text:
1. PHP Code:
 _________________________________________________________________________________________________  /                                                                                \ |    v0.04                           Al-Kharid  Cook : 00:57:06                                     | |---------------------------------------------------------------------------------------------------| |    Player    |    Type    |    Time    |    Active    |    Cooked    |    Loads    |    Levels    | |--------------|------------|------------|--------------|--------------|-------------|--------------| | Superlekker  |  Sardine   |  03:56:17  |    True      |     896      |     32      |      12      | |______________|____________|____________|______________|______________|_____________|______________| | Total        |    N/A     |  00:57:06  |    1\1       |     896      |     32      |      12      | |---------------------------------------------------------------------------------------------------|  \_________________________________________________________________________________________________/
out of food.. works perfect, just the banking could be a little bit faster(the search for bankbooth part of srl is slow)

2. Originally Posted by masterBB
PHP Code:
 _________________________________________________________________________________________________ /                                                                                \|    v0.04                           Al-Kharid  Cook : 00:57:06                                     ||---------------------------------------------------------------------------------------------------||    Player    |    Type    |    Time    |    Active    |    Cooked    |    Loads    |    Levels    ||--------------|------------|------------|--------------|--------------|-------------|--------------|| Superlekker  |  Sardine   |  03:56:17  |    True      |     896      |     32      |      12      ||______________|____________|____________|______________|______________|_____________|______________|| Total        |    N/A     |  00:57:06  |    1\1       |     896      |     32      |      12      ||---------------------------------------------------------------------------------------------------| \_________________________________________________________________________________________________/
out of food.. works perfect, just the banking could be a little bit faster(the search for bankbooth part of srl is slow)
awesome, thanks I'll make a custom banking I suppose, I thought banking was fairly fast for me but if it can be optimized I'll do it!

EDIT:

Originally Posted by Zyt3x
PHP Code:
   _________________________________________________________________________________________________ /                                                                                \|    v0.04                           Al-Kharid  Cook : 00:28:52                                     ||---------------------------------------------------------------------------------------------------||    Player    |    Type    |    Time    |    Active    |    Cooked    |    Loads    |    Levels    ||--------------|------------|------------|--------------|--------------|-------------|--------------|| ********     |  Salmon    |  148:15:57 |    False     |     420      |     15      |      3       ||______________|____________|____________|______________|______________|_____________|______________|| Total        |    N/A     |  00:28:52  |    0\1       |     420      |     15      |      3       ||---------------------------------------------------------------------------------------------------| \_________________________________________________________________________________________________/
Stopped because of SRL trying to open Lamp while your script tried to walk to the bank.

EDIT: The script got stuck in a loop while trying to bank an item that couldn't be banked (lamp)
EDIT: When it was finished cooking all the raw food I had in my bank, it withdrew cooked Salmon and started to cook that :P
hmm so I'll look into the lamp thing, not sure how to fix that :/

as for the banking thing I suppose some simple failsafes will be suffice. As for finishing cooking I do a color comparison check in the bankslot, obviously the tolerance I set was too high or something, I'll up a fix in a bit. Thanks for the input.

3. The problem with the banking was that it sometimes was searching the walls for the uptext, for like half a minute, sometimes 2 minutes... Most times it just opens the bank fine, fast enough for me.

I lost my last progie but it was for 1.2 hours! I fixed the banking problem with reflection. Than its perfect!

I never used SRL stats, but it seems that it doesn't work with this script, I get errors and the stats don't go up... But it could be my fault...

4. Originally Posted by masterBB
The problem with the banking was that it sometimes was searching the walls for the uptext, for like half a minute, sometimes 2 minutes... Most times it just opens the bank fine, fast enough for me.

I lost my last progie but it was for 1.2 hours! I fixed the banking problem with reflection. Than its perfect!

I never used SRL stats, but it seems that it doesn't work with this script, I get errors and the stats don't go up... But it could be my fault...
hmmm they should. Works for me, maybe the site is down or you didn't put your user+pass in correctly, who knows. ok then I'll quicken up the banking in the next revision, it'll be out in a few days hopefully. I'm also in the process of fixing my aircrafter again so I might delay fixing this for a bit.

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[Error] (770:6): Duplicate identifier 'autocolor' at line 769
Compiling failed.
Line 769: I, autocolor: Integer;
Anyone know why I get this error now? I never got it before when using this script. Maybe from the recent updates?

6. Originally Posted by gamer716
Anyone know why I get this error now? I never got it before when using this script. Maybe from the recent updates?
recent updates, I think Coh3n made a new Autocolor.scar um I'll have to adjust that. Thanks for pointing it out

Edit: new version up that complies (I think). I don't have the new SRL so please let me know. Thanks

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Code:
Compiled succesfully in 1500 ms
.

__________________________________________________ _______________
PHP Code:
 ________________________________  /                                                                                \ |    v0.04                           Al-Kharid  Cook : 00:55:02                                     | |---------------------------------------------------------------------------------------------------| |    Player    |    Type    |    Time    |    Active    |    Cooked    |    Loads    |    Levels    | |--------------|------------|------------|--------------|--------------|-------------|--------------| |               |  Rout      |  00:54:31  |    True      |     868      |     31      |      1       | |______________|____________|____________|______________|______________|_____________|______________| | Total        |    N/A     |  00:55:02  |    1\1       |     868      |     31      |      1       | |---------------------------------------------------------------------------------------------------|

8. fabulous glad to know it works. I don't have much inspiration at the moment to script, but I'm sure I'll get around to modifying this more sometime soon. Thanks for using

9. Running it now, it started with:
Warning! You passed a wrong ye to a finder function: 506. The client has a height of 503, thus the ye is out of bounds. Setting the value to 502 (h-1) for now.
Warning! You passed a wrong ye to a finder function: 506. The client has a height of 503, thus the ye is out of bounds. Setting the value to 502 (h-1) for now.
But than continued, proggie will come...

__________________________________________________ _______________________________________________
/ \
| v0.04 Al-Kharid Cook : 01:15:37 |
|---------------------------------------------------------------------------------------------------|
| Player | Type | Time | Active | Cooked | Loads | Levels |
|--------------|------------|------------|--------------|--------------|-------------|--------------|
| --------- | Shrim,Ps | 15:01:28 | True | 1148 | 41 | 3 |
|______________|____________|____________|________ ______|______________|_____________|______________ |
| Total | N/A | 01:15:37 | 1\1 | 1148 | 41 | 3 |
|---------------------------------------------------------------------------------------------------|
\_________________________________________________ ________________________________________________/
Banking Loop
Walking Loop
Cooking Loop
Could not Find Range.
Last edited by masterBB; 06-11-2010 at 10:50 PM.

10. yeah I get that when I call the setChat functions, but it hasn't hindered the progress of the script at all so I'm not going to change it.

As for not finding the range I'm assuming that the symbol moved too far away from the store to get inside. I will work on a fix for it later, I don't have much inspiration to script at all lately so when I do I'll fix that error.

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there is a problem with finding the bank teller, the script searches the bank for similar colors (around the walls) but does not find the teller. It happens quite frequently although i did get 2 hour+ proggy

Code:
  _________________________________________________________________________________________________
/                                                                                \
|    v0.04                           Al-Kharid  Cook : 00:30:01                                     |
|---------------------------------------------------------------------------------------------------|
|    Player    |    Type    |    Time    |    Active    |    Cooked    |    Loads    |    Levels    |
|--------------|------------|------------|--------------|--------------|-------------|--------------|
| *******  |            |  00:29:34  |    True      |     476      |     17      |      1       |
|______________|____________|____________|______________|______________|_____________|______________|
| Total        |    N/A     |  00:30:01  |    1\1       |     476      |     17      |      1       |
|---------------------------------------------------------------------------------------------------|
\_________________________________________________________________________________________________/
Banking Loop
Could not Withdraw Food. NextPlayer
NextPlayer
SwitchToPlayer(PlayerNo: 0, Active: False);
Player is not Active...
All players not active!
Walking Loop
attempting to find cooking symbol
Walking to Range Failed. NextPlayer
NextPlayer
Ran out of food to cook...
Last edited by gamer716; 06-14-2010 at 10:25 PM.

12. Thanks for the info! I will fix it up immediately I finally got some inspiration to script

Edit: I've added a few things to the script and it's running okay but it's a bit shaky and I don't know why. If anyone is willing to do a little bug testing for me I'd appreciate it.

Also is anyone interested in me creating a reflection version of the script? I am interested in reflection and it seems like an easy task to complete.
Last edited by Blumblebee; 06-15-2010 at 01:50 AM.

13. Amazing script I love it and will use it often

thnx blumblebee <---- got the name right most people dont

heres a proggy\

/ \
| v0.04 Al-Kharid Cook : 01:35:00 |
|---------------------------------------------------------------------------------------------------|
| Player | Type | Time | Active | Cooked | Loads | Levels |
|--------------|------------|------------|--------------|--------------|-------------|--------------|
| number1 | An,Cl,Ovies| 25:10:42 | True | 1400 | 50 | 4 |
|______________|____________|____________|________ ______|______________|_____________|______________ |
| Total | N/A | 01:35:00 | 1\1 | 1400 | 50 | 4 |
|---------------------------------------------------------------------------------------------------|
\_________________________________________________ ________________________________________________/

14. Thanks J_Pizzle appreciate spelling my name right and the proggie haha. I'll have a newer version up soon here, should speed up the whole banking process, etc.

