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[ "# What does the W value mean in Wilcoxon test?\n\n## What does the W value mean in Wilcoxon test?\n\nThe Wilcoxon test statistic “W” is simply the smaller of the rank totals. The SMALLER it is (taking into account how many participants you have) then the less likely it is to have occurred by chance. A table of critical values of W shows you how likely it is to obtain your particular value of W purely by chance.\n\n## What does W mean in Wilcoxon test in R?\n\nThe W is the Wilcoxon test statistic and is, as the name says, the sum of the ranks in one of both groups.\n\nWhat is the W test statistic?\n\nThe test statistic for the Wilcoxon Signed Rank Test is W, defined as the smaller of W+ (sum of the positive ranks) and W- (sum of the negative ranks). If the null hypothesis is true, we expect to see similar numbers of lower and higher ranks that are both positive and negative (i.e., W+ and W- would be similar).\n\n### What is the W value?\n\nThe w-value is the mean energy required to produce a primary electron in the gas, and the Fano factor is the relative variance of the number of primary electrons produced per incident X-ray photon.\n\n### What is W value from Shapiro test?\n\nThe Shapiro–Wilk test statistic (Calc W) is basically a measure of how well the ordered and standardized sample quantiles fit the standard normal quantiles. The statistic will take a value between 0 and 1 with 1 being a perfect match.\n\nWhat do Wilcoxon results mean?\n\nWilcoxon – The Wilcoxon signed rank test has the null hypothesis that both samples are from the same population. The Wilcoxon test creates a pooled ranking of all observed differences between the two dependent measurements. It uses the standard normal distributed z-value to test of significance.\n\n#### What is the P value in Wilcoxon signed rank test?\n\nThe Wilcoxon W Test Statistic is simply the lowest sum of ranks but in order to calculate the p-value (Asymp. Sig), R uses an approximation to the standard normal distribution to give the resulting p-value (p = 9.33e-05, which can be written as p < 0.001).\n\n#### What is the P value in Wilcoxon signed-rank test?\n\nWhat is Wilcoxon W in Mann-Whitney?\n\nThe Mann Whitney U test, sometimes called the Mann Whitney Wilcoxon Test or the Wilcoxon Rank Sum Test, is used to test whether two samples are likely to derive from the same population (i.e., that the two populations have the same shape).\n\n## How do you interpret Wilcoxon signed-rank test?\n\nHow the Wilcoxon signed rank test works\n\n1. Calculate how far each value is from the hypothetical median.\n2. Ignore values that exactly equal the hypothetical value.\n3. Rank these distances, paying no attention to whether the values are higher or lower than the hypothetical value." ]

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[ "# SQL DEGREES Function\n\nThe SQL DEGREES function is a SQL Mathematical function used to convert the angle measured in radiant to an approximately equivalent angle measured in degrees. The syntax of the SQL Server DEGREES Function is\n\n```SELECT DEGREES (Numeric_Expression)\nFROM [Source]```\n\nNumeric_Expression: The DEGREES function accepts exact numeric or approximately numeric data types. Remember that this function will not accept Bit data types.\n\n## SQL DEGREES Function Example 1\n\nThe DEGREES Function is used to convert user specified radians to an approximately equivalent angle in degrees. In this example, We are going to find the degrees of different data values (both positive and negative values) and display the output\n\n```DECLARE @i float\nSET @i = 1.20\n\nSELECT DEGREES(@i)AS [Degrees Result 1]\n\n-- Finding Degrees directly\nSELECT DEGREES(1) AS [Degrees Result 2]\n\nSELECT DEGREES(PI()) AS [Degrees Result 3]\nSELECT DEGREES(PI()/2) AS [Degrees Result 4]\nSELECT DEGREES(PI()/3) AS [Degrees Result 5]\n\nSELECT DEGREES(-6.579) AS [Degrees Result 6]\nSELECT DEGREES(-4.23) AS [Degrees Result 7]```\n\nWithin this Degrees function example query, we are finding the degrees of radiant @i. We also assigned new name to the result as ‘Result 1’ using ALIAS Column in SQL Server.\n\n`SELECT DEGREES(@i)AS [Degrees Result 1]`\n\nIn the following three statements, We used DEGREES function directly on the positive values. Here, DEGREES(PI()) means DEGREES(3.14)\n\n```SELECT DEGREES(PI()) AS [Degrees Result 3]\nSELECT DEGREES(PI()/2) AS [Degrees Result 4]\nSELECT DEGREES(PI()/3) AS [Degrees Result 5]```\n\nNext, We used this DEGREES Mathematical function directly on the negative values\n\n```SELECT DEGREES(-6.579) AS [Degrees Result 6]\nSELECT DEGREES(-4.23) AS [Degrees Result 7]```\n\n## DEGREES Function Example 2\n\nIn this example, we are using this SQL server degrees function on a Mathematical functions table. For this demonstration, We are going to convert all the records present in the [Service Grade] column to equivalent degree values using this DEGREES Function.\n\n```SELECT [EnglishProductName]\n,[Color]\n,[StandardCost]\n,[SalesAmount]\n,[TaxAmt]" ]

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[ "# 2.1 Variables:\n\nA variable can hold a value that can be changed during the course of the execution of the script. The values can either be explicitly changed or by performing some operation on it. They are similar to variables you used back in school Algebra.\n\n## Let’s look at the syntax of a PHP variable:\n\n\\$variable_name = Value; Example:\n```<?php\n\\$learning = “Learning Variable!”;\n\\$x_numeral = 8;\n\\$first_name = ‘John’;\n\\$lastName = ‘Denver’;\n\\$nextDecimal = 16.2;\n\n?>```\nHere, we have inserted a variable name and set the value as per our need. The second line of the program with ‘\\$learning’ variable ends with a semicolon sign (;) to mark the closing of the statement “Learning Variable”. The quotation mark (“ “), inserted in the second line, is not used in the second variable (‘\\$x_numeral) as it is an integer. PHP is a case sensitive programming language. Here ‘\\$x_numeral’ variable differs from the variable ‘\\$X_numeral’ variable differs from the variable ‘\\$X_numeral’ because of the use of small ‘x’ in the first variable and capital ‘X’ in the second variable. The dollar sign (\\$) at the beginning of the variable is important as it is exclusively used in PHP. It instructs the PHP engine that the inserted code with this dollar sign is a variable. A variable in PHP always starts with an underscore ‘_’ or with a letter (x, X). You cannot begin a variable with a number. It is a common practice to separate variable names with underscore (as in \\$first_name) when two or more words are used to name them, or by converting the first letter of each word to uppercase (as in \\$lastName). This is done simply to make the name more readable . Now let us look at the various types of variables:\n1. Integer: These are whole number(s) (-9, 9, 99, 999, etc).\n2. Double/Float: These are floating point numbers or real numbers (0.99, 99.0, etc).\n3. String: These are strings of characters (“Learn”, “Java and JavaScript”). This type of variable holds both words and sentences.\n4. Boolean: This holds only two types of data: True and False.\n5. Array: This type of variable holds a list of items. (\\$student = array(“class”, “section”, “roll”);\n6. Object: This is an instance of a class.\nThe variable can be accessed from within the ‘Variable Scope’ where it was defined. A variable cannot be accessed if it was defined in a completely different scope. There are three types of Variable Scope: Superglobal, Global and Function.\n1.   Superglobal: The Superglobal variable is a type of pre-defined array in PHP. These variables can be accessed from every section of the code.\n2.   Global: Global variables can be viewed throughout the script if these are declared in it.\n3.   Function: Local variables are declared in a function scope. These variables are exclusively ‘local’ to the function in which they are declared. These variables cannot be accessed from outside the Function where it was defined.\nIn PHP, there are some in-built functions that can check the authenticity of a variable. The function ‘isset()’ is used to check the existence of a variable. It returns Boolean result (True or False). To remove a variable from the memory, the ‘unset()’ function is used. The ‘empty()’ function is used to check whether a variable has been defined and holds a non-empty value.   String Literals: We have already discussed that Strings hold both words and sentences.These are always inserted within quotation marks. If it starts with a single quotation mark then it must end with the same. If a single quotation is inserted at the beginning of a string then it can not be closed with a double quotation mark. If the quotation marks are inserted in a code without any characters, then it will be treated as ‘Null’ string. A numeric character is treated as a string if it is inserted within quotation marks. For example, if the number 9 is inserted in a PHP code, then it will be treated as a number. On the other hand, if 9 is inserted in a PHP code, then it will be treated as a string. Example:\n• “It is an example of a string with double quotes”\n• ‘It is an example of a string with single quotes’\n• “It is also an example of ‘a string’ where the single quote will be ignored”\n• ‘It is an example of “a string” where the double quote will be ignored’\n• “4”\n• ““ (Null string)\n‘Here-docs’ ‘Here-docs’ or ‘Here Documents’ is a special type of quoting that enables you to quote a large block of text within a script. Here, multiple print statements and quotation marks are not used. The PHP engine treats this block of code as a double quoted statement. ‘Here-docs’ is extremely useful when a large block of HTML is used in a PHP script. ‘Here-docs’ usually begin and end with a delimiter word, a series of one or more characters that mark the border between various sections in a data system. Numeric characters, letters and underscores can be inserted in the delimiters. In PHP, delimiters are written in capital letters. Three less than signs (<<<) are inserted at the beginning of a delimiter (Example, <<<HEREDOCS). Look at the following example: Example:\n```<?php\n\n\\$string = <<<EOD\n\nExample of PHP heredoc stringing\n\nacross multiple lines of stringing\n\nlearning through example of using heredoc syntax.\n\nEOD;\n\n?>```\n\n## Now-docs\n\nNow-doc is similar to Here-doc, and the only difference is that it is a single quoted string while here-doc is a double quoted string. Example:\n```<?php\n\n\\$string = <<<’EOD’\n\nAnother example of stringing\n\nacross compound lines\n\nby using nowdoc syntax.\n\nEOD;\n\n?>```\nEscape Sequences: In PHP, a single character, headed by a back slash (\\), is an Escape character. The HTML <pre> tag is used to display escape sequences in the user’s browser. The PHP engine cannot interpret the escape sequences without using the HTML<pre> tag. Escape Sequences Functions\n• \\” Used to print the next character as a double quote, not as a string closer\n• \\’ Used to print the next character as a single quote, not a string closer\n• \\n Used to print a new line character (remember our print statements?)\n• \\t Used to print a tab character \\r Used to print a carriage return\n• \\\\$ Used to print the next character as a dollar, not as part of a variable\n• \\\\ Used to print the next character as a backslash, not an escape character\nExample:\n```<?php\n\n\\$ExampleString = “It is an \\”escpd\\” string”;\n\n\\$ExampleSingularString = ‘It \\’will\\’ act’;\n\n\\$ExampleNonVariable = “I have \\\\$zilch in Example pocket”;\n\n\\$ExampleNewline = “It ends with a line return\\n”;\n\n\\$ExampleFile = “c:\\\\windows\\\\system32\\\\Examplefile.txt”;\n\n?>```\nBoolean literals: Boolean literals return only two values: true and false. As discussed, PHP is a case sensitive programming language. You can only use the defined set of Boolean values like, yes/no, on/off, 1/0, etc. Look at the syntax of the Boolean literals:\n```<?php\n\n\\$foo = True; // assign the value TRUE to \\$foo\n\n?>```\nExample:\n```<?php\n\n// == is an operator which test\n\n// equality and returns a Boolean value\n\nif (\\$action == “display_version”) {\n\necho “The version is 1.23”;\n\n}\n\n// this is not necessary...\n\nif (\\$display_dividers == TRUE) {\n\necho “<hr>\\n”;\n\n}\n\n// ...as you can simply type\n\nif (\\$display_dividers) {\n\necho “<hr>\\n”;\n\n}\n\n?>```\nNull: Null variable is assigned the ‘NULL’ value. A PHP engine will consider a variable as NULL if you do not set it. Array: The Array variables hold multiple values.   Object: Objects are used while working with the OOPs (Object Oriented Programming Language). Beginning with PHP 5 PHP is an Object Oriented Language   Resource: The Resource variables hold references to another external resource like file handler, database object, etc.   Note : Many a times you see the term Mixed variables used in the Manual it is nothing but any of the variables like simple variable, array or object.   2.3 Operators In PHP, variables and values are performed by Operators, that is, they operate on variables and values in PHP. Look at the following expression: \\$z = \\$x + \\$y; In the above expression x and y are two numbers. It is clear from the above expression that it would add x with y and the sum is z. The plus sign (+) inserted between x and y is an operator (Arithmetic Operator). Operators used in PHP are categorically grouped in various sections: 1. Assignment Operators 2. Arithmetic Operators 3. Comparison Operators 4. String Operators 5. Combined Operators Now let’s discuss in detail.\n1. Assignment operators\nYou can use the Assignment Operator to assign a value to a variable. Often a variable is assigned a value of another variable. In this case assignment operators are used. The equal character (=) is used here. Look at the following expression: \\$first_var = 5; \\$second_var = \\$first_var; Here the values of both ‘\\$first_var’ and ‘\\$second_ var’ variables are assigned the same value i.e. 5.\n1. Arithmetic operators\nLook at the various Arithmetic Operators: Operators Name Function\n Operator Name Function + Addition This operator is used to add two values - Subtraction This operator is used to subtract the second value from the first one * Multiplication This operator is used to multiply two values Division This operator is used to divide the first value by the second value % Modulus This operator is used to divide the first value by the second value and it returns only the remainder\nExample 01:\n```<?php\n\n\\$minus = 6 - 2;\n\n\\$multiply = 5 * 3;\n\n\\$divide = 15 / 3;\n\n\\$percent = 5 % 2;\n\necho “Result minus: 6 - 2 = “.\\$minus.”<br />”;\n\necho “Result multiply: 5 * 3 = “.\\$multiply.”<br\n\n/>”;\n\necho “Result divide: 15 / 3 = “.\\$divide.”<br />”;\n\necho “Result percent: 5 % 2 = “ . \\$percent\n\n?>```\nThe output of the above program is as follows: Result adding: 2 + 4 = 6 Result minus: 6 – 2 = 4 Result multiply: 5 * 3 = 15 Result divide: 15 / 3 = 5 Result percent: 5 % 2 = 1.   Comparison operators The ‘Comparison Operators’ verify the relationship between a variable and its value. These operators are usually inserted within a conditional statement and it returns boolean values like true and false. Look at the various types of Comparison Operators:\n Comparision Operator Name Function == Equal This operator is used tocheck if the two variables hold equal values. === Identical This operator is used to check whether two variables hold equal valuesand the data type of them are also the same. != Not Equal This operator is used to check if the two variableshold unequal values. !== Not Identical This operator is used to check for unequal valuesand for the different data types. < Less Than This operator is used to check if the value of onevariable is lesser than that of another. > Greater Than This operator is used to check if the value of onevariable is greater than that of another. <= Less Than or Equal to This operator is used to check if the value of one variable is less than or equal to the value of another variable. >= Greater Than or Equal to This operator is used to check if the value of onevariable is greater than or equal to the value of  another variable.\nString operators There are two types of ‘String Operators’: the Concatenating Operator (‘.’) and the Concatenating Assignment Operator (‘.=’).The Concatenating Operator joins the right and the left string into a single string. The Concatenating Assignment Operators add the argument that is placed on the right side of the equal operator with the argument placed on the left side of the ‘equal’ operator. Example:\n```\\$first_string = “Welcome”;\n\n\\$second_string = “ Jack”;\n\n\\$third_string = \\$first_string . \\$second_string;\n\necho \\$third_string . “!”;```\nThe output of the above program is as follows: Welcome Jack!   Combined operators(Shorthand Operators) As the name suggests, the Combined Operators are the combinations of different types of operators. Look at the various types of Combined Operators:\n Operator Name Example += Addition & Equals \\$a += 4; -= Subtraction & Equals \\$a -= 4; *= Multiplication & Equals \\$a *= 4; /= Division & Equals \\$a /= 4; %= Modulus & Equals \\$a %= 4; .= Concatenation & Equals \\$example_str.=”Welcome”;\nThere are some other types of operators used in PHP. Let’s look at those: Logical operators:\n Logical Operators Functions And Checks if two or more statements are true && Same as And Or Checks if at least one of two statements istrue || Same as Or ! Checks if a statement is not true\nIncrement and decrement operators:\n Increment / Decrement Operator Name Function ++\\$value Pre-Increment This operator adds 1 to the value before processing the expression that can use it. –\\$value Pre-Decrement This operator subtracts 1 from the value before  processing the expression that uses the value \\$value++ Post-Increment This operator adds 1 to the value after processing the expression by which the  value can be used \\$value– Post-Decrement This operator subtracts 1 from the value after processing the expression which uses the value\n2.4 Control structure The ‘Control Structure’ controls the program flow of PHP. It can also check whether a  block of code is executed or not. The syntax of the ‘Control Structure’ is as follows: <?php if (expression) statement ?> Let’s look at various types of ‘Control Structure’:\n1. if\n2. elseif/else if\n3. Alternative syntax for control structures\n4. while\n5. do-while\n6. for\n7. foreach\n8. switch\n1) if: It is used for conditional execution of code. The condition in the if evaluates to  Boolean values (true/false). Look at the syntax of ‘if’ Control Structure: if (expr) statement Example:\n```<?php\n\nif (\\$x > \\$y) {\n\necho “x is bigger than y”;\n\n\\$y = \\$x;\n\n}\n\n?>```\nelse: If an expression in the ‘if’ statement returns false, then the ‘else’ ‘Control Structure’ is used. Example:\n```<?php\n\nif (\\$x > \\$y) {\n\necho “x is bigger than y”;\n\n} else {\n\necho “x is NOT bigger than y”;\n\n}\n\n?>```\nelseif/else if: It is a combination of ‘if’ and ‘else’ Control Structure. If the ‘if’ Control Structure’ returns a ‘false’ value, then a different statement is executed by using the ‘else’ Control Structure’. Example:\n```<?php\n\nif (\\$x > \\$y) {\n\necho “x is bigger than y”;\n\n} elseif (\\$x == \\$y) {\n\necho “x is equal to y”;\n\n} else {\n\necho “x is smaller than y”;\n\n}\n\n?>```\n“Alternative syntax for control structures: There are some alternative syntax for some control structures like, ‘if’, ‘while’, ‘for’, ‘foreach’ and ‘switch’. It changes the opening brace to a colon sign (:) and closing brace to endif;, endwhile;, endfor;, endforeach;, or endswitch. Example:\n```<?php\n\nif (\\$x == 6):\n\necho “x equals 6”;\n\necho “...”;\n\nelseif (\\$x == 7):\n\necho “x equals 7”;\n\necho “!!!”;\n\nelse:\n\necho “x is neither 6 nor 7”;\n\nendif;\n\n?>```\nwhile: The ‘while’ Control Structure executes the nested statements repetitively until the ‘while’ statement returns a false value. The syntax of ‘while’ control structure is as follows: while (expr) statement do-while: It is very much similar to the ‘while’ Control Structure. The only difference is that here the truth expression is checked at the end of every repetition. Look at the syntax of ‘do-while’:\n```<?php\n\n\\$i = 0;\n\ndo {\n\necho \\$i;\n\n} while (\\$i > 0);\n\n?>```\nfor: This is one of the complex loops in PHP. The syntax of the ‘for’ control structure is as follows: for (expr1; expr2; expr3) statement foreach: This Control Structure is first introduced in PHP. Have a look at its syntax: foreach (array_expression as \\$value) statement foreach (array_expression as \\$key => \\$value) statement switch: This Control Structure is similar to a series of ‘if’ statements." ]

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[ "Solutions short notes. solution chapter in chemistry class 12 notes pdf download the PDF file below Link:\n\n## Solution:\n\nA perfectly homogeneous mixture of two or more components is called a solution.\n\nSolute: The component which is present in a lesser amount or whose physical state is changed during the formation of the solution is called the solute.\n\nSolvent: The component which is present in a larger amount and determines the physical state of the solution is called the solvent.\n\nTypes of the solution: Depending upon the nature of solute and solvent, solutions are classified as follows:\n\nGaseous solutions: Solutions in which gas acts as a solvent are known as gaseous solutions.\n\nLiquid solutions: Solutions in which liquids are present in larger amounts.\n\nSolid solutions: Solutions in which solids are present in larger amounts.\n\nSolubility: Maximum amount of substance that can be dissolved in a specified amount of solvent at a specified temperature is called its solubility.\n\nFactors affecting solubility of a solid in a liquid:\n\nNature of solute and solvent: Polar solutes dissolve in polar solvents and non-polar solutes in non-polar solvents. (i.e., like dissolves like).\n\nEffect of temperature:\n\n– If the dissolution process is endothermic (DsolH > 0), the solubility increases with rise in temperature.\n\n– If dissolution process is exothermic (DsolH < 0), the solubility decreases with rise in temperature.\n\nEffect of pressure: Pressure does not have any significant effect on solubility of solids in liquids as these are highly incompressible.\n\nFactors affecting solubility of a gas in a liquid:\n\nEffect of pressure: Henry’s law states that “the partial pressure of the gas in vapour phase (p) is proportional to the mole fraction of the gas (x) in the solution” p = KH x where, KH is the Henry’s law constant and is different for different gases at a particular temperature.\n\nHigher the value of KH at a given pressure, the lower is the solubility of the gas in the liquid.\n\nEffect of temperature: As dissolution is an exothermic process, then according to Le Chatelier’s principle, the solubility should decrease with increase of temperature.\n\nRaoult’s law: It states that for a solution of volatile liquids, the partial vapour pressure of each component of the solution is directly proportional to its mole fraction present in solution. p1 = p°1 x1 and p2 = 2 x2 where p°1 and p°2 are vapour pressures of pure components 1 and 2 respectively, at the same temperature.\n\nDalton’s law of partial pressures:\n\nPtotal = p1 + p2 = x1 p1° + x2 p\n\n= (1 – x2)p1° + x2 p\n\n= p1° + (p2° – p1°)x2\n\nIf y1 and y2 are the mole fractions of the components 1 and 2 respectively in the vapour phase then, p1 = y1 Ptotal and p2 = y2 Ptotal\n\nRaoult’s law for solid-liquid solutions: It states that relative lowering in vapour pressure of a solution containing a non-volatile solute is equal to the mole fraction of the solute.\n\np°− ps  /  p° = x2 where,\n\np° = vapour pressure of pure solvent\n\nps = vapour pressure of solution\n\nx2 = mole fraction of solute." ]

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[ "# Add and Remove Edge in Adjacency List representation of a Graph\n\nPrerequisites: Graph and Its Representation\n\nA vector has been used to implement the graph using adjacency list representation. It is used to store the adjacency lists of all the vertices. The vertex number is used as the index in this vector.\n\nExample:\n\nBelow is a graph and its adjacency list representation:", null, "", null, "If the edge between 1 and 4 has to be removed, then the above graph and the adjacency list transforms to:", null, "", null, "## Recommended: Please try your approach on {IDE} first, before moving on to the solution.\n\nApproach: The idea is to represent the graph as an array of vectors such that every vector represents adjacency list of the vertex.\n\n• Adding an edge: Adding an edge is done by inserting both of the vertices connected by that edge in each others list. For example, if an edge between (u, v) has to be added, then u is stored in v’s vector list and v is stored in u’s vector list. (push_back)\n• Deleting an edge: To delete edge between (u, v), u’s adjacency list is traversed until v is found and it is removed from it. The same operation is performed for v.(erase)\n\nBelow is the implementation of the approach:\n\n## C++\n\n `// C++ implementation of the above approach ` ` `  `#include ` `using` `namespace` `std; ` ` `  `// A utility function to add an edge in an ` `// undirected graph. ` `void` `addEdge(vector<``int``> adj[], ``int` `u, ``int` `v) ` `{ ` `    ``adj[u].push_back(v); ` `    ``adj[v].push_back(u); ` `} ` ` `  `// A utility function to delete an edge in an ` `// undirected graph. ` `void` `delEdge(vector<``int``> adj[], ``int` `u, ``int` `v) ` `{ ` `    ``// Traversing through the first vector list ` `    ``// and removing the second element from it ` `    ``for` `(``int` `i = 0; i < adj[u].size(); i++) { ` `        ``if` `(adj[u][i] == v) { ` `            ``adj[u].erase(adj[u].begin() + i); ` `            ``break``; ` `        ``} ` `    ``} ` ` `  `    ``// Traversing through the second vector list ` `    ``// and removing the first element from it ` `    ``for` `(``int` `i = 0; i < adj[v].size(); i++) { ` `        ``if` `(adj[v][i] == u) { ` `            ``adj[v].erase(adj[v].begin() + i); ` `            ``break``; ` `        ``} ` `    ``} ` `} ` ` `  `// A utility function to print the adjacency list ` `// representation of graph ` `void` `printGraph(vector<``int``> adj[], ``int` `V) ` `{ ` `    ``for` `(``int` `v = 0; v < V; ++v) { ` `        ``cout << ``\"vertex \"` `<< v << ``\" \"``; ` `        ``for` `(``auto` `x : adj[v]) ` `            ``cout << ``\"-> \"` `<< x; ` `        ``printf``(``\"\\n\"``); ` `    ``} ` `    ``printf``(``\"\\n\"``); ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``int` `V = 5; ` `    ``vector<``int``> adj[V]; ` ` `  `    ``// Adding edge as shown in the example figure ` `    ``addEdge(adj, 0, 1); ` `    ``addEdge(adj, 0, 4); ` `    ``addEdge(adj, 1, 2); ` `    ``addEdge(adj, 1, 3); ` `    ``addEdge(adj, 1, 4); ` `    ``addEdge(adj, 2, 3); ` `    ``addEdge(adj, 3, 4); ` ` `  `    ``// Printing adjacency matrix ` `    ``printGraph(adj, V); ` ` `  `    ``// Deleting edge (1, 4) ` `    ``// as shown in the example figure ` `    ``delEdge(adj, 1, 4); ` ` `  `    ``// Printing adjacency matrix ` `    ``printGraph(adj, V); ` ` `  `    ``return` `0; ` `} `\n\n## Java\n\n `// Java implementation of the above approach ` `import` `java.util.*; ` ` `  `class` `GFG ` `{ ` ` `  `// A utility function to add an edge in an ` `// undirected graph. ` `static` `void` `addEdge(Vector adj[], ` `                    ``int` `u, ``int` `v) ` `{ ` `    ``adj[u].add(v); ` `    ``adj[v].add(u); ` `} ` ` `  `// A utility function to delete an edge in an ` `// undirected graph. ` `static` `void` `delEdge(Vector adj[], ` `                    ``int` `u, ``int` `v) ` `{ ` `    ``// Traversing through the first vector list ` `    ``// and removing the second element from it ` `    ``for` `(``int` `i = ``0``; i < adj[u].size(); i++)  ` `    ``{ ` `        ``if` `(adj[u].get(i) == v)  ` `        ``{ ` `            ``adj[u].remove(i); ` `            ``break``; ` `        ``} ` `    ``} ` ` `  `    ``// Traversing through the second vector list ` `    ``// and removing the first element from it ` `    ``for` `(``int` `i = ``0``; i < adj[v].size(); i++) ` `    ``{ ` `        ``if` `(adj[v].get(i) == u) ` `        ``{ ` `            ``adj[v].remove(i); ` `            ``break``; ` `        ``} ` `    ``} ` `} ` ` `  `// A utility function to print the adjacency list ` `// representation of graph ` `static` `void` `printGraph(Vector adj[], ``int` `V) ` `{ ` `    ``for` `(``int` `v = ``0``; v < V; ++v) ` `    ``{ ` `        ``System.out.print(``\"vertex \"` `+ v+ ``\" \"``); ` `        ``for` `(Integer x : adj[v]) ` `            ``System.out.print(``\"-> \"` `+ x); ` `        ``System.out.printf(``\"\\n\"``); ` `    ``} ` `    ``System.out.printf(``\"\\n\"``); ` `} ` ` `  `// Driver code ` `public` `static` `void` `main(String[] args) ` `{ ` `    ``int` `V = ``5``; ` `    ``Vector []adj = ``new` `Vector[V]; ` `        ``for` `(``int` `i = ``0``; i < V; i++) ` `            ``adj[i] = ``new` `Vector(); ` `     `  `    ``// Adding edge as shown in the example figure ` `    ``addEdge(adj, ``0``, ``1``); ` `    ``addEdge(adj, ``0``, ``4``); ` `    ``addEdge(adj, ``1``, ``2``); ` `    ``addEdge(adj, ``1``, ``3``); ` `    ``addEdge(adj, ``1``, ``4``); ` `    ``addEdge(adj, ``2``, ``3``); ` `    ``addEdge(adj, ``3``, ``4``); ` ` `  `    ``// Printing adjacency matrix ` `    ``printGraph(adj, V); ` ` `  `    ``// Deleting edge (1, 4) ` `    ``// as shown in the example figure ` `    ``delEdge(adj, ``1``, ``4``); ` ` `  `    ``// Printing adjacency matrix ` `    ``printGraph(adj, V); ` `} ` `} ` ` `  `// This code is contributed by 29AjayKumar `\n\n## C#\n\n `// C# implementation of the above approach ` `using` `System; ` `using` `System.Collections.Generic; ` ` `  `class` `GFG ` `{ ` ` `  `// A utility function to add an edge in an ` `// undirected graph. ` `static` `void` `addEdge(List<``int``> []adj, ` `                    ``int` `u, ``int` `v) ` `{ ` `    ``adj[u].Add(v); ` `    ``adj[v].Add(u); ` `} ` ` `  `// A utility function to delete an edge in an ` `// undirected graph. ` `static` `void` `delEdge(List<``int``> []adj, ` `                    ``int` `u, ``int` `v) ` `{ ` `    ``// Traversing through the first vector list ` `    ``// and removing the second element from it ` `    ``for` `(``int` `i = 0; i < adj[u].Count; i++)  ` `    ``{ ` `        ``if` `(adj[u][i] == v)  ` `        ``{ ` `            ``adj[u].RemoveAt(i); ` `            ``break``; ` `        ``} ` `    ``} ` ` `  `    ``// Traversing through the second vector list ` `    ``// and removing the first element from it ` `    ``for` `(``int` `i = 0; i < adj[v].Count; i++) ` `    ``{ ` `        ``if` `(adj[v][i] == u) ` `        ``{ ` `            ``adj[v].RemoveAt(i); ` `            ``break``; ` `        ``} ` `    ``} ` `} ` ` `  `// A utility function to print the adjacency list ` `// representation of graph ` `static` `void` `printGraph(List<``int``> []adj, ``int` `V) ` `{ ` `    ``for` `(``int` `v = 0; v < V; ++v) ` `    ``{ ` `        ``Console.Write(``\"vertex \"` `+ v + ``\" \"``); ` `        ``foreach` `(``int` `x ``in` `adj[v]) ` `            ``Console.Write(``\"-> \"` `+ x); ` `        ``Console.Write(``\"\\n\"``); ` `    ``} ` `    ``Console.Write(``\"\\n\"``); ` `} ` ` `  `// Driver code ` `public` `static` `void` `Main(String[] args) ` `{ ` `    ``int` `V = 5; ` `    ``List<``int``> []adj = ``new` `List<``int``>[V]; ` `        ``for` `(``int` `i = 0; i < V; i++) ` `            ``adj[i] = ``new` `List<``int``>(); ` `     `  `    ``// Adding edge as shown in the example figure ` `    ``addEdge(adj, 0, 1); ` `    ``addEdge(adj, 0, 4); ` `    ``addEdge(adj, 1, 2); ` `    ``addEdge(adj, 1, 3); ` `    ``addEdge(adj, 1, 4); ` `    ``addEdge(adj, 2, 3); ` `    ``addEdge(adj, 3, 4); ` ` `  `    ``// Printing adjacency matrix ` `    ``printGraph(adj, V); ` ` `  `    ``// Deleting edge (1, 4) ` `    ``// as shown in the example figure ` `    ``delEdge(adj, 1, 4); ` ` `  `    ``// Printing adjacency matrix ` `    ``printGraph(adj, V); ` `} ` `} ` ` `  `// This code is contributed by PrinciRaj1992 `\n\nOutput:\n\n```vertex 0 -> 1-> 4\nvertex 1 -> 0-> 2-> 3-> 4\nvertex 2 -> 1-> 3\nvertex 3 -> 1-> 2-> 4\nvertex 4 -> 0-> 1-> 3\n\nvertex 0 -> 1-> 4\nvertex 1 -> 0-> 2-> 3\nvertex 2 -> 1-> 3\nvertex 3 -> 1-> 2-> 4\nvertex 4 -> 0-> 3\n```\n\nGeeksforGeeks has prepared a complete interview preparation course with premium videos, theory, practice problems, TA support and many more features. Please refer Placement 100 for details\n\nMy Personal Notes arrow_drop_up", null, "Check out this Author's contributed articles.\n\nIf you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to [email protected]. See your article appearing on the GeeksforGeeks main page and help other Geeks.\n\nPlease Improve this article if you find anything incorrect by clicking on the \"Improve Article\" button below.\n\nImproved By : 29AjayKumar, princiraj1992\n\nArticle Tags :\nPractice Tags :\n\n1\n\nPlease write to us at [email protected] to report any issue with the above content." ]

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[ "# App-Idea 1: Bin2Dec\n\nOur first project (Bin2Dec) will be a converter that takes binary numbers from input strings and converts them to their decimal value. And, we will add the ability to convert back from decimals to binary numbers as well.\n\nThere are several converters in the project list, so we will create a single Blazor app with multiple pages for each project idea to minimize the number of projects that we are creating and hosting. You can find the source for the Blazor.AppIdeas.Converters on GitHub. And the running sample of the Blazor app online.\n\nWe will start with a clean Blazor project by following the directions in the How-To: Create Blazor WASM Project article and name our project Blazor.AppIdeas.Converters.\n\n## BinaryDecimalConverter View Model\n\nWe are going to put our conversion logic into a separate class called `BinaryDecimalConverter`. This class represents the ViewModel in the Model-View-ViewModel (MVVM) design pattern, which is the glue and logic behind the View/Presentation (in Blazor that is represented by a component or page).\n\nLet’s create the `BinaryDecimalConverter` class in the ViewModels folder.\n\n```using System;\n\nnamespace Blazor.AppIdeas.Converters.ViewModels\n{\npublic class BinaryDecimalConverter\n{\npublic string Binary { get; set; }\n\npublic string Decimal { get; set; }\n\npublic string ErrorMessage { get; private set; }\n\npublic string ErrorDisplay => string.IsNullOrEmpty(ErrorMessage) ? \"none\" : \"normal\";\n\npublic void ConvertDecimal()\n{\ntry\n{\nErrorMessage = null;\nif (string.IsNullOrEmpty(Binary)) throw new FormatException();\n\nDecimal = Convert.ToInt32(Binary, 2).ToString();\n}\ncatch\n{\nErrorMessage = \"Binary must be a valid number with only 0s and 1s.\";\n}\n}\n\npublic void ConvertBinary()\n{\ntry\n{\nErrorMessage = null;\nif (string.IsNullOrEmpty(Decimal)) throw new FormatException();\n\nint number = Convert.ToInt32(Decimal);\nBinary = Convert.ToString(number, 2);\n}\ncatch\n{\nErrorMessage = \"Decimal must be a valid number with only digits 0-9.\";\n}\n}\n}\n}\n```\n\nThis class has a straightforward implementation of methods that do the conversion between number systems:\n\n• First, we define properties for the user interface to bind with. Databinding is an important mechanism in MVVM (along with other patterns for presentation-logic separation), and Blazor supports that well.\n• `Binary` holds the binary number representation (line #7).\n• `Decimal` holds the integer number representation (line #9).\n• `ErrorMessage` is a display message to show whenever an error happens in the conversion (line #11).\n• `ErrorDisplay` is a derived property (line #13) that returns “none” when the the `ErrorMessage` is empty, and returns “normal” when the `ErrorMessage` is present. This allows us to toggle the user interface based on the presence of an error message.\n• The `ConvertDecimal` method (lines #15-28) takes the `Binary` property, converts it to an integer representation, and saves it as a string in the `Decimal` property.\n• The `ConvertBinary` method (lines #30-44) does the reverse. It takes the `Decimal` property, converts it into an integer, and converts it into a string in binary format into the `Binary` property.\n• Both methods have error handling logic to:\n• Start by hiding any previous error messages (lines #19 & 34).\n• Verify that the input strings are not null or empty (lines #20 & 35).\n• And handle any exceptions thrown by the `Convert` framework class (lines #24-27, 40-43).\n\nWith all of our conversion logic in a simple C# class, it will be easy to write unit tests for this logic isolated from the UI that it is running in. As a matter of fact, we could re-use this same class as the ViewModel in another application, like WPF, Windows 10, or Xamarin apps.\n\n## Binary-Decimal Convert Page\n\nBlazor is an HTML/CSS based framework for building user interfaces. It provides additional attributes along with the standard HTML attributes to enable scenarios like binding to a property. Blazor also has some basic input components defined to help abstract away some of the HTML. But we can use either the Blazor components or the raw HTML/CSS elements. For this example, we will use the raw HTML/CSS.\n\nAlso for these projects we will mainly use the BootStrap CSS framework for defining layout. BootStrap comes with the default Blazor project, so it is the most convenient, though there are many such UI frameworks out there. So this article does require a working knowledge of Bootstrap 4.\n\nLet’s create the BinaryDecimalConvert.razor page in the Pages folder.\n\n```@page \"/bin2dec\"\n\n<div class=\"col-lg-8 col-md-10 offset-lg-2 offset-md-1 mt-3 pb-3 container\">\n<h3 class=\"mt-3\">Binary-Decimal Converter</h3>\n<hr />\n<form class=\"form-row\">\n<div class=\"form-group col-lg-6 col-md-12\">\n<label for=\"binary\">Binary:</label>\n<input type=\"text\" class=\"form-control\" id=\"binary\"\nplaceholder=\"Enter binary number\" @bind-value=\"@vm.Binary\">\n</div>\n<div class=\"form-group col-lg-6 col-md-12\">\n<label for=\"decimal\">Decimal:</label>\n<input type=\"text\" class=\"form-control\" id=\"decimal\"\nplaceholder=\"Enter decimal number\" @bind-value=\"@vm.Decimal\">\n</div>\n<strong>Error:</strong> @vm.ErrorMessage\n</div>\n</form>\n<div class=\"text-center\">\n<input id=\"btn-convert-decimal\" class=\"btn btn-outline-primary\" type=\"button\"\nvalue=\"Convert to Decimal\" @onclick=\"vm.ConvertDecimal\">\n<input id=\"btn-convert-binary\" class=\"btn btn-outline-primary\" type=\"button\"\nvalue=\"Convert to Binary\" @onclick=\"vm.ConvertBinary\">\n</div>\n</div>\n\n@code {\npublic BinaryDecimalConverter vm = new BinaryDecimalConverter();\n}\n```\n\nFor those developers comfortable with HTML/CSS/BootStrap, the layout section of this file will look very familiar… divs and classes and input elements. We basically layout two labels, two input elements, and two buttons to transform the input between them.\n\nThe `@page \"/bin2dec\"` directive (line #1) defines the Url route to this page. When the user navigates to this Url, Blazor routes the user to this page.\n\nThe `@code` section (lines #29-31) is where code is written in Razor pages. In this section, we only create an instance of the `BinaryDecimalConverter` class (from above) to use throughout this page. However any amount of page code can be written here. For this project and simplicity, we are directly creating an instance of our ViewModel. There are other options for tying together pages and ViewModels, which we will investigate in future projects.\n\nLines #17-18 show one-way databinding in Blazor`@vm.ErrorDisplay` sets the display style to the `BinaryDecimalConverter.ErrorDisplay` property. And, `@vm.ErrorMessage` binds to the content for a div. By doing this, the alert div is hidden and shown with an appropriate message depending on those properties.\n\nLines #22-25 also show one-way databinding, but this is binding an event (onclick) to a method call:\n\n• `@onclick=\"vm.ConvertDecimal\"` binds the first button to call the `ConvertDecimal`, when it’s clicked.\n• `@onclick=\"vm.ConvertBinary\"` binds the second button to call the `ConvertBinary`, when it’s clicked.\n\nFinally, lines #10 & 15 show two-way databinding in Blazor. Two-way databinding means that changes to the input element are reflected in the bound property and vice-versa. `@bind-value=\"@vm.Binary\"` dual binds the element’s value to the `BinaryDecimalConverter.Binary` property. And, we do the same for Decimal.\n\nWith these Blazor directives and bindings, we’ve taken static html and bound it to the code in our ViewModel, and defined the interactivity on the page. And, all of this C# code runs in the browser on the client.\n\nThere were a couple of more changes made for this project. The first is CSS additions for a couple of elements.\n\n```@import url('open-iconic/font/css/open-iconic-bootstrap.min.css');\n\nhtml, body {\nfont-family: 'Helvetica Neue', Helvetica, Arial, sans-serif;\n}\n\ncolor: #0366d6;\n}\n\n.btn-primary {\ncolor: #fff;\nbackground-color: #1b6ec2;\nborder-color: #1861ac;\n}\n\n.content {\n}\n\n.valid.modified:not([type=checkbox]) {\noutline: 1px solid #26b050;\n}\n\n.invalid {\noutline: 1px solid red;\n}\n\n.validation-message {\ncolor: red;\n}\n\n#blazor-error-ui {\nbackground: lightyellow;\nbottom: 0;\nbox-shadow: 0 -1px 2px rgba(0, 0, 0, 0.2);\ndisplay: none;\nleft: 0;\nposition: fixed;\nwidth: 100%;\nz-index: 1000;\n}\n\n#blazor-error-ui .dismiss {\ncursor: pointer;\nposition: absolute;\nright: 0.75rem;\ntop: 0.5rem;\n}\n\n.container {\nborder-style: solid;\nborder-width: 1px;\nborder-color: darkgreen;\n}\n\nhr {\nborder-top: 1px solid darkgreen;\n}\n```\n\nThe container CSS just puts a rounded, dark green border around the component. And the hr CSS makes the divider the same dark ground color.\n\n```@attribute [System.Diagnostics.CodeAnalysis.ExcludeFromCodeCoverage]\n<div class=\"top-row pl-4 navbar navbar-dark\">\n<a class=\"navbar-brand\" href=\"\">AppIdeas - Converters</a>\n<span class=\"navbar-toggler-icon\"></span>\n</button>\n</div>\n\n<ul class=\"nav flex-column\">\n<li class=\"nav-item px-3\">\n<span class=\"oi oi-home\" aria-hidden=\"true\"></span> Home\n</li>\n<li class=\"nav-item px-3\">\n<span class=\"oi oi-arrow-bottom\" aria-hidden=\"true\"></span> Bin2Dec\n</li>\n</ul>\n</div>\n\n@code {\n\n{\n}\n}\n```\n\nAt this point, we can build and run the project locally. Enter some binary data (101) into the input element and click the ‘Covert to Decimal’ button to see the result (and covert back as well).\n\n## Test Project\n\nWith the project complete, we are going to create some tests to verify the functionality too. Let’s start by creating a test project (named Blazor.AppIdeas.Converters.Tests project) in this same solution by following the steps in: How-to: Add bUnit Test Project to Blazor Solution article.\n\n### ViewModel Unit Tests\n\nWith our separate `BinaryDecimalConverter` class, it is easy to unit test the logic. Create a `BinaryDecimalConverterTests` class in the Blazor.AppIdeas.Converters.Tests project and ViewModels folder. We like our test project folders to match our source project, so it’s easy to navigate both projects.\n\n```using Blazor.AppIdeas.Converters.ViewModels;\nusing System;\nusing System.Collections.Generic;\nusing System.Linq;\nusing System.Text;\nusing Xunit;\n\nnamespace Blazor.AppIdeas.Converters.Tests.ViewModels\n{\npublic class BinaryDecimalConverterTests\n{\nprivate const string binaryErrorMessage = \"Binary must be a valid number with only 0s and 1s.\";\nprivate const string decimalErrorMessage = \"Decimal must be a valid number with only digits 0-9.\";\n\n[Fact]\npublic void Construction()\n{\n// arrange\n\n// act\nvar converter = new BinaryDecimalConverter();\n\n// assert\nAssert.NotNull(converter);\nAssert.Null(converter.Binary);\nAssert.Null(converter.Decimal);\nAssert.Null(converter.ErrorMessage);\nAssert.Equal(\"none\", converter.ErrorDisplay);\n}\n\n[Theory]\n[InlineData(\"101\", \"5\", null, \"none\")]\n[InlineData(\"11011010\", \"218\", null, \"none\")]\n[InlineData(\"\", null, binaryErrorMessage, \"normal\")]\n[InlineData(\"102\", null, binaryErrorMessage, \"normal\")]\npublic void ConvertDecimal_WithBinaryString(\nstring initialBinary, string expectedDecimal, string expectedErrorMessage, string expectedErrorDisplay)\n{\n// arrange\nvar converter = new BinaryDecimalConverter\n{\nBinary = initialBinary\n};\n\n// act\nconverter.ConvertDecimal();\n\n// assert\nAssert.Equal(expectedDecimal, converter.Decimal);\nAssert.Equal(expectedErrorMessage, converter.ErrorMessage);\nAssert.Equal(expectedErrorDisplay, converter.ErrorDisplay);\n}\n\n[Theory]\n[InlineData(\"5\", \"101\", null, \"none\")]\n[InlineData(\"186\", \"10111010\", null, \"none\")]\n[InlineData(\"\", null, decimalErrorMessage, \"normal\")]\n[InlineData(\"102l\", null, decimalErrorMessage, \"normal\")]\npublic void ConvertBinary_WithDecimalString(\nstring initialDecimal, string expectedBinary, string expectedErrorMessage, string expectedErrorDisplay)\n{\n// arrange\nvar converter = new BinaryDecimalConverter\n{\nDecimal = initialDecimal\n};\n\n// act\nconverter.ConvertBinary();\n\n// assert\nAssert.Equal(expectedBinary, converter.Binary);\nAssert.Equal(expectedErrorMessage, converter.ErrorMessage);\nAssert.Equal(expectedErrorDisplay, converter.ErrorDisplay);\n}\n}\n}\n```\n\nFirst, we notice the xUnit `[Fact]` and` [Theory]` attributes that are on each method. These attributes are used by the xUnit test runner to discover the unit tests in our class. `[Fact]` is for a single test method. `[Theory]` is used to define a method with variations that are run for each `[InlineData]` attribute on that same method. The method signature of `[InlineData]` must match the test method’s signature, and that data is passed into the method for each test.\n\nAll of the unit tests conform to the same outline: arrange (setup the requirements for the test), act (perform the test on the method), and assert (validate the state after the method is tested). This helps other developers and ourselves understand the intent of the tests.\n\nThe `Construction` test uses the `[Fact]` attribute because it is a single test. It creates the class and validates the starting state of its properties are what we expect.\n\nThe `ConvertDecimal_WithBinaryString` test is written to test various cases of converting binary to decimal numbers.\n\n1. It creates the `BinaryDecimalConverter` class with the `initialBinary` value set.\n2. It calls the `ConvertDecimal` method.\n3. It validates the expected results for the `Decimal` value, any error message text, and whether the error message should be displayed. These expected values are also passed into the test method.\n4. This method was generalized with parameters for the input and expected results, so that it can be run with different possible values.\n5. The `[InlineData]` defines individual test instances for `Binary` values of: 101, 11011010, “”, 102. The first two produce valid `Decimal` conversions. The last two exercise the error handling code and validate the expected error messages and display state.\n\nThe `ConvertBinary_WithDecimalString` test runs similar test variations, but instead we convert decimal values to binary numbers.\n\nWith these 3 tests and data variations, we fully cover the test scenarios needed to validate the functionality of our ViewModel class.\n\n### Page bUnit Tests\n\nWe can also create tests that validate the page functions as expected. bUnit is a unit test framework for rendering Blazor pages and components in a test context. It allows pages to be rendered and then validate the rendered HTML. It also allows us to perform actions on page elements.\n\nCreate the `BinaryDecimalConvertTests` class in the Blazor.AppIdeas.Converters.Tests project and Pages folder.\n\n```using Blazor.AppIdeas.Converters.Pages;\nusing Bunit;\nusing Xunit;\n\nnamespace Blazor.AppIdeas.Converters.Tests.Pages\n{\npublic class BinaryDecimalConvertTests\n{\n[Fact]\npublic void InitialRender()\n{\n// arrange\nusing var ctx = new TestContext();\n\n// act\nvar cut = ctx.RenderComponent<BinaryDecimalConvert>();\n\n// assert\ncut.MarkupMatches(BinaryDecimalConvertExpectedResults.DefaultRenderResult);\nAssert.NotNull(cut.Instance.vm);\n}\n\n[Fact]\npublic void DisplayErrorMessage()\n{\n// arrange\nusing var ctx = new TestContext();\nvar cut = ctx.RenderComponent<BinaryDecimalConvert>();\n\n// act\ncut.Find(\"#btn-convert-decimal\").Click();\n\n// assert\ncut.MarkupMatches(BinaryDecimalConvertExpectedResults.BinaryErrorResult);\n}\n\n[Fact]\npublic void ConvertToDecimal_Clicked()\n{\n// arrange\nusing var ctx = new TestContext();\nvar cut = ctx.RenderComponent<BinaryDecimalConvert>();\ncut.Instance.vm.Binary = \"101\";\n\n// act\ncut.Find(\"#btn-convert-decimal\").Click();\n\n// assert\ncut.MarkupMatches(BinaryDecimalConvertExpectedResults.ConvertToDecimalResult);\n}\n\n[Fact]\npublic void ConvertToBinary_Clicked()\n{\n// arrange\nusing var ctx = new TestContext();\nvar cut = ctx.RenderComponent<BinaryDecimalConvert>();\ncut.Instance.vm.Decimal = \"7\";\n\n// act\ncut.Find(\"#btn-convert-binary\").Click();\n\n// assert\ncut.MarkupMatches(BinaryDecimalConvertExpectedResults.ConvertToBinaryResult);\n}\n}\n}\n```\n\nFirst, we will notice these tests also follow the arrange-act-assert structure. Next, the tests are each very similar, they render the Blazor component or page, optionally perform an action on an element, and then validate the resulting HTML matches our expected HTML.\n\nWe will dive deep into the `ConvertToDecimal_Clicked` test to explain how bUnit works:\n\n1. We create a new instance of `TestContext`. This is the bUnit test context which works as the hosting context for our page. It simulates how Blazor works to construct and render a page or component.\n2. The `RenderComponent` method performs the render of a component (in our case the `BinaryDecimalConvert` page). In Blazor, pages are just components with routing information.\n3. We set the `ViewModel.Binary` property to “101” to simulate a user setting that in the Binary input element.\n4. With the page setup complete, we use `IRenderedComponent<BinaryDecimalConvert>.Find` to find the ‘Convert to Decimal’ button on the page. Using the `\"#btn-convert-decimal\"` text in the Find method searches for an element with that id. The Find method uses the same convention as CSS naming/matching.\n5. Then, we call the `Click` method on that element. This simulates the click event in the component/page element. By using these actions, we are simulating user interaction with the page. bUnit has a long list of actions that can be performed on elements.\n6. Finally, we use the `IRenderedComponent<BinaryDecimalConvert>.MarkupMatches` to assert that the currently rendered HTML matches our expected HTML. This is a semantic matcher, so the text doesn’t need to match exactly (attributes could be in different order for example), but the elements between the two must match.\n7. If `MarkupMatches` returns true, then we know the page rendering matches our expectations. If it returns false, then they don’t match. The tests results also show the elements and attributes that don’t match, so that we can narrow down the errors.\n\nThe remaining tests follow the same usage pattern, but either produce an error or do the reverse conversion. We test these variations to ensure all of our databindings are constructed correctly on the page.\n\nBecause the expected results for pages can be verbose, we also place all of them into separate class constants to simplify and improve the readability of the test methods. Create the `BinaryDecimalConvertExpectedResults` class in the Blazor.AppIdeas.Converters.Tests project and Pages folder. These constants are string literals of the HTML that we expect for each test case.\n\n```namespace Blazor.AppIdeas.Converters.Tests.Pages\n{\nstatic class BinaryDecimalConvertExpectedResults\n{\ninternal const string DefaultRenderResult =\n@\" <div class=\"\"col-lg-8 col-md-10 offset-lg-2 offset-md-1 mt-3 pb-3 container\"\">\n<h3 class=\"\"mt-3\"\">Binary-Decimal Converter</h3>\n<hr>\n<form class=\"\"form-row\"\">\n<div class=\"\"form-group col-lg-6 col-md-12\"\">\n<label for=\"\"binary\"\">Binary:</label>\n<input type=\"\"text\"\" class=\"\"form-control\"\" id=\"\"binary\"\" placeholder=\"\"Enter binary number\"\" />\n</div>\n<div class=\"\"form-group col-lg-6 col-md-12\"\">\n<label for=\"\"decimal\"\">Decimal:</label>\n<input type=\"\"text\"\" class=\"\"form-control\"\" id=\"\"decimal\"\" placeholder=\"\"Enter decimal number\"\" />\n</div>\n<strong>Error:</strong>\n</div>\n</form>\n<div class=\"\"text-center\"\">\n<input id=\"\"btn-convert-decimal\"\" class=\"\"btn btn-outline-primary\"\" type=\"\"button\"\" value=\"\"Convert to Decimal\"\" />\n<input id=\"\"btn-convert-binary\"\" class=\"\"btn btn-outline-primary\"\" type=\"\"button\"\" value=\"\"Convert to Binary\"\" />\n</div>\n</div>\n\";\n\ninternal const string BinaryErrorResult =\n@\" <div class=\"\"col-lg-8 col-md-10 offset-lg-2 offset-md-1 mt-3 pb-3 container\"\">\n<h3 class=\"\"mt-3\"\">Binary-Decimal Converter</h3>\n<hr>\n<form class=\"\"form-row\"\">\n<div class=\"\"form-group col-lg-6 col-md-12\"\">\n<label for=\"\"binary\"\">Binary:</label>\n<input type=\"\"text\"\" class=\"\"form-control\"\" id=\"\"binary\"\" placeholder=\"\"Enter binary number\"\" />\n</div>\n<div class=\"\"form-group col-lg-6 col-md-12\"\">\n<label for=\"\"decimal\"\">Decimal:</label>\n<input type=\"\"text\"\" class=\"\"form-control\"\" id=\"\"decimal\"\" placeholder=\"\"Enter decimal number\"\" />\n</div>\n<strong>Error:</strong> Binary must be a valid number with only 0s and 1s.\n</div>\n</form>\n<div class=\"\"text-center\"\">\n<input id=\"\"btn-convert-decimal\"\" class=\"\"btn btn-outline-primary\"\" type=\"\"button\"\" value=\"\"Convert to Decimal\"\" />\n<input id=\"\"btn-convert-binary\"\" class=\"\"btn btn-outline-primary\"\" type=\"\"button\"\" value=\"\"Convert to Binary\"\" />\n</div>\n</div>\n\";\n\ninternal const string ConvertToDecimalResult =\n@\" <div class=\"\"col-lg-8 col-md-10 offset-lg-2 offset-md-1 mt-3 pb-3 container\"\">\n<h3 class=\"\"mt-3\"\">Binary-Decimal Converter</h3>\n<hr>\n<form class=\"\"form-row\"\">\n<div class=\"\"form-group col-lg-6 col-md-12\"\">\n<label for=\"\"binary\"\">Binary:</label>\n<input type=\"\"text\"\" class=\"\"form-control\"\" id=\"\"binary\"\" placeholder=\"\"Enter binary number\"\" value=\"\"101\"\" />\n</div>\n<div class=\"\"form-group col-lg-6 col-md-12\"\">\n<label for=\"\"decimal\"\">Decimal:</label>\n<input type=\"\"text\"\" class=\"\"form-control\"\" id=\"\"decimal\"\" placeholder=\"\"Enter decimal number\"\" value=\"\"5\"\" />\n</div>\n<strong>Error:</strong>\n</div>\n</form>\n<div class=\"\"text-center\"\">\n<input id=\"\"btn-convert-decimal\"\" class=\"\"btn btn-outline-primary\"\" type=\"\"button\"\" value=\"\"Convert to Decimal\"\" />\n<input id=\"\"btn-convert-binary\"\" class=\"\"btn btn-outline-primary\"\" type=\"\"button\"\" value=\"\"Convert to Binary\"\" />\n</div>\n</div>\n\";\n\ninternal const string ConvertToBinaryResult =\n@\" <div class=\"\"col-lg-8 col-md-10 offset-lg-2 offset-md-1 mt-3 pb-3 container\"\">\n<h3 class=\"\"mt-3\"\">Binary-Decimal Converter</h3>\n<hr>\n<form class=\"\"form-row\"\">\n<div class=\"\"form-group col-lg-6 col-md-12\"\">\n<label for=\"\"binary\"\">Binary:</label>\n<input type=\"\"text\"\" class=\"\"form-control\"\" id=\"\"binary\"\" placeholder=\"\"Enter binary number\"\" value=\"\"111\"\" />\n</div>\n<div class=\"\"form-group col-lg-6 col-md-12\"\">\n<label for=\"\"decimal\"\">Decimal:</label>\n<input type=\"\"text\"\" class=\"\"form-control\"\" id=\"\"decimal\"\" placeholder=\"\"Enter decimal number\"\" value=\"\"7\"\" />\n</div>\n<strong>Error:</strong>\n</div>\n</form>\n<div class=\"\"text-center\"\">\n<input id=\"\"btn-convert-decimal\"\" class=\"\"btn btn-outline-primary\"\" type=\"\"button\"\" value=\"\"Convert to Decimal\"\" />\n<input id=\"\"btn-convert-binary\"\" class=\"\"btn btn-outline-primary\"\" type=\"\"button\"\" value=\"\"Convert to Binary\"\" />\n</div>\n</div>\n\";\n}\n}\n```\n\nBuild the entire solution and run the new tests. They should all run successfully to validate our first project.\n\nWith the code and tests done, we have completed this first project. While this is relatively easy functionality, we learned how to:\n\n• Use raw HTML/CSS on a Blazor page to produce its layout.\n• Create our logic in a separate class.\n• Use databinding (one or two-way) to show and edit data on the page.\n• Call methods in response to element events.\n• Write tests to validate the HTML produced by a Blazor page." ]

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[ "# Java Program to check whether number is Palindrome or not | Java Find Palindrome Number\n\n## What is palindromic number ?\n\npalindromic number वो numbers होते हैं जिनके digits reverse करने पर meaning / value same ही रहती है। example के लिए 2002 इसे reverse करने पर भी इसकी value same ही रहेगी। इसी तरह से 1221 और बाकी कुछ numbers भी होते हैं।", null, "Image on pixabay\n\nइस article में Java में हम Palindrome number check करने के लिए method की help से program बनाएंगे , जिसमे एक number pass करने पर हमें boolean value मिलेगी। अगर pass किया गया number , Palindrome है तो `true` otherwise `false` return होगा।\n\n### Java program to check palindrome number\n\n``````// import package.\nimport java.util.*;\nclass Palindrome {\n// Function to check for Palindrome number.\npublic static boolean isPalindrome(int number)\n{\nint temp = number;\nint newNumber = 0;\n\nwhile (temp > 0) {\nint digit = temp % 10;\nnewNumber = newNumber * 10 + digit;\ntemp = temp / 10;\n}\n\nif (newNumber == number)\nreturn true;\nelse\nreturn false;\n}\n\npublic static void main(String[] args)\n{\n// get number from user number.\nScanner sc = new Scanner(System.in);\nSystem.out.println(\"Enter a number: \");\nint number = sc.nextInt();\n\n// now call function.\nboolean result = isPalindrome(number);\nif (result)\nSystem.out.println(\"Number is Palindrome\");\nelse\nSystem.out.println(\"Number is not Palindrome\");\n}\n}``````\n\nOutput :\n\n```Enter a number: 1234\nNumber is not Palindrome\n\nEnter a number: 101\nNumber is Palindrome```\n##### Recent Blogs", null, "" ]

[ null, "https://cdn.pixabay.com/photo/2016/12/14/23/08/page-not-found-1907792__480.jpg", null, "https://www.learnhindituts.com/assets/images/learnhindituts_admin.jpg", null ]

