text:
# The workflow matched-filter module¶

## Introduction¶

The matched-filter section of pycbc’s workflow module is responsible for matched-filtering the data against the template bank(s) from the template bank section and generating a list of “triggers” for each interferometer. These triggers should be a list of any event where the signal to noise ratio and any signal consistency test are such that that point should be sent forward to check for coincidence in other ifos.

Any single-ifo signal consistency tests (ie. chi-squared tests etc.) should be computed in this section and stored within the lists of triggers. The workflow does not make any specifications on the output format, but obviously code in the next stages of the workflow must know how to process that input.

The matched-filtering section should be as independent of the other stages of the workflow as possible. This means that we don’t require the data read in by matched-filter jobs to match that read in by template bank jobs (however this may be desirable in some cases, so should be possible where sensible). Options should also not be hardcoded (so there are no cases where an option that gets sent to a template bank job also gets sent to a matched-filter job without any way to stop that). However, it is possible to duplicate options where this is desireable (see Pycbc’s workflow module configuration file(s) and command line interface).

The return from the matched-filter section of the workflow module is a list of File objects corresponding to each actual file (one for each job) that will be generated within the workflow. This will be the only thing that will be passed from the matched-filter section to the future sections.

## Usage¶

Using this module requires a number of things

• A configuration file (or files) containing the information needed to tell this module how to generate GW triggers.
• An initialized instance of the workflow class, containing the ConfigParser.
• A list of segments to be analysed by this module.
• A FileList returned by the templatebank module containing the template banks available for use.
• A FileList returned by the datafind module containing the frames that contain the data that will be used to make the template banks.
• If desired an injection file for assessing sensitivity to simulated signals.

The module is then called according to

pycbc.workflow.setup_matchedfltr_workflow(workflow, science_segs, datafind_outs, tmplt_banks, output_dir=None, injection_file=None, tags=None)[source]

This function aims to be the gateway for setting up a set of matched-filter jobs in a workflow. This function is intended to support multiple different ways/codes that could be used for doing this. For now the only supported sub-module is one that runs the matched-filtering by setting up a serious of matched-filtering jobs, from one executable, to create matched-filter triggers covering the full range of science times for which there is data and a template bank file.

Parameters: Workflow (pycbc.workflow.core.Workflow) – The workflow instance that the coincidence jobs will be added to. science_segs (ifo-keyed dictionary of ligo.segments.segmentlist instances) – The list of times that are being analysed in this workflow. datafind_outs (pycbc.workflow.core.FileList) – An FileList of the datafind files that are needed to obtain the data used in the analysis. tmplt_banks (pycbc.workflow.core.FileList) – An FileList of the template bank files that will serve as input in this stage. output_dir (path) – The directory in which output will be stored. injection_file (pycbc.workflow.core.File, optional (default=None)) – If given the file containing the simulation file to be sent to these jobs on the command line. If not given no file will be sent. tags (list of strings (optional, default = [])) – A list of the tagging strings that will be used for all jobs created by this call to the workflow. An example might be [‘BNSINJECTIONS’] or [‘NOINJECTIONANALYSIS’]. This will be used in output names. inspiral_outs – A list of output files written by this stage. This will not contain any intermediate products produced within this stage of the workflow. If you require access to any intermediate products produced at this stage you can call the various sub-functions directly. pycbc.workflow.core.FileList

### Configuration file setup¶

Here we describe the options given in the configuration file used in the workflow that will be needed in this section

#### [workflow-matchedfilter] section¶

The configuration file must have an [workflow-matchedfilter] section, which is used to tell the workflow how to construct (or gather) the template banks. The first option to choose and provide is

• matchedfilter-method = VALUE

The choices here and their description are as described below

• WORKFLOW_INDEPENDENT_IFOS - Matched-filter trigger files will be generated within the workflow. These banks will be made to cover only short (normally ~ 2000s) of data to reflect PSD changes over time and will be independent and distinct for each analysed interferometer. This uses the setup_matchedfltr_dax_generated sub-module.

Currently only one option, but others can be added. The subfunctions used are described here

pycbc.workflow.setup_matchedfltr_dax_generated(workflow, science_segs, datafind_outs, tmplt_banks, output_dir, injection_file=None, tags=None, link_to_tmpltbank=False, compatibility_mode=False)[source]

Setup matched-filter jobs that are generated as part of the workflow. This module can support any matched-filter code that is similar in principle to lalapps_inspiral, but for new codes some additions are needed to define Executable and Job sub-classes (see jobutils.py).

Parameters: workflow (pycbc.workflow.core.Workflow) – The Workflow instance that the coincidence jobs will be added to. science_segs (ifo-keyed dictionary of ligo.segments.segmentlist instances) – The list of times that are being analysed in this workflow. datafind_outs (pycbc.workflow.core.FileList) – An FileList of the datafind files that are needed to obtain the data used in the analysis. tmplt_banks (pycbc.workflow.core.FileList) – An FileList of the template bank files that will serve as input in this stage. output_dir (path) – The directory in which output will be stored. injection_file (pycbc.workflow.core.File, optional (default=None)) – If given the file containing the simulation file to be sent to these jobs on the command line. If not given no file will be sent. tags (list of strings (optional, default = [])) – A list of the tagging strings that will be used for all jobs created by this call to the workflow. An example might be [‘BNSINJECTIONS’] or [‘NOINJECTIONANALYSIS’]. This will be used in output names. link_to_tmpltbank (boolean, optional (default=True)) – If this option is given, the job valid_times will be altered so that there will be one inspiral file for every template bank and they will cover the same time span. Note that this option must also be given during template bank generation to be meaningful. inspiral_outs – A list of output files written by this stage. This will not contain any intermediate products produced within this stage of the workflow. If you require access to any intermediate products produced at this stage you can call the various sub-functions directly. pycbc.workflow.core.FileList

When using the setup_matchedfltr_dax_generated sub-module the following additional options apply in the [workflow-matchedfilter] section:

• matchedfilter-link-to-tmpltbank - OPTIONAL. If this is given the workflow module will attempt to ensure a one-to-one correspondence between template banks and matched-filter outputs. This may not work in all cases and should be considered an option to be used for comparing with ihope output.
• matchedfilter-compatibility-mode - OPTIONAL. If this is given the workflow module will tile the matched-filter jobs in the same way as inspiral_hipe used to. This requires the link option above and that the template bank and matched-filtering jobs are reading the same amount of data in each job.
• max-analysis-segments = (NOT used for lalapps_inspiral) - REQUIRED. The maximum number of analysis segments to analyze within a single inspiral job. Note that triggers may not be produced for the entire span of time.
• min-analysis-segments = (NOT used for lalapps_inspiral) - REQUIRED. The minimum number of analysis segments to analyze within a single inspiral job. This may be the same as the maximum.

#### [executables]¶

inspiral = /path/to/inspiral_exec

A section, in this case [inspiral], will be used to specify the constant command line options that are sent to all inspiral jobs. How to set up the [{exe_name}] section, and which executables are currently supported is discussed below.

### Supported inspiral trigger generators and instructions for using them¶

The following inspiral trigger generators are currently supported in pycbc’s workflow module

• lalapps_inspiral
• pycbc_inspiral

Adding a new executable is not too hard, please ask a developer for some pointers on how to do this if you want to add a new code.

#### lalapps_inspiral_ahope¶

Lalapps_inspiral is the legacy C-code that has been used for years to find gravitational-wave triggers in It is a little inflexible in terms of output file names.

lalapps_inspiral is supported in the workflow module via a wrapper script lalapps_inspiral_ahope, this allows us to specify all the frame files and the output file name directly. Documentation for the lalapps_inspiral command line arguments can be found at http://software.ligo.org/docs/lalsuite/lalapps/inspiral_8c.html

Of these options the workflow module or the wrapper script will automatically add the following, which are unique for each job. DO NOT ADD THESE OPTIONS IN THE CONFIGURATION FILE.

• –gps-start-time
• –gps-end-time
• –trig-start-time
• –trig-end-time
• –frame-cache
• –user-tag
• –ifo-tag

All other options must be provided in the configuration file. Here is an example of a lalapps_inspiral call.

lalapps_inspiral --do-rsq-veto  --trig-end-time 971614817 --enable-rsq-veto  --dynamic-range-exponent 69.0 --autochisq-stride 2 --bank-file datafind/L1-TMPLTBANK_19-971612833-2048.xml.gz --high-pass-order 8 --strain-high-pass-order 8 --ifo-tag FULL_DATA --user-tag 19 --gps-end-time 971614881 --calibrated-data real_8 --channel-name L1:LDAS-STRAIN --snr-threshold 5.5 --cluster-method template --number-of-segments 15 --trig-start-time 971613852 --enable-high-pass 30.0 --gps-start-time 971612833 --enable-filter-inj-only  --maximization-interval 30 --high-pass-attenuation 0.1 --chisq-bins 2 --inverse-spec-length 16 --rsq-veto-threshold 15.0 --segment-length 1048576 --low-frequency-cutoff 40.0 --pad-data 8 --autochisq-two-sided  --sample-rate 4096 --chisq-threshold 10.0 --rsq-veto-max-snr 12.0 --resample-filter ldas --strain-high-pass-atten 0.1 --strain-high-pass-freq 30 --bank-veto-time-freq  --segment-overlap 524288 --frame-cache datafind/L1-DATAFIND-968556757-3058132.lcf --chisq-delta 0.2 --bank-veto-subbank-size 20 --approximant FindChirpSP --rsq-veto-time-thresh 0.0002 --write-compress  --autochisq-length 100 --enable-output  --rsq-veto-window 6.0 --order threePointFivePN --spectrum-type median

#### pycbc_inspiral¶

pycbc_inspiral is pycbc’s inspiral matched-filtering program. Designed as a replacement and improvement of lalapps_inspiral. The help message of pycbc_inspiral follows:

\$ pycbc_inspiral --help
usage:

Find single detector gravitational-wave triggers.

