the Power Rule): fâ(x) = 2x . I looked for resources that describe the application of the chain rule to these types of partial derivatives, but I can find nothing. The chain rule for this case will be âzâs=âfâxâxâs+âfâyâyâsâzât=âfâxâxât+âfâyâyât. In this article students will learn the basics of partial differentiation. For example, the surface in Figure 1a can be represented by the Cartesian equation z=x^{2}-y^{2}. Next Section . This calculator calculates the derivative of a function and then simplifies it. Chain Rules for Higher Derivatives H.-N. Huang, S. A. M. Marcantognini and N. J. However, the same surface can also be represented in polar coordinates \left(r,\,\theta \right), by the equation z=r^{2}\cos \,2\theta (see Figure 1b). The Chain Rule for Partial Derivatives Implicit Differentiation: Examples & Formula Double Integration: Method, Formulas & Examples Is there a YouTube video or a book that better describes how to approach a problem such as this one? Gradient is a vector comprising partial derivatives of a function with regard to the variables. Young September 23, 2005 We deï¬ne a notion of higher-order directional derivative of a smooth function and use it to establish three simple formulae for the nth derivative of the composition of two functions. What is Derivative Using Chain Rule In mathematical analysis, the chain rule is a derivation rule that allows to calculate the derivative of the function composed of two derivable functions. Related Topics: More Lessons for Engineering Mathematics Math Worksheets A series of free Engineering Mathematics video lessons. Partial derivatives are usually used in vector calculus and differential geometry. Chain Rule and Partial Derivatives. The Chain Rule Something we frequently do in mathematics and its applications is to transform among different coordinate systems.

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The MOLLER experiment

# The MOLLER experiment

The MOLLER experiment at Jefferson Lab will measure the weak charge of the electron, , $Q^e _W = 1 - 4 sin^2 \theta _W$ by measuring the PV asymmetry in electron-electron scattering. The measured asymmetry will be sensitive to faint but measurable deviations from precisely calculable predictions from SM. The MOLLER experiment will provide the best contact interaction search for leptons at low or high energy making it a probe of physics beyond the SM with sensitivities to mass scales of new PV physics up to 7.5 TeV. Such unprecedented sensitivity will results in a unique opportunity to new physics at the multi-TeV scale complementary to direct searches at high energy colliders. Possible new physics sensitivities include new $Z^0$ bosons and low mass dark-Z bosons. Best current limit on contact interaction scales available from LEP2 but LEP2 is only sensitive to parity conserving quantities ($g^2 _{RL}$ and $g^2 _{RR}+ g^2 _{LL}$) while MOLLER will be sensitive to parity violating new physics interactions.


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# Using Green's Theorem

Tags:
1. Apr 28, 2015

### Calpalned

1. The problem statement, all variables and given/known data
Use Green's Theorem to evaluate the line integral along the given positively oriented curve.

1) Is the statement above the same as finding the area enclosed?
2) $\int_C \cos ydx + x^2\sin ydy$, C is the rectangle with vertices (0,0) (5,0) (5,2) and (0,2).
3) $\int_C y^4 dx + 2xy^3dy$, C is the ellipse $x^2 + xy^2 = 2$
4) $\int_C {(1-y^3)dx + (x^3+e^\psi)dy}$, where $\psi = y^2$ and C is the boundary of the region between the circles $x^2 + y^2 =4$ and $x^2 + y^2 =9$

2. Relevant equations
n/a

3. The attempt at a solution
I solved all of these questions, with the exception of the first one. Unfortunately, these do not come with answers, so I would like to check if my answers are correct. For questions 2 to 3, I just wrote out Green's double integral.

1) Yes
2) $\int_0^2 \int_0^5 (\sin y(2x+1)) dxdy$
3) $\int \int -2\sin ^3 \theta d \theta$
4) $\int_0^{2\pi} \int_2^3 3r^3 drd \theta$

I think I got #1 and #3 wrong. If they are wrong, I will put up my original solution attempt. .

Note to self: Stewart, page 1090, 1 refers to question 6, 2 = 8 and 3 = 10.

Thanks everyone!

Last edited: Apr 28, 2015
2. Apr 28, 2015

### HallsofIvy

Staff Emeritus
To evaluate what line integral? Do you mean each of 2, 3, 4, below? (So this does not apply to 1.)