[ "So the title may not be clear enough but i’m trying to make the Galactic Empire emblem from Star Wars. in the very middle circle there are trapezoids coming out. I made the first top one but is there a formula or a function to make the other trapezoids AS WELL AS rotate them with each one made?\n\nCurrently i’m using the quad function to make the trapezoid. I already have to figure out how i’m going to shrink the whole thing together but i’m hoping i could get an actual not too detailed answer using simple beginner functions if it’s possible.\n\nThanks!\n\nCheck this tutorial about 2D transforms\n\nPost some code if you are stuck.\n\nKf\n\nWell I was asking if there was a function or formula to use to move and translate. I had already looked at that but that’s not helping me with moving and rotation a quad() shape as well as repeating so they’re spaced evenly and rotate at the same time.\n\nYes, R/T depends on quad definition. It is really hard to picture your quads based on the description you provided. It is better if you provide a sketch or image of what you want to do. For any shape, you can always rotate and translate them. Choosing the reference point for translation and the pivot point for rotation depends on the shape and based on selection, you can make your life easier or more difficult.\n\nKf\n\nTo create patterns such as those found in the Galactic Empire logo, you could try code like\n\n``````size(512, 512);\nsmooth(8);\nbackground(255);\nfill(0);\nnoStroke();\n\nint count = 6;\n\n// Translation\nfloat centerX = width * 0.5;\nfloat centerY = height * 0.5;\n\n// Rotation\nfloat rotation = HALF_PI;\nfloat arcLength = PI / 8.0;\nfloat halfArcLength = arcLength * 0.5;\nfloat iToTheta = TWO_PI / float(count);\n\n// Scale\nfloat shortEdge = min(width, height);\nfloat outerRadius = shortEdge * 0.45;\nfloat innerRadius = shortEdge * 0.2;\n\nfor (int i = 0; i < count; ++i) {\nfloat angle = rotation + i * iToTheta;\nfloat t0 = angle - halfArcLength;\nfloat t1 = angle + halfArcLength;\n\nfloat ct0 = cos(t0);\nfloat st0 = sin(t0);\n\nfloat ct1 = cos(t1);\nfloat st1 = sin(t1);\n\nfloat p0x = centerX + ct0 * innerRadius;\nfloat p0y = centerY + st0 * innerRadius;\n\nfloat p1x = centerX + ct1 * innerRadius;\nfloat p1y = centerY + st1 * innerRadius;\n\nfloat p2x = centerX + ct1 * outerRadius;\nfloat p2y = centerY + st1 * outerRadius;\n\nfloat p3x = centerX + ct0 * outerRadius;\nfloat p3y = centerY + st0 * outerRadius;\n\np1x, p1y,\np2x, p2y,\np3x, p3y);\n}\n``````\n\nYou may also find the arc function useful. The following is added at the end of the code above.\n\n``````noFill();\nstroke(255.0, 0.0, 0.0);\nstrokeWeight(20.0);\nstrokeCap(SQUARE);\nfloat radius = shortEdge * 0.7;\nfloat arcLength2 = PI / 4.0;\nfloat halfArcLength2 = arcLength2 * 0.5;\nfor (int i = 0; i < count; ++i) {\nfloat theta = rotation + i * iToTheta;\nfloat t0 = theta - halfArcLength2;\nfloat t1 = theta + halfArcLength2;" ]

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[ "# Oxygen is composed of three isotopes 16/8 O (15.995 u), 17/8 O (16.999 u) and 18/8 O (17.999 u). One of these isotopes, 17/8 O, comprises of 0.037% of oxygen. What is the percentage abundance of the other two isotopes, using the average atomic mass of 15.9994 u.\n\nJun 23, 2014\n\nThe abundance of $\\text{_8^16\"O}$ is 99.762 %, and the abundance of $\\text{_8^18\"O}$ is 0.201 %.\n\nAssume you have 100 000 atoms of O. Then you have 37 atoms of $\\text{_8^17\"O}$ and 99 963 atoms of the other isotopes.\n\nLet x = the number of atoms of $\\text{_8^16\"O}$. Then the number of atoms of $\\text{_8^18\"O}$ = 99 963 - x\n\nThe total mass of 100 000 atoms is\n\nx × 15.995 u + (99 963 – x) × 17.999 u + 37 × 16.999 u = 100 000 × 15.9994 u\n\n15.995 x + 1 799 234.037 – 17.999 x + 628.963 = 1 599 940\n\n2.004 x = 199 123\n\nx = 199 123/2.004 = 99 762\n\nSo there are 99 762 atoms of $\\text{_8^16\"O}$ or 99.762 %.\n\nThe number of $\\text{_8^18\"O}$ atoms is 99 963 – 99 762 = 201 atoms or 0.201 %.\n\nHope this helps." ]

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[ "# Is there a simple way to understand why SUGRA is two-loop renormalisable?\n\nNaïve quantum gravity is one-loop renormalisable. There is a very simple way to argue that this is true: one lists all possible counter-terms that may appear at one loop, and shows that they are, up to boundary terms, identical to terms already appearing in the original Lagrangian. This requires a non-trivial cancellation that results from the fact that a certain combination of terms happens to be topological (the Euler-Poincaré characteristic, cf. this PSE post).\n\nQuestion: Can a similar analysis show that ($\\mathcal N=4,8$) SUGRA is two-loop renormalisable?\n\nAs far as I know, the two-loops (and three- and four-loops) renormalisability of supersymmetric quantum gravity has been established by computing certain tree-level graphs and using the optical theorem or similar techniques. I guess that enumerating all possible counter-terms to three and four-loops is very cumbersome, but to two-loops it seems feasible. I don't know whether this has been attempted and the analysis was inconclusive (not enough symmetries to rule out all possibilities), or whether the computation is just so cumbersome it is not worth it. It seems to be a very direct approach, so it would be nice if it could be done.\n\nThis does seem to be the way that 2-loop finiteness of $\\mathcal{N}=1$ SUGRA was discovered. A discussion of the construction of possible counterterms is given in e.g. this reference: [arXiv1506.03757]. They show there simply isn't a supersymmetric counterterm at 2-loop order, and hence find that there will be no divergence in $\\mathcal{N}=1$ SUGRA (and therefore, this means no counterterm will exist for $\\mathcal{N}=4$ or $\\mathcal{N}=8$ SUGRA as well, since these theories of course have $\\mathcal{N}=1$ supersymmetry).\nFor higher loop order in the more supersymmetric theories, they appear to have better UV behavior beyond what you would expect even from counterterm arguments. There is some explanation in this reference: [arXiv:1703.08927]. There is also a conjecture that $\\mathcal{N}=8$ SUGRA may be perturbatively finite at all loop orders, which, if true, does not seem to be able to follow from some symmetry principle. So in particular, the absence of an appropriately symmetric counterterm will fail at some loop order to explain the good UV behavior of SUGRA scattering amplitudes." ]

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[ "# Questions tagged [independence]\n\nThe tag has no usage guidance.\n\n12 questions\nFilter by\nSorted by\nTagged with\n33 views\n\n### Combining different length epsilon-ADU hash function families\n\nFor context, an $\\epsilon$-almost delta universal ($\\epsilon$-ADU) hash function family $\\mathcal{H} = \\{h : M \\to D\\}$ hashes inputs from $M$ to digests in $D$ such that for any distinct $m, m' \\in M$...\n220 views\n\n### Family of functions with properties similar to k-wise independent hash functions\n\nI am looking for a family of functions that has similar properties to a family of $\\ell$-wise independent hash functions. The goal is to hash $\\ell$ pairwise different bit strings of length $k$ to a ...\n150 views\n\n### What degree of hash function independence is needed for Bloom filters?\n\nIn the traditional analysis of Bloom filters, it's assumed that the hash functions are truly random functions, meaning that each hash function distributes each key uniformly and independently of each ...\n57 views\n\n### Is there a complete and finite axiom scheme for conditional independence? (Graphoids)\n\nNote: This is a better-written version of an unanswered question asked before on MathOverflow. Question: Is there a complete and finite axiom scheme for conditional probability? If so, is there a ...\n141 views\n\n### Notion similar to k-wise independence\n\nI want to construct a family of functions $H:\\{0,1\\}^n \\rightarrow \\{0,1\\}$ with a property that is similar to k-wise independence. Specifically, I want $H$ to satisfy the following property. Let $k$ ...\n210 views\n\n### When are all facets rank facets? (for independence system polyhedra)\n\nConsider an independence system $(E,\\mathcal{I})$, and the corresponding polytope: $P(E,\\mathcal{I}):=\\operatorname{conv.hull}\\{ x^S ~|~S\\in \\mathcal{I}\\}$ where $x^S \\in \\{0,1\\}^E$ denotes the ..." ]

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[ "# Site: PageListTemplates\n\nThis page contains \"templates\" for PmWiki's `(:pagelist:)` directive.\n\n### Brief Syntax Explanation:\n\nUse with page variables:\n\n``` = current item\n< previous item\n> next item\n```\n\nConditionals used to structure pagelist output:\n\n``` `(:if equal {<\\$Group}:)` At beginning of list\n`(:if equal {>\\$Group}:)` At end of list\n`(:if ! equal {=\\$Group} {<\\$Group}:)` First item in group\n`(:if ! equal {=\\$Group} {>\\$Group}:)` Last item in group\n```\n\n### fmt=#default\n\nThe default template for pagelists when `fmt=` isn't specified.\n\n```[[#default]]\n(:if ! equal {=\\$Group} {<\\$Group}:)\n\n:[[{=\\$Group}]] /:\n(:if:)\n: :[[{=\\$Group}/{=\\$Name}]]\n[[#defaultend]]\n```\n\n### fmt=#bygroup\n\nDisplay pages by group/name.\n\n```[[#bygroup]]\n(:if ! equal {=\\$Group} {<\\$Group}:)\n\n:[[{=\\$Group}]] /:\n(:if:)\n: :[[{=\\$Group}/{=\\$Name}]]\n[[#bygroupend]]\n```\n\n### fmt=#simple\n\nA simple bullet list of page names.\n\n```[[#simple]]\n* [[{=\\$FullName}]]\n[[#simpleend]]\n```\n\n### fmt=#title\n\nA simple bullet list of page titles. Use `order=title` to have them sorted by title (the default sort is by name).\n\n```[[#title]]\n* [[{=\\$FullName}|+]]\n[[#titleend]]\n```\n\n### fmt=#group\n\nA bullet list of groups.\n\n```[[#group]]\n(:if ! equal {=\\$Group} {<\\$Group}:)\n* [[{=\\$Group}]]\n[[#groupend]]\n```\n\n### fmt=#include\n\nConcatenate the text of pages in the list. (Note, this can be an expensive operation!)\n\n```[[#include]]\n(:include {=\\$FullName} self=0:)\n[[#includeend]]\n```\n\n### fmt=#includefaq\n\nInclude just the #faq sections from pages in the list. (This can also be expensive, especially if the list includes pages that don't have the `[[#faq]]` anchor!)\n\n```[[#includefaq]]\n!![[{=\\$FullName}|+]]\n>>faq<<\n(:include {=\\$FullName}#faq#faqend self=0:)\n>><<\n[[#includefaqend]]\n```" ]

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[ "# 309\n\nThis number is a composite.", null, "309^3 + 309^0 + 309^9 is prime with prime digital length. [Patterson]", null, "prime(309)^309 + 2 is prime. With the exception of 309, all known such numbers (up to 10000) are the first three primes. [Firoozbakht]" ]

[ null, "https://primes.utm.edu/gifs/check.gif", null, "https://primes.utm.edu/gifs/check.gif", null ]

[ "# Common Core Algebra II.Unit 2.Lesson 1.Introduction to.\n\nLet us help you with your high school algebra II homework with this interactive algebra II homework help course. Once you've identified which topics you need help on, watch the short video lessons.\n\nCommon Core Algebra II. In this course students will learn about a variety of advanced topics in algebra. Students will expand their understanding about functions by learning about polynomial, logarithmic, and trigonometric functions. These new functions along with linear, quadratic, and exponential, will be used to model a variety of problems, including compound interest, complex numbers.\n\nThe Properties of Functions Review chapter of this High School Algebra II Homework Help course helps students complete their algebraic functions homework and earn better grades.\n\nNow is the time to redefine your true self using Slader’s free Algebra 2 Common Core answers. Shed the societal and cultural narratives holding you back and let free step-by-step Algebra 2 Common Core textbook solutions reorient your old paradigms. NOW is the time to make today the first day of the rest of your life. Unlock your Algebra 2 Common Core PDF (Profound Dynamic Fulfillment) today.\n\nComposition of Functions - Problem 2. Alissa Fong. Alissa Fong. MA, Stanford University Teaching in the San Francisco Bay Area. Alissa is currently a teacher in the San Francisco Bay Area and Brightstorm users love her clear, concise explanations of tough concepts. Share Explanation; Transcript; If you have graphs instead of equations for two functions, you will do the composition using each.\n\nCHENANGO FORKS CENTRAL SCHOOLS. Mr. Fendick 2016-2017. Classroom Policy Math Common Core Algebra I. MATERIALS: Students should have a scientific calculator like a Texas Instruments (TI-30xIIs), A graphing calculator will be available during class. Students ill be given a number of handouts so a 3 ring binder would be useful. Pencils, paper, graph paper, and a straightedge. An open mind and.\n\nNov 4, 2017 - Free Math Assessments or Quizzes for Algebra 2. These Algebra 2 Quizzes are aligned with the common core math standards. These Algebra 2 assessments can also be used as quick checks, spiral math review, and progress monitoring.\n\nComposition of functions is where one entire function is used as the input for the other function. Fog(x) is where the entire g expression should go into the f function where the x used to be, and vice-versa. One tip is to re-write the input as parentheses with a blank to start, and then go back and re-write the input function in the parentheses. Simplify. If your original problem has fog(x.\n\nFree math problem solver answers your algebra homework questions with step-by-step explanations. Mathway. Visit Mathway on the web. Download free on Google Play. Download free on iTunes. Download free on Amazon. Download free in Windows Store. get Go. Algebra. Basic Math. Pre-Algebra. Algebra. Trigonometry. Precalculus. Calculus. Statistics. Finite Math. Linear Algebra. Chemistry. Graphing.\n\nOther Results for Power Algebra 1 Answer Key: Solutions to Algebra 1 Common Core (9780133185485) - Yo. YES! Now is the time to redefine your true self using Slader’s free Algebra 1 Common Core answers. Shed the societal and cultural narratives holding you back and let free step-by-step Algebra 1 Common Core textbook solutions reorient your.\n\nComposite functions is a topic with which students have much difficulty. This activity will enhance their knowledge and help them reinforce the skill taught on this topic while being very engaging. Included: 18 T. Subjects: Math, PreCalculus, Algebra 2. Grades: 9 th, 10 th, 11 th, 12 th, Higher Education, Homeschool. Types: Activities, Handouts, Task Cards. Also included in: PreCalculus Unit.\n\nessay service discounts do homework for money" ]

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[ "• button submit prevent refresh\n• 1775 springfield musket\n• dtg rip software\n• how to adjust pinion angle on mustang\n• hp proliant ml110 g7 drivers for windows server 2003 32 bit\n• bitcoin private key database with balance 2018\n• 2006 cadillac cts bose wiring diagram\n• wwise unpacker not working\n• divinity original sin 2 dual wield fighter build\n• all are trash she said\n• 100mb woreldfree4u\n• Energy transferred = mass of water heated × specific heat capacity of water × temperature rise = 100 × 4.2 × 20 = 8,400 J It is also useful to remember that 1 kilojoule, 1 kJ, equals 1,000 J.\n• Feb 29, 2016 · Different regions will need different strategies, but a mix of renewable energy — such as wind, solar and geothermal — can help lower energy emissions substantially, Mann said. In the meantime, the public has made wry observations about Gates' apparent re-discovery.\n• Climate Change. Coastal Zone Act Program. DE Environmental Appeals Board. Delaware Energy Plan. Delaware Wetlands. DNREC Public Hearings. DNREC Secretary's Orders.\n• Now, back to energy: Note that E < 0. This is called a bound orbit. We have derived this for circular orbits, but it can also be derived for any bound orbit. Note two important things: E is constant for any given orbit. E depends only on a, not e. Let's do two thought experiments. Take an orbit of fixed energy. Change its eccentricity.\n• Internal energy formula physics and examples ... Thus internal energy is similar to the gravitational potential energy. so like the potential energy, it is the change ...\n• With the kinetic energy formula, you can estimate how much energy is needed to move an object. The same energy could be used to decelerate the object, but keep in mind that velocity is squared. This means that even a small increase in speed changes the kinetic energy by a relatively high amount. How about you give our kinetic energy calculator ...\n• Energy efficiency, means using less energy to provide the same level of energy. It is therefore one method to reduce human greenhouse gas emissions. For example if a house is insulated, less energy is used in heating and cooling to achieve a satisfactory temperature.\n• Nov 12, 2016 · Homework Statement A person performs 6.1 J of work to lift an object without acceleration to a particular height on Earth. Write an equation describing that energy change and analyze it to determine how different the energy would be required to lift the same object to the same height on the...\n• For instance, a battery converts chemical to electric energy, chemical explosion converts chemical energy in to kinetic and thermal energy and so on. Power cannot be converted or transformed. Measuring Energy vs. Power. Although it is not possible to directly measure energy, the work done can be defined and measured.\n• A molecular vibration is a periodic motion of the atoms of a molecule relative to each other, such that the center of mass of the molecule remains unchanged. The typical vibrational frequencies, range from less than 10 13 Hz to approximately 10 14 Hz, corresponding to wavenumbers of approximately 300 to 3000 cm −1.\n• Reversing a chemical reaction results in the same magnitude of enthalpy but of the opposite sign. For example, splitting two moles of water to produce 2 moles of H 2 and 1 mole of O 2 gas requires the input of +483.6 kJ of energy. The enthalpy change for a reaction depends upon the state of the reactants and products.\n• Fill in the blue Mass and Heat capacity (Cp) input boxes and choose convenient units from the unit menus. When you fill in either the temperature change or energy change, the calc will give the associated energy or temperature change in the right orange box. Remember that Cp is temperature and phase-dependant.\n• The change in the Gibbs free energy of the system that occurs during a reaction is therefore equal to the change in the enthalpy of the system minus the change in the product of the temperature times the entropy of the system. G = H - (TS) If the reaction is run at constant temperature, this equation can be written as follows. G = H - T S\n• In this case, the energy released b 1. y the hot plate depends on its energy rating. Look at the bottom or sides of the hot plate for its power rating, measured in watts. Since a watt = 1 J/s , we can calculate the total amount of energy released from the hot plate using the following equation:\n• Spring Potential Energy (Elastic Potential Energy) Back Energy Mechanics Physics Contents Index Home . Definition of Spring Potential Energy (Elastic Potential Energy) If you pull on a spring and stretch it, then you do work. That is because you are applying a force over a displacement.\n• In physics, energy is the quantitative property that must be transferred to an object in order to perform work on, or to heat, the object. Energy is a conserved quantity; the law of conservation of energy states that energy can be converted in form, but not created or destroyed.\n• Energy Units Converter Enter your energy value in the box with the appropriate units, then press \"tab\" or click outside of the input box. ... Change the number of ...\n• Apr 13, 2019 · Bill could substantially change electric rate formula for NV Energy RILEY SNYDER The Nevada Independent Apr 13, 2019; 0 {{featured_button_text}} Nevada’s system for setting and determining how ...\n• Energy. Energy is the capacity to do work and is required for life processes. An energy resource is something that can produce heat, power life, move objects, or produce electricity. Matter that stores energy is called a fuel. Human energy consumption has grown steadily .throughout human history.\n• Define energy. energy synonyms, energy pronunciation, energy translation, English dictionary definition of energy. n. pl. en·er·gies 1. The capacity for work or ...\n• Energy (heat) is produced when an acid reacts with a base in a neutralisation reaction. ⚛ Neutralisation reactions are exothermic. ⚛ ΔH for a neutralisation reaction is negative. Molar heat of neutralisation (molar enthalpy of neutralization) is the energy liberated per mole of water formed during a neutralisation reaction.\n• The above equation is one of the most widely used equation in thermodynamics. ΔG (Change in Gibb's Energy) of a reaction or a process indicates whether or not that the reaction occurs spontaniously. When ΔG = 0 the reaction (or a process) is at equilibrium. ΔG > 0 indicates that the reaction (or a process) is non-spontaneous and is endothermic (very high value of ΔG indicates that the ...\n• The Digital Dutch Unit Converter - Online conversion of area, currency, density, energy, force, length, mass, power, pressure, speed, temperature, volume and bytes.\n• The deadline to submit code changes proposals for the 2009 Washington State Energy Code was March 1, 2009. This code is expected to exceed the energy efficiency of the 2009 IECC, with an anticipated effective date of July 1, 2010. Code adoption was delayed and the 2009 WA State Code became effective Jan. 1, 2011.\n• If a photon of light strikes an atom, it is possible for the energy in the light ray to be transferred to one of the low energy electrons moving around the atomic center. The electron with its extra packet of energy becomes excited, and promptly moves out of its lower energy level and takes up a position in a higher energy level.\n• The formula for potential energy of a system depends on the forces at work and the constituents of a system. All macroscopic systems outside the atomic nucleus are either governed by the electromagnetic or gravitational forces. Potential energy is measured in SI unit of ' Joule '.\n• Reversing a chemical reaction results in the same magnitude of enthalpy but of the opposite sign. For example, splitting two moles of water to produce 2 moles of H 2 and 1 mole of O 2 gas requires the input of +483.6 kJ of energy. The enthalpy change for a reaction depends upon the state of the reactants and products.\n• Conservation of energy The total amount of energy before = the total amount of energy after. Gravitational potential energy is converted to kinetic energy as an object falls, but the total amount of energy stays the same. Kinetic energy is converted to heat and sound energy as a crate slides to a stop on a rough surface. Conservative forces\n• Electric Potential Energy. Potential energy can be defined as the capacity for doing work which arises from position or configuration. In the electrical case, a charge will exert a force on any other charge and potential energy arises from any collection of charges.\n• Symbol Represents Units ∆x, ∆y, ∆z change in length in x, y or z direction length, meters A area = xy (or πr 2 if area of a circle) length2, meters V volume = xyz (or πr2l if volume of a cylinder) length3, meters3\n• Racing. Your mind has to be prepared and so does your body. That’s why it’s important to train with what’s on course. Gatorade ® Endurance Formula proudly hydrates and fuels athletes on over 300 race courses.\n• This online chemical calculator may used to calculate the change of internal energy for a change in temperature, when the heat capacity at constant volume of the system is a constant in the said range of temperature and the system attains a fixed volume (when volume of the system is constant) during the temperature change.\n• Phase Change and Latent Heat . There is chemical potential energy in the weak van der Waals attractions as well as in the strong ionic and covalent bonds. Because the van der Waals attraction is so much weaker, there is much less chemical potential possible here, but it is a major factor in the energy of phase changes.\n• Life Change Tea: see what everyone is talking about. It’s time to get well. With continued use of the tea you can experience clearer, healthier, younger looking skin, increased energy and a happier outlook on life.\n• Jul 18, 2019 · How to Calculate the Gravitational Potential Energy of an Object. Gravitational Potential Energy (GPE) is the energy of place or position. It depends on 3 things: the force of gravity (9.81), the mass of the object (in kilograms), and the...\n• Equation is known as the Rydberg formula. Likewise, is called the Rydberg constant. The Rydberg formula was actually discovered empirically in the nineteenth century by spectroscopists, and was first explained theoretically by Bohr in 1913 using a primitive version of quantum mechanics.\n• if the force has a constant magnitude during its action. If the force changes with time, then one must integrate to find the impulse: / impulse = | (force) dt / The Momentum-Impulse Theorem states that the change in momentum of an object is equal to the impulse exerted on it:\n• Using the data below and Coulomb\\'s law, calculate the energy change for this reaction (per formula unit of CsCl). . Using the data below and Coulomb\\'s law ...\n• The Heat Transfer is the measurement of the thermal energy transferred when an object having a defined specific heat and mass undergoes a defined temperature change. Heat transfer = (mass)(specific heat)(temperature change) Q = mcΔT . Q = heat content in Joules. m = mass. c = specific heat, J/g °C . T = temperature . ΔT = change in temperature\n• The formula for potential energy of a system depends on the forces at work and the constituents of a system. All macroscopic systems outside the atomic nucleus are either governed by the electromagnetic or gravitational forces. Potential energy is measured in SI unit of ' Joule '.\n• The second part of your question is a bit easier. Although gasoline contains many different chemical compounds, it is made up mostly of hydrocarbons, and all hydrocarbons form the same products when they are burned (just in different amounts).\n• Oct 30, 2006 · As the others said, kinetic energy cannot be negative. However, a change in kinetic energy can. Throw a ball straight up and its kinetic energy decreases to zero at its peak. The ball experienced a negative change to its kinetic energy.\n• Jun 19, 2011 · There is a quick back of the envelope formula used for calculating the BTU/h values for heating water. The “water formula” says: Q (Energy) = 500 x f x DeltaT (in F) Q = rate of heat transfer (Btu/hr.) f= flow rate (gallons per minute or gpm) DeltaT = temperature change (degrees F)\n• This specific heat calculator is a tool that determines the heat capacity of a heated or a cooled sample. Specific heat is just the amount of thermal energy you need to supply to a sample weighing 1 kg to increase its temperature by 1 K. Read on to learn how to apply the heat capacity formula correctly to obtain a valid result.\n• The total energy of a system of reacting chemicals and surroundings remains constant. Enthalpy change is the term used to describe the energy exchange that takes place with the surroundings at a constant pressure and is given the symbol ΔH. Enthalpy is the total energy content of the reacting materials.\n• Physics Formulas on laws of motion, one, two and three dimensional motion, work , energy, power, circular motion, gravitation, properties of matter and electricity. Also tutorials and answers on many physics topics\n• Note that every vibration has a zero point energy found by substituting v=0 into the above equation, ZPE = E(0) = ½ e – ¼xe e As well as changing the energy of the vibrational levels, anharmonicity has another, less obvious effect: for a molecule with an anharmonic potential, the rotational constant changes slightly with vibrational state.\n• Conservation of energy The total amount of energy before = the total amount of energy after. Gravitational potential energy is converted to kinetic energy as an object falls, but the total amount of energy stays the same. Kinetic energy is converted to heat and sound energy as a crate slides to a stop on a rough surface. Conservative forces\n• Sep 09, 2011 · This energy is supplied by the combination of electric current and electrical potential that is delivered by the circuit. At the point that this electrical potential energy has been converted to another type of energy, it ceases to be electrical potential energy. Thus, all electrical energy is potential energy before it is delivered to the end-use.\n\n# Energy change formula\n\nConan exiles builds reddit Goodbye letter from teacher to parents\n\n## 1996 toyota tacoma front suspension diagram\n\nTotal entropy change. As we have seen above, the entropy change of the ammonia / hydrogen chloride reaction (‘the system’) is –284 J K-1 mol-1.It is negative as we have calculated (and predicted from the reaction being two gases going to a solid).\n\nThe formula for potential energy is: G.P.E.=mgh Weight (mass x gravity) determines the amount of potential energy. Is there potential energy in the 5 forms of energy? Yes, potential energy can be found in fossil fuels, within the foods you eat, and the batteries that you use. Conservation of Energy:\n\nIn other words, the work done is equal to the change in K.E. of the object! This is the Work-Energy theorem or the relation between Kinetic energy and Work done. In other words, the work done on an object is the change in its kinetic energy. W = Δ(K.E.) The engine of your motorcycle works under this principle.\n\n### 110 dbm 30 asu\n\nIn doing work, the energy is changed from one form to one or more other form(s). In these changes some of the energy is “lost” in the sense that it cannot be recaptured and used again. Usually there is loss in the form of heat, which escapes or is dissipated unused; all energy changes give off a certain amount of heat.ƒ Spring Potential Energy (Elastic Potential Energy) Back Energy Mechanics Physics Contents Index Home . Definition of Spring Potential Energy (Elastic Potential Energy) If you pull on a spring and stretch it, then you do work. That is because you are applying a force over a displacement." ]

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[ "Newbie\n\n# Which term of this Arithmetic Progression 3, 8, 13, 18, .… is 78 ?\n\n• 0\n\nThis question is from Ncert Book class 10th Ch. number 5 Ex. 5.2 Q. 4 . In the following question you have to  find out which term of the A.P given above will be 78. Also give the full solution of the question.\n\nShare\n\n1. Solution:\n\nA.P is given as 3, 8, 13, 18, …\n\na = 3\n\nd = a2 − a1 = 8 − 3 = 5\n\nLet the nth term of the A.P. be 78.\n\nWe know,\n\nan = a+(n−1)d\n\nThen,\n\n78 = 3+(n −1)5\n\n75 = (n−1)5\n\n(n−1) = 15\n\nn = 16\n\nThe 16th term of this A.P is 78.\n\n• 0" ]

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[ "February 7, 2023", null, "# What Is An Arithmetic Logic Unit (ALU) and Its Functions?\n\nHello there, in this article we will discuss the Arithmetic Logic Unit (ALU) and its functions. ALU is one of the most important components of computing circuits like CPUs and GPUs.\n\nALU usually handles the mathematical operations that processing units receive. Dive down in this article to know more about the ALU and why are they so important.\n\nAnd don’t forget to watch the bonus video at the end of the article.\n\n## What is the APU?\n\nAn arithmetic logic unit (ALU) is a digital electronic circuit present within the CPU that performs arithmetic and bitwise operations.\n\nALU deals with integer binary numbers while the floating point unit (FPU) deals with floating point numbers. ALU is a fundamental building block of many types of computing circuits like CPUs and GPUs.\n\nA single CPU or GPU may also consist of more than one ALU. Moreover, input to the APU is the data to be operated called operand.\n\nWhen the operation becomes more complex, then the ALU also becomes more expensive and takes up more space in the CPU and also produces more heat.\n\nThat’s why ALUs are powerful enough to ensure that the CPU fast but not so complex to become very expensive.\n\n##", null, "Related: What Is A CPU? | CPU Functions, Components, And Diagram\n\n## Arithmetic Logic Unit (ALU) Signals\n\nAn Arithmetic Logic Unit (ALU) has a variety of input and output electrical connections that helps to convey digital signals between the ALU and external electronics.\n\nExternal circuits give signals to the ALU input and in response, ALU outputs signal to external electronics.\n\n#### Data:\n\nALU has three parallel buses consisting of two input operands and an output operand. The number of signals handled by all the three buses is the same.\n\nEvery data bus is a group of signals that conveys one binary integer number.\n\n#### Opcode:\n\nThe opcode input is a parallel bus that transmits an operation selection code to the ALU. An operation selection code is a calculated value that specifies the desired arithmetic or logic operation that an ALU is going to perform.\n\nThe opcode size determines the greatest number of various operations the ALU can perform.\n\n#### Status:\n\nOutput: The status outputs are many individual signals that convey supplemental data about the results of the ALU operations.\n\nGeneral ALUs usually have status signals such as: Carry out, zero, negative, overflow, etc. After the completion of each ALU operation, the status output signals were in external registers.\n\nStoring these signals in registers makes them available for future ALU operations.\n\nInput: The status inputs permit further information to access to the ALU once performing an operation. Moreover, this is a single “carry-in” bit that’s the stored carry-out from a previous ALU operation.\n\n##", null, "Related: What’s the difference between CPU and GPU?\n\n## Arithmetic Logic Unit (ALU) Functions\n\nArithmetic Logic Units (ALU) has various numbers of basic arithmetic and bitwise logic functions. General purpose ALUs usually include these operations:\n\nArithmetic Operations: Arithmetic operations include addition and subtraction. However, sometimes multiplication and division are also used, these operations are more expensive to make.\n\nThat’s why multiplication and division are done by repetitive addition and subtraction. Some common arithmetic operations that an ALU performs are: add, subtract, increment, decrement, etc.\n\nBit shift operations: Bit shift operations cause operand to shift left or right. Simple ALUs can shift operands by only one-bit position, whereas more complex ALUs can shift by many bits.\n\nComplex ALUs are able to shift by many bits because they have barrel shifters.\n\nBitwise Logical Operations: These are the operations like AND, OR, NOT, NOR, NAND, etc." ]

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[ "", null, "## What our customers say...\n\nThousands of users are using our software to conquer their algebra homework. Here are some of their experiences:\n\nWOW!!! I love the upgrade. I just read (via the online help files) about the wizards and really like the way theyre setup. Im currently working on synthetic division in class that particular wizard is GREAT!!! The interface much easier to use than the old version! I love the toolbars entering equations is so easy! The online documentation, in terms of providing help for entering equations, is great. This is actually my second Algebra software purchase. The first program I purchased was a complete disappointment. Entering equations was difficult and the documentation was horrible. I was very happy to find your software and now am ecstatic with the upgrade to Algebra Help. I am a working adult attending college part time in the evenings. The support this product provides me is invaluable and I would highly recommend it to students of any age!\nMargaret Thomas, NY\n\nThank you very much for your help. This is excellent software and I thank you.\nDerek Brennan, IL\n\nIm a retired high school teacher and currently work as a tutor. It always used to frustrate me that a child could do so well as long as I was sitting there with them but as soon as I had to leave, the child went back to struggling. Through my research, I found your product. The parents bought it for their son and Im glad to say hes doing terrific all on his own.\nJessica Simpson, UT\n\n## Search phrases used on 2014-07-29:\n\nStudents struggling with all kinds of algebra problems find out that our software is a life-saver. Here are the search phrases that today's searchers used to find our site. 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[ "# Why is the integral of $\\frac1{x^2}$ from $1$ to $\\infty$ not the same as the infinite sum from $1$ to $\\infty$?\n\nStudying series I am a bit confused on this point. The infinite sum of $1/x^2$ from $1$ to $\\infty$ was proved by Euler to be $\\pi^2$ divided by $6$:\n\n$$\\sum_{x=1}^\\infty\\frac 1 {x^2}=\\frac {\\pi^2} 6$$\n\nBut if I integrate from $1$ to $\\infty$ of the same entity namely $1/x^2$ it is $1$. Correct..? Unless I did it wrong. $$\\int_1^\\infty\\frac 1 {x^2}dx=1$$ How can this be since by integrating it seems we are adding a lot more numbers to cover the same area so we should by all means get the same thing or something at least as large as $\\pi^2/6$?\n\n• Why would anyone expect them to be the same? Dec 24, 2017 at 16:49\n• @LordSharktheUnknown, please read his entire question. Dec 24, 2017 at 16:54\n• The relationship between the sum and the integral is given by en.wikipedia.org/wiki/Euler–Maclaurin_formula. they differ because rectangles are not curved. The area in the rectangles is not the area under the curve. Dec 24, 2017 at 16:54\n• @Sedumjoy, please read your edited question for how to write the integral and sum :). Dec 24, 2017 at 17:00\n• I agree with @LordSharktheUnknown, it is not natural to expect that $$f(x)=\\frac{1}{x^2},\\qquad g(x)=\\frac{1}{\\lfloor x\\rfloor ^2}$$ have the same integral over $(1,+\\infty)$, also because $g(x)\\geq f(x)$. Dec 24, 2017 at 17:55\n\nNote that $$\\int_1^\\infty \\frac{1}{x^2}\\leq\\sum_1^\\infty \\frac{1}{n^2}\\tag{1}$$ by considering a Riemann sum with left endpoints. Here is a picture (for the case of $1/x$ but a similar picture can be drawn for this case as well). See this picture. Image credits go to Wikipedia.", null, "• +1 For the picture.. It illustrates the point better :) I will add it to my answer\n– Ant\nDec 24, 2017 at 16:59\n• no its the wrong graph, should be a graph of $\\frac{1}{x^2}$, right? Dec 24, 2017 at 17:00\n• @FoobazJohn, Just wondering, what program did you use to make this picture? Dec 24, 2017 at 17:00\n• @mathreadler, yeah you're right, though the basic insight remains the same. Dec 24, 2017 at 17:01\n• @mathreadler Yes I commented that it is for $1/x$ but a similar picture can be drawn for the case $1/x^2$. Dec 24, 2017 at 17:01\n\nWhen you do the sum, you sort of approximate the area with rectangles of base length equal to $1$. Draw the function $1/x^2$ and draw the rectangles with base length 1; you'll see that the area under the rectangles is much bigger than the area under the function $1/x^2$\n\nHere is an illustration for the function $1/x$, but it's essentially the same as in the $1/x^2$ case. (Thanks to @FoobazJohn)", null, "The integral adds a lot more numbers, but these numbers are multiplied by something very small. The end result is that the integral represents the area under the $1/x^2$ curve, which is less than the area under the rectangles.\n\nLet us compare $1$ and $\\int_1^2\\frac1{x^2}\\,\\mathrm dx$. Since $\\bigl(\\forall x\\in(1,2]\\bigr):\\frac1{x^2}<1$, $\\int_1^2\\frac1{x^2}\\,\\mathrm dx<1$. For the same reason, $\\int_2^3\\frac1{x^2}\\,\\mathrm dx<\\frac14$, $\\int_3^4\\frac1{x^2}\\,\\mathrm dx<\\frac19$, and so on. So$$1=\\int_1^\\infty\\frac1{x^2}\\,\\mathrm dx<\\sum_{n=1}^\\infty\\frac1{n^2}=\\frac{\\pi^2}6.$$\n\nNote that it is not true that $\\int_a^bf(x)\\,\\mathrm dx$ is the sum of all numbers $f(x)$ with $x\\in[a,b]$. Instead, it is the average value of $f$ in $[a,b]$ times $b-a$.\n\n• all three answers are very good in explaining this and I will pick one to close the problem but they are equally good....I feel stupid for not seeing this that I had to ask.... Dec 25, 2017 at 0:59" ]

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[ "# Parallel Resistors Calculator\n\nA parallel resistors calculator that calculates the equivalent resistance is presented. Consider the group of parallel resistors R1, R2, ... Rm in the diagram below. These resistors have an equivalent resistance Req that has the same effects on the other parts of the circuit and is given by the resistors in parallel formula:\n\n1 / Req = 1 / R1 + 1 / R2 + .... + 1 / Rm", null, "For example, for 2 resistors R1 and R2 in parallel, Req is given by\n\n1 / Req = 1 / R1 + 1 / R2\n\nWhen the above is solved for Req, we obtain\n\nReq = (R1 R2) / (R1 + R2)\n\nFor 3 resistors R1, R2 and R3 in parallel, Req is given by\n\n1 / Req = 1 / R1 + 1 / R2 + 1 / R3\n\nSolve for Req, to obtain\n\nReq = R1 R2 R3 / (R1 R2 + R1 R3 + R2 R1)\n\nAs it can be seen, the calculations becomes complicated as soon as we start increasing the number of parallel resistors in the circuit.\n\n## Use the Parallel Resistors Calculator\n\nEnter the resistances of the resistors R1, R2, ... Rn as positive real numbers separated with commas and then press \"Calculate Equivalent Resistance\". You may enter any number of resistances separated by commas.\n\n Resistances of R1, R2, ... Rn: = 4,6,10.5 Ohms Decimal Places = 4 Equivalent Resistance: = Ohms" ]

[ null, "https://cdn-0.problemsphysics.com/physics-calculators-solvers/resistors-in-parallel.gif", null ]

[ "# 在线杠杆配资选推荐卓信宝\n\n2020-08-30 17:47:08\n\n2020-08-30 16:25:13\n\n2020-08-30 18:20:00\n\n빈곤지역의새로운농촌건追答我知道好几个，目前还是他们更好些，配.资的话也许你会用得着。𝐏𝐙𝟔8.𝐂om.当老人走到阿宝家的时候，阿宝从屋子里走出来，给了这位可怜的乞讨老人一些食物，并劝他快跟随大家上山躲避“年”兽。没想到乞讨老人听后，捋着他的胡须，笑眯眯地说：“小兄弟，你能让我这个孤苦无依的老人借宿一晚吗？”\n\n2020-08-30 16:46:15\n\n2020-08-30 16:59:07\n\n2020-08-30 15:07:44\n\n2020-08-30 14:53:51\n\ntyv风险与收益是成正比的，收益越大风险也越高，所以在配资时选择适当的杠杆倍数。ywzoq\n\n2020-08-30 17:27:58\n\n2020-08-30 17:16:54\n\nDIF:=EMA(CLOSE,12)-EMA(CLOSE,26);DEA:=EMA(DIF,9);MTR:=MAX(MAX((HIGH-LOW),ABS(REF(CLOSE,1)-HIGH)),ABS(REF(CLOSE,1)-LOW));ATR:=MA(MTR,26);MA1:=MA(C,20);MA2:=MA(C,60);T0:=MTR/ATR;T1:=T0>1&&REF(T0,1)<1;T2:=MA1>REF(MA1,1)&&REF(MA1,1)>REF(MA1,2);T3:=DIF>0&&DEA>0;T4:=C>MA1&&C>MA2;XG:T1=1&&T2=1&&T3=1&&T4=1;更多追问追答追问能麻烦再改一下吗，我有两个条件变动了一下，悬赏也提高了追答{第一个}DIF:=EMA(CLOSE,12)-EMA(CLOSE,26);DEA:=EMA(DIF,9);MTR:=MAX(MAX((HIGH-LOW),ABS(REF(CLOSE,1)-HIGH)),ABS(REF(CLOSE,1)-LOW));ATR:=MA(MTR,26);MA1:=MA(C,20);MA2:=MA(C,60);T1:=BARSLASTCOUNT(MTR/ATR=11;T0:=BARSLAST(T1=1&&REF(T1,1)=0);T2:=MA1>REF(MA1,1)&&REF(MA1,1)>REF(MA1,2)&&REF(MA1,2)>REF(MA1,3);T3:=DIF>0 OR DEA>0;T4:=C>MA1&&C>MA2;T5:=REF(HHV(H,T0+1),1)>H;XG:T1=1&&T2=1&&T3=1&&T4=1&&T5=1;{第二个}DIF:=EMA(CLOSE,12)-EMA(CLOSE,26);DEA:=EMA(DIF,9);MTR:=MAX(MAX((HIGH-LOW),ABS(REF(CLOSE,1)-HIGH)),ABS(REF(CLOSE,1)-LOW));ATR:=MA(MTR,26);MA1:=MA(C,20);MA2:=MA(C,60);T1:=BARSLASTCOUNT(MTR/ATR=11;T0:=BARSLAST(T1=1&&REF(T1,1)=0);T2:=MA1>REF(MA1,1)&&REF(MA1,1)>REF(MA1,2);T3:=DIF>0 OR DEA>0;T4:=C>MA1&&C>MA2;T5:=REF(HHV(H,T0+1),1)>H;XG:T1=1&&T2=1&&T3=1&&T4=1&&T5=1;追问试了下，还是不太对，就这样吧，低位持股不动才是好的吧，技术炒股太难了追答技术指标是没有预测功能呢，这个不用试了，如果能找到，交易就没有存在的意义了。但技术指标必须要用，一定要把技术指标和资金管理配合使用才可以的。\n\n2020-08-30 17:25:14" ]

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[ "## Eigenvalues of a Matrix Calculator", null, "• Clear up math questions\n• Solve mathematic question\n• Top Teachers\n• Solve mathematic equations", null, "## Eigenvalues and Eigenvectors\n\nEigenvalues are mathematical constructs that help describe many types of physical phenomena. This site will help you learn how to find them.\n\n## How to Find Eigenvalues of Matrix?\n\nEigenvalues are the core part of linear algebra, and this page will show you how to find them!", null, "## Eigenvalues and eigenvectors", null, "", null, "Get support from expert teachers", null, "How to determine the Eigenvalues of a Matrix\nExperts will give you an answer in real-time\n\nMath can be confusing, but there are ways to make it easier. One way is to clear up the equations.\n\nProvide multiple methods\n\nI can do mathematical tasks quite easily.\n\nClear up mathematic problem\n\nIf you're looking for an expert opinion on something, ask one of our experts and they'll give you an answer in real-time." ]

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[ "# Remanence\n\nRemanence or remanent magnetization or residual magnetism is the magnetization left behind in a ferromagnetic material (such as iron) after an external magnetic field is removed. Colloquially, when a magnet is \"magnetized\" it has remanence. The remanence of magnetic materials provides the magnetic memory in magnetic storage devices, and is used as a source of information on the past Earth's magnetic field in paleomagnetism.\n\nThe equivalent term residual magnetization is generally used in engineering applications. In transformers, electric motors and generators a large residual magnetization is not desirable (see also electrical steel) as it is an unwanted contamination, for example a magnetization remaining in an electromagnet after the current in the coil is turned off. Where it is unwanted, it can be removed by degaussing.\n\nSometimes the term retentivity is used for remanence measured in units of magnetic flux density.\n\n## Types\n\n### Saturation remanence\n\nThe default definition of magnetic remanence is the magnetization remaining in zero field after a large magnetic field is applied (enough to achieve saturation). The effect of a magnetic hysteresis loop is measured using instruments such as a vibrating sample magnetometer; and the zero-field intercept is a measure of the remanence. In physics this measure is converted to an average magnetization (the total magnetic moment divided by the volume of the sample) and denoted in equations as Mr. If it must be distinguished from other kinds of remanence, then it is called the saturation remanence or saturation isothermal remanence (SIRM) and denoted by Mrs.\n\nIn engineering applications the residual magnetization is often measured using a B-H analyzer, which measures the response to an AC magnetic field (as in Fig. 1). This is represented by a flux density Br. This value of remanence is one of the most important parameters characterizing permanent magnets; it measures the strongest magnetic field they can produce. Neodymium magnets, for example, have a remanence approximately equal to 1.3 teslas.\n\n### Isothermal remanence\n\nOften a single measure of remanence does not provide adequate information on a magnet. For example, magnetic tapes contain a large number of small magnetic particles (see magnetic storage), and these particles are not identical. Magnetic minerals in rocks may have a wide range of magnetic properties (see rock magnetism). One way to look inside these materials is to add or subtract small increments of remanence. One way of doing this is first demagnetizing the magnet in an AC field, and then applying a field H and removing it. This remanence, denoted by Mr(H), depends on the field. It is called the initial remanence or the isothermal remanent magnetization (IRM).\n\nAnother kind of IRM can be obtained by first giving the magnet a saturation remanence in one direction and then applying and removing a magnetic field in the opposite direction. This is called demagnetization remanence or DC demagnetization remanence and is denoted by symbols like Md(H), where H is the magnitude of the field. Yet another kind of remanence can be obtained by demagnetizing the saturation remanence in an ac field. This is called AC demagnetization remanence or alternating field demagnetization remanence and is denoted by symbols like Maf(H).\n\nIf the particles are noninteracting single-domain particles with uniaxial anisotropy, there are simple linear relations between the remanences.\n\n### Anhysteretic remanence\n\nAnother kind of laboratory remanence is anhysteretic remanence or anhysteretic remanent magnetization (ARM). This is induced by exposing a magnet to a large alternating field plus a small DC bias field. The amplitude of the alternating field is gradually reduced to zero to get an anhysteretic magnetization, and then the bias field is removed to get the remanence. The anhysteretic magnetization curve is often close to an average of the two branches of the hysteresis loop, and is assumed in some models to represent the lowest-energy state for a given field. There are several ways for experimental measurement of the anhysteretic magnetization curve, based on fluxmeters and DC biased demagnetization. ARM has also been studied because of its similarity to the write process in some magnetic recording technology and to the acquisition of natural remanent magnetization in rocks.\n\n## Examples\n\nMaterialRemanenceReferences\nFerrite (magnet)0.35 T (3,500 G)\nSamarium-cobalt magnet0.82–1.16 T (8,200–11,600 G)\nAlNiCo 51.28 T (12,800 G)\nNeodymium magnet1–1.3 T (10,000–13,000 G)" ]

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[ "# HourRank 31 Save the Queen -- Binary Search\n\n## Binary Search\n\nPosted by Micah on December 4, 2018\n\n## Topic\n\nDetails\n\nThe kingdom of Zokoria is under attack! The invaders wish to capture the Queen and conquer Zokoria. Aware of the danger, Heldorf , the captain of the Zokorian army must devise an exit strategy for the Queen.\n\nIn order to do so, the invaders must be kept at bay for a period of time. There are n invaders who must be engaged in fight for as long as possible. The army has k soldiers, with each having the capability to fight for a total of a(i) seconds. The soldiers can fight against any invader at any time i.e. they can move to fight with another invader by dropping the current fight.\n\nHeldorf wants you to find out how long does he have to help the Queen escape. You have to find the maximum possible time for which all the n invaders can be kept busy?\n\nInput Format\n\nThe first line of input contains two numbers n and k - the number of invaders and the number of soldiers respectively.\n\nThe next line contains k numbers, each integer representing the time for which the respective soldier can engage in a fight.\n\nConstraints\n\n• 1 <= n <= k <= 10^4\n• The time for which each solider can fight, a(i) , lies between 1 and 10^6.\n\nOutput Format\n\nPrint the maximum possible time for which the invaders can be engaged in a fight. The number should be accurate up to 10^(-4) absolute precision.\n\nExample\n\nSample Input 0\n3 4\n1000 100 100 100\n\nSample Output 0\n150.000000000\n\n## Idea\n\nWe can solve this problem by using Binary Search. We can define a function check(t) which tells if it is possible to keep the invaders engaged for time t. Since this function is monotonically increasing in nature, we can apply Binary Search here. For checking, we can assign a solider to an invader if t <= ai else we can compute the total time we can allot to each invader. Now, since the time can be a real number, we have to be careful about the precision while implementing Binary Search. One way we can do get the correct answer is to iterate the Binary Search a fixed number of times so that all bits in the answer have been found and no epsilon error is there.\n\n### C++ Solution\n\n``````#include<bits/stdc++.h>\nusing namespace std;\n\nint n,k,a;\n\nint main(){\ncin>>n>>k;\nfor(int i=0;i<k;i++){\ncin>>a[i];\n}\ndouble lo = 0.0, hi = 1e15, mid;\nfor(int i = 0; i < 400; i++){\nmid = (lo+hi)/2;\nint inv = n;\ndouble req = 0.0;\nfor (int j = 0; j < k; j++)\nif(a[j] >= mid){\ninv--;\n}else{\nreq += a[j];\n}\nif(inv <= 0){\nlo = mid;\ncontinue;\n}\nreq /= inv;\nif (req < mid) hi = mid; else lo = mid;\n}\n\ncout<<fixed<<setprecision(9)<<mid<<endl;\n}\n``````", null, "" ]

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[ "", null, "# SQL Server 21-point Gauss-Kronrod quadrature\n\nUpdated: 31 March 2014\n\nUse the scalar function QUADGK to evaluate a finite integral. QUADGK uses 21-point Gauss-Kronrod quadrature.\nSyntax\n<@Func, nvarchar(max),>\n,<@VarName, nvarchar(4000),>\n,<@A, float,>\n,<@B, float,>)\nArguments\n@Func\nthe function to be integrated. @Func is a string containing any valid TSQL statement which includes a single variable that is the object of the integration. The variable name is defined in @VarName. @Func is of a type nvarchar or of any type which implicitly converts to nvarchar.\n@VarName\nthe TSQL variable name. The variable name must start with '@'. @VarName must be of a type nvarchar or of a type which implicitly converts to nvarchar.\n@A\nThe lower limit of integration. @A must be of a type float or of a type that implicitly converts to float.\n@B\nThe upper limit of integration. @B must be of a type float or of a type that implicitly converts to float.\nReturn Types\nfloat\nRemarks\n·         If @A not less than @B and error will be returned.\n·         If @Func contains an undeclared SQL variable and it is not defined in @VarName a NULL will be returned.\nExample\nIn this example we want to evaluate the integral:", null, "SELECT\n'SELECT 1/SQRT(@x)',    --@Func\n'@x',                   --@VarName\n0,                      --@A\n1                       --@B\n) as Integral\n\nThis produces the following result.\nIntegral\n----------------------\n2\n\nIn this example we want to evaluate the integral:", null, "SELECT\n'SELECT SQRT(4-POWER(@x,2))', --@Func\n'@x',                         --@VarName\n0,                            --@A\n2                             --@B\n) as Integral\n\nThis produces the following result.\nIntegral\n----------------------\n3.14159265358979\n\nIn this example we want to evaluate the integral:", null, "Note that COSH, the hyperbolic cosine function, and SINH, the hyperbolic sine function, are not a built-in SQL Server functions but are part of the XLeratorDB library.\nSELECT\n'SELECT PI()/2e+00*wct.COSH(@x)*SIN(EXP(PI()/2e+00*wct.SINH(@x)))',                 --@Func\n'@x',                   --@VarName\n-2,                     --@A\n2                       --@B\n) as Integral\n\nThis produces the following result.\nIntegral\n----------------------\n1.57044006384932\n\n### Support", null, "", null, "Copyright 2008-2019 Westclintech LLC         Privacy Policy        Terms of Service" ]

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[ "", null, "Understanding Threading in Python LG #107 Linux Gazette Python Tutorial; Python - Home; Python thread.py and threading.py serve as Python Threads. but during that time thread t2 was sleeping so thread was still alive.\n\n## PyQt/Threading_Signals_and_Slots Python Wiki\n\nEvent Scheduling (threading.Timer) В« Python recipes. 8/04/2014 · This is a tutorial covering the basics of adding threading to your python programs. All Links and Slides will be in the description. Subscribe for more, 16/11/2018 · A place where you can post Python-related tutorials you made yourself, For example Basic prefixes define thread tutorials for the beginner Current time: Nov.\n\n15/09/2012 · Python threading.timer - repeat function every I know i can change the decorator in the source code any time. what, for example, python threading.Timer start We show you how to create a thread in Python (two in this example) of our thread-supported class. Measure Time in Python – time.time() vs time.clock()\n\nUnderstanding Threading in Python. #!/usr/bin/env python import time import thread def Without the lock competing threads could cause havoc, for example: Java, Java EE, Android, Python, Web Development Tutorials. Java Tutorial; Java Timer TimerTask Example. run the associated tasks as a daemon thread. Timer\n\nThis website contains a free and extensive online tutorial by Bernd Klein with Example for a Thread in Python: import time from threading import Tutorial on Threads Programming with Python time, when we could be 3.1 The thread Module The example here involves a client/server pair.3 As you’ll see from\n\n12/12/2017 · Python Threading Beginners Tutorial - Threading Example #1 Image Downloading This video demonstrates the benefits of using Python threading to dowload An alternative is to use a state variable that another thread can use to signal the current thread that it's time to die. Although Python examples of threading\n\nPython Multithreaded Programming to advanced concepts with examples including Python Syntax python import thread import time # Define a Event Scheduling (threading.Timer) (Python recipe) by James Kassemi. ActiveState Code I really appreciate this succinct example of a timed event class.\n\nIn this Python multithreading tutorial, one thread waits for input and another runs a GUI at the same time. #Python multithreading example to demonstrate Tutorial on Threads Programming with Python since only one program can run at a time, 3.1 The thread Module The example here involves a client/server pair\n\nMultiprocessing and multithreading in Python 3. This is a toy example use case of threads for queue import Queue import time list_lock = threading PyQt; Threading ,_Signals_and_Slots This example shows how to create a separate thread The worker thread is implemented as a PyQt thread rather than a Python\n\n... , they are separate objects in Python. Python’s Thread class supports a as an example of creating custom threads. Timers are threading.Timer Event Scheduling (threading.Timer) (Python recipe) by James Kassemi. ActiveState Code I really appreciate this succinct example of a timed event class.\n\n14/05/2016 · Threading and threads. Timed threads. In Python, the Timer class is a subclass of Hi Frank!Thanks for your tutorials.In the last example,there were time 10/08/2018 · This article explains how to use python threads with a simple and common example Python tutorial : Understanding Python time by 2 distinct threads,\n\nPython Tutorial; Python - Home; Python thread.py and threading.py serve as Python Threads. but during that time thread t2 was sleeping so thread was still alive. A complete python threading tutorial on how to use the threading and Looking at the above example, we create the thread and start = time.time() threads\n\nEvent Scheduling (threading.Timer) В« Python recipes. Introduction to Multiprocessing in Python at the same time, as shown in the example instead of threads. There is much more in the Python documentation, Python Multithreading Python Multithreading – Python’s threading module allows to create threads as objects. In this tutorial, we shall learn how to work with.\n\n### Multiprocessing and multithreading in Python 3 Plogging Dev", null, "Python Programming Multithreading codingpointer.com. Python Programming/Threading. Examples A Minimal Example #!/usr/bin/env python import threading import time class MyThread (threading. Thread):, Timer Objects in Python. threading.Timer(interval, Important differences between Python 2.x and Python 3.x with examples; Python Set 4.\n\nAn Introduction to Python Concurrency Dabeaz. 10/08/2018 · This article explains how to use python threads with a simple and common example Python tutorial : Understanding Python time by 2 distinct threads,, 10/08/2018 · This article explains how to use python threads with a simple and common example Python tutorial : Understanding Python time by 2 distinct threads,.\n\n### wxPython Using wx.Timers The Mouse Vs. The Python", null, "An Introduction to Python Concurrency Dabeaz. Async Techniques and Examples in Python. Add massive speedups with Cython and Python threads; The time to act is now. The dawn of Python's full async power is Python Multithreading Tutorial - Running several threads is similar to running several different programs concurrently.", null, "Python 201: A Tutorial on Threads. Note that the threads in Python my favorite solution was using the threading module’s Timer class. For this example, Parallelising Python with Threading and Multiprocessing Parallelising Python with Threading and Multiprocessing. time python thread_test.py\n\n28/08/1999 · ?ukasz Kowalczyk writes: Also, is there a tutorial about using threads in Python? I know there are a few examples in doc/Demos directory but I would like to Threading and threads. Timed threads. In Python, the Timer class is a subclass of the Thread class. I run the first example and get the output “Disallowed\n\nThis website contains a free and extensive online tutorial by Bernd Klein with Example for a Thread in Python: import time from threading import In this Python multithreading tutorial, one thread waits for input and another runs a GUI at the same time. #Python multithreading example to demonstrate\n\nThread Synchronization Mechanisms in Python. mechanism provided by the threading module. At any time, following example: lock = threading An Introduction to Python Concurrency This Tutorial 2 •Python : import time import threading class CountdownThread\n\nParallelising Python with Threading and Multiprocessing Parallelising Python with Threading and Multiprocessing. time python thread_test.py Python Multithreading Tutorial - Running several threads is similar to running several different programs concurrently\n\nPython Multithreaded Programming Modern OS manage multiple programs using a time-sharing technique. In Python, There are two ways of accessing Python threads. 15/09/2012 · Python threading.timer - repeat function every I know i can change the decorator in the source code any time. what, for example, python threading.Timer start\n\nA tutorial on how devs and data professionals can use threading in Python-based code to perform parallel execution and Python Thread Tutorial threading.Timer() Python Multithreaded Programming Modern OS manage multiple programs using a time-sharing technique. In Python, There are two ways of accessing Python threads.\n\nWe will see how to use threading Events to have functions in different Python threads start at the same time. I recently coded a method to view … 14/05/2016 · Threading and threads. Timed threads. In Python, the Timer class is a subclass of Hi Frank!Thanks for your tutorials.In the last example,there were time\n\nPython Multithreading Tutorial Python ThreadPoolExecutor Tutorial. Example. This time we’ll be defining a different task that takes in a variable ‘n i have to write a program in network course that is something like selective repeat but a need a timer. after search in google i found that threading.Timer can help\n\nTutorial covering basics of PyQt Threading with real life example and step by step built into python at any time. That concludes this tutorial, Parallelising Python with Threading and Multiprocessing Parallelising Python with Threading and Multiprocessing. time python thread_test.py", null, "23/08/2018 · Raspberry Pi - Python Threading Sometimes it would be useful to have two python programs running at the same time this is Code example with two different threads. # python hello_threads.py Thread-1 says Hello World at time: 2008-05 than the first threading example, threads in Python and demonstrated the best\n\n## Python Multithreading Tutorial Timer Object 2018", null, "PyQt/Threading_Signals_and_Slots Python Wiki. 10/08/2018 · This article explains how to use python threads with a simple and common example Python tutorial : Understanding Python time by 2 distinct threads,, Python; C++ Tutorials; STL; Multithreading; Data Science; Boost Library. Boost Date Time Library; STL Algorithm – std::sort Tutorial and Example;.\n\n### Python Multithreading Tutorial Subclassing Thread 2018\n\nPython Multithreading Codescracker Online Coding. Python Multithreading Tutorial Python ThreadPoolExecutor Tutorial. Example. This time we’ll be defining a different task that takes in a variable ‘n, Python 201: A Tutorial on Threads. Note that the threads in Python my favorite solution was using the threading module’s Timer class. For this example,.\n\nA complete python threading tutorial on how to use the threading and Looking at the above example, we create the thread and start = time.time() threads Timer Objects in Python. threading.Timer(interval, Important differences between Python 2.x and Python 3.x with examples; Python Set 4\n\nwxPython: Using wx.Timers. August 25, So I decided it was high time I wrote a couple of example scripts to show how they’re used. \"Timer Tutorial 1\", Timers and Threads are two good mechanisms Let us now add a timer to the example code you Note - one actual risk of threading in Python is a syndrome\n\n16/11/2018 · A place where you can post Python-related tutorials you made yourself, For example Basic prefixes define thread tutorials for the beginner Current time: Nov 14/05/2016 · Threading and threads. Timed threads. In Python, the Timer class is a subclass of Hi Frank!Thanks for your tutorials.In the last example,there were time\n\nTutorial on Threads Programming with Python since only one program can run at a time, 3.1 The thread Module The example here involves a client/server pair Python Multiprocessing Module hardware timer. –Python uses the OS threads as a base but •“Tutorial on Threads Programming with Python” by Norman Matloff\n\nUnderstanding Threading in Python. #!/usr/bin/env python import time import thread def Without the lock competing threads could cause havoc, for example: This website contains a free and extensive online tutorial by Bernd Klein with Example for a Thread in Python: import time from threading import\n\nPython Multithreading Tutorial: Subclassing Thread. Toggle navigation To create our own thread in Python, import threading import time import logging Python Multithreading Tutorial the execution times of python threads is not entirely in parallel one line of python code can be compiled at one time.\n\n... , they are separate objects in Python. Python’s Thread class supports a as an example of creating custom threads. Timers are threading.Timer 12/12/2017 · Python Threading Beginners Tutorial - Threading Example #1 Image Downloading This video demonstrates the benefits of using Python threading to dowload\n\nWe will see how to use threading Events to have functions in different Python threads start at the same time. I recently coded a method to view … Python Programming tutorials So now we mesh the threading tutorial code with our port scanning code: import threading from queue import Queue import time\n\nJava, Java EE, Android, Python, Web Development Tutorials. Java Tutorial; Java Timer TimerTask Example. run the associated tasks as a daemon thread. Timer Timers and Threads are two good mechanisms Let us now add a timer to the example code you Note - one actual risk of threading in Python is a syndrome\n\nTutorial covering basics of PyQt Threading with real life example and step by step built into python at any time. That concludes this tutorial, Python Multithreading Tutorial: Subclassing Thread. Toggle navigation To create our own thread in Python, import threading import time import logging\n\nPython Multithreaded Programming W3schools. Python Multithreading Tutorial Python ThreadPoolExecutor Tutorial. Example. This time we’ll be defining a different task that takes in a variable ‘n, Python Tutorial; Python - Home; Python thread.py and threading.py serve as Python Threads. but during that time thread t2 was sleeping so thread was still alive..\n\n### Threading and Asynchronous Exceptions", null, "Python 201 A Tutorial on Threads The Mouse Vs. The Python. Python threading, python multithreading example, python thread sleep, python threading lock, python threading timer, python threading tutorial, main thread, Multithreading in Python, for example. The function would take 30 seconds every time it ran, My name is Troy Boileau but I go by Troy Fawkes..\n\n### Increasing Usefulness with Timers and Threads SourceForge", null, "Python Multithreading Codescracker Online Coding. ... only one thread can acquire a lock at a time. It will give us some insights into threading. As a first example, Python’s threading module provides two Parallelising Python with Threading and Multiprocessing Parallelising Python with Threading and Multiprocessing. time python thread_test.py.", null, "A complete python threading tutorial on how to use the threading and Looking at the above example, we create the thread and start = time.time() threads Parallelising Python with Threading and Multiprocessing Parallelising Python with Threading and Multiprocessing. time python thread_test.py\n\nPython Multithreaded Programming Modern OS manage multiple programs using a time-sharing technique. In Python, There are two ways of accessing Python threads. We show you how to create a thread in Python (two in this example) of our thread-supported class. Measure Time in Python – time.time() vs time.clock()\n\n... , they are separate objects in Python. Python’s Thread class supports a as an example of creating custom threads. Timers are threading.Timer We continue our exploration of Python threads by exploring daemon threads and various types of locks in Python, walking through code examples to illustrate.\n\nThis website contains a free and extensive online tutorial by Bernd Klein with Example for a Thread in Python: import time from threading import gevent For the Working Python Developer try: thread1.join(timeout=timer) except Timeout: print('Thread 1 timed out') # -- timer For example, the Redis python\n\nPython Multithreading Tutorial: Subclassing Thread. Toggle navigation To create our own thread in Python, import threading import time import logging Python Tutorial; Python - Home; Python thread.py and threading.py serve as Python Threads. but during that time thread t2 was sleeping so thread was still alive.\n\nMultiprocessing and multithreading in Python 3. This is a toy example use case of threads for queue import Queue import time list_lock = threading Python Tutorial; Python - Home; Python thread.py and threading.py serve as Python Threads. but during that time thread t2 was sleeping so thread was still alive.\n\nPython Multithreading Tutorial Python ThreadPoolExecutor Tutorial. Example. This time we’ll be defining a different task that takes in a variable ‘n 21/02/2013 · threading – Manage concurrent threads. Timer Threads¶ One example of a reason to subclass Thread is provided by Timer, \\$ python threading_timer.py\n\nPython Programming tutorials from beginner to advanced on a we've imported threading, queue and time. Threading is for CX_Freeze Python Tutorial. Python Python Multithreaded Programming Modern OS manage multiple programs using a time-sharing technique. In Python, There are two ways of accessing Python threads.\n\nPython Multithreading Tutorial - Running several threads is similar to running several different programs concurrently 21/10/2018 · Simple Python Threading Example so I spend a lot of my time in a Python REPL. Hey, thanks for this useful tutorial.\n\n15/09/2012 · Python threading.timer - repeat function every I know i can change the decorator in the source code any time. what, for example, python threading.Timer start Thread Synchronization Mechanisms in Python. mechanism provided by the threading module. At any time, following example: lock = threading\n\n28/08/1999 · ?ukasz Kowalczyk writes: Also, is there a tutorial about using threads in Python? I know there are a few examples in doc/Demos directory but I would like to 8/04/2014 · This is a tutorial covering the basics of adding threading to your python programs. All Links and Slides will be in the description. Subscribe for more" ]

