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Home

#### Integration by Parts

Integration by Parts
Examples
Integration by Parts with a definite integral
Going in Circles

#### Integrals of Trig Functions

Antiderivatives of Basic Trigonometric Functions
Product of Sines and Cosines (mixed even and odd powers or only odd powers)
Product of Sines and Cosines (only even powers)
Product of Secants and Tangents
Other Cases

#### Trig Substitutions

How Trig Substitution Works
Summary of trig substitution options
Examples
Completing the Square

#### Partial Fractions

Introduction to Partial Fractions
Linear Factors
Improper Rational Functions and Long Division
Summary

#### Strategies of Integration

Substitution
Integration by Parts
Trig Integrals
Trig Substitutions
Partial Fractions

#### Improper Integrals

Type 1 - Improper Integrals with Infinite Intervals of Integration
Type 2 - Improper Integrals with Discontinuous Integrands
Comparison Tests for Convergence

#### Modeling with Differential Equations

Introduction
Separable Equations
A Second Order Problem

#### Euler's Method and Direction Fields

Direction Fields
Euler's method revisited

#### Separable Equations

The Simplest Differential Equations
Separable differential equations
Mixing and Dilution

#### Models of Growth

Exponential Growth and Decay
The Zombie Apocalypse (Logistic Growth)

#### Linear Equations

Linear ODEs: Working an Example
The Solution in General
Saving for Retirement

#### Parametrized Curves

Three kinds of functions, three kinds of curves
The Cycloid
Visualizing Parametrized Curves
Tracing Circles and Ellipses
Lissajous Figures

#### Calculus with Parametrized Curves

Video: Slope and Area
Video: Arclength and Surface Area
Summary and Simplifications
Higher Derivatives

#### Polar Coordinates

Definitions of Polar Coordinates
Graphing polar functions
Video: Computing Slopes of Tangent Lines

#### Areas and Lengths of Polar Curves

Area Inside a Polar Curve
Area Between Polar Curves
Arc Length of Polar Curves

#### Conic sections

Slicing a Cone
Ellipses
Hyperbolas
Parabolas and Directrices
Shifting the Center by Completing the Square

#### Conic Sections in Polar Coordinates

Foci and Directrices
Visualizing Eccentricity
Astronomy and Equations in Polar Coordinates

#### Infinite Sequences

Examples of Infinite Sequences
Limit Laws for Sequences
Theorems for and Examples of Computing Limits of Sequences
Monotonic Covergence

#### Infinite Series

Introduction
Geometric Series
Limit Laws for Series
Test for Divergence and Other Theorems
Telescoping Sums

#### Integral Test

Preview of Coming Attractions
The Integral Test
Estimates for the Value of the Series

#### Comparison Tests

The Basic Comparison Test
The Limit Comparison Test

#### Convergence of Series with Negative Terms

Introduction, Alternating Series,and the AS Test
Absolute Convergence
Rearrangements

The Ratio Test
The Root Test
Examples

#### Strategies for testing Series

Strategy to Test Series and a Review of Tests
Examples, Part 1
Examples, Part 2

#### Power Series

Finding the Interval of Convergence
Power Series Centered at $x=a$

#### Representing Functions as Power Series

Functions as Power Series
Derivatives and Integrals of Power Series
Applications and Examples

#### Taylor and Maclaurin Series

The Formula for Taylor Series
Taylor Series for Common Functions
Adding, Multiplying, and Dividing Power Series
Miscellaneous Useful Facts

#### Applications of Taylor Polynomials

Taylor Polynomials
When Functions Are Equal to Their Taylor Series
When a Function Does Not Equal Its Taylor Series
Other Uses of Taylor Polynomials

#### Functions of 2 and 3 variables

Functions of several variables
Limits and continuity

#### Partial Derivatives

One variable at a time (yet again)
Definitions and Examples
An Example from DNA
Geometry of partial derivatives
Higher Derivatives
Differentials and Taylor Expansions

#### Differentiability and the Chain Rule

Differentiability
The First Case of the Chain Rule
Chain Rule, General Case
Video: Worked problems

#### Multiple Integrals

General Setup and Review of 1D Integrals
What is a Double Integral?
Volumes as Double Integrals

#### Iterated Integrals over Rectangles

How To Compute Iterated Integrals
Examples of Iterated Integrals
Fubini's Theorem
Summary and an Important Example

#### Double Integrals over General Regions

Type I and Type II regions
Examples 1-4
Examples 5-7
Swapping the Order of Integration
Area and Volume Revisited

#### Double integrals in polar coordinates

dA = r dr (d theta)
Examples

#### Multiple integrals in physics

Double integrals in physics
Triple integrals in physics

#### Integrals in Probability and Statistics

Single integrals in probability
Double integrals in probability

#### Change of Variables

Review: Change of variables in 1 dimension
Mappings in 2 dimensions
Jacobians
Examples
Bonus: Cylindrical and spherical coordinates

We begin with functions of one variable. We say a function $f(x)$ is differentiable at $x=a$ if the limit $$\lim_{x\to a} \frac{f(x)-f(a)}{x-a}$$ exists. However, the equation $$\lim_{x\to a} \frac{f(x)-f(a)}{x-a}=c$$ means exactly the same thing as $$\lim_{x \to a} \frac{f(x)-f(a)-c(x-a)}{x-a}=0.$$ In other words, a function $f(x)$ is differentiable at $a$ if and only if there is a linear function $$L(x) = f(a) + c(x-a)$$ such that $$\lim_{x \to a} \frac{f(x)-L(x)}{x-a}=0.$$ That last expression generalizes naturally to functions of two (or more) variables.

 A function $f(x,y)$ is differentiable at $(a,b)$ if there is a linear function $$L(x,y)=f(a,b) + c_1 (x-a) + c_2 (y-b)$$ such that $$\lim_{(x,y) \to (a,b)} \frac{|f(x,y)-L(x,y)|}{\|\langle x-a, y-b \rangle \|}=0.$$

You may wonder why we didn't just say `a function is differentiable at $(a,b)$ if its partial derivatives exist at $(a,b)$?' Because it isn't true! If a function is differentiable, then its partial derivatives exist (and equal $c_1$ and $c_2$), but a function can have partial derivatives without being differentiable!

 Example 1: Compute the partial derivatives of $$f(x,y) = \begin{cases} \frac{xy}{x^2+y^2} & (x,y) \ne (0,0); \cr 0 & (x,y)=(0,0). \end{cases}$$ at $(x,y)=(0,0)$. Solution: Since $f(h,0)=0$ for all $h$, $$f_x(0,0) = \lim_{h \to 0} \frac{f(h,0)-f(0,0)}{h} = \lim_{h \to 0}\frac{0}{h}=0.$$ Similarly, $f(0,h)=0$ for all $h$, so $$f_y(0,0) = \lim_{h \to 0} \frac{f(0,h)-f(0,0)}{h} = \lim_{h \to 0}\frac{0}{h}=0.$$

 Example 2: Is $$f(x,y) = \begin{cases} \frac{xy}{x^2+y^2} & (x,y) \ne (0,0); \cr 0 & (x,y)=(0,0). \end{cases}$$ differentiable at $(x,y)=(0,0)$? Solution: No. $f(x,y)$ isn't even continuous at $(x,y)=(0,0)$, since $f(x,y)=\frac{1}{2}$ whenever $x=y\ne 0$ and $f(x,y)=\frac{-1}{2}$ whenever $x = -y \ne 0$. The function is well-behaved on the $x$-axis and the $y$-axis, so it has partial derivatives, but it behaves badly in every other direction.

So for a function to be differentiable, we need more than just the existence of partial derivatives. We need continuity of partial derivatives:

 Theorem: Suppose that $f(x,y)$ is continuous on a region $D$ containing $(a,b)$, and that $f_x$ and $f_y$ exist and are continuous on $D$. Then $f(x,y)$ is differentiable at $(a,b)$.

The composition of differentiable functions is differentiable. In particular, if $x(t)$ and $y(t)$ are differentiable functions of a parameter $t$, and if $f(x,y)$ is a differentiable function of $x$ and $y$, then $f(x(t),y(t))$ is a differentiable function of $t$. In the next slide, we'll compute its derivative.


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## Human identifier associated with a wallet

-1

I know that, strong anonymity is one of the important aspects of Bitcoin; however, the mandate for us is clear. For audit purposes, we need to be able to prove that, the buyer's name in the web form exactly matches with the name associated with the payment instrument. When paying with BTC, it means, every address used to make a payment should be co-related with an human identifier e.g. name, passport number, etc.

Is there a wallet provider who exposes an API responding with a simple true or a false when the wallet identifier, address and human identifiers are passed as input?

"the mandate for us is clear. For audit purposes, we need to be able to prove that, the buyer's name in the web form exactly matches with the name associated with the payment instrument." If this is the case, then BitCoin is not an appropriate instrument for your transaction. – abelenky – 2017-11-21T15:54:33.993

1

When you say that the "mandate is clear for us", who is 'us'?

Bitcoin isn't designed to provide full auditable clarity on individuals using/spending it. It has pseudonimity. See conversation in link below.

https://english.stackexchange.com/q/224254

1

The way you track payments is to hand out unique addresses to each customer. This way you know who to attribute payments to. However the customer could always ask someone else to pay to your address. There is no way to be sure that he made the payment himself.

format: plain


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# deviance.gl1ce

0th

Percentile

##### Deviance Method for gl1ce' Objects

This is a method of the generic function deviance() for objects inheriting from class gl1ce (see help(gl1ce.object)).

Keywords
models
##### Usage
## S3 method for class 'gl1ce':
deviance(object, \dots)
deviance for the general behavior of this function and for the interpretation of object`.


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# Properties

 Modulus $2100$ Structure $$C_{60}\times C_{2}\times C_{2}\times C_{2}$$ Order $480$

# Learn more about

Show commands for: Pari/GP / SageMath

sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed

sage: H = DirichletGroup_conrey(2100)

pari: g = idealstar(,2100,2)

## Character group

 sage: G.order()  pari: g.no Order = 480 sage: H.invariants()  pari: g.cyc Structure = $$C_{60}\times C_{2}\times C_{2}\times C_{2}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{2100}(2077,\cdot)$, $\chi_{2100}(349,\cdot)$, $\chi_{2100}(701,\cdot)$, $\chi_{2100}(1051,\cdot)$

## First 32 of 480 characters

Each row describes a character. When available, the columns show the orbit label, order of the character, whether the character is primitive, and several values of the character.

