text:
# How can recursive editing of a comma-separated list be handled in expl3?

How can I recursively process a comma-separated list in expl3? How to make a recursive Latex macro with comma separated argument list looks like a (more general) duplicate and offers no fewer than two expl3 answers. However, I'm obviously an idiot because I still can't figure out how to do it. I understand that expansion always confuses me, but I don't understand why none of the many variants I've played with have worked - or even given me errors. (OK, I do more-or-less understand why they don't give me errors, given that they don't work.)

I've also tried with sequences. Unsurprisingly, I couldn't get those to work either. I tried using an aux function along (I thought) the lines shown in Scott H.'s answer. However, I apparently can't discern the salient features of that solution well enough to adapt it here. I didn't understand egreg's answer well enough to try anything.

\documentclass[border=10pt]{standalone}
\usepackage{expl3}
\begin{document}
\ExplSyntaxOn
\cs_new_protected_nopar:Nn \subsets_construct_subset:nn
{
\clist_set:Nn \l_tmpa_clist { #1 }
\int_zero:N \l_tmpa_int
\tl_clear:N \l_tmpa_tl
\clist_map_inline:Nn \l_tmpa_clist
{
\int_incr:N \l_tmpa_int
\int_compare:nF { \l_tmpa_int = #2 }{
\int_compare:nTF { #2 = 1 }{
\int_compare:nF { \l_tmpa_int = 2 } { \tl_put_right:Nn \l_tmpa_tl { , } }
}{
\int_compare:nF { \l_tmpa_int = 1 } { \tl_put_right:Nn \l_tmpa_tl { , } }
}
\tl_put_right:Nn \l_tmpa_tl { ##1 }
}
}
\tl_use:N \l_tmpa_tl
}
\cs_generate_variant:Nn \clist_set:Nn { Nx }
\subsets_construct_subset:nn { 2, 3, 4, 5 } { 2 } ~ : ~
\subsets_construct_subset:nn { 2, 4, 5 } { 1 } ~ : ~
\subsets_construct_subset:nn { \subsets_construct_subset:nn { 2, 3, 4, 5 } { 2 } } { 1 } ??
\ExplSyntaxOff
\end{document}

Sometimes, expansion seems more difficult to deal with in expl3 than it did before the revolution!

EDIT I wanted to use this in an answer to The way to list subsets of the set {1, 2, 3, 4, 5} with forest or tree package. However, my answer there actually does it differently. I rewrote the Forest code in order to avoid the need for applying the expl3 function recursively. I wanted to avoid needing to do that, partly because a recursive approach seemed to reflect what was needed (or what I thought was needed) and partly because adding cycles to a Forest tree makes things very slow, very quickly. Also, I thought I must be missing some simple and obvious solution, as what I wanted seemed a pretty mundane sort of thing to need to do. So I wanted, as each node was added, to construct its content based on its parent's content and its n value. However, to do this, its necessary to repeatedly apply the expl3 function as the tree grows. My current solution just adds the nodes and populates them only when the entire structure is in place (using an expl3 function very similar to the one Christian suggests below, as it happens). But this seems a less transparent approach ....

• Would you please add what's the expected output from the last call? Anyway, passing \subsets_construct_subset:nn { 2, 3, 4, 5 } { 2 } as the second argument to \clist_set:Nn will not build a clist and only one item will be seen; since \subsets_construct_subset:nn doesn't work by expansion alone, I can't see what you're after. – egreg Aug 6 '17 at 8:00
• @egreg: The output should be 4,5 I think. The first strips the 3 from the 2,3,4,5 list, leaving 2,4,5 and this should be feeded again, stripping the first element in the list, so 4,5 remains. But I agree that this not expandable and the \clist_set:Nn will not generate a \clist – user31729 Aug 6 '17 at 8:23
• @egreg 4,5. I realise it doesn't work. But I don't know how to make it work. How can I get something which is expanded to the list produced by the first step, which I can feed back in for the second step? – cfr Aug 6 '17 at 12:55
• @egreg Because expansion just expands the tokens? I already said I don't understand it! – cfr Aug 6 '17 at 12:56

I can offer a recursion based on what the first token in the first argument is; if it is \subsets_construct_subset:nn, the function is executed and the result passed as argument to the same function.

I see several cases in which this can fail, though. Anyway, this is obviously not a problem of expansion: \subsets_construct_subset:nn doesn't work by pure expansion, so you cannot hope some f expansion magic can work (and x expansion definitely won't, because it doesn't work by pure expansion).

\documentclass{article}
\usepackage{expl3}
\begin{document}

\ExplSyntaxOn
\cs_new_protected:Nn \subsets_construct_subset:nn
{
\clist_set:Nn \l_tmpa_clist { #1 }
\exp_last_unbraced:Nx \token_if_eq_meaning:NNTF { \tl_head:n { #1 } } \subsets_construct_subset:nn
{
\cs_set_eq:NN \__subsets_use:n \use_none:n
#1
\cs_set_eq:NN \__subsets_use:n \use:n
\subsets_construct_subset:xn { \tl_use:N \l_tmpa_tl } { #2 }
}
{
\__subsets_construct_subset:nn { #1 } { #2 }
\__subsets_use:n { \tl_use:N \l_tmpa_tl }
}
}
\cs_set_eq:NN \__subsets_use:n \use:n % initialize
\cs_new_protected:Nn \__subsets_construct_subset:nn
{
\int_zero:N \l_tmpa_int
\tl_clear:N \l_tmpa_tl
\clist_map_inline:Nn \l_tmpa_clist
{
\int_incr:N \l_tmpa_int
\int_compare:nF { \l_tmpa_int = #2 }{
\int_compare:nTF { #2 = 1 }{
\int_compare:nF { \l_tmpa_int = 2 } { \tl_put_right:Nn \l_tmpa_tl { , } }
}{
\int_compare:nF { \l_tmpa_int = 1 } { \tl_put_right:Nn \l_tmpa_tl { , } }
}
\tl_put_right:Nn \l_tmpa_tl { ##1 }
}
}
}
\cs_generate_variant:Nn \subsets_construct_subset:nn { x }

\subsets_construct_subset:nn { 2, 3, 4, 5 } { 2 } \par
\subsets_construct_subset:nn { 2, 4, 5 } { 1 } \par
\subsets_construct_subset:nn { \subsets_construct_subset:nn { 2, 3, 4, 5 } { 2 } } { 1 }
\ExplSyntaxOff

\end{document}

• Thanks very much. I've actually rewritten the Forest code to use a non-recursive approach (similar to Christian's answer, as it happens). But it would be nice not to have to do it that way. What does it mean for something to work or not work 'by pure expansion'? – cfr Aug 6 '17 at 20:45
• It seems weird to me that there's no simple way to do this. (That is, this is very impressive, of course, but it seems quite a fragile and roundabout way to have to do something which seemed to me fairly mundane.) – cfr Aug 6 '17 at 20:51

A solution without recursion, by 'double' - looping over the second argument which is a comma separated list as well:

\documentclass{article}
\usepackage{expl3}
\begin{document}
\ExplSyntaxOn

\clist_new:N \l_cfr_subset_clist

\cs_new:Nn \subsets_construct_subset:nn
{
\group_begin:
\clist_set:Nn \l_cfr_subset_clist {#1}
\clist_set:Nn \l_tmpb_clist { #2 }
\clist_map_inline:Nn \l_tmpb_clist {% Loop over the indices
\int_zero:N \l_tmpa_int
\clist_set_eq:NN \l_tmpa_clist \l_cfr_subset_clist
\clist_clear:N \l_cfr_subset_clist
\clist_map_inline:Nn \l_tmpa_clist
{% Loop over the current temp list
\int_incr:N \l_tmpa_int
\int_compare:nF { \l_tmpa_int = ##1 }{
\clist_put_right:Nn \l_cfr_subset_clist {####1}
}
}
}
\clist_use:Nn \l_cfr_subset_clist {,}
\group_end:
}

\subsets_construct_subset:nn { 2, 3, 4, 5 } { 2 } ~ : ~
\par
\subsets_construct_subset:nn { 2, 4, 5 } { 1 } ~ : ~
\par
\subsets_construct_subset:nn { 2, 3, 4, 5 } { 2, 1 } ~ : ~
\par
\subsets_construct_subset:nn { 2, 3, 4, 5 } { 2, 1,1 } ~ : ~
\ExplSyntaxOff
\end{document}

• Yes, thanks. This is pretty similar to what I've got. But it means rewriting the Forest code, which I'd hoped to avoid. – cfr Aug 6 '17 at 20:38
• @cfr: It's not recursive, I know. – user31729 Aug 6 '17 at 20:39
• tex.stackexchange.com/questions/384906/… is my rewrite. But it means more Forest cycling .... ;( – cfr Aug 6 '17 at 20:49


text:
# [SOLVED] 1st Order Diff Equation

• September 22nd 2008, 01:20 PM
Ian1779
[SOLVED] 1st Order Diff Equation
Hi - I am just checking that I have got the right idea

The following first-order differential equation can be solved by separting the variables

${\frac{dy}{dx}} = x^2 + 2x^2y^2(y>0)$

Am I right in saying that the following is the right separation so I can integrate and solve?

