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## Friday, December 16, 2011
### Flow Meters : An Introduction
An introduction to flow meters:
Flow meters have a wide selection of applications and are utilized in nearly every industry and in some laboratories too. A flow meter is a machine to measure large quantity fluid movement. You will find many methods used to calculate flow. Considered one of the common kinds of flow meters is the positive displacement flow meter. It basically gathers an allocated volume of the fluid then it will count the number of instances the volume is filled to sum up the flow. Others have a constriction and by calibrating the forces produced by the running stream across the constriction, this will compute the flow indirectly. If we need to employ a flow meter for any application, it is always good to purchase a top quality unit since it will give long years of trouble free service.
Much of the applications for flow meters are:
- Production process.
- To compute effluent emission.
- Steam movement
- Oil flows
- Air flows
- Gas movement
- For laboratory use.
- To compute water and gas usage.
- To measure stream of rivers and opportunities.
- To calculate fuel being dispensed.
These are only some of the uses. Flow meters have hundreds of applications and are of the various types. The form of flow meter depends upon its application. Flow meters can measure in minute quantities and in some massive applications they could measure fluid flow in large volumes.
Some of the different types of flow gauge are:
- Piston meter/Rotary piston: They are one of the commonest flow meters and are utilized to measure domestic water utilization.
- Variable area meter: This flow meter is also called a 'rotameter' and consists of a tapered tube with a float inside that is pushed upwards by the fluid flow and downwards by gravity. While the flow rate keeps increasing, the ball moves up in the tapered tube till the upward and down forces are in a state of equilibrium. The reading at that point is the flow. It is used mainly to measure flow of water or air and it is precise up to =/- 1%.
- Turbine flow meter: It obstructs the stream of the liquid only minimally and this design allows for measurement of greater flow rates. They are mostly used by large commercial users.
- Some of the other kinds of meters are Woltmann gauge, Single jet gauge, Paddle wheel meter, multiple jet meter, Pelton wheel, Oval gas meter, Nutating disk gauge, Current meter etc.
These are generally only a few of the many types of flow meters available. Some of the other types are Pressure based meters. They function on Bernoulli's principle by measuring differential pressure. Venturi meters shrink the flow of the fluid and by utilizing pressure sensors to measure the differential pressure, before and after constriction, the flow is calculated. The Pitot tube measures the fluid flow by computing the stagnation pressure and by making use of Bernoulli's equation, the rate of flow is determined.
Flow meters are regular and we are certain to encounter a flow meter practically daily. One of the most common flow meters is the diesel dispenser. The other is our domestic water meter. A flow meter may be manual or electronic, simple or sophisticated, but plays important part in our way of life either directly or indirectly.
Article Source : www.clintbrownlee.com
## Labels
Automation (4) Basics (48) DCS (1) Flow (27) Flow Meters (22) Level (19) PLC (2) Pressure (12) SCADA (2) Sensors (7) Temperature (17) Transducer (17)
Hai friends…welcome to my blog. This blog is exclusively for instrumentation engineering students which will provide sources for their reference and studies. As you all know Instrumentation is now a fast emerging and developing field in Engineering. This blog has different categories like PLC, SCADA, DCS, Sensors and Transducers, Computer control of process, Industrial Instrumentation, etc.
This blog will also provide an exclusive ‘ASK ME’ section where you can make any queries and share your ideas about instrumentation. The solution for your queries will be given to you by mail from best of my knowledge and reference.
So I wish this blog may be very useful for your studies and reference. | 878 | 4,229 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.5625 | 3 | CC-MAIN-2024-33 | latest | en | 0.946995 |
https://www.jiskha.com/questions/1466105/a-car-is-traveling-at-40-miles-per-hour-write-a-rational-expression-that-gives-the-time | 1,627,948,471,000,000,000 | text/html | crawl-data/CC-MAIN-2021-31/segments/1627046154408.7/warc/CC-MAIN-20210802234539-20210803024539-00135.warc.gz | 869,691,991 | 4,858 | # Jefferson
A car is traveling at
40 miles per hour.
Write a rational expression that gives the time that it takes the car to travel
Upper M miles.
1. 👍
2. 👎
3. 👁
1. time = M/40 hours
1. 👍
2. 👎
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http://blog.pkh.me/p/3-masquerade-ball-with-eight-queens.html | 1,632,878,545,000,000,000 | text/html | crawl-data/CC-MAIN-2021-39/segments/1631780061350.42/warc/CC-MAIN-20210929004757-20210929034757-00626.warc.gz | 9,292,346 | 5,170 | A small freedom area.
# Masquerade ball with eight queens
Sat 16 Apr 2011
A while ago, I had some fun writing a solution for the classic eight queens puzzle. But rather than focusing on the recursive issue which is finally just a dozen of SLOC, I played with the board representation in memory. The recursive algorithm won't be much detailed here, it's not the aim of this post.
## Plate declaration
We need a 8x8 array to represent the plate, so instinctively, we start with the following declaration:
``````int t[8][8];
``````
Then, we realized a two-dimensional array is not specially useful since we'll brute-force with an index from 0 to 63:
``````int t[64];
``````
An `int` is a bit overkill for a `boolean` value, isn't it?
``````uint8_t t[64];
``````
Hey, maybe could just use 8 bits per line:
``````uint8_t t[8];
``````
Right, so we have 8x8 bits, then let's use a simpler representation:
``````uint64_t t;
``````
Here we go, much better. We can now start.
## Ascii art
Being able to visually represent our board is the first thing to do. Here is an example:
``````static void disp_board(uint64_t t)
{
for (int i = 0; i < 64; i++, mask <<= 1)
printf("%c%c", t & mask ? '@' : '.', (i + 1) % 8 == 0 ? '\n' : ' ');
printf("\n");
}
``````
This function displays:
``````@ . . . . . . .
. . . . @ . . .
. . . . . . . @
. . . . . @ . .
. . @ . . . . .
. . . . . . @ .
. @ . . . . . .
. . . @ . . . .
``````
...for `t = 577094088726155265`, or in binary:
``````00001000 00000010 01000000 00000100 00100000 10000000 00010000 00000001
``````
You'll notice I choose the LSB for the bit corresponding to the position (0, 0) on the board (`1` means a queen, `0` means no queen).
## Recursion
About the recursion, here is the code with the appropriate `main()`:
``````#define sq(i) do { t |= 1ULL << i; qleft--; } while (0)
#define rq(i) do { t &= ~(1ULL << i); qleft++; } while (0)
static int solve(uint64_t t, int qleft, int idx)
{
int n = 0;
if (idx == 64)
return 0;
if (ok(t, idx)) {
sq(idx);
if (qleft == 0) {
disp_board(t);
n = 1;
} else {
n = solve(t, qleft, (idx / 8 + 1) * 8);
}
rq(idx);
}
return n + solve(t, qleft, idx + 1);
}
int main()
{
printf("%d\n", solve(0, 8, 0));
return 0;
}
``````
A few notes on this code:
• The macros `sq` et `rq` (respectively `set queen` et `remove queen`) set and unset the queen's bit with index `idx`, and increment/decrement the number of left queens to place.
• The `ok()` function we will study soon let you know if it's possible to put a queen at index `idx` or not.
• The `main()` function runs the recursion with an empty board (`t=0`), eight queens left to place (`qleft=8`) starting at position `idx=0`, or (0,0).
• When all the queens are set, we display the plate, and we continue.
• `solve()` returns the number of solutions when we found and displayed them all.
The fun can now begin with the writing of the last function:
``````static int ok(uint64_t t, int idx);
``````
To simplify a few operations, we fetch the `x` and `y` coordinates:
``````static int ok(uint64_t t, int idx)
{
int y = idx / 8;
int x = idx - y * 8;
// ...
}
``````
And the function's return will look like something like this:
``````return !(t & (MASK_LINE | MASK_COLUMN | MASK_DIAGONAL1 | MASK_DIAGONAL2));
``````
All the masks will form a bit field in which no queen should be. A simple binary `AND` with the board will allow to say if it's the case or not.
Let's start by determining `MASK_LINE` for a given `idx`. A mask for the line could be the following:
``````#define MLI 0x00000000000000ffULL /* 00000000 00000000 00000000 00000000 00000000 00000000 00000000 11111111 */
``````
This mask allow to scratch the first line of the board, so we need to shift it to the given queen line:
``````#define MASK_LINE(y) (MLI << (y) * 8)
``````
And in the same way for the columns starting with the left one:
``````#define MCL 0x0101010101010101ULL /* 00000001 00000001 00000001 00000001 00000001 00000001 00000001 00000001 */
``````
Since we have the two masks for lines and columns, we now need to do the diagonals. Let's take the first case:
If we take the case where `x > y`, we have to shift to the left (the right on the board) eight time the difference:
However, the diagonal gets extended (red frame) while it shouldn't, so we need to filter that part. For this diagonal and `x > y`, we can use the following mask:
``````d = x - y
(MD1 & ~0ULL >> 8 * d) << d
^ ^^^^^ ^^^^^ ^^^^
| | | |
| | | `-- 4. And we shift the diagonal.
| | |
| | `-- 2. ...we shift them in order to create zeroes in the lowest part of the board.
| |
| `-- 1. All bits to 1...
|
`-- 3. We only keep higher part of the board.
``````
With `MD1` (mask for the middle diagonal):
``````#define MD1 0x8040201008040201ULL /* 10000000 01000000 00100000 00010000 00001000 00000100 00000010 00000001 */
``````
To handle the case where `x < y`, we just have to shift in the other direction, and toggle the difference sign:
``````d = x - y
(d > 0 ? (MD1 & ~0ULL >> 8 * d) << d : (MD1 & ~0ULL << 8 * -d) >> -d)
^^^^^^^^^^^^^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Shift to the right on the Shift to the left on the board.
board.
``````
The case for the second diagonal is almost the same; the difference is not obtained with `x - y` but `x + y - 7`, and the mask change:
``````d1 = x - y
d2 = x + y - 7
First diagonal: (d1 > 0 ? (MD1 & ~0ULL >> 8 * d1) << d1 : (MD1 & ~0ULL << 8 * -d1) >> -d1)
Second diagonal: (d2 > 0 ? (MD2 & ~0ULL << 8 * d2) << d2 : (MD2 & ~0ULL >> 8 * -d2) >> -d2)
``````
With the following `MD2`:
``````#define MD2 0x0102040810204080ULL /* 00000001 00000010 00000100 00001000 00010000 00100000 01000000 10000000 */
``````
If we now merge our four masks (line, column, diagonal 1 and diagonal 2), we get this code:
``````#define MLI 0x00000000000000ffULL /* 00000000 00000000 00000000 00000000 00000000 00000000 00000000 11111111 */
#define MCL 0x0101010101010101ULL /* 00000001 00000001 00000001 00000001 00000001 00000001 00000001 00000001 */
#define MD1 0x8040201008040201ULL /* 10000000 01000000 00100000 00010000 00001000 00000100 00000010 00000001 */
#define MD2 0x0102040810204080ULL /* 00000001 00000010 00000100 00001000 00010000 00100000 01000000 10000000 */
static int ok(uint64_t t, int idx)
{
int y = idx / 8;
int x = idx - y * 8;
int d1 = x - y;
int d2 = x + y - 7;
return !(t & ((MLI << y * 8) | (MCL << x)
| (d1 > 0 ? (MD1 & ~0ULL >> 8 * d1) << d1 : (MD1 & ~0ULL << 8 * -d1) >> -d1)
| (d2 > 0 ? (MD2 & ~0ULL << 8 * d2) << d2 : (MD2 & ~0ULL >> 8 * -d2) >> -d2)));
}
``````
The result is a binary `AND` between the memory board, and a mask which looks like for example:
## Conclusion
We can do better, with less than 64 bits, but I found this approach entertaining (and I got this last link when I was almost done with my code).
For those interested, here is the complete code:
``````#include <stdio.h>
#include <stdint.h>
static void disp_board(uint64_t t)
{
printf("t = %llx\n", t);
for (int i = 0; i < 64; i++, mask <<= 1)
printf("%c%c", t & mask ? '@' : '.', (i + 1) % 8 == 0 ? '\n' : ' ');
printf("\n");
}
#define MLI 0x00000000000000ffULL /* 00000000 00000000 00000000 00000000 00000000 00000000 00000000 11111111 */
#define MCL 0x0101010101010101ULL /* 00000001 00000001 00000001 00000001 00000001 00000001 00000001 00000001 */
#define MD1 0x8040201008040201ULL /* 10000000 01000000 00100000 00010000 00001000 00000100 00000010 00000001 */
#define MD2 0x0102040810204080ULL /* 00000001 00000010 00000100 00001000 00010000 00100000 01000000 10000000 */
static int ok(uint64_t t, int idx)
{
int y = idx / 8;
int x = idx - y * 8;
int d1 = x - y;
int d2 = x + y - 7;
return !(t & ((MLI << y * 8) | (MCL << x)
| (d1 > 0 ? (MD1 & ~0ULL >> 8 * d1) << d1 : (MD1 & ~0ULL << 8 * -d1) >> -d1)
| (d2 > 0 ? (MD2 & ~0ULL << 8 * d2) << d2 : (MD2 & ~0ULL >> 8 * -d2) >> -d2)));
}
#define sq(i) do { t |= 1ULL << i; qleft--; } while (0)
#define rq(i) do { t &= ~(1ULL << i); qleft++; } while (0)
static int solve(uint64_t t, int qleft, int idx)
{
int n = 0;
if (idx == 64)
return 0;
if (ok(t, idx)) {
sq(idx);
if (qleft == 0) {
disp_board(t);
n = 1;
} else {
n = solve(t, qleft, (idx / 8 + 1) * 8);
}
rq(idx);
}
return n + solve(t, qleft, idx + 1);
}
int main()
{
printf("%d\n", solve(0, 8, 0));
return 0;
}
``````
index | 2,966 | 8,380 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.4375 | 3 | CC-MAIN-2021-39 | longest | en | 0.79114 |
https://www.carboncollective.co/sustainable-investing/free-cash-flow-to-equity | 1,726,231,459,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725700651513.89/warc/CC-MAIN-20240913101949-20240913131949-00598.warc.gz | 637,571,504 | 29,380 | Free Cash Flow to Equity (FCFE) is a valuation metric that determines the amount of cash that is potentially available to equity shareholders after all the expenses of the company have been taken care of. Put simply, it is the amount of cash that the company generates after meeting various obligations such as capital expenditure, re-investment, debt, and other expense obligations.
## Free Cash Flow to Equity Formula
• Cash from Operations can be found in the Cash Flow statement under the “Cash from Operations” section
• Capital Expenditure can also be found in the Cash Flow statement under the “Cash from Investing” section
• Net borrowing can be calculated by subtracting the amount of debt repaid in the year from the total debt borrowed during the year. Both these figures can also be found in the Cash Flow statement under the “Cash from Investing” section.
If the cash flow statement is not readily available, we can calculate FCFE directly from the income statement of the company. This can be calculated in one of the following ways.
### From Net Income
The formula for FCFE can be rewritten as follows:
This is because:
• Net Income
• can be found at the bottom of the income statement
• Depreciation and amortization and other non-cash expenses can also be found on the income statement under the “Expenses” section
• Changes in Working capital are the net of current assets and current liabilities. Therefore, it could be either positive or negative. If changes in working capital are positive, add that amount else subtract it from the net figure.
• Current Assets are usually inventory and receivables while Current liabilities are payables and other accrued liabilities and all of them are listed in the balance sheet under the Current Assets and Current liabilities section respectively
• Net borrowings is the net of debt issued and debt repaid during the year and therefore can be both positive or negative. Debt includes both long-term and short-term debt and can be found in the balance sheet under the Liabilities section
### From Earnings before Income and Tax (EBIT)
We know that:
We also know that:
This means we can also rewrite the formula as:
EBIT can be found in the company’s income statement and both Interest and taxes will also be listed in the income statement below EBIT.
### From Earnings before Interest, Taxes, Depreciation, and Amortization (EBITDA)
EBITDA provides a better measure of the operating profitability of the company since it excludes depreciation and amortization expenses. We know that net income can be calculated using EBITDA through the following formula:
Substituting the above equation for net income in the FCFE formula, we get:
This can be rewritten as:
EBITDA can also be found in the income statement of the company.
## Free Cash Flow to Equity Example
You have been provided with the following details from Company A’s Balance Sheet and Income statement:
The company’s net income for the year 2019 is \$200 million. Find out the free cash flow to equity of the firm.
Since net income has been provided to us, let’s solve for FCFE using the formula:
• Net Income is \$200m
• Depreciation & Amortization for 2019 is \$15m
• Let’s now calculate the changes in Working Capital
• Difference in Current Assets = 100-150 = -50
• Difference in Current Liabilities = 30-30 = 0
• Therefore, change in working capital would be (-50-0) = -50
• Change in Capital Expenditure would be equal to 250-200 = 50
• Net borrowings would be the total of short term and long term debt
• Difference in short term debt = 40-30 =10
• Difference in long term debt = 30-20 = 10
• Net Borrowings = Short term Debt+Long term Debt = 10+10 = 20
From this we can see that company A has a positive FCFE of \$135m which is potentially available for equity shareholders.
## Free Cash Flow to Equity Analysis
Free Cash Flow to Equity is an alternative to the Dividend Discount Model for estimating the value of a firm under the Discounted Cash Flow (DCF) valuation model. The dividend Discount Model of valuation can be used only when a firm maintains a regular discount payout. But there are multiple companies that do not pay dividends regularly. Some of them despite being profitable does not pay dividends. Instead, they might reinvest the excess cash generated, back in the business either to sustain or increase the growth rate of the company. In such cases, it is impossible to value the company based on the Dividend Discount Model (DDM). Another disadvantage of using the DDM is that dividends paid by the company might not exactly reflect the true picture of the business capacity of the company.
FCFE was developed as an alternative to estimate the value of a firm since it uses equity as the basis for firm valuation. It is especially useful for calculating the value of a firm that pays little or no dividends. Using the FCFE, you can find out the Net Present Value of the company’s equity. Under the DCF model, this can be done by discounting the FCFE at the required rate of return on equity. We can now use this equity value to calculate the theoretical share price of the firm.
FCFE can also be used to find out if the firm is paying for stock buybacks and dividends using free cash flow available to equity holders or whether it is using debt to finance them. If the FCFE is less than the cost of dividend payments and stock buybacks, one can conclude that the company is using debt to finance the payments. Another possibility is that the company is issuing new shares or is using retained earnings of previous years to fund the same. You can find that out by noticing the difference in Share Capital and/or retained earnings between the current financial year and the previous financial year.
## Conclusion
To sum up:
• FCFE is used to determine the amount of cash that is potentially available to the equity shareholders of a company after meeting all its debt, re-investment, and expense obligations.
• FCFE is an alternative to the Dividend Discount Model for calculating the fair value of the stock of a company.
• FCFE is used to calculate the equity value of a firm under the DCF model, especially when the firm pays little or no dividends.
• FCFE can be used to find out if a firm is using debt to finance its stock repurchases or dividend payments
## Free Cash Flow to Equity Calculator
You can use the free cash flow to equity calculator below to easily find the amount of cash that is available to equity shareholders after expenses by entering the required numbers.
## FAQs
### 1. What is free cash flow to equity?
Free cash flow to equity (FCFE) is the cash generated by a company that is available to be paid to its equity shareholders after meeting all of its debt and reinvestment obligations. This is an important metric for estimating a company's value under the discounted cash flow (DCF) valuation model.
### 2. What is the formula of free cash flow to equity?
The formula for FCFE is: FCFE = Cash from Operations − Capital Expenditure (Capex) + Net Borrowing
• Cash from Operations can be found in the Cash Flow statement under the “Cash from Operations” section
• Capital Expenditure can also be found in the Cash Flow statement under the “Cash from Investing” section
• Net borrowing can be calculated by subtracting the amount of debt repaid in the year from the total debt borrowed during the year. Both these figures can also be found in the Cash Flow statement under the “Cash from Investing” section.
### 3. Is Free Cash Flow (FCF) the same as FCFE?
No, FCF is not the same as FCFE. Free cash flow (FCF) is the total cash generated by a company, including cash from operating activities, investing activities, and financing activities. However, FCFE only includes the cash generated by operations and investing activities (excluding financing activities). This is because the net borrowing used to calculate FCFE is the amount of debt that was repaid during the year, which is a financing activity.
### 4. When should a company use the free cash flow?
A company should use free cash flow when it wants to assess its ability to pay dividends, repurchase shares, or service debt. FCFE can also be used to estimate the value of a company under the discounted cash flow model.
### 5. What is an example of a free cash flow to equity?
An example of FCFE would be a company that generated \$100 million in cash from operations, spent \$50 million on capital Expenditures, and had net borrowing of \$10 million. In this case, the FCFE would be \$40 million (\$100 million − \$50 million + \$10 million).
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# Ameer Hamza
### Hong Kong Polytechnic University
Last seen: 4 meses hace Con actividad desde 2016
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Rescale Scores
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Verify Law of Large Numbers
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Who Has the Most Change?
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Must be in the front row...
