text:
All Questions

5 views

ParametricPlot two Piecewise functions

I am trying to ParametricPlot two Piecewise functions. Here are my two Piecewise functions: ...
10 views

How can I set an axes scale on x in terms of Pi?

If I plot a function just like that Plot[Sin(x), {x, 0, 3Pi}] I'll Get a plot whit the x betwenn 0 and 10, I'll like to know how can I could modufy the x axes ...
6 views

Debugging NDSolve to see numerical values at each time-step

I wish to debug my NDSolve function and this is my first time using the Mathematica debugger. I have read around and attempted various different ways of debugging but I cannot figure it out. I want to ...
11 views

How to use vector plot and gradient vectors?

How do I plot a sampling of gradient vectors for fby using the vectorplot command? I’m confused how to use both these commands.
18 views

Multidimensional Matlab conversion

I try to convert this code Matlab code: ...
16 views

Custom Property interface on my own objects

I know I can use the Property interface for things like Graph but I want to use it for all of my objects. This includes: ...
13 views

Shading between two regions of two separate parametric curves/function

I have two long functions g12 and g14 in terms of g2: ...
50 views

How can I order this list on mathematica?

This is my list Matrix = {{1, -2, 3, -4}, {{a, b}, {f, e}, {a, b}, {f, e}}} I want to order the columns in ascending order depending on the values on the first ...
22 views

Finding all roots of a function within an interval

I have the following code: ...
17 views

Problem with building graphic using ListPlot

I want to build the graphic using ListPlot but it doesn't work. I get list in next form: ...
20 views

Understanding conditional expressions returned from definite integral

I dont understand how to interpret C[i] returned from a definite integral when there are no C[i] terms in the actual answer, only in the conditional expr. Thanks! Dan
20 views

Plotting points with different marker and different plotlegend

Currently i'm stuck at problem, where i have a sets of points, and I wish to plot these point with different plot markers, and also with different plot legend. The code is the following: ...
13 views

RunProcess returns a confusing error message when using ProcessDirectory options

Here is one way to find the names of the files in one's home directory: FileNames["*", "~"] (* { "~/.account", "~/Applications", "~/.bash_sessions", ... } *) ...
34 views

How to solve the system of two equations to get the approximation value

I'm a Ph.D. student in Banking and Finance and I'm not familiar with the solving system of equations. I don't know how to solve the two equations below to get the approximation value of x, and y. All ...
17 views

Command line arguments to wolframscript interact strangely with -file option

In order to avoid script-defined command-line arguments clashing with existing arguments to wolframscript, it appears you are supposed to use the ...
28 views

Solve second order differential equation with boundary values

I'm a bit new to solving differential equations in Mathematica. I want to solve the differential equation for f(R): Eq = f''[R] + K2[R]*f[R] (*=0*) With the ...
37 views

Easy way of integrating the same integrand over several intervals?

I was wondering if there is some shorthand in Mathematica for expressions such as $$\left(\int_A + \int_B + \int_C + \cdots\right)F(x_1,\ldots, x_n) dx_1\cdots dx_n$$ where $A,B,C,\ldots$ each ...
50 views

Can this integral be calculated using Mathematica?

I have the following integral:  \int_{-\infty}^{\infty} \frac{\mathrm d\tau}{2\pi \mathrm i} \int_{-\infty}^{\infty} \frac{\mathrm d\tau'}{2\pi \mathrm i} \frac{\mathrm e^{-c^2(\tau - \tau')^2}}{(\...
34 views

Manipulate does not work with random and text display

I would like to do a small demonstration of Monte Carlo integration. However, When I generated the plot code, it does not work properly. ...
21 views

Invert color in MatrixPlot

How can I invert the grayscale colors when using MatrixPlot? My data is between 0 and 1 and the color scheme when using GrayLevel...
19 views

InputField enabled or disabled with two dynamic variables

Dynamic has been really useful for me but it is as well not easy to understand also. I am doing a calculation where I want some of the input fields enabled or disabled depending on where I am in the ...
66 views

Interactive Labeling of Images

I have a list of pictures: pictures = {im1,im2,im3,im4,im5,im6} Where im1: im2: im3: im4: im5: im6: I want to assign the pictures to labels (1,2,3,4,5 ...
41 views

Unable to use Solve to solve simultaneous equations, or use Maximize for exact maximum solution

Mathematica has found that the maximum of the following function is negative using NMaximize, but I am trying to prove that the maximum is negative (i.e. that the ...
280 views

Deleting duplicates only if they are a certain kind of duplicate

I have a list of tuples like this: {{1,a,b},{1,1,b},{1,a,a},{b,a,1},{b,a,b}} I would like to find a way to delete all those tuples in the list that contain a ...
63 views

Solve or Reduce don't work with Integer functions

I had been trying to limit for some c++ programs, the bigest whole number they can handle is lim = 18446744073709551615 and the different functions are: ...
46 views

Problem using Nonlinearfit on integral function

I tried to fit my data with a very complicate Integrated function. But I get many errors messages when I perform the fit. For exemple I get : NIntegrate::inumr: The integrand ....has evaluated to ...
20 views

Table of SystemModelSimulate Data

I am trying to simulate a model in SystemModeler from Mathematica 11.3. I wish to simulate this model for various parameter values and make a table of the output data. To attempt this I do the ...
36 views

Solved: Randomizing Initial Conditions of NDSolve Differential Equation Phase Space Plots with Looping Structures

I am looking for a way to randomize the initial conditions on the numerical approximation for the angular displacement of a plane pendulum. I have been trying for hours, and believe a For loop is ...
45 views

Changing the values of variables throughout a notebook

I have a model with many parameters, and I'd like to see how the model changes when some of those parameters change. Right now many of those parameters are set to prescribed values, i.e., ...
37 views

Why is my GroebnerBasis = 0 in this case?

I recently asked a question: Finding Intersections Between Arbitrary Surface and A Line whose solution required me to use the GroebnerBasis function. I successfully ...
98 views

How do we cluster separate curves in a set of data?

Below, I have included some data. (It is long, but I don't like to host data elsewhere and provide links that might some day be broken.) Plotting this set of data,...
37 views

Representing an interpolating function

I just want to figure out how to "represent" or to inject an interpolating function into a numerical calculation. So, suppose i have an interpolating function $int$ and then i want to use NDSolve or ...
50 views

Manipulation of 3D matrix

Assume that we have a 3D array x, and we would like to split it into 2D slices then cut every slice into some small patches and get all patches in single list ...
32 views

Find minimum precision setting

I am using FindMinimum command to find a local minimum of an object function. My code is below ...
45 views

Assume a variable is a Matrix

Is it possible to tell Mathematica to assume a variable is a matrix, analogous to assuming a variable is real with the Assuming command?
24 views

How put a matrix in a row (with or without index titles) using mathematica

I am trying to put a 16x16 complex matrix in a row, with separated columns to real and imaginary parts (i.e a 1x512 matrix). Additionally this 16x16 matrix is generated by an operator ...
53 views

How to run a CellularAutomaton until a configuration is repeated?

I would like to do something like CellularAutomaton[10, {1, 0, 0, 0, 0}, 2^5], but instead of running for 2^5, it should stop as ...
28 views

Not getting solution to simple equation [on hold]

qThis is my code. R = 12.17 g = 9.8 θ = 36 Degree Solve[R==v*cos[θ]*(v*sin[θ]+sqrt[(v*sin[θ])^\.1d2 \[Minus] 2*g]), v]` What is the problem with this code?
115 views

Transferring DownValues

I have a code in which I define something like this: cc[1, 2] = 1; cc[2, 6] = 12; cc[3, 7] = 3; After some manipulation I define a sort of temporary variable ...
58 views

Is there a way to automate this procedure?

I have some code which numerically solves a differential equation for a given value of the parameter $M0$ and for some initial conditions. The initial conditions will remain fixed throughout the ...
82 views

Convert Unicode to Math Input

Any Ideas how I could convert unicode to Mathematica Input ? For instance : I have the following Unicode: test= {"a", "\\:1d62"} So here I would like to convert ...
53 views

Deleting sub-list that contains duplicates

I have a large list of uniform-length lists. What is an efficient way to delete component lists that contain duplicates? For three-item sub-lists, I have used the following code: ...
83 views

How to make a frustum of a cone

For finite element purposes I need a frustum of a cone with a finite wall thickness, i.e. a tapered pipe. To make a cone is easy ...
45 views

Series expansion of a multi-variable function with singularities

Can anyone help me to find the series expansion as a polynomial of the following multi-variable function with singularities? f[x_, t_] := 1/(x - t)^(1/4) Where <...
47 views

How can I better formulate a conditional statement?

To solve optimization problems I have seen this: Is there a more elegant way to do this with alternative conditional expressions? Is there something equivelant to ...
25 views

Solving a Volterra integral Equation with singularities

Dears, I am trying to solve the equation in the below picture. What I did is: I used wavelet functions and substitute the wavelet instead of u, where I have the ...
86 views

Unexpected behaviour of PowerSpectralDensity

I recently wanted to calculate the power spectral density of a surface profile. I was happy to find out that there is a built in PowerSpectralDensity[] function in Mathematica (version 10). However, I'...
54 views

Create a cross-section, time series data set using Matrix operations

I have developed the following code, which produces what I aim to obtain. ...


text:
# Derivating a Yukawa theory loop-integral !

1. Jan 20, 2014

### Ace10

Hello fellow physicists,

during some calculations for a project regarding Renormalization, I had a difficulty in computing a derivative of a loop integral in Yukawa theory. The thing i'm reffering to can be found in Peskin and Schroeder's book, Introduction to QFT , in Chapter 10 page 329-330.

Question #1:

How the gamma function's argument changes from "1-d/2" (10.33) to "2-d/2" (10.35) ?

Question #2:

Could please somebody show me a detailed calculation of the derivation? I cannot get the finel form, with "x(1-x)" in the numerator and plus the denominator has power "2-d/2" and i think that normally the power should be "-d/2"

Thank you very much in advance..

2. Jan 20, 2014

### Bill_K

When you take the derivative of the denominator, a factor of 1-d/2 comes out, and then use the identity zΓ(z) = Γ(z+1).

format: plain


text:
# At what point would we stop seeing a star?

• B
The universe is expanding and at some point faster than light so once it reaches that point we wont see the light from those stars. I forget what this point is called.

If someone happened to be watching a star as it crossed that point would we see it simply blink out or close to that or would it kind of fade away to blackness. It seems to me that there should be a precise point where the speed of light is reached and one mile an hour faster than that would stop us from seeing it.