$\int {\frac{dy}{1+2y^2}}= \int x^2 dx$

Thanks in anticipation.
• September 22nd 2008, 01:21 PM
Moo
Hello,
Quote:

Originally Posted by Ian1779
Hi - I am just checking that I have got the right idea

The following first-order differential equation can be solved by separting the variables

${\frac{dy}{dx}} = x^2 + 2x^2y^2(y>0)$

Am I right in saying that the following is the right separation so I can integrate and solve?

$\int {\frac{dy}{1+2y^2}}= \int x^2 dx$

Thanks in anticipation.

Yes you are right :)
• September 22nd 2008, 01:21 PM
icemanfan
Yes, that differential equation is separable and your setup is correct.
• September 22nd 2008, 01:22 PM
Matt Westwood
Looks okay to me.
• September 22nd 2008, 01:24 PM
Ian1779
Brilliant - thanks for the swift reply. It's really important I get this assignment right so trying to make sure it's all right (Happy)

format: plain


text:
Browse Questions

# The flame colours of metal ions are due to

Metal excess defect
Hence (D) is the correct answer.


text:
Home > Programming > Programming an estimation command in Stata: A first ado-command using Mata

## Programming an estimation command in Stata: A first ado-command using Mata

I discuss a sequence of ado-commands that use Mata to estimate the mean of a variable. The commands illustrate a general structure for Stata/Mata programs. This post builds on Programming an estimation command in Stata: Mata 101, Programming an estimation command in Stata: Mata functions, and Programming an estimation command in Stata: A first ado-command.

This is the thirteenth post in the series Programming an estimation command in Stata. I recommend that you start at the beginning. See Programming an estimation command in Stata: A map to posted entries for a map to all the posts in this series.

I begin by reviewing the structure in mymean5.ado, which I discussed in Programming an estimation command in Stata: A first ado-command.

*! version 5.0.0 20Oct2015
program define mymean5, eclass
version 14

syntax varlist(max=1)

tempvar e2
tempname b V
quietly summarize varlist'
local sum            = r(sum)
local N              = r(N)
matrix b'           = (1/N')*sum'
generate double e2' = (varlist' - b'[1,1])^2
quietly summarize e2'
matrix V'           = (1/((N')*(N'-1)))*r(sum)
matrix colnames b'  = varlist'
matrix colnames V'  = varlist'
matrix rownames V'  = varlist'
ereturn post b' V'
ereturn display
end

The syntax command on line 5 stores the name of the variable for which the command estimates the mean. The tempvar and tempname commands on lines 7 and 8 put temporary names into the local macros e2, b, and V. Lines 9-15 compute the point estimates and the estimated variance-covariance of the estimator (VCE), using the temporary names for objects, so as not to overwrite user-created objects. Lines 16–18 put the column name on the point estimate and row and column names on the estimated VCE. Line 19 posts the point estimate and the estimated VCE to e(b) and e(V), respectively. Line 20 produces a standard output table from the information stored in e(b) and e(V).

By the end of this post, I will have a command that replaces the Stata computations on lines 9–15 with Mata computations. To illustrate the structure of Stata-Mata programming, I start off only computing the point estimate in myregress6.

*! version 6.0.0 05Dec2015
program define mymean6, eclass
version 14

syntax varlist(max=1)

mata: x  = st_data(., "varlist'")
mata: w  = mean(x)
mata: st_matrix("Q", w)

display "The point estimates are in Q"
matrix list Q

end

Line 7 executes a one-line call to Mata; in this construction, Stata drops down to Mata, executes the Mata expression, and pops back up to Stata. Popping down to Mata and back up to Stata takes almost no time, but I would like to avoid doing it three times. (Lines 8 and 9 are also one-line calls to Mata.)

Line 7 puts a copy of all the observations on the variable for which the command estimates the mean in the Mata column vector named x, which is stored in global Mata memory. Line 8 stores the mean of the column vector in the 1$$\times$$1 matrix named w, which is also stored in global Mata memory. Line 9 copies the Mata matrix w to the Stata matrix named Q. Lines 11 and 12 display the results stored in Stata.

I illustrate what myregress6 produces in example 1.

Example 1: myregress6 uses global Mata memory

. sysuse auto
(1978 Automobile Data)

. mymean6 price
The point estimates are in Q

symmetric Q[1,1]
c1
r1  6165.2568

. matrix dir
Q[1,1]

. mata: mata describe

# bytes   type                        name and extent
-------------------------------------------------------------------------------
8   real scalar                 w
592   real colvector              x[74]
-------------------------------------------------------------------------------

I use matrix dir to illustrate that Q is a Stata matrix, and I use mata describe to illustrate that x and w are objects in global Mata memory. Using fixed names for an object in Stata memory or in global Mata memory should be avoided, because you can overwrite users’ data.

mymean7 does not put anything in global Mata memory; all computations are done using objects that are local to the Mata function mymean_work(). mymean7 uses temporary names for objects stored in Stata memory.

*! version 7.0.0 07Dec2015
program define mymean7, eclass
version 14

syntax varlist(max=1)

tempname b
mata: mymean_work("varlist'", "b'")

display "b is "
matrix list b'
end

mata:
void mymean_work(string scalar vname, string scalar mname)
{
real vector    x
real scalar    w

x  = st_data(., vname)
w  = mean(x)
st_matrix(mname, w)
}
end

There are two parts to mymean7.ado: an ado-program and a Mata function. The ado-program is defined on lines 2–12. The Mata function mymean_work() is defined on lines 14–24. The Mata function mymean_work() is local to the ado-program mymean7.

Line 8 uses a one-line call to Mata to execute mymean_work(). mymean_work() does not return anything to global Mata memory, and we are passing in two arguments. The first argument is a string scalar containing the name of the variable for which the function should compute the estimate. The second argument is a string scalar containing the temporary name stored in the local macro b. This temporary name will be the name of a Stata matrix that stores the point estimate computed in mymean_work().

Line 15 declares the function mymean_work(). Function declarations specify what the function returns, the name of the function, and the arguments that the function accepts; see Programming an estimation command in Stata: Mata functions for a quick introduction.

The word void on line 15 specifies that the function does not return an argument; in other words, it returns nothing. What precedes the ( is the function name; thus, mymean_work() is the name of the function. The words string scalar vname specify that the first argument of mymean_work() is a string scalar that is known as vname inside mymean_work(). The comma separates the first argument from the second argument. The words string scalar mname specify that the second argument of mymean_work() is a string scalar that is known as mname inside mymean_work(). ) closes the function declaration.

Lines 17-22 define mymean_work() because they are enclosed between the curly braces on lines 16 and 23. Lines 17 and 18 declare the real vector x and real scalar w, which are local to mymean_work(). Lines 20 and 21 compute the estimate. Line 22 copies the estimate stored in the scalar w, which is local to the Mata function mymean_work(), to the Stata matrix whose name is stored in the string scalar mname, which contains the temporary name contained in the local macro b that was passed to the function on line 8.

The structure used in mymean7 ensures three important features.

1. It does not use global Mata memory.
2. It uses temporary names for global Stata objects.
3. It leaves nothing behind in Mata memory or Stata memory.

Examples 2 and 3 combine to illustrate feature (3); example 2 clears Stata and Mata memory, and example 3 shows that mymean7 leaves nothing in the previously cleared memory.

Example 2: Removing objects from Stata and Mata memory

. clear all

. matrix dir

. mata: mata describe

# bytes   type                        name and extent
-------------------------------------------------------------------------------
-------------------------------------------------------------------------------

In detail, I use clear all to drop all objects from Stata and Mata memory, use matrix dir to illustrate that no matrices were left in Stata memory, and use mata describe to illustrate that no objects were left in Mata memory.

Example 3: mymean7 leaves nothing in Stata or Mata memory

. sysuse auto
(1978 Automobile Data)

. mymean7 price
b is

symmetric __000000[1,1]
c1
r1  6165.2568

. matrix dir

. mata: mata describe

# bytes   type                        name and extent
-------------------------------------------------------------------------------
-------------------------------------------------------------------------------

In example 3, I use mymean7 to estimate the mean, and use matrix dir and mata describe to illustrate that mymean7 did not leave Stata matrices or Mata objects in memory. The output also illustrates that the temporary name __000000 was used for the Stata matrix that held the result before the ado-program terminated.

While it is good that mymean7 leaves nothing in global Stata or Mata memory, it is bad that mymean7 does not leave the estimate behind somewhere, like in e().

mymean8 stores the results in e() and has the features of mymean5, but computes its results in Mata.