Character Orbit Order Primitive $$-1$$ $$1$$ $$11$$ $$13$$ $$17$$ $$19$$ $$23$$ $$29$$ $$31$$ $$37$$ $$41$$ $$43$$
$$\chi_{2100}(1,\cdot)$$ 2100.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{2100}(11,\cdot)$$ 2100.dd 30 yes $$1$$ $$1$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$-1$$
$$\chi_{2100}(13,\cdot)$$ 2100.co 20 no $$1$$ $$1$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$i$$
$$\chi_{2100}(17,\cdot)$$ 2100.dm 60 no $$-1$$ $$1$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{7}{60}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{59}{60}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{11}{60}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$-i$$
$$\chi_{2100}(19,\cdot)$$ 2100.cy 30 no $$1$$ $$1$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$1$$
$$\chi_{2100}(23,\cdot)$$ 2100.dq 60 yes $$-1$$ $$1$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{59}{60}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{43}{60}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{37}{60}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$-i$$
$$\chi_{2100}(29,\cdot)$$ 2100.ca 10 no $$-1$$ $$1$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$-1$$
$$\chi_{2100}(31,\cdot)$$ 2100.da 30 no $$1$$ $$1$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$-1$$
$$\chi_{2100}(37,\cdot)$$ 2100.dp 60 no $$-1$$ $$1$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{11}{60}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{37}{60}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{43}{60}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$-i$$
$$\chi_{2100}(41,\cdot)$$ 2100.cb 10 no $$1$$ $$1$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$1$$
$$\chi_{2100}(43,\cdot)$$ 2100.t 4 no $$1$$ $$1$$ $$-1$$ $$i$$ $$-i$$ $$1$$ $$-i$$ $$-1$$ $$-1$$ $$-i$$ $$1$$ $$-i$$
$$\chi_{2100}(47,\cdot)$$ 2100.do 60 yes $$1$$ $$1$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{23}{60}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{1}{60}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{19}{60}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$i$$
$$\chi_{2100}(53,\cdot)$$ 2100.dk 60 no $$1$$ $$1$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{43}{60}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{41}{60}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{29}{60}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$i$$
$$\chi_{2100}(59,\cdot)$$ 2100.de 30 yes $$-1$$ $$1$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$1$$
$$\chi_{2100}(61,\cdot)$$ 2100.dg 30 no $$-1$$ $$1$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$1$$
$$\chi_{2100}(67,\cdot)$$ 2100.dn 60 no $$1$$ $$1$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{7}{60}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{59}{60}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{11}{60}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$i$$
$$\chi_{2100}(71,\cdot)$$ 2100.br 10 no $$1$$ $$1$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$-1$$
$$\chi_{2100}(73,\cdot)$$ 2100.dr 60 no $$1$$ $$1$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{19}{60}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{23}{60}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{17}{60}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$i$$
$$\chi_{2100}(79,\cdot)$$ 2100.cz 30 no $$-1$$ $$1$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$1$$
$$\chi_{2100}(83,\cdot)$$ 2100.cp 20 yes $$1$$ $$1$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$-i$$
$$\chi_{2100}(89,\cdot)$$ 2100.cv 30 no $$1$$ $$1$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$-1$$
$$\chi_{2100}(97,\cdot)$$ 2100.co 20 no $$1$$ $$1$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$-i$$
$$\chi_{2100}(101,\cdot)$$ 2100.bi 6 no $$1$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$-1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$-1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$1$$ $$1$$
$$\chi_{2100}(103,\cdot)$$ 2100.dl 60 no $$-1$$ $$1$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{23}{60}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{1}{60}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{49}{60}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$-i$$
$$\chi_{2100}(107,\cdot)$$ 2100.cf 12 no $$-1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$-i$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$-1$$ $$i$$
$$\chi_{2100}(109,\cdot)$$ 2100.dh 30 no $$1$$ $$1$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$-1$$
$$\chi_{2100}(113,\cdot)$$ 2100.ct 20 no $$1$$ $$1$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$i$$
$$\chi_{2100}(121,\cdot)$$ 2100.cm 15 no $$1$$ $$1$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$1$$
$$\chi_{2100}(127,\cdot)$$ 2100.cs 20 no $$1$$ $$1$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$i$$
$$\chi_{2100}(131,\cdot)$$ 2100.dj 30 yes $$-1$$ $$1$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$-1$$
$$\chi_{2100}(137,\cdot)$$ 2100.dk 60 no $$1$$ $$1$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{1}{60}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{47}{60}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{23}{60}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$-i$$
$$\chi_{2100}(139,\cdot)$$ 2100.bw 10 no $$1$$ $$1$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$1$$