Of course since the star is huge the light from the leading edge of the star would be the first to go out then it would progress to the trailing edge so maybe it would not quite be a blink but close to it.

Am I thinking right?

tex

George Jones
Staff Emeritus
Gold Member
The universe is expanding and at some point faster than light so once it reaches that point we wont see the light from those stars. I forget what this point is called.
Care is needed with respect to the definition of "speed" in a cosmological setting.

this isn't true. It is true that recession speeds of galaxies that we now see will eventually exceed c, but it is not true that we loose sight of a galaxy once its recession speed exceeds c. If we see a galaxy now, then we will (in principle) always see the galaxy, even when its recession speed exceeds c.

Suppose we now see galaxy A. Assume that at time t in the future, A's recession speed is greater than c, and that at this time someone in galaxy A fires a laser pulse directly at us. Even though the pulse is fired directly at us, the proper distance between us and the pulse will initially increase. After a while, however, the pulse will "turn around", and the proper distance between us and the pulse will decrease, and the pulse will reach us, i.e., we still see galaxy A.
This can happen because the Hubble constant decreases with time (more on this near the end of this post) in the standard cosmological model for our universe. Consider the following diagram:

Code:
O                                B        A        C
*                                *        *        *

*                    *     *     *
O                    B     A     C
The bottom row of asterisks represents the positions in space (proper distances) of us (O) and galaxies B, A, and C, all at the same instant of cosmic time, $t_e$. The top row of asterisks represents the positions in space of us (O) and galaxies B, A, and C, all at some later instant of cosmic time, $t$. Notice that space has "expanded" between times $t_e$ and $t$.

Suppose that at time $t_e$: 1) galaxy A has recession speed (from us) greater than c; 2) galaxy A fires a laser pulse directed at us. Also suppose that at time $t$, galaxy B receives this laser pulse. In other words, the pulse was emitted from A in the bottom row and received by B in the top row. Because A's recession speed at time $t_e$ is greater than c, the pulse fired towards us has actually moved away from us between times $t_e$ and $t$.

Now, suppose that the distance from us to galaxy B at time $t$ is the same as the distance to galaxy C at time $t_e$. Even though the distances are the same, the recession speed of B at time $t$ is less than than the recession speed of C at time $t_e$ because:

1) recession speed equals the Hubble constant multiplied by distance;

2) the value of the Hubble constant decreases between times $t_e$ and $t$.

Since A's recession speed at time $t_e$ is greater than c, and galaxy C is farther than A, galaxy C's recession speed at time $t_e$ also is greater than c. If, however, the Hubble constant decreases enough between times $t_e$ and $t$, then B's recession speed at time $t$ can be less than c. If this is the case, then at time $t$ (and spatial position B), the pulse is moving towards us, i.e., the pulse "turned around" at some time between times $t_e$ and $t$.

If the value of the Hubble constant changes with time, what does the "constant" part of "Hubble constant" mean? It means constant in space. At time $t_e$, galaxies O, B, A, and C all perceive the same value for the Hubble constant. At time $t$, galaxies O, B, A, and C all perceive the same value for the Hubble constant. But these two values are different.

Probably some of my explanation is unclear. If so, please ask more questions.

Since the speed of recession is approaching the speed of light the star would be red-shifting. The horizon of the Universe behave very much like a black hole event horizon, the star would appear frozen at the horizon and red shift out of existence.

Jorrie
Gold Member
Since the speed of recession is approaching the speed of light the star would be red-shifting. The horizon of the Universe behave very much like a black hole event horizon, the star would appear frozen at the horizon and red shift out of existence.
This is not quite correct. The distance to the cosmological horizon D_Hor is larger than the Hubble radius R, where the recession rate equals c.

They only approach each other in the far future, when H becomes constant. Distant stars were always moving through the Hubble radius and we will see them farther and farther away, just red-shifting out of detectability, but never "frozen" at the horizon.

#### Attachments

• 9.3 KB Views: 328
|Glitch|
Jorrie


text:
# Types of programming languages used for optimization in finance

I'm currently taking graduate finance courses, and wish to pursue a career in finance - in particular $\textbf{optimization in finance}$. To date, I've only been taught the GAMS programming language (some models can be found at: https://www.gams.com/latest/finlib_ml/libhtml/index.html).

I've looked up What programming languages are most commonly used in quantitative finance? but found no other programming language that solves optimization problems in finance. Are there any other possible programs I can pick up which are still relevant in the industry?

• I believe this question will be closed as off topic but for what its worth most of this is done in general purpose programming languages in industry. As far as I have seen in terms of my work and from job postings these will be R, python, C++ & java. Some places also use Haskell or Scala and I've heard of places using Matlab. They are all as good at solving optimization problems as the programmer. – MD-Tech Nov 3 '17 at 11:03
• I would learn R and C++ if I were going to try to get to where I am now. – MD-Tech Nov 3 '17 at 11:06
• I use C#, Java, Python, and VBA. As mentioned above though, the languages are only as good as the developer. You will find lots of strong opinions and attitudes within the programming world though...It's as if an arrogance course is a prerequisite nowadays. – amdopt Nov 3 '17 at 13:53
• FWIW I use python not because I believe it to be the best optimising language (R, c++, MATLAB etc. can all implement the required algos as other have said) but because I find it easier to manipulate the inputs and outputs in a user interface, or for example with web interaction. – Attack68 Nov 5 '17 at 15:00
• Most of the optimization routines out there are written in Fortran/C/C++. Languages like R and Python typically call these Fortran/C/C++ libraries. You can write an optimization function in just about any languages. What has the best performance? Fortran/C/C++. However, it can be more productive in higher-level languages like R/Python. – John Nov 10 '17 at 3:44


text:
# Mathematica Moravica, Vol. 14-1 (2010)

A Class of Polynomials in Two Variables
Mathematica Moravica, Vol. 14-1 (2010), 1–14.

Download PDF file: (341kB) | Abstract and keywords
Abstract. In this paper, we present some families of polynomials in two variables. Some further results of these polynomials as generating function, Rodriguez formula and recurrence relations are discussed. We derive various families of bilinear and bilateral generating functions. We also give some particular cases reduced to Hermite-Hermite and Laguerre-Laguerre polynomials.
Keywords. Rodriguez formula, recurrence relation, generating function, bilinear and bilateral generating function.

Warped Product Semi-Invariant Submanifolds in Almost Paracontact Metric Manifolds
Mathematica Moravica, Vol. 14-1 (2010), 15–21.

Download PDF file: (333kB) | Abstract and keywords
Abstract. In this paper we have investigated the existence of warped product semi-invariant submanifolds in almost paracontact metric manifolds. Finally, we see that there exists no any warped product semi invariant submanifold in almost paracontact metric manifolds such that the contra variant vector field tangent to submanifold.
Keywords. Paracontact metric manifold, warped product, warped product semi-invariant submanifold.

Geometry of Semi-Invariant Submanifolds of a Riemannian Product Manifold
Mathematica Moravica, Vol. 14-1 (2010), 23–34.

Download PDF file: (363kB) | Abstract and keywords
Abstract. In this paper, we show new results on semi-invariant submanifolds of a Riemannian product manifold and introduce equations related with geometry of semi-invariant submanifold in real product space forms. We characterize and study the geometry of the semiinvariant submanifolds in a Riemannian product manifold.
Keywords. Riemannian product manifold, real space form; semiinvariant submanifold, Semi-Riemannian product, partially integrable and Ricci tensor and Scalar curvature.

Some Remarks on the Notion of Contraction of Lie Group Representations
Mathematica Moravica, Vol. 14-1 (2010), 35–46.

Download PDF file: (381kB) | Abstract and keywords
Abstract. In the series of papers [1-4], L. Barker developed a general notion of convergence for sequences of Hilbert spaces and related objects (vectors, operators...). In this paper, we remark that Barker's convergence for sequences of operators provides a notion of contraction of Lie group (unitary) representations and we compare it to the usual one introduced by J. Mickelsson and J. Niederle. This allows us to illustrate Barker's convergence of operators by various examples taken from contraction theory.
Keywords. Contractions, Lie groups, unitary representations, sequences of Hilbert spaces.

Some Equalities which Hold in the $(n,m)$-Group $(Q,A)$ for $n\geq 2m$
Mathematica Moravica, Vol. 14-1 (2010), 47–51.

Download PDF file: (340kB) | Abstract and keywords
Abstract. In this paper, we have proved two equalities which hold in an $(n,m)$-group $(Q,A)$ for $n\geq 2m$. The first of them is a generalization of the equality $(a\cdot b)^{-1} = b^{-1}\cdot a^{-1}$, which holds in the binary group $(Q,\cdot)$. The second of them is equality $A(x_{1}^{m}, b_{1}^{n-2m}, y_{1}^{m}) = A\bigl(A(x_{1}^{m}, a_{1}^{n-2m}, (a_{1}^{n-2m}, e(b_{1}^{n-2m}))^{-1}), a_{1}^{n-2m}, y_{1}^{m}\bigr).$ Keywords. $(n,m)$-group, $\{1, n-m+1\}$-neutral operation, inverse operation of the $(n,m)$-groupoid.

Central Operation of the $(n,m)$-Group
Mathematica Moravica, Vol. 14-1 (2010), 53–59.

Download PDF file: (341kB) | Abstract and keywords
Abstract. In this paper we have defined a central operation of the $(n,m)$-group, as a mapping $\alpha$ of the set $Q^{n-2m}$ into the set $Q^{m}$, such that for every $a_{1}^{n-2m}, b_{1}^{n-2m}\in Q$ and for every $x_{1}^{m}\in Q^{m}$ the following equality holds: $A(\alpha(a_{1}^{n-2m}), a_{1}^{n-2m}, x_{1}^{m}) = A(x_{1}^{m}, \alpha(b_{1}^{n-2m}), b_{1}^{n-2m}).$ This is a generalization of the notion of a central operation of the $n$-group, i.e. of the central element of a binary group. The notion of the central operation of the $n$-group was defined by Janez Ušan in [4]. Furthermore, in this paper we have proved some claims which hold for the central operation of the $(n, m)$-group.
Keywords. $(n, m)$-group, $\{1, n-m+1\}$-neutral operation, inverse operation of the $(n, m)$-groupoid, central operation.

The γ-open Open Topology for Function Spaces
Mathematica Moravica, Vol. 14-1 (2010), 61–67.

Download PDF file: (354kB) | Abstract and keywords
Abstract. In this paper we have introduced the notion of $\gamma$-open open topology and proved some properties which the topology does possess. We have also introduced the concept of convergence of nets in $\gamma H(X)$ (where $\gamma H(X)$ is the set of all self $\gamma$-homeomorphisms on a topological space $X$) and showed when $\gamma H(X)$ is complete.
Keywords. $\gamma$-open sets, $\gamma$-open open topology, $\gamma H(X)$-the set of all self $\gamma$-homeomorphisms on $X$, $\gamma$-convergence, $\gamma$-regular.

