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### Author Topic: Has anyone experiences with the german ”NEO“ layout?  (Read 4056 times)

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#### RC-1140

• Posts: 100
##### Has anyone experiences with the german ”NEO“ layout?
« on: Mon, 17 October 2011, 13:52:23 »
Hey,
I have just come across the German ”NEO-Ergonomic“ Layout which can be seen here. (The page is on German, but at the Bottom is a graphic. Hover your mouse over ”Ebene 1-6“ to see the various layers, which make this layout pretty unique in my opinion.)

I think the Idea of the six layers is pretty interesting. I’ve set up my arch linux to use it, and typing texts still takes ages, but even though I noticed how seldom I have to leave the homerow, and how useful the third and fourth layer are. (the fourth is for anything outside the main cluster like ”Enter“, Arrow keys, Backspace and a numpad) If I should really manage to get used to this layout I might even consider Tenkeyless Boards. But now I really feel like having to learn this as I would miss these sweet layers when returning to QWERTZ. (damn I had to search for these keys a while)

How long does it usually take to get used to a new layout, so one is able to type at least half as fast as in QWERTZ/QWERTY?

RC
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#### fossala

•  Guest
##### Has anyone experiences with the german ”NEO“ layout?
« Reply #1 on: Mon, 17 October 2011, 14:00:21 »
I'm on the way from qwerty to dvorak and I am about half the speed 3 weeks in

#### RC-1140

• Posts: 100
##### Has anyone experiences with the german ”NEO“ layout?
« Reply #2 on: Mon, 17 October 2011, 14:12:32 »
This sounds good and gives me some hope, as I feared I would have to port the layers to QWERTZ when switching back, as these are nearly addictive. There is nearly two weeks of Holiday left, so I will have some time to train, and never switch back. Luckily the developers provide a takeaway-solution as a AHK script and I'm an Admin at school, so I am not forced to use QWERTZ there…
[SIGPIC][/SIGPIC] Unicomp 122-Key Terminal Emulator - IBM Model M 1394309 - IBM Model M 1394312 (Terminal) - Cherry G84-4100 - Cherry G80-1800 MX Black - Cherry G80-2551HAD (with a spare NIB)

#### sinis

• Posts: 470
##### Has anyone experiences with the german ”NEO“ layout?
« Reply #3 on: Mon, 17 October 2011, 14:21:20 »
only I can tell for this is that ktouch, a ubuntu/kubuntu software, has lections to neo, too.

#### Playtrumpet

• Posts: 275
##### Has anyone experiences with the german ”NEO“ layout?
« Reply #4 on: Mon, 17 October 2011, 14:26:25 »
There are some striking similarities to Dvorak in that layout. Makes me happy. ^_^

Six layers? Sure, why not? You can program extra layers to your layout; just make sure to set the right modifiers and using the right keyboard would help.
Das S Ultimate Brown | Dvorak

#### RC-1140

• Posts: 100
##### Has anyone experiences with the german ”NEO“ layout?
« Reply #5 on: Mon, 17 October 2011, 14:29:19 »
Edit: Typing this took long enough for another post to appear. This refers to the post above Playtrumpet's.

Yeah, I knew about this too, (ktouch isn't ubuntu only, it's part of the ”KEdu suite“, and as thus available for any Linux/*BSD and even on Windows) but I don't have much disk space left, and somehow don't want to install all these qt ane KDE libs on my slick Xmonad Arch Linux machine. Im picky about my software.

And well, I had a look on German Dvorak too, but I had the feeling, that the NEO layout would be optimized for German better, and I really liked the possibilities NEO provides for coding. Only downside is that it totally destroys my vim habits. (no more hjkl navigation... :Cry: )
« Last Edit: Mon, 17 October 2011, 14:36:27 by RC-1140 »
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#### Tony

• Posts: 1171
##### Has anyone experiences with the german ”NEO“ layout?
« Reply #6 on: Mon, 17 October 2011, 21:37:45 »
It took around 3 weeks for me to type Colemak with half Qwerty speed.
Keyboard: Filco MJ1 104 brown, Filco MJ2 87 brown, Compaq MX11800, Noppoo Choc Brown/Blue/Red, IBM Model M 1996, CMStorm Quickfire Rapid Black
Layout: Colemak experience, speed of 67wpm

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##### Has anyone experiences with the german ”NEO“ layout?
« Reply #7 on: Tue, 18 October 2011, 00:27:29 »
Took me a less than a week to regain my pathetic QWERTY speed in Dvorak. Typing a paper that day helped.

I really mean pathetic. It was like 20 keystrokes a minute in QWERTY.
---
I really like the many layers, though. I use greek letters all the time, but it's usually in the form of $\alpha \Beta$ or similar (in LaTeX).
---
Why isn't layer six shift+mod3? That follows the pattern, while what they have doesn't.

layer 1 is nothing.
2 is shift
3 is 3
4 is 4
5 is shift+3
6 is 3+4
6 sholud be shift+3
---
They could add another two layers by using shift+3 or shift+4. Not like they'd need it.
« Last Edit: Tue, 18 October 2011, 00:32:01 by dorkvader »
Kleptomaniacs are bad with puns: they take everything, literally.
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#### bugybunny

• Posts: 2
##### Has anyone experiences with the german ”NEO“ layout?
« Reply #8 on: Tue, 01 November 2011, 16:59:40 »
I started using Neo in June this year; I switched from one day to the other at home but typed QWERTZ at work for the first 4 weeks before I changed completely. After this 4 weeks I felt I could write fluently and work nearly as fast as with QWERTZ. Now I have about 400cpm (better that with QWERTZ) and sometimes when I have to type at another computer it’s just a pain. So if you have the possibility to exercise with NEO the whole day and don’t have to switch back for a few hours while working, you should feel confident after a week.
I’m working as a software developer and the 3rd and 4th layer is like heaven. Thanks to the Eclipse IDE and its many shortcuts I rarely leave my keyboard to use the mouse or even leave the homerow.
It’s optimized for German but they considered English too (y on your right pinky for example).

You started about 2 weeks ago, how is it now? :-)

(sorry for my English^^)

#### Duraxel

• Posts: 1
##### Has anyone experiences with the german ”NEO“ layout?
« Reply #9 on: Thu, 10 November 2011, 18:43:50 »
I'm German, a software developer and I'm considering using Neo 2.0 as my future keyboard layout. Hearing that Neo is heaven when it comes to programming really wants me to begin working on it.  And if anybody knows a way to get keycaps for my Filco blue (ISO layout) printed with Neo 2.0 symbols - that would be perfect!

Here my little story why I'm considering Neo 2.0:
It is literally painful to enter some of the special characters (e.g. '[', ']', '{', '}') needed for programming on a default german keyboard. Although it is possible to enter those characters comfortably with the common english layouts out there, I still have to write german sometimes. Writing german umlauts (ö, ä, ü) for example becomes then rather annoying.
And I don't want to switch between english and german layouts all the time.

I also considered the Colemak and the Dvorak layout, but  both miss an option to enter german characters comfortably. Aside from that I also like that Neo leaves the often used short cuts for copy, cut and paste unchanged ;-)

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##### Has anyone experiences with the german ”NEO“ layout?
« Reply #10 on: Thu, 10 November 2011, 22:36:59 »
Quote from: Duraxel;449628
I'm German, a software developer and I'm considering using Neo 2.0 as my future keyboard layout. Hearing that Neo is heaven when it comes to programming really wants me to begin working on it.  And if anybody knows a way to get keycaps for my Filco blue (ISO layout) printed with Neo 2.0 symbols - that would be perfect!

Yeah, you can get most of them from WASD. They only have ANSI now, so you'll have to forego the enter and shift, etc. They will have ISO, soon. If you want to wait a little.
Kleptomaniacs are bad with puns: they take everything, literally.
let me put together your keyboard!

#### RC-1140

• Posts: 100
##### Has anyone experiences with the german ”NEO“ layout?
« Reply #11 on: Fri, 11 November 2011, 10:26:39 »
Yeah I was thinking about a set from WASD (damn, this combination is somewhat hard to find in neo) too, but it was literally impossible to enter all the symbols. I asked them once about it, and they told me, that support for all UTF-8 symbols will come around the same time as ISO. But atm I'm in love with my unicomp, so i wouldn't be able to use these keycaps at all.

And about my current experiences using Neo: I finally stopped switching back to QWERTZ when having to type long texts for school. When at school I get some strange looks for my neo g84-4100. But overall I'm happy about the decision to learn Neo.
[SIGPIC][/SIGPIC] Unicomp 122-Key Terminal Emulator - IBM Model M 1394309 - IBM Model M 1394312 (Terminal) - Cherry G84-4100 - Cherry G80-1800 MX Black - Cherry G80-2551HAD (with a spare NIB)

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##### Has anyone experiences with the german ”NEO“ layout?
« Reply #12 on: Sat, 12 November 2011, 20:27:27 »
Quote from: RC-1140;449966
Yeah I was thinking about a set from WASD (damn, this combination is somewhat hard to find in neo) too, but it was literally impossible to enter all the symbols. I asked them once about it, and they told me, that support for all UTF-8 symbols will come around the same time as ISO. But atm I'm in love with my unicomp, so i wouldn't be able to use these keycaps at all.

And about my current experiences using Neo: I finally stopped switching back to QWERTZ when having to type long texts for school. When at school I get some strange looks for my neo g84-4100. But overall I'm happy about the decision to learn Neo.

You can still upload custom graphics to the WASD one, so you can came up with keycaps still.

Nevertheless, I'd wait for UTF-8 and ISO

Kleptomaniacs are bad with puns: they take everything, literally.
let me put together your keyboard!

#### RC-1140

• Posts: 100
##### Has anyone experiences with the german ”NEO“ layout?
« Reply #13 on: Mon, 26 December 2011, 15:24:15 »
Just if anybody is interested in my current progress in learning this new layout, here is the current state:

I’m really getting used to Neo. Typing on QWERTZ feels absolutely strange now, though I can still type as fast in it as before. But I have no intention of leaving Neo. My typing speed in Neo is now 33 WPM, compared to 42 WPM in QWERTZ. That’s fast enough to use it for anything I have to do on a PC, so I never switch back anymore. I’ve found a Keyboard app for Android that allows me to use NEO on my mobile too.

