content string | quality_label int64 | meta string | all-MiniLM-L6-v2_embedding list | doc_id int64 | unique_id string |
|---|---|---|---|---|---|
Positive Solutions for a Nonhomogeneous Kirchhoff Equation with the Asymptotical Nonlinearity in
Abstract and Applied Analysis
Volume 2014 (2014), Article ID 710949, 10 pages
http://dx.doi.org/10.1155/2014/710949
Research Article
Positive Solutions for a Nonhomogeneous Kirchhoff Equation with the Asymptotical Nonlin... | 5 | [
-0.10888671875,
0.0225830078125,
0.029296875,
0.09033203125,
-0.021240234375,
-0.042724609375,
-0.06591796875,
-0.0439453125,
0.0810546875,
-0.0019378662109375,
0.045654296875,
-0.033447265625,
0.06640625,
0.0010528564453125,
0.004791259765625,
-0.002227783203125,
-0.039794921875,
... | 24,200 | 24200 | |
Fourier Series and the first term
Remember that the general term of a Fourier series is
[tex]<f,e_i>[/tex]
where the [itex]e_i[/itex] is normalized (has norm 1)
We want to define
[tex]a_n=\frac{1}{\pi}\int_{-\pi}^\pi f(x)\cos(nx)dx[/tex]
If n>0, then this holds. The [itex]1/\pi[/itex] comes from normalizing the co... | 4 | [
-0.07666015625,
0.01007080078125,
0.0615234375,
0.0203857421875,
-0.031005859375,
0.047119140625,
-0.01397705078125,
0.03662109375,
-0.001495361328125,
-0.033447265625,
0.059814453125,
-0.00225830078125,
0.0128173828125,
-0.039794921875,
-0.03515625,
-0.1337890625,
0.0167236328125,
... | 24,201 | 24201 | |
Need to construct an equation
April 8th 2013, 06:26 AM #1
Newbie
Joined
Apr 2013
From
Cape Town
Posts
3
Thanks
1
Need to construct an equation
Hi--I'm new to the forum (and suck at maths) and need to construct an equation for the following:
[(Sum of(A + B))/C] x [D/E] x[(Sum of (F)) to the po... | 4 | [
-0.10107421875,
0.049560546875,
0.034423828125,
0.0146484375,
-0.05517578125,
0.0281982421875,
0.040283203125,
-0.04296875,
0.0771484375,
0.08154296875,
0.0269775390625,
-0.0703125,
0.00885009765625,
0.0400390625,
-0.00714111328125,
0.08837890625,
-0.041015625,
0.083984375,
-0.06... | 24,202 | 24202 | |
addition theorems
October 23rd 2009, 01:06 PM #1
Super Member
Joined
Aug 2009
Posts
639
addition theorems
Hi!
How do you prove that tan(∅+Φ) = (tan ∅ + tan Φ)/ (1- tanΦtan∅)?
I'm able to prove the formulas for sin and cos (∅+Φ) but when i use sin/ cos = tan, it doesnt give me the above formula.... | 4 | [
-0.0947265625,
0.03857421875,
0.006561279296875,
0.03955078125,
-0.03857421875,
0.0576171875,
0.04345703125,
-0.03955078125,
0.04296875,
0.078125,
0.055908203125,
-0.07763671875,
-0.05029296875,
0.00543212890625,
0.04443359375,
-0.0255126953125,
-0.0306396484375,
-0.0167236328125,
... | 24,203 | 24203 | |
Asteroid: Potential/Kinetic Energy, Angular Momentum
1. The problem statement, all variables and given/known data
Suppose an asteroid of mass 5e20 kg is nearly at rest outside the solar system, far beyond Pluto. It falls toward the Sun and crashes into the Earth at the equator, coming in at an angle of 30
degrees to t... | 5 | [
0.045654296875,
0.09033203125,
0.10693359375,
-0.0615234375,
0.06982421875,
-0.03271484375,
-0.025146484375,
0.134765625,
-0.04541015625,
0.11962890625,
0.006622314453125,
-0.03076171875,
-0.01123046875,
-0.06396484375,
0.04736328125,
0.0380859375,
0.0247802734375,
0.06640625,
-0... | 24,204 | 24204 | |
Yarn Strength Prediction: A Practical Model Based on Artificial Neural Networks
Advances in Mechanical Engineering
Volume 2010 (2010), Article ID 640103, 11 pages
http://dx.doi.org/10.1155/2010/640103
Research Article
Yarn Strength Prediction: A Practical Model Based on Artificial Neural Networks
^1Department of Mec... | 4 | [
-0.12890625,
-0.04150390625,
-0.0135498046875,
0.054931640625,
0.000362396240234375,
-0.0101318359375,
-0.0126953125,
0.060791015625,
-0.07763671875,
0.0166015625,
-0.0830078125,
0.0693359375,
-0.01263427734375,
0.04833984375,
-0.11083984375,
0.03173828125,
0.049072265625,
0.003890... | 24,205 | 24205 | |
Improved Rao-Blackwellized Particle Filter by Particle Swarm Optimization
Journal of Applied Mathematics
Volume 2013 (2013), Article ID 302170, 7 pages
http://dx.doi.org/10.1155/2013/302170
Research Article
Improved Rao-Blackwellized Particle Filter by Particle Swarm Optimization
^1Shandong Province Key Laboratory o... | 4 | [
-0.017822265625,
-0.0030517578125,
0.042724609375,
-0.01446533203125,
0.0040283203125,
-0.051513671875,
0.042724609375,
-0.09033203125,
-0.05810546875,
0.034912109375,
0.059326171875,
0.0208740234375,
0.0654296875,
-0.06396484375,
-0.07763671875,
0.06103515625,
0.038330078125,
0.03... | 24,206 | 24206 | |
Accelerated Particle Swarm for Optimum Design of Frame Structures
Mathematical Problems in Engineering
Volume 2013 (2013), Article ID 649857, 6 pages
http://dx.doi.org/10.1155/2013/649857
Research Article
Accelerated Particle Swarm for Optimum Design of Frame Structures
^1Marand Faculty of Engineering, University of... | 5 | [
-0.01031494140625,
0.0517578125,
-0.06396484375,
-0.060546875,
-0.0303955078125,
-0.032470703125,
-0.00830078125,
0.0311279296875,
-0.05615234375,
0.031982421875,
-0.005859375,
0.050048828125,
-0.029052734375,
-0.044677734375,
-0.06494140625,
0.007080078125,
0.049560546875,
0.05297... | 24,207 | 24207 | |
1,1,1,1 Matrix general formula!!!
April 27th 2008, 04:30 AM #16
hmm are you sure?
when i did (X+Y)^2, i got
l4 0l
l0 4l
and i thought maybe A^n would be something like
l2^n-1 0l
l0 2^n-1l
that would work for all constants right?
No.You have computed it wrongly then
First of ... | 4 | [
-0.0228271484375,
0.000396728515625,
-0.0732421875,
0.0189208984375,
-0.0279541015625,
-0.059814453125,
0.031494140625,
-0.123046875,
-0.0084228515625,
-0.016845703125,
0.07958984375,
0.0283203125,
-0.0159912109375,
0.0184326171875,
-0.0072021484375,
0.1611328125,
-0.08935546875,
0... | 24,208 | 24208 | |
Physics Forums - View Single Post - How do you guys deal with problems having only 2 variable? Good fomula sheet?
jtbell
All constant-acceleration problems can be solved using these two equations:
[tex]x = x_0 + v_0 t + \frac{1}{2} a t^2[/tex]
[tex]v = v_0 + a t[/tex]
All those other equations can be derived from ... | 4 | [
-0.09130859375,
0.0089111328125,
0.09326171875,
0.05078125,
-0.078125,
0.029052734375,
-0.07373046875,
0.06201171875,
-0.051025390625,
0.0341796875,
0.123046875,
-0.031494140625,
0.0126953125,
-0.021484375,
-0.03369140625,
0.050537109375,
-0.0306396484375,
0.1337890625,
-0.002044... | 24,209 | 24209 | |
Integration By Parts
March 20th 2013, 08:46 PM
knag95
Integration By Parts
Could someone please do me a favor and show me the steps to integrate this problem: 2PI fnInt((x)(-10cos((PI/6.44)x)+18 - 1 ),x,0,0.2)? Thanks.
March 21st 2013, 02:36 AM
chiro
Re: Integration By Parts
Hey knag95.
It is usuall... | 5 | [
-0.0947265625,
0.0400390625,
0.1005859375,
-0.012939453125,
0.0380859375,
0.037353515625,
-0.02587890625,
0.09423828125,
-0.017333984375,
0.00024127960205078125,
0.04052734375,
-0.0306396484375,
0.023681640625,
-0.0198974609375,
0.004119873046875,
-0.04833984375,
-0.01324462890625,
... | 24,210 | 24210 | |
Rotational control of a satellite
We're working on a mathematic project, which is about rotational control of a satellite. It's in some ways connected to physics,because we're supposed to analyse the dynamics of a satellite. First a
one-axis, then a three axis model.