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Replace Nonzero Numbers with 1
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subtract central cross
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*Description* Given an integer _X_, determine if it is a palindrome number. That is, _X_ is equal to the _X_ with the digits ...
casi 5 años hace | 1,605 | 5,773 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.140625 | 3 | CC-MAIN-2023-06 | latest | en | 0.48782 |
https://studymaterialcenter.in/question/if-a-and-b-are-the-roots-of-the-equation-2x-2x-1-1-then-b-is-equal-to-33548/ | 1,685,996,706,000,000,000 | text/html | crawl-data/CC-MAIN-2023-23/segments/1685224652161.52/warc/CC-MAIN-20230605185809-20230605215809-00362.warc.gz | 591,370,844 | 24,306 | # If a and b are the roots of the equation 2x(2x + 1) = 1, then b is equal to:
Question:
If $\alpha$ and $\beta$ are the roots of the equation $2 x(2 x+1)=1$, then $\beta$ is equal to:
1. $2 \alpha(\alpha+1)$
2. $-2 \alpha(\alpha+1)$
3. $2 \alpha(\alpha-1)$
4. $2 \alpha^{2}$
Correct Option: 2
JEE Main Previous Year 1 Question of JEE Main from Mathematics Complex Numbers and Quadratic Equations chapter.
JEE Main Previous Year Sep. 06, 2020 (II)
Solution:
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https://15worksheets.com/worksheet-category/subtracting-fractions/ | 1,721,288,887,000,000,000 | text/html | crawl-data/CC-MAIN-2024-30/segments/1720763514826.9/warc/CC-MAIN-20240718064851-20240718094851-00696.warc.gz | 59,765,175 | 35,175 | # Subtracting Fractions Worksheets
## All About These 15 Worksheets
This series of worksheets on subtracting fractions is a comprehensive and effective set of materials designed to help students master this essential math concept. Subtracting fractions is a critical skill that forms the foundation of many more advanced math topics, and these worksheets can provide students with ample practice and guidance to master this skill.
The worksheets are organized into several different sections, each of which focuses on a specific aspect of subtracting fractions. These sections include basic subtraction, subtracting mixed numbers, subtracting fractions with unlike denominators, and subtracting fractions with borrowing. The exercises are designed to be both challenging and engaging, with a variety of problems ranging from basic to advanced difficulty. The worksheets are suitable for use in a classroom setting or as homework, and they can be easily customized to meet the needs of individual students.
Overall, this series of worksheets on subtracting fractions is an excellent resource for learners of all ages and skill levels. With clear instructions, engaging problems, and ample practice opportunities, these materials are sure to help students master this critical math concept and build a strong foundation for future learning.
## How to subtract fractions
Subtracting fractions may seem a bit challenging at first, but with the right approach, it can be a straightforward process. Here’s a step-by-step process on how to subtract fractions that teachers can guide their students through.
Step 1: Find a common denominator.
The first step is to make sure the fractions have a common denominator. If they don’t already have one, you’ll need to find the least common denominator (LCD). To do this, you’ll need to identify the factors of the denominators and find the least common multiple (LCM) of these factors. The LCM is the LCD.
Step 2: Convert the fractions.
Once you’ve found the common denominator, convert each fraction so that they have the same denominator. To do this, multiply both the numerator and denominator of each fraction by the same factor. The factor is usually the denominator of the other fraction.
Step 3: Subtract the numerators.
Now that the fractions have the same denominator, you can simply subtract the numerators. Be sure to keep the denominator the same. For example, to subtract 2/5 from 3/4, you would find the common denominator of 20, convert both fractions to have a denominator of 20 (3/4 becomes 15/20 and 2/5 becomes 8/20), and then subtract the numerators: 15/20 – 8/20 = 7/20. | 529 | 2,639 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.78125 | 5 | CC-MAIN-2024-30 | latest | en | 0.936379 |
http://mathhelpforum.com/algebra/124301-algebra-quadratic-formula-word-problem-print.html | 1,503,184,216,000,000,000 | text/html | crawl-data/CC-MAIN-2017-34/segments/1502886105927.27/warc/CC-MAIN-20170819220657-20170820000657-00124.warc.gz | 265,514,987 | 4,135 | # Algebra quadratic formula word problem
• Jan 18th 2010, 01:11 PM
lightstevoo
I have two problems I am new here and I want to see how this site works...
so...
#1. two positive real numbers have a sum of 5 and product of 5. Find the numbers.
2. A rectangular animal pen with area 1200m^2 has one side along a barn. The other three sides are enclosed by 100m of fencing. Find the dimensions of the pen.
• Jan 18th 2010, 01:24 PM
General
Quote:
Originally Posted by lightstevoo
I have two problems I am new here and I want to see how this site works...
so...
#1. two positive real numbers have a sum of 5 and product of 5. Find the numbers.
2. A rectangular animal pen with area 1200m^2 has one side along a barn. The other three sides are enclosed by 100m of fencing. Find the dimensions of the pen.
Try to obtain equations from your problems.
For the first one:
Let a be the first number, and b be the second number,
thier sum = 5 $\implies a+b=5 .... (1)$
thier product = 5 $\implies ab=5 .... (2)$
Now, If we subtract a from the both sides in equation (1), we will get:
$b = 5 - a .... (3)$
By substituting (3) in (2), we get:
$a(5-a)=5$
$5a-a^2=5$
Now, Solve the last quadratic equation for a.
Once you have the values of a, substitute them in (3) to obtain the value of b.
Do not remember to reject the negative values; because the question said that : the two numbers are positive.
I will leave the second for you.
Try to obtain some equations from it.
• Jan 18th 2010, 01:29 PM
pickslides
Hi there lightstevoo, welcome to MHF!
Quote:
Originally Posted by lightstevoo
I have two problems I am new here and I want to see how this site works...
so...
On this forum we try to 'help' you solve the problem not just solve it for you.
Quote:
Originally Posted by lightstevoo
#1. two positive real numbers have a sum of 5 and product of 5. Find the numbers.
Lets say your numbers are $x$ and $y$. From the problem
$x+y = 5$
and
$x\times y = 5$
The first statement can be writtien as
$x = 5-y$
Lets use that to put into the secons statement which becomes
$(5-y)\times y = 5$
Now you need to exapnd this and solve
$5y-y^2 = 5$
Have a go from here
Quote:
Originally Posted by lightstevoo
2. A rectangular animal pen with area 1200m^2 has one side along a barn. The other three sides are enclosed by 100m of fencing. Find the dimensions of the pen.
This is similar to the first
Lets call the $x$ the length and $y$ the width. As one side (lets call it the width of your triangle) of your rectangle is the barn then only 3 sides need to be fenced.
So you have
$x+x+y= 100$
and
$x\times y = 1200$
The first statement can be writtien as
$2x+y= 100$ then $y= 100-2x$
Can you take it from here?
(Sleepy)
• Jan 18th 2010, 01:31 PM
Q1.
$(x-a)(x-b)=x^2-(a+b)x+ab=x^2-5x+5$
$a\ and\ b\ are\ \frac{5+\sqrt{25-20}}{2}\ and\ \frac{5-\sqrt{25-20}}{2}$
Q2.
The barn side dimensions are
$x,\ 50-\frac{x}{2}$
Use the area to solve for x.
• Jan 18th 2010, 01:52 PM
lightstevoo
thank you
i got the answer thanks to you guys
so ㅡㅡㅡ ㅡ ㅡ ㅡ
l l
x l l x
l l
l l
ㅡ ㅡ ㅡ ㅡ ㅡ ㅡ
100-2x
(100-2x)x= 1200
x^2-50x+600
and then you do the quadratic formula.
20, and 30
then you plug it in
30,40
20, 60
thank you!
• Jan 18th 2010, 01:53 PM
lightstevoo
yes and i got it thank you!
emm
5 plus or minus radiacal 5 /2
• Jan 18th 2010, 02:28 PM
I hope my pen dimensions were not confusing, lightstevoo.
My x was the side against the barn.
• Jan 18th 2010, 02:29 PM
Jameson
Quote:
Originally Posted by lightstevoo
yes and i got it thank you!
emm | 1,134 | 3,546 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 21, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.28125 | 4 | CC-MAIN-2017-34 | longest | en | 0.923132 |
https://www.scribd.com/document/346483630/matrix-review-worksheet | 1,542,459,393,000,000,000 | text/html | crawl-data/CC-MAIN-2018-47/segments/1542039743521.59/warc/CC-MAIN-20181117123417-20181117145417-00295.warc.gz | 1,017,913,315 | 31,890 | You are on page 1of 4
# Matrix Review Worksheet
Name______________________________________ Name__________________________________
For questions 1 - 4 refer to the following matrices.
3 1
2 0 2 1 6 8
A =
B =
4 0 3 2
1 4
1. What are the dimensions of A? 2. What are the dimensions of B?
3. What is A22 ? 4. What is B21 ?
For questions 5 - 14, refer to the following matrices.
3 1
2 0 2 1 6 8 1
1 2
4 0 3 2
2 4
3 2
C =
A = B = D = E = 2 1 6
0 1 4
0 3 0
1
1 4
2 1
1 8
G = 3 1
0
1 1
3
F = H = 2 0
0 2
0 4 0
0 4
Find the following.
5. 3A 6. ½ D
7. F - 2D 8. D + 3F
9. DB 10. EH
11. F2 12. AF
13. |D| 14. |E|
For questions 15 - 20, refer to the following matrices.
3 1 2 0 5 2 2 1
A = B = C = D=
4 1 1 3 15 6 3 1
15. Find the inverse of A. 16. Find the inverse of B.
Find the missing matrix.
1 0 11 2
17. EA = 18. AF =
0 1 17 2
1 3
19. GD = 9
2 2
20. BL =
13
2 1
For questions 21 & 22, solve each system of equations by using Cramer’s rule.
21. 2x - 3y = 32 22. 2x + y - z = 15
x + 4y = -20 4x - 3y + 7z = -11
x + y + z = 2
For questions 23 - 24, solve each system of equations by using the inverse matrix method.
23. x + 4y = -19 24. x + 4y = -2
-3x + 2y = -13 -3x + 2y = 6
\$ \$ \$
1300 1400 1600
Sofa and love seat Sofa and two chairs Sofa, love seat, one chair
How much does each piece of furniture cost individually?
26. The table below shows the percent of comedies, drama, and action videos available at a video
store. Assume that the store has a collection of 3,405 general videos to be rented, 1,070
children’s videos to be rented, and 1,225 videos for sale. Write and solve a system of equations
to find out how many comedies, dramas, and action movies are at the store.
Store Section
Comedy Drama Action
General rental
55% 65% 60%
Children’s rental
25% 10% 20%
Videos for sale 20% 25% 20% | 1,235 | 2,074 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.25 | 3 | CC-MAIN-2018-47 | latest | en | 0.674048 |
yfcv.istitutocomprensivoascea.it | 1,600,491,156,000,000,000 | text/html | crawl-data/CC-MAIN-2020-40/segments/1600400190270.10/warc/CC-MAIN-20200919044311-20200919074311-00211.warc.gz | 256,139,747 | 22,559 | # Thin Walled Cylinder Stress Problems
Shahani and Nabavi [16] solved the transient thermal stress problem for a hollow cylinder analytically, using finite the Hankel. The most desirable among the pre-1987 blocks, are the “high-nickel” ones. 1-prediction of both hoop and longitudinal stress in the thin-walled cylinder. If the cylinder bore is worn and can't be re-bored to a uniform diameter, the external piston ring diameter should be the same as the smallest diameter of the bore (usually crank shaft end) - to avoid possible ring breakage due to an insufficient expansion gap. 2: Flow near a wall suddenly set in motion (approximate solution) Problem 4D. When the maximum stress, which in th is case lies inside the cylinder, surpasses the yield point, yielding will occur with a corresponding deformation and the stress curve will be given by Fig. 2 Geometry for °ow through a rectangular duct. If a factor of safety 4 was used in the design, what is the ultimate tensile stress in the pipe material? (Ans ?C100 MPa, ?L50. Roll forming of channels is a continuous alternative to a discrete channel bending process, such as the one illustrated in figure 269. Considering an element of material: H will cause strains of:-. It doesn't have to stretch until it becomes "thin" before it fails. 7) Slide No. Thin Shells of menting problem solutions on a programmable calculator, or espe-cially, a personal computer. I'm trying to find shear stress, which should come only as a result of the 40kN from the collar correct? Need Help With Thin Walled Pressure Vessel Problem. thin-walled beam theory, on one hand [12, 13], and the basic assumptions of the optimum design on the other [1-5]. So the Diameter to thickness ratio is more than 100. Peterson 9. A wide variety of panelized metal wall systems are available for installation as a buildings exterior wall cladding. Stress intensity factor for a circumferential crack in a finite-length thin to thick-walled cylinder under an arbitrary biquadratic stress distribution on the crack surfaces From Fig. The end result is a cylinder. Also, unlike thin cylinders, the radial stress in thick cylinders are not small but instead, varies from inner surface where it is equal to the magnitude of the fluid pressure to the outer surface where. Not surprisingly, problems with pile driving usually are related to adverse or unexpected soil conditions, which can lead to pile damage, hammer-pile alignment problems, and other issues. A wide selection of hot water cylinders in a range of materials for various heating systems. Generally, an indirect hot water cylinder will be heated by a coil with an immersion heater(s) as a back-up heat source. If the cylinder has closed ends, the axial stress can be found separately using only force equilibrium considerations as was done for the thin walled cylinder. Calculate changes in diameter and volume due to pressure. Often, these horses will be more tender following a trim than before, leaving horse owners upset and wondering if their farrier/trimmer trimmed their horse too short. To calculate hoop stress just multiply internal pressure (MPa) and internal diameter (mm), thickness (mm) with 2(two) and. This plant had a high economic value and widely demanded throughout the world for the usage of the nicotine, cigarettes, cigars and other tobacco product (Akerhust, 1981). stresses and the maximum shearing stress. (b) Maximum Distortion Energy Theory. Note that for the radial stress distributions, the maximum and minimum values occur, respectively, at the outer wall (σ r =0) and at the (σ r =-p) as noted already for the thin walled pressure vessel. Matoković, Bending of Thin-Walled Beams of Symmetrical B. Tensile stress. Thin Walled Cylinders and Spheres; Circular Plates; Compound Stress and StrainPart 2; Compound Stress and Strain part 1; Curved Beams; Direct Stress; Direct Stress and Strain; Elastic Constants; Notations; Plastic Theory of Bending; Rotating Discs and Cylinders; Shear Force and Bending Moment; Shear Stress. Stresses in Thick-Walled Cylinders • Thick-Walled cylinders have an average radius less than 20 times the wall thickness. It may be that even if you’re able to have a friendly conversation with her and she’s. If the object/vessel has walls with a thickness greater than one-tenth of the overall diameter, then these objects can be assumed to be ‘thick-walled’. In this study an analytical solution for elastic thin-walled cylinder-truncated cone shell intersection under internal pressure is presented. With single-acting cylinders, the piston rod is usually loaded in push-only mode so that fatigue is. Having cracks appear on your wall may just be a cosmetic problem, or it could indicate a more serious, structural issue. Failure occurs when the von Mises stress exceeds the material's 0. Thin Walled Cylinders 2. Shear Flow from Shear Stress. Typical shear stress and pressure distributions are shown in Fig. a) We need to find all three principal stresses to substitute into von Mises criterion; using thin walled pressure vessel theory we get: and substituting these values into the von Mises yield criterion gives: hence meeting the criterion, thus failure would NOT have been expected on the basis of yield. 1-prediction of both hoop and longitudinal stress in the thin-walled cylinder. Nowadays, in Malaysia, Tobacco industry is very crucial in uplifting the socio. For a hollow shaft 32 D d J 4. Driving Stress: 0. 01949 m = 19. 47, but now fixed axially and rotated inside the sleeve. C h_refine - Mesh refinement to increase the solution accuracy. (a) Normal Stress. 3 equation for the displacement stress. The width and height is taken to the center of each wall. Wall Stresses in a Sphere (under pressure) Cut again: total force (to the left) due to pressure = πr2P (not shown, but can be obtained by integrating horizontal terms over entire hemispherical area) equating: 2πrtτ wall= πr2P Note - this is the same as a cylinder axial stress which is half the cylinder hoop stress. NASA Techinal Note D-271: Analysis of Elactic-Plastic Stress Distribution in Thin-Wall Cylinders and Spheres Subjected to internal Pressure [Donald F. 01949 m = 19. Figure 1: Thin wall cylinder schematic with cross. The second term, which comes from the bending stress dose not appear in the case of the cylinder as there is no bending. This specification results from the effort to make walls as thin as possible is a natural optimization strategy to reduce dead weight and to minimize. [13] have established displacement function , temperature distribution and stresses of a semi-infinite cylinder. Magnetic Tape Essay Magnetic tape is a medium for magnetic recording, made of a thin magnetizable coating on a long, narrow strip of plastic film. Solve problems involving the compression of fluids into pressure vessels. Theoretical and numerical methods used to. Homework Statement A long cylindrical boiler shell is 1. Thin Shells of Revolution under Distributed Loadings Producing Membrane Stresses Only. By thin wall pressure vessel we will mean a container whose wall thickness is less than 1/10 of the. 0 cm and diameter 28. It is subjected to an internal pressure of 3. The wall has a thickness of 0. pricefrom 7. 6 MPa in Eq. Stress Intensity Factor for a Thin-Walled Cylinder Containing an Edge Circumferential Crack under Bending Home Applied Mechanics and Materials Advances in Structural Engineering Stress Intensity Factor for a Thin-Walled Cylinder Stress Intensity Factor for a Thin-Walled Cylinder Containing an Edge Circumferential Crack under Bending. tloel compressive stress E Young's modulxis. Theoretical and numerical methods used to. The result is the minimum wall thickness assuming ideal conditions. TORSION IN THIN WALLED VESSELS and THIN STRIPS 1. These are most readily available near the soil surface where precipitation infiltrates the soil and oxygen from the atmosphere diffuses into the porous soil. In their treatment. The failures that cylinders are designed against are stress dependent. For the thin walled equations below the wall thickness is less than 1/20 of tube or cylinder diameter. The cylinder has a 10 inch mean radius, sits 20 inches high and has a constant thickness of 0. Chapter 6 SOLUTION OF VISCOUS-FLOW PROBLEMS 6. SHAPE-THIN determines the effective cross-sections according to EN 1993-1-3 and EN 1993-1-5 for cold-formed sections. 1, 2017 Title 14 Aeronautics and Space Parts 110 to 199 Revised as of January 1, 2017 Containing a codification of documents of general applicability and future effect As of January 1, 2017. Solve circumferential, radial and longitudinal stresses in thick walled cylinders. Normally Caesar II is widely used for stress analysis of all piping systems. The two major thick walled storage and transport cask manufacturers are Areva (TN-24 series) and Siempelkamp (e. Determine the state of stress in the wall of the cylinder for both cases if the piston Pcauses the internal pressure to be 65 psi. Shear stress, often denoted by τ (Greek: tau), is the component of stress coplanar with a material cross section. This section deals with the related work done in the area of thick walled cylinders with and without holes subjected to varying internal pressure amplitudes. Final total thickness : t = q/ τ = (750 kN/m) / (350,000 kN/m 2) = 0. Shear on the Horizontal Face of a Beam Element. Stress Analysis of a Cantilevered Thin-Wall Cylinder within a Cylindrical Cavity 720285 A semiempirical procedure has been developed to determine the stresses in a thin-wall cylinder extending from a block cavity and subjected to cantilever loading. The change in diameter the cylinder can be determined using the formula for thermal linear expansion. The design incorporated both high strength 60 MPa (8. These are the stress intensity factor and the crack mouth opening displacement for a crack under uniform loading. For I and Z -sections s. this chapter cover several additional topics related to torsion, such statically indeterminate members, strain energy, thin-walled tube of noncircular section, stress concentration, and nonlinear behavior 3. on the buckling load of a thin cylinder under an applied. 