Everything is sorted into layers. I feel good about things. But I can’t read the label, because I'm a hologram. (Let's see if somebody realizes where this comes from)

greetings,

RC
[SIGPIC][/SIGPIC] Unicomp 122-Key Terminal Emulator - IBM Model M 1394309 - IBM Model M 1394312 (Terminal) - Cherry G84-4100 - Cherry G80-1800 MX Black - Cherry G80-2551HAD (with a spare NIB)

#### Playtrumpet

• Posts: 275
##### Has anyone experiences with the german ”NEO“ layout?
« Reply #14 on: Mon, 26 December 2011, 20:44:07 »
Quote from: RC-1140;478033
Everything is sorted into layers. I feel good about things. But I can’t read the label, because I'm a hologram. (Let's see if somebody realizes where this comes from)

greetings,

RC

30 Rock?

Neo seems to have a lot of similarities to Dvorak. Nice to see people using it. ^_^
Das S Ultimate Brown | Dvorak

#### sordna

• Posts: 2826
##### Has anyone experiences with the german ”NEO“ layout?
« Reply #15 on: Mon, 26 December 2011, 22:18:21 »
I've experimented with NEO a bit, just because I was trying to find a way to enable 5th level shift and assign multiple functions onto a single key (the goal was to have embedded numpad, mousekeys, etc). Out of several layouts I tried only de(neo) and ca(multix) had 5th level shift:

I ended up settling on us(altgr-intl) which at least has a 3rd level shift (sadly no 5th level) since US layout works best for my needs.
Kinesis Contoured Advantage LF with Cherry MX Red switches / Extra keys mod / O-ring dampening mod / Dvorak layout. ErgoDox with buzzer and LED mod.
Also: Kinesis Advantage Classic, Kinesis Contoured Model 110, Data911 TG3, Fingerworks Touchstream LP, KBC Poker (Cherry MX Red), IBM Space Saving keyboard (Buckling spring), Goldtouch GTU-0077 keyboard

#### What's that? It's NEO!

• Posts: 55
##### Has anyone experiences with the german ”NEO“ layout?
« Reply #16 on: Thu, 26 January 2012, 04:44:26 »
Hi,
as far as I can say, the NEO layout when writing german is pretty much better than QUERTZ, writing english does not feel weired either. I switched 100 percent last year when I ordered my filco keyboard and I have never regretted it. Before the switch I wasn't able to type without looking at the characters... oh my.

I started with sticking the characters onto the keys but quickly after some rounds of typing games, I removed them. It took quite a while to get used to NEO but now I really like the functions it has: especially helpful when setting texts with LaTeX. It's just the routine that get's you going.

#### boli

• Posts: 350
##### Has anyone experiences with the german ”NEO“ layout?
« Reply #17 on: Thu, 26 January 2012, 05:06:21 »
Quote from: RC-1140;432882
How long does it usually take to get used to a new layout, so one is able to type at least half as fast as in QWERTZ/QWERTY?

Haven't tried NEO, but for the QWERTY to Colemak switch it took me about 3 weeks to get to half my previous QWERTY-speed.
Keyboard: Kinesis Ergo Advantage (two LF editions with red Cherry switches, one regular with brown switches)
Keyboard layout: basically Colemak, with some remapping to end up with my custom Kinesis Advantage layout
Typing test profiles: typeracer.com / hi-games.net / keybr.com

#### Icarium

• Posts: 385
• I AM A MONKEY!
##### Has anyone experiences with the german ”NEO“ layout?
« Reply #18 on: Thu, 26 January 2012, 06:51:52 »
Does anybody have a list of semi-common layouts? And by semi-common I mean let's leave those that are used by only one person out.
I had a sig once but it's gone. It used to display an icon of a Kinesis. Just imagine that.

#### pyro

• Posts: 182
##### Has anyone experiences with the german ”NEO“ layout?
« Reply #19 on: Thu, 26 January 2012, 10:42:04 »
Colemak and Dvorak seem to be the most common alternative layouts. QGMLWB (Carpalx best) is pretty well known, too, but I think very few actually bother to learn it.

Although I haven't encountered anyone in real life using anything besides QWERTZ or QWERTY.

#### sordna

• Posts: 2826
##### Has anyone experiences with the german ”NEO“ layout?
« Reply #20 on: Thu, 26 January 2012, 11:17:56 »
Really? At work I have bumped into at least 2 people that use Dvorak. One of them was a Kinesis Advantage user, the other was not.
Kinesis Contoured Advantage LF with Cherry MX Red switches / Extra keys mod / O-ring dampening mod / Dvorak layout. ErgoDox with buzzer and LED mod.
Also: Kinesis Advantage Classic, Kinesis Contoured Model 110, Data911 TG3, Fingerworks Touchstream LP, KBC Poker (Cherry MX Red), IBM Space Saving keyboard (Buckling spring), Goldtouch GTU-0077 keyboard

#### boli

• Posts: 350
##### Has anyone experiences with the german ”NEO“ layout?
« Reply #21 on: Thu, 26 January 2012, 13:39:47 »
I know only two people beside myself who use alternative layouts IRL: one uses Dvorak, the other Colemak. Both are software engineers like myself, one of them works in the same company with 140ish employees (Dvorak user, using Typematrix 2030, has a TE as well but not used yet last I heard); the other I've known since childhood and encouraged to switch to Colemak.
« Last Edit: Thu, 26 January 2012, 13:51:42 by boli »
Keyboard: Kinesis Ergo Advantage (two LF editions with red Cherry switches, one regular with brown switches)
Keyboard layout: basically Colemak, with some remapping to end up with my custom Kinesis Advantage layout
Typing test profiles: typeracer.com / hi-games.net / keybr.com

#### sordna

• Posts: 2826
##### Has anyone experiences with the german ”NEO“ layout?
« Reply #22 on: Thu, 26 January 2012, 13:43:49 »
Does any linux distro have colemak built in ? i tried "setxkbmap colemak" on my ubuntu 11.10 and it didn't work, while I can choose other layouts that way.
Kinesis Contoured Advantage LF with Cherry MX Red switches / Extra keys mod / O-ring dampening mod / Dvorak layout. ErgoDox with buzzer and LED mod.
Also: Kinesis Advantage Classic, Kinesis Contoured Model 110, Data911 TG3, Fingerworks Touchstream LP, KBC Poker (Cherry MX Red), IBM Space Saving keyboard (Buckling spring), Goldtouch GTU-0077 keyboard

#### boli

• Posts: 350
##### Has anyone experiences with the german ”NEO“ layout?
« Reply #23 on: Thu, 26 January 2012, 13:46:40 »
Quote from: sordna;499794
Does any linux distro have colemak built in ? i tried "setxkbmap colemak" on my ubuntu 11.10 and it didn't work, while I can choose other layouts that way.

Yes, they say Colemak comes installed by default with most modern distributions, and doesn't require any download.
Source: Linux/Unix in graphical mode (preinstalled)

Dunno if it works, I'm using Mac OS X.
« Last Edit: Thu, 26 January 2012, 14:00:43 by boli »
Keyboard: Kinesis Ergo Advantage (two LF editions with red Cherry switches, one regular with brown switches)
Keyboard layout: basically Colemak, with some remapping to end up with my custom Kinesis Advantage layout
Typing test profiles: typeracer.com / hi-games.net / keybr.com

#### sordna

• Posts: 2826
##### Has anyone experiences with the german ”NEO“ layout?
« Reply #24 on: Thu, 26 January 2012, 13:50:11 »
doh, didn't realize it's a us layout variant, thanks! This worked: setxkbmap 'us(colemak)'
Any idea why dvorak is a separate layout but colemak is a variant of the us layout ?
Kinesis Contoured Advantage LF with Cherry MX Red switches / Extra keys mod / O-ring dampening mod / Dvorak layout. ErgoDox with buzzer and LED mod.
Also: Kinesis Advantage Classic, Kinesis Contoured Model 110, Data911 TG3, Fingerworks Touchstream LP, KBC Poker (Cherry MX Red), IBM Space Saving keyboard (Buckling spring), Goldtouch GTU-0077 keyboard

#### boli

• Posts: 350
##### Has anyone experiences with the german ”NEO“ layout?
« Reply #25 on: Thu, 26 January 2012, 13:55:16 »
Quote from: sordna;499799
Any idea why dvorak is a separate layout but colemak is a variant of the us layout ?

No clue. From what I understand both are optimized for English (though I don't think American or British English makes a difference really). Maybe something hardware related, maybe British keyboards have an extra key compared to a US keyboard or something (like many international keyboards do).

BTW even though my native language is (Swiss) German, Colemak works pretty well for me, as German shares 9 of the 10 most frequent letters (those on the home row) with English IIRC. I can't think of any common German letter sequences that are uncomfortable to type, but then again I type a lot of English and code as well...
« Last Edit: Thu, 26 January 2012, 14:12:29 by boli »
Keyboard: Kinesis Ergo Advantage (two LF editions with red Cherry switches, one regular with brown switches)
Keyboard layout: basically Colemak, with some remapping to end up with my custom Kinesis Advantage layout
Typing test profiles: typeracer.com / hi-games.net / keybr.com

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##### Has anyone experiences with the german ”NEO“ layout?
« Reply #26 on: Fri, 27 January 2012, 01:37:17 »
I'd say it's because of how the punctuation is arranged. Colemak is basically a varient, with only capslock being the weird key. Dvorak has all the punctuation changed as well as / ][- and

I've only met two: one each of dvorak and colemak. Only one was fluent.
Kleptomaniacs are bad with puns: they take everything, literally.
let me put together your keyboard!

#### sordna

• Posts: 2826
##### Has anyone experiences with the german ”NEO“ layout?
« Reply #27 on: Fri, 27 January 2012, 09:24:10 »
Sean Wrona recommends using Caps Lock. I do too. It's silly of them to get rid of it, it should be up to the user. Controversial stuff like that (reminds me of TE moving Shift on the ASD row) should be left to the user and not forced down one's throat.
Kinesis Contoured Advantage LF with Cherry MX Red switches / Extra keys mod / O-ring dampening mod / Dvorak layout. ErgoDox with buzzer and LED mod.
Also: Kinesis Advantage Classic, Kinesis Contoured Model 110, Data911 TG3, Fingerworks Touchstream LP, KBC Poker (Cherry MX Red), IBM Space Saving keyboard (Buckling spring), Goldtouch GTU-0077 keyboard

#### Icarium

• Posts: 385
• I AM A MONKEY!
##### Has anyone experiences with the german ”NEO“ layout?
« Reply #28 on: Fri, 27 January 2012, 10:11:56 »
Do you use caps lock instead of the normal shift key or just for multiple caps in a row?
I had a sig once but it's gone. It used to display an icon of a Kinesis. Just imagine that.