Anyway, most of the tasks are about differential ... | 5 | [
-0.119140625,
-0.0439453125,
-0.0247802734375,
-0.03125,
-0.06298828125,
0.01287841796875,
-0.052734375,
0.06591796875,
0.1328125,
0.087890625,
0.0771484375,
0.0252685546875,
0.056884765625,
-0.1064453125,
-0.02734375,
0.04541015625,
-0.06201171875,
0.053466796875,
-0.03564453125... | 24,211 | 24211 | |
a number proof or disproof question
if a>0 then we can write $a^3=b^2-c^2$$b,c\in\mathbb{Z}$ how can ı prove the truthness this equation
Don't you see that $\forall a \in \mathbb{N}^{*},\ a^{3}=\left( \frac{a^{2}+a}{2}\right)^{2}-\left( \frac{a^{2}-a}{2} \right)^{2}$ ? :p Actually, you can write $a^{3}=(b+c)(b-c)$, an... | 5 | [
-0.08203125,
0.10498046875,
-0.083984375,
0.103515625,
-0.087890625,
0.006805419921875,
0.01025390625,
-0.0277099609375,
0.09033203125,
-0.064453125,
-0.016845703125,
-0.006988525390625,
0.047119140625,
0.040771484375,
0.040283203125,
-0.0286865234375,
-0.006317138671875,
0.0668945... | 24,212 | 24212 | |
Help with these two geometry!
October 19th 2009, 10:37 PM #1
Newbie
Joined
Oct 2009
Posts
19
Help with these two geometry!
Help with these two hard problems:
Problem 12
Let M be a point inside the angle A. From point M perpendiculars MP and MQ are dropped to the angle sides. From point A, perpen... | 4 | [
-0.10107421875,
0.1376953125,
0.0281982421875,
-0.0634765625,
-0.0556640625,
0.038818359375,
0.0830078125,
-0.003082275390625,
0.038330078125,
0.05078125,
0.12158203125,
-0.05419921875,
0.0732421875,
0.001861572265625,
0.045166015625,
0.078125,
-0.033203125,
0.046630859375,
0.001... | 24,213 | 24213 | |
Special Factoring: Recognizing Factoring Patterns
Special Factoring:
Recognizing Factoring Patterns (page 3 of 3)
Sections: Differences of squares, Sums and differences of cubes, Recognizing patterns
You've learned the difference-of-squares formula and the difference- and sum-of-cubes formulas. But how do you know wh... | 4 | [
0.0361328125,
-0.0137939453125,
-0.0244140625,
0.0751953125,
0.053466796875,
0.078125,
-0.059326171875,
-0.042724609375,
0.000774383544921875,
-0.03271484375,
-0.01507568359375,
-0.01953125,
-0.00148773193359375,
0.0322265625,
0.0031280517578125,
0.0380859375,
-0.0284423828125,
0.1... | 24,214 | 24214 | |
Imaginary Area? Huh?
October 12th 2009, 01:06 PM
pflo
Imaginary Area? Huh?
I don't understand the answer to the following definite integral. Can anyone help me explain why it is the way it is?
$\int_0^2{\frac{1}{^3\sqrt{t-1}}}dt$
I think the easiest way to see my point on this is to use u-substitution ... | 5 | [
-0.01287841796875,
-0.0791015625,
-0.016845703125,
-0.031005859375,
-0.0169677734375,
-0.11474609375,
-0.0233154296875,
0.006622314453125,
0.00046539306640625,
0.005767822265625,
0.046142578125,
-0.015869140625,
-0.01202392578125,
0.044189453125,
-0.08203125,
-0.07421875,
-0.01116943... | 24,215 | 24215 | |
Complex line
October 10th 2012, 02:25 PM #1
Junior Member
Joined
Jan 2011
Posts
73
Thanks
1
Complex line
Quick question, why does the equation z=(a+b)-a*b*conjugate(z) determine the line that passes through points a and b on the unit circle in the complex plane?
Thanks,
$y = \frac{i (a+b-x-a... | 5 | [
-0.212890625,
0.01708984375,
-0.060791015625,
0.1044921875,
-0.0218505859375,
-0.037109375,
0.10986328125,
-0.0301513671875,
0.00162506103515625,
-0.0439453125,
0.0303955078125,
-0.00885009765625,
0.076171875,
0.018310546875,
-0.03759765625,
0.034912109375,
-0.0986328125,
-0.115234... | 24,216 | 24216 | |
Homogeneity analysis of hierarchical classifications
August 10, 2010
By Michael Bedward
I've spent more years than I care to remember analysing vegetation survey data (typically species abundances in plots) using a variety of software including my own algorithms coded in FORTRAN and
C++. A recent query on the r-help... | 4 | [
-0.011962890625,
-0.01348876953125,
0.01434326171875,
-0.0303955078125,
0.05859375,
-0.0274658203125,
-0.109375,
-0.035400390625,
-0.0291748046875,
-0.058837890625,
0.00927734375,
-0.078125,
0.00653076171875,
-0.017578125,
-0.049072265625,
-0.017578125,
-0.061767578125,
-0.04980468... | 24,217 | 24217 | |
uzzy sets
Fuzzy sets
From Scholarpedia
Milan Mares (2006), Scholarpedia, 1(10):2031. doi:10.4249/scholarpedia.2031 revision #91291 [link to/cite this article]
Fuzzy set is a mathematical model of vague qualitative or quantitative data, frequently generated by means of the natural language. The model is based on th... | 4 | [
0.0206298828125,
-0.0001773834228515625,
-0.040283203125,
0.01806640625,
-0.13671875,
0.06982421875,
0.087890625,
-0.00872802734375,
-0.0032958984375,
0.0286865234375,
0.017578125,
0.00848388671875,
0.1298828125,
-0.0179443359375,
-0.055908203125,
0.050537109375,
0.025390625,
-0.19... | 24,218 | 24218 | |
Practice with Arithmetic and Geometric Sequences Word Problems
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃ Practice with ┃
┃ Arithmetic and Geometric Sequences Word Problems ┃
┃ Topic Index | Algebra2/Trig Index | Regents Exam Prep Center┃
┗... | 4 | [
-0.059326171875,
0.047607421875,
0.0260009765625,
-0.059326171875,
-0.1181640625,
0.04736328125,
0.00052642822265625,
0.00921630859375,
-0.000027060508728027344,
0.046142578125,
0.0283203125,
-0.044677734375,
0.0299072265625,
0.059326171875,
-0.0081787109375,
0.019775390625,
-0.05273... | 24,219 | 24219 | |
Radioactive Decay
May 17th 2008, 12:20 PM
akasixcon
Radioactive Decay
I'm new here, first post.
I honestly forgot the concept of half-life and this week we are having our final exams. Good thing that the teacher provided us with a review test. So would someone refresh my memory.
Quote:
Originally ... | 5 | [
0.031982421875,
-0.0142822265625,
0.0255126953125,
-0.0238037109375,
0.00579833984375,
-0.1328125,
0.0191650390625,
0.0849609375,
-0.007049560546875,
0.07763671875,
0.06494140625,
-0.0247802734375,
0.058349609375,
0.080078125,
0.028564453125,
0.0308837890625,
-0.064453125,
-0.07470... | 24,220 | 24220 | |
Series Expansion
$f(x)=(1+x^2)^\frac{1}{4}$ How would you expand this exactly? Would you use the binomial theorem?
the binomial expansion doesn't give rise to series, it simply shows you how to expand brackets. you can write the Taylor series for this. perhaps that's what you want?
Well I thought it was either that o... | 5 | [
0.06591796875,
-0.07861328125,
-0.034423828125,
0.1552734375,
-0.06982421875,
-0.01373291015625,
-0.0087890625,
-0.035888671875,
0.103515625,
0.039306640625,
0.0191650390625,
-0.030517578125,
-0.06396484375,
0.048095703125,
-0.0262451171875,
0.03955078125,
-0.00909423828125,
-0.007... | 24,221 | 24221 | |
partition of unity
September 11th 2009, 05:36 AM #1
Newbie
Joined
Mar 2009
Posts
19
partition of unity
Hi, I have the follow question:
Construct a function $\phi\in C_c^\infty (\mathbb{R})$ such that $\phi\geq 0$, $supp\phi\subset (-1,1)$
$\psi_n(x)=\phi(x-n)/\displaystyle_{m\in\mathbb{Z}}\phi(... | 5 | [
-0.1298828125,
0.006927490234375,
0.049072265625,
0.0284423828125,
-0.032470703125,
0.09912109375,
0.08349609375,
0.037109375,
-0.08056640625,
-0.046630859375,
0.0220947265625,
0.0308837890625,
-0.0179443359375,
-0.0233154296875,
-0.0595703125,
-0.0791015625,
0.0185546875,
-0.09277... | 24,222 | 24222 | |
Some Generalized Dependent Aggregation Operators with Interval-Valued Intuitionistic Fuzzy Information and Their Application to Exploitation Investment Evaluation
Journal of Applied Mathematics
Volume 2013 (2013), Article ID 705159, 24 pages
http://dx.doi.org/10.1155/2013/705159
Research Article
Some Generalized Depe... | 4 | [
-0.0189208984375,
0.0184326171875,
0.0263671875,
-0.0230712890625,
-0.072265625,
-0.0084228515625,
0.051513671875,
0.01556396484375,
0.04931640625,
-0.011962890625,
-0.005218505859375,
0.036865234375,
0.0947265625,
0.037353515625,
-0.03662109375,
0.039794921875,
0.058837890625,
-0.... | 24,223 | 24223 | |
Partial Differential Equations Problems
September 21st 2010, 09:54 AM
Creebe
Partial Differential Equations Problems
Hello.