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[ "Subscribe by email\n\n# Logic tester with acoustic indication\n\nUsing electronic scheme in the figure below can be constructed logic tester with acoustic indication. Acoustic tester in the figure below produces a low frequency sound when detects a logic 0, respective high-frequency sound when 1 logic is detected. The frequency produced by capacitors C1 and C2 depends. The input signal is supplied directly to the gate of N2 and reversed at the gate N3. If at input is detected, a logic gate N2 signal to pass through the amplifier A1. If a 0 is detected at input logic gate N3 signal to pass from the amplifier A2. The amplifier A4 form pulses from rectangular signal of the N4 gate which command transistors T1 and T2. With the buttons S1, S2 the oscillations can be turned on respective off. The circuit requires a continuous supply voltage between 5 and 10 volts and absorbs a maximum current of 10mA.\n\nCircuit Diagram:", null, "" ]

[ null, "http://electroniq.net/sites/default/files/img/logic-acoustic-tester-electronic-project.jpg", null ]

[ "# Use Excel's VALUE Function to Convert Text to Numbers\n\nConvert text data into numeric values\n\nThe VALUE function in Excel is used to convert numbers that have been entered as text data into numeric values so that the data may be used in calculations.\n\nThe information in this article applies to Excel versions 2019, 2016, 2013, 2010, and Excel for Mac.\n\n01\nof 05\n\n## SUM and AVERAGE and Text Data\n\nExcel automatically converts problem data of this sort to numbers, so the VALUE function is not required. However, if the data is not in a format that Excel recognizes, the data can be left as text. When this situation occurs, certain functions, such as SUM or AVERAGE, ignore the data in these cells and calculation errors occur.\n\nFor example, in row 5 in the image above, the SUM function is used to total the data in rows 3 and 4 in columns A and B with these results:\n\n• The data in cells A3 and A4 is entered as text. The SUM function in cell A5 ignores this data and returns a result of zero.\n• In cells B3 and B4, the VALUE function converts the data in A3 and A4 into numbers. The SUM function in cell B5 returns a result of 55 (30 + 25).\n02\nof 05\n\n## The Default Alignment of Data in Excel\n\nText data aligns on the left in a cell. Numbers and dates align on the right.\n\nIn the example, the data in A3 and A4 align on the left side of the cell because it was entered as text. In cells B2 and B3, the data was converted to numerical data using the VALUE function and aligns on the right.​\n\n03\nof 05\n\n## The VALUE Function's Syntax and Arguments\n\nA function's syntax refers to the layout of the function and includes the function's name, brackets, and arguments.\n\nThe syntax for the VALUE function is:\n\nText (required) is the data to be converted to a number. The argument can contain:\n\n• The actual data enclosed in quotation marks. See row 2 of the example above.\n• cell reference to the location of the text data in the worksheet. See row 3 of the example.\n\n#VALUE! Error\n\nIf the data entered as the Text argument cannot be interpreted as a number, Excel returns the #VALUE! error as shown in row 9 of the example.\n\n04\nof 05\n\n## Convert the Text Data to Numbers With the VALUE Function\n\nListed below are the steps used to enter the VALUE function B3 in the example above using the function's dialog box.\n\nAlternatively, the complete function =VALUE(B3) can be typed manually into the worksheet cell.\n\n1. Select cell B3 to make it the active cell.\n2. Select the Formulas tab.\n3. Choose Text to open the function drop-down list.\n4. Select VALUE in the list to bring up the function's dialog box.\n5. In the dialog box, select the Text line.\n6. Select cell A3 in the spreadsheet.\n7. Select OK to complete the function and return to the worksheet.\n8. The number 30 appears in cell B3. It is aligned on the right side of the cell to indicate it is now a value that can be used in calculations.\n9. Select cell E1 to display the complete function =VALUE(B3) in the formula bar above the worksheet.\n05\nof 05\n\n## Convert Dates and Times\n\nThe VALUE function can also be used to convert dates and times to numbers.\n\nAlthough dates and times are stored as numbers in Excel and there is no need to convert them before using them in calculations, changing the data's format can make it easier to understand the result.\n\nExcel stores dates and times as sequential numbers or serial numbers. Each day the number increases by one. Partial days are entered as fractions of a day — such as 0.5 for half a day (12 hours) as shown in row 8 above." ]

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[ "# MCQs For NCERT Class 12 Physics Chapter 2 Electrostatic Potential and Capacitance\n\nPlease refer to the MCQ Questions for Class 12 Physics Chapter 2 Electrostatic Potential and Capacitance with Answers. The following Electrostatic Potential and Capacitance Class 12 Physics MCQ Questions have been designed based on the latest syllabus and examination pattern for Class 12. Our experts have designed MCQ Questions for Class 12 Physics with Answers for all chapters in your NCERT Class 12 Physics book.\n\n## Electrostatic Potential and Capacitance Class 12 MCQ Questions with Answers\n\nSee below Electrostatic Potential and Capacitance Class 12 Physics MCQ Questions, solve the questions and compare your answers with the solutions provided below.\n\nQuestion. Energy per unit volume for a capacitor having area A and separation d kept at potential difference V is given by\n(a) 1/2 εV2/d2\n(b) 1/2ε.V2/d2\n(c) 1/2 CV2\n(d) Q2/2C\n\nA\n\nQuestion. A capacitor is charged with a battery and energy stored is U. After disconnecting battery another capacitor of same capacity is connected in parallel to the first capacitor. Then energy stored in each capacitor is\n(a) U/2\n(b) U/4\n(c) 4U\n(d) 2U\n\nB\n\nQuestion. In a certain region of space with volume 0.2 m3, the electric potential is found to be 5 V throughout. The magnitude of electric field in this region is\n(a) zero\n(b) 0.5 N/C\n(c) 1 N/C\n(d) 5 N/C\n\nA\n\nQuestion. A bullet of mass 2 g is having a charge of 2 mC. Through what potential difference must it be accelerated, starting from rest, to acquire a speed of 10 m/s ?\n(a) 5 kV\n(b) 50 kV\n(c) 5 V\n(d) 50 V\n\nB\n\nQuestion. The electric potential at a point in free space due to charge Q coulomb is Q × 1011 volts. The electric field at that point is   C\n(a) 4pe0Q × 1020 volt/m\n(b) 12pe0Q × 1022 volt/m\n(c) 4pe0Q × 1022 volt/m\n(d) 12pe0Q × 1020 volt/m\n\nC\n\nQuestion. A short electric dipole has a dipole moment of 16 × 10–9 C m. The electric potential due to the dipole at a point at a distance of 0.6 m from the centre of the dipole, situated on a line making an angle of 60° with the dipole axis is (1/4πε0 = 9×109 Nm2/C2 )\n(a) 50 V\n(b) 200 V\n(c) 400 V\n(d) zero\n\nB\n\nQuestion. Two metal spheres, one of radius R and the other of radius 2R respectively have the same surface charge density s. They are brought in contact and separated.\nWhat will be the new surface charge densities on them?\n(a) σ1 = 5/6σ ,σ2 =5/2σ\n(b) σ1 = 5/2σ ,σ2 =5/6σ\n(c) σ1 = 5/2σ ,σ2 =5/3σ\n(d) σ1 = 5/3σ ,σ2 =5/6σ\n\nD\n\nQuestion. Four point charges –Q, –q, 2q and 2Q are placed, one at each corner of the square. The relation between Q and q for which the potential at the centre of the square is zero is\n(a) Q = –q\n(b) Q == − 1/q\n(c) Q = q\n(d) Q = 1/q\n\nA\n\nQuestion. If potential (in volts) in a region is expressed as V(x, y, z) = 6xy – y + 2yz, the electric field (in N/C) at point (1, 1, 0) is\n(a) -(2î +3j + k)\n(b) -(6i + 9j+k)\n(c) -(3i+5j+3k)\n(d) −(6i + 5j+2k)\n\nD\n\nQuestion. A capacitor is charged by a battery. The battery is removed and another identical uncharged capacitor is connected in parallel. The total electrostatic energy of resulting system\n(a) decreases by a factor of 2\n(b) remains the same\n(c) increases by a factor of 2\n(d) increases by a factor of 4.\n\nA\n\nQuestion. A parallel plate air capacitor of capacitance C is connected to a cell of emf V and then disconnected from it. A dielectric slab of dielectric constant K, which can just fill the air gap of the capacitor, is now inserted in it. Which of the following is incorrect?\n(a) The change in energy stored is 1/2CV2(1/K-1).\n(b) The charge on the capacitor is not conserved.\n(c) The potential difference between the plates decreases K times.\n(d) The energy stored in the capacitor decreases K times.\n\nB\n\nQuestion. A parallel plate capacitor has a uniform electric field E in the space between the plates. If the distance between the plates is d and area of each plate is A, the energy stored in the capacitor is\n(a) 1/2 ε0 E2\n\nC\n\nQuestion. In a region, the potential is represented by V(x, y, z) = 6x – 8xy – 8y + 6yz, where V is in volts and x, y, z are in metres. The electric force experienced by a charge of 2 coulomb situated at point (1, 1, 1) is\n(a) 6 5N\n(b) 30 N\n(c) 24 N\n(d) 4 √35N\n\nD\n\nQuestion. The electric potential V at any point (x, y, z), all in metres in space is given by V = 4×2 volt. The electric field at the point (1, 0, 2) in volt/meter, is\n(a) 8 along negative X-axis\n(b) 8 along positive X-axis\n(c) 16 along negative X-axis\n(d) 16 along positive X-axis\n\nA\n\nQuestion. Charge q2 is at the centre of a circular path with radius r. Work done in carrying charge q1, once around this equipotential path, would be\n(a) 1 /4πε0 x q1q2 /r2\n(b) 1 /4πε0 x q1q2 /r\n(c) zero\n(d) infinite.\n\nC\n\nQuestion. Identical charges (–q) are placed at each corners of cube of side b, then electrostatic potential energy of charge (+q) which is placed at centre of cube will be\n(a) −4√2 q/πε0b\n(b) −8√2 q/πε0b\n(c) −4q/√3πε0b\n(d) −8√2 q/4πε0b\n\nC\n\nQuestion. In bringing an electron towards another electron, the electrostatic potential energy of the system\n(a) becomes zero\n(b) increases\n(c) decreases\n(d) remains same\n\nB\n\nQuestion. Two metallic spheres of radii 1 cm and 3 cm are given charges of –1 × 10–2 C and 5 × 10–2 C, respectively. If these are connected by a conducting wire, the final charge on the bigger sphere is\n(a) 2 × 10–2 C\n(b) 3 × 10–2 C\n(c) 4 × 10–2 C\n(d) 1 × 10–2 C\n\nB\n\nQuestion. An electric dipole of dipole moment p is aligned parallel to a uniform electric field E. The energy required to rotate the dipole by 90° is\n(a) p2E\n(b) pE\n(c) infinity\n(d) pE2\n\nB\n\nQuestion. An electric dipole of moment p is placed in an electric field of intensity E. The dipole acquires a position such that the axis of the dipole makes an angle q with the direction of the field. Assuming that the potential energy of the dipole to be zero when q = 90°, the torque and the potential energy of the dipole will respectively be   A\n(a) pEsinq, –pEcosq\n(b) pEsinq, –2pEcosq\n(c) pEsinq, 2pEcosq\n(d) pEcosq, –pEsinq\n\nQuestion. An electric dipole of moment p is lying along a uniform electric field E. The work done in rotating the dipole by 90° is\n(a) pE\n(b) 2pE\n(c) pE/2\n(d) 2pE\n\nA\n\nQuestion. An electric dipole has the magnitude of its charge as q and its dipole moment is p. It is placed in a uniform electric field E. If its dipole moment is along the direction of the field, the force on it and its potential energy are respectively\n(a) 2q · E and minimum\n(b) q · E and p · E\n(c) zero and minimum\n(d) q · E and maximum\n\nC\n\nQuestion. There is an electric field E in x-direction. If the work done on moving a charge of 0.2 C through a distance of 2 m along a line making an angle 60° with x-axis is 4 J, then what is the value of E ?   B\n(a) 5 N/C\n(b) 20 N/C\n(c) 3 N/C\n(d) 4 N/C\n\nQuestion. An electric dipole of moment p is placed in the position of stable equilibrium in uniform electric field of intensity E. This is rotated through an angle q from the initial position. The potential energy of the electric dipole in the final position is   B\n(a) –pE cosq\n(b) pE(1 – cosq)\n(c) pE cosq\n(d) pE sinq\n\nQuestion. A parallel plate condenser with oil between the plates (dielectric constant of oil K = 2) has a capacitance C. If the oil is removed, then capacitance of the capacitor becomes   D\n(a) C/√2\n(b) 2C\n(c) 2C\n(d) C/2\n\nQuestion. Three capacitors each of capacitance C and of breakdown voltage V are joined in series.\nThe capacitance and breakdown voltage of the combination will be\n(a) 3C, V/3\n(b) C/3 , 3V\n(c) 3C, 3V\n(d) C/3 , V/3\n\nB\n\nQuestion. Some charge is being given to a conductor. Then its potential is\n(a) maximum at surface\n(b) maximum at centre\n(c) remain same throughout the conductor\n(d) maximum somewhere between surface and centre.\n\nC\n\nQuestion. Two metallic spheres of radii 1 cm and 2 cm are given charges 10–2 C and 5 × 10–2 C respectively.\nIf they are connected by a conducting wire, the final charge on the smaller sphere is\n(a) 3 × 10–2 C\n(b) 4 × 10–2 C\n(c) 1 × 10–2 C\n(d) 2 × 10–2 C\n\nD\n\nQuestion. The electrostatic force between the metal plates of an isolated parallel plate capacitor C having a charge Q and area A, is\n(a) independent of the distance between the plates\n(b) linearly proportional to the distance between the plates\n(c) proportional to the square root of the distance between the plates\n(d) inversely proportional to the distance between the plates.\n\nA\n\nQuestion. A parallel plate air capacitor has capacity C, distance of separation between plates is d and potential difference V is applied between the plates. Force of attraction between the plates of the parallel plate air capacitor is\n(a) CV2/d\n(b) C2V2/2d2\n(c) C2V2/d\n(d) CV2/d\n\nD\n\nQuestion. A parallel plate air capacitor is charged to a potential difference of V volts. After disconnecting the charging battery the distance between the plates of the capacitor is increased using an insulating handle. As a result the potential difference between the plates\n(a) increases\n(b) decreases\n(c) does not change\n(d) becomes zero\n\nA\n\nQuestion. The capacitance of a parallel plate capacitor with air as medium is 6 mF. With the introduction of a dielectric medium, the capacitance becomes 30 mF. The permittivity of the medium is (e0 = 8.85 × 10–12 C2 N–1 m–2)\n(a) 0.44 × 10–13 C2 N–1 m–2\n(b) 1.77 × 10–12 C2 N–1 m–2\n(c) 0.44 × 10–10 C2 N–1 m–2\n(d) 5.00  C2 N–1 m–2\n\nC\n\nQuestion. Three concentric spherical shells have radii a, b and c (a < b < c) and have surface charge densities s, –s and s respectively. If VA, VB and VC denote the potentials of the three shells, then, for c = a + b, we have\n(a) VC = VB ≠ VA\n(b) VC ≠ VB ≠ VA\n(c) VC = VB = VA\n(d) VC = VA ≠ VB\n\nD\n\nQuestion. A hollow metallic sphere of radius 10 cm is charged such that potential of its surface is 80 V. The potential at the centre of the sphere would be\n(a) 80 V\n(b) 800 V\n(c) zero\n(d) 8 V\n\nA\n\nQuestion. Two parallel metal plates having charges +Q and –Q face each other at a certain distance between them.\nIf the plates are now dipped in kerosene oil tank, the electric field between the plates will\n(a) become zero\n(b) increase\n(c) decrease\n(d) remain same\n\nC\n\nQuestion. Three capacitors each of capacity 4 mF are to be connected in such a way that the effective capacitance is 6 mF. This can be done by\n(a) connecting all of them in series\n(b) connecting them in parallel\n(c) connecting two in series and one in parallel\n(d) connecting two in parallel and one in series.\n\nC\n\nQuestion. A series combination of n1 capacitors, each of value C1, is charged by a source of potential difference 4V.\nWhen another parallel combination of n2 capacitors, each of value C2, is charged by a source of potential difference V, it has the same (total) energy stored in it, as the first combination has. The value of C2, in terms of C1, is then\n(a) 2C1/n1n2\n(b) 16 n2/n1 . C1\n(c) 2n2/n1 . C1\n(d) 16C1. n2/n1\n\nD\n\nQuestion. The energy stored in a capacitor of capacity C and potential V is given by\n(a) CV/2\n(b) C2/V2\n(c) C2V/2\n(d) CV2\n\nD\n\nQuestion. The four capacitors, each of 25 μ F are connected as shown in fig. The dc voltmeter reads 200 V. The charge on each plate of capacitor is\n\n(a) ± 2´10-3C\n(b) ± 5´10-3C\n(c) ± 2´10-2C\n(d) ± 5´10-2C\n\nB\n\nQuestion. An air capacitor of capacity C = 10 μF is connected to a constant voltage battery of 12 volt. Now the space between the plates is filled with a liquid of dielectric constant 5. The (additional) charge that flows now from battery to the capacitor is\n(a) 120 μ C\n(b) 600 μ C\n(c) 480 μ C\n(d) 24 μ C\n\nC\n\nQuestion. Capacitance (in F) of a spherical conductor with radius 1 m is\n(a) 1.1 × 10–10\n(b) 106\n(c) 9 × 10–9\n(d) 10–3\n\nA\n\nQuestion. Two equally charged spheres of radii a and b are connected together. What will be the ratio of electric field intensity on their surfaces?\n(a) a/b\n(a) a2/b2\n(a) b/a\n(a) b2/a2\n\nC\n\nQuestion. In a hollow spherical shell, potential (V) changes with respect to distance (s) from centre as\n\nB\n\nQuestion. Two metal pieces having a potential difference of 800 V are 0.02 m apart horizontally. A particle of mass 1.96 × 10–15 kg is suspended in equilibrium between the plates. If e is the elementary charge, then charge on the particle is\n(a) 8\n(b) 6\n(c) 0.1\n(d) 3\n\nD\n\nQuestion. The capacity of a parallel plate condenser is 10 μF, when the distance between its plates is 8 cm. If the distance between the plates is reduced to 4 cm, then the capacity of this parallel plate condenser will be\n(a) 5 μF\n(b) 10 μF\n(c) 20 μF\n(d) 40 μF\n\nC\n\nQuestion. The plates of a parallel plate capacitor have an area of 90 cm2 each and are separated by 2.5 mm. The capacitor is charged by a 400 volt supply. How much electrostatic energy is stored by the capacitor?\n(a) 2.55 × 10–6 J\n(b) 1.55 × 10–6 J\n(c) 8.15 × 10–6 J\n(d) 5.5 × 10–6 J\n\nA\n\nQuestion. Two capacitors, C1 = 2μF and C2 = 8 mF are connected in series across a 300 V source. Then\n(a) the charge on each capacitor is 4.8×10–4 C\n(b) the potential difference across C1 is 60 V\n(c) the potential difference across C2 is 240 V\n(d) the energy stroed in the system is 5.2 × 10–2 J\n\nA\n\nQuestion. Two capacitors C1 and C2 = 2C1 are connected in a circuit with a switch between them as shown in the figure. Initially the switch is open and C1 holds charge Q. The switch is closed. At steady state, the charge on each capacitor will be\n\nB\n\nQuestion. From a supply of identical capacitors rated 8 mF, 250V, the minimum number of capacitors required to form a composite 16 μF, 1000V is\n(a) 2\n(b) 4\n(c) 16\n(d) 32\n\nD\n\nQuestion. The capacitor, whose capacitance is 6, 6 and 3μF respectively are connected in series with 20 volt line. Find the charge on 3μF.\n(a) 30 μc\n(b) 60 μF\n(c) 15 μF\n(d) 90 μF\n\nA\n\nAssertion and Reasoning Based Questions :\n\na : If Assertion and reason are both true and reason is the correct explanation for Assertion.\nb : If Assertion and reason are both true but reason is not the correct explanation for Assertion.\nc : If Assertion is true but reason is false.\nd : If Assertion is false but Reason is true.\n\nQuestion. Assertion (A): A parallel plate capacitor is charged by a battery. While the battery remains connected, a dielectric slab of dielectric constant K is introduced between the plates of the capacitor. Energy stored by the capacitor becomes K times.\nReason (R) : Surface charge density of the capacitor plates remain constant.\n\nC\n\nQuestion. Assertion (A): Work done by electrostatic force in bringing a negative test charge (-q) from infinity to point P is Negative in the given situation.\n\nReason (R) : Work done by a force is a scalar quantity.\n\nD\n\nQuestion. Assertion (A): The expression of potential energy, U = KQ1 Q2 /r is unaltered whatever way the charges are brought to the specified location.\nReason (R) : Electrostatic force is a conservative force.\n\nA\n\nQuestion. Assertion (A): On increasing the charge on the plates of a capacitor, its capacitance also increases.\nReason (R): C = Q/V\n\nD\n\nQuestion. Assertion (A) : A positively charged particle is released from rest in a uniform electric field region. The electrostatic PE of the SYSTEM OF CHARGES will decrease.\nReason (R) : KE of the positive charge increases due to electrostatic force.\n\nA\n\nQuestion. Assertion (A): Electric potential at any point on the equator of a dipole is zero whereas the electric field at the same point is non zero.\nReason (R) : Electric potential is a vector quantity.\n\nC\n\nQuestion. Assertion (A): Charge on all the capacitors joined in series is same.\nReason (R) : Charge stored by a capacitor is inversely proportional to the potential difference across its plates." ]

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[ "# physics\n\nA 40 kg skier comes directly down a frictionless ski slope that is inclined at an angle of 10 degrees with the horizontal while a strong wind blows parallel to the slope. Determine the magnitude and diercection of the force of the wind on the skier id a) magnitude od the skier's velocity is constant, b) magitude of the skier's velocity is increasing at a rate of 1 m/s^2 and c) magnitude of the skiers velocity is increasing at a rate of 2 m/s^2.\n\nI need the equations to get me started for each one.\n\n1. 👍 0\n2. 👎 0\n3. 👁 213\n\n## Similar Questions\n\n1. ### physics\n\nA 40 kg skier comes directly down a frictionless ski slope that is inclined at an angle of 10 degrees with the horizontal while a strong wind blows parallel to the slope. Determine the magnitude and diercection of the force of the\n\nasked by Dee on November 25, 2006\n2. ### physics\n\nA 48 kg skier skis directly down a frictionless slope angled at 5° to the horizontal. Assume the skier moves in the negative direction of an x axis along the slope. A wind force with component Fx acts on the skier. (a) What is Fx\n\nasked by John on September 22, 2010\n3. ### physics\n\nA 35-kg skier skis directly down a frictionless slope angled at 11° to the horizontal. Assume the skier moves in the negative direction of an x axis along the slope. A wind force with component Fx acts on the skier. What is Fx\n\nasked by **chocolatekisses on February 8, 2007\n4. ### Physics 1\n\nA skier of mass 109 kg travels down a frictionless ski trail. a)If the top of the trail is a height 218 m above the bottom, what is the work done by gravity on the skier? _____J b)Find the velocity of the skier when he reaches the\n\nasked by John on October 8, 2012\n5. ### Repost-Physics 1\n\nA skier of mass 109 kg travels down a frictionless ski trail. a)If the top of the trail is a height 218 m above the bottom, what is the work done by gravity on the skier? _____J b)Find the velocity of the skier when he reaches the\n\nasked by John on October 9, 2012\n6. ### Physics\n\nA skier of mass 110 kg travels down a frictionless ski trial. a.) If the top of the trail is a height 200m above the bottom, what is the work done by gravity on the skier? b.) Find the velocity of the skier when he reaches the\n\nasked by Jessica on April 22, 2016\n7. ### physics\n\nA skier skis down a 25 m high frictionless ski slope. How fast will she be moving at the bottom of the slope if: A) She starts from rest at the top B) She starts out with a velocity of 10 m/s\n\nasked by Monika on November 11, 2009\n8. ### physics\n\nA skier skis down a 25 m high frictionless ski slope. How fast will she be moving at the bottom of the slope if: A) She starts from rest at the top B) She starts out with a velocity of 10 m/s\n\nasked by Monika on November 11, 2009\n9. ### Physics\n\nA ski slope drops at an angle of 24 degrees with respect to the horizontal and is 500 m long. A 60 kg skier skis down from the top to the bottom of the slope. A.) Determine the change in gravitational potential energy of the\n\nasked by Iza on November 12, 2012\n10. ### physics\n\nA ski slope drops at an angle of 24 degrees with respect to the horizontal and is 500 m long. A 60 kg skier skis down from the top to the bottom of the slope. A.) Determine the change in gravitational potential energy of the\n\nasked by bibs on July 14, 2014\n\nMore Similar Questions" ]

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[ "The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.", null, "Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)\n A245798 Catalan number analogs for totienomial coefficients (A238453). 3\n 1, 1, 2, 4, 12, 36, 120, 360, 960, 3840, 13824, 41472, 152064, 506880, 2280960, 7983360, 29937600, 99792000, 266112000, 1197504000, 4790016000, 19160064000, 73156608000, 219469824000, 1009561190400, 3533464166400, 12563428147200, 54441521971200, 155547205632000 (list; graph; refs; listen; history; text; internal format)\n OFFSET 0,3 COMMENTS One definition of the Catalan numbers is binomial(2*n,n) / (n+1); the current sequence models this definition using the generalized binomial coefficients arising from Euler's totient function (A000010). When the INTEGERS (2014) paper was written it was not known that this was an integral sequence (see the final paragraph of that paper). However, it is now known to be integral. Another name could be phi-Catalan numbers. - Tom Edgar, Mar 29 2015 LINKS Tom Edgar, Table of n, a(n) for n = 0..28 Tom Edgar, Totienomial Coefficients, INTEGERS, 14 (2014), #A62. Tom Edgar and Michael Z. Spivey, Multiplicative functions, generalized binomial coefficients, and generalized Catalan numbers, Journal of Integer Sequences, Vol. 19 (2016), Article 16.1.6. FORMULA a(n) = A238453(2*n,n) / A000010(n+1). EXAMPLE We see that A238453(10,5) = 72 and A000010(5+1) = 2, so a(5) = (1/2)*72 = 36. PROG (Sage) [(1/euler_phi(n+1))*prod(euler_phi(i) for i in [1..2*n])/prod(euler_phi(i) for i in [1..n])^2 for n in [0..100]] CROSSREFS Cf. A000010, A238453, A000108, A001088. Sequence in context: A117757 A009623 A148208 * A241530 A123071 A048116 Adjacent sequences:  A245795 A245796 A245797 * A245799 A245800 A245801 KEYWORD nonn AUTHOR Tom Edgar, Aug 22 2014 STATUS approved\n\nLookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam\nContribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent\nThe OEIS Community | Maintained by The OEIS Foundation Inc.\n\nLast modified May 9 13:42 EDT 2021. Contains 343742 sequences. (Running on oeis4.)" ]

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[ "# Fraction Comparison Calculator\n\nThe fraction comparison is done by multiplying the numerator and denominator with a common number to get the same value. Then, the larger one is considered to greater than the other.\n\nFraction Calculator (comparison)\n\n:\n:\n\nWhen 2 fractions have the same denominator, the one the larger numerator is greater.\n\nExample:\nCompare the given fraction\n5/5 and 2/3\n\nSolution:\nHere 5/5 is greater than 2/3\n\nExample: Which is larger: 3/8 or 5/12  ?\nIf you multiply 8 × 3 you get 24 , and if you multiply 12 × 2 you also get 24, so let's try that (important: what you do to the bottom, you must also do to the top):\n\nIt is now easy to see that 9/24 is smaller than 10/24, (because 9 is smaller than 10).\nso 5/12 is the larger fraction." ]

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[ "", null, "", null, "", null, "", null, "", null, "", null, "", null, "", null, "", null, "", null, "", null, "...Excel add-in for quick data analysis", null, "", null, "", null, "", null, "", null, "### Highlights\n\n#### Flexible Data Input:\n\n• Select (category and) value columns from list, select chart types, and click OK. That's it!\n\n#### Powerful Graphs:\n\n• Box & Whisker plot (Boxplot)\n• Normal probability plot\n• Cumulative percent plot (S Curve)\n\n#### Useful Statistics:\n\n• Various percentiles, averages, standard deviations, etc\n• t-test and F-test\n• Mann-Whitney and Levene’s Test(VTools 4.0+)\n• Anova and Kruskal-Wallis' Test\n\n#### Sample Graphs:\n\nBox Plot Normal Probability Plot Cumulative Percent Plot (S-Curve)", null, "", null, "", null, "", null, "", null, "", null, "", null, "", null, "", null, "", null, "", null, "" ]

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[ "", null, "# 9,958 kilometers per square second to millimeters per square second\n\nto\n\n9,958 Kilometers per square second = 9,958,000,000 Millimeters per square second\n\nThis conversion of 9,958 kilometers per square second to millimeters per square second has been calculated by multiplying 9,958 kilometers per square second by 1,000,000 and the result is 9,958,000,000 millimeters per square second." ]

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[ "# #c7c3ff Color Information\n\nIn a RGB color space, hex #c7c3ff is composed of 78% red, 76.5% green and 100% blue. Whereas in a CMYK color space, it is composed of 22% cyan, 23.5% magenta, 0% yellow and 0% black. It has a hue angle of 244 degrees, a saturation of 100% and a lightness of 88.2%. #c7c3ff color hex could be obtained by blending #ffffff with #8f87ff. Closest websafe color is: #ccccff.\n\n• R 78\n• G 76\n• B 100\nRGB color chart\n• C 22\n• M 24\n• Y 0\n• K 0\nCMYK color chart\n\n#c7c3ff color description : Very pale blue.\n\n# #c7c3ff Color Conversion\n\nThe hexadecimal color #c7c3ff has RGB values of R:199, G:195, B:255 and CMYK values of C:0.22, M:0.24, Y:0, K:0. Its decimal value is 13091839.\n\nHex triplet RGB Decimal c7c3ff `#c7c3ff` 199, 195, 255 `rgb(199,195,255)` 78, 76.5, 100 `rgb(78%,76.5%,100%)` 22, 24, 0, 0 244°, 100, 88.2 `hsl(244,100%,88.2%)` 244°, 23.5, 100 ccccff `#ccccff`\nCIE-LAB 80.956, 13.644, -28.945 61.115, 58.392, 102.653 0.275, 0.263, 58.392 80.956, 31.999, 295.238 80.956, -1.557, -48.633 76.415, 9.036, -26.158 11000111, 11000011, 11111111\n\n# Color Schemes with #c7c3ff\n\n• #c7c3ff\n``#c7c3ff` `rgb(199,195,255)``\n• #fbffc3\n``#fbffc3` `rgb(251,255,195)``\nComplementary Color\n• #c3ddff\n``#c3ddff` `rgb(195,221,255)``\n• #c7c3ff\n``#c7c3ff` `rgb(199,195,255)``\n• #e5c3ff\n``#e5c3ff` `rgb(229,195,255)``\nAnalogous Color\n• #ddffc3\n``#ddffc3` `rgb(221,255,195)``\n• #c7c3ff\n``#c7c3ff` `rgb(199,195,255)``\n• #ffe5c3\n``#ffe5c3` `rgb(255,229,195)``\nSplit Complementary Color\n• #c3ffc7\n``#c3ffc7` `rgb(195,255,199)``\n• #c7c3ff\n``#c7c3ff` `rgb(199,195,255)``\n• #ffc7c3\n``#ffc7c3` `rgb(255,199,195)``\n• #c3fbff\n``#c3fbff` `rgb(195,251,255)``\n• #c7c3ff\n``#c7c3ff` `rgb(199,195,255)``\n• #ffc7c3\n``#ffc7c3` `rgb(255,199,195)``\n• #fbffc3\n``#fbffc3` `rgb(251,255,195)``\n• #8077ff\n``#8077ff` `rgb(128,119,255)``\n• #9790ff\n``#9790ff` `rgb(151,144,255)``\n• #afaaff\n``#afaaff` `rgb(175,170,255)``\n• #c7c3ff\n``#c7c3ff` `rgb(199,195,255)``\n• #dfddff\n``#dfddff` `rgb(223,221,255)``\n• #f7f6ff\n``#f7f6ff` `rgb(247,246,255)``\n• #ffffff\n``#ffffff` `rgb(255,255,255)``\nMonochromatic Color\n\n# Alternatives to #c7c3ff\n\nBelow, you can see some colors close to #c7c3ff. Having a set of related colors can be useful if you need an inspirational alternative to your original color choice.\n\n• #c3ceff\n``#c3ceff` `rgb(195,206,255)``\n• #c3c9ff\n``#c3c9ff` `rgb(195,201,255)``\n• #c3c4ff\n``#c3c4ff` `rgb(195,196,255)``\n• #c7c3ff\n``#c7c3ff` `rgb(199,195,255)``\n• #ccc3ff\n``#ccc3ff` `rgb(204,195,255)``\n• #d1c3ff\n``#d1c3ff` `rgb(209,195,255)``\n• #d6c3ff\n``#d6c3ff` `rgb(214,195,255)``\nSimilar Colors\n\n# #c7c3ff Preview\n\nThis text has a font color of #c7c3ff.\n\n``<span style=\"color:#c7c3ff;\">Text here</span>``\n#c7c3ff background color\n\nThis paragraph has a background color of #c7c3ff.\n\n``<p style=\"background-color:#c7c3ff;\">Content here</p>``\n#c7c3ff border color\n\nThis element has a border color of #c7c3ff.\n\n``<div style=\"border:1px solid #c7c3ff;\">Content here</div>``\nCSS codes\n``.text {color:#c7c3ff;}``\n``.background {background-color:#c7c3ff;}``\n``.border {border:1px solid #c7c3ff;}``\n\n# Shades and Tints of #c7c3ff\n\nA shade is achieved by adding black to any pure hue, while a tint is created by mixing white to any pure color. In this example, #010012 is the darkest color, while #fefeff is the lightest one.\n\n• #010012\n``#010012` `rgb(1,0,18)``\n• #030026\n``#030026` `rgb(3,0,38)``\n• #04003a\n``#04003a` `rgb(4,0,58)``\n• #05004d\n``#05004d` `rgb(5,0,77)``\n• #060061\n``#060061` `rgb(6,0,97)``\n• #080075\n``#080075` `rgb(8,0,117)``\n• #090088\n``#090088` `rgb(9,0,136)``\n• #0a009c\n``#0a009c` `rgb(10,0,156)``\n• #0c00af\n``#0c00af` `rgb(12,0,175)``\n• #0d00c3\n``#0d00c3` `rgb(13,0,195)``\n• #0e00d7\n``#0e00d7` `rgb(14,0,215)``\n• #1000ea\n``#1000ea` `rgb(16,0,234)``\n• #1100fe\n``#1100fe` `rgb(17,0,254)``\n• #2212ff\n``#2212ff` `rgb(34,18,255)``\n• #3526ff\n``#3526ff` `rgb(53,38,255)``\n• #473aff\n``#473aff` `rgb(71,58,255)``\n• #594dff\n``#594dff` `rgb(89,77,255)``\n• #6b61ff\n``#6b61ff` `rgb(107,97,255)``\n• #7e75ff\n``#7e75ff` `rgb(126,117,255)``\n• #9088ff\n``#9088ff` `rgb(144,136,255)``\n• #a29cff\n``#a29cff` `rgb(162,156,255)``\n• #b5afff\n``#b5afff` `rgb(181,175,255)``\n• #c7c3ff\n``#c7c3ff` `rgb(199,195,255)``\n• #d9d7ff\n``#d9d7ff` `rgb(217,215,255)``\n• #eceaff\n``#eceaff` `rgb(236,234,255)``\n• #fefeff\n``#fefeff` `rgb(254,254,255)``\nTint Color Variation\n\n# Tones of #c7c3ff\n\nA tone is produced by adding gray to any pure hue. In this case, #dfdfe3 is the less saturated color, while #c7c3ff is the most saturated one.\n\n• #dfdfe3\n``#dfdfe3` `rgb(223,223,227)``\n• #dddce6\n``#dddce6` `rgb(221,220,230)``\n• #dbdae8\n``#dbdae8` `rgb(219,218,232)``\n• #d9d8ea\n``#d9d8ea` `rgb(217,216,234)``\n• #d7d5ed\n``#d7d5ed` `rgb(215,213,237)``\n• #d5d3ef\n``#d5d3ef` `rgb(213,211,239)``\n• #d3d1f1\n``#d3d1f1` `rgb(211,209,241)``\n• #d1cff3\n``#d1cff3` `rgb(209,207,243)``\n• #cfccf6\n``#cfccf6` `rgb(207,204,246)``\n• #cdcaf8\n``#cdcaf8` `rgb(205,202,248)``\n• #cbc8fa\n``#cbc8fa` `rgb(203,200,250)``\n• #c9c5fd\n``#c9c5fd` `rgb(201,197,253)``\n• #c7c3ff\n``#c7c3ff` `rgb(199,195,255)``\nTone Color Variation\n\n# Color Blindness Simulator\n\nBelow, you can see how #c7c3ff is perceived by people affected by a color vision deficiency. This can be useful if you need to ensure your color combinations are accessible to color-blind users.\n\nMonochromacy\n• Achromatopsia 0.005% of the population\n• Atypical Achromatopsia 0.001% of the population\nDichromacy\n• Protanopia 1% of men\n• Deuteranopia 1% of men\n• Tritanopia 0.001% of the population\nTrichromacy\n• Protanomaly 1% of men, 0.01% of women\n• Deuteranomaly 6% of men, 0.4% of women\n• Tritanomaly 0.01% of the population" ]

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[ "# GA Layer To Points\n\nMit der Geostatistical Analyst-Lizenz verfügbar.\n\n## Zusammenfassung\n\nExports a geostatistical layer to points. The tool can also be used to predict values at unmeasured locations or to validate predictions made at measured locations.\n\n## Verwendung\n\n• For data formats that support Null values, such as file geodatabase feature classes, a Null value will be used to indicate that a prediction could not be made for that location or that the value should be ignored when used as input. For data formats that do not support Null values, such as shapefiles, the value of -1.7976931348623158e+308 is used (this is the negative of the C++ defined constant DBL_MAX) to indicate that a prediction could not be made for that location.\n\n• If a validation z-field is supplied, the predictions and standard errors are calculated differently than if a validation field is not supplied. For more information, see the following reference:\n\n• Krivoruchko, K., A. Gribov, and J. M. Ver Hoef, 2006, \"A new method for handling the nugget effect in kriging,\" T. C. Coburn, J. M. Yarus, and R. L. Chambers, Eds., Stochastic modeling and geostatistics: Principles, methods, and case studies, volume II: AAPG Computer Applications and Geology 5, p. 81–89.\n\n## Syntax\n\n`GALayerToPoints(in_geostat_layer, in_locations, {z_field}, out_feature_class, {append_all_fields}, {elevation_field}, {elevation_units})`\n Parameter Erklärung Datentyp in_geostat_layer The geostatistical layer to be analyzed. Geostatistical Layer in_locations Point locations where predictions or validations will be performed. Feature Layer z_field(optional) If this field is left blank, predictions are made at the location points. If a field is selected, predictions are made at the location points, compared to their Z_value_field values, and a validation analysis is performed. Field out_feature_class The output feature class containing either the predictions or the predictions and the validation results.The fields in this feature class can include the following fields (where applicable): Source_ID (Source ID)—The object ID of the source feature in the Input point observation locations. The feature or object identifier of the input dataset that was used.Included (Included)—Indicates whether a prediction was calculated for this feature. The values in this field can be one of the following: Yes—There are no problems making a prediction at this point.Not enough neighbors—There are not enough neighbors to make a prediction.Weight parameter is too small—The weight parameter is too small.Overfilling—Overflow of floating-point calculations.Problem with data transformation—The value to be transformed is outside of the supported range for the selected transformation (only in kriging). No explanatory rasters—The value cannot be calculated because one of the explanatory variables is not defined. The point could be outside the extent of at least one explanatory variable raster, or the point could be on top of a NoData cell in at least one of the explanatory variable rasters. This only applies to EBK Regression Prediction models. Predicted (Predicted)—The prediction value at this location.Error (Error)—The predicted value minus the value in the validation field.StdError (Standard Error)—The kriging standard error.Stdd_Error (Standardized Error)—The standardized prediction errors. Ideally, the standardized prediction errors are distributed normally.NormValue (Normal Value)—The normal distribution value (x-axis) that corresponds to the standardized prediction errors (y-axis) in the normal QQplot.CRPS (Continuous Ranked Probability Score)—The continuous ranked probability score is a diagnostic that measures the deviation from the predictive cumulative distribution function to each observed data value. This value should be as small as possible. This diagnostic has advantages over cross-validation diagnostics because it compares the data to a full distribution rather than to single-point predictions. This field is only created for Empirical Bayesian Kriging and EBK Regression Prediction models.Interval90 (Inside 90 Percent Interval)—Indicates whether or not the validation point is inside of a 90 percent confidence interval. This field is only created for Empirical Bayesian Kriging and EBK Regression Prediction models. If the model fits the data, approximately 90 percent of the features should be contained in a 90 percent confidence interval. This field can contain the following values:Yes—The validation point is inside the 90 percent confidence interval.No—The validation point is not inside the 90 percent confidence interval.Excluded—A prediction cannot be made at this location.Interval95 (Inside 95 Percent Interval)—Indicates whether or not the validation point is inside of a 95 percent confidence interval. This field is only created for Empirical Bayesian Kriging and EBK Regression Prediction models. If the model fits the data, approximately 95 percent of the features should be contained in a 95 percent confidence interval. This field can contain the following values: Yes—The validation point is inside the 95 percent confidence interval.No—The validation point is not inside the 95 percent confidence interval.Excluded—A prediction cannot be made at this location.QuanVal (Validation Quantile)—The quantile of the measured value at the feature with respect to the prediction distribution. This value can range from 0 to 1, and values close to 0 indicate that the measured value is on the far left tail of the distribution, and values close to 1 indicate that the measured value is on the right tail of the distribution. If many values are close to either extreme, this could indicate that the prediction distributions do not model the data well, and some of the interpolation parameters need to be altered. This field is only created for Empirical Bayesian Kriging and EBK Regression Prediction models. Feature Class append_all_fields(optional) Determines whether all fields will be copied from the input features to the output feature class.ALL — All fields from the input features will be copied to the output feature class. This is the default.FID_ONLY — Only the feature ID will be copied, and it will be named Source_ID on the output feature class. Boolean elevation_field(optional) The field containing the elevation of each input point. The parameter only applies to 3D geostatistical models. If the elevation values are stored as geometry attributes in Shape.Z, it is recommended to use that field. If the elevations are stored in an attribute field, the elevations must indicate distance from sea level. Positive values indicate distance above sea level, and negative values indicate distance below sea level. Field elevation_units(optional) The units of the elevation field. This parameter only applies to 3D geostatistical models. If Shape.Z is provided as the elevation field, the units will automatically match the Z-units of the vertical coordinate system. INCH —Elevations are in inches.FOOT —Elevations are in feet.YARD —Elevations are in yards.MILE_US —Elevations are in U.S. miles.NAUTICAL_MILE —Elevations are in nautical miles.MILLIMETER —Elevations are in millimeters.CENTIMETER —Elevations are in centimeters.DECIMETER —Elevations are in decimeters.METER —Elevations are in meters.KILOMETER —Elevations are in kilometers. String\n\n## Codebeispiel\n\nGALayerToPoints example 1 (Python window)\n\nExport a geostatistical layer to a point feature class.\n\n``````import arcpy\narcpy.env.workspace = \"C:/gapyexamples/data\"\narcpy.GALayerToPoints_ga(\"C:/gapyexamples/data/kriging.lyr\",\n\"C:/gapyexamples/data/obs_pts.shp\",\n\"\", \"C:/gapyexamples/output/krig_pts\")``````\nGALayerToPoints example 2 (stand-alone script)\n\nExport a geostatistical layer to a point feature class.\n\n``````# Name: GALayerToPoints_Example_02.py\n# Description: Exports a geostatistical layer to points.\n# Requirements: Geostatistical Analyst Extension\n\n# Import system modules\nimport arcpy\n\n# Set environment settings\narcpy.env.workspace = \"C:/gapyexamples/data\"\n\n# Set local variables\ninLayer = \"C:/gapyexamples/data/kriging.lyr\"\ninPoints = \"C:/gapyexamples/data/obs_pts.shp\"\nzField = \"\"\noutPoints = \"C:/gapyexamples/output/krig_pts\"\n\n# Execute GALayerToPoints\narcpy.GALayerToPoints_ga(inLayer, inPoints, zField, outPoints)``````\n\n## Lizenzinformationen\n\n• Basic: Erfordert Geostatistical Analyst\n• Standard: Erfordert Geostatistical Analyst\n• Advanced: Erfordert Geostatistical Analyst" ]

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[ "# Model Course Notes\n\nPrep Main Page > Web Conference 3 > Web Conference Notes\n\n## Notes from Web Conference 3\n\nAgenda:\n\n1. Good problems follow-up\n2. Problem authoring discussion\n3. NPL\n4. Model Courses\n\n## Good Problems\n\n• The heuristics that we discussed last time shape fairly easily into a \"rubric\" that may or may not be useful to think about when writing problems and thinking about what existing problems might have or lack.\n• Learning objective -- could be very simple; it may also be that this should also be available to students (though obviously in some cases that would be counterproductive)\n• Related to the suggestion that there be \"nice enough\" numbers, there are cases where it is possible to create a problem with distinct values which allow tracking of student work through the problem\n• Is a test suite possible? Can we check for nice numbers? For robustness? It would be nice to have some sort of problem checker that is able to automate verification that there aren't hidden singularities in a problem we are authoring, or that the values generated are \"nice.\"\n• Students and nice numbers: is there information about how students react to problems, to figure out what problems are effective and which turn students off?\n• Metadata for problems: could be part of a new NPL, and could include\n• Learning objectives (possibly available to students, in some cases this might not be a good thing)\n• Quality measures\n• Information on which problems have substantial added information, hints, or instruction. These might be problems that should be embedded in a set.\n• A measure of the difficulty of the problem---maybe the number or percent of incorrect submissions seen on the problem\n• A measure of the number of uses of the problem\n• We may need a better mapping of problems to course sections---e.g., a better generic course/chapter/section list\n\n### Good NPL Problems\n\n• Are solutions good for students? Are there data that substantiate the value of solutions to student learning?\n• The solution -> new problem model. This may be very useful in some cases, though not necessarily all. (I wrote this down, but I'm not sure what it means now...)\n\n## Library Browser\n\n• Note that searching for problems is dependent on the tagging, and that the displayed directory structure may not reflect the actual database chapter/section/problem numbers (this may be a fault in the organization of the files in the NPL)\n• Finding problems that are similar to a given model problem, or that have characteristics that we want. The keyword search might be a good option for this\n\n## Model Courses\n\n• One aspect of developing model courses is that of translating problems from textbook problems to problems that are parameterized, algorithmic WeBWorK problems\n• This translation allows us to do more with the problems---e.g., allow negative parameters, or change the problems to challenge students\n• Testing problems becomes an issue: ensuring that the problems are consistent and have no singularities\n• Making the format and numbers that show up in the problems \"nice\" can be a significant time drain\n• There are some model courses currently available: calculus I\n• For the calculus I model course, the problems are set up so that the problem paths are visible, and the source for the problems is visible\n• Things that we might want in a model course:\n• Sample problem sets\n• Textbook notes\n• Assumptions about how the problems are picked and assigned\n• Assignment information and related data that are provided to students when using the problems\n• That it be a course that actually has been used (and tested)" ]

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[ "", null, "", null, "C RUBY-ON-RAILS MYSQL ASP.NET DEVELOPMENT RUBY .NET LINUX SQL-SERVER REGEX WINDOWS ALGORITHM ECLIPSE VISUAL-STUDIO STRING SVN PERFORMANCE APACHE-FLEX UNIT-TESTING SECURITY LINQ UNIX MATH EMAIL OOP LANGUAGE-AGNOSTIC VB6 MSBUILD", null, "# OpenCV 3D Mat to Vector", null, "", null, "» opencv » OpenCV 3D Mat to Vector\n\nBy : zigmo\nDate : November 19 2020, 12:41 AM\nit helps some times I have 3D Mat and would like to convert it to Vector. I tried opencv's reshape() function but it seems to not work with matrices that have dimensions more than 2. How can I convert to 3D Mat to Vector ? I can do it by accessing all elements in the Mat. Is there any efficient way? , If we have the following 3D matrix:", null, "code :\n``````const int ROWS=2, COLS=3, PLANES=4;\nint dims = {ROWS, COLS, PLANES};\ncv::Mat m = cv::Mat(3, dims, CV_32SC1); // works with other types (e.g. float, double,...)\n``````\n``````const int* p3 = m3.ptr<int>(0);\nstd::vector<int> flat0(p3, p3+m3.total());\n``````\n``````cv::Mat m2(ROWS, COLS*PLANES, CV_32SC1, m3.data); // no copying happening here\ncv::Mat m2xPlanes = m2.reshape(PLANES); // not sure if this involves a copy\nstd::vector<Mat> planes;\ncv::split(m2xPlanes, planes); // usually used for splitting multi-channel matrices\n\nstd::vector<int> flat;\nfor(size_t i=0; i<planes.size(); i++) {\ncv::Mat plane_i = planes[i];\nconst int* plane_i_ptr = plane_i.ptr<int>(0);\nflat.insert(flat.end(), plane_i_ptr, plane_i_ptr+plane_i.total());\n}\n``````\n``````int index = row * COLS * PLANES + col * PLANES + p\n``````", null, "##", null, "How do I create a vector of cv::matrix in opencv and assign submatrix of image data to matrices on all index of vector\n\nBy : Jason H\nDate : March 29 2020, 07:55 AM\nI wish this helpful for you I want to create a vector of cv::Matrix in a c++ program and on each index i want to copy the submatrix of an image, for example; , To make a real copy you can do\ncode :\n``````VectorMat[i]=threshImage(cv::Rect(x,y,max.x-min.x,max.y-min.y)).clone();\n``````\n``````threshImage(cv::Rect(x,y,max.x-min.x,max.y-min.y)).copyTo(VectorMat[i]);\n``````", null, "##", null, "How to access vector<vector<Point>> contours in opencv like matrix element?\n\nBy : Micah Carpenter II\nDate : March 29 2020, 07:55 AM\nThis might help you If my situation was so urgent, I would ask my question more carefully.\nIf I try hard to understand your question, you basically want to consider a contour in pixel level. In order to do that, you should draw the contour into a blank matrix with drawContour. And then compare two matrices or match a pixel in that matrix in case you want pixel by pixel.", null, "##", null, "calling OpenCV calibration functions to calculate rotation vector and translation vector\n\nBy : Neo\nDate : March 29 2020, 07:55 AM\nTo fix the issue you can do If I understand you well, you have 4 points in the image and you know their world coordinates (you have 4 2D-3D correspondences) to find the rotation matrix and translation vector (known as the camera pose), you can use the solvePnP function.\nThis function takes as inputs the 3D coordinates, 2D coordinates, the camera matrix (focal distance and center of projection) and the distortion coefficients, which you should have obtained by an intrinsic calibration process. The output is the rotation and translation vectors. The obtained rotation vector can be transformed in to a rotation matrix with the function Rodrigues.", null, "##", null, "OpenCV: Conversion of vector<vector<Point>> to vector<Mat>, problems with call by reference\n\nBy : user2673380\nDate : March 29 2020, 07:55 AM\nThis might help you You are using the right constructor but incorrectly accepting the default for the second parameter. The declaration for the Mat constructor taking std::vector as an input:\ncode :\n``````//! builds matrix from std::vector with or without copying the data\ntemplate<typename _Tp> explicit Mat(const vector<_Tp>& vec, bool copyData=false);\n``````", null, "##", null, "OpenCV, findContours - Why do we need a <vector<vector<Point>> to store the contours? Why not just <ve\n\nBy : Rashedul Hasan\nDate : March 29 2020, 07:55 AM\nWith these it helps For your first question, why there are no contour points stored in contours[n][k] for all n > 0, you may have only one contour in your contours vector, which is contours.\nThe reason for the vector in a vector is because the\ncode :\n``````vector<Point>\n``````\n`````` vector<vector<Point>>\n``````", null, "Related Posts :", null, "" ]

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[ "", null, "# Triangular prism surface area made easy\n\nTo find the triangular prism surface area, we add the areas of all the five faces.\n\n## How to find the surface area of a triangular prism?\n\nAs you saw in the triangular prism nets section of this site, all kinds of triangular prisms are made up of two triangular and three rectangular faces.\n\nFind the area of all the five faces and add them together to find the total triangular prism surface area.\n\nHence, the key to find the surface area of a triangular prism is to find the area of five of its faces.\n\nTriangular Prism Volume\n\nTriangular prism surface area is the sum of areas of its five faces. There is no need to be panic, and if kids know how to find the area of a rectangle and the area of a triangle, then they can easily find the surface area of a triangular prism.\n\nThe need is to know how to make the net of a prism. The alternative method is to imagine all the faces of the prism one by one. This way adding the area of all the faces the surface area of the shape can be obtained.\n\n### What it takes to find the surface area of a triangular prism?\n\nIf you know how to find the area of a rectangle and the area of a triangle; then you can find the surface area of a triangular prism easily.\n\nTo find the area of a rectangle we need to multiply base and height or the rectangle. Some times base and height of a rectangle are called length and breadth (width) of the rectangle.\n\nStudents need not to confuse with these terms, as they need to multiply both the given lengths of adjacent sides of a rectangle to find its area.\n\nTo find the area of a triangle, multiply the length of base to the height of triangle from the same base and divide the answer by 2.\n\nGrades six and seven give a very good opportunity for kids to learn how to find the area of basic two dimensional shapes. This curriculum includes the lessons on finding areas of rectangles and triangles.\n\n#### Lessons to find triangular prism surface area\n\nBelow are the key lessons to find the surface area of a triangular prism. We encourage the learner to go through the lessons before printing the worksheets for practice. Most of these lessons have step by step instructions so that students understand the concept of surface area.\n\nReviewing lessons give a hang of the concept to students and give them confidence to do any kind of problem on the concept.\n\nThe above methods were to find the surface area of the triangular prism without using its net. Below are two more lessons on finding the surface are but this time we will use the net of the triangular prism.\n\n Worksheets to practice finding the triangular prism surface area   Now its your turn to show your competensce on the topic of finding the surface area of a triangular prism. Below are the key worksheets having questions on finding the surface area of triangular prisms. Print these worksheets and try to solve all of the problems contained in them.   If still having problems solving the problems in the following exercises, we urge you to go back to lessons and try to do those lesson questions yourself. Most students get successful once they get able to solve the lesson problems on their own." ]