15. Hey blumblebee, I saw you said you needed a few bugs, and I got a few for you

#1 is that in the furnace next door, right next to the door, on the wall there's something with very similar colors to the range, and it will sometimes bug out there (it's the curtain that would otherwise be the door). Suggested fix? new colors on the range w/ confirming uptext

#2 definitely needs new and/or updated/more failsafes on banking... you've probably noticed that it sometimes bugs out standing next to the booths.

#3 I didn't look through the actual script of this part, but how is it distinguishing when all the inventory is done? is it based on a time? cause sometimes it will leave the range w/o doing the whole inventory, which also screws up the proggy D: (Yeah, I'm watching it currently for bugs, and it most definitely needs a better way to detect when the inventory is finished)

Obviously more antiban and antirandoms (but i think you have those covered) could always be cool, as cooking is one of things you need minimal attention for. I could recommend calling the mouse off the screen more, like as if you were going to another tab or window on your computer, as I tend to do that actually, so I'd say that could be realistic.

#4 proggy is messed up d: that shouldn't be hard. If/when you do fix it, don't worry about the food being cooked. Just worry about the # of food cooked. You could also consider pulling exp gained from the new exp bar. Some people had a discussion about this on another page, you could see if they got that working.

In any case, this is the best cooker right now (: Really looking forward to a fix!

EDIT: You may actually want to consider calling FindNormalRandom more too cause it has bugged out nearly every random, and most of the randoms are working fine

EDIT1: Also, needs a better failsafe on the range, as if it misses click (clicked use food on some player and logged out) on the range.
Last edited by c0rrupt f1r3; 06-19-2010 at 10:31 PM.

16. Originally Posted by c0rrupt f1r3
Hey blumblebee, I saw you said you needed a few bugs, and I got a few for you

#1 is that in the furnace next door, right next to the door, on the wall there's something with very similar colors to the range, and it will sometimes bug out there (it's the curtain that would otherwise be the door). Suggested fix? new colors on the range w/ confirming uptext

#2 definitely needs new and/or updated/more failsafes on banking... you've probably noticed that it sometimes bugs out standing next to the booths.

#3 I didn't look through the actual script of this part, but how is it distinguishing when all the inventory is done? is it based on a time? cause sometimes it will leave the range w/o doing the whole inventory, which also screws up the proggy D: (Yeah, I'm watching it currently for bugs, and it most definitely needs a better way to detect when the inventory is finished)

Obviously more antiban and antirandoms (but i think you have those covered) could always be cool, as cooking is one of things you need minimal attention for. I could recommend calling the mouse off the screen more, like as if you were going to another tab or window on your computer, as I tend to do that actually, so I'd say that could be realistic.

#4 proggy is messed up d: that shouldn't be hard. If/when you do fix it, don't worry about the food being cooked. Just worry about the # of food cooked. You could also consider pulling exp gained from the new exp bar. Some people had a discussion about this on another page, you could see if they got that working.

In any case, this is the best cooker right now (: Really looking forward to a fix!

EDIT: You may actually want to consider calling FindNormalRandom more too cause it has bugged out nearly every random, and most of the randoms are working fine

EDIT1: Also, needs a better failsafe on the range, as if it misses click (clicked use food on some player and logged out) on the range.
the cooking is relative to color changes in the last slot. If you open the Smart window or close it, it can bug the isCooking() function. I have fixed banking, I will release the new version soon. I have yet to have the range finding fail, but I will definatly work on fixing it. And I like the XP bar idea I just worry that it looks bottish to do that continually :/

nevertheless thank you for your contributions, I will fix them up when I get a chance here. Diploma Exams and other stuff are difficult right now for me.

17. Originally Posted by Blumblebee
the cooking is relative to color changes in the last slot. If you open the Smart window or close it, it can bug the isCooking() function. I have fixed banking, I will release the new version soon. I have yet to have the range finding fail, but I will definatly work on fixing it. And I like the XP bar idea I just worry that it looks bottish to do that continually :/

nevertheless thank you for your contributions, I will fix them up when I get a chance here. Diploma Exams and other stuff are difficult right now for me.
Good deal, and no problem! It's the least I can do without being able to contribute with a script atm...

18. new version will be up soon, added "findPixelLine" and "openBankCustom".

Test report,

PHP Code:
   _________________________________________________________________________________________________ /                                                                                \|    v0.05                           Al-Kharid  Cook : 00:45:55                                     ||---------------------------------------------------------------------------------------------------||    Player    |    Type    |    Time    |    Active    |    Cooked    |    Loads    |    Levels    ||--------------|------------|------------|--------------|--------------|-------------|--------------|| Apothevel    |            |  00:44:35  |    True      |     756      |     27      |      0       ||______________|____________|____________|______________|______________|_____________|______________|| Total        |    N/A     |  00:45:55  |    1\1       |     756      |     27      |      0       ||---------------------------------------------------------------------------------------------------| \_________________________________________________________________________________________________/
manually stopped.

19. Originally Posted by Blumblebee
new version will be up soon, added "findPixelLine" and "openBankCustom".

Test report,

PHP Code:
   _________________________________________________________________________________________________  /                                                                                \ |    v0.05                           Al-Kharid  Cook : 00:45:55                                     | |---------------------------------------------------------------------------------------------------| |    Player    |    Type    |    Time    |    Active    |    Cooked    |    Loads    |    Levels    | |--------------|------------|------------|--------------|--------------|-------------|--------------| | Apothevel    |            |  00:44:35  |    True      |     756      |     27      |      0       | |______________|____________|____________|______________|______________|_____________|______________| | Total        |    N/A     |  00:45:55  |    1\1       |     756      |     27      |      0       | |---------------------------------------------------------------------------------------------------|  \_________________________________________________________________________________________________/
manually stopped.
Yay! I need something to cook 35k fish and the current version can cook... at most 1k before logging

20. new version upped. I will be making some major changes to the script in a week or so, as for now your going to have to live with this. If errors occur, please revert to older version(s) and post bugs. Thanks

21. well, i have about 15k fish to cook, when i finish my bows i'll try it out

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Code:
_________________________________________________________________________________________________
/                                                                                \
|    v0.05                           Al-Kharid  Cook : 01:30:52                                     |
|---------------------------------------------------------------------------------------------------|
|    Player    |    Type    |    Time    |    Active    |    Cooked    |    Loads    |    Levels    |
|--------------|------------|------------|--------------|--------------|-------------|--------------|
| ******** |  Trout     |  02:31:38  |    True      |     1340     |     48      |      1       |
|______________|____________|____________|______________|______________|_____________|______________|
| Total        |    N/A     |  01:30:52  |    1\1       |     1340     |     48      |      1       |
|---------------------------------------------------------------------------------------------------|
\_________________________________________________________________________________________________/
Working great!

EDIT: Another progress Report

Code:
  _________________________________________________________________________________________________
/                                                                                \
|    v0.05                           Al-Kharid  Cook : 01:31:17                                     |
|---------------------------------------------------------------------------------------------------|
|    Player    |    Type    |    Time    |    Active    |    Cooked    |    Loads    |    Levels    |
|--------------|------------|------------|--------------|--------------|-------------|--------------|
| ******** |  Salmon    |  02:37:46  |    True      |     1384     |     50      |      0       |
|______________|____________|____________|______________|______________|_____________|______________|
| Total        |    N/A     |  01:31:17  |    1\1       |     1384     |     50      |      0       |
|---------------------------------------------------------------------------------------------------|
\_________________________________________________________________________________________________/
Last edited by gamer716; 06-25-2010 at 03:58 PM.

23. Originally Posted by Blumblebee
new version upped. I will be making some major changes to the script in a week or so, as for now your going to have to live with this. If errors occur, please revert to older version(s) and post bugs. Thanks
I was going to say to just steal MyOpenBank from my smelter. It works good

Edit:
Just looked at yours, your going to want to change ChooseOption to WaitOption('', 2000). The former has stopped my script working before. I'd also would use a WaitUpText instead of waiting beforehand. (less code, works nicer)

24. Originally Posted by gamer716
Code:
_________________________________________________________________________________________________
/                                                                                \
|    v0.05                           Al-Kharid  Cook : 01:30:52                                     |
|---------------------------------------------------------------------------------------------------|
|    Player    |    Type    |    Time    |    Active    |    Cooked    |    Loads    |    Levels    |
|--------------|------------|------------|--------------|--------------|-------------|--------------|
| ******** |  Trout     |  02:31:38  |    True      |     1340     |     48      |      1       |
|______________|____________|____________|______________|______________|_____________|______________|
| Total        |    N/A     |  01:30:52  |    1\1       |     1340     |     48      |      1       |
|---------------------------------------------------------------------------------------------------|
\_________________________________________________________________________________________________/
Working great!
fabulous, glad to see it working

Originally Posted by Narcle
I was going to say to just steal MyOpenBank from my smelter. It works good

Edit:
Just looked at yours, your going to want to change ChooseOption to WaitOption('', 2000). The former has stopped my script working before. I'd also would use a WaitUpText instead of waiting beforehand. (less code, works nicer)
I've never been a big fan of WaitOption or WaitUpText, but maybe that's because I'm old school haha. I'll give those functions a try, thanks for the heads up

25. PHP Code:
   _________________________________________________________________________________________________ /                                                                                \|    v0.05                           Al-Kharid  Cook : 00:52:12                                     ||---------------------------------------------------------------------------------------------------||    Player    |    Type    |    Time    |    Active    |    Cooked    |    Loads    |    Levels    ||--------------|------------|------------|--------------|--------------|-------------|--------------|| Apothevel    |  Salmon,   |  00:51:37  |    True      |     840      |     30      |      1       ||______________|____________|____________|______________|______________|_____________|______________|| Total        |    N/A     |  00:52:12  |    1\1       |     840      |     30      |      1       ||---------------------------------------------------------------------------------------------------| \_________________________________________________________________________________________________/
Updated Script (slightly). Found a bug I don't know how to fix, happens with the logging in and out of the script. I would suggest changing the constant AVG_loads from 15 to 30+ to negate the logging in and out of the script repetitively. Any other bug fixes/reports I'll keep posted.


text:
# Doppler Effect Of Gravitational Field

Discussion in 'Alternative Theories' started by TonyYuan, May 27, 2020.