Question 1
Find the temperature distribution T(x,t) in a long thin bar $-a \leq x \leq a$ with given initial temperature $u(x,0) = f(x)$
The side walls of the bar are insulated... | 4 | [
-0.034423828125,
0.053466796875,
0.1005859375,
-0.010009765625,
-0.0166015625,
0.060302734375,
-0.03466796875,
0.02197265625,
-0.0908203125,
0.0458984375,
0.0634765625,
-0.09326171875,
0.0859375,
-0.0673828125,
0.07080078125,
-0.005340576171875,
0.02783203125,
-0.1298828125,
-0.0... | 24,224 | 24224 | |
functions
June 19th 2008, 12:35 AM
Tangera
functions
Question:
a) f(x) = | (3-x)/(x-2) |, x > 2
Define the inverse funtion of f corresponding to the domain of f.
b) g(x) = ln (x+2), x > -2
h(x) = 2 + (e ^ -x) , x > b and b > 0
The composite function gh is well defined and the range of gh ... | 4 | [
-0.0859375,
-0.0238037109375,
-0.00119781494140625,
-0.0595703125,
0.043212890625,
-0.020751953125,
0.0072021484375,
0.06982421875,
-0.01904296875,
0.0238037109375,
0.048583984375,
-0.13671875,
-0.0225830078125,
-0.06201171875,
0.0361328125,
0.048095703125,
-0.0595703125,
-0.152343... | 24,225 | 24225 | |
Fourth Derivitive Problem ~ (Need Help for Calc Midterm)
January 14th 2009, 06:08 PM #1
Newbie
Joined
Jan 2009
Posts
5
Fourth Derivitive Problem ~ (Need Help for Calc Midterm)
I've got a question that asks me to take the 4th derivitive of (2x+1)^4 ~ The problem I come across is once it becomes 24(2x+1)^... | 5 | [
0.080078125,
0.008056640625,
0.031494140625,
0.0322265625,
-0.01226806640625,
-0.000743865966796875,
0.01458740234375,
-0.0213623046875,
0.00106048583984375,
0.04443359375,
0.099609375,
-0.032958984375,
0.0419921875,
0.043701171875,
-0.026123046875,
0.0234375,
-0.068359375,
0.07421... | 24,226 | 24226 | |
Check whether root 17 is rational or irrational?
The square root of any positive non-square integer is irrational.
Thanks a lot friend... but i need this to be proved by proof by contradiction.. Anybody there to help me?
The square root of any positive non-square integer is irrational. Proof: Suppose that $n$ is a po... | 5 | [
0.026611328125,
0.09228515625,
0.047607421875,
0.0380859375,
-0.006591796875,
0.005615234375,
0.02783203125,
0.0015106201171875,
0.0177001953125,
-0.04345703125,
-0.026611328125,
-0.0021820068359375,
0.06396484375,
0.036865234375,
-0.047607421875,
-0.109375,
0.07763671875,
0.026611... | 24,227 | 24227 | |
Convex polynomial homogenization and convexity
up vote 1 down vote favorite
I have a polynomial that I know to be convex. If I homogenize the polynomial, is the resulting homogeneous polynomial also convex? I know that the perspective of a convex function is convex, but
cannot find a citation for the homogenization of... | 5 | [
-0.0225830078125,
-0.0283203125,
-0.034423828125,
-0.032470703125,
-0.004608154296875,
0.03173828125,
0.050048828125,
-0.03125,
0.006500244140625,
0.01202392578125,
-0.02294921875,
0.0810546875,
0.0035247802734375,
-0.0006103515625,
-0.0235595703125,
-0.008056640625,
-0.0006256103515... | 24,228 | 24228 | |
Facebook Friends' Birthdays: A Probability Question
January 10th 2010, 06:56 AM
probabilitydunce
Facebook Friends' Birthdays: A Probability Question
Hey guys,
I have 2,000 Facebook friends and noticed that not one of them has a birthday today (January 10th). I quickly calculated the probability of this as (... | 5 | [
0.05126953125,
0.0478515625,
0.01348876953125,
0.0458984375,
-0.01318359375,
-0.064453125,
0.0137939453125,
0.005035400390625,
-0.041259765625,
-0.029296875,
0.04296875,
-0.08349609375,
0.0283203125,
-0.0211181640625,
0.053955078125,
-0.00830078125,
-0.08251953125,
-0.037841796875,... | 24,229 | 24229 | |
Finding the tangent line
(X^3)y + (x^2)y = 5xy find dy/dx @(2,5) and the equation of the tangent line.
You have to use implicit differentiation. $yx^3+yx^2=5xy$ Apply the product rule to each term. Since each term is a product of two functions, the derivative will have 6 terms: $(x^3\frac{dy}{dx}+3x^
2y)+(\frac{dy}{dx... | 5 | [
-0.0673828125,
-0.0888671875,
0.0150146484375,
-0.044921875,
-0.01202392578125,
0.0224609375,
0.021240234375,
0.042236328125,
-0.03125,
-0.038818359375,
0.046142578125,
0.0263671875,
0.022216796875,
-0.027587890625,
0.034423828125,
0.138671875,
-0.1201171875,
0.01300048828125,
-0... | 24,230 | 24230 | |
Schauder Basis
April 27th 2009, 06:18 AM #1
Junior Member
Joined
Apr 2009
Posts
39
Schauder Basis
Show that if a Normed Space X has a Schauder Basis => X is Seperable.
Definition of a Schauder Basis:
If a Normed Space X contains a sequence (e_n) with the property that for every x element of X t... | 5 | [
-0.08251953125,
-0.03955078125,
-0.052978515625,
0.019287109375,
0.0196533203125,
0.1025390625,
0.09521484375,
-0.068359375,
-0.037353515625,
-0.12255859375,
0.055419921875,
-0.017333984375,
-0.01129150390625,
-0.022216796875,
-0.052001953125,
-0.134765625,
0.00555419921875,
-0.078... | 24,231 | 24231 | |
Patent US8138963 - Method for detecting targets using space-time adaptive processing and shared knowledge of the environment
FIELD OF THE INVENTION
This invention relates generally to signal processing, and in particular to space-time adaptive processing (STAP) for target detection using radar signals.
BACKGROUND OF ... | 4 | [
-0.007659912109375,
-0.0546875,
-0.047607421875,
-0.00958251953125,
0.049560546875,
-0.050537109375,
0.037109375,
-0.0191650390625,
0.0166015625,
-0.07275390625,
-0.06201171875,
0.01422119140625,
0.028564453125,
-0.037353515625,
-0.01904296875,
-0.0517578125,
-0.0235595703125,
-0.0... | 24,232 | 24232 | |
[Haskell-cafe] speeding up fibonacci with memoizing
ajb at spamcop.net ajb at spamcop.net
Sun Feb 18 18:15:25 EST 2007
G'day all.
On 2/18/07, Yitzchak Gale <gale at sefer.org> wrote:
> Besides memoizing, you might want to use the fact
> that:
>
> fib (2*k) == (fib (k+1))^2 - (fib (k-1))^2
> fib (2*k-1) == (fib k)^2... | 4 | [
-0.0225830078125,
0.0240478515625,
-0.0286865234375,
0.002105712890625,
-0.0712890625,
0.0189208984375,
-0.0115966796875,
-0.01513671875,
0.0111083984375,
-0.0123291015625,
0.003997802734375,
0.01904296875,
0.003173828125,
0.0286865234375,
-0.06103515625,
0.0257568359375,
-0.04296875... | 24,233 | 24233 | |
Game theory and baseball, Part 5: Generalizing the pitch selection model
For the past four articles, I have discussed various applications of game theory to baseball analysis. Last time, I developed a new framework for pitch selection wherein a pitcher named Chuck decides
whether to throw a fastball or a curveball, aft... | 5 | [
0.0172119140625,
-0.036376953125,
0.0098876953125,
-0.109375,
0.047607421875,
0.064453125,
-0.03271484375,
0.0235595703125,
0.0703125,
0.10498046875,
0.01361083984375,
0.00946044921875,
-0.0167236328125,
0.011474609375,
0.06591796875,
0.0128173828125,
0.04296875,
0.0181884765625,
... | 24,234 | 24234 | |
Simultaneous equations question
March 8th 2010, 03:41 AM #1
Simultaneous equations question
Hi there, I'm trying to work out this question, but not having much luck:
Solve this system of equations for all possible values of $a$ and $b$, where $a$ and $b$ are real constants.
$ax+y+z=1$
$x+by+z=1$
... | 4 | [
-0.1083984375,
-0.057861328125,
-0.068359375,
0.004730224609375,
-0.0277099609375,
-0.0028228759765625,
0.06884765625,
-0.06689453125,
-0.00543212890625,
0.00701904296875,
0.000499725341796875,
0.035400390625,
0.1201171875,
0.031005859375,
-0.0263671875,
0.0225830078125,
-0.083496093... | 24,235 | 24235 | |
Learn about Classification of Real Numbers
Learn about Classification of Real Numbers In this lesson, let's learn how to classify real numbers. We tried different numbers and learned how to classify them. Let's start with 1/3. 1/3 is a real
number. It's written as a/b, well we know b is not equal to zero. So I'm not di... | 4 | [
-0.0859375,
-0.06982421875,
-0.06201171875,
-0.01904296875,
-0.03759765625,
-0.02587890625,
0.06201171875,
-0.06298828125,
0.1025390625,
-0.046142578125,
-0.05859375,
-0.11279296875,
0.0130615234375,
0.06982421875,
0.00970458984375,
-0.033447265625,
-0.00811767578125,
0.0439453125,... | 24,236 | 24236 | |
Poisson Problem
January 6th 2009, 11:16 PM #1
Banned
Joined
Dec 2008
From
Mauritius
Posts
523
Poisson Problem
If the number of accidents occuring in an industrial plant during aa day is given by a Poisson random variable with parameter 3.