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[ "# R-alpha: Bugs in R-0.50-a1.\n\nPatrick Lindsey [email protected]\nTue, 29 Jul 1997 11:28:50 +0200 (MET DST)\n\n```Problems in R but not in S:\n---------------------------\n\n1) 'unlist' seems to have several other problems than the ones\nreported up to now. For instance, 'unlist' can be used on almost any\nobject in S without much trouble. Eg.:\nS> unlist(c(2))\n 2\nS>\n---\nR> unlist(c(2))\nSegmentation fault (core dumped)\nThis occurs in R-0.49 and in R-0.50-a1.\n\n2) Problem with the parser: When a function contains a condition\nbetween brackets the closing bracket must be adjacent to the last item\nin R but not in S. Here is an example:\nS> new <- function (x,y,z,k) {\nS+ message <- list(x,y,a=if(z) k\nS+ )\nS+ message\nS+ }\nS>\n---\nR> new <- function (x,y,z,k) {\nR+ message <- list(x,y,a=if(z) k\nR+ )\n)\n^\nError: syntax error\nR>\nThis occurs in R-0.49 and in R-0.50-a1.\n\nProblems in R:\n--------------\n\n1) The 'R Graphics' window does not have any X class or resource and\ntherefore cannot be given a default size or geometry. Would it be\npossible to give the graphic window a class name so that the size\ncould be specified in the '.Xdefaults' file?\n\n2) It does not appear to be possible to specify the 'xlim' when using\nboxplot. This might also be the case in S but would be nice to\nhave. Eg., when plotting several boxplots together, lets say 7. One\nwould generally plot 4 first and then 3. Hence, if they are fitted on\nthe same page the boxplots of the first line will be wider than on the\nsecond...\n\n3) Some problems occur when using the help. Eg.,\nR> ?\"+\"\nsorry, no help for \"Arithmetic\".\nR>\nThis occurs in R-0.49 and in R-0.50-a1 and seems to be the case for\nany item contained in a help file starting with a capital letter.\n\n4) The option 'right' when using print gives an error. In S,\n'print.default' calls 'print.structure' and then 'print.matrix'. This\nlast one allows this option. Can anything be done as 'print.default'\nis internal in R?\n\n5) The control-c still does not work on R-0.50-a1 under certain\nvariants of Linux. What is the easiest way to fix this?\n\nPatrick.\n=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-\nr-devel mailing list -- Read http://www.ci.tuwien.ac.at/~hornik/R/R-FAQ.html\nSend \"info\", \"help\", or \"[un]subscribe\"\n(in the \"body\", not the subject !) To: [email protected]\n=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-\n\n```" ]

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[ "NOTE: A Pascal is a derived unit equal to 1 N/m. Dimensions, Units, Conversion Factors, and Significant Digits . For example, the base unit for length is meters. 0000015886 00000 n NOTE: This page relies on JavaScript to format equations for proper display. 0000004973 00000 n kg and kgf units are not consistent units on the paper, but looks equal on non scientific conversations. More than 4500 entries covering traditional English, conventional metric, and SI units in the fields of civil, mechanical, electrical, and chemical engineering make conversions a snap. 0000002115 00000 n 0000002820 00000 n endstream endobj 17 0 obj<>stream 4-2.4 accuracy in the conversion of units 4-6 4-3 mass, force, and weight 4-8 4-3.1 basic concepts 4-8 4-3.2 systems of-mechanical units 4-9 4-4 conversion of the units of derived quantities 4-12 4-5 conversion of temperature units 4-16 4-6 electromagnetic units 4-18 4-7 equations 4-19 4-7.1 dimensional analysis of equations 4-22 While these multipliers are most often used with metric basic or derived units, the multipliers are sometimes used with english units, creating confusing combinations. And there are list of units of selected features. 0000006088 00000 n M�u���ϥF`.cZ��A7v#�*i%j+(�,�6t�S�{cJ������ �b�G�C�2\\�흀�PH�Pj�'d��B�E��� �Y�����A�5W`_��l���������R i~4��tjRL`2Bd\\Ti�n�������i�� m�����[�%���&�Tj�*e�������{+�%�,R���+���}�Y&,��߶D����[!sP��2����i_>��fmӲ��,�.~�۱:)�U�N�~����Y���:�՗�̘���E�|B3�Xo�4ӱԤ��&��N��G=N\\B��� ��%� 0000005475 00000 n This page provides a calculator for performing unit conversion, with a focus on engineering units. The unit of time, seconds (s, sec) is the same in both systems. As you see beneath that list, there are two of little boxes that you can enter values. Machinery's Handbook, 27th Ed., Industrial Press Inc., 2004. All engineering unit conversions are derived from a base unit. Installing ‘Convert’ The Engineering Unit Conversion Calculator On Your PC Convert consists of a single 548KB file named convert.exe which is contained within the 154KB file named ‘convert.zip’ that you have downloaded to your preferred folder. In the following tables, a number in bold and blue indicates an exact conversion value. Conversions between units in the metric system are defined by their prefixes (for example, 1 kilogram = 1000 grams, 1 milligram = 0.001 grams) and are thus not listed in this article. While these multipliers are most often used with metric basic or derived units, the multipliers are sometimes used with english units, creating confusing combinations. Engineering Conversion Factors. Conversion Factors for Units of Area (Large Units) Conversion Factors for Units of Area (Small Units) A table of conversion factors between common length units is provided below: A table of conversion factors between common area units is provided below: A table of conversion factors between common volume units is provided below: A table of conversion factors between common mass units is provided below: A table of conversion factors between common density units is provided below: A table of conversion factors between common force units is provided below: A table of conversion factors between common units of moment and torque is provided below: A table of conversion factors between common units of pressure and stress is provided below: A table of conversion factors between common fluid pressure units is provided below: A table of conversion factors between common velocity units is provided below: A table of conversion factors between common acceleration units is provided below: A table of conversion factors between common angular velocity units is provided below: A table of conversion factors between common volumetric flow rate units is provided below: A table of conversion factors between common units of energy and work is provided below: A table of conversion factors between common power units is provided below: Stress intensity is an important quantity in fracture mechanics. Introduction ; There is a difference between dimensions and units. Unit of Length, Area, Volume, Force, Pressure etc. The U.S.Customary System (English, imperial, engineering system) uses pounds (lb) and feet (ft) or inches (in.). Factors for converting units of Length, Angle, Area, Weight, Volume, Power, Pressure, Engergy, Force and Electricity. and English Systems. Dimensions, Units, Conversion Factors, and Significant Digits . 0000007996 00000 n endstream endobj 7 0 obj<> endobj 8 0 obj<> endobj 9 0 obj<>/ProcSet[/PDF/Text]/ExtGState<>>> endobj 10 0 obj<> endobj 11 0 obj<> endobj 12 0 obj<> endobj 13 0 obj<> endobj 14 0 obj<>stream In the fields of civil engineering, unit conversion of various measurements is must have knowledge now-a-days. The System International (International Standard System) use newtons (N) and meters (m) for its units of force and length. ���P.��P�ەh�,���c�\\$ͦI�Q/V���f�%��O�%4l��;�ڡu��=4�E �bE�!��\"9/м**�����P��~l�;�_b�\\Z8:'���~�5�ͦ%��s�5�ޒDm2tB-�y��kUk�S�j��&������l�i\"Xh�������;@���v{���������Zl��1�\"��x,l4��_��F*g��:`����Q,4���0V0)o���+Q�d?0��q(�Ԇ�N흲EA?b���W��� ; For example, length is a dimension, but it is measured in units of feet (ft) or meters (m). The conversion factors presented are for general measurements as well as those primarily associated with energy calculations; additional conversion multipliers can be … Exceptions are made if the unit is commonly known by another name (for example, 1 micron = 10 −6 metre). ��3�� NOTE: The units of Joule and N•m are equivalent and are both commonly used to express quantities of energy and work. Mechanical Engineering Units and Quantities. Access Free Mechanical Engineering Unit Conversion Table juggled next … Speed 11 J. Therefore, we must know the basic conversion of different units. Users can add new engineering unit conversions and modify existing engineering unit conversions. Mechanical Engineering Units and Quantities . Derived Units. Below are tables that convert units from USCS to S.I. 0000007267 00000 n The speed of sound varies depending on the medium (substance) the sound is travelling through and the temperature. Please enable JavaScript. The S.I. so if we conventionally assume: 1 kgf = 1 kg, eq1 and eq2 can be combined like this: \\$\\$ kgf/mm^3 = 0.01 \\ kN / mm^3 = 93.53 \\ lbf \\ sec^2 / in^4 \\$\\$ A dimension is a measure of a physical variable (without numerical values), while a unit is a way to assign a number or measurement to that dimension. endstream endobj 18 0 obj<>stream 0000001755 00000 n How to use Torque Converter Select the unit to convert from in the input units list. A table of conversion factors between common mass units is provided below: 1. Quick, free, online unit converter that converts common units of measurement, along with 77 other converters covering an assortment of units. 0000000016 00000 n H��T;o�0��+8��Y�!Y��K��]��k�=\\����~)�q\\?�L\"�I�g�Cq�A�S���j:�����6o���NŚ^a�m ��K�+i�&p9~�s���\"�P-I�\"��m(�B�����V! FingerCAD - FingerCAD is a computer aided design application for technical drawing. 4vet���+��P��n��O���)�@�wōo������ ������p�tz/��d�|_k����I����\\.��޵��w�����S�-� ��;o 0000002690 00000 n However, its use is required to produce a consistent set of units. Mechanical 6 B. This comprehensive unit conversion tool makes conversion calculations easy-peasy, covering all the dimensions engineers need on a daily basis. Third part. ; For example, length is a dimension, but it is measured in units of feet (ft) or meters (m). ��&X�]:v��7K�=[ ݫ��?�T���zB+3�Zi�ɕP:�4F˪��B?���{�*�/�M�Z�V�i�=s{ �G8��J����':��qUgtr��1��Fw�g�m�N�B�l.�~�\"�:_`�%�����j�v�Kv\"��uh��.�0xQ�E��]���埻�&�r�u�T�e�q�0 tO�R�` YG2- The conversion result will immediately appear in the output box. H��T�n�0��+t���DJ��u@�+�a�A�b�!M�nK�����Gɪ�D �Ƈ����#�Y�u��Ш��i����.�V�6���6�/7k�M�71zy�m�#��)������ �5��7c�{�\\$]zsH!�@S^T�cU�KTy�\\$��p��]��m :��3�vӪ�7�y q��!y��zۅV�4���X�w����g0�U����'L<4�xC:�l;� I�Iw��\\?JЈIA)Ҙ�<8�,��uɚ�F \"�28b�qq��S��,7� pK3 � �:��J���3Y=|}��~-l60i�B�����s�ӌ.&���R�~����_�����)~�~?z%c�2����ˎ�m'�z�Kee'F��;Lr\\$r��e�s���Kw���>]�Գ�&T�&|��l��Z-��T��9�Ơ\\���Nta��\\$s�;q�������z�Ny��e�k�@�!�T��0 67, Covering more than 4,500 entries on traditional English, conventional metric, and SI units found in the civil, mechanical, electrical, and chemical engineering fields. InstaConvert – Converter tool for Engineers InstaConvert is an essential tool for Instrumentation / Electrical/Industrial automation / Mechanical Engineers and Technicians. 0000016115 00000 n Reference Tables useful for Mechanical or Industrial Engineers . Introduction ; There is a difference between dimensions and units. 0000004392 00000 n Recommended Textbooks Passing the PE Exam Overview of Mechanical Engineering Skills of a Mechanical Engineer Software for Mechanical Engineers Useful Gadgets. ;Mh�N��NRɈ,��^ (\"��U���C�)hpO��l�u Derived Units. Engineering Conversions and Equivalents. Where: Length = L Mass = M Time = T Current = Q/T Charge = Q. meter/sec 2. 6 27 �4r�q&R����r͖��7y�r� Note that the force unit conversion factor gc [lbm-ft/(lbf-sec2)] should not be confused with the local acceleration of gravity g, which 0000007775 00000 n A very useful tool for every mechanical, electrical and process engineer! endstream endobj 20 0 obj<>stream H���[k�@F��W�������@چ^Hoa�RBJ���[Zȯ��J�e�Il�\"-;Gg��=BL�8�R�Y}P������1j��y�\\�O�F=͊АFy�סc����rw %�V{ y������U�8jo�l�4ƒCAg�B��tt@cC��1'H����!�es~�^�眴l�.���-�MJ�ۂ`.:=c�`f��G�R���g'�u�P����HI�b[�p%`%\\6��߿�O�r��;�np�qsS����ŕ|r�%�.? It converts a large variety of engineering units that are often not included in other converters. 0000016866 00000 n H��TKo�0��W��ŠzzX���C �P���N��q��[�?J��ݰ!�(\"�=H*'�7�]�*N�JA�,H�����F��ZV�\\��@UD�tP��%�m���v�nz�� ���y���쮺*�A� �r�>g0������1��L�0�AA:�u(Y��hl�%�TO>�\\7��E�֋.�U�7Ͷ�WSY{=�}mVj�F��ÁGF��x�V��z��o3��l������#�Y��>�u���.����� Table 15 Kinematic Viscosity Units Table 16 Temperature Conversion Formulas . 0000001408 00000 n As you see beneath that list, there are two of little boxes that you can enter values. 1 lbf/in2= 1 psi = 6894.6 Pa = 2.0418 in Hg = 144 lbf/ft2 1 in Hg = 3376.8 Pa = 0.4898 lbf/in2= 13.57 in H 2O 1 in H2O = 248.8 Pa = 0.0361 lbf/in 2 perform conversions between Torque units. Moles are often reported as a fundamental unit, but it is not; it is just a bookkeeping convenience to avoid carrying around factors of 10 23 everywhere. meter/sec 2. This engineering unit conversion calculator makes engineering unit conversion fast and simple. Key Features: Contains many new basic conversions that have developed or have been encountered or sought out. Unit Converter with commonly used Units Common converting units for Acceleration, Area, Density, Energy, Energy per unit mass, Force, Heat flow rate, Heat flux, Heat generation per unit volume and many more Unit symbols are given in [brackets] Plane Angle 8 B. Description: Dimensions. endstream endobj 15 0 obj<> endobj 16 0 obj<>stream It contains basic units and its conversion. In all these examples, gc should be regarded as a force unit conversion factor. %%EOF 0 And there are list of units of selected features. ��R���Խ,��-JxY��P�ݶ�Y�V�m�|Ҁ�C���2�Hl��[��2 �D�c ڭL��V���B�t%S��v�s��4������v;Q���������UQamu�iA�X������6O�������&�UT�V�9:G�;\"�:�g�M0 [��~��u�^�|AΫ7�k�RD~�E8��ݑ)!����bݒ.��l_���(;�S[0{#�l]�U�r�n*�[M�*�+����7'.w@�҄^���h+�E�u��/�iQ�Y:h�Z�)Rﻙ�]��>��9=|֪��y�Rݳy�с���΍yh%�߁��#�EU):S!���0�UQ�¦��wޢn�)�` ��00 Mechanical Engineering Units and Quantities. International System of Units. NOTE: 1 g is the acceleration due to gravity. It is frequently not written explicitly in engineering equations. Thermal 7 C. Electric and Magnetic 7 VI. 0000006662 00000 n trailer The site also includes a predictive tool that suggests possible conversions based on input, allowing for easier navigation while learning more about various unit … ����R���tbESt��!!�!A��R�}\\$%! *���Q��C�*� Enter the value to convert from into the input box on the left. %PDF-1.4 %���� Engineering Conversion Factors. The engineering unit conversions are also user configurable. Select the unit to convert to in the output units list. Mechanical Engineering Units and Quantities . It is frequently not written explicitly in engineering equations. mechanical engineering unit conversion table, but end in the works in harmful downloads. This page provides conversion tables for common engineering units. Engineering Unit Conversions by Lindeburg is essential in preparing for, and taking the PE exam. Reference tables for the International System of Units, or the SI System. The use of MB-Unit Converter is very easy. ��!��ʜcy���uji�CfB����N��C�I�z\\w9B����u>4�����:ǧ*�U�[و�9~��� |��MKC����M]/�7�D�s�\\��]B���/{�'����k�:���G��~�<7�}zn6��#c��-c4\"�kj]sه׼�W6�. ���nʛIQ�r��)=�1\\1gs���t� 0000003537 00000 n Unit Converter with commonly used Units Common converting units for Acceleration, Area, Density, Energy, Energy per unit mass, Force, Heat flow rate, Heat flux, Heat generation per unit volume and many more Unit symbols are given in [brackets] Agreed with SMott. MechaniCalc Pricing. A dimension is a measure of a physical variable (without numerical values), while a unit is a way to assign a number or measurement to that dimension. Angle: 0. Engineering Conversions and Equivalents. 100% FREE. Note that the force unit conversion factor gc [lbm-ft/(lbf-sec2)] should not be confused with the local acceleration of gravity g, which This is a comprehensive engineering unit converter with an intuitive spinning wheel interface. Mach 1 is equal to the speed of sound, which is 343 m/s in dry air at 20 °C (68 °F). xref Where: Length = L Mass = M Time = T Current = Q/T Charge = Q. Angle: 0. This page provides a calculator for performing unit conversion, with a focus on engineering units. Click on the pop-up list, then select what do you want to calculate from them such as torque, electricity etc. Rather than enjoying a good book later a mug of coffee in the afternoon, on the other hand they Page 6/10. NOTE: The Avoirdupois ounce is what is typically used in engineering work, as opposed to the Troy ounce (which is used for weighing gold and silver). Engineering Unit Conversion - Number crunch with ease. Acceleration: LT-2. This converter app consists of engineering calculation tools related to Instrumentation, Electrical, Industrial Automation and Mechanical engineering. 0000016618 00000 n Moles are often reported as a fundamental unit, but it is not; it is just a bookkeeping convenience to avoid carrying around factors of 10 23 everywhere. Unit conversion multipliers are presented in this fact sheet along with several examples to describe the use of these multipliers. Engineering Calculator is a tiny software program whose purpose is to aid people in converting a wide range of measurement units and making simple calculations.. Conversion of mksq Units to Gaussian Units 8 VII. 32 0 obj<>stream bǃ�t��ѲE��u֟Vd��K%�櫸�����Uj�dZ�R w��ܥtԂ'�Ҵ�_�g��:)l����;�=�FM�'��)Y\"٠s�����+Hڸ�V�!�2v�,���v�^J�R~J�� �:g5�{٬`��l���l�d^y��4%��GJ�r�s��k�9�T��s� The conversions you need for exam day success. Description: Dimensions. Solid Angle 8 C. Length 9 D. Area 9 E. Volume 9 F. Mass 10 G. Density 10 H. Time 11 I. In all these examples, gc should be regarded as a force unit conversion factor. Conversions listed alphabetically for easy referencing. The use of MB-Unit Converter is very easy. 0000001281 00000 n 0000008465 00000 n In addition, new base units can also be added to the historian system. x�b``�```�� �wP3�0p,``@��b^f�Cr�~6�P��WQ��8�'���D��;�8'�2Om��dd`p��L@lĬ��!�� �� NOTE: The Avoirdupois ounce is what is typically used in engineering work, as opposed to the Troy ounce (which is used for weighing gold and silver). Acceleration: LT-2. For example someone can say this chair mass is 10kg or it's weight is 10kgf, both refers to same chair with same mass and weight. AEMT - Association of Electrical and Mechanical Trades ... SI Units Classification of Insulation Systems Glossary of Terms Formulae Conversion Factors. <<8E56AE49D9F60646BEC7335F86A85AF8>]>> startxref H��T͎�0��)�\"e֞q��� 0000000836 00000 n This book will come in handy during your open-book exam as well as throughout your engineering career. AEMT - Association of Electrical and Mechanical Trades About AEMT Membership Buy/Sell Bulletin Helpline Contact Conversion Factors for Units of Area (Large Units) Conversion Factors for Units of Area (Small Units) Start using it early in your preparation so you can get a feel for how to flip through it quickly. Today it is very important to be able to understand measurements in both the English system of units and the SI (Systems International) system of units. A standard unit conversion tool is also included in the App. 0000003853 00000 n A. 6 0 obj <> endobj This is light and simple unit converter designed specifically for engineers. H��T�n�@��+x=\\$g�=]�M4�=\\$줱S�N�?��+g�D� �P����Ң�D��&)������@h}�����B0,�uV�8�0� However, its use is required to produce a consistent set of units. endstream endobj 19 0 obj<>stream \"Guide for the Use of the International System of Units (SI),\" National Institute of Standards and Technology (NIST), 2008. Recommended Textbooks Passing the PE Exam Overview of Mechanical Engineering Skills of a Mechanical Engineer Software for Mechanical Engineers Useful Gadgets. Conversion Factors 8-23 A. 0000008223 00000 n The modified or developed form of Metric System (one of the system of units for measurement consist of three fundamental units which are meter, kilogram, second) is called as International System of Units or SI Units.SI Units are considered as standard units of measurement and are most widely used. MechaniCalc Pricing. 0000001105 00000 n 0000016313 00000 n It features a quick \"Paste\" button for input value, \"Copy\" button of the result. Click on the pop-up list, then select what do you want to calculate from them such as torque, electricity etc. 0000001029 00000 n Conversions between the most common units are given in the table below: A table of conversions between common temperature units is provided below: Subscribe to receive occasional updates on the latest improvements: Affordable PDH credits for your PE license. Format equations for proper display - Association of Electrical and Mechanical Trades... SI units Classification of systems... Commonly used to express quantities of energy and work Mass 10 G. Density H.... Addition, new base units can also be added to the historian.. Must know the basic conversion of mksq units to Gaussian units 8.. Engineers Useful Gadgets tools related to Instrumentation, Electrical, Industrial automation and Mechanical engineering conversions...: 1 g is the acceleration due to gravity written explicitly in engineering equations do you want to calculate them... = Q Time = T Current = Q/T Charge = Q fact sheet along several... Length is meters the value to convert from in the afternoon, on pop-up. Is essential in preparing for, and Significant Digits 20 °C ( °F. Box on the medium ( substance ) the sound is travelling through and the temperature Length = Mass! Focus on engineering units that are often not included in other converters dimensions, units, or the System. Glossary of Terms Formulae conversion Factors for units of Joule and N•m are equivalent are... Consistent set of units, or the SI System ) conversion Factors for units of Area ( Small )... Conversion of different units calculation tools related to Instrumentation, Electrical and Mechanical Trades... SI units Classification of systems. Sec ) is the same in both systems multipliers are presented in this fact sheet with! Instaconvert is an essential tool for Engineers boxes that you can enter values for proper display with... Output box standard unit conversion, with a focus on engineering units calculation tools to! And process Engineer difference between dimensions and units Current = Q/T Charge = Q Press,. Included in the following unit conversion for mechanical engineering, a number in bold and blue indicates an exact conversion value new units. Is a comprehensive engineering unit conversions and modify existing engineering unit conversions therefore we... Engineering career set of units, or the SI System torque converter select the unit to convert from into input! In all these examples, gc should be regarded as a force unit conversion with! There is a computer aided design application for technical drawing 9 D. Area 9 Volume. And work written explicitly in engineering equations due to gravity, Pressure etc is essential! Of these multipliers of energy and work it is frequently not written explicitly in equations. ( 68 °F ) is essential in preparing for, and taking the PE Exam Overview of engineering! Provides a calculator for performing unit conversion multipliers are presented in this fact sheet along with several to... Mksq units to Gaussian units 8 VII, conversion Factors for units of selected.... Tools related to Instrumentation, Electrical, Industrial automation and Mechanical engineering unit conversions is 343 m/s dry. A good book later a mug of coffee in the output box you can enter values is travelling through the. Units list where: Length = L Mass = M Time = Current! – converter tool for Instrumentation / Electrical/Industrial automation / Mechanical Engineers Useful Gadgets Instrumentation / automation. Of coffee in the output box Press Inc., 2004 provides a for... Insulation systems Glossary of Terms Formulae conversion Factors, and Significant Digits performing conversion... The afternoon, on the paper, but looks equal on non scientific conversations units that often! Is an essential tool for Engineers instaconvert is an essential unit conversion for mechanical engineering for Instrumentation / Electrical/Industrial automation / Mechanical and... Mug of coffee in the output units list for example, 1 micron = −6! Bold and blue indicates an exact conversion value Passing the PE Exam Overview Mechanical. Common Mass units is provided below: 1 new base units can also be added the... Units that are often not included in the output box between common Mass units is provided below: 1 other... Set of units, or the SI System 8 C. Length 9 D. Area E.. Conversion result will immediately appear in the afternoon, on the paper, but looks equal on non conversations! Base unit 20 °C ( 68 °F ) number in bold and blue indicates an exact conversion value commonly to. Current = Q/T Charge = Q quick `` Paste '' button for input value, `` ''. = Q the basic conversion of mksq units to Gaussian units 8 VII the to... Is commonly known by another name ( for example, 1 micron = 10 −6 metre.... All these examples, gc should be regarded as a force unit conversion tool makes calculations! Between dimensions and units below: 1 g is the same in both systems light and simple converter. A focus on engineering units indicates an exact conversion value of mksq units to Gaussian units 8 VII, etc... Difference between dimensions and units 27th Ed., Industrial Press Inc., 2004 conversion. N•M are equivalent and are both commonly used to express quantities of and... With a focus on engineering units between common Mass units is provided below: 1 on! ( substance ) the sound is travelling through and the temperature consistent units on the other they... Tool for Engineers instaconvert is an essential tool for Engineers instaconvert is an essential for... This fact sheet along with several examples to describe unit conversion for mechanical engineering use of these multipliers you see beneath that,! To convert from into the input units list unit conversion for mechanical engineering need on a daily basis for technical drawing converts. 1 N/m conversion multipliers are presented in this fact sheet along with several examples to describe the of. Rather than enjoying a good book later a mug of coffee in the afternoon, on the pop-up list there... Torque, electricity etc with a focus on engineering units flip through it quickly blue indicates exact! °F ) they page 6/10 of Mechanical engineering Skills of a Mechanical Engineer Software for Mechanical Engineers and.! A focus on engineering units that are often not included in the afternoon, on the paper, but in! In all these examples, gc should be regarded as a force unit conversion factor, Industrial Press,! A feel for how to flip through it quickly input units list an intuitive wheel. Engineering career 10 H. Time 11 I conversion Factors unit conversion for mechanical engineering units of Joule and N•m are equivalent and are commonly. Daily basis a base unit quick `` Paste '' button for input value, `` ''! Due to gravity known by another name ( for example, 1 micron = 10 −6 metre.! Trades... SI units Classification of Insulation systems Glossary of Terms Formulae conversion Factors, and Significant Digits this will! Of Area ( Small units ) conversion Factors for units of selected features electricity! Introduction ; there is a computer aided design application for technical drawing Technicians! As torque, electricity etc a good book later a mug of coffee in the input units list ''... Area ( large units ) Agreed with SMott converter select the unit to convert to in the output units.!: 1 System of units are two of little boxes that you can enter values is the acceleration to! = Q/T Charge = Q, gc should be regarded as a force unit conversion factor or been... Select what do you want to calculate from them such as torque electricity... The dimensions Engineers need on a daily basis tools related to Instrumentation, Electrical process! And taking the PE Exam Overview of Mechanical engineering unit conversions and modify existing engineering unit multipliers! / Electrical/Industrial automation / Mechanical Engineers Useful Gadgets it is frequently not explicitly! Many new basic conversions that have developed or have been encountered or sought out many. Need on a daily basis 1 micron = 10 −6 metre ) conversion multipliers are presented in this sheet. Unit is commonly known by another name ( for example, 1 micron 10! Engineering Skills of a Mechanical Engineer Software for Mechanical Engineers and Technicians units! This converter app consists of engineering calculation tools related to Instrumentation, Electrical, Press! = L Mass = M Time = T Current = Q/T Charge Q. Included in other converters Electrical, Industrial automation and Mechanical Trades... SI units Classification of Insulation systems Glossary Terms... Convert to in the following tables, a number in bold and blue an... A standard unit conversion factor bold and blue indicates an exact conversion value features! Formulae conversion Factors for units of Joule and N•m are equivalent and are both commonly used express! Volume 9 F. Mass 10 G. Density 10 H. Time 11 I conversion of different.! Express quantities of energy and work converter app consists of engineering units that are often not included other... Tool makes conversion calculations easy-peasy, covering all the dimensions Engineers need on a daily basis new... Aemt - Association of Electrical and Mechanical Trades... SI units Classification of Insulation systems Glossary Terms!, seconds ( s, sec ) is the same in both systems button of result. Exam as well as throughout your engineering career are not consistent units the. This page provides a calculator for performing unit conversion tool makes conversion calculations easy-peasy, covering all the dimensions need. Your preparation so you can enter values the basic conversion of mksq to! Javascript to format equations for proper display a table of conversion Factors bold blue... Express quantities of energy and work handy during your open-book Exam as as. Is also included in other converters input units list conversion value conversion unit conversion for mechanical engineering will appear... Mechanical Engineer Software for Mechanical Engineers and Technicians express quantities of energy and work tool! Mass 10 G. Density 10 H. Time 11 I want to calculate from such..." ]

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[ "# A Treatise on Electricity and Magnetism/Part IV/Chapter XXII\n\nJump to navigation Jump to search\nA Treatise on Electricity and Magnetism by James Clerk Maxwell\nFerromagnetism and Diamagnetism Explained by Molecular Currents\n\nCHAPTER XXII.\n\nFERROMAGNETISM AND DIAMAGNETISM EXPLAINED BY MOLECULAR CURRENTS.\n\nOn Electromagnetic Theories of Magnetism.\n\n832.] WE have seen (Art. 380) that the action of magnets on one another can be accurately represented hy the attractions and repulsions of an imaginary substance called * magnetic matter. We have shewn the reasons why we must not suppose this magnetic matter to move from one part of a magnet to another through a sensible distance, as at first sight it appears to do when we magnetize a bar, and we were led to Poisson s hypothesis that the magnetic matter is strictly confined to single molecules of the mag netic substance, so that a magnetized molecule is one in which the opposite kinds of magnetic matter are more or less separated to wards opposite poles of the molecule, but so that no part of either can ever be actually separated from the molecule (Art. 430).\n\nThese arguments completely establish the fact, that magnetiza tion is a phenomenon, not of large masses of iron, but of molecules, that is to say, of portions of the substance so small that we cannot by any mechanical method cut one of them in two, so as to obtain a north pole separate from a south pole. But the nature of a mag netic molecule is by no means determined without further investi gation. We have seen (Art. 442) that there are strong reasons for believing that the act of magnetizing iron or steel does not consist in imparting magnetization to the molecules of which it is com posed, but that these molecules are already magnetic, even in un- magnetized iron, but with their axes placed indifferently in all directions, and that the act of magnetization consists in turning the molecules so that their axes are either rendered all parallel to one direction, or at least. are deflected towards that direction.\n\n�� � 834-] AMPERE S THEORY. 419\n\n833.] Still, however, we have arrived at no explanation of the nature of a magnetic molecule, that is, we have not recognized its likeness to any other thing of which we know more. We have therefore to consider the hypothesis of Ampere, that the magnetism of the molecule is due to an electric current constantly circulating in some closed path within it.\n\nIt is possible to produce an exact imitation of the action of any magnet on points external to it, by means of a sheet of electric currents properly distributed on its outer surface. But the action of the magnet on points in the interior is quite different from the action of the electric currents on corresponding points. Hence Am pere concluded that if magnetism is to be explained by means of electric currents, these currents must circulate within the molecules of the magnet, and must not flow from one molecule to another. As we cannot experimentally measure the magnetic action at a point in the interior of a molecule, this hypothesis cannot be dis proved in the same way that we can disprove the hypothesis of currents of sensible extent within the magnet.\n\nBesides this, we know that an electric current, in passing from one part of a conductor to another, meets with resistance and gene rates heat ; so that if there were currents of the ordinary kind round portions of the magnet of sensible size, there would be a constant expenditure of energy required to maintain them, and a magnet would be a perpetual source of heat. By confining the circuits to the molecules, within which nothing is known about resistance, we may assert, without fear of contradiction, that the current, in cir culating within the molecule, meets with no resistance.\n\nAccording to Ampere s theory, therefore, all the phenomena of magnetism are due to electric currents, and if we could make ob servations of the magnetic force in the interior of a magnetic mole cule, we should find that it obeyed exactly the same laws as the force in a region surrounded by any other electric circuit.\n\n834.] In treating of the force in the interior of magnets, we have supposed the measurements to be made in a small crevasse hollowed out of the substance of the magnet, Art. 395. We were thus led to consider two different quantities, the magnetic force and the magnetic induction, both of which are supposed to be observed in a space from which the magnetic matter is removed. We were not supposed to be able to penetrate into the interior of a mag netic molecule and to observe the force within it.\n\nIf we adopt Ampere s theory, we consider a magnet, not as a\n\nE e 2\n\n�� � 420 ELECTE1C THEORY OF MAGNETISM. [8 35.\n\ncontinuous substance, the magnetization of which varies from point to point according to some easily conceived law,, but as a multitude of molecules, within each of which circulates a system of electric currents, giving rise to a distribution of magnetic force of extreme complexity, the direction of the force in the interior *pf a molecule being generally the reverse of that of the average force in its neigh bourhood, and the magnetic potential, where it exists at all, being a function of as many degrees of multiplicity as there are molecules in the magnet.\n\n835.J But we shall find, that, in spite of this apparent complexity, which, however, arises merely from the coexistence of a multitude of simpler parts, the mathematical theory of magnetism is greatly simplified by the adoption of Ampere s theory, and by extending our mathematical vision into the interior of the molecules.\n\nIn the first place, the two definitions of magnetic force are re duced to one, both becoming the same as that for the space outside the magnet. In the next place, the components of the magnetic force everywhere satisfy the condition to which those of induction are subject, namely, j a JQ j\n\n��In other words, the distribution of magnetic force is of the same nature as that of the velocity of an incompressible fluid, or, as we have expressed it in Art. 25, the magnetic force has no convergence.\n\nFinally, the three vector functions the electromagnetic momen tum, the magnetic force, and the electric current become more simply related to each other. They are all vector functions of no convergence, and they are derived one from the other in order, by the same process of taking the space-variation, which is denoted by Hamilton by the symbol V.\n\n836.] But we are now considering magnetism from a physical point of view, and we must enquire into the physical properties of the molecular currents. We assume that a current is circulating in a molecule, and that it meets with no resistance. If L is the coefficient of self-induction of the molecular circuit, and M the co efficient of mutual induction between this circuit and some other circuit, then if y is the current in the molecule, and y that in the other circuit, the equation of the current y is\n\n-Ry, (2)\n\n�� � 838.] CIRCUITS OF NO RESISTANCE. 421\n\nand since by the hypothesis there is no resistance, R = 0, and we get by integration\n\nLy + My =. constant, = Zy , say. (3)\n\nLet us suppose that the area of the projection of the molecular circuit on a plane perpendicular to the axis of the molecule is A, this axis being defined as the normal to the plane on which the projection is greatest. If the action of other currents produces a magnetic force, X, in a direction whose inclination to the axis of the molecule is 6, the quantity My becomes XA cos0, and we have as the equation of the current\n\nLy + XAco\\$0 Ly , (4)\n\nwhere y is the value _of y when X = 0.\n\nIt appears, therefore, that the strength of the molecular current depends entirely on its primitive value y , and on the intensity of the magnetic force due to other currents.\n\n837.] If we suppose that there is no primitive current, but that the current is entirely due to induction, then\n\n• XA\n\ny = -- -COS0. (o)\n\n��The negative sign shews that the direction of the induced cur rent is opposite to that of the inducing current, and its magnetic action is such that in the interior of the circuit it acts in the op posite direction to the magnetic force. In other words, the mole cular current acts like a small magnet whose poles are turned towards the poles of the same name of the inducing magnet.\n\nNow this is an action the reverse of that of the molecules of iron under magnetic action. The molecular currents in iron, therefore, are not excited by induction. But in diamagnetic substances an action of this kind is observed, and in fact this is the explanation of diamagnetic polarity which was first given by Weber.\n\nWeber s Theory of Diamagnetism.\n\n838.] According to Weber s theory, there exist in the molecules of diamagnetic substances certain channels round which an electric current can circulate without resistance. It is manifest that if we suppose these channels to traverse the molecule in every direction, this amounts to making the molecule a perfect conductor.\n\nBeginning with the assumption of a linear circuit within the mo lecule, we have the strength of the current given by equation (5).\n\n�� � 422 ELECTRIC 'IIIEDHY OF mrow/1*1SlL [839. Thu moguulic moment af the eimvet in the product ol` its etmngdi lg lhs arm ot' the circuit, or yu, and the mwlvonl part ui this in the dlractiun of the iuagnutizing iowa ix yi} our 0, or, hy (S), ¤ - # sm a, (M) lf them are u such mnlseulns in nnitaf volume, and if their axes nin distritnxtnd inditforeiitly in all directions, than the avuznga vsluc of eo¤’0 will hs Q, and tha intensity of magnetization of tho sabslnnes will he 1# (7) Neumann; couliicieut r»l'mngar:ti.uhl¤n is therefore wil s - Mg T - wt Thu inngimtimtion ol' the sulxstanu is therefore iu the opposite tlireeticn to the magnetiziug A`or¤s_,or, in other wnnls, the sulmannn is rlinmzgnutie. It is also exactly proportional to the ningautizing fame, and llocs not will to it linits limit., as iu the casa uf ordinary magnetic indizctiun, Sse Arts. M2, Sac. E39.] It tho directions af the axes ul' the mcleeular channels ara nrinngerl, not inrliii`ei·eatly in all diieelions, but with n pi·epanrlt·i»- ating numbor in certain directions, than thu sum s we it extended to all the molnsules will have tliflhmni: values aceording tu the dirautiou of the line from which 0 is mcasumnl, and the Aim trihutiou of Lhnsc values in dillbrent ilirootians will hu similar to tho distrilzation of the values of moments el' inertia nhoub nm: in dif. fsmnf. directions through the same paint, Such in distribution will explain the magnetic plienomann related to axes in the body, described by Pltiokor, which Faraday has collorl Magracrystollis plisaoinaim. See Art. U5. 840,] Let us naw consider whnt would lm the effect, it inawnrl ol' the eluetiiu current being cantinell to it certain channel within thc molecule, the whale molecule wm snppnretl a parfeet eemluemr. Lot us Login with tho earn of n lmdy the Form of which is ncyclie, that is tn any, which is not in the ibrm of a ring; or peifuiatcll body, and lot us suppose that this livxly is cveryxvlierc surrenndul by u thin shall of pcri\"¤¤tl_v ouxidaoting matter. l We have proved in Art, GM, that a closed sheet of perfectly l canrlueting matter of any {`urm, originally free hom enrrunts, he· ` 842.] PERFECTLY CONDUCTING MOLECULES. 423\n\ncomes, when exposed to external magnetic force, a current-sheet, the action of which on every point of the interior is such as to make the magnetic force zero.\n\nIt may assist us in understanding this case if we observe that the distribution of magnetic force in the neighbourhood of such a body is similar to the distribution of velocity in an incompressible fluid in the neighbourhood of an impervious body of the same form.\n\nIt is obvious that if other conducting shells are placed within the first, since they are not exposed to magnetic force, no currents will be excited in them. Hence, in a solid of perfectly conducting material, the effect of magnetic force is to generate a system of currents which are entirely confined to the surface of the body.\n\n841.] If the conducting body is in the form of a sphere of radius r, its magnetic moment is\n\n-ir&gt;JT,\n\nand if a number of such spheres are distributed in a medium, so that in unit of volume the volume of the conducting matter is , then, by putting ^=1, and ^ = in equation (1 7), Art. 314, we find the coefficient of magnetic permeability,\n\n2 ~ U/ , (9)\n\n��whence we obtain for Poisson s magnetic coefficient\n\n• =-**, (10)\n\nand for Neumann s coefficient of magnetization by induction\n\n��_\n\nSince the mathematical conception of perfectly conducting bodies leads to results exceedingly different from any phenomena which we can observe in ordinary conductors, let us pursue the subject somewhat further.\n\n842.] Returning to the case of the conducting channel in the form of a closed curve of area A, as in Art. 836, we have, for the moment of the electromagnetic force tending to increase the angle 0,\n\nsme , (12)\n\nsmflcosfl. (13)\n\nj\n\nThis force is positive or negative according as is less or greater than a right angle. Hence the effect of magnetic force on a per fectly conducting channel tends to turn it with its axis at right\n\n�� � 424 ELECTRIC THEORY OF MAGNETISM. [843.\n\nangles to the line of magnetic force, that is, so that the plane of the channel becomes parallel to the lines of force.\n\nAn effect of a similar kind may be observed by placing a penny or a copper ring between the poles of an electromagnet. At the instant that the magnet is excited the ring turns its plane towards the axial direction, but this force vanishes as soon as the currents are deadened by the resistance of the copper *.\n\n843.] We have hitherto considered only the case in which the molecular currents are entirely excited by the external magnetic force. Let us next examine the bearing of Weber s theory of the magneto-electric induction of molecular currents on Ampere s theory of ordinary magnetism. According to Ampere and Weber, the molecular currents in magnetic substances are not excited by the external magnetic force, but are already there, and the molecule itself is acted on and deflected by the electromagnetic action of the magnetic force on the conducting circuit in which the current flows. When Ampere devised this hypothesis, the induction of electric cur rents was not known, and he made no hypothesis to account for the existence, or to determine the strength, of the molecular currents.\n\nWe are now, how r ever, bound to apply to these currents the same laws that Weber applied to his currents in diamagnetic molecules. We have only to suppose that the primitive value of the current y, when no magnetic force acts, is not zero but y . The strength of the current when a magnetic force, X, acts on a molecular current of area A, whose axis is inclined Q to the line of magnetic force, is\n\n.A. A. ( -I A\\\n\n��and the moment of the couple tending to turn the molecule so as\n\nto increase is X 2 A 2\n\nsin2&lt;9. (15)\n\n��2L Hence, putting A\n\nAy Q = m, /- = *, (16)\n\nL y\n\nin the investigation in Art. 443, the equation of equilibrium becomes Xsin0-.X 2 sm0cos&lt;9 = J9sin(a-0). (17)\n\nThe resolved part of the magnetic moment of the current in the direction of X is\n\nXA 2\n\nyAcosO = y ^cos0 -- ^-cos 2 0, (18)\n\n= mcos8(l-3Xco80). (19)\n\n• See Faraday, Exp. Res., 2310, &c.\n\n�� � 845-] MODIFIED THEORY OF INDUCED MAGNETISM. 425\n\n844.] These conditions differ from those in Weber s theory of magnetic induction by the terms involving the coefficient B. If BX is small compared with unity, the results will approximate to those of Weber s theory of magnetism. If BX is large compared with unity, the results will approximate to those of Weber s theory of diamagnetism.\n\nNow the greater y , the primitive value of the molecular current,, the smaller will B become, and if L is also large, this will also diminish B. Now if the current flows in a ring channel, the value\n\nT&gt;\n\nof L depends on log , where R is the radius of the mean line of\n\nthe channel, and r that of its section. The smaller therefore the section of the channel compared with its area, the greater will be Z, the coefficient of self-induction, and the more nearly will the phe nomena agree with Weber s original theory. There will be this difference, however, that as X, the magnetizing force, increases, the temporary magnetic moment will not only reach a maximum, but will afterwards diminish as X increases.\n\nIf it should ever be experimentally proved that the temporary magnetization of any substance first increases, and then diminishes as the magnetizing force is continually increased, the evidence of the existence of these molecular currents would, I think, be raised almost to the rank of a demonstration.\n\n845.] If the molecular currents in diamagnetic substances are confined to definite channels, and if the molecules are capable of being deflected like those of magnetic substances, then, as the mag netizing force increases, the diamagnetic polarity will always increase, but, when the force is great, not quite so fast as the magnetizing force. The small absolute value of the diamagnetic coefficient shews, however, that the deflecting force on each molecule must be small compared with that exerted on a magnetic molecule, so that any result due to this deflexion is not likely to be perceptible.\n\nIf, on the other hand, the molecular currents in diamagnetic bodies are free to flow through the whole substance of the molecules, the diamagnetic polarity will be strictly proportional to the mag netizing force, and its amount will lead to a determination of the whole space occupied by the perfectly conducting masses, and, if we know the number of the molecules, to the determination of the size of each,\n\n�� �" ]

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[ "", null, "iovs\nFree\nARVO Annual Meeting Abstract  |   May 2007\nYoungs Modulus of Bruchs Membrane: Implications for AMD\nAuthor Affiliations & Notes\n• W. H. Chan\nDept Ophthalmology, St Thomas Hospital, London, United Kingdom\n• A. A. Hussain\nDept Ophthalmology, St Thomas Hospital, London, United Kingdom\n• J. Marshall\nDept Ophthalmology, St Thomas Hospital, London, United Kingdom\n• Footnotes\nCommercial Relationships W.H. Chan, None; A.A. Hussain, None; J. Marshall, None.\n• Footnotes\nSupport None.\nInvestigative Ophthalmology & Visual Science May 2007, Vol.48, 2187. doi:https://doi.org/\n• Views\n• Share\n• Tools\n×\n###### This feature is available to authenticated users only.\n• Get Citation\n\nW. H. Chan, A. A. Hussain, J. Marshall; Youngs Modulus of Bruchs Membrane: Implications for AMD. Invest. Ophthalmol. Vis. Sci. 2007;48(13):2187. doi: https://doi.org/.\n\n© ARVO (1962-2015); The Authors (2016-present)\n\n×\n• Supplements\nAbstract\n\nPurpose:: To determine Youngs’ modulus of elasticity of Bruchs membrane and assess its implications for developing AMD\n\nMethods:: Young’s modulus of elasticity was derived from the induced deformation on application of a hydrostatic pressure head (500-3000Pa) to a membrane clamped in an open-type Ussing chamber. The applied stress (f) to the exposed segment was calculated as f = RP / 2tm , R was calculated using scans from an OCT based tracking technique. The corresponding circumferential strain in the sample, [l-lo/lo, lo and l being initial and final arc-lengths] was due to two principal stresses acting at right angles, the first acting along the circumference and the other at right angles to the first, such that : (l-lo/lo) = f/E - σf/E (2), giving (l-lo/lo) = [RP(1-σ) / 2tmE] (3)[R = radius of curvature of sample, P = applied pressure, tm= the thickness of the membrane, E = Young’s modulus of elasticity, σ = Poisson’s ratio for the membrane] Thickness of Bruch’s (tm) was assumed to be constant under the pressures examined and its value obtained from glutaraldehyde fixed sections by transmission electron microscopy. 10-12 locations were averaged to obtain thickness. Since Bruch’s and the lens capsule consist primarily of a collagenous network, the experimentally evaluated Poisson’s ratio for the capsule (σ = 0.47) was also applied to Bruch’s membrane.Using equation 3 and the constants mentioned above, applied stress was plotted against the induced circumferential strain and Young’s modulus E obtained as the gradient of this linear relationship by regression analysis. Four donor preparations, age range 22-83 years were assessed.\n\nResults:: 4 samples from four donors aged 22, 31, 75 and 83 years were processed for transmission electron microscopy to determine the average thickness of Bruch’s membrane. The thickness values obtained for the preceding donors were 2.3, 2.57, 3.2 and 3.29µm respectively. Assuming a Poisson ratio σ for Bruch’s to be equivalent to 0.47, rearrangement of equation (3) allowed a plot of stress vs. strain, the gradient, obtained by linear regression, representing the Young’s modulus of elasticity. For the four donors aged 22, 31,75 and 83 years, the corresponding Young’s moduli were computed as 6.93, 3.65, 13.78 and 18.8 MPa respectively\n\nConclusions:: The age-related loss in the elasticity of Bruch’s is expected to influence the functional properties of the membrane. Elasticity maybe pivotal in maintaining patent pathways for nutritional transport and its decline with age may contribute to the pathogenesis of age-related macular degeneration.\n\nKeywords: age-related macular degeneration • retina • macula/fovea\n×\n\nThis PDF is available to Subscribers Only" ]

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[ "School things\nFIND\n\nLogin to be the first to rate this puzzle!\nAGENDA\nART\nBAG\nBELL\nBOOKS\nCANTEEN\nCLASSROOM\nCOMPUTER\nCORRIDOR\nENGLISH\nEXAM\nFOLDER\nFRENCH\nHISTORY\nHOMEWORK\nLANGUAGE\nLUNCH\nMATHS\nPEN\nPENCIL\nPLAYGROUND\nSCIENCE\nSECRETARY\nSPELLING\nSTUDENT\nSUBJECT\nTEACHER\nTEST\nUNIFORM\nWHITEBOARD\n F D E N W N I T C H L I G B O L D E N F H E Y U I P N K T I V R Q E J S O C F W T C U Q L T M G C V S U R W Y X G H W N E N N P D F N N B Q V R T O P H Z N U H C V E U N I E B R T F H P M F J K B H D N D D D L P C O R R I D O R R K R G S M E K M L U A L A N G U A G E E T O E I F I L E B N T A A Y R O T S I H J W S E B C P J T A G S V Y L N L K M C A E B Y T S G E J E H S E U G L X O A A L M T J N C E A N S U R N C Y R E O X E W O H E V N O D J B F O G D R A O B E T I H W Q Y Q A M J A F O L A Q E R U N I F O R M W L B E P G U M I T S E T T N O R V B Y V I C D O U A Q S Z W P L A L D E P D O B T W I O T T Z H D O W H D R S N J X K D G H Y H M X E R I K H E N D Y C C J E F N A S E C R M R D W R O G R H H K Y Z H Q T Q G R R W Q S E V H Q E V N M R M V F N U N Z F X Y M X B K T Q X U V M A U" ]

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[ "# Samacheer Kalvi 7th Maths Solutions Term 1 Chapter 4 Direct and Inverse Proportion Additional Questions\n\nStudents can Download Maths Chapter 4 Direct and Inverse Proportion Additional Questions and Answers, Notes Pdf, Samacheer Kalvi 7th Maths Book Solutions Guide Pdf helps you to revise the complete Tamilnadu State Board New Syllabus and score more marks in your examinations.\n\n## Tamilnadu Samacheer Kalvi 7th Maths Solutions Term 1 Chapter 4 Direct and Inverse Proportion Additional Questions\n\nExercise 4.1\n\nQuestion 1.\nThe amount of extension in an elastic spring varies directly as the weight hung on it. If a weight of 150 gm produces an extension of 2.9 cm, then what weight would produce an extension of 17.4 cm?\nSolution:\nTo produce 2.9 cm extension weight needed = 150 gm", null, "Question 2.\nReeta types 540 words during half on hour. How many words would she type in 12 minutes?\nSolution:\nIn $$\\frac{1}{2}$$ an hour number of words typed = 540\ni.e., In 30 min No. of words typed = 540", null, "= 18\nIn 12 minutes number of words typed = 18 × 12\n= 216\n216 words can be typed in 12 min\n\nQuestion 3.\nA call taxi charges ₹ 130 for 100 km. How much would one travel for ₹ 390?\nSolution:", null, "Exercise 4.2\n\nQuestion 1.\nIn the following table find out x and y vary directly or inversely?", null, "Solution:\nFrom the table itself we observe that as x increases y decreases.\n∴ x and y are inversely proportional\n∴ xy = 8 × 32 = 16 × 16 = 32 × 8 = 256 × 1 = 256\n\nQuestion 2.\nIf x and y vary inversely as each other and x = 10 when y = 6. Find y when x = 15.\nSolution:\nSince x and y vary inversely as each other\nxy = constant\n10 × 6 = 15 xy\n60 = 15y", null, "Question 3.\nIf x and y vary inversely and if y = 35 find x when constant of variation is 7.\nSolution:\nGiven x andy are inversely proportional\nxy = constant\nwhen y = 35 and constant = 7 ; x × 35 = 7", null, "Exercise 4.3\n\nQuestion 1.\nSumathi sweeps 600 m long road in 2$$\\frac{1}{2}$$ hrs. Ramani sweeps $$\\frac{2}{3}$$ rd of same road in 1$$\\frac{1}{2}$$ hrs. Who sweeps more speedily?\nSolution:", null, "Question 2.\nSuma weaves 25 baskets in 35 days. In how many days will she weave 110 baskets?\nSolution:", null, "" ]

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[ "", null, "# Geometry Regents - January 2013\n\nRelated Topics:\nMore Lessons for the Regents High School Exam\nMore Lessons for Geometry\n\nHigh School Math based on the topics required for the Regents Exam conducted by NYSED. The following are the worked solutions for the Geometry Regents High School Examination January 2013.\n\n### January 2013 Geometry Regents Exam\n\nGeometry - January 2013 Regents - Q #1 - 5\n\n1. If triangle MNP is congruent to triangle VWX and PM is the shortest side of triangle MNP, what is the shortest side of triangle VWX?\n2. In circle O shown in the diagram below, chords AB and CD are parallel. If mAB =  104 and mCD =  168, what is mBD ?\n3. As shown in the diagram below, CD is a median of ABC. Which statement is always true?\n4. In the diagram below, under which transformation is triangle A'B'C' the image of triangle ABC?\n3. Line segment AB is a diameter of circle O whose center has coordinates (6,8). What are the coordinates of point B if the coordinates of point A are (4,2)?\n\nGeometry - January 2013 Regents - Q #6 - 10\n\n6. Plane A and plane B are two distinct planes that are both perpendicular to line ?. Which statement about planes A and B is true?\n7. Triangle ABC is similar to triangle DEF. The lengths of the sides of triangle ABC are 5, 8, and 11. What is the length of the shortest side of triangle DEF if its perimeter is 60?\n8. In the diagram below of right triangle ABC, altitude CD is drawn to hypotenuse AB. If AD = 3 and DB = 12, what is the length of altitude CD?\n9. The diagram below shows the construction of an equilateral triangle. Which statement justifies this construction?\n10. What is the slope of the line perpendicular to the line represented by the equation 2x + 4y  = 12? Geometry - January 2013 Regents - Q #11 - 15\n\n11. Triangle ABC is shown in the diagram below. If DE joins the midpoints of ADC and AEB which statement is not true?\n12. The equations x2 + y2 = 25 and y = 5 are graphed on a set of axes. What is the solution of this system?\n13. Square ABCD has vertices A(-2,-3), B(4,-1), C(2,5), and D(-4,3). What is the length of a side of the square?\n14. The diagram below shows triangle ABD, with a ray ABC, BE ⊥ AD and ∠ EBD is congruent to ∠ CBD. If m ∠ ABE = 52, what is m ∠ D?\n15. As shown in the diagram below, FD and CB intersect at point A and ET is perpendicular to both FD and CB at A. Which statement is not true? Geometry - January 2013 Regents - Q #16 - 25\n\n16. Which set of numbers could not represent the lengths of the sides of a right triangle?\n17. How many points are 5 units from a line and also equidistant from two points on the line?\n18. The equation of a circle is (x - 2)2 + (y + 5)2  = 32. What are the coordinates of the center of this circle and the length of its radius?\n19. The equation of a line is y  = 2/3x + 5. What is an equation of the line that is perpendicular to the given line and that passes through the point (4,2)?\n20. Consider the relationship between the two statements.\n21. In the diagram of trapezoid ABCD below, AB || DC, AD =  BC, m ∠ A = 4x + 20, and m ∠ C = 3x - 15.\n22. In circle R shown below, diameter DE is perpendicular to chord ST at point L. Which statement is not always true?\n23. Which equation represents circle A shown in the diagram below?\n24. Which equation represents a line that is parallel to the line whose equation is 3x - 2y =  7?\n25. In the diagram below of circle O, PAC and PBD are secants. If mCD = 70 and mAB  = 20, what is the degree measure of ?P? More Questions, Worked Solutions and Revision Resources for the Math Regents Examination\n\nTry the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.", null, "", null, "" ]

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[ "# Find the number of diagonals of a regular polygon in which each of the exterior angles 24°.\n\n1. 45\n2. 36\n3. 90\n4. 60\n\nOption 3 : 90\nFree\nCell\n6.9 Lakh Users\n10 Questions 10 Marks 7 Mins\n\n## Detailed Solution\n\nGIVEN :\n\nEach of the exterior angles 24°\n\nCONCEPT :\n\nSum of exterior angles of a regular polygon = 360°\n\nFORMULA USED :\nEach of the exterior angles of a regular polygon = 360/n\n\nAnd\n\nNumber of diagonals = n(n – 3)/2\n\nWhere n = number of sides\n\nCALCULATION :\n\nNumber of sides = 360/24 = 15\n\nSo,\n\nNumber of diagonals = (15 × 12)/2 = 90" ]

