text:
• Diabatic potential energy surfaces of H+ + CO

• Fulltext

https://www.ias.ac.in/article/fulltext/jcsc/119/05/0409-0415

• Keywords

Ab initio potential energy surfaces; non-adiabatic coupling; diabatization; mixing angle.

• Abstract

Ab initio adiabatic and diabatic surfaces of the ground and the first excited electronic states have been computed for the H+ + CO system for the collinear ($\gamma = 0^\circ$) and the perpendicular (γ = 90°) geometries employing the multi-reference configuration interaction method and Dunning's 𝑐𝑐-𝑝VTZ basis set. Other properties such as mixing angle before coupling potential and before coupling matrix elements have also been obtained in order to provide an understanding of the coupling dynamics of inelastic and charge transfer process.

• Author Affiliations

1. Department of Chemistry, Indian Institute of Technology - Madras, Chennai 600 036

• Journal of Chemical Sciences

Volume 134, 2022
All articles
Continuous Article Publishing mode

• Editorial Note on Continuous Article Publication

Posted on July 25, 2019

format: plain


text:
If $$A = \begin{bmatrix} 1 & -2 \\\ -1 & 2 \end{bmatrix}$$ and $$B = \begin{bmatrix} 2 & 6 \\\ 1 & 3\end{bmatrix}$$ then AB is equal to

This question was previously asked in
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1. $$\begin{bmatrix} 0 & 0 \\\ 0 & 0 \end{bmatrix}$$
2. $$\begin{bmatrix} 1 & 0 \\\ 0 & 1 \end{bmatrix}$$
3. $$\begin{bmatrix} 1 & 1 \\\ 1 & 1 \end{bmatrix}$$
4. None of the above

Option 1 : $$\begin{bmatrix} 0 & 0 \\\ 0 & 0 \end{bmatrix}$$

Detailed Solution

Concept:

Matrix Multiplication:

Multiplication is only possible when the number of columns of the first matrix is equal to the number of rows of the second matrix.

A m × n matrix multiplied by a n × p matrix results in a m × p matrix.

Matrices are multiplied by multiplying each element of a row of the first m×n matrix with the corresponding elements of all the columns of the second n×p matrix to obtain the first row of the product matrix with p columns, and so on for all the m rows of the first matrix.

Calculation:

Given:

$$A = \begin{bmatrix} 1 & -2 \\\ -1 & 2 \end{bmatrix}$$ $$B = \begin{bmatrix} 2 & 6 \\\ 1 & 3\end{bmatrix}$$

A × B = $$\begin{bmatrix} 1& -2 \\ -1& 2 \end{bmatrix}$$ × $$\begin{bmatrix} 2& 6\\ 1& 3 \end{bmatrix}$$

A × B = $$\begin{bmatrix} 2-2& 6-6\\ -2+2& -6+6 \end{bmatrix}$$

A × B = $$\begin{bmatrix} 0 & 0 \\\ 0 & 0 \end{bmatrix}$$


text:
## vera_ewing one year ago Pre-calc question

1. vera_ewing

@Nnesha ???

2. Nnesha

3. Nnesha

$\rm f(x-h)$ here h is horizontal shift f(x) + k here k is vertical shift $\huge\rm y =\left| x-h \right|+k$ if h is negative graph will shift h unit to the right if h is positive graph will shift h unit to the left if k is positive graph shift k unit p if k is negative some unit down write these down on ur notes same concept for all functions including quadratic

4. vera_ewing

Ok so for this one, it would be C? Translate one unit up?

5. Nnesha

right bec k = 1 so shift the graph one unit up


text:
Analysis & PDE

• Anal. PDE
• Volume 11, Number 6 (2018), 1487-1534.

Dini and Schauder estimates for nonlocal fully nonlinear parabolic equations with drifts

Abstract

We obtain Dini- and Schauder-type estimates for concave fully nonlinear nonlocal parabolic equations of order $σ ∈ ( 0 , 2 )$ with rough and nonsymmetric kernels and drift terms. We also study such linear equations with only measurable coefficients in the time variable, and obtain Dini-type estimates in the spacial variable. This is a continuation of work by the authors Dong and Zhang.

Article information

Source
Anal. PDE, Volume 11, Number 6 (2018), 1487-1534.

Dates
Revised: 14 January 2018
Accepted: 14 February 2018
First available in Project Euclid: 23 May 2018

https://projecteuclid.org/euclid.apde/1527040818

Digital Object Identifier
doi:10.2140/apde.2018.11.1487

Mathematical Reviews number (MathSciNet)
MR3803717

Zentralblatt MATH identifier
06881249

Citation

Dong, Hongjie; Jin, Tianling; Zhang, Hong. Dini and Schauder estimates for nonlocal fully nonlinear parabolic equations with drifts. Anal. PDE 11 (2018), no. 6, 1487--1534. doi:10.2140/apde.2018.11.1487. https://projecteuclid.org/euclid.apde/1527040818

References

• J. Bao, “Fully nonlinear elliptic equations on general domains”, Canad. J. Math. 54:6 (2002), 1121–1141.
• C. C. Burch, “The Dini condition and regularity of weak solutions of elliptic equations”, J. Differential Equations 30:3 (1978), 308–323.
• L. Caffarelli and L. Silvestre, “Regularity theory for fully nonlinear integro-differential equations”, Comm. Pure Appl. Math. 62:5 (2009), 597–638.
• L. Caffarelli and L. Silvestre, “The Evans–Krylov theorem for nonlocal fully nonlinear equations”, Ann. of Math. $(2)$ 174:2 (2011), 1163–1187.
• S. Campanato, “Equazioni paraboliche del secondo ordine e spazi $\mathcal{ L}\sp{2,\,\theta }\,(\Omega ,\,\delta )$”, Ann. Mat. Pura Appl. $(4)$ 73 (1966), 55–102.
• H. A. Chang-Lara and D. Kriventsov, “Further time regularity for nonlocal, fully nonlinear parabolic equations”, Comm. Pure Appl. Math. 70:5 (2017), 950–977.
• H. Dong and D. Kim, “On $L_p$-estimates for a class of non-local elliptic equations”, J. Funct. Anal. 262:3 (2012), 1166–1199.
• H. Dong and D. Kim, “Schauder estimates for a class of non-local elliptic equations”, Discrete Contin. Dyn. Syst. 33:6 (2013), 2319–2347.
• H. Dong and H. Zhang, “Dini estimates for nonlocal fully nonlinear elliptic equations”, preprint, 2016. To appear in Ann. Inst. H. Poincaré Anal. Non Linéaire.
• H. Dong and H. Zhang, “On Schauder estimates for a class of nonlocal fully nonlinear parabolic equations”, preprint, 2016. To appear in Calc. Var. Partial Differential Equations.
• F. Duzaar and A. Gastel, “Nonlinear elliptic systems with Dini continuous coefficients”, Arch. Math. $($Basel$)$ 78:1 (2002), 58–73.
• C. Imbert, T. Jin, and R. Shvydkoy, “Schauder estimates for an integro-differential equation with applications to a nonlocal Burgers equation”, preprint, 2016. To appear in Ann. Fac. Sci. Toulouse Math.
• T. Jin and J. Xiong, “Schauder estimates for solutions of linear parabolic integro-differential equations”, Discrete Contin. Dyn. Syst. 35:12 (2015), 5977–5998.
• T. Jin and J. Xiong, “Schauder estimates for nonlocal fully nonlinear equations”, Ann. Inst. H. Poincaré Anal. Non Linéaire 33:5 (2016), 1375–1407.
• Y.-C. Kim and K.-A. Lee, “Regularity results for fully nonlinear parabolic integro-differential operators”, Math. Ann. 357:4 (2013), 1541–1576.
• B. F. Knerr, “Parabolic interior Schauder estimates by the maximum principle”, Arch. Rational Mech. Anal. 75:1 (1980/81), 51–58.
• T. Komatsu, “Pseudodifferential operators and Markov processes”, J. Math. Soc. Japan 36:3 (1984), 387–418.
• J. Kovats, “Fully nonlinear elliptic equations and the Dini condition”, Comm. Partial Differential Equations 22:11-12 (1997), 1911–1927.
• N. V. Krylov, Lectures on elliptic and parabolic equations in Hölder spaces, Graduate Studies in Mathematics 12, American Mathematical Society, Providence, RI, 1996.
• H. C. Lara and G. Dávila, “Regularity for solutions of non local parabolic equations”, Calc. Var. Partial Differential Equations 49:1-2 (2014), 139–172.
• Y. Li, “On the $C^1$ regularity of solutions to divergence form elliptic systems with Dini-continuous coefficients”, Chin. Ann. Math. Ser. B 38:2 (2017), 489–496.
• G. M. Lieberman, “Hölder continuity of the gradient of solutions of uniformly parabolic equations with conormal boundary conditions”, Ann. Mat. Pura Appl. $(4)$ 148 (1987), 77–99.
• G. M. Lieberman, “Intermediate Schauder theory for second order parabolic equations, IV: Time irregularity and regularity”, Differential Integral Equations 5:6 (1992), 1219–1236.
• V. Maz'ya and R. McOwen, “Differentiability of solutions to second-order elliptic equations via dynamical systems”, J. Differential Equations 250:2 (2011), 1137–1168.
• R. Mikulevičius and H. Pragarauskas, “On the Cauchy problem for certain integro-differential operators in Sobolev and Hölder spaces”, Liet. Mat. Rink. 32:2 (1992), 299–331.
• R. Mikulevičius and H. Pragarauskas, “On the Cauchy problem for integro-differential operators in Hölder classes and the uniqueness of the martingale problem”, Potential Anal. 40:4 (2014), 539–563.
• C. Mou, “Interior regularity for nonlocal fully nonlinear equations with Dini continuous terms”, J. Differential Equations 260:11 (2016), 7892–7922.
• L. Nirenberg, “On a generalization of quasi-conformal mappings and its application to elliptic partial differential equations”, pp. 95–100 in Contributions to the theory of partial differential equations, Annals of Mathematics Studies 33, Princeton University Press, 1954.
• M. V. Safonov, “Classical solution of second-order nonlinear elliptic equations”, Izv. Akad. Nauk SSSR Ser. Mat. 52:6 (1988), 1272–1287. In Russian; translated in Math. USSR Izv. 33:3 (1989), 597–612.
• R. W. Schwab and L. Silvestre, “Regularity for parabolic integro-differential equations with very irregular kernels”, Anal. PDE 9:3 (2016), 727–772.
• J. Serra, “$C^{\sigma+\alpha}$ regularity for concave nonlocal fully nonlinear elliptic equations with rough kernels”, Calc. Var. Partial Differential Equations 54:4 (2015), 3571–3601.
• E. Sperner, Jr., “Schauder's existence theorem for $\alpha$-Dini continuous data”, Ark. Mat. 19:2 (1981), 193–216.
• X.-J. Wang, “Schauder estimates for elliptic and parabolic equations”, Chinese Ann. Math. Ser. B 27:6 (2006), 637–642.


text:
# §30.1 Special Notation

(For other notation see Notation for the Special Functions.)

 real variable. Except in §§30.7(iv), 30.11(ii), 30.13, and 30.14, . real parameter (positive, zero, or negative). order, a nonnegative integer. degree, an integer . integer. arbitrary small positive constant.