Find
i) probability that no accident occurs on a day
... | 5 | [
0.0341796875,
-0.029296875,
0.02294921875,
-0.02880859375,
0.01055908203125,
-0.03369140625,
0.1259765625,
-0.031494140625,
0.044921875,
0.0439453125,
0.1435546875,
-0.1005859375,
0.037109375,
-0.03515625,
0.0751953125,
-0.015380859375,
-0.0341796875,
-0.0751953125,
-0.0649414062... | 24,237 | 24237 | |
Numerical Simulation of Size Effects on Countercurrent Flow Limitation in PWR Hot Leg Models
Science and Technology of Nuclear Installations
Volume 2012 (2012), Article ID 907364, 7 pages
http://dx.doi.org/10.1155/2012/907364
Research Article
Numerical Simulation of Size Effects on Countercurrent Flow Limitation in P... | 4 | [
-0.059814453125,
0.0291748046875,
0.004974365234375,
0.0537109375,
-0.005645751953125,
-0.08837890625,
-0.0810546875,
0.1357421875,
-0.05419921875,
0.04248046875,
-0.00836181640625,
0.02734375,
0.0703125,
0.00360107421875,
-0.032958984375,
0.03515625,
-0.062255859375,
-0.0011749267... | 24,238 | 24238 | |
Reverse ratios and percentages....
September 27th 2013, 10:52 AM
lisach
Reverse ratios and percentages....
The teachers were right.... we will need this one day!!! I didn't do so well in math class. Thank you for forums like this! :)
I am working with dilutions of a concentrate. (I will give both gallons an... | 4 | [
0.04052734375,
-0.035400390625,
0.042724609375,
-0.005584716796875,
-0.015869140625,
-0.03173828125,
0.0017852783203125,
0.07763671875,
-0.01263427734375,
0.048828125,
-0.0277099609375,
-0.068359375,
0.018798828125,
0.08447265625,
-0.0306396484375,
0.005767822265625,
0.0810546875,
... | 24,239 | 24239 | |
A Resource Allocation Evolutionary Algorithm for OFDM Based on Karush-Kuhn-Tucker Conditions
Mathematical Problems in Engineering
Volume 2013 (2013), Article ID 406143, 8 pages
http://dx.doi.org/10.1155/2013/406143
Research Article
A Resource Allocation Evolutionary Algorithm for OFDM Based on Karush-Kuhn-Tucker Cond... | 4 | [
-0.08984375,
0.0732421875,
-0.029052734375,
-0.028076171875,
-0.039306640625,
0.0030517578125,
-0.005950927734375,
-0.0079345703125,
-0.0216064453125,
0.038330078125,
-0.0625,
0.04638671875,
0.02685546875,
-0.00341796875,
-0.076171875,
0.0260009765625,
0.041748046875,
-0.0524902343... | 24,240 | 24240 | |
A Weather Generator for Use in Construction Simulation Models
International Journal of Architecture, Engineering and Construction
Vol 2, No 2, June 2013, pp. 73-87
A Weather Generator for Use in Construction Simulation Models
Adham Shahin^1,*^*Corresponding author. Email: adham.shahin@gmail.com , Simaan M. AbouRizk^... | 4 | [
-0.09423828125,
0.048828125,
0.025146484375,
0.09423828125,
-0.0625,
-0.11279296875,
-0.09228515625,
-0.0223388671875,
0.0201416015625,
0.01129150390625,
-0.083984375,
-0.060546875,
0.0859375,
-0.041015625,
0.0439453125,
-0.015625,
-0.0595703125,
-0.087890625,
-0.037109375,
-0.... | 24,241 | 24241 | |
Methods for Inhomogeneous Difference Equations
July 13th 2007, 07:47 AM
topsquark
Methods for Inhomogeneous Difference Equations
I believe that the term "inhomogeneous difference equation" describes the following problem:
$a_{n + 2} - 2a_{n + 1} + a_n = 4$ with the conditions $a_0 = 1$ and $a_1 = 2$. (This p... | 5 | [
-0.11376953125,
0.012939453125,
0.040283203125,
0.0289306640625,
-0.032958984375,
0.031982421875,
-0.05078125,
0.0189208984375,
0.00518798828125,
0.008544921875,
0.06591796875,
-0.03466796875,
0.02880859375,
-0.039794921875,
-0.030517578125,
0.023193359375,
-0.0012664794921875,
-0.... | 24,242 | 24242 | |
Math Help
prove that if n>6 then $\exists a,b \in N \ a,b >1 , \ gcd (a,b)=1$ such that n= a+b
Hello, $n > 6$. Consider two cases : $\Rightarrow n$ is odd. Let $a = \frac{n - 1}{2}$ and $b = \frac{n + 1}{2}$. $a + b = \frac{2n}{2} = n$, and $b - a = \frac{n + 1 - n + 1}{2} = 1$. Since $b = a +
1$, $gcd(a, b) = 1$. $\... | 4 | [
-0.047607421875,
-0.02978515625,
0.0234375,
0.00506591796875,
-0.0303955078125,
0.0966796875,
0.01373291015625,
0.06787109375,
-0.029541015625,
-0.05908203125,
-0.0576171875,
0.033447265625,
-0.038330078125,
-0.07177734375,
-0.00182342529296875,
0.00372314453125,
-0.0015716552734375,... | 24,243 | 24243 | |
Antidifferentiation Help
Hello, please assist with the following: Find An Antiderivative of the following: 1.) X/(X+1) 2.) 1/(X+1)^2 Please show working, thanks!
Ok, for the first one: x / (x + 1) = 1 - (1 / (x+1)) ∫ 1 dx - ∫ (1 / (x+1) dx = x - log (x+1) + C For the second one: ∫ (x+1)^-2 . dx = (-1)(x+1)^(-2+1) = -1... | 5 | [
-0.005767822265625,
-0.011962890625,
0.07666015625,
0.036376953125,
0.044677734375,
-0.099609375,
-0.04248046875,
-0.010986328125,
0.035888671875,
0.02392578125,
0.06494140625,
-0.053955078125,
0.0098876953125,
0.080078125,
-0.0556640625,
0.0035247802734375,
-0.03564453125,
-0.0033... | 24,244 | 24244 | |
Plz help....meeeee induction
November 14th 2006, 06:40 PM #1
Member
Joined
Mar 2006
Posts
82
Plz help....meeeee induction
I am studying for my 2nd midterm, but then I am stuck..plz help me..thank you so much.
1) prove by induction that for each nonnegative integer k, the integer k^2 + 5k is even.
... | 5 | [
-0.002685546875,
-0.005645751953125,
0.06494140625,
-0.0262451171875,
-0.04638671875,
0.007476806640625,
0.0732421875,
-0.042724609375,
-0.02197265625,
0.0361328125,
-0.06884765625,
0.0091552734375,
0.040771484375,
-0.035400390625,
-0.09765625,
0.09033203125,
0.0252685546875,
-0.00... | 24,245 | 24245 | |
Sharp Bounds for the Weighted Geometric Mean of the First Seiffert and Logarithmic Means in terms of Weighted Generalized Heronian Mean
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 721539, 4 pages
http://dx.doi.org/10.1155/2013/721539
Research Article
Sharp Bounds for the Weighted Geometric Mean of th... | 5 | [
0.0213623046875,
-0.0272216796875,
0.046875,
-0.047119140625,
-0.0576171875,
-0.12890625,
0.000316619873046875,
0.068359375,
-0.0026702880859375,
-0.0308837890625,
-0.031005859375,
-0.018310546875,
0.059814453125,
-0.01556396484375,
-0.04931640625,
-0.052978515625,
0.0009574890136718... | 24,246 | 24246 | |
Combining Cross-Validation and Confidence to Measure Fitness :: Institutional Repository
Combining Cross- Validation and Confidence to Measure Fitness
D. Randall Wilson
fonix corporation
WilsonR @ fonix. corn
Abstract
Neural network and machine learning algorithms often
have parameters that must be tuned ... | 4 | [
-0.05859375,
-0.07763671875,
-0.07666015625,
0.00064849853515625,
0.00506591796875,
-0.004302978515625,
0.005462646484375,
0.007171630859375,
-0.064453125,
-0.10791015625,
-0.0546875,
-0.138671875,
0.05810546875,
-0.0517578125,
-0.056640625,
-0.04248046875,
0.036865234375,
0.042724... | 24,247 | 24247 | |
A Simple and Efficient Artificial Bee Colony Algorithm
Mathematical Problems in Engineering
Volume 2013 (2013), Article ID 526315, 9 pages
http://dx.doi.org/10.1155/2013/526315
Research Article
A Simple and Efficient Artificial Bee Colony Algorithm
^1School of Computer Science and Technology, Huazhong University of ... | 4 | [
0.00732421875,
0.029541015625,
-0.01177978515625,
-0.0361328125,
-0.09765625,
-0.0498046875,
0.054931640625,
-0.08056640625,
0.0198974609375,
0.0634765625,
0.0191650390625,
-0.005218505859375,
0.125,
-0.0294189453125,
-0.07177734375,
0.080078125,
0.0264892578125,
-0.0361328125,
-... | 24,248 | 24248 | |
Planes in 3-space; Equations of planes
March 29th 2008, 05:46 AM #1
Newbie
Joined
Mar 2008
Posts
21
Planes in 3-space; Equations of planes
Hi guys,
I've got this exercise where I'm required to describe the equation of the plane determined by the fact that the following
three points lie in it: (−... | 5 | [
-0.0556640625,
0.027099609375,
-0.06787109375,
-0.02099609375,
-0.01031494140625,
0.07421875,
0.07373046875,
-0.00072479248046875,
-0.038330078125,
0.035888671875,
-0.00021457672119140625,
-0.0272216796875,
-0.01312255859375,
-0.007171630859375,
-0.06689453125,
0.03466796875,
-0.0712... | 24,249 | 24249 | |
Find a formula for the sequence....