#### sordna

• Posts: 2826
##### Has anyone experiences with the german ”NEO“ layout?
« Reply #29 on: Fri, 27 January 2012, 10:12:48 »
i use it for let's say 3 or more capital letters in a row.
Kinesis Contoured Advantage LF with Cherry MX Red switches / Extra keys mod / O-ring dampening mod / Dvorak layout. ErgoDox with buzzer and LED mod.
Also: Kinesis Advantage Classic, Kinesis Contoured Model 110, Data911 TG3, Fingerworks Touchstream LP, KBC Poker (Cherry MX Red), IBM Space Saving keyboard (Buckling spring), Goldtouch GTU-0077 keyboard


text:
# Question

Refer to Exercise 11.25.
a. Determine the margin of error for the estimate of p.
b. Obtain a sample size that will ensure a margin of error of at most 0.01 for a 95% confidence interval without making a guess for the observed value of pˆ.
c. Find a 95% confidence interval for p if, for a sample of the size determined in part (b), the proportion of asthmatics sampled who are allergic to sulfites is 0.071.
d. Determine the margin of error for the estimate in part (c) and compare it to the margin of error specified in part (b).
e. Repeat parts (b)–(d) if you can reasonably presume that the proportion of asthmatics sampled who are allergic to sulfites will be at most 0.10.
f. Compare the results you obtained in parts (b)–(d) with those obtained in part (e).

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text:
Probability distribution of Fourier coefficients

Suppose I have $N$ independent random numbers with a uniform distribution in $[+1, -1]$. Suppose I take the discrete Fourier transform of these numbers. What would the probability distribution of each frequency coefficient be?

Each frequency coefficient is the weighted sum of $N$ independent random numbers with the same distribution. If it were an unweighted sum, then the distribution would presumably tend towards a normal distribution as $N$ increases.

But since it's a weighted sum... The only fact I have which seems relevant is that the PDF of the sum of some random variables supposedly equals the convolution of the PDFs of the individual variables. (Assuming they are all independent, obviously.) I'm not sure what you get if you convolve several unequal uniform distributions thought...

• It is easy to compute the characteristic function of a weighted sum of independent uniform random variables. But in general it is not the characteristic function of a standard distribution. Apr 27 '12 at 17:24
• Even a weighted sum of i.i.d. variates with finite mean and variance tends towards Normality as long as, loosely speaking, the maximum weight (when the weights sum to 1 regardless of sample size) goes to zero as the sample size goes to infinity. Apr 27 '12 at 19:52

The complex Fourier coefficients of a random series form a 2-D normal distribution in the complex plane (a Gaussian rotated around zero). When taking the magnitude of the complex spectrum, at each magnitude $r$ (the distance from the origin) the probability density will be $\int 2 \pi r dr$, multiplied by the Gaussian, which gives (up to some constants) $r\times e^{-r^2}$. Incidentally, this does not depend on the shape of the original random distribution (from the central limit theorem, I guess). I tried in Matlab randn(...) (normally distributed), rand(...) (uniformly distributed) or rand(...)>.5 (zeros and ones only). Magic!


text:
Dotcpp  >  编程题库  >  信息学奥赛一本通T1448-电路维修

# 信息学奥赛一本通T1448-电路维修

## 题目描述

Casper is designing an electronic circuit on a N×M rectangular grid plate. There are N×M square tiles that are aligned to the grid on the plate. Two (out of four) opposite corners of each tile are connected by a wire.

A power source is connected to the top left corner of the plate. A lamp is connected to the bottom right corner of the plate. The lamp is on only if there is a path of wires connecting power source to lamp. In order to switch the lamp on, any number of tiles can be turned by

90° (in both directions).

In the picture above the lamp is off. If any one of the tiles in the second column from the right is turned by 90° , power source and lamp get connected, and the lamp is on.

Write a program to find out the minimal number of tiles that have to be turned by 90° to switch the lamp on.

## 输入格式

The first line of input contains two integer numbers N and M, the dimensions of the plate. In each of the following N lines there are M symbols – either  \ or / – which indicate the direction of the wire connecting the opposite vertices of the corresponding tile.

## 输出格式

There must be exactly one line of output. If it is possible to switch the lamp on, this line must contain only one integer number: the minimal number of tiles that have to be turned to switch on the lamp. If it is not possible, output the string: NO SOLUTION

## 样例输入

1
3 5
\\/\\
\\///
/\\\\

## 样例输出

1


text:
# Math Help - Log simplification.

1. ## Log simplification.

1. logx + log sqroot x^3 - 2log x
ANS: 1/2log

2. log x/(sqroot x) + log sq.root x^5 - 7/3 log x
ANS: 2/3log

3. 2log2x - log 4y - log sqroot (xy)
ANS: x^(3/2) y^(-3/2)

how do i do these?, you dont have to answer them fully, since i would like to learn or if you show all steps so i can learn.

Can someone guide me through these?

2. ## Re: Log simplification.

Hey skg94.

For these recall that log(xy) = log(x) + log(y) and that log(x/y) = log(x) - log(y).

In terms of your answers are you looking for terms in terms of log(x) (You write log but is it instead log(x))?

3. ## Re: Log simplification.

To simplify these expressions, you need to know a few properties of logs and concerting from radical notation to rational exponent notation.

$\log_a(x)+\log_a(y)=\log_a(xy)$

$\log_a(x)-\log_a(y)=\log_a\left(\frac{x}{y} \right)$

$\log_a(b^c)=c\cdot\log_a(b)$

$\sqrt[n]{x^m}=x^{\frac{m}{n}}$

The answers you have supplied are incomplete, although I can tell what is intended.

Using the above properties, see if you can get the desired result. If you get stuck, post your working and state where you are stuck.

4. ## Re: Log simplification.

Well they are the answers in my textbook i cant really do much about them, since im pretty sure my teachers look for the same, maybe not.

if they are incomplete what are the correct answers?

x* x^1.5 / x^2

x^2.5/x^2
2.5-2 = x^.5

so is that why its 1/2 log x? suppose i got that one at least.

2. x*x^2.5/x^1/2 * x^(7/3) =x^3.5/ x^ 17/6 = x^ 2/3

2/3 log x

3. 4x^2 / 4y * x^1/2 * y^1/2
4x^2/ 4y^1.5 * x^1/2

x^1.5 y^1.5 -- hm not negative 1.5?

well i got it now if you see any errors let me know

5. ## Re: Log simplification.

The first two answer provided by the book do not contain an argument for the log function, which is meaningless. The last one does not include the log function, but just the argument. It certainly is not the way the answers should be given.

If I were working these problems, this is the way I would show my work for the first one:

1.) $\log(x)+\log(\sqrt{x^3})-2\log(x)$

$\log(x)+\log({x^{\frac{3}{2}}})-\log(x^2)$

$\log\left(\frac{x\cdot x^{\frac{3}{2}}}{x^2} \right)$

$\log(x^{\frac{1}{2}})$

$\frac{1}{2}\log(x)$

6. ## Re: Log simplification.

yes it was just my laziness it does have the x and such in the textbook my apologies.


text:
Review question

Can we evaluate these log expressions without using a calculator? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R9976

Question

1. Without using tables [or calculators], find the value of \begin{align*} 2 \lg 5 - \frac{1}{2} &\lg 9 + \lg 0.12.\\ [\lg x &= \log_{10} x] \end{align*}
2. If $\lg 2 = 0.30103$ and $\lg 3 = 0.47712$, find, without using tables [or calculators], the values of $\lg 6$ and $\lg 15$.


text:
# Angle between two vectors

This topic is 4584 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic.

## Recommended Posts

Hi! I have this very simple question. I've totally forgot how dot product in 2D space works. I am using OpenGL to render something in 2D, the origo is in the middle of the screen, everything below is negative y, and everything to the left of the origo is negative x. So I have two positions given as 2 2D vectors pos1, and pos2 for example. I dot product the pos1 with (pos2-pos1), acos -> convert to degrees, but I get totally wrong angles. And if my pos2 is ie. (200, 100) and when it is (100, 200) the angle equals. Do you guys can help me out, and explain what I am doing wrong. btw: I am using glRotatef(angle, 0.0f, 0.0f, 1.0f) for rotating the sprite. Thank you!!

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The formula is
    A dot B = |A| |B| cos θ
Thus
    θ = cos-1 ( A dot B ) / ( |A| |B| )
You probably need to divide A dot B by the lengths of the vectors (or normalize the vectors first, it's the same) before doing cos-1.

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Remember that acos() returns the angle in radians, so you'll have to convert before calling glRotate(). Also, an alternate way of finding the (signed) angle between vectors of arbitrary (non-zero) length in 2d is:
angle = atan2(perpdot(a,b), dot(a,b));

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Sorry, forgot to add, that I normalized the vectors. Do I have to use the current position vector, and the pos2-pos1 vector? Or other vectors? :s
pos1 is my current position, pos2 is the goal position.

Thanks!

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Quote:
 Original post by jykRemember that acos() returns the angle in radians, so you'll have to convert before calling glRotate(). Also, an alternate way of finding the (signed) angle between vectors of arbitrary (non-zero) length in 2d is:angle = atan2(perpdot(a,b), dot(a,b));

I have no idea why, but still doesn't work :(((((
I've tried it your way, but still no luck. I am posting some code:

public double dot(Vector2D v1) {		double dot = (this.dX*v1.dX + this.dY*v1.dY);   	return dot;}   public double perpDot(Vector2D v1) {   	double pdot =  this.dX*v1.dY-this.dY*v1.dX;	return pdot;}//...pos = new Vector2D((double)x, (double)y);goal_pos = new Vector2D(201.0, 101.0);		Vector2D dirVector = goal_pos.sub(pos);		dir = Math.toDegrees(Math.atan2(pos.perpDot(dirVector), pos.dot(dirVector)));//...gl.glRotated(dir, 0.0, 0.0, 1.0);

I've tried negating values, tried using goal_pos instead of dirVector, also tried changing parameters in the atan2 function, but still no-no for luck. :(((

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Here is what i have used

float CVector2D::getAngle(CVector2D & rVector)
{
return atan2(rVector.m_y - m_y , rVector.m_x - m_x);
}

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Ah, I see. The solutions John and I posted are for (signed or unsigned) relative angles. It looks like you want an absolute angle, in which case you should use MTclip's solution. (If you ever need the relative angle though, at least you have the answer :)

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Quote:
 Original post by jykAh, I see. The solutions John and I posted are for (signed or unsigned) relative angles. It looks like you want an absolute angle, in which case you should use MTclip's solution. (If you ever need the relative angle though, at least you have the answer :)

Thanks for all your help, for the first tries it went great, then when I did some random going there, going there it failed. Here is what I want to implement. I have a littleobject, I want it to face a position defined by a 2D vector. I worked many times with 3D engines, wrote some engines using pixelshader, and etc... never thought that in 2D finding two coordinates between an object and a point is so hard. :D:D

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dir = Math.toDegrees(Math.atan2(pos.perpDot(dirVector), pos.dot(dirVector)));

Should be
dir = Math.toDegrees(Math.atan2(dirVector.y,dirVector.x);

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Thanks all for your help. Actually I needed signed relative angle between the two vectors. The equation pointed out by jyk was working fine, I did a mistake that I wasn't multiplying like heading x directionVector, but I was using position x directionVector. I first get the current heading vector like
xh = Math.cos(dir);
yh = Math.sin(dir);
Then I used jyk's equation to multiply that with the direction vector pointing to goal position. Thanks again for your help!