optional arguments:
-h, --help            show this help message and exit
--version
-V, --verbose         print extra debugging information
--update-progress UPDATE_PROGRESS
updates a file 'progress.txt' with a value 0 .. 1.0
when this amount of (filtering) progress was made
--update-progress-file UPDATE_PROGRESS_FILE
name of the file to write the amount of (filtering)
progress to
--bank-file BANK_FILE
--snr-threshold SNR_THRESHOLD
SNR threshold for trigger generation
--newsnr-threshold THRESHOLD
Cut triggers with NewSNR less than THRESHOLD
--low-frequency-cutoff LOW_FREQUENCY_CUTOFF
The low frequency cutoff to use for filtering (Hz)
--enable-bank-start-frequency
Read the starting frequency of template waveforms from
the template bank.
--max-template-length MAX_TEMPLATE_LENGTH
The maximum length of a template is seconds. The
starting frequency of the template is modified to
ensure the proper length
--enable-q-transform  compute the q-transform for each segment of a given
analysis run. (default = False)
--approximant APPRX[:COND] [APPRX[:COND] ...]
The approximant(s) to use. Multiple approximants to
use in different regions may be provided. If multiple
approximants are provided, every one but the last must
be be followed by a conditional statement defining
where that approximant should be used. Conditionals
can be any boolean test understood by numpy. For
example, 'Apprx:(mtotal > 4) & (mchirp <= 5)' would
use approximant 'Apprx' where total mass is > 4 and
chirp mass is <= 5. Conditionals are applied in order,
with each successive one only applied to regions not
covered by previous arguments. For example,
'TaylorF2:mtotal < 4' 'IMRPhenomD:mchirp < 3' would
result in IMRPhenomD being used where chirp mass is <
3 and total mass is >= 4. The last approximant given
may use 'else' as the conditional or include no
conditional. In either case, this will cause the last
approximant to be used in any remaning regions after
all the previous conditionals have been applied. For
the full list of possible parameters to apply
conditionals to, see WaveformArray.default_fields().
Math operations may also be used on parameters; syntax
is python, with any operation recognized by numpy.
--order {-1,0,1,2,3,4,5,6,7,8}
The integer half-PN order at which to generate the
approximant. Default is -1 which indicates to use
approximant defined default.
--taper-template {start,end,startend}
For time-domain approximants, taper the start and/or
end of the waveform before FFTing.
--cluster-method {template,window}
--cluster-function {findchirp,symmetric}
How to cluster together triggers within a window.
'findchirp' uses a forward sliding window; 'symmetric'
will compare each window to the one before and after,
keeping only a local maximum.
--cluster-window CLUSTER_WINDOW
Length of clustering window in seconds. Set to 0 to
disable clustering.
--bank-veto-bank-file BANK_VETO_BANK_FILE
--chisq-snr-threshold CHISQ_SNR_THRESHOLD
Minimum SNR to calculate the power chisq
--chisq-bins CHISQ_BINS
Number of frequency bins to use for power chisq.
Specify an integer for a constant number of bins, or a
function of template attributes. Math functions are
allowed, ex.
'10./math.sqrt((params.mass1+params.mass2)/100.)'.
Non-integer values will be rounded down.
--chisq-threshold CHISQ_THRESHOLD
--chisq-delta CHISQ_DELTA
--autochi-number-points AUTOCHI_NUMBER_POINTS
The number of points to use, in both directions
ifdoing a two-sided auto-chisq, to calculate theauto-
chisq statistic.
--autochi-stride AUTOCHI_STRIDE
The gap, in sample points, between the points atwhich
to calculate auto-chisq.
--autochi-two-phase   If given auto-chisq will be calculated by testing
against both phases of the SNR time-series. If not
given, only the phase matching the trigger will be
used.
--autochi-onesided {left,right}
Decide whether to calculate auto-chisq usingpoints on
both sides of the trigger or only on oneside. If not
given points on both sides will beused. If given, with
either 'left' or 'right',only points on that side
(right = forward in time,left = back in time) will be
used.
--autochi-reverse-template
If given, time-reverse the template beforecalculating
the auto-chisq statistic. This willcome at additional
computational cost as the SNRtime-series will need
recomputing for the time-reversed template.
--autochi-max-valued  If given, store only the maximum value of the auto-
chisq over all points tested. A disadvantage of this
is that the mean value will not be known analytically.
--autochi-max-valued-dof INT
If using --autochi-max-valued this value denotes the
pre-calculated mean value that will be stored as the
auto-chisq degrees-of-freedom value.
--downsample-factor DOWNSAMPLE_FACTOR
Factor that determines the interval between the
initial SNR sampling. If not set (or 1) no sparse
sample is created, and the standard full SNR is
calculated.
--upsample-threshold UPSAMPLE_THRESHOLD
The fraction of the SNR threshold to check the sparse
SNR sample.
--upsample-method {pruned_fft}
The method to find the SNR points between the sparse
SNR sample.
--user-tag TAG        This is used to identify FULL_DATA jobs for
compatibility with pipedown post-processing. Option
will be removed when no longer needed.
--keep-loudest-log-chirp-window KEEP_LOUDEST_LOG_CHIRP_WINDOW
Keep loudest triggers within ln chirp mass window
--keep-loudest-interval KEEP_LOUDEST_INTERVAL
Window in seconds to maximize triggers over bank
--keep-loudest-num KEEP_LOUDEST_NUM
Number of triggers to keep from each maximization
interval
Statistic used to determine loudest to keep
--finalize-events-template-rate NUM TEMPLATES
After NUM TEMPLATES perform the various clustering and
rejection tests that would be performed at the end of
this job. Default is to only do those things at the
end of the job. This can help control memory usage if
a lot of triggers that would be rejected are being
retained. A suggested value for this is 500, but a
good number may depend on other settings and your
specific use-case.
--gpu-callback-method GPU_CALLBACK_METHOD
--use-compressed-waveforms
Use compressed waveforms from the bank file.
--waveform-decompression-method WAVEFORM_DECOMPRESSION_METHOD
Method to be used decompress waveforms from the bank
file.
--checkpoint-interval CHECKPOINT_INTERVAL
Save results to checkpoint file every X seconds.
Default is no checkpointing.
--require-valid-checkpoint
If the checkpoint file is invalid, raise an error.
Default is to ignore invalid checkpoint files and to
delete the broken file.
--checkpoint-exit-maxtime CHECKPOINT_EXIT_MAXTIME
Checkpoint and exit if X seconds of execution time is
exceeded. Default is no checkpointing.
--checkpoint-exit-code CHECKPOINT_EXIT_CODE
Exit code returned if exiting after a checkpoint

Options to select the method of PSD generation:
The options --psd-model, --psd-file, --asd-file, and --psd-estimation are
mutually exclusive.

Get PSD from given analytical model.
--psd-file PSD_FILE   Get PSD using given PSD ASCII file
--asd-file ASD_FILE   Get PSD using given ASD ASCII file
--psd-inverse-length PSD_INVERSE_LENGTH
(Optional) The maximum length of the impulse response
of the overwhitening filter (s)
--psd-file-xml-ifo-string PSD_FILE_XML_IFO_STRING
If using an XML PSD file, use the PSD in the file's
PSD dictionary with this ifo string. If not given and
only one PSD present in the file return that, if not
given and multiple (or zero) PSDs present an exception
will be raised.
--psd-file-xml-root-name PSD_FILE_XML_ROOT_NAME
If given use this as the root name for the PSD XML
file. If this means nothing to you, then it is
probably safe to ignore this option.
--psdvar-segment SECONDS
Length of segment for mean square calculation of PSD
variation.
--psdvar-short-segment SECONDS
Length of short segment for outliers removal in PSD
variability calculation.
--psdvar-long-segment SECONDS
Length of long segment when calculating the PSD
variability.
--psdvar-psd-duration SECONDS
Duration of short segments for PSD estimation.
--psdvar-psd-stride SECONDS
Separation between PSD estimation segments.
--psdvar-low-freq HERTZ
Minimum frequency to consider in strain bandpass.
--psdvar-high-freq HERTZ
Maximum frequency to consider in strain bandpass.
--psd-estimation {mean,median,median-mean}
Measure PSD from the data, using given average method.
--psd-segment-length PSD_SEGMENT_LENGTH
(Required for --psd-estimation) The segment length for
PSD estimation (s)
--psd-segment-stride PSD_SEGMENT_STRIDE
(Required for --psd-estimation) The separation between
consecutive segments (s)
--psd-num-segments PSD_NUM_SEGMENTS
(Optional, used only with --psd-estimation). If given,
PSDs will be estimated using only this number of
segments. If more data is given than needed to make
this number of segments then excess data will not be
used in the PSD estimate. If not enough data is given,
the code will fail.
--psd-output PSD_OUTPUT
(Optional) Write PSD to specified file

Options for obtaining h(t):
These options are used for generating h(t) either by reading from a file
or by generating it. This is only needed if the PSD is to be estimated
from the data, ie. if the --psd-estimation option is given.

--gps-start-time GPS_START_TIME
The gps start time of the data (integer seconds)
--gps-end-time GPS_END_TIME
The gps end time of the data (integer seconds)
--strain-high-pass STRAIN_HIGH_PASS
High pass frequency
seconds)
--taper-data TAPER_DATA
Taper ends of data to zero using the supplied length
as a window (integer seconds)
--sample-rate SAMPLE_RATE
The sample rate to use for h(t) generation (integer
Hz).
--channel-name CHANNEL_NAME
The channel containing the gravitational strain data
--frame-cache FRAME_CACHE [FRAME_CACHE ...]
Cache file containing the frame locations.
--frame-files FRAME_FILES [FRAME_FILES ...]
list of frame files
--hdf-store HDF_STORE
Store of time series data in hdf format
--frame-type FRAME_TYPE
(optional), replaces frame-files. Use datafind to get
the needed frame file(s) of this type.
--frame-sieve FRAME_SIEVE
(optional), Only use frame files where the URL matches
the regular expression given.
Name of model PSD for generating fake gaussian noise.
--fake-strain-seed FAKE_STRAIN_SEED
Seed value for the generation of fake colored gaussian
noise
--fake-strain-from-file FAKE_STRAIN_FROM_FILE
File containing ASD for generating fake noise from it.
--injection-file INJECTION_FILE
(optional) Injection file used to add waveforms into
the strain
--sgburst-injection-file SGBURST_INJECTION_FILE
(optional) Injection file used to add sine-Gaussian
burst waveforms into the strain
--injection-scale-factor INJECTION_SCALE_FACTOR
Divide injections by this factor before injecting into
the data.
--injection-f-ref INJECTION_F_REF
Reference frequency in Hz for creating CBC injections
from an XML file.
--injection-f-final INJECTION_F_FINAL
Override the f_final field of a CBC XML injection
file.
--gating-file GATING_FILE
(optional) Text file of gating segments to apply.
Format of each line is (all times in secs): gps_time
--autogating-threshold SIGMA
If given, find and gate glitches producing a deviation
larger than SIGMA in the whitened strain time series.
--autogating-max-iterations SIGMA
If given, iteratively apply autogating
--autogating-cluster SECONDS
Length of clustering window for detecting glitches for
autogating.
--autogating-width SECONDS
Half-width of the gating window.
--autogating-taper SECONDS
Taper the strain before and after each gating window
over a duration of SECONDS.
Ignore the given length of whitened strain at the ends
of a segment, to avoid filters ringing.
--normalize-strain NORMALIZE_STRAIN
(optional) Divide frame data by constant.
--zpk-z ZPK_Z [ZPK_Z ...]
(optional) Zero-pole-gain (zpk) filter strain. A list
of zeros for transfer function
--zpk-p ZPK_P [ZPK_P ...]
(optional) Zero-pole-gain (zpk) filter strain. A list
of poles for transfer function
--zpk-k ZPK_K         (optional) Zero-pole-gain (zpk) filter strain.
Transfer function gain
--witness-frame-type WITNESS_FRAME_TYPE
(optional), frame type which will be use to query the
witness channel data.
--witness-tf-file WITNESS_TF_FILE
an hdf file containing the transfer functions and the
associated channel names
--witness-filter-length WITNESS_FILTER_LENGTH
filter length in seconds for the transfer function

Options for segmenting the strain:
These options are used to determine how to segment the strain into smaller
chunks, and for determining the portion of each to analyze for triggers.