May 13th 2010, 03:00 PM #1
Member
Joined
Jul 2008
Posts
212
Find a formula for the sequence....
The two questions are here, they're probably easy but I'm having a brain freeze lol
http://img29.imageshack.us/img29/5626/file.png
The 4(c) sequence is 5, 7, 9, 11... | 4 | [
-0.09619140625,
0.0025482177734375,
0.053955078125,
-0.140625,
-0.0174560546875,
0.0673828125,
-0.0184326171875,
0.04443359375,
0.039794921875,
0.0341796875,
0.052001953125,
-0.04833984375,
-0.046630859375,
-0.000568389892578125,
-0.0634765625,
-0.001617431640625,
-0.0128173828125,
... | 24,250 | 24250 | |
Secant Line Slope and Tangent Line Slope
August 26th 2009, 05:11 PM #1
Banned
Joined
Aug 2009
Posts
3
Secant Line Slope and Tangent Line Slope
I have answered these problems already but I am not sure what the correct answers were.
Point P=(3,1/9) lies on 1/x^2
Find slope of secant line PQ for c... | 4 | [
-0.060791015625,
-0.028076171875,
0.0205078125,
-0.01275634765625,
-0.02685546875,
0.02001953125,
0.0299072265625,
0.1328125,
0.04296875,
-0.0172119140625,
0.055419921875,
-0.0986328125,
0.00830078125,
0.04443359375,
0.01153564453125,
0.06640625,
-0.061767578125,
-0.01806640625,
... | 24,251 | 24251 | |
Proof for Hilbert's third problem
See Hilbert's third problem for what we want to prove, motivation, discussion and importance. Due to the moderate length of the proof, I give an outline of the ideas and principal constructs used.
More details are in the linked nodes.
Max Dehn proved a counterexample to Hilbert's thir... | 4 | [
-0.0537109375,
0.048583984375,
0.01507568359375,
-0.06982421875,
-0.03759765625,
0.017578125,
0.0279541015625,
-0.0203857421875,
0.03466796875,
-0.0093994140625,
-0.0712890625,
-0.037841796875,
0.061767578125,
0.0654296875,
-0.0264892578125,
-0.08642578125,
-0.022216796875,
0.06884... | 24,252 | 24252 | |
Constrained Optimization again
April 4th 2010, 04:46 PM #1
Member
Joined
Sep 2009
Posts
242
Thanks
1
Constrained Optimization again
Hi. I still need help with a constrained optimization problem. A couple days ago I posted a similar problem. MHF Member "Anonymous" helped me to get farther along, but n... | 5 | [
-0.024169921875,
-0.0390625,
-0.032470703125,
-0.0556640625,
-0.01190185546875,
0.040771484375,
-0.0184326171875,
0.00848388671875,
-0.10498046875,
0.020751953125,
-0.058837890625,
-0.000701904296875,
-0.00921630859375,
0.034912109375,
0.021484375,
0.056884765625,
0.059814453125,
-... | 24,253 | 24253 | |
Limit of a Trig Function
June 2nd 2010, 05:57 PM #1
Newbie
Joined
Nov 2009
Posts
17
Limit of a Trig Function
I'm quite confused on this question.
Limit Cos [ (pi * x) / (1- 4x) ]
X -> infinity
What I thought it was was to divide everything by x so it would be
Cos (pi / (1/x) - 4)
... | 5 | [
-0.05078125,
-0.011962890625,
-0.009521484375,
0.01275634765625,
-0.033447265625,
-0.0174560546875,
0.01055908203125,
0.0269775390625,
0.0498046875,
0.032958984375,
0.0252685546875,
-0.0206298828125,
0.048583984375,
0.039306640625,
0.036376953125,
0.005279541015625,
0.06787109375,
... | 24,254 | 24254 | |
A Sphere-Based Calibration Method for Line Structured Light Vision Sensor
Advances in Mechanical Engineering
Volume 2013 (2013), Article ID 580417, 8 pages
http://dx.doi.org/10.1155/2013/580417
Research Article
A Sphere-Based Calibration Method for Line Structured Light Vision Sensor
Key Laboratory of Precision Opto... | 4 | [
-0.002655029296875,
0.00732421875,
-0.02978515625,
-0.05859375,
0.05859375,
-0.040283203125,
0.038330078125,
0.038818359375,
0.011962890625,
0.02880859375,
0.033447265625,
-0.02490234375,
0.0306396484375,
0.052978515625,
-0.07958984375,
-0.01397705078125,
-0.02734375,
0.0625,
0.0... | 24,255 | 24255 | |
The WKB approximation to the Schrodinger Equation
December 8th 2010, 02:16 PM
bugatti79
The WKB approximation to the Schrodinger Equation
Hi all,
I am examining the approximate solutions to the Schrodinger equation using the WKB method. I have a simple differentiation query as follows. I want to find A.
... | 5 | [
-0.07421875,
0.0400390625,
0.06689453125,
0.09033203125,
-0.056884765625,
0.041748046875,
-0.03759765625,
0.05126953125,
0.043212890625,
0.05419921875,
0.12890625,
0.002288818359375,
-0.0216064453125,
-0.04150390625,
-0.0263671875,
0.03369140625,
0.01251220703125,
-0.01507568359375... | 24,256 | 24256 | |
On Second Order of Accuracy Difference Scheme of the Approximate Solution of Nonlocal Elliptic-Parabolic Problems
Abstract and Applied Analysis
Volume 2010 (2010), Article ID 705172, 17 pages
http://dx.doi.org/10.1155/2010/705172
Research Article
On Second Order of Accuracy Difference Scheme of the Approximate Solu... | 5 | [
-0.061279296875,
0.109375,
0.08642578125,
-0.0078125,
0.01611328125,
-0.10498046875,
-0.039306640625,
0.01171875,
0.02685546875,
-0.031494140625,
0.06005859375,
0.012451171875,
-0.0087890625,
-0.0311279296875,
-0.044921875,
-0.08056640625,
-0.0123291015625,
-0.054931640625,
-0.02... | 24,257 | 24257 | |
Vectors, Hamming Distance, Coding Theory
September 15th 2010, 10:14 PM #1
Vectors, Hamming Distance, Coding Theory
This problem is causing me some trouble, and I fear that I am overthinking it.
Prove that a binary $[n,M]$-code C of distance $d=2t+1$ exists if and only if a binary $[n+1,M]$-code C' of distanc... | 4 | [
0.0022430419921875,
0.00013256072998046875,
-0.05078125,
-0.057373046875,
-0.02685546875,
0.0272216796875,
-0.00830078125,
-0.0014495849609375,
-0.037353515625,
0.0206298828125,
0.0191650390625,
-0.022216796875,
0.0556640625,
-0.08984375,
-0.07958984375,
0.060791015625,
0.01696777343... | 24,258 | 24258 | |
Law of Cosine Word Problems Pt. 2
July 12th 2009, 06:00 PM #1
Newbie
Joined
Jul 2009
Posts
15
Law of Cosine Word Problems Pt. 2
Two ships leave a port at 9 A.M. One travels at a bearing of N 53 degrees W at 12 mph and the other travels at a bearing of S 67 degrees W at 16 mph. Approximate how far apart t... | 4 | [
-0.013916015625,
0.09814453125,
-0.056884765625,
0.033935546875,
-0.034912109375,
-0.03271484375,
-0.06884765625,
0.006683349609375,
-0.04296875,
0.0159912109375,
0.0791015625,
0.0150146484375,
-0.035400390625,
0.011474609375,
0.017333984375,
0.0150146484375,
-0.05419921875,
-0.055... | 24,259 | 24259 | |
Numerical Simulation for General Rosenau-RLW Equation: An
Average Linearized Conservative Scheme
Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 517818, 15 pages
http://dx.doi.org/10.1155/2012/517818
Research Article
Numerical Simulation for General Rosenau-RLW Equation: An Average Linearized Con... | 5 | [
-0.10302734375,
0.016845703125,
0.03466796875,
0.07421875,
0.0203857421875,
-0.00775146484375,
-0.0546875,
0.050048828125,
-0.0245361328125,
0.009033203125,
-0.04052734375,
0.01556396484375,
0.04541015625,
-0.02490234375,
-0.039306640625,
0.060546875,
-0.1103515625,
-0.024169921875... | 24,260 | 24260 | |
An Interesting Problem
An Interesting Problem July 23, 2009
Posted by genericme in Uncategorized.
trackback
Though this post isn’t necessarily characteristic of what I’d like to post on in the future, I have an interesting problem that I must share with you all. To encourage everyone to try it, I will not
include a ... | 5 | [
-0.053466796875,
-0.01953125,
-0.00341796875,
-0.11181640625,
0.044189453125,
0.051513671875,
-0.041259765625,
-0.053955078125,
0.007476806640625,
0.00041961669921875,
0.01904296875,
0.01806640625,
-0.017822265625,
0.07666015625,
0.00567626953125,
0.07373046875,
-0.006011962890625,
... | 24,261 | 24261 | |
Propagation Behavior of Virus Codes in the Situation That Infected Computers Are Connected to the Internet with Positive Probability
Discrete Dynamics in Nature and Society
Volume 2012 (2012), Article ID 693695, 13 pages
http://dx.doi.org/10.1155/2012/693695
Research Article
Propagation Behavior of Virus Codes in the... | 5 | [
-0.09765625,
-0.02685546875,
-0.0032501220703125,
-0.012939453125,
0.00665283203125,
-0.0986328125,
0.0234375,
-0.01611328125,
0.09619140625,
0.041259765625,
0.05908203125,
0.083984375,
0.11767578125,
-0.052001953125,
-0.06787109375,
-0.037109375,
-0.0216064453125,
-0.0673828125,
... | 24,262 | 24262 | |
Common Denominator ?