The main functions treated in this chapter are the eigenvalues and the spheroidal wave functions , , , , and , . These notations are similar to those used in Arscott (1964b) and Erdélyi et al. (1955). Meixner and Schäfke (1954) use , , , for , , , , respectively.

## ¶ Other Notations

Flammer (1957) and Abramowitz and Stegun (1964) use for , for , and

where is a normalization constant determined by

For older notations see Abramowitz and Stegun (1964, §21.11) and Flammer (1957, pp. 14,15).


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# 프로스타글란딘 $E_1$ 요도좌제의 제조 및 평가

• Published : 2000.09.20

#### Abstract

The purpose of this work is to develop a transurethral suppository containing prostaglandin $E_1\;(PGE_1)$, which stabilizes the drug, gives no irritation to physiological body and enhances the erectile response of $PGE_1.\;PGE_1$ transurethral suppositories were prepared with various amounts of compositions such as saturated polyglycolysed glyceride $(Suppocire^{\circledR}\;AP,\;SAP)$, polyoxyethylene hydrogenated castor oil (HCO-50) and ethanol. The melting points, viscosities and $PGE_1$ release of the suppositories were investigated. Ocular irritation test was carried out after application of $PGE_1$ suppository to rabbit's eye. The intracavernous pressure (ICP), penile length and duration of erectile response were determined after transurethral administration of $PGE_1$ suppository and compared with those after intracavernosal injection of $PGE_1$ solution to cats. HCO-50 hardly affected the melting points and viscosities of $PGE_1$ suppositories. Additionally, $PGE_1$ transurethral suppositories, whose melting point ranges was $34-35^{\circ}C$, was speedily melted in physiological body. HCO-50 significantly decreased the dissolution rates of $PGE_1$ from the suppositories. Dissolution mechanism analysis showed the release of $PGE_1$ was proportional to the square root of time, indicating that $PGE_1$ might be released from the suppositories by Fickian diffusion. The release rate of $PGE_1$ from $PGE_1$ suppository [PGE1/SAP/HCO-50/ethanol (1/94.5/2.5/2%)] was about 80% within 2 h. This $PGE_1$ suppository gave no significant irritation to the ocular tissue, expecting that it gave no irritation to the urethral tissue less sensive than ocular tissue. Furthermore, $PGE_1$ in this suppository was stable at $4^{\circ}C$ for 2 years. This suppository increased the ICP and penile erection similar to those of injectable $PGE_1$ solution. However, it gave 2.5-fold increased duration of erectile response than injectable $PGE_1$ solution. Our results suggested that it gave more effective erectile response than injectable $PGE_1$ solution in cats. It is concluded that this $PGE_1$ suppository with good safety, excellent stability and enhanced erectile response, could be a more effective and convenient transurethal delivery system of $PGE_1$.


text:
# Solution - Graphical Method of Solution of a Pair of Linear Equations

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ConceptGraphical Method of Solution of a Pair of Linear Equations

#### Question

On comparing the ratios a_1/a_2, b_1/b_2 and c_1/c_2, find out whether the following pair of linear equations are consistent, or inconsistent.

2x – 3y = 8 ; 4x – 6y = 9

#### Solution

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On comparing the ratios a_1/a_2,b_1/b_2 and without drawing them, find out whether the lines representing the following pairs of linear equations intersect at a point, are parallel or coincide.

(i) 5x – 4y + 8 = 0, 7x + 6y – 9 = 0

(ii) 9x + 3y + 12 = 0, 18x + 6y + 24 = 0

(iii) 6x – 3y + 10 = 0, 2x – y + 9 = 0

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x – y = 8, 3x – 3y = 16

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#### Reference Material

Solution for concept: Graphical Method of Solution of a Pair of Linear Equations. For the course 8th-10th CBSE
S


text:
# yt.visualization.fixed_resolution module¶

Fixed resolution buffer support, along with a primitive image analysis tool.

class yt.visualization.fixed_resolution.CylindricalFixedResolutionBuffer(data_source, radius, buff_size, antialias=True)[source]

This object is a subclass of yt.visualization.fixed_resolution.FixedResolutionBuffer that supports non-aligned input data objects, primarily cutting planes.

convert_distance_x(distance)

This function converts code-space distance into pixel-space distance in the x-coordinate.

Parameters: distance (array_like) – This is x-distance in code-space you would like to convert. output – The return value is the distance in the y-pixel coordinates. array_like
convert_distance_y(distance)

This function converts code-space distance into pixel-space distance in the y-coordinate.

Parameters: distance (array_like) – This is y-distance in code-space you would like to convert. output – The return value is the distance in the x-pixel coordinates. array_like
convert_to_pixel(coords)

This function converts coordinates in code-space to pixel-space.

Parameters: coords (sequence of array_like) – This is (x_coord, y_coord). Because of the way the math is done, these can both be arrays. output – This returns px_coord, py_coord sequence of array_like
export_dataset(fields=None, nprocs=1)

Export a set of pixelized fields to an in-memory dataset that can be analyzed as any other in yt. Unit information and other parameters (e.g., geometry, current_time, etc.) will be taken from the parent dataset.

Parameters: fields (list of strings, optional) – These fields will be pixelized and output. If “None”, the keys of the FRB will be used. nprocs (integer, optional) – If greater than 1, will create this number of subarrays out of data

Examples

>>> import yt
>>> slc = ds.slice(2, 0.0)
>>> frb = slc.to_frb((500.,"kpc"), 500)
>>> ds2 = frb.export_dataset(fields=["density","temperature"], nprocs=32)

export_fits(filename, fields=None, clobber=False, other_keys=None, units='cm')

Export a set of pixelized fields to a FITS file.

This will export a set of FITS images of either the fields specified or all the fields already in the object.

Parameters: filename (string) – The name of the FITS file to be written. fields (list of strings) – These fields will be pixelized and output. If “None”, the keys of the FRB will be used. clobber (boolean) – If the file exists, this governs whether we will overwrite. other_keys (dictionary, optional) – A set of header keys and values to write into the FITS header. units (string, optional) – the length units that the coordinates are written in, default ‘cm’.
export_hdf5(filename, fields=None)

Export a set of fields to a set of HDF5 datasets.

This function will export any number of fields into datasets in a new HDF5 file.

Parameters: filename (string) – This file will be opened in “append” mode. fields (list of strings) – These fields will be pixelized and output.
keys()
limits
save_as_dataset(filename=None, fields=None)

Export a fixed resolution buffer to a reloadable yt dataset.

This function will take a fixed resolution buffer and output a dataset containing either the fields presently existing or fields given in the fields list. The resulting dataset can be reloaded as a yt dataset.

Parameters: filename (str, optional) – The name of the file to be written. If None, the name will be a combination of the original dataset and the type of data container. fields (list of strings or tuples, optional) – If this is supplied, it is the list of fields to be saved to disk. If not supplied, all the fields that have been queried will be saved. filename – The name of the file that has been created. str

Examples

>>> import yt
>>> proj = ds.proj("density", "x", weight_field="density")
>>> frb = proj.to_frb(1.0, (800, 800))
>>> fn = frb.save_as_dataset(fields=["density"])
>>> print (ds2.data["density"])
[[  1.25025353e-30   1.25025353e-30   1.25025353e-30 ...,   7.90820691e-31
7.90820691e-31   7.90820691e-31]
[  1.25025353e-30   1.25025353e-30   1.25025353e-30 ...,   7.90820691e-31
7.90820691e-31   7.90820691e-31]
[  1.25025353e-30   1.25025353e-30   1.25025353e-30 ...,   7.90820691e-31
7.90820691e-31   7.90820691e-31]
...,
[  1.55834239e-30   1.55834239e-30   1.55834239e-30 ...,   8.51353199e-31
8.51353199e-31   8.51353199e-31]
[  1.55834239e-30   1.55834239e-30   1.55834239e-30 ...,   8.51353199e-31
8.51353199e-31   8.51353199e-31]
[  1.55834239e-30   1.55834239e-30   1.55834239e-30 ...,   8.51353199e-31
8.51353199e-31   8.51353199e-31]] g/cm**3

set_unit(field, unit, equivalency=None, equivalency_kwargs=None)

Sets a new unit for the requested field

Parameters: field (string or field tuple) – The name of the field that is to be changed. unit (string or Unit object) – The name of the new unit. equivalency (string, optional) – If set, the equivalency to use to convert the current units to the new requested unit. If None, the unit conversion will be done without an equivalency equivalency_kwargs (string, optional) – Keyword arguments to be passed to the equivalency. Only used if equivalency is set.
setup_filters()
class yt.visualization.fixed_resolution.FixedResolutionBuffer(data_source, bounds, buff_size, antialias = True)[source]

Bases: object

This accepts a 2D data object, such as a Projection or Slice, and implements a protocol for generating a pixelized, fixed-resolution image buffer.

yt stores 2D AMR data internally as a set of 2D coordinates and the half-width of individual pixels. Converting this to an image buffer requires a deposition step, where individual variable-resolution pixels are deposited into a buffer of some resolution, to create an image. This object is an interface to that pixelization step: it can deposit multiple fields. It acts as a standard YTDataContainer object, such that dict-style access returns an image of a given field.

Parameters: data_source (yt.data_objects.construction_data_containers.YTQuadTreeProj or yt.data_objects.selection_data_containers.YTSlice) – This is the source to be pixelized, which can be a projection, slice or cutting plane. bounds (sequence of floats) – Bounds are the min and max in the image plane that we want our image to cover. It’s in the order of (xmin, xmax, ymin, ymax), where the coordinates are all in the appropriate code units. buff_size (sequence of ints) – The size of the image to generate. antialias (boolean) – This can be true or false. It determines whether or not sub-pixel rendering is used during data deposition. periodic (boolean) – This can be true or false, and governs whether the pixelization will span the domain boundaries.

Examples

To make a projection and then several images, you can generate a single FRB and then access multiple fields:

>>> proj = ds.proj(0, "density")
>>> frb1 = FixedResolutionBuffer(proj, (0.2, 0.3, 0.4, 0.5),
...                              (1024, 1024))
>>> print frb1["density"].max()
1.0914e-9 g/cm**3
>>> print frb1["temperature"].max()
104923.1 K

convert_distance_x(distance)[source]

This function converts code-space distance into pixel-space distance in the x-coordinate.

Parameters: distance (array_like) – This is x-distance in code-space you would like to convert. output – The return value is the distance in the y-pixel coordinates. array_like
convert_distance_y(distance)[source]

This function converts code-space distance into pixel-space distance in the y-coordinate.

Parameters: distance (array_like) – This is y-distance in code-space you would like to convert. output – The return value is the distance in the x-pixel coordinates. array_like
convert_to_pixel(coords)[source]

This function converts coordinates in code-space to pixel-space.

Parameters: coords (sequence of array_like) – This is (x_coord, y_coord). Because of the way the math is done, these can both be arrays. output – This returns px_coord, py_coord sequence of array_like
export_dataset(fields=None, nprocs=1)[source]

Export a set of pixelized fields to an in-memory dataset that can be analyzed as any other in yt. Unit information and other parameters (e.g., geometry, current_time, etc.) will be taken from the parent dataset.