Not open for further replies.
1. ### river

Messages:
15,655
Now physically what is going on . With objects .

What are the objects doing , physically .

3. ### TonyYuanRegistered Senior Member

Messages:
440
I derived this equation F=GMm/R^2 * [(c-v) / c] from the basic laws of mathematics and physics. From the formula, it reflects the Doppler effect of a gravitational field. And I verified the calculation of Mercury's precession deviation, and my calculated result is 43.05".

This result 43.05" is almost identical to the 43" obtained by GR calculation.

In other words, the physical problem revealed by the GR physical model is the Doppler effect of the gravitational field. They may be equivalent.

5. ### river

Messages:
15,655
So this gravitational field , is a real physical thing .

7. ### TonyYuanRegistered Senior Member

Messages:
440
Yes. If it is not true, then you cannot perceive.

Einstein used time-space distortion to describe gravity. Also recognized that space is a substance.
Newton used the gravitational field to describe gravitation, and also recognized that the gravitational field is a substance.

They are all different physical models that describe gravity.

8. ### river

Messages:
15,655
Highlighted

Disagree

Space is not a substance .

There is substance within space .

9. ### TonyYuanRegistered Senior Member

Messages:
440
Doppler effect of gravitational field, this theory can explain many physical phenomena and physical experiments.
For example: Morley experiment, light bending, Mercury precession, gravity redshift, etc, and it's very easy.

10. ### river

Messages:
15,655
How so ?

So far we have a gravitational field , made of what ?

Doppler effect from this gravitational field , give me a picture of what this looks like .

11. ### TonyYuanRegistered Senior Member

Messages:
440
What constitutes a gravitational field?
What constitutes a magnetic field?
What constitutes an electric field?
What constitutes time and space?
There are so many reasons why we need to explore.

What we are discussing now is just what the laws show under the action of these fields. Newton gave us a model, it has some defects, we have corrected it.

The Doppler effect of the gravitational field unifies Newton's gravitation and general relativity. It makes our exploration of the universe simple.

Last edited: Jun 17, 2020
12. ### river

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15,655
You said this before post#107 . You didn't answer my question . And In my post#107 , Doppler effect from this gravitational field , give me a picture of what this looks like .

13. ### TonyYuanRegistered Senior Member

Messages:
440
Last edited: Jun 17, 2020
14. ### river

Messages:
15,655
Tony you have mathematically shown your thinking .

Now the challenge is to prove it physically .

15. ### TonyYuanRegistered Senior Member

Messages:
440
I have given detailed mathematical and physical derivations in the paper.
The calculation of Mercury's precession has also been verified, and the results obtained are completely consistent with GR.

By the way, GR does not show correctness in the calculation of the precession of Venus, Earth, Mars and other planets. You can find the data in the link below.
http://farside.ph.utexas.edu/teaching/336k/Newtonhtml/node115.html

16. ### river

Messages:
15,655
Thats not what I'm getting at Tony . The mathematics must represent a physical object(s) .

What is physically In This Space that makes you more correct ?

What is the energy and matter environment that Mercury is in , ?

17. ### TonyYuanRegistered Senior Member

Messages:
440
Sorry, I do not quite understand you.

Newton's law of gravity is great. I just made some corrections based on him. It can calculate the celestial orbit as accurately as GR.

18. ### river

Messages:
15,655

Where ? Just say .

Last edited: Jun 17, 2020
19. ### TonyYuanRegistered Senior Member

Messages:
440
What is physically In This Space that makes you more correct ?
Ans:Newton's law of gravity is great. I just made some corrections based on him. It can calculate the celestial orbit as accurately as GR.

What is the energy and matter environment that Mercury is in , ?
Ans:I don’t know. I think there might be something we don’t know besides the gravitational field.

The mathematics must represent a physical object(s) .
Ans: I don’t know what is your mean.
F =G * M * m / R^2 * (c-v) / c, it is just doppler effect.

You can also write like this:
F =G' * M * m / R^2. G' = G * (c-v) / c

G is the value when the velocity of the gravitational field relative to the object is equal to c.
G’ is the value when the velocity of the gravitational field relative to the object is equal to c-v.

Last edited: Jun 17, 2020
20. ### river

Messages:
15,655
Fine to your first statement , but it doesn't tell me what physically must go on , to make the calculation accurate .

Inotherwords , it is the physical that is the essence of any calculation .

21. ### river

Messages:
15,655

Physical objects are real . They exist . Our bodies are from them .

If the mathematics is only real in the realm of mathematics , then this mathematics is a fantasy .

22. ### TonyYuanRegistered Senior Member

Messages:
440
Calculating the precession of Mercury by the classic universal gravitation F=GMm/R^2 will have a deviation of 43" per century.
And by the modified gravitation formula F=GMm/R^2*(c-v)/c, the results obtained can eliminate the 43" deviation.

23. ### TonyYuanRegistered Senior Member

Messages:
440
Newton's universal gravitation equation F=GMm/R^2, I think it has always been true. Although it is a mathematical formula, humans have been using it for hundreds of years.

format: plain


text:
# a.

The partial-tree procedure take an ordered list of element and the size of this list as arguments. At the beginning, if there are arguments, the procedure split the list of element in two lists, one list for the left branch, another one for the right branch and the element in the middle of the list is kept (the entry). The procedure calls itself to compute the left and right branches. At the end a pair is returned, the car is a tree constructed with the entry and both branches, the cdr is the elements remaining.

Here is the tree produced by list->tree for the list (1 3 5 7 9 11).

# b.

The procedure requires $$n$$ steps as the procedure is called for each node.


text:
# 13 In the following cases, determine whether the given planes are parallel or perpendicular, and in case they are neither, find the angles between them.     (a)      7x + 5y + 6z + 30 = 0 and 3x – y – 10z + 4 = 0

Two planes

$L_{1}:a_{1}x+b_{1}y+c_{1}z = 0$ whose direction ratios are $a_{1},b_{1},c_{1}$ and $L_{2}:a_{2}x+b_{2}y+c_{2}z = 0$ whose direction ratios are $a_{2},b_{2},c_{2}$,

are said to Parallel:

If, $\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}}=\frac{c_{1}}{c_{2}}$

and Perpendicular:

If, $a_{1}a_{2}+b_{1}b_{2}+c_{1}c_{2} = 0$

And the angle between $L_{1}\ and\ L_{2}$ is given by the relation,

$A = \cos^{-1}\left | \frac{a_{1}a_{2}+b_{1}b_{2}+c_{1}c_{2}}{\sqrt{a_{1}^2+b_{1}^2+c_{1}^2}.\sqrt{a_{2}^2+b_{2}^2+c_{2}^2}} \right |$
So, given two planes  $7x + 5y + 6z + 30 = 0\ and\ 3x -y - 10z + 4 = 0$

Here,

$a_{1} = 7,b_{1} = 5, c_{1} = 6$   and   $a_{2} = 3,b_{2} = -1, c_{2} = -10$

So, applying each condition to check:

Parallel check:   $\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}}=\frac{c_{1}}{c_{2}}$

$\Rightarrow \frac{a_{1}}{a_{2}} =\frac{7}{3}, \frac{b_{1}}{b_{2}}=\frac{5}{-1},\frac{c_{1}}{c_{2}} = \frac{6}{-10}$

Clearly, the given planes are NOT parallel.$\frac{a_{1}}{a_{2}} \neq \frac{b_{1}}{b_{2}} \neq \frac{c_{1}}{c_{2}}$

Perpendicular check: $a_{1}a_{2}+b_{1}b_{2}+c_{1}c_{2} = 0$

$\Rightarrow 7(3)+5(-1)+6(-10) = 21-5-60 = -44 \neq 0$.

Clearly, the given planes are NOT perpendicular.

Then find the angle between them,

$A = \cos^{-1}\left | \frac{a_{1}a_{2}+b_{1}b_{2}+c_{1}c_{2}}{\sqrt{a_{1}^2+b_{1}^2+c_{1}^2}.\sqrt{a_{2}^2+b_{2}^2+c_{2}^2}} \right |$

$= \cos^{-1}\left | \frac{-44}{\sqrt{7^2+5^2+6^2}.\sqrt{3^2+(-1)^2+(-10)^2}} \right |$

$= \cos^{-1}\left | \frac{-44}{\sqrt{110}.\sqrt{110}} \right |$

$= \cos^{-1}\left ( \frac{44}{110} \right )$

$= \cos^{-1}\left ( \frac{2}{5} \right )$

## Related Chapters

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text:
# box

0th

Percentile

##### Draw a Box around a Plot

This function draws a box around the current plot in the given color and linetype. The bty parameter determines the type of box drawn. See par for details.

Keywords
aplot
##### Usage
box(which = "plot", lty = "solid", …)
##### Arguments
which

character, one of "plot", "figure", "inner" and "outer".

lty

line type of the box.

further graphical parameters, such as bty, col, or lwd, see par. Note that xpd is not accepted as clipping is always to the device region.

##### Details

The choice of colour is complicated. If col was supplied and is not NA, it is used. Otherwise, if fg was supplied and is not NA, it is used. The final default is par("col").