1, where t is the wall thickness and r is the internal radius of either the sphere or cylinder. Thin−Walled Cylinders And Spheres. The stress calculated is the tangential stress. On the other hand, as opposition to the thin wall assumption or membrane theory, there is the curved plate or thick wall pipe formulas derived from Lame´s theory whose use is more complicated, sometimes with iterations, and requires a careful approach like, for instance, in ASME B 31. La Crosse Technology WT-3143A-INT 14-Inch Atomic Wall Clock. D is the outer diameter and d the inner diameter. Stress is the average amount of force exerted per unit area. Non-Structural Cracks – Non-structural wall cracks can occur almost anywhere in a foundation wall; they are likely to emanate from openings in the wall, like windows, doors and pipe intrusions. The hoop stress for the thin walled cylinder can be calculated the second analyzes a few general problems, such as stresses of the membrane. You’ve finally found it… the “treasure map” to building an unstoppable career or business in the cannabis industry. analyze thick and thin cylinder through stress-strain diagram: Stresses in thick cylinders For thick cylinders such as guns, pipes to hydraulic presses, high pressure hydraulic pipes the wall thickness is relatively large and the stress variation across the thickness is also significant. Von Mises stress The von Mises stress is a combination of the three principal stresses (axial, radial, tangential/hoop) and the shear stress caused by torque. Shahani and Nabavi [16] solved the transient thermal stress problem for a hollow cylinder analytically, using finite the Hankel. the resulting thermal stresses in pipes, two solids namely; steel and cooper and three fluids namely; water, coolanol-25, and mercury are used in the study. For reasons of symmetry, all four normal stresses on a small stress element in the wall must be identical. The cylinder has inner radius r = 2. Typical shear stress and pressure distributions are shown in Fig. Poisson's ratio will typically be between 0 to 0. A woman gave birth to a healthy 7-pound, 13-ounce infant girl. , • For the thin-wall pressure vessels where D >> t, the cylindrical cross-section area may be approximated by πDt. The primary criterion for consideration of papers in Thin-Walled Structures is that they must be concerned with thin-walled structures or the basic problems inherent in thin-walled structures. As a general rule, pressure vessels are considered to be thin -walled when the ratio of. Thick Cylinder Subjected to Internal Pressure Only [8] From the follow equilibrium equation for thick cylinder dr r dðsr ð=ðsðqð-ðsr. KEY POINTS TO REMEMBER A cylinder is said to be 'THIN' if the ratio of its inner diameter to the thickness of wall is more than 20. Evaluation with an. Note that for the radial stress distributions, the maximum and minimum values occur, respectively, at the outer wall (σ r =0) and at the (σ r =-p) as noted already for the thin walled pressure vessel. As an added bonus this analysis works for any regular polygon:. Shear stress, often denoted by τ (Greek: tau), is the component of stress coplanar with a material cross section. Circumstances and General State of Stress. Matoković, Bending of Thin-Walled Beams of Symmetrical B. BENDING STRESS. Increase of the outer radius of the hoop All calculations assume zero external pressure. Generally, a pressure vessel is considered to be "thin-walled" if its radius r is larger than 5 times its wall thickness t (r > 5 · t). circumferential) direction. l), and also that there is no pressure gradient across the wall. An empirical equation is given for the buckling of cylinders having. The thin cylindrical shell structures are prone to a large number of imperfections, due to their manufacturing difficulties. His solution very logically assumed that a thick cylinder to consist of series of thin cylinders such that each exerts pressure on the other. And wall thickness t = 0. This plant had a high economic value and widely demanded throughout the world for the usage of the nicotine, cigarettes, cigars and other tobacco product (Akerhust, 1981). A pressure vessel is assumed to be a thin walled pressure vessel when the thickness of the vessel is less than 1/20 of its radius. A major difference between a thick and a thin wall cross-section, is that the shear stresses for thin-walled beams are always aligned with the median line of the cross-section, see the figure below. The most desirable among the pre-1987 blocks, are the “high-nickel” ones. TANGENTIAL STRESS, σ t (Circumferential Stress) Consider the tank shown being subjected to an internal pressure p. The expression can be derived from the Lamé equation for tangential stress by making the thin-wall assumption that D/t >> 1. The theoretical results gave good correlation with existing experimental data. Online Thin Walled Circle Property Calculator. Consider a thick walled cylinder having an inner radius = a; outer radius = b. Correct analyses of stability of thin-walled structures can prevent many problems and save a lot of money in the future. The magnitude of pressure a vessel can withstand is predicted with the von Mises combined stress model. Also compute the radial stress at the mid-thickness. Pressure and weight i. The pelvis provides a solid platform for the spine—whether the spine is hoisting the body upright or bending it forward, the pelvis will provide the fulcrum for the movement. All plants need water, oxygen, and nutrients. Non-Structural Cracks – Non-structural wall cracks can occur almost anywhere in a foundation wall; they are likely to emanate from openings in the wall, like windows, doors and pipe intrusions. A thin walled cylinder has a wall thickness < r/10, with r being the radius of the cylinder. stresses and the maximum shearing stress. Divided by 2. 3: Creeping flow around a spherical bubble: Problem 4D. critical axial stress for a cylinder with an elastic core axial stress circumferential stress shear stress torsional buckling stress of an unfilled cylinder shear stress in the x-y plane. NR 302 Exam: Chamberlain University The nurse is interviewing the client. In this course I will be discussing about Thin And Thick Cylinders And Spheres,Stresses in Thin Cylinders, Expression For Hoop and Longitudinal Stresses, Various Numerical Problems, Efficiency of a joint,wire winding of thin Cylinders,Thick Cylinders. 2 Geometry for °ow through a rectangular duct. The resulting stresses and expansion of the vessels are calculated by this calculator. The study of the behavior of a thin-walled cylinder under. Determine the maximum shearing stresses and associated normal stresses in the cylindrical wall. 3 Stress Concentration as a Two-Dimensional Problem 10 1. The nurse is aware that the initiation of breastfeeding is most effective during the first 30 minutes after birth. Axisymmetric Problems. If the cylinder has closed ends, the axial stress can be found separately using only force equilibrium considerations as was done for the thin walled cylinder. () 2 ()/ 2 / , Newtonian fluid zzrrrL vrzL θθ θ τ τπµ π ==−Ω =Ω The stress is a function of the radius and if the fluid is non-Newtonian, the viscosity may be changing with radial position. Name the stresses induced in a thin walled cylinder subjected to internal fluid pressure. The plastic instability of thin-walled tubes subjected to internal pressure and independent axial load is investigated. This compares very well to the value of -10,000 Pa predicted by the analytical theory for Thick Walled cylinders subjected to internal pressure. ANALYSIS OF RESIDUAL STRESSES AND DISTORTIONS IN CIRCUMFERENTIALLY WELDED THIN-WALLED CYLINDERS: Authors: QURESHI, MUHAMMAD EJAZ: Keywords: Technology Engineering & allied operations Mechanical engineering Civil engineering Other branches of engineering: Issue Date: 2008: Publisher: NATIONAL UNIVERSITY OF SCIENCES & TECHNOLOGY, PAKISTAN. Thin Shells of menting problem solutions on a programmable calculator, or espe-cially, a personal computer. The wall has a thickness of 0. And so that's the method that we're going to use as we move along and analyze and design thin walled pressure vessels. Homework Statement A long cylindrical boiler shell is 1. and the inner diameter of the cylinder is 8 in. Stress-Strain Relations As you will be measuring strains in our thin-wall vessel, you will need to convert them to stresses. distribution, displacement function, and stresses of a thin as well as thick hollow cylinder and Khobragade et al. The nurse is aware that the initiation of breastfeeding is most effective during the first 30 minutes after birth. The pressure P o acts on area given by πr o 2. Stress tests, nuclear and otherwise, are helpful for identifying areas of poor blood flow. 2 Thin Walled Cylinders The analysis of a thin-walled internally-pressurised cylindrical vessel is similar to that of the spherical vessel. If you have any problem locating or obtaining a copy of material listed in the Finding Aids of this volume as an approved incorporation by reference, please contact the agency that issued the regulation containing that incorporation. Magnetic Tape Essay Magnetic tape is a medium for magnetic recording, made of a thin magnetizable coating on a long, narrow strip of plastic film. shear stresses, and there is no necessary relation between the two viscosities. Suggestion: Use the result of Example 23. the bending limit of the thin-walled tube are improved evidently with internal pressure increasing. 18), using the initial data. NSG6430 Exam Study Guide / NSG 6430 Exam Question Bank (Latest): South University South University NSG6430 Exam Study Guide for Final and Midterm / South University NSG 6430 Exam Question Bank for Final and Midterm • Abnormal uterine bleeding (AUB) has multiple causes. To relate stress and strain distributions to material properties and cylinder geometry. The basic difference between the two is that in Thick wall Raidal stresses are also there in addition to Hoop and longitudinal stresses. 726 m and its mass is m = 1. Open thin-walled steel sections subjected to twisting moments are generally prone to large warping stresses and excessive angles of twist. [16] have established displacement function, temperature distribution and stresses of a semi-infinite cylinder. PETER VAN DYKE ; PETER VAN DYKE. Sharp cracks 11. E (steel)= 200 GPa. • The principal stresses are circumferential (hoop) σ c, radial σ r, and longitudinal (axial) σ l. This specification results from the effort to make walls as thin as possible is a natural optimization strategy to reduce dead weight and to minimize. The failures that cylinders are designed against are stress dependent. at in SolidWorks and one does need a good baseline from which to start. If the cylinder bore is worn and can't be re-bored to a uniform diameter, the external piston ring diameter should be the same as the smallest diameter of the bore (usually crank shaft end) - to avoid possible ring breakage due to an insufficient expansion gap. The material is Fig. com Argentina Calle 14 nro. The minimum cylinder wall thickness (in mm) for safe design must be ____. Elastoplastic stress state of a long thin-walled cylinder under the influence of a magnetic field. Section 5: Thin-Walled Pressure Vessels Thin-walled pressure vessels are defined as having the ratio t/r ≤ 0. Stress Analysis of Thin-Walled Pressure Vessels. It is proposed to conduct stress analysis of thick walled cylinder and composite tubes (Shrink fits) subjected to internal and external pressure. • Therefore, the longitudinal stress in the cylinder is given by: t pD Dt D p A P l 4 4 2. Question: HW Problem 2 A Thin-walled Hollow Cylinder Is Subjected To An Axial Force N= 7. The can's moment of inertia is: The moment of inertia of the empty soup can is approximately. The stresses on the outside surface of a thin-walled pressure vessel are shown in Fig. Stresses in Thick-Walled Cylinders • Thick-Walled cylinders have an average radius less than 20 times the wall thickness. to/2SRJWkQ 2) Circle/Angle Maker https://amzn. Author(s) James P. There is no friction anywhere in the problem. Similar to what we would see in the skin panels of aircraft. its like trying to machine a big tin can! Im trying to hold very tight tolerances on the diameter and im having trouble. The resulting stresses and expansion of the vessels are calculated by this calculator. In the present paper, an attempt is made to study the theoretical solution for a thermoelastic problem to. Calculate the hoop and longitudinal stresses induced in the pipe material. SHAPE-THIN determines the effective cross-sections according to EN 1993-1-3 and EN 1993-1-5 for cold-formed sections. The magnitude of the radial stress is usually small when compared with the longitudinal and hoop stresses; consequently it is not specifically limited by the design codes. stresses serve to reduce the tensile stresses developed as a result of subsequent application of an operating pressure, thus increasing the load beari ng capacity [1, 2]. Common Stress Problems in Thin Walled Pressure Vessels. length having simply supported edges is cr-c. Stresses in thin- walled cylinders. ) t―wall thickness (in. P (a)(b) P. According to theory, Thin-wall Theory is justified for In practice, typically use a less conservative rule, State of Stress Definition 1. P=internal pressure of cylinder, P a. (b) Determine the outside diameter required to give the same outer surface stress if a hollow shaft of inside diameter 0. The stress acting at a point on a specific plane is a vector. Then equation (1. this chapter cover several additional topics related to torsion, such statically indeterminate members, strain energy, thin-walled tube of noncircular section, stress concentration, and nonlinear behavior 3. Longitudinal Shear on a Beam Element of. 1 The shape and method of stressing. It is subjected to an internal pressure of 3. 4 Stress Concentration as a Three-Dimensional Problem 11 1. If bending stress exceeds the materials yield strength it will be permanently deformed and not return to its original shape. In this example problem we consider the overall deformation and failure behavior of a thin-wall, double-chambered aluminum extrusion under quasi-static three-point bending and dynamic axial loading conditions. If the inner radius of the vessel is 20 cm and the outer radius is 40 cm, both circumferences will grow ~6. AE 3610 Transient Stress Measurements in Thin-Wall Pressure Vessel 3 p t R L 2. Spherical Pressure Vessels Shell structures: When pressure vessels have walls that are thin in comparison to their radii and length. Hoop Stress: Wall thickness. The first thing is torsion. If the cylinder has a wall thickness of 2 mm, determine the. Thin Walled Cylinder Hoop Stress Calculator. (b) Stresses produced by the combination of shrink-fit and internal pressure. K c is referred to as the fracture toughness of the material. For example, at (,), = The out-of-plane displacements can be obtained by solving for the warping function. and lower buckling stresses can be established for dead-weight loading. It clearly shows the principles, theories and analytical techniques, and provides effective, practical support to studies. It is therefore a common practice to avoid twisting moments in steel assemblies. Fort Lauderdale, FL 33322 Ted. Notes: Thin-walled pressure vessel is a condition where the thickness of the wall is negligible in comparison to other significant dimensions. at intersection of the two straight limbs, i. INTRODUCTION. We assume that the beam’s material is linear-elastic (i. Usually large scale yielding occurs in the autofrettaged thick-walled cylinder wall [3]. Reducing Stress Concentration Around a Hole in a Thin-Wall Cylinder Subjected to Internal Pressure Using Piezoelectric Patches. Find the maximum hoop stress in the material and the radial and hoop stress at a point in the barrel 19 mm from the inner surface when the fluid pressure inside the cylinder is 9. The results of this analysis allow one to the determination of the stresses and distortions for the case of thick walled cylinder. 1" but for shear stress is not useful because it seem that our formula for shear stress is not the same like RSAP one - and we could not find RSAP formula for thin walled cross section shear stress in HELP system. Consequently, most designers of hydraulic cylinders will strive, insofar as possible, to avoid side loading. To analyze thin-walled tubes, the concept of shear flow, q, needs to be understood. critical axial stress for a cylinder with an elastic core axial stress circumferential stress shear stress torsional buckling stress of an unfilled cylinder shear stress in the x-y plane. Piston and cylinder, in mechanical engineering, sliding cylinder with a closed head (the piston) that is moved reciprocally in a slightly larger cylindrical chamber (the cylinder) by or against pressure of a fluid, as in an engine or pump. A thin rectangular plate under a uniaxial tension has a uniform stress distribution. Cylindrical Pressure Vessel Uniform Axial Load Equation and Calculator. Circumferential stress and longitudinal stress. Hoop (Circumferential) Stress. The cylinder is subjected to an internal pressure of 300 MPa. 6, a guideline βH⩾5 (which Labbens et al. 320 m, but maintaining the same mass, which pulley design would give the fastest speed for the 4. A wide variety of panelized metal wall systems are available for installation as a buildings exterior wall cladding. Points A and B are on a circular part of the track having radius R. Stress-Strain Relations As you will be measuring strains in our thin-wall vessel, you will need to convert them to stresses. Everything I've read points to under-extrusion being the cause, but it seems odd that everything but cylinders would print just fine. 4 Stress Concentration as a Three-Dimensional Problem 11 1. Question: HW Problem 2 A Thin-walled Hollow Cylinder Is Subjected To An Axial Force N= 7. The edge where a boss meets the nominal wall should be radiused to reduce the sharp corner without increasing the wall thickness enough that it creates a sink problem. Three cylinder geometries were considered; defined by the pipe radius (R) to wall thickness (t) ratios: R/t = 5, 10, and. On arrival, chest compressions are being performed and 2 operators are mask ventilating the patient. The present study is carried out under conditions of plane stress, according to the thin-walled shell assumption. Closed thin-walled sections are widely used in structures subjected to torsional moments because compared to other sections, they can resist torsional stress and deformations more efficiently. Heat and matter flow 15. If K c is known the following can be derived from the equation: The crack length, a, that will result in fast fracture for a given applied stress. Prepared By: Muhammad Farooq. The inner radius of the cylinder is 2 m with a wall thickness of 20 mm. Chapter 8 Lecture Problems Problem 8-10 The A-36 steel band is 2 in wide and is secured around the smooth rigid cylinder. We start to actually solve thin-walled pressure vessel problems. Thick walled casks do not have the thin canister problems. Points A and B are on a circular part of the track having radius R. &sigma = (M x y)/I x. Find the direct stress acting in the direction perpendicular to the weld line. Thick Cylinders • The problem of determination of stresses in a thick cylinders was first attempted more than 160 years ago by a French mathematician Lame in 1833. Many problems of practical importance are concerned with solids of revolution which are deformed symmetrically with respect to the axis of revolution. Empirical design curves are presented for the critical stress of thin-walled cylinders loaded in axial compression. The concept of transition theory based on Lebesgue strain measure has been used to simplify the constitutive equations. 4(a) and Fig. 3\u201394 to A pressure cylinder has an outer diameter do, wall thickness t, internal pressure pi, and maximum 3\u201396 allowable shear stress \u3c4max. The pelvis provides a solid platform for the spine—whether the spine is hoisting the body upright or bending it forward, the pelvis will provide the fulcrum for the movement. Longitudinal Shear on a Beam Element of. Stresses in thin- walled cylinders. This set of Strength of Materials Multiple Choice Questions & Answers (MCQs) focuses on “Bending Stress”. relatively thin walled (. Finite element analysis of stresses in beam structures 4 1 PREFACE Determining of stresses in beam structures is standard teaching material in basic courses on mechanics of materials and structural mechanics [1], [2]. 7 , we analyzed the motion of a block sliding down a frictionless incline. It needs to be done in three steps. Vaginal Problems That Affect Your Sex Life. A woman gave birth to a healthy 7-pound, 13-ounce infant girl. Using Tresca and Von Mises yield criteria, determine the maximum allowable gas pressure pmax so that no yielding occurs. Further Discussion of the Distribution of Stresses in a Sample Problem 6. Note that for the radial stress distributions, the maximum and minimum values occur, respectively, at the outer wall (σ r =0) and at the (σ r =-p) as noted already for the thin walled pressure vessel. Likewise, to restore the cylinders to like-new dimensions, all the cylinders in the block can be re-sleeved if all of the cylinders are heavily worn. Author(s) James P. Plane Stress Examples. The effects of the internal pres-sure on the section distortion, the wall thickness distribution and the bending limit are investigated. This is because shear and torsion generate shear flow through the cross-section, as seen below:. We start to actually solve thin-walled pressure vessel problems. The magnitude of the radial stress is usually small when compared with the longitudinal and hoop stresses; consequently it is not specifically limited by the design codes. P=internal pressure of cylinder, P a. Contact stresses 9. Physiologic and Behavioral Adaptations of the Newborn 1. Torsional Stress. Problems 384. Note: Used for vessels with inner radiuses larger than five times it's wall thickness; e. In the cylinder below, the only stress acting on. 7 Thin-Wall Circular Cylinders 378. Everything I've read points to under-extrusion being the cause, but it seems odd that everything but cylinders would print just fine. The value given "by the small-deflection theory for the "buckling stress of a thin-walled cylinder of moderate. Thin Walled Cylinder Hoop Stress Calculator. Their thickness is. sublayer, and make suitable assumptions about how the near- wall velocity prole behaves, in order to obtain the wall shear st ress. Problem: I want to calculate the stress in the walls of a hexagonal pressure vessel but I can't manage to get coherent results. The main component of this benchtop unit is a thin-walled metal cylinder. Investigation of the stresses and strains in a thin-walled cylinder under internal pressure; Cylinder usable as open pipe or as closed tank; Strain gauge application on cylinder surface at various angles; Hydraulic cylinder with hydraulic pump to generate pressure; Hermetically sealed hydraulic system, maintenance-free. This bending stress will dominate the expression for thin walled vessels to the point were it is likely they would just deform until they resembled a cylinder. Atthe surfacesofthevesselwall,aradialstress σ Consider a compound cylinder, one having a cylinder of brass fitted snugly inside another of steel as. In a thin wall pressure vessel, two significant stresses exist: the longitudinal stress and the hoop stress. From D onward the cylinder begins. a closed-form solution for transient pure thermal stresses in a thick-walled cylinder subjected to heating on the internal surface of the cylinder with convection to the surrounding external environment. (a) If the lateral surfaces of the rod are insulated, the heat transfer surface area of the cylindrical rod is the bottom or the top surface area of the rod, A = (PI (D^2)) /4. 67A106B C 3. The study of the behavior of a thin-walled cylinder under. Figure 6 – Hoop Stress. This is often called "membrane action". Not surprisingly, problems with pile driving usually are related to adverse or unexpected soil conditions, which can lead to pile damage, hammer-pile alignment problems, and other issues. The maximum bending stress is given by: where c is the centroidal distance of. ARLINGTON, Texas — There's plenty to eat and drink on most grocery store shelves. C h_refine - Mesh refinement to increase the solution accuracy. Thin Soles: diagnosis and treatment It is extremely common for a horse to be tender-footed simply due to thin soles. It Is Assumed That The Yield Stress Is Oy= 280 MPa, The Radius Is A = 1 M, And Wall Thickness Is T= 5x10-3 M. Determine the electric field at a point a distance d from the right side of the cylinder as shown in Figure P23. [16] have established displacement function, temperature distribution and stresses of a semi-infinite cylinder. For a hollow shaft 32 D d J 4. pressure, p, at the inner wall, and decreases through the wall to zero at the outer wall (plane stress condition) since the gage pressure there is zero. (crumpling) of the cylinder. A thin gas cylinder with an internal radius of 100 mm is subject to an internal pressure of 10 MPa. The nurse suggests that the client place the infant to her breast within 15 minutes after birth. stress is rotated 45 o from the faces of the element shown above. A thin-walled cylindrical pressure vessel of radius 120 mm and a wall thickness of 5 mm is subjected to an internal pressure of. 5 triangular 1. The cylinder will undergo pressure loading that will introduce hoop and longitudinal stresses on the surface of the material. Torsional Stress and Rotation of Thin-Walled Section Thin-walled sections can be analyzed for torsion using somewhat similar assumptions as for circular. The cylinder liner, serving as the inner wall of a cylinder, forms a sliding surface for the piston rings while retaining the lubricant within. Maybe a little thicker. Whether cracks occur on the finished surfaces of masonry, wood or metal stud walls, the most common cause is the movement of building materials. Stress Components in a Thick Walled Cylinder. Cylinder liners from older lower powered engines had a uniform wall thickness and the cooling was achieved by circulating cooling water through a space formed between liner and jacket. We see hollow cylinders every day in our day to day lives. 