On the Hyper Order of Solutions of Linear Differential Equations with Entire Coefficients
Mathematica Moravica, Vol. 14-1 (2010), 69–82.

Download PDF file: (404kB) | Abstract and keywords
Abstract. In this paper, we investigate higher order homogeneous linear differential equations with entire coefficients of finite order. We improve and extend the results due to the second author and Hamouda by introducing the concept of hyper-order. We also consider non homogeneous linear differential equations.
Keywords. Differential equations, meromorphic function, hyper-order.

Convergence to Common Fixed Points of Two Asymptotically Nonexpansive Type Mappings
Mathematica Moravica, Vol. 14-1 (2010), 83–88.

Download PDF file: (337kB) | Abstract and keywords
Abstract. Common fixed points of two asymptotically non expansive type mappings have been approximated by strong convergence of an iteration scheme in a uniformly convex Banach space.
Keywords. Asymptotically nonexpansive type mappings, strong convergence, iteration scheme; common fixed points.

Common Random Fixed Point and Random Best Approximation in Non-Starshaped Domain of $q$-Normed Spaces
Mathematica Moravica, Vol. 14-1 (2010), 89–99.

Download PDF file: (366kB) | Abstract and keywords
Abstract. The aim of this paper is to obtain some common random fixed point by extending the concept of uniformly $\mathcal{R}$-subweakly commuting mappings to the case of non-star shaped domain in $q$-normed space. Random best approximation results have also been obtained as its application. This work provides extension as well as substantial improvement of some results in the existing literature.
Keywords. Asymptotically non-expansive maps, uniformly asymptotically regular map, random best approximation, random fixed point, random operator, non-expansivemapping, uniformly $\mathcal{R}$-subweakly commuting maps, property $(N)$, property $(C)$, $q$-normed space.

Convergence of Common Fixed Point for Asymptotically Quasi-Nonexpansive Mappings in Convex Metric Spaces
Mathematica Moravica, Vol. 14-1 (2010), 101–111.

Download PDF file: (361kB) | Abstract and keywords
Abstract. In this paper, the necessary and sufficient conditions for three-step iterative sequences with errors to converge to a common fixed point for three asymptotically quasi-nonexpansive mappings is established in convex metric spaces. The results of this paper are generalizations and improvements of the corresponding results of Chang [1] - [3], Kim et al. [8], Liu [9] - [11], Ghosh and Debnath [4], Xu and Noor [15], Shahzad and Udomene [13], Khan and Takahashi [6] and Khan and Uddin [7].
Keywords. Convex metric space, asymptotically quasi-nonexpansive mapping, asymptotically nonexpansive mapping, three-step iterative sequence with errors, common fixed point.

On the Convergence of Ishikawa Iterates to a Common Fixed Point for a Pair of Nonexpansive Mappings in Banach Spaces
Mathematica Moravica, Vol. 14-1 (2010), 113–119.

Download PDF file: (344kB) | Abstract and keywords
Abstract. In the present paper we prove a common fixed point theorem for Ishikawa iterates of a pair of multivalued mappings on a Banach space, satisfying nonexpansive type condition which extend and generalize the results of Rhoades [16, 17] and others.
Keywords. Ishikawa-type iteration, Banach spaces, multivalued nonexpansive mappings, common fixed point.

The Matrix Transformations on Double Sequence Space of χπ2
Mathematica Moravica, Vol. 14-1 (2010), 121–127.

Download PDF file: (397kB) | Abstract and keywords
Abstract. Let $\xi$ denote the space of all prime sense double gai sequences and $\Lambda^{2}$ the space of all prime sense double analytic sequences. First we show that the set $E = \{s^{(mn)}: m,n = 1, 2, 3, \dots\}$ is a determining set for $\chi_{\pi}^{2}$. The set of all finite matrices transforming $\chi_{\pi}^{2}$ into FK-space $Y$ denoted by $(\chi_{\pi}^{2}: Y)$. We characterize the classes $(\chi_{\pi}^{2}: Y)$ when $Y = c_{0}^{2}, c^{2}, \chi^{2}, l^{2}, \Lambda^{2}$. But the approach to obtain these result in the present paper is by determining set for $\chi_{\pi}^{2}$. First, we investigate a determining set for $\chi_{\pi}^{2}$ and then we characterize the classes of matrix transformations involving $\chi_{\pi}^{2}$ and other known sequence spaces.
Keywords. Determining set, gai sequence, analytic sequence, doublesequence.

CR-Warped Product Submanifolds of Lorentzian Manifolds
Mathematica Moravica, Vol. 14-1 (2010), 129–136.

Download PDF file: (350kB) | Abstract and keywords
Abstract. In this paper, we study warped product $CR$-submanifolds of a Lorentzian Sasakian manifold. We show that the warped product of the type $M = N_{\perp}\times_{f} N_{T}$ in a Lorentzian Sasakian manifold is simply $CR$-product and obtain a characterization of $CR$-warped product submanifolds.
Keywords. Warped product, $CR$-submanifold, contact $CR$-warped product, Lorentzian Sasakian manifold.

©2010 Mathematica Moravica


text:
# Bulk Modulus Formula

Bulk modulus is the modulus associated with volume strain. The strain equal to the change in volume divided by the original volume is called volume strain. The change in the relative volume of the object when a unit compressive or tensile stress acts on the surface of the object uniformly is called Bulk modulus. The units for the bulk modulus is the pascalThe Bulk modulus helps us understand how an object reacts when compressed from all sides equally.

## Bulk modulus formula

K = V(∆P) / ∆V

Where,

K= bulk modulus in pascal

∆P denotes the change in pressure in pascal

∆V denotes the change in volume in m3

V denotes the actual volume of the object in m3

Example 1

In ammunition testing centre the pressure is found to be 255 MPa. Calculate the change in volume of the piece of the copper piece when subjected to this pressure in percentage. The bulk modulus of copper is 1.38 x $10^{11}$ Pa.

Solution

The pressure in the testing centre is 255 MPa.

Bulk modulus,K = V(∆P) / ∆V

Substituting the values,

(ΔV / V) = 255×106/ 1.38×1011× 100

Therefore, the change in volume percentage is 0.184 %


text:
# sum of alternating series

• December 30th 2013, 11:29 AM
hedi
sum of alternating series
Hi,
I am trying to prone that the sum of the following series is log3.

1+1/2-2/3+1/4+1/5-2/6+1/7+1/8-2/9+1/10+1/11-2/12...

• December 30th 2013, 02:59 PM
chiro
Re: sum of alternating series
Hey hedi.

Hint: Look at the taylor series expanded around a = 1 (i.e. taylor series for log(1+x)).
• December 30th 2013, 03:06 PM
hedi
Re: sum of alternating series
This gives the harmonic alternating series,it is not so helpfull here.
• December 30th 2013, 03:21 PM
chiro
Re: sum of alternating series
Can you collect terms together to show that both are the same series?
• December 30th 2013, 03:25 PM
romsek
Re: sum of alternating series
Quote:

Originally Posted by hedi
Hi,
I am trying to prone that the sum of the following series is log3.

1+1/2-2/3+1/4+1/5-2/6+1/7+1/8-2/9+1/10+1/11-2/12...

I think this is the continued fraction form of the natural log. Take a look at the wiki page on continued fractions here or here
• December 31st 2013, 05:43 AM
SlipEternal
Re: sum of alternating series
Quote:

Originally Posted by hedi
Hi,
I am trying to prone that the sum of the following series is log3.

1+1/2-2/3+1/4+1/5-2/6+1/7+1/8-2/9+1/10+1/11-2/12...

Let $H_n$ be the $n$-th Harmonic number (the sum of the first $n$ terms of the Harmonic series). Consider partial sums of three terms of your series at a time. Show that $S_n = H_{3n}-H_n$ gives the correct partial sums for your series. So, your series is given by $\lim_{n \to \infty}S_n$.

Next, use common inequalities for the Harmonic numbers. For example, Young (1991) showed that $\dfrac{1}{2n+2} < H_n - \ln n - \gamma < \dfrac{1}{2n}$. So,

$\dfrac{1}{6n+2} < H_{3n} - \ln (3n) - \gamma < \dfrac{1}{6n}$ and $-\dfrac{1}{2n} < \gamma + \ln n - H_n < -\dfrac{1}{2n+2}$

$\dfrac{1}{6n+2} - \dfrac{1}{2n} < H_{3n} + \gamma + \ln n - \ln (3n) - \gamma - H_n < \dfrac{1}{6n} - \dfrac{1}{2n+2}$

Simplifying gives:

$-\dfrac{2n+1}{2n(3n+1)} < S_n - \ln 3 < \dfrac{1-2n}{6n(n+1)}$

Finally, use the Squeeze Theorem to show that $\lim_{n \to \infty} (S_n - \ln 3) = 0$, so $\lim_{n \to \infty} S_n = \ln 3$
• December 31st 2013, 07:31 AM
SlipEternal
Re: sum of alternating series
Btw, to show that $S_n = H_{3n} - H_n$, you can write your series as follows:

\begin{align*}1+\frac{1}{2} -\frac{2}{3} +\cdots + \frac{1}{3n-2} + \frac{1}{3n-1} - \frac{2}{3n} & = \sum_{k= 1}^n \left(\dfrac{1}{3k-2} + \dfrac{1}{3k-1} -\dfrac{2}{3k}\right) \\ & = \sum_{k= 1}^n \left(\dfrac{1}{3k-2} + \dfrac{1}{3k-1} + \dfrac{1}{3k} -\dfrac{3}{3k}\right) \\ & = \sum_{k= 1}^n \left(\dfrac{1}{3k-2} + \dfrac{1}{3k-1} + \dfrac{1}{3k}\right) -\sum_{k=1}^n\dfrac{1}{k} \\ & = \sum_{k=1}^{3n}\dfrac{1}{k} - \sum_{k=1}^n \dfrac{1}{k} \\ & = H_{3n} - H_n\end{align*}
• December 31st 2013, 08:03 AM
hedi
Re: sum of alternating series
Thanks to both of you so much.
• December 31st 2013, 11:50 AM
romsek
Re: sum of alternating series
I'm curious what course (if any) this would be learned in. I've had a fair bit of math and never ran into a detailed analysis of the Harmonic series like this.