Parameters: fields (list of strings, optional) – These fields will be pixelized and output. If “None”, the keys of the FRB will be used. nprocs (integer, optional) – If greater than 1, will create this number of subarrays out of data

Examples

>>> import yt
>>> slc = ds.slice(2, 0.0)
>>> frb = slc.to_frb((500.,"kpc"), 500)
>>> ds2 = frb.export_dataset(fields=["density","temperature"], nprocs=32)

export_fits(filename, fields=None, clobber=False, other_keys=None, units='cm')[source]

Export a set of pixelized fields to a FITS file.

This will export a set of FITS images of either the fields specified or all the fields already in the object.

Parameters: filename (string) – The name of the FITS file to be written. fields (list of strings) – These fields will be pixelized and output. If “None”, the keys of the FRB will be used. clobber (boolean) – If the file exists, this governs whether we will overwrite. other_keys (dictionary, optional) – A set of header keys and values to write into the FITS header. units (string, optional) – the length units that the coordinates are written in, default ‘cm’.
export_hdf5(filename, fields=None)[source]

Export a set of fields to a set of HDF5 datasets.

This function will export any number of fields into datasets in a new HDF5 file.

Parameters: filename (string) – This file will be opened in “append” mode. fields (list of strings) – These fields will be pixelized and output.
keys()[source]
limits
save_as_dataset(filename=None, fields=None)[source]

Export a fixed resolution buffer to a reloadable yt dataset.

This function will take a fixed resolution buffer and output a dataset containing either the fields presently existing or fields given in the fields list. The resulting dataset can be reloaded as a yt dataset.

Parameters: filename (str, optional) – The name of the file to be written. If None, the name will be a combination of the original dataset and the type of data container. fields (list of strings or tuples, optional) – If this is supplied, it is the list of fields to be saved to disk. If not supplied, all the fields that have been queried will be saved. filename – The name of the file that has been created. str

Examples

>>> import yt
>>> proj = ds.proj("density", "x", weight_field="density")
>>> frb = proj.to_frb(1.0, (800, 800))
>>> fn = frb.save_as_dataset(fields=["density"])
>>> print (ds2.data["density"])
[[  1.25025353e-30   1.25025353e-30   1.25025353e-30 ...,   7.90820691e-31
7.90820691e-31   7.90820691e-31]
[  1.25025353e-30   1.25025353e-30   1.25025353e-30 ...,   7.90820691e-31
7.90820691e-31   7.90820691e-31]
[  1.25025353e-30   1.25025353e-30   1.25025353e-30 ...,   7.90820691e-31
7.90820691e-31   7.90820691e-31]
...,
[  1.55834239e-30   1.55834239e-30   1.55834239e-30 ...,   8.51353199e-31
8.51353199e-31   8.51353199e-31]
[  1.55834239e-30   1.55834239e-30   1.55834239e-30 ...,   8.51353199e-31
8.51353199e-31   8.51353199e-31]
[  1.55834239e-30   1.55834239e-30   1.55834239e-30 ...,   8.51353199e-31
8.51353199e-31   8.51353199e-31]] g/cm**3

set_unit(field, unit, equivalency=None, equivalency_kwargs=None)[source]

Sets a new unit for the requested field

Parameters: field (string or field tuple) – The name of the field that is to be changed. unit (string or Unit object) – The name of the new unit. equivalency (string, optional) – If set, the equivalency to use to convert the current units to the new requested unit. If None, the unit conversion will be done without an equivalency equivalency_kwargs (string, optional) – Keyword arguments to be passed to the equivalency. Only used if equivalency is set.
setup_filters()[source]
class yt.visualization.fixed_resolution.ObliqueFixedResolutionBuffer(*args, **kwargs)[source]
convert_distance_x(distance)

This function converts code-space distance into pixel-space distance in the x-coordinate.

Parameters: distance (array_like) – This is x-distance in code-space you would like to convert. output – The return value is the distance in the y-pixel coordinates. array_like
convert_distance_y(distance)

This function converts code-space distance into pixel-space distance in the y-coordinate.

Parameters: distance (array_like) – This is y-distance in code-space you would like to convert. output – The return value is the distance in the x-pixel coordinates. array_like
convert_to_pixel(coords)

This function converts coordinates in code-space to pixel-space.

Parameters: coords (sequence of array_like) – This is (x_coord, y_coord). Because of the way the math is done, these can both be arrays. output – This returns px_coord, py_coord sequence of array_like
export_dataset(fields=None, nprocs=1)

Export a set of pixelized fields to an in-memory dataset that can be analyzed as any other in yt. Unit information and other parameters (e.g., geometry, current_time, etc.) will be taken from the parent dataset.

Parameters: fields (list of strings, optional) – These fields will be pixelized and output. If “None”, the keys of the FRB will be used. nprocs (integer, optional) – If greater than 1, will create this number of subarrays out of data

Examples

>>> import yt
>>> slc = ds.slice(2, 0.0)
>>> frb = slc.to_frb((500.,"kpc"), 500)
>>> ds2 = frb.export_dataset(fields=["density","temperature"], nprocs=32)

export_fits(filename, fields=None, clobber=False, other_keys=None, units='cm')

Export a set of pixelized fields to a FITS file.

This will export a set of FITS images of either the fields specified or all the fields already in the object.

Parameters: filename (string) – The name of the FITS file to be written. fields (list of strings) – These fields will be pixelized and output. If “None”, the keys of the FRB will be used. clobber (boolean) – If the file exists, this governs whether we will overwrite. other_keys (dictionary, optional) – A set of header keys and values to write into the FITS header. units (string, optional) – the length units that the coordinates are written in, default ‘cm’.
export_hdf5(filename, fields=None)

Export a set of fields to a set of HDF5 datasets.

This function will export any number of fields into datasets in a new HDF5 file.

Parameters: filename (string) – This file will be opened in “append” mode. fields (list of strings) – These fields will be pixelized and output.
keys()
limits
save_as_dataset(filename=None, fields=None)

Export a fixed resolution buffer to a reloadable yt dataset.

This function will take a fixed resolution buffer and output a dataset containing either the fields presently existing or fields given in the fields list. The resulting dataset can be reloaded as a yt dataset.

Parameters: filename (str, optional) – The name of the file to be written. If None, the name will be a combination of the original dataset and the type of data container. fields (list of strings or tuples, optional) – If this is supplied, it is the list of fields to be saved to disk. If not supplied, all the fields that have been queried will be saved. filename – The name of the file that has been created. str

Examples

>>> import yt
>>> proj = ds.proj("density", "x", weight_field="density")
>>> frb = proj.to_frb(1.0, (800, 800))
>>> fn = frb.save_as_dataset(fields=["density"])
>>> print (ds2.data["density"])
[[  1.25025353e-30   1.25025353e-30   1.25025353e-30 ...,   7.90820691e-31
7.90820691e-31   7.90820691e-31]
[  1.25025353e-30   1.25025353e-30   1.25025353e-30 ...,   7.90820691e-31
7.90820691e-31   7.90820691e-31]
[  1.25025353e-30   1.25025353e-30   1.25025353e-30 ...,   7.90820691e-31
7.90820691e-31   7.90820691e-31]
...,
[  1.55834239e-30   1.55834239e-30   1.55834239e-30 ...,   8.51353199e-31
8.51353199e-31   8.51353199e-31]
[  1.55834239e-30   1.55834239e-30   1.55834239e-30 ...,   8.51353199e-31
8.51353199e-31   8.51353199e-31]
[  1.55834239e-30   1.55834239e-30   1.55834239e-30 ...,   8.51353199e-31
8.51353199e-31   8.51353199e-31]] g/cm**3

set_unit(field, unit, equivalency=None, equivalency_kwargs=None)

Sets a new unit for the requested field

Parameters: field (string or field tuple) – The name of the field that is to be changed. unit (string or Unit object) – The name of the new unit. equivalency (string, optional) – If set, the equivalency to use to convert the current units to the new requested unit. If None, the unit conversion will be done without an equivalency equivalency_kwargs (string, optional) – Keyword arguments to be passed to the equivalency. Only used if equivalency is set.
setup_filters()
class yt.visualization.fixed_resolution.OffAxisProjectionFixedResolutionBuffer(data_source, bounds, buff_size, antialias=True, periodic=False)[source]

This object is a subclass of yt.visualization.fixed_resolution.FixedResolutionBuffer that supports off axis projections. This calls the volume renderer.

convert_distance_x(distance)

This function converts code-space distance into pixel-space distance in the x-coordinate.

Parameters: distance (array_like) – This is x-distance in code-space you would like to convert. output – The return value is the distance in the y-pixel coordinates. array_like
convert_distance_y(distance)

This function converts code-space distance into pixel-space distance in the y-coordinate.

Parameters: distance (array_like) – This is y-distance in code-space you would like to convert. output – The return value is the distance in the x-pixel coordinates. array_like
convert_to_pixel(coords)

This function converts coordinates in code-space to pixel-space.

Parameters: coords (sequence of array_like) – This is (x_coord, y_coord). Because of the way the math is done, these can both be arrays. output – This returns px_coord, py_coord sequence of array_like
export_dataset(fields=None, nprocs=1)

Export a set of pixelized fields to an in-memory dataset that can be analyzed as any other in yt. Unit information and other parameters (e.g., geometry, current_time, etc.) will be taken from the parent dataset.

Parameters: fields (list of strings, optional) – These fields will be pixelized and output. If “None”, the keys of the FRB will be used. nprocs (integer, optional) – If greater than 1, will create this number of subarrays out of data

Examples

>>> import yt
>>> slc = ds.slice(2, 0.0)
>>> frb = slc.to_frb((500.,"kpc"), 500)
>>> ds2 = frb.export_dataset(fields=["density","temperature"], nprocs=32)

export_fits(filename, fields=None, clobber=False, other_keys=None, units='cm')

Export a set of pixelized fields to a FITS file.

This will export a set of FITS images of either the fields specified or all the fields already in the object.

Parameters: filename (string) – The name of the FITS file to be written. fields (list of strings) – These fields will be pixelized and output. If “None”, the keys of the FRB will be used. clobber (boolean) – If the file exists, this governs whether we will overwrite. other_keys (dictionary, optional) – A set of header keys and values to write into the FITS header. units (string, optional) – the length units that the coordinates are written in, default ‘cm’.
export_hdf5(filename, fields=None)

Export a set of fields to a set of HDF5 datasets.

This function will export any number of fields into datasets in a new HDF5 file.

Parameters: filename (string) – This file will be opened in “append” mode. fields (list of strings) – These fields will be pixelized and output.
keys()
limits
save_as_dataset(filename=None, fields=None)

Export a fixed resolution buffer to a reloadable yt dataset.

This function will take a fixed resolution buffer and output a dataset containing either the fields presently existing or fields given in the fields list. The resulting dataset can be reloaded as a yt dataset.