622 1/2 entre 44 y 45 La Plata (B1900AND), Buenos Aires Argentina +54-221-425-1266. In the table given, determine the appropriate value of x. A major difference between a thick and a thin wall cross-section, is that the shear stresses for thin-walled beams are always aligned with the median line of the cross-section, see the figure below. Problem: I want to calculate the stress in the walls of a hexagonal pressure vessel but I can't manage to get coherent results. Note the hoop stresses are twice the axial stresses. The defòrmed shape looks correct, so let's look closer at the computed solution. The value of the maximum. D is the outer diameter and d the inner diameter. It is sealed on one side with a piston which can be repositioned with a hand wheel. relatively thin walled (. the mean diameter D m = ( D i + D o)/2, as used in AS 1210, or ; the outside diameter D o (giving the so-called 'Barlow's formula'). Imperial Steel manufactures a wide assortment of thin wall steel tubing. If you have any problem locating or obtaining a copy of material listed in the Finding Aids of this volume as an approved incorporation by reference, please contact the agency that issued the regulation containing that incorporation. 2 Thin Walled Cylinders The analysis of a thin-walled internally-pressurised cylindrical vessel is similar to that of the spherical vessel. (e) Unequal cylinders crossed at right angles (f) Unequal diameter cylinders crossed with their axes at any angle (g) Sphere on a cylinder (h) Sphere inside a cylinder (i) Cylinders in contact along a line parallel to their axes and a cylinder on a plane IV. stress τ in the transverse section of a thin-walled hollow shaft (2) the distribution of the velocities v in water flowing through a closed channel of unit depth and variable width. 8 MPa As Shown In Fig. Usually large scale yielding occurs in the autofrettaged thick-walled cylinder wall [3]. Strength of Materials Questions Answers (SoM) – Civil Engineering MCQ 1) A thin walled cylindrical vessel of wall thickness ‘t’ and diameter ‘d’ is filled with gas to a gauge pressure of ‘p’. Principal Strain, (c) Tresca and (d) Von. Nonsingular boundary integral equations are derived for. From D onward the cylinder begins. The Figure 8. Other causes of thin uterine lining include inadequate blood flow, endometrial tissue damage, use of the medication clomid and long-term birth control use (containing progestins). PROBLEM 3 A gravity main 2m in diameter and 15mm in thickness. A hollow cylinder is one which is empty from inside and has some difference between the internal and external radius. Shear Stress in Beams and Sample Problem 6. The hoop stress distribution in the cylinder prior to introduction of the crack is arbitrary. Therefore, solutions based on Lame’s equations for values of tangential and radial stresses at both the inside and outside surfaces of a thick‐wall cylinder are. Usmle step 3 Question and Answers 2020 You are called emergently to the medical floor where a 66-year-old man was found to be minimally responsive. 3 code (Process Piping),and ASME B 31. of CEE;Uttara University// | Thin walled pressure vessel 6 Problem-1: A cylinder is 300 mm mean diameter with a wall 2 mm thick. 2: Flow near a wall suddenly set in motion (approximate solution) Problem 4D. , it is an ideal elastic material. Shear stress in beams. Lame's equations are used for determination of various stresses in Thick shell. A thin, light string is wrapped around the outer rim of a uniform hollow cylinder of mass 4. However, before examining stress plots, it is helpful to have some expectation of magnitudes associated with these two stresses. at centroid. A sphere is the theoretical ideal shape for a vessel that resists internal pressure. We can therefore say that fast fracture occurs when a critical stress intensity factor, K c, is reached, ie. l), and also that there is no pressure gradient across the wall. 29), has an inside diameter of 20mm, and has an outside diameter of 100mm. Stresses in thin- walled cylinders. and have the same sign. Considering an element of material: H will cause strains of:-. Calculate the stresses. dimensional problems turning thin walled Ti cylinder ( 35") dia. a) Open Ends Condition The cylinder in this condition has no end constraint and therefore the longitudinal component of stress L will be zero, but there will be some s train in this direction due to the Poisson effect. His past medical history is unclear but his arm band lists allergies to penicillin and sulfa medications. The problems of weld induced imperfections like residual stresses and shape change behavior evolve almost simultaneously with the introduction of welding as a joining method and harmful stresses. To relate failure. Thus, P 0 = p 0 at z= 0 and P L= p LˆgLat z= L, giving p 0p L+ ˆgL= P 0P L P. This makes it possible to create either the dual-axis stress state of a sealed container or the single-axis stress state of a tube. , where bending shear stresses cause zero torsional moment. Since the vessel is thin, the load due to the tensile stress in the wall is. In the determination of air on the surface of thin-walled cylindrical principal stress and principal strain, and the resistance strain measurement technique was used for the direct measurement. thin-walled structures with large diameters, and hence buckling may occur when they are subjected to wind loads at their empty or partially filled state. The change in diameter the cylinder can be determined using the formula for thermal linear expansion. The cylinder bore should be uniform in diameter throughout it's full length. Cylindrical Vessel Under Combined Loads. OnAllCylinders is an automotive blog powered by the gearheads and car enthusiasts at Summit Racing Equipment. A theoretical solution is_given for the critical_stress of thin-walled cylinders loaded in torsion} The results are presented in terms of a few simple formulas and curves _which are applicable to a wide range of cylinder dimensions from very short cylinders of large radius to long cylinders of small radius. the mean diameter D m = ( D i + D o)/2, as used in AS 1210, or ; the outside diameter D o (giving the so-called 'Barlow's formula'). 003 inch [75μm] wall thickness of metal nickel titanium (NiTi / Nitinol) stent tubing. Cylinder is a Mechanical device, which is used for supplying, carrying, storing, or processing of the fluids (liquids, gases or mixture sometimes slurry) under pressure. It does a great job of catching excess batter that squeezes out as you cook, but it gets as hot as 300. Failure Criteria for Yielding Comparison and Example Example : Thin pressurized tube with end caps Given a thin walled tube (radius r, thickness t) containing gas. Depending on how slender the structural member is, it may buckle or crush under compression stresses. However, buckling does not occur when a structural member is. Thin-walled tube: τmax = 2 ⋅ V Basic Stress Equations Dr. The primary criterion for consideration of papers in Thin-Walled Structures is that they must be concerned with thin-walled structures or the basic problems inherent in thin-walled structures. The cylinder is subjected to an internal pressure of 300 MPa. Determine The Factor Of Safety Based On (a) Tresca Criterion, (b) Von Mises Criterion. proposed for thin-walled cylinders) F. _ t wall thlclmess of cylinder r radius of cylinder :. Therefore the web shear stress: fs = (VQ / It) PSI. Strain has no units due to simply being the ratio between the extension and original length of a material, so Young's Modulus is measured by the same units as stress, i. Previous exposure to thin walled pressure vessel theoffy is helpful, but not required. The failures that cylinders are designed against are stress dependent. For L and T -sections s. 5 MN, T = 0 And An Internal Pressure P = 0. The stress in axial direction at a point in the tube or cylinder wall can be expressed as: σa = (pi ri2 - po ro2 )/ (ro2 - ri2) (1) σa = stress in axial direction (MPa, psi). Top 15 Items Every Engineering Student Should Have! 1) TI 36X Pro Calculator https://amzn. Longitudinal Stress, σ • Exists for cylinders with capped ends;. distribution, displacement function, and stresses of a thin as well as thick hollow cylinder and Khobragade et al. Solution:. Therefore the web shear stress: fs = (VQ / It) PSI. Find the maximum hoop stress in the material and the radial and hoop stress at a point in the barrel 19 mm from the inner surface when the fluid pressure inside the cylinder is 9. Tables of elastic constants and. It's important to remember that normal stresses add together, and shear stresses add together. Longitudinal Shear on a Beam Element of. Results from the. If the cylinder has closed ends, the axial stress can be found separately using only force equilibrium considerations as was done for the thin walled cylinder. From automotive to agriculture and everything in between. Stress Analysis of a Cantilevered Thin-Wall Cylinder within a Cylindrical Cavity 720285 A semiempirical procedure has been developed to determine the stresses in a thin-wall cylinder extending from a block cavity and subjected to cantilever loading. Similar to what we would see in the skin panels of aircraft. in the wall on a cross-sectional plane between the ends. Empirical design curves are presented for the critical stress of thin-wall cylinders loaded in axial compression. 7 ksi) concrete and thin walled tubes with. The problems of weld induced imperfections like residual stresses and shape change behavior evolve almost simultaneously with the introduction of welding as a joining method and harmful stresses. KEY POINTS TO REMEMBER A cylinder is said to be 'THIN' if the ratio of its inner diameter to the thickness of wall is more than 20. The first step to fixing the problem is identifying which one it is: Structural damage vs hairline cracks. First, it's important to understand the basic difference between athin-walled plastic bushing and a thicker-walled bronze bushing. Strength of Materials Questions Answers (SoM) – Civil Engineering MCQ 1) A thin walled cylindrical vessel of wall thickness ‘t’ and diameter ‘d’ is filled with gas to a gauge pressure of ‘p’. Coca cola soda can. With single-acting cylinders, the piston rod is usually loaded in push-only mode so that fatigue is. 156 Thin shells under internal pressure Problem 6. The real problem is the cast-iron overflow moat that runs around the rim of the irons. The effect of curvature of the cylinder wall is neglected. Since the vessel is thin, the load due to the tensile stress in the wall is. Normally the sign convention for the wall shear stress, τ w, that the fluid applies to the interior surface of thepipeissuchthat τ w = −(σ rr) r=R = RΔp 2 (Bic13). Many problems of practical importance are concerned with solids of revolution which are deformed symmetrically with respect to the axis of revolution. Suggestion: Use the result of Example 23. OnAllCylinders is an automotive blog powered by the gearheads and car enthusiasts at Summit Racing Equipment. CIVE 2200 [0. For objects that are not circular the resulting stress field is different. Note also how the $${\bf Q}$$ matrix transforms. Like the normal stress there is a stress profile that is based off of the neutral axis of the particular cross-sectional area. The material in these first sections is based on the assumption that failure by buckling under external pressures does not occur. TORSION IN THIN WALLED VESSELS and THIN STRIPS 1. Maximum shear stress in the wall of the cylinder (not in-plane shear stress) is given by : τ max = h 2 = Pd 4t 5. In the present paper, T-stress solutions are provided for circumferential through-wall cracks in thin-walled cylinders. To decrease the amount of work involved and to enhance the reliability of the results, a short thin-walled cylindrical. If the butt-welded seams form an angle of 33° with the longitudinal axis of the vessel, a. Wall Thickness. Theoretical treatments of the problem are discussed, in particular the plastic straining of tubes under constant ratio of circumferential to axial stress. There’s just good or better. Determine the maximum shearing stresses and associated normal stresses in the. , where bending shear stresses cause zero torsional moment. 0 cm and diameter 28. 0580 kg, the inner radius is R 1 = 0. ) is closed by plates. Usmle step 3 Question and Answers 2020 You are called emergently to the medical floor where a 66-year-old man was found to be minimally responsive. On the stress problem of large elliptical cutouts and cracks in circular cylindrical shells. In this course I will be discussing about Thin And Thick Cylinders And Spheres,Stresses in Thin Cylinders, Expression For Hoop and Longitudinal Stresses, Various Numerical Problems, Efficiency of a joint,wire winding of thin Cylinders,Thick Cylinders. Consider such a vessel subjected to an internal pressure above atmospheric pressure. Roll forming of channels is a continuous alternative to a discrete channel bending process, such as the one illustrated in figure 269. For I and Z -sections s. If the rolled-up piece of paper were a perfect cylinder, the strength would be even stronger!. Further Discussion of the Distribution of Stresses in a Sample Problem 6. Sharp cracks 11. to/2SRJWkQ 2) Circle/Angle Maker https://amzn. • The cross-sectional area of the cylinder wall is characterized by the product of its wall thickness and the mean circumference. Model 2 in a series of four thin-shell cylinder-to-cylinder models was tested, and the experimentally determined elastic stress distributions were compared with theoretical predictions. 1 Thin-Walled Pressure Vessels. Sim-ilarly to that collection the aim here is to present the most important ideas us-ing which one can solve most (> 95%) of olympiad problems on. Android Application - https://play. Heat and matter flow 15. 6-4 Determine the flexural stress distribution in the thin-walled section shown that is produced by a positive bending moment Mx. Poisson's ratio will typically be between 0 to 0. The results can be checked by applying Eq. The material in these first sections is based on the assumption that failure by buckling under external pressures does not occur. Installing a repair sleeve can often save the block if a cylinder has excessive taper wear, or is cracked, scored or otherwise damaged, and boring out the damaged cylinder. Thin-walled open sections may be considered as combinations of narrow rectangular sections so that 3T ___- - - T rmax = Ckldb2 Cdb2 0 - - T - - 3T - L Xk2db’G GCdb’ The relevant formulae for other non-rectangular, non-tubular solid shafts are given in For thin-walled closed sections the stress at any point is given by Table 5. A major difference between a thick and a thin wall cross-section, is that the shear stresses for thin-walled beams are always aligned with the median line of the cross-section, see the figure below. 1 Ahmad Mansour. 276 Chapter 6|Solution of Viscous-Flow Problems Momentum balances. Having cracks appear on your wall may just be a cosmetic problem, or it could indicate a more serious, structural issue. Thin Shells of Revolution under Distributed Loadings Producing Membrane Stresses Only. It Is Assumed That The Yield Stress Is Oy= 280 MPa, The Radius Is A = 1 M, And Wall Thickness Is T= 5x10-3 M.\endgroup\$ - alephzero Jul 3 '18 at 22:42. (b) Determine the outside diameter required to give the same outer surface stress if a hollow shaft of inside diameter 0. Piston and cylinder, in mechanical engineering, sliding cylinder with a closed head (the piston) that is moved reciprocally in a slightly larger cylindrical chamber (the cylinder) by or against pressure of a fluid, as in an engine or pump. The program is calculating the outside diameter hoop stress instead of the mid-plane hoop stress when the 2012 code is used. Also, unlike thin cylinders, the radial stress in thick cylinders are not small but instead, varies from inner surface where it is equal to the magnitude of the fluid pressure to the outer surface where. The required tensile stresses may be in the form of directly applied stresses or in the form of residual stresses. Using the structural engineering calculator located at the top of the page (simply click on the the "show/hide calculator" button) the following properties can be calculated: Calculate the Area of a Thin Walled Circle; Calculate the Perimeter of a Thin Walled Circle. 1" but for shear stress is not useful because it seem that our formula for shear stress is not the same like RSAP one - and we could not find RSAP formula for thin walled cross section shear stress in HELP system. Solutions for diffusion equations 16. Consider free body diagram of half portion of the cylinder as shown in figure 31. In the case of thin walled pressure vessels of spherical shape the ratio of radius r to wall thickness t is greater than 10. The Figure 8. For the purpose of analysis, thick walled cylinder can be considered to consist of a series of thin rings (Figure 1a. Learn about its definition, formula, units, types - longitudinal stress, bulk stress, shear stress along with practice questions. Chapter 6 Stresses in Beam (Advanced Topics) 6. Cylinder may be * Pressure vessel * Storing vessel * Pipes * Engine cylinder. 67A106B C 3. Application of Perpendicular Axis and Parallel axis Theorems. 4 x Outer diameter of piston pin Allowable bending stress of piston pin - 84 N/mm 2. Heat and matter flow 15. Vaginal Problems That Affect Your Sex Life. 29, 30 evaluated the behavior of welding residual stress of thin-walled pipes with 2" diameter and found high levels of stresses in the FZ and HAZ. Stating Moment of Inertia of a infinitesimally thin Disk. These curves are plotted in terms of the nondimensional parameters of small-deflection theory and are compared with theoretical curves derived for the buckling of cylinders with simply supported and clamped edges. Longitudinal Stress, σ • Exists for cylinders with capped ends;. CYLINDERS AND SPHERES. P (a)(b) P. Thick Cylinder Subjected to Internal Pressure Only [8] From the follow equilibrium equation for thick cylinder dr r dðsr ð=ðsðqð-ðsr. 2- Draw stress distribution over the thickness of thin-walled cylinder with closed ends. Lame's equation should be used for thick wall pipes. All plants need water, oxygen, and nutrients. , where bending shear stresses cause zero torsional moment. Cite this chapter as: Shama M. Measurement of residual stresses in the coating deposited by brush-plating on a thin-walled short cylinder. Q13: With a diameter of 21 mm and a wall thickness of 1. The failures that cylinders are designed against are stress dependent. Tensile stresses stretch a member and compressive stresses squeeze a member. Calculate changes in diameter and volume due to pressure. If the butt-welded seams form an angle of 33° with the longitudinal axis of the vessel, a. Determine the state of stress in the wall of the cylinder for both cases if the piston P causes the There is no moment in this problem. Calculate the hoop and longitudinal stresses in the spherical vessel. As a result of this differential shrinkage, a stress develops that the part will want to relieve upon ejection, and the part can then exhibit excessive warpage. 7 (see Problem 10. under stay-at-home orders until recently, Americans have rediscovered the art of. Ask us how. Determine The Factor Of Safety Based On (a) Tresca Criterion, (b) Von Mises Criterion. CIRCULAR SECTIONS When a circular section shaft is subjected to a torque T, the shear stress at any radius r is given by J Tr 2 J is the polar second moment of area. These stresses are all linear, and can therefore be added together in the case of combined loading (like, bending a thin-walled pressure vessel). Whether cracks occur on the finished surfaces of masonry, wood or metal stud walls, the most common cause is the movement of building materials. A woman gave birth to a healthy 7-pound, 13-ounce infant girl. 5 MN, T = 0 And An Internal Pressure P = 0. For example in a 200 mm diameter tube with a wall thickness of 20 mm the shear stress is 10% larger than predicted by the latter formula. 29), has an inside diameter of 20mm, and has an outside diameter of 100mm. The failures that cylinders are designed against are stress dependent. The magnitude of the radial stress is usually small when compared with the longitudinal and hoop stresses; consequently it is not specifically limited by the design codes. AE 3610 Transient Stress Measurements in Thin-Wall Pressure Vessel 3 p t R L 2. 00-kg block? m 1 m 2 (a) Solid disk (b) Solid sphere (c) Thin-walled hollow cylinder Problem 2 (25 points) - Chapter 9 You design three pulley with radius the floor if the pulley is R. My first thought was that it could be the bed, since it vibrates quite a bit when moving, but it only affected the cylinders, so I doubt it's that. This is because shear and torsion generate shear flow through the cross-section, as seen below:. In this situation only the membrane stresses are considered and the stresses are assumed to be constant throughout the wall thickness, t. Key words: elastic-plastic, creep, transition, stresses, strain, pressure, cylinder. ) is one of the most important non- food crop and widely grown commercially (Akerhust, 1981). The inner radius of the cylinder is 2 m with a wall thickness of 20 mm. 1" but for shear stress is not useful because it seem that our formula for shear stress is not the same like RSAP one - and we could not find RSAP formula for thin walled cross section shear stress in HELP system. A device that stores computer data on magnetic tape is a tape drivOver. When a thick-walled tube or cylinder is subjected to internal and external pressure a hoop and longitudinal stress are produced in the wall. Boundary layer separation is an important issue for aircraft wings as it induces a large wake that completely changes the flow downstream of the point of separation. Failure of such tanks results, in most cases, in a tremendous loss of financial and human resources, as well as composes. La Crosse Technology WT-3143A-INT 14-Inch Atomic Wall Clock. distribution, displacement function, and stresses of a thin as well as thick hollow cylinder and Khobragade et al. 0 cm and diameter 28. Solution: Concepts: Static equilibrium; Reasoning:. It Is Assumed That The Yield Stress Is Oy= 280 MPa, The Radius Is A = 1 M, And Wall Thickness Is T= 5x10-3 M. In operation, in a thin wall pressure vessel, stresses developed in the (thin) wall can conservatively be assumed to be uniform. You can optionally check the geometric conditions for the applicability of the standard specified in EN 1993‑1‑3, Section 5. The concept of transition theory based on Lebesgue strain measure has been used to simplify the constitutive equations. Question: HW Problem 2 A Thin-walled Hollow Cylinder Is Subjected To An Axial Force N= 7. on the buckling load of a thin cylinder under an applied. | 13,186 | 60,032 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.921875 | 3 | CC-MAIN-2020-40 | latest | en | 0.903685 |
http://www.transtutors.com/questions/stock-valuation-and-research-321145.htm | 1,454,996,365,000,000,000 | text/html | crawl-data/CC-MAIN-2016-07/segments/1454701156520.89/warc/CC-MAIN-20160205193916-00123-ip-10-236-182-209.ec2.internal.warc.gz | 705,166,334 | 16,355 | +1.617.933.5480
# Q: stock valuation and research
Research online trading sites and DRIPS as outlined below, and summarize your findings. Make sure to include a summary table of the relevant information.