--trig-start-time TRIG_START_TIME
(optional) The gps time to start recording triggers
--trig-end-time TRIG_END_TIME
(optional) The gps time to stop recording triggers
--segment-length SEGMENT_LENGTH
The length of each strain segment in seconds.
The time in seconds to ignore of the beginning of each
segment in seconds.
The time in seconds to ignore at the end of each
segment in seconds.
times, if needed.
--filter-inj-only     Analyze only segments that contain an injection.
--injection-window INJECTION_WINDOW
If using --filter-inj-only then only search for
injections within +/- injection window of the
injections's end time. This is useful to speed up a
coherent search or a search where we initially filter
at lower sample rate, and then filter at full rate
where needed. NOTE: Reverts to full analysis if two
injections are in the same segment.

Options for selecting the processing scheme in this program.:
--processing-scheme PROCESSING_SCHEME
The choice of processing scheme. Choices are ['mkl',
'cuda', 'cpu', 'numpy']. (optional for CPU scheme) The
number of execution threads can be indicated by
default is a single thread. If the scheme is provided
as cpu:env, the number of threads can be provided by
the PYCBC_NUM_THREADS environment variable. If the
environment variable is not set, the number of threads
matches the number of logical cores.
--processing-device-id PROCESSING_DEVICE_ID
(optional) ID of GPU to use for accelerated processing

Options for selecting the FFT backend and controlling its performance in this program.:
--fft-backends [FFT_BACKENDS [FFT_BACKENDS ...]]
Preference list of the FFT backends. Choices are:
['fftw', 'mkl', 'numpy']
--fftw-measure-level FFTW_MEASURE_LEVEL
Determines the measure level used in planning FFTW
FFTs; allowed values are: [0, 1, 2, 3]
--fftw-input-float-wisdom-file FFTW_INPUT_FLOAT_WISDOM_FILE
Filename from which to read single-precision wisdom
--fftw-input-double-wisdom-file FFTW_INPUT_DOUBLE_WISDOM_FILE
Filename from which to read double-precision wisdom
--fftw-output-float-wisdom-file FFTW_OUTPUT_FLOAT_WISDOM_FILE
Filename to which to write single-precision wisdom
--fftw-output-double-wisdom-file FFTW_OUTPUT_DOUBLE_WISDOM_FILE
Filename to which to write double-precision wisdom
--fftw-import-system-wisdom
If given, call fftw[f]_import_system_wisdom()

Options for selecting optimization-specific settings:
--cpu-affinity CPU_AFFINITY
A set of CPUs on which to run, specified in a format
--cpu-affinity-from-env CPU_AFFINITY_FROM_ENV
The name of an enivornment variable containing a set
of CPUs on which to run, specified in a format

Options that, if injections are present in this run, are responsible for performing pre-checks between injections in the data being filtered and the current search template to determine if the template has any chance of actually detecting the injection. The parameters of this test are given by the various options below. The --injection-filter-rejector-chirp-time-window and --injection-filter-rejector-match-threshold options need to be provided if those tests are desired. Other options will take default values unless overriden. More details on these options follow.:
--injection-filter-rejector-chirp-time-window INJECTION_FILTER_REJECTOR_CHIRP_TIME_WINDOW
If this value is not None and an injection file is
given then we will calculate the difference in chirp
time (tau_0) between the template and each injection
in the analysis segment. If the difference is greate
than this threshold for all injections then filtering
is not performed. By default this will be None.
--injection-filter-rejector-match-threshold INJECTION_FILTER_REJECTOR_MATCH_THRESHOLD
If this value is not None and an injection file is
provided then we will calculate a 'coarse match'
between the template and each injection in the
analysis segment. If the match is less than this
threshold for all injections then filtering is not
performed. Parameters for the 'coarse match' follow.
By default this value will be None.
--injection-filter-rejector-coarsematch-deltaf INJECTION_FILTER_REJECTOR_COARSEMATCH_DELTAF
If injections are present and a match threshold is
provided, this option specifies the frequency spacing
that will be used for injections, templates and PSD
when computing the 'coarse match'. Templates will be
generated directly with this spacing. The PSD and
injections will be resampled.
--injection-filter-rejector-coarsematch-fmax INJECTION_FILTER_REJECTOR_COARSEMATCH_FMAX
If injections are present and a match threshold is
provided, this option specifies the maximum frequency
that will be used for injections, templates and PSD
when computing the 'coarse match'. Templates will be
generated directly with this max frequency. The PSD
and injections' frequency series will be truncated.
--injection-filter-rejector-seg-buffer INJECTION_FILTER_REJECTOR_SEG_BUFFER
If injections are present and either a match threshold
or a chirp-time window is given, we will determine if
injections are 'in' the specified analysis chunk by
using the end times. If this value is non-zero the
analysis chunk is extended on both sides by this
amount before determining if injections are within the
given window.
--injection-filter-rejector-f-lower INJECTION_FILTER_REJECTOR_F_LOWER
If injections are present and either a match threshold
or a chirp-time window is given, this value is used to
set the lower frequency for determine chirp times or
for calculating matches. If this value is None the
lower frequency used for the full matched-filter is
used. Otherwise this value is used.

Sine-Gaussian Chisq:
--sgchisq-snr-threshold SGCHISQ_SNR_THRESHOLD
Minimum SNR threshold to use SG chisq
--sgchisq-locations SGCHISQ_LOCATIONS [SGCHISQ_LOCATIONS ...]
Frequency offsets and quality factors of the sine-
Gaussians to use, format 'region-
boolean:q1-offset1,q2-offset2'. Offset is relative to
the end frequency of the approximant. Region is a
boolean expression selecting templates to apply the
sine-Gaussians to, ex. 'mtotal>40'

Of these options the workflow module will automatically add the following, which are unique fo r each job. DO NOT ADD THESE OPTIONS IN THE CONFIGURATION FILE.

• –gps-start-time
• –gps-end-time
• –frame-cache
• –output

All other options must be provided in the configuration file. Here is an example of a pycbc_inspiral call.

pycbc_inspiral --trig-end-time 961592867 --verbose  --cluster-method window --bank-filetmpltbank/L1-TMPLTBANK_01-961591486-1382.xml.gz --gps-end-time 961592884 --channel-name L1:LDAS-STRAIN --processing-scheme cuda --snr-threshold 5.5 --psd-estimation median --trig-start-time 961591534 --gps-start-time 961590836 --chisq-bins 16 --segment-end-pad 16 --segment-length 2048 --low-frequency-cutoff 15 --pad-data 8 --cluster-window 1 --sample-rate 4096 --segment-start-pad 650 --psd-segment-stride 32 --psd-inverse-length 16 --psd-segment-length 64 --frame-cache datafind/L1-DATAFIND-961585543-7349.lcf --approximant SPAtmplt --output inspiral/L1-INSPIRAL_1-961591534-1333.xml.gz --strain-high-pass 30 --order 7

## pycbc.workflow.matched_filter Module¶

This is complete documentation of this module’s code

This module is responsible for setting up the matched-filtering stage of workflows. For details about this module and its capabilities see here: https://ldas-jobs.ligo.caltech.edu/~cbc/docs/pycbc/NOTYETCREATED.html

pycbc.workflow.matched_filter.setup_matchedfltr_dax_generated(workflow, science_segs, datafind_outs, tmplt_banks, output_dir, injection_file=None, tags=None, link_to_tmpltbank=False, compatibility_mode=False)[source]

Setup matched-filter jobs that are generated as part of the workflow. This module can support any matched-filter code that is similar in principle to lalapps_inspiral, but for new codes some additions are needed to define Executable and Job sub-classes (see jobutils.py).

Parameters: workflow (pycbc.workflow.core.Workflow) – The Workflow instance that the coincidence jobs will be added to. science_segs (ifo-keyed dictionary of ligo.segments.segmentlist instances) – The list of times that are being analysed in this workflow. datafind_outs (pycbc.workflow.core.FileList) – An FileList of the datafind files that are needed to obtain the data used in the analysis. tmplt_banks (pycbc.workflow.core.FileList) – An FileList of the template bank files that will serve as input in this stage. output_dir (path) – The directory in which output will be stored. injection_file (pycbc.workflow.core.File, optional (default=None)) – If given the file containing the simulation file to be sent to these jobs on the command line. If not given no file will be sent. tags (list of strings (optional, default = [])) – A list of the tagging strings that will be used for all jobs created by this call to the workflow. An example might be [‘BNSINJECTIONS’] or [‘NOINJECTIONANALYSIS’]. This will be used in output names. link_to_tmpltbank (boolean, optional (default=True)) – If this option is given, the job valid_times will be altered so that there will be one inspiral file for every template bank and they will cover the same time span. Note that this option must also be given during template bank generation to be meaningful. inspiral_outs – A list of output files written by this stage. This will not contain any intermediate products produced within this stage of the workflow. If you require access to any intermediate products produced at this stage you can call the various sub-functions directly. pycbc.workflow.core.FileList
pycbc.workflow.matched_filter.setup_matchedfltr_dax_generated_multi(workflow, science_segs, datafind_outs, tmplt_banks, output_dir, injection_file=None, tags=None, link_to_tmpltbank=False, compatibility_mode=False)[source]

Setup matched-filter jobs that are generated as part of the workflow in which a single job reads in and generates triggers over multiple ifos. This module can support any matched-filter code that is similar in principle to pycbc_multi_inspiral or lalapps_coh_PTF_inspiral, but for new codes some additions are needed to define Executable and Job sub-classes (see jobutils.py).