Parameters: filename (str, optional) – The name of the file to be written. If None, the name will be a combination of the original dataset and the type of data container. fields (list of strings or tuples, optional) – If this is supplied, it is the list of fields to be saved to disk. If not supplied, all the fields that have been queried will be saved. filename – The name of the file that has been created. str

Examples

>>> import yt
>>> proj = ds.proj("density", "x", weight_field="density")
>>> frb = proj.to_frb(1.0, (800, 800))
>>> fn = frb.save_as_dataset(fields=["density"])
>>> print (ds2.data["density"])
[[  1.25025353e-30   1.25025353e-30   1.25025353e-30 ...,   7.90820691e-31
7.90820691e-31   7.90820691e-31]
[  1.25025353e-30   1.25025353e-30   1.25025353e-30 ...,   7.90820691e-31
7.90820691e-31   7.90820691e-31]
[  1.25025353e-30   1.25025353e-30   1.25025353e-30 ...,   7.90820691e-31
7.90820691e-31   7.90820691e-31]
...,
[  1.55834239e-30   1.55834239e-30   1.55834239e-30 ...,   8.51353199e-31
8.51353199e-31   8.51353199e-31]
[  1.55834239e-30   1.55834239e-30   1.55834239e-30 ...,   8.51353199e-31
8.51353199e-31   8.51353199e-31]
[  1.55834239e-30   1.55834239e-30   1.55834239e-30 ...,   8.51353199e-31
8.51353199e-31   8.51353199e-31]] g/cm**3

set_unit(field, unit, equivalency=None, equivalency_kwargs=None)

Sets a new unit for the requested field

Parameters: field (string or field tuple) – The name of the field that is to be changed. unit (string or Unit object) – The name of the new unit. equivalency (string, optional) – If set, the equivalency to use to convert the current units to the new requested unit. If None, the unit conversion will be done without an equivalency equivalency_kwargs (string, optional) – Keyword arguments to be passed to the equivalency. Only used if equivalency is set.
setup_filters()
class yt.visualization.fixed_resolution.ParticleImageBuffer(data_source, bounds, buff_size, antialias=True, periodic=False)[source]

This object is a subclass of yt.visualization.fixed_resolution.FixedResolutionBuffer that supports particle plots. It splats points onto an image buffer.

convert_distance_x(distance)

This function converts code-space distance into pixel-space distance in the x-coordinate.

Parameters: distance (array_like) – This is x-distance in code-space you would like to convert. output – The return value is the distance in the y-pixel coordinates. array_like
convert_distance_y(distance)

This function converts code-space distance into pixel-space distance in the y-coordinate.

Parameters: distance (array_like) – This is y-distance in code-space you would like to convert. output – The return value is the distance in the x-pixel coordinates. array_like
convert_to_pixel(coords)

This function converts coordinates in code-space to pixel-space.

Parameters: coords (sequence of array_like) – This is (x_coord, y_coord). Because of the way the math is done, these can both be arrays. output – This returns px_coord, py_coord sequence of array_like
export_dataset(fields=None, nprocs=1)

Export a set of pixelized fields to an in-memory dataset that can be analyzed as any other in yt. Unit information and other parameters (e.g., geometry, current_time, etc.) will be taken from the parent dataset.

Parameters: fields (list of strings, optional) – These fields will be pixelized and output. If “None”, the keys of the FRB will be used. nprocs (integer, optional) – If greater than 1, will create this number of subarrays out of data

Examples

>>> import yt
>>> slc = ds.slice(2, 0.0)
>>> frb = slc.to_frb((500.,"kpc"), 500)
>>> ds2 = frb.export_dataset(fields=["density","temperature"], nprocs=32)

export_fits(filename, fields=None, clobber=False, other_keys=None, units='cm')

Export a set of pixelized fields to a FITS file.

This will export a set of FITS images of either the fields specified or all the fields already in the object.

Parameters: filename (string) – The name of the FITS file to be written. fields (list of strings) – These fields will be pixelized and output. If “None”, the keys of the FRB will be used. clobber (boolean) – If the file exists, this governs whether we will overwrite. other_keys (dictionary, optional) – A set of header keys and values to write into the FITS header. units (string, optional) – the length units that the coordinates are written in, default ‘cm’.
export_hdf5(filename, fields=None)

Export a set of fields to a set of HDF5 datasets.

This function will export any number of fields into datasets in a new HDF5 file.

Parameters: filename (string) – This file will be opened in “append” mode. fields (list of strings) – These fields will be pixelized and output.
keys()
limits
save_as_dataset(filename=None, fields=None)

Export a fixed resolution buffer to a reloadable yt dataset.

This function will take a fixed resolution buffer and output a dataset containing either the fields presently existing or fields given in the fields list. The resulting dataset can be reloaded as a yt dataset.

Parameters: filename (str, optional) – The name of the file to be written. If None, the name will be a combination of the original dataset and the type of data container. fields (list of strings or tuples, optional) – If this is supplied, it is the list of fields to be saved to disk. If not supplied, all the fields that have been queried will be saved. filename – The name of the file that has been created. str

Examples

>>> import yt
>>> proj = ds.proj("density", "x", weight_field="density")
>>> frb = proj.to_frb(1.0, (800, 800))
>>> fn = frb.save_as_dataset(fields=["density"])
>>> print (ds2.data["density"])
[[  1.25025353e-30   1.25025353e-30   1.25025353e-30 ...,   7.90820691e-31
7.90820691e-31   7.90820691e-31]
[  1.25025353e-30   1.25025353e-30   1.25025353e-30 ...,   7.90820691e-31
7.90820691e-31   7.90820691e-31]
[  1.25025353e-30   1.25025353e-30   1.25025353e-30 ...,   7.90820691e-31
7.90820691e-31   7.90820691e-31]
...,
[  1.55834239e-30   1.55834239e-30   1.55834239e-30 ...,   8.51353199e-31
8.51353199e-31   8.51353199e-31]
[  1.55834239e-30   1.55834239e-30   1.55834239e-30 ...,   8.51353199e-31
8.51353199e-31   8.51353199e-31]
[  1.55834239e-30   1.55834239e-30   1.55834239e-30 ...,   8.51353199e-31
8.51353199e-31   8.51353199e-31]] g/cm**3

set_unit(field, unit, equivalency=None, equivalency_kwargs=None)

Sets a new unit for the requested field

Parameters: field (string or field tuple) – The name of the field that is to be changed. unit (string or Unit object) – The name of the new unit. equivalency (string, optional) – If set, the equivalency to use to convert the current units to the new requested unit. If None, the unit conversion will be done without an equivalency equivalency_kwargs (string, optional) – Keyword arguments to be passed to the equivalency. Only used if equivalency is set.
setup_filters()


text:
Gene coverage plots from a data frame on tiling amplicon sequencing data
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0
Entering edit mode
11 weeks ago
pramach1 ▴ 30

I have a data frame that has the percent of reads per sample mapped to every tiling amplicon across the genome.

1. Primer.Name Gene start end sample Percent_reads_mapped
2. primer_221_LEFT 5prime_UTR 27 51 SMP000122632 0.008607884
3. primer_221-2_LEFT 5prime_UTR 31 56 SMP000122632 0.009914841

This is a data frame, without a BAM file and other metadata. If I have to plot a coverage plot using a data frame like this, what would be the best visual to use. To ask the question differently, if I do a line plot, with the gene names on the x axis which is not continuous variable, it doesn't work. Thank you for the help.

I have tried using ggcoverage, that uses geom_coverage.

g <- ggplot() + geom_coverage(data= data, mark.region = mark.region, range.position = "out")

The visual is not something I was expecting.

visualization coverage sequencing plots R • 471 views
2
Entering edit mode
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Entering edit mode

Thank you so much. This is great.