How do I do this? (1/ 3x^(2/3)) + (2/3x^(5/3)) thanks
I guess this is the exercice: $\frac{1}{3\cdot x^{\frac{2}{3}}}+\frac{2}{3\cdot x^{\frac{5}{3}}}$ ? Write: $3x^{\frac{5}{3}}=3x^{\frac{2}{3}}.x^{\frac{3}{3}}= 3x^{\frac{2}{3}}.x$ Can you now finish
it? ...
sorry but can you please clarify? I s... | 4 | [
0.034912109375,
-0.08203125,
-0.0439453125,
0.031494140625,
-0.0174560546875,
-0.0595703125,
0.060302734375,
-0.11376953125,
0.02587890625,
0.055419921875,
0.032958984375,
-0.0281982421875,
0.0235595703125,
0.08203125,
0.111328125,
0.07373046875,
-0.0966796875,
0.087890625,
-0.04... | 24,263 | 24263 | |
Strutures - groups
May 19th 2013, 02:23 PM
YoungStudent
Strutures - groups
Hy guys .... I hope that are all fine with you ....
I had this exercises to do, and I'm having problems to solving them, can some of you,help me?
**** find the subgroup of the group (Z, +, 0) generated by the set {10, 15} .
... | 5 | [
-0.052490234375,
0.1201171875,
0.01336669921875,
-0.00159454345703125,
0.062255859375,
0.0206298828125,
0.06640625,
-0.00823974609375,
-0.08154296875,
-0.0869140625,
0.08203125,
-0.04150390625,
0.03271484375,
-0.0751953125,
-0.08642578125,
-0.006134033203125,
0.002685546875,
-0.016... | 24,264 | 24264 | |
A New Approach to the Design of Helical Shape Memory Alloy Spring Actuators
Smart Materials Research
Volume 2011 (2011), Article ID 167195, 5 pages
http://dx.doi.org/10.1155/2011/167195
Research Article
A New Approach to the Design of Helical Shape Memory Alloy Spring Actuators
Department of Applied Mechanics, IIT M... | 4 | [
-0.046630859375,
0.01031494140625,
-0.045166015625,
0.0869140625,
-0.0732421875,
0.068359375,
0.018310546875,
0.04638671875,
-0.0322265625,
0.0419921875,
0.00433349609375,
0.10107421875,
0.04833984375,
0.044677734375,
0.04443359375,
-0.03271484375,
-0.01953125,
0.005859375,
-0.01... | 24,265 | 24265 | |
Work Problem
September 11th 2010, 07:29 AM #1
Newbie
Joined
Apr 2010
Posts
15
Work Problem
A heavy rope, 50 ft. long, weighs .5 lb/ft and hangs over the edge of a building 120 ft. high.
The first part of the question asks you to approximate the work by a Riemann sum and then an integral for how much... | 5 | [
-0.08349609375,
0.08447265625,
0.0830078125,
-0.0478515625,
-0.00003838539123535156,
-0.0791015625,
0.0076904296875,
0.10009765625,
-0.0751953125,
0.07373046875,
-0.01446533203125,
-0.0018463134765625,
-0.00017642974853515625,
0.047119140625,
-0.095703125,
0.080078125,
-0.00086975097... | 24,266 | 24266 | |
Changing the subject of a formula
November 14th 2010, 01:23 PM #1
Newbie
Joined
Nov 2010
Posts
3
Changing the subject of a formula
Hello
I'm new to this forum and I was hoping someone could please help me with something.
I'm trying to learn algebra and am working through a book doing all the pr... | 4 | [
-0.00151824951171875,
0.10546875,
0.04345703125,
0.054443359375,
0.009521484375,
0.061279296875,
0.037353515625,
0.0380859375,
-0.037353515625,
0.09716796875,
0.00933837890625,
-0.09619140625,
-0.037353515625,
0.0194091796875,
0.07421875,
0.019287109375,
-0.08544921875,
0.017578125... | 24,267 | 24267 | |
Proposition 62
The square on the second bimedial straight line applied to a rational straight line produces as breadth the third binomial.
Let AB be a second bimedial straight line divided into its medials at C, so that AC is the greater segment, let DE be any rational straight line, and to DE let there be applied th... | 5 | [
0.0244140625,
-0.0269775390625,
0.020751953125,
-0.1015625,
-0.076171875,
0.02978515625,
0.044921875,
0.0174560546875,
0.056640625,
0.0169677734375,
-0.032470703125,
-0.00183868408203125,
0.036865234375,
-0.0028076171875,
-0.0206298828125,
0.0012664794921875,
-0.0771484375,
0.02575... | 24,268 | 24268 | |
Analytical Solution for the Pressure Oscillations Caused by Trains of Solitary Waves within Confined Coastal Aquifers
ISRN Civil Engineering
Volume 2012 (2012), Article ID 953204, 7 pages
http://dx.doi.org/10.5402/2012/953204
Research Article
Analytical Solution for the Pressure Oscillations Caused by Trains of Solit... | 4 | [
-0.08349609375,
0.040771484375,
0.09375,
0.005340576171875,
-0.050537109375,
-0.032470703125,
-0.048583984375,
0.00909423828125,
-0.0047607421875,
-0.048095703125,
-0.05126953125,
-0.09619140625,
0.05126953125,
-0.0252685546875,
-0.00130462646484375,
0.062255859375,
-0.0537109375,
... | 24,269 | 24269 | |
A Novel Sensitivity Analysis Method in Structural Performance of Hydraulic Press
Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 647127, 21 pages
http://dx.doi.org/10.1155/2012/647127
Research Article
A Novel Sensitivity Analysis Method in Structural Performance of Hydraulic Press
School of Mecha... | 4 | [
-0.018798828125,
0.045654296875,
0.0225830078125,
-0.0152587890625,
-0.072265625,
-0.08447265625,
-0.032958984375,
0.1005859375,
-0.01422119140625,
-0.04248046875,
-0.08837890625,
-0.0011749267578125,
0.10107421875,
0.037353515625,
-0.10693359375,
-0.029541015625,
0.018798828125,
0... | 24,270 | 24270 | |
Converge or diverge plus show why
January 9th 2012, 07:41 AM #1
Junior Member
Joined
Oct 2011
From
United States
Posts
41
Converge or diverge plus show why
show why the con/diverge:
$\sum_{r=1}^{\infty}\frac{r^{2}-1}{r^{2}+1}$
i think she diverges. because the terms get bigger (closer to 1 ... | 5 | [
-0.045166015625,
-0.0751953125,
-0.0272216796875,
0.0478515625,
0.016845703125,
0.00147247314453125,
-0.037841796875,
-0.0252685546875,
0.107421875,
-0.0084228515625,
-0.07763671875,
0.01806640625,
-0.04150390625,
0.1044921875,
-0.041015625,
-0.03515625,
0.0361328125,
0.01116943359... | 24,271 | 24271 | |
Find the soulution set for each inequality...Help Please!
3(12 - x) - 2 < 28 The answer i got was x < 30 over 36...Is this correct?
You have to carefully move things from one side to the other, you start with: $3(12 - x) - 2 \leq 28$ 1. Add 2 to both sides: $3(12 - x) \leq 30$ 2. Divide both sides by 3: $12 - x \leq 1... | 4 | [
0.043701171875,
0.08251953125,
-0.012451171875,
-0.1083984375,
-0.10986328125,
0.025634765625,
0.00653076171875,
0.06103515625,
-0.0732421875,
0.0120849609375,
-0.042236328125,
0.0150146484375,
0.0732421875,
-0.0303955078125,
0.07080078125,
0.031494140625,
0.0142822265625,
-0.02758... | 24,272 | 24272 | |
Prediction of Building Limestone Physical and Mechanical Properties by Means of Ultrasonic P-Wave Velocity
The Scientific World Journal
Volume 2014 (2014), Article ID 508073, 8 pages
http://dx.doi.org/10.1155/2014/508073
Research Article
Prediction of Building Limestone Physical and Mechanical Properties by Means of ... | 4 | [
-0.04541015625,
-0.00885009765625,
0.0751953125,
0.045654296875,
-0.0284423828125,
-0.04833984375,
-0.08740234375,
0.01904296875,
-0.0595703125,
-0.024658203125,
-0.07470703125,
-0.0927734375,
-0.021240234375,
0.01373291015625,
0.0517578125,
-0.00738525390625,
0.08837890625,
0.0693... | 24,273 | 24273 | |
Need help solving this problem with fractions
January 27th 2013, 03:03 PM #1
Newbie
Joined
Jan 2013
From
montral
Posts
3
Need help solving this problem with fractions
Can someone help me and give me a step by step to solve the following?