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# Help with Gibbs' Free Energy!

There's an equation that states ΔG = - RT ln K, where ΔG is the Gibbs' free energy at standard conditions, R is the universal gas constant, T is the temperature, and K is the equilibrium constant.

Is K = Kc (in terms of concentrations) or K = Kp (in terms of partial pressures)?

According to this equation it seems to be dimensionless!

Note by Ameya Daigavane
1 year, 10 months ago

Sort by:

Both Kp nd Kc I guess, because any sort of equilibrium is considered in the equilibrium, it's just a particular value of the reaction quotient attained at equilibrium. · 1 year, 4 months ago

It is $$K_{c}$$ i.e. in terms of concentration. · 1 year, 5 months ago


text:
# The effects of 2015 El Nino on smallholder maize production in the transitional ecological zone of Ghana

Kwadwo Owusu (Department of Geography and Resource Development, University of Ghana, Legon, Greater Accra, Ghana)
Ayisi Kofi Emmanuel (University of Ghana Business School, Accra, Ghana)
Issah Justice Musah-Surugu (Department of Public Administration, University of Ghana, Legon, Greater Accra, Ghana)
Paul William Kojo Yankson (Department of Geography and Resource Development, University of Ghana, Legon, Greater Accra, Ghana)

ISSN: 1756-8692

Publication date: 18 November 2019

## Abstract

### Purpose

This paper aims to provide empirical evidence on the El Nino and its effects on maize production in three municipalities: Ejura, Techiman and Wenchi in the transitional zone of Ghana. Using a mixed approach, the study details the effects of the El Nino on rainy season characteristics, particularly, rainfall amounts and distribution, onset and cessation of rains, duration of the rainy season and total seasonal rainfall and how it impacted smallholder maize production.

### Design/methodology/approach

The study used a mixed method approach in collecting and analyzing data. For stronger evidence building, (Creswell, 2013) the authors combined interviews and focus group discussions (FGD) to collect the qualitative data. Semi-structured questionnaires were administered to extension officers, management information system officers and other relevant personnel of the Ministry of Agriculture in the three municipalities. Six FGD’s were held for maize farmers in six communities in all three municipalities.

### Findings

The study shows that the 2015 El Nino had dire consequences on farm yields, subsequently affecting farmer’s incomes and livelihoods. The study further finds that complex socio-cultural factors, some unrelated to the El Nino, aggravated the effects on maize farmers. These include the lack of adequate climatic information, predominance of rain-fed farming, a lack of capacity to adapt and existing levels of poverty.

### Originality/value

The study recommends inter alia, appropriate use of seasonal rainfall forecasting to enhance better farming decision-making and the development of elaborate climate variability interventions by national and local agencies.

## Keywords

#### Citation

Owusu, K., Emmanuel, A., Musah-Surugu, I. and Yankson, P. (2019), "The effects of 2015 El Nino on smallholder maize production in the transitional ecological zone of Ghana", International Journal of Climate Change Strategies and Management, Vol. 11 No. 5, pp. 609-621. https://doi.org/10.1108/IJCCSM-02-2018-0014

### Publisher

:

Emerald Publishing Limited

## 1. Introduction

One of the topical issues in the world today is climate variability and its effect on crop production. According to Rowhani et al. (2011), climate variability is expected to increase in some regions, with significant consequences on food production beyond climate change impacts. The issue attracts much attention because among other things, such changes have implications for food security globally (Godfray et al., 2010; Frelat et al., 2016). For Africa in particular, climate variability impact is pertinent because the continent receives the most food aid, with some 30 million of its people requiring emergency food aid in any one single year (Godfray et al., 2010; FAO, 2016). As indicated by the 2015 global food security index, malnutrition, starvation and deaths still persist in Sub-Saharan Africa despite significant food security improvements over the past decade. Although this situation is attributed to a number of factors including distribution obstacles, (Godfray et al., 2010; FAO, 2016), ineffective local agriculture (Antwi-Agyei et al., 2013) and poor governance (Clover, 2003), it is the changes in climate and climate variability that seem to have a stronger explanatory weight in the whole food security discourse (Sasson, 2012; Mawunya and Adiku, 2013).

The El Nino-Southern Oscillation (ENSO), the largest known source of climate variability in the tropics, has severe impacts particularly on agricultural activities (Goddard et al., 2001; Woli et al., 2012). Although the phenomenon is pretty much predictable, sometimes a year or more ahead (Chen and Cane, 2007; Adiku et al., 2007), its impacts are still devastating on sectors that are climate sensitive such as smallholder agricultural and hydropower production (Schaeffer et al., 2012; Boadi and Owusu, 2017). In Ghana and other developing countries, vulnerability to El Nino event is exacerbated by the predominance of rain-fed agricultural systems and the absence of reliable climatic information (Rockström et al., 2004; Mongi et al., 2010). However, the risks associated with the El Nino cycles may be mitigated if effective plans are instituted. Adaptation to within season or terminal drought could be improved by irrigation efficiency and the timeous dissemination of information among farmers as well as the use of seasonal rainfall forecasting to help in decision-making (Adiku et al., 2007). Thomas et al. (2007), highlight the success of such strategies in Southern Africa for example, where farmers cultivate lands closer to a water source during drought periods.

The effect of ENSO on rainfall in the Guinea Coast area of Ghana is evident in many studies (Opoku-Ankomah and Cordery, 1994; Adiku et al., 2007 Owusu and Waylen,2009). The 1982/83 ENSO season for instance is known to be associated with a severe drought that caused general crop failure (Owusu and Waylen, 2009), resulting in Ghana receiving food aid. Given the severity of the 2015 El Nino, it becomes imperative to assess how the phenomenon impacted food production in Ghana. The main objective of the study is to investigate the effect of the 2015 El Nino on maize production in three municipalities in the transitional agro ecological zone of Ghana. We concentrate on maize in particular because of the important socio-economic consequences it has on smallholder farmers. Maize is widely produced by smallholder farmers and serves as the main staple food for most households and livestock in Ghana (Asantewah, 2003; Braimoh and Vlek, 2006). However, because it is mostly cultivated under rain-fed conditions, it becomes vulnerable to extreme climate events like the El Nino. Among its specific objectives, the study details the extent to which the El Nino affected rainfall and its impacts on yields and livelihoods of smallholder maize farmers. In addition, the coping strategies used by these farmers are explored, with the aim of contributing to the formulation of appropriate policies to reduce food insecurity associated with ENSO events.

The study is relevant in understanding how ENSO impacts agriculture and maize production: an enterprise that could move the country closer to eliminating hunger and meeting goal one of the Sustainable Development Goals.

## 2. El Nino and Maize production

The ENSO commonly referred to as “El Nino” has been the subject of scholarly efforts in the last four decades (Babkina, 2003). Occurring every three to seven years and lasting between 9 to 24 months, it represents an irregular periodic variation in winds and sea surface temperatures (Wang et al., 2004; Cane, 2005). El Nino is attributed to a weakening of the trade winds which result in atmospheric modifications (Trenberth, 1997). Selvaraju (2003) explains that heated surface water becomes concentrated near the equator of the eastern Pacific where it then spreads up and down the coasts of North and South America. The expanse of warm waters in the Pacific causes such a huge increase in evaporation from the ocean resulting in a natural mode of oscillation from unstable interactions between the tropical Pacific Ocean and the atmosphere leading to El Nino. The effects of El Nino have global tele-connections resulting in pressure, temperature and rainfall variability with the severest impacts in the tropics.

During El Nino years, the dry period separating the two rainy seasons gets longer through a reduced occurrence of the rainy seasons in Equatorial Africa (Camberlin et al., 2001). The dry periods of the 1980s and the associated crop failures in West Africa is known to have been caused by droughts resulting from the El Nino (Mohino et al., 2011). Drought over West Africa is mostly characterized by the growth of positive SST anomalies in the Eastern Pacific complimented by a negative SST anomaly in the Northern Atlantic (Fontaine and Janicot, 1996), which according to Owusu and Waylen (2009) has been accompanied by declining rainfall amounts and a decreasing agricultural productivity since the 1970s. The occurrence of this phenomenon implies that economies largely dependent on the agricultural sector which is climate sensitive become even more vulnerable. Different economic sectors in different locations across the globe are affected differently by the occurrence of an El Nino event (Davey et al., 2011).

The literature on El Nino is replete with empirical evidence on how it impacts crop production generally across the globe (Hansen et al., 2009; Subash et al., 2014; Kellner and Niyogi, 2015). These and other studies discuss the impact of El Nino on food production, value and prices and highlight how ENSO’s intensification of climatic variations and shifts in climatic conditions has major implications for crop production. With particular regards to its effects on maize production, there are useful descriptions of associations between ENSO and maize yields in different environments (Hall et al., 1992; Carlson et al., 1996; Iizumi et al., 2014; Shuai et al., 2016). Hall et al. (1992), for example, present a description of the climate, soils and crop production systems in the Pampas of Argentina and establish a clear relationship between maize yields and ENSO-related climate variability in one of the major maize producing areas of the world. They conclude that low yields are more likely during El Nino years than in normal ones. Similarly, Ferreyra et al. (2001) developed a risk assessment framework for the characterization of maize vulnerability to ENSO and found less precipitation, a common feature of the El Nino as the one variable that influences maize yields in rain-fed production systems. Amissah‐Arthur et al. (2002) also explore the link between El Nino-related variability in rainfall at annual and seasonal scales and national-level maize yield in Kenya and report of a fall although spatial and regional differences were also recorded. Beyond these, ENSO has been found to have a negative socio-economic impact by decreasing farm income, employment and adversely affecting prices, trade, and market access (Iizumi et al., 2014).