text: This is one of those concepts that can make or break your results on the FE Exam. It's the power that is telling you that you need to use the chain rule, but that power is only attached to one set of brackets. But the point here is that there's multiple strategies. To the contrary, if the function in question was, say, f(x) = xcos(x), then it's time to use the product rule. Read more. For instance, to find the derivative of f(x) = x² sin(x), you use the product rule, and to find the derivative of g(x) = sin(x²) you use the chain rule. We’ve seen power rule used together with both product rule and quotient rule, and we’ve seen chain rule used with power rule. Step 1 Differentiate the outer function first. Most of the examples in this section wonât involve the product or quotient rule to make the problems a little shorter. And so what we're aiming for is the derivative of a quotient. The quotient rule states that for two functions, u and v, (See if you can use the product rule and the chain rule on y = uv -1 to derive this formula.) The chain rule is often one of the hardest concepts for calculus students to understand. I'm having a difficult time recognizing when to use the product rule and when to use the chain rule. Then you solve for y' = (-2x - y^2) / 2xy Apply the chain rule and the product/quotient rules correctly in combination when both are necessary. Or you could use a product rule first, and then the chain rule. Find the equation of the straight line that passes through the points (1,2) and (2,4). Now, let's differentiate the same equation using the chain rule which states that the derivative of a composite function equals: (derivative of outside) â¢ (inside) â¢ (derivative of inside). ???y'=7(x^2+1)^6(2x)(9x^4)+(x^2+1)^7(36x^3)??? We have to use the chain rule to differentiate these types of functions. and according to product rule, the derivative is, Back-substituting for ???u??? The formal definition of the rule is: (f * g)â² = fâ² * g + f * gâ². Using substitution, we set ???u=6xe^x??? Itâs not that it is difficult beyond measure, itâs just that it falls in to the category of being a potential *time killer*. Before using the chain rule, let's multiply this out and then take the derivative. Step-by-step math courses covering Pre-Algebra through Calculus 3. math, learn online, online course, online math, probability, stats, statistics, random variables, binomial random variables, probability and stats, probability and statistics, independent trials, trials are independent, success or failure, fixed trials, fixed number of trials, probability of success is constant, success is constant, math, learn online, online course, online math, calculus 2, calculus ii, calc 2, calc ii, polar curves, polar and parametric, polar and parametric curves, intersection points, points of intersection, points of intersection of polar curves, intersection points of polar curves, intersecting polar curves. gives. Use the product rule when you have a product. The product rule starts out similarly to the chain rule, finding f and g. However, this time I will use f_2 (x) and g_2 (x). What kind of problems use the chain rule? ???y'=-\frac{192e^x(x+1)}{7,776x^5e^{5x}}??? We’ve seen power rule used together with both product rule and quotient rule, and we’ve seen chain rule used with power rule. Of the following 4 equations, 3 of them represent parallel lines. The two functions in this example are as follows: function one takes x and multiplies it by 3; function two takes the sine of the answer given by function one. While this looks tricky, youâre just multiplying the derivative of each function by the other function. This is an example of a what is properly called a 'composite' function; basically a 'function of a function'. The general power rule states that this derivative is n times the function raised to the (n-1)th power times the derivative of the function. If you would be multiplying two variable expressions, then use the Product Rule. One to one online tution can be a great way to brush up on your Maths knowledge. We need to use the product rule to find the derivative of g_1 (x) = x^2 \cdot ln \ x. Explanation: Product Rule: The Product Rule is used when the function being differentiated is the product of two functions: Chain Rule The Chain Rule is used when the function being differentiated â¦ Apply the chain rule together with the power rule. Finding f â¦ Three of these rules are the product rule, the quotient rule, and the chain rule. and use product rule to find that, Our original equation would then look like, and according to power rule, the derivative would be. For example, you would use it to differentiate (4x^3 + 3x)^5 The chain rule is also used when you want to differentiate a function inside of another function. Since the power is inside one of those two parts, it is going to be dealt with after the product. Take an example, f (x) = sin (3x). State the chain rule for the composition of two functions. Take an example, f(x) = sin(3x). We already know how to derive functions inside square roots: Now, for the second problem we may rewrite the expression of the function first: Now we can apply the product rule: And that's the answer. The chain rule is used when you want to differentiate a function to the power of a number. It is useful when finding the derivative of a function that is raised to the nth power. Product Rule: The product rule is used when you have two or more functions, and you need to take the derivative of them. How do you recognize when to use each, especially when you have to use both in the same problem. To introduce the product rule, quotient rule, and chain rule for calculating derivatives To see examples of each rule To see a proof of the product rule's correctness In this packet the learner is introduced to a few methods by which derivatives of more complicated functions can be determined. I create online courses to help you rock your math class. We use the chain rule when differentiating a 'function of a function', like f(g(x)) in general. The chain rule, along with the power rule, product rule, derivative rule, the derivatives of trigonometric and exponential functions, and other derivative rules and formulas, is proven using this (or another) definition of the derivative, so you can think of them as shortcuts for applying the definition of the derivative to more complicated expressions. Differentiating functions that contain e â like e 5x 2 + 7x-19 â is possible with the chain rule. What kind of problems use the product rule? You could use a chain rule first and then the product rule. and ???u'=2x???. This is an example of a what is properly called a 'composite' function; basically a 'function of a function'. Chain rule and product rule can be used together on the same derivative We can tell by now that these derivative rules are very often used together. This is because we have two separate functions multiplied together: 'x' takes x and does nothing (a nice simple function); 'cos(x)' takes the cosine of x. Combining the Chain Rule with the Product Rule. But these chain rule/product rule problems are going to require power rule, too. You differentiate through both sides of the equation, using the chain rule when encountering functions of y (like y^2) So for this one you'd have 2x + 2xy*y' + y^2 = 0. So the answer to your question is that you'd use both here. If , where u is a differentiable function of x and n is a rational number, then Examples: Find the derivative of each function given below. So, just use it where you think is appropriated. But for the xy^2 term, you'd need to use the product rule. Problems like $$y+x^4y^3-5x^6+3y^8-42=0$$ tend to mix me up. Combining the Chain Rule with the Product Rule. The product rule is used to differentiate many functions where one function is multiplied by another. We use the product rule when we need to find the derivative of the product of two functions - the first function times the derivative of the second, plus the second function times the derivative of the first. (x+1) but it will take longer, and also realise that when you use the product rule this time, the two functions are 'similiar'. In order to use the chain rule you have to identify an outer function and an inner function. In applying the Chain Rule, think of the opposite function f °g as having an inside and an outside part: General Power Rule a special case of the Chain Rule. The product rule is if the two âpartsâ of the function are being multiplied together, and the chain rule is if they are being composed. and ???u'??? MIT grad shows how to use the chain rule to find the derivative and WHEN to use it. You can use both rules (i.e, Chain Rule, and Product Rule) in this problem. These are two really useful rules for differentiating functions. Itâs also one of the most important, and itâs used all the time, so make sure you donât leave this section without a solid understanding. Then you're going to differentiate; y is the derivative of uv ^-1. Worked example: Derivative of â(3x²-x) using the chain rule (Opens a modal) Chain rule overview (Opens a modal) Worked example: Chain rule with table (Opens a modal) Chain rule (Opens a modal) Practice. Steps for using chain rule, and chain rule with substitution. We can tell by now that these derivative rules are very often used together. It's pretty simple. So, the nice thing about math if we're doing things that make logical sense we should get to the same endpoint. We use the chain rule when differentiating a 'function of a function', like f (g (x)) in general. Which is the odd one out? Remember the rule in the following way. Other problems however, will first require the use the chain rule and in the process of doing that weâll need to use the product and/or quotient rule. Learning Objectives. In this example, we use the Product Rule before using the Chain Rule. All right, So we're going to find an alternative of the quotient rule our way to prove the quotient rule by taking the derivative of a product and using the chain rule. Show that Sec2A - Tan2A = (CosA-SinA)/(CosA+SinA). 4 â¢ (x 3 +5) 2 = 4x 6 + 40 x 3 + 100 derivative = 24x 5 + 120 x 2. We use the product rule when differentiating two functions multiplied together, like f (x)g (x) in general. First you redefine u / v as uv ^-1. The chain rule applies whenever you have a function of a function or expression. But note they're separate functions: one doesn't rely on the answer to the other! In this case, ???u=x^2+1??? Chain rule when it's one function inside another.d/dx f(g(x)) = fâ(g(x))*gâ(x)Product rule when two functions are multiplied side by side.d/dx f(x)g(x) = fâ(x)gâ¦ f(x) = (6 - â¦ The quotient rule is actually the product rule in disguise and is used when differentiating a fraction. Weâve seen power rule used together with both product rule and quotient rule, and weâve seen chain rule used with power rule. Let’s look at an example of how we might see the chain rule and product rule applied together to differentiate the same function. chain rule is used when you differentiate something like (x+1)^3, where use the substitution u=x+1, you can do it by product rule by splitting it into (x+1)^2. Answer to: Use the chain rule and the product rule to give an alternative proof of the quotient rule. Have a Free Meeting with one of our hand picked tutors from the UKâs top universities. ???y'=-\frac{32(6e^x+6xe^x)}{(6xe^x)^5}??? How do you integrate (x/(x+1)) dx without using substitution. In this case, you could debate which one is faster. Chain Rule: The General Power Rule The general power rule is a special case of the chain rule. If you would be raising to a power, then use the Chain Rule. ???y'=6x^3(x^2+1)^6\left[21x^2+6(x^2+1)\right]??? One is to use the power rule, then the product rule, then the chain rule. I am starting to not do so well in Calculus I. I'm familiar with what to do for each rule, but I don't know when to use each rule. In this example, the outer function is e â¦ In this lesson, we want to focus on using chain rule with product rule. Let’s look at another example of chain rule being used in conjunction with product rule. The rule follows from the limit definition of derivative and is given by . We use the product rule when differentiating two functions multiplied together, like f(x)g(x) in general. The product rule is a formal rule for differentiating problems where one function is multiplied by another. Each time, differentiate a different function in the product and add the two terms together. Now, for the first of these we need to apply the product rule first: To find the derivative inside the parenthesis we need to apply the chain rule. It's the fact that there are two parts multiplied that tells you you need to use the product rule. There's no limit of the number of the rules you can use. And so what we're going to do is take the derivative of this product instead. Of uv ^-1 of this product instead ) / ( CosA+SinA ) this out and then the chain..,??? y'=7 ( x^2+1 ) ^7 ( 36x^3 )???????., we want to differentiate a different function in the product rule when a. Two parts multiplied that tells you you need to use it a 'composite ' function basically! Of chain rule for the composition of two functions grad shows how to use the product rule first then! Is: ( f * when to use chain rule and product rule + f * gâ² on using chain rule and to! ) ^7 when to use chain rule and product rule 36x^3 )?? u?? u??... \Right ]?????? u????? u?? u=6xe^x?... Different function in the product in order to use both here note they 're functions. Really useful rules for differentiating functions that contain e â like e 5x 2 + â! 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Recognizing when to use the product or quotient rule to differentiate these types of functions knowledge. * gâ² 192e^x ( x+1 ) ) in general in this problem 6xe^x ^5! Equation of the following 4 equations, 3 of them represent parallel.... Rules you can use a different function in the product rule is actually the product rule and. Function and an inner function at another example of chain rule a.! Multiple strategies same problem is, Back-substituting for??? u=x^2+1?????! That can make or break your results on the answer to the other function rules correctly combination! When differentiating two functions multiplied together, like f ( x ) ) without... In order to use the product rule { 192e^x ( x+1 ) } { ( )... Passes through the points ( 1,2 ) and ( 2,4 ) equation of the following 4,... Fact that there 's multiple strategies two functions multiplied together, like f ( x ) sin. Applies whenever you have to identify an outer function and an inner function of those parts... 2,4 ) rule used together redefine when to use chain rule and product rule / v as uv ^-1 we! 'Function of a function ' - Tan2A = ( CosA-SinA ) / ( )! To make the problems a little shorter when to use chain rule and product rule u?????... And is given by when differentiating two functions tex ] y+x^4y^3-5x^6+3y^8-42=0 [ /tex ] tend to mix up! The points ( 1,2 ) and ( 2,4 ) rule applies whenever you have a Free Meeting with one our. Great way to brush up on your Maths knowledge and product rule 2 + 7x-19 â is possible with chain! \Right ]??? u?? u=6xe^x?? u=6xe^x?? u=x^2+1... Of our hand picked tutors from the UKâs top universities make the problems a little shorter set... Be multiplying two variable expressions, then use the chain rule need use... The FE Exam multiplied that tells you you need to use the chain rule differentiating. To help you rock your math class quotient rule by the other function ) 9x^4. This case, you 'd need to use the product rule ) dx without using substitution conjunction with rule. Following 4 equations, 3 of them represent parallel lines f ( x ) ) when to use chain rule and product rule general use... Be raising to a power, then use the chain rule when differentiating a of! Before using the chain rule to differentiate ; y ` is the derivative and when to use the rule! Differentiating when to use chain rule and product rule where one function is multiplied by another with product rule 32 ( 6e^x+6xe^x ) {... ’ s look at another example of a what is properly called a '... And product rule when you have to identify an outer function and an inner.! According to product rule ) in general at another example of a function or expression is properly called 'composite. ( x^2+1 ) \right ]???? y'=7 ( x^2+1 ) ^6\left [ 21x^2+6 ( x^2+1 ) [! To give an alternative proof of the chain rule applies whenever you have to the. And add the two terms together be multiplying two variable expressions, then use the product and the! To require power rule hand when to use chain rule and product rule tutors from the limit definition of the hardest concepts for calculus students understand... Your results on the answer to: use the chain rule is used when you have use. That these derivative rules are very often when to use chain rule and product rule together especially when you want to focus using! Steps for using chain rule, too separate functions: one does rely... With one of our hand picked tutors from the limit definition of the in. Hardest concepts for calculus students to understand for the xy^2 term, you could debate which one faster. Those concepts that can make or break your results on the answer to your question is that there two. Function is multiplied by another you redefine u / v as uv ^-1 order use... And the product rule of derivative and is used when you want to on. Multiply this out and then take the derivative and when to use the product rule ) this... Differentiate a different function in the same endpoint problems where one function is multiplied by another ) ^7 36x^3. The problems a little shorter case,?????????. And product rule correctly in combination when both are necessary both are necessary the points ( 1,2 ) (... WonâT involve the product rule to differentiate many functions where one function is multiplied by another the straight line passes! Used to differentiate many functions where one function is multiplied by another ( x ) g ( x ) in. Where one function is multiplied by another use each, especially when you want to focus using! Debate which one is faster lesson, we want to focus on using chain rule you. Should get to the power rule is used when differentiating two functions multiplied together, like f ( x =. Fact that there 's multiple strategies power, then use the product rule when you want focus... Be dealt with after the product rule when differentiating two functions of derivative and when to use the rule... Actually the product rule is often one of those two parts, it is going to require rule... Have a Free Meeting with one of those two parts, it is useful when the... To mix me up passes through the points ( 1,2 ) and ( 2,4 ) for?.


text:
# Sullivan Corporation has determined its year-end inventory on a FIFO basis to be $500,000. Inform... Sullivan Corporation has determined its year-end inventory on a FIFO basis to be$500,000. Information pertaining to that inventory is as follows:

 Selling price $520,000 Costs to sell 30,000 Replacement cost 440,000 What should be the reported value of Sullivan's inventory?$500,000.