Green's Theorem says that $\oint_C P(x,y)dx+ Q(x,y)dy= \int\int_D \left(\frac{\partial Q}{\partial x}- \frac{\partial P}{\partial y}\right)dxdy$
Since area is given by $\int\int_D dxdy$ that will give the area if and only if $\frac{\partial Q}{\partial x}- \frac{\partial P}{\partial y}= 1$ and that will depend upon what P and Q are.

This is not an ellipse. At first I thought you meant just $x^2+ y^2= 2$ but that would be called a circle, not ellipse.

I would have thought Green's Theorem would be a "relevant equation"!

In (2), P(x,y)= y and $Q(x,y)= x^2 sin(y)$ So $Q_x- P_y= 2x sin(y)- 1$ NOT $sin(y)(2x+ 1)$

Assuming the "ellipse" was actually the circle $x^2+ y^2= 2$ then you are missing a factor of $\sqrt{2}$

This one is set up correctly. What did you get for the actual integrals?

3. Apr 28, 2015

### Zondrina

#1 is correct. Green's theorem allows you to find the area of a region $D$ with a positively oriented, piecewise-smooth, simple closed curve $C$ making up the boundary.

#2 is correct.

#3 needs some work. First of all, the boundary curve $C$ is not $x^2 + xy^2 = 2$, but is actually $x^2 + 2y^2 = 2$ according to Stewart question #8. Now that we actually have an ellipse of the form $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 2$, it can be parametrized by means of the equations:

$$x = a \text{cos}(\theta) = \text{cos}(\theta)$$
$$y = b \text{sin}(\theta) = \frac{1}{\sqrt{2}} \text{sin}(\theta)$$

Now, what happens to $-2y^3$? What will be the limits of integration?

#4 is correct.

Last edited: Apr 28, 2015
4. Apr 28, 2015

### Calpalned

Oops, number three should have been $x^2+ 2y^2= 2$

5. Apr 28, 2015

### Calpalned

I solved number two again and I still got the same integral. Additionally, Zondrina says I'm right


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Dor Marciano: On the first undefinable ordinal

BGU Seminar in Logic, Set Theory and Topology.

Please take note of the one-time change in room!

Time: Tuesday, March 29th, 12:30-13:45.

Place: Room 124, building 72.
Speaker:

Dor Marciano (HUJI).

Title: On the first undefinable ordinal

Abstract:
The argument “there are only countably many definitions in the language of set theory, therefore there are uncountably many undefinable reals” is fallacious. The same applies for the argument suggesting that the first undefinable (first order, no parameters) ordinal must be countable, and the two statements are closely linked.

In the paper “Pointwise definable models of Set Theory” by Joel Hamkins et all, countable models of set theory are constructed in which every element is definable.
We shall demonstrate a couple of these constructions,
and then move on to consider models in which there are undefinable ordinals.
We’ll show that in well-founded models of V=L there exists a dichotomy: Either the first undefinable ordinal is countable (according to the model), or it does not exist.
We’ll construct well-founded models of ZFC (given very low-strength consistency hypotheses) in which the first undefinable ordinal is uncountable (according to the model).
We’ll show that the consistency strength of “The first undefinable ordinal is a cardinal” is roughly that of an inaccessible cardinal, and that the consistency strength of “The first undefinable ordinal is a regular cardinal” is roughly that of a Mahlo cardinal.

Note: The lecture will be given in two sessions (this week, and the next). Basic knowledge of forcing is recommended, but not completely required – as notions and facts about the relevant forcings will be stated.

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# App does not run with VS 2008 SP1 DLLs, previous version works with RTM versions

Since our switch from Visual Studio 6 to Visual Studio 2008, we've been using the MFC90.dll and msvc[pr]90.dlls along with the manifest files in a private side-by-side configuration so as to not worry about versions or installing them to the system.

Pre-SP1, this was working fine (and still works fine on our developer machines). Now that we've done some testing post-SP1 I've been pulling my hair out since yesterday morning.

First off, our NSIS installer script pulls the dlls and manifest files from the redist folder. These were no longer correct, as the app still links to the RTM version.

So I added the define for _BIND_TO_CURRENT_VCLIBS_VERSION=1 to all of our projects so that they will use the SP1 DLLs in the redist folder (or subsequent ones as new service packs come out). It took me hours to find this.

I've double checked the generated manifest files in the intermediate files folder from the compilation, and they correctly list the 9.0.30729.1 SP1 versions. I've double and triple checked depends on a clean machine: it all links to the local dlls with no errors.