## 3. Methodology

### 3.1 Study area

The research was conducted in the transitional agro-ecological zone of Mid-Ghana which coincides with Ghana Meteorological Agency’s (GMet) Zone C agro-climatological classification. The specific municipalities studied were Techiman, and Wenchi in the Brong Ahafo region and Ejura in the Ashanti region all of which are noted for maize production in Ghana.The zone has a mean annual rainfall totals ranging between 1,200 to a peak of 1,500 mm which decreases from south to north in accordance with the general rainfall pattern of Ghana. The migrating inter-tropical convergence zone and monsoons flows produce peak rains in May/June and September/October, with a long dry season (harmattan) lasting from November through March (Owusu and Waylen, 2013) which is associated with high inter-annual and multi decadal variability. The major rainy season begins in late March/early April and runs until mid-July. The bi-modal rainfall pattern allows for two crops per season under rain-fed agriculture. The regime however presents variability in the time of the onset of each rainy season and the beginning of the short dry spell (Adiku and Stone, 1995; Yorke and Omotosho, 2010). The study area is a major agricultural region of Ghana characterized by a highly diversified agricultural production of both tuber crops of the forest region of the South and the grains and cereals of the North (Cudjoe et al., 2010). The study area has been described as the bread basket of Ghana (Egyir et al., 2014; Owusu and Waylen, 2013), even though production here like all parts of the country is almost entirely rain-fed. According to Owusu and Waylen (2013), rainfall variability in the area has a significant impact on crop yields and general food security in Ghana.

### 3.2 Data and methods

The study used a mixed method approach in collecting and analyzing data. For stronger evidence building (Creswell, 2013), we combined interviews and focus group discussions (FGD) to collect the qualitative data. The purposive sampling technique was used to select key informants in the Municipal offices of the Ministry of Agriculture who were deemed to possess relevant information to answer the study’s research questions. These included Directors of Agriculture, management information system officers and Extension officers who were purposively selected and interviewed (Table I). Interviews took a semi-structured format to make it possible for interviews to be steered along the research objectives while allowing respondents adequate room to explain issues in depth. The projected sample was 12, but saturation was reached after 11 interviews overall.

Six FGD’s were held for maize farmers in six communities in all three municipalities. Whereas the interviews offered in-depth understanding of the climatic conditions that accompanied the El Nino and its impact on overall maize production, the FGD approach on the other hand generated rich insights on farmer’s perceptions and experiences on rainfall patterns over the years, maize cultivation practices, community relations and relationships with extension officers as well as the overall impact of the El Nino on farmers livelihoods. The group interactions among farmers provided a better appreciation of common issues, the people’s socio-cultural views and how these inform decision-making.

With the benefit of using multiple sources and methods of data collection, the qualitative data were effectively validated and triangulated. Interviews were recorded and then transcribed verbatim. This transcribed data were not coded but systematically analyzed according to themes initially developed from the literature and those that emerged from fieldwork.

In addition, the study drew on quantitative rainfall data for Wenchi and Ejura from the GMet to contextualize the reduction in rainfall for the 2015 season associated with El Nino. Yield data for the three study areas obtained from the District Agricultural offices were compared between El Nino and normal years to corroborate the results obtained from the FGD’s and key informant interviews.

## 4. Results

### 4.1 Effects of El Nino on rainfall

Given that El Nino is associated with a reduction in rainfall in the study area (Owusu and Waylen, 2013; Adiku and Stone, 1995), the study among other things sought to examine the severity of rainfall reduction in the transitional zone during the 2015 El Nino year. As shown in Figure 1, the 2014 normal and (2015) El Nino years rainfall recorded in the study area was approximately 1,200 (698) mm 1,400 (843) mm and 1,300 (1,264) mm for Techiman, Wenchi and Ejura respectively. Ejura had an appreciable amount of rainfall, but that goes to buttress the spatial component of El Nino effect and the strong variability associated with rainfall in West Africa in general (Owusu, 2017). Even though the farmers did not record the rainfall, they recounted that the amount received in 2015 was not near the previous years as revealed in the FGDs as follows:

Although rainfall has been reducing by the years, the 2015 season was exceptional. The rains were just inadequate and it was clear something went wrong [Male FGD Akrobi].

In addition to the reduction in the rainfall totals, it was also found that there was a reduction in the number of rainy days, thus, the average number of days when a measurable amount (defined as 1 mm) of rain falls. As shown in Figure 2, the number of rainfall days reduced considerably during the 2015 El Nino year as opposed to the previous year. While farmers report of a late onset of the rainy season, they also experienced dry spells over most parts of the zone around mid-May instead of the normal cessation at the end of June. The usual major farming season which begins in March-April, delayed during the 2015 farming season and started in May. A farmer intimated:

I usually begin planting at the end of March through to April for the main season and August for the minor season. This year, I planted in anticipation of rains that took forever to come and I had to plant and re-plant several times. Because there was no rainfall, the seeds could not germinate [Male FGD, Wenchi].

Farmers generally decried their helplessness in terms of having no prior information on weather changes and for which reason they were caught off-guard. The few farmers who acknowledged getting some weather information from the meteorological agency, mainly through local media, pointed out that, it did not inform their farming decisions as the forecasts tended to be largely unreliable. They therefore depended on their own experience and indigenous knowledge acquired over time.

### 4.2 Effects of El Nino-Southern Oscillation on maize production

Data from our fieldwork shows a significant reduction in maize production in all the three municipalities in 2016 compared to the previous year (see Figure 3). According to the data provided by the District Agricultural offices, all the three study districts recorded a deficit in production over the previous year. Techiman had a deficit of 7,708 tons, Wenchi 6,434 tons and Ejura 2,452 tons. The reduction in yield is consistent with the reduction in rainfall totals as shown in Figure 1. Farmers in the communities recounted the seriousness of low yields for the same pieces of land cultivated in previous years. They attributed their losses to the reduction in rainfall that characterized the El Nino year. One distraught farmer observed:

I cultivated four (4) acres with a yield of 40 bags in 2015 […]. but in 2016, I had only 15bags for the same piece of land because the rains failed me [Ejura FGD].

Although the data showed a general reduction in yield, a few farmers reported minimal reduction in yields that was attributed to sheer luck and not planning based on weather information. Such experiences could also be as a result of localized factors like soils and rainfall variability in addition to the variety of maize planted. Farmers attributed the general low yields to inadequate rains, indicating that fertilizer application delayed and in some cases was simply not possible because of the unavailability of adequate moisture in the soil. In addition to inadequate rainfall and lack of weather information, the farmers also lamented the fact that they did not get any technical or financial assistance. Weather index insurance that could have helped the farmers is nonexistent in the study area.

The respondents reported that the poor harvest resulting from the El Nino induced drought also resulted in price inflation across the zone. Checks from the markets for prices of maize revealed increases over the past year as depicted in Figure 3. In Techiman, a 100 kg bag of maize which sold for $14 in May 2015 was reported to be$24 around the same month in 2016. Similar increases were recorded for Wenchi and Ejura which went for $17 and$23 and $15 and$22 in 2015 and 2016 respectively. With production slashed by about 15 per cent, as shown in Figure 3, these increases were to be expected. However, while the increases were quite significant in all the study areas, it still remained unclear whether the maize price inflation experienced was as a result of the fall in maize production due to the El Nino droughts as price could be influenced by production and demand outside the study area. However, the study established that prices could have gone up further but for inflows from the Northern parts of the country particularly Hamile and Tumu as well as neighboring Burkina Faso as reported by maize traders in the Techiman market. These inflows augment the local supply and keep prices from soaring beyond normal. Therefore, the effects of the El Nino and its associated impacts on food availability also depend on external factors including trade policies such as open borders.

### 4.3 Effects of 2015 El Nino on farmer’s livelihood

With about 60 per cent of people in the study area deriving their livelihood from maize cultivation and other related farming activities, the El Nino and its associated reduction in rainfall had a number of local effects. The implications were dire and ranged from less food for subsistence to loss of investments and increased household poverty. As has been indicated earlier, the reduction in rainfall had a serious toll on farming activities, delaying preparation of land, planting, fertilizer application and harvesting. Stalled farming activities resulted in crop failure and poor harvest at best. One director of agriculture in Wenchi noted that “more than 50 per cent of farmers lost everything because of inadequate rainfall last year”.

The fall in maize production as a result of the El Nino negatively affected the farmers by way of unavailability of food and income for subsistence. Farmers struggled to make ends meet with some having virtually nothing to subsist on. One woman lamented:

The cheapest foods in this area are those prepared from maize including, porridge (koko), ‘kenkey’ and ‘banku’. But with poor harvests from our maize farms, we cannot even have these foods to eat and that makes life very difficult [Ejura FGD].

The expectations of these farmers, in terms of incomes from the sale of their produce were cut short. For most of the people in the study area, agriculture provides the main source of income from which household responsibilities are catered for. The lack of income due to poor harvest was reported to have brought untold hardship to households. The effects are captured by one farmer who lamented the impact on her children’s education.

My expectations regarding my maize farm were cut short. I am now struggling to pay my children’s school fees and meeting other needs like books and transport [Akrobi FGD].

The El Nino adversely affected the poorest and most vulnerable people in the study area, further worsening their poverty situations. The interviews revealed that the impact varied, severely affecting some districts like Wenchi, but much less in Ejura. The study also found out that the outcomes and responses to the effects of the El Nino have been dependent on the safety-net structures available in a particular municipality, as well as the general food security policies in Ghana. One widespread effect of the El Nino on farmers is the loss of investments. Farmers, particularly those in the rural communities noted that low productivity in 2016 had negative consequences on their productivity and future investments. One farmer illustrated this point as follows:

Maize cultivation has become capital intensive in modern times. From preparation of the land, through planting, application of fertilizers and spraying of farms, to harvesting, so much money and time is invested. Yet, for this year in particular, these investments proved not to be worth our while as the farms did not do well [Ejura FGD].

The farmers’ losses were compounded by the absence of farm insurance in the study area. For those who invested their own capital but lost out, they had no money to reinvest in the new season. Farmers expressed a lot of apprehension for the post El Nino year, as the drought that caused so much damage to their farms in 2015 had protracted into the new 2016 farming season.

### 4.4 Famers’ coping strategies

Confronted with the debilitating effects of the 2015 El Nino, smallholder farmers devised a number of strategies, mostly upon the advice of extension officers to manage the unexpected situation. Extension officers visited farms especially after sensing delays in the onset of rains and advised farmers to plant early maturing and drought resistant breeds like “opeburow” and “Omankwa”. One municipal director of agriculture at Techiman noted that “it is the planting of early maturing varieties like Dodi and Omankwa which mature in 70 days that saved some farmers from recording total losses”.

Even then, they note that some farmers planted old breeds because of the high costs of the new ones. Farmers were also directed to plant and replant deep in anticipation of rains. They were advised to use folia to conserve moisture and protect their seeds. However, most of the seeds could not even germinate, with those surviving neither tasseling nor reaching full maturity before the rains ceased. This affected production and yields. Farmers also managed the El Nino induced droughts by diversification where they mixed crops and varieties in the same field, staggered planting times and scattered crops in different soils and locations. Some farmers mixed their maize with other crops like beans and okra. This was found to be useful when the maize failed although the other crops did not do too well either.