##### References

Becker, R. A., Chambers, J. M. and Wilks, A. R. (1988) The New S Language. Wadsworth & Brooks/Cole.

rect for drawing of arbitrary rectangles.
library(graphics) # NOT RUN { plot(1:7, abs(stats::rnorm(7)), type = "h", axes = FALSE) axis(1, at = 1:7, labels = letters[1:7]) box(lty = '1373', col = 'red') # }


text:
Welcome to ZOJ
 Problem Sets Information Select Problem Runs Ranklist
ZOJ Problem Set - 4059
Kawa Exam

Time Limit: 3 Seconds      Memory Limit: 65536 KB

BaoBao is taking an online exam of the Kawa programming language, which consists of $n$ multiple choice questions. The exam is not easy, as for each question, BaoBao needs to select the one and only one correct answer from $10^5$ available choices! But don't worry, as an active committer of the famous open-kdk, BaoBao obviously knows all the correct answers.

Although BaoBao is an expert in Kawa, the developers of the exam system are definitely not experts in software engineering. There are $m$ bugs in the exam system, and the $i$-th bug can be described as $(u_i, v_i)$, which means that BaoBao must select the same choice for question $u_i$ and $v_i$ (even if the choice he selects is incorrect!).

Time is limited, and the exam must go on. The developers only have time to fix one bug. Now the developers are wondering, for all $1 \le i \le m$, what's the maximum possible number of questions BaoBao can correctly answer if they fix the $i$-th bug. Please write a program to solve this problem so that the developers can select a proper bug to fix.

This image is the cover of an album by muzzle lab.
It's not related to this problem. It only serves the purpose of making this problemset less boring.
By the way, the 3rd, 5th, 8th and 9th track in this album are really, really nice.

#### Input

There are multiple test cases. The first line of the input contains an integer $T$, indicating the number of test cases. For each test case:

The first line contains two integers $n$ and $m$ ($1 \le n \le 10^5$, $1 \le m \le 10^5$), indicating the number of questions and the number of bugs.

The second line contains $n$ integers $a_1, a_2, \dots, a_n$ ($1 \le a_i \le 10^5$), where $a_i$ indicates the correct answer for question $i$.

For the following $m$ lines, the $i$-th line has two integers $u_i$ and $v_i$ ($1 \le u_i, v_i \le n$), indicating the $i$-th bug.

It's guaranteed that neither the sum of $n$ nor the sum of $m$ over all test cases will exceed $10^6$.

#### Output

For each test case output one line containing $m$ integers $c_1, c_2, \dots, c_m$ separated by a space, where $c_i$ indicates the maximum possible number of questions BaoBao can correctly answer if the $i$-th bug is fixed.

Please, DO NOT output extra spaces at the end of each line, or your answer may be considered incorrect!

#### Sample Input

3
7 5
1 2 1 2 1 2 1
1 2
1 3
2 4
5 6
5 7
3 3
1 2 3
1 2
1 3
2 3
2 3
12345 54321
1 2
1 2
1 1

#### Sample Output

6 5 5 5 4
1 1 1
1 1 1

#### Hint

The following table explains the first sample test case.

• The "possible choices" column indicates a possible set of choices to each question BaoBao can select, leading to a maximum possible number of correctly answered questions;
• The "correct" column indicates the number of correctly answered questions using the set of choices provided in the "possible choices" column.

Bug No.Possible ChoicesCorrect
1(1, 2, 1, 2, 1, 1, 1)6
2(2, 2, 1, 2, 1, 1, 1)5
3(1, 1, 1, 2, 1, 1, 1)5
4(1, 1, 1, 1, 1, 2, 1)5
5(1, 1, 1, 1, 1, 1, 1)4

For the second sample test case, no matter which bug is fixed, BaoBao has to select the same choice for all the three questions. As the correct answer for each question is different, BaoBao can only correctly answer 1 question.

For the third sample test case, note that even if the developers fix the first bug, the second bug is still taking effect and BaoBao still has to select the same choice for the two problems. It's the same if the second bug is fixed.

Author: WENG, Caizhi
Source: The 2018 ACM-ICPC Asia Qingdao Regional Contest
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# Open Physics

### formerly Central European Journal of Physics

Editor-in-Chief: Seidel, Sally

Managing Editor: Lesna-Szreter, Paulina

IMPACT FACTOR 2017: 0.755
5-year IMPACT FACTOR: 0.820

CiteScore 2017: 0.83

SCImago Journal Rank (SJR) 2017: 0.241
Source Normalized Impact per Paper (SNIP) 2017: 0.537

ICV 2017: 162.45

Open Access
Online
ISSN
2391-5471
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Volume 17, Issue 1

# Radiation effects of nuclear physics rays on hepatoma cells

Wenhui Zhao
/ Lu Cong
/ Yolanda Guerrero-Sánchez
• Departamento de Demartología, Estomatología y Medicna Física. Área de Medicina Bucal. Universidad de Murcia, Murcia, Spain
• Email
• Other articles by this author:
Published Online: 2019-04-11 | DOI: https://doi.org/10.1515/phys-2019-0017

## Abstract

PACS: 21.65.+f; 28.41.Te; 29.30.Kv

## 1 Introduction

Cancer is one of the most lethal diseases. Radiotherapy is currently one of the main means of liver cancer treatment. Radiobiologists study the radiation effects of different kinds of nuclear physics rays on hepatocellular carcinoma cells as the main objective to determine the radiation results and efficacy of different nuclear physics rays on hepatocellular carcinoma cells [1, 2]. Accurate research on radiation effects of hepatocellular carcinoma cells can not only provide theoretical basis for cancer treatment, but also provide great help for clinicians in choosing treatment options. But the same treatment dose caused different damage to different tissues and cells [3]. Radiation effects of different nuclear physics rays on hepatocellular carcinoma cells are different in clinic, and the effects of radiotherapy are also very different.

Previous studies involving different cell lines and different types of radiation, such as X-rays, γ-rays and heavy ion beams, showed a linear dose-dependent relationship after radiation [4]. There are many methods to study the radiation effect of γ-rays on hepatocellular carcinoma cells. Cloning is a common method to study the radiation effect of hepatocellular carcinoma cells. However, as a conventional method, the results obtained by single cloning method are not reliable, and it is not suitable for clinical diagnosis and treatment [5]. Premature chromosome agglutination (PCC) technique was used to study the radiation effect of hepatocellular carcinoma (HCC), which took only 2 days from cell treatment to result statistics, but its application was limited. After chromosome damage, PCC technology has become a mature method to study radiation-induced primary chromosome damage in different cell cycle phases, especially in G2 phase [6]. However, most of the studies focused on G2 phase of hepatocellular carcinoma cells, and there were few reports on the correlation between G1 phase and G2 phase. There are few effective methods to study the radiation effect of X-ray on hepatoma cells, such as cloning, electrophoresis and so on [7].

In view of the shortcomings of the current research on X-ray and γ-ray radiation to hepatoma cells, a new and effective method is adopted to re-study the radiation effects of X-ray and γ-ray [8, 9]. The main methods were as follows: the radiation effects of human hepatoma HepG2 cells were studied by chemical-induced PCC technique. The radiation effects of X-rays on hepatocellular carcinoma cells were studied by cloning formation assay, neutral comet electrophoresis and γH2AX focal detection. The aim was to provide effective radiation methods for different nuclear physical rays on hepatocellular carcinoma cells in clinical radiotherapy.

## 2.1.1 Cell culture

Human hepatoma cell HepG2 (purchased from CCTCC) was cultured in RMPI-1640 medium containing 10% fetal bovine serum in a constant temperature incubator at 37°C and 5% CO2.

HepG2 hepatoma cells in exponential growth stage were irradiated with γ-rays (dose rate 0.2Gy/min) from Co source in a medical school.

## 2.1.3 PCC method and chromosome preparation

Calyculin-A (purchased from BIOMOL, USA) is a good inducer for PCC. It is dissolved in 100% ethanol and made into 1 mmol/L storage solution [10]. Before irradiation, it was added to the culture medium of irradiated cells, and the final concentration was 50nmol/L. After irradiation, the cells were cultured in a constant temperature incubator with 37°C and 5% CO2 for 30 minutes. The cells were treated with 75 mMKCl for 20 minutes and fixed with Carnot’s solution [11]. At last, the cells were suspended in a small amount of stationary solution. The cells were dried in hot steam and stained with 5% Giemsa.

## 2.1.4 Chromosome observation and enumeration

According to Savage’s criteria, G2 phase cells at no less than 40 doses were observed and the number of chromatid breaks and isochromatid breaks were calculated. At the same time, the G1 phase cells in the process were recorded and the number of chromatid breakage was calculated. Each chromatid breakage is equal to two fractures.

## 2.2.1 Material

Human hepatoma cell HepG2 is frozen in our central laboratory; DMEM (Dulbecco’s modified Eagle medium) is from Gibco; MTT (3-(4, 5-Dimethylthiazol-2-yl) -2, 5-diphenyltetrazolium bromide) is from Sigma; DAPI (4, 6-diamino-2-phenyl indole) is from Molecular Probes; propidium iodide (4, 6-diamino-2-phenyl indole) is from Molecular Probes, USA. Propidium iodide, (PI) is provided by Lsbio Company of USA; mouse anti-γH2AX monoclonal antibody comes from Upstate Technology Company of USA; the other reagents are all domestic analytical purity.

Olympus AX70 fluorescence microscope is from Olympus Company of Japan; enzyme-linked immunoassay analyzer is from Bio-Rad Company of America; DYY-6C electrophoresis analyzer is from Beijing 61 Instrument Factory. The X-ray irradiation device is RX-650 Cabinet X-Radiator System: the energy is 100 kVp (Kilovolt peak, peak voltage); the current is 5 mA; the absorbed dose rate is 1.38 Gy/min; the irradiation field is 20 cm×20 cm.