Is this something you just naturally come across post-grad in the course of solving other problems?
• December 31st 2013, 01:06 PM
SlipEternal
Re: sum of alternating series
Quote:

Originally Posted by romsek
I'm curious what course (if any) this would be learned in. I've had a fair bit of math and never ran into a detailed analysis of the Harmonic series like this.

Is this something you just naturally come across post-grad in the course of solving other problems?

Are you asking hedi or me? If you are asking me, then this comes about from examining Euler's constant, which is $\gamma = \lim_{n \to \infty} H_n - \ln n$. Young was showing how quickly the sequence $H_n - \ln n$ converges to $\gamma$.
• December 31st 2013, 01:13 PM
hedi
Re: sum of alternating series
This question comes from a course in problem solving.
• December 31st 2013, 01:46 PM
SlipEternal
Re: sum of alternating series
Actually, I just thought of a more direct way to show that the series converges to $\ln 3$. By definition, $\gamma := \lim_{n \to \infty} (H_n - \ln n)$, so

\begin{align*}0 & = \gamma - \gamma \\ & = \lim_{n \to \infty} \left(H_{3n} - \ln (3n) \right) - \lim_{n \to \infty} \left( H_n - \ln n \right) \\ & = \lim_{n \to \infty} \left( H_{3n} - H_n - \ln 3 \right)\end{align*}
• January 1st 2014, 04:14 PM
Prove It
Re: sum of alternating series
This is not an alternating series...


text:
# How to show curve vertex tilt + radius value slider in custom toolshelf panel

Is it possible to generate a field in the a custom toolshelf panel that displays the curve vertex tilt value and make it editable like the tilt slider insider the transform tab in the properties panel?

I see that the operator is transform.tilt but I have no idea how to generate a UI value slider that displays the value and can edit it.

Is that even possible with Blender?

Curve vertex tilt transform command:

bpy.ops.transform.tilt(value=8.36929, mirror=False, proportional='DISABLED', proportional_edit_falloff='SPHERE', proportional_size=0.0323492)

Unfortunately the content of that Transform panel are defined outside of the Python api. But you could have something monsterously convoluted like this to show up the Tilt value of a single selected Control Point of a bezier_point

    if context.active_object:
if not context.active_object.data:
pass
else:
# you do more checking here to verify the kind of active_object
# I will ommit this from the example.

data = context.active_object.data
points = data.splines.active.bezier_points

selected_points = [idx for idx, p in enumerate(points) if p.select_control_point]
print(selected_points)
if len(selected_points) == 1:
idx = selected_points[0]
point = points[idx]
col = layout.column()
col.prop(point, "weight_softbody", text='weight')


text:
## Friday, April 10, 2015

### [OlymPri20150408CBP] Paths to avoid {#Combinatorics}

Question

Introduction
This is an mathematics olympiad question for primary schools, and it is also a good mind-stretching exercise for students taking H2 Mathematics or IB Mathematics.  The problem can be solved using good tactics (heuristics) and some knowledge of combinations.  The number of ways to choose  r  objects out of  n  (a.k.a. “n choose r”) is
For example, if you have  8  different balls  and you want to choose  3  out of the  8, the number of combinations is  8C3 = 56.   You write 8 on top and 3 below and then introduce new factors by successively decreasing each number by one, until the bottom factor reaches 1.  Notice that the number of factors in the numerator is equal to the number of factors in the denominator.
Sometimes, nCr is written like a  2 by 1  column vector.  Many teachers introduce the concept with a formula using factorials, but the above formula is more practical for calculations.  Combinations have a nice symmetrical property.  For example, 8C5 = 8C3 = 56.  Why?  That is because choosing  5  objects out of  8  is the same as choosing  3  to be rejected.  This can be verified by writing  8C5  out in full and cancelling the factors.

Solution

First, let us note that every path from  A  to  B  is equivalent to a sequence of right arrows (®) and up arrows (á).  In the above example, the path corresponds to a sequence “®áá®®á®®á”.  There are  9  symbols in each sequence, of which  5  must be “go right” and  4  must be “go forward”.  [H12* Think of a related problem]  The number of such paths is
W = # of paths from  A  to  B  = 9C4  = 9C4  =  126.

However, we do not want the paths that pass through  P  or  Q.  So we need to consider
X = # of paths from  A  to  B  passing through  P
Y = # of paths from  A  to  B  passing through  Q

The problem is, if you added these, the paths that pass through  P  and  Q  would have been double-counted.  So we also need to consider
Z = # of paths from  A  to  B  passing through  P  and  Q
The required number of paths would be  W – (X + YZ) = WXY + Z.  Let us calculate part by part.
X = # of paths from  A  to  B  passing through  P
= (# of paths from  A  to  P) ´ (# of paths from  P  to  B)
= 3C1 ´ 6C3  = 3 ´ 20 = 60
Y = # of paths from  A  to  B  passing through  Q
= (# of paths from  A  to  Q) ´ (# of paths from  Q  to  B)
= 6C2 ´ 3C2  = 15 ´ 3 = 45
Z = # of paths from  A  to  B  passing through  P  and  Q
= (# paths A  to  P) ´ (# paths  P  to  Q) ´ (# paths  Q  to  B)
= 3C1 ´ 3C1 ´ 3C2  = 3 ´ 3 ´ 3 = 27
The paths from  A  to  P  are chosen independently from the paths from  P  to  B.  That is why we are able to multiply the numbers.  Likewise, the other multiplications are justified because of independence.  Putting everything together,
# of paths from  A  to  B  passing through neither  P  nor  Q
= WXY + Z = 126 – 60 – 45 + 27 = 48   J

H02. Use a diagram / model
H09. Restate the problem in another way
H10. Simplify the problem
H11. Solve part of the problem
H12* Think of a related problem

Suitable Levels
* GCE ‘A’ Level H2 Mathematics (“Permutations and Combinations”)
*  IB Mathematics HL / SL (“Counting Principles”)


text:
# Scattering Without Scale, Or The S-Matrix In N=4

My research focuses on an unrealistic theory called massless $\mathcal{N}=4$ super Yang-Mills (SYM). This sounds pretty pointless, at least at first. But actually this model shares many features with more complete accounts of reality.  So it’s not all pie in the sky.

The reason I look at  SYM is because it contains lots of symmetry. This simplifies matters a lot. Studying SYM is like going to an adventure playground – you can still have great fun climbing and jumping, but it’s a lot safer than roaming out into a nearby forest.

Famously SYM has a conformal symmetry. Roughly speaking, this means that the theory looks the same at every length scale. (Whether conformal symmetry is equivalent to scale invariance is a hot topic, in fact)! Put another way, SYM has no real notion of length. I told you it was unrealistic.

This is a bit unfortunate for me, because I’d like to use SYM to think about particle scattering. To understand the problem, you need to know what I want to calculate. The official name for this quantity is the S-matrix.

The jargon is quite straightforward. “S” just stands for scattering. The “matrix” part tells you that this quantity encodes many possible scattering outcomes. To get an S-matrix, you have to assume you scatter particles from far away. That’s certainly the case in big particle accelerators – the LHC is huge compared to a proton!

But remember I said that SYM doesn’t have a length scale. So really you can’t get an S-matrix. And without an S-matrix, you can’t say anything about particle scattering. Things aren’t looking good.

Fortunately all is not lost. You can try to define an S-matrix using the usual techniques that worked in normal theories. All the calculations go through fine, unless there are any low energy particles around. Any of these so-called soft particles will cause your S-matrix to blow up to infinity!

But hey, we should expect our S-matrix to be badly behaved. After all, we’ve chosen a theory without a sense of scale! These irritating infinities go by the name of infrared divergences. Thankfully there’s a systematic way of eliminating them.

Remember that I said our SYM theory is massless. All the particles are like photons, constantly whizzing about that the speed of light. If you were a photon, life would be very dull. That’s because you’d move so fast through space you couldn’t move through time. This means that essentially our massless particles have no way of knowing about distances.

Viewed from this perspective it’s intuitive that this lack of mass yields the conformal symmetry. We can remove the troublesome divergences by destroying the conformal symmetry. We do this in a controlled way by giving some particles a small mass.

Technically our theory is now called Coulomb branch SYM. Who’s Coulomb, I hear you cry? He’s the bloke who developed electrostatics 250 years ago. And why’s he cropped up now? Because when we dispense with conformal symmetry, we’re left with some symmetries that match those of electromagnetism.

In Coulomb branch SYM it’s perfectly fine to define an S-matrix! You get sensible answers from all your calculations. Now imagine we try to recover our original theory by decreasing all masses to zero. Looking closely at the S-matrix, we see it split into two pieces – finite and infinite. Just ignore the infinite bit, and you’ve managed to extract useful scattering data for the original conformal theory!

You might think I’m a bit blasé in throwing away these divergences. But this is actually well-motivated physically. The reason is that such infinities cancel in any measurable quantity. You could say that they only appear in the first place because you’re doing the wrong sum!

This perspective has been formalized for the realistic theories as the KLN theorem. It may even be possible to get a rigorous version for our beloved massless $\mathcal{N}=4$ SYM.

So next time somebody tells you that you can’t do scattering in a conformal theory, you can explain why they’re wrong! Okay, I grant you, that’s an unlikely pub conversation. But stranger things have happened.

And if you’re planning to grab a pint soon, make it a scientific one!


text:
An Iso – Quant Curve always slopes downward from left to right. i.e., It should always have a Negative Slope

This is because, if producer wants to increase the proportion of one factor, it is possible only by reducing the proportion of another factor because of limited resources. The negative slope of Isoquants implies substitutability between the inputs. It means that if one of the inputs is reduced, the other inputs has to be so increased that the total output remains unaffected. To represent this concept, it should always slope downward. This can be explained with the help of a diagram:

An Iso – Quant will be always convex to the origin

The Law of Diminishing Marginal Rate of Technical Substitution (MRTS) could be explained only if it is convex to the origin. The rate at which one factor is substituted for another factor is known as Technical Substitution.

An Iso-Quant curve drawn to the right hand side of an existing Iso-Quant curve represents higher output

If the manufacturer selects combination M, he would be using 2 units of capital and 4 units of labour, but if he selects combination N, he will be using 4 units of capital and 4 units of labour. Higher the inputs higher would be the output.

The collection of iso-quant curves/the family of iso-quants, is known as “Iso-Quants Map”. In an iso-quants map, an iso-quant curve at the extreme right represents highest level of out put and the curve at the extreme left represents lowest amount of out put. Hence IQ4>IQ3>IQ2>IQ1.

No two Iso-Quant curves should intersects each other

Each iso-quant curve represents a particular level of output and iso-quant curve to the right represents higher output. If they intersect each other, at one point both will give the same level of out put, which is untrue.