1. Search three online trading sites, and determine the requirements for trading, including the price per trade. Compare and contrast the online trading companies. (2–3 pages)
2. Search the Web for three companies (look for investor information) that offer DIPs or DRIPs. (2–3 pages)
3. Compare and contrast the requirements, including minimum investments, nature of the return, costs, and other features. (1–2 pages)
Part B: Research Market Data on Bonds
Research the current (within the last two months) market data on bonds from AT&T, Dell, and IBM. Assume each bond has a par value of $1000, unless otherwise indicated. Cite your sources. AT&T Dell IBM Coupon Maturity Frequency Rating Required: 1. Complete the table above. 2. Calculate the value of the bond if your required return is 5% on AT&T, 6.5% on Dell, and 8% on IBM. 3. Determine the yield to maturity (YTM) on the bonds given the current price. Based on each bond’s ratings and your determination of its yield to maturity, explain how you rank each bond for risk and return. 1. Stock. What is the value of a stock with a a.$2.50 dividend just paid and an 8% required return with 0% growth? b. $3 dividend just paid and a 8% required return with 2% growth? c.$7 dividend to be paid and a 10% required return with 2% growth? 2. Stock. What is the required rate of return on a stock with a a. $2.50 expected dividend and a$19 price with 6% growth? b. $2.75 expected dividend and a$20 price with 8% growth? c. $2.50 expected dividend and a$19 price with 9% growth? 3. Stock. What is the growth rate of the stock with a a. $3.00 expected dividend and a$20.60 price with 15% required return? b. $2.40 expected dividend and a$25.35 price with 10% required return? c. $2 expected dividend and a$8.30 price with 11% required return?
## Solutions:
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Question Status: Solved | 856 | 3,369 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.640625 | 3 | CC-MAIN-2016-07 | longest | en | 0.881446 |
https://www.physicsforums.com/threads/fluid-problem-piston-moving-in-an-oil-filled-cylinder.800728/ | 1,571,434,714,000,000,000 | text/html | crawl-data/CC-MAIN-2019-43/segments/1570986684854.67/warc/CC-MAIN-20191018204336-20191018231836-00446.warc.gz | 1,005,830,189 | 19,016 | # Fluid problem -- Piston moving in an oil-filled cylinder
#### Queren Suriano
1. Homework Statement
A piston 10 is coaxially in diameter moves within a cylinder whose inner diameter is 10.006 in;
The annular space between piston and cylinder is filled with oil having a kinematic viscosity is 0.004 feet ^ 2 / s and specific gravity of 0.85
If the piston makes its way with a speed of 30 ft / min and the length of the piston within the cylinder is 10 feet, calculate the shear force and the friction opposing the motion of the piston
2. Homework Equations
(tangencial force) / area = (dynamic viscosity) (velocity/space betwteen the two surfaces)
3. The Attempt at a Solution
I can know the dynamic viscosity of the equation kinematic viscosity = dynamic viscosity/density and the density it can be known from the specific gravit.
So if I draw a Diagram of piston, I have two tangent forces and the weight. But I know that (tangencial force) / area = (dynamic viscosity) (velocity/space betwteen the two surfaces) and the area of contact it can be calculated from 2(pi)(radio) (Lenght)???
Last edited by a moderator:
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#### Chestermiller
Mentor
1. Homework Statement
A piston 10 is coaxially in diameter moves within a cylinder whose inner diameter is 10.006 in;
The annular space between piston and cylinder is filled with oil having a kinematic viscosity is 0.004 feet ^ 2 / s and specific gravity of 0.85
If the piston makes its way with a speed of 30 ft / min and the length of the piston within the cylinder is 10 feet, calculate the shear force and the friction opposing the motion of the piston
2. Homework Equations
(tangencial force) / area = (dynamic viscosity) (velocity/space betwteen the two surfaces)
3. The Attempt at a Solution
I can know the dynamic viscosity of the equation kinematic viscosity = dynamic viscosity/density and the density it can be known from the specific gravit.
So if I draw a Diagram of piston, I have two tangent forces and the weight. But I know that (tangencial force) / area = (dynamic viscosity) (velocity/space betwteen the two surfaces) and the area of contact it can be calculated from 2(pi)(radio) (Lenght)???
It looks like you're on the right track, but where are there two tangent forces acting on the piston? I see only one.
What do you get for the dynamic viscosity?
What do you get for the distance between the two surfaces?
What do you get for the velocity/space between the two surfaces (in reciprocal seconds)?
What do you get for the tangential shear stress (i.e., (tangential force) / area)?
What do you get for the tangential force?
I don't understand what they mean by "friction opposing the motion of the piston"
Chet
#### Queren Suriano
It looks like you're on the right track, but where are there two tangent forces acting on the piston? I see only one.
What do you get for the dynamic viscosity?
What do you get for the distance between the two surfaces?
What do you get for the velocity/space between the two surfaces (in reciprocal seconds)?
What do you get for the tangential shear stress (i.e., (tangential force) / area)?
What do you get for the tangential force?
I don't understand what they mean by "friction opposing the motion of the piston"
Chet
With you answer I realized I don't have understand where act the tangent force, It acts in the area of the piston like a circle (bases of the piston) ????
#### Chestermiller
Mentor
With you answer I realized I don't have understand where act the tangent force, It acts in the area of the piston like a circle (bases of the piston) ????
No. It acts on the cylindrical surface of the piston. That's why you use 2πrL.
Chet
#### Queren Suriano
Why it's only one?? Because there are many tangent forces acting in the contour of the cylinder?? or do you refer to the resultant??
Last edited:
#### Queren Suriano
I calculated the dynamic viscosity it gives me 3.16 g / (cm -s). So Should I apply directly the equation
(tangencial force) / area = (dynamic viscosity) (velocity/space betwteen the two surfaces)
Because the area=2pi(R)(L)= 2pi (25.4 cm / 2) (304.8 cm)
velocity=15.24 cm/s
space between= 25.4152 cm - 25.4 =0.01520 cm
#### Chestermiller
Mentor
Why it's only one?? Because there are many tangent forces acting in the contour of the cylinder?? or do you refer to the resultant??
Yes. Just the resultant.
Ok, thank you!
#### Chestermiller
Mentor
I calculated the dynamic viscosity it gives me 3.16 g / (cm -s). So Should I apply directly the equation
(tangencial force) / area = (dynamic viscosity) (velocity/space betwteen the two surfaces)
Because the area=2pi(R)(L)= 2pi (25.4 cm / 2) (304.8 cm)
velocity=15.24 cm/s
space between= 25.4152 cm - 25.4 =0.01520 cm
The space between is half of that. You took the difference between the diameters, and it should be the clearance, which is the difference between the radii. The velocity gradient in the gap should be 2000 reciprocal seconds.
Chet
#### Queren Suriano
The velocity gradient in the gap should be 2000 reciprocal seconds.
You are right! Thank you!!
"Fluid problem -- Piston moving in an oil-filled cylinder "
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• Solo and co-op problem solving | 1,354 | 5,523 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.703125 | 4 | CC-MAIN-2019-43 | latest | en | 0.896731 |
https://solvedlib.com/n/solution-general-find-a-complex-roots-sey-uoqenba-difierential,4978331 | 1,669,792,426,000,000,000 | text/html | crawl-data/CC-MAIN-2022-49/segments/1669446710733.87/warc/CC-MAIN-20221130060525-20221130090525-00142.warc.gz | 569,481,235 | 20,209 | # Solution general Find a complex roots. sey uoqenba difierential equaton for the given 3 12y' + The aruliary <
###### Question:
solution general Find a complex roots. sey uoqenba difierential equaton for the given 3 12y' + The aruliary < 2
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##### Untitled SectionTwo parallel conducting plates are separated by 2.0 mm and carry equal 10 points but opposite surface charge densities. If the potential difference between them is 2.0 V, what is the magnitude of the surface charge density on each plate? (Take electric permittivity 0=8.85*10*(-12) C^2INm 2) (10 pts)17.7 nclm 28.85 nc/m 24.43 nclm 24.43 pC/m*2
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##### The initial volume the volume reading of NaOH in the buret before you start the titration_ The final volume the volume reading of NaOH in the buret once that titration run is complete. Trial Initial Volume 92 mL Final Volume: 34.15 mLTrial 2: Initial Volumez 2.55 mLFinal Volume- 25.05 mLTrial Initial Volume: 0.25 mLFinal Volume 24.52 mLTrial 2: Initial Volume_ 13.40 mLFinal Volume: 38.00 mLWrite chemical equation describing the reaction between hydrochloric acid and sodium hydroxide. Include sta
The initial volume the volume reading of NaOH in the buret before you start the titration_ The final volume the volume reading of NaOH in the buret once that titration run is complete. Trial Initial Volume 92 mL Final Volume: 34.15 mL Trial 2: Initial Volumez 2.55 mL Final Volume- 25.05 mL Trial Ini...
##### Lets imagine a car in an amusement park roller coaster ridemoving uphill and downhill. If the total mass of the car and theriders is 459 kg, traveling at 8 m/s, and the radius of circle(both uphill and downhill) is 20 m, a. Calculate the magnitude ofcentripetal force acting on the car. b. What is the magnitude anddirection of the force exerted on the car from the rail a. At thetop of the hill b. At the bottom of the hill.
Lets imagine a car in an amusement park roller coaster ride moving uphill and downhill. If the total mass of the car and the riders is 459 kg, traveling at 8 m/s, and the radius of circle (both uphill and downhill) is 20 m, a. Calculate the magnitude of centripetal force acting on the car. b. What i... | 1,856 | 6,706 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.171875 | 3 | CC-MAIN-2022-49 | latest | en | 0.822408 |
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C. Day at the Beach
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output
One day Squidward, Spongebob and Patrick decided to go to the beach. Unfortunately, the weather was bad, so the friends were unable to ride waves. However, they decided to spent their time building sand castles.
At the end of the day there were n castles built by friends. Castles are numbered from 1 to n, and the height of the i-th castle is equal tohi. When friends were about to leave, Squidward noticed, that castles are not ordered by their height, and this looks ugly. Now friends are going to reorder the castles in a way to obtain that condition hi ≤ hi + 1 holds for all i from 1 to n - 1.
Squidward suggested the following process of sorting castles:
• Castles are split into blocks — groups of consecutive castles. Therefore the block from i to j will include castles i, i + 1, ..., j. A block may consist of a single castle.
• The partitioning is chosen in such a way that every castle is a part of exactly one block.
• Each block is sorted independently from other blocks, that is the sequence hi, hi + 1, ..., hj becomes sorted.
• The partitioning should satisfy the condition that after each block is sorted, the sequence hi becomes sorted too. This may always be achieved by saying that the whole sequence is a single block.
Even Patrick understands that increasing the number of blocks in partitioning will ease the sorting process. Now friends ask you to count the maximum possible number of blocks in a partitioning that satisfies all the above requirements.
Input
The first line of the input contains a single integer n (1 ≤ n ≤ 100 000) — the number of castles Spongebob, Patrick and Squidward made from sand during the day.
The next line contains n integers hi (1 ≤ hi ≤ 109). The i-th of these integers corresponds to the height of the i-th castle.
Output
Print the maximum possible number of blocks in a valid partitioning.
Sample test(s)
input
3
1 2 3
output
3
input
4
2 1 3 2
output
2
Note
In the first sample the partitioning looks like that: [1][2][3].
In the second sample the partitioning is: [2, 1][3, 2]
0
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Last Updated on May 13, 2024 by Francis
Converting between milliliters and fluid ounces is a handy skill, especially when it comes to accurately measuring liquids, whether at home or when traveling. If you’ve ever wondered how to convert 100ml (milliliters) to oz (ounces), we’ve got you covered. In this guide, we’ll walk you through the conversion process, so you’ll never have to second-guess your measurements again.
When it comes to liquid measurements, understanding the difference between mass and volume is crucial. Mass refers to weight and can be measured in grams or ounces, while volume relates to size or capacity and can be measured in fluid ounces or milliliters. Abiding by TSA regulations when traveling also requires knowledge of these measurements. According to the TSA’s liquids rule, containers must hold no more than 3.4 fluid ounces (100 milliliters) and fit into a quart-sized bag. However, it’s essential to note that the conversion from 100 milliliters to fluid ounces is actually 3.3814, which can affect how certain liquids fill a 3.4 fluid ounce container.
To make your conversions easier, consider referring to a reliable chart that provides weight in ounces for common liquids. This chart can assist you in accurately measuring and packing liquids, ensuring compliance with TSA regulations during your travels. With this knowledge, you’ll be able to convert 100 milliliters to fluid ounces effortlessly and confidently.
Key Takeaways:
• Converting between milliliters and fluid ounces is crucial for measuring liquids accurately.
• Understanding the difference between mass and volume is essential for complying with TSA regulations when traveling.
• Refer to a chart that provides weight in ounces for common liquids to make your conversions easier.
• The conversion from 100 milliliters to fluid ounces is 3.3814.
• Know the density of liquids to determine the amount of weight needed to fill a 3.4 fluid ounce container.
Understanding Mass and Volume in Liquid Measurements
When it comes to measuring liquids, understanding the concepts of mass and volume is essential. Mass refers to the weight of an object, which can be measured in grams or ounces. On the other hand, volume relates to the size or capacity of an object and can be measured in fluid ounces or milliliters.
Knowing the difference between mass and volume is particularly important when converting between 100 milliliters and fluid ounces accurately. This knowledge is not only helpful in everyday cooking and baking but also crucial when adhering to TSA regulations for carrying liquids during travel.
“Mass and volume play a significant role in achieving precise liquid measurements.”
To grasp the distinction between mass and volume in liquid measurements, consider the following:
1. Mass: Mass refers to the weight of a substance or the amount of matter it contains. In liquid measurements, mass can be measured in grams or ounces. Grams are the preferred unit of measurement in the metric system, while ounces are commonly used in the imperial system.
2. Volume: Volume refers to the amount of space occupied by a substance. In liquid measurements, volume is measured in fluid ounces or milliliters. Fluid ounces are commonly used in the United States, while milliliters are frequently used in the metric system.
Understanding the relationship between mass and volume is vital in accurately converting between 100 milliliters and fluid ounces. By grasping these concepts, you’ll be well-equipped to make precise measurements and follow recipes with ease. Whether you’re a seasoned chef or a beginner in the kitchen, mastering mass and volume in liquid measurements is key to achieving culinary success.
The Importance of Precise Measurements
Precise measurements are crucial in cooking and baking. Inaccurate measurements can affect the taste, texture, and overall outcome of your dishes. Understanding the principles of mass and volume allows you to follow recipes accurately and achieve consistent results.
When it comes to liquids, using the correct amount is especially critical. Too much or too little liquid can impact the balance of flavors and affect the texture of your recipes. By taking the time to measure liquids accurately, you can ensure that your dishes turn out as intended.
Measuring Tools for Liquid Measurements
To measure liquids effectively, you’ll need the right tools. Here are some commonly used measuring tools for liquid measurements:
• Measuring Cups: Liquid measuring cups are specially designed for measuring liquid volumes. They typically have a spout for easy pouring and markings on the side to indicate different quantities.
• Measuring Spoons: Measuring spoons are used for smaller liquid measurements, such as teaspoons and tablespoons. They are essential for precise measurements of liquid ingredients in recipes.
Having these tools on hand will make it easier to measure liquids accurately and achieve consistent results in your cooking and baking endeavors.
In addition to using the right tools, following accurate measurement techniques is essential. Pour liquids into a liquid measuring cup on a level surface, ensuring that the bottom of the meniscus aligns with the measurement markings for precise results. Double-check the measurement by bringing your eyes to the same level as the markings on the cup. Avoid estimating or eyeballing measurements, as this can lead to inaccuracies.
The TSA Liquids Rule and Conversions
When it comes to traveling, complying with TSA regulations is essential to ensure a smooth airport experience. One of the most important rules to be aware of is the TSA liquids rule, also known as the 3-1-1 rule.
The TSA liquids rule states that passengers can only carry liquids in containers that hold no more than 3.4 fluid ounces (100 milliliters). These containers must also fit comfortably inside a quart-size bag. This rule is in place to maintain airport security and prevent any potential threats from liquids.
It’s important to note that the conversion from 100 milliliters to fluid ounces is actually 3.3814, so it’s crucial to be aware of this slight difference when measuring your liquids for air travel. Understanding this conversion is key to complying with the TSA liquids rule and ensuring that your liquids are within the approved limit.
By knowing the difference between mass and volume, you can accurately measure and pack your liquids to avoid any issues at security checkpoints. Remember that mass refers to weight and can be measured in grams or ounces, while volume relates to size and can be measured in fluid ounces or milliliters.
To help you better understand the TSA liquids rule and make accurate conversions, here is a table summarizing the key information:
Liquid MeasurementConversion
100 milliliters3.3814 fluid ounces
3.4 fluid ounces100 milliliters
Quart-size bag capacityNo more than 3.4 fluid ounces or 100 milliliters combined
By following the TSA liquids rule and understanding the conversions between fluid ounces and milliliters, you can pack your liquids effectively and adhere to airport security regulations. This knowledge will help you have a hassle-free travel experience without any issues at the security checkpoint.
Converting Weight Ounces to 100ml
When it comes to converting weight ounces to 100 milliliters (ml), understanding the density of the substance is key. Different substances have varying densities, which directly affect the ratio of weight ounces to fluid ounces. For instance, substances with a density similar to water have a ratio of 1 fluid ounce to 1 weight ounce, equivalent to approximately 28.3495 grams. However, it’s important to note that substances with different densities may not have a perfect ratio.
To simplify the conversion process, it’s beneficial to refer to a weight ounces to 100ml conversion chart. This chart provides approximate conversions for various common substances, making it easier to determine the weight ounces equivalent to 100 milliliters.
SubstanceWeight Ounces
Water1 oz
Milk1.03 oz
Olive Oil0.91 oz
Keep in mind that the conversion values may differ depending on the exact composition and density of the substance. However, the chart provides a reliable reference for most situations.
By utilizing a weight ounces to 100ml conversion chart, you can easily determine the weight in ounces that corresponds to 100 milliliters. This knowledge allows for accurate measurements when working with liquids in various applications, be it in the kitchen or other industries.
Milliliters to Fluid Ounces Conversion Chart
When it comes to converting milliliters (ml) to fluid ounces, having a conversion chart on hand can be incredibly useful. The chart provides approximate conversions for different amounts of milliliters to their corresponding fluid ounces. While the exact conversion may vary slightly depending on the substance’s composition, the values in the chart should give you a good estimate.
Milliliters (ml)Fluid Ounces (fl oz)
10 ml0.34 fl oz
50 ml1.69 fl oz
100 ml3.38 fl oz
250 ml8.45 fl oz
500 ml16.91 fl oz
It’s important to note that these conversions are approximate and may vary based on the specific substance. Nevertheless, this chart serves as a handy reference for most common situations where you need to convert milliliters to fluid ounces accurately.
By referring to this conversion chart, you can easily and accurately convert milliliters to fluid ounces, ensuring precise measurements in your culinary endeavors.
Liquid Measurement Tools and Conversions
Accurate measurement of liquids is crucial to cooking and baking. To achieve precise results, it is necessary to have the right tools at your disposal. Two essential liquid measurement tools are liquid measuring cups and measuring spoons.
Liquid Measuring Cups
When measuring larger volumes of liquids, such as cups, pints, quarts, or gallons, liquid measuring cups are indispensable. These cups are usually made of clear glass or plastic, allowing you to accurately measure the desired quantity. The measurement markings on the cups make it easy to read the volume precisely.
Measuring Spoons
For smaller quantities of liquids, measuring spoons come in handy. These spoons are designed to measure both dry and liquid ingredients. Measuring spoons ensure accuracy when adding small amounts of liquids to your recipes, such as vanilla extract or lemon juice.
Moreover, it’s worth noting that you may come across recipes with metric measurements, especially if you explore international cuisines. To adapt these metric measurements to the commonly used imperial system in the United States, you will need a liquid measurement conversion chart.
The chart will assist you in converting liquid metric measurements to fluid ounces and other units in the imperial system. With the help of the chart, you can confidently switch between metric and imperial measurements, ensuring consistent and precise results in your culinary endeavors.
Now that you’re equipped with the right tools and conversion resources, you can effectively measure liquids, accurately convert between various units, and confidently tackle any recipe that comes your way.
Understanding Fluid Ounce Conversions
Fluid ounces are a common unit of measurement in the United States for liquid volume. Whether you’re following a recipe or scaling ingredients up or down, understanding fluid ounce conversions is essential for cooking and baking success. By knowing how to convert between fluid ounces and other commonly used measurements, such as tablespoons to cups or cups to pints, you can easily adjust quantities to suit your needs.
Converting Tablespoons to Cups
When a recipe calls for tablespoons but you prefer to work with cups, a simple conversion can help. Here’s a handy table to guide you:
TablespoonsCups
1 tbsp1/16 cup
2 tbsp1/8 cup
4 tbsp1/4 cup
8 tbsp1/2 cup
16 tbsp1 cup
Converting Cups to Pints and Pints to Quarts
Converting between cups, pints, and quarts allows you to measure and scale liquid volumes effectively. Here’s a helpful conversion chart:
CupsPintsQuarts
1 cup1/2 pint1/4 quart
2 cups1 pint1/2 quart
4 cups2 pints1 quart
8 cups4 pints2 quarts
These conversions will help you measure liquids accurately and confidently in your cooking and baking adventures. Being able to convert between different units of measurement ensures that your recipes turn out just right every time.
With a solid understanding of fluid ounce conversions, you’ll have the knowledge and tools to tackle any liquid volume measurements with ease.