Trading and other non-farm incomes such as remittances served as alternatives in assisting households meet their needs and to survive the post 2015 El Nino season. We found that while some of the male farmers had moved into other ventures like driving and working as laborers in poultry farms to earn a living, most of the women engaged in petty trading to help support their families. One woman noted”:

Because the rains disappointed us, there was not much to be done on our farm. I got a loan which I invested in selling used clothing at Techiman market. That is how I managed to support my family [Female FGD, Bonsu].

However, the low production of maize as a result of the El Nino had made local trading and non-farm activities less profitable because the local people had lost their purchasing power. The loss of incomes and investments from maize farms affected patronage of commodities like used clothing. With the decline in household incomes, the already alarming poverty situation had worsened especially amongst the lower income earners.

## 5. Discussion

This study found evidence on the El Nino and its linkage with reduced rainfall in the transitional zone of Ghana. The findings presented indicate that rainfall was significantly reduced in terms of amounts and distribution during the 2015 El Nino year with some spatial variability. The reduction in rainfall as a result of the El Nino is consistent with findings of other studies which report of such rainfall patterns associated with the phenomenon in other parts of the world and the study area as well (Adiku et al., 2007; Owusu and Waylen, 2009; Collins et al., 2010; Davey et al., 2011). In other jurisdictions like the Philippines, Indonesia and Australia, El Nino events have been found to cause similar rainfall deficits (Davey et al., 2011). There was a reduction in the number of rainy days which could have more severe impact on crop production. The reduction in rainfall had negative consequences for maize production by smallholder farmers. Given that maize is largely cultivated under rain-fed conditions, farmers suffered the worst of crop failure with low yields recorded across the towns and villages. These observations also resonate with other studies in Ghana and elsewhere (Akpalu et al., 2008; Hansen et al., 2009; Acquah and Kyei, 2012; Adamgbe and Ujoh, 2013; John and Olanrewaju, 2014; Huang et al., 2015), which report of a significant relationship between maize yield and climate variability. A study by Araújo et al. (2015) for instance, found the occurrence of El Nino to cause about 50 per cent of productivity losses for corn and beans in northeast Brazil.

Low productivity of maize resulting from El Nino induced cuts in rainfall had implications for farmers’ livelihoods and incomes. With maize serving as the main staple food and source of income for these farmers, low yields resulted in shortages of maize stock for food and income for other needs like health and education. This worsened the poverty situations of smallholder farmers most of whom live from “hand to mouth”. As earlier observed by Akpalu et al. (2008), reduced rainfall as a result of climate variability has detrimental effects on crop yield, food security and livelihoods.

The severity of the rainfall reduction on maize yields was mainly because of the fact that smallholder farmers did not receive adequate information on the impending El Nino and therefore, were unable to adjust and adapt their initial farming decisions to the situation. The extension service intensified their contact with farmers after the rainfall had delayed and the early crops had been destroyed by late onset. The fact that the farmers who yielded to the information provided by the extension service and used drought resistant maize varieties sustained lower losses confirms observations of earlier works by Amegnaglo and Mensah-Bonsu (1999); Adesina and Elasha (2007); Fosu-Mensah et al. (2012) and Jiri et al. (2016), that the application and use of forecast information, science and technology is still limited among poor rural farmers, thereby affecting their productivity. This also implies that to build resilience against climate variability and climate change, smallholder farmers would have to embrace the use of climate information and technology as well as careful crop selection, as proposed by Owusu (2017). Like this study, we also found that farmers depended on their own indigenous knowledge and experience to cope with the El Nino and that affected their ability to make appropriate responses.

## 6. Conclusion and recommendation

It was established that like other severe El Nino’s, there were significant reductions in rainfall and increased variability with the within season characteristics. The number of rainy days was found to be fewer than normal years. Productivity of smallholder farmers was found to be low and in the Techiman Municipality in particular, production was reduced by as much as 15 per cent. In the Ejura Municipality, however, the impact was not that severe indicating that there is a spatial component to the El Nino induced rainfall variability in mid-Ghana.

The major impacts of the El Nino induced rainfall failure and yield reduction were household food insecurity, loss of income, indebtedness and deepening poverty. These were exacerbated by the lack of institutional support; save for the agronomic services of extension officers. Households survived mainly through income and crop diversification, and off-farm practices like petty trading and remittances. Some of the adaptation strategies were found not to be effective due to households’ total dependence on agriculture for employment and income generation and the general lack of application of climate information and technology in smallholder farming in Ghana.

Based on our findings, we make the following recommendations. First, although El Nino cycles are a natural occurrence, we note that they may have a less devastating impact on food production and livelihoods of communities if effective plans are put in place. Based on what we know about the effect of El Nino on rainfall and the fact that the IPCC (2017) has projected an increase in the frequency and intensity of El Nino due to global warming, we recommend that provision and conservation of water for agriculture in the study area should be improved. If El Nino becomes frequent and severe, the current smallholder practice which is almost entirely rain-fed will not be resilient enough to ensure food security. Therefore, local government units and the Ministry of Food and Agriculture should work together to develop community irrigation to help smallholders improve maize and other food crop production.

Against the backdrop that most farmers did not get sufficient information on the El Nino and were therefore left to their own devices, we recommend a close collaboration between the meteorological agency and the Ministries of Agriculture on the application of climatic information and relaying same to farmers in a timely manner. In peripheral communities, such information could be circulated through text messages, local radio and television networks to ensure effectiveness. In developing country contexts like Ghana where poverty is at biting levels especially among rural farmers, subsidies on drought-resistant breeds must be provided during unusual periods like the El Nino to make them affordable for farmers.

## Figures

#### Figure 1.

Rainfall amount for 2014/15 in the study districts

#### Figure 2.

Maize production in municipalities (in metric tons) normal year versus El Nino year

#### Figure 3.

Maize price per 100 kg bag for 2015 and 2016 in dollars

## Table I.

Breakdown of interviews and FGDs

Target groups Data collection tool Location
Directors of the ministry of Agriculture in municipalities (3), Extension officers (3), Management Information system officers (3) and meteorological officers (2) the Ministry of Agriculture in the three municipalities.
N = 11
Key informant interviews Techiman Wenchi and Ejura Municipal offices
Smallholder farmers in the communities
N = 6
FGDs, Composition – (Female only, male only)
8 participants on average
Techiman – Bonsu, Forikrom
Wenchi – Nkonsia, Akrobi
Ejura – Dromankuma and Ejura Sekyere Dumase

Source: Fieldwork data

## References

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#### Supplementary materials

IJCCSM_11_5.pdf (17 MB)

## Acknowledgements

The authors would like to thank the Office of Research, Innovation and Development (ORID), University of Ghana (UG) for offering support [grant number UG-ORID/BSU/II/WP2/2015-2016/002] through the BSU II initiative Building Stronger Universities project to support the fieldwork that resulted in the production of this paper.

## Corresponding author

Issah Justice Musah-Surugu can be contacted at: musah123@gmail.com


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# Limit of f(x) knowing limit of f(x)/x

Given that: $$\lim_{x\to0} \frac{f(x)}{x}=0$$ How can I prove that: $$\lim_{x\to0} f(x)=0$$ ?

Would the L'Hospital's Rule be applicable?

• Given that the first limit exists, I think that $\lim_{x\to0}f(x)=0$ must hold. Apr 13, 2015 at 8:38
• thing which is given , we can write limit of [f(x)-0]/[x-0]=0, hence given thing is derivative of f(x) at 0 i.e. f'(0)=0 Apr 13, 2015 at 8:40
• L'Hospital's rule applies to calculating derivatives, but you have no assumptions about $f(x)$ being differentiable.. Apr 14, 2015 at 8:53

Hint :

$f(x)=\frac{f(x)}{x}{x}$ and product rule.

• Clearly the best method in this case. Apr 13, 2015 at 12:41
• Product rule is a rule of derivative calculations, but the problem assumes nothing about differentiability.... Apr 14, 2015 at 8:51
• @CiaPan By "product rule" I mean product rule for limits
– John
Apr 14, 2015 at 10:12

If by contradiction $f(x)\to a\neq0,\;\infty$, your limit $\lim f(x)/x$ would be $\infty$. How can you obtain a contradiction if $\lim f(x)$ doesn't exist?

• ....How indeed? Apr 13, 2015 at 9:38
• It actually suffices to consider what happens if the limit doesn't tend to 0. You can construct a sequence $\{x_n\}$ tending to $0$ such that $f(x_n)<\epsilon$ where $\epsilon$ is fixed.
– ktoi
Apr 13, 2015 at 10:14

By definition, if $\lim_{x \to 0} f(x)/x = 0$ then for all $\epsilon>0$ there exist small enough $x$ such that

$$-\epsilon<f(x)/x<\epsilon$$ therefore, since $x\ne0$ $$-\epsilon\cdot x<f(x)<\epsilon\cdot x$$ and when $x\in (0, 1)\cup(-1, 0)$ we get $$-\epsilon<f(x)<\epsilon$$ which implies that $\lim_{x \to 0} f(x) = 0$

Because the $\lim_{x\to0} \frac{f(x)}{x}=0$, this means that $f(x)$ tends to $0$ faster than $x$, or that $|f(x)|\le x$.

Therefore:

$$0\le|f(x)|\le x$$

Using the squeeze theorem, and because $\lim_{x\to0} x=0$, $\lim_{x\to0} f(x){x}=0$.

• Although there may exist a point of view in which your first sentence is right, I believe that it is not at all a rigorous thing to say (i.e. if I get an homework with those words, I won't never give full mark). This said, in order to deduce $|f(x)<x$ there must be some work required (perhaps using the formal definition of limit applied to the hypothesis). Apr 13, 2015 at 11:30
• To expand on rafforaffo's comments: there is nothing wrong with saying $|f(x)| < x$ for $x$ sufficiently close to zero (well, if you justify the statement formally, at any rate), but it may not hold in general. For example, let $f(x) = x^2$.
– user88319
Apr 13, 2015 at 18:15

By the definition of a limit, f (x) / x < eps for every eps if x is small enough. Take eps = 1, so f (x) / x < 1 if x < eps1, or f (x) < x if x < eps1. Take the definition of the limit again; f (x) < eps if you take x < min (eps, eps1).

Obviously you don't need that the limit of f (x) / x is 0. If the limit is c, then f (x) / x < c+1 for small x, so f (x) < x * (c + 1) for small x, and f (x) < eps if x < eps / (c + 1).