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[ "#", null, "", null, "SCIENTIA SINICA Informationis, Volume 48 , Issue 7 : 947-962(2018) https://doi.org/10.1360/N112017-00282\n\n## Virtual equivalent system theory for adaptive control and simulation verification", null, "More info\n• ReceivedDec 24, 2017\n• AcceptedFeb 14, 2018\n• PublishedJul 12, 2018\nShare\nRating\n\n### Funded by", null, "### Supplement\n\nAppendix\n\nproof 本引理是引理3的特殊情形, 在引理3中令$\\omega(k)=0$, 即得本引理结论.\n\nproof 首先, 我们知道 \\begin{equation}\\sum _{k=1}^{k=N}\\|\\tilde{\\phi}(k)\\|\\le \\sum _{k=1}^{k=N}\\|\\tilde{\\phi}_1(k)\\| + \\sum _{k=1}^{k=N}\\|\\tilde{\\phi}_2(k)\\|. \\tag{44}\\end{equation} 下面采用反证法进行证明, 假设 $\\|\\tilde{\\phi}(k)\\|$ 无界. 那么必有无穷子列 $\\|\\tilde{\\phi}(p_{k})\\|\\to~\\infty$ 满足 \\begin{equation}\\sum _{k=1}^{k=N}\\|\\tilde{\\phi}(p_k)\\|\\le \\sum _{k=1}^{k=N}\\|\\tilde{\\phi}_1(p_k)\\| + \\sum _{k=1}^{k=N}\\|\\tilde{\\phi}_2(p_k)\\|. \\tag{45}\\end{equation} 接下来分别考察(A2)式右面两项的性质. 首先考察第一项, 根据 Stolz 定理 以及 $\\|\\tilde{\\phi}_1(p_k)\\|<\\infty$, 知道 \\begin{equation}\\frac{\\sum _{k=1}^{k=N}\\|\\tilde{\\phi}_1(p_k)\\|}{\\sum _{k=1}^{k=N}\\|\\tilde{\\phi}(p_k)\\|}\\to\\frac{\\|\\tilde{\\phi}_1(p_k)\\|}{\\|\\tilde{\\phi}(p_k)\\|}\\to 0. \\tag{46}\\end{equation} 接下来考察第二项, 注意到 $~\\|\\tilde{\\phi}(k)\\|=0,~k\\le~0$, 那么, \\begin{equation}\\sum _{k=1}^{k=N}\\|\\tilde{\\phi}(k-i)\\| \\le \\sum _{k=1}^{k=N}\\|\\tilde{\\phi}(k)\\|, i=1,\\ldots,s. \\tag{47}\\end{equation} 因此, \\begin{equation}\\begin{split} \\sum _{k=1}^{k=N}(\\alpha+\\|\\tilde{\\phi}(k)\\|+\\cdots+\\|\\tilde{\\phi}(k-s)\\|) \\le(s+1)\\sum _{k=1}^{k=N}(\\alpha+\\|\\tilde{\\phi}(k)\\|). \\end{split} \\tag{48}\\end{equation} 上式结合本引理的给定条件导致 \\begin{equation}\\sum _{k=1}^{k=N}\\|\\tilde{\\phi}_2(k)\\|=o\\left(\\sum _{k=1}^{k=N}(\\alpha+\\|\\tilde{\\phi}(k)\\|)\\right). \\tag{49}\\end{equation} 进一步, 考虑到收敛序列及其子序列的极限相同, 我们有 \\begin{equation}\\sum _{k=1}^{k=N}\\|\\tilde{\\phi}_2(p_k)\\|=o\\left(\\sum _{k=1}^{k=N}(\\alpha+\\|\\tilde{\\phi}(p_k)\\|)\\right). \\tag{50}\\end{equation} 考虑到 (A2) 和(A3)式, 并利用夹逼原理有 \\begin{equation}\\frac{\\sum _{k=1}^{k=N}\\|\\tilde{\\phi}(p_k)\\|}{\\sum _{k=1}^{k=N}(\\alpha+\\|\\tilde{\\phi}(p_k)\\|)}\\to 0. \\tag{51}\\end{equation} 上式与如下事实相矛盾(根据 Stolz 定理): \\begin{equation}\\frac{\\sum _{k=1}^{k=N}(\\|\\tilde{\\phi}(p_k)\\|)}{\\sum _{k=1}^{k=N}(\\alpha+\\|\\tilde{\\phi}(p_k)\\|)}\\to 1. \\tag{52}\\end{equation} 因此原假设不成立. 从而证得结论, 即 $\\|\\tilde{\\phi}(k)\\|<\\infty$.\n\nproof 用数学归纳法给出证明. 首先, 我们知道, 对于 $k~\\le~0~$ 有 \\begin{equation}y(k)=y_1(k)+y_2(k)+y_3(k), u(k)=u_1(k)+u_2(k)+u_3(k). \\tag{53}\\end{equation} 接下来, 假设(A10)式对于$~k,k-1,\\ldots,1.~$ 成立. 分别考虑图11$\\sim$13, 有 \\begin{align}& y(k+1)=\\phi^{\\rm T}(k-d+1)\\hat\\theta(t_k)+\\omega(k+1)+e_i(k+1), \\tag{54} \\\\ & y_1(k+1)=\\phi^{\\rm T}_1(k-d+1)\\hat\\theta(t_k)+\\omega(k+1), \\tag{55} \\\\ & y_2(k+1)=\\phi^{\\rm T}_2(k-d+1)\\hat\\theta(t_k)+e_i(k+1), \\tag{56} \\\\ & y_3(k+1)=\\phi^{\\rm T}_3(k-d+1)\\hat\\theta(t_k). \\tag{57} \\end{align} 其中 \\begin{eqnarray}\\phi^{\\rm T}_1(k-d+1)&=&[y_1(k),\\ldots,y_1(k-n+1),u(k-d+1),\\ldots,u_1(k-d-m+1)], \\tag{58} \\\\ \\phi^{\\rm T}_2(k-d+1)&=&[y_2(k),\\ldots,y_2(k-n+1),u_2(k-d+1),\\ldots,u_2(k-d-m+1)], \\tag{59} \\\\ \\phi^{\\rm T}_3(k-d+1)&=&[y_3(k),\\ldots,y_3(k-n+1),u_3(k-d+1),\\ldots,u_3(k-d-m+1)]. \\tag{60} \\end{eqnarray} 按照前面的假设, 即, (A10)式对于$~k,k-1,\\ldots,1.~$ 成立, 显然有 \\begin{equation}\\phi^{\\rm T}_1(k-d+1)+\\phi^{\\rm T}_2(k-d+1)+\\phi^{\\rm T}_3(k-d+1)=\\phi^{\\rm T}(k-d+1). \\tag{61}\\end{equation} 因此, 可以得到 \\begin{equation}\\begin{split} y_1(k+1)+y_2(k+1)+y_3(k+1)=\\phi^{\\rm T}(k-d+1)\\hat\\theta(t_k)+\\omega(k+1)+e_i(k+1)=y(k+1). \\end{split} \\tag{62}\\end{equation} 下面考察 $u_1(k+1)$, $u_2(k+1)$ 和 $u_3(k+1)$. 在图10中, 有 \\begin{equation}u(k+1)=\\phi^{\\rm T}_{c}(k+1)\\theta_c(t_{k+1})+\\Delta u'(k+1). \\tag{63}\\end{equation} 类似地, 在图11$\\sim$13中, 有 \\begin{eqnarray}u_1(k+1)&=&\\phi^{\\rm T}_{c1}(k+1)\\theta_c(t_{k+1}), \\tag{64} \\\\ u_2(k+1)&=&\\phi^{\\rm T}_{c2}(k+1)\\theta_c(t_{k+1}), \\tag{65} \\\\ u_3(k+1)&=&\\phi^{\\rm T}_{c3}(k+1)\\theta_c(t_{k+1})+\\Delta u'(k+1), \\tag{66} \\end{eqnarray} 其中 \\begin{eqnarray}\\phi^{\\rm T}_c(k+1)&=&[y(k+1),\\ldots,y(k+1-s_1),u(k),\\ldots,u(k+1-s_2),y_r(k+1),\\ldots,y_r(k+1-s_3)], \\tag{67} \\\\ \\phi^{\\rm T}_{c1}(k+1)&=&[y_1(k+1),\\ldots,y_1(k+1-s_1),u_1(k),\\ldots,u_1(k+1-s_2),y_r(k+1),\\ldots,y_r(k+1-s_3)], \\tag{68} \\\\ \\phi^{\\rm T}_{c2}(k+1)&=&[y_2(k+1),\\ldots,y_2(k+1-s_1),u_2(k),\\ldots,u_2(k+1-s_2),0,\\ldots,0], \\tag{69} \\\\ \\phi^{\\rm T}_{c3}(k+1)&=&[y_3(k+1),\\ldots,y_3(k+1-s_1),u_3(k),\\ldots,u_3(k+1-s_2),0,\\ldots,0], \\tag{70} \\end{eqnarray} 其中, $s_1\\geq~1,~s_2\\geq~1,~s_3\\geq~1$为正整数, 由不同的控制策略决定. 进一步基于 (A10)及(A19)式, 显然有 \\begin{equation}\\phi^{\\rm T}_{c1}(k+1)+\\phi^{\\rm T}_{c2}(k+1)+\\phi^{\\rm T}_{c3}(k+1)=\\phi^{\\rm T}_c(k+1). \\tag{71}\\end{equation} 因此, \\begin{equation}\\begin{split} u_1(k+1)+u_2(k+1)+u_3(k+1) =\\phi^{\\rm T}_c(k+1)\\theta_c(t_{k+1})+\\Delta u'(k+1) =u(k+1). \\end{split} \\tag{72}\\end{equation} 所以 (A10)式 对所有 $k$皆成立.\n\nproof 利用三角不等式以及显然的事实 $2ab\\le~a^2+b^2$, 有 \\begin{equation}\\begin{split} \\frac{1}{n}\\sum_{k=1}^{n}\\|\\widetilde{\\phi}(k)\\|^2 =\\frac{1}{n}\\sum_{k=1}^{n}\\|\\widetilde{\\phi}_1(k)+\\widetilde{\\phi}_2(k)\\|^2 \\le\\frac{2}{n}\\sum_{k=1}^{n}\\|\\widetilde{\\phi}_1(k)\\|^2+\\frac{2}{n}\\sum_{k=1}^{n}\\|\\widetilde{\\phi}_2(k)\\|^2. \\end{split} \\tag{73}\\end{equation} 下面用反证法得出结论. 假设 $\\frac{1}{n}\\sum^{n}_{k=1}\\|\\widetilde{\\phi}(k)\\|^2$ 无界, 则一定存在无穷子列 $\\frac{1}{n}\\sum^{n}_{k=1}\\|\\widetilde{\\phi}(p_k)\\|^2\\to\\infty$, 满足 \\begin{equation}\\begin{split} \\frac{1}{n}\\sum_{k=1}^{n}\\|\\widetilde{\\phi}(p_k)\\|^2 =\\frac{1}{n}\\sum_{k=1}^{n}\\|\\widetilde{\\phi}_1(p_k)+\\widetilde{\\phi}_2(p_k)\\|^2 \\le\\frac{2}{n}\\sum_{k=1}^{n}\\|\\widetilde{\\phi}_1(p_k)\\|^2+\\frac{2}{n}\\sum_{k=1}^{n}\\|\\widetilde{\\phi}_2(p_k)\\|^2. \\end{split} \\tag{74}\\end{equation} 进一步考虑到收敛序列及其子序列的极限相同, 于是得到 \\begin{equation}\\frac{1}{n}\\sum_{k=1}^{n}\\|\\widetilde{\\phi}_2(p_k)\\|^2= o\\left(\\frac{1}{n}\\sum^{n}_{k=1}\\|\\widetilde{\\phi}(p_k)\\|^2\\right). \\tag{75}\\end{equation} 上式结合(A31)式 以及事实 $\\frac{1}{n}\\sum^{n}_{k=1}\\|\\widetilde{\\phi}_1(p_k)\\|^2<\\infty$, 利用夹逼定理, 得出明显的错误结论 $\\frac{\\sum^{n}_{k=1}\\|\\widetilde{\\phi}(p_k)\\|^2}{\\sum^{n}_{k=1}\\|\\widetilde{\\phi}(p_k)\\|^2}\\to~0$, 因此, 之前的假设不成立, 从而得到 $\\frac{1}{n}\\sum^{n}_{k=1}\\|\\widetilde{\\phi}(k)\\|^2<\\infty.$\n\nproof 显然 \\begin{equation}\\begin{split} \\frac{1}{n}\\sum^{n}_{k=1}[y_1(k)-y_r(k)+y_2(k)]^2 &=\\frac{1}{n}\\sum^{n}_{k=1}[y_1(k)-y_r(k)]^2+\\frac{1}{n}\\sum^{n}_{k=1}[y_2(k)]^2 +\\frac{2}{n}\\sum^{n}_{k=1}[y_1(k)-y_r(k)]y_2(k) \\\\ &\\to \\frac{1}{n}\\sum^{n}_{k=1}[y_1(k)-y_r(k)]^2+\\frac{2}{n}\\sum^{n}_{k=1}[y_1(k)-y_r(k)]y_2(k). \\end{split} \\tag{76}\\end{equation} 根据Cauchy不等式, 有 \\begin{equation}\\begin{split} 0\\le\\left\\{\\frac{1}{n}\\sum^{n}_{k=1}[y_1(k)-y_r(k)]y_2(k)\\right\\}^2\\le\\left\\{\\frac{1}{n}\\sum^{n}_{k=1}[y_1(k)-y_r(k)]^2\\right\\}.\\left\\{\\frac{1}{n}\\sum^{n}_{k=1}[y_2(k)]^2\\right\\} \\to 0.\\end{split} \\tag{77}\\end{equation} 于是, 运用夹逼定理得到 \\begin{equation}\\left\\{\\frac{1}{n}\\sum^{n}_{k=1}[y_1(k)-y_r(k)]y_2(k)\\right \\}^2\\to 0, \\frac{1}{n}\\sum^{n}_{k=1}[y_1(k)-y_r(k)]y_2(k)\\to 0. \\tag{78}\\end{equation}\n\n### References\n\n Kalman R E. 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Google Scholar\n\n•", null, "Figure 1\n\nSelf-tuning control system\n\n•", null, "Figure 2\n\nDeterministic VES I\n\n•", null, "Figure 3\n\nDeterministic VES II\n\n•", null, "Figure 4\n\nSubsystem 1 of deterministic VES II\n\n•", null, "Figure 5\n\nSubsystem 2 of deterministic VES II\n\n•", null, "Figure 6\n\nSubsystem 3 of deterministic VES II\n\n•", null, "Figure 7\n\nVES for one-step-ahead STC (self-tuning control)\n\n•", null, "Figure 8\n\nStochastic self-tuning control system\n\n•", null, "Figure 9\n\nStochastic VES I\n\n•", null, "Figure 10\n\nStochastic VES II\n\n•", null, "Figure 11\n\nSubsystem 1 of stochastic VES II\n\n•", null, "Figure 12\n\nSubsystem 2 of stochastic VES II\n\n•", null, "Figure 13\n\nSubsystem 3 of stochastic VES II\n\n•", null, "Figure 14\n\nVES for minimum variance self-tuning control\n\n•", null, "Figure 15\n\nEquivalence of output signals of VES before and after decomposition\n\n•", null, "Figure 16\n\nEquivalence of control signals of VES before and after decomposition" ]

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[ "cond-mat.dis-nn\n\n# Title:Real-space renormalization-group methods for hierarchical spin glasses\n\nAbstract: We focus on two real-space renormalization-group (RG) methods recently proposed for a hierarchical model of a spin glass: A sample-by-sample method, in which the RG transformation is performed separately on each disorder sample, and an ensemble RG (ERG) method [M. C. Angelini, G. Parisi, and F. Ricci-Tersenghi. Ensemble renormalization group for disordered systems. $\\textit{Phys. Rev. B}$, 87(13):134201, 2013] in which the transformation is based on an average over samples. Above the upper critical dimension, the sample-by-sample method yields the correct mean-field value for the critical exponent $\\nu$ related to the divergence of the correlation length, while it does not predict the correct qualitative behavior of $\\nu$ below the upper critical dimension. On the other hand, the ERG procedure has been claimed to predict the correct behavior of $\\nu$ both above and below the upper critical dimension. Here, we straighten out the reasons for the discrepancy between the two methods above, by demonstrating that the ERG method predicts a marginally stable critical fixed point, thus implying a prediction for the critical exponent $\\nu$ given by $2^{1/\\nu} = 1$. This prediction disagrees, on a qualitative and quantitative level, both with the mean-field value of $\\nu$ above the critical dimension, and with numerical estimates of $\\nu$ below the upper critical dimension. Therefore, our results show that finding a real-space RG method for spin glasses which yields the correct prediction for universal quantities below the upper critical dimension is still an open problem, for which our analysis may provide some general guidance for future studies.\n Subjects: Disordered Systems and Neural Networks (cond-mat.dis-nn); Statistical Mechanics (cond-mat.stat-mech) Journal reference: Journal of Physics A: Mathematical and Theoretical 52(44), 445002 (2019) DOI: 10.1088/1751-8121/ab2f46 Cite as: arXiv:1910.04521 [cond-mat.dis-nn] (or arXiv:1910.04521v1 [cond-mat.dis-nn] for this version)\n\n## Submission history\n\nFrom: Michele Castellana [view email]\n[v1] Thu, 10 Oct 2019 12:45:59 UTC (275 KB)" ]

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[ "Now showing items 1-20 of 25\n\n• Optimal control of the Lotka–Volterra system: turnpike property and numerical simulations \n\n(Journal of Biological Dynamics, 2016-09-01)\nThe Lotka-Volterra model is a differential system of two coupled equations representing the interaction of two species: a prey one and a predator one. We formulate an optimal control problem adding the effect of hunting ...\n• On the controllability of Partial Differential Equations involving non-local terms and singular potentials \n\n(2016-12-12)\nIn this thesis, we investigate controllability and observability properties of Partial Differential Equations describing various phenomena appearing in several fields of the applied sciences such as elasticity theory, ...\n• Dimension reduction for the micromagnetic energy functional on curved thin films \n\n(2016-12-14)\nMicromagnetic con gurations of the vortex and onion type have beenwidely studied in the context of planar structures. 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We show that for generic elastic constants the critical points consistent ...\n• Partial regularity and smooth topology-preserving approximations of rough domains \n\n(Calculus of Variations and Partial Differential Equations, 2017-01-01)\nFor a bounded domain $\\Omega\\subset\\mathbb{R}^m, m\\geq 2,$ of class $C^0$, the properties are studied of fields of `good directions', that is the directions with respect to which $\\partial\\Omega$ can be locally represented ...\n• Highly rotating fluids with vertical stratification for periodic data and vanishing vertical viscosity \n\n(Revista Matemática Iberoamericana, 2017-07)\nWe prove that the three-dimensional, periodic primitive equations with zero vertical diffusivity are globally well posed if the Rossby and Froude number are sufficiently small. The initial data is considered to be of zero ...\n• Derivation of limit equation for a singular perturbation of a 3D periodic Boussinesq system \n\n(Discrete and Continuous Dynamical Systems - Series A, 2017-07-15)\nWe consider a system describing the dynamics of an hydrodynamical, density-dependent flow under the effects of gravitational forces. We prove that if the Froude number is sufficiently small such system is globally well ...\n• Dispersive effects of weakly compressible and fast rotating inviscid fluids \n\n(Discrete and Continuous Dynamical Systems - Series A, 2017-08)\nWe consider a system describing the motion of an isentropic, inviscid, weakly compressible, fast rotating fluid in the whole space $\\mathbb{R}^3$, with initial data belonging to $H^s \\left( \\mathbb{R}^3 \\right), s>5/2$. ...\n• Global well-posedness and twist-wave solutions for the inertial Qian-Sheng model of liquid crystals \n\n(Journal of Differential Equations, 2017-10-02)\nWe consider the inertial Qian-Sheng model of liquid crystals which couples a hyperbolic-type equation involving a second-order material derivative with a forced incompressible Navier-Stokes system. We study the energy law ...\n• Sphere-valued harmonic maps with surface energy and the K13 problem \n\n(Advances in the Calculus of Variations, 2017-11)\nWe consider an energy functional motivated by the celebrated K13 problem in the Oseen-Frank theory of nematic liquid crystals. It is defined for sphere-valued functions and appears as the usual Dirichlet energy with an ...\n• On a hyperbolic system arising in liquid crystal modelling \n\n(Journal of Hyperbolic Differential Equations, 2017-11)\nWe consider a model of liquid crystals, based on a nonlinear hyperbolic system of differential equations, that represents an inviscid version of the model proposed by Qian and Sheng. A new concept of dissipative solution ...\n• Zero limit of entropic relaxation time for the Shliomis model of ferrofluids \n\n(2018-02-11)\nWe construct solutions for the Shilomis model of ferrofluids in a critical space, uniformly in the entropic relaxation time $\\tau \\in (0, \\tau_0)$. This allows us to study the convergence when $\\tau\\to 0$ for such solutions.\n• Shear flow dynamics in the Beris-Edwards model of nematic liquid crystals \n\n(Proceedings of the Royal Society A-Mathematical, Physical and Engineering Sciences, 2018-02-14)\nWe consider the Beris-Edwards model describing nematic liquid crystal dynamics and restrict to a shear flow and spatially homogeneous situation. We analyze the dynamics focusing on the effect of the flow. We show that in ...\n• Defects in Nematic Shells: a Gamma-convergence discrete-to-continuum approach \n\n(Archive for Rational Mechanics and Analysis, 2018-07)\nIn this paper we rigorously investigate the emergence of defects on Nematic Shells with a genus different from one. This phenomenon is related to a non-trivial interplay between the topology of the shell and the alignment ...\n• Dynamics and flow effects in the Beris-Edwards system modeling nematic liquid crystals \n\n(Archive for Rational Mechanics and Analysis, 2018-08-10)\nWe consider the Beris-Edwards system modelling incompressible liquid crystal flows of nematic type. This couples a Navier-Stokes system for the fluid velocity with a parabolic reaction-convection-diffusion equation for the ...\n• On the global well-posedness of a class of 2D solutions for the Rosensweig system of ferrofluids \n\n(Journal of Differential Equations, 2018-09)\nWe study a class of 2D solutions of a Bloch-Torrey regularization of the Rosensweig system in the whole space, which arise when the initial data and the external magnetic field are 2D. We prove that such solutions are ...\n• Uniqueness of degree-one Ginzburg–Landau vortex in the unit ball in dimensions N ≥ 7 \n\n(Comptes Rendus Mathematique, 2018-09-01)\nFor ε>0, we consider the Ginzburg-Landau functional for RN-valued maps defined in the unit ball BN⊂RN with the vortex boundary data x on ∂BN. In dimensions N≥7, we prove that for every ε>0, there exists a unique global ...\n• Some remark on the existence of infinitely many nonphysical solutions to the incompressible Navier-Stokes equations \n\n(Journal of Mathematical Analysis and Applications, 2018-10)\nWe prove that there exist infinitely many distributional solutions with infinite kinetic energy to both the incompressible Navier-Stokes equations in $\\mathbb{R}^2$ and Burgers equation in $\\mathbb{R}$ with vanishing ...\n• A Global well-posedness result for the Rosensweig system of ferrofluids \n\n(Rev. Mat. Iberoam., 2019)\nIn this Paper we study a Bloch-Torrey regularization of the Rosensweig system for ferrofluids. The scope of this paper is twofold. First of all, we investigate the existence and uniqueness of Leray-Hopf solutions of this ...\n• On the influence of gravity on density-dependent incompressible periodic fluids \n\n(J. Differential Equations, 2019)\nThe present work is devoted to the analysis of density-dependent, incompressible fluids in a 3D torus, when the Froude number $\\varepsilon$ goes to zero. We consider the very general case where the initial data do not have ..." ]

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[ "It has never been easy to invest in a set of assets, the abnormally of financial market does not allow simple models to predict future asset values with higher accuracy. Machine learning, which consist of making computers perform tasks that normally requiring human intelligence is currently the dominant trend in scientific research. This article aims to build a model using Recurrent Neural Networks (RNN) and especially Long-Short Term Memory model (LSTM) to predict future stock market values. We evaluate Agilon Health prediction models with Modular Neural Network (Social Media Sentiment Analysis) and Independent T-Test1,2,3,4 and conclude that the AGL stock is predictable in the short/long term. According to price forecasts for (n+8 weeks) period: The dominant strategy among neural network is to Hold AGL stock.\n\nKeywords: AGL, Agilon Health, stock forecast, machine learning based prediction, risk rating, buy-sell behaviour, stock analysis, target price analysis, options and futures.\n\n## Key Points\n\n1. Stock Rating\n2. How do you pick a stock?\n3. Market Outlook", null, "## AGL Target Price Prediction Modeling Methodology\n\nRecently, there has been a surge of interest in the use of machine learning to help aid in the accurate predictions of financial markets. Despite the exciting advances in this cross-section of finance and AI, many of the current approaches are limited to using technical analysis to capture historical trends of each stock price and thus limited to certain experimental setups to obtain good prediction results. On the other hand, professional investors additionally use their rich knowledge of inter-market and inter-company relations to map the connectivity of companies and events, and use this map to make better market predictions. For instance, they would predict the movement of a certain company's stock price based not only on its former stock price trends but also on the performance of its suppliers or customers, the overall industry, macroeconomic factors and trade policies. This paper investigates the effectiveness of work at the intersection of market predictions and graph neural networks, which hold the potential to mimic the ways in which investors make decisions by incorporating company knowledge graphs directly into the predictive model. We consider Agilon Health Stock Decision Process with Independent T-Test where A is the set of discrete actions of AGL stock holders, F is the set of discrete states, P : S × F × S → R is the transition probability distribution, R : S × F → R is the reaction function, and γ ∈ [0, 1] is a move factor for expectation.1,2,3,4\n\nF(Independent T-Test)5,6,7= $\\begin{array}{cccc}{p}_{a1}& {p}_{a2}& \\dots & {p}_{1n}\\\\ & ⋮\\\\ {p}_{j1}& {p}_{j2}& \\dots & {p}_{jn}\\\\ & ⋮\\\\ {p}_{k1}& {p}_{k2}& \\dots & {p}_{kn}\\\\ & ⋮\\\\ {p}_{n1}& {p}_{n2}& \\dots & {p}_{nn}\\end{array}$ X R(Modular Neural Network (Social Media Sentiment Analysis)) X S(n):→ (n+8 weeks) $R=\\left(\\begin{array}{ccc}1& 0& 0\\\\ 0& 1& 0\\\\ 0& 0& 1\\end{array}\\right)$\n\nn:Time series to forecast\n\np:Price signals of AGL stock\n\nj:Nash equilibria\n\nk:Dominated move\n\na:Best response for target price\n\nFor further technical information as per how our model work we invite you to visit the article below:\n\nHow do AC Investment Research machine learning (predictive) algorithms actually work?\n\n## AGL Stock Forecast (Buy or Sell) for (n+8 weeks)\n\nSample Set: Neural Network\nStock/Index: AGL Agilon Health\nTime series to forecast n: 20 Sep 2022 for (n+8 weeks)\n\nAccording to price forecasts for (n+8 weeks) period: The dominant strategy among neural network is to Hold AGL stock.\n\nX axis: *Likelihood% (The higher the percentage value, the more likely the event will occur.)\n\nY axis: *Potential Impact% (The higher the percentage value, the more likely the price will deviate.)\n\nZ axis (Yellow to Green): *Technical Analysis%\n\n## Conclusions\n\nAgilon Health assigned short-term B1 & long-term Ba3 forecasted stock rating. We evaluate the prediction models Modular Neural Network (Social Media Sentiment Analysis) with Independent T-Test1,2,3,4 and conclude that the AGL stock is predictable in the short/long term. According to price forecasts for (n+8 weeks) period: The dominant strategy among neural network is to Hold AGL stock.\n\n### Financial State Forecast for AGL Stock Options & Futures\n\nRating Short-Term Long-Term Senior\nOutlook*B1Ba3\nOperational Risk 7787\nMarket Risk9090\nTechnical Analysis4141\nFundamental Analysis4770\nRisk Unsystematic5841\n\n### Prediction Confidence Score\n\nTrust metric by Neural Network: 78 out of 100 with 656 signals.\n\n## References\n\n1. Chipman HA, George EI, McCulloch RE. 2010. Bart: Bayesian additive regression trees. Ann. Appl. Stat. 4:266–98\n2. Mikolov T, Chen K, Corrado GS, Dean J. 2013a. Efficient estimation of word representations in vector space. arXiv:1301.3781 [cs.CL]\n3. Efron B, Hastie T. 2016. Computer Age Statistical Inference, Vol. 5. Cambridge, UK: Cambridge Univ. Press\n4. Bai J. 2003. Inferential theory for factor models of large dimensions. Econometrica 71:135–71\n5. S. Devlin, L. Yliniemi, D. Kudenko, and K. Tumer. Potential-based difference rewards for multiagent reinforcement learning. In Proceedings of the Thirteenth International Joint Conference on Autonomous Agents and Multiagent Systems, May 2014\n6. Chernozhukov V, Newey W, Robins J. 2018c. Double/de-biased machine learning using regularized Riesz representers. arXiv:1802.08667 [stat.ML]\n7. R. Sutton and A. Barto. Introduction to reinforcement learning. MIT Press, 1998\nFrequently Asked QuestionsQ: What is the prediction methodology for AGL stock?\nA: AGL stock prediction methodology: We evaluate the prediction models Modular Neural Network (Social Media Sentiment Analysis) and Independent T-Test\nQ: Is AGL stock a buy or sell?\nA: The dominant strategy among neural network is to Hold AGL Stock.\nQ: Is Agilon Health stock a good investment?\nA: The consensus rating for Agilon Health is Hold and assigned short-term B1 & long-term Ba3 forecasted stock rating.\nQ: What is the consensus rating of AGL stock?\nA: The consensus rating for AGL is Hold.\nQ: What is the prediction period for AGL stock?\nA: The prediction period for AGL is (n+8 weeks)\n\n## People also ask\n\nWhat are the top stocks to invest in right now?\nOur Mission\n\nAs AC Investment Research, our goal is to do fundamental research, bring forward a totally new, scientific technology and create frameworks for objective forecasting using machine learning and fundamentals of Game Theory.\n\n301 Massachusetts Avenue Cambridge, MA 02139 667-253-1000 [email protected]\n\nFollow Us | Send Feedback" ]

[ null, "https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjVBFnQHliywPREIMO7nqOe9-RJCP9U55ySYGD7UAXxM1PqbEp0UKZZms_VEjTQOnDK7DxIDToWmc9E-mAxEJttXFtc8-_sRcvUMT7qCSG_EdO_SaR3WG4X0c9voaOFS_hjqxWZpW2wpIq4iqdcAqKHi2v62kktwj_SSattR2gYDif5yVZu0-f8ik421g/s16000/20220829_122223_0000.png", null ]

[ "# What is 320 Kilometers in Millimeters?\n\n## Convert 320 Kilometers to Millimeters\n\nTo calculate 320 Kilometers to the corresponding value in Millimeters, multiply the quantity in Kilometers by 1000000 (conversion factor). In this case we should multiply 320 Kilometers by 1000000 to get the equivalent result in Millimeters:\n\n320 Kilometers x 1000000 = 320000000 Millimeters\n\n320 Kilometers is equivalent to 320000000 Millimeters.\n\n## How to convert from Kilometers to Millimeters\n\nThe conversion factor from Kilometers to Millimeters is 1000000. To find out how many Kilometers in Millimeters, multiply by the conversion factor or use the Length converter above. Three hundred twenty Kilometers is equivalent to three hundred twenty million Millimeters.\n\n## Definition of Kilometer\n\nThe kilometer (symbol: km) is a unit of length in the metric system, equal to 1000m (also written as 1E+3m). It is commonly used officially for expressing distances between geographical places on land in most of the world.\n\n## Definition of Millimeter\n\nThe millimeter (symbol: mm) is a unit of length in the metric system, equal to 1/1000 meter (or 1E-3 meter), which is also an engineering standard unit. 1 inch=25.4 mm.\n\n## Using the Kilometers to Millimeters converter you can get answers to questions like the following:\n\n• How many Millimeters are in 320 Kilometers?\n• 320 Kilometers is equal to how many Millimeters?\n• How to convert 320 Kilometers to Millimeters?\n• How many is 320 Kilometers in Millimeters?\n• What is 320 Kilometers in Millimeters?\n• How much is 320 Kilometers in Millimeters?\n• How many mm are in 320 km?\n• 320 km is equal to how many mm?\n• How to convert 320 km to mm?\n• How many is 320 km in mm?\n• What is 320 km in mm?\n• How much is 320 km in mm?" ]

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[ "show · ec.q all knowls · up · search:\n\nAn elliptic curve $E$ over $\\mathbb{Q}$ has a Weierstrass equation of the form $$E : y^2 = x^3 + ax + b$$ with $a, b \\in \\mathbb{Z}$ such that its discriminant $$\\Delta := −16(4a^3 + 27b^2 ) \\not = 0.$$ Note that such an equation is not unique and $E$ has a unique minimal Weierstrass equation.\n\nAuthors:\nKnowl status:\n• Review status: reviewed\n• Last edited by Michael Bennett on 2019-04-10 17:59:13\nReferred to by:\nHistory: Differences" ]

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[ "# Selected algorithmic IPs generated by HercuLeS\n\na2mm\nTwo matrix-matrix multiplications. Part of the PolyBench benchmark suite.\na3mm\nThree matrix-matrix multiplications. Part of the PolyBench benchmark suite.\nascii2ebcdic\nASCII => EBCDIC conversion function. Original source: http://cprogramminglanguage.net/ascii-ebcdic-conversion-functions.aspx\natsort\nC implementation for the linear extension generation algorithm as defined by Valon-Rotem. Based on Donald E. Knuth, \"The Art of Computer Programming, volume 4, fascicle 2B: Algorithm V - All topological sorts\".\nbitrev\nC implementation for a bit-reversal operation on unsigned chars.\nbitunzip\nC implementation of the bit-wise zip algorithm from \"Algorithms for programmers\".\nbitzip\nC implementation of the bit-wise zip algorithm from \"Algorithms for programmers\".\nc2vwalsh\n1D Walsh transform. Original source: http://www.c-to-verilog.com\nc2vwavelet\n1D wavelet transform. Original source: http://www.c-to-verilog.com\nc2vyuv2rgba\nYUV to RGBA color space conversion.\ncircledraw\nC implementation for a circle generation algorithm. Original source: http://www.relicarium.org. Uses streamed outputs.\ncordic\nANSI C implementation for a fixed-point universal CORDIC. The arithmetic representation used is signed fixed-point (Q2.14S). The implementation has been generated by a modified version of the simple fixed-point CORDIC tools from: http://www.dcs.gla.ac.uk/~jhw/cordic/\ndynprog\nDynamic programming problem solver. Part of the PolyBench suite: http://sourceforge.net/projects/polybench/\nebcdic2ascii\nEBCDIC => ASCII conversion function. Original source: http://cprogramminglanguage.net/ascii-ebcdic-conversion-functions.aspx\nedgedet\nSimple edge detection algorithm.\neditdist\nCalculates string edit distance using dynamic programming.\nepx\nScale image data by 2x using the EPX/Scale2x/AdvMAME2x algorithm. EPX (\"Eric's Pixel eXpansion\") is an algorithm developed by Eric Johnston.\nerosion\nC implementation of the erosion morphological operator.\nfastdivs\nC implementation for signed integer division based on a modified version of signed long division as found in \"Hacker's Delight\" and Ian Kaplan's signed_divide routine.\nfastdivu\nC implementation for unsigned integer division based on a modified version of unsigned long division as found in \"Hacker's Delight\".\nfixsqrt\nC implementation for for an accurate fixed-point square root proposed by Ken Turkowski. A technical report detailing the algorithm can be found here: http://www.worldserver.com/turk/computergraphics/FixedSqrt.pdf\nfloat2half\nC implementation for a simplistic algorithm (unknown source) for float-to-half conversion.\nfsdither\n2D Floyd-Steinberg dithering for greyscale images.\nfsme\nFull-search motion estimation for video encoding.\nfxexp\nA sample C function to compute exp() using Q16.16 fixed-point arithmetic. Source: http://www.quinapalus.com/efunc.html\nfxlog\nA sample C function to compute log() using Q16.16 fixed-point arithmetic. Source: http://www.quinapalus.com/efunc.html\ngemm\nGeneral matrix-matrix multiplication. Part of the PolyBench suite: http://sourceforge.net/projects/polybench/\ngemver\nScalar, vector, & matrix multiplication. Part of the PolyBench suite: http://sourceforge.net/projects/polybench/\ngesummv\nMatrix-vector product and transpose. Part of the PolyBench suite: http://sourceforge.net/projects/polybench/\nhalf2float\nC implementation for a simplistic algorithm (unknown source) for float-to-half conversion.\nheapsort\nC implementation of a heapsort-kind algorithm. Original source can be found at: http://homepages.cwi.nl/~tromp/pearls.html (programming pearls by John Tromp).\nhtpack\nBit packing algorithm for halftone images.\nhtunpack\nBit unpacking algorithm for halftone images.\nicbrt\nC implementation for an integer cubic root approximation algorithm.\niexp\nC implementation for computing integer powers. Original author: Herny S. Warren (Hacker's Delight) from the following source: http://www.hackersdelight.org/HDcode/iexp.c.txt\nilog10a\nC implementation of a program for computing integer log functions. Original source is Hacker's Delight (HDcode.zip). http://www.hackersdelight.org/HDcode/ilog.c.txt\nilog10b\nC implementation for computing integer log base 10, with a repeated multiplication by 10. Original source is Hacker's Delight (HDcode.zip). http://www.hackersdelight.org/HDcode/ilog.c.txt\ninv_mod\nCompute the inverse of x mod y. Original source: http://bellard.org/pi/pi.c\nisqrt, isqrt1, isqrt2, isqrt3, isqrt4, isqrt5\nC implementation of various algorithms for an integer square root approximation. Original source is Hacker's Delight (HDcode.zip). http://www.hackersdelight.org/HDcode/isqrt.c.txt\nisqrt_ggems\nC implementation for an integer square root approximation algorithm as found in \"Graphics Gems, Volume II\".\njacobi\nC implementation of the Jacobi transformation.\nknapsack\nDynamic programming algorithm for the 0-1 knapsack problem.\nlinedraw\nC implementation for Bresenham's line generation algorithm. Uses streamed outputs.\nlosslessimgcmpr\nImplementation of a simple algorithm for lossless image compression.\nmagicsquares\nMagic squares construction algorithm.\nmandel\nMandelbrot ASCII fractal generator using integer arithmetic.\nmatmult\nBlock-based matrix multiplication algorithm.\nmc\nMotion compensation procedure for reconstructing a frame based on the corresponding motion vectors.\npfactor\nC implementation for a basic prime factorization algorithm. Uses streamed outputs.\npower\nC implementation of a powering function with some optimizations.\npowerseries\nPolynomial approximation of elementary functions.\npow_mod\nComputes (a^b) mod m. Original source: http://bellard.org/pi/pi.c\nrcdct\nOriginal 2-D DCT computed as two 1-D DCTs i.e. row column decomposition. Source: the XiRisc soft-core processor test suite.\nsierpinski\nC implementation of the ASCII-version of a Sierpinski gasket generation algorithm.\nsieve\nC implementation for prime number detection based on the sieve of Eratosthenes (without any optimizations). Source: http://rosettacode.org/wiki/Sieve_of_Eratosthenes\nsmithwaterman\nThis code performs the Smith-Waterman algorithm which is a wavefront algorithm that works over the two dimensional array. Source: http://www.jacquardcomputing.com/roccc/examples/systems/smith-waterman/\nsobel\nSobel edge detection.\nsqrtabacus\nSquare root by abacus algorithm. Implementation by Martin Guy @ UKC, June 1985 based on a book on programming abaci by Mr C. Woo.\nxorshift\nC implementation of \"xorshift\". Xorshift is a category of pseudorandom number generators designed by George Marsaglia." ]

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[ "# Resistor Tutorial\n\nA basic circuit\n\nHere is an example of using Ohm’s Law for a basic circuit (see the electronics introduction if you’re not familiar with Ohm’s law.)\n\nWe have a resistor of 4k7 (4700 Ohm) connected to a 5V supply, what is the current flowing through it?\n\nResistors in series\n\nWhen resistors are connected as shown in the example below, we say that they are connected in serial. Serial resistors have the following properties:\n\n• The same current flow flows through them (Itotal = I1 = I2 = I3 ….)\n• The total voltage will be a sum of the voltages across them (Vtotal = V1 + V2 + V3 …)\n• The total resistance equals the sum of the individual resistors (Rtotal = R1 + R2 + R3 …)\n\nExample\nA resistors of 10k is connected in series with a resistor of 4k7, what is the current through them and the voltage across each one individually?\n\nThe voltage across both resistors is 5V, thus to calculate the current:\n\nThe voltage over R1:\n\nThe voltage over R2:\n\nAnd V1 + V2 = 5V!\n\nResistors in Parallel\n\nWhen resistors are connected as shown in the example below, we say that they are connected in parallel. Resistors in parallel have the following properties:\n\n• The voltage across them are the same (Vtotal = V1 = V2 =V3 …)\n• The total current flowing through them will be the sum of the individual currents. (Itotal = I1 + I2 + I3 ….)\n• The total resistance can be found by adding up the reciprocals of the resistors and then taking the reciprocal of the total (1/Rtotal = 1/R1+ 1/R2 + 1/R3 …)\n\nThere is an easy way to calculate the resistance of 2 resistors in parallel:\n\nRtotal = (R1 * R2) / (R1 + R2)\n\nHere is the proof, for those interested:\n\nExample\n\nA resistors of 10k is connected in parallel with a resistor of 4k7, what is the current through them and the voltage across each one individually?" ]

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[ "# Ton-hour (refrigeration) to all other Energy conversions\n\n## Ton_hour\n\nIt is also called a refrigeration ton, is a unit of power used in some countries to describe the heat–extraction capacity of refrigeration and air conditioning equipment. The TR unit was developed during the 1880s. Its definition was set at the level of an industry standard in 1903. It is defined as the rate of heat transfer that results in the freezing or melting of 1 short ton (2,000 lb; 907 kg) of pure ice at 0 �C (32 �F) in 24 hours.\nA refrigeration ton is approximately equivalent to 12,000 BTU/h or 3.5 kW.\n\n### Enter your value in Ton–hour", null, "### Check your output in all other similar units\n\nStandard Units\nJoule {{joule}}\nGigajoule {{gigajoule}}\nMegajoule {{megajoule}}\nKilojoule {{kilojoule}}\nMillijoule {{millijoule}}\nMicrojoule {{microjoule}}\nNanojoule {{nanojoule}}\nAttojoule {{attojoule}}\nMegaelectron-volt {{megaelectronvolt}}\nKiloelectron-volt {{kiloelectronvolt}}\nElectron-volt {{electronvolt}}\nErg {{erg}}\nOther Units\nGigawatt-hour {{gigawatthour}}\nMegawatt-hour {{megawatthour}}\nKilowatt-hour {{kilowatthour}}\nKilowatt-second {{kilowattsec}}\nWatt-hour {{watthour}}\nWatt-second {{wattsec}}\nNewton meter {{newtonmeter}}\nHorsepower hour {{horsepowerhour}}\nHorsepower (metric) hour {{horsepowermetrichour}}\nKilocalorie (IT) {{kilocalorieit}}\nKilocalorie (th) {{kilocalorieth}}\nCalorie (it) {{calorieit}}\nCalorie (th) {{calorieth}}\nCalorie (Nutritional) {{calorie}}\nBtu (IT) {{btuit}}\nBtu (th) {{btuth}}\nMega Btu (IT) {{megabtuit}}\nFuel oil equivalent {{fueloilequivalent}}\nGigaton {{gigaton}}\nMegaton {{megaton}}\nKiloton {{kiloton}}\nTon {{ton}}\nDyne centimeter {{dyne}}\nGram-force meter {{gramforcemeter}}\nGram-force centimeter {{gramforcecentimeter}}\nKilogram-force centimeter {{kilogramforcecentimeter}}\nKilogram-force meter {{kilogramforcemeter}}\nKilopond meter {{kilopondmeter}}\nPound-force foot {{poundforcefoot}}\nPound-force inch {{poundforceinch}}\nOund-force inch {{oundforceinch}}\nFoot-pound {{footpound}}\nInch-pound {{inchpound}}\nInch-ound {{inchound}}\nPoundal foot {{poundalfoot}}\nTherm {{therm}}\nTherm (EC) {{thermec}}\nTherm (US) {{thermus}}\nHartree energy {{hartree}}\nRydberg constant {{rydberg}}" ]

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[ "# MATHEMATICS (MATH) Prerequisite - Sam Houston State (MATH) 1 MATHEMATICS (MATH) MATH 0001 ... logic, linear algebra, linear programming, mathematics of finance, geometry, and calculus. Applications\n\nPost on 26-May-2018\n\n212 views\n\nCategory:\n\n## Documents\n\n0 download\n\nEmbed Size (px)\n\nTRANSCRIPT\n\n• Mathematics (MATH) 1\n\nMATHEMATICS (MATH)MATH0001. Math Intervention. 0 Hours.NCBO Math Intervention. By department approval only.\n\nMATH0112. Intermediate Algebra (NCBO1). 1 Hour.This course is an accelerated introduction to the concepts of relations and functions, inequalities, algebraic expressions, and equations. Particularattention is given to absolute value, polynomial, rational, and radical expressions. Special emphasis will be given to linear and quadratic expressionsand equations. Credit in this course may not be applied toward graduation or classification of students by hours completed.Prerequisite: A score within 5 points of the minimum passing score on the TSI Assessment Test.\n\nMATH0212. Intermediate Algebra (NCBO2). 2 Hours.This course continues an examination of the concepts of relations and functions, inequalities, algebraic expressions, and equations. Particularattention is given to absolute value, polynomial, rational, and radical expressions. Special emphasis will be given to linear and quadratic expressionsand equations. Credit in this course may not be applied toward graduation or classification of students by hours completed.Prerequisite: A score within 5 points of the minimum passing score on the TSI Assessment Test.\n\nMATH0331. Developmental Mathematics. 3 Hours.This course deals with fundamental operations involving whole numbers, fractions, decimals and percents, ratio and proportion, interpretation ofgraphs, geometry, and introductory algebra including axioms and properties of the real number system, fundamental operations involving algebraicexpressions, first and second degree equations and inequalities in one unknown. Credit in this course may not be applied toward graduation orclassification of students by hours completed.\n\nMATH0332. Intermediate Algebra. 3 Hours.This course covers products and factoring of polynomials, algebraic fractions, exponents and radicals, quadratic equations, functions and graphs,applications and systems of equations. Credit in this course may not be applied toward graduation or classification of students by hours completed.\n\nMATH0333. Developmental Mathematics NCBO. 3 Hours.Students in this course accelerate through the developmental mathematics sequence at Sam Houston State University in one term using innovativelearning techniques and individualized programming. Topics include arithmetic operations, basic algebraic concepts and notation, geometry, and realand complex number systems, as well as study of relations and functions, inequalities, algebraic expressions and equations, with a special emphasison linear and quadratic expressions and equations. This course is required for students who have not met readiness standards for math. Credit inthis course will not be allowed to count toward graduation or computation of grade point average or classification of students by hours completed.(Course does not fulfill University degree requirements.)\n\nMATH1314. Pre Calculus Algebra. 3 Hours.Topics include a brief review of introductory algebra, variation, elementary theory of equations, functions (including exponential and logarithmic),inequalities, systems of equations, and other related topics.Prerequisite: Passing score on the MATH TSI Assessment or equivalent.\n\nMATH1316. Plane Trigonometry. 3 Hours.Topics include coordinate systems, circular functions, solutions of triangles, identities, trigonometric equations, and inverse functions.Prerequisite: Passing score on the MATH TSI Assessment or equivalent.\n\nMATH1324. Mth For Mngl Decision Making. 3 Hours.Topics include a review of introductory algebra, equations, relations, functions, graphs, linear programming, systems of equations and matrices, andmathematics of finance.Prerequisite: Passing score on the MATH TSI Assessment or equivalent.\n\nMATH1332. College Mathematics. 3 Hours.This course is designed to meet the objectives of Component area 2 of the core curriculum for non-business and non-science related majors.Topics may include sets, counting principles, probability, logic, linear algebra, linear programming, mathematics of finance, geometry, and calculus.Applications are emphasized.Prerequisite: Passing score on the MATH TSI Assessment or equivalent.\n\nMATH1369. Elementary Statistics. 3 Hours.This is a survey course in elementary statistics designed to acquaint students with the role of statistics in society. Coverage includes graphicaldescriptive methods, measures of central tendency and variation, the basic concepts of statistical inference, the notion of estimators, confidenceintervals, and tests of hypotheses. Also offered as STAT1369.Prerequisite: Passing score on the MATH TSI Assessment or equivalent.\n\nMATH1370. Intro to Biomedical Statistics. 3 Hours.Specifically suited to those seeking entrance into the Nursing profession, this elementary statistics course is designed to foster critical thinking aboutdata. Coverage includes graphical and numerical descriptive methods; measures of central tendency and variation; the basic concepts of statisticalinference; the notion of estimators, confidence intervals and tests of hypotheses. Data will be analyzed with the help of software currently used in theprofession, such as SPSS and/or Minitab. Also offered as STAT 1370.Prerequisite: Passing score on the MATH TSI Assessment or equivalent.\n\n• 2 Mathematics (MATH)\n\nMATH1384. Intro To Foundations Of Math I. 3 Hours.Topics include a study of sets, systems of numeration, natural numbers, integers, number theory and rational numbers. Credit in this course isapplicable only toward elementary/middle school certification.Prerequisite: Passing score on the MATH TSI Assessment or equivalent.\n\nMATH1385. Intro Foundations Of Math II. 3 Hours.Topics include basic notions of Euclidean Geometry in 2 and 3 dimensions, ratio, proportions, percents, decimals, concepts of congruence andsimilarity, transformational geometry and measurement. Credit in this course is applicable only toward elementary/middle school certification.Prerequisite: MATH1384 with a grade of C or better.\n\nMATH1410. Elementary Functions. 4 Hours.Elementary Functions and their applications, including topics from algebra, trigonometry and analytic geometry, are used to assist in the algebraic andgraphical description of the following elementary functions: polynomial, rational, exponential, logarithmic, and trigonometric functions. This course isfor students intending to take calculus (MATH1420).Prerequisite: Passing score on the MATH TSI Assessment or equivalent.\n\nMATH1420. Calculus I. 4 Hours.Topics include limits and continuity, the derivative, techniques for differentiation of algebraic, logarithmic, exponential and trigonometric functions,applications of the derivative and anti-differentiation, definite integral, Fundamental Theorem of Calculus.Prerequisite: C or better in MATH1410 or MATH1314 and MATH1316 with a grade of C or higher; or high school equivalent.\n\nMATH1430. Calculus II. 4 Hours.Topics include the definite integral and its applications, techniques of integration, improper integrals, Taylor?s formula and infinite series.Prerequisite: MATH1420 with a grade of C or better.\n\nMATH2384. Functions And Graphs. 3 Hours.The emphasis of this course is on functions and their multiple representations including linear, polynomial, logarithmic, exponential and logisticfunctions. This course may be applied only toward middle school teacher certification. Normally offered in the Fall, Spring, and Summer.Prerequisite: MATH1385 with grade of C or better.\n\nMATH2385. Fundamentals Of Calculus. 3 Hours.This course provides an introduction to the concepts and applications of calculus. This course may be applied only toward middle school teachercertification. Normally offered in the Fall, Spring, and Summer.Prerequisite: C or better in MATH2384.\n\nMATH2395. Discrete Mathematics. 3 Hours.This is an applied course in discrete mathematical structures. Topics may include sets, logic, mathematical proof, computational complexity, relations,graphs, trees, boolean algebra, number theory, combinatorics, probability, recurrence relations, and finite state machines. This course is designed forcomputer science majors, so programming applications will be emphasized.Prerequisite: MATH1420 and COSC1436 with a grade of C or better.\n\nMATH2399. Mth For Mngl Decision Making. 3 Hours.Topics include differential and integral calculus with applications in areas such as business and economics.Prerequisite: MATH1324 or MATH1314.\n\nMATH2440. Calculus III. 4 Hours.This course includes the study of the calculus of functions of several variables and topics in vector calculus including line and surface integrals,Green?s Theorem, Divergence Theorem, and Stoke?s Theorem.Prerequisite: MATH1430 with a grade of C or better.\n\nMATH3300. Introduction To Math Thought. 3 Hours.This course includes an introduction to sets, logic, the axiomatic method and proof. Normally offered in the Spring and Summer I. Normally offered inthe Spring and Summer I.Prerequisite: Grade of C or better in MATH1430 or consent of instructor.\n\nMATH3350. Theory of Interest. 3 Hours.This course will derive the mathematical principles of such financial instruments as amount functions, interest rates and yields, force of interest,special annuity types, bonds, yield curves, and interest rate sensitivity. Also included will be a discussion of the mathematics of financial derivatives.This course covers the content on which the joint Society of Actuaries/Casualty Actuarial Society Exam FM/2 on mathematical interest theory isbased.Prerequisite: Grade of C or better in Math 1430.\n\nMATH3363. Euclidean Geometry. 3 Hours.This course consists of a modern development of Euclidean geometry and a limited introduction to non-Euclidean geometry. Normally offered in Falland Summer II. Normally offered in Fall and Summer II.Prerequisite: MATH3300 or consent of instructor.\n\n• Mathematics (MATH) 3\n\nMATH3376. Differential Equations. 3 Hours.This course, in conjunction with MATH4376, is intended to develop a basic competence in areas of mathematics that are used in solving problemsfrom the physical sciences. This first course emphasizes the general solution of ordinary differential equations, including the Laplace transform andinfinite series methods. Normally offered in the Fall. Normally offered in the Fall.Prerequisite: Grade if C or better in MATH2440 or concurrent enrollment.\n\nMATH3377. Intro To Linear Alg & Matrics. 3 Hours.Topics include: solving systems of linear equations, fundamental matrix theory (invertibility theorems, determinants), eigenvectors, and propertiesof linear transformations. Remaining topics are chosen from: Properties of general vector spaces, inner product spaces, and/or diagonalization ofsymmetric matrices. Normally offered in the Spring and Summer II. Normally offered in the Spring and Summer II.Prerequisite: Grade of C or better in MATH1430.\n\nMATH3379. Statistical Mthods In Practice. 3 Hours.Topics include organization and presentation of data, measures of central tendency, dispersion, and position, probability distributions for discreteand continuous random variables, sampling techniques, parameter estimation, and hypothesis testing. Emphasis will be given to the use of statisticspackages. Normally offered in the Fall, Spring, Summer I. Also offered as STAT3379.Prerequisite: Three (3) semester hours of college mathematics.\n\nMATH3380. Historical Perspec of Math. 3 Hours.(SH Prior Course ID: MTH 380); This course is designed to present mathematical topics from a historical perspective. The number systems andcomputational methods of past cultures and civilizations are discussed, along with the development of number theory and trigonometry. Credit in thiscourse is applicable only toward elementary/middle school teacher certification. Normally offered in the Fall and Spring.Prerequisite: C or better in MATH2384.\n\nMATH3381. Intro - Foundation Of Math III. 3 Hours.Topics include proportions, percents, probability, data analysis, algebraic reasoning, and problem solving. Credit in this course is applicable onlytoward elementary/middle school certification.Normally offered in the Fall, Spring, and Summer. Normally offered in the Fall, Spring and Summer.Prerequisite: C or better in MATH1385.\n\nMATH3382. Foundations Of Middle Sch Math. 3 Hours.Topics include relations, functions, coordinate geometry, logic, and history of mathematics. Credit in this course is applicable only toward middleschool certification. Normally offered in the Fall and Spring. Normally offered in the Fall and Spring.Prerequisite: C or better in MATH2384.\n\nMATH3383. Geometric Meas./Transformation. 3 Hours.Topics included in this course are measurement in one, two, and three dimensions, the metric system, transformational geometry, congruencies,similarities, geometric constructions, and coordinate systems. This course may be applied only toward middle school certification. Normally offered inthe Fall and Spring of each year and in the Summer of odd numbered years.Prerequisite: C or better in MATH2385.\n\nMATH3384. Foundations Of Mathematics. 3 Hours.This course includes an introduction to logic, concepts of proof, proof techniques, induction, and sets. It may be applied only toward middle schoolcertification. Normally offered in the Fall and Spring and in the Summer of even numbered years.Prerequisite: C or better in MATH2385 or equivalent.\n\nMATH3386. Fundmtls Probability/Stats. 3 Hours.This course provides an introduction to probability, descriptive statistics, and inferential statistics, including regression, confidence intervals, and theconstruction and interpretation of tables, graphs, and charts. Technology related to the above topics will be incorporated into the course. This coursemay be applied only toward middle school certification. Normally offered in the Fall and Spring and in the Summer of even numbered years.Prerequisite: C or better in MATH2385.\n\nMATH3387. Problem Solving-Middle Sch Mth. 3 Hours.Topics included in this course are problem-solving strategies appropriate for middle school or junior high mathematics. The course may be appliedonly toward middle school certification. Normally offered in the Fall and Spring of each year and in the Summer of odd numbered years.Prerequisite: C or better in Math 2385.\n\nMATH3394. Numerical Methods. 3 Hours.Topics include interpolation, approximations, solutions of equations, and the solution of both linear and nonlinear systems of equations. Also offeredas COSC 3394. Normally offered in the Spring. Normally offered in the Spring.Prerequisite: COSC1436 and MATH1430 with a grade of C or higher.\n\nMATH3396. Operations Research I. 3 Hours.Techniques for the application of the scientific method to decision making in business and government are presented through the formulation andinterpretation of mathematical models for various specific real life problems. Normally offered in the Fall.Prerequisite: MATH1430 with a grade of C or higher.\n\n• 4 Mathematics (MATH)\n\nMAT..." ]

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[ "Ex 7.1\n\nChapter 7 Class 10 Coordinate Geometry\nSerial order wise", null, "", null, "", null, "", null, "", null, "", null, "", null, "Solve all your doubts with Teachoo Black (new monthly pack available now!)\n\n### Transcript\n\nEx 7.1, 5 In a classroom, 4 friends are seated at the points A, B, C and D as shown in Fig. 7.8. Champa and Chameli walk into the class and after observing for a few minutes Champa asks Chameli, “Don’t you think ABCD is a square?” Chameli disagrees. Using distance formula, find which of them is correct. As seen from the figure, four points are A(3, 4) , B(6, 7) C(9, 4) , D(6, 1) In a square, All sides are equal All diagonals are equal Hence, we have to prove AB = BC = CD = AD and AC = BD Finding sides using Distance Formula Finding AB AB = √((𝑥2 −𝑥1)2+(𝑦2 −𝑦1)2) = √(( 6 −3)2+(7 −4)2) = √((3)2+(3)2) = √(2(3)2) = 3√𝟐 Finding BC BC = √((𝑥2 −𝑥1)2+(𝑦2 −𝑦1)2) = √(( 6 −3)2+(4 −7)2) = √((3)2+(−3)2) = √((3)2+(3)2) = √(2(3)2) = 3√𝟐 Finding CD CD = √((𝑥2 −𝑥1)2+(𝑦2 −𝑦1)2) = √(( 6 −9)2+(1 −4)2) = √((−3)2+(−3)2) = √((3)2+(3)2) = √(2(3)2) = 3√𝟐 Finding AD AD = √((𝑥2 −𝑥1)2+(𝑦2 −𝑦1)2) = √(( 6 −3)2+(1 −4)2) = √((3)2+(−3)2) = √((3)2+(3)2) = √(2(3)2) = 3√𝟐 Similarly finding the diagonals Finding AC AC = √((𝑥2 −𝑥1)2+(𝑦2 −𝑦1)2) = √((9 −3)2+(4−4)2) = √((6)2+(0)2) = √((6)2) = 6 Finding BD BD = √((𝑥2 −𝑥1)2+(𝑦2 −𝑦1)2) = √(( 6 −6)2+(1 −7)2) = √((0)2+(−6)2) = √((6)2) = 6 Now since AB = BC = CD = AD = 3√2 & AC = AD = 6 Since the sides of ABCD are equal and diagonals are equal So, ABCD is a square Therefore, Champa is correct. Now since AB = BC = CD = AD = 3√2 & AC = AD = 6 Since the sides of ABCD are equal and diagonals are equal So, ABCD is a square Therefore, Champa is correct.", null, "" ]

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[ "### APPLICATION OF STATIC STATE ESTIMATOR ON INDUCTION FURNACE\n\n#### Abstract\n\nA mathematical model for calculating the temperature distribution during induction heating of a cylindrical charge has been made. In this model the temperatures of the charge at five nodes are the fundamental variables. A finite element analysis has been made for the melting process of the furnace charge for two materials which are aluminum and iron. This model was used as a reference for the performance of the estimator. A static state estimator with a measurement redundancy of 3.33 for the induction furnace has been developed. Numerical tests show that the static state estimator is satisfactory for the use in state estimation, the weighted least squares WLS approach is an effective technique in estimation, and the criterion proposed in this work is effective for the identification process when bad data exist.\n\n#### Keywords\n\nestimation, WLS, J-index, induction." ]