*! version 8.0.0 07Dec2015
program define mymean8, eclass
version 14

syntax varlist(max=1)

tempname b V
mata: mymean_work("varlist'", "b'", "V'")
matrix colnames b'  = varlist'
matrix colnames V'  = varlist'
matrix rownames V'  = varlist'
ereturn post b' V'
ereturn display
end

mata:
void mymean_work(                  ///
string scalar vname,     ///
string scalar mname,     ///
string scalar vcename)
{
real vector    x, e2
real scalar    w, n, v

x  = st_data(., vname)
n  = rows(x)
w  = mean(x)
e2 = (x :- w):^2
v   = (1/(n*(n-1)))*sum(e2)
st_matrix(mname,   w)
st_matrix(vcename, v)
}
end

Line 8 is a one-line call to mymean_work(), which now has three arguments: the name of the variable whose mean is to be estimated, a temporary name for the Stata matrix that will hold the point estimate, and a temporary name for the Stata matrix that will hold the estimated VCE. The declaration mymean_work() on lines 17-20 has been adjusted accordingly; each of the three arguments is a string scalar. Lines 22 and 23 declare objects local to mymean_work(). Lines 25-29 compute the mean and the estimated VCE. Lines 30 and 31 copy these results to Stata matrices, under the temporary names in the second and third arguments.

There is a logic to the order of the arguments in mymean_work(); the first argument is the name of an input, the second and third arguments are temporary names for the outputs.

Returning to the ado-code, we see that lines 9–11 put row or column names on the point estimate or the estimated VCE. Line 12 posts the results to e(), which are displayed by line 13.

Example 4 illustrates that mymean8 produces the same point estimate and standard error as produced by mean.

Example 4: Comparing mymean8 and mean

. mymean8 price
------------------------------------------------------------------------------
|      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
price |   6165.257   342.8719    17.98   0.000      5493.24    6837.273
------------------------------------------------------------------------------

. mean price

Mean estimation                   Number of obs   =         74

--------------------------------------------------------------
|       Mean   Std. Err.     [95% Conf. Interval]
-------------+------------------------------------------------
price |   6165.257   342.8719      5481.914      6848.6
--------------------------------------------------------------

The confidence intervals produced by mymean8 differ from those produced by mean because mymean8 uses a normal distribution while mean uses a $$t$$ distribution. The mymean_work() in mymean9 uses a fourth argument to remove this difference.

*! version 9.0.0 07Dec2015
program define mymean9, eclass
version 14

syntax varlist(max=1)

tempname b V dfr
mata: mymean_work("varlist'", "b'", "V'", "dfr'")
matrix colnames b'  = varlist'
matrix colnames V'  = varlist'
matrix rownames V'  = varlist'
ereturn post b' V'
ereturn scalar df_r  = dfr'
ereturn display
end

mata:
void mymean_work(                  ///
string scalar vname,     ///
string scalar mname,     ///
string scalar vcename,   ///
string scalar dfrname)
{
real vector    x, e2
real scalar    w, n, v

x  = st_data(., vname)
n  = rows(x)
w  = mean(x)
e2 = (x :- w):^2
v   = (1/(n*(n-1)))*sum(e2)
st_matrix(mname,   w)
st_matrix(vcename, v)
st_numscalar(dfrname, n-1)
}
end

On line 8, mymean_work() accepts four arguments. The fourth argument is new; it contains the temporary name that is used for the Stata scalar that holds the residual degrees of freedom. Line 34 copies the value of the expression n-1 to the Stata numeric scalar whose name is stored in the string scalar dfrname; this Stata scalar now contains the residual degrees of freedom. Line 13 stores the residual degrees of freedom in e(df_r), which causes ereturn display to use a $$t$$ distribution instead of a normal distribution.

Example 5: mymean9 uses a t distribution

. mymean9 price
------------------------------------------------------------------------------
|      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
price |   6165.257   342.8719    17.98   0.000     5481.914      6848.6
------------------------------------------------------------------------------
`

mymean9 has five basic parts.

1. It parses the user input.
2. It uses a one-line call to a Mata work routine to compute results and to store these results in Stata matrices whose temporary names are passed to the Mata work routine.
3. It puts on the column and row names and stores the results in e().
4. It displays the results.
5. It defines the Mata work routine after the end that terminates the definition of the ado-program.

This structure can accommodate any estimator whose results we can store in e(). The details of each part become increasingly complicated, but the structure remains the same. In future posts, I discuss Stata/Mata programs with this structure that implement the ordinary least-squares (OLS) estimator and the Poisson quasi-maximum-likelihood estimator.

Done and undone

I discussed a sequence of ado-commands that use Mata to estimate the mean of a variable. The commands illustrated a general structure for Stata/Mata programs.

In the next post, I show some Mata computations that produce the point estimates, an IID VCE, a robust VCE, and a cluster-robust VCE for the OLS estimator.

Categories: Programming Tags:


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Algebra has a reputation for being difficult, but Math Games makes struggling with it a thing of the past. Feel free to try them now. The unknown is also called a variable. ∂Q ∂x = ∂P ∂y. it cost40 to produce each canoe. 4x4 System of. Solving an Equation In the equation above we could just tell by looking at it that x = 2, however, this isn't always the case. Click "Show Answer" underneath the problem to see the answer. William Stein (2007-07-16): added arithmetic with symbolic equations; sage. Setting IgnoreAnalyticConstraints to true can give you simple solutions for the equations for which the direct use of the solver returns complicated results. Clear of fractions as follows: Multiply both sides of the equation -- every term -- by the LCM of denominators. In a system of linear equations, each equation corresponds with a straight line corresponds and one seeks out the point where the two lines intersect. Solving an Equation Date: 11/30/2002 at 11:11:59 From: Amanda Parrish Subject: Solving an Equation Dear Dr. If this is the case, let me tell you about great features of our equation solver - Equation Wizard. Trigonometric Form of Complex Numbers. Society & Culture › Words & Linguistics. Study guide for my Math course Wednesday May 06, 2020. Solving two-step equations. The word equation and its cognates in other languages may have subtly different meanings; for example, in French an équation is defined as containing one or more variables, while in English any equality is an equation. #N#Build your own widget » Browse widget gallery » Learn more » Report a problem » Powered by Wolfram|Alpha. pdf: File Size: 664 kb: Download File. It is free to use. Free student math practice Feedback: Solve (y) Solve 0. The worksheets suit pre-algebra and algebra 1 courses (grades 6-9). 4 Write and solve equations that represent diagrams S. To solve a system of linear equations graphically we graph both equations in the same coordinate system. Math is a hard and complicated thing for most of us, but not for this awesome app! Equation solving and graphing are as easy as shelling peas for this new math equation solver and helper for android! Equation solver with steps Are you in search of an equation calculator for free in order to solve math equations step-by-step? You came to the. Feel free to try them now. Step 2: Solve your equation. Solving Equations. Generally speaking, converting a word problem into an equation involves reading through the problem and setting up word equations — that is, equations that contain words as well as numbers. All of the cases I worked on boil down to how to transform the higher-order equation(s) given to a system of first order equations. Solve any quadratic equation by using the quadratic formula. Singular linear systems are detected automatically: Linear Equation Solver and Grapher: Linear equation solver graphs any linear equation, and calculates slope. Free math problem solver answers your algebra homework questions with step-by-step explanations. In mathematics, the order of operations define the priority in which complex equations are solved. Algebraic Equation. Microsoft Mathematics Add-in 2013 for Microsoft Word and Microsoft OneNote makes it easy to plot graphs in 2D and 3D, solve equations or inequalities, and simplify algebraic expressions in your Word documents and OneNote notebooks. Plots & Geometry. Click on the question mark button (s) for more details. We test the proposed method to solve nonlinear fractional Burgers equations in one, two coupled, and three dimensions. com add to compare. 6726 x 10-11 N-m 2 /kg 2. 5 out of 5 stars. This compilation of a meticulously drafted equation word problems is designed to get students to write and solve a variety of one-step, two-step and multi-step equations that involve integers, fractions, and decimals. How to Use the Calculator. Write, insert, or change an equation or formula. UMS solves a homework math problem. In the section about linear algebra, you can solve system of linear equations using Cramer's rule or an augmented matrix, find the null space, the rank, or the nullity, find the eigenvalues, eigenvectors, and eigenspace of a matrix. Beginning of the Year Documentation M1. Paolo Ruffini was the first person to develop the theory of permutation groups, and like his predecessors, also in the context of solving algebraic equations. ; Puzzles like this require you to look and find the one loose end you can pull to. Someone might want to make a document, such as a business manager, finance manager, school teacher, university professor and for them Word provides the facility to add mathematics equations or. The program SolveLinearEquations solves simultaneous equations. Calculator. The solve for variable calculator identifies the variables then add or subtract variables on one side and add or subtract the whole numbers on other side. mathportal. In this section, we will learn, how to solve word problems using linear equations. There are two methods for solving exponential equations. The standard form of a quadratic equation is ax 2 + bx + c = 0. When you enter an equation into the calculator, the calculator will begin by expanding (simplifying) the problem. a can't be 0. This resource is designed for UK teachers. Derivative Calculator. Any lowercase letter may be used as a. Please use at your own risk, and please alert us if something isn't working. 6 Solve two-step equations S. Best of all, this file is FREE!Students must be able to work with simple fractions in order to complete these puzzles. Return from this Equation Puzzle to the Equation Games page or to the Math Puzzles Page. Visualize Concepts - learn how trig functions can be used to draw and animate. Write, insert, or change an equation or formula. Feb 20, 20 08:44 AM. Calculadora gratuita de ecuaciones – Resolver ecuaciones lineales, cuadráticas, bicuadradas, con valor absoluto y con radicales paso por paso. Math Problem Solver Questions Answered Free Algebra Geometry Trigonometry Calculus Number Theory Combinatorics Probability. To solve an equation means to find the variable or unknown. Mathematics › Step-by-Step Solutions. Not only do I still have to help my sisters out with their elementary school maths homework (trust me, it’s surprisingly difficult), but every time I log into Facebook, there’s always some tantalizing equation thrown at me, asking me to solve it. This equation of an ellipse calculator is a handy tool for determining the basic parameters and most important points on an ellipse. The slope intercept form of the equation of a straight line. In this post I. The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. Fractions should be entered with a forward slash such as '3/4. The game is based on the following Common Core Math Standard: 1. The following translation tables help convert word problems into Algebra expressions and equations. It’s simply your ticket towards a successful pre algebra journey, so make sure to seize this opportunity and try out the app. Computational Lab Tools. 5x+2 and y=x-2. x are all nonnegative rational numbers. The steps of calculations required to solve an inequality are also given. These tutorials focus on solving equations and understanding solutions to inequalities. There are different kinds of exponential equations. Calculus & Analysis. txt) or read online for free. You'll be able to enter math problems once our session is over. x + 4 = 20 2. Scroll down below for a quick intro. Here is a simple online 4 unknown calculator to solve the 4x4 equations. A simple equation that contains one variable like x-4-2 = 0 can be solved using the SymPy's solve() function. It can be used to solve problems that are not as simple one-step addition, subtraction, multiplication or division ones. A "one-step equation" means there is only one step that needs to be done to solve for the variable. Algebra Four is one of the Interactivate assessment games. Graphing calculator. For example, x + 2 = 5. Solve Systems of Equations: Solves 2 by 2 and 3 by 3 systems of linear equations. Enter an equation or expression using the common 'calculator notation'. 5 out of 5 stars. Solve the equation with the initial condition y(0) == 2. Algebra Calculator Tutorial. Feel free to try them now. These tutorials focus on solving equations and understanding solutions to inequalities. With the information at hand, you can calculate which loan is the best choice for you. In other words, SolveMathProblems’ app is a calculator for pre algebra, no, is the best pre algebra calculator, for a variety of uses, no matter on which level you are. Using the Matrix Calculator we get this: (I left the 1/determinant outside the matrix to make the numbers simpler) Then multiply A-1 by B (we can use the Matrix Calculator again): And we are done! The solution is: x = 5, y = 3, z = −2. Since the Renaissance, every century has seen the solution of more mathematical problems than the century before, yet many mathematical problems, both major and minor, still remain unsolved. Attempting to solve an equation that does not fit these criteria returns undefined. Clear Equation Solver ». Equation Calculator. When it comes to evaluating expressions that contain parentheses, you can follow these steps: Evaluate the contents of parentheses, from the inside out. A simple equation that contains one variable like x-4-2 = 0 can be solved using the SymPy's solve() function. Related Articles. solving an equation for x, solvang and santa ynez, solving an inequality in interval notation, solving and writing linear equations, solving an ivp, FACEing Math Awesome math resource that MAKES MATH REVIEW FUN from Solving And Graphing Inequalities Worksheet Answer Key. These equations can be classified into 2 types. Background. ( 6 + 3) ⋅ ( 10 − 7) (6+3)\cdot (10-7). Thinking Blocks Tool. Equation Calculator. The differential equation now becomes: We now consider the two equations:. 3 solutions/day. txt) or read online for free. Solution can be expressed either in radians or degrees. Society & Culture › Words & Linguistics. Ask a friend to pick a number from 1 through 1,000. Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more. Division by Integers. Enter your queries using plain English. Algebra Calculator Tutorial. Easily solve equations of the form ax = c with the click of a button! Algebra lessons. After you enter the expression, Algebra Calculator will solve the equation 4x+7=2x+1 for x to get x=-3. To solve a system of linear equations graphically we graph both equations in the same coordinate system. Two questions now become very important. As they do so, have students complete the Worksheet , writing down the number of steps it takes them to solve each equation as compared with the recommended minimum number of steps. The simplest are adding, subtracting, multiplying, and dividing. With the information at hand, you can calculate which loan is the best choice for you. Algebra Solver, Simplifier and Evaluator. Enter the values in the boxes below and click Solve. Solution is by factorising the quadratic into two bracketed expressions. The parabola equation cal be expressed in two ways, standard form and vertex form. How to enter numbers: Enter any integer, decimal or fraction. The Algebra column shows what happens to the unknown. Begin by writing your equation. Math is a hard and complicated thing for most of us, but not for this awesome app! Equation solving and graphing are as easy as shelling peas for this new math equation solver and helper for android! Equation solver with steps Are you in search of an equation calculator for free in order to solve math equations step-by-step? You came to the. Also, it can find equation of a circle given its center and radius. 1) x2 − 9x + 18 = 0 2) x2 + 5x + 4 = 0 3) n2 − 64 = 0 4) b2 + 5b = 0. I charge $2 for steps, or$1 for answers only. These unsolved problems occur in. Equation Solver. So if you encounter an equation in standard form that you are required to graph, you must convert it to slope intercept form. Other than that, this program has no graphical user interface and a slightly modified equation format. In the Symbols group, you'll find math related symbols. Free math problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with step-by-step explanations, just like a math tutor. Related Topics: Common Core for Grade 6 More Lessons for Grade 6 Examples, solutions, videos, and lessons to help Grade 6 students learn how to solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers. Chegg Math Solver. Now our equation is simplified. The Algebra column shows what happens to the unknown. Math Equations Sites search in title. Identifying Perfect Cubes. The algebra calculator helps you find solution to a wide range of mathematical problems. T O SOLVE AN EQUATION WITH fractions, we transform it into an equation without fractions -- which we know how to solve. com add to compare. The dsolve function finds a value of C1 that satisfies the condition. Related Articles. 4 Write and solve equations that represent diagrams S. Physics Formulas. Very easy to understand! Algebra Lessons at Cool math. This book is available at Google Play and Amazon. Slope intercept equations (y=mx+b) are the easiest to graph. Step 1: Enter your equation. MathType is a powerful equation editor for Windows and Mac that lets you create mathematical notation for word processing, presentations and many of your other favorite applications. Solving Radical Equations Learning how to solve radical equations requires a lot of practice and familiarity of the different types of problems. This online solver will show steps and explanations for common math problems. Math Problem Solver Below is a math problem solver that lets you input a wide variety of math problems and it will provide the final answer for free. When it is applied, the functions are physical quantities while the derivatives are their rates of change. Automatically number and reference your equations. Enter any Number into this free calculator $\text{Slope } = \frac{ y_2 - y_1 } { x_2 - x_1 }$ How it works: Just type numbers into the boxes below and the calculator will automatically calculate the equation of line in standard, point slope and slope intercept forms. Khan Academy Video: Solving Simple Equations. Practice solving one-variable equations like 20 - 7x = 6x - 6, where the variable appears on both sides of the equals sign. 30000019073486 5. Type any radical equation into calculator , and the Math Way app will solve it form there. Learn more: Problem types supported by Math Assistant. for -x-7y=14 and -4x-14y=28. Let us see, how to translate the information given in a word problem into an algebraic expression or equation in the following examples. This bundle contains all of the resources you will need to teach a summer school algebra class. a fun little algebra starter, make sure you change teachers names to suit your school. The available choices in this drop-down menu depend on the selected equation. Literal equations are solved by isolating the unknown variable on one side of the equation, and all of the remaining literal variables on the other side of the equation. The point-slope formula. When expr involves only polynomial conditions over real or complex domains, Solve [ expr, vars] will always be able to eliminate quantifiers. This course covers the foundational concepts in algebra that students need to solve equations. Add and Subtract B. For some calculations, in addition to the result, the different calculation steps are returned. Evaluate […]. On the right, 18 plus 6 is 24, so x = 24. x 2 − 2 a x + a 2 = 0 \displaystyle x^2-2ax+a^2=0. Add and Subtract A. Multiple-version printing. The calculator will generate a step by step explanations and circle graph. Improve your math knowledge with free questions in "Solve equations using order of operations" and thousands of other math skills. In the previous section we applied separation of variables to several partial differential equations and reduced the problem down to needing to solve two ordinary differential equations. Solve b+1=-2b: b+1=-2b. Included is an example solving the heat equation on a bar of length L but instead on a thin circular ring. To solve your equation using the Equation Solver, type in your equation like x+4=5. The differential equation P(x,y)dx+ Q(x,y)dy = 0 is an exact equation if and only if. Pulling Out Like Terms. It's simply your ticket towards a successful pre algebra journey, so make sure to seize this opportunity and try out the app. How hard it is depends on the complexity of equations. The solve command is not only used for solving for zeros, it can be used to solve other equations as well. This helps you to find the order of precedence when you work with equations. 