Running the app still gets the following error:

The application failed to initialize properly (0xc0150002). Click on OK to terminate the application.

None of the searches I've done on google or microsoft have come up with anything that relates to my specific issues (but there are hits back to 2005 with this error message).

Any one had any similar problem with SP1?

Options:

• Find the problem and fix it so it works as it should (preferred)
• Install the redist
• dig out the old RTM dlls and manifest files and remove the #define to use the current ones. (I've got them in an earlier installer build, since Microsoft blasts them out of your redist folder!)

Edit: I've tried re-building with the define turned off (link to RTM dlls), and that works as long as the RTM dlls are installed in the folder. If the SP1 dlls are dropped in, it gets the following error:

c:\Program Files\...\...\X.exe

This application has failed to start because the application configuration is incorrect. Reinstalling the application may fix this problem.

Has no-one else had to deal with this issue?

Edit: Just for grins, I downloaded and ran the vcredist_x86.exe for VS2008SP1 on my test machine. It works. With the SP1 DLLs. And my RTM linked app. But NOT in a private side-by-side distribution that worked pre-SP1.

I have battled this problem myself last week and consider myself somewhat of an expert now ;)

I'm 99% sure that not all dlls and static libraries were recompiled with the SP1 version. You need to put

#define _BIND_TO_CURRENT_MFC_VERSION 1
#define _BIND_TO_CURRENT_CRT_VERSION 1

into every project you're using. For every project of a real-world size, it's very easy to forget some small lib that wasn't recompiled.

There are more flags that define what versions to bind to; it's documented on http://msdn.microsoft.com/en-us/library/cc664727%28v=vs.90%29.aspx . As an alternative to the lines above, you can also put

#define _BIND_TO_CURRENT_VCLIBS_VERSION 1

which will bind to the latest version of all VC libs (CRT, MFC, ATL, OpenMP).

Then, check what the embedded manifest says. Download XM Resource Editor: http://www.wilsonc.demon.co.uk/d10resourceeditor.htm. Open every dll and exe in your solution. Look under 'XP Theme Manifest'. Check that the 'version' attribute on the right-hand side is '9.0.30729.1'. If it's '9.0.21022', some static library is pulling in the manifest for the old version.

What I found is that in many cases, both versions were included in the manifest. This means that some libraries use the sp1 version and others don't.

A great way to debug which libraries don't have the preprocessor directives set: temporarily modify your platform headers so that compilation stops when it tries to embed the old manifest. Open C:\Program Files\Microsoft Visual Studio 9.0\VC\crt\include\crtassem.h. Search for the '21022' string. In that define, put something invalid (change 'define' to 'blehbleh' or so). This way, when you're compiling a project where the _BIND_TO_CURRENT_CRT_VERSION preprocessor flag is not set, your compilation will stop and you'll know that you need to add them or made sure that it's applied everywhere.

Also make sure to use Dependency Walker so that you know what dlls are being pulled in. It's easiest to install a fresh Windows XP copy with no updates (only SP2) on a virtual machine. This way you know for sure that there is nothing in the SxS folder that is being used instead of the side-by-side dlls that you supplied.

• Depends never showed what was missing on my clean VM (might need to make sure I've got the latest version!), but using the Resource Editor, I found the offending DLL. It was a DLL we compile but that is not part of our project. Thanks for the help. – crashmstr Sep 16 '08 at 13:59
• I got the newer version of Dependency Walker, and it called out problems immediately with the specific DLLs that were a problem. – crashmstr Sep 16 '08 at 17:28
• Roel's crtassem.h edit technique is great for finding compilation units that don't include stdafx.h that may still be binding the wrong lib versions. – Aidan Ryan Apr 28 '11 at 2:28
• Raises hands to the sky Thank you, thank you, thank you! Not only did that work, but I actually understand why. A combination of sxstrace to determine which component was crying about what sxs dependency and these defines to make the manifest point in the right direction, woot! – Erikest Apr 29 '14 at 0:02

To understand the problem, I think it is important to realize that there are four version numbers involved:

• (A) The version of the VC header files to which the .exe is compiled.
• (B) The version of the manifest file that is embedded in the resources section of that .exe. By default, this manifest file is automatically generated by Visual Studio.
• (C) The version of the VC .DLLs (part of the side-by-side assembly) you copy in the same directory as the .exe.
• (D) The version of the VC manifest files (part of the side-by-side assembly) you copy in the same directory as the .exe.