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## Robert J Le Roy

University of Waterloo, Canada

#### Articles in Scholarly Journals [Incomplete List]

1. Full configuration interaction calculation of the low lying valence and Rydberg states of BeH
Journal of Computational Chemistry, vol. 29, no. 4, pp. 523–532, 2008
2. A comparative study of single reference correlation methods of the coupled-pair type
Chemical Physics, vol. 343, no. 2-3, pp. 217–230, 2008
3. Accurate Kr–CO interaction potential energy surface with vibrational coordinate dependence
Chemical Physics Letters, vol. 454, no. 1-3, pp. 7–11, 2008
4. Spectroscopic characterization of the potential energy functions of Ne2 Rydberg states in the vicinity of the Ne(1S0)+Ne(4p') dissociation limits
Journal of Molecular Spectroscopy, vol. 247, no. 1, pp. 85–99, 2008
5. Potential energy function of CN-CN-
Journal of Molecular Spectroscopy, vol. 248, no. 1, pp. 77–80, 2008
6. On the Theory of Time-Resolved X-ray Diffraction
Journal of Physical Chemistry B, vol. 112, no. 2, pp. 558–567, 2008
7. Ab initio study of ground state MH2, HMHe+ and MHe22+, M = Mg, Ca
Physical Chemistry Chemical Physics, vol. 10, no. 9, p. 1285, 2008
8. Predicting the infrared transition intensities in the Ar–HF complex: The key role of the dipole moment surface accuracy
The Journal of Chemical Physics, vol. 128, no. 3, p. 034308, 2008
9. Ab initio potential energy surface and bound states of the Xe–CO complex
The Journal of Chemical Physics, vol. 128, no. 4, p. 044309, 2008
10. Valence transitions of Br[sub 2] in Ar matrices: Interaction with the lattice and predissociation
The Journal of Chemical Physics, vol. 128, no. 6, p. 064504, 2008
11. A new potential energy surface and predicted infrared spectra of He–CO[sub 2]: Dependence on the antisymmetric stretch of CO[sub 2]
The Journal of Chemical Physics, vol. 128, no. 12, p. 124323, 2008
12. Steering dissociation of Br[sub 2] molecules with two femtosecond pulses via wave packet interference
The Journal of Chemical Physics, vol. 128, no. 13, p. 134303, 2008
13. Toward accurate thermochemical models for transition metals: G3Large basis sets for atoms Sc–Zn
The Journal of Chemical Physics, vol. 128, no. 14, p. 144122, 2008
14. Pure rotational spectra of PbSe and PbTe: potential function, Born–Oppenheimer breakdown, field shift effect and magnetic shielding
Physical Chemistry Chemical Physics, vol. 10, no. 15, p. 2078, 2008
15. Long range dispersion interactions of the low lying states of Mg with H, He, Ne, Ar, Kr and Xe
Molecular Physics, vol. 106, no. 1, pp. 127–132, 2008
16. Interplay between theory and experiment in investigations of molecules embedded in superfluid helium nanodroplets
International Reviews in Physical Chemistry, vol. 27, no. 2, pp. 273–316, 2008
17. Near-threshold quantization and scattering lengths
Physical Review A, vol. 77, no. 1, 2008
18. Two-color photoassociation spectroscopy of ytterbium atoms and the precise determinations of s -wave scattering lengths
Physical Review A, vol. 77, no. 1, 2008
19. Resonant double Auger decay in carbon K -shell excitation of CO
Physical Review A, vol. 77, no. 4, 2008
20. Improved potentials and Born-Oppenheimer corrections by new measurements of transitions of 129I2 and 127I 129I  in the B3 $\Pi_{\rm O^+_u}$ - X1 $\Sigma^+_{\rm g}$ band system
The European Physical Journal D, vol. 47, no. 2, pp. 171–179, 2008
21. Combined analysis of the PFOODR data on the a 3S u + , 23?g, 23S g + , 33?g, and 43S g + states of the K2 molecule
Optics and Spectroscopy, vol. 103, no. 5, pp. 723–727, 2007
22. Correction for Triples in Reduced Multireference Coupled-Cluster Approaches
Collection of Czechoslovak Chemical Communications, vol. 72, no. 1, pp. 100–120, 2007
23. Study on the (HI)
Zeitschrift f�r Physikalische Chemie, vol. 221, no. 6, pp. 815–824, 2007
24. Laser-enhanced molecular-ionization spectrometry of BaO and LuO in low-temperature flame
Moscow University Chemistry Bulletin, vol. 62, no. 5, pp. 295–297, 2007
25. Ultracold atom-molecule collisions and bound states in magnetic fields: Tuning zero-energy Feshbach resonances in He-NH (^{3}S^{-})
Physical Review A, vol. 75, no. 2, 2007
26. Absorption spectroscopy of the rubidium dimer in an overheated vapor: An accurate check of molecular structure and dynamics
Physical Review A, vol. 75, no. 3, 2007
27. Preparation of highly polarized nuclei: Observation and control of time-dependent polarization transfer from H^{35}Cl molecular rotation to ^{35}Cl nuclear spin
Physical Review A, vol. 76, no. 1, 2007
28. Enhancement of the formation of ultracold ^{85}Rb_{2} molecules due to resonant coupling
Physical Review A, vol. 76, no. 2, 2007
29. Absolute cross sections and kinetic energy release for doubly and triply charged fragments produced by electron impact on CO +
Journal of Physics B: Atomic, Molecular and Optical Physics, vol. 40, no. 1, pp. 85–100, 2007
30. Experimental evidence for an isotopic effect in the formation of ultracold ground-state rubidium dimers
Journal of Physics B: Atomic, Molecular and Optical Physics, vol. 40, no. 16, pp. 3283–3293, 2007
31. Ab initio calculation on accurate analytic potential energy functions and harmonic frequencies of c3?g+ and B1?u states of dimer 7Li2
Chinese Physics, vol. 16, no. 8, pp. 2371–2377, 2007
32. Ab initio calculations on the a3S+u state properties of dimer 7Li2
Chinese Physics, vol. 16, no. 9, pp. 2701–2708, 2007
33. Molecular collisions in ultracold atomic gases
International Reviews in Physical Chemistry, vol. 26, no. 1, pp. 1–28, 2007
34. Potential energy surfaces and predicted infrared spectra for van der Waals complexes: dependence on one intramolecular vibrational coordinate
International Reviews in Physical Chemistry, vol. 26, no. 3, pp. 487–520, 2007
35. Magnesium Isotopes in Metal-poor Dwarfs: The Rise of AGB Stars and the Formation Timescale of the Galactic Halo
The Astrophysical Journal, vol. 659, no. 1, pp. L25–L28, 2007
36. Accurate ab initio-based molecular potentials: from extrapolation methods to global modelling
Physica Scripta, vol. 76, no. 3, pp. C28–C35, 2007
37. A new potential function form incorporating extended long-range behaviour: application to ground-state Ca2
Molecular Physics, vol. 105, no. 5, pp. 663–677, 2007
38. Metastable rovibrational f-symmetry levels of the I 1?g state of H2, HD and D2: experiment and theory
Molecular Physics, vol. 105, no. 11, pp. 1643–1651, 2007
39. An isotopic error compensation method for rovibrational spectra of isotopic diatomic molecules
Molecular Physics, vol. 105, no. 17, pp. 2289–2303, 2007
40. Nuclear electric quadrupole moment of gold
The Journal of Chemical Physics, vol. 126, no. 6, p. 064314, 2007
41. Experimental Vibrational Zero-Point Energies: Diatomic Molecules
Journal of Physical and Chemical Reference Data, vol. 36, no. 2, p. 389, 2007
42. The rotational spectra, potential function, Born-Oppenheimer breakdown, and magnetic shielding of SnSe and SnTe
The Journal of Chemical Physics, vol. 126, no. 11, p. 114305, 2007
43. Ab initio calculation of the electronic structures of the [sup 3]F ground and [sup 5]F excited states of CoH
The Journal of Chemical Physics, vol. 126, no. 14, p. 144307, 2007
44. A full analytic potential energy curve for the a [sup 3]Σ[sup +] state of KLi from a limited vibrational data set
The Journal of Chemical Physics, vol. 126, no. 19, p. 194313, 2007
45. Photodissociation of gas-phase I[sub 3][sup -]: Comprehensive understanding of nonadiabatic dissociation dynamics
The Journal of Chemical Physics, vol. 126, no. 20, p. 204311, 2007
46. An ab initio study of the CH[sub 3]I photodissociation. II. Transition moments and vibrational state control of the I[sup
The Journal of Chemical Physics, vol. 126, no. 23, p. 234103, 2007
47. Calculations of the ground states of BeH and BeH[sup +] without the Born-Oppenheimer approximation
The Journal of Chemical Physics, vol. 126, no. 21, p. 214305, 2007
48. Geminal model chemistry III: Partial spin restriction
The Journal of Chemical Physics, vol. 126, no. 23, p. 234112, 2007
49. New spectroscopic data, spin-orbit functions, and global analysis of data on the A [sup 1]S[sub u][sup +] and b [sup 3]?[sub u] states of Na[sub 2]
The Journal of Chemical Physics, vol. 127, no. 4, p. 044301, 2007
50. Interactions and dynamics in Li+Li[sub 2] ultracold collisions
The Journal of Chemical Physics, vol. 127, no. 7, p. 074302, 2007
51. Accuracy of recent potential energy surfaces for the He–N[sub 2] interaction. I. Virial and bulk transport coefficients
The Journal of Chemical Physics, vol. 127, no. 5, p. 054302, 2007
52. Optical control of ground-state atomic orbital alignment: Cl([sup 2]P[sub 3/2]) atoms from HCl(v=2,J=1) photodissociation
The Journal of Chemical Physics, vol. 127, no. 14, p. 144307, 2007
53. Hg+Br?HgBr recombination and collision-induced dissociation dynamics
The Journal of Chemical Physics, vol. 127, no. 16, p. 164304, 2007
54. Interaction of CO with Kr: Potential energy surface and bound states
The Journal of Chemical Physics, vol. 127, no. 17, p. 174301, 2007
55. Photodissociation spectroscopy of stored CH[sup +] and CD[sup +] ions: Analysis of the b [sup 3]S[sup -]-a [sup 3]? system
The Journal of Chemical Physics, vol. 127, no. 20, p. 204304, 2007
56. Accurate ab initio potential energy curve of F[sub 2]. I. Nonrelativistic full valence configuration interaction energies using the correlation energy extrapolation by intrinsic scaling method
The Journal of Chemical Physics, vol. 127, no. 16, p. 164317, 2007
57. The B [sup 1]? state of NaCs: High resolution laser induced fluorescence spectroscopy and potential construction
The Journal of Chemical Physics, vol. 127, no. 22, p. 224302, 2007
58. Accurate ab initio potential energy curve of F[sub 2]. III. The vibration rotation spectrum
The Journal of Chemical Physics, vol. 127, no. 20, p. 204313, 2007
59. The mechanism of H-bond rupture: the vibrational pre-dissociation of C2H2–HCl and C2H2–DCl
Physical Chemistry Chemical Physics, vol. 9, no. 47, p. 6241, 2007
60. Adiabatic and non-adiabatic corrections to rovibrational energies of diatomic molecules: variational calculations with experimental accuracy
Physical Chemistry Chemical Physics, vol. 9, no. 20, p. 2538, 2007
61. Theoretical study of the ArH+ photodissociation
Physical Chemistry Chemical Physics, vol. 9, no. 37, p. 5088, 2007
62. Ground State Potential Energy Curve and Dissociation Energy of MgH
Journal of Physical Chemistry A, vol. 111, no. 49, pp. 12495–12505, 2007
63. Unraveling Excited States of Doped Helium Clusters
Journal of Physical Chemistry A, vol. 111, no. 49, pp. 12749–12753, 2007
64. Interactions in Diatomic Dimers Involving Closed-Shell Metals
Journal of Physical Chemistry A, vol. 111, no. 49, pp. 12822–12838, 2007
65. Vibrational Energy Relaxation Rates of H2 and D2 in Liquid Argon via the Linearized Semiclassical Method
Journal of Physical Chemistry A, vol. 111, no. 3, pp. 460–467, 2007
66. Computational Spectroscopy of Carbon Monoxide Isotopomers in Helium Clusters
Journal of Physical Chemistry A, vol. 111, no. 31, pp. 7640–7645, 2007
67. Mass-Resolved Resonance Enhanced Ionization Study of Complicated Excited Electronic States of Rb2 near 430 nm and Their Predissociation Dynamics
Journal of Physical Chemistry A, vol. 111, no. 46, pp. 11750–11758, 2007
68. The pure rotational spectrum of ZnCl (X2S+): Variations in zinc halide bonding
Journal of Molecular Spectroscopy, vol. 244, no. 2, pp. 153–159, 2007
69. Infrared spectroscopic studies of the rare gas atom perturbed S1(0) rovibron band of solid parahydrogen
Journal of Molecular Spectroscopy, vol. 244, no. 2, pp. 138–145, 2007
70. Broadening of the R(0) and P(2) lines in the 13CO fundamental by helium atoms from 300K down to 12K: Measurements and comparison with close-coupling calculations
Journal of Molecular Spectroscopy, vol. 246, no. 1, pp. 118–125, 2007
71. New observation of the 6Li7Li33Sg+, 13?g, and 23?g states and molecular constants with all 6Li2, 7Li2, and 6Li7Li data
Journal of Molecular Spectroscopy, 2007
72. Studies on the photodissociation dynamics of HI molecule within the A band range
Chemical Physics, vol. 342, no. 1-3, pp. 119–125, 2007
73. The C1?u and 21Su+ states in Li2: Experiment and comparison with theory
Chemical Physics, vol. 333, no. 2-3, pp. 214–218, 2007
74. Negative ion photoelectron spectroscopy of copper hydrides
Chemical Physics Letters, vol. 442, no. 1-3, pp. 12–16, 2007
75. Formation of HF through radiative association in the early universe
Chemical Physics Letters, vol. 443, no. 1-3, pp. 40–42, 2007
76. Potential energy curves of the quasi-stable states of CO2+ determined using Auger spectroscopy
Chemical Physics Letters, vol. 445, no. 1-3, pp. 6–11, 2007
77. The 51?u electronic state of the lithium dimer
Chemical Physics Letters, vol. 444, no. 4-6, pp. 229–231, 2007
78. Photodissociation dynamics of HI and DI at 157nm
Chemical Physics Letters, 2007
79. Controlling the spreading of wave packets of a dissociating molecule
Chemical Physics Letters, vol. 450, no. 1-3, pp. 6–11, 2007
80. Separation ofortho- andpara-Hydrogen in Van der Waals Complex Formation
ChemPhysChem, vol. 8, no. 6, pp. 815–818, 2007
81. The photodissociation of hydrogen iodide: Is it adiabatic?
International Journal of Quantum Chemistry, vol. 107, no. 14, pp. 2665–2671, 2007
82. Tunable diode laser spectroscopy of helium clusters
Applied Physics B, vol. 90, no. 2, pp. 213–225, 2007
83. A new equation of state for rubidium vapors at temperatures up to 1600 K and pressures up to 4 MPa
High Temperature, vol. 44, no. 1, pp. 67–82, 2006
84. F + H2 ? FH + H potential energy surface: Construction of the reference configuration state function space and MR-ACPF-2 results
International Journal of Quantum Chemistry, vol. 106, no. 7, pp. 1516–1527, 2006
85. Systematic calculation of molecular vibrational spectra through a complete Morse expansion
International Journal of Quantum Chemistry, vol. 107, no. 4, pp. 782–797, 2006
86. The effect of cluster environment on a chemical reaction
Chemical Physics, vol. 328, no. 1-3, pp. 338–344, 2006
87. Application of direct potential fitting to line position data for the X1Sg+ and A1Su+ states of Li2
Journal of Molecular Spectroscopy, vol. 235, no. 2, pp. 235–247, 2006
88. Analysis of the Na2 43Sg+ state above and below the 3s+3d atomic limit
Journal of Molecular Spectroscopy, vol. 236, no. 1, pp. 35–41, 2006
89. On the X2S+, A2?, and C2S+ states of BeH, BeD, and BeT
Journal of Molecular Spectroscopy, vol. 236, no. 2, pp. 178–188, 2006
90. Near infrared emission spectra of CoH and CoD
Journal of Molecular Spectroscopy, vol. 237, no. 1, pp. 11–18, 2006
91. Multi-isotopologue analyses of new vibration–rotation and pure rotation spectra of ZnH and CdH
Journal of Molecular Spectroscopy, vol. 237, no. 1, pp. 87–96, 2006
92. Infrared combination and difference bands of the NO dimer
Journal of Molecular Spectroscopy, vol. 238, no. 1, pp. 127–134, 2006
93. Resolution of a convergence problem in direct-potential-fit data analyses: Applications to GaH(X1S+) and ArH+(X1S+)
Journal of Molecular Spectroscopy, vol. 238, no. 2, pp. 260–263, 2006