Obviously you'll have to add a few absolute values in the argument.

This is not a fancy proof. It is a grinding one from the epsilon-delta definition of limit suitable for an introductory calculus class.

The core of the idea is that if $f(x)$ is bounded away from $0$ as $x$ goes to zero, then $f(x)/x$ is also bounded away from zero, as for small $x$, dividing by $x$ makes things further from zero.

And things bounded away from zero don't have a limit of zero.

Suppose the limit as $x$ goes to zero of $f(x)$ is $a$, and $a > 0$.

Let $\epsilon = a/2$. Then there is a $\delta$ such that for all $0 < x < \delta$, $a/2 < f(x) < 3a/3$.

Let $\delta_0$ be the minimum of $1/2$ and $\delta$.

(statement 1): Then for $0 < x < \delta_0$, $f(x)/x \geq f(x)*2 \geq 2a/2 = a$

If the limit of $f(x)/x$ as $x$ goes to zero is $0$, then let $\epsilon = a/2$.

(statement 2): Then there exists a $\delta_1 > 0$ such that for all $0 < x < \delta_1$, $-a/2 < f(x)/x < a/2$

Let $\delta_2$ be the least of $\delta_0$ and $\delta_1$.

For $x < \delta_2 <= \delta_1$, $f(x)/x < a/2$ by (2).

For $x < \delta_2 <= \delta_1$, $f(x)/x \geq a$ by (1).

Thus $a/2 > a$ or $1/2 > 1$, a contradiction.

A similar result holds of $a < 0$. Spotting the places where I implicitly assumed $a$ was positive may be interesting.


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# zbMATH — the first resource for mathematics

## Li, Chengju

Compute Distance To:
 Author ID: li.chengju Published as: Li, C.; Li, C. J.; Li, ChengJu; Li, Chengju
 Documents Indexed: 56 Publications since 1993, including 1 Book
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#### Co-Authors

 1 single-authored 19 Yue, Qin 6 Bae, Sunghan 4 Ding, Cunsheng 4 Li, Fengwei 3 Mesnager, Sihem 3 Yang, Shudi 2 Ahn, Jaehyun 2 Carlet, Claude 2 Fu, Fangwei 2 Heng, Ziling 2 Li, Shuxing 2 Liu, Hao 2 Peng, Wei 2 Wu, Peng 2 Yan, Haode 1 Dinh, Hai Quang 1 Du, Zongrun 1 Hu, Liqin 1 Huang, Yiwei 1 Jiang, Tongsong 1 Ka, Dongseok 1 Kang, Pyung-Lyun 1 Li, Xiuqing 1 Liu, Fengmei 1 Liu, Hao 1 Wang, Zilong 1 Wu, Mengna 1 Wu, Xiumei 1 Xia, Yongbo 1 Yao, Zhengan 1 Zeng, Peng
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#### Serials

 8 Designs, Codes and Cryptography 7 IEEE Transactions on Information Theory 6 Finite Fields and their Applications 4 Discrete Mathematics 3 Advances in Mathematics of Communications 3 Cryptography and Communications 2 Applicable Algebra in Engineering, Communication and Computing 1 Mathematics in Practice and Theory 1 Chinese Annals of Mathematics. Series A 1 Journal of Qufu Normal University. Natural Science 1 Algebra Colloquium 1 Science China. Mathematics 1 Journal of Algebra, Combinatorics, Discrete Structures and Applications
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#### Fields

 34 Information and communication theory, circuits (94-XX) 27 Number theory (11-XX) 3 Combinatorics (05-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Commutative algebra (13-XX) 1 Algebraic geometry (14-XX) 1 Operator theory (47-XX)

#### Citations contained in zbMATH

36 Publications have been cited 375 times in 202 Documents Cited by Year
Weight distributions of cyclic codes with respect to pairwise coprime order elements. Zbl 1366.94641
Li, Chengju; Yue, Qin; Li, Fengwei
2014
Hamming weights of the duals of cyclic codes with two zeros. Zbl 1360.94401
Li, Chengju; Yue, Qin; Li, Fengwei
2014
LCD cyclic codes over finite fields. Zbl 1370.94585
Li, Chengju; Ding, Cunsheng; Li, Shuxing
2017
Complete weight enumerators of some cyclic codes. Zbl 1402.94102
Li, Chengju; Yue, Qin; Fu, Fang-Wei
2016
Weight distributions of two classes of cyclic codes with respect to two distinct order elements. Zbl 1364.94655
Li, Chengju; Yue, Qin
2014
Two families of LCD BCH codes. Zbl 1374.94845
Li, Shuxing; Li, Chengju; Ding, Cunsheng; Liu, Hao
2017
Complete weight enumerators of some linear codes and their applications. Zbl 1379.94058
Li, Chengju; Bae, Sunghan; Ahn, Jaehyun; Yang, Shudi; Yao, Zheng-An
2016
Kuznetsov’s trace formula and the Hecke eigenvalues of Maass forms. Zbl 1314.11038
Knightly, A.; Li, C.
2013
Passivity and passification of stochastic impulsive memristor-based piecewise linear system with mixed delays. Zbl 1312.93098
Wen, S. P.; Zeng, Z. G.; Huang, T. W.; Li, C. J.
2015
The minimum Hamming distances of irreducible cyclic codes. Zbl 1332.94105
Li, Fengwei; Yue, Qin; Li, Chengju
2014
Hermitian LCD codes from cyclic codes. Zbl 1408.94982
Li, Chengju
2018
Complete weight enumerators of a class of linear codes. Zbl 1379.94054
Ahn, Jaehyun; Ka, Dongseok; Li, Chengju
2017
Recent progress on weight distributions of cyclic codes over finite fields. Zbl 1371.94683
Dinh, Hai Q.; Li, Chengju; Yue, Qin
2015
On the complete weight enumerators of some reducible cyclic codes. Zbl 1321.94129
Bae, Sunghan; Li, Chengju; Yue, Qin
2015
Parameters of LCD BCH codes with two lengths. Zbl 1401.94223
Yan, Haode; Liu, Hao; Li, Chengju; Yang, Shudi
2018
A class of cyclic codes from two distinct finite fields. Zbl 1392.94943
Li, Chengju; Yue, Qin
2015
Irreducible cyclic codes of length $$4p^n$$ and $$8p^n$$. Zbl 1392.94930
Li, Fengwei; Yue, Qin; Li, Chengju
2015
Dimensions of three types of BCH codes over $$\mathrm{GF}(q)$$. Zbl 1422.94051
Liu, Hao; Ding, Cunsheng; Li, Chengju
2017
Torsional impact response of a penny-shaped interface crack in bonded materials with a graded material interlayer. Zbl 1110.74552
Li, C.; Duan, Z.; Zou, Z.
2002
Three classes of linear codes with two or three weights. Zbl 1372.94455
Heng, Ziling; Yue, Qin; Li, Chengju
2016
Two families of nearly optimal codebooks. Zbl 1393.94321
Li, Chengju; Yue, Qin; Huang, Yiwei
2015
Infinite families of 2-designs and 3-designs from linear codes. Zbl 1367.05029
Ding, Cunsheng; Li, Chengju
2017
A construction of codes with linearity from two linear codes. Zbl 1380.94145
Li, Chengju; Bae, Sunghan; Yan, Haode
2017
The Walsh transform of a class of monomial functions and cyclic codes. Zbl 1365.94673
Li, Chengju; Yue, Qin
2015
Learning algorithms for neural networks based on quasi-Newton methods with self-scaling. Zbl 0775.93081
Beigi, H. S. M.; Li, C. J.
1993
Transverse free vibration and stability of axially moving nanoplates based on nonlocal elasticity theory. Zbl 1446.74028
Liu, J. J.; Li, C.; Fan, X. L.; Tong, L. H.
2017
A construction of several classes of two-weight and three-weight linear codes. Zbl 1384.94126
Li, Chengju; Yue, Qin; Fu, Fang-Wei
2017
Dissipative dynamics of two-photon Jaynes-Cummings model with the Stark shift in the dispersive approximation. Zbl 0983.81535
Zhou, L.; Song, H. S.; Luo, Y. X.; Li, C.
2001
On two classes of primitive BCH codes and some related codes. Zbl 1432.94187
Li, Chengju; Wu, Peng; Liu, Fengmei
2019
Nonlinear maps preserving product $$X^{*}Y+Y^{*}X$$ on von Neumann algebras. Zbl 07040690
Li, C.; Zhao, F.; Chen, Q.
2018
Constructions of linear codes with one-dimensional hull. Zbl 1431.94157
Li, Chengju; Zeng, Peng
2019
Some two-weight and three-weight linear codes. Zbl 1415.94482
Li, Chengju; Bae, Sunghan; Yang, Shudi
2019
Weight distributions of a class of cyclic codes from $$\mathbb F_l$$-conjugates. Zbl 1357.94093
Li, Chengju; Yue, Qin; Heng, Ziling
2015
Some results on strongly regular graphs from unions of cyclotomic classes. Zbl 1257.05180
Li, ChengJu; Yue, Qin; Hu, LiQin
2012
Three-dimensional numerical simulation of compound meandering open channel flow by the Reynolds stress model. Zbl 1156.76037
Jing, H.; Guo, Y.; Li, C.; Zhang, Jisheng
2009
Three-dimensional analysis of the coupled thermo-piezoelectro-mechanical behaviour of multilayered plates using the differential quadrature technique. Zbl 1120.74601
Liew, K. M.; Zhang, Jordan Z.; Li, C.; Meguid, S. A.
2005
On two classes of primitive BCH codes and some related codes. Zbl 1432.94187
Li, Chengju; Wu, Peng; Liu, Fengmei
2019
Constructions of linear codes with one-dimensional hull. Zbl 1431.94157
Li, Chengju; Zeng, Peng
2019
Some two-weight and three-weight linear codes. Zbl 1415.94482
Li, Chengju; Bae, Sunghan; Yang, Shudi
2019
Hermitian LCD codes from cyclic codes. Zbl 1408.94982
Li, Chengju
2018
Parameters of LCD BCH codes with two lengths. Zbl 1401.94223
Yan, Haode; Liu, Hao; Li, Chengju; Yang, Shudi
2018
Nonlinear maps preserving product $$X^{*}Y+Y^{*}X$$ on von Neumann algebras. Zbl 07040690
Li, C.; Zhao, F.; Chen, Q.
2018
LCD cyclic codes over finite fields. Zbl 1370.94585
Li, Chengju; Ding, Cunsheng; Li, Shuxing
2017
Two families of LCD BCH codes. Zbl 1374.94845
Li, Shuxing; Li, Chengju; Ding, Cunsheng; Liu, Hao
2017
Complete weight enumerators of a class of linear codes. Zbl 1379.94054
Ahn, Jaehyun; Ka, Dongseok; Li, Chengju
2017
Dimensions of three types of BCH codes over $$\mathrm{GF}(q)$$. Zbl 1422.94051
Liu, Hao; Ding, Cunsheng; Li, Chengju
2017
Infinite families of 2-designs and 3-designs from linear codes. Zbl 1367.05029
Ding, Cunsheng; Li, Chengju
2017
A construction of codes with linearity from two linear codes. Zbl 1380.94145
Li, Chengju; Bae, Sunghan; Yan, Haode
2017
Transverse free vibration and stability of axially moving nanoplates based on nonlocal elasticity theory. Zbl 1446.74028
Liu, J. J.; Li, C.; Fan, X. L.; Tong, L. H.
2017
A construction of several classes of two-weight and three-weight linear codes. Zbl 1384.94126
Li, Chengju; Yue, Qin; Fu, Fang-Wei
2017
Complete weight enumerators of some cyclic codes. Zbl 1402.94102
Li, Chengju; Yue, Qin; Fu, Fang-Wei
2016
Complete weight enumerators of some linear codes and their applications. Zbl 1379.94058
Li, Chengju; Bae, Sunghan; Ahn, Jaehyun; Yang, Shudi; Yao, Zheng-An
2016
Three classes of linear codes with two or three weights. Zbl 1372.94455
Heng, Ziling; Yue, Qin; Li, Chengju
2016
Passivity and passification of stochastic impulsive memristor-based piecewise linear system with mixed delays. Zbl 1312.93098
Wen, S. P.; Zeng, Z. G.; Huang, T. W.; Li, C. J.
2015
Recent progress on weight distributions of cyclic codes over finite fields. Zbl 1371.94683
Dinh, Hai Q.; Li, Chengju; Yue, Qin
2015
On the complete weight enumerators of some reducible cyclic codes. Zbl 1321.94129
Bae, Sunghan; Li, Chengju; Yue, Qin
2015
A class of cyclic codes from two distinct finite fields. Zbl 1392.94943
Li, Chengju; Yue, Qin
2015
Irreducible cyclic codes of length $$4p^n$$ and $$8p^n$$. Zbl 1392.94930
Li, Fengwei; Yue, Qin; Li, Chengju
2015
Two families of nearly optimal codebooks. Zbl 1393.94321
Li, Chengju; Yue, Qin; Huang, Yiwei
2015
The Walsh transform of a class of monomial functions and cyclic codes. Zbl 1365.94673
Li, Chengju; Yue, Qin
2015
Weight distributions of a class of cyclic codes from $$\mathbb F_l$$-conjugates. Zbl 1357.94093
Li, Chengju; Yue, Qin; Heng, Ziling
2015
Weight distributions of cyclic codes with respect to pairwise coprime order elements. Zbl 1366.94641
Li, Chengju; Yue, Qin; Li, Fengwei
2014
Hamming weights of the duals of cyclic codes with two zeros. Zbl 1360.94401
Li, Chengju; Yue, Qin; Li, Fengwei
2014
Weight distributions of two classes of cyclic codes with respect to two distinct order elements. Zbl 1364.94655
Li, Chengju; Yue, Qin
2014
The minimum Hamming distances of irreducible cyclic codes. Zbl 1332.94105
Li, Fengwei; Yue, Qin; Li, Chengju
2014
Kuznetsov’s trace formula and the Hecke eigenvalues of Maass forms. Zbl 1314.11038
Knightly, A.; Li, C.
2013
Some results on strongly regular graphs from unions of cyclotomic classes. Zbl 1257.05180
Li, ChengJu; Yue, Qin; Hu, LiQin
2012
Three-dimensional numerical simulation of compound meandering open channel flow by the Reynolds stress model. Zbl 1156.76037
Jing, H.; Guo, Y.; Li, C.; Zhang, Jisheng
2009
Three-dimensional analysis of the coupled thermo-piezoelectro-mechanical behaviour of multilayered plates using the differential quadrature technique. Zbl 1120.74601
Liew, K. M.; Zhang, Jordan Z.; Li, C.; Meguid, S. A.
2005
Torsional impact response of a penny-shaped interface crack in bonded materials with a graded material interlayer. Zbl 1110.74552
Li, C.; Duan, Z.; Zou, Z.
2002
Dissipative dynamics of two-photon Jaynes-Cummings model with the Stark shift in the dispersive approximation. Zbl 0983.81535
Zhou, L.; Song, H. S.; Luo, Y. X.; Li, C.
2001
Learning algorithms for neural networks based on quasi-Newton methods with self-scaling. Zbl 0775.93081
Beigi, H. S. M.; Li, C. J.
1993
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#### Cited by 300 Authors