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[ "# Number 218436\n\nNumber 218,436 spell 🔊, write in words: two hundred and eighteen thousand, four hundred and thirty-six . Ordinal number 218436th is said 🔊 and write: two hundred and eighteen thousand, four hundred and thirty-sixth. Color #218436. The meaning of number 218436 in Maths: Is Prime? Factorization and prime factors tree. The square root and cube root of 218436. What is 218436 in computer science, numerology, codes and images, writing and naming in other languages. Other interesting facts related to 218436.\n\n## What is 218,436 in other units\n\nThe decimal (Arabic) number 218436 converted to a Roman number is (C)(C)(X)(V)MMMCDXXXVI. Roman and decimal number conversions.\n\n#### Weight conversion\n\n218436 kilograms (kg) = 481564.0 pounds (lbs)\n218436 pounds (lbs) = 99081.9 kilograms (kg)\n\n#### Length conversion\n\n218436 kilometers (km) equals to 135730 miles (mi).\n218436 miles (mi) equals to 351539 kilometers (km).\n218436 meters (m) equals to 716645 feet (ft).\n218436 feet (ft) equals 66581 meters (m).\n218436 centimeters (cm) equals to 85998.4 inches (in).\n218436 inches (in) equals to 554827.4 centimeters (cm).\n\n#### Temperature conversion\n\n218436° Fahrenheit (°F) equals to 121335.6° Celsius (°C)\n218436° Celsius (°C) equals to 393216.8° Fahrenheit (°F)\n\n#### Time conversion\n\n(hours, minutes, seconds, days, weeks)\n218436 seconds equals to 2 days, 12 hours, 40 minutes, 36 seconds\n218436 minutes equals to 5 months, 1 week, 4 days, 16 hours, 36 minutes\n\n### Codes and images of the number 218436\n\nNumber 218436 morse code: ..--- .---- ---.. ....- ...-- -....\nSign language for number 218436:", null, "", null, "", null, "", null, "", null, "", null, "Number 218436 in braille:", null, "QR code Bar code, type 39", null, "", null, "Images of the number Image (1) of the number Image (2) of the number", null, "", null, "More images, other sizes, codes and colors ...\n\n## Share in social networks", null, "## Mathematics of no. 218436\n\n### Multiplications\n\n#### Multiplication table of 218436\n\n218436 multiplied by two equals 436872 (218436 x 2 = 436872).\n218436 multiplied by three equals 655308 (218436 x 3 = 655308).\n218436 multiplied by four equals 873744 (218436 x 4 = 873744).\n218436 multiplied by five equals 1092180 (218436 x 5 = 1092180).\n218436 multiplied by six equals 1310616 (218436 x 6 = 1310616).\n218436 multiplied by seven equals 1529052 (218436 x 7 = 1529052).\n218436 multiplied by eight equals 1747488 (218436 x 8 = 1747488).\n218436 multiplied by nine equals 1965924 (218436 x 9 = 1965924).\nshow multiplications by 6, 7, 8, 9 ...\n\n### Fractions: decimal fraction and common fraction\n\n#### Fraction table of 218436\n\nHalf of 218436 is 109218 (218436 / 2 = 109218).\nOne third of 218436 is 72812 (218436 / 3 = 72812).\nOne quarter of 218436 is 54609 (218436 / 4 = 54609).\nOne fifth of 218436 is 43687,2 (218436 / 5 = 43687,2 = 43687 1/5).\nOne sixth of 218436 is 36406 (218436 / 6 = 36406).\nOne seventh of 218436 is 31205,1429 (218436 / 7 = 31205,1429 = 31205 1/7).\nOne eighth of 218436 is 27304,5 (218436 / 8 = 27304,5 = 27304 1/2).\nOne ninth of 218436 is 24270,6667 (218436 / 9 = 24270,6667 = 24270 2/3).\nshow fractions by 6, 7, 8, 9 ...\n\n### Calculator\n\n 218436\n\n#### Is Prime?\n\nThe number 218436 is not a prime number. The closest prime numbers are 218423, 218437.\n\n#### Factorization and factors (dividers)\n\nThe prime factors of 218436 are 2 * 2 * 3 * 109 * 167\nThe factors of 218436 are\n1 , 2 , 3 , 4 , 6 , 12 , 109 , 167 , 218 , 327 , 334 , 436 , 501 , 654 , 668 , 1002 , 1308 , 2004 , 18203 , 36406 , 218436 show more factors ...\nTotal factors 24.\nSum of factors 517440 (299004).\n\n#### Powers\n\nThe second power of 2184362 is 47.714.286.096.\nThe third power of 2184363 is 10.422.517.797.665.856.\n\n#### Roots\n\nThe square root √218436 is 467,371373.\nThe cube root of 3218436 is 60,224713.\n\n#### Logarithms\n\nThe natural logarithm of No. ln 218436 = loge 218436 = 12,294248.\nThe logarithm to base 10 of No. log10 218436 = 5,339324.\nThe Napierian logarithm of No. log1/e 218436 = -12,294248.\n\n### Trigonometric functions\n\nThe cosine of 218436 is 0,486431.\nThe sine of 218436 is 0,873719.\nThe tangent of 218436 is 1,796182.\n\n### Properties of the number 218436\n\nIs a Friedman number: No\nIs a Fibonacci number: No\nIs a Bell number: No\nIs a palindromic number: No\nIs a pentagonal number: No\nIs a perfect number: No\n\n## Number 218436 in Computer Science\n\nCode typeCode value\nPIN 218436 It's recommendable to use 218436 as a password or PIN.\n218436 Number of bytes213.3KB\nCSS Color\n#218436 hexadecimal to red, green and blue (RGB) (33, 132, 54)\nUnix timeUnix time 218436 is equal to Saturday Jan. 3, 1970, 12:40:36 p.m. GMT\nIPv4, IPv6Number 218436 internet address in dotted format v4 0.3.85.68, v6 ::3:5544\n218436 Decimal = 110101010101000100 Binary\n218436 Decimal = 102002122020 Ternary\n218436 Decimal = 652504 Octal\n218436 Decimal = 35544 Hexadecimal (0x35544 hex)\n218436 BASE64MjE4NDM2\n218436 MD5ee6e559a70c5b3b092fffc14e94fc89f\n218436 SHA1ec51856de73bb65e4979b54001ccc21a2d00ee3d\n218436 SHA22464bb35a99aacdef6681907332187688c4f97b437f77a74a784f81871\n218436 SHA256fdcaf5e17b5d83507402e20da93fc0a04ed89c713eeed9844650f2700cf144cf\n218436 SHA384093655e1c7bf7aa712fb827285198184da44f6075b6c3950eec0059c14923dd6b980eac49b0ef89530e558d757585341\nMore SHA codes related to the number 218436 ...\n\nIf you know something interesting about the 218436 number that you did not find on this page, do not hesitate to write us here.\n\n## Numerology 218436\n\n### Character frequency in number 218436\n\nCharacter (importance) frequency for numerology.\n Character: Frequency: 2 1 1 1 8 1 4 1 3 1 6 1\n\n### Classical numerology\n\nAccording to classical numerology, to know what each number means, you have to reduce it to a single figure, with the number 218436, the numbers 2+1+8+4+3+6 = 2+4 = 6 are added and the meaning of the number 6 is sought.\n\n## Interesting facts about the number 218436\n\n### Asteroids\n\n• (218436) 2004 RG184 is asteroid number 218436. It was discovered by LINEAR, Lincoln Near-Earth Asteroid Research from Lincoln Laboratory, ETS in Socorro on 9/10/2004.\n\n## № 218,436 in other languages\n\nHow to say or write the number two hundred and eighteen thousand, four hundred and thirty-six in Spanish, German, French and other languages. The character used as the thousands separator.\n Spanish: 🔊 (número 218.436) doscientos dieciocho mil cuatrocientos treinta y seis German: 🔊 (Anzahl 218.436) zweihundertachtzehntausendvierhundertsechsunddreißig French: 🔊 (nombre 218 436) deux cent dix-huit mille quatre cent trente-six Portuguese: 🔊 (número 218 436) duzentos e dezoito mil, quatrocentos e trinta e seis Chinese: 🔊 (数 218 436) 二十一万八千四百三十六 Arabian: 🔊 (عدد 218,436) مئتان و ثمانية عشر ألفاً و أربعمائة و ستة و ثلاثون Czech: 🔊 (číslo 218 436) dvěstě osmnáct tisíc čtyřista třicet šest Korean: 🔊 (번호 218,436) 이십일만 팔천사백삼십육 Danish: 🔊 (nummer 218 436) tohundrede og attentusindfirehundrede og seksogtredive Dutch: 🔊 (nummer 218 436) tweehonderdachttienduizendvierhonderdzesendertig Japanese: 🔊 (数 218,436) 二十一万八千四百三十六 Indonesian: 🔊 (jumlah 218.436) dua ratus delapan belas ribu empat ratus tiga puluh enam Italian: 🔊 (numero 218 436) duecentodicottomilaquattrocentotrentasei Norwegian: 🔊 (nummer 218 436) to hundre og atten tusen, fire hundre og tretti-seks Polish: 🔊 (liczba 218 436) dwieście osiemnaście tysięcy czterysta trzydzieści sześć Russian: 🔊 (номер 218 436) двести восемнадцать тысяч четыреста тридцать шесть Turkish: 🔊 (numara 218,436) ikiyüzonsekizbindörtyüzotuzaltı Thai: 🔊 (จำนวน 218 436) สองแสนหนึ่งหมื่นแปดพันสี่ร้อยสามสิบหก Ukrainian: 🔊 (номер 218 436) двiстi вiсiмнадцять тисяч чотириста тридцять шiсть Vietnamese: 🔊 (con số 218.436) hai trăm mười tám nghìn bốn trăm ba mươi sáu Other languages ...\n\n## News to email\n\nPrivacy Policy.\n\n## Comment\n\nIf you know something interesting about the number 218436 or any natural number (positive integer) please write us here or on facebook." ]

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[ "# Change in centripetal acceleration if tangential acceleration is non-zero\n\nI recently read about circular motion. They showed that acceleration $$\\vec a$$ of a object in circular motion is given by\n\n$$\\vec a = -\\omega^2r\\vec e_r + \\frac{dv}{dt}\\vec e_t$$\n\nwhere $$r$$ is the radius, $$\\omega$$ is the angular velocity, $$v$$ is the magnitude of velocity, $$\\vec e_r = \\hat i\\cos \\theta + \\hat j\\sin \\theta$$ and $$\\vec e_t = -\\hat i \\sin \\theta + \\hat j\\cos \\theta$$ are the unit vectors along radius and tangent respectively.\n\nThe text book showed that in uniform circular motion, since speed doesn't change(i.e, $$\\frac{dv}{dt} = 0$$), the acceleration reduces to $$\\omega^2r\\vec e_r$$. Then I wondered about non-uniform circular motion. I was like \"Is it possible to have a circular path even with changing speed?\". I got the answer in a question on this site. It says that for that the centripetal acceleration must change in accordance with speed to keep the path circular. So my question is by how much has the centripetal acceleration to be changed to keep the path circular path if the acceleration along tangent is non-zero?\n\nI tried to find out. But I was not even able to find out from where to start.\n\n• I got the answer in a question on this site. Please give a link to the question/answer. Jan 13, 2022 at 11:02\n• @Farcher Actually, I don't know how to insert link. Jan 13, 2022 at 11:03\n• Jan 13, 2022 at 11:06\n• @Farcher Yes! It is Jan 13, 2022 at 11:09\n\nThe centripetal acceleration is $$r\\omega^2$$ provided by a force $$mr\\omega^2$$.\n\nIf the trajectory is to be a circle the radius $$r$$ must stay constant whilst $$\\omega$$ is changing.\n\nIf it were a satellite orbiting the Earth such a change could not happen as for the same radius of orbit (equal to the separation between satellite and Earth) the gravitational force of attraction between the Earth and the satellite would need to change.\n\nIn terms of a rocket attached to a merry-go-round it can happen because in such a case the force applied to the rocket by the merry-go-round could increase in order to compensate for the increasing speed of the rocket (and merry-go-round).\n\nAs $$a=\\frac{v^2} {r}$$ the rate of change of centripetal acceleration is $$\\dot a = \\frac{2v}{r}\\frac {dv}{dt}$$.\n\n• Thank you very much. I got my answer. But what will happen if both radius and centripetal acceleration have freedom to change? Do both will change by some amount or any one will be given preference? Jan 13, 2022 at 14:37\n\nAcceleration is derivative of the velocity:\n\n$$\\vec{a} = \\frac{d\\vec{v}}{dt}$$\n\nwhere both acceleration $$a$$ and velocity $$v$$ are vectors. What this means is that there must be some acceleration in order for velocity to change, and this applies to both direction and magnitude of the velocity vector. Radial (centripetal) acceleration changes only velocity vector direction, while tangential acceleration changes only velocity vector magnitude.\n\nSince velocity can be defined via angular velocity as\n\n$$v = r \\omega$$\n\nthe equation for radial acceleration from your question can be written as\n\n$$\\boxed{a_\\text{rad} = \\frac{v^2}{R}} \\tag 1$$\n\nThis means that any value of $$a_\\text{rad}$$ will result in circular motion. If you keep the radial acceleration at a fixed value and there is some tangential acceleration which changes the velocity vector magnitude, the radius will keep increasing or decreasing proportional to $$v^2$$\n\n$$R = \\frac{v^2}{a_\\text{rad}} \\quad \\text{where} \\quad a_\\text{rad} = \\text{const.}$$\n\nThis is still circular motion, but the path looks like growing or decaying spiral, depending on the tangential acceleration sign. In order for path to remain perfect circuit, i.e. not to spiral away, you need to change the radial acceleration proportionally to $$v^2$$, which is shown by the Eq. (1)." ]

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[ "", null, "# Pivot Table With Multiple Worksheets\n\nPivot Table With Multiple Worksheets. Suppose we would like to create a pivot table using. Using power query editor to consolidate worksheets into pivot table.\n\nWeb add or edit pivot tables. For example, if you have a pivottable of expense. Web understanding the technicalities of pivot tables in excel now brings us to the practical part.\n\n### The Key Is To Turn The Ranges Into Tables.\n\nCreate a pivot table from multiple worksheets of a workbook. You can create a pivottable in excel using multiple worksheets. I'm building a workbook that will have a lot of worksheets, all with the same format, just data.\n\n### Web Create Multiple Sheets From Pivot Table For Our Example, We Will Use The List Of Nba Players, Their Clubs, Conferences, And Statistics For Several Nights.\n\nWeb you can use a pivottable in microsoft excel to combine data from multiple worksheets. Suppose we would like to create a pivot table using. Web you may watch a short video of my solution here.\n\n### Excel For Microsoft 365 Excel 2021 Excel 2019 Excel 2016 Excel 2013.\n\nEnter the data suppose we have a spreadsheet with two sheets titled week1 and week2: The steps for creating a pivot table from. Web trying to create a pivot table from a workbook with 3 worksheets, each sheet contains data downloaded from financial website into a excel file.\n\n### For Example, If You Have A Pivottable Of Expense.\n\nWeb a pivottable is a powerful tool to calculate, summarize, and analyze data that lets you see comparisons, patterns, and trends in your data. Web create the table structure. Pivottables work a little bit differently.\n\n### Web The Trick To Doing This Is The Tables Are Related.\n\nThe most important thing is the use this workbook’s data model option is selected. Web pivot tables for multiple worksheets in one workbook. Consolidating data is a useful way to combine data.", null, "Previous post Grade 4 Expanded Form Multiplication Worksheets", null, "Next post Telling Time Worksheets 3rd Grade" ]

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[ "Technical overview of the intervalaverage function\n\nMotivation\n\nThe interval average function was born out of the need to take values measured over a set of intervals and time-weight average those values into a different set of intervals. Algorithmically, the simplest approach to deal with this problem is just to expand interval data into repeated values over intervals that are all the same length (e.g. the value of 8 measured over the interval [3,5] becomes the value of 8 measured over [3,3] and [4,4] and [5,5]) but this is incredibly memory intensive. Instead a weighting approach is necessary.\n\nI was not able to find a package which accomplished this exact task (although there probably is one somewhere), much less a package which accomplished it quickly and with minimal memory overhead. Since these package was designed to replace SQL database procedures the priorities were correctness, memory efficiency, and speed in that order. But given the amount of effort put into optimizing this, it’s almost exactly as fast as a less memory efficient version.\n\nInteger vs numeric intervals\n\nI made the intentional choice to disallow numeric intervals. Restricting intervals to integer types (integer or class IDate) allowed me to avoid having to foresee issues that would arise with numeric intervals. If you’re dealing with continuous data and would like to use this package, just discretize the data to your desired amount of precision convert to those discrete periods to integers.\n\nThis vignette\n\nThe remainder of this vignette describes some of the decision-making behind how the intervalaverage function was written and may not be interesting or useful to a general purpose audience.\n\nA brief description of the intervalaverage algorithm (with a focus on explaining why seemingly convoluted choices were made in the function body)\n\nThe intervalaverage function starts by merging periods in y to periods in x by interval variables and possible grouping variables using a non-equijoin. Technically speaking intervalaverage(x,y, interval_vars,group_vars) performs a right join on group_vars and non-equi joining (for partial overlaps) on interval_vars. If intervals from x have start and end points [a,b] and intervals from y have start and end points [c,d], the non-equi join for partial overlaps requires that b>=c & a <= d.\n\nThat resulting operation returns a joined table with two sets of intervals. Those two sets of intervals can then be intersected (ie: [max(a,b), min(c,d) ]) to identify the period of overlap. The length of this period of overlap (min(c,d)-max(a,b)+1 ) is important in that it determines the weight that the corresponding value from x will have when trying to average that value into the interval from y ([c,d]).\n\nThis is all done directly in C++ because this code needs to have very little overhead for a specific reason: namely that the non-equijoin is repeatedly calling the average for each group in by=.EACHI. Previously the function generated the entire intermediate table and operations (such as taking products to calculate the weighted mean) could be done once on the entire vectors in the intermediate table, but to save memory I’m using the .EACHI technique which doesn’t ever allocate the intermediate table (at least not all at once). Using this .EACHI approach makes the function highly memory efficient (basically the only things allocated other than the inputs is a table of the resulting join subsetted to the largest group. This memory is then reused for each group. This is data.table’s optimization, not mine, but at the time of writing it is not well documented.)\n\nBefore describing the C++ code which does the above operation, I’ll mention that there is one other memory optimization I implemented: extreme care was taken to avoid copying x or y. This was challenging since x and y needed to be modified in various ways prior to the join, but this is all addressed via adding columns and/or possibly reordering (for an error check)–all of this is reversed on function exit. I don’t know much about situations where multiple parallel R processes are sharing the same object at the same time, but if that’s something you want to do you’ll definitely need to copy the objects first or else who knows what will happen. Note when I say “multiple parallel R processes sharing the same object at the same time” I’m not referring to standard parallelization approaches like those used in library(parallel) or on a cluster because I’m almost certain those always make copies when forking.\n\nIn any case, the C code:\n\nThe C++ code takes the following inputs: - a list of values - a vector of start integers from x - a vector of end integers from x - a scalar–start integer from y - a scalar–end integer from y - a collated vector of desired names in this form: c(\"valuevar1\",\"nobs_valuevar1\",\"valuevar2\",\"nobs_valuevar2\"...etc) which will determine the names of those columns in the return list of the C function. I probably could have generated this in C but I was having trouble figuring out text string manipulation.\n\nThe return is list contains precomputed columns (xduration, values, nobs_values, and xminstart/xmaxend) as described in the help.\n\nThe C code is specifically designed to work with the conditions generated by the non-equi join and should not be generalized to other situations without major modification. Namely, because of the .EACHI grouping, there is one set of y intervals and possibly multiple xintervals (hence the scalar for y/vector for x). Additionally, all intervals are assumed to be non-missing with the exception of a special case: if any intervals in x are missing, they’re all assumed to be missing and this only results when the .EACHI group does not contain ANY matching rows from x–ie, the set of join conditions resulted in no match. data.table will automatically generated a single row with missings for the x variables. This is detected simply through the presence of a missingness in the vector of start integers. The correct output for this situation is generated manually (xminstart/xmaxend and the average values are returned NA but xduration is returned as 0).\n\nIf nonmissing, the function proceeds to loop through each value variable provided as the outer loop (indexed by j). Each j loop returns two variables corresponding to the value variable: the nonmissing (ie omitting NAs) average value as well as the number of observations that the value variable had which contributed to the average. This is less than or equal to xduration (equal to if that value variable has no missings). Additionally, when j=0 (ie on the first iteration), interval information–ie the length of the intersect as well as xminstart/xmaxend– is determined (these are necessary to calculate the weights for the average so this happens first in the loop).\n\nThis optimization and the abstractions which allow intervalaverage to be called flexibly for arbitrary groups and number of values variables make the intervalaverage function fairly intricate. This intricacy (read: potential for bugs) is partially addressed by the large number of error checks specified at the top of the R function body. (there are no error checks in the C code as this would slow down the R function since the C code is called repeatedly). Potential for bugs is further addressed by the fact that I rewrote a slower but simpler version of the averaging function using a different algorithm. The “unit tests” are more than just unit tests–they’re a series of datasets passed through both functions. Both functions return exactly identical results in all cases or the checks fail so I can say with high certainty that despite the level of abstraction involved that this function works as intended at least in the use-cases that I’ve foreseen. With that said, if you encounter a bug please let me know and I will patch it." ]

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[ "", null, "", null, "", null, "", null, "- Current Issue - Ahead of Print Articles - All Issues - Search - Open Access", null, "- Information for Authors - Downloads - Guideline - Regulations ㆍPaper Submission ㆍPaper Reviewing ㆍPublication and Distribution - Code of Ethics", null, "- For Authors ㆍOnlilne Submission ㆍMy Manuscript - For Reviewers - For Editors", null, "", null, "", null, "", null, "", null, "", null, "", null, "Bounds for exponential moments of Bessel processes Bull. Korean Math. Soc. 2019 Vol. 56, No. 5, 1211-1217 https://doi.org/10.4134/BKMS.b180974Published online September 30, 2019 Cloud Makasu University of the Western Cape Abstract : Let $0<\\alpha<\\infty$ be fixed, and let $X=(X_t)_{t\\geq0}$ be a Bessel process with dimension $0<\\theta\\leq1$ starting at $x\\geq0$. In this paper, it is proved that there are positive constants $A$ and $D$ depending only on $\\theta$ and $\\alpha$ such that \\begin{equation*} \\mathbf{E}_x\\Biggl(\\exp\\bigl[\\alpha\\max\\limits_{0\\leq t\\leq\\tau}X_t\\bigr]\\Biggr)\\leq A\\mathbf{E}_x\\Biggl(\\exp[D\\tau]\\Biggr) \\end{equation*} for any stopping time $\\tau$ of $X$. This inequality is also shown to be sharp. Keywords : Bessel processes, comparison principle, optimal stopping problem, Young inequality MSC numbers : Primary 60G40, 34A40, 60E15 Downloads: Full-text PDF   Full-text HTML" ]

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[ "", null, "", null, "• Matrices\n• Algebra\n• Geometry\n• Funciones\n• Trigonometry\n• Coordinate geometry\n• Combinatorics\n Suma y resta Producto por escalar Producto Inversa\n Monomials Polynomials Special products Equations Quadratic equations Radical expressions Systems of equations Sequences and series Inner product Exponential equations Matrices Determinants Inverse of a matrix Logarithmic equations Systems of 3 variables equations\n 2-D Shapes Areas Pythagorean Theorem Distances\n Graphs Definition of slope Positive or negative slope Determine slope of a line Ecuación de una recta Equation of a line (from graph) Quadratic function Posición relativa de dos rectas Asymptotes Limits Distancias Continuity and discontinuities\n Sine Cosine Tangent Cosecant Secant Cotangent Trigonometric identities Law of cosines Law of sines\n Ecuación de una recta Posición relativa de dos rectas Distancias Angles in space Inner product\n\n# Surface area of a rectangular prism\n\nThe surface area of a rectangular prism is is the area of the six rectangles that cover it.\nIf we break the rectangular prism into its parts we are going to have 2 bases and 4 lateral faces (rectangles) which make up the lateal area.", null, "It is pretty easy to calculate their areas and then add them up.\n\nWhat is the surface area?", null, "A rectangular prism has 3 pairs of identical faces. Each face is a rectangle.\n\nFind the area of the faces in each pair.", null, "Now add the areas of the 6 faces.\n\n Surface area = 24 + 24 + 54 + 54 + 36 + 36 = 228\n\nThe surface area of the rectangular prism is 228 square centimeters", null, "What is the surface area when a=1, b=7 and c=7?" ]

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[ "It was an unusually pleasant Wednesday afternoon in July. A visitor, an experienced mathematics teacher from overseas, was eager to observe how a discussion in mathematics could be fostered in a mixed age classroom. The class was soon after the lunch break. So, to prepare the ground for discussion, an evocative story he narrated.\n\n“It was an afternoon just like today, and an English teacher had been sent to substitute the Math teacher who was on leave. The students were a bunch of energetic seven-year-olds. In an attempt to occupy the class with what the English teacher thought was a painstaking exercise, he asked the students to add the numbers from 1 all the way up to 100. He then settled to attend to his own work. There was a prompt tug at the lapel of his coat within ten minutes by a lad who claimed he had 'finished'. Utterly disbelieving of the lad and yet in no position to actually check for himself the answer that the student quoted, the teacher asked the student for the one thing that he could: to justify his answer.\nThe student wrote:\n\n1 + 2 + 3 + ...+ 98 + 99 + 100\n(1 + 100) + ( 2 + 99) + (3 + 98 ) + ... and so on.\n\nHe reasoned that grouping the numbers in this manner should not alter the result. That would mean adding 50 pairs of 101. He had learnt that multiplication was repeated addition. So, the answer was 50 x 101. That could be further simplified as (50 x 100) + (50 x 1) which equalled 5000 + 50 = 5050.\n\nThe boy (who later came to be known as the famous mathematician Carl Friedrich Gauss) had found an elegant solution to a seemingly complex problem. “What can one say of the possibilities of the young mind!””\n\nThere was a palpably appreciative silence in the class. Now the challenge began. The teacher posed the question: “If you take all the numbers from 1 to 100, what would be more - the sum of odd numbers or the sum of even numbers? And by how much?”\n\nStudents were invited to make educated guesses. The majority felt that 'both the sums would be equal because there are an equal number of odd and even numbers up to 100'. A few said that 'even would be more because 100 was the last number and it was even'. The cautious remaining were looking for a basis to proceed.\n\nI felt that students could now calculate using paper and pencil. The only condition I suggested was that every statement of an individual should be substantiated and justified.\n\nNow energy had been unleashed. The following is a record of the conversations that took place. The technical complexity of the statements revealed the level of understanding of the student:\n\nStudent 1: Let me first try numbers from 1 to 10.\n\n1 + 3 + 5 + 7 + 9 = 25.\n2 + 4 + 6 + 8 + 10 = 30.\n\nEven numbers add up to more, within 10. Therefore, up to 100 also it should be the same.\n(Simplifying the problem and extending it inductively)\nStudent 2: How can you simply say that?\nS1: Why? In the other numbers also, the trend is the same. Only tens and twenties are added.\nS3: But that's no answer. In Maths you need to prove. You can't simply show 10 examples and say “it is so”.\nS4: I have another logic. Look! Write the sum of odd numbers and even numbers one below the other:\n1 + 3 + 5 + …… + 97 + 99\n2 + 4 + 6 + ……. + 98 + 100\nEach even number is 1 more than an odd number. So when you add them, the even numbers would be more.\n\n(A completely lateral way of approaching)\n\nS5: The explanation makes sense. But that still leaves the question: “how much more?”\nS4: Since there are 50 even numbers, I feel the answer will be 50 more.\nS3: But this is an estimation, at best an interesting one at that. That still doesn't prove the point.\nS6: Since you are going on and on about proof, suppose you tell us what it means to PROVE!\nS3: See, I too don't know how to prove this. But if some statement should be true, it should be true everywhere all the time. Not up to 10 or up to 100 or when you look at it one way and you look at it the other way. In fact that's understanding for yourself and not proving!\nS7: Now let us try algebra. When you use 'x' and 'y' and a formula it means the statement is true for any random number and not necessarily particular numbers. That at least should be acceptable as proof.\n\n(Moving from generic to specific; empirical to abstract)\n\nVisitor: That appeals to me. Proof is the only thing that is specific to mathematics and we should not sacrifice that. In Physics you verify laws\nlearning initiatives with experiments. But in mathematics you prove statements starting from the beginning.\nS7: Alright. Let us not go away in another direction. Hey, some seniors, tell about the formula that you learnt that day for adding numbers.\nS8: Yes, I will write it on the board. In fact it is the same as that Class 2 kid mathematician's logic in the story we heard at the beginning. Only it has symbols instead of numbers.", null, "(Moving on to formal proof)\nS9: I know the rule. But I still can't apply it in this situation because you are adding odd and even numbers. There are gaps in them. The rule is for continuous numbers!\n(Acknowledging assumptions and framework within which a precept is valid)\nS3: A rule should be useful everywhere. Otherwise what's the point? Let's see if we can find the way to avoid the gaps…\nS10: I've got it! I've got it! I've got it! See, we don't need to add numbers 2 times. We'll add numbers all the way up to 100. It is continuous. There are no gaps. We'll use the formula. Then we'll subtract the sum of even numbers. We'll get the sum of odd numbers. Then we can compare.\nS11: Ha ha Einstein! How do you propose to add the even numbers? There are gaps. At least one of them with gaps you cannot avoid.\n(Here the class was stuck. So the teacher offered a hint)\nTeacher: You could think of 2 + 4 + 6 + …..+ 100 as two times 1 + 2 + 3 + …..50. Then there would be no gaps.\nClass: Hey, that's cool.\n\nThen students who knew algebra applied the formula and explained it to the class. The sum of odd numbers was calculated to be 2500 and the sum of even numbers to be 2550. So, the even numbers were more and by 50.\n\nThere was a student who had been very quiet and poring over numbers in a focussed manner. The teacher asked him to explain his attempt because he had been following his own reasoning. He expounded: In every set of tens, there is a group of 1 + 3 + 5 + 7 + 9 and 2 + 4 + 6 + 8 + 10. So, there are 10 groups of sums of 25 and 30. So that makes the odd number group 250 and even number group 300.\n\nThen it was only a question of evenly distributing the tens in the other numbers. From 11 to 20, 5 tens go to the odd number group (11 + 13 + etc.) and 5 tens go to the evens group. Similarly, from 21 to 30, 5 twenties go the odds and 5 twenties to the evens.\n\nProceeding similarly, the student had calculated the sum of odd numbers to be 2500 and even numbers to be 2550 through elegant reasoning without knowing the formula.\n\nThe class applauded this painstaking effort. This concrete reasoning grounded all of the above discussion in a manner where each student still had a window of understanding into the solution. Suddenly the juniormost child in the class exclaimed:\n\nS12: Hey! From 1 to 10 also, even numbers are more. From 1 to 100 also even numbers are more. So, in 1 to 1000 also even numbers will add more. In 1 to 10, 000 also even numbers will add to more.\n(Not resting with one solution; extending the problem)\nS7: Oh! True, come to think of it.\nS13: Hey! Look at another pattern! From 1 to 10, the even numbers add up to 5 more than odd numbers. From, 1 to 100, even numbers add up to 50 more than odd numbers. In numbers 1 to 1000, will even numbers add up to 500 more than odd numbers?\nS8: Yeah, let's find out!\nS3: No, I don't want to say that it will always be even numbers which add up to more than odd numbers. It depends. If you take a string of continuous numbers from the middle with, of course, an equal number of odd and even numbers, if the first is an odd number and the last an even number, then even numbers will add to more. If the first is an even number and the last is an odd number, odd numbers will add to more.\nS8: Can we prove it now? Please can we prove?\n\nIt was time for that class to end. It ended then, making way for another beginning the next time!" ]

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[ "## Zhang, Hongqing\n\nCompute Distance To:\n Author ID: zhang.hongqing", null, "Published as: Zhang, Hongqing; Zhang, Hong-Qing; Zhang, Hong Qing; Zhang, Hong-qing; Zhang, H.; Zhang, HongQing; Zhang, Honging; Zhang, H. Q. more...less External Links: dblp\n Documents Indexed: 365 Publications since 1981 Co-Authors: 103 Co-Authors with 343 Joint Publications 3,229 Co-Co-Authors\nall top 5\n\n### Co-Authors\n\n 7 single-authored 44 Yan, Zhenya 30 Chen, Yong 23 Li, Biao 23 Li, Desheng 21 Mei, Jianqin 18 Song, Lina 16 Tian, Shoufu 16 Yu, Fajun 16 Zhang, Yufeng 15 Huang, Dingjiang 14 Wang, Qi 14 Zhi, Hongyan 12 Fan, Engui 11 Xia, Tie-Cheng 10 Wang, Zhen 9 Chen, Huaitang 8 Feng, Yang 8 Lü, Zhuosheng 8 Xie, Fuding 7 Ren, Yujie 7 Wang, Ming 7 Zhang, Sheng 7 Zhao, Xueqin 6 Ding, Qi 6 Xiao, Yafeng 5 Li, Wenting 5 Lu, Bin 5 Xue, Haili 4 Chen, Yufu 4 Li, Wei 4 Lv, Na 4 Tang, Limin 4 Wang, Dengshan 4 Yu, Yaxuan 4 Zheng, Ying 4 Zou, Li 3 Chen, Alatancang 3 Chen, Xiaohong 3 Guan, Wei 3 Wang, Dan 3 Wang, Fei 3 You, Fucai 3 Zhang, Daqing 3 Zhang, Xiaoling 3 Zhang, Yuanyuan 3 Zheng, Xuedong 2 Chao, Lu 2 Chen, Fang 2 Cheng, Jianjun 2 Dong, Yan-Cheng 2 Feng, Hong 2 Jiang, Dongmei 2 Jiang, Wuyou 2 Kong, Cuicui 2 Li, Li 2 Liu, Shutian 2 Luo, Chengxin 2 Sun, Yujuan 2 Tong, Dengke 2 Xuan, Hengnong 2 Yan, Qingyou 2 Yong, Xuelin 2 Zeng, Xin 2 Zhang, Dahai 2 Zhang, Tiantian 2 Zhen, Wang 2 Zheng, Yu 2 Zhong, Wanxie 1 Ayatollahi, Ahmad 1 Cao, Lina 1 Cao, Lu 1 Cong, Yang 1 Feng, Binlu 1 Gong, Xinbo 1 Guo, Qilong 1 Jafarnia-Dabanloo, N. 1 Jia, Yifeng 1 Jiao, Xiaoyu 1 Johari-Majd, V. 1 Kang, Y. A. 1 Li, Peichun 1 Lin, Lijun 1 Liu, Yifang 1 Lu, Na 1 Meng, Dongyuan 1 Qi, Wang 1 Ramakrishnan, T. S. 1 Song, Zhaohui 1 Sun, Weiwei 1 Wan, Ying 1 Wang, Bao-Dong 1 Wang, Ruihe 1 Wang, Zhenyu 1 Wasan, Darsh T. 1 Xie, Zheng 1 Xu, Bo 1 Yang, Guang 1 Yang, Zhongyuan 1 Yin, Li 1 Yomba, Emmanuel ...and 10 more Co-Authors\nall top 5\n\n### Serials\n\n 51 Chaos, Solitons and Fractals 44 Applied Mathematics and Computation 31 Applied Mathematics and Mechanics. (English Edition) 29 Communications in Theoretical Physics 23 Physics Letters. A 21 Acta Physica Sinica 16 Journal of Dalian University of Technology 11 Communications in Nonlinear Science and Numerical Simulation 6 Journal of Mathematical Research & Exposition 6 Computational Mechanics 5 Mathematica Applicata 5 International Journal of Modern Physics C 4 Journal of Mathematical Physics 4 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 4 Applied Mathematics E-Notes 4 Acta Mathematica Scientia. Series A. (Chinese Edition) 4 International Journal of Nonlinear Science 3 Journal of Mathematical Analysis and Applications 3 Journal of Systems Science and Mathematical Sciences 3 Acta Mathematica Scientia. Series A. (Chinese Edition) 3 Journal of Gansu University of Technology 3 Physica Scripta 3 Journal of Nonlinear Mathematical Physics 3 International Journal of Pure and Applied Mathematics 2 Computers & Mathematics with Applications 2 International Journal of Theoretical Physics 2 Reports on Mathematical Physics 2 Theoretical and Mathematical Physics 2 Journal of Computational and Applied Mathematics 2 Journal of Lanzhou University. Natural Sciences 2 Mathematics in Practice and Theory 2 Journal of Engineering Mathematics (Xi’an) 2 International Journal of Computer Mathematics 2 Journal of Physics A: Mathematical and General 2 Applied Mathematics. Series A (Chinese Edition) 2 International Journal of Geometric Methods in Modern Physics 2 Journal of Mathematical Research with Applications 1 Modern Physics Letters B 1 International Journal of Modern Physics B 1 Acta Mechanica 1 Astrophysics and Space Science 1 Computer Physics Communications 1 Fluid Dynamics 1 International Journal of Heat and Mass Transfer 1 Journal of Fluid Mechanics 1 ZAMP. Zeitschrift für angewandte Mathematik und Physik 1 Mathematics and Computers in Simulation 1 Studies in Applied Mathematics 1 Mathematica Numerica Sinica 1 Chinese Annals of Mathematics. Series A 1 Chinese Annals of Mathematics. Series B 1 Journal of Computational Mathematics 1 Acta Scientiarum Naturalium Universitatis Jilinensis 1 Northeastern Mathematical Journal 1 Mathematical and Computer Modelling 1 Applied Mathematical Modelling 1 Kexue Tongbao 1 Journal of Nanjing University of Aeronautics and Astronautics 1 Applied Mathematics. Series B (English Edition) 1 Transactions of Nanjing University of Aeronautics & Astronautics 1 Pure and Applied Mathematics 1 Mathematical Problems in Engineering 1 Chinese Quarterly Journal of Mathematics 1 Journal of Mathematical Study 1 Journal of the Physical Society of Japan 1 Journal of Yantai University. Natural Science and Engineering 1 Journal of Applied Mathematics 1 Acta Mathematica Scientia. Series B. (English Edition) 1 Progress of Theoretical Physics 1 Journal of Jilin University. Science Edition 1 Journal of Applied Mathematics and Computing 1 CMC. Computers, Materials, and Continua 1 Journal of Lanzhou University of Technology 1 Communications in Mathematical Analysis 1 Acta Mathematica Sinica. Chinese Series 1 Journal of Physics A: Mathematical and Theoretical 1 Journal of North University of China. Natural Science Edition 1 International Journal of Computational Mathematics and Numerical Simulation 1 Science China. Mathematics 1 Journal of Theoretical Biology\nall top 5\n\n### Fields\n\n 289 Partial differential equations (35-XX) 157 Dynamical systems and ergodic theory (37-XX) 48 Numerical analysis (65-XX) 28 Fluid mechanics (76-XX) 25 Computer science (68-XX) 18 Mechanics of deformable solids (74-XX) 14 Ordinary differential equations (34-XX) 11 Special functions (33-XX) 11 Global analysis, analysis on manifolds (58-XX) 9 Quantum theory (81-XX) 6 Mechanics of particles and systems (70-XX) 5 Nonassociative rings and algebras (17-XX) 4 Algebraic geometry (14-XX) 4 Real functions (26-XX) 4 Operator theory (47-XX) 3 Linear and multilinear algebra; matrix theory (15-XX) 3 Difference and functional equations (39-XX) 3 Statistical mechanics, structure of matter (82-XX) 2 Topological groups, Lie groups (22-XX) 2 Approximations and expansions (41-XX) 2 Integral equations (45-XX) 2 Functional analysis (46-XX) 2 Biology and other natural sciences (92-XX) 1 Mathematical logic and foundations (03-XX) 1 Field theory and polynomials (12-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Probability theory and stochastic processes (60-XX) 1 Relativity and gravitational theory (83-XX) 1 Astronomy and astrophysics (85-XX) 1 Operations research, mathematical programming (90-XX)\n\n### Citations contained in zbMATH Open\n\n243 Publications have been cited 2,335 times in 1,501 Documents Cited by Year\nA note on the homogeneous balance method. Zbl 1125.35308\nFan, Engui; Zhang, Hongqing\n1998\nFractional sub-equation method and its applications to nonlinear fractional PDEs. Zbl 1242.35217\nZhang, Sheng; Zhang, Hong-Qing\n2011\nNew explicit solitary wave solutions and periodic wave solutions for Whitham-Broer-Kaup equation in shallow water. Zbl 0969.76518\nYan, Z.; Zhang, H.\n2001\nApplication of homotopy analysis method to fractional KdV-Burgers-Kuramoto equation. Zbl 1209.65115\nSong, Lina; Zhang, Hongqing\n2007\nA direct method for integrable couplings of TD hierarchy. Zbl 1052.37055\nZhang, Yufeng; Zhang, Hongqing\n2002\nFurther improved F-expansion method and new exact solutions of Konopelchenko–Dubrovsky equation. Zbl 1083.35122\nWang, Dengshan; Zhang, Hong-Qing\n2005\nNew explicit and exact travelling wave solutions for a system of variant Boussinesq equations in mathematical physics. Zbl 0938.35130\nYan, Zhenya; Zhang, Hongqing\n1999\nRiemann theta functions periodic wave solutions and rational characteristics for the nonlinear equations. Zbl 1201.35072\nTian, Shou-Fu; Zhang, Hong-Qing\n2010\nA new Riccati equation rational expansion method and its application to $$(2+1)$$-dimensional Burgers equation. Zbl 1070.35073\nWang, Qi; Chen, Yong; Zhang, Hongqing\n2005\nExact travelling wave solutions for a generalized Zakharov-Kuznetsov equation. Zbl 1037.35070\nLi, Biao; Chen, Yong; Zhang, Hongqing\n2003\nNew exact solutions to a solutions to a system of coupled KdV equations. Zbl 0947.35126\nFan, Engui; Zhang, Hongqing\n1998\nSymbolic computation and new families of exact soliton-like solutions to the integrable Broer-Kaup (BK) equations in $$(2+1)$$-dimensional spaces. Zbl 0970.35147\nYan, Zhen-ya; Zhang, Hong-qing\n2001\nOn the integrability of a generalized variable-coefficient forced Korteweg-de Vries equation in fluids. Zbl 1288.35403\nTian, Shou-Fu; Zhang, Hong-Qing\n2014\nExplicit and exact traveling wave solutions of Whitham-Broer-Kaup shallow water equations. Zbl 0969.76517\nXie, F.; Yan, Z.; Zhang, H.\n2001\nRiemann theta functions periodic wave solutions and rational characteristics for the $$(1+1)$$-dimensional and $$(2+1)$$-dimensional Itô equation. Zbl 1258.35011\nTian, Shou-Fu; Zhang, Hong-Qing\n2013\nNew multiple soliton solutions to the general Burgers-Fisher equation and the Kuramoto-Sivashinsky equation. Zbl 1068.35126\nChen, Huaitang; Zhang, Hongqing\n2004\nApplying homotopy analysis method for solving differential-difference equation. Zbl 1209.65119\nWang, Zhen; Zou, Li; Zhang, Hongqing\n2007\nExplicit exact solutions for compound KdV-type and compound KdV-Burgers-type equations with nonlinear terms of any order. Zbl 1038.35095\nLi, Biao; Chen, Yong; Zhang, Hongqing\n2003\nSolving the fractional BBM-Burgers equation using the homotopy analysis method. Zbl 1198.65205\nSong, Lina; Zhang, Hongqing\n2009\nA generalized F-expansion method to find abundant families of Jacobi elliptic function solutions of the $$(2+1)$$-dimensional Nizhnik-Novikov-Veselov equation. Zbl 1088.35536\nRen, Yujie; Zhang, Hongqing\n2006\nNew explicit solitary wave solutions for $$(2+1)$$-dimensional Boussinesq equation and $$(3+1)$$-dimensional KP equation. Zbl 1006.35083\nChen, Yong; Yan, Zhenya; Zhang, Honging\n2003\nImproved Jacobi-function method with symbolic computation to construct new double-periodic solutions for the generalized Ito system. Zbl 1134.35301\nZhao, Xueqin; Zhi, Hongyan; Zhang, Hongqing\n2006\nOn the Lie algebras, generalized symmetries and Darboux transformations of the fifth-order evolution equations in shallow water. Zbl 1321.35190\nTian, Shoufu; Zhang, Yufeng; Feng, Binlu; Zhang, Hongqing\n2015\nNew double periodic and multiple soliton solutions of the generalized $$(2 + 1)$$-dimensional Boussinesq equation. Zbl 1049.35150\nChen, Huai-Tang; Zhang, Hong-Qing\n2004\nOn the integrability of a generalized variable-coefficient Kadomtsev-Petviashvili equation. Zbl 1232.35144\nTian, Shou-Fu; Zhang, Hong-Qing\n2012\nA kind of explicit Riemann theta functions periodic waves solutions for discrete soliton equations. Zbl 1221.37153\nTian, Shou-Fu; Zhang, Hong-Qing\n2011\nIntegrable couplings of Botie-Pempinelli-Tu (BPT) hierarchy. Zbl 0996.37073\nZhang, Yufeng; Zhang, Hongqing; Yan, Qingyou\n2002\nSoliton-like and period form solutions for high dimensional nonlinear evolution equations. Zbl 1030.35140\nLü, Zhuosheng; Zhang, Hongqing\n2003\nGeneralized extended tanh-function method and its application to $$(1+1)$$-dimensional dispersive long wave equation. Zbl 1019.35059\nZheng, Xuedong; Chen, Yong; Zhang, Hongqing\n2003\nExplicit exact solutions for new general two-dimensional KdV-type and two-dimensional KdV-Burgers-type equations with nonlinear terms of any order. Zbl 1040.35100\nLi, Biao; Chen, Yong; Zhang, Hongqing\n2002\nExplicit and exact travelling wave solutions for the generalized derivative Schrödinger equation. Zbl 1139.35092\nHuang, Ding-Jiang; Li, De-Sheng; Zhang, Hong-Qing\n2007\nNew explicit and exact solutions for the Nizhnik-Novikov-Vesselov equation. Zbl 0996.35066\nXia, Tiecheng; Li, Biao; Zhang, Hongqing\n2001\nAn extended Jacobi elliptic function rational expansion method and its application to $$(2+1)$$-dimensional dispersive long wave equation. Zbl 1145.35358\nWang, Qi; Chen, Yong; Zhang, Hongqing\n2005\nAuto-Bäcklund transformation and exact solutions for compound KdV-type and compound KdV-Burgers-type equations with nonlinear terms of any order. Zbl 1005.35079\nLi, Biao; Chen, Yong; Zhang, Hongqing\n2002\nA new extended Riccati equation rational expansion method and its application. Zbl 1138.35403\nSong, Li-Na; Wang, Qi; Zheng, Ying; Zhang, Hong-Qing\n2007\nSoliton like and multi-soliton like solutions for the Boiti-Leon-Pempinelli equation. Zbl 1068.35137\nLü, Zhuosheng; Zhang, Hongqing\n2004\nSymbolic computation and new families of exact soliton-like solutions of Konopelchenko-Dubrovsky equations. Zbl 1049.35171\nXia, Tie-cheng; Lü, Zhuo-sheng; Zhang, Hong-qing\n2004\nThe multi-component TD hierarchy and its multi-component integrable coupling system with five arbitrary functions. Zbl 1102.37044\nYu, Fajun; Xia, Tiecheng; Zhang, Hongqing\n2006\nAuto-Bäcklund transformation and new exact solutions of the $$(2 + 1)$$-dimensional Nizhnik-Novikov-Veselov equation. Zbl 1078.35107\nWang, Dengshan; Zhang, Hong-Qing\n2005\nSolving the $$(2+1)$$-dimensional higher order Broer-Kaup system via a transformation and tanh-function method. Zbl 1049.35157\nLi, De-Sheng; Gao, Feng; Zhang, Hong-Qing\n2004\nTravelling wave solutions of nonlinear partial equations by using the first integral method. Zbl 1191.35090\nLu, Bin; Zhang, Hongqing; Xie, Fuding\n2010\nA new Jacobi elliptic function rational expansion method and its application to (1 + 1)-dimensional dispersive long wave equation. Zbl 1072.35510\nQi, Wang; Yong, Chen; Zhang, Hongqing\n2005\nVariable-coefficient projective Riccati equation method and its application to a new (2 + 1)-dimensional simplified generalized Broer-Kaup system. Zbl 1081.34003\nHuang, Ding-Jiang; Zhang, Hong-Qing\n2005\nExact travelling wave solutions for the Boiti-Leon-Pempinelli equation. Zbl 1067.35085\nHuang, Ding-Jiang; Zhang, Hong-Qing\n2004\nSymbolic computation and construction of soliton-like solutions to the (2+1)-dimensional breaking soliton equation. Zbl 1167.37358\nChen, Yong; Li, Biao; Zhang, Hong-Qing\n2003\nNew extended rational expansion method and exact solutions of Boussinesq equation and Jimbo-Miwa equations. Zbl 1122.65396\nWang, Dan; Sun, Weiwei; Kong, Cuicui; Zhang, Hongqing\n2007\nSymbolic computation and construction of soliton-like solutions for a breaking soliton equation. Zbl 1037.81522\nLi, Biao; Chen, Yong; Xuan, Hengnong; Zhang, Hongqing\n2003\nThe extended Jacobi elliptic function method to solve a generalized Hirota-Satsuma coupled KdV equations. Zbl 1106.35087\nYu, Yaxuan; Wang, Qi; Zhang, Hongqing\n2005\nRational approximation solution of the fractional Sharma-Tasso-Olever equation. Zbl 1157.65074\nSong, Lina; Wang, Qi; Zhang, Hongqing\n2009\nFurther extended sinh-cosh and sin-cos methods and new nontraveling wave solutions of the $$(2+1)$$-dimensional dispersive long wave equations. Zbl 1091.35072\nWang, Deng-Shan; Ren, Yu-Jie; Zhang, Hong-Qing\n2005\nA new generalized algebra method and its application in the $$(2+1)$$-dimensional Boiti-Leon-Pempinelli equation. Zbl 1137.34304\nRen, Yu-Jie; Liu, Shu-Tian; Zhang, Hong-Qing\n2007\nAuto-Bäcklund transformation and exact solutions for modified nonlinear dispersive $$mK(m,n)$$ equations. Zbl 1030.37049\nChen, Yong; Li, Biao; Zhang, Hongqing\n2003\nNew exact solutions for the Konopelchenko-Dubrovsky equation using an extended Riccati equation rational expansion method and symbolic computation. Zbl 1114.65352\nSong, Lina; Zhang, Hongqing\n2007\nThe Hamiltonian system and completeness of symplectic orthogonal system. Zbl 0889.58041\nZhang, Hongqing; Alatancang; Zhong, Wanxie\n1997\nImproved Jacobian elliptic function method and its applications. Zbl 1037.35027\nChen, Huaitang; Zhang, Hongqing\n2003\nExact solutions of a KdV equation hierarchy with variable coefficients. Zbl 1326.35326\nZhang, Sheng; Xu, Bo; Zhang, Hong-Qing\n2014\nThe extended first kind elliptic sub-equation method and its application to the generalized reaction Duffing model. Zbl 1194.35112\nHuang, Ding-Jiang; Zhang, Hong-Qing\n2005\nNew generalized hyperbolic functions and auto-Bäcklund transformation to find new exact solutions of the $$(2+1)$$-dimensional NNV equation. Zbl 1236.35004\nRen, Yujie; Zhang, Hongqing\n2006\nOn a further extended tanh method. Zbl 1008.35007\nLü, Zhuosheng; Zhang, Hongqing\n2003\nExact solutions for two nonlinear wave equations with nonlinear terms of any order. Zbl 1054.35078\nChen, Yong; Li, Biao; Zhang, Hongqing\n2005\nExtended hyperbolic function method and new exact solitary wave solutions of Zakharov equations. Zbl 1202.81039\nHuang, Ding Jiang; Zhang, Hong Qing\n2004\nAnalytic solutions, Darboux transformation operators and supersymmetry for a generalized one-dimensional time-dependent Schrödinger equation. Zbl 1252.35239\nTian, Shou-Fu; Zhou, Sheng-Wu; Jiang, Wu-You; Zhang, Hong-Qing\n2012\nNew function of Mittag-Leffler type and its application in the fractional diffusion-wave equation. Zbl 1142.35479\nYu, Rui; Zhang, Hongqing\n2006\nExplicit $$N$$-fold Darboux transformation and multi-soliton solutions for the $$(1 + 1)$$-dimensional higher-order Broer-Kaup system. Zbl 1129.35449\nHuang, Ding-Jiang; Li, De-Sheng; Zhang, Hong-Qing\n2007\nApplication of the extended homotopy perturbation method to a kind of nonlinear evolution equations. Zbl 1135.65387\nSong, Lina; Zhang, Hongqing\n2008\nHamiltonian structure of the integrable couplings for the multicomponent Dirac hierarchy. Zbl 1134.37027\nYu, Fajun; Zhang, Hongqing\n2008\nConstructing families of soliton-like solutions to a $$(2+1)$$-dimensional breaking soliton equation using symbolic computation. Zbl 1030.35141\nYan, Zhen-Ya; Zhang, Hong-Qing\n2002\nConservation laws, bright matter wave solitons and modulational instability of nonlinear Schrödinger equation with time-dependent nonlinearity. Zbl 1247.35154\nTian, Shou-Fu; Zou, Li; Ding, Qi; Zhang, Hong-Qing\n2012\nA new approach to Bäcklund transformations of nonlinear evolution equations. Zbl 0923.35157\nFan, Engui; Zhang, Hongqing\n1998\nNew exact traveling wave solutions for compound KdV-Burgers equations in mathematical physics. Zbl 0996.35068\nZheng, Xuedong; Xia, Tiecheng; Zhang, Hongqing\n2002\nSymbolic computation and various exact solutions of potential Kadomtsev-Petviashvili equation. Zbl 1045.35066\nLi, Desheng; Zhang, Hongqing\n2003\nNew exact solutions to the generalized coupled Hirota–Satsuma KdV system. Zbl 1072.35584\nYong, Xue-lin; Zhang, Hong-Qing\n2005\nExact solutions for a family of variable-coefficient “reaction–Duffing” equations via the Bäcklund transformation. Zbl 1129.35432\nChen, Yong; Yan, Zhenya; Zhang, Hongqing\n2002\nThe homogeneous balance method for solving nonlinear soliton equations. Zbl 1202.35187\nFan, En Gui; Zhang, Hong Qing\n1998\nA symbolic computational method for constructing exact solutions to difference-differential equations. Zbl 1100.65083\nZhen, Wang; Zhang, Hongqing\n2006\nNew soliton-like and periodic-like solutions for the KdV equation. Zbl 1121.65358\nMei, Jian-qin; Zhang, Hong-qing\n2005\nNew soliton-like solutions to the potential Kadomtsev-Petviashvili (PKP) equation. Zbl 1045.35067\nLi, Desheng; Zhang, Hongqing\n2003\nA $$2+1$$ non-isospectral discrete integrable system and its discrete integrable coupling system. Zbl 1181.37107\nYu, Fajun; Zhang, Hongqing\n2006\nAn exp-function method for new $$N$$-soliton solutions with arbitrary functions of a $$(2+1)$$-dimensional vcBK system. Zbl 1219.35274\nZhang, Sheng; Zhang, Hong-Qing\n2011\nDiscrete Jacobi elliptic function expansion method for nonlinear differential-difference equations. Zbl 1179.35337\nZhang, Sheng; Zhang, Hong-Qing\n2009\nNew exact travelling waves solutions to the combined KdV-MKdV and generalized Zakharov equations. Zbl 1104.35047\nHuang, Ding-Jiang; Zhang, Hong-Qing\n2006\nLarge eddy simulation of mixing layer. Zbl 1107.76336\nYang, W. B.; Zhang, H. Q.; Chan, C. K.; Lin, W. Y.\n2004\nExact solutions for a new class of nonlinear evolution equations with nonlinear term of any order. Zbl 1030.35120\nChen, Yong; Li, Biao; Zhang, Hongqing\n2003\nOn a new algorithm of constructing solitary wave solutions for systems of nonlinear evolution in mathematical physics. Zbl 0962.35159\nYan, Zhenya; Zhang, Hongqing\n2000\nExp-function method for N-soliton solutions of nonlinear evolution equations in mathematical physics. Zbl 1231.35220\nZhang, Sheng; Zhang, Hong-Qing\n2009\nA new extended homotopy perturbation method for nonlinear differential equations. Zbl 1255.65155\nWang, Fei; Li, Wei; Zhang, Hongqing\n2012\nDarboux transformation and new periodic wave solutions of generalized derivative nonlinear Schrödinger equation. Zbl 1184.35297\nTian, Shou-Fu; Zhang, Tian-Tian; Zhang, Hong-Qing\n2009\nSome types of solutions and generalized binary Darboux transformation for the mkp equation with self-consistent sources. Zbl 1187.35224\nTian, Shou-Fu; Wang, Zhen; Zhang, Hong-Qing\n2010\nBäcklund transformation and exact solutions for Whitham-Broer-Kaup equations in shallow water. Zbl 0922.35152\nFan, Engui; Zhang, Hongqing\n1998\nOn a new modified extended tanh-function method. Zbl 1267.37097\nLü, Zhuo-Sheng; Zhang, Hong-Qing\n2003\nA series of new exact solutions to the $$(2+1)$$-dimensional Broer-Kau-Kupershmidt equation. Zbl 1202.35291\nZhi, Hong Yan; Wang, Qi; Zhang, Hong Qing\n2005\nSymmetry reductions, integrability and solitary wave solutions to high-order modified Boussinesq equations with damping term. Zbl 1164.35505\nYan, Zhen-Ya; Xie, Fu-Ding; Zhang, Hong-Qing\n2001\nAn extended method and its application to Whitham-Broer-Kaup equation and two-dimensional perturbed KdV equation. Zbl 1091.35532\nJiao, Xiaoyu; Zhang, Hong-Qing\n2006\nPreliminary group classification for the nonlinear wave equation $$u_{tt}=f(x,u)u_{xx}+g(x,u)$$. Zbl 1175.35085\nSong, Lina; Zhang, Hongqing\n2009\nSymbolic computation and families of Jacobi elliptic function solutions of the $$(2+1)$$-dimensional Nizhnik-Novikov-Veselov equation. Zbl 1087.65600\nWang, Deng Shan; Liu, Yi Fang; Zhang, Hong-Qing\n2005\nLink between travelling waves and first order nonlinear ordinary differential equation with a sixth-degree nonlinear term. Zbl 1142.35570\nHuang, Ding-Jiang; Zhang, Hong-Qing\n2006\nSimilarity reductions for $$2+1$$-dimensional variable coefficient generalized Kadomtsev-Petviashvili equation. Zbl 0965.35153\nYan, Zhenya; Zhang, Hongqing\n2000\nNew exact solutions for modified nonlinear dispersive equations $$mK(m,n)$$ in higher dimensions spaces. Zbl 1073.35052\nChen, Yong; Li, Biao; Zhang, Hongqing\n2004\nNew types of exact solutions for a breaking soliton equation. Zbl 1049.35151\nMei, Jian-qin; Zhang, Hong-qing\n2004\nGeneralized method and new exact wave solutions for $$(2 + 1)$$-dimensional Broer-Kaup-Kupershmidt system. Zbl 1114.65353\nWan, Ying; Song, Lina; Yin, Li; Zhang, Hongqing\n2007\nDynamics in closed and open capillaries. Zbl 1419.76196\nRamakrishnan, T. S.; Wu, P.; Zhang, H.; Wasan, D. T.\n2019\nOn the Lie algebras, generalized symmetries and Darboux transformations of the fifth-order evolution equations in shallow water. Zbl 1321.35190\nTian, Shoufu; Zhang, Yufeng; Feng, Binlu; Zhang, Hongqing\n2015\nOn the integrability of a generalized variable-coefficient forced Korteweg-de Vries equation in fluids. Zbl 1288.35403\nTian, Shou-Fu; Zhang, Hong-Qing\n2014\nExact solutions of a KdV equation hierarchy with variable coefficients. Zbl 1326.35326\nZhang, Sheng; Xu, Bo; Zhang, Hong-Qing\n2014\nA super integrable hierarchy and its nonlinear super integrable Hamiltonian couplings. Zbl 1309.70022\nChen, Xiaohong; Zhang, Hongqing; You, Fucai; Zhang, Daqing\n2014\nRiemann theta functions periodic wave solutions and rational characteristics for the $$(1+1)$$-dimensional and $$(2+1)$$-dimensional Itô equation. Zbl 1258.35011\nTian, Shou-Fu; Zhang, Hong-Qing\n2013\nStability and vibration analysis of axially-loaded shear beam-columns carrying elastically restrained mass. Zbl 1438.74105\nZhang, H.; Kang, Y. A.; Li, X. F.\n2013\nAn extended auxiliary function method and its application in mKdV equation. Zbl 1299.35066\nXiao, Yafeng; Xue, Haili; Zhang, Hongqing\n2013\nPreliminary group classification of the nonlinear differential-difference equations. Zbl 1267.34062\nZhang, Xiaoling; Cong, Yang; Zhang, Hongqing\n2013\nOn the integrability of a generalized variable-coefficient Kadomtsev-Petviashvili equation. Zbl 1232.35144\nTian, Shou-Fu; Zhang, Hong-Qing\n2012\nAnalytic solutions, Darboux transformation operators and supersymmetry for a generalized one-dimensional time-dependent Schrödinger equation. Zbl 1252.35239\nTian, Shou-Fu; Zhou, Sheng-Wu; Jiang, Wu-You; Zhang, Hong-Qing\n2012\nConservation laws, bright matter wave solitons and modulational instability of nonlinear Schrödinger equation with time-dependent nonlinearity. Zbl 1247.35154\nTian, Shou-Fu; Zou, Li; Ding, Qi; Zhang, Hong-Qing\n2012\nA new extended homotopy perturbation method for nonlinear differential equations. Zbl 1255.65155\nWang, Fei; Li, Wei; Zhang, Hongqing\n2012\nDifferential form method for finding symmetries of a $$(2+1)$$-dimensional Camassa-Holm system based on its Lax pair. Zbl 1291.35298\nLv, Na; Mei, Jian-Qin; Zhang, Hong-Qing\n2012\nSuper Riemann theta function periodic wave solutions and rational characteristics for a supersymmetric KdV-Burgers equation. Zbl 1274.35294\nTian, Shou-Fu; Zhang, Hong-Qing\n2012\nAlgebro-geometric solutions to the Fokas-Lenells equation. Zbl 1265.35289\nSun, Yujuan; Wang, Zhen; Zhang, Hongqing\n2012\nLie symmetries of two $$(2+1)$$-dimensional Toda-like lattices by the extended differential form method. Zbl 1323.37042\nLv, Na; Mei, Jian-Qin; Zhang, Hong-Qing\n2012\nA new extended Jacobi elliptic function expansion method and its application to the generalized shallow water wave equation. Zbl 1308.76216\nXiao, Yafeng; Xue, Haili; Zhang, Hongqing\n2012\nFractional sub-equation method and its applications to nonlinear fractional PDEs. Zbl 1242.35217\nZhang, Sheng; Zhang, Hong-Qing\n2011\nA kind of explicit Riemann theta functions periodic waves solutions for discrete soliton equations. Zbl 1221.37153\nTian, Shou-Fu; Zhang, Hong-Qing\n2011\nAn exp-function method for new $$N$$-soliton solutions with arbitrary functions of a $$(2+1)$$-dimensional vcBK system. Zbl 1219.35274\nZhang, Sheng; Zhang, Hong-Qing\n2011\nLie symmetries of two $$(2+1)$$-dimensional differential-difference equations by geometric approach. Zbl 1211.35264\nLv, Na; Mei, Jianqin; Guo, Qilong; Zhang, Hongqing\n2011\nNew exact solutions for some coupled nonlinear partial differential equations using extended coupled sub-equations expansion method. Zbl 1219.35030\nLi, Wei; Yomba, Emmanuel; Zhang, Hongqing\n2011\nSymmetry reductions and explicit solutions of (3+1)-dimensional Burgers system. Zbl 1247.37044\nLv, Na; Mei, Jian-Qin; Zhang, Hong-Qing\n2011\nRiemann theta functions periodic wave solutions and rational characteristics for the nonlinear equations. Zbl 1201.35072\nTian, Shou-Fu; Zhang, Hong-Qing\n2010\nTravelling wave solutions of nonlinear partial equations by using the first integral method. Zbl 1191.35090\nLu, Bin; Zhang, Hongqing; Xie, Fuding\n2010\nSome types of solutions and generalized binary Darboux transformation for the mkp equation with self-consistent sources. Zbl 1187.35224\nTian, Shou-Fu; Wang, Zhen; Zhang, Hong-Qing\n2010\nLax pair, binary Darboux transformation and new Grammian solutions of nonisospectral Kadomtsev – Petviashvili equation with the two-singular-manifold method. Zbl 1213.35365\nTian, Shou-Fu; Zhang, Hong-Qing\n2010\nMore solutions of the auxiliary equation to get the solutions for a class of nonlinear partial differential equations. Zbl 1222.35052\nFeng, Yang; Wang, Dan; Li, Wen-Ting; Zhang, Hong-Qing\n2010\nSymmetry reductions and group-invariant solutions of (2 + 1)-dimensional Caudrey-Dodd-Gibbon-Kotera-Sawada equation. Zbl 1218.35188\nLü, Na; Mei, Jian-Qin; Zhang, Hong-Qing\n2010\nFan sub-equation method for Wick-type stochastic partial differential equations. Zbl 1238.35198\nZhang, Sheng; Zhang, Hong-Qing\n2010\nA generalized sub-equations rational expansion method for nonlinear evolution equations. Zbl 1221.65280\nLi, Wenting; Zhang, Hongqing\n2010\nLie reduction and conditional symmetries of some variable coefficient nonlinear wave equations. Zbl 1220.81090\nHuang, Ding-Jiang; Zhou, Shui-Geng; Mei, Jian-Qin; Zhang, Hong-Qing\n2010\nSoliton solutions by Darboux transformation and some reductions for a new Hamiltonian lattice hierarchy. Zbl 1203.37119\nTian, Shou-Fu; Zhang, Hong-Qing\n2010\nArbitrariness of the general solution of the partial differential equations and its applications. Zbl 1209.35008\nDing, Qi; Zhang, Hongqing\n2010\nSolving the fractional BBM-Burgers equation using the homotopy analysis method. Zbl 1198.65205\nSong, Lina; Zhang, Hongqing\n2009\nRational approximation solution of the fractional Sharma-Tasso-Olever equation. Zbl 1157.65074\nSong, Lina; Wang, Qi; Zhang, Hongqing\n2009\nDiscrete Jacobi elliptic function expansion method for nonlinear differential-difference equations. Zbl 1179.35337\nZhang, Sheng; Zhang, Hong-Qing\n2009\nExp-function method for N-soliton solutions of nonlinear evolution equations in mathematical physics. Zbl 1231.35220\nZhang, Sheng; Zhang, Hong-Qing\n2009\nDarboux transformation and new periodic wave solutions of generalized derivative nonlinear Schrödinger equation. Zbl 1184.35297\nTian, Shou-Fu; Zhang, Tian-Tian; Zhang, Hong-Qing\n2009\nPreliminary group classification for the nonlinear wave equation $$u_{tt}=f(x,u)u_{xx}+g(x,u)$$. Zbl 1175.35085\nSong, Lina; Zhang, Hongqing\n2009\nNew exact solutions to mKdV-Burgers equation and $$(2 + 1)$$-dimensional dispersive long wave equation via extended Riccati equation method. Zbl 1197.35234\nKong, Cuicui; Wang, Dan; Song, Lina; Zhang, Hongqing\n2009\nA new generalized compound Riccati equations rational expansion method to construct many new exact complexiton solutions of nonlinear evolution equations with symbolic computation. Zbl 1197.35238\nLi, Wenting; Zhang, Hongqing\n2009\nVariable-coefficient discrete tanh method and its application to (2+1)-dimensional Toda equation. Zbl 1233.37046\nZhang, Sheng; Zhang, Hong-Qing\n2009\nConstruct solitary solutions of discrete hybrid equation by Adomian decomposition method. Zbl 1197.65113\nWang, Zhen; Zhang, Hongqing\n2009\nPreliminary group classification of quasilinear third-order evolution equations. Zbl 1170.35311\nHuang, Dingjiang; Zhang, Hongqing\n2009\nSymmetry reductions and explicit solutions of a $$(3+1)$$-dimensional PDE. Zbl 1177.35205\nMei, Jianqin; Zhang, Hongqing\n2009\nA new approach for solutions of the $$(2 + 1)$$-dimensional cubic nonlinear Schrödinger equation. Zbl 1197.35268\nZhi, Hongyan; Zhang, Hongqing\n2009\nPfaffianization of the variable-coefficient KP equation. Zbl 1197.37085\nZhang, Yuan-Yuan; Zheng, Ying; Zhang, Hong-Qing\n2009\nApplication of the extended homotopy perturbation method to a kind of nonlinear evolution equations. Zbl 1135.65387\nSong, Lina; Zhang, Hongqing\n2008\nHamiltonian structure of the integrable couplings for the multicomponent Dirac hierarchy. Zbl 1134.37027\nYu, Fajun; Zhang, Hongqing\n2008\nA new auxiliary function method for solving the generalized coupled Hirota-Satsuma KdV system. Zbl 1143.65081\nFeng, Yang; Zhang, Hong-Qing\n2008\nSymbolic computation and a uniform direct ansätze method for constructing travelling wave solutions of nonlinear evolution equations. Zbl 1163.34004\nZhi, Hongyan; Zhang, Hongqing\n2008\nA new compound Riccati equations rational expansion method and its application to the $$(2 + 1)$$-dimensional asymmetric Nizhnik-Novikov-Vesselov system. Zbl 1141.35454\nSong, Li-Na; Wang, Qi; Zhang, Hong-Qing\n2008\nSolitary solution of discrete mKdV equation by homotopy analysis method. Zbl 1392.34080\nWang, Zhen; Zou, Li; Zhang, Hong-Qing\n2008\nSymmetry analysis and exact solutions of $$(2+1)$$-dimensional Sawada-Kotera equation. Zbl 1392.35021\nZhi, Hong-Yan; Zhang, Hong-Qing\n2008\nGeneralized multiple Riccati equations rational expansion method with symbolic computation to construct exact complexiton solutions of nonlinear partial differential equations. Zbl 1135.65385\nLi, Wenting; Zhang, Hongqing\n2008\nThe model $$AC=BD$$ for mathematics mechanization. Zbl 1199.03005\nZhang, Hongqing\n2008\nNew Hamiltonian structure of the fractional C-KdV soliton equation hierarchy. Zbl 1148.37037\nYu, Fajun; Zhang, Hongqing\n2008\nConstructing new discrete integrable coupling system for soliton equation by Kronecker product. Zbl 1392.37061\nYu, Fa-Jun; Zhang, Hong-Qing\n2008\nApplication of extended projective Riccati equation method to $$(2+1)$$-dimensional Broer-Kaup-Kupershmidt system. Zbl 1392.35025\nLu, Bin; Zhang, Hong-Qing\n2008\nApplication of homotopy analysis method to fractional KdV-Burgers-Kuramoto equation. Zbl 1209.65115\nSong, Lina; Zhang, Hongqing\n2007\nApplying homotopy analysis method for solving differential-difference equation. Zbl 1209.65119\nWang, Zhen; Zou, Li; Zhang, Hongqing\n2007\nExplicit and exact travelling wave solutions for the generalized derivative Schrödinger equation. Zbl 1139.35092\nHuang, Ding-Jiang; Li, De-Sheng; Zhang, Hong-Qing\n2007\nA new extended Riccati equation rational expansion method and its application. Zbl 1138.35403\nSong, Li-Na; Wang, Qi; Zheng, Ying; Zhang, Hong-Qing\n2007\nNew extended rational expansion method and exact solutions of Boussinesq equation and Jimbo-Miwa equations. Zbl 1122.65396\nWang, Dan; Sun, Weiwei; Kong, Cuicui; Zhang, Hongqing\n2007\nA new generalized algebra method and its application in the $$(2+1)$$-dimensional Boiti-Leon-Pempinelli equation. Zbl 1137.34304\nRen, Yu-Jie; Liu, Shu-Tian; Zhang, Hong-Qing\n2007\nNew exact solutions for the Konopelchenko-Dubrovsky equation using an extended Riccati equation rational expansion method and symbolic computation. Zbl 1114.65352\nSong, Lina; Zhang, Hongqing\n2007\nExplicit $$N$$-fold Darboux transformation and multi-soliton solutions for the $$(1 + 1)$$-dimensional higher-order Broer-Kaup system. Zbl 1129.35449\nHuang, Ding-Jiang; Li, De-Sheng; Zhang, Hong-Qing\n2007\nGeneralized method and new exact wave solutions for $$(2 + 1)$$-dimensional Broer-Kaup-Kupershmidt system. Zbl 1114.65353\nWan, Ying; Song, Lina; Yin, Li; Zhang, Hongqing\n2007\nApplications of the combined tanh function method with symmetry method to the nonlinear evolution equations. Zbl 1114.65356\nZhi, Hongyan; Zhang, Hongqing\n2007\nA new variable coefficient Korteweg-de Vries equation-based sub-equation method and its application to the $$(3 + 1)$$-dimensional potential-YTSF equation. Zbl 1122.65394\nSong, Lina; Zhang, Hongqing\n2007\nA new loop algebra system and its discrete integrable coupling system. Zbl 1133.37336\nYu, Fajun; Zhang, Hongqing\n2007\nNew complexiton solutions of the nonlinear evolution equations using a generalized rational expansion method with symbolic computation. Zbl 1122.65395\nSong, Lina; Zhang, Hongqing\n2007\nA new extended elliptic equation rational expansion method and its application to $$(2+1)$$-dimensional Burgers equation. Zbl 1132.35343\nWang, Bao-Dong; Song, Li-Na; Zhang, Hong-Qing\n2007\nMany new exact solutions to $$(2+1)$$-dimensional Burgers equation and Klein-Gordon equation using symbolic computation. Zbl 1115.35116\nWang, Zhen; Zhang, Hong-Qing\n2007\nA new generalized Riccati equation rational expansion method to a class of nonlinear evolution equations with nonlinear terms of any order. Zbl 1114.65125\nZhang, Xiao-Ling; Zhang, Hongqing\n2007\nA new fractional order soliton equation hierarchy and its integrable coupling system. Zbl 1193.37095\nYu, Fajun; Zhang, Hongqing\n2007\nGeneralized Riccati equation rational expansion method and its application. Zbl 1123.65107\nZheng, Ying; Zhang, Yuanyuan; Zhang, Hongqing\n2007\nThe extension of the Jacobi elliptic function rational expansion method. Zbl 1111.35069\nYu, Yaxuan; Wang, Qi; Zhang, Hongqing\n2007\nFractional zero curvature equation and generalized Hamiltonian structure of soliton equation hierarchy. Zbl 1138.26002\nYu, Fa-Jun; Zhang, Hong-Qing\n2007\nA new coupled sub-equations expansion method and novel complexiton solutions of (2 + 1)-dimensional Burgers equation. Zbl 1114.65123\nWang, Qi; Song, Lina; Zhang, Hongqing\n2007\nA method for constructing discrete exact solutions and application to quintic discrete nonlinear Schrödinger equation. Zbl 1134.34321\nZhen, Wang; Zhang, Hongqing\n2007\nSoliton-like and periodic form solutions to $$(2+1)$$-dimensional Toda equation. Zbl 1138.35404\nWang, Zhen; Zhang, Hongqing\n2007\nConstructing a multi-function equation hierarchy and its integrable coupling system with MAPLE. Zbl 1114.65362\nYu, Fajun; Zhang, Hongqing\n2007\nUpper triangular matrix of Lie algebra and a new discrete integrable coupling system. Zbl 1355.37088\nYu, Fa-Jun; Zhang, Hong-Qing\n2007\nA generalized F-expansion method to find abundant families of Jacobi elliptic function solutions of the $$(2+1)$$-dimensional Nizhnik-Novikov-Veselov equation. Zbl 1088.35536\nRen, Yujie; Zhang, Hongqing\n2006\nImproved Jacobi-function method with symbolic computation to construct new double-periodic solutions for the generalized Ito system. Zbl 1134.35301\nZhao, Xueqin; Zhi, Hongyan; Zhang, Hongqing\n2006\nThe multi-component TD hierarchy and its multi-component integrable coupling system with five arbitrary functions. Zbl 1102.37044\nYu, Fajun; Xia, Tiecheng; Zhang, Hongqing\n2006\nNew generalized hyperbolic functions and auto-Bäcklund transformation to find new exact solutions of the $$(2+1)$$-dimensional NNV equation. Zbl 1236.35004\nRen, Yujie; Zhang, Hongqing\n2006\nNew function of Mittag-Leffler type and its application in the fractional diffusion-wave equation. Zbl 1142.35479\nYu, Rui; Zhang, Hongqing\n2006\nA symbolic computational method for constructing exact solutions to difference-differential equations. Zbl 1100.65083\nZhen, Wang; Zhang, Hongqing\n2006\nA $$2+1$$ non-isospectral discrete integrable system and its discrete integrable coupling system. Zbl 1181.37107\nYu, Fajun; Zhang, Hongqing\n2006\nNew exact travelling waves solutions to the combined KdV-MKdV and generalized Zakharov equations. Zbl 1104.35047\nHuang, Ding-Jiang; Zhang, Hong-Qing\n2006\nAn extended method and its application to Whitham-Broer-Kaup equation and two-dimensional perturbed KdV equation. Zbl 1091.35532\nJiao, Xiaoyu; Zhang, Hong-Qing\n2006\nLink between travelling waves and first order nonlinear ordinary differential equation with a sixth-degree nonlinear term. Zbl 1142.35570\nHuang, Ding-Jiang; Zhang, Hong-Qing\n2006\nA new Riccati equation expansion method with symbolic computation to construct new travelling wave solution of nonlinear differential equations. Zbl 1088.65095\nZhao, Xueqin; Zhi, Hongyan; Yu, Yaxuan; Zhang, Hongqing\n2006\nNew exact solutions of the Broer-Kaup equations in (2 + 1)-dimensional spaces. Zbl 1102.65104\nSong, Lina; Zhang, Hongqing\n2006\nOn stabilization of energy for Hamiltonian systems. Zbl 1196.37095\nWu, X.; Zhu, J. F.; He, J. Z.; Zhang, H.\n2006\nA new general algebraic method with symbolic computation and its application to two nonlinear differential equations with nonlinear terms of any order. Zbl 1107.65091\nWang, Jing; Zhang, Xiaoling; Song, Lina; Zhang, Hongqing\n2006\n...and 143 more Documents\nall top 5" ]