## 2.2.2 Method

Cell culture

Human hepatoma cells were incubated in incubators incubated at 5% CO2 and 37 degrees. The culture medium was DMEM containing 10% inactivated calf serum and antibiotics (100 μg/mL penicillin and 100 μg/mL streptomycin). Each 3-4d was passaged once, and logarithmic growth phase cells were used for the experiment.

Cell grouping setup

X-ray irradiation was used to irradiate hepatocellular carcinoma cells with absorbed doses of 2 Gy, 4 Gy, 6 Gy and 8 Gy, respectively. The experiment was carried out after irradiation for 0.5 h, 4 h and 24 h in non-irradiated group.

Effect of X-ray on the radiation of human hepatoma cells by colony formation assay.

The cells with concentration of 4×108 L−1 were inoculated into the bottle of human hepatoma cells. The cells were incubated in 2 mL DMEM medium for 24 hours at 37°Cand for X-ray irradiation, then further culture at 37°C. 0.25% trypsin is used to digest cells and make single cell suspension. Cell suspension was diluted by gradient dilution and inoculated in a 100 mm diameter dish. Each dose group consisted of 4 dishes, with two cell density groups (except control group) (cell density: control group 5×102 / dish; 2 Gy group, 8×102 / dish and 4 ×103 / dish; 4 Gy group, 1 ×103 / dish and 5 ×103 / dish; 6 Gy group, 3×103 / dish and 1.5×104 / dish; 8Gy group, 6 ×103 / dish and 3 ×104 / dish), the final volume of each dish DMEM is 10 mL. The cells were cultured for 10-14 days in incubator at 37 °C and 5% CO2. The incubator was discarded. Phosphate buffer saline (PBS) was carefully washed twice. The fixed solution (methanol: glacial acetic acid = 3:1) was fixed for 15 minutes. The fixed solution was discarded and dried. The cells were stained with 0.4% crystal violet for 20 minutes, with water washing and air drying [12]. The number of clones consisting of more than 50 cells was counted under an inverted microscope. The plating efficiency (PE) and survival fraction (SF)were calculated according to the Formula (1), (2).

$PE=ACNNIC×100%$(1)$SF=NCFAINIC×CFRUC×100%$(2)

In the form of Average number of clones is CAN, number of clones formed after irradiation is NCFAI, The number of inoculated cells is NIC, Colony formation rate of unirradiated cells is CFRUC.

Detection of DNA double strand damage by neutral comet electrophoresis

Digest and adjust the cell concentration to 4×107L-1. 50 μL 1% low melting point agarose gel was evenly spread on the glass slide and placed at room temperature [13]. The above 400 μL cells and 1.2 mL 1% low melting point agarose gel were preheated at 40°C, then mixed and quickly spread on the first layer of gel (about 1.4 mL), and cured at room temperature for 3 min. The slides were immersed in the newly prepared pre-cooled pyrolysis solution (containing 0.4-0.5 mg/ml protease K, added before use), pyrolysis at 4°C for 1 h, and carefully incubated in incubator at 37 °C for 18-20 h; TBE buffer (45mmol/L Tris-boric acid; 1mmol/L EDTA, pH = 8.5) was used to rinse the slides three times for 30 minutes each time. Place the slide in the electrophoresis tank for 30 minutes, pay attention that the liquid level should be 2 mm higher than the slide, and avoid light; adjust the buffer liquid level, so that the voltage is 16-18 V, current is about 7 mA, electrophoresis time is 25 minutes. 1%H2O2 is used to fix glass for 10minutes, and fully washed by double distilled water. PI (5 μg/mL) is stained for 30 minutes, placed in an airtight wet box, stored at 4 °C (observed within 24 hours to prevent fluorescence quenching). Under the excitation of fluorescence microscope (10×40) ultraviolet (UV), the DNA image is orange red. Each slide was taken for at least 50 cells, and each drug dose was taken for 3 slides [14]. The images were analyzed by CASP software. The comet tail length, head DNA content, tail DNA content, tail moment (Talmoment, TM and Olive tail moment, OTM) were calculated. TM is defined as the product of the average distance of migration and the DNA fraction of comet tail [15]. OTM calculation: the distance between the center of gravity of the tail light density and the center of gravity of the head light density × the percentage content of DNA in the tail.

Immunofluorescence staining was used to detect the formation of γH2AX foci.

The cells with a concentration of 2×108L-1 were inoculated into a 35 mm×10mmdish with a cover slide (soaked in 95% ethanol after cleaning and overheated, pre-placed in the dish). The cells were incubated at 37°C for 2 h, added to DMEM medium for 2 mL, and cultured for 24 h. Remove the cover slides, pre-cool TBS buffer (25 mmol/L Tris, 137 mmoL/L sodium chloride, 2.7 mmol/L potassium chloride) to wash twice, 4% paraformaldehyde is used to fix for 20 minutes; TBS washing for 5 min×3 times; 0.2% Triton-X 100 is used to break film, the shaking table speed for 100 r/min, 15 min; TBS washing, 5 min×3 times; TTN sealing solution (BSA, volume fraction, 1% TBS weight concentration, 0.2% Tween 20 ) was soaked for 10 minutes, PBS was washed for 5 min×3 times, TTN diluted mouse γH2AX monoclonal antibody (1:500) was labeled and incubated for 2 hours, TBS was washed for 1 min×2 times, TTN was washed for 1 min, TTN diluted goat anti-rat FITC-lgG (1:200), incubated for 1 h: TBS washed for 5 min×3 times, and avoided light; DAPI (0.05 μg/mL) is stained for 5 min, TBS washed for 5 min×3 times, attention should be taken to avoid light; fixed fluid seals were observed under OlympusIX51 fluorescence microscope. The quantitative method of γH2AX focus was: the number of γH2AX focus was counted by image pro plus software, and the number of γH2AX focus was more than 5 positive cells. Each film counts at least 800 cells.

Statistical analysis method

The experimental data were expressed by ¯x±s, and then analyzed by SPSS 11.5. The difference between the mean values of multiple groups was tested by one-way ANOVA. When P <0.05, the results showed that the difference was statistically significant.

## 3.1 Cell viability assay

Figure 1 is the survival curve of HepG2 hepatoma cells irradiated by γ-rays. The fitting function is S= exp (−αDβD2), and the correlation coefficient is R2 = 1, α and βare 0.03 and 0.06, respectively. The β value greater than the α value indicates that high dose radiation can better overcome the immediate effect of cell repair, and the survival rate decreases exponentially, unlike the linear attenuation in low dose radiation [16, 17, 18, 19, 20, 21, 22].

Figure 1

HepG2 hepatoma cell survival curve

## 3.2 PCC induction efficiency

Caly Culin A is a protein serine/tyrosine phosphatase inhibitor that can induce PCC formation at different stages of cell cycle, especially at G2 stage. Caly Culin A can induce premature chromosome agglutination in mixed cells at 50 nm. Among the agglutinated chromosomes, about 20% of G1 phase cells and about 80% of G2 phase cells. The proportion of these two phase cells is called PCC induction efficiency. At each dose point, when 40 G2 phase cells were counted, 5-8 G1 phase cells entered the counting range, indicating that the induction efficiency of PCC in this experiment was 12.5%-20%, the results are shown in Table 1.

Table 1

Data ratio of G1 and G2 precocious chromosome agglutination cells

## 3.3 Chromatid breakage after irradiation of Gl and G2 Cells

Figure 2 shows the relationship between G1 and G2 cell chromatid breakage and irradiation dose. As can be seen from Figure 2, the number of chromatid breaks increases linearly with the dose at G1 and G2 stages.At the same dose point, the number of G2 phase chromatids is about 3 to 4 times that of G1.

Figure 2

Dose effect relationship between G1 and G2 chromatid breakage

## 3.4 G2 phase isochromatid breakage

Figure 3 is the relationship between the chromatid breakage and the dose of G2 isochromatic cells. By linear regression analysis, the regression equation is y = 0.01 + 0.2x, R2 = 0.99, indicating that there is a good linear correlation between the two.

Figure 3

Dose effect relationship of G2 phase isochromosome chromosome breakage

## 3.5 Relationship between chromatid breakage and cell survival fraction

Figure 4 is the relationship between the number of G2 chromatid breakup and the number of chromatid breakpoints and cell survival. Linear regression analysis showed that there was a good correlation between the number of chromatid and isochromatid breaks and cell survival rate in G2 phase cells.

Figure 4

Relationship between G2 chromatid breakup and isochromatid breakage and cell survival rate

## 3.6 X-ray inhibits proliferation of HepG2 hepatoma cells

The results of clone formation assay showed that the survival fraction of HepG2 hepatoma cells decreased in a dose-dependent manner (p < 0.05) from 2, 4, 6, 8 Gy to 0.5, 4 and 24 h after X-ray irradiation. At 4 and 24 h after irradiation, the survival fraction of each dose group recovered, as shown in Figure 5.

Figure 5

Effect of X-ray on the clone formation of HepG2 hepatoma cells

## 3.7 X-ray induced DNA double strand damage in HepG2 hepatoma cells

The results of neutral comet electrophoresis showed that 0.5, 4, and 24 h after irradiation of Hela, MEC-1 and HepG2 cells with X-ray irradiation of 2, 4, 6, 8 Gy, the three cells showed typical changes of comet cell indices. At 0.5 h after irradiation, TMin each dose group increased significantly, and the 4h group had the highest value after irradiation. Among them, the TM of MEC-1 cells increased significantly at 4 hours after irradiation, reaching 84.56 in 6 Gy irradiation group, while the TM of Hela cells increased relatively little, which was significantly different from that of MEC-1 cells and HepG2 hepatoma cells (p < 0.05); at 24 hours after irradiation, the TMvalues of each dose group decreased in varying degrees (Figure 6, Table 2).