5x+2 and y=x-2. However, it is often necessary to use a logarithm when solving an exponential equation. Graph y=x^2+2x: y=x^2+2x. Sets of Linear Equations. To solve bx = e, divide both sides of the equation by. Physics calculators for solving engineering equations and science formulas Physics Equations Formulas Calculator Home: Popular Index 1 Index 2 Index 3 Index 4 Infant Chart Math Geometry Physics Force Fluid Mechanics Finance Loan Calculator Nursing Math. Critical Thinking. Improve your math knowledge with free questions in "Solve equations using order of operations" and thousands of other math skills. If in your equation a some variable is absent, then in this place in the calculator, enter zero. We will practice translating word sentences into algebraic equations. As you might've noticed, an exponential equation is just a special type of equation. The word equation and its cognates in other languages may have subtly different meanings; for example, in French an équation is defined as containing one or more variables, while in English any equality is an equation. Quick video demo for the Windows 10 App version of OneNote. All you need to do is to write the ellipse standard form equation and watch this calculator do the math for you. Finding the roots of polynomials with TI-86 Graphing Calculator [Using Flash] Drill in solving equations involving trigonometric functions. This helps you to find the order of precedence when you work with equations. This calculator computes volumes for a few of the most usual basic shapes. Math formula shows how things work out with the help of some equations like the equation for force or acceleration. Quadratic Equation Solver. Teaching aims: Translate. pdf), Text File (. Then it will attempt to solve the equation by using one or more of the following: addition, subtraction, division, taking the square root of each side, factoring, and completing the square. Visit Mathway on the web. The consecutive integer after the. Quick! I need help with:. Just enter the equation in the field below and click the "Solve Equation" button. If before the variable in equation no number then in the appropriate field, enter the number "1". This method will use the following fact about. Special emphasis is given to methods for solving functional equations that appear in mathematics contests, such as the Putnam competition and the International Mathematical Olympiad. Evaluate […]. This video shows students how to solve 2-step Algebra equations involving one addition. Includes examples and answers. Solve 2a+4=12: 2a+4=12. To solve the current equation, do any of the following: Click or tap the Select an action box and then choose the action you want Math Assistant to take. Algebra Calculator Calculate equations, inequatlities, line equation and system of equations step-by-step. Challenge Board: Score points by answering questions correctly. [Math Processing Error] The formula can be used to solve any. It has an easy to use GUI that can solve up to 16 terms functions. Some sentences will translate into equations with variables. Stop searching. Easily solve equations of the form ax = c with the click of a button! Algebra lessons. Just like on the Systems of Linear Equations page. x - 4 = 10. Math loves simplicity and our calculator is. Systems of Equations Calculator is a calculator that solves systems of equations step-by-step. Check the solution by substituting 14 in the original equation for x. True or false question about algebra Sunday February 16, 2020. If you can be explicit about delta solve equation, I could provide help to solve the math problem. It supports polynomial equations as well as some equations with exponents, logarithms and trigonometric functions. pdf), Text File (. Free Pre-Algebra, Algebra, Trigonometry, Calculus, Geometry, Statistics and Chemistry calculators step-by-step This website uses cookies to ensure you get the best experience. Based on the promo clip, PhotoMath, dubbed a “smart camera calculator,” appears to use smartphone cameras to scan a photo of a math equation in a textbook and display the answer instantly. Enter equation to solve, e. Geometry lessons. Quadratic Equations. The Equation Solver solves your equation in one click. Really clear math lessons (pre-algebra, algebra, precalculus), cool math games, online graphing calculators, geometry art, fractals, polyhedra, parents and teachers areas too. The Equation Solver on your TI-84 Plus calculator is a great tool for solving one-variable equations. Series and Progressions. F>Zero Graphing Inequalities. Solving for gravitational force exerted between two objects. Select Settings if you want to switch between solving real numbers and complex numbers, or if you want to set the angle measurement of graphs to. In this study, a relatively new method to solve partial differential equations (PDEs) called the fractional reduced differential transform method (FRDTM) is used. 4 Solve Rational Equations A2. 2 jk 8uztbap qsbouflt1wmaxrfex sllljc h2 5 xaalflg 5rieguhwtgsf orve8sdetrjv 0eidyh n pmta 3dsea jwoiltfhs niknyf7ign4iitbe0 caxllg ce1b8rra4 s2gt worksheet by kuta software llc answers to solving quadratic equations practice 2 id. The problems are of various difficulty. x + 6 = 10) is to realize that the equation is an equality. We can help you solve an equation of the form "ax 2 + bx + c = 0" Just enter the values of a, b and c below: Is it Quadratic? Only if it can be put in the form ax 2 + bx + c = 0, and a is not zero. Geometric Representation of Complex Numbers. ( x − 1) ( x − 8) = 0 \displaystyle (x-1) (x-8)=0 ( x − 1) ( x − 8) = 0, so the roots are x=1 and x=8. 4 Solve simple equations in one variable using inverse relationships between operations such as addition and subtraction (taking the opposite), multiplication and division (multiplying by the reciprocal), raising to a power and taking a root;. Here is a simple online 4 unknown calculator to solve the 4x4 equations. To solve your equation using the Equation Solver, type in your equation like x+4=5. Type in any equation to get the solution, steps and graph. Very easy to understand! Algebra Lessons at Cool math. But a math professor at Carnegie Mellon University in Pittsburgh may have come up with a better way of solving it. The steps of calculations required to solve an inequality are also given. For example, let's solve it using the logarithm with base 5. Equation generator, yields an equation from three points When 3 points are input, this calculator will generate a second degree equation. Relevant links and theory. Easy to use online geometry calculators and solvers for various topics in geometry such as calculate area, volume, distance, points of intersection. Math is a hard and complicated thing for most of us, but not for this awesome app! Equation solving and graphing are as easy as shelling peas for this new math equation solver and helper for android! 🙾 Equation solver with steps Are you in search of an equation calculator for free in order to solve math equations step-by-step? You came to the right place!. There are three basic methods for solving quadratic equations: factoring, using the quadratic formula, and completing the square. In this video the instructor shows the different methods of solving quadratic equations. Coolmath Algebra has hundreds of really easy to follow lessons and examples. Pre-Algebra. SolveMyMath - Your math help website. Reducing Fractions to Lowest Terms. Finding the Area of a Rectangle; Finding the Perimeter of a Rectangle. The simplest are adding, subtracting, multiplying, and dividing. The axis of symmetry is also known as line of symmetry. Learn more about fsolve, variable, symbolic, function, nonlinear, equation. Math for Everyone. Mathematics › Step-by-Step Solutions. Stack Overflow for Teams is a private, secure spot for you and your coworkers to find and share information. This method will use the following fact about. For equation solving, Wolfram|Alpha calls the Wolfram Language's Solve and Reduce functions, which contain a broad range of methods for all kinds of algebra, from basic linear and quadratic equations to multivariate nonlinear systems. Solves equations, showing work and detailed explanation. With a smart calculator, you just need to enter the formula and the equation calculator will give you answers automatically. can be entered as: x 1 + x 2 + x 3 + x 4 = Additional features of Cramer's rule calculator. Four less than a number is twenty. Free math lessons and math homework help from basic math to algebra, geometry and beyond. equations where the unknown variable is found in the denominator. Solving an Equation Date: 11/30/2002 at 11:11:59 From: Amanda Parrish Subject: Solving an Equation Dear Dr. Feel free to try them now. From the drop-down menu in Math pane, select the option to Graph in 2D. To see all the symbols, click the More button. Find other activities. In other words, SolveMathProblems’ app is a calculator for pre algebra, no, is the best pre algebra calculator, for a variety of uses, no matter on which level you are. Hui's XP Math features free math games aligned to Common Core State Standards: Number Sense and Operations, Algebra, Geometry, Measurement, and Data Analysis. Equation Solver. Enter expression to be simplified, or equation to be solved. Recent Articles. It will have an equals sign "=" like this: That equations says: what is on the left (x − 2) is equal to what is on the right (4) So an equation is like a statement " this equals that " A Solution is a value we can put in place of a variable (such as x) that makes the equation true. It is the one which separates the typical parabola into exactly half. Download free on Google Play. Example 1: Solve for x in the following equation. Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more. Relevant links and theory. Solve b+1=-2b: b+1=-2b. This calculator solves quadratic equation using two methods. com and discover intermediate algebra syllabus, rational numbers and countless additional math subject areas. Related Articles. They will generally have two solutions; that is, two different values of x that make the equation true. Best Math Problem Solver App 2018. Using x as the unknown and other letters to represent known quantities, consider the following example equation: + = +. Computational Lab Tools. You just need to type in the expressions on the left. Hagan's Museum of Art October 2013 (9) September 2013 (4) August 2013 (14) July 2013 (5) June 2013 (10) May 2013 (16) April 2013 (6). X K fATlHl8 5r KigChOtWsU 6r JeHsae 3rxv 6e1ds. Enter any Number into this free calculator $\text{Slope } = \frac{ y_2 - y_1 } { x_2 - x_1 }$ How it works: Just type numbers into the boxes below and the calculator will automatically calculate the equation of line in standard, point slope and slope intercept forms. Solves many common math problems found in school and everyday life. Multiplication and division can be used to solve for variables in equations. Try it free!. Brush up on your knowledge of the techniques needed to solve. Or click the "Show Answers" button at the bottom of the page to see all the answers at once. These solving proportions worksheets will help students meet Common Core Standards for Expressions & Equations as well as Ratios & Proportional Relationships. Further Help. the selling price is 80 per canoeTags: cost, profit, revenue. Solve any equation with this free calculator! Just enter your equation carefully, like shown in the examples below, and then click the blue arrow to get the result! You can solve as many equations as you like completely free. This should give you an Solve the equation. The addition rule for equations tells us that the same quantity can be added to both sides of an equation without changing the solution set of the equation. Part of the Algebra Basics Series: https://www. Understand solving an equation or inequality as a process of. Solutions and calculations for solving math problems used by nurses. The program SolveLinearEquations solves simultaneous equations. There are also packets, practice problems, and answers provided on the site. We can help you solve an equation of the form "ax 2 + bx + c = 0" Just enter the values of a, b and c below: Is it Quadratic? Only if it can be put in the form ax 2 + bx + c = 0, and a is not zero. Solving Equations. This course focuses on the equations and techniques most useful in science and engineering. A truth table is a table representing the output boolean values of a logical expression based on their entries. Here are more examples of how to solve equations in Algebra Calculator. Easily solve equations of the form ax = c with the click of a button! Algebra lessons. Free graphing calculator instantly graphs your math problems. " x " is the variable or unknown (we don't know it yet). An equation says that two things are equal. Physics calculators for solving engineering equations and science formulas Physics Equations Formulas Calculator Home: Popular Index 1 Index 2 Index 3 Index 4 Infant Chart Math Geometry Physics Force Fluid Mechanics Finance Loan Calculator Nursing Math. Integral calculus offers a precise method of calculating the region below the curve of a mathematical function. To solve bx = e, divide both sides of the equation by. In addition to supplying the outcome, the calculator offers detailed measures and calculations that resulted in the resolution of the logarithmic equation. Using the Matrix Calculator we get this: (I left the 1/determinant outside the matrix to make the numbers simpler) Then multiply A-1 by B (we can use the Matrix Calculator again): And we are done! The solution is: x = 5, y = 3, z = −2. Hui's XP Math features free math games aligned to Common Core State Standards: Number Sense and Operations, Algebra, Geometry, Measurement, and Data Analysis. \[\begin{align*}25 - {x^2} & = 9\\ 16 & = {x^2}\hspace{0. Solve and Practice your K-14 math homework. Slope intercept equations (y=mx+b) are the easiest to graph. (PEMDAS Warning) This calculator solves math equations that add, subtract, multiply and divide positive and negative numbers and exponential numbers. Relevant links and theory. Test your child's math accuracy with action-packed game! Fifth graders can join Penelope as she dribbles, shoots, and scores her way across the court by solving basic algebraic equations. When you enter an equation into the calculator, the calculator will begin by expanding (simplifying) the problem. 5th Grade Math 6th Grade Math Pre-Algebra Algebra 1 Geometry Algebra 2 College Students learn to solve equations that involve fractions by either multiplying both sides of the equation by the reciprocal of the fraction, or multiplying both sides of the equation by the denominator of the fraction. Each equation has containing the unknown variables X, Y and Z. Feel free to try them now. 1_practice_solutions. Algebra - multiplication, divisibility, fractions, functions, radicals, equations, inequalities, progressions, log, lim. To turn the English into Algebra it helps to: Read the whole thing first. If you need detailed step-by-step answers you'll have to sign up for Mathway's premium service (provided by a third party). Math for Everyone. Math is a hard and complicated thing for most of us, but not for this awesome app! Equation solving and graphing are as easy as shelling peas for this new math equation solver and helper for android! 🙾 Equation solver with steps Are you in search of an equation calculator for free in order to solve math equations step-by-step? You came to the right place! This best of all math apps free. A 4x4 linear equation is one which has 4 linear equations with 4 unknown variables each. Geometry lessons. Hagan's Museum of Art October 2013 (9) September 2013 (4) August 2013 (14) July 2013 (5) June 2013 (10) May 2013 (16) April 2013 (6). Symbolic Math Toolbox™ offers both symbolic and numeric equation solvers. Summary : Calculator that allows the calculation of the discriminant of a quadratic equation online. A-level Physics. Look for and make use of structure. Taxes, Tips, Sales. Download free on iTunes. Get the free "General Differential Equation Solver" widget for your website, blog, Wordpress, Blogger, or iGoogle. 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BELLE2-CONF-PH-2020-005