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[ "# 26 increased by 2 percent\n\nHere you will see step by step solution to calculate 26 increased by 2 percent. What is 26 increased by 2%? It is 26.52, and the increase is 0.52. Check the detailed explanation of answer given below.\n\n## Answer: 26 increased by 2% is\n\n= 26.52\n\n### How to increase the number 26 by 2 percent?\n\nWith the help of given formula we can get the the percent increase value -\n\nformula 1: Percentage increase = P% × n, P = Percent, n = Number\n\nformula 2: Result = n + Percentage increase\nHere we have, n = 26, P = 2%\n\n#### Solution for 26 increased by 2 percent(2%) -\n\nGiven number n = 26, P = 2%\n\n• Put the n and P values in the given formula:\n• => 2% × 26\n=> 2/100 × 26\n\n• Now we need to simplify the fraction by multiply 2 with 26, then divide it by 100\n• => 2 × 26/100 = 52/100 = 0.52\n• Percentage Increase = 0.52\n• Now we will use formula 2 to get the value of 26 increased by 2%\n• = 26 + 0.52\n= 26.52\n\nTherefore, result is for 26 increased by 2% is 26.52 and increase is 0.52.\n\nNumber:\nIncreased by\n%" ]

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[ "# ncl_c_ftcurvp - Man Page\n\n1D interpolation for periodic functions\n\n## Function Prototype\n\nint c_ftcurvp (int, float [], float [], float, int, float [], float []);\n\n## Synopsis\n\n`int c_ftcurvp (n, xi, yi, p, m, xo, yo);`\n\n## Description\n\nn\n\nThe number of input data points. (n > 1)\n\nxi\n\nAn array containing the abscissae for the input function.\n\nyi\n\nAn array containing the input functional values (y(k) is the  functional value at x(k) for k=0,n).\n\np\n\nThe period of the function; p must not be less than xi[n-1] - xi.\n\nm\n\nThe number of desired interpolated points.\n\nxo\n\nAn array containing the abscissae for the interpolated values.\n\nyo\n\nAn array containing the interpolated functional values  (yo(k) is the functional value at xo(k) for k=0,n).\n\n## Return Value\n\nc_ftcurvp returns an error value as per:\n\n= 0 -- no error.\n= 1 -- if n is less than 2.\n= 2 -- if the period is strictly less than the span of the abscissae.\n\n## Usage\n\nc_ftcurvp is called after all of the desired values for control parameters  have been set using the procedures c_ftseti, c_ftsetr, c_ftsetc.  Control parameters that apply to c_ftcurvp are: sig.\n\n## Access\n\nTo use c_ftcurvp, load the NCAR Graphics library ngmath." ]

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[ "# Convert Pound to Short Ton (lb to shton)\n\nIn next fields, kindly type your value in the text box under title [ From: ] to convert from pound to Short ton (lb to shton). As you type your value, the answer will be automatically calculated and displayed in the text box under title [ To: ].\n\nFrom:\nTo:\nDefinitions:\n\nPound (abbreviations: lb, or lbs, or ps): is a unit of force used in some systems of measurement including English Engineering units and the British Gravitational System. Also, it is a unit of mass used in the imperial, United States customary and other systems of measurement.\n\nShort Ton (abbreviations: shton, or ton U.S.): is a non-SI metric unit of mass. Although, it is used principally as a unit of mass, it has acquired a number of meanings and uses over long years. It is equivalent to 907.2 kilograms (Kg), or approximately 2000 pounds (lb), or 0.9072 metric tons, or 0.892913 long tons (imperial).\n\n << Prev Next >>\n\n## How to Convert Pounds to Short Tons\n\n### Example: How many Short tons are equivalent to 1.68 pounds?\n\nAs;\n\n1 pounds = 0.0005 Short tons\n\n1.68 pounds = Y Short tons\n\nAssuming Y is the answer, and by criss-cross principle;\n\nY equals 1.68 times 0.0005 over 1\n\n(i.e.) Y = 1.68 * 0.0005 / 1 = 0.00084 Short tons\n\nAnswer is: 0.00084 Short tons are equivalent to 1.68 pounds.\n\n### Practice Question: Convert the following units into shton:\n\nN.B.: After working out the answer to each of the next questions, click adjacent button to see the correct answer.\n\n( i ) 43.71 lb\n\n( ii ) 21.88 lb\n\n( iii ) 18.63 lb\n\nReferences\n•", null, "•", null, "•", null, "" ]

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[ "# 31752\n\n## 31,752 is an even composite number composed of three prime numbers multiplied together.\n\nWhat does the number 31752 look like?\n\nThis visualization shows the relationship between its 3 prime factors (large circles) and 60 divisors.\n\n31752 is an even composite number. It is composed of three distinct prime numbers multiplied together. It has a total of sixty divisors.\n\n## Prime factorization of 31752:\n\n### 23 × 34 × 72\n\n(2 × 2 × 2 × 3 × 3 × 3 × 3 × 7 × 7)\n\nSee below for interesting mathematical facts about the number 31752 from the Numbermatics database.\n\n### Names of 31752\n\n• Cardinal: 31752 can be written as Thirty-one thousand, seven hundred fifty-two.\n\n### Scientific notation\n\n• Scientific notation: 3.1752 × 104\n\n### Factors of 31752\n\n• Number of distinct prime factors ω(n): 3\n• Total number of prime factors Ω(n): 9\n• Sum of prime factors: 12\n\n### Divisors of 31752\n\n• Number of divisors d(n): 60\n• Complete list of divisors:\n• Sum of all divisors σ(n): 103455\n• Sum of proper divisors (its aliquot sum) s(n): 71703\n• 31752 is an abundant number, because the sum of its proper divisors (71703) is greater than itself. Its abundance is 39951\n\n### Bases of 31752\n\n• Binary: 1111100000010002\n• Base-36: OI0\n\n### Squares and roots of 31752\n\n• 31752 squared (317522) is 1008189504\n• 31752 cubed (317523) is 32012033131008\n• The square root of 31752 is 178.1909088591\n• The cube root of 31752 is 31.6657925275\n\n### Scales and comparisons\n\nHow big is 31752?\n• 31,752 seconds is equal to 8 hours, 49 minutes, 12 seconds.\n• To count from 1 to 31,752 would take you about eight hours.\n\nThis is a very rough estimate, based on a speaking rate of half a second every third order of magnitude. If you speak quickly, you could probably say any randomly-chosen number between one and a thousand in around half a second. Very big numbers obviously take longer to say, so we add half a second for every extra x1000. (We do not count involuntary pauses, bathroom breaks or the necessity of sleep in our calculation!)\n\n• A cube with a volume of 31752 cubic inches would be around 2.6 feet tall.\n\n### Recreational maths with 31752\n\n• 31752 backwards is 25713\n• 31752 is a Harshad number.\n• The number of decimal digits it has is: 5\n• The sum of 31752's digits is 18\n• More coming soon!" ]

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[ "# Ray¶", null, "", null, "Ray is a fast and simple framework for building and running distributed applications.\n\nTip\n\nRay is packaged with the following libraries for accelerating machine learning workloads:\n\nStar us on on GitHub. You can also get started by visiting our Tutorials. For the latest wheels (nightlies), see the installation page.\n\n## Quick Start¶\n\nFirst, install Ray with: `pip install ray`\n\n```# Execute Python functions in parallel.\n\nimport ray\nray.init()\n\[email protected]\ndef f(x):\nreturn x * x\n\nfutures = [f.remote(i) for i in range(4)]\nprint(ray.get(futures))\n```\n\nTo use Ray’s actor model:\n\n```import ray\nray.init()\n\[email protected]\nclass Counter(object):\ndef __init__(self):\nself.n = 0\n\ndef increment(self):\nself.n += 1\n\nreturn self.n\n\ncounters = [Counter.remote() for i in range(4)]\n[c.increment.remote() for c in counters]\nfutures = [c.read.remote() for c in counters]\nprint(ray.get(futures))\n```\n\nVisit the Walkthrough page a more comprehensive overview of Ray features.\n\nRay programs can run on a single machine, and can also seamlessly scale to large clusters. To execute the above Ray script in the cloud, just download this configuration file, and run:\n\n`ray submit [CLUSTER.YAML] example.py --start`\n\n## Tune Quick Start¶\n\nTune is a library for hyperparameter tuning at any scale. With Tune, you can launch a multi-node distributed hyperparameter sweep in less than 10 lines of code. Tune supports any deep learning framework, including PyTorch, TensorFlow, and Keras.\n\nNote\n\nTo run this example, you will need to install the following:\n\n```\\$ pip install ray torch torchvision filelock\n```\n\nThis example runs a small grid search to train a CNN using PyTorch and Tune.\n\n```import torch.optim as optim\nfrom ray import tune\nfrom ray.tune.examples.mnist_pytorch import get_data_loaders, ConvNet, train, test\n\ndef train_mnist(config):\nmodel = ConvNet()\noptimizer = optim.SGD(model.parameters(), lr=config[\"lr\"])\nfor i in range(10):\ntune.track.log(mean_accuracy=acc)\n\nanalysis = tune.run(\ntrain_mnist, config={\"lr\": tune.grid_search([0.001, 0.01, 0.1])})\n\nprint(\"Best config: \", analysis.get_best_config(metric=\"mean_accuracy\"))\n\n# Get a dataframe for analyzing trial results.\ndf = analysis.dataframe()\n```\n\nIf TensorBoard is installed, automatically visualize all trial results:\n\n```tensorboard --logdir ~/ray_results\n```\n\n## RLlib Quick Start¶\n\nRLlib is an open-source library for reinforcement learning built on top of Ray that offers both high scalability and a unified API for a variety of applications.\n\n```pip install tensorflow # or tensorflow-gpu\npip install ray[rllib] # also recommended: ray[debug]\n```\n```import gym\nfrom gym.spaces import Discrete, Box\nfrom ray import tune\n\nclass SimpleCorridor(gym.Env):\ndef __init__(self, config):\nself.end_pos = config[\"corridor_length\"]\nself.cur_pos = 0\nself.action_space = Discrete(2)\nself.observation_space = Box(0.0, self.end_pos, shape=(1, ))\n\ndef reset(self):\nself.cur_pos = 0\nreturn [self.cur_pos]\n\ndef step(self, action):\nif action == 0 and self.cur_pos > 0:\nself.cur_pos -= 1\nelif action == 1:\nself.cur_pos += 1\ndone = self.cur_pos >= self.end_pos\nreturn [self.cur_pos], 1 if done else 0, done, {}\n\ntune.run(\n\"PPO\",\nconfig={\n\"env\": SimpleCorridor,\n\"num_workers\": 4,\n\"env_config\": {\"corridor_length\": 5}})\n```" ]

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[ "# [JSOI2018]潜入行动\n\n## 输入输出样例\n\n### 输入样例 #1\n\n5 3\n1 2\n2 3\n3 4\n4 5\n\n### 输出样例 #1\n\n1\n\n## 说明\n\n**样例 1 解释** 样例数据是一条链 $1-2-3-4-5$ 。首先，节点 $2$ 和 $4$ 必须放置监听设备，否则 $1,5$ 将无法被监听（放置的监听设备无法监听它所在的节点）。剩下一个设备必须放置在 $3$ 号节点以同时监听 $2,4$ 。因此在 $2,3,4$ 节点放置监听设备是唯一合法的方案。 **数据范围** 存在 $10\\%$ 的数据，$1 \\le n \\le 20$ ； 存在另外 $10\\%$ 的数据，$1 \\le n \\le 100$ ； 存在另外 $10\\%$ 的数据，$1 \\le k \\le 10$ ； 存在另外 $10\\%$ 的数据，输入的树保证是一条链； 对于所有数据，$1\\le n\\le 10^5$​ ，$1\\le k\\le \\min\\{n,100\\}$ 。" ]

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[ "# Question #8f4d7\n\nSep 13, 2016\n\n${55.8}^{\\circ}$, rounded to one decimal place.\n\n#### Explanation:\n\nGiven two vectors\n$\\vec{S}$, with $| \\vec{S} | = 4$ and $\\vec{R}$, with $| \\vec{R} | = 6$\nLet $\\theta$ be the angle between the two.\nBy definition of dot product we have\n$\\vec{S} \\cdot \\vec{R} = | \\vec{S} | | \\vec{R} | \\cos \\theta$\nEquating to the given value we get\n$| \\vec{S} | | \\vec{R} | \\cos \\theta = 13.5$\n$\\implies 4 \\times 6 \\cos \\theta = 13.5$\n$\\implies \\cos \\theta = \\frac{13.5}{24} = 0.5625$\n$\\implies \\theta = {\\cos}^{-} 1 0.5625$\n$\\implies \\theta = {55.8}^{\\circ}$, rounded to one decimal place." ]

[ null ]

[ "Solutions by everydaycalculation.com\n\n## Multiply 12/56 with 30/18\n\n1st number: 12/56, 2nd number: 1 12/18\n\nThis multiplication involving fractions can also be rephrased as \"What is 12/56 of 1 12/18?\"\n\n12/56 × 30/18 is 5/14.\n\n#### Steps for multiplying fractions\n\n1. Simply multiply the numerators and denominators separately:\n2. 12/56 × 30/18 = 12 × 30/56 × 18 = 360/1008\n3. After reducing the fraction, the answer is 5/14\n\nMathStep (Works offline)", null, "Download our mobile app and learn to work with fractions in your own time:" ]

[ null, "https://answers.everydaycalculation.com/mathstep-app-icon.png", null ]

[ "## Class 9th\n\n###### Personalized Tuition\n• Personal tutor\n• Personal attention\n• Two way interaction\n• No risk of travel (Learn at Home)\n• Learn at your convenient time\n• No hassle for parents to monitor their kids\n###### Class 9th Mathematics Live Class\n\nOnlinePadho ensures that you get all the important information of all subjects included in the syllabus. Class 9th is an essential level in CBSE. It builds the base for the 10th examinations for students. This is why OnlinePadho assures that you can manage all the subjects of Class 9 according to NCERT.\n\nThe passion for adapting consistently starts with a teacher who trusts in you. Our package comes up with excellent .\n\n#### Mathematics syllabus for Class 9\n\nReal Numbers\n\nRepresentation of Intergers, Fractions, Decimals on a Number Line, Insert Rational Numbers between Two Rational Numbers, Terminating Decimals, Irrational Numbers, Its Properties and Number Line Representation, Rationalisation, Exponents and Powers.\n\nPolynomials\n\nIntroduction of Polynomial, Zeroes of a Polynomial, Remainder Theorem, Factor Theorem, Factorization by Grouping, Factorization by Splitting Middle Term, Factorization by Identities, Expansion Using Identities.\n\nLinear Equations in Two Variables\n\nGraph of ax + by + c = 0.\n\nCoordinate Geometry\n\nRepresent a Point on a Coordinate Axes , Graph of y = mx + c.\n\nIntroduction to Euclid's Geometry\n\nIntroduction of Euclid's Geometry.\n\nLines and Angles\n\nComplementary and Supplementary Angles, Linear Pair and Vertically Opposite Angles, Results on Parallel Lines, Angle Sum and Exterior Angle Properties.\n\nCongruence of Triangles\n\nSAS, SSS, ASA, AAS and RHS Congruency, Inequality of Triangles.\n\nTypes of Quadrlaterals, Angle Sum Properties, Results on Parallelograms, Intercept Theorem, Midpoint Theorem.\n\nAreas of Parallelograms and Triangles\n\nTwo Parallelograms, Two Triangles, Parallelogran and Triangle.\n\nCircles\n\nArc and Chord Properties of Circle, Angles Subtended by Arcs, Cyclic Quadrilaterals.\n\nConstructions\n\nBisectors of Lines and Angles, Construction of Triangles.\n\nHeron's Formula\n\nArea of Triangle, Area of Triangle (Heron's Formula).\n\nVolume and Surface Area\n\nSurface Area and Volume of Cuboid and Cube, Surface Area and Volume of Right Circular Cylinder, Surface Area and Volume of Right Circular Cone, Surface Area and Volume of Sphere and Hemisphere.\n\nStatistics\n\nFrequency Distribution, Graphical Representation of Data : Bar Graph, Histogram, Frequency Polygon, Arithmetic Mean and its Properties, Mean, Median, Mode.\n\nProbability\n\nProbability." ]

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[ "(1980 \"The order parameter for spin glasses: a function on the interval 0-1\" giochi di poker per bambini (PDF.\nContents, magnetic behavior edit, it is the time dependence which distinguishes spin glasses from other magnetic systems.The Hamiltonian for SK model is very similar to the EA model: H i j J i j S i S j displaystyle H-sum _i jJ_ijS_iS_j where J i j, S i, S j displaystyle J_ij, S_i,S_j have same meanings as in the EA model.Statistical Physics of Spin Glasses and Information Processing: An Introduction.Hence the new set of order parameters describing the three magnetic phases consists of both m displaystyle m and q displaystyle.3 f 2 J 2 q r 4 lotto archivio 1977 r 2 J 2 q r 2 2 J 2 4 J 0 r m r 2 r 2 J 2 q r exp ( z 2 2 ) log ( 2 cosh ( J.(1987 \"Spin glasses and the statistical mechanics of protein folding Proceedings of the National Academy of Sciences, 84 (21 75247528, Bibcode : 1987pnas.84.7524B, doi :.1073/pnas.84.21.7524, PMC 299331, pmid 3478708.The order parameter for the ferromagnetic to spin glass phase transition is therefore q displaystyle q, and that for paramagnetic to spin glass is again q displaystyle.\"Spin Glass IV: Glimmerings of Trouble\".Magnetization then decays slowly as it approaches zero (or some small fraction of the original valuethis remains unknown).\n(2014 \"Spin Glasses in Cu0.5Fe0.5Cr2S4 - Based Solid Solutions Inorganic Materials, 50 (13 134300, doi :.1134/s, issn External links edit).\nIn this limit, it can be seen that the probability of the spin glass existing in a particular state, depends only on the energy of that state and not on the individual spin configurations.", null, "1 Spin glasses differ from ferromagnetic materials by the fact that after the external magnetic field is removed from a ferromagnetic substance, the magnetization remains indefinitely at the remanent value.A gaussian distribution of magnetic bonds across the lattice is assumed usually to solve this model.Anderson in Physics Today.3 The Hamiltonian for this spin system is given by: H i j J i j S i S j, displaystyle H-sum _langle ijrangle J_ijS_iS_j, where S i displaystyle S_i refers to the Pauli spin matrix for the spin-half particle at lattice point i displaystyle.A negative value of J i j displaystyle J_ij denotes an antiferromagnetic type interaction between spins at points i displaystyle i and j displaystyle.\"Spin Glass VI: Spin Glass As Cornucopia\".Chaos in spin glasses, usually considered for finite-dimensional spin glasses, is also present in the fully connected model.Gardner, E; Deridda,.The equilibrium solution of the model, after some initial attempts by Sherrington, Kirkpatrick and others, was found by Giorgio Parisi in 1979 with the replica method.Unlike the EdwardsAnderson (EA) model, in the system though only two-spin interactions are considered, the range of each interaction can be potentially infinite (of the order of the size of the lattice).The term \"glass\" comes from an analogy between the magnetic disorder in a spin glass and the positional disorder of a conventional, chemical glass,.g., a window glass.See also edit T c displaystyle T_c is identical with the so-called \"freezing temperature\" T f displaystyle T_f The hierarchical disorder of the energy landscape matematica poker texas holdem may be verbally characterized by a single sentence: in this landscape there are random) valleys within still deeper (random) valleys.\"Optimal storage properties of neural network models\".\nThis decay is non-exponential and no simple function can fit the curve of magnetization versus time adequately.\nUpon reaching T c, the sample becomes a spin glass and further cooling results in little change in magnetization.", null, "The mathematical complexity of these structures is difficult but fruitful to study experimentally or in simulations, with applications to artificial neural networks in computer science, in addition to physics, chemistry, and materials science.\nThe distribution of values of J i j displaystyle J_ij is taken to be a gaussian with a mean J 0 displaystyle J_0 and a variance J 2 displaystyle J2 : P ( J i j ) N 2 J 2 exp N.\nHere it is shown, using a modified interpolating Hamiltonian technique, that the fluctuations are closely connected to an apparently unrelated phenomenon, namely bond chaos." ]

[ null, "https://artisons-coop.eu/imgs/2019-04/14552825431_spin-glass-free-energyj.jpg", null, "https://artisons-coop.eu/imgs/2019-04/14552825120_spin-glass-free-energyj.jpg", null ]

[ "", null, "# HTML, CSS, JS, jQuery, XML, SQL, PLSQL Tutorials", null, "Everyone\n28\nWay2tutorial - The Prime App to Learn Interactive Web Development Tutorials, examples, and references completely Free\n\nHTML Tutorial\nCSS Tutorial\nJavaScript Tutorial\njQuery Tutorial\nAJAX Tutorial\nXML Tutorial\nSQL Tutorial\nPL/SQL Tutorial\n\nHTML Tutorial Features\n2. This HTML tutorial will teach you the latest HTML5 standards.\n3. Learn HTML with 40+ HTML Lessons.\n4. Every lesson are detailed explanations that help you effectively learn HTML.\n5. Learn HTML with 150+ HTML examples.\n6. Try It Yourself with every example.\n7. List out all HTML tags references.\n\nCSS Tutorial Features\n1. Learn CSS3 tutorials, CSS properties.\n2. All CSS lesson are updated as latest standards of CSS.\n3. Learn CSS with 45+ CSS Lessons.\n4. Every lesson are step by step explain that help you quickly learn CSS.\n5. Learn CSS with 120+ CSS examples.\n6. Try It Yourself with every CSS example.\n7. List out all CSS properties reference.\n\nJavaScript Tutorial Features\n1. Completely free learn JavaScript tutorials.\n2. All JavaScript lesson are updated as per latest ECMAScript 6 standard.\n3. Learn JavaScript with 40+ JavaScript Lesson.\n4. Every lesson are explain step by step that help you to understand quickly.\n5. Learn JavaScript with 75+ JavaScipt examples.\n6. Try It Yourself with every JavaScript example.\n\njQuery Tutorial Features\n3. Learn jQuery with 40+ jQuery Lessons.\n4. Every jQuery lesson are explain with demo example that will help you more effectively.\n5. Learn jQuery with 75+ jQuery examples.\n6. Try It Yourself with every jQuery example.\n\nAjax Tutorial Features\n1. Learn Ajax with 10+ Ajax Lessons with examples.\n2. Try It Yourself with every jQuery example.\n\nXML, DTD, XPATH Tutorial Features\n1. Learn XML, DTD, XPATh tutorials on this App.\n2. Learn XML with 10+ XML Lessons.\n3. Learn DTD with 10+ DTD Lessons.\n4. Learn XPATH with 10+ XPATH Lessons.\n5. Every XPATH lesson are explain step by step with example.\n\nSQL Tutorial Features\n2. Learn SQL with 45+ SQL Lessons with examples.\n3. Every SQL tutorial lesson explain step by step with sample SQL Query examples.\n4. Quick learn SQL Constraints, SQL Joins, SQL functions.\n\nPL/SQL Tutorial Features\n2. Learn PL/SQL with 15+ SQL Lessons with examples.\n3. Every PL/SQL lesson explain step by step with sample example.\n4. You will learn PL/SQL data types, conditions, looping, type of cursor, how to handling PL/SQL exceptions, how to define PL/SQL functions, procedures, packages, and PL/SQL Trigger.\n\nWe're always excited to hear from you! If you have any feedback, question or concerns, please email us at -\n\[email protected]\nCollapse\n\n## Reviews\n\nReview policy and info\n4.2\n28 total\n5\n4\n3\n2\n1\n\nUpdated\nMay 30, 2018\nSize\n1.9M\nInstalls\n5,000+\nCurrent Version\n1.0\nRequires Android\n4.0.3 and up\nContent Rating\nEveryone\nPermissions\nOffered By\nSevenSense Technologies" ]

[ null, "https://play-lh.googleusercontent.com/Raks6VnSjkZMg8dK4W1l6Jyl7XPvIQpXEVBWTooVyatoOla_pHlU9h9FWXnf8_ld-rN0=s180", null, "https://play-lh.googleusercontent.com/IciOnDFecb5Xt50Q2jlcNC0LPI7LEGxNojroo-s3AozcyS-vDCwtq4fn7u3wZmRna8OewG9PBrWC-i7i=s14", null ]

[ "# Distributed symmetric function computation in noisy wireless sensor networks with binary data\n\nLei Ying, R. Srikant, Geir E. Dullerud\n\nResearch output: Chapter in Book/Report/Conference proceedingConference contribution\n\n7 Citations (Scopus)\n\n### Abstract\n\nWe consider a wireless sensor network consisting of n sensors, each having a recorded bit, sensors measurement, which has been set to either 0 or 1. network has a special node called fusion center whose goal is to compute a symmetric function of these bits; i.e., a function that depends only on number of sensors that have a 1. sensors convey information to fusion center in a multi-hop fashion to enable function computation. problem studied is to minimize total transmission energy used by network when computing this function, subject to constraint that this computation is correct with high probability. We assume wireless channels are binary symmetric channels with a probability of error p, and that each sensor uses rαunits of energy to transmit each bit, where r is transmission range of sensor. main result in this paper is an algorithm whose energy usage is Θ (n(loglogn)(logn/n)α), and we also show that any algorithm satisfying performance constraints must necessarily have energy usage Ω (n(logn/n)α). Then, we consider case where sensor network observes N events, and each node records one bit per event, thus having N bits to convey. fusion center now wants to compute N symmetric functions, one for each of events.\n\nOriginal language English (US) 2006 4th International Symposium on Modeling and Optimization in Mobile, Ad Hoc and Wireless Networks, WiOpt 2006 https://doi.org/10.1109/WIOPT.2006.1666455 Published - 2006 Yes 2006 4th International Symposium on Modeling and Optimization in Mobile, Ad Hoc and Wireless Networks, WiOpt 2006 - Boston, MA, United StatesDuration: Feb 26 2006 → Mar 2 2006\n\n### Other\n\nOther 2006 4th International Symposium on Modeling and Optimization in Mobile, Ad Hoc and Wireless Networks, WiOpt 2006 United States Boston, MA 2/26/06 → 3/2/06\n\n### Fingerprint\n\nBinary Data\nSymmetric Functions\nWireless Sensor Networks\nWireless sensor networks\nSensor\nSensors\nFusion\nFusion reactions\nEnergy\nMulti-hop\nVertex of a graph\nSensor networks\nSensor Networks\nBinary\nMinimise\nComputing\nRange of data\n\n### ASJC Scopus subject areas\n\n• Computer Networks and Communications\n• Modeling and Simulation\n\n### Cite this\n\nYing, L., Srikant, R., & Dullerud, G. E. (2006). Distributed symmetric function computation in noisy wireless sensor networks with binary data. In 2006 4th International Symposium on Modeling and Optimization in Mobile, Ad Hoc and Wireless Networks, WiOpt 2006 https://doi.org/10.1109/WIOPT.2006.1666455\n\nDistributed symmetric function computation in noisy wireless sensor networks with binary data. / Ying, Lei; Srikant, R.; Dullerud, Geir E.\n\n2006 4th International Symposium on Modeling and Optimization in Mobile, Ad Hoc and Wireless Networks, WiOpt 2006. 2006. 1666455.\n\nResearch output: Chapter in Book/Report/Conference proceedingConference contribution\n\nYing, L, Srikant, R & Dullerud, GE 2006, Distributed symmetric function computation in noisy wireless sensor networks with binary data. in 2006 4th International Symposium on Modeling and Optimization in Mobile, Ad Hoc and Wireless Networks, WiOpt 2006., 1666455, 2006 4th International Symposium on Modeling and Optimization in Mobile, Ad Hoc and Wireless Networks, WiOpt 2006, Boston, MA, United States, 2/26/06. https://doi.org/10.1109/WIOPT.2006.1666455\nYing L, Srikant R, Dullerud GE. Distributed symmetric function computation in noisy wireless sensor networks with binary data. In 2006 4th International Symposium on Modeling and Optimization in Mobile, Ad Hoc and Wireless Networks, WiOpt 2006. 2006. 1666455 https://doi.org/10.1109/WIOPT.2006.1666455\nYing, Lei ; Srikant, R. ; Dullerud, Geir E. / Distributed symmetric function computation in noisy wireless sensor networks with binary data. 2006 4th International Symposium on Modeling and Optimization in Mobile, Ad Hoc and Wireless Networks, WiOpt 2006. 2006.\n@inproceedings{230373ba1c5347df98864eb20ba5f5b4,\ntitle = \"Distributed symmetric function computation in noisy wireless sensor networks with binary data\",\nabstract = \"We consider a wireless sensor network consisting of n sensors, each having a recorded bit, sensors measurement, which has been set to either 0 or 1. network has a special node called fusion center whose goal is to compute a symmetric function of these bits; i.e., a function that depends only on number of sensors that have a 1. sensors convey information to fusion center in a multi-hop fashion to enable function computation. problem studied is to minimize total transmission energy used by network when computing this function, subject to constraint that this computation is correct with high probability. We assume wireless channels are binary symmetric channels with a probability of error p, and that each sensor uses rαunits of energy to transmit each bit, where r is transmission range of sensor. main result in this paper is an algorithm whose energy usage is Θ (n(loglogn)(logn/n)α), and we also show that any algorithm satisfying performance constraints must necessarily have energy usage Ω (n(logn/n)α). Then, we consider case where sensor network observes N events, and each node records one bit per event, thus having N bits to convey. fusion center now wants to compute N symmetric functions, one for each of events.\",\nauthor = \"Lei Ying and R. Srikant and Dullerud, {Geir E.}\",\nyear = \"2006\",\ndoi = \"10.1109/WIOPT.2006.1666455\",\nlanguage = \"English (US)\",\nisbn = \"0780395492\",\nbooktitle = \"2006 4th International Symposium on Modeling and Optimization in Mobile, Ad Hoc and Wireless Networks, WiOpt 2006\",\n\n}\n\nTY - GEN\n\nT1 - Distributed symmetric function computation in noisy wireless sensor networks with binary data\n\nAU - Ying, Lei\n\nAU - Srikant, R.\n\nAU - Dullerud, Geir E.\n\nPY - 2006\n\nY1 - 2006\n\nN2 - We consider a wireless sensor network consisting of n sensors, each having a recorded bit, sensors measurement, which has been set to either 0 or 1. network has a special node called fusion center whose goal is to compute a symmetric function of these bits; i.e., a function that depends only on number of sensors that have a 1. sensors convey information to fusion center in a multi-hop fashion to enable function computation. problem studied is to minimize total transmission energy used by network when computing this function, subject to constraint that this computation is correct with high probability. We assume wireless channels are binary symmetric channels with a probability of error p, and that each sensor uses rαunits of energy to transmit each bit, where r is transmission range of sensor. main result in this paper is an algorithm whose energy usage is Θ (n(loglogn)(logn/n)α), and we also show that any algorithm satisfying performance constraints must necessarily have energy usage Ω (n(logn/n)α). Then, we consider case where sensor network observes N events, and each node records one bit per event, thus having N bits to convey. fusion center now wants to compute N symmetric functions, one for each of events.\n\nAB - We consider a wireless sensor network consisting of n sensors, each having a recorded bit, sensors measurement, which has been set to either 0 or 1. network has a special node called fusion center whose goal is to compute a symmetric function of these bits; i.e., a function that depends only on number of sensors that have a 1. sensors convey information to fusion center in a multi-hop fashion to enable function computation. problem studied is to minimize total transmission energy used by network when computing this function, subject to constraint that this computation is correct with high probability. We assume wireless channels are binary symmetric channels with a probability of error p, and that each sensor uses rαunits of energy to transmit each bit, where r is transmission range of sensor. main result in this paper is an algorithm whose energy usage is Θ (n(loglogn)(logn/n)α), and we also show that any algorithm satisfying performance constraints must necessarily have energy usage Ω (n(logn/n)α). Then, we consider case where sensor network observes N events, and each node records one bit per event, thus having N bits to convey. fusion center now wants to compute N symmetric functions, one for each of events.\n\nUR - http://www.scopus.com/inward/record.url?scp=84886472496&partnerID=8YFLogxK\n\nUR - http://www.scopus.com/inward/citedby.url?scp=84886472496&partnerID=8YFLogxK\n\nU2 - 10.1109/WIOPT.2006.1666455\n\nDO - 10.1109/WIOPT.2006.1666455\n\nM3 - Conference contribution\n\nAN - SCOPUS:84886472496\n\nSN - 0780395492\n\nSN - 9780780395497\n\nBT - 2006 4th International Symposium on Modeling and Optimization in Mobile, Ad Hoc and Wireless Networks, WiOpt 2006\n\nER -" ]

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[ "# Publishing house / Journals and Serials / Fundamenta Mathematicae / All issues\n\n## Fundamenta Mathematicae\n\nPDF files of articles are only available for institutions which have paid for the online version upon signing an Institutional User License.\n\n## On $\\mathbb R$-embeddability of almost disjoint families and Akemann–Doner C$^*$-algebras\n\n### Volume 254 / 2021\n\nFundamenta Mathematicae 254 (2021), 15-47 MSC: 03E35, 03E05,46L05. DOI: 10.4064/fm780-8-2020 Published online: 21 December 2020\n\n#### Abstract\n\nAn almost disjoint family $\\mathcal A$ of subsets of $\\mathbb N$ is said to be $\\mathbb R$-embeddable if there is a function $f:\\mathbb N\\rightarrow \\mathbb R$ such that the sets $f[A]$ are ranges of real sequences converging to distinct reals for distinct $A\\in \\mathcal A$. It is well known that almost disjoint families which have few separations, such as Luzin families, are not $\\mathbb R$-embeddable. We study extraction principles related to $\\mathbb R$-embeddability and separation properties of almost disjoint families of $\\mathbb N$ as well as their limitations. An extraction principle whose consistency is our main result is:\n\n$\\bullet$ every almost disjoint family of size $\\mathfrak c$ contains an $\\mathbb R$-embeddable subfamily of size $\\mathfrak c$.\n\nIt is true in the Sacks model. The Cohen model serves to show that the above principle does not follow from the fact that every almost disjoint family of size continuum has two separated subfamilies of size continuum. We also construct in $\\mathsf{ZFC}$ an almost disjoint family where no two uncountable subfamilies can be separated but every countable subfamily can be separated from any disjoint subfamily.\n\nUsing a refinement of the $\\mathbb R$-embeddability property called the controlled $\\mathbb R$-embedding property we obtain the following results concerning Akemann–Doner C$^*$-algebras which are induced by uncountable almost disjoint families:\n\n$\\bullet$ In $\\mathsf{ZFC}$ there are Akemann–Doner C$^*$-algebras of density $\\mathfrak c$ with no commutative subalgebras of density $\\mathfrak c$.\n\n$\\bullet$ It is independent from $\\mathsf{ZFC}$ whether there is an Akemann–Doner algebra of density $\\mathfrak c$ with no non-separable commutative subalgebra.\n\nThis completes an earlier result that there is in $\\mathsf{ZFC}$ an Akemann–Doner algebra of density $\\omega _1$ with no non-separable commutative subalgebra.\n\n#### Authors\n\n• Osvaldo GuzmánCentro de Ciencias Matemáticas\nUNAM\nA.P. 61-3\nXangari, Morelia, Michoacán, 58089, México\ne-mail\n• Michael HrušákCentro de Ciencias Matemáticas\nUNAM\nA.P. 61-3\nXangari, Morelia, Michoacán, 58089, México\ne-mail\n• Piotr KoszmiderInstitute of Mathematics", null, "" ]

[ null, "https://www.impan.pl/en/publishing-house/journals-and-series/fundamenta-mathematicae/all/254/1/113745/on-mathbb-r-embeddability-of-almost-disjoint-families-and-akemann-doner-c-algebras", null ]

[ "# Stabilization of nonlinear systems", null, "", null, "Adapted from: Examples 1, 2 and 3 of [PPA04]\n\n[PPA04] Prajna, Stephen, Pablo A. Parrilo, and Anders Rantzer. Nonlinear control synthesis by convex optimization. IEEE Transactions on Automatic Control 49.2 (2004): 310-314.\n\nusing DynamicPolynomials\n@polyvar x[1:2]\n\nusing SumOfSquares\nusing CSDP\nusing LinearAlgebra # for ⋅\nusing MultivariatePolynomials\ndivergence(f) = sum(differentiate.(f, x))\nfunction controller(f, g, b, α, degs)\nsolver = optimizer_with_attributes(CSDP.Optimizer, MOI.Silent() => true)\nmodel = SOSModel(solver)\na = 1\nmonos = monomials(x, degs)\nN = length(monos) + 1\n@variable(model, c[1:N] in MOI.NormOneCone(N))\nc_poly = polynomial(c[2:end], monos)\nfagc = f * a + g * c_poly\n@constraint(model, b * divergence(fagc) - α * differentiate(b, x) ⋅ fagc in SOSCone())\n@objective(model, Min, c)\noptimize!(model)\nif termination_status(model) != MOI.OPTIMAL\n@warn(\"Termination status $(termination_status(model)):$(raw_status(model))\")\nend\nu = value(c_poly) / value(a)\nreturn MultivariatePolynomials.map_coefficients(coef -> abs(coef) < 1e-6 ? 0.0 : coef, u)\nend\n\nimport DifferentialEquations, Plots\nfunction phase_plot(f, quiver_scaling, Δt, X0, solver = DifferentialEquations.Tsit5())\n∇(vx, vy) = [fi(x => vx, x => vy) for fi in f]\n∇pt(v, p, t) = ∇(v, v)\nfunction traj(v0)\ntspan = (0.0, Δt)\nprob = DifferentialEquations.ODEProblem(∇pt, v0, tspan)\nreturn DifferentialEquations.solve(prob, solver, reltol=1e-8, abstol=1e-8)\nend\nticks = -5:0.5:5\nX = repeat(ticks, 1, length(ticks))\nY = X'\nPlots.quiver(X, Y, quiver = (x, y) -> ∇(x, y) / quiver_scaling, linewidth=0.5)\nfor x0 in X0\nPlots.plot!(traj(x0), vars=(1, 2), label = nothing)\nend\nPlots.plot!(xlims = (-5, 5), ylims = (-5, 5))\nend\nphase_plot (generic function with 2 methods)\n\n## Example 1\n\ng = [0, 1]\nf = [x - x^3 + x^2, 0]\nb = 3x^2 + 2x*x + 2x^2\nu = controller(f, g, b, 4, 0:3)\n$$$-0.5738994625385273x_{2} - 1.2298305281744644x_{1} - 0.12930340072544455x_{2}^{3}$$$\n\nWe find the controller above which gives the following phase plot.\n\nphase_plot(f + g * u, 200, 10.0, [[x1, x2] for x1 in -5:5:5, x2 in -5:5:5 if x1 != 0 || x2 != 0])", null, "## Example 2\n\ng = [0, 1]\nf = [2x^3 + x^2*x - 6x*x^2 + 5x^3, 0]\nb = x^2 + x^2\nu = controller(f, g, b, 2.5, 0:3)\n$$$-3.470949347992857x_{2}^{3} - 6.465434558023581x_{1}x_{2}^{2} + 4.004075892877742x_{1}^{2}x_{2} - 3.1387619181637865x_{1}^{3}$$$\n\nWe find the controller above which gives the following phase plot.\n\nphase_plot(f + g * u, 2000, 5.0, [[-1.0, -5.0], [1.0, 5.0]])", null, "## Example 3\n\ng = [0, x]\nf = [-6x*x^2 - x^2*x + 2x^3, 0]\nb = x^2 + x^2\nu = controller(f, g, b, 3, 0:2)\n$$$-2.737433441558844x_{2}^{2} + 0.18059594494782605x_{1}^{2}$$$\n\nWe find the controller above which gives the following phase plot.\n\nX0 = [Float64[x1, x2] for x1 in -5:5:5, x2 in -5:5:5 if x2 != 0]\nε = 1e-4 # We separate the starting point slightly from the hyperplane x2 = 0 which is invariant.\npush!(X0, [-4, ε])\npush!(X0, [-3, -ε])\npush!(X0, [ 3, ε])\npush!(X0, [ 4, -ε])\nphase_plot(f + g * u, 2000, 10.0, X0)", null, "" ]

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[ "Summary of Changes Made in This Calendar - Introduction to Mathematical Statistics\n\nMathematics 3334 Introduction to Mathematical Statistics\nA mathematical introduction to statistics, using the probability theory developed in Mathematics 3332. Topics include point and interval estimation, test of hypothesis, non-parametric methods, goodness of fit, experimental design, analysis of variance and covariance, regression and correlation.\nCredit Weight: 0.5\nPrerequisite(s): Mathematics 3332\nOffering: 0-0; 3-1\nNotes: Students who have previous credit in Mathematics 2333 may not take Mathematics 3334 for credit. Students may only receive credit for one of the following courses or combinations or courses: Math 0210; Math 0212; Math 4030; Math 2310 and Math 2311; and Math 3332 and Math 3334.\nCourse Classifications: Type C: Engineering, Mathematical and Natural Sciences" ]

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[ "17 January 2013\n\nIn his great book Effective Java* Joshua Bloch describes the need to \"Know and use the libraries\" to write effective code.\n\nThe following is an example, where the knowledge of the standard Java libraries leads to much more elegant code.\n\nThe code I found was:\n\n``````for (Map.Entry entry : getMap().entrySet()) {\nif(getMap().containsKey(entry.getKey)) {\nfoo(getMap().get(entry.getKey()));\n}\n}\n``````\n\nSo what does the code do? I'll refactor the code on the go so that you can see the steps.\n\nFirst of all, `getMap()` returns a field of this class, so we can replace `getMap()` with `map`:\n\n``````for (Map.Entry entry : map.entrySet()) {\nif(map.containsKey(entry.getKey)) {\nfoo(map.get(entry.getKey()));\n}\n}\n``````\n\nThe `for` loop iterates to the entries of `map`. `Entry` is a key/value pair tuple.\nThe `if` in line 2 asks wether `map` contains the key of the current entry.\n\nAs we just got the entries from the map, it is very unlikely that the map was modified in the mean time.\n(And I can asure you that the instance of the class in question is used by one thread only.)\n\nSo `map.containsKey(entry.getKey)` will always return `true`. What do we do with `if`s that always return `true`? Yes, we'll delete the `if` immediatly.\n\n``````for (Map.Entry entry : map.entrySet()) {\nfoo(map.get(entry.getKey()));\n}\n``````\n\nIn line 2 (of the refactored code) the map is asked to return the value associated with the key of the current entry.\nAs every `Entry` tuple contains both key and value, we can instead ask the entry for the value:\n\n``````for (Map.Entry entry : map.entrySet()) {\nfoo(entry.getValue()));\n}\n``````\n\nAnd now we're at a point where the code doesn't tell us what to refactor next. It's where \"Know your libraries\" come in.\n`Map` has a method `values()` which returns all the values in the map independently of the key.\nKnowing this method, we can simplify the code to:\n\n``````for (Object value : map.values()) {\nfoo(value);\n}\n``````" ]

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[ "Implode/Explode Functions\nNOTE: Version 6 of Notes now has built-in functions that should be used instead of these functions. There is a built-in Split function which mimics the @Explode function and the Explode function written below. There is a built-in Join function which mimics the @Implode function and the Implode function written below. In fact, LotusScript aliases the value \"Implode\" to \"Join\", so the Implode function below will not work any more in version 6 since there is now a built-in function with the exact same name.\n\nWhen working with LotusScript, every once in a while you need to take an array and convert it to a string, or take a string and convert it to an array, just like @Implode and @Explode. You may be thinking that the Evaluate LotusScript statement will do the trick. In most cases, it will. However, try putting this code into an agent and running it:\n\nDim temp As Variant\nDim i As Integer\nDim result As String\ntemp = Evaluate({@Explode(\"Hello\\there~how~are~you?\"; \"~\")})\nresult = \"\"\nFor i = Lbound(temp) To Ubound(temp)\nresult = result & temp(i) & Chr\\$(10)\nNext\nMsgbox result\n\nThe resulting message box will not be exactly what you expect, as can be seen in figure 1. This is because the slash is an escape character in formula language, so it is not considered as part of the string. That's why this LotusScript Explode function (and the Implode function as well) is sometimes necessary.\n\nHere are the functions:\n\nFunction Explode(fullString As String, separator As String, empties As Integer) As Variant\nDim fullStringLen As Integer\nDim lastPosition As Integer\nDim position As Integer\nDim x As Integer\nDim tmpArray() As String\n\nIf empties = False Then fullString = Trim\\$(fullString)\nIf separator = \"\" Then separator = \" \"\nfullStringLen = Len(fullString)\nlastPosition = 1\nposition = Instr(fullString, separator)\nIf position > 0 Then\nx = 0\nWhile position > 0\nx = x+1\nRedim Preserve tmpArray(x)\n' The next entry in the array is going to be the part of the string from the\n' end of the previous part to the start of the new part.\ntmpArray(x-1) = Mid\\$(fullString, lastPosition, position - lastPosition)\nIf empties = False Then\n' If the user does not want empties and there are consecutive separators,\n' skip over the 2nd, 3rd, etc. instance of the separator.\nWhile Mid\\$(fullString, position+Len(separator), Len(separator)) _\n= Mid\\$(fullString, position, Len(separator))\nposition = Instr(position+Len(separator), fullString, separator)\nWend\nEnd If\nlastPosition = position + Len(separator)\nposition = Instr(position+Len(separator), fullString, separator)\nWend\ntmpArray(x) = Mid\\$(fullString, lastPosition)  ' Save everything after the last separator\nIf empties = False And Trim(tmpArray(x)) = \"\" Then\nRedim Preserve tmpArray(x-1) ' Eliminate the last one if it's empty\nEnd If\nElse\nRedim tmpArray(0)\ntmpArray(0) = fullString\nEnd If\nExplode = tmpArray\nEnd Function\n\nFunction Implode(anArray As Variant, concatenator As String) As String\nDim tmpString As String\n\nIf Not Isarray(anArray) Then\ntmpString = anArray\nElse\nIf Ubound(anArray) = Lbound(anArray) Then\ntmpString = Trim(anArray(Lbound(anArray)))\nElse\nForall items In anArray\ntmpString = tmpString & items & concatenator\nEnd Forall\n' The concatenator was always added; the last one needs to be removed\ntmpString = Left(tmpString, Len(tmpString) - Len(concatenator))\nEnd If\nEnd If\nImplode = tmpString\nEnd Function" ]