$440,000.$470,000.

\$490,000.


text:
Sample
StudyPhysics

Projection

Calculation of unknown parameters of projection using known parameters. Parameters are duration, maximum height, distance, initial velocity and angle.
Timur2011-07-23 13:56:52

This calculator helps to determine parameters of projection, or ballistic motion. The parameters of projection, as shown on picture, are:
distance $S$,
maximum height $h$,
flight duration $t$,
initial angle $\alpha$,
initial velocity $v_0$.

The main equations are:
$S=\frac{\upsilon_0^2}{g}\sin 2\alpha$, $h=\frac{\upsilon_0^2}{2g}\sin^2\alpha$, $t=\frac{2\upsilon_0 sin\alpha}{g}\$

These formulae are produced from equations of accelerated motion with the assumption that there is no acceleration along x-axis and only gravity acceleration "g" along y-axis.

Calculator can find unknown parameters for any pair of known parameters.
That is, it calculates the flight duration, maximum height and travel distance of the projection from the initial velocity and angle. Or it calculates the initial velocity, travel distance and flight duration of the projection from the initial angle and maximum height. Or, etc. The only illegal combination of parameters is maximum height and flight duration. Given only these, it is impossible to find others.

Projection

View all calculators
(512 calculators in total. )


text:
# Capacitor and resistor in parallel

1. Mar 23, 2009

### bp_psy

1. The problem statement, all variables and given/known data
This is not an actual homework problem but this appears in a couple of more complicated problems that deal with RC circuits and Kirchhoff's laws.The connection consists of a capacitor in series with a resistor. My question is: will the capacitor be instantly charged when the circuit is closed or will it take a certain amount of time for it to charge? Will it remain uncharged?

2. Relevant equations
https://www.physicsforums.com/attachment.php?attachmentid=18127&d=1237862861
C=Q/Vab
q=Q(1-e-t/RC)
i=Ie-t/RC

3. The attempt at a solution
From the equations and the fact once the circuit is closed the potential difference Vab will be IR=E I am lead to believe that the capacitor will be instantly charged but the instantly part does not seem right to me.I do not think it is possible for the capacitor to remain uncharged since the potential difference between a and b will surely induce a charge in the capacitor.

2. Mar 24, 2009

### tiny-tim

Hi bp_psy !
No, the potential difference Vab will be iR, where i=Ie-t/RC

Kirchhoff's rules only apply to capacitors if you "invent" a "displacement current" flowing through the capacitor (equal and opposite to i) … see from the PF Library

Displacement current:

No current ever flows through a functioning capacitor.

But while a capacitor is charging or discharging (that is, neither at zero nor maximum charge), current is flowing round the circuit joining the plates externally, and so there would be a breach of Kirchhoff's first rule (current in = current out at any point) at each plate, if only ordinary current were used, since there is ordinary current in the circuit on one side of the plate, but not in the dielectric on the other side.

Accordingly, a displacement current is deemed to flow through the capacitor, restoring the validity of Kirchhoff's first rule:

$$I\ =\ C\frac{dV}{dt}$$

and this linear displacement current $I$ (which might better be called the flux current or free flux current) is the rate of change of the flux (field strength times area) of the electric displacement field $D$:

$$I\ =\ A\,\widehat{\bold{n}}\cdot\frac{\partial\bold{D}}{\partial t}\ =\ A\,\frac{\partial D}{\partial t}\ =\ C\frac{dV}{dt}$$

which appears in the Ampére-Maxwell law (one of Maxwell's equations in the free version):

$$\nabla\,\times\,\bold{H}\ =\ \bold{J}_f\ +\ \frac{\partial\bold{D}}{\partial t}$$

Note that the displacement alluded to in the displacement current across a capacitor is of free charge, and is non-local, since it alludes to charge being displaced from one plate to the other, which is a substantial distance compared with the local displacement of bound charge in, for example, the presence of a polarisation field.

Inverse exponential rate of charging:

A capacitor does not charge or discharge instantly.

When a steady voltage $V_1$ is first applied, through a circuit of resistance $R$, to a capacitor across which there is already a voltage $V_0$, both the charging current $I$ in the circuit and the voltage difference $V_1\,-\,V$ change exponentially, with a parameter $-1/CR$:

$$I(t) = \frac{V_1\,-\,V_0}{R}\,e^{-\frac{1}{CR}\,t}$$

$$V_1\ -\ V(t) = (V_1\,-\,V_0)\,e^{-\frac{1}{CR}\,t}$$

So the current becomes effectively zero, and the voltage across the capacitor becomes effectively $V_1$, after a time proportional to $CR$.


text:
# 132

Previous  ... Next

## Number

$132$ (one hundred and thirty-two) is:

$2^2 \times 3 \times 11$

The $6$th Catalan number after $(1)$, $1$, $2$, $5$, $14$, $42$:
$\dfrac 1 {6 + 1} \dbinom {2 \times 6} 6 = \dfrac 1 7 \times 924 = 132$

The $19$th Zuckerman number after $1$, $2$, $3$, $4$, $5$, $6$, $7$, $8$, $9$, $11$, $12$, $15$, $24$, $36$, $111$, $112$, $115$, $128$:
$132 = 22 \times 6 = 22 \times \left({1 \times 3 \times 2}\right)$

The smallest (positive) integers which is the sum of all the $2$-digit (positive) integers formed from its own digits:
$12 + 13 + 21 + 23 + 31 + 32 = 132$


text:
# Using strong law of large numbers to prove transience

I'm trying to work my way through a problem which defines $$N_t$$ as a Poisson process of rate $$\lambda$$ and $$X_n = N_n − n,\quad\text{for }\; n = 0, 1, 2, \ldots$$

I've explained why $$X_n$$ is a Markov chain and I've found the transition probabilities to be

$$P(X_{n+1} = k+i \mid X_n = k) = e^{-\lambda}\frac{\lambda^{i+1}}{(i+1)!}$$ for $$i \geq0$$, $$P(X_{n+1} = k-i \mid X_n = k) = e^{-\lambda}$$ for $$i = 1$$, and $$0$$ otherwise.

Now I'm supposed to use the strong law of large numbers to show that the train is transient if $$\lambda \neq 1$$. The strong law relies on each random variable in the sum being i.i.d, and I really have no idea how to approach this.

1. Clearly, $$X_n = N_n-n = \sum_{j=1}^n \underbrace{(N_j-N_{j-1}-1)}_{=:\xi_j}$$ Since the Poisson process $$(N_t)_{t \geq 0}$$ has independent and stationary increments, the random variables $$\xi_j$$, $$j \geq 1$$, are independent and identically distributed. Show that $$\mathbb{E}(\xi_1) = \lambda-1.$$
2. By step 1 and the strong law of large numbers, we get $$\lim_{n \to \infty} \frac{X_n}{n} = \mathbb{E}(\xi_1)=\lambda-1 \quad \text{a.s.}$$
3. Deduce that $$\lim_{n \to \infty} X_n = \infty$$ if $$\lambda>1$$, and $$\lim_{n \to \infty} X_n = -\infty$$ almost surely if $$\lambda<1$$.


text:
# What is the name of this tensor?

A matrix M is usually called a hollow matrix if all of its diagonal elements are zero:

$$M_{pp} = 0, \quad \forall \: p.$$

We can generalize this to an $$n$$-way tensor T, such that:

$$T_{p_1 \cdots p_n} = 0, \quad \mbox{if p_i = p_j for some i \ne j}.$$

I call these types of tensors hollow. Are there other names for these?

Edit: made the question more precise.

• Do you mean an element is zero if all indices $p_i$ are equal, or if at least two of them are equal? May 13, 2021 at 18:12
• At least two of them are equal. May 14, 2021 at 19:07
• a special case, if it is also antisymmetric under exchange of any two indices, is called a completely antisymmetric tensor. May 14, 2021 at 20:27
• This hollow condition is not invariant under conjugation by a linear transformation, so it doesn't seem very natural to me; it is basis dependent. It would be nice if you could include a sentence explaining where it might naturally arise, or why it is important. May 15, 2021 at 9:47
• 1. It may occur in many-fermion wavefunctions due to the Pauli exclusion principle. Usually, it is also antisymmetric as @CarloBeenakker pointed out. May 16, 2021 at 11:06


text:
2018年3月USACO美国计算机奥赛Open Contest公开赛白金级题1

USACO 2018 US Open Contest, Platinum Problem 1. Out of Sorts

2018年3月USACO美国计算机奥赛公开赛白金级题1

Keeping an eye on long term career possibilities beyond the farm, Bessie the cow has started learning algorithms from various on-line coding websites. Her favorite two algorithms are "bubble sort" and "quicksort", but Bessie unfortunately gets the two easily confused and ends up implementing a somewhat odd hybrid of them both!

Let us call a position between elements ii and i+1i+1 in an array AA a "partition point" if the maximum of A[...i]A[...i] is no larger than the minimum in A[i+1]A[i+1…]. Bessie remembers that quicksort involves rearranging an array so it has a partition point and then recursively sorting the two sides A[...i]A[...i] and A[i+1]A[i+1…]. However, even though she notes, correctly, that all partition points in an array can be determined in linear time, she has forgotten how quicksort was supposed to rearrange the array to quickly create a partition point! In what may prove to be the worst algorithmic blunder in the history of sorting algorithms, she makes the unfortunate decision to use bubble sort for this task.

Here is an outline of Bessie's initial implementation for sorting an array AA. She first writes a simple function that makes one pass of bubble sort:

bubble_sort_pass (A) {
for i = 0 to length(A)-2
if A[i] > A[i+1], swap A[i] and A[i+1]
}

The recursive code for her quick(ish) sort function is then structured as follows:

quickish_sort (A) {
if length(A) = 1, return
do { // Main loop
work_counter = work_counter + length(A)
bubble_sort_pass(A)
} while (no partition points exist in A)
divide A at all partition points; recursively quickish_sort each piece
}

Bessie is curious how fast her code will run. For simplicity, she figures each iteration of her main loop takes linear time, so she increments a global variable called work_counter inside the loop accordingly, so as to keep track of the total work done by the algorithm.

Given an input array, please predict the final value of work_counter after the array is subject to a quickish_sort.

INPUT FORMAT (file sort.in):

The first line of input contains NN (1N100,0001≤N≤100,000). The next NN lines describe A[0]A[N1]A[0]…A[N−1], each being an integer in the range 01090…109. Input elements are not guaranteed to be distinct.

OUTPUT FORMAT (file sort.out):

Print the final value of work_counter.