Converting Milliliters and Cubic Centiliters to Ounces and Drams
When it comes to accurately measuring liquid volumes, converting milliliters (ml) and cubic centiliters (cc) to ounces and drams is key. This conversion is especially important in the medical and pharmaceutical fields, where precise quantities of liquids need to be administered or dispensed. To make these conversions quick and easy, refer to the handy conversion chart below:
Milliliters (ml)Ounces (oz)Drams (dr)
1 ml0.0338 oz0.2705 dr
5 ml0.1691 oz1.3526 dr
10 ml0.3381 oz2.7051 dr
25 ml0.8454 oz6.7627 dr
50 ml1.6907 oz13.5254 dr
100 ml3.3814 oz27.0509 dr
Whether you’re working with milliliters, ounces, or drams, this conversion chart will help you accurately measure and administer liquids in the desired quantities. Keep in mind that fluid ounces and drams are commonly used in the United States, while milliliters and cubic centiliters are more prevalent in other parts of the world.
Now that you have the knowledge to convert liquid volumes between different units of measurement, you can confidently handle medical or pharmaceutical tasks that require specific quantities. Remember to consult this conversion chart whenever you need to convert milliliters or cubic centiliters to ounces or drams, ensuring precise liquid measurements every time.
Glass and Plastic Container Size Conversion Chart
Are you unsure about the volume of different glass and plastic containers? Don’t worry, we’ve got you covered! Our handy glass and plastic container size conversion chart provides all the information you need to understand the capacity of various containers. Whether you’re working with drams, milliliters, or ounces, this chart will help you easily determine the right container size for your needs.
Here’s a glimpse of what you’ll find in our comprehensive chart:
Container SizeDramsMillilitersOunces
Small13.70.125
Medium27.40.25
Large414.80.5
X-Large829.61
Keep in mind that the volumes listed in the chart are approximate and may vary slightly depending on the specific container. However, this chart serves as a valuable reference to help you make informed decisions when selecting the right container size.
Whether you’re storing homemade cosmetics, spices, or other household items, our glass and plastic container size conversion chart will be your go-to resource. Next time you’re in doubt, consult our chart for accurate measurements and confident choices.
Remember, knowing the right container size is the key to keeping your items organized and stored properly. So bookmark our chart for easy access and never struggle with container capacity again!
Tips for Accurate Liquid Measurements
Accurate liquid measurements are crucial for successful cooking and baking. To ensure precision, follow these tips:
1. Pour liquids into a liquid measuring cup on a level surface to ensure an accurate measurement. This helps eliminate any tilt or imbalance that could affect the quantity.
2. Confirm the measurement by bending down to eye level and aligning with the markings on the cup. This technique reduces the margin of error and gives you a more accurate reading.
3. Avoid eyeballing measurements from above, as it can be difficult to gauge exact quantities. Always rely on the markings on the measuring cup for precise measurements.
4. When measuring smaller quantities, such as tablespoons, be careful to fill them to the rim without letting the liquid spill over. This ensures that you’re getting the exact amount needed for your recipe.
By following these techniques, you can achieve precise and consistent results in your recipes, ensuring that your dishes turn out just right every time.
Remember: Accurate liquid measurements are the key to culinary success!
Measurement TechniqueTips for Accuracy
Pouring liquids on a level surfaceUse a liquid measuring cup on a flat surface to avoid tilting and ensure accurate measurements.
Bending down to eye levelAlign your eyes with the markings on the cup to get a precise measurement.
Avoiding eyeballingAlways rely on the markings on the measuring cup instead of estimating the quantity visually.
Filling smaller measurements to the rimCarefully fill tablespoons and other small measuring tools to the rim without any spills for accuracy.
Conclusion
Mastering liquid measurement conversions is crucial for achieving accurate cooking and baking results. By understanding the relationship between milliliters, fluid ounces, grams, and weight ounces, you can confidently convert between different units of measurement. This knowledge allows you to adapt recipes, comply with TSA regulations when traveling, and ensure consistent precision in your culinary endeavors.
To ensure accuracy, make use of the appropriate tools like liquid measuring cups and spoons. Additionally, refer to conversion charts to simplify the process of converting liquid measurements. By following these accurate measuring techniques, you can confidently measure liquids and achieve precise results.
Whether you’re a home cook or a professional chef, accurate liquid measurements are the key to culinary success. So take the time to understand liquid measurement conversions, use the right tools, and practice accurate measuring techniques. Your dishes will be perfectly balanced, and your baking creations will turn out just right. Happy cooking!
FAQ
Can you convert 100ml to oz?
Yes, you can convert 100 milliliters to fluid ounces. The conversion from 100ml to oz is approximately 3.3814 fluid ounces.
How do I convert ml to oz?
To convert milliliters (ml) to fluid ounces (oz), you can use a conversion chart that provides the corresponding values for various amounts of milliliters to fluid ounces.
What is the conversion ratio for ml to oz?
The conversion ratio for milliliters to fluid ounces may vary slightly depending on the density of the substance. Generally, the conversion ratio is approximately 1 milliliter equals 0.0338 fluid ounces.
How many ounces are in 100ml?
There are approximately 3.3814 fluid ounces in 100 milliliters.
Is there a calculator to convert ml to oz?
Yes, you can use an online ml to oz calculator to quickly and accurately convert milliliters to fluid ounces.
What is the TSA liquids rule?
The TSA liquids rule, also known as the 3-1-1 rule, states that passengers can only carry liquids in containers that hold no more than 3.4 fluid ounces (100 milliliters). These containers must also fit comfortably inside a quart-sized clear bag.
Why is the conversion from 100ml to oz not exactly 3.4?
The conversion from 100 milliliters to fluid ounces is actually 3.3814. Different substances have varying densities, which affect the ratio of weight ounces to fluid ounces.
How do I convert weight ounces to 100ml?
Converting weight ounces to 100 milliliters (or approximately 3.4 fluid ounces) requires knowing the density of the substance. Different substances have different ratios of weight ounces to fluid ounces.
What is a milliliters to fluid ounces conversion chart?
A milliliters to fluid ounces conversion chart provides the approximate values for converting different amounts of milliliters to fluid ounces. This chart can be used as a reference for converting ml to oz easily and accurately.
What are some common liquid measurement tools?
Liquid measuring cups, made of clear glass or plastic, are essential for measuring volumes such as cups, pints, quarts, and gallons. Measuring spoons are used for smaller quantities of liquid and can measure both dry and liquid ingredients.
How do I convert metric measurements to the imperial system?
To convert metric measurements to the imperial system commonly used in the United States, you can refer to a liquid measurement conversion chart. This chart will help you convert liquid metric measurements to fluid ounces and other units in the imperial system.
What are some common fluid ounce conversions?
Common fluid ounce conversions include tablespoons to cups, cups to pints, and pints to quarts. Understanding these conversions allows you to adjust recipes according to your needs.
How do I convert milliliters and cubic centiliters to ounces and drams?
To convert milliliters (ml) and cubic centiliters (cc) to ounces and drams, you can refer to a conversion chart that provides the corresponding values for these units of measurement.
What is a glass and plastic container size conversion chart?
A glass and plastic container size conversion chart provides information on the volume of different containers. This chart includes conversions between drams, milliliters, and ounces, helping you determine the capacity of various containers.
What are some tips for accurate liquid measurements?
To achieve accurate liquid measurements, pour liquids into a liquid measuring cup on a level surface and confirm the measurement by aligning with the markings on the cup at eye level. Avoid eyeballing measurements from above and be careful with smaller measurements, such as tablespoons, by filling them to the rim without spilling over.
Why are accurate liquid measurements important?
Accurate liquid measurements are crucial for successful cooking and baking. They ensure that the right quantities of ingredients are used, resulting in precise and consistent results in recipes. | 4,350 | 21,981 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.234375 | 3 | CC-MAIN-2024-22 | latest | en | 0.918665 |
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## News:
IWBasic runs in Windows 11!
## Fireworks
Started by Steven Picard, November 26, 2006, 05:16:58 PM
0 Members and 1 Guest are viewing this topic.
#### Steven Picard
##### November 26, 2006, 05:16:58 PM
This was originally written by Fletchie and modified by Boris (where are you?) I got this from the off-line forum (any chance of making it available again since that info is now useful?) The code worked like a charm right away:
`autodefine "off" def fps,ext:int def t,n,nn:int type pixel def x:float def y:float def c:int endtype const total=10000def test[total]:pixel def vx[total]:float def vy[total]:float def an,x,y:floatcreatescreen 640,480,32 for t=1 to 200 /* A bit of a delay for screen warm-up */ fillscreen 0 flip next t nn=1001do fillscreen 0 if nn>20 nn=0 gosub set_pixels endif nn=nn+1 WritePixelGroupFast(test,total,backbuffer) for t=0 to total-1 /* Add the x,y velocities... */ vx[t]=vx[t]*.995 vy[t]=vy[t]+.05 test[t].x=test[t].x+vx[t] test[t].y=test[t].y+vy[t] next t writetext 0,0,str\$(fps) fps = flipuntil keydown(1)endsub set_pixelsdef start:intdef force:floatext=rand(10,400)select 1 case ext<100:fillscreen 0x111111 case ext<300:fillscreen 0x222222 case ext<370:fillscreen 0x333333 default:fillscreen 0x999999endselectstart=rand(0,total-ext)x=rand(0,640)y=rand(0,480)force=rand(1,4)*1000for n=start to start+ext test[n].x=x test[n].y=y test[n].c=rgb(rand(0,255),rand(0,255),rand(0,255)) an=rand(0,35999)/100f vx[n]=fsind(an)*rand(50,5000)/force vy[n]=fcosd(an)*rand(50,5000)/forcenext nreturnendsubdef bpointer,bpitch:int def pp:pointer def pcount:int sub WritePixelGroupFast(p:pointer,qty:int,w:window) lockbuffer w bpointer=getbufferpointer() bpitch=getbufferpitch() pp=p pcount=qty_asm push ebp push ebp mov ebp,[\$pp] mov ecx,[\$pcount] mov esi,[\$bpitch] mov edi,[\$bpointer] another: ; mov ebx,[ebp+72] ; Enabling this increases fps slightly (kinda pre-caching), needs a bit of extra space at the end of an array fld dword [ebp] fistp dword [esp] mov ebx,[esp] cmp ebx,639 ; one less than screen width jg nextone test ebx,0x8000000 jnz nextone fld dword [ebp+4] shl bx,2 mov eax,esi fistp dword [esp] cmp dword [esp],479 ; one less than screen height jg nextone test dword [esp],0x80000000 jnz nextone mul dword [esp] add eax,ebx add eax,edi mov ebx,[ebp+8] mov dword [eax],ebx nextone: add ebp,12 loop another pop ebp pop ebp _endasm unlockbuffer w return endsub` | 930 | 2,643 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.65625 | 3 | CC-MAIN-2024-30 | latest | en | 0.365226 |
http://us.metamath.org/ilegif/iunxiun.html | 1,653,068,002,000,000,000 | text/html | crawl-data/CC-MAIN-2022-21/segments/1652662533972.17/warc/CC-MAIN-20220520160139-20220520190139-00205.warc.gz | 61,367,153 | 5,020 | Intuitionistic Logic Explorer < Previous Next > Nearby theorems Mirrors > Home > ILE Home > Th. List > iunxiun Unicode version
Theorem iunxiun 3765
Description: Separate an indexed union in the index of an indexed union. (Contributed by Mario Carneiro, 5-Dec-2016.)
Assertion
Ref Expression
iunxiun
Distinct variable groups: , , ,
Allowed substitution hints: () (,) ()
Proof of Theorem iunxiun
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 eliun 3690 . . . . . . . 8
21anbi1i 446 . . . . . . 7
3 r19.41v 2511 . . . . . . 7
42, 3bitr4i 185 . . . . . 6
54exbii 1537 . . . . 5
6 rexcom4 2623 . . . . 5
75, 6bitr4i 185 . . . 4
8 df-rex 2355 . . . 4
9 eliun 3690 . . . . . 6
10 df-rex 2355 . . . . . 6
119, 10bitri 182 . . . . 5
1211rexbii 2374 . . . 4
137, 8, 123bitr4i 210 . . 3
14 eliun 3690 . . 3
15 eliun 3690 . . 3
1613, 14, 153bitr4i 210 . 2
1716eqriv 2079 1
Colors of variables: wff set class Syntax hints: wa 102 wceq 1285 wex 1422 wcel 1434 wrex 2350 ciun 3686 This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-io 663 ax-5 1377 ax-7 1378 ax-gen 1379 ax-ie1 1423 ax-ie2 1424 ax-8 1436 ax-10 1437 ax-11 1438 ax-i12 1439 ax-bndl 1440 ax-4 1441 ax-17 1460 ax-i9 1464 ax-ial 1468 ax-i5r 1469 ax-ext 2064 This theorem depends on definitions: df-bi 115 df-tru 1288 df-nf 1391 df-sb 1687 df-clab 2069 df-cleq 2075 df-clel 2078 df-nfc 2209 df-ral 2354 df-rex 2355 df-v 2604 df-iun 3688 This theorem is referenced by: (None)
Copyright terms: Public domain W3C validator | 755 | 1,611 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.140625 | 3 | CC-MAIN-2022-21 | latest | en | 0.115175 |
https://groupprops.subwiki.org/wiki/Transpose-inverse_map_induces_inner_automorphism_on_projective_general_linear_group_of_degree_two | 1,590,737,166,000,000,000 | text/html | crawl-data/CC-MAIN-2020-24/segments/1590347402457.55/warc/CC-MAIN-20200529054758-20200529084758-00183.warc.gz | 367,779,831 | 7,734 | # Transpose-inverse map induces inner automorphism on projective general linear group of degree two
## Statement
Suppose $R$ is any commutative unital ring. Let $G = GL(2,R)$ be the General linear group (?) of degree two over $R$, $Z$ be the center of $G$ (which is also the group of scalar matrices, because Center of general linear group is group of scalar matrices over center), and let $PGL(2,R) = G/Z$ be the Projective general linear group (?) of degree two over $R$.
Then, the automorphism of $PGL(2,R)$ induced by the Transpose-inverse map (?) automorphism of $G$ is an inner automorphism of $PGL(2,R)$. | 163 | 614 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 10, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.609375 | 3 | CC-MAIN-2020-24 | longest | en | 0.869012 |
https://eandt.theiet.org/content/articles/2010/06/the-science-of-predicting-football-results/ | 1,675,052,607,000,000,000 | text/html | crawl-data/CC-MAIN-2023-06/segments/1674764499801.40/warc/CC-MAIN-20230130034805-20230130064805-00489.warc.gz | 239,188,258 | 39,025 | # The science of predicting football results
A statistician explains some mathematical models behind predicting results of international soccer games and risks his reputation by trying to guess the winners of the 2010 World Cup.
Predicting football results is a rapidly growing area of academic interest. Economists use models to assess the efficiency of betting markets, operational researchers use models to experiment with the various effects of tournament design, and statisticians showcase their proficiency with advanced statistical techniques by modelling the intricacies of football data.
It is not, of course, just academics who are mining the archives of football scores. Bookmakers live and breathe football prediction models - as do the more committed flutterers. Mistakes cost money and jobs, whilst finding a small advantage can carry great rewards.
#### Betting markets
In academia, the most common application of football forecasting models is to test for betting market efficiency. The Efficient Markets Hypothesis (EMH) is a cornerstone of financial theory and, in its simplest form, states that an investor should not be able to consistently obtain returns above the average. Finding a forecasting model of football that can generate better-than-average - or even positive - returns usually results in a publication for the academic as an example of a violation of the EMH, but the proprietary nature of the models means that the published ones rarely (if ever) represent the very best models, and even less often generate positive returns consistently.
The best performing models are the reserve of the gambling industry. It is paramount for a bookmaker to set odds at a value that realistically represent the probabilities of a match being won, drawn or lost. If the bookmaker fails to do this, it will risk huge losses.
For instance, Asian bookmakers would think nothing of taking an individual bet of US\$200,000 - and regularly receive bets of \$400,000 - and a typical weekend in the English Premier League typically attracts \$500m turnover in Asia. With such tides of cash being wagered, it is not surprising that bookmakers make use of every possible tool at their disposal - one of them being mathematical models.
A mathematical model is not typically used on its own to set odds. An expert odds-setter is employed to adjust the model-generated odds given any extra information. For example, a typical model might take into account recent results of a team and each team's position in the league only. The odds-setter will then adjust these predicted odds to account for, say, an injury to a star player.
On the other side of the market, are the bettors. Specialist companies offer services to advise clients which bets to make. Maciej Jarowek is a betting consultant for AsianConnect88.com, a betting broker. I asked him for his thoughts on the use of mathematics in the industry. As a bookmaker does, he uses a model to give him a starting point and then adjusts the odds as he sees fit.
Jarowek is an expert on Polish football, and when he finds a discrepancy between his odds and those of the bookmakers, he can choose whether the discrepancy is enough to advise placing a bet. He says the biggest advantage professional gamblers have over the bookmaker is that they do not have to bet on every match - they can pick and choose. Given that Jarowek is one of many professional gamblers working for AsianConnect88.com, and that there are numerous such agencies in operation, it appears there is considerable scope for beating the market.
Compared with other sports, the result of a football match is relatively difficult to predict. Some academics believe this is one of the sources of the popularity of football - fans never really know the outcome of a match before it has happened making watching the game an exciting proposition.
Pundits make careers based on this uncertainty of outcome and spend endless hours contemplating each and every possible event in a match. There are countless upsets in domestic football every weekend, and the World Cup throws up its fair share of giant-killings. Given this inherent unpredictability, how can we make predictions?
There are two broad approaches to modelling football match outcomes. First, one can predict the result directly - whether the result will be a win, a draw or a loss. In this case, the outcome (win, loss, draw) is an ordinal variable (a win is better than a draw which is better than a loss). The model of choice here is an ordinal regression one, such as ordered probit. The output from such a model is the probability of each outcome, so that for an upcoming match one can use the model to calculate the probability of a win, draw or loss.
The second approach for modelling a match outcome is an indirect method where the analyst models the exact score of the game. In this case, the analyst estimates the probability of each possible number of goals scored by each team. One can then infer the probability of a team winning, drawing or losing the match by summing the relevant exact score probabilities.
#### An ordered probit
Evidence suggests very little difference in performance of each approach in modelling match outcome. Here, I build a model of the first type, namely an 'ordered probit' model.
The ordered probit model can be used to estimate the probability of the three outcomes of a match. To do this, it uses information on each team. For instance, it seems reasonable that a team that has won its last three matches has a higher probability of winning its next match than a team that has lost its last three matches. Similarly, a team that is ranked higher than the opposition has a higher probability of winning the match than does the lower-ranked team. The amount of the win probability changes, given these nuggets of information are governed by the model parameters. In a statistical model, the parameters are estimated to best explain what has happened in the past.
My model here is based on nearly 9,000 international match results over an eight-year period. The information and the effects on the probability of a team winning a match are:
• Venue - home/away or neutral. A team is more likely to win if at home;
• Distance from capital city to game location. A team is more likely to win the shorter the distance travelled (by fans and the team itself);
• Difference in world ranking between the teams. A higher ranked team is more likely to win;
• Change in world rankings for each team during the previous 12 months. An improving team is more likely to win;
• Type of match, namely: major tournament (World Cup or confederation championship), minor tournament (other FIFA- sanctioned one), qualifier or friendly. Better teams take major tournaments more seriously;
• Past match results. For each game, I use the previous eight results for each team (on average a national team plays eight matches in a 12-month period). In addition to the results, I know the world rankings for each of the eight opposition teams at the time of the game.
Using the information of past results needs a little extra thought. A 1-0 win for a team ranked 200 versus a team ranked 4 clearly represents a better performance than if the teams were ranked 200 and 198 respectively. As a consequence, the past results should be weighted relative to the result and relative to the strength of the opposition. A past performance metric (ppm), which captures this relationship, is given by the formula at the top (left) of this page.
This ppm goes from '-1' to '1', where '-1' represents the worst result possible - the top-ranked team losing to the bottom-ranked team - and '1' represents the worst-ranked team beating the best-ranked team. Note that 204 is the maximum value of the ranking of any team during the period under consideration. The past performance metric is plotted at the top (right) of this page.
(Sshhh - I predict the World Cup winner)
The ordered probit model described above can be used to estimate the probability of each outcome (win/draw/loss) in one match. A bookmaker might use these probabilities to help inform odds-setters, whilst a bettor might use them to assess whether a bet should be placed.
In order to predict the winner of the World Cup 2010, one needs to predict the winner of a series of matches. To do this, I use simulation, and have written code that uses the fitted model of match outcome to simulate the entire tournament. The World Cup starts with eight mini-leagues (groups) of four teams, playing each other once. The first- and second-placed teams in each group then progress to the knockout stages. This tournament structure affects the probability of a team winning.
For example, in the upcoming World Cup, the most likely teams to progress from Group G are Brazil and Portugal. The most likely team to win Group H is Spain. The winners (runners-up) of Group H then meet the runners-up (winners) of group G in the first knockout round. Thus Spain are almost guaranteed a difficult match in the first knockout round. Compare this to Group A favourites, France, who will most likely face the runner-up of Group B. Given Group B favourites, Argentina, are much stronger than the other teams in the group, France (and Argentina) are likely to have less difficult matches in the first knockout stage than Spain, Brazil and Portugal.