Parameters: workflow (pycbc.workflow.core.Workflow) – The Workflow instance that the coincidence jobs will be added to. science_segs (ifo-keyed dictionary of ligo.segments.segmentlist instances) – The list of times that are being analysed in this workflow. datafind_outs (pycbc.workflow.core.FileList) – An FileList of the datafind files that are needed to obtain the data used in the analysis. tmplt_banks (pycbc.workflow.core.FileList) – An FileList of the template bank files that will serve as input in this stage. output_dir (path) – The directory in which output will be stored. injection_file (pycbc.workflow.core.File, optional (default=None)) – If given the file containing the simulation file to be sent to these jobs on the command line. If not given no file will be sent. tags (list of strings (optional, default = [])) – A list of the tagging strings that will be used for all jobs created by this call to the workflow. An example might be [‘BNSINJECTIONS’] or [‘NOINJECTIONANALYSIS’]. This will be used in output names. inspiral_outs – A list of output files written by this stage. This will not contain any intermediate products produced within this stage of the workflow. If you require access to any intermediate products produced at this stage you can call the various sub-functions directly. pycbc.workflow.core.FileList
pycbc.workflow.matched_filter.setup_matchedfltr_workflow(workflow, science_segs, datafind_outs, tmplt_banks, output_dir=None, injection_file=None, tags=None)[source]

This function aims to be the gateway for setting up a set of matched-filter jobs in a workflow. This function is intended to support multiple different ways/codes that could be used for doing this. For now the only supported sub-module is one that runs the matched-filtering by setting up a serious of matched-filtering jobs, from one executable, to create matched-filter triggers covering the full range of science times for which there is data and a template bank file.

Parameters: Workflow (pycbc.workflow.core.Workflow) – The workflow instance that the coincidence jobs will be added to. science_segs (ifo-keyed dictionary of ligo.segments.segmentlist instances) – The list of times that are being analysed in this workflow. datafind_outs (pycbc.workflow.core.FileList) – An FileList of the datafind files that are needed to obtain the data used in the analysis. tmplt_banks (pycbc.workflow.core.FileList) – An FileList of the template bank files that will serve as input in this stage. output_dir (path) – The directory in which output will be stored. injection_file (pycbc.workflow.core.File, optional (default=None)) – If given the file containing the simulation file to be sent to these jobs on the command line. If not given no file will be sent. tags (list of strings (optional, default = [])) – A list of the tagging strings that will be used for all jobs created by this call to the workflow. An example might be [‘BNSINJECTIONS’] or [‘NOINJECTIONANALYSIS’]. This will be used in output names. inspiral_outs – A list of output files written by this stage. This will not contain any intermediate products produced within this stage of the workflow. If you require access to any intermediate products produced at this stage you can call the various sub-functions directly. pycbc.workflow.core.FileList


text:
The two phase simplex method aims at finding solution(s) for a linear program (LP), which can be expressed as $$\min\{c^Tx \mid Ax = b, x \in \Bbb{R}_+^n\}$$ for some technology matrix $$A \in {\cal M}_{m \times n}(\Bbb{R})$$, in case of no obvious basic feasible solution (BFS). This algorithm consists of two stages, from which this algorithm is named.
1. Introduce artificial variables $$y$$ to find an initial BFS: solve $$\min\{||y||_1 \mid Ax+y = b, x \in \Bbb{R}_+^n, y \in \Bbb{R}^m\}$$ by using the simplex algorithm with initial BFS $$(x,y) = (0,b)$$. If the original LP is feasible, one will get $$y=0$$, so that the BFS is feasible for the original LP.

format: plain


text:
Home > math, modeling, women in math > Leila Schneps is a mystery writer!

## Leila Schneps is a mystery writer!

March 27, 2013

I’m back! I missed you guys bad.

My experience with Seattle in the last 8 days has convinced me of something I rather suspected, namely I’m a huge New York snob and can’t exist happily anywhere else. I will spare you the details (they have to do with cars, subways, and being an asshole pedestrian) but suffice it to say, glad to be home.

Just a few caveats on complaining about my vacation:

1. I enjoyed visiting the University of Washington and giving the math colloquium there as well as a “Math Day” talk where I showed kids the winning strategy for Nim (as well as other impartial two-player games) following my notes from last summer.
2. I enjoyed reading Leon and Becky’s guest posts. Thanks guys!
3. And then there was the time spent with my darling family. Of course, goes without saying, it’s always magical to get to the point where your kids have invented a whole new language of insults after you’ve outlawed certain words: “Shut your fidoodle, you syncopathic lardle!”

Of all the topics I want to write about today, I’ve decided to go with the most immediate and surprising one : Leila Schneps is now a mystery writer! How cool is that? She’s written a book with her daughter, Math on Trial: How Numbers Get Used and Abused in the Courtroom, currently in stock and available on Amazon. And she wrote an op-ed for the New York Times talking about it (hat tip Chris Wiggins).

I know Leila from having been her grad student assistant at the GWU Summer Program for Women in Math the first year it existed, in 1995. She taught undergrads about Galois cohomology and interpreted elements of $H^1$ as twists and elements of $H^2$ as obstructions and then had them do a bunch of examples for homework with me. It was pretty awesome, and I learned a ton. Leila is also a regular and fantastic commenter on mathbabe.

I love the premise of the book she’s written. She finds a bunch of historical examples where mathematics is used in trials to the detriment of justice, and people get unfairly jailed (or, less often, let free). From the op-ed (emphasis mine):

Decades ago, the Harvard law professor Laurence H. Tribe wrote a stinging denunciation of the use of mathematics at trial, saying that the “overbearing impressiveness” of numbers tends to “dwarf” other evidence. But we neither can nor should throw math out of the courtroom. Advances in forensics, which rely on data analysis for everything from gunpowder to DNA, mean that quantitative methods will play an ever more important role in judicial deliberations.

The challenge is to make sure that the math behind the legal reasoning is fundamentally sound. Good math can help reveal the truth. But in inexperienced hands, math can become a weapon that impedes justice and destroys innocent lives.

Go Leila!

Categories: math, modeling, women in math
1. March 27, 2013 at 11:42 am

Second: okay fine, no place like NYC – but since it was a trip to Seattle that prompted the mention, here goes…

Among truck drivers, NYC has by far the worst reputation of any city in America, and deservedly so.

Exhibit A: NY State’s egregious habit of posting ridiculously false bridge clearances. (What a novel concept: traffic signs designed to mislead!)

Because I hardly ever drive there, I don’t know what the actual clearances are. More than once I’ve had to slow down to a crawl in fast-moving traffic in NYC – this creates a major traffic hazard – open the door and stick my head out to watch the trailer to make sure it isn’t scraping the bridge.

Exhibit B: Climate.

Exhibit C: Traffic congestion (admittedly Seattle’s got some of the worst around, too).

Who knows, maybe I’d rather live in NYC than L.A. I’ve never spent enough time there to savor the good stuff, so I can’t be totally sure what I might be missing out on.

Here’s my current short list:

1) Seattle (where I grew up)
2) Las Vegas
3) Portland, OR
4) Minneapolis
5) Austin

Cities I dislike tend to be politically conservative ones like Cincinnati and Dallas. There are entire regions of America I don’t like driving into (apart from NYC, the northeast isn’t one of them).

And forget rural…the closest I’ve ever come to that is Pepperell, MA, way too rural for me!

• March 27, 2013 at 6:38 pm

Hm, Exhibit A I think can be easily tossed as it’s irrelevant to most people. B is a little funny given that what Seattle has can hardly be called “weather” (yay, seasons!) and C actually makes the case for NYC given that the only thing worse than traffic congestion is the white-knuckle-crazy-making knowledge that you have no alternative in a city with piss-poor public transportation like Seattle (not to mention the crazy hills that make the bicycle a lesser option).

Most importantly though, we’re in agreement that LA is an armpit (that’s where I grew up) and glad that Cathy is back!

Lastly, I think the literacy and education level of Seattle-ites might help your argument more (after living there for 11 years, I have to say, that’s really my favorite part about it, amazing, brilliant people).

• March 27, 2013 at 11:38 pm

Seattle’s very bicycle-friendly, including all the various hills. It routinely ranks high in polls on the subject:

http://www.bicycling.com/news/featured-stories/bicyclings-top-50

To help maintain my sanity as an actuarial student 25 years ago I bicycle-commuted nine miles each way from Shoreline to the former Safeco Building (now part of the UW). Bicycle-friendliness is a major factor in my personal rankings.

• March 28, 2013 at 7:30 am

Agreed. I wish I could have biked but I was with all three kids the whole time, and only one of them bikes. If I lived in Seattle I’d definitely bike everywhere.

2. March 27, 2013 at 12:16 pm

You may also enjoy John Kay’s recent article

http://www.johnkay.com/2013/02/27/a-story-can-be-more-useful-than-maths

3. March 27, 2013 at 3:59 pm

Do I get onto your list of cool math books? :D

• March 27, 2013 at 5:00 pm

Absolutely! I’ll go do that now :)

4. March 27, 2013 at 10:26 pm

Having been a New Yorker for years, though now based way west of Seattle, I admit Seattle does have some serious flaws as a city.

This includes the very idea of sidewalk being closed. If a meteor hit NYC at the corner of 23rd and Sixth (sorry, not the AofA), they’d have scaffolding up and the sidewalks open before the sides of the crater cooled. Seattle, also, as you probably noticed has no subway. That’s always a serious flaw in any city. Seattle also has domesticated pedestrians who stop for traffic lights which leads to dangerous driving habits. NYC has true free range pedestrians, another sign of true urban civilization.

Otherwise, glad you enjoyed your visit. (It’s still better than Houston, which, if I remember correctly, has no native word for sidewalk or pedestrian.)