There are two versions of the VC 2008 DLL's in the running:

• v1: 9.0.21022.8
• v2: 9.0.30729.4148

For clarity, I'll use the v1/v2 notation. The following table shows a number of possible situations:

Situation | .exe (A) | embedded manifest (B) | VC DLLs (C) | VC manifests (D)
-----------------------------------------------------------------------------
1         | v2       | v1                    | v1          | v1
2         | v2       | v1                    | v2          | v2
3         | v2       | v1                    | v2          | v1
4         | v2       | v2                    | v2          | v2

The results of these situations when running the .exe on a clean Vista SP1 installation are:

• Situation 1: a popup is shown, saying: "The procedure entry point XYZXYZ could not be located in the dynamic link library".

• Situation 2: nothing seems to happen when running the .exe, but the following event is logged in Windows' "Event Viewer / Application log":

Activation context generation failed for "C:\Path\file.exe".Error in manifest or policy file "C:\Path\Microsoft.VC90.CRT.MANIFEST" on line 4. Component identity found in manifest does not match the identity of the component requested. Reference is Microsoft.VC90.CRT,processorArchitecture="x86",publicKeyToken="1fc8b3b9a1e18e3b",type="win32",version="9.0.21022.8". Definition is Microsoft

• Situation 3: everything seems to work fine. This is remicles2's solution.

• Situation 4: this is how it should be done. Regrettably, as Roel indicates, it can be rather hard to implement.

Now, my situation (and I think it is the same as crashmstr's) is nr 1. The problem is that Visual Studio for one reason or another generates client code (A) for v2, but for one reason or another, generates a v1 manifest file (B). I have no idea where version (A) can be configured.

Note that this whole explanation is still in the context of private assemblies.

Update: finally I start to understand what is going on. Apparently, Visual Studio generates client code (A) for v2 by default, contrary to what I've read on some Microsoft blogs. The _BIND_TO_CURRENT_VCLIBS_VERSION flag only selects the version in the generated manifest file (B), but this version will be ignored when running the application.

## Conclusion

An .exe that is compiled by Visual Studio 2008 links to the newest versions of the VC90 DLLs by default. You can use the _BIND_TO_CURRENT_VCLIBS_VERSION flag to control which version of the VC90 libraries will be generated in the manifest file. This indeed avoids situation 2 where you get the error message "manifest does not match the identity of the component requested". It also explains why situation 3 works fine, as even without the _BIND_TO_CURRENT_VCLIBS_VERSION flag the application is linked to the newest versions of the VC DLLs.

The situation is even weirder with public side-by-side assemblies, where vcredist was run, putting the VC 9.0 DLLs in the Windows SxS directory. Even if the .exe's manifest file states that the old versions of the DLLs should be used (this is the case when the _BIND_TO_CURRENT_VCLIBS_VERSION flag is not set), Windows ignores this version number by default! Instead, Windows will use a newer version if present on the system, except when an "application configuration file" is used.

Am I the only one who thinks this is confusing?

So in summary:

• For private assemblies, use the _BIND_TO_CURRENT_VCLIBS_VERSION flag in the .exe's project and all dependent .lib projects.
• For public assemblies, this is not required, as Windows will automatically select the correct version of the .DLLs from the SxS directory.
• How ironic that this MESS is supposed to solve the DLL hell. Now we have SxS hell, which is even worse. – Tamás Szelei Jun 30 '11 at 19:37

I just remembered another trick that I used to find out which static libraries were ill-behaving: 'grep' through the static libraries for the string '21022'. HOWEVER, don't use the 'normal' grep tools like wingrep because they won't show you these strings (they think it's a binary file and look for the raw, non-unicode string). Use the 'strings' utility from the resource kit (now in the Russinovich site I think). That one will grep through binaries ok. So you let this 'strings' go through your whole source tree and you'll see the binary files (dlls and static libraries) that contain references to the wrong manifest (or to the manifest with the wrong version in it).

Another nice tool for viewing exe and dll manifests is Manifest View, which fittingly enough will not run on a clean install of XP, because it depends on 9.0.21022.

For your third option, you can probably find the DLLs and manifests for the 9.0.21022 version in the C:\WINDOWS\WinSxS directory on your dev machine. If you can, then you can setup your own redist directory and install those files with your app.

Alternatively, you can use the 9.0.30729.1 ones supplied with Visual Studio and forge the manifest you install with your app to report that it supplies the 9.0.21022 DLLs, and not 9.0.30729.1. The runtime linker doesn't seem to mind. See this blog, which has been immensely helpful for solving these problems, for more information.