94. The breakdown of the Born–Oppenheimer approximation for protonated rare gas ions
Journal of Molecular Spectroscopy, vol. 240, no. 1, pp. 52–57, 2006
95. Isotopically invariant analysis of vibration–rotation transitions of HBr and its isotopologues
Journal of Molecular Spectroscopy, vol. 240, no. 1, pp. 69–74, 2006
96. Ab initio excitation spectrum of the CO–Ar van der Waals molecule
Journal of Molecular Structure: THEOCHEM, vol. 801, no. 1-3, pp. 1–5, 2006
97. Analytical Chemistry, vol. 78, no. 7, pp. 2382–2387, 2006
98. The pure rotational spectrum of TeSe: Rotational parameters, Born–Oppenheimer breakdown corrections, and hyperfine constants
Journal of Molecular Structure, vol. 795, no. 1-3, pp. 163–172, 2006
99. Analysis of bound-state spectra near the threshold of neutral particle interaction potentials
Physics Letters A, vol. 352, no. 1-2, pp. 133–137, 2006
100. The Journal of Physical Chemistry A, vol. 110, no. 19, pp. 6261–6270, 2006
101. Journal of Physical Chemistry A, vol. 110, no. 30, pp. 9344–9351, 2006
102. Journal of Physical Chemistry A, vol. 110, no. 39, pp. 11260–11264, 2006
103. Rotational spectroscopy of AuH and AuD in the 1S+ electronic ground state
Chemical Physics Letters, vol. 422, no. 1-3, pp. 58–61, 2006
104. Direct fit of extended Hartree–Fock approximate correlation energy model to spectroscopic data
Chemical Physics Letters, vol. 424, no. 4-6, pp. 425–431, 2006
105. Theoretical study of the femtosecond-resolved photoelectron spectrum of the I2- anion
Chemical Physics Letters, vol. 433, no. 1-3, pp. 28–31, 2006
106. The Journal of Physical Chemistry A, vol. 110, no. 2, pp. 564–571, 2006
107. Importance of long-range interactions in chemical reactions at cold and ultracold temperatures
International Reviews in Physical Chemistry, vol. 25, no. 3, pp. 283–311, 2006
108. Oriented xenon hydride molecules in the gas phase
International Reviews in Physical Chemistry, vol. 25, no. 4, pp. 583–612, 2006
109. Formation, detection and spectroscopy of ultracold Rb2 in the ground X1Sg+ state
Journal of Physics B: Atomic, Molecular and Optical Physics, vol. 39, no. 19, pp. S857–S869, 2006
110. Ultracold scattering of Rb atoms and bound states of Rb2
Journal of Physics B: Atomic, Molecular and Optical Physics, vol. 39, no. 22, pp. 4563–4573, 2006
111. Physics-Uspekhi, vol. 49, no. 11, p. 1113, 2006
112. Calculation of absolute scattering phase shifts
Molecular Physics, vol. 104, no. 1, pp. 147–150, 2006
113. Accurate computations of the rovibrational spectrum of the He–HF van der Waals complex
Molecular Physics, vol. 104, no. 9, pp. 1413–1420, 2006
114. Reference potential approach to the inverse problem in quantum mechanics
Molecular Physics, vol. 104, no. 16-17, pp. 2671–2684, 2006
115. Chemical Properties of Electronically Excited Halogen Atoms X([sup 2]P[sub 1/2]) (X=F,Cl,Br,I)
Journal of Physical and Chemical Reference Data, vol. 35, no. 2, p. 869, 2006
116. New exchange-Coulomb N[sub 2]–Ar potential-energy surface and its comparison with other recent N[sub 2]–Ar potential-energy surfaces
The Journal of Chemical Physics, vol. 124, no. 3, p. 034308, 2006
117. Energetics and dynamics of threshold photoion-pair formation in HF/DF
The Journal of Chemical Physics, vol. 124, no. 7, p. 074311, 2006
118. Interaction-induced dipole moment of the Ar–H[sub 2] dimer: Dependence on the H[sub 2] bond length
The Journal of Chemical Physics, vol. 124, no. 15, p. 154309, 2006
119. High-resolution laser excitation spectroscopy of the A~ [sup 2]E-X~ [sup 2]A[sub 1] transition of SrCH[sub 3]
The Journal of Chemical Physics, vol. 124, no. 17, p. 174309, 2006
120. High resolution spectroscopy and potential determination of the (3)[sup 1]? state of NaCs
The Journal of Chemical Physics, vol. 124, no. 17, p. 174310, 2006
121. Experimental long range potential of the B [sup 1]? state in NaRb
The Journal of Chemical Physics, vol. 124, no. 20, p. 204308, 2006
122. Computed lifetimes of metastable states of CO[sup 2+]
The Journal of Chemical Physics, vol. 124, no. 21, p. 214303, 2006
123. Erratum: “A hierarchical family of three dimensional potential energy surfaces for He-CO” [J. Chem. Phys. 123, 084314 (2005)]
The Journal of Chemical Physics, vol. 124, no. 22, p. 229901, 2006
124. Construction and calibration of an instrument for three-dimensional ion imaging
The Journal of Chemical Physics, vol. 125, no. 13, p. 133503, 2006
125. An accurate analytic potential function for ground-state N[sub 2] from a direct-potential-fit analysis of spectroscopic data
The Journal of Chemical Physics, vol. 125, no. 16, p. 164310, 2006
126. Helium clusters seeded with CO molecules: New results for He[sub N]–[sup 13]C[sup 18]O and the approach to the nanodroplet limit
The Journal of Chemical Physics, vol. 125, no. 16, p. 164328, 2006
127. Rovibrational resonance effects in collision-induced electronic energy transfer: I[sub 2](E,v=0–2)+CF[sub 4]
The Journal of Chemical Physics, vol. 125, no. 19, p. 194313, 2006
128. CO oxidation on electrically charged gold nanotips
The Journal of Chemical Physics, vol. 125, no. 21, p. 214707, 2006
129. Atomic polarization in the photodissociation of diatomic molecules
Physical Chemistry Chemical Physics, vol. 8, no. 48, p. 5591, 2006
130. Phase control of the photofragment branching ratio of the HI molecule in two intense few-cycle laser pulses
Physical Review A, vol. 74, no. 4, 2006
131. Control of photodissociation pathway for oriented adsorbed molecules using polarized light
Journal of Physics: Condensed Matter, vol. 18, no. 30, pp. S1345–S1356, 2006
132. Probing phonon-rotation coupling in helium nanodroplets: Infrared spectroscopy of CO and its isotopomers
Physical Review B, vol. 73, no. 5, 2006
133. ION PAIR DISSOCIATION: Spectroscopy and Dynamics
Annual Review of Physical Chemistry, vol. 57, no. 1, pp. 431–465, 2006
134. Monte Carlo approach to identification of the composition of stratospheric aerosols from infrared solar occultation measurements
Applied Optics, vol. 44, no. 22, p. 4785, 2005
135. Attacking a Small Beast: Ar?CO, a Prototype for Intermolecular Forces
Zeitschrift f�r Physikalische Chemie, vol. 219, no. 8, pp. 1053–1088, 2005
136. Potential Energy Curve of N2 in Its Ground Electronic State
Collection of Czechoslovak Chemical Communications, vol. 70, no. 6, pp. 731–739, 2005
137. Dipole moment functions for electronic transitions from ion-pair states of the second tier of molecular iodine
Optics and Spectroscopy, vol. 99, no. 1, pp. 36–42, 2005
138. Ab initio study for the intermolecular interaction potential surface of Ar-N2 complex
The European Physical Journal D, vol. 33, no. 1, pp. 43–48, 2005
139. The D1? state of the NaRb molecule
The European Physical Journal D, vol. 36, no. 1, pp. 49–55, 2005
140. Nonthermal Power Law Decay of Metal Dimer Anions
Physical Review Letters, vol. 94, no. 11, 2005
141. Ab initio calculation on the analytic potential energy functions for the state a3S+u and the state b3?u of spin-aligned trimer 7Li2
Chinese Physics, vol. 14, no. 8, pp. 1566–1570, 2005
142. Exact quantization of nonsolvable potentials: The role of the quantum phase
Physical Review A, vol. 72, no. 5, 2005
143. Studies on full vibrational spectra and dissociation energies of some diatomic molecular electronic states using algebraic approaches
Molecular Physics, vol. 103, no. 17, pp. 2335–2345, 2005
144. Absorption and fluorescence laser spectroscopy of Rb 2 molecules
Journal of Modern Optics, vol. 52, no. 16, pp. 2373–2380, 2005
145. State-to-state dynamics of elementary chemical reactions using Rydberg H-atom translational spectroscopy
International Reviews in Physical Chemistry, vol. 24, no. 1, pp. 37–98, 2005
146. The isomers of HF–HCN formed in helium nanodroplets: Infrared spectroscopy and ab initio calculations
The Journal of Chemical Physics, vol. 122, no. 2, p. 024306, 2005
147. Quantum mechanical investigation of rovibrational relaxation of H[sub 2] and D[sub 2] by collisions with Ar atoms
The Journal of Chemical Physics, vol. 122, no. 2, p. 024304, 2005
148. Close-coupling calculations of low-energy inelastic and elastic processes in [sup 4]He collisions with H[sub 2]: A comparative study of two potential energy surfaces
The Journal of Chemical Physics, vol. 122, no. 2, p. 024307, 2005
149. High resolution infrared spectra of H[sub 2]–Kr and D[sub 2]–Kr van der Waals complexes
The Journal of Chemical Physics, vol. 122, no. 8, p. 084320, 2005
150. A reliable new three-dimensional potential energy surface for H[sub 2]–Kr
The Journal of Chemical Physics, vol. 122, no. 8, p. 084321, 2005
151. Photodissociation of HI and DI: Polarization of atomic photofragments
The Journal of Chemical Physics, vol. 122, no. 8, p. 084301, 2005
152. Small para-hydrogen clusters doped with carbon monoxide: Quantum Monte Carlo simulations and observed infrared spectra
The Journal of Chemical Physics, vol. 122, no. 9, p. 094314, 2005
153. Time-resolved imaging of the reaction coordinate
The Journal of Chemical Physics, vol. 122, no. 17, p. 174305, 2005
154. Helium induced pressure broadening and shifting of HCN hyperfine transitions between 1.3 and 20 K
The Journal of Chemical Physics, vol. 122, no. 18, p. 184319, 2005
155. Low temperature pressure broadening of OCS by He
The Journal of Chemical Physics, vol. 122, no. 20, p. 204308, 2005
156. Electronic structure, reactivity, and spectroscopy of dihydrides of group-IB metals
The Journal of Chemical Physics, vol. 122, no. 20, p. 204325, 2005
157. On equilibrium structures of the water molecule
The Journal of Chemical Physics, vol. 122, no. 21, p. 214305, 2005
158. Time-dependent four-component relativistic density-functional theory for excitation energies. II. The exchange-correlation kernel
The Journal of Chemical Physics, vol. 123, no. 5, p. 054102, 2005
159. Computing resonance energies, widths, and wave functions using a Lanczos method in real arithmetic
The Journal of Chemical Physics, vol. 122, no. 24, p. 244107, 2005
160. Spectroscopy of Ar–SH and Ar–SD. II. Determination of the three-dimensional intermolecular potential-energy surface
The Journal of Chemical Physics, vol. 123, no. 5, p. 054325, 2005
161. A hierarchical family of three-dimensional potential energy surfaces for He-CO
The Journal of Chemical Physics, vol. 123, no. 8, p. 084314, 2005
162. Accurately solving the electronic Schro¨dinger equation of atoms and molecules using explicitly correlated (r[sub 12]-) multireference configuration interaction. VII. The hydrogen fluoride molecule
The Journal of Chemical Physics, vol. 123, no. 2, p. 024304, 2005
163. Photodissociation of HI and DI: Testing models for electronic structure via polarization of atomic photofragments
The Journal of Chemical Physics, vol. 123, no. 5, p. 054301, 2005
164. Close-coupling study of rotational energy transfer of CO (?=2) by collisions with He atoms
The Journal of Chemical Physics, vol. 123, no. 13, p. 134326, 2005
165. Direct-potential-fit analysis of new infrared and UV/visible A [sup 1]S[sup +]-X [sup 1]S[sup +] emission spectra of AgH and AgD
The Journal of Chemical Physics, vol. 123, no. 20, p. 204304, 2005
166. Direct deperturbation analysis of the A [sup 2]?~B [sup 2]S[sup +] complex of [sup 7,6]LiAr isotopomers
The Journal of Chemical Physics, vol. 123, no. 20, p. 204307, 2005
167. Near-UV photodissociation of oriented CH[sub 3]I adsorbed on Cu(110)–I
The Journal of Chemical Physics, vol. 123, no. 20, p. 204709, 2005
168. Photoinduced ion-pair formation in the (HI)[sub m](H[sub 2]O)[sub n] cluster system
The Journal of Chemical Physics, vol. 123, no. 21, p. 214308, 2005
169. The Journal of Physical Chemistry A, vol. 109, no. 46, pp. 10547–10553, 2005
170. Vibrational dynamics of the hydrogen bonded complexes (CH2)2O?HF and ?DF investigated by combined jet- and cell-Fourier transform infrared spectroscopy
Physical Chemistry Chemical Physics, vol. 7, no. 4, p. 592, 2005
171. Continuum and discrete pulsed cavity ring down laser absorption spectra of Br vapor
Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy, vol. 61, no. 9, pp. 2115–2120, 2005
172. Ab initio molecular orbital studies of the vibrational spectra of the van der Waals complexes of boron trifluoride with the noble gases
Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy, vol. 61, no. 7, pp. 1403–1409, 2005
173. Ab initio study of low-lying triplet states of the lithium dimer
Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy, vol. 62, no. 4-5, pp. 790–799, 2005
174. Flow injection chemical vapor generation of Au using a mixed reductant
Spectrochimica Acta Part B: Atomic Spectroscopy, vol. 60, no. 1, pp. 101–107, 2005
175. The Journal of Physical Chemistry A, vol. 109, no. 13, pp. 3094–3096, 2005
176. The Journal of Physical Chemistry B, vol. 109, no. 17, pp. 8407–8414, 2005
177. The Journal of Physical Chemistry A, vol. 109, no. 42, pp. 9402–9413, 2005
178. Fourier transform infrared emission spectra of MnH and MnD
Journal of Molecular Spectroscopy, vol. 229, no. 1, pp. 145–149, 2005
179. Revision of the K 3? and states: new vibrational numberings and new potential functions
Journal of Molecular Spectroscopy, vol. 229, no. 1, pp. 122–130, 2005
180. Geometry of the CaOCH radical from isotope effects in the transition
Journal of Molecular Spectroscopy, vol. 229, no. 2, pp. 224–230, 2005
181. Infrared and near infrared emission spectra of SbH and SbD
Journal of Molecular Spectroscopy, vol. 229, no. 2, pp. 257–265, 2005
182. Infrared and near infrared emission spectra of TeH and TeD
Journal of Molecular Spectroscopy, vol. 230, no. 2, pp. 105–116, 2005
183. The Lamb-dip spectrum of the =1?0 transition of DF: Crossing resonances and hyperfine components
Journal of Molecular Spectroscopy, vol. 231, no. 2, pp. 124–130, 2005
184. A build-up cavity for Fourier transform emission experiments
Journal of Molecular Spectroscopy, vol. 232, no. 1, pp. 14–25, 2005
185. The ? state of Na revisited: A comprehensive study by polarization labeling spectroscopy technique
Journal of Molecular Spectroscopy, vol. 232, no. 2, pp. 291–295, 2005
186. New experimental data on the K state analyzed with the multi-parameter approach
Journal of Molecular Spectroscopy, vol. 234, no. 1, pp. 41–52, 2005
187. High-resolution Fourier transform spectroscopy of the CaO A1S+-X1S+ transition: New insights into perturbations by the a3?0+a3?0+ and A1? states?
Journal of Molecular Spectroscopy, vol. 234, no. 2, pp. 255–263, 2005
188. Reexamination of the structures and energies of LiC and LiC
Chemical Physics Letters, vol. 411, no. 4-6, pp. 484–491, 2005
189. Prediction of spectroscopic constants for diatomic molecules in the ground and excited states using time-dependent density functional theory
Journal of Computational Chemistry, vol. 27, no. 2, pp. 163–173, 2005
190. Photodissociation of HBr on the surface of Ar clusters at 193nm
Chemical Physics, vol. 315, no. 1-2, pp. 161–170, 2005
191. Accurate intermolecular ground state potential of the Ar-N[sub 2] van der Waals complex
The Journal of Chemical Physics, vol. 121, no. 21, p. 10419, 2004
192. Infrared spectrum and predissociation dynamics of H[sub 2]O[sup +]–Ar
The Journal of Chemical Physics, vol. 121, no. 24, p. 12345, 2004