No Iso-Quant curve should touch the horizontal or either the vertical axis

The basic assumption is that the producer will use a combination of factor inputs. If an Iso-Quant curve touches either vertical or horizontal axis, this assumption will be violated.

The Iso-Quant curves need not be parallel to each other

The iso-quant curves need not be parallel to each other because the marginal rate of Technical Substitution mayn’t be the same in all the iso-quant curves. Hence it is not a necessary condition that all the iso-quant curves should be parallel to each other.


text:
Control Surface main MIDI Control Surface library for Arduino
Bankable/NoteButtons.cpp
Go to the documentation of this file.


text:
load_all() loads a package. It roughly simulates what happens when a package is installed and loaded with library(), without having to first install the package. It:

• Loads all data files in data/. See load_data() for more details.

• Sources all R files in the R directory, storing results in environment that behaves like a regular package namespace. See load_code() for more details.

• Adds a shim from system.file() to shim_system.file() in the imports environment of the package. This ensures that system.file() works with both development and installed packages despite their differing directory structures.

• Adds shims from help() and ? to shim_help() and shim_question() to make it easier to preview development documentation.

• Compiles any C, C++, or Fortran code in the src/ directory and connects the generated DLL into R. See pkgbuild::compile_dll() for more details.

• Loads any compiled translations in inst/po.

• Runs .onAttach(), .onLoad() and .onUnload() functions at the correct times.

• If you use testthat, will load all test helpers so you can access them interactively. devtools sets the DEVTOOLS_LOAD environment variable to "true" to let you check whether the helpers are run during package loading.

is_loading() returns TRUE when it is called while load_all() is running. This may be useful e.g. in .onLoad hooks.

## Usage

load_all(
path = ".",
reset = TRUE,
compile = NA,
attach = TRUE,
export_all = TRUE,
export_imports = export_all,
helpers = TRUE,
attach_testthat = uses_testthat(path),
quiet = NULL,
recompile = FALSE,
warn_conflicts = TRUE
)

is_loading(pkg = NULL)

## Arguments

path

Path to a package, or within a package.

reset

clear package environment and reset file cache before loading any pieces of the package. This largely equivalent to running unload(), however the old namespaces are not completely removed and no .onUnload() hooks are called. Use reset = FALSE may be faster for large code bases, but is a significantly less accurate approximation.

compile

If TRUE always recompiles the package; if NA recompiles if needed (as determined by pkgbuild::needs_compile()); if FALSE, never recompiles.

attach

Whether to attach a package environment to the search path. If FALSE load_all() behaves like loadNamespace(). If TRUE (the default), it behaves like library(). If FALSE, the export_all, export_imports, and helpers arguments have no effect.

export_all

If TRUE (the default), export all objects. If FALSE, export only the objects that are listed as exports in the NAMESPACE file.

export_imports

If TRUE (the default), export all objects that are imported by the package. If FALSE export only objects defined in the package.

helpers

if TRUE loads testthat test helpers.

attach_testthat

If TRUE, attach testthat to the search path, which more closely mimics the environment within test files.

quiet

if TRUE suppresses output from this function.

recompile

DEPRECATED. force a recompile of DLL from source code, if present. This is equivalent to running pkgbuild::clean_dll() before load_all()

warn_conflicts

If TRUE, issues a warning if a function in the global environment masks a function in the package. This can happen when you accidentally source a .R file, rather than using load_all(), or if you define a function directly in the R console. This is frustrating to debug, as it feels like the changes you make to the package source aren't having the expected effect.

pkg

If supplied, is_loading() only returns TRUE if the package being loaded is pkg.

load_all() tries its best to reproduce the behaviour of loadNamespace() and library(). However it deviates from normal package loading in several ways.

• load_all() doesn't install the package to a library, so system.file() doesn't work. pkgload fixes this for the package itself installing a shim, shim_system.file(). However, this shim is not visible to third party packages, so they will fail if they attempt to find files within your package. One potential workaround is to use fs::path_package() instead of system.file(), since that understands the mechanisms that devtools uses to load packages.

• load_all() loads all packages referenced in Imports at load time, but loadNamespace() and library() only load package dependencies as they are needed.

• load_all() copies all objects (not just the ones listed as exports) into the package environment. This is useful during development because it makes internal objects easy to access. To export only the objects listed as exports, use export_all = FALSE. This more closely simulates behavior when loading an installed package with library(), and can be useful for checking for missing exports.

## Examples

if (FALSE) {
# Load the package in the current directory


text:
# Hilbert scheme of 2 points on an elliptic curve

The Hilbert scheme of 2 points on an elliptic curve $C$, $Hilb^2(C)$, has a natural structure of ruled surface, given by the map $f:Hilb^2(C) \to C$ such that $f(P,Q)=P+Q$.

What can we say about the corresponding locally free sheaf of rank 2 on $C$?

-

In this case the corresponding locally free sheaf or rank $2$ on $C$ is the unique indecomposable one.
Dimitri means that it is (up to translations) the unique nontrivial extension of degree 1 $1 \to \mathcal{O}_C→E→\mathcal{O}_C(o) \to 1$, where $o \in C$ is the origin in the group law. –  Francesco Polizzi Nov 5 '12 at 12:35
The curves of the form $D_P=\{x+P \, | \, x \in C \}$ are a $1$-dimensional algebraic family of sections with self-intersection $1$, and moreover one cannot find two disjoint sections... –  Francesco Polizzi Nov 5 '12 at 16:51


text:
Angular 2 – Two Ways to Pass Data to Components

This article represents concepts and code samples in relation to how one could pass data from one component to another in an Angular app. Please feel free to comment/suggest if I missed mentioning one or more important points. Also, sorry for the typos.

As Angular is primarily based on components and components interaction, it is important to understand how data is passed from one component to another. Data is passed between the component using property bindings. Take a look at the syntax below:

<user [value]="user"></user>

In above syntax, user component’s property “value” is bound to “user” property of the parent component. The data type of the bound property needs to be matched. Thus, if the “value” is an object, the “user” property of parent component also needs to be an object. To achieve the contractual requirement, one could take define a user “interface” and then create a property of interface type for consistency. Following is sample code for the user interface. The code below could be saved in a separate file such as user.ts and the interface could be imported in different component appropriately.

export interface User {
id: number,
name: string,
email: string,
age: number
}

Following are two different syntax that could be used in the Child component for it to receive the input from the parent component.

Usage of @Input Decorator

@Input decorator is used to define the property which receives the data from parent property. In other words, the @Input decorator adds metadata to the class that makes the “value” property, in the code below, available for property binding under the “value” alias. Take a look at the User component below and usage of @Input decorator.

import {Component, View} from 'angular2/core';
import {User} from './user';

@Component({
selector: 'user',
})
@View({
template: '{{value.name}}'
})
export class UserComponent {
@Input('value') value: User;
}

Usage of inputs Array

Another way is to use “inputs” array in the @Component metadata. Take a look at the following code:

import {Component, View} from 'angular2/core';
import {User} from './user';

@Component({
selector: 'user',
inputs: ['value']
})
@View({
template: '{{value.name}}'
})
export class UserComponent {
value: User;
}


text:
The OrinaryLeastSquares regressor in Mahout implements a closed-form solution to Ordinary Least Squares. This is in stark contrast to many “big data machine learning” frameworks which implement a stochastic approach. From the users perspecive this difference can be reduced to:

• Stochastic- A series of guesses at a line line of best fit.
• Closed Form- A mathimatical approach has been explored, the properties of the parameters are well understood, and problems which arise (and the remedial measures), exist. This is usually the preferred choice of mathematicians/statisticians, but computational limititaions have forced us to resort to SGD.

### Parameters

Parameter Description Default Value
'calcCommonStatistics Calculate commons statistics such as Coeefficient of Determination and Mean Square Error true
'calcStandardErrors Calculate the standard errors (and subsequent "t-scores" and "p-values") of the $$\boldsymbol{\beta}$$ estimates true
'addIntercept Add an intercept to $$\mathbf{X}$$ true

### Example

In this example we disable the “calculate common statistics” parameters, so our summary will NOT contain the coefficient of determination (R-squared) or Mean Square Error

import org.apache.mahout.math.algorithms.regression.OrdinaryLeastSquares

val drmData = drmParallelize(dense(
(2, 2, 10.5, 10, 29.509541),  // Apple Cinnamon Cheerios
(1, 2, 12,   12, 18.042851),  // Cap'n'Crunch
(1, 1, 12,   13, 22.736446),  // Cocoa Puffs
(2, 1, 11,   13, 32.207582),  // Froot Loops
(1, 2, 12,   11, 21.871292),  // Honey Graham Ohs
(2, 1, 16,   8,  36.187559),  // Wheaties Honey Gold
(6, 2, 17,   1,  50.764999),  // Cheerios
(3, 2, 13,   7,  40.400208),  // Clusters
(3, 3, 13,   4,  45.811716)), numPartitions = 2)

val drmX = drmData(::, 0 until 4)
val drmY = drmData(::, 4 until 5)

val model = new OrdinaryLeastSquares[Int]().fit(drmX, drmY, 'calcCommonStatistics → false)
println(model.summary)


text:
Time series data is widely present in our lives. Stock prices, house prices, weather information, and sales data captured over time are just a few examples. As businesses increasingly look for new ways to gain meaningful insights from time-series data, the ability to visualize data and apply desired transformations are fundamental steps. However, time-series data possesses unique characteristics and nuances compared to other kinds of tabular data, and require special considerations. For example, standard tabular or cross-sectional data is collected at a specific point in time. In contrast, time series data is captured repeatedly over time, with each successive data point dependent on its past values.

Because most time series analyses rely on the information gathered across a contiguous set of observations, missing data and inherent sparseness can reduce the accuracy of forecasts and introduce bias. Additionally, most time series analysis approaches rely on equal spacing between data points, in other words, periodicity. Therefore, the ability to fix data spacing irregularities is a critical prerequisite. Finally, time series analysis often requires the creation of additional features that can help explain the inherent relationship between input data and future predictions. All these factors differentiate time series projects from traditional machine learning (ML) scenarios and demand a distinct approach to its analysis.

This post walks through how to use Amazon SageMaker Data Wrangler to apply time series transformations and prepare your dataset for time series use cases.