A calibration of the Belle II hadronic tag-side reconstruction algorithm with $B \rightarrow X\ell \nu$ decays

William Sutcliffe ; Florian Bernlochner

08 May 2020

Abstract: Tag-side reconstruction is an important method for reconstructing $B$ meson decays with missing energy. The Belle II tag-side reconstruction algorithm, Full Event Interpretation, relies on a hierarchical reconstruction of $B$ meson decays with multivariate classification employed at each stage of reconstruction. Given the large numbers of classifiers employed and decay chains reconstructed, the performance of the algorithm on data and simulation differs significantly. Here, calibration factors are derived to correct for this effect for the case of hadronic tag-sides using $B\rightarrow X\ell\nu$ decays in $34.6$ fb$^{-1}$ of Belle II data. For a loose selection on the tag-side $B$ multivariate classifier the calibration factors are $0.65 \pm 0.02$ and $0.83 \pm 0.03$ for tag-side $B^{+}$ and $B^{0}$ mesons, respectively.

Keyword(s): tagging ; tag-side reconstruction ; FEI ; Full Event Interpretation ; calibration

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Conference Submissions > Papers


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# American Institute of Mathematical Sciences

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June  2013, 33(6): 2469-2494. doi: 10.3934/dcds.2013.33.2469

## Multiple solutions for nonlinear elliptic equations with an asymmetric reaction term

 1 Department of Mathematics, Hellenic Naval Academy, Piraeus 18539 2 Department of Mathematics, National Technical University of Athens, Zografou Campus, Athens 15780