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## "Purification, Determination Molecular Weight and Study Kinetic Properties of G6PD Enzyme from Diabetes Patient"

Abdulkader W Rasheed1Firas T Maher1*, Akeel H Al-Aisse2

1Department of Chemistry, College of Science, University of Tikrit, Tikrit, Iraq

2Department of Biology, College of Science, University of Tikrit, Tikrit, Iraq

*Corresponding author: Firas T Maher, Department of Chemistry, College of Science, University of Tikrit, Tikrit, Iraq. Tel: 009647702658972; Email:firastaher3@gmail.com

Received Date: 31July, 2017; Accepted Date:31 August, 2017; Published Date:7September, 2017

1.                  Abstract

This study was conducted to purification G6PD enzyme from diabetic patients by using simple and cheap methodthe technique gel filtration onSephadex G100 and determine molecular weight of enzyme and compare it with true molecular weight of enzyme and determine kinetic constant (Km,Vmax) and study the effect of temperature and substrate and pH and known the best condition to give optimum work of enzyme. Study contain (60) patients with diabetes and (60) control Glucose and activity of G6PD were measured and the enzyme precipitated by Ammonium Sulfate with concentration (75%) and purification enzyme gel filtration onSephadex G-100 with dimensions (1.5×30)cm and using the buffer solution from (Tris-HCl) at pH 8.2 to isolate the enzyme and determine molecular weight with same method. Specific activity was calculated (21.5UI\mg), total activity(706.8UI), number of purification (3.45) enzyme yield(23.188%) and enzyme activity (17.67UI\ml). and the molecular weight was calculated with using same technique (57.82) k.D. Effect of increased concentration of substrate on enzyme activityand found the activity increase with increase substrateand amount constant level not change howeverincrease of concentration of substratewhen drawing relation between activity and concentration of substrate format appear exchange excess and after study effect of pH found the optimum value (8.4) and study effect of temperature on activity found (38ºC) the optimum temperature . Study of kinetic constant was done and the and the Michaelis- Menten (Km) value was (3.8 mM)and Vmax value (8IU\ml).

2.      Keywords: Diabetes Mellitus; G6PD; Molecular Weight; Purification.

1.                  Introduction

Diabetes mellitus is a metabolic disease clinically and genetically heterogeneous group characterized by hyperglycemia due to defects in insulin metabolism. If the hyperglycemia of diabetes is not managed properly, it causes long-term damage, dysfunction, and failure of different organism [1]. notably the eyes, kidneys, nerves, heart, and blood diabetes mellitus is a multifactorial disease resulting from interaction of both genetic and environmental It has been stated that oxidative stress and impaired release of nitric oxide may be the contributory factors in the pathogenesis of diabetes[2,3].

One of themaincauses of diabetes is functional causes such aspancreatic disorders, this occurs when the pancreas is infected with tumors (benign and malignant), internal bleeding or when the pancreas is removed leading to an absolute inability to secrete insulin to lead to diabetes induced by excessive use of thiazide diuretics, anti-inflammatory drugs and antiviral[2]. Genetic causes Individuals with parents who have diabetes or individuals from a family with a family history of the disease are more likely to develop diabetes than others obesity is a cause of diabetes, Obese people who store high amounts of fat in the abdomen are more likely to develop diabetes[5]. Those who accumulate fat in the limbs and increase the amount of fats affect the blood sugar level because it is one of the main factors that cause insulin resistance of cells by reducing the sensitivity of insulin receptors on the surface of target cells[4]. One of the other reasons is also lack of physical activity as it affects the increased incidence of diabetes. In some cases, emotional emotions have an effect on diabetes, such as anxiety, fear or sudden shocks, and susceptibility to disease [6]. Viral infections have a major role in the development of type 1 diabetes, Self-infection due toviral infection or by the destruction of beta cells in the pancreas[7].

1.1.  Diagnosis of Diabetes

1.1.1.         Clinical Diagnosis: Patients with diabetes of all types have the following symptoms:Polyuria, polydipsia, lethargy, boils, slow healing wounds, frequent infections persist for a long time. Patients with Type I diabetes suffer from weight loss dehydration, ketonuria, and hyperventilation [6]. Symptoms of type 1 diabetes tend to be short-term, whereas patients with type 2 diabetes tend to have chronic symptoms with longer duration of symptoms [5]. This is a significant difference between the two. Lack of secretion of insulin also causes excessive metabolism of free fatty acids, and this leads to confusion in fat metabolism [7].

1.1.2.         Laboratory Diagnosis: High blood sugar hyperglycemia and the emergence of glucose in the blood glucose is a distinctive phenomenon of diabetes, so some tests are used to diagnose diabetes, including: Fasting Plasma Glucose (FPG),Random plasma Glucose (RPG), Oral glucose Tolerance test(OGTT), Glycosylated Haemoglobin (HbA1c), Glucose in Urine, Ketone body in Blood or Urine[8,9]

3.1.2.1      Glucose-6-Phosphate Dehydrogenase(G6PD)

Enzyme: Are vital catalysts that accelerate the rate of chemical reactions. They have a high molecular weight protein structure. Like other proteins, the enzyme is composed of a combination of a large number of amino acids that have one or more polypeptides. Is a three-dimensional form of the protein. amino acids are found in these sequences according to a particular sequence of each enzyme, leading to a specific vacuum structure that enables the enzyme to accelerate its own reaction.

Glucose-6-Phosphate Dehydrogenase (G6PD ((Oxidoreductase,EC1.1.1.1-49)(G6PD) is one of the cytoplasmic enzymes is spread throughout the body, especially in the red blood cells, which is one of the most important enzymes of the egg, as it is the main enzyme and the key to the Pentose phosphate pathway[10].It stimulates the oxidation process of the glucose-6-phosphate (G-6-P) (NADP) and to convert it to an effective reduced form (NADP) to preserve the life-producing pathways of several important substances, particularly in red blood cells because they have no other source of production(NADP) to preserve the life-producing pathways of several important substances, particularly in red blood cells because they do not have another source of NADPH production. NADPH product produced by G6PD is complementary to the reduced triglyceride enzyme (GRG), which converts and converts oxidative glutathione (GSSG) (GSH), [7]which protects human red blood cells from partial and planned [1], shows the pathway of pentose phosphate sugar and rule of G6PD in reactions of pathway.

The enzyme was first discovered by the scientists Warburg (Christian) in 1931 in the red blood cells of the horse and since then studies and research have been conducted to extract and purify the enzyme from various sources[12].