Figure 6

Neutral comet electrophoresis of 4H cells after X-ray irradiation

Table 2

Comparison of TM in three cell lines at different time points after X-ray irradiation

## 3.8 X-ray induced γH2AX formation has time and dose effects

Immunofluorescence staining showed that the focal γH2AX was expressed in different degrees at 0.5, 4 and 24 h after irradiation of HepG2 hepatoma cells to 2, 4, 6, 8 Gy. After 0.5 h, the green fluorescent focus appeared in the nuclei of HepG2 hepatoma cells, as shown in Figure 7. Compared with the control group, the percentage of γH2AX positive cells in HepG2 hepatoma cells increased significantly at 0.5, 4 and 24 hours after irradiation (p < 0.05). The percentage of γH2AX positive cells in HepG2 hepatoma cells reached 100% at 0.5 hours after irradiation in 2 Gy group, and decreased gradually at 24 hours after irradiation, but there was still significant difference compared with the control group (p < 0.05), as shown in Figure 8.

Figure 7

HHepG2 hepatoma cells X radiation of 8 Gy group after 0.5 h focus image formation

Figure 8

Time and dose effect of γH2AX focus formation in HepG2 hepatoma cells after X-ray irradiation

## 4.1 Discussion on the radiation effects of γ-rays on hepatoma cells

Radiotherapy is currently one of the main means of cancer treatment. The radiation effects of cancer cells on radiotherapy are affected by various factors. Caly Culin A is an effective inducer of PCC. It can induce chromosome aggregation at various stages of cell cycle, especially at G2 stage. In this study, we found that Caly Culin A induced chromosome aggregation in G2 phase was 5-8 times as efficient as that in G1 phase, whichwas consistent with Goodwin’s and Durante’s results, but its mechanism needs further study. In this study, the linear relationship between cell survival rate and irradiation dose of HepG2 hepatoma cells irradiated by γ-rays has been confirmed by many studies. At G1 and G2 stages, the increase of the number of chromatid breaks was linearly correlated with the decrease of cell viability.

In our study, both the number of chromatid breaks and the isochromatid breaks in HepG2 hepatocellular carcinoma cells linearly increased with the increase of the dose of γ-rays, suggesting that at higher doses, more electrons would hit the target substance - the chromosome, so the yield of chromosome breaks would increase in response.

However, the absolute increment of G2 isochromatid breakage in HepG2 hepatoma cells was much less than that of chromatid breakage. After studying the biological effects of different LET rays, chromosome breakage was mainly caused by chromatid breakage, while in high LET irradiation, isochromatid breakage was the main form of chromosome breakage, probably because most isochromatid breaks were caused by isochromatid breakage. The body fracture is caused by the electron hitting sister chromatid. For low LET radiation, it loses not enough energy per unit range to cause sister chromatid breakage, so after hitting one of the sister chromatids, the energy loss is exhausted or the remaining energy is insufficient to cause damage to another chromatid. Therefore, after low LET ray irradiation, chromosome breakage is mostly chromatid breakage.

In the G1 phase of HepG2 hepatocellular carcinoma cells, chromosomes are relatively loose aggregated, but in the G2 phase of HepG2 hepatocellular carcinoma cells, the aggregation of chromosomes is much tighter than in the G1 phase because of the replication of chromosomes and the preparation for mitosis. Therefore, the same energy of γ- rays on chromosome cross section is greater than G1, and the G2 chromosome breakage yield will be higher than G1.

## 4.2 Discussion on the radiation effects of X-ray on hepatocellular carcinoma cells

DNA damage response (DDR) is an exceptionally complex regulatory system in DNA. When ionizing radiation causes DSB, members of the phosphatidylinositol-3-kinase family: ATM (Ataxia telangiectasia mutatedgene), ATR (Ataxia-telangiectasia and Rad-3related) and DNA-PK (DNA-dependent protein kinase) are activated, mobilizing a series of phosphorylation cascades, activating the stress system, and activating the DDR signal. Downstream molecules of the pathway, such as γH2AX, MRN, Chk2 and p53, repair DNA, produce cell cycle arrest or initiate apoptosis. The results showed that phosphorylated histone H2AX (γH2AX) was the index reflecting the radiation effect of DSB, and the focal point of γH2AX was one-to-one corresponding to the quantity of DSB. The γH2AX fluorescence staining was the gold standard for detecting the presence of DSB. In this paper, a series of studies on γH2AX as radiation and chemotherapeutic radiation effect indicators have been carried out. It has been proved that γH2AX is an effective research parameter for studying radiation effect of radiotherapy and chemotherapy.

The expression of H2AX was detected by immunofluorescence staining. This method can directly count the number of focal points formed by γH2AX, which is more convenient and sensitive than the traditional DSB method. The results showed that only 0.5 h after irradiation, the positive rate of γH2AX cells reached 100% in each dose group, and the high expression rate of γH2AX cells persisted until 4 h after irradiation; 24 h after irradiation, the positive rate of γH2AX cells in HepG2 hepatoma cells gradually decreased, but there was still significant difference compared with the control group.

## 5 Conclusions

PCC method was used to study the radiation effect of γ-rays on hepatocellular carcinoma cells. Clone formation assay,neutral comet electrophoresis and γH2AX focal point detection were used to study the radiation effect of X-rays on hepatocellular carcinoma cells.

study provides a useful reference for clinical radiotherapy of liver cancer.

According to the radiation effects of nuclear physics ray on hepatoma cells, the application prospects are as follows:

Radiation therapy for nuclear physics is as a downstage treatment before liver transplantation. Liver transplantation is one of the most effective treatment methods for patients with early liver cancer, which can eliminate liver cancer, reduce the risk of disease progression and metastasis, and is conducive to the recovery of liver function. Liver transplantation should try to choose the limited lesion, and it is expected to get better survival after liver transplantation. Local treatment such as TACE, RFA and TACE can reduce the survival rate of 24% to 69% of patients who do not meet the transplantation criteria, and the survival rate of patients who do liver transplantation after the transplantation is better than those who do liver transplantation directly.

Combination of radiation therapy and sensitizing drugs in nuclear physics. Patients with advanced hepatocellular carcinoma (HCC) have rapid progression, short survival time, and poor effects of chemotherapy and radiotherapy alone. Theoretically, combined use of radiotherapy and chemotherapy may improve the therapeutic effect. SHARP and Oriental studies are two large prospective randomized studies, not only confirmed the survival benefits of sorafenib in patients with advanced liver cancer, but also demonstrated its safety. The efficacy of sorafenib in the treatment of advanced liver cancer provides a basis for multidisciplinary treatment of liver cancer based on sorafenib. Since Sorafenib was approved by the Food and Drug Administration of the United States and the European Drug Evaluation Agency (EMEA) as a targeted molecule drug for the treatment of liver cancer in 2007, several clinical guidelines for liver cancer have recommended Sorafenib as a standard first-line treatment for patients with inoperable or advanced liver cancer, and a combination of multiple sorafenib and RT for clinical purposes. The experiment is under way. Among them, RTOG1112 is an exploratory study of sorafenib combined with stereotactic radiotherapy in patients with middle-term liver cancer in Europe and America. Nearly 400 patients with unresectable liver cancer who are not suitable for TACE were randomly divided into solafenib group and somatic stereotactic radiotherapy plus solafenib group. The results are expected.

## Acknowledgement

This research has been financed by the International Science & Technology Cooperation Program of China (2014DFE10030).

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Huo Y., Wang LQ., Chen C., Solution of medium power grid-connected PV inverter radiation emission, J. Pow. Supp., 2016, 14(1), 109-113. Google Scholar

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Tomita M.,Maeda M., Mechanisms and biological importance of photon-induced bystander responses: Do they have an impact on low-dose radiation responses, J. Radiat. Res., 2016, 56(2), 205-219.

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Liu L.X., Deng W., Zhou X.T., Chen R.P., Xiang M.Q., Guo Y.T., et al., The Mechanism of adenosine-mediated activation of lncRNA MEG3 and its antitumor effects in human hepatoma cells, Int. J. Oncol., 2016, 48(1), 421-9.

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Lazzarini A., Macchiarulo A., Floridi A.,Coletti A., Cataldi S., Codini M., et al., Very-long-chain fatty acid sphingomyelin in nuclear lipid microdomains of hepatocytes and hepatoma cells: Can the exchange from C24:0 to C16:0 affect signal proteins and vitamin D receptor, Mol. Biol. Cell, 2015, 26(13), 2418-2425.

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Accepted: 2019-01-28

Published Online: 2019-04-11

Citation Information: Open Physics, Volume 17, Issue 1, Pages 167–176, ISSN (Online) 2391-5471,

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text:
# All composition and Chief series for $S_n$ $n \geq 4$

All composition and Chief series for $$S_n$$ $$n \geq 4$$

So a composition series is a series $$1 \leq G_1 \leq G_2 \leq ... \leq S_n$$

s.t. $$\frac{G_{i+1}}{G_i}$$ is simple.

A Chief series is the same thing except now every factor is characteristically simple i.e. has no characteristic subgroups.

So Is this easy for $$n \geq 5$$ because then $$A_n$$ is simple? How do I handle when $$n=4$$?