Received  January 2012 Revised  September 2012 Published  December 2012

We consider a nonlinear Dirichlet problem driven by the $p$-Laplace differential operator. We assume that the Carathéodory reaction term $f(z,x)$ exhibits an asymmetric behavior on the two semiaxes of $\mathbb{R}$. Namely, $f(z,\cdot)$ is $(p-1)$-linear near $-\infty$ and $(p-1)$-superlinear near $+\infty$, but without satisfying the well-known Ambrosetti--Rabinowitz condition (AR-condition). Combining variational methods based on critical point theory, with suitable truncation techniques and Morse theory, we show that the problem has at least three nontrivial smooth solutions, two of which have constant sign (one positive, the other negative).
Citation: Sophia Th. Kyritsi, Nikolaos S. Papageorgiou. Multiple solutions for nonlinear elliptic equations with an asymmetric reaction term. Discrete & Continuous Dynamical Systems - A, 2013, 33 (6) : 2469-2494. doi: 10.3934/dcds.2013.33.2469
##### References:
 [1] W. Allegretto and Y. H. Huang, A Picone's identity for the $p$-Laplacian and applications,, Nonlin. Anal., 32 (1998), 819.  doi: 10.1016/S0362-546X(97)00530-0.  Google Scholar [2] D. Arcoya and S. Villegas, Nontrivial solutions for a Neumann problem with a nonlinear term asymptotically linear at $-\infty$ and superlinear at $+\infty$,, Math. Z., 219 (1995), 499.  doi: 10.1007/BF02572378.  Google Scholar [3] P. Bartolo, V. Benci and D. Fortunato, Abstract critical point theorems and applications to some nonlinear problems with strong resonance at infinity,, Nonlin. Anal., 7 (1983), 981.  doi: 10.1016/0362-546X(83)90115-3.  Google Scholar [4] T. Bartsch and S. Li, Critical point theory for asymptotically quadratic functionals and applications to problems with resonance,, Nonlin. Anal., 28 (1997), 419.  doi: 10.1016/0362-546X(95)00167-T.  Google Scholar [5] T. Bartsch and Z. Liu, On a superlinear elliptic $p$-Laplacian equation,, J. Differential Eqns, 198 (2004), 149.  doi: 10.1016/j.jde.2003.08.001.  Google Scholar [6] S. Carl and K. Perera, Sign changing amd multiple solutions for the $p$-Laplacian,, Abstr. Appl. Anal., 7 (2003), 613.  doi: 10.1155/S1085337502207010.  Google Scholar [7] J.-N. Corvellec, On the second deformation lemma,, Topol. Methods Nonlin. Anal., 17 (2001), 55.   Google Scholar [8] D. Costa and C. Magalhaes, Existence results for perturbation of the $p$-Laplacian,, Nonlin. Anal., 24 (1995), 409.  doi: 10.1016/0362-546X(94)E0046-J.  Google Scholar [9] N. Dancer and K. Perera, Some remarks on the Fučik spectrum of the $p$-Laplacian and critical groups,, J. Math. Anal. Appl., 254 (2001), 164.  doi: 10.1006/jmaa.2000.7228.  Google Scholar [10] Y. Deng, S. Peng and L. Wang, Existence of multiple solutions for a nonhomogeneous semilinear elliptic system involving critical exponent,, Discrete and Continuous Dynamical Systems, 32 (2012), 795.   Google Scholar [11] G. Fei, On periodic solutions of superquadratic Hamiltonian systems,, Electr. Jour. Diff. Eqns, 8 (2002).   Google Scholar [12] S. Th. Kyritsi-Yiallourou and N. S. Papageorgiou, "Handbook of Applied Analysis, Advances in Mechanics and Mathematics 19,", Springer, (2009).  doi: 10.1007/b120946.  Google Scholar [13] J. Garcia Azorero, J. Manfredi and I. Peral Alonso, Sobolev versus Hölder local minimizers and global multiplicity for some quasilinear elliptic equations,, Comm. Contemp. Math., 2 (2000), 385.  doi: 10.1142/S0219199700000190.  Google Scholar [14] L. Gasiński and N. S. Papageorgiou, "Nonlinear Analysis,", Chapman & Hall/CRC Press, (2006).   Google Scholar [15] A. Granas and J. Dugundji, "Fixed Point Theory,", Springer-Verlag, (2003).   Google Scholar [16] Z. Guo and Z. Liu, Perturbed elliptic equations with oscillatory nonlinearities,, Discrete and Continuous Dynamical Systems, 32 (2012), 3567.  doi: 10.3934/dcds.2012.32.3567.  Google Scholar [17] O. Ladyzhenskaya and N. Uraltseva, "Linear and Quasilinear Elliptic Equations,", Academic Press, (1968).   Google Scholar [18] G. Lieberman, Boundary regularity for solutions of degenerate elliptic equations,, Nonlin. Anal., 12 (1988), 1203.  doi: 10.1016/0362-546X(88)90053-3.  Google Scholar [19] S. Liu, Multiple solutions for coercive $p$-Laplacian equations,, J. Math. Anal. Appl., 316 (2006), 229.  doi: 10.1016/j.jmaa.2005.04.034.  Google Scholar [20] J. Liu and S. Liu, The existence of multiple solutions to quasilinear elliptic equations,, Bull. London Math. Soc., 37 (2005), 592.  doi: 10.1112/S0024609304004023.  Google Scholar [21] J. Mawhin, Multiplicity of solutions for variational systems involving $\varphi$-Laplacians with singular $\varphi$ and periodic potentials,, Discrete and Continuous Dynamical Systems, 32 (2012), 4015.  doi: 10.3934/dcds.2012.32.4015.  Google Scholar [22] D. Motreanu, V. V. Motreanu and N. S. Papageorgiou, Nonautonomous resonant periodic systems with indefinite linear part and a nonsmooth potential,, Communications on Pure and Applied Analysis, 10 (2011), 1401.  doi: 10.3934/cpaa.2011.10.1401.  Google Scholar [23] D. Motreanu, Donal O'Regan and N. S. Papageorgiou, A unified treatment using critical point methods of the existence of multiple solutions for superlinear and sublinear Neumann problems,, Communications on Pure and Applied Analysis, 10 (2011), 1791.  doi: 10.3934/cpaa.2011.10.1791.  Google Scholar [24] J. Mawhin and M. Willem, "Critical Point Theory and Hamiltonian Systems,", Springer-Verlag, (1989).   Google Scholar [25] O. Miyagaki and M. A. S. Souto, Superlinear problems without Ambrosetti and Rabinowitz growth condition,, J. Diff. Eqns, 245 (2008), 3628.  doi: 10.1016/j.jde.2008.02.035.  Google Scholar [26] D. Motreanu, V. Motreanu and N. S. Papageorgiou, A degree theoretic approach for multiple solutions of constant sign for nonlinear elliptic equations,, Manuscripta Math., 124 (2007), 507.  doi: 10.1007/s00229-007-0127-x.  Google Scholar [27] F. O. de Paiva, Multiple solutions for a class of quasilinear problems,, Discrete Cont. Dynam. Systems, 15 (2006), 669.  doi: 10.3934/dcds.2006.15.669.  Google Scholar [28] R. Palais, Homotopy theory of finite dimensional manifolds,, Topology, 5 (1966), 1.   Google Scholar [29] E. Papageorgiou and N. S. Papageorgiou, A multiplicity theorem for problems with the $p$-Laplacian,, J. Funct. Anal., 244 (2007), 63.  doi: 10.1016/j.jfa.2006.11.015.  Google Scholar [30] N. S. Papageorgiou, E. Rocha and V. Staicu, Multiplicity theorems for superlinear elliptic problems,, Calc. Var., 33 (2008), 199.  doi: 10.1007/s00526-008-0172-7.  Google Scholar [31] K. Perera, Existence and multiplicity results for a Sturm-Liouville equation asymptotically linear at $-\infty$ and superlinear at $+\infty$,, Nonlin. Anal., 39 (2000), 669.  doi: 10.1016/S0362-546X(98)00228-4.  Google Scholar [32] M. Schechter and W. Zou, Superlinear problems,, Pacific J. Math., 214 (2004), 145.  doi: 10.2140/pjm.2004.214.145.  Google Scholar [33] M. Tanaka, Existence of a nontrivial solution for a $p$-Laplacian equation with Fu\vcik type resonance at infinity,, Nonlin. Anal., 72 (2010), 507.  doi: 10.1016$|$j. na. 2008.02.117.  Google Scholar [34] J. Vazquez, A strong maximum principle for some quasilinear elliptic equations,, Appl. Math. Optim., 12 (1984), 191.  doi: 10.1007/BF01449041.  Google Scholar [35] Z. Q. Wang, On a superlinear elliptic equation,, Annales IHP, 8 (1991), 43.   Google Scholar [36] M. Willem and W. Zou, On a Schrödinger equation with periodic potential and spectrum point zero,, Indiana Univ. Math. Jour., 52 (2003), 109.  doi: 10.1512/iumj.2003.52.2273.  Google Scholar [37] Z. Zhang, J. Chen and S. Li, Construction of pseudogradient vector field and sign-changing multiple solutions involving the $p$-Laplacian,, Jour. Diff. Eqns, 201 (2004), 287.  doi: 10.1016/j.jde.2004.03.019.  Google Scholar [38] Z. Zhang and S. Li, On sign-changing and multiple solutions of the $p$-Laplacian,, J. Funct. Anal., 197 (2003), 447.  doi: 10.1016/S0022-1236(02)00103-9.  Google Scholar [39] Z. Zhang, S. Li, S. Liu and W. Feng, On an asymptotically linear elliptic Dirichlet problem,, Abstract Appl. Anal., 7 (2002), 509.  doi: 10.1155/S1085337502207046.  Google Scholar