There are other important reasons to study as the change in the effectiveness of this enzyme G6PD enzyme in the body's various tissues is linked to many diseases in humans and these diseases is the disease of jaundice in children and hemolytic anemia [13]. G6PD deficiency is a disease that is prevalent in different parts of the world. The number of infected people is 400 million males, females, neonates and other ages, according to the World Health Organization (WHO) report [1]. More than 442 types of enzyme (G6PD variants) have been identified using a large number of biological techniques, including molecular analytical methods, which identify genetic mutations that occur in the genes responsible for the biological processing of different types of enzyme [14]. Genefound thatThe enzyme gene was found to be carried on the sex chromosome (X) [15]. The shortening of enzyme efficacy is associated with genetic and hereditary disorders[16]. This shortage is widespread in the world, especially in the Mediterranean region Patients with this type of hemorrhagic deficiency are generally affected by certain drugs and foods in the case of a paroxysmal or neonatal jaundice found in natural erythrocytes, enzymatic activity decreases with age[16].Many mutations of this enzymatic deficiency are widespread in the world and by geographic location. Moreover, genetic defects and age can lead to Enzymatic Deficiency An enzyme deficiency leads to the production of some red blood cell anemia due to exposure to certain chemical agents or certain infections and wounds [15]

3.1.2.2.    Classification

Numerous G6PD variants have been described These have been classified by the World Health Organization according to the magnitude of the enzyme deficiency and the severity of hemolysis. This classification gives some approximation of the magnitude of hemolysis an individual might incur in the setting of an oxidative stress. Only class I, II, and III are of clinical significance.

Class I - Class I variants have severe enzyme deficiency (<10 percent of normal) relation with chronic hemolytic anemia.

Class II - Class II variants also have severe enzyme deficiency (<10 percent of normal), but there is usually only intermittent hemolysis, typically on exposure to oxidant stress such as fava bean exposure or ingestion of certain drugs and the classic example is (G6PD Mediterranean)

Class III - Class III variants have moderate enzyme deficiency (10 to 60 percent of normal) with intermittent hemolysis, typically associated with significant oxidant stress the classic example is(G6PD A-).

Class IV - Class IV variants have no enzyme deficiency or hemolysis the wild-type (normal) enzyme is considered a class IV variant, as are numerous other genetic changes that do not alter levels of the enzyme and these variants are of no clinical significance.

Class V - Class V variants have increased enzyme activity (more than twice normal). These are typically uncovered during testing for G6PD deficiency and they are of no clinical significance [10].

3.1.3.         Clinical Significance of the Enzyme

·         Acute Hemolytic Anemia: Some individuals with G6PD deficiency have acute hemolytic anemia at the site of the wound when some medications, acute diseases, and certain foods are taken [17].

·         Neonatal Jaundice: Anemiaand jaundice are most often observed in newborns in individuals with severe enzyme deficiency[18].

·         Neutrophil Dysfunction: - The enzyme is used in addition to red blood cells in white cells to reduce the oxidizing factors. Some people with severe enzyme deficiency suffer from a defect in the function of white blood cells, which causes weak respiratory resistance to diseases and also weakens The presence of beneficial bacteria in the body[19].

·         Diabetic Mellitus-Induced Hemolysis: In people with an enzyme deficiency, hemolyticysis starts with an increase in ketone content in diabetics and has the lowest levels when blood glucose levels are abnormal in diabetics[20]. Studies have indicated that high sugar leads to the deposition of decomposed blood in patients with deficiency [17].

3.1.4.         The Relationship between (G6PD) Enzyme and Diabetes

An epidemiological study fromsuggested a positive correlation between diabetes and deficiency [21]. (G6PD) has conducted a study on Indian society being the most potential to give this relationshipSerum samples were collected for healthy people and of both sexes. A higher incidence among Indians provided an excellent opportunity to study the possible association of G6PD deficiency in diabetes mellitus [5]. G6 PD deficiency is one of the common enzymopathy in human being affecting about 400 million people worldwide. It is suggested that there may be a positive association of G6PD deficiency with diabetes mellitus.Although G6PD deficiency is not uncommon in our country but there is scarcity of data on this regards especially on diabetes. Therefore, this study was undertaken to observe the G6PD status in patients with type 2 diabetes mellitus in order to explore the role of this enzyme deficiency as one of the risk factor for diabetes mellitus[7].a positive association of G6PD deficiency with diabetes mellitus Although G6PD deficiency is not uncommon in our country but there is scarcity of data on this regards especially on diabetes. Therefore, this study was undertaken to observe the G6PD status in patients with type 2 diabetes mellitus in order to explore the role of this enzyme deficiency as one of the risk factor for diabetes mellitus[6].

4.              Materials and Methods

4.1.          Collection of Sample

The total number of these samples was (60) samples, serum samples were collected for people with diabetes and both sexes. They reached (60) satisfactory samples of both types of diabetes (type I and type II)Diagnosis of the disease using a blood glucose test.

Blood was drawn from the vein using a 5ml plastic syringe with one use. The blood was placed in clean, sterile plastic tubes free of anticoagulant EDTA. And left to coagulate at room temperature. The blood serum was then separated from the centrifuged portion of the centrifuge and at a velocityof 5000 G for 15 minutes to ensure adequate serum red blood cell extraction, Micro pipette. The effectiveness of the enzyme was measured directly and the study was done outside the body (in vitro).

4.2.          Diagnosis Kits

The kits Clarifiers in table2 were used in procedures of this study.

4.3.          Estimation of Biochemical Parameters in Blood Serum

4.3.1.         Estimationof Glucose Concentration in serum

Principle: glucose level in serum was measured by using (kit Aflu Italia)depending on enzyme method that stated onTrinder reaction[8].

4.3.2.         Determination of Total Protein in serum

Total proteinlevel in serum was measured by using (kit Aflu Italia)depending on enzyme method [9].

4.3.3.         Determination of G6PD Activity in Serum

G6PD activity in serum was measured by usingBiolabo kit according this equation[22].

A = AbsorbanceV= enzyme volume in ml6.22= absorbance confection of (NADPH) in length 340nm

4.3.4.         Separation and purification of the enzyme G6PDH from serum diabetes patients:

G6PDH was purified from the serum of diabetic patients using the following steps:

Serum proteins were precipitated using gradual concentrations of ammonium sulphate until 75%. 3.75gm of ammonium sulphate was added to 5 ml of serum during 60-45 minutes by placing the serum in a snow bath with constant stirring, and then dissolved Deposition using 4ml of 1M Tris - HCl regulated solution(pH= 7.8).

4.4.     Dialysis

Which is one of the most important methods used in the purification of enzymes and the oldest, and the goal is to remove the remaining ammonium sulphate added to the deposition of proteins by placing the dissolved protein in the above step in the membrane bag dialysis bag after measuring the effectiveness of the enzyme G6PD and protein concentration, and immerses the bag in the solution solution. 1M Tris - HCl pH 7.8 The regulator solution was changed from time to time for 16 hours. This step was performed at (4°C±1°C) to maintain the efficacy of G6PD. After the membrane separation process After the membrane separation process, G6PD and protein concentration were measured.

4.4.1.         Gel Filtration Chromatography

Gel Filtration technology is one of the most important techniques in the field of biochemistry, one of the methods used in the separation of compounds depending on the size of their molecules and their molecular weights. The proteins with large molecular weights are not carried out through the gel but move outside the gel layer with the solvent that is removed in sequence. This solvent is often distilled water or a dilute regulator. Therefore, the large particles first filter during the separation. Small molecules can penetrate the gel granules. finally. The fraction of the gel filtration is collected using the Fraction Collector. The volume of distilled water or solution is calculated to displace each protein from the separation column, and the protein is isolated by reading the absorption at 280 nm[13].

The gel filtration technology is also used as a method for estimating the approximate molecular weight of protein by drawing a graph showing the relationship between the size of the elution and the known molecular weight. The protein with the molecular weight is then passed through the separation column and calculated. The size of the Rogan accurately and in comparison with the known molecular weights can estimate the approximate molecular weight of the unknown protein [23,24].

4.4.2.         Used solutions

·         Buffer solution 0. 1M Tris-HCl pH 7.8

Prepare to dissolve 15.76 gm of Tris-HCl per liter of distilled water and adjust

pH at 7.8.

Prepare to dissolve 2.5 gm of the Sephadex G100 column filler in 200 ml of the 0.1M Tris-HCl pH solution 7.2 and leave the solution for 28-24 hours at 4°C. During this time the solution was changed several times to remove the soft minutes from the solution Because its presence reduces the velocity of the flow of the liquid solution through the column.

·         Sodium chloride solution at 500 mM concentration Prepare 29.25 g of NaCl per liter of 0.1M Tris-HCl pH 7.8 solution.

4.4.3.         Procedure

a)       Use a glass column with a diameter of 1.5 cm and a length of 30 cm. A small amount of glass wool is placed at the end of the column to prevent the gel particles from leaking out of the column. The gel solution is slowly and homogeneously poured into the column to prevent air bubbles from forming. (11cm), wash the column with sufficient amounts of 0.1M Tris-HCl pH solution until a flow velocity of 2.5 ml / min was obtained [25].

b)       Add 5 ml of enzyme after membrane separation slowly over the surface of the G100 Sephadex gel and leave for 5 minutes to soak in the gel column.

c)       The process of separation was started using 150ml of the structured solution containing 500 ml of NaCl, collecting 5 ml per part.

d)       After collecting the extracting parts of the separation column, the efficacy of the G6PD enzyme was evaluated by paragraph and protein concentration by the method (kit Aflu).

4.4.3.1.    Kinetics of G6PD

The kinetics of G6PD were studied after its separation and partially purified from the serum of diabetic patients by gel filtration. These included

4.4.3.2.    Effect of Glucose 6-Phosphate Concentration (G6P)

The effect of different concentrations of G6P on the activity of G6PD was studied by using different concentrations(0.6,0.0512,0.0256,0.0128,0.064.0.048,0.024,0.012)M to determine the effect of the concentration of substrate on the work of the enzyme G6PD,G6PD reaction (G6PD kit Biolabo), and plotting the relationship between the reaction rate and the concentration of substrate to determine that the enzyme is subject to the Michaelis-Menten equation.The Km values were obtained using the Linover-Burke graphical method, which links the inverse values of both velocity and G6P concentration

(1 / (S)vs. 1/ V).

4.4.3.3.    Optimized pH Mapping:

The pH effect of the regulated solution (0.1M Tris-HCl pH 7.8) was studied at the velocityof the G6PD reaction. Different pH solutions (11, 10, 9, 8, 7.6) were used with G6P at 0.6 mM and 37° C (G6PD kit Biolabo), and by plotting the relationship between reaction velocity and pH, the optimal pH was identified.

4.4.3.4.    Effect of Temperature

G6PD kit Biolabo was used to measure the effectiveness of G6PD. The reaction was conducted at different temperatures (57, 47, 37, 27, 17 and 7) with the regulated solution (0.1M Tris - HCl pH 7.8) Basically (G6P) 0.6mM, and then painted the relationship between the reaction velocity and the temperature to find out the optimal temperature of the reaction.