Just keep factoring stuff out of $$S_4$$ until you can't anymore!
We can factor out $$A_4$$ giving us a factor of $$\mathbb{Z}_2$$. But $$A_4$$ is not simple. The biggest normal subgroup of it we can find is the one with all the 2+2-cycles in it: $$\{1,(12)(34),(13)(24),(14)(23)\}$$. Let's factor this out of $$A_4$$. We get another factor of order 3. But wait, the klein 4-group still isn't simple because it has $$\cyclic{(12)(34)}$$ as a normal subgroup. Factor that out too.
$$1\norm \cyclic{(12)(34)}\norm \{1,(12)(34),(13)(24),(14)(23)\}\norm A_4\norm S_4$$


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# Input Made Easy

Jiro's pick this week is settingsdlg by Rody Oldenhuis.

Last December, I wrote this post on inputsdlg by Kesh. I really liked the flexibility of inputsdlg in creating a complex user input dialog. Today, I came across settingsdlg by Rody. There are a lot of similarities between the two functions. For example, they both allow prompting for multiple inputs, specifying input format, and storing output as a structure. While the customizability of settingsdlg is not as exhaustive as inputsdlg, I am impressed at the ease of use of the function.

[settings, button] = settingsdlg(...
'Description'                        , ['This dialog will set the ', ...
'parameters used by FMINCON()'], ...
'title'                              , 'FMINCON() options', ...
'separator'                          , 'Unconstrained/General', ...
{'This is a checkbox'; 'Check'}      , [false, false],...
{'Tolerance X';'TolX'}               , 1e-6, ...
{'Tolerance on Function';'TolFun'}   , 1e-6, ...
'Algorithm'                          , {'active-set','interior-point'}, ...
'separator'                          , 'Constrained', ...
{'Tolerance on Constraints';'TolCon'}, 1e-6)
settings =
Check: 0
TolX: 1.0000e-006
TolFun: 1.0000e-006
Algorithm: 'active-set'
TolCon: 1.0000e-006
button =
ok

As you can see, it takes parameter-value pairs. The type of input is automatically determined by the value: numbers and strings use edit boxes, cell arrays use list boxes, and logical arrays use check boxes. You can also group fields by creating separators.

I also like the detailed documentation (.pdf) that Rody includes with the entry. And finally, if you're looking for an example of a well-written MATLAB code, take a look at this entry. It's very well-commented and has a lot of error checking to make it robust.

Published with MATLAB® 7.10

|


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JenniferSmart1 2 years ago I'm having trouble cancelling out my units. $(N \cdot \cancel{m^2}/\cancel{C^2)}\left[\frac{\cancel{C}}{\cancel{m}^2}+\frac{\cancel{C}}{\cancel{m}^2}\right]$ I've N left, but I should have N/C

1. jtvatsim

$N \cdot \cancel{m^2}/\cancel{C^2)}\left[\frac{\cancel{C}}{\cancel{m}^2}+\frac{\cancel{C}}{\cancel{m}^2}\right]$

2. jtvatsim

Just reposting the question :)

3. JenniferSmart1

@phi

4. JenniferSmart1

nevermind I think I see my mistake, C^2 doesn't cancel out C

5. klimenkov

Very nice. You solved your own problem by yourself.

6. klimenkov

But where is 2 in the numerator?

7. JenniferSmart1

2 in the numerator?

8. JenniferSmart1

m^2

9. klimenkov

$$\frac{C}{m^2}+\frac{C}{m^2}=\frac{2C}{m^2}$$

10. JenniferSmart1

The m's are different, I can't add them. $8.99\times10^9N\cdot m^2/C^2\left[\frac{(-5\times10^{-6}C)}{(0.11m)^2}+\frac{(5\times10^-6C)}{(0.09m)^2}\right]$

11. JenniferSmart1

I just needed to cancel my units out to make sure I'm doing the calculations correctly, because the answer is supposed to be in N/C

12. JenniferSmart1

$\vec{E}=N/C$

13. klimenkov

Ah, i understood, that is ok.


text:
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# Approximate first passage time distribution for barrier crossing in a double well under fractional Gaussian noise

Chaudhury, Srabanti and Cherayil, Binny J (2006) Approximate first passage time distribution for barrier crossing in a double well under fractional Gaussian noise. In: Journal of Chemical Physics, 125 (11). 114106 (8 pages).

 PDF Approximate_first_passage_time_distribution_for_barrier_crossing.pdf Restricted to Registered users only Download (157Kb) | Request a copy

## Abstract

The distribution of waiting times, f(t), between successive turnovers in the catalytic action of single molecules of the enzyme ${\beta}$-galactosidase has recently been determined in closed form by Chaudhury and Cherayil [J. Chem. Phys. 125, 024904 2006] using a one-dimensional generalized Langevin equation GLE formalism in combination with Kramers’ flux-over-population approach to barrier crossing dynamics. The present paper provides an alternative derivation of f(t) that eschews this approach, which is strictly applicable only under conditions of local equilibrium. In this alternative derivation, a double well potential is incorporated into the GLE, along with a colored noise term representing protein conformational fluctuations, and the resulting equation transformed approximately to a Smoluchowski-type equation. f(t) is identified with the first passage time distribution for a particle to reach the barrier top starting from an equilibrium distribution of initial points, and is determined from the solution of the above equation using local boundary conditions. The use of such boundary conditions is necessitated by the absence of definite information about the precise nature of the boundary conditions applicable to stochastic processes governed by non-Markovian dynamics. f(t) calculated in this way is found to have the same analytic structure as the distribution calculated by the flux-over-population method.

Item Type: Journal Article Copyright of this article belongs to American institute of Physics. Division of Chemical Sciences > Inorganic & Physical Chemistry 11 Jan 2007 19 Sep 2010 04:32 http://eprints.iisc.ernet.in/id/eprint/8870

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# Proof of a series having infinitely many zeros in the unit disc

I have read an interesting question recently. This is about a series having infinitely many zeros inside the unit disc $$U$$. The series is $$\begin{equation*} f(z)=\sum_{k=1}^\infty 5^k z^{n_k}, \end{equation*}$$ where $$\{n_k\}$$ is a sequence of integers such that $$n_1 \ge 2$$ and $$n_{k+1}>2kn_k$$. I have shown that $$f \in H(U)$$ and it does not have radial limit at any point of the unit circle $$\partial U$$. However, I can't show that it has infinitely many zeros inside $$U$$. The tools that I can apply are graduate level complex analysis such as Rouche's theorem, the open mapping theorem, the maximum modulus theorem, Schwarz lemma, Runge's theorem, the Mittag-Leffler theorem and etc. Anyone can help?

This function has the property that on the circle $$|z|=1-\frac{1}{n_k}, k \ge 10$$, $$|h(z)|>C5^k$$, where we can take for example $$C=\frac{1}{100}$$

(note that $$(1-\frac{1}{n_k})^{n_k} \ge \frac{1}{3}$$ as that sequence converges increasingly to $$\frac{1}{e}$$ with the inequality already happening for $$k \ge 10$$ and $$n_k>k$$, while for $$m>k,(1-\frac{1}{n_k})^{n_m} \le (\frac{1}{e})^{2^{m-k}(m-1)...k} < 6^{-m}$$ so the corresponding terms form a geometric sum that converges to a small finite number, while the smaller terms sum in absolute value to obviously less than $$\frac{1}{4}5^{k}$$ by the trivial estimate and the corresponding geometric series)

Assume now that $$h$$ has finitely many zeroes only (could be none here of course). Let $$B$$ a finite Blaschke product with the same zeroes (including multiplicities etc, where we take $$B=1$$ if $$h$$ has no zeroes). Then $$g=\frac{h}{B}$$ has no zeroes in the unit disc and is analytic and still satisfying $$|g(z)| > C5^k, |z|=1-\frac{1}{n_k}$$, since $$|B(z)| <1, |z| <1$$.

But then $$\frac{1}{g}$$ is analytic in the unit disc and by maximum modulus, $$|\frac{1}{g}| < \frac{1}{C5^k}, |z| \le 1-\frac{1}{n_k}$$. If we let $$k \to \infty$$ we get $$\frac{1}{g}=0$$ in the unit disc and that is a contradiction.

Note that $$h(z)-w$$ has the same properties as $$h$$ (taking all $$k$$ large enough so $$5^k > 200|w|$$ say, so we can use $$C=\frac{1}{200}$$ say, so the same proof applies to show that $$h$$ takes every complex value infinitely many times in the unit disc!

• This is a very nice solution. – KK Wong Mar 6 at 4:47

Here is another solution to the problem following the hint in W. Rudin's Real and Complex analysis boo for problem 6, chaser 13.

The key, as also pointed put in the OP and by others is to show that there is $$c>0$$ such that along any circle of radius $$r_m:=1-\tfrac{1}{n_m}$$ \begin{align} |f(z)|\geq |5^mz^{n_m}|-|f(z) - 5^mz^{n_m}|\geq 5^m(r_m)^{n_m} -\sum_{\substack{k\geq1\\ k\neq m}}5^k(r_m)^{n_k}> 5^mc\tag{1}\label{one} \end{align}

Zeroes of $$f$$: Once this is proven, one can appeal to Rouché's theorem. Let $$p_m(z):=5^m z^{n_m}$$. The polynomial $$p_m$$ has only one zero $$z=0$$ of multiplicity $$n_m$$ in $$\mathcal{C}$$. From \eqref{one}, $$|f(z)-p_m(z)|<|p_m(z)|,\qquad |z|=r_m$$ By Rouché's theorem $$f$$ has the same number of zeroes, $$n_m$$, as $$g$$ counted according to their multiplicities inside the disk $$D(0;r_m)$$. This implies that the number of zeroes of $$f$$ in $$U$$ us countably infinite ($$r_m\xrightarrow{m\rightarrow\infty}1$$ and $$n_m>m$$).