147/20/2-x = 147/10
So 147 over 20 over 2-x equals 14... | 4 | [
-0.076171875,
0.041259765625,
0.09130859375,
0.0283203125,
-0.0234375,
-0.033203125,
-0.051025390625,
0.023681640625,
-0.0206298828125,
0.0098876953125,
0.0556640625,
-0.0947265625,
0.0546875,
0.0390625,
0.01531982421875,
0.0264892578125,
-0.00848388671875,
0.064453125,
-0.047851... | 24,274 | 24274 | |
A Projection-Type Method for Multivalued Variational Inequality
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 836720, 6 pages
http://dx.doi.org/10.1155/2013/836720
Research Article
A Projection-Type Method for Multivalued Variational Inequality
Institute of Applied Mathematics, Chongqing University of... | 5 | [
-0.033935546875,
0.0038604736328125,
0.0289306640625,
-0.083984375,
-0.055419921875,
0.0888671875,
0.03662109375,
0.05517578125,
-0.021728515625,
-0.03662109375,
-0.04248046875,
-0.003692626953125,
0.09765625,
0.0147705078125,
-0.068359375,
0.0093994140625,
0.047119140625,
0.009399... | 24,275 | 24275 | |
Math Help
Let $f(x)=a_0x+\frac{a_1}{2}x^2+...+\frac{a_n}{n+1}x^{n +1}$ Clearly, this function is differentiable in the interval $[0,1]$. Let's apply the mean value theorem on that interval: $f(1)-f(0)=f'(c)
(1-0)$ where $c\in(0,1)$. Hence: $f(x)=a_0+\frac{a_1}{2}+...+\frac{a_n}{n+1}-0=a_0+a_1c+a_2c^2+...+a_nc^n$ (chec... | 4 | [
-0.057373046875,
-0.01708984375,
0.004730224609375,
0.1142578125,
-0.0966796875,
-0.0020904541015625,
0.013671875,
-0.00579833984375,
0.020263671875,
0.02294921875,
-0.033203125,
-0.09375,
0.0732421875,
-0.0255126953125,
-0.130859375,
-0.03076171875,
-0.0240478515625,
-0.0495605468... | 24,276 | 24276 | |
Need help evaluating this integral.
February 14th 2013, 03:37 PM #1
Newbie
Joined
Sep 2012
From
Ohio
Posts
14
Need help evaluating this integral.
$\int cos^7(5x)\dif dx$
This problem coincides with my Calculus II course chapter on trigonometric integrals. I am unsure if I should be using the red... | 5 | [
-0.040283203125,
0.05029296875,
0.0927734375,
0.051025390625,
0.0262451171875,
0.000244140625,
0.029052734375,
0.00173187255859375,
-0.027587890625,
0.0859375,
0.01153564453125,
-0.0308837890625,
-0.0810546875,
0.07666015625,
-0.0341796875,
-0.036865234375,
0.0191650390625,
0.05737... | 24,277 | 24277 | |
series
John Hughes rjmh@cs.chalmers.se
Wed, 15 Aug 2001 12:05:31 +0200 (MET DST)
hello, i just want to ask a simple question: does somebody have or know =
where to find a haskell program that calculates the number e, that is =
the list of infinite digits? Because i thin... | 4 | [
-0.044921875,
0.064453125,
-0.025634765625,
0.0322265625,
-0.01531982421875,
-0.0107421875,
0.05419921875,
0.1298828125,
-0.08349609375,
-0.040771484375,
-0.06689453125,
0.043212890625,
0.01953125,
-0.003570556640625,
-0.076171875,
-0.04443359375,
-0.04052734375,
0.0152587890625,
... | 24,278 | 24278 | |
Trig Equation
December 28th 2012, 02:36 PM
kinhew93
Trig Equation
1 + 4sin[A](3sin[A] - 4) = cosec[A](cosec[A]-4)
Find the possible values of sin[A]
I tried writing as a quartic equation but I couldn't factorise it and I am now totally void of ideas. Could someone point me in the right direction?
Dec... | 4 | [
-0.053955078125,
-0.02099609375,
-0.07373046875,
-0.04248046875,
-0.036865234375,
0.08642578125,
0.0125732421875,
0.01318359375,
0.0810546875,
-0.007568359375,
0.01544189453125,
-0.0732421875,
0.03369140625,
0.04443359375,
-0.006195068359375,
0.01470947265625,
0.007293701171875,
-0... | 24,279 | 24279 | |
please help with discrete math
April 13th 2008, 01:04 PM #1
Newbie
Joined
Apr 2008
Posts
3
please help with discrete math
Which properties do each of the following relations satisfy among the properties relexive, symmetric transitiv, irreflexive, and antisymmetric?
1. R = {(a,b) l a squared = b squa... | 4 | [
0.01904296875,
0.014892578125,
0.04248046875,
-0.031982421875,
-0.049560546875,
0.0439453125,
0.0184326171875,
-0.026611328125,
-0.01531982421875,
0.031494140625,
-0.026611328125,
-0.0145263671875,
0.07421875,
0.0279541015625,
0.048095703125,
0.07568359375,
0.06396484375,
0.0093994... | 24,280 | 24280 | |
the encyclopedic entry of bernoulli's theorem
In fluid dynamics, Bernoulli's principle states that for an inviscid flow, an increase in the speed of the fluid occurs simultaneously with a decrease in pressure or a decrease in the fluid's
gravitational potential energy. Bernoulli's principle is named after the inventor ... | 4 | [
-0.078125,
-0.0247802734375,
0.031005859375,
0.051025390625,
0.07373046875,
-0.03369140625,
-0.0026092529296875,
0.04931640625,
0.036865234375,
-0.029541015625,
-0.07568359375,
0.037109375,
0.08203125,
0.016845703125,
0.0174560546875,
-0.0267333984375,
-0.09130859375,
0.07666015625... | 24,281 | 24281 | |
Perturbation Theory for Abstract Volterra Equations
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 307684, 26 pages
http://dx.doi.org/10.1155/2013/307684
Research Article
Perturbation Theory for Abstract Volterra Equations
Faculty of Technical Sciences, University of Novi Sad, Trg Dositeja Obradovića 6... | 4 | [
-0.11376953125,
-0.0010528564453125,
0.0908203125,
0.06689453125,
-0.04638671875,
0.07275390625,
0.016357421875,
0.03759765625,
0.08984375,
-0.062255859375,
0.0263671875,
-0.0296630859375,
-0.01434326171875,
-0.01300048828125,
-0.0130615234375,
0.029541015625,
-0.045654296875,
0.05... | 24,282 | 24282 | |
Finding Volume using spherical coordinates
March 26th 2010, 03:39 PM #1
Member
Joined
Nov 2009
Posts
92
Finding Volume using spherical coordinates
Question: Find the spherical coordinate limits for the integral that calculates the volume of the solid between the sphere $\rho=4 cos\phi$ and the hemisphere... | 5 | [
0.044189453125,
0.060302734375,
-0.0194091796875,
-0.06298828125,
0.01806640625,
-0.0260009765625,
-0.07275390625,
0.04052734375,
-0.013671875,
0.0206298828125,
-0.04931640625,
0.033203125,
-0.04296875,
0.031982421875,
-0.00537109375,
-0.0250244140625,
-0.01226806640625,
0.02099609... | 24,283 | 24283 | |
Math Help
Hi, If $a$ is irrational, show that the set {m $a$+n; m $\in$N, n $\in$Z} is dense in R. Thanks!
I can’t explain in English very well, but I will try: A={m $\alpha$+n} I make ( or do?): (1) $\forall$$\epsilon$ >0 A $\cap$(0, $\epsilon$) is true, if x $\in$A $\cap$(0, $\epsilon$) then, sequence
{x, 2x,3x...}... | 5 | [
0.0220947265625,
0.005462646484375,
-0.004150390625,
-0.01385498046875,
-0.03662109375,
0.06640625,
0.1455078125,
-0.06640625,
-0.035888671875,
-0.05615234375,
0.03271484375,
-0.07177734375,
0.07177734375,
0.0194091796875,
-0.00074005126953125,
-0.0673828125,
0.035400390625,
0.0067... | 24,284 | 24284 | |
Adaptive-AR Model with Drivers’ Prediction for Traffic Simulation
International Journal of Computer Games Technology
Volume 2013 (2013), Article ID 904154, 8 pages
http://dx.doi.org/10.1155/2013/904154
Research Article
Adaptive-AR Model with Drivers’ Prediction for Traffic Simulation
^1Zhejiang University, Hangzhou ... | 4 | [
-0.042724609375,
-0.0322265625,
-0.0634765625,
0.0054931640625,
-0.00147247314453125,
-0.0120849609375,
0.0025177001953125,
-0.002349853515625,
0.007476806640625,
-0.002288818359375,
-0.064453125,
-0.01019287109375,
0.0263671875,
0.054931640625,
-0.031494140625,
-0.01043701171875,
0.... | 24,285 | 24285 | |
Noise Suppression in ECG Signals through Efficient One-Step Wavelet Processing Techniques
Journal of Applied Mathematics
Volume 2013 (2013), Article ID 763903, 13 pages
http://dx.doi.org/10.1155/2013/763903
Research Article
Noise Suppression in ECG Signals through Efficient One-Step Wavelet Processing Techniques
Dep... | 4 | [
-0.056396484375,
0.0712890625,
0.061279296875,
-0.040771484375,
-0.0016326904296875,
-0.0869140625,
0.0234375,
-0.078125,
0.08935546875,
-0.111328125,
0.0027923583984375,
0.0289306640625,
-0.0140380859375,
-0.095703125,
-0.0322265625,
-0.0084228515625,
-0.02099609375,
0.07470703125... | 24,286 | 24286 | |
Unsupervised Topographic Learning for Spatiotemporal Data Mining
Advances in Artificial Intelligence
Volume 2010 (2010), Article ID 832542, 12 pages
http://dx.doi.org/10.1155/2010/832542
Research Article
Unsupervised Topographic Learning for Spatiotemporal Data Mining
LIPN-CNRS, UMR 7030, Université de Paris 13. 99,... | 4 | [
-0.0167236328125,
-0.09814453125,
0.0546875,
0.0296630859375,
0.08447265625,
0.00518798828125,
0.00634765625,
-0.0712890625,
-0.0137939453125,
0.0250244140625,
-0.0196533203125,
-0.09326171875,
0.0162353515625,
0.103515625,
-0.035400390625,
-0.00445556640625,
0.0019683837890625,
-0... | 24,287 | 24287 | |
Normed sequence space
April 13th 2010, 06:25 AM
ejgmath
Normed sequence space
Let $\ell^1(\mathbb{N},\mathbb{R})$ denote the space of sequences $x(j)$ such that $\sum_{j=1}^{\infty}|x(j)|<\infty$, equipped with the norm $\|x\|_1=\sum_{j=1}^{\infty}|x(j)|$. Let $\|x\|_2$
denote the usual norm $(\sum_{j=1}^{\i... | 4 | [
-0.0157470703125,
-0.0537109375,
0.03515625,
-0.01190185546875,
0.03466796875,
0.0673828125,
0.04052734375,
-0.021728515625,
-0.021728515625,
-0.08203125,
0.01190185546875,
0.045166015625,
0.06298828125,
-0.09375,
-0.032958984375,
-0.022216796875,
0.031494140625,
-0.000587463378906... | 24,288 | 24288 | |
Homogeneous Equations with Constant Coefficients
April 19th 2007, 08:03 PM #1
Member
Joined
Jun 2006
Posts
93
Homogeneous Equations with Constant Coefficients
Find the general solution of the given differential equation.