5.         Results and Discussion

5.1. Purification of Enzyme

5.1.1.         Precipitation by Ammonium Sulphate

The basic principle of the method is to equalize the charges on the surface of the protein and the degradation of the water layer surrounding the protein and reduce the degree of watering and reduce the solubility of the protein and sedimentation[26].Add the stages to get rid of some of the protein content with the enzymatic extract[27].The result in table 4 showing the efficiency of quality (10.77 units / mg) with the number of times of purification (1.73) and the yield (35.02) during the satisfaction rate of ammonium sulfate sulfate estimated (75%). The results differed with the studies of enzyme extraction. In a study involving red blood cell extraction, the specific activity was 1.251 (units / mg) with 121.5 purification number and 53.8% enzymatic yield when using ammonium sulphate salt at 35-65%[28]. Another study showed that the specific efficacy was 0.37 mg / ml and the number of purification times was 39.79 times and the yield of 79.18 units / mg after adding the salt with saturation concentration (40-60%) of the red blood cells of the geese[29]. In the Penicillium duPonti fungi, the salt was used by saturation (45-60%), giving the result a quality efficacy of (1.04 units/mg) and the number of times the purification of 8.67 times and proceeds 63.4%[30].

5.1.2.         Gel Filtration

The different methods used to purify the enzyme from bacterial, fungal, plant, or animal sources were obtained in obtaining high purity of the enzyme, During this research the use of gel filtration technique with the Sephadex G-100 was the result of the specific efficacy (21.5 units / mg), total activity (706.8 units), purification number 3.45, enzymatic yield (23.188%) and enzymatic efficacy (17.67 units / ml). Results were obtained with other studies of enzyme purification. In one study, using the Sephacryl-S200 column to purify the enzyme from rat liverit was found that the specific efficacy was 24.75 units / mg and the total efficiency was 198 units with 6.17 times purification and an enzyme yield of 60.57% [31].In a study that included several steps, first transfer the concentrated enzymatic extract with ammonium sulphate salt on the calcium phosphate column and then transfer the extract to the ion exchanger DEAE-Cellulose and then the gel filtration column Bio-Gel A-150 these steps gave a quality effect of 470 units / mg with a frequency of 2.42 times and an enzyme yield of 10% [32]. A studyof the purified enzyme from calf tissue using the gel filter column Sephadex G-25an enzyme yield of 91% with 450 times purification[33]. Another study included enzyme purification from Coriander Leaves The first two-step purification was performed with ammonium sulphate deposition and the use of the Sephadex G-200 gel. The enzymatic activity was 1.82 units / mg and the enzymatic yield was 26.4% and the number of purification times was 74 [34]. Also using gelatin filtration of the Sephadex G-200 column and concentration of sulphate salts prior to filtration, the results included (326 unit\ mg) the enzymatic yield was 19.9% and the frequency of purification was 2.5 when purifying the enzyme from the pituitary gland of caw[35]

In another study to Saccharomyces cerevisiae include using saturated concentration of ammonium sulphate salt(40-80)and gel filtration column on Sephacryl S-200 gave specific activity 65.68 unit/ mg and the enzymatic yield was 20.62% and the number of purification times was 2.94 [32] Table 3.

5.1.3.         Determination of Molecular Weight in Gelatin Filtration Technology

The researcher's method[29]was based on the gel filter method in estimating the approximate molecular weight of the G6PD enzyme from the protein package [23]which showed the highest concentration of the protein. and passed a number of known molecular weight indicated in Table 5 and the molecular weight ranges between (20000000-13700) Dalton for the purpose of specifying the characteristics of the column in terms of internal volume (Elution Volume Ve) for each material as well as the free or empty size of the granules (Void Volume Vo), which was estimated from the standard curve of blue dextran at 3 mL per part. The Vo value was equal to 33 mL and the recovery volume of the standard Ve proteins to the volume of the recovery of dextran blue Vo, represented by the Ve / Vo relationship [31].As shown in Table 4 (Sephadex G-100), molecular weight and recovery volume The Elution Volume of each material versus its molecular weight logarithm shows the appearance of a straight line in which the approximate molecular weight of the protein packet separated by the gel filtration technique is shown in Figure 1. The recovery volume of the package (18ml) To approximate molecular weight Figure 2, the approximate molecular weight of the G6PD is (57.82) kDa for the enzymatic extract using gel filtration technique.

We see these results contrasted with a range of studies and studies conducted to estimate the molecular weight of the enzyme from its various sources[36]. The molecular weight was 133 kDa for the purified enzyme from pig liver using ammonium sulphate and Sephadex G-200 for the bilateral body the single molecule had a molecular weight of 67.50 and other studies showed that the molecular weight of the enzyme was purified from the liver of the mice, and the pituitary gland for cows had a molecular weight of 64 kDa[37]. The molecular weight of the purified enzyme from human red blood cells was estimated to be 43 kDa[36]. and in another study using gelatin filtration with the Sephadex G150 the molecular weight was (40 KDa) from Bean plant [38] The molecular weight of the purified enzyme from diabetics was within the range mentioned [39]ranging from 22-58 KDa. Due to the difference in the scientific basis in the different methods used in the Dalton of the enzyme purified from yeast Saccharomyces cerevisiaePurification of enzymes The molecular weights vary from one study to another [40].The difference is also due to the length of the purification steps of some of the different studies which may lead to the enzyme breaking through these long stages and therefore the resulting molecular weights are less than the real G6PD Study of Enzyme kinetics[41].

5.1.4.         G6PD Study of Enzyme kinetics

5.1.4.1.    Effect of the pH

pH has a significant effect on the enzyme's effectiveness for controlling ionization Ionic aggregates at the active site of the enzyme The optimal pH of enzyme stability is an important characteristic of enzymes [42].The results of the kinetic study of the enzyme showed that the optimal pH of the enzymatic extract was in the range (8-8.4)as shown in figure 3. The optimal basis for the stability of the enzyme was (8-9) Extreme pH values affect substrate and the ionic state of the enzyme and lead to enzyme protein mutagenesis by altering the enzyme body [26]. In a study people with enzymatic deficiency and a group of healthy patients, pH was (8.5-7).as in figure3.[43]

Filter column the gel filtration column using the Sephadex gel and the solution of regulating the hydrochloride gear with different hydrogen numbers ranging from 5-11, respectively.

5.1.4.2.    Effect of Temperature on Enzyme Activity

The optimum temperature of the activity, the highest temperature, where the rate of enzymatic reaction rate is maximal, while the enzyme is highly effective, and is affected by pH and other factors[44]The optimum temperature of the enzyme activity when the pH was confirmed and the concentration of Substrate was (37-38C). The results varied with the studies carried out, including a study on the enzymatic extract extracted from coriander leaves(30C) [35].and another study indicated that the optimum degree of the enzyme purified from bacteria Azotobacter and human placenta is (50C) [45]In a study of the purified extract from the lamb marrow, the optimum grade was (38C) [46].

5.1.4.3.    Effect of Substrate Concentration

The Michaelis-Menten constant (Km) was defined as the affinity between the enzyme and substrate. The higher its value, the less the value of the substance is reduced. In order to stimulate the biological reactions and to determine the stability of enzymes and the effect of inhibitory and activating substances on enzymatic efficacy[40]The results of the kinetic constants estimated for the enzymatic extract were shown in Figure 5. The constant value of the Michaelis-Menten ofsubstrate(G6P) was(3.8mM) and the maximum velocity value Vmax (8 UI\ml). The differences between all these studies were clear and almost natural as a result of the different sources of the enzyme which were cleared and the different methods In the Iraqi study to purify the enzyme from human blood, the value of Michaelis-Menten was found in the substrate after the use of two purification methods (103 and 114 micro mole) and the maximum velocity(362 and 403 micromole / min /mg) respectively [39].In another study on coriander leaves, the value of the Michaelis-Menten constant was 0.11 mmol and the maximum velocity was 0.038 units / ml. In a study to purify the enzyme from the pituitary gland for cows, the values of the Michaelis-Menten constant were 0.042 mmol and the maximum velocity was 9 units / ml[37]. In a WHO report for 2015, MichaelisMenten - purified from malaria patients is an average (30-50 micro mole)[1].In a study on fungusPenicillium duPonti the Michaelis constant and the maximum velocity were respectively (0.43 mmol, 9 unit/mg)for the purified enzyme of the fungus [30].The value of the Michaelis constant(Km) from the human placenta was (0.4 mmol) and the maximum velocity was (8 unit\mg) [45]. study of the enzyme purification of the local isolation of yeast Saccharomyces cerevisiae showed that the value of the Michaelis-Menten(Km) constant was (0.343 mmol) and the maximum velocity of substrate G6P (4.08 mmol\ min)[47,48]

PlanningPentose phosphate pathway [1,11]

Figure 1: Purification of G6PD Enzyme with Gill filtration technology on Sephadex G-100 (Elution curve).

Figure 2:Stander Curve to Determine Proximal Molecular Weight of G6PD Enzyme with Gel Filtration Chromatography.

Figure 3:Effect of pH on G6PD Activity.

Figure 4:Effect of Temperature on G6PD Activity.

Figure5:Lineweaver-Burk to calculate (Km) and (Vmax) to G6PD enzyme that purification from diabetes patient with Gill filtration on Sephadex G-100 towards substrate G6P with concentration between(0.6-0.0512mM) with Coenzyme (NADP+ = 0.2Mm).

Figure6:Effect of Substrate Concentration on Enzyme Activity.

 Country Year 2010 Year 2030 Iraq 968 2.009.000 Egypt 2.873.000 6.725.000 Jordan 315 680 Saudi Arabia 895 2.523.000 Bahrain 38 99 Lebanon 149 378 Morocco 437 1.138.000

Table 1: Statistical Represents the Number of Patients with Diabetes in the Arab States in 2010, and it is Expected in 2030 [4].

 1 Glucose 6-Phosphate dehydrogenase (G6PDH) kit Biolabo- France 2 Total protein kit Aflu-Italia 3 Glucose kit Aflu-Italia

Table 2:The Kits and its Source.

 Step of purification Elute (ml) Activity (IU ∕ ml) Protein conc. mg/ml Specific Activity (IU ∕ mg) Total Activity (IU) Purification (fold) Yield (%) Total Protein conc. (mg) Crud serum 5 30.48 24.5 6.22 3048 1 100 4.9 Ammonium sulphate (75%) 4 21.54 8 10.77 1077 1.73 35 2 Dialysis 3.5 19.1 6.37 10.49 1049 1.68 34.4 1.82 Gel filtration (Sephadex G-100) 3 17.67 2.46 21.5 706.8 3.45 23.188 0.82

Table3:Steps of Enzyme Purification.

 Standard protein Molecular weight (Dalton) Log Molecular weight Number of fraction (ml) Elution volume(Ve)in(ml) Ve\Vo Blue Dextran 2000000 6.3 11 33 1 BSA 67000 4.82 15 45 1.36 alpha-Amylase Enzyme 58000 4.7 20 60 1.3 ovalbumin 43000 4.63 24 72 2.18 Chymotrypsinogen 23000 4.39 27 81 2.45 Ribonuclease 13700 4.13 31 93 2.81

Table4: Relation Between Molecular Weight and Elution Volume to Standard Protein.