show all references

##### References:
 [1] W. Allegretto and Y. H. Huang, A Picone's identity for the $p$-Laplacian and applications,, Nonlin. Anal., 32 (1998), 819.  doi: 10.1016/S0362-546X(97)00530-0.  Google Scholar [2] D. Arcoya and S. Villegas, Nontrivial solutions for a Neumann problem with a nonlinear term asymptotically linear at $-\infty$ and superlinear at $+\infty$,, Math. Z., 219 (1995), 499.  doi: 10.1007/BF02572378.  Google Scholar [3] P. Bartolo, V. Benci and D. Fortunato, Abstract critical point theorems and applications to some nonlinear problems with strong resonance at infinity,, Nonlin. Anal., 7 (1983), 981.  doi: 10.1016/0362-546X(83)90115-3.  Google Scholar [4] T. Bartsch and S. Li, Critical point theory for asymptotically quadratic functionals and applications to problems with resonance,, Nonlin. Anal., 28 (1997), 419.  doi: 10.1016/0362-546X(95)00167-T.  Google Scholar [5] T. Bartsch and Z. Liu, On a superlinear elliptic $p$-Laplacian equation,, J. Differential Eqns, 198 (2004), 149.  doi: 10.1016/j.jde.2003.08.001.  Google Scholar [6] S. Carl and K. Perera, Sign changing amd multiple solutions for the $p$-Laplacian,, Abstr. Appl. Anal., 7 (2003), 613.  doi: 10.1155/S1085337502207010.  Google Scholar [7] J.-N. Corvellec, On the second deformation lemma,, Topol. Methods Nonlin. Anal., 17 (2001), 55.   Google Scholar [8] D. Costa and C. Magalhaes, Existence results for perturbation of the $p$-Laplacian,, Nonlin. Anal., 24 (1995), 409.  doi: 10.1016/0362-546X(94)E0046-J.  Google Scholar [9] N. Dancer and K. Perera, Some remarks on the Fučik spectrum of the $p$-Laplacian and critical groups,, J. Math. Anal. Appl., 254 (2001), 164.  doi: 10.1006/jmaa.2000.7228.  Google Scholar [10] Y. Deng, S. Peng and L. Wang, Existence of multiple solutions for a nonhomogeneous semilinear elliptic system involving critical exponent,, Discrete and Continuous Dynamical Systems, 32 (2012), 795.   Google Scholar [11] G. Fei, On periodic solutions of superquadratic Hamiltonian systems,, Electr. Jour. Diff. Eqns, 8 (2002).   Google Scholar [12] S. Th. Kyritsi-Yiallourou and N. S. Papageorgiou, "Handbook of Applied Analysis, Advances in Mechanics and Mathematics 19,", Springer, (2009).  doi: 10.1007/b120946.  Google Scholar [13] J. Garcia Azorero, J. Manfredi and I. Peral Alonso, Sobolev versus Hölder local minimizers and global multiplicity for some quasilinear elliptic equations,, Comm. Contemp. Math., 2 (2000), 385.  doi: 10.1142/S0219199700000190.  Google Scholar [14] L. Gasiński and N. S. Papageorgiou, "Nonlinear Analysis,", Chapman & Hall/CRC Press, (2006).   Google Scholar [15] A. Granas and J. Dugundji, "Fixed Point Theory,", Springer-Verlag, (2003).   Google Scholar [16] Z. Guo and Z. Liu, Perturbed elliptic equations with oscillatory nonlinearities,, Discrete and Continuous Dynamical Systems, 32 (2012), 3567.  doi: 10.3934/dcds.2012.32.3567.  Google Scholar [17] O. Ladyzhenskaya and N. Uraltseva, "Linear and Quasilinear Elliptic Equations,", Academic Press, (1968).   Google Scholar [18] G. Lieberman, Boundary regularity for solutions of degenerate elliptic equations,, Nonlin. Anal., 12 (1988), 1203.  doi: 10.1016/0362-546X(88)90053-3.  Google Scholar [19] S. Liu, Multiple solutions for coercive $p$-Laplacian equations,, J. Math. Anal. Appl., 316 (2006), 229.  doi: 10.1016/j.jmaa.2005.04.034.  Google Scholar [20] J. Liu and S. Liu, The existence of multiple solutions to quasilinear elliptic equations,, Bull. London Math. Soc., 37 (2005), 592.  doi: 10.1112/S0024609304004023.  Google Scholar [21] J. Mawhin, Multiplicity of solutions for variational systems involving $\varphi$-Laplacians with singular $\varphi$ and periodic potentials,, Discrete and Continuous Dynamical Systems, 32 (2012), 4015.  doi: 10.3934/dcds.2012.32.4015.  Google Scholar [22] D. Motreanu, V. V. Motreanu and N. S. Papageorgiou, Nonautonomous resonant periodic systems with indefinite linear part and a nonsmooth potential,, Communications on Pure and Applied Analysis, 10 (2011), 1401.  doi: 10.3934/cpaa.2011.10.1401.  Google Scholar [23] D. Motreanu, Donal O'Regan and N. S. Papageorgiou, A unified treatment using critical point methods of the existence of multiple solutions for superlinear and sublinear Neumann problems,, Communications on Pure and Applied Analysis, 10 (2011), 1791.  doi: 10.3934/cpaa.2011.10.1791.  Google Scholar [24] J. Mawhin and M. Willem, "Critical Point Theory and Hamiltonian Systems,", Springer-Verlag, (1989).   Google Scholar [25] O. Miyagaki and M. A. S. Souto, Superlinear problems without Ambrosetti and Rabinowitz growth condition,, J. Diff. Eqns, 245 (2008), 3628.  doi: 10.1016/j.jde.2008.02.035.  Google Scholar [26] D. Motreanu, V. Motreanu and N. S. Papageorgiou, A degree theoretic approach for multiple solutions of constant sign for nonlinear elliptic equations,, Manuscripta Math., 124 (2007), 507.  doi: 10.1007/s00229-007-0127-x.  Google Scholar [27] F. O. de Paiva, Multiple solutions for a class of quasilinear problems,, Discrete Cont. Dynam. Systems, 15 (2006), 669.  doi: 10.3934/dcds.2006.15.669.  Google Scholar [28] R. Palais, Homotopy theory of finite dimensional manifolds,, Topology, 5 (1966), 1.   Google Scholar [29] E. Papageorgiou and N. S. Papageorgiou, A multiplicity theorem for problems with the $p$-Laplacian,, J. Funct. Anal., 244 (2007), 63.  doi: 10.1016/j.jfa.2006.11.015.  Google Scholar [30] N. S. Papageorgiou, E. Rocha and V. Staicu, Multiplicity theorems for superlinear elliptic problems,, Calc. Var., 33 (2008), 199.  doi: 10.1007/s00526-008-0172-7.  Google Scholar [31] K. 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2018 Impact Factor: 1.143


text:
• A new pixel detector for the CMS experiment was built in order to cope with the instantaneous luminosities anticipated for the Phase~I Upgrade of the LHC. The new CMS pixel detector provides four-hit tracking with a reduced material budget as well as new cooling and powering schemes. A new front-end readout chip mitigates buffering and bandwidth limitations, and allows operation at low comparator thresholds. In this paper, comprehensive test beam studies are presented, which have been conducted to verify the design and to quantify the performance of the new detector assemblies in terms of tracking efficiency and spatial resolution. Under optimal conditions, the tracking efficiency is $99.95\pm0.05\,\%$, while the intrinsic spatial resolutions are $4.80\pm0.25\,\mu \mathrm{m}$ and $7.99\pm0.21\,\mu \mathrm{m}$ along the $100\,\mu \mathrm{m}$ and $150\,\mu \mathrm{m}$ pixel pitch, respectively. The findings are compared to a detailed Monte Carlo simulation of the pixel detector and good agreement is found.
• ### Towards an Understanding of the Correlations in Jet Substructure(1504.00679)

Aug. 19, 2015 hep-ph, hep-ex
Over the past decade, a large number of jet substructure observables have been proposed in the literature, and explored at the LHC experiments. Such observables attempt to utilize the internal structure of jets in order to distinguish those initiated by quarks, gluons, or by boosted heavy objects, such as top quarks and W bosons. This report, originating from and motivated by the BOOST2013 workshop, presents original particle-level studies that aim to improve our understanding of the relationships between jet substructure observables, their complementarity, and their dependence on the underlying jet properties, particularly the jet radius and jet transverse momentum. This is explored in the context of quark/gluon discrimination, boosted W boson tagging and boosted top quark tagging.
• The degradation of signal in silicon sensors is studied under conditions expected at the CERN High-Luminosity LHC. 200 $\mu$m thick n-type silicon sensors are irradiated with protons of different energies to fluences of up to $3 \cdot 10^{15}$ neq/cm$^2$. Pulsed red laser light with a wavelength of 672 nm is used to generate electron-hole pairs in the sensors. The induced signals are used to determine the charge collection efficiencies separately for electrons and holes drifting through the sensor. The effective trapping rates are extracted by comparing the results to simulation. The electric field is simulated using Synopsys device simulation assuming two effective defects. The generation and drift of charge carriers are simulated in an independent simulation based on PixelAV. The effective trapping rates are determined from the measured charge collection efficiencies and the simulated and measured time-resolved current pulses are compared. The effective trapping rates determined for both electrons and holes are about 50% smaller than those obtained using standard extrapolations of studies at low fluences and suggests an improved tracker performance over initial expectations.
• ### Boosted objects and jet substructure at the LHC(1311.2708)

Dec. 4, 2013 hep-ph, hep-ex
This report of the BOOST2012 workshop presents the results of four working groups that studied key aspects of jet substructure. We discuss the potential of the description of jet substructure in first-principle QCD calculations and study the accuracy of state-of-the-art Monte Carlo tools. Experimental limitations of the ability to resolve substructure are evaluated, with a focus on the impact of additional proton proton collisions on jet substructure performance in future LHC operating scenarios. A final section summarizes the lessons learnt during the deployment of substructure analyses in searches for new physics in the production of boosted top quarks.


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# 5.1 Introduction

Memory access有两个局部性（principle of locality）：这里直接复制书中的内容

Temporal locality (locality in time): if an item is referenced, it will tend to be referenced again soon.

Spatial locality (locality in space): if an item is referenced, items whose

addresses are close by will tend to be referenced soon

Cache既利用了空间局部性，也利用了时间局部性。空间局部性是cache中的每一个cache line包含一段地址相邻的数据；时间局部性，缓存在cache中的数据，下次被访问的时候，直接从cache中取。

hit rate The fraction of memory accesses found  in a level of the memory hierarchy.

miss rate The fraction of memory accesses not found in a level of the memory hierarchy.

hit time The time required to access a level of the memory hierarchy, including the time needed to determine whether the access is a hit or a miss.

miss penalty The time required to fetch a block into a level of the memory hierarchy from the lower level, including the time to access the block, transmit it from one level to the other, insert it in the level that experienced

the miss, and then pass the block to the requestor.

# 5.2 memory technology

SRAM （static  random access memory）

DRAM（dynamic random access memory）

- the value kept in a cell is stored as a charge in a capacitor.

- A single transistor is then used to access this stored charge。 So one transistor per

bit of storage

- must periodically be refreshed

refresh方式：读出来，再写进去。

DDR SDRAM。