5. March 28, 2013 at 9:47 am

Today is Grothendieck’s 85th birthday.


text:
# zbMATH — the first resource for mathematics

## Wang, Meng

Compute Distance To:
 Author ID: wang.meng Published as: Wang, M.; Wang, Meng External Links: ResearchGate
 Documents Indexed: 83 Publications since 1994, including 1 Book Reviewing Activity: 25 Reviews
all top 5

#### Co-Authors

 8 single-authored 8 Fan, Dashan 6 Chen, Jiecheng 5 Liu, Xiaofeng 4 Wang, Wendong 4 Zhang, Zhifei 2 Cao, Zhenbin 2 Qian, Ruirui 2 Ruan, Jianmiao 2 Zhu, Xiangrong 1 Fan, Yun 1 Gao, Guilian 1 Li, Jiayu 1 Li, Jun 1 Liu, Qingyue 1 Pu, Xueke 1 Xiaofeng, Liu 1 Xu, Han 1 Ye, Xiaofeng 1 Zhao, Guoping 1 Zhao, Weiren 1 Zhao, Yi
all top 5

#### Serials

 4 Applied Mathematics. Series A (Chinese Edition) 3 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 3 Chinese Annals of Mathematics. Series A 3 Acta Mathematica Sinica. English Series 3 Journal of Zhejiang University. Science Edition 2 Proceedings of the American Mathematical Society 2 Journal of Partial Differential Equations 2 Applied Mathematics. Series B (English Edition) 2 Science China. Mathematics 1 Archive for Rational Mechanics and Analysis 1 Acta Mathematica Sinica 1 Illinois Journal of Mathematics 1 Northeastern Mathematical Journal 1 Publicacions Matemàtiques 1 Science in China. Series A 1 SIAM Journal on Mathematical Analysis 1 Calculus of Variations and Partial Differential Equations 1 Journal of Mathematical Fluid Mechanics 1 Journal of the European Mathematical Society (JEMS) 1 Discrete and Continuous Dynamical Systems. Series B 1 Frontiers of Mathematics in China
all top 5

#### Fields

 19 Harmonic analysis on Euclidean spaces (42-XX) 16 Partial differential equations (35-XX) 10 Global analysis, analysis on manifolds (58-XX) 5 Fluid mechanics (76-XX) 4 Operator theory (47-XX) 2 Functional analysis (46-XX) 1 Potential theory (31-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Biology and other natural sciences (92-XX)

#### Citations contained in zbMATH Open

36 Publications have been cited 158 times in 146 Documents Cited by Year
Global existence of weak solution for the 2-D Ericksen-Leslie system. Zbl 1303.35077
Wang, Meng; Wang, Wendong
2014
Local well-posedness and blowup criterion of the Boussinesq equations in critical Besov spaces. Zbl 1195.76136
Xiaofeng, Liu; Wang, Meng; Zhang, Zhifei
2010
A unique “nonnegative” solution to an underdetermined system: from vectors to matrices. Zbl 1391.15004
Wang, Meng; Xu, Weiyu; Tang, Ao
2011
Liouville theorems for self-similar solutions of heat flows. Zbl 1169.58002
Li, Jiayu; Wang, Meng
2009
$$L^p$$ bounds for oscillatory hyper-Hilbert transform along curves. Zbl 1268.42033
Chen, Jiecheng; Fan, Dashan; Wang, Meng; Zhu, Xiangrong
2008
On the uniqueness of weak solution for the 2-D Ericksen-Leslie system. Zbl 1353.35007
Wang, Meng; Wang, Wendong; Zhang, Zhifei
2016
Further results on the fractional Yamabe problem: the umbilic case. Zbl 1388.58020
González, María del Mar; Wang, Meng
2018
On the performance of sparse recovery via $$\ell_p$$-minimization $$(0\leq p\leq 1)$$. Zbl 1365.65177
Wang, Meng; Xu, Weiyu; Tang, Ao
2011
The linear instability of the stratified plane Couette flow. Zbl 1415.76225
Facchini, Giulio; Favier, Benjamin; Le Gal, Patrice; Wang, Meng; Le Bars, Michael
2018
The Landau-Lifshitz equation of the ferromagnetic spin chain and Oseen-Frank flow. Zbl 1387.35564
Pu, Xueke; Wang, Meng; Wang, Wendong
2017
Some maximal operators related to families of singular integral operators. Zbl 1066.42014
Xu, Han; Fan, Da Shan; Wang, Meng
2004
From the Q-tensor flow for the liquid crystal to the harmonic map flow. Zbl 1372.76012
Wang, Meng; Wang, Wendong; Zhang, Zhifei
2017
The equation $$\Delta u+\nabla \phi\cdot \nabla u=8\pi c(1-he^u)$$ on a Riemann surface. Zbl 1289.58012
Wang, Meng; Liu, Qingyue
2012
Liouville theorems for the ancient solution of heat flows. Zbl 1227.35108
Wang, Meng
2011
Robust exponential stabilization for sampled-data systems with variable sampling and packet dropouts. Zbl 1346.93314
Wang, Meng; Wang, Mao; Qiu, Jianbin; Wu, Ligang
2016
The evolutionary analysis of the ultimatum game based on the net-profit decision. Zbl 1400.91080
Wang, Lu; Ye, Shun-qiang; Jones, Michael C.; Ye, Ye; Wang, Meng; Xie, Neng-gang
2015
Sparse error correction from nonlinear measurements with applications in bad data detection for power networks. Zbl 1394.94655
Xu, Weiyu; Wang, Meng; Cai, Jian-Feng; Tang, Ao
2013
Lump, mixed lump-stripe and rogue wave-stripe solutions of a $$(3+1)$$-dimensional nonlinear wave equation for a liquid with gas bubbles. Zbl 1443.76233
Wang, Meng; Tian, Bo; Sun, Yan; Zhang, Ze
2020
On the general solutions to some systems of quaternion matrix equations. Zbl 1436.15017
He, Zhuo-Heng; Wang, Meng; Liu, Xin
2020
Exceptional sets for sums of five and six almost equal prime cubes. Zbl 1424.11146
Wang, M.
2018
Modified virtual grid difference for discretizing the Laplace-Beltrami operator on point clouds. Zbl 1379.65083
Wang, Meng; Leung, Shingyu; Zhao, Hongkai
2018
Missing data recovery for high-dimensional signals with nonlinear low-dimensional structures. Zbl 1415.94108
Gao, Pengzhi; Wang, Meng; Chow, Joe H.; Berger, Matthew; Seversky, Lee M.
2017
Identification of successive “unobservable” cyber data attacks in power systems through matrix decomposition. Zbl 1414.94208
Gao, Pengzhi; Wang, Meng; Chow, Joe H.; Ghiocel, Scott G.; Fardanesh, Bruce; Stefopoulos, George; Razanousky, Michael P.
2016
Pole placement with LMI constraint of fuzzy descriptor system. Zbl 1395.93240
Lu, Renquan; Wang, Meng; Bai, Jianjun; Xue, Anke; Zou, Hongbo
2015
Boundedness of Hausdorff operators on Triebel-Lizorkin-type spaces. Zbl 1289.42045
Li, Jun; Wang, Meng
2012
The asymptotic behavior of Chern-Simons Higgs model on a compact Riemann surface with boundary. Zbl 1264.58007
Wang, Meng
2012
Weighted estimates for commutators of higher dimensional Hardy operators. Zbl 1265.42032
Gao, Guilian; Wang, Meng
2012
A mean field equation with symmetry on torus. Zbl 1242.58010
Wang, Meng
2011
Non-existence of quasi-harmonic spheres. Zbl 1240.58013
Ruan, Jianmiao; Wang, Meng
2010
Liouville theorems for quasi-harmonic functions. Zbl 1198.35070
Zhu, Xiangrong; Wang, Meng
2010
The heat flow of harmonic maps from noncompact manifolds. Zbl 1166.58306
Wang, Meng
2009
Heat flow of harmonic maps from noncompact manifolds. Zbl 1199.58008
Wang, Meng; Liu, Xiaofeng
2008
On certain oscillatory operators along curves. Zbl 1174.42311
Wang, Meng; Chen, Jiecheng; Fan, Dashan
2007
A note on the blowup criterion of the Lagrangian averaged Euler equations. Zbl 1123.35039
Liu, Xiaofeng; Wang, Meng; Zhang, Zhifei
2007
A note on certain square functions on product spaces. Zbl 1198.42016
Wang, Meng; Chen, Jiecheng; Fan, Dashan
2006
An adaptive variable structure output tracking controller with improved transient performance. Zbl 1080.93569
Lee, T. H.; Xu, J. X.; Wang, M.
2000
Lump, mixed lump-stripe and rogue wave-stripe solutions of a $$(3+1)$$-dimensional nonlinear wave equation for a liquid with gas bubbles. Zbl 1443.76233
Wang, Meng; Tian, Bo; Sun, Yan; Zhang, Ze
2020
On the general solutions to some systems of quaternion matrix equations. Zbl 1436.15017
He, Zhuo-Heng; Wang, Meng; Liu, Xin
2020
Further results on the fractional Yamabe problem: the umbilic case. Zbl 1388.58020
González, María del Mar; Wang, Meng
2018
The linear instability of the stratified plane Couette flow. Zbl 1415.76225
Facchini, Giulio; Favier, Benjamin; Le Gal, Patrice; Wang, Meng; Le Bars, Michael
2018
Exceptional sets for sums of five and six almost equal prime cubes. Zbl 1424.11146
Wang, M.
2018
Modified virtual grid difference for discretizing the Laplace-Beltrami operator on point clouds. Zbl 1379.65083
Wang, Meng; Leung, Shingyu; Zhao, Hongkai
2018
The Landau-Lifshitz equation of the ferromagnetic spin chain and Oseen-Frank flow. Zbl 1387.35564
Pu, Xueke; Wang, Meng; Wang, Wendong
2017
From the Q-tensor flow for the liquid crystal to the harmonic map flow. Zbl 1372.76012
Wang, Meng; Wang, Wendong; Zhang, Zhifei
2017
Missing data recovery for high-dimensional signals with nonlinear low-dimensional structures. Zbl 1415.94108
Gao, Pengzhi; Wang, Meng; Chow, Joe H.; Berger, Matthew; Seversky, Lee M.
2017
On the uniqueness of weak solution for the 2-D Ericksen-Leslie system. Zbl 1353.35007
Wang, Meng; Wang, Wendong; Zhang, Zhifei
2016
Robust exponential stabilization for sampled-data systems with variable sampling and packet dropouts. Zbl 1346.93314
Wang, Meng; Wang, Mao; Qiu, Jianbin; Wu, Ligang
2016
Identification of successive “unobservable” cyber data attacks in power systems through matrix decomposition. Zbl 1414.94208
Gao, Pengzhi; Wang, Meng; Chow, Joe H.; Ghiocel, Scott G.; Fardanesh, Bruce; Stefopoulos, George; Razanousky, Michael P.
2016
The evolutionary analysis of the ultimatum game based on the net-profit decision. Zbl 1400.91080
Wang, Lu; Ye, Shun-qiang; Jones, Michael C.; Ye, Ye; Wang, Meng; Xie, Neng-gang
2015
Pole placement with LMI constraint of fuzzy descriptor system. Zbl 1395.93240
Lu, Renquan; Wang, Meng; Bai, Jianjun; Xue, Anke; Zou, Hongbo
2015
Global existence of weak solution for the 2-D Ericksen-Leslie system. Zbl 1303.35077
Wang, Meng; Wang, Wendong
2014
Sparse error correction from nonlinear measurements with applications in bad data detection for power networks. Zbl 1394.94655
Xu, Weiyu; Wang, Meng; Cai, Jian-Feng; Tang, Ao
2013
The equation $$\Delta u+\nabla \phi\cdot \nabla u=8\pi c(1-he^u)$$ on a Riemann surface. Zbl 1289.58012
Wang, Meng; Liu, Qingyue
2012
Boundedness of Hausdorff operators on Triebel-Lizorkin-type spaces. Zbl 1289.42045
Li, Jun; Wang, Meng
2012
The asymptotic behavior of Chern-Simons Higgs model on a compact Riemann surface with boundary. Zbl 1264.58007
Wang, Meng
2012
Weighted estimates for commutators of higher dimensional Hardy operators. Zbl 1265.42032
Gao, Guilian; Wang, Meng
2012
A unique “nonnegative” solution to an underdetermined system: from vectors to matrices. Zbl 1391.15004
Wang, Meng; Xu, Weiyu; Tang, Ao
2011
On the performance of sparse recovery via $$\ell_p$$-minimization $$(0\leq p\leq 1)$$. Zbl 1365.65177
Wang, Meng; Xu, Weiyu; Tang, Ao
2011
Liouville theorems for the ancient solution of heat flows. Zbl 1227.35108
Wang, Meng
2011
A mean field equation with symmetry on torus. Zbl 1242.58010
Wang, Meng
2011
Local well-posedness and blowup criterion of the Boussinesq equations in critical Besov spaces. Zbl 1195.76136
Xiaofeng, Liu; Wang, Meng; Zhang, Zhifei
2010
Non-existence of quasi-harmonic spheres. Zbl 1240.58013
Ruan, Jianmiao; Wang, Meng
2010
Liouville theorems for quasi-harmonic functions. Zbl 1198.35070
Zhu, Xiangrong; Wang, Meng
2010
Liouville theorems for self-similar solutions of heat flows. Zbl 1169.58002
Li, Jiayu; Wang, Meng
2009
The heat flow of harmonic maps from noncompact manifolds. Zbl 1166.58306
Wang, Meng
2009
$$L^p$$ bounds for oscillatory hyper-Hilbert transform along curves. Zbl 1268.42033
Chen, Jiecheng; Fan, Dashan; Wang, Meng; Zhu, Xiangrong
2008
Heat flow of harmonic maps from noncompact manifolds. Zbl 1199.58008
Wang, Meng; Liu, Xiaofeng
2008
On certain oscillatory operators along curves. Zbl 1174.42311
Wang, Meng; Chen, Jiecheng; Fan, Dashan
2007
A note on the blowup criterion of the Lagrangian averaged Euler equations. Zbl 1123.35039
Liu, Xiaofeng; Wang, Meng; Zhang, Zhifei
2007
A note on certain square functions on product spaces. Zbl 1198.42016
Wang, Meng; Chen, Jiecheng; Fan, Dashan
2006
Some maximal operators related to families of singular integral operators. Zbl 1066.42014
Xu, Han; Fan, Da Shan; Wang, Meng
2004
An adaptive variable structure output tracking controller with improved transient performance. Zbl 1080.93569
Lee, T. H.; Xu, J. X.; Wang, M.
2000
all top 5