## Use cases for Data Wrangler

Data Wrangler provides a no-code/low-code solution to time series analysis with features to clean, transform, and prepare data faster. It also enables data scientists to prepare time series data in adherence to their forecasting model’s input format requirements. The following are a few ways you can use these capabilities:

• Descriptive analysis– Usually, step one of any data science project is understanding the data. When we plot time series data, we get a high-level overview of its patterns, such as trend, seasonality, cycles, and random variations. It helps us decide the correct forecasting methodology for accurately representing these patterns. Plotting can also help identify outliers, preventing unrealistic and inaccurate forecasts. Data Wrangler comes with a seasonality-trend decomposition visualization for representing components of a time series, and an outlier detection visualization to identify outliers.
• Explanatory analysis– For multi-variate time series, the ability to explore, identify, and model the relationship between two or more time series is essential for obtaining meaningful forecasts. The Group by transform in Data Wrangler creates multiple time series by grouping data for specified cells. Additionally, Data Wrangler time series transforms, where applicable, allow specification of additional ID columns to group on, enabling complex time series analysis.
• Data preparation and feature engineering– Time series data is rarely in the format expected by time series models. It often requires data preparation to convert raw data into time series-specific features. You may want to validate that time series data is regularly or equally spaced prior to analysis. For forecasting use cases, you may also want to incorporate additional time series characteristics, such as autocorrelation and statistical properties. With Data Wrangler, you can quickly create time series features such as lag columns for multiple lag periods, resample data to multiple time granularities, and automatically extract statistical properties of a time series, to name a few capabilities.

## Solution overview

This post elaborates on how data scientists and analysts can use Data Wrangler to visualize and prepare time series data. We use the bitcoin cryptocurrency dataset from cryptodatadownload with bitcoin trading details to showcase these capabilities. We clean, validate, and transform the raw dataset with time series features and also generate bitcoin volume price forecasts using the transformed dataset as input.

The sample of bitcoin trading data is from January 1 – November 19, 2021, with 464,116 data points. The dataset attributes include a timestamp of the price record, the opening or first price at which the coin was exchanged for a particular day, the highest price at which the coin was exchanged on the day, the last price at which the coin was exchanged on the day, the volume exchanged in the cryptocurrency value on the day in BTC, and corresponding USD currency.

## Prerequisites

Download the Bitstamp_BTCUSD_2021_minute.csv file from cryptodatadownload and upload it to Amazon Simple Storage Service (Amazon S3).

Import bitcoin dataset in Data Wrangler

To start the ingestion process to Data Wrangler, complete the following steps:

1. On the SageMaker Studio console, on the File menu, choose New, then choose Data Wrangler Flow.
2. Rename the flow as desired.
3. For Import data, choose Amazon S3.
4. Upload the Bitstamp_BTCUSD_2021_minute.csv file from your S3 bucket.

You can now preview your data set.

1. In the Details pane, choose Advanced configuration and deselect Enable sampling.

This is a relatively small data set, so we don’t need sampling.

1. Choose Import.

You have successfully created the flow diagram and are ready to add transformation steps.

To add data transformations, choose the plus sign next to Data types and choose Edit data types.

Ensure that Data Wrangler automatically inferred the correct data types for the data columns.

In our case, the inferred data types are correct. However, suppose one data type was incorrect. You can easily modify them through the UI, as shown in the following screenshot.

Let’s kick off the analysis and start adding transformations.

## Data cleaning

We first perform several data cleaning transformations.

### Drop column

Let’s start by dropping the unix column, because we use the date column as the index.

1. Choose Back to data flow.
2. Choose the plus sign next to Data types and choose Add transform.
3. Choose + Add step in the TRANSFORMS pane.
4. Choose Manage columns.
5. For Transform, choose Drop column.
6. For Column to drop, choose unix.
7. Choose Preview.
8. Choose Add to save the step.

### Handle missing

Missing data is a well-known problem in real-world datasets. Therefore, it’s a best practice to verify the presence of any missing or null values and handle them appropriately. Our dataset doesn’t contain missing values. But if there were, we would use the Handle missing time series transform to fix them. Commonly used strategies for handling missing data include dropping rows with missing values or filling the missing values with reasonable estimates. Because time series data relies on a sequence of data points across time, filling missing values is the preferred approach. The process of filling missing values is referred to as imputation. The Handle missing time series transform allows you to choose from multiple imputation strategies.

1. Choose + Add step in the TRANSFORMS pane.
2. Choose the Time Series transform.
3. For Transform, Choose Handle missing.
4. For Time series input type, choose Along column.
5. For Method for imputing values, choose Forward fill.

The Forward fill method replaces the missing values with the non-missing values preceding the missing values.

Backward fill, Constant Value, Most common value and Interpolate are other imputation strategies available in Data Wrangler. Interpolation techniques rely on neighboring values for filling missing values. Time series data often exhibits correlation between neighboring values, making interpolation an effective filling strategy. For additional details on the functions you can use for applying interpolation, refer to pandas.DataFrame.interpolate.

### Validate timestamp

In time series analysis, the timestamp column acts as the index column, around which the analysis revolves. Therefore, it’s essential to make sure the timestamp column doesn’t contain invalid or incorrectly formatted time stamp values. Because we’re using the date column as the timestamp column and index, let’s confirm its values are correctly formatted.

1. Choose + Add step in the TRANSFORMS pane.
2. Choose the Time Series transform.
3. For Transform, choose Validate timestamps.

The Validate timestamps transform allows you to check that the timestamp column in your dataset doesn’t have values with an incorrect timestamp or missing values.

1. For Timestamp Column, choose date.
2. For Policy dropdown, choose Indicate.

The Indicate policy option creates a Boolean column indicating if the value in the timestamp column is a valid date/time format. Other options for Policy include:

• Error – Throws an error if the timestamp column is missing or invalid
• Drop – Drops the row if the timestamp column is missing or invalid
1. Choose Preview.

A new Boolean column named date_is_valid was created, with true values indicating correct format and non-null entries. Our dataset doesn’t contain invalid timestamp values in the date column. But if it did, you could use the new Boolean column to identify and fix those values.

1. Choose Add to save this step.

## Time series visualization

After we clean and validate the dataset, we can better visualize the data to understand its different component.

### Resample

Because we’re interested in daily predictions, let’s transform the frequency of data to daily.

The Resample transformation changes the frequency of the time series observations to a specified granularity, and comes with both upsampling and downsampling options. Applying upsampling increases the frequency of the observations (for example from daily to hourly), whereas downsampling decreases the frequency of the observations (for example from hourly to daily).

Because our dataset is at minute granularity, let’s use the downsampling option.

2. Choose the Time Series transform.
3. For Transform, choose Resample.
4. For Timestamp, choose date.
5. For Frequency unit, choose Calendar day.
6. For Frequency quantity, enter 1.
7. For Method to aggregate numeric values, choose mean.
8. Choose Preview.

The frequency of our dataset has changed from per minute to daily.

1. Choose Add to save this step.

### Seasonal-Trend decomposition

After resampling, we can visualize the transformed series and its associated STL (Seasonal and Trend decomposition using LOESS) components using the Seasonal-Trend-decomposition visualization. This breaks down original time series into distinct trend, seasonality and residual components, giving us a good understanding of how each pattern behaves. We can also use the information when modelling forecasting problems.

Data Wrangler uses LOESS, a robust and versatile statistical method for modelling trend and seasonal components. It’s underlying implementation uses polynomial regression for estimating nonlinear relationships present in the time series components (seasonality, trend, and residual).

1. Choose Back to data flow.
2. Choose the plus sign next to the Steps on Data Flow.
4. In the Create analysis pane, for Analysis type, choose Time Series.
5. For Visualization, choose Seasonal-Trend decomposition.
6. For Analysis Name, enter a name.
7. For Timestamp column, choose date.
8. For Value column, choose Volume USD.
9. Choose Preview.

The analysis allows us to visualize the input time series and decomposed seasonality, trend, and residual.

1. Choose Save to save the analysis.

With the seasonal-trend decomposition visualization, we can generate four patterns, as shown in the preceding screenshot:

• Original – The original time series re-sampled to daily granularity.
• Trend – The polynomial trend with an overall negative trend pattern for the year 2021, indicating a decrease in Volume USD value.
• Season – The multiplicative seasonality represented by the varying oscillation patterns. We see a decrease in seasonal variation, characterized by decreasing amplitude of oscillations.
• Residual – The remaining residual or random noise. The residual series is the resulting series after trend and seasonal components have been removed. Looking closely, we observe spikes between January and March, and between April and June, suggesting room for modelling such particular events using historical data.

These visualizations provide valuable leads to data scientists and analysts into existing patterns and can help you choose a modelling strategy. However, it’s always a good practice to validate the output of STL decomposition with the information gathered through descriptive analysis and domain expertise.

To summarize, we observe a downward trend consistent with original series visualization, which increases our confidence in incorporating the information conveyed by trend visualization into downstream decision-making. In contrast, the seasonality visualization helps inform the presence of seasonality and the need for its removal by applying techniques such as differencing, it doesn’t provide the desired level of detailed insight into various seasonal patterns present, thereby requiring deeper analysis.

## Feature engineering

After we understand the patterns present in our dataset, we can start to engineer new features aimed to increase the accuracy of the forecasting models.

### Featurize datetime

Let’s start the feature engineering process with more straightforward date/time features. Date/time features are created from the timestamp column and provide an optimal avenue for data scientists to start the feature engineering process. We begin with the Featurize datetime time series transformation to add the month, day of the month, day of the year, week of the year, and quarter features to our dataset. Because we’re providing the date/time components as separate features, we enable ML algorithms to detect signals and patterns for improving prediction accuracy.

2. Choose the Time Series transform.
3. For Transform, choose Featurize datetime.
4. For Input Column, choose date.
5. For Output Column, enter date (this step is optional).
6. For Output mode, choose Ordinal.
7. For Output format, choose Columns.
8. For date/time features to extract, select Month, Day, Week of year, Day of year, and Quarter.
9. Choose Preview.

The dataset now contains new columns named date_month, date_day, date_week_of_year, date_day_of_year, and date_quarter. The information retrieved from these new features could help data scientists derive additional insights from the data and into the relationship between input features and output features.

1. Choose Add to save this step.

### Encode categorical

Date/time features aren’t limited to integer values. You may also choose to consider certain extracted date/time features as categorical variables and represent them as one-hot encoded features, with each column containing binary values. The newly created date_quarter column contains values between 0-3, and can be one-hot encoded using four binary columns. Let’s create four new binary features, each representing the corresponding quarter of the year.

2. Choose the Encode categorical transform.
3. For Transform, choose One-hot encode.
4. For Input column, choose date_quarter.
5. For Output style, choose Columns.
6. Choose Preview.

### Lag feature

Next, let’s create lag features for the target column Volume USD. Lag features in time series analysis are values at prior timestamps that are considered helpful in inferring future values. They also help identify autocorrelation (also known as serial correlation) patterns in the residual series by quantifying the relationship of the observation with observations at previous time steps. Autocorrelation is similar to regular correlation but between the values in a series and its past values. It forms the basis for the autoregressive forecasting models in the ARIMA series.