2.                   American Diabetes Association (2016)Diagnosis and classification of diabetes mellitus Diabetes Care 33: S62-S98.

3.                   AmerianDiabetic Associat. Ion. (2009) Diagnosis and Classification of Diabetes mellitus; Diab car 20: 1183-1197.

4.                   Engelgan MM (2014) Diabetes diagnostic criteria and impaired glycemic states. EvolEvid Base Clin Diab 22: 69-77.

7.                   H Kirkman, E Hendrickson (2012) G6PD from Human erythrocytes. II. Subactive states of the enzyme from normal persons. Journal of Biological Chemistry 237: pp2371-pp2376.

8.                   Bregmeyer HU (1984) Method of enzymatic analysis, 4th education. Verlag chemie. Weinheim.

9.                   Grandall GD (1983) Biochemistry Laboratory New York, Oxford university press 29: 83.

10.                D Cappellini, G Fiorelli (2008) Glucose 6-Phosphate Dehydrogenase Deficiency. Lancet 371: 64-74.

11.                JD Cronk (2014) Pentose phosphate pathway.

12.                Cappellini MD, Fiorelli G (2008) Glucose-6-phosphate dehydrogenase deficiency. Lancet: 371: 64-74.

13.                Plummer TD (1978) An introduction of practical Biochemistry 2nd ed., McGraw-Hill Book Co., U.K. 54.

17.                Gellady AM, Greenwood RD (1972) G-6-PD hemolytic anemia complicating diabetic ketoacidosis. J Pediatr 80: 1037.

22.                CihangirFiengezer, NuriyeNurayUlusu (2007) Three Different Purification Protocols in Purification of G6PD from Sheep Brain Cortex. FABAD J. Pharm. Sci 32: 65-72.

24.                Robyt FJ, White JB (1987) Biochemical Techniques. Theory and practice". Books/cole publishing Co., U.S.A 141: 235-236.

25.                Morris CJ, Morris P (1998) Separation method in Biochemistry. 5nd ed., pitman publishing 443-444.

26.                ErwiniacarotovoraMM-3 from L-asparaginase al-Ani, Mohamed Qais Abdel Moustafa. Production of Enzyme-23 in inhibition of cancer cells (outside the body of the organism). PhD thesis - Faculty of Science - Anbar University (2005).

27.                White Ahandler P, Smith E (1973) Principle of Biochemistry McGrew-hill book company.New York.

28.                Beydemir S, Gulcin I, Kufrevioglu OI, Ceftice M (2003) G6PD For normal and G6PD in Vitro and in vivo effect of Dantrolene Sodium. Pol J Pharmacol 55: 787-792.

29.                Beydemir S, Ylmaz H Ceftice M, Bakan E, Kufrevioglu OL (2003) Purification and kinetics of glucose-6-phosphate From Erythrocyte Goose. dehydrogenase. Comp BiochemPhysiol B Biochem Turk J. Vet. Anim. Sci. 27: 1179-1185.

30.                A Malcolm, M Shepherd (1972) Purification and properties of Penicillium G6PD. Biochemical Journal 128: 817-831.

31.                Karlsoon E, Ryden L, Brewer J (1998) Ion exchange chromatography: Introduction to protein purification.A.Lohn Whiley and Sons INC U.S.A. New York: 40-67.

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33.                Nguyen K, David A, Lee P, Anderson J, Epstein DL (1986) G6PD of Calf trabecular meshwork, Invest.Opthalmol and Vis Sci 27:991-998.

35.                HÖzdemir, VTürkoglu, M Çiftçi(2007) Purification and Characterization of Glucose-6- phosphate Dehydrogenase from Lake Van Fish (ChalcalburnustarichiiPallas, 1811) Erythrocytes. Asian Journal of Chemistry 19: 5695-5702.

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Citation:Rasheed AW,Maher FT, Al-Aisse AH (2017)Purification, Determination Molecular Weight and Study Kinetic Properties of G6PD Enzyme from Diabetes Patient. Adv BiochemBiotehcnol: ABIO-139. DOI: 10.29011/2574-7258.000039


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## College Algebra (10th Edition)

Published by Pearson

# Chapter 7 - Section 7.2 - The Parabola - 7.2 Assess Your Understanding - Page 514: 5

#### Answer

right $3$ units $up$ 1 unit

#### Work Step by Step

We know that for a parabola, the equation $y=(x-h)^2+k$ is shifted h units to the right and k units up. Thus, the blanks should be filled with: right $3$ units $up$ 1 unit

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.


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# Motivic stuff

## What is cohomology?

Posted by Andreas Holmstrom on December 13, 2008

Cohomology (or homology) means different things to different people. The common theme of all notions of cohomology, is the idea of using algebraic invariants to study geometric objects. More precisely, a cohomology theory is a functor from a geometric category (for example CW complexes or schemes) to an algebraic category (for example abelian groups, vector spaces, or modules). This is an extremely powerful idea, as the algebraic objects are often easier to work with, so a problem in geometry can be solved by transferring it to algebra.

We will be a bit sloppy in that we won’t really distinguish between cohomology and homology in the discussion below. Homology usually refers to functors which are covariant, while cohomology refers to functors which are contravariant.

Most commonly, the word cohomology is used to refer to singular cohomology, one of the fundamental notions of algebraic topology. More generally, algebraic topology studies and makes use of generalized cohomology and homology theories, such as K-theory, complex cobordism, and stable homotopy groups. Good online references for these things include this book of May (pdf) and the books of Hatcher.

In mathematics as a whole, there are over 400 different notions of cohomology. The reason for this multitude of cohomologies seems to be that almost any interesting functor from geometry to algebra is referred to as a cohomology theory, regardless of its properties. One of the very few things that all cohomology theories seem to have in common, is the appearance of long exact sequences, which is one of the most important tools for doing actual computations. More generally, the power of cohomology comes from the use of homological algebra, see for example these lecture notes (pdf) of Schapira.

Most of the cohomology theories in mathematics seem to appear in algebraic and arithmetic geometry. Many of these have helped solve some of the major mathematical problems of the past century. I will come back with more posts discussing these in more detail.

1. ### Akhil Mathewsaid

Just curious- why is the word “group cohomology” applied to a covariant functor? Is it just because group homology already exists? What about sheaf cohomology then?

• ### Andreas Holmstromsaid

I think the behaviour of group cohomology is contravariant in the first variable and covariant in the second. You have to be a bit careful though in order to state precisely on which category you have your functor, see for example the brief and clear discussion in Brown: Cohomology of groups, starting at the bottom of p 78. Here is a direct link to the page at Google Books, hope it works.

A different answer is that the group cohomology of a group is related to the singular cohomology of the corresponding Eilenberg-MacLane space, and similarly for group homology and singular homology. This is probably the historical reason for the terminology. You might enjoy Mac Lane’s survey on the origin of group cohomology, which should be freely available here.

• ### Andreas Holmstromsaid

Aha, I now saw that you just wrote a nice post on group cohomology. And I forgot to say that for sheaf cohomology it’s similar, it behaves contravariantly in the first variable and covariantly in the second.

• ### Akhil Mathewsaid

Ok, so it’s basically restriction in the first variable (or corestriction, I forget which). Thanks!

By the way, for sheaf cohomology are you referring to the $Ext$ functors of two sheaf variables, or is the underlying topological space one of the variables?

• ### Andreas Holmstromsaid

I come from algebraic geometry, so when talking about sheaf cohomology I think of the scheme (or the manifold) as the first variable and the sheaf as the second variable. But any Hom or Ext bifunctor (when taking two sheaves or other objects in an abelian category as input) would be contravariant in the first variable and covariant in the second.


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# [CvGmt News] [cvgmt seminar] The low temperature limit of Dirichlet energies

matteo.novaga at unipi.it matteo.novaga at unipi.it
Sat Dec 8 08:58:10 CET 2018

The low temperature limit of Dirichlet energies
-----------------------------------------

http://cvgmt.sns.it/seminar/670/

Date: Monday, Dec 17, 2018

Time: 10:30

Place: Aula Marie Curie, Scuola Normale Superiore

Speaker: Mauro Mariani  (High School of Economics, Moscow)

Abstract. Let $M$ be a Riemannian manifold equipped with a reference measure $m$ with density $\exp(- V/T)$  with respect to the volume measure, where $V$ represents a potential and the positive constant $T$ represents the temperature. The Dirichlet energy with reference measure m is a classical functional defined on the space of probability measures on $M$. I will discuss the variational convergence of such a functional in the limit $T \to 0$. In particular, if $V$ is not convex, a non-trivial expansion by $\Gamma$-convergence holds under generic hypotheses on $V$.
The results are based on a joint work with G. DiGesu (TU Wien).


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# RFC: Drop embedded MathJax in favor of using distro-packaged one? #158

Closed
opened this Issue Sep 7, 2015 · 9 comments

None yet

### 7 participants

Member
commented Sep 7, 2015
 Well, it has been done in Debian here - as a patch. Can we do the same upstream and drop the excessive amount of source code? @infirit @flexiondotorg @NiceandGently @willysr @posophe @obache thoughts? yes, some of you have already confirmed that MathJax is in your distros, I know 😄
Contributor
commented Sep 7, 2015
 I am not against removing and relying on the distro's packaged version. I am only concerned about distro's that do not have this packaged, slackware was one but then I don't think @willysr enabled epub in atril..
added the confirmed label Sep 7, 2015
changed the title from Drop embedded MathJax in favor of using distro-packaged one? to RFC: Drop embedded MathJax in favor of using distro-packaged one? Sep 7, 2015
Member
 I agree with this proposal.
commented Sep 7, 2015
 yes, go on with this idea :) just let me know when it has become a mandatory dep
commented Sep 8, 2015
 I agree with this idea too. I don't know whether "/usr/share/javascript/mathjax" is the de facto standard location for MathJax installation or not, but it is better to add a configure option to specify the location (with existence and required version check). I will also avoid potential missing dependency from packaging.
commented Sep 8, 2015
 I agree too. And don't worry, I'll package it by basing it on Fedora's
added a commit to monsta/atril that referenced this issue Sep 10, 2015
 monsta epub: drop embedded MathJax in favor of using distro-packaged one closes mate-desktop#158 d2f1cf6
referenced this issue Sep 10, 2015
Merged

#### epub: drop embedded MathJax in favor of using distro-packaged one #160

Member
commented Sep 10, 2015
 Ok, there goes #160.
Member
 @monsta Do i have to include MathJax as runtime require in downstream package?
Member
 ok. i see it is already in debian control
Member
commented Oct 14, 2015
 Yes, runtime dep has to be there - in debian it's libjs-mathjax.


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DEPRECATION WARNING

This documentation is not using the current rendering mechanism and will be deleted by December 31st, 2020. The extension maintainer should switch to the new system. Details on how to use the rendering mechanism can be found here.

# Using the sr_feuser_register autologin feature¶

If you use sr_feuser_register with autologin, you need to set the following constants so this works:

plugin.tx_srfeuserregister_pi1 {
enablePreviewRegister = 0

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