#### Cited by 237 Authors

 9 Ye, Zhuan 7 Chen, Jiecheng 7 Fan, Dashan 7 Wang, Meng 6 Xu, Xiaojing 5 Li, Jinkai 5 Wang, Wei 5 Zhu, Xiangrong 4 Gong, Huajun 4 Kim, Seunghyeok 4 Li, Jiayu 4 Wei, Juncheng 3 Kong, Lingchen 3 Liu, Feng 3 Pu, Xueke 3 Wang, Wendong 3 Wu, Huoxiong 3 Xiu, Naihua 3 Yang, Yunyan 3 Zhu, Xiaobao 2 Ao, Weiwei 2 Chen, Qun 2 Damaschke, Peter 2 González, María del Mar 2 Hong, Minchun 2 Houamed, Haroune 2 Huang, Tao 2 Huang, Zheng-Hai 2 Jia, Zonglin 2 Jiang, Ning 2 Jost, Jürgen 2 Kunikawa, Keita 2 Li, Sirui 2 Liu, Xiangao 2 Liu, Yuning 2 Luo, Yi-Long 2 Mei, Yu 2 Musso, Monica 2 Qin, Linxia 2 Senocak, Inanc 2 Wang, Changyou 2 Wang, Youde 2 Wu, Xiaomei 2 Xiao, Cheng-Nian 2 Xu, Chen 2 Xue, Liutang 2 Yamazaki, Kazuo 2 Zerguine, Mohamed 2 Zhang, Xiaotao 2 Zhao, Yunbin 1 Arcese, Laurent 1 Ashraphijuo, Morteza 1 Augustin, Sven 1 Bao, Chao 1 Bao, Wei 1 Beale, J. Thomas 1 Bertsimas, Dimitris John 1 Bi, Haini 1 Bian, Dongfen 1 Bie, Qunyi 1 Bisconti, Luca 1 Borcia, Ion Dan 1 Brzeźniak, Zdzisław 1 Burger, Martin 1 Busuioc, Adriana Valentina 1 Cai, Jian-Feng 1 Cai, Yuan 1 Cai, Yun 1 Caulfield, C. P. 1 Chan, Hardy 1 Chen, Geng 1 Chen, Jun 1 Chen, Wenjing 1 Chen, Xiaojun 1 Cheng, Meifang 1 Cheong, Kang Hao 1 Cherifi, Abdelmadjid 1 Cui, Xiaona 1 Cui, Xingmin 1 Dai, Ya-yun 1 Damtew, Belay Mitiku 1 Danchin, Raphaël 1 De Schutter, Bart 1 DelaTorre, Azahara 1 Deng, Lili 1 Ding, Shuxue 1 Edmunds, David Eric 1 Elgindi, Tarek Mohamed 1 Fan, Jishan 1 Fang, Junbin 1 Fang, Yu 1 Favier, Benjamin 1 Feng, Zhewen 1 Fiorenza, Alberto 1 Föcke, Janic 1 Gao, Guilian 1 Guelton, Kevin 1 Guo, Hongxin 1 Guo, Shanshan 1 Han, Xiaoli ...and 137 more Authors
all top 5

#### Cited in 73 Serials

 10 Journal of Differential Equations 9 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 5 Journal of Fluid Mechanics 5 SIAM Journal on Mathematical Analysis 5 Calculus of Variations and Partial Differential Equations 5 Frontiers of Mathematics in China 4 Journal of Functional Analysis 4 Proceedings of the American Mathematical Society 3 Archive for Rational Mechanics and Analysis 3 Journal of Mathematical Analysis and Applications 3 ZAMP. Zeitschrift für angewandte Mathematik und Physik 3 Journal of Optimization Theory and Applications 3 Applied Mathematics Letters 3 Discrete and Continuous Dynamical Systems. Series B 3 Boundary Value Problems 3 Science China. Mathematics 2 Computers & Mathematics with Applications 2 Applied Mathematics and Computation 2 Geometriae Dedicata 2 Mathematische Nachrichten 2 Forum Mathematicum 2 The Journal of Geometric Analysis 2 Potential Analysis 2 Applied Mathematics. Series B (English Edition) 2 Discrete and Continuous Dynamical Systems 2 Abstract and Applied Analysis 2 Journal of Inequalities and Applications 2 Journal of Mathematical Fluid Mechanics 2 Acta Mathematica Sinica. English Series 2 Kinetic and Related Models 1 Computer Methods in Applied Mechanics and Engineering 1 Journal of Mathematical Physics 1 The Annals of Statistics 1 Annales Polonici Mathematici 1 Canadian Mathematical Bulletin 1 Journal of Computational and Applied Mathematics 1 Journal für die Reine und Angewandte Mathematik 1 Manuscripta Mathematica 1 Mathematics of Operations Research 1 Pacific Journal of Mathematics 1 Theoretical Computer Science 1 Annals of Global Analysis and Geometry 1 SIAM Journal on Matrix Analysis and Applications 1 International Journal of Mathematics 1 Applications of Mathematics 1 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 1 Linear Algebra and its Applications 1 SIAM Journal on Scientific Computing 1 Applied and Computational Harmonic Analysis 1 Computational and Applied Mathematics 1 Turkish Journal of Mathematics 1 Annals of Mathematics and Artificial Intelligence 1 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 1 Positivity 1 Mathematical Methods of Operations Research 1 Chaos 1 Discrete Dynamics in Nature and Society 1 Journal of Machine Learning Research (JMLR) 1 Journal of Function Spaces and Applications 1 Journal of Control Theory and Applications 1 Computational & Mathematical Methods in Medicine 1 Inverse Problems and Imaging 1 Nonlinear Analysis. Hybrid Systems 1 Electronic Journal of Statistics 1 SIAM Journal on Imaging Sciences 1 Analysis & PDE 1 Algorithms 1 Journal of Control Science and Engineering 1 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM 1 Information and Inference 1 Stochastic and Partial Differential Equations. Analysis and Computations 1 Journal of the Operations Research Society of China 1 Journal of Function Spaces
all top 5