It is clear then, that predicting the winners of the tournament overall is not just a case of picking the best team. One needs to take into account the effect of the tournament structure. The results of 100,000 simulated tournaments are shown in the table, left.
Despite their seemingly difficult draws, Spain and Brazil are still first and second in terms of number of wins. The number of wins can easily be converted into a predicted probability of winning the tournament for each team which is shown in the third column of the table (left).
It is interesting to compare the predicted win probabilities with the FIFA World Rankings. France are big movers upwards - possibly because of their easier draw, whilst Portugal fall to ninth favourites, despite being the third-ranked team in the world.
Given that the most frequent use of such a model is to compare the probabilities with those of bookmakers, the fifth and sixth columns of the table give the odds and implied probabilities from Bet365, as at the date I made my predictions (14 May 2010). I have to admit, when I saw the similarities, I was pleased - it confirms the model and simulation exercise give sensible results. However, closer inspection reveals some discrepancies. Disclaimer time: Please note I do not suggest you use these odds to place a bet. The bookies really do know what they are doing and incorporate far more information I have used to inform their odds - they are also paid much more than I am for doing this sort of thing!
It appears the bookmakers think Spain and Brazil are more likely to win than I do, suggesting these are actually not good teams to back (at these odds). This might be because they are protecting themselves against the market which is keen to be on these teams - a similar story is true for England.
France, on the other hand, offers good value - the model suggests the probability of victory is nearly twice the probability assumed by the bookmaker. It will be hard to take for any Republic of Ireland fan, if France were to go on to win the World Cup, given that they were knocked out of the World Cup by France forward Thierry Henry's 21st-century spin on the 'hand of God' goal.
So here it is - I put my neck on the line (at least the model does) to give you some tips, based purely on statistics (not my opinion):
Spain are the tournament favourites, but may not offer value for money. (The more astute reader will recognise this as a bit of a politician's answer: if Spain win, I can say 'I told you they were favourites', whilst if they lose, I can say 'I told you they weren't a good bet - there was an 88.4 per cent probability of them not winning'!)
France to win is a good bet.
I also persuaded Jarowek to give me a tip:
Brazil not to win. (Typically reserved and cautious).
##### The model's predictions for the latter stages of the tournament are:
QF1: Holland vs Brazil
QF2: France vs England
QF3: Germany vs Argentina
QF4: Italy vs Spain
##### Semi-final line up:
SF1: Brazil vs France
SF2: Argentina vs Spain
##### Final:
Brazil vs. Spain
Pretty obvious really! I should say that, although my reputation as a statistician rests on these tips being reasonably good, I will be cheering on my native England no matter whom the opposition. I wait in anticipation for kick-off on 11 June...
##### Further information:
Download the article as a PDF to see the equations and simulation results table.
Sign up to the E&T News e-mail to get great stories like this delivered to your inbox every day. | 2,646 | 12,933 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.890625 | 3 | CC-MAIN-2023-06 | latest | en | 0.949298 |
https://forum.ozgrid.com/forum/index.php?user-post-list/253303-gdoddaiah/ | 1,695,418,985,000,000,000 | text/html | crawl-data/CC-MAIN-2023-40/segments/1695233506423.70/warc/CC-MAIN-20230922202444-20230922232444-00670.warc.gz | 300,021,362 | 11,544 | # Posts by gdoddaiah
• ## Calculate Resolution date and time based on priority SLA
Re: Calculate Resolution date and time based on priority SLA
Thanks for all the help Herbds7, you are too good!
• ## Calculate Resolution date and time based on priority SLA
Re: Calculate Resolution date and time based on priority SLA
Thanks Herbsd7. I need one more help from you.
Please help me find the resolution date and response dates for service requests and incidents. I have put the response SLA and other details required in the attached xls.
Thanks and Regards,
Girish
• ## Calculate Resolution date and time based on priority SLA
Re: Calculate Resolution date and time based on priority SLA
Thanks a lot Herbds7, it works perfectly now. Thanks for the detailed explanation as well on the latest xls shared.
I have another question, how do I read the priority and open date from one xls and update? Also I need to change color of the Close date cell, if the date is nearing the close date.
Thanks once again...Can you please tell me how the Fin() works in the xls.
• ## Calculate Resolution date and time based on priority SLA
Re: Calculate Resolution date and time based on priority SLA
Sorry the answer should be Monday 02/09/2102 14:01.
• ## Calculate Resolution date and time based on priority SLA
Re: Calculate Resolution date and time based on priority SLA
ok thanks Herbd7.
But I am not getting the desired result.
For eg:- row 7 in your xls
Open date is: Friday 31/08/2012 6:01:29 PM and priority is 2.
As per my requirement the answer should be Monday 02/08/2012 14:01. As the next workday is monday and the time to resolve is 8 hrs. Hence the answer should be 02/08/2102 14:01, as the monday start time is 7 AM. The clock should start from 7 AM from monday and 1 hour on Friday till 19:00 hrs. The working time is 7 AM - 7 PM.
Also can you please explain your xls :).
Thanks
• ## Calculate Resolution date and time based on priority SLA
Re: Calculate Resolution date and time based on priority SLA
thanks for the response Herbds7. But I want the reolution date and time be always as per the SLA timelines given below.
also is there a easier way using WORKDAY and IF commands. thanks.
SLA timelines based on priority:
2-High - 8 hours
3-Medium - 48 hours(4 days)
4-Low - 240 hours(20 days)
• ## Calculate Resolution date and time based on priority SLA
Hi,
I need to find the resolution date and time based on priority from the reported date of the incident.
Working hours is from 7 AM to 7 PM weekdays, excluding weekends.
SLA timelines based on priority:
2-High - 8 hours
3-Medium - 48 hours(4 days)
4-Low - 240 hours(20 days)
For eg:- If the incident is reported at 6:30 pm on a friday, the resolution date should move to monday along with appropriate time and date.
Thanks | 696 | 2,813 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.859375 | 3 | CC-MAIN-2023-40 | latest | en | 0.901434 |
https://www.experts-exchange.com/questions/28270848/Excel-Lookup-Question.html | 1,534,531,854,000,000,000 | text/html | crawl-data/CC-MAIN-2018-34/segments/1534221212768.50/warc/CC-MAIN-20180817182657-20180817202657-00414.warc.gz | 893,179,692 | 15,502 | # Excel Lookup Question
Hi Experts,
I think I have a basic excel lookup question. I am using Excel 2007 and simply have two worksheets within a single workbook. One sheet has the item numbers and the prices, and the other has more detailed information. I simply want Excel to search the Price List sheet for the Part #, and enter the price into the appropriate field on the Item Details sheet. I have attached an example spreadsheet that I created. I think it might be a vlookup or lookup function but am unsure. Thank you! So if item B20 is \$5.23 on the Price List, I want Excel to search for item B20 in the Price List and enter the Price for that item into the Item Details sheet. Hope that makes sense!
LookupPriceQuestion.xlsx
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Commented:
Hi,
pls try this
place in C2
=VLOOKUP(A2,'Price List'!A:B,2)
LookupPriceQuestionv1.xlsxRegards
0
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Author Commented:
Hi Rgonzo, that seems to work for the first few and then doesn't pull the right number over time. Do you know of any other ways to do this. At least when I copy the formula down my column it pulls inaccurate data after a few.
Hmmm--I'm sure it's something straightforward.
0
Author Commented:
Scratch that -- Had to be an absolute reference to the rannge in the formula--Then it worked fine.
Thank you
0
Author Commented:
Thanks!
0
Commented:
Hi,
I suppose you use row numbers you have to have absolute ranges
``````=VLOOKUP(A3,'Price List'!\$A\$1:\$B\$10000,2)
``````
Regards
0
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From novice to tech pro — start learning today. | 580 | 2,528 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.546875 | 3 | CC-MAIN-2018-34 | latest | en | 0.929436 |
https://blupee.jimdo.com/2016/03/18/7-7/ | 1,550,352,218,000,000,000 | text/html | crawl-data/CC-MAIN-2019-09/segments/1550247481122.31/warc/CC-MAIN-20190216210606-20190216232410-00058.warc.gz | 496,612,920 | 10,326 | 7 = +7
7 = +7 (The sigh + can be omitted.) (*)
using (*), we get
+7 = +(+7)
-7 = +(-7)
-7 = -(+7).
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Comments: 0 | 56 | 133 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.78125 | 3 | CC-MAIN-2019-09 | longest | en | 0.364568 |
https://www.ajjacobson.us/fundamentals-corporate/simplifying-the-dividend-discount-model.html | 1,568,747,630,000,000,000 | text/html | crawl-data/CC-MAIN-2019-39/segments/1568514573105.1/warc/CC-MAIN-20190917181046-20190917203046-00177.warc.gz | 705,557,696 | 7,764 | Simplifying the Dividend Discount Model
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the dividend discount model with no growth
Consider a company that pays out all its earnings to its common shareholders. Such a company could not grow because it could not reinvest.6 Stockholders might enjoy a generous immediate dividend, but they could forecast no increase in future dividends. The company's stock would offer a perpetual stream of equal cash payments, DIV1 = DIV2 = . . . = DIVt = . . ..
6 We assume it does not raise money by issuing new shares.
J8<r
144 part two Value
The dividend discount model says that these no-growth shares should sell for the present value of a constant, perpetual stream of dividends. We learned how to do that calculation when we valued perpetuities in Chapter 3. Just divide the annual cash payment by the discount rate. The discount rate is the rate of return demanded by investors in other stocks of the same risk:
Since our company pays out all its earnings as dividends, dividends and earnings are the same, and we could just as well calculate stock value by
Value of a no-growth stock _ P0 _ —^r where EPS1 represents next year's earnings per share of stock. Thus some people loosely say, "Stock price is the present value of future earnings" and calculate value by this formula. Be careful—this is a special case. We'll return to the formula later in this chapter.
V Self-Test 5.5 Moonshine Industries has produced a barrel per week for the past 20 years but cannot grow because of certain legal hazards. It earns \$25 per share per year and pays it all out to stockholders. The stockholders have alternative, equivalent-risk ventures yielding 20 percent per year on average. How much is one share of Moonshine worth? Assume the company can keep going indefinitely.
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Get My Free Ebook | 468 | 2,156 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.828125 | 3 | CC-MAIN-2019-39 | latest | en | 0.929127 |
https://www.alecjacobson.com/weblog/1281.html | 1,722,703,778,000,000,000 | text/html | crawl-data/CC-MAIN-2024-33/segments/1722640372747.5/warc/CC-MAIN-20240803153056-20240803183056-00017.warc.gz | 516,385,824 | 2,055 | # Block matrices in LaTeX, part one
## weblog/
When I'm writing out complicated linear systems by hand I usually draw the system as block matrices. And when I say block matrices, I mean that I really draw the boxes around each part of the matrix with matching row and column dimensions. So when I draw a single matrix it is just a single box. And when I draw a partitioned (block) matrix I draw a stack of these boxes (I realize "block matrix" technically refers to these partitioned matrices and not drawing them as blocks). This helps me see the matrix multiplication in my head and keep track of whether the system is determined, underdetermined, or over determined. Here's an example of my hand drawn block matrices in action:
I looked around and found that most packages print block matrices like this, with at most vertical or horizontal lines (not boxes) sectioning off entries in an array:
So I fiddled around with LaTeX box commands and came up with a first attempt to create the sort of boxed, block matrices that I use in my notes. Here're the commands that I define:
\newcommand{\blockmatrix}[3]{%These end of the line comments are neccessary
\begin{minipage}[t][#2][c]{#1}%
\center%
#3%
\end{minipage}%
}%
\newcommand{\fblockmatrix}[3]{%
\fbox{%
\begin{minipage}[t][#2][c]{#1}%
\center%
#3%
\end{minipage}%
}%
}
Note: The end of line comments are necessary to prevent fbox from adding spurious spacing. And here's a document using the commands:
\documentclass[letterpaper,11pt]{article}
\newcommand{\blockmatrix}[3]{%These end of the line comments are neccessary
\begin{minipage}[t][#2][c]{#1}%
\center%
#3%
\end{minipage}%
}%
\newcommand{\fblockmatrix}[3]{%
\fbox{%
\begin{minipage}[t][#2][c]{#1}%
\center%
#3%
\end{minipage}%
}%
}
\begin{document}
\fblockmatrix{0.5in}{0.5in}{A} \fblockmatrix{0.1in}{0.5in}{x}
\blockmatrix{0.1in}{0.5in}{=} \fblockmatrix{0.1in}{0.5in}{b}
\\
\\
\fblockmatrix{0.5in}{0.3in}{A} \fblockmatrix{0.1in}{0.5in}{x}
\blockmatrix{0.1in}{0.5in}{=} \fblockmatrix{0.1in}{0.3in}{b}
\\
\\
\fblockmatrix{0.5in}{0.3in}{L}
\fblockmatrix{0.5in}{0.5in}{M}
\fblockmatrix{0.3in}{0.5in}{L}
\fblockmatrix{0.1in}{0.3in}{x}
\blockmatrix{0.25in}{0.3in}{=}
\fblockmatrix{0.1in}{0.3in}{b}
\\
\\
\fblockmatrix{0.6in}{0.4in}{L}
\fblockmatrix{0.6in}{0.6in}{M}
\fblockmatrix{0.4in}{0.6in}{L}
\fblockmatrix{0.1in}{0.4in}{x}
\blockmatrix{0.1in}{0.3in}{=}
\fblockmatrix{0.6in}{0.4in}{L}
\fblockmatrix{0.6in}{0.6in}{M}
\fblockmatrix{0.2in}{0.6in}{L}
\fblockmatrix{0.1in}{0.2in}{b}
\\
\\
\fblockmatrix{0.525in}{0.375in}{$L$}
\fblockmatrix{0.525in}{0.525in}{$M$}
\fblockmatrix{0.375in}{0.525in}{$L$}
\fblockmatrix{0.1in}{0.375in}{$x$}
\blockmatrix{0.1in}{0.275in} {$=$}
\fblockmatrix{0.525in}{0.375in}{$L$}
\fblockmatrix{0.525in}{0.525in}{$M$}
\blockmatrix{0.1in}{0.375in}{\Huge{ $($}}
\fblockmatrix{0.175in}{0.525in}{$L$}
\fblockmatrix{0.1in}{0.175in}{$b$}
\blockmatrix{0.1in}{0.4in}{$+$}
\fblockmatrix{0.1in}{0.525in}{$b_n$}
\blockmatrix{0.1in}{0.375in}{\Huge{ $)$}}
\\
\\
\begin{tabular}{llll}
\fblockmatrix{0.5in}{0.5in}{A}&
\fblockmatrix{0.1in}{0.5in}{x}&
\blockmatrix{0.1in}{0.5in}{=}&
\fblockmatrix{0.1in}{0.5in}{b}
\\
\fblockmatrix{0.5in}{0.25in}{G} & & &
\fblockmatrix{0.1in}{0.25in}{0}
\\
\end{tabular}
\\\\
\end{document}
Which produces this: Admittedly there's a lot left to do. The parenthesis behavior is annoying and it's not terribly easy to stack them. | 1,257 | 3,392 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.53125 | 3 | CC-MAIN-2024-33 | latest | en | 0.810806 |
https://books.google.com.jm/books?qtid=f47e787a&lr=&id=ygMFAAAAQAAJ&sa=N&start=20 | 1,680,080,989,000,000,000 | text/html | crawl-data/CC-MAIN-2023-14/segments/1679296948965.80/warc/CC-MAIN-20230329085436-20230329115436-00090.warc.gz | 179,168,680 | 5,723 | Books Books
And the same thing is to be understood when it is more briefly expressed by saying, a has to d the ratio compounded of the ratios of e to f, g to h, and k to l. In like manner, the same things being supposed, if m has to n the same ratio which a has to...
Euclid's Elements of plane geometry [book 1-6] explicitly enunciated, by J ... - Page 117
by Euclides - 1860
## The First Six Books of the Elements of Euclid, with a Commentary and ...
Euclid, Dionysius Lardner - Euclid's Elements - 1828 - 544 pages
...briefly expressed by saying, A has to D the ratio compounded of the ratios of E to F, G to H, and K to L. In like manner, the same things being supposed, if...then, for shortness' sake, M is said to have to N the ratio compounded of the ratios of E to F, G to H, and K to L. The term compound ratio, like all...
## Elements of Geometry: Containing the First Six Books of Euclid : with a ...
John Playfair - Euclid's Elements - 1832 - 333 pages
...the ratio compounded of the ratios which are the same with the ratios of E to F, G to H, and K to L. In like manner, the same things being supposed, if...ratio which A has to D, then, for shortness' sake, Mis said to have to N a ratio compounded of the same ratios, which compound the ratio of A to D ; that...
## Elements of Geometry: Containing the First Six Books of Euclid, with a ...
John Playfair - Euclid's Elements - 1835 - 316 pages
...F, G to H, and K to L. In like manner, the same things being supposed, if M has to'N the sameratio which A has to D, then, for shortness' sake, M is...compounded of the ratios of E to F, G to H, and K to L. 11. If three magnitudes are continual proportionals, the ratio of the first to the third is said to...
## The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...
Euclid - 1835 - 540 pages
...expressed, by saying, A has to D the ratio compounded of the ratios of E to F, G to H, and K to L. In like manner, the same things being supposed, if...; then, for shortness sake, M is said to have to N the ratio compounded of the ratios of E to F, G to H, and K to L. XII. In proportionals, the antecedent...
## Elements of Geometry: Containing the First Six Books of Euclid, with a ...
John Playfair - Euclid's Elements - 1836 - 488 pages
...ratio compounded of the ratios which -sJre the same with the ratios of E to F, G to H, and K to L. In like manner, the same things being supposed, if...is, a ratio compounded of the ratios of E to F, G to Hr and K to L. XI. Ef three magnitudes are continual proportionals, tlie ratio of the first to the...
## The First Six Books of the Elements of Euclid: With a Commentary and ...
Dionysius Lardner - Geometry - 1838 - 386 pages
...expressed by saying, A has to D the ratio compounded of the ratios of E to F, G to H, and K to L. I n like manner, the same things being supposed, if M...then, for shortness' sake, M is said to have to N the ratio compounded of the ratios of E to F, G to H, and K to L. The term compound ratio, like all...
## The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...
Robert Simson - Geometry - 1838 - 434 pages
...the ratios of E to F, G to H, and K to L. In like manner the same things being supposed, if M have to N the same ratio which A has to D: then for shortness' sake, M is said to have to N, the ratio compounded of the ratios of E to F, G to H, and K to L. XII. In proportionals, the antecedent...
## The Elements of Euclid
Euclid - Geometry - 1838 - 478 pages
...ratios of E to F, G to H, and K to L. In like manner the same things being supposed, if M have tl^N the same ratio which A has to D: then for shortness' sake, M is said to have to N, the ratio compounded of the ratios of E to F, G to H, and K to L. XII. 'Geometers make use of the following... | 1,063 | 3,821 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.625 | 3 | CC-MAIN-2023-14 | latest | en | 0.956336 |
https://www.geeksforgeeks.org/design-asynchronous-up-down-counter/?ref=rp | 1,669,636,499,000,000,000 | text/html | crawl-data/CC-MAIN-2022-49/segments/1669446710503.24/warc/CC-MAIN-20221128102824-20221128132824-00666.warc.gz | 824,168,027 | 24,120 | # Design asynchronous Up/Down counter
• Difficulty Level : Medium
• Last Updated : 26 May, 2021
Prerequisite : Ripple counter.
In asynchronous/ripple counter output of the first flip-flop is provided as the clock to the second flip-flop i.e flip-flop(FF) are not clocked simultaneously.
Circuit is simpler, but speed is slow.
Asynchronous counter basics :
1 bit asynchronous/ripple counter
When -ve edge clock pulse is applied and input is given to FF logic 1 then the output state of FF will toggle for every falling edge. The output frequency will be f/2 (If f is clock frequency). It is known as binary or mod -2 counter or bit ripple counter.
It has 2 unique output states (0 and 1).
2 bit asynchronous Up counter.
When two FFs are connected in series and output of one FF is act as clock for 2nd FF. So the state of 2nd FF will change only when output and 1st FF is logic 1 and falling edge occur. The output frequency of Q1 is f/4(if f is clock frequency).
It can generate 4 different unique states. This is known as divide by 4 circuits or mod 4 ripple counter.
Here output is taken as Q1(MSB) Q0(LSB).
By this, we can conclude that –
If there are n FFs then the output frequency will be divide by 2n. Also generate 2n unique states.
So the frequency division basically forms counting state.
Here we are seeing that the output of the 1st FF act as clock for 2nd FF. Suppose the FF takes 30ns for generating output(i.e. propagation delay because of gates). Therefore, the output of second FF will be obtained after 60 ns. So the propagation delay is ripples through the FFs and becomes more when the number of FFs increases.
Therefore, asynchronous counter are too slow for generating big counting.
• As we know, when the output state (i.e. Q) of previous FF is feed as clock to next FF then the counter will perform up counting as you seen above(i.e. 0 1 2 3).
After 4th -ve edge clock pulse the sequence will repeat.
• When the complemented output state (i.e. Q’) of previous FF is feed as clock to next FF then the counter will perform down counting as you seen below(i.e. 3 2 1 0).
After 4th -ve edge clock pulse the sequence will repeat.