 34 Yue, Qin 18 Li, Chengju 14 Wu, Yansheng 14 Yang, Shudi 11 Cao, Xiwang 9 Heng, Ziling 8 Ding, Cunsheng 8 Tang, Chunming 7 Li, Fengwei 6 Liu, Hongwei 6 Luo, Gaojun 6 Mesnager, Sihem 6 Yao, Zhengan 6 Zhu, Shi-xin 5 Fu, Fangwei 5 Li, Fei 5 Wang, Qiuyan 5 Wang, Xiaoqiang 5 Zheng, Dabin 5 Zhou, Zhengchun 4 Bae, Sunghan 4 Carlet, Claude 4 Huang, Tingwen 4 Li, Nian 4 Li, Xia 4 Lin, Dongdai 4 Liu, Zihui 4 Shi, Xueying 4 Xu, Shanding 4 Yan, Haode 4 Zhu, Xiaomeng 3 Fan, Cuiling 3 Itou, Shouetsu 3 Kong, Xiangli 3 Liu, Xiusheng 3 Pang, Binbin 3 Qi, Yanfeng 3 Sun, Zhonghua 3 Xu, Guangkui 3 Zeng, Xiangyong 3 Zhao, Changan 2 Ahn, Jaehyun 2 Blomer, Valentin 2 Cao, Yanyi 2 Chen, Bocong 2 Ding, Kelan 2 Du, Xiaoni 2 Fan, Shuqin 2 Feng, Keqin 2 Guo, Li-Cheng 2 Hu, Lei 2 Hu, Liqin 2 Knightly, Andrew H. 2 Li, Chunlei 2 Liao, Qunying 2 Lin, Zhouchen 2 Ling, Xin 2 Liu, Chunlei 2 Liu, Fengmei 2 Liu, Haibo 2 Liu, Hualu 2 Liu, Yiwei 2 Lu, Wei 2 Peng, Wei 2 Petrow, Ian N. 2 Razeghi, Mehran 2 Shi, Zexia 2 Tang, Deng 2 Vega, Gerardo 2 Wen, Shiping 2 Xia, Yongbo 2 Xiang, Can 2 Xiao, Jianying 2 Young, Matthew P. 2 Yu, Long 2 Zhong, Shou-Ming 1 Aghdam, Mohammad Mohammadi 1 Aiobi, H. 1 Assing, Edgar 1 Bagchi, Satya 1 Bandi, Ramakrishna 1 Bao, Jingjun 1 Batoul, Aicha 1 Batra, Sudhir 1 Batur, Celal 1 Benahmed, Fatma-Zohra 1 Benbelkacem, N. 1 Bhowmick, Sanjit 1 Borges, Joaquim 1 Boripan, Arunwan 1 Byrne, Eimear 1 Cai, Zuowei 1 Cao, Yonglin 1 Cao, Yuan 1 Cao, Yuting 1 Chen, Ming 1 Chen, Wenbing 1 Cheng, Feng 1 Cherchem, Ahmed 1 Cuén-Ramos, Jesús E. ...and 200 more Authors
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#### Cited in 51 Serials

 31 Finite Fields and their Applications 29 Designs, Codes and Cryptography 26 Cryptography and Communications 21 Discrete Mathematics 8 Applicable Algebra in Engineering, Communication and Computing 8 Advances in Mathematics of Communications 7 Discrete Applied Mathematics 6 Journal of Applied Mathematics and Computing 4 Applied Mathematical Modelling 3 Acta Mechanica 3 Applied Mathematics and Computation 3 Circuits, Systems, and Signal Processing 3 Mathematical Problems in Engineering 2 International Journal of Solids and Structures 2 International Journal of Theoretical Physics 2 Journal of Number Theory 2 Bulletin of the Korean Mathematical Society 2 SIAM Journal on Discrete Mathematics 2 Neural Networks 2 The Ramanujan Journal 2 Journal of Systems Science and Complexity 2 Algebra & Number Theory 2 Journal of Algebra, Combinatorics, Discrete Structures and Applications 1 International Journal for Numerical Methods in Fluids 1 Journal of the Franklin Institute 1 Mathematical Notes 1 Annales de l’Institut Fourier 1 Canadian Journal of Mathematics 1 Functiones et Approximatio. Commentarii Mathematici 1 Information Sciences 1 Journal of Functional Analysis 1 Meccanica 1 Transactions of the American Mathematical Society 1 Journal of Information & Optimization Sciences 1 Optimization 1 Geometric and Functional Analysis. GAFA 1 Pattern Recognition 1 Archive of Applied Mechanics 1 International Journal of Robust and Nonlinear Control 1 Documenta Mathematica 1 Nonlinear Dynamics 1 Annals of Mathematics. Second Series 1 Journal of Modern Optics 1 Journal of Applied Mathematics 1 South East Asian Journal of Mathematics and Mathematical Sciences 1 Journal of Algebra and its Applications 1 Advances in Difference Equations 1 International Journal of Number Theory 1 Proyecciones 1 Acta Mechanica Sinica 1 Asian-European Journal of Mathematics
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#### Cited in 26 Fields

 146 Information and communication theory, circuits (94-XX) 112 Number theory (11-XX) 12 Systems theory; control (93-XX) 11 Combinatorics (05-XX) 11 Mechanics of deformable solids (74-XX) 6 Computer science (68-XX) 6 Biology and other natural sciences (92-XX) 4 Algebraic geometry (14-XX) 4 Quantum theory (81-XX) 3 Field theory and polynomials (12-XX) 3 Associative rings and algebras (16-XX) 3 Ordinary differential equations (34-XX) 3 Mechanics of particles and systems (70-XX) 2 Partial differential equations (35-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Commutative algebra (13-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Group theory and generalizations (20-XX) 1 Topological groups, Lie groups (22-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Functional analysis (46-XX) 1 Operator theory (47-XX) 1 Probability theory and stochastic processes (60-XX) 1 Fluid mechanics (76-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Operations research, mathematical programming (90-XX)