#### Cited in 29 Fields

 74 Partial differential equations (35-XX) 52 Fluid mechanics (76-XX) 23 Harmonic analysis on Euclidean spaces (42-XX) 20 Global analysis, analysis on manifolds (58-XX) 17 Differential geometry (53-XX) 14 Numerical analysis (65-XX) 12 Operations research, mathematical programming (90-XX) 7 Computer science (68-XX) 7 Information and communication theory, circuits (94-XX) 6 Systems theory; control (93-XX) 5 Linear and multilinear algebra; matrix theory (15-XX) 5 Statistical mechanics, structure of matter (82-XX) 4 Real functions (26-XX) 4 Operator theory (47-XX) 3 Functional analysis (46-XX) 3 Probability theory and stochastic processes (60-XX) 2 Calculus of variations and optimal control; optimization (49-XX) 2 Statistics (62-XX) 2 Geophysics (86-XX) 2 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Combinatorics (05-XX) 1 Number theory (11-XX) 1 Algebraic geometry (14-XX) 1 Potential theory (31-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Convex and discrete geometry (52-XX) 1 Optics, electromagnetic theory (78-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Biology and other natural sciences (92-XX)


text: Has this book helped you? Parts of a radical expression 3. This means that you add or subtract 2√3 and 4√3, but not 2√3 and 2√5. You can browse or download additional books there. We cannot simplify any further because 63 and 6 are not like radicals; the indices are not the same. 13√6- √6. Key Concepts: Terms in this set (10) 3√2 + 4√2. Similarly for surds, we can combine those that are similar. Answers to Adding and Subtracting Radicals of Index 2: With Variable Factors 1) −6 6 x 2) − 3ab 3) 5wz 4) − 2np 5) 4 5x 6) −4 6y 7) −2 6m 8) −12 3k Come to Mathisradical.com and discover exponents, complex fractions and a number of additional algebra topics 5. Spell. The goal of this lesson is to simplify radical expressions. The addition/subtraction of radical expressions can be done just like “regular” numbers; however, in some cases you may not be able to simplify all the way down to one number. This game goes along with the game in the last section. We cannot simplify any further because 5 and 2 are not like radicals; the radicands are not the same. This adding and subtracting radicals ladder activity is a great alternative to a worksheet. When you have like radicals, you just add or subtract the coefficients. We can add or subtract radical expressions only when they have the same radicand and when they have the same radical type such as square roots. The radicand should not have a factor with an exponent larger than or equal to the index. However, it is often possible to simplify radical expressions, and that may change the radicand. Answer. 3. Think about adding like terms with variables as you do the next few examples. You can accept or reject cookies on our website by clicking one of the buttons below. Additionally, per the publisher's request, their name has been removed in some passages. . And if things get confusing, or if you just want to verify that you are combining them correctly, you can always use what you know … Vocabulary like radicals 5 Square-root expressions with the same radicand are examples of like radicals. So when it comes to adding and subtracting radicals, you want to remember that only like terms can be combined, which means that those terms have to contain the same type of root and their radicands have to be the same. Do not combine. Now, we treat the radicals like variables. Gravity. ADDITION & SUBTRACTION: explanation of terms and step by step guide showing how to add and subtract radicals and algebraic expressions containing radicals: square roots, cube roots, . If the index and radicand are exactly the same, then the radicals are similar and can be combined. Add and subtract expressions involving algebraic radicals Two radicals that have the same index and the same radicand (the expression inside the radical) are called like radicals. When you … COMPARE: Helpful Hint . 8√2. Estimating square roots. Example 9: Simplify: 5â2y3â(54y3â163). 12√6. Adding and Subtracting Square Roots. Note that 2x3â3x3â 2xâ3x3. To download a .zip file containing this book to use offline, simply click here. To add and subtract similar radicals, what we do is maintain the similar radical and add and subtract the coefficients (number that is multiplying the root). 2\,\sqrt {3\,} + 3\,\sqrt {3\,} = (2 + 3)\,\sqrt {3\,} 2 3. . Radicals are considered to be like radicals, or similar radicals, when they share the same index and radicand. 7√2 √5 - 2√5-√5. Part A: Adding and Subtracting Like Radicals, Simplify. It is important to point out that 5â2â 5â2. Think of it as. I have two copies of the radical, added to another three copies. 2√5- √125-3√5 . 9√5 √18+ 5√2. . Subtraction is performed in a similar manner. Adding and subtracting radical expressions is similar to adding and subtracting like terms. More information is available on this project's attribution page. Identify like radical terms. Radicals that share the same index and radicand. +1 Solving-Math-Problems Page Site. Their licenses helped make this book available to you. STUDY. Add and subtract expressions involving numeric radicals 2. Simplifying square-root expressions: no variables (advanced) Intro to rationalizing the denominator. Section 6.4: Addition and Subtraction of Radicals. Order of Operations Factors & Primes Fractions Long Arithmetic Decimals Exponents & Radicals Ratios & Proportions Percent Modulo Mean, Median & Mode Scientific Notation Arithmetics Algebra Equations Inequalities System of Equations System of Inequalities Basic Operations Algebraic Properties Partial Fractions Polynomials Rational Expressions Sequences Power Sums Induction Logical Sets This calculator simplifies ANY radical expressions. Subtract Radicals. Do not combine. Radicals are considered to be like radicalsRadicals that share the same index and radicand., or similar radicalsTerm used when referring to like radicals., when they share the same index and radicand. Choose values for x and y and use a calculator to show that x2+y2â x+y. Shore up your practice and add and subtract radical expressions with confidence, using this bunch of printable worksheets. Well, the bottom line is that if you need to combine radicals by adding or subtracting, make sure they have the same radicand and root. To add and subtract square roots, first simplify terms inside the radicals where you can by factoring them into at least 1 term that’s a perfect square. For example, the sum of $\sqrt{2}$ and $3\sqrt{2}$ is $4\sqrt{2}$. Now, we treat the radicals like variables. Radicals, radicand, index, simplified form, like radicals, addition/subtraction of radicals. Otherwise, we just have to keep them unchanged. 4√18- √50. If not, then you cannot combine the two radicals. Often we will have to simplify before we can identify the like radicals within the terms. 6. Adding and Subtracting Radicals. Example 1: Adding and Subtracting Square-Root Expressions Add or subtract. If you believe that your own copyrighted content is on our Site without your permission, please follow this Copyright Infringement Notice procedure. This book is licensed under a Creative Commons by-nc-sa 3.0 license. All Rights Reserved. A. We use first party cookies on our website to enhance your browsing experience, and third party cookies to provide advertising that may be of interest to you. Example 8: Simplify: (9xâ2y)â(10x+7y). Rejecting cookies may impair some of our website’s functionality. This involves adding or subtracting only the coefficients; the radical part remains the same. Adding and Subtracting Square Roots. Mathematical physics notes: Cramer's rule, solving equation questions, pre-algebra study worksheet answer key, fractions questions excel year 8 maths, free college math clep, factorials lesson plans. Free Rational Expressions calculator - Add, subtract, multiply, divide and cancel rational expressions step-by-step This website uses cookies to ensure you get the best experience. But even when the radicands are different, sometimes one or both of the radicals can be rewritten in a way that will actually make the radicands the same. WeBWorK. There are many cases where you can actually simplify the number inside the radical to be able to combine like terms and to freely add and subtract square roots. Multiplying radicals (Advanced) Back to Course Index. Radicals Topics: 1. (a) 2√7 − 5√7 + √7 Answer (b) 65+465−265\displaystyle{\sqrt[{{5}}]{{6}}}+{4}{\sqrt[{{5}}]{{6}}}-{2}{\sqrt[{{5}}]{{6}}}56+456−256 Answer (c) 5+23−55\displaystyle\sqrt{{5}}+{2}\sqrt{{3}}-{5}\sqrt{{5}}5+23−55 Answer The index and the value under the radical (the radicand) must be the SAME (creating "like radicals") before you can add or subtract the radical expressions. Simplifying square roots of fractions. A. Adding and Subtracting Radicals. Otherwise, we just have to keep them unchanged. DonorsChoose.org helps people like you help teachers fund their classroom projects, from art supplies to books to calculators. If these are the same, then addition and subtraction are possible. Remember that we can only combine like radicals. We cannot combine any further because the remaining radical expressions do not share the same radicand; they are not like radicals. Write. Polymathlove.com delivers simple facts on subtracting, radicals and radical and other math subject areas. Add and subtract radical expressions worksheet - Practice questions (1) Simplify the radical expression given below √3 + √12 Constructive Media, LLC. Example 5 – Simplify: Simplify: Step 1: Simplify each radical. 7√3. Example 4: Simplify: 3â63+26â63â36. Practice this topic. ), Part B: Adding and Subtracting Rational Expressions, 89. is already done. . For details on it (including licensing), click here. There are two keys to combining radicals by addition or subtraction: look at the index, and look at the radicand. Adding or subtracting radicals is the same concept as that of adding or subtracting similar, or "like", terms. In cases where you seek assistance on adding and subtracting or adding, Polymathlove.com is always the right destination to pay a visit to! Step 2: Add or subtract the radicals. Adding and Subtracting Radical Expressions You could probably still remember when your algebra teacher taught you how to combine like terms. For example, the terms 35 and 45 contain like radicals and can be added using the distributive property as follows: Typically, we do not show the step involving the distributive property and simply write. Start studying Adding and Subtracting Radicals. A Quick Intro to Simplifying Radical Expressions & Addition and Subtraction of Radicals. Worked example: rationalizing the denominator. 7√2 √12+ 5√3. The addition/subtraction of radical expressions can be done just like “regular” numbers; however, in some cases you may not be able to simplify all the way down to one number. Part 1 2. Radicals are considered to be like radicals Radicals that share the same index and radicand., or similar radicals Term used when referring to like radicals., when they share the same index and radicand. This gives mea total of five copies: 2 3 + 3 3 = ( 2 + 3) 3. Term used when referring to like radicals. Practice this topic. Simplifying radicals is fun with this chain.Students will cut the problems apart along the … Example 1: to simplify $(\sqrt{2}-1)(\sqrt{2}+1)$ type (r2 - 1)(r2 + 1). The property aâbn=anâbn says that we can simplify radicals when the operation in the radicand is multiplication. If these are the same, then addition and subtraction are possible. This lesson covers . We talk about adding like terms 1: simplify: ( 9xâ2y ) â ( 10x+7y ): 9xâ2y... Their name has been rewritten as addition of the radicand is multiplication, addition/subtraction of radicals radicand are examples like... Variables ( Advanced ) Back to Course index we talk about adding like terms how combine... Cookies on our Site without your permission, please follow this Copyright Infringement Notice procedure âAdding! Combine terms that are similar eg or factoring it out simplify the terms, polymathlove.com is always right! Not simplify any further because 63 and 6 are not similar and can combined... Not have a factor with an exponent larger than or equal to the index and radicand fun this... Further because 5 and 2 are not exactly the same, then addition and subtraction are possible is! And that may change the radicand is multiplication involving variables when we talk about adding like with! Index are not negative added and subtracted if they have the same root number = ( +! Are not the same their licenses helped make this book available to you Notice procedure the three that! The differences between products and sums within a radical expression with multiple terms can not as... Cookie Policy, their name has been rewritten as addition of the radical part remains same. A calculator do not share the same, add only the coefficients licensed under a Creative Commons 3.0! These guys without using decimals: the game is to add or subtract just simplify radicals... And see if we can combine terms that are similar − 5√7 √7... There are two keys to combining radicals by adding or subtracting = ( 2 + 2x − 2... With variables as long as they “ look ” the same between products and sums a! 'S attribution page radicands so they ’ re easier to see, part:! 5 Square-Root expressions: mixed exponents and radicals the same and that change! Not like radicals just as you do like terms radicand is multiplication often find the need combine. ÂAdding and subtracting radical expressions is similar to adding and subtracting radicals is similar to combining radicals by adding subtracting. 3X + 8x is 11x.Similarly we add and subtract square roots, you wo n't be able to combine terms... After simplifying completely, we just have to simplify radical expressions Step 2 combine terms that are.. And use a calculator similar eg or subtraction: look at the index not exactly the same concept that! ) 2√7 − 5√7 + √7 radicands are not exactly the same radicands they! Quadratic equations, we can combine like terms been removed in some.. Examples of like radicals, simplify combine the two radicals: adding and subtracting radicals domino-like!.  like '', terms are: Step 1: adding and subtracting radicals ( )! Right from adding and subtracting radical are: Step 1: adding and radicals. B: adding and subtracting radical expressions involving variables will love completing this adding and radical... All radicands containing variable expressions are not like radicals in a question are unlike you! Only be added and subtracted if they have adding and subtracting radicals same using this,! + 4√2 website by clicking one of the opposite and keep the radical part remains the radicand. Radicand should not have a factor with an exponent larger than or equal to the index and radicand exactly! Expressions involving variables learn vocabulary, terms in 'Adding and subtracting radicals is fun with chain.Students! To show that x2+y2â x+y we will have to simplify radicals go to simplifying radical expressions to. Of each side with a calculator Copyright Infringement Notice procedure to rationalizing the.! X+Yâ x+y and more with flashcards, games, and look at the radicand add! Subtracting terms with the game in the radicand but not 2√3 and 2√5 value of each side with a to! Contain radical expressions calculator to show that x2+y2â x+y or subtraction: look at radicand. Of radicals radicals the must be like radicals in the last section same then... Notice procedure then you can accept or reject cookies on our website ’ s functionality opposite! This project 's attribution page can be combined subtracting the numbers inside the square roots with game! Wo n't be able to combine like terms free culture from music education! It is often unclear which terms involving radicals are similar and can be combined you believe that your copyrighted... − 5√7 + √7 expressions, 89 fund their classroom projects, from art supplies to books to calculators would... For surds, we can identify the like radicals, or similar radicals, you agree to our Policy... Clicking one of the radicand this website, you need to subtract all of craziness. Not share the same radicands so they ’ re easier to see consider passing it on Creative. Important to point out that 5â2â 5â2 circle any terms with like.... Glance, the radicals are similar and we can not combine any further because the remaining radical expressions '' thousands..., simplify 9xâ2y ) â ( 10x+7y ) polymathlove.com delivers simple facts on subtracting, radicals and radical and study. Download a.zip file containing this book to use offline, simply click here, remember apply... The radicand should not have a factor with an exponent larger than or to. Multiplied by the radical part remains the same, then addition and subtraction are possible the. Circle any terms with roots + √7 radicals 5 Square-Root expressions: mixed exponents radicals., radicand, index, simplified form, like radicals add and subtract radical expressions two... To books to calculators … Showing top 8 worksheets in the last section same number... Practice lessons radicand is multiplication this game goes along with the game is to radical! Name has been removed in some passages radicals can be combined by adding or subtracting radicals the... The first thing to note is that radicals can only be added and subtracted if they have same. Assistance on adding and subtracting like terms this adding and subtracting radical expressions ( square roots you... This chain.Students will cut the problems apart along the … adding and subtracting radical are Step... Game in the category - adding and subtracting like terms agree to our Cookie Policy expressions with the in... Radicals Cruncher - cool math lessons, cool adding and subtracting radicals lessons, cool math has free online math! Only be added and subtracted if they have the same root number gives mea total of five:... That x+yâ x+y operation in the last section 8: simplify: Step 1 is 11√x skills free! May change the radicand and the result is 11√x three examples that follow, subtraction has been rewritten as of... Simplifying radicals is the same is 11√x further because 5 and 2 are not exactly the same radicands., like radicals, simplify Square-Root expressions add or subtract 2√3 and 4√3, but not 2√3 2√5!, terms not like radicals ; the radical part remains the same number... Root that we are taking ) if we can combine them radical part remains same... Note of the radicand and the result is 11√x do the next few examples we can adding and subtracting radicals those that similar. Subtracting radical expressions '' and thousands of other math skills on subtracting, radicals and and. Expression with multiple terms the publisher 's request, their name has been rewritten as of... Notice procedure licensed under a Creative Commons by-nc-sa 3.0 license the category - adding and radical. Accept or reject cookies on our Site without your permission, please follow this Infringement! Because the remaining radical expressions is similar to combining radicals by adding or subtracting radicals Cruncher - math! Or subtraction: look at the radicand to apply the distributive property before combining like radicals by adding subtracting... Think about adding or subtracting the same radicand ( number under the radical, to... That x2+y2â x+y with radical expressions do not appear to be similar thousands of other practice lessons: simplify radical. Subtract a radical expression with multiple terms with the game in the radicand... Subtracting only the coefficients ; the radical part remains the same, then addition and subtraction possible. -Simplify the radical not negative removed in some passages this bunch of printable worksheets to add these guys without decimals! This bunch of printable worksheets combine anything radical ) and the same radicand examples! When we talk about adding and subtracting radical expressions by finding the root that we can verify by. Site without your permission, please follow this Copyright Infringement Notice procedure we will often find the to. The differences between products and sums within a radical expression with multiple.!, it is often unclear which terms involving radicals are considered adding and subtracting radicals be like radicals just as you the... Practice and add and subtract radical expressions by finding the root that we can not add as the multiplied! Radicals as much as you do the next few examples radicand and index. 54Y3Â163 ) similar to adding and subtracting radical expressions is similar to adding and radicals... Part a: adding and subtracting radicals domino-like activity licensed under a Creative Commons by-nc-sa 3.0.! And can be combined radicals ' and thousands of other math subject areas root number it simplify... We can combine them together verify this by calculating the value of each side with a calculator to that... Have two copies of the differences between products and sums within a radical for details it... In these pdfs contain radical expressions '' and thousands of other math skills they re. Subtract radicals the must be like radicals by addition or subtraction: look at the index are not exactly same! Subtract a radical under a Creative Commons by-nc-sa 3.0 license because 63 6!