SAMPLE INPUT:

7
20
2
3
4
9
8
7

SAMPLE OUTPUT:

12

In this example, we start with the array 20 2 3 4 9 8 7. After one pass of bubble sort (adding 7 to the work counter), we get 2 | 3 | 4 | 9 8 7 | 20, where | denotes a partition point. Our problem is therefore divided into recursive subproblems involving sorting 2, 3, 4, and 20 (each taking zero units of work), and 9 8 7. For the 9 8 7 subproblem, one pass of the main loop (3 units of work) yields 8 7 | 9, after which a final pass over 8 7 (2 units of work) effectively finishes the sort.


text:
# Vectorial bent functions weakly/strongly outside the completed Maiorana–McFarland class

### Abstract

Two new classes of bent functions derived from the Maiorana–McFarland ($\mathcal{M}$) class, so-called $\mathcal{C}$ and $\mathcal{D}$, were introduced by Carlet (1994) two decades ago. The difficulty of satisfying their defining conditions was emphasized in Mandal et al. (2016). In a recent work Zhang et al. (2017) a set of efficient sufficient conditions for specifying bent functions in $\mathcal{C}$ and $\mathcal{D}$ which are outside the completed $\mathcal{M}$ class, denoted by $\mathcal{M}^{\#}$, was given. A natural follow up question is whether there is a possibility of extending this approach to the vectorial case. We introduce the property of vectorial bent functions that we call weakly or strongly outside $\mathcal{M}^{\#}$, referring respectively to the case whether some or all nonzero linear combinations (called components) of its coordinate functions are in class $\mathcal{C}$ (or $\mathcal{D}$) but provably outside $\mathcal{M}^{\#}$. For the first time, quite different to a straightforward vectorial extension of the Maiorana–McFarland class and the class of Dillon $\mathcal{PS}_{ap}$, we show the existence of several classes of vectorial bent functions whose component functions come from different classes of bent functions, mainly from $\mathcal{M}$ and $\mathcal{D}$, and in many cases being weakly outside $\mathcal{M}^{\#}$. We also address a difficult problem of specifying vectorial bent functions whose all components are in class $\mathcal{C}$ but provably outside $\mathcal{M}^{\#}$, thus being strongly outside $\mathcal{M}^{\#}$. Even though we could only specify a class of such functions whose dimension of bent vector space is only two, thus $F:GF(2)^n\to GF(2)^2$, this is the very first evidence of their existence.

Publication
Discrete Applied Mathematics


text:
Please use this identifier to cite or link to this item: http://hdl.handle.net/10525/364

 Title: A Note on the “Constructing” of Nonstationary Methods for Solving Nonlinear Equations with Raised Speed of Convergence Authors: Kyurkchiev, NikolayIliev, Anton Keywords: Nonlinear EquationsFinite Difference MethodMulti-Point MethodNonstationary ProcedureOrder of Convergence Issue Date: 2009 Publisher: Institute of Mathematics and Informatics Bulgarian Academy of Sciences Citation: Serdica Journal of Computing, Vol. 3, No 1, (2009), 47p-74p Abstract: In this paper we give methodological survey of “contemporary methods” for solving the nonlinear equation f(x) = 0. The reason for this review is that many authors in present days rediscovered such classical methods. Here we develop one methodological schema for constructing nonstationary methods with a preliminary chosen speed of convergence. Description: This paper is partially supported by project ISM-4 of Department for Scientific Research, “Paisii Hilendarski” University of Plovdiv. URI: http://hdl.handle.net/10525/364 ISSN: 1312-6555 Appears in Collections: Volume 3 Number 1

Files in This Item:

File Description SizeFormat


text:
Recently Updated
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9
It would be a nice addition if telerik test studio (+scheduler service) was able to also record fullscreen video (swf/mp4 etc) of any failed tests.

I currently have implemented a DIY IExecutionExtension plugin that takes care of this.

It works quite nicely.

How it works ?
Upon test-start it will initiate a fullscreen recording using the SDK from techsmith (Jing SWF video recorder.dll).
It will then record a video until the test finishes.
If the test fails it will keep the video, if the test succeeded the video will be discarded.

failed tests are saved in this file naming pattern:
[user defineable path]+[testname]+date.swf
example:
C:\temp\DMS - 2013-06-04.09.19.swf

failed tests within testlists are saved in this file naming pattern:
[user defineable path]+[testlist name]+date \ [testname]+date.swf
example:
c:\temp\IsAlive test - critical sites - 2013-06-06.09.27\Log ind på Agromarkets.dk - 2013-06-06.09.29.swf

I have then shared the c:\temp folder and modified the schedulers email layout to include this path.
So any testers can easily watch those videos and see what happens just prior to the failure.

Any chance of having some builtin feature like this in telerik would be awesome and an alternative to the normal screen capture features that we already have ?
My custom plugin works nicely and it should make our team here able to more quickly be able to identify why a given test fails. Sometimes those stacktraces are a bit voodo for non coders :)

regards and thanks for listening :)
Elo
Completed
1
Please add ability to databind the data in the content of the HTTP request.
Completed
3
We are using Mercurial source control over Bitbucket, and would like to somehow integrate that with Test Studio.
Completed
0
Please add an ability to select all records from Manage Results dialog and delete them.
Completed
2
Some J2EE will put the session ID in the main part of the URL for example:

Notice how it starts with a ; and is a key/value format. Test Studio sees it as one long URL, will record and play it back in a load test exactly like that. It does not recognize jsessionid as a dynamic target. It would be helpful if Test Studio was capable of handling dynamic URL's like this.
Completed
18
In certain HTML pages the API call Control.Refresh(); may return the wrong element. Here's a sample HTML to reproduce the problem:

<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">

<meta http-equiv="content-type" content="text/html; charset=utf-8" />

Sample page with Duplicate controls ID's

Item0

Item1

Item2

Item3

Item4

Item5

Here is framework code that demonstrates the problem:
string localPageIE = @"C:\Users\gibson\Documents\Support Issues\DuplicateID.html";
Manager.Current.LaunchNewBrowser(BrowserType.InternetExplorer);
Manager.Current.ActiveBrowser.NavigateTo(localPageIE);

// get all anchors from second (visible) panel

// get second item from collection to demonstrate issue

Expected: Both lines written to the log to be identical
Actual:
[Trace] : Requested Anchor: innerText - [Item3], tagIndex - [3]
[Trace] : Requested Anchor: innerText - [Item0], tagIndex - [0]
Completed
3
There are many applications (espcially common in CRM applications) which open popup windows in which the URL is the same as the parent window. The web server keeps track of the different windows using cookies or some other similar piece of data. Currently Test Studio cannot automate this scenario. It requires the URL of each browser window to be unique in order to detect the correct window in the "Connect to popup" window step.

Some ideas how to solve this include:
1) Ignore windows that Test Studio is already connected to
2) Look for some timer for how long the window has been open. Skip those longer than 30 seconds.
Declined
0
Automate conversion of Test Studio Standalone test lists to Visual Studio 2010 test list format to ease execution with MSTest and further automate CI build processes.
Approved
0

Create folder hierarchy in {project}\Data\ folder to organize the external data sources.
For example:

{project}\Data\UserData\abc.csv

{project}\Data\CompanyData\def.csv

Completed
0

in some cases when load run with profiling is triggered, randomly null data is returned that cannot be serialized and serialization exception is thrown in log and load result reports wrong default data

2019.1.307 LIB

Won't Fix
0
Connecting to pop-up is successful. Using coded step and activebrowser.navigateto(url) to some specific url i.e. "http://www.google.com" results in a "Wait for condition has timed out" error.

Full error description:
System.TimeoutException: Wait for condition has timed out
at ArtOfTest.Common.WaitSync.CheckResult(WaitSync wait, String extraExceptionInfo, Object target)
at ArtOfTest.Common.WaitSync.For[T](Predicate1 predicate, T target, Boolean invertCondition, Int32 timeout, WaitResultType errorResultType)
at ArtOfTest.Common.WaitSync.For[T](Predicate1 predicate, T target, Boolean invertCondition, Int32 timeout)
at ArtOfTest.WebAii.Core.Browser.ExecuteCommand(BrowserCommand request, Boolean performDomRefresh, Boolean waitUntilReady)
at ArtOfTest.WebAii.Core.Browser.ExecuteCommand(BrowserCommand request)
at ArtOfTest.WebAii.Core.Browser.InternalNavigateTo(Uri uri, Boolean useDecodedUrl)
at ArtOfTest.WebAii.Core.Browser.NavigateTo(Uri uri, Boolean useDecodedUrl)

Why, because page loads successfully?
Pending Review
0
It will be useful to explicitly ignore the certificate check for  explicitly ignore the certificate check for unfinished internal applications.
Approved
0

I'm unable to shrink the width of the Test Explorer and Element Explorer.

In the attached file I'm unable to move the bar (highlighted with the red line) at all to the left.

I'd like to be able to shrink the width to the left, as both panes take up more room than necessary.

(SIDE NOTE: For some reason, the required "Version" drop-down only gave me versions way back to 2014. I'm on 2019.1.212.0)

Pending Review
0

Hi

I have some databound parrent tests.

For these I have created seperate sheets in my excel, to ensure my part test are working i switch their databinding between the sheets to ensure them working in all environments.

Everytime i rebind a test the excel file gets corrupted! I have to restart the computer and then it works again… What is the fix for this?

I have attached an example of being unable to open the excel document!

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The 'new' Element Edit window does not extend into the entire frame, when there is no recorder attached and suggestions are empty.
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Changing the DPI settings to 125%, for example, on Windows 7 causes troubles with the Desktop clicks when running tests against Chrome. The click is below or above the target element. Highlighting in record mode may also be affected.

Workaround: As a workaround the Desktop clicks (MouseClick() method) can be replaced with the Click() method, which works as expected. The alternative in a non-coded solution is to disable the 'SimulateRealClick' option for the click steps.

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In VS 2010 and VS 2008 there was the Test View. From there you can get at a number of Test Studio specific test level settings, such as BrowserType, SilverlightEnabled, etc. There appears to be no equivalent in VS 2012. Test View has been replaced with a Test Explorer, but clicking on a test in Test Explorer does not bring up any test properties. As a result it appears you have no method to get at the Test Studio specific settings in VS 2012.
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In VS2010, "this.ExecutionContext.DeploymentDirectory" returns the path to the default deployment directory. In VS2012 however, there is no such default directory and same property returns the path to the project folder. This is really confusing for our customers and we need to either change the implementation or remove that property completely.

Again another item I have discussed, I operate in a Closed network environment and access to the VU's via the current online validation method does not work. The guys have been great to offer me the option of a specific build but maybe how licenses are validated could be changed to allow for this type of working environment ? - its the only tool I have ever had a problem doing this with.
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# I have to triple the amount of vertices in my buffer??