Proof of \eqref{one}: Here is a rather pedestrian approach. Notice that from $$n_1>1$$ and $$n_{k+1}>2k n_k$$, it follows that \begin{align} n_{k+m}> 2^k\Big((k-1+m)\cdot\ldots\cdot m \Big) n_m >2kmn_m \tag{2}\label{two} \end{align} for all $$k,\, m\geq1$$. Along the circle $$|z|=r_m$$ \begin{align} \Big|\sum^{m-1}_{k=1}5^kz^{n_k}\Big|\leq \sum^{m-1}_{k=1}5^k(r_m)^{n_k}\leq \frac{5^m}{4}\tag{3}\label{three} \end{align} Since $$g(x)=\big(1-\tfrac{1}{x}\Big)^x$$ is strictly monotone increasing in $$[1,\infty)$$ and $$\lim_{x\rightarrow1-}g(x)=e^{-1}$$, \begin{align} \Big|\sum^\infty_{k=m+1}5^kz^{n_k}\Big|&\leq 5^m\sum^\infty_{k=1}5^k(r_m)^{n_{k+m}}< 5^m\sum^\infty_{k=1} 5^k(r_m)^{2mkn_m}\\ &< 5^m\sum^\infty_{k=1} 5^k e^{-2mk}= 5^m\frac{5e^{-2m}}{1-5e^{-2m}}<5^m\frac{5e^{-6}}{1-5e^{-6}}\tag{4}\label{four} \end{align} for $$m\geq3$$. Combining \eqref{three} and \eqref{four} we obtain $$5^m(r_m)^{n_m}-\sum_{\substack{k\geq1\\ k\neq m}}5^k(r_m)^{n_k}>5^m\Big((r_m)^{n_m}-\frac{1}{4}-\frac{5e^{-6}}{1-5e^{-6}}\Big)\geq 5^m\Big((r_3)^{n_3}-\frac{1}{4}-\frac{5e^{-6}}{1-5e^{-6}}\Big)$$ for all $$n\geq 3$$. $$n_3>8n_1>16$$. A numeric calculation gives $$(r_3)^{n_3}-\frac{1}{4}-\frac{5e^{-6}}{1-5e^{-6}}>\big(1-\frac{1}{17}\big)^{17} -\frac14-\frac{5e^{-6}}{1-5e^{-6}}>0.09$$ Inequality \eqref{one} follows from this.

• From \eqref{two} we habe that the the radius of convergcen of $$f$$ is $$\lim_{k\rightarrow\infty}\sqrt[n_k]{5^k}=1$$. That $$\limsup_{r\rightarrow1-}|f(re^{i\theta}|=\infty$$ for all $$\theta$$ shows that $$f$$ cannot be extended analytically to any region containing $$U$$.
• As pointed out by others, one can also show that for any $$w\in\mathbb{C}$$, there are infinitely many solutions to the equation $$f(z)=w$$, $$z\in U$$. Indeed, along $$|z|=r_m$$ $$|f(z)-w|\geq |p_m(z)|-|f(z)-w-p_m(z)|\geq |p_m(z)|-|f(z)-p_n(z)|-|w|> 5^mc-|w|>0$$ for all sufficiently large $$m$$. Another application of Rouche's theorem shows that $$f-w$$ has $$n_m$$ solutions (counted according to their multiplicities) inside the disk $$D(0;r_m)$$ (for each $$m$$ large enough).


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# Integrating an absolute value on exponential

This might be a bit rusty but hopefully it can be brushed up.

I need to integrate $$\int_{-\infty}^{\infty}xe^{-2\lambda \left | x \right |}dx$$

Recall:

$$\left | x \right |=\left\{\begin{matrix} x &x\geq 0 \\ -x& x< 0 \end{matrix}\right.$$

Then,

$$\lim_{t\rightarrow \infty}\int_{-t}^{0}xe^{-2\lambda(-x)}dx+\lim_{t\rightarrow \infty}\int_{0}^{t}xe^{-2\lambda(x)}dx$$

I would appreciate a nudge. Intuition suggest odd and even function have a role to play. Absolute values are nasty.

• As Ron Gordon explained, the answer slides out nicely given the fact the function is odd. But you should also be able to integrate $xe^{kx}$ (hint: by parts). Absolute values aren't too bad: you just need to split them up in their two cases (as you've done) and then look at each case as you would for any other normal question ^^ – bilaterus Dec 15 '15 at 11:53

Absolute value is even, so exponential is even. $x$ is odd. Odd times even is odd. Thus, an integral of an odd function about a symmetric interval is...
• Well, technically it's 0 iff the two branches converge, since this is an improper integral. Pretty sure that's the case iff $\lambda \ne 0$ – Alan Dec 15 '15 at 12:07
• @Alan: I think I know what you mean, but I do not know what a "branch" is nor how it converges. I do know, though, that if $\lambda=0$, the integral is a Cauchy principal value defined as the limit of a symmetric finite interval. – Ron Gordon Dec 15 '15 at 12:09


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## JFraser 2 years ago Tutorial: Ionization Energy

1. JFraser

Ionization energy is defined as the energy input required to remove 1 mole of electrons from 1 mole of gaseous atoms, and is summarized by the general equation:$X(g) \rightarrow X^{+1}(g) + e^{-1}$The ease with which this process occurs will vary from element to element, but varies in a regular, periodic fashion. A second ionization may occur, so long as the atom has a second electron to remove (so any atom other than H), and the generalized equation looks similar:$X^{+1}(g) \rightarrow X^{+2}(g) + e^{-1}$ Successive ionizations are always more difficult, since we are removing electrons from an increasingly unbalanced system. Consider an atom of aluminum, with 3 valence electrons. A neutral atom will have 13 protons pulling on 13 electrons, 3 of which occupy the 3rd principle energy level. Aluminum's electron configuration is$[Ne]3s^23p^1$ Removal of a valence electron leaves aluminum with 12 electrons, still being attracted by 13 protons. Each electron now "feels" more than a full proton's equivalent attraction, and the electrons in the 3s-orbital are drawn in slightly, decreasing the radius of the Al^{+1} ion. In order to remove a second electron, a larger energy "cost" is needed, and the remaining ion's radius is decreased further still, as the nucleus becomes, in effect, stronger, as valence electrons are removed (see table)

2. JFraser

As the table shows, repeatedly removing electrons from the same atom gets more and more difficult, but the table also shows a HUGE increase in IE (shown by the yellow line) occurring at a different point for each atom in the second period. In the case of a sodium atom, removing a second electron "costs" nearly 10 times as much as removing the first, where the second IE of magnesium is only twice as much as the first. The huge jump in the ionizations of magnesium occurs when the third electron is removed. This jump is easily explained if we look at WHICH electrons are being removed. Sodium has just one valence electron, sitting in the 3s orbital. If we personalize the sodium atom, we can imagine it being "desperate" to lose that electron, empty that level, and gain a configuration just like neon. So the loss of a single electron from an atom of sodium isn't particularly costly, since the sodium atom benefits from this loss energetically. If a second electron were to be removed, it would come from a different principle energy level.$Na: 1s^12s^22p^63s^1$$Na^{+1}: 1s^22s^22p^6$ Removing an electron from a full principle level would result in a loss of stability, so the cost to remove one of the 2p-electrons will be a several-fold increase in IE. A magnesium atom, with 2 valence electrons to lose, doesn't see a huge increase in IE until the THIRD ionization, once the 2 valence electrons have already been removed. This pattern allows us to use the successive ionizations of an unknown atom to place the unknown atom in a particular group, based on when the jump in IE occurs. We may not be able to identify the atom, but with information about its successive ionizations, we can, at least, identify its group number.

3. JFraser

This table shows the first ionizations for the main group of the periodic table (s- and p-block only), and we see two reliable trends. Firstly, moving from top to bottom within any group, ionization energy decreases. This trend is most easily explained by looking at the atomic radii of the atoms within the group. Atoms at the top of a group are filling a principle energy level that is fairly close to the nucleus, so the force of attraction of the oppositely charged particles (an inverse-square law) is fairly strong. As we move down the group, the principle level being filled becomes larger, so the orbitals being filled are farther and farther away from the nucleus. As a result, the inverse-square law shows that the force of attraction is weaker, and the valence electrons themselves are also shielded from the nucleus by more and more layers of core electrons. For example:$Na: 1s^22s^22p^63s^1$$Cs: 1s^22s^22p^63s^23p^64s^23d^{10}4p^65s^24d^{10}5p^66s^1$ Where the valence level of a sodium atom is shielded by only 2 layers and 10 electrons, the valence level of a cesium atom is shielded by portions of five different layers and 54 core electrons. The 6s-electron in cesium is very weakly-held, and is very easy to remove. Down any group we see the same general decrease, because each atom within a group has an electron configuration similar to those above it, simply within a principle energy level that is farther from the nucleus

4. JFraser

When we look across the period, we see a general increase in IE. As each principle level is in the process of being filled, atoms at the left of the period have a low resistance to the removal of a valence electron, where atoms at the right of each period have a decreasing willingness to have one of their valence electrons removed. Where lithium has an electron configuration of $$1s^22s^1$$, fluorine's electron configuration is: $$1s^22s^22p^5$$, one electron shy of full. The fluorine atom will be in no "mood" to have one of its valence electrons removed, so its IE is the second highest of any in its period, after neon for obvious reasons

5. quintess

You lost me