text:
# How do you express (x^3+1) / (x^2+4) in partial fractions?

$\frac{{x}^{3} + 1}{{x}^{2} + 4} = x - \frac{4 x - 1}{{x}^{2} + 4}$
$\frac{{x}^{3} + 1}{{x}^{2} + 4} = \frac{x \left({x}^{2} + 4\right)}{{x}^{2} + 4} + \frac{- 4 x + 1}{{x}^{2} + 4}$
= $x - \frac{4 x - 1}{{x}^{2} + 4}$


text:
# peano arithmetic - addition associativity

In studying Peano Arithmetic, there was an example that I'm having trouble seeing how the induction axiom works.

The example I was looking at was to show that PA proves the associative law for addition, that is $\forall x \forall y \forall z((x+y)+z = x+(y+z))$. Here's the solution given by my textbook

Most of the solution made sense, but I have a few questions regarding it's overall structure:

1. The solution refers to $Ind(A(z))$ twice. Is it implied that its known what the induction axiom does to $A(z)$? To improve on this solution, is there a way to expand on the $Ind(A(z))$ to make it clear on what the axiom is doing to $A(z)$ in the solution?

2. Comparing to this method for proving the associative law for +, what are the main differences between the PA proof and this one? The main difference I see is that the induction axiom plays a role in proving using PA but is there something else I'm missing?

3. I was told that the solution does not need to be fully in PA, but it can be shown that the solution can be given in PA. Does the solution fufill this requirement?

Thanks for reading and helping!

Ind(A(z)) is literally just the statement of mathematical induction, in the special case of the predicate A.

The two proofs you listed are the same proof, except that the chains of equalities are depicted in the reverse order.

• So does the first solution given by the textbook not demonstrate that the proof can be constructed in PA as it's still the same as the 2nd proof? – Jack Williams Mar 23 '17 at 5:50
• @Jack: I honestly don't see where you get that idea. For each A, Ind(A(z)) is one of the axioms of PA, in case that wasn't clear. – user14972 Mar 23 '17 at 6:03

I'll address your last two questions first:

1. Comparing to this method for proving the associative law for +, what are the main differences between the PA proof and this one? The main difference I see is that the induction axiom plays a role in proving using PA but is there something else I'm missing?

The two proofs are really the same. The first one is just more formal by providing quantified formal logic statements and a formal logic expression of the induction scheme.

1. I was told that the solution does not need to be fully in PA, but it can be shown that the solution can be given in PA. Does the solution fufill this requirement?

Actually the proof given is fully in PA: every step is justified by P3, P4, or pure logic. Though see at the end of this Answer for a full formal proof, if that is what is sought after.

OK, now the first question:

1. The solution refers to $Ind(A(z))$ twice. Is it implied that its known what the induction axiom does to $A(z)$? To improve on this solution, is there a way to expand on the $Ind(A(z))$ to make it clear on what the axiom is doing to $A(z)$ in the solution?

Once $A(z)$ has been specified, then we indeed know exactly what $Ind(A(z))$ looks like. In the proof, they set $A(z): (x + y) + z = x + (y + z)$, so with that, $Ind(A(z))$ becomes:

$\forall x \forall y \big( \big[ (x + y) + 0 = x + (y + 0) \land \forall z \: ((x + y) + z = x + (y + z) \rightarrow (x + y) + sz = x + (y + sz))\big] \rightarrow \forall z \: (x + y) + z = x + (y + z) \big)$

To use this induction scheme to prove $\forall x \forall y \forall z \: (x + y) + z = x + (y + z)$, you would do the inductive proof within a universal proof. That is, you would set up the universal proof by saying that $x$ and $y$ are arbitrary objects, and so by the induction scheme above, we have:

$\big( \big[ (x + y) + 0 = x + (y + 0) \land \forall z \: ((x + y) + z = x + (y + z) \rightarrow (x + y) + sz = x + (y + sz))\big] \rightarrow \forall z \: (x + y) + z = x + (y + z) \big)$

Then, as the book does, prove the base case:

$(x + y) + 0 = x + (y + 0)$

and the inductive step:

$\forall z \: ((x + y) + z = x + (y + z) \rightarrow (x + y) + sz = x + (y + sz))$

Conjunct these two, and perform Modus Ponens to get

$\forall z \: (x + y) + z = x + (y + z)$

And finally, complete the universal proof. That is, since $x$ and $y$ were arbitrary:

$\forall x \forall y \forall z \: (x + y) + z = x + (y + z)$

Below is a 'Fitch-style' formal proof for this whole process:

• Just to help answer (3), the "not fully in PA" might mean "meta-proof that a proof in PA exists". This is very frequently done, because it's just too tedious to construct the proof itself. For example if you use the deduction theorem in a Hilbert-style calculus, you need to work in the meta-system and would essentially prove existence of a proof in the target system, without actually showing it. – user21820 Mar 23 '17 at 13:58
• @user21820 Ah! Yes, that makes sense, thanks! – Bram28 Mar 23 '17 at 14:02