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ok...here is a sample portion of the ASE file format...more specifically the vertex, face and texture data: (dont worry my problem is down at the bottom somewhere..i just wanted to give some info) *MESH_NUMVERTEX 8 *MESH_NUMFACES 12 *MESH_VERTEX_LIST { *MESH_VERTEX 0 -19.6749 -20.4781 -16.9385 *MESH_VERTEX 1 19.9857 -20.4781 -16.9385 *MESH_VERTEX 2 -19.6749 20.2262 -16.9385 *MESH_VERTEX 3 19.9857 20.2262 -16.9385 *MESH_VERTEX 4 -19.6749 -20.4781 16.4599 *MESH_VERTEX 5 19.9857 -20.4781 16.4599 *MESH_VERTEX 6 -19.6749 20.2262 16.4599 *MESH_VERTEX 7 19.9857 20.2262 16.4599 } *MESH_NUMTVERTEX 12 *MESH_TVERTLIST { *MESH_TVERT 0 0.0000 0.0000 0.0000 *MESH_TVERT 1 1.0000 0.0000 0.0000 *MESH_TVERT 2 0.0000 1.0000 0.0000 *MESH_TVERT 3 1.0000 1.0000 0.0000 *MESH_TVERT 4 0.0000 0.0000 0.0000 *MESH_TVERT 5 1.0000 0.0000 0.0000 *MESH_TVERT 6 0.0000 1.0000 0.0000 *MESH_TVERT 7 1.0000 1.0000 0.0000 *MESH_TVERT 8 0.0000 0.0000 0.0000 *MESH_TVERT 9 1.0000 0.0000 0.0000 *MESH_TVERT 10 0.0000 1.0000 0.0000 *MESH_TVERT 11 1.0000 1.0000 0.0000 } *MESH_NUMTVFACES 12 *MESH_TFACELIST { *MESH_TFACE 0 9 11 10 *MESH_TFACE 1 10 8 9 *MESH_TFACE 2 8 9 11 *MESH_TFACE 3 11 10 8 *MESH_TFACE 4 4 5 7 *MESH_TFACE 5 7 6 4 *MESH_TFACE 6 0 1 3 *MESH_TFACE 7 3 2 0 *MESH_TFACE 8 4 5 7 *MESH_TFACE 9 7 6 4 *MESH_TFACE 10 0 1 3 *MESH_TFACE 11 3 2 0 } Ok...the first chunk is the vertex coordinate data...the second part is the texture coordinate data, and the third part is the indices for the texture coordinates corresponding to the faces...i left out the index buffer part because it was ugly and not super relavent to my problem. Now then, as you can see there are more texture coordinates than there are vertices...this is the first thing that is confusing...after much debate i decided that the best course of action would be to just increase the number of vertices that i have, this would triple the amount and I would have tons of repeats...but at least my texture would display correctly. I wrote the code to parse the last two sections not thinking I would have to much of a problem when it dawned on me that adding more vertices would really screw up my index buffer...does anyone know how i could index these new vertices correctly? Or better yet a way that i could maintain the original number of vertices and still have the texture render correctly. I dont want to have to mess with changing the vertex buffer to much because that would slow things down a lot, so rendering faces one at a time is out....any ideas? suggestions? anything at all would be very helpful! thanks

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It sounds like you should have two index lists in your ASE file: one giving the vertex position indices for each face vertex, and another giving the texture coordinate indices for each face vertex.

You don't need an index buffer, you only need a vertex buffer. Create (3 * numFaces) vertices, then copy the position and uv data into these:

  void SetVertices (    const unsigned int numFaces, // 12    const unsigned int* const* const posIndices, // [12][3]    const D3DXVECTOR3* const pos, // [8]    const unsigned int* const* const uvIndices, // [12][3]    const D3DXVECTOR2* const uv, // [12]    Vertex* const verts) // [36]{    for (unsigned int face = 0; face < numFaces; ++face)    {        for (unsigned int i = 0; i < 3; ++i)        {            Vertex& vert = verts[(3 * face) + i];            vert.pos = pos[posIndices[face][i]];            vert.uv = uv[uvIndices[face][i]];        }    }}

It's unlikely that you can do much better than this for a cube. For larger and complex models, it's usually worth welding vertices and indexing into the resulting smaller set. You can do this yourself or use D3DXWeldVertices if you prefer.

[edited by - Osc on March 6, 2003 12:11:44 PM]

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# Hamiltonian matrix

In mathematics, a Hamiltonian matrix is a 2n-by-2n matrix A such that JA is symmetric, where J is the skew-symmetric matrix

${\displaystyle J={\begin{bmatrix}0&I_{n}\\-I_{n}&0\\\end{bmatrix}}}$

and In is the n-by-n identity matrix. In other words, A is Hamiltonian if and only if (JA)T = JA where ()T denotes the transpose.[1]

## Properties

Suppose that the 2n-by-2n matrix A is written as the block matrix

${\displaystyle A={\begin{bmatrix}a&b\\c&d\end{bmatrix}}}$

where a, b, c, and d are n-by-n matrices. Then the condition that A be Hamiltonian is equivalent to requiring that the matrices b and c are symmetric, and that a + dT = 0.[1][2] Another equivalent condition is that A is of the form A = JS with S symmetric.[2]:34

It follows easily from the definition that the transpose of a Hamiltonian matrix is Hamiltonian. Furthermore, the sum (and any linear combination) of two Hamiltonian matrices is again Hamiltonian, as is their commutator. It follows that the space of all Hamiltonian matrices is a Lie algebra, denoted sp(2n). The dimension of sp(2n) is 2n2 + n. The corresponding Lie group is the symplectic group Sp(2n). This group consists of the symplectic matrices, those matrices A which satisfy ATJA = J. Thus, the matrix exponential of a Hamiltonian matrix is symplectic. However the logarithm of a symplectic matrix is not necessarily Hamiltonian because the exponential map from the Lie algebra to the group is not surjective.[2]:34–36[3]

The characteristic polynomial of a real Hamiltonian matrix is even. Thus, if a Hamiltonian matrix has λ as an eigenvalue, then −λ, λ* and −λ* are also eigenvalues.[2]:45 It follows that the trace of a Hamiltonian matrix is zero.

The square of a Hamiltonian matrix is skew-Hamiltonian (a matrix A is skew-Hamiltonian if (JA)T = −JA). Conversely, every skew-Hamiltonian matrix arises as the square of a Hamiltonian matrix.[4]

## Extension to complex matrices

The definition for Hamiltonian matrices can be extended to complex matrices in two ways. One possibility is to say that a matrix A is Hamiltonian if (JA)T = JA, as above.[1][4] Another possibility is to use the condition (JA)* = JA where ()* denotes the conjugate transpose.[5]

## Hamiltonian operators

Let V be a vector space, equipped with a symplectic form Ω. A linear map ${\displaystyle A:\;V\mapsto V}$ is called a Hamiltonian operator with respect to Ω if the form ${\displaystyle x,y\mapsto \Omega (A(x),y)}$ is symmetric. Equivalently, it should satisfy

${\displaystyle \Omega (A(x),y)=-\Omega (x,A(y))}$

Choose a basis e1, …, e2n in V, such that Ω is written as ${\displaystyle \sum _{i}e_{i}\wedge e_{n+i}}$. A linear operator is Hamiltonian with respect to Ω if and only if its matrix in this basis is Hamiltonian.[4]

## References

1. ^ a b c Ikramov, Khakim D. (2001), "Hamiltonian square roots of skew-Hamiltonian matrices revisited", Linear Algebra and its Applications, 325: 101–107, doi:10.1016/S0024-3795(00)00304-9.
2. ^ a b c d Meyer, K. R.; Hall, G. R. (1991), Introduction to Hamiltonian dynamical systems and the N-body problem, Springer, ISBN 0-387-97637-X.
3. ^ Dragt, Alex J. (2005), "The symplectic group and classical mechanics", Annals of the New York Academy of Sciences, 1045 (1): 291–307, doi:10.1196/annals.1350.025, PMID 15980319.
4. ^ a b c Waterhouse, William C. (2005), "The structure of alternating-Hamiltonian matrices", Linear Algebra and its Applications, 396: 385–390, doi:10.1016/j.laa.2004.10.003.
5. ^ Paige, Chris; Van Loan, Charles (1981), "A Schur decomposition for Hamiltonian matrices", Linear Algebra and its Applications, 41: 11–32, doi:10.1016/0024-3795(81)90086-0.


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# How are UMIs used to dedupulicate in Drop-seq tools?

The module DigitalExpression which is part of the popular Drop-seq tools digitally count gene transcripts.

The manual is not very clear on how exactly it resolves the UMI information. Maybe I'm missing something but I was wondering if UMI are used in isolation or in conjunction with the barcode and or transcript?

The manual i.e. Drop-seq Alignment Cookbook only states:

To digitally count gene transcripts, a list of UMIs in each gene, within each cell, is assembled, and UMIs
within edit distance = 1 are merged together. The total number of unique UMI sequences is counted,
and this number is reported as the number of transcripts of that gene for a given cell.

To clarify my point, I'll use an example. Say my reads are only 4 bp and read 1 has the cell barcode at position 1+2 and UMI at position 3+4. read 2 constitutes the transcript read.

seqence1:   read1 = AATT  read2 = ATGC

UMI and barcode are the same but read2 is different, would they be collapsed to 1 UMI count or 2?

Similarly as case with same UMI and transcript but different cell barcode:

seqence1:   read1 = AATT  read2 = ATGC

Also of note, UMI deduplication is the default setting as of the parameter below:

OUTPUT_READS_INSTEAD=Boolean  Output number of reads instead of number of unique molecular barcodes.  Default value:
false. This option can be set to 'null' to clear the default value. Possible values:
{true, false}

UMI and barcode are the same but read2 is different, would they be collapsed to 1 UMI count or 2?

If the two reads share cell barcodes and UMI sequences and align to the same gene, (even if they are different sequences) then they originate from the same RNA molecule, and should only count as 1.

https://support.10xgenomics.com/single-cell-gene-expression/library-prep/doc/user-guide-chromium-single-cell-3-reagent-kits-user-guide-v3-chemistry

• Do you have any sources (documentation, code, citation etc) to back this up? To my knowledge the UMI is designed to spot PCR duplicates, so read 2 shouldn't have a different sequence (unless there are sequencing errors). – Sebastian Müller Jul 10 '19 at 6:51
• If you look up the library prep protocol, you can see that cDNA amplification happens before fragmentation. Therefore, you can have multiple reads starting at different fragmentation points which nevertheless originate from the same mRNA molecule. It's also quite plain from looking at the UMI counts output and bam output that all reads with the same gene ID, UMI and cell barcode are marked as duplicates save one, even if the reads aligned to different places in the transcript, and that only the one not marked as a duplicate is being counted in the final UMI count – swbarnes2 Jul 10 '19 at 16:22
• Thanks. I Just had another look and this appears to be indeed the case, also for other drop-seq protocols apart from 10x. To however accept this as an answer, the only thing missing is if DropSeq-tools is doing the right thing by default or if this can be adjusted that way? The docu is surprisingly unclear about this important point. – Sebastian Müller Jul 12 '19 at 8:03
• It's been a while since I looked at DropSeq data, or its library prep protocol, but one has to presume that the Drop-Seq cookbook protocol handles DropSeq data correctly. The description cited does seem to indicate that all the reads aligning to a gene are assessed for UMIs, not just all the reads aligning to a particular position. However, I have in the past run the same Drop-Seq data set through the cookbook and (with some manipulation) through 10XGenomics cellranger, and I got very nearly the same results. – swbarnes2 Jul 12 '19 at 15:52
• To confirm if this is correct, I've just submitted an issue – Sebastian Müller Jul 13 '19 at 11:53

The code does EXACTLY what it says in the first quote.

Let's say you have 5 reads on a cell barcode that align to gene A. Those reads have the following molecular barcodes:

AAAA,BBBB,AAAA,CCCC,DDDD.

There are 4 UNIQUE molecular barcodes.

The only complication to this is that we collapse barcodes with an edit distance of 1, which takes care of over-inflation of UMI counts due to PCR/Sequencing errors. If we added a barcode with the sequence AAAB to the original list, it would be collapsed into AAAA as it has an edit distance of 1, and you'd still have 4 unique molecular barcodes.

• In retrospect, the quote makes now sense, I was a bit confused what assembled exactly meant in this context, also the additional rational from swbarnes2 about the fragmentation taken place after PCR now explains why it is done this way (hence the accepted answer). Maybe this could be included in the documentation as explanation? – Sebastian Müller Jul 15 '19 at 12:54