With the Data Wrangler Lag feature transform, you can easily create lag features n periods apart. Additionally, we often want to create multiple lag features at different lags and let the model decide the most meaningful features. For such a scenario, the Lag features transform helps create multiple lag columns over a specified window size.

1. Choose Back to data flow.
2. Choose the plus sign next to the Steps on Data Flow.
4. Choose Time Series transform.
5. For Transform, choose Lag features.
6. For Generate lag features for this column, choose Volume USD.
7. For Timestamp Column, choose date.
8. For Lag, enter 7.
9. Because we’re interested in observing up to the previous seven lag values, let’s select Include the entire lag window.
10. To create a new column for each lag value, select Flatten the output.
11. Choose Preview.

Seven new columns are added, suffixed with the lag_number keyword for the target column Volume USD.

1. Choose Add to save the step.

### Rolling window features

We can also calculate meaningful statistical summaries across a range of values and include them as input features. Let’s extract common statistical time series features.

Data Wrangler implements automatic time series feature extraction capabilities using the open source tsfresh package. With the time series feature extraction transforms, you can automate the feature extraction process. This eliminates the time and effort otherwise spent manually implementing signal processing libraries. For this post, we extract features using the Rolling window features transform. This method computes statistical properties across a set of observations defined by the window size.

2. Choose the Time Series transform.
3. For Transform, choose Rolling window features.
4. For Generate rolling window features for this column, choose Volume USD.
5. For Timestamp Column, choose date.
6. For Window size, enter 7.

Specifying a window size of 7 computes features by combining the value at the current timestamp and values for the previous seven timestamps.

1. Select Flatten to create a new column for each computed feature.
2. Choose your strategy as Minimal subset.

This strategy extracts eight features that are useful in downstream analyses. Other strategies include Efficient Subset, Custom subset, and All features. For full list of features available for extraction, refer to Overview on extracted features.

1. Choose Preview.

We can see eight new columns with specified window size of 7 in their name, appended to our dataset.

1. Choose Add to save the step.

## Export the dataset

We have transformed the time series dataset and are ready to use the transformed dataset as input for a forecasting algorithm. The last step is to export the transformed dataset to Amazon S3. In Data Wrangler, you can choose Export step to automatically generate a Jupyter notebook with Amazon SageMaker Processing code for processing and exporting the transformed dataset to a S3 bucket. However, because our dataset contains just over 300 records, let’s take advantage of the Export data option in the Add Transform view to export the transformed dataset directly to Amazon S3 from Data Wrangler.

1. Choose Export data.

1. For S3 location, choose Browser and choose your S3 bucket.
2. Choose Export data.

Now that we have successfully transformed the bitcoin dataset, we can use Amazon Forecast to generate bitcoin predictions.

## Clean up

If you’re done with this use case, clean up the resources you created to avoid incurring additional charges. For Data Wrangler you can shutdown the underlying instance when finished. Refer to Shut Down Data Wrangler documentation for details. Alternatively, you can continue to Part 2 of this series to use this dataset for forecasting.

## Summary

This post demonstrated how to utilize Data Wrangler to simplify and accelerate time series analysis using its built-in time series capabilities. We explored how data scientists can easily and interactively clean, format, validate, and transform time series data into the desired format, for meaningful analysis. We also explored how you can enrich your time series analysis by adding a comprehensive set of statistical features using Data Wrangler. To learn more about time series transformations in Data Wrangler, see Transform Data.


text:
# Fortran solver for the Sparse LSE problem

I was wondering if there is a Fortran library that contains a solver for the Sparse LSE(linear equality-constrained least squares) problem $$min_{x}\|Cx-d\|^2 \text{ subject to } Ax=b$$ where $A$ and $C$ are large and sparse.

For dense linear systems, LAPACK has the subroutine DGGLSE, but I am looking for a solver for sparse systems.


text:
Author Bio: Sam started Financial Samurai in 2009 to help people achieve financial freedom sooner, rather than later. He spent 13 years working in investment banking, earned his MBA from UC Berkeley, and retired at age 34 in San Francisco. Everything Sam writes is based on first-hand experience because money is too important to be left up to pontification.
I do remember you mentioning that & how it was your ticket to exit softly and give you time to build the passive income side. Most likely when I do exit it will either be through a sale of the business which would come along with a employment contract or if a worthy successor(s) can take it over, then the business is just another annuity throwing off income. Anyway, I’d enjoy writing a guest article after I survive the next few weeks of work and weddings.

In 2011, the Indian government concluded that most spending fails to reach its intended recipients, as the large and inefficient bureaucracy consumes budgets.[381] India's absence rates are among the worst in the world; one study found that 25% of public sector teachers and 40% of government-owned public-sector medical workers could not be found at the workplace.[382][383] Similarly, there are many issues facing Indian scientists, with demands for transparency, a meritocratic system, and an overhaul of the bureaucratic agencies that oversee science and technology.[384]
What I Do: I’ve set up multiple investment accounts outside my main operations bank that deals with working capital e.g checking, paying bills. By transferring my money to a couple brokerage accounts and two other banks as soon as it hits my main bank I no longer have temptation to spend on frivolous things. As a result, I can wake up 10 years later and reap the rewards of compounding. My 401(k) is the best example where constant contributions over 18 years has grown to over $500,000 without any savings pain given it just became a part of life. Real estate is also a fantastic asset class for the long term. It’s fantastic to enjoy your home, pay down your mortgage each month, and end up with a paid off asset that has likely appreciated during your time of ownership. Since I knew I’d eventually be losing my day job income, I had to set realistic goals. There was no way I was going to make a six figure salary blogging and working online after only 2 years but I thought it might be possible to cover our monthly expenses for a few months while I took time off and looked for a new job. I already had some secondary sources of income and there were others that I specifically tried to build up. This is the best post I’ve seen on passive income streams. I’m similar to you in that I worked in IBanking for a few years but wanted out. My approach is a little different, instead of starting with the CD’s, I’m trying to build up my net worth with riskier asset classes such as stocks and real estate to get the benefit of compounding. Then, as I approach my retirement year goal, I’ll start moving them into CD and bond ladders. In theory at least, it’s best to have the highest net worth just before retirement, then convert them to risk free passive income. You’re method is more patient and probably more practical than mine. I guess I’m willing to take more risks. ###### P2P lending started in San Francisco with Lending Club in mid-2000. The idea of peer-to-peer lending is to disintermediate banks and help denied borrowers get loans at potentially lower rates compared to the rates of larger financial institutions. What was once a very nascent industry has now grown into a multi-billion dollar business with full regulation. Lots of good insights here. I’ve just recently gotten my own website for making online income. Also gotten a website for my fledgling voice over business. There’s a lot to learn when it comes to making passive income online, especially if you’re not financially savy, this is a very helpful blog in that regard, with all the useful tools and reference materials, it certainly removes a lot of guesswork. It has been always observed that diversity wherever persists balances the nature, same rule applies with the money as well. When an income source is diversified, it becomes feasible for a person to fight with the crucial situations of life and to protect their loved ones from ups and downs of life. Diversification of income becomes important because if one source of income dries up; you still are running everything smoothly with the other sources of income and it keeps your life going without hitting your financial situations massively. The key here is not worry about getting picked. Just do it for your enjoyment and satisfaction. Rewards will come to you. You only have to stick to the topic of the blog. Once you've achieved some decent number of followers, you can combine your posts into an ebook and sell it on amazon.com or smashwords.com. Advertise about the book on your blog and social media platforms, give out some special discounts to those who order from your blog and plan to gift a freebie to the first 100 buyers or so. Be creative with it. My first ebook got me 7,000 rupees and I had made it in just 1 day. Imagine if you put more effort into it, you could write a bestseller, dude! As interest rates have been going down over the past 30 years, bond prices have continued to go up. With the 10-year yield (risk free rate) at roughly 2.55%, and the Fed Funds rate at 1.5% (two more 0.25% hikes are expected in 2018), it’s hard to see interest rates declining much further. That said, long term interest rates can stay low for a long time. Just look at Japanese interest rates, which are negative (inflation is higher than nominal interest rate). Question: You mention receiving$200k of passive income a year, but your chart shows half of that coming from real estate holdings, and reading between the lines it appears that you hold mortgages against those holdings. Then you conclude that $200k/yr of passive income should be enough to live comfortably anywhere in the world. So are you subtracting your real estate expenses (taxes, insurance, mortgage payments, maintenance, remote property management company fees, etc.) when you report your passive income from those properties? Really I think it’s the net (after taxes and everything) that tells us what is left over to “spend” on living, right? When I set up my spreadsheet to retire early at age 47, I calculated the after-tax income I would need to live. Then I compared that to my income streams (estimating tax on the taxable income streams) to measure the surplus/shortfall. Also some good advice from GoCurryCracker: If you can minimize your taxes so you’re in the 15% tax bracket, you can possibly receive tax-free long term capital gains. I agree with your philosophy that time is more important than money as we age. I am not sure I agree with a philosophy that is fixated on needing such a large income, and would rather minimize taxes if it’s all the same on the happiness meter. Furthermore, having 20 plus income sources in the name of diversification adds stress and requires more management (TIME!). I think this is fine for those of us while young, as we have the energy to work hard. But as time becomes more important, the extra headache of managing, planning, and buying/selling our assets becomes a resented hindrance on par with the resentment we felt when working for an employer and fighting traffic each day to go to a job we hated. Every thing we own in actuality owns us, by virtue of its demands on our time and affections, and that includes investments. It also includes our home, and is a good reason for downsizing. As long as we have food on our table, a roof over our heads, and clothes on our bodies, what more do we need? I think we need to consider freeing ourselves from the weight of the chains of managing too many ventures. Personally, I plan on investing in no more than 5 simultaneous ventures ever, with the exception of some IRAs that I just plan to let sit for the next 20 years (and therefore no thought or anxiety required). Passive income is the Holy Grail for online marketers. It's automatic. Effortless. But, not at first. In the beginning, it's grueling. I liken this to doing the most amount of work for the least initial return. However, over time, as your passive income begins to increase, your reliance on an active income plummets. That's when the real magic starts to happen. India ranks second worldwide in farm output.[citation needed] Agriculture and allied sectors like forestry, logging and fishing accounted for 17% of the GDP.[citation needed]The sector employed 49% of its total workforce in 2014.[152] Agriculture accounted for 23% of GDP, and employed 59% of the country's total workforce in 2016.[153] As the Indian economy has diversified and grown, agriculture's contribution to GDP has steadily declined from 1951 to 2011, yet it is still the country's largest employment source and a significant piece of its overall socio-economic development.[154] Crop-yield-per-unit-area of all crops has grown since 1950, due to the special emphasis placed on agriculture in the five-year plans and steady improvements in irrigation, technology, application of modern agricultural practices and provision of agricultural credit and subsidies since the Green Revolution in India. However, international comparisons reveal the average yield in India is generally 30% to 50% of the highest average yield in the world.[155] The states of Uttar Pradesh, Punjab, Haryana, Madhya Pradesh, Andhra Pradesh, Telangana, Bihar, West Bengal, Gujarat and Maharashtra are key contributors to Indian agriculture. India started recovery in 2013–14 when the GDP growth rate accelerated to 6.4% from the previous year's 5.5%. The acceleration continued through 2014–15 and 2015–16 with growth rates of 7.5% and 8.0% respectively. For the first time since 1990, India grew faster than China which registered 6.9% growth in 2015.[needs update] However the growth rate subsequently decelerated, to 7.1% and 6.6% in 2016–17 and 2017–18 respectively,[144] partly because of the disruptive effects of 2016 Indian banknote demonetisation and the Goods and Services Tax (India).[145] As of October 2018, India is the world's fastest growing economy, and is expected to maintain that status for at least three more years.[146] Blogs and authority websites are different than niche websites, because they generally imply on-going content generation. Sure, I could stop writing on this blog today and let it sit forever, but that’s not the intention of the blog. Furthermore, blogs and authority websites tend to include a community or social aspect. We have Facebook pages and Twitter accounts (can someone explain to me why the hell I haven’t made a Facebook page yet?), and we discuss various topics in the comments of each article or blog post. Although SEO does affect traffic, community is more important. ## In January 2018, I missed my chance of raising the rent on my new incoming tenants because it didn't come to mind until very late in the interview process. I didn't write about my previous tenant's sudden decision to move out in December 2017 after 1.5 years, because they provided a relatively seamless transition by introducing their longtime friends to replace them. I didn't miss a month of rent and didn't have to do any marketing, so I felt I'd just keep the rent the same. One thing I notice about the debates on both tax policy and income inequality is that a lot of people seem to have relatively hazy ideas about how income is earned in America, and how much of each kind of income there is. For example, if someone is earning$300,000 a year, where is their income likely to be coming from? How much revenue is drawn from capital gains taxes? And how is income distributed between corporate shareholders and workers? People don't tend to have very strong priors about the answers to these questions, because they simply haven't yet learned what the relative sizes of different sources of income actually are.
The thing is, I’m not talking about buying brick-and-mortar buildings. I tried that many years ago with my father-in-law, and with devastating results. We tried to buy a duplex once, and the deal fell apart after we realized we weren’t really prepared for the purchase. I secretly wanted to become a landlord, but at the same time, I knew it wasn’t for me.
Unfortunately, it took a while for the real lessons to sink in. I was probably 20 or 21 when I read Rich Dad, Poor Dad the first time, which means I wasn’t exactly sure who I was yet. I knew I wanted to work hard and make money, but I wasn’t sure how. This made me a prime candidate for  multi-level marketing pitches, and the dream of “getting rich quick.”
5 months ago, I decided to create my own online business. I was really exacted because It was always my dream to earn cash by working from home to be able to unite my family and to retire my father that had been working as a security far away from home. My family and I only used to see him three times a year. I would like to change it, and online business gave me a possibility to make my dream to become real. I really was committed to giving all my self to succeed in building a successful online business. As a matter of fact, I failed to do it on my own. I was so disappointed because it seems that I was born to fail. It was 22nd June at night, I was hearing a motivational speech, so one of the guys said,” Copy what successful people’s strategy as your own, and you will get the same result that they have”. That opened my mind because that was the secret, I did not realize that there are a lot of people in this marketing a year. So, I took some online courses from gurus. Following their steps. right now where am I? I am now a successful online business of 22 years old trying to retire his father. I really thank people a lot that have the mindset to share this priceless information in this blog. Indeed, thank you.