Both workarounds fixed the problems I had with deploying the DLLs as private assemblies with VS2008 Express.

Roel's answer is the way to go for your first option ("fix it right"), but if you depend on a library that depends on 9.0.21022 (and your manifest therefore lists both versions), then the third option may be the only way to go if you don't want to run vcredist_x86.exe.


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Courses

# Doc - MCQ:- Calculus, Integrals, Multiple, integrals Mathematics Notes | EduRev

## Topic-wise Tests & Solved Examples for IIT JAM Mathematics

Created by: Veda Institute

## Mathematics : Doc - MCQ:- Calculus, Integrals, Multiple, integrals Mathematics Notes | EduRev

The document Doc - MCQ:- Calculus, Integrals, Multiple, integrals Mathematics Notes | EduRev is a part of the Mathematics Course Topic-wise Tests & Solved Examples for IIT JAM Mathematics.
All you need of Mathematics at this link: Mathematics

Question:-1
Solution:
Region bounded  by
x = 0, x = 1 and y = x, y = 1
Now we evaluate the integral by hanging the order of integral

Question:-2 The value of the double integral
Solution:
Region of integration is bounded  y=0, y = x and x = 0, x = π
changing the order of integration

= 2

Question:-3 Evaluate
Solution:

Question4:- Change the order of integration in the double integral
Solution:
Domain of integration is bounded  by the following curves

point of intersection of the curve y =2 - x2 and y = -x we get when

So (-1,1 ) and (2,-2 ) are the points of intersection.
Now the given integral modify by changing the order of integration we get

Question5:- Changing the order of integration of

Solution:

The region of integration is bounded by y = 0, y = x, x = 1, x = 2 after changing the order the integration changes to

Question6:- Let D the trianle bounded by the y-axis the line 2y = π. Then the value of the integral
(a) 1/2 (b) 1 (c) 3/2 (d) 2
Solution:

Question7:- Change the order of integration in the integral
Solution:  The domain of the double integration is bounded  by the curves y = x - 1,

Question8:- Let I =   Then using the transformation x = rcosθ, y = rsinθ, integral is equal to

Solution:
Region of integration is bounded  by curves

for first integral,

Question9:- Evaluate integral
(a) 0 (b) 1/2 (c) 1 (d)2
Solution:
Region of integration is bounded  by curves

changing the order

Question 10:- The value of  equals
(a) π/4 (b) 1/2π (c) 1/4 (d) 1/2
Solution:

Question11:- (a) Find in the area of the smaller of the two regions enclose between

Solution:-

Solution (b)
The region of integration is bounded  by x = 0, x = y, y = 1, y = ∞ and shown in figure changing the order

Question12:- Let f , be a continuous function with
Solution:
Given,  be a continuous function with

Now apply change of order of integration
Domain of integration is given by graph

Question13:- By changing the order of integration, the integral  can be expressed as

Solution:
The domain of integration is bounded  y = 1,   changing the order

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# Tag Info

Here's a one-liner that also plays nice with dodgy user input (say, injecting ]" into the #selectVal field, which would break Andy E's approach. function setSelect() { $("#mySelect").val($("#selectVal").val()).val($("#mySelect").val());$("#selectVal").select(); } Why this works: the first call to \$("#mySelect").val(...) selects the option if it ...


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# Function with continuous components, Zariski topology

I am trying to understand how the Zariski topology is different from the usual topology on the affine space $A^n$. Let $X$ be an affine algebraic subset of $A^n$, the $n$-dimensional affine space over $k$. Let $f_i:X\rightarrow A^1$, $i=1,...,k$ be continuous functions, both $X$ and $A^1$ being equipped with the Zariski topology. Is the function $f:X\rightarrow A^k, x\mapsto (f_1(x),...,f_k(x))$ continuous when $A^k$ is equipped with the Zariski topology? I know that $f$ is continuous for the product topology, but the Zariski topology is finer the the product topology.

I appreciate any help.