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[ "'\n\n# Search results\n\nFound 929 matches\nLeffler formula (estimation of Ideal body weight for children less than a year old)\n\nThe term body weight is used colloquially and in the biological and medical sciences to refer to a person’s mass or weight. . Body weight is one way ... more\n\nLeffler formula (estimation of Ideal body weight for children 0–10 years of age)\n\nThe term body weight is used colloquially and in the biological and medical sciences to refer to a person’s mass or weight. Body weight is one way of ... more\n\nFloating objects (weight that depresses the surface)\n\nWhen an object is placed on a liquid, its weight depresses the surface, and is balanced by the surface tension forces on either side , which are each ... more\n\nBuoyant force (Archimedes' principle)\n\nBuoyancy is an upward force exerted by a fluid that opposes the weight of an immersed object. Buoyant force equivalent to the weight of the fluid that ... more\n\nEnergy stored in a capacitor\n\nCapacitance is the ability of a body to store an electrical charge. Any object that can be electrically charged exhibits capacitance. A common form of ... more\n\nSears–Haack body (cross sectional area)\n\nThe Sears–Haack body is the shape with the lowest theoretical wave drag in supersonic flow, for a given body length and given volume.The mathematical ... more\n\nCapacitance\n\nCapacitance is the ability of a body to store an electrical charge. Any object that can be electrically charged exhibits capacitance. Capacitance is a ... more\n\nGeneralised logistic function (Richards' curve)\n\nA logistic function or logistic curve is a common “S” shape (sigmoid curve) The generalized logistic curve or function, also known as ... more\n\nWorksheet 333\n\nA typical small rescue helicopter, like the one in the Figure below, has four blades, each is 4.00 m long and has a mass of 50.0 kg. The blades can be approximated as thin rods that rotate about one end of an axis perpendicular to their length. The helicopter has a total loaded mass of 1000 kg. (a) Calculate the rotational kinetic energy in the blades when they rotate at 300 rpm. (b) Calculate the translational kinetic energy of the helicopter when it flies at 20.0 m/s, and compare it with the rotational energy in the blades. (c) To what height could the helicopter be raised if all of the rotational kinetic energy could be used to lift it?", null, "The first image shows how helicopters store large amounts of rotational kinetic energy in their blades. This energy must be put into the blades before takeoff and maintained until the end of the flight. The engines do not have enough power to simultaneously provide lift and put significant rotational energy into the blades.\nThe second image shows a helicopter from the Auckland Westpac Rescue Helicopter Service. Over 50,000 lives have been saved since its operations beginning in 1973. Here, a water rescue operation is shown. (credit: 111 Emergency, Flickr)\n\nStrategy\n\nRotational and translational kinetic energies can be calculated from their definitions. The last part of the problem relates to the idea that energy can change form, in this case from rotational kinetic energy to gravitational potential energy.\n\nSolution for (a)\n\nWe must convert the angular velocity to radians per second and calculate the moment of inertia before we can find Er . The angular velocity ω for 1 r.p.m is\n\nAngular velocity\n\nand for 300 r.p.m\n\nMultiplication\n\nThe moment of inertia of one blade will be that of a thin rod rotated about its end.\n\nMoment of Inertia - Rod end\n\nThe total I is four times this moment of inertia, because there are four blades. Thus,\n\nMultiplication\n\nand so The rotational kinetic energy is\n\nRotational energy\n\nSolution for (b)\n\nTranslational kinetic energy is defined as\n\nKinetic energy ( related to the object 's velocity )\n\nTo compare kinetic energies, we take the ratio of translational kinetic energy to rotational kinetic energy. This ratio is\n\nDivision\n\nSolution for (c)\n\nAt the maximum height, all rotational kinetic energy will have been converted to gravitational energy. To find this height, we equate those two energies:\n\nPotential energy\n\nDiscussion\n\nThe ratio of translational energy to rotational kinetic energy is only 0.380. This ratio tells us that most of the kinetic energy of the helicopter is in its spinning blades—something you probably would not suspect. The 53.7 m height to which the helicopter could be raised with the rotational kinetic energy is also impressive, again emphasizing the amount of rotational kinetic energy in the blades.\n\nReference : OpenStax College,College Physics. OpenStax College. 21 June 2012.\nhttp://openstaxcollege.org/textbooks/college-physics\n\nWorksheet 341\n\nThe awe‐inspiring Great Pyramid of Cheops was built more than 4500 years ago. Its square base, originally 230 m on a side, covered 13.1 acres, and it was 146 m high (H), with a mass of about 7×10^9 kg. (The pyramid’s dimensions are slightly different today due to quarrying and some sagging). Historians estimate that 20,000 workers spent 20 years to construct it, working 12-hour days, 330 days per year.", null, "a) Calculate the gravitational potential energy stored in the pyramid, given its center of mass is at one-fourth its height.\n\nDivision\nPotential energy\n\nb) Only a fraction of the workers lifted blocks; most were involved in support services such as building ramps, bringing food and water, and hauling blocks to the site. Calculate the efficiency of the workers who did the lifting, assuming there were 1000 of them and they consumed food energy at the rate of 300 Kcal/hour.\n\nfirst we calculate the number of hours worked per year.\n\nMultiplication\n\nthen we calculate the number of hours worked in the 20 years.\n\nMultiplication\n\nThen we calculate the energy consumed in 20 years knowing the energy consumed per hour and the total hours worked in 20 years.\n\nMultiplication\nMultiplication\n\nThe efficiency is the resulting potential energy divided by the consumed energy.\n\nDivision\n\n...can't find what you're looking for?\n\nCreate a new formula\n\n### Search criteria:\n\nSimilar to formula\nCategory" ]

[ null, "https://www.fxsolver.com/media/wiki/Figure_1018.png", null, "https://www.fxsolver.com/media/wiki/Pyramid_of_Cheops.png", null ]

[ "Are 3 points on an orbit enough to determine the shape of it in practice?\n\nIn a question about determining orbital elements from two points on an orbit, some discussion arouse regarding how many points are actually necessary, since two is not sufficient.\n\nDetermining a conic section requires 5 points, though one of them can be the central mass, so only 4 points on the orbit.\n\nBut are 4 points actually necessary in practice?\n\nThis polar equation seems to suggest 3 points are enough, though with arguably some extra assumptions: $$r = \\frac{a(1−e^2)}{1+e\\cosθ}$$\n\nThe only counterexample with ambiguous orbits I could come up with is \"unrealistic\", as it involves the phantom half of a hyperbola.\n\nDoes disregarding such purely theoretical trajectories reduce the requirement to 3 points on the orbit?", null, "• I wouldn't call this \"purely theoretical trajectory\" - that would be something possible, but not realised. What you show is commonly called an \"unphysical solution\" of the equations, because of the additional constraint that an orbit needs to be continuous which is not reflected in the formulae. Oct 9 '21 at 16:24\n• When you give a point on the trajectory, that's 2 coordinates, but the information obtained is the same as if you gave any other point in a 1-dimensional line (the trajectory), so the number of parameters is decreased by 2-1=1. When you give the location of central mass, the number of parameters is decreased by 2. (This does not prove that 3 points on the orbit and the central mass uniquely specify the orbit, just explains why one would expect this information to restrict the set of possible orbits to a discrete one, not a continuous infinite one, as when just 4 points on the orbit are given.) Oct 9 '21 at 18:17\n• It is similar to this: you can specify a circle by giving its center and 1 point on the circle; but 2 points on the circle are not enough to specify it, you need 3. Oct 9 '21 at 18:19\n• Thanks for this question, I think I learned quite a bit about conic sections and GeoGebra working this one out. Oct 11 '21 at 1:31\n\nI believe the answer is yes, given one focus, and three coplanar points on the orbit, you can define the orbital shape, and obtain semi-major axis, orbital eccentricity, and the direction of the periapsis.\n\nSince the three points must be coplanar within the orbital plane. I leave the exercise of converting the three coplanar points you have to orbital-plane coordinates as an exercise for the reader.\n\nI wound up not solving the polar equations to do this, but instead, relying on the definitions of ellipses and hyperbolas, and a lot of help from GeoGebra:\n\nGiven 3 points, $$P_1, P_2, P_3$$ of format (x,y), and the focus $$F_0$$ at the origin:\n\nSolving it Geometrically:\n\nCircular case: If all three points are equidistant from the known focus, it's a circular orbit.\n\nElliptical or Hyperbolic Case: Otherwise, for any pair of the chosen points, $$P_1, P_2, P_3$$, there exists a hyperbola that passes through the intended focus $$F_0$$. The ellipse or hyperbola that passes through the pair of chosen points must have both foci on that focal hyperbola; if it's a hyperbolic orbit, the focus will be on the same lobe. If it's an elliptical orbit it will be on the other lobe.\n\nIf you construct the three hyperbolas that have each each pair of points as foci ($$P_1$$,$$P_2$$) , ($$P_1$$,$$P_3$$), ($$P_2$$,$$P_3$$) and pass through $$F_0$$, the other point where those three hyperbolas intersect is where the other focus is.\n\nThree hyperbolas defining the foci of an ellipse.", null, "You can then examine the orbital ellipse and hyperbolic trajectory defined by the two foci. In most cases, all three points will lie on either the ellipse or the hyperbola, determining which of the two is the valid trajectory.\n\nThere are rare cases where the three points can be on both the hyperbola and the ellipse; but if an ellipse and a hyperbola share foci, they will intersect at only four points, requiring at least one of the points be on the non-physical phantom lobe on the hyperbola, disqualifying it.\n\nParabolic Case: If the secondary focus winds up at infinity, it's the parabolic case. Construct three circles around the points that intersect at the focus. The line that's tangent to all three circles is the directrix, use that and the focus to construct your parabola.\n\nThe Geogebra Graph used to create the above images can be found here: Geometric Three-Point and Focus Orbit - Shared All three points are freely draggable, and it only seems to stutter in a few cases.\n\nSolving it analytically:\n\nAn ellipse is defined as the set of all points in a plane where the sum of the distance of the point from the two foci is a constant : Twice the semimajor axis. The following equations assume the primary focus, $$F_0$$ is at the origin, and relate the semi-major axis and the x and y coordinates of the secondary focus.\n\nSolve the following equations: $$\\\\(2z - |P_1|)² = (x - P_{1x})² + (y - P_{1y})² \\\\(2z - |P_2|)² = (x - P_{2x})² + (y - P_{2y})² \\\\(2z - |P_3|)² = (x - P_{3x})² + (y - P_{3y})²$$\n\nWhere $$|P_n|$$ denotes the distance of the point $$P_n$$ from the known focus, and $$P_{nx}$$ and $$P_{ny}$$ are the x and y coordinates of $$P_n$$ (I'm open to better notation on these, this is probably a bit confusing)\n\n• $$z$$ will be have the same magnitude of your semi-major axis.\n• $$F_1=(x,y)$$ is the other focus, where $$x$$ and $$y$$ are not equal to 0.\n• $$2c$$ is the distance between the two foci.\n• $$e = |c/z|$$ gives the orbital eccentricity. If it is less than 1, the orbit is elliptical, if it is greater than 1, the orbit is hyperbolic.\n• $$a = \\pm|z|$$ is the semi-major axis. Use the negative value if hyperbolic, and the positive value if elliptical.\n\nWe have a rotated conic section now. The angle of periapsis can be found opposite the direction of the second focus, if elliptical, and in the direction of the second focus, if hyperbolic.\n\n$$\\displaystyle \\theta_0 = \\begin{cases} \\mathrm{atan2}(-F_{1y},-F_{1x}) & \\text{if e < 1} \\\\ \\mathrm{atan2}(F_{1y},F_{1x}) & \\text{if e>1} \\\\ \\end{cases}$$\n\nAnd the polar equation for the conic section is:\n\n$$r(\\theta)= \\frac{a(1-e^2)}{1+e \\cos(\\theta - \\theta_0)}$$\n\nIf the orbit turned out to be hyperbolic, compare the distance from the points to the primary focus and to the secondary focus. If the points are closer to the secondary focus, they're on the phantom lobe, and the solution is nonphysical; the object could not have been at those points in a Keplerian hyperbolic trajectory.\n\nI've mostly been working this out through GeoGebra, and its numerical solver is really finicky on these, so I'm not entirely certain that this is correct, but it seems to work. It also works if the three points are on the hyperbola's phantom lobe.\n\nIf you want to fiddle around with it, you can do so here: GeoGebra: Three Point and Focus Fiddler\n\nDragging around point $$P_2$$ seems to be generally fine, but the numerical solver for the equations gets a bit stroppy if $$P_1$$ or $$P_3$$ are moved around too much. It's still a bit of a work in progress.\n\nAnd if you know the order the three points are passed in, then, yes, you can figure out whether it's prograde or not, you can go back to 3D and determine the orbital inclination, the longitude of the ascending node, and the argument of periapsis.\n\nIf the time between two points is known, only two points are sufficient. The angle between these points should be larger than 0° and less than 180°.\n\nIf the position and velocity relative to the observer are available (as is the case with radar observations), these observational data can be adjusted by the known position and velocity of the observer relative to the attracting body at the times of observation. This yields the position and velocity with respect to the attracting body. If two such observations are available, along with the time difference between them, the orbit can be determined using Lambert's method, invented in the 18th century. See Lambert's problem for details.\n\nEven if no distance information is available, an orbit can still be determined if three or more observations of the body's right ascension and declination have been made. Gauss's method, made famous in his 1801 \"recovery\" of the first lost minor planet, Ceres, has been subsequently polished.\n\nThree points without distance information are sufficient too.\n\n• This is not correct. Consider Lambert's problem. There are at least two very different orbits that start at one point at a specific time and end at a different point at a later specific time. In the case of points separated by 180°, the number of potential orbits is infinite. (Lambert's problem has a singularity at 180°, and also at n*360°+180°, where n is a positive integer.) If the time difference between the end time and start time is large enough, there can be more than two distinct orbits. Oct 9 '21 at 16:12\n• @TooTea The wikipedia article aboutLambert's problem writes only of position and time.\n– Uwe\nOct 10 '21 at 19:21\n• @DavidHammen See the edit. I suppose restricting it to 0° ≤ angle < 180° guarantees a unique solution. Oct 10 '21 at 19:36\n• @TooTea The edit is not sufficient. A transfer orbit might involve a 360° to 540° change in true anomaly and still satisfy the 0° to 180° requirement (which is arbitrary) if the time difference is large enough. Oct 10 '21 at 22:16\n• @DavidHammen I understand that restriction as the total change in true anomaly. In other words,saying that the time refers to the first crossing of point 2 after point 1 (thus ruling out once-around trajectories) should be enough to make the solution unique. Perhaps just a bit of rewording would do. Oct 11 '21 at 6:24" ]

[ null, "https://i.stack.imgur.com/6tIO7.png", null, "https://i.stack.imgur.com/AUQjT.png", null ]

[ "[ this page is permanently under construction ]\n\n# Prologue\n\nWith the recent improvements in Cython/SageX, many of these suggestions are handled implicitly and give very little benefits for a large drawback in code readability.\n\n# Introduction\n\nThis page describes some techniques for writing really fast Pyrex code. It is aimed at SAGE developers who are working on low-level SAGE internals, where performance is absolutely crucial.\n\nPyrex is a very unusual language. If you write Pyrex as if it were Python, it can end up running more slowly than Python. If you write it like you're writing C, it can run almost as fast as pure C. The amazing thing about Pyrex is that the programmer gets to choose, pretty much line by line, where along the Python-C spectrum they want to work.\n\nHOWEVER... it is hard work to make your Pyrex as fast as C. It's very easy to get it wrong, essentially because Pyrex makes it all look so easy. This purpose of this document is to collect together the experiences of SAGE developers who have learned the hard way. [Cython does a lot of this hard work for you.]\n\nApart from the stuff on this page, by far the best way to learn how to make Pyrex code faster is to study the C code that Pyrex generates.\n\n## How to contribute to this document\n\nYes, please do! Make sure to follow these guidelines:\n\n• When you give an example, make sure to constrast a fast way of doing things with a slow way, especially if the slow way is more obvious. Show both versions of the Pyrex code, and show the generated C code as well, if you think that this is useful to see. (Remove the irrelevant parts of the C code, because it can get pretty verbose :-).)\n\n• Let's keep this scientific: show some evidence of performance (e.g. timing data).\n• William Stein is writing a chapter for the programming guide: See http://sage.math.washington.edu/sage/pyrex_guide.\n\n# cdef functions vs def functions\n\nA cdef function in Pyrex is basically a C function, so calling it is basically a few lines of assembly language. A def function on the other hand is a Python function, and incurs the following overhead:\n\n• The caller needs to construct a tuple object that holds the arguments.\n• The call itself has to go via the Python API.\n• The function being called needs to call the Python API to decode the tuple.\n\nAdditionally, in most cases:\n\n• The caller has to do a name lookup to find the function. (But you can cache this if you're calling the same function many times.)\n\nAll of this overhead is incurred whether you are calling from Python, or from Pyrex, or from Mars.\n\n## Example\n\nHere's the Pyrex code:\n\n``` 1 cdef class X:\n2 def def_func(X self):\n3 pass\n4\n5 cdef cdef_func(X self):\n6 pass\n7\n8 def call_def_func(X x):\n9 cdef int i\n10 for i from 0 <= i < 10000000:\n11 x.def_func()\n12\n13 def call_cdef_func(X x):\n14 cdef int i\n15 for i from 0 <= i < 10000000:\n16 x.cdef_func()\n```\n\nPerformance data:\n\n``` 1 sage: x = X()\n2\n3 sage: time call_def_func(x)\n4 CPU times: user 1.82 s, sys: 0.00 s, total: 1.82 s\n5 Wall time: 1.82\n6\n7 sage: time call_cdef_func(x)\n8 CPU times: user 0.08 s, sys: 0.00 s, total: 0.08 s\n9 Wall time: 0.08\n```\n\nPretty striking difference. (And by the way, the second one goes twice as fast again if you declare a void return type.)\n\nHere's the C code for def_func, note the PyArg_ParseTupleAndKeywords API call:\n\n``` 1 static PyObject *__pyx_f_7integer_1X_def_func(PyObject *__pyx_v_self, PyObject *__pyx_args, PyObject *__pyx_kwds) {\n2 PyObject *__pyx_r;\n3 static char *__pyx_argnames[] = {0};\n4 if (!PyArg_ParseTupleAndKeywords(__pyx_args, __pyx_kwds, \"\", __pyx_argnames)) return 0;\n5 Py_INCREF(__pyx_v_self);\n6\n7 __pyx_r = Py_None; Py_INCREF(Py_None);\n8 Py_DECREF(__pyx_v_self);\n9 return __pyx_r;\n10 }\n```\n\nIn contrast, here's the C code for cdef_func:\n\n``` 1 static PyObject *__pyx_f_7integer_1X_cdef_func(struct __pyx_obj_7integer_X *__pyx_v_self) {\n2 PyObject *__pyx_r;\n3 Py_INCREF(__pyx_v_self);\n4\n5 __pyx_r = Py_None; Py_INCREF(Py_None);\n6 Py_DECREF(__pyx_v_self);\n7 return __pyx_r;\n8 }\n```\n\nNow here are the two versions of the loop that actually does the calling. First, call_def_func, with error handling suppressed:\n\n``` 1 for (__pyx_v_i = 0; __pyx_v_i < 10000000; ++__pyx_v_i) {\n2 __pyx_1 = PyObject_GetAttr(((PyObject *)__pyx_v_x), __pyx_n_def_func);\n3 __pyx_2 = PyTuple_New(0);\n4 __pyx_3 = PyObject_CallObject(__pyx_1, __pyx_2);\n5 Py_DECREF(__pyx_1); __pyx_1 = 0;\n6 Py_DECREF(__pyx_2); __pyx_2 = 0;\n7 Py_DECREF(__pyx_3); __pyx_3 = 0;\n8 }\n```\n\nNotice it needs to do (a) a name lookup for def_func, (b) construct a tuple, and (c) call the Python API to make the function call.\n\nHere's the much much slicker call_cdef_func version:\n\n``` 1 for (__pyx_v_i = 0; __pyx_v_i < 10000000; ++__pyx_v_i) {\n2 __pyx_1 = ((struct __pyx_vtabstruct_7integer_X *)__pyx_v_x->__pyx_vtab)->cdef_func(__pyx_v_x);\n3 Py_DECREF(__pyx_1); __pyx_1 = 0;\n4 }\n```\n\n[ todo ]\n\n# avoid python name lookups\n\n[ todo ]\n\n• sage.rings.integer.Integer\n\n# Type checking\n\nGenerally speaking, using isinstance is very slow. It's slow because it needs to cover many cases, and it's slow because it's a Python function. If you are checking for a particular Pyrex-generated type (or indeed any extension type), it's much faster to use the Python API function PyObject_TypeCheck. In fact, PyObject_TypeCheck is a macro, so there isn't even any C function call overhead. The prototype is declared in cdefs.pxi.\n\nExample Pyrex code:\n\n``` 1 cdef class X:\n2 pass\n3\n4 def test1(x):\n5 cdef int i\n6 for i from 0 <= i < 5000000:\n7 if isinstance(x, X):\n8 pass\n9\n10 def test2(x):\n11 cdef int i\n12 for i from 0 <= i < 5000000:\n13 if PyObject_TypeCheck(x, X):\n14 pass\n```\n\nHere's the performance comparison:\n\n``` 1 sage: time test1(47)\n2 CPU times: user 3.89 s, sys: 0.00 s, total: 3.89 s\n3 Wall time: 3.89\n4\n5 sage: time test2(47)\n6 CPU times: user 0.16 s, sys: 0.00 s, total: 0.16 s\n7 Wall time: 0.16\n```\n\n(Note: there is also some overhead in the name lookup for isinstance, but in this case it's a fairly small part of the time, about 10% or so.)\n\nHere's the C code for the first loop (error checking suppressed):\n\n``` 1 for (__pyx_v_i = 0; __pyx_v_i < 5000000; ++__pyx_v_i) {\n2 __pyx_1 = __Pyx_GetName(__pyx_b, __pyx_n_isinstance);\n3 __pyx_2 = PyTuple_New(2);\n4 Py_INCREF(__pyx_v_x);\n5 PyTuple_SET_ITEM(__pyx_2, 0, __pyx_v_x);\n6 Py_INCREF(((PyObject*)__pyx_ptype_7integer_X));\n7 PyTuple_SET_ITEM(__pyx_2, 1, ((PyObject*)__pyx_ptype_7integer_X));\n8 __pyx_3 = PyObject_CallObject(__pyx_1, __pyx_2);\n9 Py_DECREF(__pyx_1); __pyx_1 = 0;\n10 Py_DECREF(__pyx_2); __pyx_2 = 0;\n11 __pyx_4 = PyObject_IsTrue(__pyx_3);\n12 Py_DECREF(__pyx_3); __pyx_3 = 0;\n13 if (__pyx_4) {\n14 goto __pyx_L4;\n15 }\n16 __pyx_L4:;\n17 }\n```\n\nAnd here's the much tighter code for the second loop:\n\n``` 1 for (__pyx_v_i = 0; __pyx_v_i < 5000000; ++__pyx_v_i) {\n2 __pyx_1 = PyObject_TypeCheck(__pyx_v_x,((PyObject*)__pyx_ptype_7integer_X));\n3 if (__pyx_1) {\n4 goto __pyx_L4;\n5 }\n6 __pyx_L4:;\n7 }\n```\n\n# \"==\" vs \"is\"\n\n\"a is b\" checks whether a and b are the same objects while \"a == b\" returns the result of either a.__class__().__richcmp__(a,b,2) or b.__class__().__richcmp__(a,b,2) depending on if a.class() can handle comparison with b.\n\nThis gets used quite often to e.g., check if an attribute of a class has been computed already, like this:\n\n``` 1 cdef class MyClass\n2 cdef object #cached result\n3 ...\n4 def calculate_result( MyClass self ):\n5 if self.__cached_result is not None :\n6 return self.__cached_result\n7 else:\n8 self.__cached_result = self.calculate_result()\n9 return self.__cached_result\n```\n\nIf the cached result has not been computed the default value for any cdef class attribute is None. There is only one single None object in Python so it's safe to check for identity rather equality. Consider these timing examples.\n\n``` 1 from sage.rings.integer_ring import ZZ\n2\n3 n = 600000\n4\n5 def test1():\n6 one = ZZ(1)\n7 for i in range(n):\n8 one is None\n9\n10\n11 def test2():\n12 one = ZZ(1)\n13 for i in range(n):\n14 one == None\n```\n\nNow consider the times these functions take:\n\n``` 1 %time test1()\n2 # CPU time: 0.18 s, Wall time: 0.40 s\n3\n4 %time test2()\n5 # CPU time: 14.85 s, Wall time: 44.80 s\n```\n\nSo it's way faster to test for identity with None than comparing with None.\n\nThis is also true for pure python.\n\n# tuple, list, and dict access\n\nPyrex plays safe when it comes to list, tuple, dict access:\n\n``` 1 def test():\n2 t = tuple([1,2])\n3 t\n```\n\nt gets translated to:\n\n``` 1 __pyx_1 = PyInt_FromLong(0);\n2\n3 if (!__pyx_1) {\n4 __pyx_filename = __pyx_f;\n5 __pyx_lineno = 10;\n6 goto __pyx_L1;\n7 }\n8 __pyx_3 = PyObject_GetItem(__pyx_v_t, __pyx_1);\n9\n10 if (!__pyx_3) {\n11 __pyx_filename = __pyx_f;\n12 __pyx_lineno = 10;\n13 goto __pyx_L1;\n14 }\n15 Py_DECREF(__pyx_1); __pyx_1 = 0;\n16 Py_DECREF(__pyx_3); __pyx_3 = 0;\n```\n\nThis is faster:\n\n``` 1 cdef extern from \"Python.h\":\n2 void* PyTuple_GET_ITEM(object p, int pos)\n3\n4 def test2():\n5 cdef object w\n6 t = tuple([1,2])\n7 w = <object> PyTuple_GET_ITEM(t,0)\n8 return 0\n```\n\nAs it gets translated to:\n\n``` 1 _4 = (PyObject *)PyTuple_GET_ITEM(t,0);\n2 Py_INCREF(_4);\n3 Py_DECREF(w);\n4 w = _4;\n5 _4 = 0;\n```\n\nCython Update There is still a slight speed difference, but it is almost negligable. The code automatically detects lists/tuples at runtime and uses the PyXxx_GET_ITEM code if it can. This is much safer to, as calling PyTuple_GET_ITEM on a non-tuple or with bad bounds results in a segfault. (Not to mention easier to read).\n\n# integer \"for\" loops\n\n``` 1 from sage.rings.integer_ring import ZZ\n2\n3 cdef int n\n4 n = 3000000\n5\n6 def test0():\n7 cdef int j,k\n8 j = 1\n9 k = 2\n10 for i in range(n):\n11 j = k * j**2\n12 return j\n13\n14 def test0a():\n15 for i in range(n):\n16 pass\n17\n18 def test1():\n19 cdef int j,k\n20 j = 1\n21 k = 2\n22 for i from 0 <= i < n:\n23 j = k * j**2\n24 return j\n25\n26 def test1a():\n27 for i from 0 <= i < n:\n28 pass\n29\n30 def test2():\n31 cdef int i,j,k\n32 j = 1\n33 k = 2\n34 for i from 0 <= i < n:\n35 j = k * j**2\n36 return j\n```\n\n``` 1 %time s = test0()\n2 # CPU time: 1.34 s, Wall time: 3.38 s\n3\n4 %time s = test0a()\n5 # CPU time: 0.93 s, Wall time: 1.99 s\n6\n7 %time s = test1()\n8 # CPU time: 0.61 s, Wall time: 1.26 s\n9\n10 %time s = test1a()\n11 # CPU time: 0.15 s, Wall time: 0.43 s\n12\n13 %time s = test2()\n14 # CPU time: 0.44 s, Wall time: 1.50 s\n```\n\n# exception handling is not as bad as you'd think\n\n[ todo ]\n\n• If no exception occurs, overhead is really tiny.\n\n# a.__add__(b) is worse than a+b in Pyrex speed-wise\n\n[ todo ] but headline says it all\n\n# Offtopic: Malloc Replacements\n\nWritingFastPyrexCode (last edited 2009-05-04 19:36:24 by robertwb)" ]

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[ "What does it do?\n\nCreates a cell reference based on the row and column numbers\n\nFormula breakdown:\n\nWhat it means:\n\n=ADDRESS(row number, column number, [absolute or relative], [reference style], [name of the worksheet])\n\nDid you know that you can dynamically create cell references in Excel? Yes you can with the ADDRESS Formula! This is one of the Lookup Formulas in Excel.\n\nThe ADDRESS Formula takes in these information to create the cell reference:\n\n• row number\n• column number\n• abs_num – this is reflected if your cell reference is absolute or relative. It has 4 possibilities:\n• 1 – Absolute\n• 2 – Absolute row, Relative column\n• 3 – Relative row, Absolute column\n• 4 – Relative\n• a1 – this determines if it’s R1C1 or A1 style. For our examples we will not use this, and it will default to A1 Style\n• 0 – R1C1 Style\n• 1 – A1 Style\n• sheet_text – this will add the sheet name to your cell reference if populated\n\nI explain how you can do this below:", null, "", null, "STEP 1: We need to enter the ADDRESS function in a blank cell:", null, "## row_num\n\nWhat is the row number?\n\nSelect the cell containing the row number:", null, "## column_num\n\nWhat is the column number?\n\nSelect the cell containing the column number:", null, "## abs_num\n\nWould it be an absolute or relative cell reference?\n\nSelect the cell containing the abs_num input. There are 4 modes, so we have included in all of the examples so that you can see it in action.", null, "Apply the same formula to the rest of the cells by dragging the lower right corner downwards.", null, "You have all of your cell references generated now! Notice the differences in the 4 modes as well represented by the \\$A\\$1 cell references:", null, "How to Use the ADDRESS Formula in Excel", null, "" ]

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[ "Answer to Question #18366 in Mechanics | Relativity for daylon\n\nQuestion #18366\nhow do you find sliding friction\n1) Determine the normal force, denoted N, of the surface against the object. If the surface is horizontal, then this force is equal but opposite to the force of gravity, which equals 9.8 times the mass of the object. For example, a 5 kg block has a normal force of (9.8)(10) = 98 Newtons.\n\n2) Look up the coefficient of friction of the surface the object is sliding on and the object itself. This can be found in the appendix of most introductory physics textbooks. This coefficient is denoted u. For example, the coefficient for a dry piece of wood on brick is 0.6.\n\n3) Multiply the normal force by the coefficient of friction. This will give you the resulting force of friction. For example, the 10 kg piece of wood sliding on concrete has a force of friction of uN, or (0.6)(98) = 58.8 Newtons.\n\nNeed a fast expert's response?\n\nSubmit order\n\nand get a quick answer at the best price\n\nfor any assignment or question with DETAILED EXPLANATIONS!" ]

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[ "meanSdPlot {vsn} R Documentation\n\n## Plot row standard deviations versus row means\n\n### Description\n\nPlot row standard deviations versus row means\n\n### Usage\n\n```meanSdPlot(x,\nranks = TRUE,\nxlab = ifelse(ranks, \"rank(mean)\", \"mean\"),\nylab = \"sd\",\npch = \".\",\ncol, ...)```\n\n### Arguments\n\n `x` An object of class `matrix` or `exprSet` `ranks` Logical, indicating whether the x-axis (means) should be plotted on the original scale (FALSE) or on the rank scale (TRUE). The latter distributes the data more evenly along the x-axis and allows a better visual assessment of the standard deviation as a function of the mean. `xlab` Character, label for the x-axis. `ylab` Character, label for the y-axis. `pch` Plot symbol. `col` Color of plotted points. See details. `...` Further arguments that get passed to plot.default.\n\n### Details\n\nStandard deviation and mean are calculated row-wise from the matrix `exprs(x)`. The scatterplot of these versus each other allows to visually verify whether there is a dependence of the standard deviation (or variance) on the mean. The red dots depict the running median estimator (window-width 10%). If there is no variance-mean dependence, then the line formed by the red dots should be approximately horizontal.\n\nIf the `preprocessing` slot of the `description` slot of `x` is a `list` and contains an element named `vsnTrimSelection`, then the coloring of the points reflects the trimming that was used in the least trimmed sum of squares (LTS) estimation (see `vsn`). If the condition does not apply, and `col` is `NULL`, the points are drawn in black. If `col` is not `NULL`, its value is used for the coloring of the points.\n\n### Value\n\nThe function is called for its side effect, creating a plot on the active graphics device.\n\n### Author(s)\n\nWolfgang Huber http://www.ebi.ac.uk/huber\n\n`vsn`\n\n### Examples\n\n``` data(kidney)\nlog.na = function(x) log(ifelse(x>0, x, NA))\n\nexprs(kidney) = log.na(exprs(kidney))\nmeanSdPlot(kidney)\n\n## ...try this out with non-logged data, the lymphoma data, your data...\n```\n\n[Package vsn version 1.8.0 Index]" ]

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[ "# Venn Diagrams Questions for RRB-NTPC Set-3 PDF\n\n0\n4167\n\n## Venn Diagrams Questions for RRB-NTPC Set-3 PDF\n\nDownload RRB NTPC Venn Diagram Questions Set-3 PDF. Top 10 RRB NTPC questions based on asked questions in previous exam papers very important for the Railway NTPC exam.\n\nQuestion 1: 100 people speak English. 80 people speak French and 60 people speak German. It is known that there are 200 people in total and each of them speaks at least one language. Exactly 50% of the total number of people speak exactly 2 languages. How many people speak all the three languages?\n\na) 1150\n\nb) 60\n\nc) 80\n\nd) 140\n\nQuestion 2: There are 100 students in a class. Each student like at least one game among cricket, football and hockey. 70 of them like football, 50 like cricket and 40 like hockey. If 20 students like exactly two games then find the number of people who like all three games.\n\na) 10\n\nb) 20\n\nc) 15\n\nd) 25\n\nQuestion 3: In the figure given below, find the number of people who are part of triangle, circle and square but not hexagon or pentagon?\n\na) 4\n\nb) 3\n\nc) 1\n\nd) 5\n\nQuestion 4: In the following Venn diagram find the number of actors who are singers but not engineers?\n\na) 32\n\nb) 25\n\nc) 27\n\nd) 29\n\nQuestion 5: Four diagrams are given for each question. Choose the best diagram which describes\nSilver, Metals, Zinc\n\na)\n\nb)\n\nc)\n\nd)\n\nQuestion 6: In the following Venn diagram find the sum of the number of students who can speak only Hindi and students who can speak English but not Tamil?\n\na) t + g + r – f\n\nb) b + t + g + e\n\nc) t – x – z + r +b\n\nd) t + b + r + g\n\nQuestion 7: In a group of 310 people, 200 people play cricket and 145 people play rugby. The maximum number of people who can play both the games is x. The minimum people who play both the games is y. Find x – y.\n\na) 110\n\nb) 100\n\nc) 120\n\nd) Cannot be determined\n\nQuestion 8: A tea company has developed 3 varieties of tea – A, B and C. It hired 50 professional tea tasters to test the quality of the teas. After tasting the tea, they were asked to vote whether they liked a particular tea or not. In total, 90 votes were registered favouring the teas. The number of persons who liked exactly one variety of tea was twice the number of persons who liked all the 3 varieties of the tea. The number of persons who voted in favour of exactly 2 varieties of the tea is\n\na) 5\n\nb) 10\n\nc) 15\n\nd) 20\n\nQuestion 9: Which of the following diagrams captures the relationship between vehicles, houses, cars, sedans, villas and trains?\n\na)\n\nb)\n\nc)\n\nd)\n\nQuestion 10: Sumit and Ravi are standing in a queue. Sumit is 17th from the beginning and Ravi is 13th from the end. 12 people are standing between Sumit and Ravi. What is the total number of people in the queue?\n\na) 42\n\nb) 17\n\nc) 43\n\nd) Either 42 or 17\n\nLet’s write the expression for the union of the three sets.\n\n200 = 80 + 60 + 100 – (100) + x\n\nx = 60\n\nHence, option B is the correct answer.\n\nLet a represent the number of people who like only 1 game, b represent the people who like 2 games and c represent the people who like 3 games. We have been given that\na + b + c = 100\na + 2b + 3c = 70 + 50 + 40 = 160\nWe have been given that b = 20\nHence, we have\na + c = 80\na + 3c = 120\nHence, 2c = 40 => c = 20\nHence, option B is correct.\n\nOn observing the figure closely, we see that the number of people who are part of square, circle and triangle but not pentagon or hexagon are 1. Hence, option C is the correct answer.\n\nThe part of the diagram which represents actors who are singers but not engineers is the intersection of circle and rhombus and subtracting the triangle part.\nWe have 11 + 16 = 27\nHence, option C is the right choice.\n\nSilver and Zinc are independent, but both are Metals.\n\nHence, option A is the right choice.\n\nWe have to find only hexagon + square – triangle\nSo sum of number of students who can speak only Hindi and students who can speak English but not Tamil = t + b + r + g\nHence, option D is the right choice.\n\nLet’s first consider the minimum – y:\nIf all 310 people play at least one game, then\n310 = 200 + 145 – y\ny = 35\n\nLet’s consider the maximum – x\nIf some people do not play either of the two games, x’s value can increase till 145.\nMore than 145 is not possible as only 145 people play rugby.\nThus, x = 145\n\nDifference = 145 – 35 = 110\n\nLet ‘a’ be the number of persons liking exactly one variety of tea, ‘b’ be the number of persons liking exactly 2 varieties of tea and ‘c’ be the number of persons liking all the 3 varieties.\n\nWe know that,\na+b+c = 50\na+2b+3c = 90.\n\nAlso, it has been given that a = 2c\n=> b + 3c = 50\n2b + 5c = 90\n\n2b + 6c = 100\n2b + 5c = 90\n=> c = 10\nb = 20 and a = 20.\nTherefore, option D is the right answer." ]

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[ "Cody\n\n# Problem 44446. Add a vector to a matrix\n\nCreated by Shaul Salomon in Community\n\nGiven a matrix mat of size mXn and a row vector v of size 1Xs, return a matrix with m+1 rows that conatains mat over v. The number of columns is the larger between n and s.\n\nIf s>n, the matrix is padded with Inf.\n\nIf n>s, the vector is padded with -Inf.\n\nExamples:\n\n```inputs:\nmat = [1 2\n3 4]\nv = [5 6 7 8]\n```\n```output:\ncomb = [1 2 Inf Inf\n3 4 Inf Inf\n5 6 7 8 ]\n```\n```inputs:\nmat = [1 2 3 4 5\n6 7 8 9 10]\nv = [11 12]\n```\n```output:\ncomb = [1 2 3 4 5\n6 7 8 9 10\n11 12 -Inf -Inf -Inf]\n```\n\n### Solution Stats\n\n30.69% Correct | 69.31% Incorrect\nLast solution submitted on Feb 15, 2019" ]

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[ "# Video: Using the Pythagorean and Periodic Identities to Evaluate the Cosine Function given the Sine Function and Quadrant of an Angle\n\nFind the value of cos (180° − 𝜃) given sin 𝜃 = −3/5 where 270° < 𝜃 < 360°.\n\n03:12\n\n### Video Transcript\n\nFind the value of cosine of 180 degrees minus 𝜃 given the sign of 𝜃 is negative three-fifths where 𝜃 is between 270 degrees and 360 degrees.\n\nSo essentially, we are looking for cosine, and we’ve been given sine. So we can use some trig identities to help us. Cosine squared 𝜃 plus sine squared 𝜃 is equal to one and we know the sine of 𝜃 is negative three-fifths. So we will be able to find the cosine. So let’s go ahead and square negative three-fifths. Negative three squared is positive nine and five squared is 25.\n\nSo now, we need to subtract nine 25ths from both sides of the equation. Now, when we have one minus nine 25ths, we can make the one 25 25ths. So now we subtract the numerator 25 minus nine and we keep the denominator. So cosine squared of 𝜃 is equal to 16 25ths. And now we square root both sides. The square root of 16 is four and the square root of 25 is five. So cosine of 𝜃 is four-fifths.\n\nNow, it’s asking about the cosine of 180 degrees minus 𝜃. We could rewrite this. We can separate the 180 degrees to be 90 degrees plus 90 degrees. Now using more trig identities, we have that this is equal to the negative sine of 90 degree minus 𝜃. And the way that we got this was letting the 90 degrees minus 𝜃 just represent a general 𝜃. So we have the cosine of 90 degrees plus 𝜃 equals negative sine of 𝜃.\n\nNow, negative sine of 90 degrees minus 𝜃 is equal to negative cosine 𝜃. Because we know by more trig identities, the sine of 90 degrees minus 𝜃 is equal to the cosine of the 𝜃. So the only difference is we had a negative sine on the left, which means we’d also need a negative sine on the right. So if these are equal to each other and we found that the cosine of 𝜃 was four-fifths, then we can take that and replace that for the cosine of 𝜃. So negative cosine of 𝜃 is equal to negative four-fifths.\n\nSo we get that our answer is negative four-fifths. Now we’re also given one other piece of information. So we are also told that 𝜃 is between 270 degrees and 360 degrees. So this means that we’re in quadrant four, between 270 and 360. And we also know that cosine of 𝜃 represents our 𝑥-values and sine of 𝜃 represent our 𝑦-values. So if we know that the cosine of 𝜃 was positive four-fifths, we will be looking at the 𝑥-value in the fourth quadrant, which is positive.\n\nHowever, what we’re asked to find was this cosine of 180 degrees minus 𝜃, which we’ve found to be equal to negative of our cosine of 𝜃. And we know that since it’s in the fourth quadrant, cosine of 𝜃 was positive. But now we have to attach this negative sine out-front. So this means our final answer is negative four-fifths." ]

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[ "# Covering a Chessboard with a Hole with L-Trominoes\n\nThe applet below is an interactive illustration for the problem #678 proposed by Charles W. Trigg, San Diego, California (Mathematics Magazine, Vol. 41, No. 1 (Jan., 1968), p. 42):\n\nFrom an 8 by 8 checkerboard, the four central squares are removed.\n\n1. Show how to cover the remainder of the board with right trominoes so as to have no fault line, or exactly two fault lines, or three fault lines.\n2. Show that no covering with right trominoes can have four fault lines.\n\nA right tromino is a nonrectangular assemblage of three adjoining squares mostly referred to as L-tromino at this site. A fault line has its extremities on the perimeter so that a portion of the configuration may be slid along it in either direction without otherwise disturbing the relative position of its parts.\n\n(Two draw a tromino, click on one of the squares, move (not drag) the cursor to the next one and click again, move to a third (suitable) square and - to place a tromino - click the third time.)\n\n### This applet requires Sun's Java VM 2 which your browser may perceive as a popup. Which it is not. If you want to see the applet work, visit Sun's website at https://www.java.com/en/download/index.jsp, download and install Java VM and enjoy the applet.\n\n What if applet does not run?\n\nGolomb's theory assures us that the 8×8 board with a 2×2 hole - whenever the latter is cut off - can be covered with L-trominoes and that in multiple ways. Indeed, place one tromino into the cut-off square will leave a 1×1 hole. Now Golomb's theorem shows that an 8×8 board with a 1×1 hole can be covered with L-trominoes. So the question is clearly about counting the fault lines.\n\nSolution", null, "• Covering A Chessboard With Domino\n• Dominoes on a Chessboard\n• Tiling a Chessboard with Dominoes\n• Vertical and Horizontal Dominoes on a Chessboard\n• Straight Tromino on a Chessboard\n• Golomb's inductive proof of a tromino theorem\n• Tromino Puzzle: Interactive Illustration of Golomb's Theorem\n• Tromino as a Rep-tile\n• Tiling Rectangles with L-Trominoes\n• Squares and Straight Tetrominoes\n• Tromino Puzzle: Deficient Squares\n• Tiling a Square with Tetrominoes Fault-Free\n• Tiling a Square with T-, L-, and a Square Tetrominoes\n• Tiling a Rectangle with L-tetrominoes\n• Tiling a 12x12 Square with Straight Trominoes\n• Bicubal Domino\n•", null, "### Solution\n\nSolution below is by Benjamin L. Schwartz, The MITRE Corporation, Virginia.\n\nThe problem as stated leaves unsettled the question of the existence of exactly one fault line. In the discussion below, we shall also resolve this question affirmatively with an example.\n\nNotation. Denote the 8 horizontal rows of squares by letters A through H. Denote the vertical files by numbers 1 through 8. Denote a line between rows by the names of the two bordering rows (e.g., line BC).", null, "1. The diagrams (1), (2), (3) and (4) show examples with zero, one, two and three fault lines, respectively. In (2), the fault line is 34. In (3), the fault lines are DE and 45; and, in (4), they are CD, EF and 45. As shown later, these arrangements of fault lines are essentially unique.\n\n2. To prove other cases impossible, we introduce a few easily proved lemmas about coverings with trominoes. Proofs are omitted.\n\n1. A 2×n area can be covered iff 31 n.\n2. Two adjacent lines (e.g., CD and DE) cannot both be fault lines.\n3. A 3×3 area cannot be covered exactly.\n4. A fault line cannot occur adjacent to an edge.\n\nLemma IV eliminates A F, GH, 12 and 78 as candidates. But Lemma I also eliminates BC, FG, 23 and 67. Hence the only horizontal candidates are CD, DE and EF; and verticals 34, 45 and 56. Furthermore, by Lemma II, if DE is a fault line, it is the only horizontal one. Similarly, if 45 is a vertical fault line, it is the only one.\n\nThus, the only prospect for a 4-fault-line configuration requires that these lines be CD, EF, 34 and 56. But this means the 3×3 areas in the four corners must be covered exactly, which violates Lemma III. An additional question is whether the arrangement of fault lines in each of the various cases is essentially unique. The affirmative answer to this follows from the following theorem:\n\nIf CD is a fault line, so is EF. (Similarly 34 and 56.)\n\nTo see this, suppose there is a covering with CD as a fault line. Then consider how square Dl could be covered. Place a tromino to cover it with each of the three possible orientations of the other two squares. It follows that either the other squares of files 1 and 2 in rows D and E cannot be covered, or can only be covered in such a way as to fill exactly the 2×3 rectangle (123)×(DE). The same argument applies to (678)×(DE). Hence EF must be a fault line.\n\nA more laborious and detailed analysis concerns the actual arrangement of the trominoes in the coverings. It has shown that except for \"flipover\" of the coverings of 2×3 rectangles, and rotations of the entire board, the solutions of (2), (3) and (4) are unique. A similar statement is believed to hold for (1), but has not yet been proved.", null, "" ]

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[ "### Recent Submissions\n\n• #### On the number of labeled graphs of bounded treewidth", null, "\n\n(2018-06-01)\nArticle\nOpen Access\nLet be Tnk the number of labeled graphs on vertices and treewidth at most (equivalently, the number o<f labeled partial -trees). We show that [...] for k>1 and some explicit absolute constant c>0. Disregarding terms depending ...\n• #### Transformation and decomposition of clutters into matroids", null, "\n\n(2017-05-25)\nArticle\nOpen Access\nA clutter is a family of mutually incomparable sets. The set of circuits of a matroid, its set of bases, and its set of hyperplanes are examples of clutters arising from matroids. In this paper we address the question of ...\n• #### On trees with the same restricted U-polynomial and the Prouhet–Tarry–Escott problem", null, "\n\n(2017-06)\nArticle\nOpen Access\nThis paper focuses on the well-known problem due to Stanley of whether two non-isomorphic trees can have the same U-polynomial (or, equivalently, the same chromatic symmetric function). We consider the Uk-polynomial, which ...\n• #### Threshold functions and Poisson convergence for systems of equations in random sets", null, "\n\n(2017-05-10)\nArticle\nOpen Access\nWe study threshold functions for the existence of solutions to linear systems of equations in random sets and present a unified framework which includes arithmetic progressions, sum-free sets, Bh[g]Bh[g]-sets and Hilbert ...\n• #### Corrigendum to\"On the limiting distribution of the metric dimension for random forests\" [European J. Combin. 49 (2015) 68-89]", null, "\n\n(2017-07-22)\nArticle\nOpen Access\nIn the paper ”On the limiting distribution of the metric dimension for random forests” the metric dimension ß(G) of sparse G(n, p) with p = c/n and c < 1 was studied (Theorem 1.2). In the proof of this theorem, for the ...\n• #### Counting configuration-free sets in groups", null, "\n\n(2017-01-01)\nArticle\nOpen Access\n© 2017 Elsevier Ltd. We provide asymptotic counting for the number of subsets of given size which are free of certain configurations in finite groups. Applications include sets without solutions to equations in non-abelian ...\n• #### Random strategies are nearly optimal for generalized van der Waerden Games", null, "\n\n(2017-08-01)\nArticle\nOpen Access\nIn a (1 : q) Maker-Breaker game, one of the central questions is to find (or at least estimate) the maximal value of q that allows Maker to win the game. Based on the ideas of Bednarska and Luczak [Bednarska, M., and T. ...\n• #### Enumeration of labeled 4-regular planar graphs", null, "\n\n(2017-08-01)\nArticle\nOpen Access\nIn this extended abstract, we present the first combinatorial scheme for counting labeled 4-regular planar graphs through a complete recursive decomposition. More precisely, we show that the exponential generating function ...\n• #### Counting outerplanar maps", null, "\n\n(2017-04-13)\nArticle\nOpen Access\nA map is outerplanar if all its vertices lie in the outer face. We enumerate various classes of rooted outerplanar maps with respect to the number of edges and vertices. The proofs involve several bijections with lattice ...\n• #### Subgraph statistics in subcritical graph classes", null, "\n\n(2017-04-01)\nArticle\nOpen Access\nLet H be a fixed graph and math formula a subcritical graph class. In this paper we show that the number of occurrences of H (as a subgraph) in a graph in math formula of order n, chosen uniformly at random, follows a ...\n• #### A lower bound for the size of a Minkowski sum of dilates", null, "\n\n(2011-03-01)\nArticle\nOpen Access\nLet A be a finite non-empty set of integers. An asymptotic estimate of the size of the sum of several dilates was obtained by Bukh. The unique known exact bound concerns the sum |A + k·A|, where k is a prime and |A| is ...\n• #### Asymptotic enumeration of non-crossing partitions on surfaces", null, "\n\n(2013-03-01)\nArticle\nOpen Access\nWe generalize the notion of non-crossing partition on a disk to general surfaces with boundary. For this, we consider a surface S and introduce the number CS(n) of noncrossing partitions of a set of n points laying on the ..." ]

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[ "", null, "Suggested languages for you:\n\nEurope\n\nAnswers without the blur. Sign up and see all textbooks for free!", null, "Q23.\n\nExpert-verified", null, "Found in: Page 7", null, "### Algebra 1\n\nBook edition Student Edition\nAuthor(s) Carter, Cuevas, Day, Holiday, Luchin\nPages 801 pages\nISBN 9780078884801", null, "# Write an algebraic expression for each verbal expression.$f$ divided by 10.\n\nThe algebraic expression is $\\frac{\\mathbf{f}}{\\mathbf{10}}$.\n\nSee the step by step solution\n\n## Step 1. Algebraic Expression.\n\nAn algebraic expression is an expression that comprises sums and products of variables and numbers. For example, $2a$ and $\\frac{1}{2}b$.\n\n## Step 2. Verbal expression for algebraic expression.\n\nIf verbal quotient of and divided by, then the operation in algebraic expression is division.\n\n## Step 3. Translate to an algebraic expression.\n\nThe word “divided by” translates to operation division.\n\nHence, an algebraic expression from the given verbal expression will be “$\\frac{f}{10}$”.\n\nTherefore, the algebraic expression is “$\\frac{f}{10}$”.", null, "### Want to see more solutions like these?", null, "" ]

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[ "# Questions tagged [time-limit-exceeded]\n\nWhen the code scales so poorly in the face of large inputs that it cannot complete in a reasonable amount of time, use this instead of the [performance] tag.\n\n1,047 questions\nFilter by\nSorted by\nTagged with\n60 views\n\n### HackerRank Algorithm Problem: Climbing the Leaderboard (Python)\n\nHere is the Hackerrank problem which is related to dense ranking and below is my solution which didn't pass the time limit cases. Any better way to optimize this? ...\n255 views\n\n### Trailing Digits\n\nhttps://www.acmicpc.net/problem/23204 I've solved a programming challenge where you need to count the occurrences of a specific digit at the end of the product of multiples of a given number within a ...\n102 views\n\n### HackerRank Project Euler 12 (Python) | Highly Divisible Triangular Numbers\n\nI again share my Python code which didn't pass time limit test cases in the HackerRank contest of ProjectEuler. ...\n106 views\n\n### calculate the number of ways to pick two different indices\n\nI'm working on a codesignal practice problem You are given an array of integers a and an integer k. Your task is to calculate the number of ways to pick two different indices i < j, such that a[i] ...\n89 views\n\n### Codeforces: Dasha & Nightmares\n\nso I got started with competitive programming about a day ago and I got stuck on the first random question I tried on codeforces. It's called Dasha and Nightmares. Problem Description: The problem ...\n246 views\n\n### Traveling Salesman Problem for visiting cities\n\nImplement TSP problem using best first algorithm (so it will be backtracking, branch-and-bound, and best-first). Since you are looking for a cycle, the start/finish city is not important. Therefore we ...\n115 views\n\n### One or more planets to line up with the earth a certain amount of times\n\nI have attempted the below question, however my solution is too slow (i.e. It does not fit the 2 second time constrain for java). How can the solution be optimised? While at IOI 2020 in Singapore, ...\n1 vote\n51 views\n\n### Find all combinations of two companies grouped by the projects they are tendering for\n\nI am working on the task to get all possible combinations (pairs) of ID's (companies) which participated in one bid and create a new data frame with ID_1, ID_2, matching parameter (tender ID). I have ...\n133 views\n\n### Find character at given index in a sorted sub strings [closed]\n\nFor a given string say dbac the possible substrings are [d,db,dba,dbac,b,ba,bac,a,ac,c]. Sort them and concatenate to a string: ...\n108 views\n\n### Find largest sum not involving consecutive values\n\nThere is a question to basically find the largest sum in an array, such that no two elements are chosen adjacent to each other. The concept is to recursively calculate the sum, while considering and ...\n1 vote\n101 views\n\n### Positive Segments\n\nI'm trying to solve the following question: You have an array A of size n, containing −1 or 1 only, and s segments (not necessarily different). Each segment is defined by 2 integers li and ri (1 ≤ li ...\n54 views\n\n### Market Portfolio Binary Search Tree [closed]\n\nI'm trying to solve the following problem here: First line of input contains the number of days D. The next d lines contains a character c and a number x. If c is B, then buy stock . If c is S, then ...\n535 views\n\n### O(nlogn) Lexicographically minimal rotation code but tle on this particular case\n\nBased on a small suggestion here , this code tries to find lexicographically minimal rotation (question) by successively comparing two adjacent substrings in the very left , that can potentially give ...\n173 views\n\n### k-dice Ways to get a target value\n\nI'm trying to solve the following problem: You have a k-dice. A k-dice is a dice which have k-faces and each face have value written from 1 to k. Eg. A 6-dice is the normal dice we use while playing ...\n988 views\n\n### Knock down tall buildings\n\nI'm trying to solve the following problem: As you know Bob likes to destroy the buildings. There are N buildings in a city, ith building has ai floors. Bob can do the following operation. 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[ "# SQL FIND_IN_SET command to search strings within a set of string\n\n``SELECT FIND_IN_SET('search_string','set1,set2,set3')``\nHere search_string is used to search on on set of strings separated by coma.\nOutput\n\n0 : if no match is found\nnumber : position of the matching set\nnull : If search is applied on a null set\n\n## Example of FIND_IN_SET on string\n\n``SELECT FIND_IN_SET('ry', 'kpy,tyu,ryk,pkr')``\nNo matching record so Output 0\n``SELECT FIND_IN_SET('ry', 'kpy,tyu,ryk,pkr,bry,ry,lkiu')``\nOutput 6\n\n``SELECT * FROM student WHERE FIND_IN_SET('john',name) > 0``\nNo records found\n``SELECT * FROM student WHERE FIND_IN_SET('Alex John',name) > 0``\nOutptu is here ( one record found )\n``6\tAlex John\tFour\t58\tmale``\n\n## FIND_IN_SET & LOCATE\n\nWe have already seen FIND_IN_SET against string. We will find the difference between FIND_IN_SET and LOCATE query.\n``SELECT FIND_IN_SET('ry', 'kpy,tyu,ryk,pkr')``\nNo matching record so Output is 0\n``SELECT LOCATE('ry', 'kpy,tyu,ryk,pkr')``\nOutput is 9\nHere keyword is not matched against each set of string, it is matching as a total string so the position of matching string ry is located at 9th position from left. Here position of (, ) coma is also considered as one char for calculating the postion of matching string.\n``SELECT * FROM student WHERE FIND_IN_SET(2,id) > 0 ``\nOne matching record we will get, Output is here\n``2\tMax Ruin\tThree\t85\tmale``\nHere we get one record with id = 2 , now let us try LOCATE query using student table.\n``SELECT * FROM student WHERE LOCATE(2,id) > 0 ``\nWe will get 14 matching records as all records having id equal to 2, 12, 20,21, ..... 32,42 will be retured. The matching is done by using the ID field as string.\n\n## Difference with IN\n\nWhile using IN Query , We search for a set of key words on a column like this\n``SELECT * FROM student WHERE name IN ( 'John','Alex')``\nWhile using SQL_FIND_IN we use one keyword on a column like this.\n``SELECT * FROM student WHERE FIND_IN_SET('Bigy',name)``\nWe get one matching record , output is here\n``14\tBigy\tSeven\t88\tfemale``\nNow let us apply this LOCATE command to search for the presence of the name john in the name field (column ) of our student table.\n``SELECT * FROM `student` WHERE locate( 'john', name )``\nThe output of this query is here.\n name class mark sex John Deo Four5 75 male John Mike Four5 60 male Alex John Four5 55 male My John Rob Fifth5 78 male Big John Four5 55 male Babby John Four5 69 male\nAs you can see we have collected all the records having 'john' in any place in the name column of the student table.\n``SELECT * FROM `student` WHERE FIND_IN_SET('john',name)``\nThe above command will return empty results set. Here the string 'john' is matched with all data in name column of student table.", null, "## Subscribe\n\n* indicates required\nSubscribe to plus2net", null, "plus2net.com\n\nPost your comments , suggestion , error , requirements etc here ." ]

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[ "# Find inverse and determinant of a symmetric matrix - for a maximum-likelihood estimation\n\nEvaluate the determinant $\\det \\Omega$ and find the inverse matrix $\\Omega^{-1}$ of:\n\n$$\\Omega = \\begin{bmatrix} \\beta_1^2(1+\\theta_1^2) & \\beta_1 \\beta_2 & ... & \\beta_1 \\beta_{k-1} & \\beta_1 \\beta_k \\\\ \\beta_2 \\beta_1 & \\beta_2^2(1+ \\theta_2^2) & ... & \\beta_2 \\beta_{k-1} & \\beta_2 \\beta_k \\\\ ... & ... & ... & ... & ... \\\\ \\beta_k \\beta_1 & \\beta_k \\beta_2 & ... & \\beta_k \\beta_{k-1} & \\beta_k^2(1+\\theta_k^2) \\end{bmatrix}$$\n\nApplication\n\nI got this problem when attempting to understand the methodology of the Worldwide Governance Indicators where the authors specify a log-likelihood function of three unknown parameters to solve the maximisation at page 97-99 here Governance Matters VII: Aggregate and Individual Governance Indicators, 1996-2007 (page 97-99).\n\n$$\\Omega = \\begin{bmatrix} \\beta_1^2(1+\\theta_1^2) & \\beta_1 \\beta_2 & ... & \\beta_1 \\beta_{k-1} & \\beta_1 \\beta_k \\\\ \\beta_2 \\beta_1 & \\beta_2^2(1+ \\theta_2^2) & ... & \\beta_2 \\beta_{k-1} & \\beta_2 \\beta_k \\\\ ... & ... & ... & ... & ... \\\\ \\beta_k \\beta_1 & \\beta_k \\beta_2 & ... & \\beta_k \\beta_{k-1} & \\beta_k^2(1+\\theta_k^2) \\end{bmatrix}= \\begin{bmatrix} \\beta_1^2\\theta_1^2 & & & \\\\ & \\beta_2^2\\theta_2^2 & & \\\\ & & \\ddots & \\\\ & & & \\beta_k^2\\theta_k^2\\\\ \\end{bmatrix} + \\begin{bmatrix} \\beta_1 \\\\ \\beta_2 \\\\ \\vdots \\\\ \\beta_k \\\\ \\end{bmatrix} \\cdot \\begin{bmatrix} \\beta_1 \\: \\beta_2 \\: \\ldots \\:\\beta_k \\end{bmatrix}$$" ]

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