India's retail industry mostly consists of local mom-and-pop stores, owner-manned shops and street vendors. Retail supermarkets are expanding, with a market share of 4% in 2008.[247] In 2012, the government permitted 51% FDI in multi-brand retail and 100% FDI in single-brand retail. However, a lack of back-end warehouse infrastructure and state-level permits and red tape continue to limit growth of organised retail.[248] Compliance with over thirty regulations such as "signboard licences" and "anti-hoarding measures" must be made before a store can open for business. There are taxes for moving goods from state to state, and even within states.[247] According to The Wall Street Journal, the lack of infrastructure and efficient retail networks cause a third of India's agriculture produce to be lost from spoilage.[249]
any income you received related to a business, trade, profession, or occupation previously carried on in New York State, including but not limited to covenants not to compete and termination agreements (see TSB-M-10(9)I, Income Received by a Nonresident Related to a Business, Trade, Profession, or Occupation Previously Carried on Within New York State); and

The gems and jewellery industry has been economically active in India for several thousand years.[187] Until the 18th century, India was the only major reliable source of diamonds.[183] Now, South Africa and Australia are the major sources of diamonds and precious metals, but along with Antwerp, New York, and Ramat Gan, Indian cities such as Surat and Mumbai are the hubs of world's jewellery polishing, cutting, precision finishing, supply and trade. Unlike other centres, the gems and jewellery industry in India is primarily artisan-driven; the sector is manual, highly fragmented, and almost entirely served by family-owned operations.
It is hard to do both but you’re not supposed to. You’re supposed to get your safety net down THEN try to do high wire acrobatics above it – not set up the two at the same time. So get retirement and your emergency fund squared away, then consider the stock market (taxable) and real estate. There’s no rush! Don’t let others dictate your future because they don’t have the same priorities as you. 🙂
became \$1,000,000 during an 18 year period (about 3x better than Berkshire Hathaway). Five – ten shares, or more, invested in a ROTH Ira and held *consistently* come h..l or highwater, with dividends and splits reinvested, may provide you a very pleasant surprise in 20 years or so. Asset Managers often do better than the assets they manage. Eaton Vance (EV) and T. Rowe Price (TROW) also did exceedingly well over a 25 year period.

### If you are unfortunate enough to find yourself no longer able to physically work in your chosen position, developing a skill set that will allow for a complete career change is a must. The passive income route as a second career is a great backup allowing you to hire out what you can’t physically do. Early on in my career I found I was unable to physically tolerate exposure to tobacco smoke. At that time, smoking was allowed in all offices, restaurants, etc. I was blindsided; who ever thought? It virtually removed me from most positions I had schooling for. As luck would have it, I had purchased a duplex while working and saved a small sum. When I had to leave my career, I made a down payment on another duplex doing any maintenance I could myself. If a physical setback of another sort should happen, I can hire.

Nah you misunderstood me. I’m working 50 hours a week now to get residency and only taking a couple of classes. I’ll be working 10-20 hours a week when I go back to schoool full time a year from now. I tried working 35 hours and school full time but got burned out last year so no more of that. My grades are so-so. I got a 3.7gpa in all my GE’s and really on a conservative basis planning to remain around there which would mean 1 B for every 2 A’s. To get residency realistically I got to earn 300 dollars in taxable income a week for a year, and in the meantime am allowed to go to school part time given the fact that I can pay for school with the money I have earned within the period I began to establish residency, so no outside cash because my bank accounts will be audited at the end of the year.
This equation implies two things. First buying one more unit of good x implies buying {\displaystyle {\frac {P_{x}}{P_{y}}}} less units of good y. So, {\displaystyle {\frac {P_{x}}{P_{y}}}} is the relative price of a unit of x as to the number of units given up in y. Second, if the price of x falls for a fixed {\displaystyle Y} , then its relative price falls. The usual hypothesis is that the quantity demanded of x would increase at the lower price, the law of demand. The generalization to more than two goods consists of modelling y as a composite good.
An obvious example is over exposure to bank stocks, which have been excellent investments for over a century.  Though a foundation of most portfolios, bank stocks do involve more risk at certain stages of the economic cycle than many realise.  Being less exposed to bank shares in the last few months could have preserved some capital.  So, a more diversified approach can help mitigate some of these risks.


text:
<meta http-equiv="refresh" content="1; url=/nojavascript/"> Heat Capacity and Specific Heat ( Real World ) | Chemistry | CK-12 Foundation

# Heat Capacity and Specific Heat

%
Best Score
Practice Heat Capacity and Specific Heat
Best Score
%

# Everything Has a Price

### Whether they are low or high, what do heat capacity and specific heat say about a substance?

Credit: sergis blog & Luigi Crespo
Source: http://www.flickr.com/creativecommons/by-2.0/

[Figure1]

All merchandise we find in stores have a price. The more money we put up, the more we can buy, either quantity-wise or quality-wise. Maybe a set of kids’ watches costs $30, but a single men’s luxury watch costs$300! Also, as we buy more of a certain item, our bill is surely going to go up!

Similarly, all substances have a heat capacity, that is a required amount of heat to raise the temperature of the substance by one degree Celsius. Some substances have a higher heat capacity than others, so they require more heat to experience a rise in temperature. Sometimes, also, a substance’s required heat input can be larger than that of another simply because it has a larger mass.

Credit: rychlepozicky.com & Images_of_Money
Source: http://www.flickr.com/creativecommons/by-2.0/

[Figure2]

Sometimes in the world of money, however, it doesn’t matter how much of something we have. Let’s say you want to purchase a few souvenirs at a gift shop in England, but first you need to convert your U.S. dollars to British pounds. Although you will need to shell out more money because you are buying several products, the number of pounds you get per dollar will ultimately stay the same.

Specific heat is the required amount of heat per unit of mass to raise the temperature of a substance by one degree Celsius, and it works in a similar manner. The specific heat of a substance does not depend on its mass, remaining the same whether 1 gram or a kilogram is involved.

### Creative Applications

1. It takes 243.5 J to heat 36 grams of a substance from 45 °C to 65 °C. What is its specific heat in J/g·°C? Use the formula q = m × c × ΔT (q = heat energy, m = mass, c = specific heat, ΔT = change in temperature).
2. Research: What substance has the highest known specific heat at room temperature? You may use the link provided in the "Resources" section.

3. Each of the following substances have a different required heat input to raise their temperature by 5 degrees Celsius. Order them from least to greatest required input: 5 grams of solid copper, 5 grams of solid aluminum, 50 grams of solid aluminum. Look up the specific heats of the substances if necessary, or use the link in the "Resources" section.
4. What might be some useful applications of a substance with a heat capacity and specific heat that are high? low?