y'' + 5y' = 0
The answer is y = C1 + C2*e^(-5t)
I don't know where to... | 4 | [
-0.09912109375,
-0.00347900390625,
0.11083984375,
0.034912109375,
0.0294189453125,
0.028076171875,
0.0123291015625,
-0.026611328125,
0.00677490234375,
0.0703125,
0.08447265625,
-0.0810546875,
-0.068359375,
0.005859375,
-0.08349609375,
0.0086669921875,
-0.060791015625,
-0.068359375,... | 24,289 | 24289 | |
Physics Forums - Visualizing integration
-
Calculus
(
http://www.physicsforums.com/forumdisplay.php?f=109
)
quietrain Feb22-12 02:16 AM
Visualizing integration
Lets say I want to integrate sin from 0 to pi
The answer is 2
But how do visualize it in terms of the graph?
am I summing up the area under the g... | 4 | [
-0.0177001953125,
-0.015380859375,
-0.0286865234375,
-0.050537109375,
0.0306396484375,
-0.06298828125,
-0.033203125,
0.09130859375,
0.0211181640625,
0.00482177734375,
0.0303955078125,
0.0286865234375,
0.00653076171875,
0.078125,
0.01177978515625,
-0.0240478515625,
0.030517578125,
-... | 24,290 | 24290 | |
physics question
1. June 29th 2013, 08:30 AM #1
2. June 29th 2013, 08:50 AM #2
Re: physics question
A body moving in a circle, with radius R, with angular velocity $\omega$ can be represented by the parametric equations $x= R cos(\omega t)$, $y= R sin(\omega t)$. Differentiating, the
velocity ve... | 4 | [
-0.0986328125,
0.039794921875,
-0.048583984375,
0.0130615234375,
0.06201171875,
0.002777099609375,
0.0247802734375,
0.039794921875,
0.0283203125,
0.0021514892578125,
0.1171875,
0.00093841552734375,
-0.0140380859375,
-0.01123046875,
0.036376953125,
0.03857421875,
-0.03369140625,
0.0... | 24,291 | 24291 | |
Accelerated motion in two dimensions
Let us have a look at two dimensional motions that we have so far studied. We observe that projectile motion is characterized by a constant acceleration, “g”, i.e. acceleration due to gravity. What
it means that though the motion itself is two dimensional, but acceleration is one di... | 4 | [
0.0244140625,
-0.08740234375,
-0.01300048828125,
-0.025390625,
0.0274658203125,
0.005767822265625,
-0.0546875,
-0.01312255859375,
0.06201171875,
0.0225830078125,
0.05810546875,
0.0203857421875,
0.0400390625,
-0.0262451171875,
0.000461578369140625,
-0.04345703125,
0.0087890625,
0.04... | 24,292 | 24292 | |
Trignometric Equations
March 18th 2008, 07:41 PM
lemontea
Trignometric Equations
Let f(x)=1-tan^2x and g(x)=tanx. Find the value of x in the interval (0, pie/2) where f(x)=g(x)
Can anyone help me with this question?
March 18th 2008, 07:46 PM
o_O
$f(x) = g(x)$
$1 - \tan^{2}x = \tan x$
$0 = tan... | 4 | [
-0.0294189453125,
-0.0076904296875,
0.087890625,
0.054931640625,
-0.07470703125,
0.01025390625,
0.01806640625,
0.046630859375,
0.029296875,
-0.05419921875,
0.0634765625,
-0.01031494140625,
-0.007080078125,
0.012451171875,
-0.03564453125,
0.043212890625,
0.07421875,
-0.10302734375,
... | 24,293 | 24293 | |
Calculus Max and Min
November 5th 2009, 01:49 PM
Velvet Love
Calculus Max and Min
Consider the function f(x)=sin(x)+(1/4)*sin(2x) on the interval [0,2pi].
Find numbers a, b and c so that a < b < c and f(x) is concave in one direction
on each of the intervals (0,a),(a,b),(b,c) and (c,2pi).
November 5th... | 5 | [
-0.0128173828125,
-0.043212890625,
0.00058746337890625,
-0.017578125,
-0.01165771484375,
0.0284423828125,
-0.06689453125,
0.1005859375,
-0.059814453125,
0.047119140625,
0.01324462890625,
-0.060791015625,
0.09912109375,
-0.006378173828125,
0.01300048828125,
0.041015625,
0.05126953125,... | 24,294 | 24294 | |
Proof involving invertible matrices
February 21st 2010, 11:36 AM
madmartigano
Proof involving invertible matrices
I need to prove that if A is an invertible matrix and B is row equivalent to A, then B is also invertible.
I understand the logic of that statement, but I'm not experienced enough to know how to... | 5 | [
-0.140625,
0.0126953125,
-0.06640625,
-0.01312255859375,
0.005706787109375,
-0.06689453125,
0.00567626953125,
-0.07958984375,
-0.03271484375,
0.047119140625,
-0.03173828125,
-0.0185546875,
0.055908203125,
-0.03662109375,
0.019775390625,
0.07763671875,
-0.048828125,
-0.0037231445312... | 24,295 | 24295 | |
Prove that for every prime p, there is an irreducible quadratic in Z_p[x]
April 12th 2009, 01:14 PM
Dark Sun
Prove that for every prime p, there is an irreducible quadratic in Z_p[x]
Prove that for every prime p, there is an irreducible quadratic in $Z_p[x]$ (the polynomial ring of the integers mod p).
I ha... | 5 | [
0.0023345947265625,
0.0546875,
0.06640625,
0.048583984375,
0.04296875,
0.039794921875,
0.0712890625,
0.036376953125,
-0.003662109375,
-0.1337890625,
-0.01348876953125,
0.0159912109375,
0.08984375,
0.01263427734375,
-0.07275390625,
-0.048095703125,
0.0262451171875,
0.0201416015625,
... | 24,296 | 24296 | |
another challenging integral
April 18th 2010, 08:23 PM
Random Variable
another challenging integral
Most of us know that $\int^{\pi/2}_{0} \ln (\sin x) \ dx = \int^{\pi/2}_{0} \ln (\cos x) \ dx = - \frac{\pi}{2} \ln 2$
But what about $\int^{\pi/2}_{0} \ln (\sin x) \ln (\cos x) \ dx$?
The worked solutio... | 5 | [
-0.0751953125,
-0.00041961669921875,
0.06884765625,
-0.00445556640625,
0.1083984375,
-0.03955078125,
0.02392578125,
-0.056640625,
-0.0218505859375,
0.01153564453125,
0.08251953125,
-0.0120849609375,
-0.048828125,
0.0233154296875,
0.0284423828125,
-0.060302734375,
-0.044677734375,
-... | 24,297 | 24297 | |
A Novel Flexible Model for the Extraction of Features from Brain Signals in the Time-Frequency Domain
International Journal of Biomedical Imaging
Volume 2013 (2013), Article ID 759421, 12 pages
http://dx.doi.org/10.1155/2013/759421
Research Article
A Novel Flexible Model for the Extraction of Features from Brain Sign... | 4 | [
-0.0223388671875,
-0.040771484375,
0.0966796875,
-0.01068115234375,
0.0634765625,
0.06640625,
-0.0089111328125,
-0.0458984375,
0.00579833984375,
-0.0306396484375,
0.0306396484375,
-0.0264892578125,
-0.06103515625,
0.04248046875,
0.00823974609375,
-0.044677734375,
0.000230789184570312... | 24,298 | 24298 | |
Qualitative Analysis of a Diffusive Ratio-Dependent Holling-Tanner Predator-Prey Model with Smith Growth
Discrete Dynamics in Nature and Society
Volume 2013 (2013), Article ID 267173, 9 pages
http://dx.doi.org/10.1155/2013/267173
Research Article
Qualitative Analysis of a Diffusive Ratio-Dependent Holling-Tanner Pred... | 5 | [
-0.05517578125,
0.016357421875,
0.0009918212890625,
0.06591796875,
0.042236328125,
-0.080078125,
-0.0137939453125,
-0.04833984375,
0.0015106201171875,
0.038818359375,
0.0194091796875,
-0.038818359375,
0.00823974609375,
0.1220703125,
-0.029296875,
0.025146484375,
-0.01019287109375,
... | 24,299 | 24299 |