• Excellent, precise question! – Georges Elencwajg Mar 28 '18 at 6:38

NO, $f$ need not be continuous in the Zariski topology !
For a counterexample take $X=\mathbb A^1$ and let $f_1:\mathbb A^1\to \mathbb A^1$ be the map permuting $0$ and $1$ and leaving $x$ fixed if $x\neq 0,1$.
Like all permutations of $\mathbb A^1$ the map $f_1$ is continuous in the Zariski topology.
Now taking the identity for $f_2:\mathbb A^1\to\mathbb A^1$, let us show that the map $$f:\mathbb A^1\to \mathbb A^1\times \mathbb A^1:x\mapsto (f_1(x),f_2(x)=(f_1(x),x)$$ is not continuous for the Zariski topology.
Indeed the diagonal $\Delta=\{(x,x)\vert x\in \mathbb A^1\} \subset \mathbb A^1\times \mathbb A^1$ is closed in the product endowed with its Zariski topology but its inverse image $f^{-1}{\Delta}=\mathbb A^1\setminus \{0,1\}\subset \mathbb A^1$ is not closed if $k$ is an infinite field.


text:
Ok, Cassian says forking does not sound completely healthy thing to do. Well, for those none geeks out there, what it means is that if there is that in github, a bunch of code is collected together in a repository.

If you want to work on someone's software, then there is the concept of a fork. That is make an exact copy of the entire history and then you have your own copy.

The language of revision control is all about trees, so when you want to do some of your own editing, you create the branch (of a tree).

When you make a complete copy, it's like a fork in the road, so you go on your path and I go on mine.

This works really well except for Github issues. That is the problems that you have. YOu don't get a copy of these. So you decide if you are really transferring a repo or forking.

## Transfer a repo including issues

Transferring makes sense when you are working and want to move the work from same your private world to a new startup organization (hooray). This way all your issues and things get moved and tracked.

The way to do this is to:

1. Delete all invitations and make sure that all the collaborators in the destination organization exist. For instance, if you have a invitation outstanding, you need to delete that. This makes sense because issues and everything move over. Otherwise, you will get obscure error about insufficient collaborator seats.
2. Go to the repo in questions and choose settings > options. Scroll down all the way to the very, very, very bottom and click on Transfer and then you can put it any place including any organization for which you have access rights. Pretty cool.

This is really nice as all issues are right there.

## Moving issues

If you didn't do this and just recreate the repo, then all your issues will be lost. However, if it is still in the same organization. All is not lost, because git now lets you move issues from one repo to another. Hooray, that is super great.

So now an issue can move if you discover it is really for a different project. In the old days, you had to recreate it.


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# Creating unique junk data with pwgen

… when you need to generate many files with unique payloads … enter pwgen and some shell scripting.

Though I use 1Password to manage access to accounts, I seldom use its password creation mechanism and instead generate and (sometimes) augment the result of pwgen for that purpose.

I’ve also found pwgen useful for generating many junk files with different payloads such that, say, they have different content signatures as the result of various hashing methods. The following snippet shows the generation of these files:

for j in {1..5}; do mkdir $j && for i in {1..100}; do pwgen -n$(expr $j \*$i \* 1000) 1 > $j/$i.txt; done & done

…where the command uses pwgen to create a file at 1K, 2K, … to 5K then multiplies that argument by 1-100 to generate a set of files with random contents. This, of course, is not the most efficient way of achieving this, as you could simply have a prefixed-seed value for each size of file you need and concatenate a random value or counter to obtain different hash results.

Also, I really should upgrade to sf-pwgen.


text:
Different width of spectral lines for different groups of stars

As seen in an HR-diagram, a certain stellar classification can correspond to more than one group/sequence of stars (G5 could for instance be either a giant, main sequence star or a white dwarf and so on). I have read in my textbook that even though these groups might have the same absorption spectrum, they can be distinguished by the thickness of their absorption-lines. For instance, giants have narrow lines and dwarfs broad ones. What is the physical explanation of this?

Many of the strongest spectral lines (e.g. Balmer absorption lines and resonance lines of metals) are very sensitive to the surface gravity of the star. This enables a distinction between dwarfs and giants because a giant star's surface gravity is factors of $$\sim 100$$ lower than that of a dwarf star of the same temperature.


text:
run.shiny.calc {credsubs} R Documentation

Run a calculator

Description

Runs the specified calculator using the shiny package. Calculators must be built using build.shiny.calc.

Usage

run.shiny.calc(
app.dir = system.file("shiny", "alzheimers", package = "credsubs")
)

Arguments

 app.dir A character string pointing to the application directory.

Details

The app.dir argument need not exactly match the value recommended by build.shiny.calc(), as long as it points to the correct directory. For example, "./calc/", "calc/", and "calc" are all equivalent. If no value is supplied, an example is run.

[Package credsubs version 1.1.1 Index]