2 bit asynchronous down counter
Now we are designing Up/Down counter.
Up/Down counter is the combination of both the counters in which we can perform up or down counting by changing the Mode control input.
Design of 3 bit Asynchronous up/down counter
It is used more than separate up or down counter.
1. In this a mode control input (say M) is used for selecting up and down mode.
2. A combinational circuit is required between each pair of flip-flop to decide whether to do up or do down counting.
For n = 3, i.e for 3 bit counter –
Maximum count = 2n -1 and number of states are 2n.
Steps involve in design are :
Step 1 : Decision for Mode control input –
Decision for mode control input
When M = 0, then Y= Q, therefore it will perform Up counting (As discussed above).
When M = 1, then Y= Q’ therefore it will perform Down counting (As discussed above).
Combinational circuit is required for deciding mode control(i.e whether counter will perform Up counting or Down counting).
So the all possible combinations are –
K-map for finding output Y that will be given as clock to next FF.
K map for finding Y
Step 2 : Insertion of Combinational logic between every pair of FFs –
Up/Down Counter
Timing diagram :
Initially Q3 = 0, Q2 = 0, Q1 = 0.
Timing diagram for 3 bit asynchronous up/down counter
Case 1 – When M=0, then M’ =1.
Put this in Y= M’Q + MQ’= Q So Q is acting as clock for next FFs.
Therefore, the counter will act as Up counter.
Explanation of Up counter –
• The 1st FF is connected to logic 1. Therefore, it will toggle for every falling edge.
• The 2nd FF input is connected to Q1.Therefore it changes its state when Q1= 1 and there is falling edge of clock.
• Similarly, 3rd FF is connected to Q2. Therefore, it changes its state when Q2= 1 and there is falling edge of clock.
• By this we can generate counting states of Up counter.
• After every 8th falling edge the counter is again reaching to state 0 0 0.
Therefore, it is also known as divide by 8 circuit or mod 8 counter.
Case 2 – When M=1, then M’ =0.
Put this in Y= M’Q + MQ’= Q’. So Q’ is acting as clock for next FFs.
Therefore, the counter will act as Down counter.
Explanation of Down counter –
• The 1st FF is connected to logic 1. Therefore, it will toggle for every falling edge.
• The 2nd FF input is connected to Q’1.Therefore it changes its state when Q’1= 1 and there is falling edge of clock.
• Similarly, 3rd FF is connected to Q’2. Therefore, it changes its state when Q’2= 1 and there is falling edge of clock.
• By this we can generate counting states of down counter.
• After every 8th falling edge the counter is again reaching to state 0 0 0.
Therefore, it is also known as divide by 8 circuit or mod 8 counter.
My Personal Notes arrow_drop_up | 1,249 | 4,921 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.171875 | 3 | CC-MAIN-2022-49 | latest | en | 0.92104 |
https://www.jiskha.com/display.cgi?id=1337642184 | 1,501,329,855,000,000,000 | text/html | crawl-data/CC-MAIN-2017-30/segments/1500549427766.28/warc/CC-MAIN-20170729112938-20170729132938-00278.warc.gz | 798,635,626 | 3,918 | # math 8
posted by .
3 1/4 x 2 1/2 = 65/8 or 8 1/8 is this right
• math 8 -
Right.
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Post a New Question | 500 | 1,755 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.984375 | 3 | CC-MAIN-2017-30 | longest | en | 0.793484 |
https://www.lawnsite.com/threads/dry-creek-bed-construction.280199/ | 1,516,624,688,000,000,000 | text/html | crawl-data/CC-MAIN-2018-05/segments/1516084891316.80/warc/CC-MAIN-20180122113633-20180122133633-00626.warc.gz | 918,343,365 | 30,263 | # Dry Creek Bed Construction
Discussion in 'Water Features' started by VO Landscape Design, Jun 24, 2009.
1. ### VO Landscape DesignLawnSite Senior MemberMale, from Mt. Pleasant Ia.Messages: 366
Trying this in a different forum.
A client wants a dry creek bed in their yard. It starts out about 6' at the top and 10' at the end and 41' long. I know the basics of design but am having problems with the amount of rocks for it. With the different size on the bottom building up to larger on the top is there a easy way to figure out approx. how much of each? It will be about 12" deep at the deepest part.
I am thinking Rock A (the smallest) at about 300 sq.ft. X 2" depth = 600sq.ft. Plus another 82sq.ft. X 10" depth = 820sq.ft.for the deepest part. Rock B (larger) at 208sq.ft. X 3" depth = 624sq.ft. Rock C (largest) at 129sq.ft. X 2" depth = 252sq.ft.
I hope this is clearer than it sounds to me.
Here is a picture of the area. The shaded area is where they would like it.
Thank you
VO
2. ### wurkn with amishLawnSite Senior Memberfrom in the bathroomMessages: 662
will water ever flow this route?
3. ### VO Landscape DesignLawnSite Senior MemberMale, from Mt. Pleasant Ia.Messages: 366
Yes. Some will be coming off the porch above but not much.
VO
4. ### wurkn with amishLawnSite Senior Memberfrom in the bathroomMessages: 662
Well to start you off 300ft2 x 2" doesn't equal 6ooft2 . It equals 50ft3 so that would be roughly 3ton ( I always round up)
Here's what I came up with in amounts.
A. 7tons
B.3-4tons
C.2tons
What I would do is have 10-12 nice size boulders planted in and out of the stream and run a 3"-4" size gravel mixed with #4 gravel down thru the stream. Hope that makes sense.
5. ### VO Landscape DesignLawnSite Senior MemberMale, from Mt. Pleasant Ia.Messages: 366
Thanks. With limited space didn't want a lot of extra rock. This is in a nice area so this could be my "in"
VO | 542 | 1,907 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.828125 | 3 | CC-MAIN-2018-05 | latest | en | 0.920591 |
https://cnchou.github.io/notes/RS.html | 1,558,311,771,000,000,000 | text/html | crawl-data/CC-MAIN-2019-22/segments/1558232255251.1/warc/CC-MAIN-20190520001706-20190520023706-00436.warc.gz | 434,675,460 | 9,049 | Back to Coding Theory
Back to notes
# Reed-Solomon Code
In this note, we introduce some basic properties of Reed-Solomon code and present a simple decoding algorithm.
## Definition and basic facts
Let $n$ denote the block length, prime power $q$ denote the alphabet size, $k$ denote the message length, and $d$ denote the minimum distance. Define the Reed-Solomon code as follows.
For integer $1\leq k<n\leq q$ and a set $S={\alpha_1,\dots,\alpha_n}\subseteq\mathbb{F}_q$, we define the Reed-Solomon code
$\text{RS}_{q,S}[n,k] := \{(p(\alpha_1),\dots,p(\alpha_n)):\ p\text{ is a polynomial of degree at most }k-1 \}.$
Intuitively, we think of the code of Reed-Solomon code as a low degree ($k-1$) polynomial and the codeword is the evaluation of the polynomial on set $S$ of size $n$. Thus, we have the following facts directly from the definition and the properties of polynomials.
• The rate is $1-k/n$.
• The minimum distance is $n-k+1$.
• This follows from the fact (“Degree Mantra”) that two distinct univariate degree $d$ polynomial intersect on at most $d$ points.
The good thing about Reed-Solomon code is that its rate achieves the Singleton bound, i.e., Reed-Solomon code has optimal rate. However, the alphabet size required is pretty large: $q>n$. Thus, many people have been worked hard to reduce the alphabet size of the Reed-Solomon code while preserving the optimality of code rate.
### Linear code characterization
Recall that there are three important issues in linear code: the generator matrix, the parity checking matrix, and the dual code. In the following, we consider a special case of Reed-Solomon code where $n=q$ and $S={0,1,2,\dots,q-1}$.
• The generator matrix of Reed-Solomon code
The generating matrix of Reed-Solomon code is simply the sumatrix of Vandermonde matrix of $S$ up to degree $k-1$. We denote the code as $\text{RS}_q[n,k]$.
• The parity checking matrix of Reed-Solomon code
From the generator matrix characterization of Reed-Solomon code, one can see that every codeword lie in the row space of $G$. Thus, to find the parity checking matrix, it is equivalent to find the perp of the row space of $G$. Thus, we need some properties from the Vandermonde matrix as follows. (Note that these properties hold when $n=q$)
Let $V_i$ denote the $i$th row of the Vandermonde matrix, then for any $i,j\in[n]$,
$% $
From the above lemma, we know that the first $n-k$ row of the Vandermonde matrix is perpendicular to $\text{RS}_q[n,k]$. As the dimension of $\text{RS}_q[n,k]$ is $k$ and the dimension of the universe is $n$, we conclude that the parity checking matrix of $\text{RS}_q[n,k]$ is
• The dual code of Reed-Solomon code
By the property of linear code, we know that the generator matrix of the dual code of $\text{RS}_q[n,k]$ is the transpose of the parity checking matrix of $\text{RS}_q[n,k]$. That is, the dual code of $\text{RS}_q[n,k]$ is $\text{RS}_q[n,n-k+1]$.
## Nice resources
• Book chapter by Madu Sudan, Venkatesan Guruswami, and Atri Rudra.
• Background in polynomials and finite fields.
• A very comprehensive introduction to Reed-Solomon code.
• A property of MDS codes.
• Nice exercises cover many useful properties of Reed-Solomon code and some variants.
• Lecture notes of an IT course at University of Wyoming.
• Short and self-contained. | 884 | 3,322 | {"found_math": true, "script_math_tex": 2, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.5 | 4 | CC-MAIN-2019-22 | latest | en | 0.827426 |
http://mathhelpforum.com/business-math/210566-calculate-forward-price-range-based-historic-volatility.html | 1,524,313,262,000,000,000 | text/html | crawl-data/CC-MAIN-2018-17/segments/1524125945143.71/warc/CC-MAIN-20180421110245-20180421130245-00349.warc.gz | 212,180,021 | 11,161 | # Thread: calculate forward price range based on historic volatility
1. ## calculate forward price range based on historic volatility
I am an absolute Math Dummy but I'm sure there is a solution for my issue, but I didn't find any in the net. I would like to calculate the potential forward price for an equity by knowing what todays equity-price is and what the historic volatility of the last 30 days is. Assuming that the stock-price is currently at 100 and the 30day volatility is 10%, what would be the price-assumption for day1, day2, day3.... as each following day the spread of the price gets bigger, I assume the chart has to look like
or will it look like
http://qvmgroup.com/invest/wp-conten...ilityCones.png
because here the cone looks much different then I assume.
Any idea of a formula that would work in Excel? I think it is correct that I only go forward with the price the many days as the historic volatility is = 30day vola = 30day price assumption.
Thx in advance for any input
rgds
PS: I tried in the attacheded Excel, but I calculated 30d Volatility for the lower band of the forward pricing that gives me a much higher Vola then the historic vola is, shouldn't this be same at the end?
2. ## Re: calculate forward price range based on historic volatility
Hey ColumA.
In finance we have what is called a Martingale approach.
Basically we say that all the information for potential future prices is contained in the current existing price and also (and this is the Martingale part) that the conditional expectation for later prices only depends on the current price.
You also have option pricing which takes a very similar approach but the volatility is captured in what is called a Brownian Motion or Wiener process.
If you have volatility information, then what you can do is simulate the process so many thousands of times and then get the average path for the amount of time simulated and this can be used to see the behavior of the process under the Wiener/Brownian motion process assumptions.
For this you will need to simulate from a Normal distribution and in Excel this is given by the function NORMDIST:
An Introduction to Excel's Normal Distribution Functions
So what you would do is calculate say 5000 simulations for each tick and then get the average and standard deviation of each tick and plot that if you wanted to.
Also this model is a simple one and if you have other assumptions or extra information, then it may not be adequate at all.
What kind of tick size were you thinking of?
3. ## Re: calculate forward price range based on historic volatility
Hi chiro
What kind of extra information are you thinking of? Is ex-dividend within the coming 30 days I would like to simulate one of them, and if yes, I should take this into account on/after ex-date i assume.
I read the Introduction and understood most (I'm Swiss) by the meaning and imagine that I add the ,Gausche Glockenkurve, at the end of the historic price which comes close to the clone in the gold-chart.
As I would like to simulate couple of hundreds equities each day, I do not want to take care on each specific ticksize and therefore would go for 0.01. To simulate 5000 on each tick shouldn't be a problem as I am programming on SQL, but Excel is a good way for me to see/get the way and it should be easy to implement later by VBA into SQL db
4. ## Re: calculate forward price range based on historic volatility
you mean like my modified xls? How do you go for 30 days or is this not needed? | 778 | 3,522 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.5 | 4 | CC-MAIN-2018-17 | latest | en | 0.956515 |
https://vibrationresearch.com/resources/test-my-product-using-sine-or-random/ | 1,713,805,205,000,000,000 | text/html | crawl-data/CC-MAIN-2024-18/segments/1712296818312.80/warc/CC-MAIN-20240422144517-20240422174517-00096.warc.gz | 532,484,541 | 20,238 | # Test My Product Using Sine or Random?
#### Author John & Philip Van Baren
This paper originally appeared in Test Engineering & Management Magazine, June/July 2004.
In vibration testing, there are quite a few test types to which you can expose your product. The primary choices are sine, random, classical shock, transient shock, field-recorded time history, sine-on-random, random-on-random, and sine-and-random-on-random. Our customers often request advice on which test type to run and, in particular, how to choose between the two most common test types: sine and random. They want to know which test, sine or random, most quickly pinpoints flaws in their product. If they can only run one of the two tests, which should it be?
Recently, I received an even more specific request from a customer. They presented data from a sine test and a random test and wanted to know: given both a sine test and a random test, how he could determine which is the most severe? Let’s take a look at the two tests and decide how to answer his question.
### The Question
How would the following specifications compare in amplitude/severity?
Sine Test (Figure 1)
• 3.5G at 5Hz to 50Hz
• 1.5G at 50Hz to 300Hz
• Limit vibration to 0.4in double amplitude
• Test all axes at the same level
Figure 1: Sample sine test profile.
Random (Figure 2)
• 0.01500 G2/Hz from 10Hz to 0.01500G2/Hz at 40Hz
• 0.01500 G2/Hz at 40Hz to 0.00015G2/Hz at 500Hz
• Results in 1.05GRMS
• Test all axes at the same level
Figure 2: Sample random test profile.
### The Response
This is a valid and interesting question. Why? Because the answer is not obvious. The sine vibration is measured in G peak (Gpk), while the random vibration is measured as GRMS, with the peak G levels typically left to a statistical assumption. A quick calculation tells us that the random test, which can have peak values up to 4 or even 5 times the RMS level, will apply 4 x 1.05 GRMS, or 4.20Gpk to our product. Since the sine test is only 3.5 Gpk, we would expect the random test to be more damaging, right?
#### Analysis
Looking for support from some equations, let’s make some reasonable assumptions: 1) failures due to vibration are caused at the peak G level seen by the product, 2) most products have resonances at one or more frequencies, and 3) at these resonances the vibration levels applied to the product are amplified by the Q factor of the resonance. Following this train of logic, we conclude that the failures will occur when the vibration is at one of the resonant frequencies. Now when we use a sine vibration, the full vibration levels are concentrated at the resonant frequency, and the vibration levels are simply amplified by the amplification factor Q.
(1) Aproduct,sine = Q x Acontrol,sine
When we use a random vibration, it is not so simple because not all of the vibration is amplified by the resonance. Let’s further assume the resonance has a Q factor of 5 or more. In that case, the resonance will act as an amplifying band-pass filter with amplification equal to Q, and a bandwidth equal to Df, where
(2) Q = fn / Δf
fn = resonant frequency
Δf = half-power bandwidth of the resonance
It will also be helpful to refer to the following relationship, which tells us that, for a given RMS level, the PSD level is inversely proportional to the full bandwidth of the random spectrum. In more general terms, a more concentrated random vibration will have a higher PSD value.
(3) PSDcontrol = Acontrol,rms2 / ΔF *
ΔF = full bandwidth of the random PSD
*equation (3) applies to flat spectrum only
A random test is defined in terms of a PSD, which is an amplitude-squared measure. So, at the resonant frequency, the PSD levels of the product will be amplified by Q2. Since the resonance acts as an amplifying band-pass filter, we can approximate the vibration levels at the product by looking at just the energy at the resonant frequency that passes through and is amplified by the resonance (again assuming the random waveform has up to 4 sigma peaks):
(4) Aproduct,peak = 4 x Aproduct,rms
= 4 x [ PSDproduct x Δf ]1/2
= 4 x [ Q2 x PSDcontrol x Δf ]1/2
= 4 x [ PSDcontrol x Q x fn ]1/2
From equation (4) we note three features of the peak amplitude for a random test:
1. It is proportional to only the square root of Q. As a result, a high-Q resonance will result in a more severe test in sine than it will in random if all other parameters are equal.
2. It is proportional to the square root of the resonant frequency, fn, so the higher the resonant frequency, the higher the peak values in the output.
3. Referring back to equation (3), we also note that the more concentrated the random vibration is, the higher the peak vibration levels will be.
Now we can also compare the peak vibration levels on the product for both Sine and Random tests by comparing equations (1) and (4) with Aproduct,sine = Aproduct,peak,random.
(5) Acontrol,sine = Aproduct,sine / Q
= Aproduct,peak,random / Q
= 4 x [ fn x PSDcontrol / Q ]1/2
Equation (5) allows a direct comparison of a random test with a sine test, for a given value for the Q factor. We plotted our two test specifications in Figure 3, where we see that the sine equivalent to our random test is actually a much lower test level than our sine test. Only in the case of resonance at 50Hz, where the sine test steps down in amplitude, with Q=5 does the random test level even come close to the sine test level. So the equations are telling us that the sine test will be more severe than the random test.
Figure 3: Comparison of the Sine equivalents to the Random profile, with various Q. For higher Q, the Sine equivalent to the Random profile has a lower amplitude.
### Application
At the time the customer asked his question, I was at Sperry Marine in Charlottesville Virginia, setting up for some equipment installation training. This was a great time to demonstrate and test for the differences. As a single test is worth a thousand opinions, we set up to run both the random test and the sine test on a slip plate (Figure 9). The slip plate had two elements mounted on it, each with different resonant frequencies. The elements were aluminum masses attached by threaded rods of different lengths and thicknesses, with accelerometers mounted on the mass at the top of each rod connected to channels 4 and 6.
What we needed to do for the comparison was run the tests, and then look at the G levels seen. We knew they would be 3.5Gpk for the sine test at the control point, and, making a 4-sigma peak assumption, we expected to find 4.2Gpk at the control point for the random test also. The two plots in Figures 4 and 5 show the controlled test along with the response data for the two vertical rods with masses attached.
Figure 4: Sine test results.
Figure 5: Random test results.
While running the tests, we also simultaneously streamed the accelerometer data to the hard disk drive for later analysis. This allowed us to be able to make a direct comparison of the peak G levels for each of the tests. As expected, at the control point, the peak G levels for the Sine test were 3.5Gpk and 1.5Gpk. The random test levels at the control point were 1.05GRMS, as expected, and 4.8Gpk, which is a little bit higher than the 4-sigma peaks we predicted, but not unusual for a Gaussian random vibration (Figure 6).
Figure 6: At the control point, the Random test vibration levels showed a 4.8Gpk.
Now, as we were running the test, we observed the resonant elements mounted to the slip table going berserk. This also showed up on the controller plots (Figures 4 and 5), which showed much larger accelerations on channels 4 and 6 than measured at the control point. What could be going on here? Recall from equations (1) and (4) above, that when we have resonances in the product, they will amplify the vibration levels. The accelerometers monitoring our two resonant elements show the resonance frequencies are 27Hz and 62Hz, right in the middle of our test range.
Let us examine the time data for those accelerometers, which we had conveniently streamed to the hard disk drive, and see what is happening at the resonant elements. This may shed more light on the test equivalences. First looking at the frequency response for the Ch4 accelerometer (Figure 5), we estimate a Q factor of 48 and a resonant frequency of 27Hz. However, we note that the bandwidth, Δf = fn / Q = 0.6Hz, which is less than the frequency resolution of the PSD plot (using 800 lines). This is a good indication that the Q factor estimated from this PSD will be underestimated. Since we had recorded the time waveforms to disk, we are able to load these waveforms into Matlab™ and use high-resolution spectral post-processing (13,000 lines) to zoom in on the peaks. With this more accurate estimate, we find the Q level to be 140. Computing using equation (4), we expect a peak level of 4 x [ 0.015 x 140 x 27 ]1/2, or 30Gpk. Figure 7 shows the actual acceleration levels on Ch4, where we find the peak G level was 28G.
Next looking at the frequency response for the Ch6 accelerometer (Figure 5) we estimate a Q factor of 110 and a resonant frequency of 62Hz. Again we find the bandwidth, 0.6Hz, to be less than the frequency resolution of the PSD plot, so we need to post-process this recorded waveform to obtain a more accurate estimate of the Q factor. Using 13,000 lines of resolution we estimate the Q factor to be 200. Computing using equation (4), we expect to see peak levels of 4 x [ 0.00673 x 200 x 62 ]1/2, or 37Gpk. Figure 8 shows the actual acceleration levels on Ch6, where we find the peak G level was 42G.
Figure 7: On Ch4, the Random test vibration levels showed a 28Gpk.
Figure 8: On Ch6, the Random test vibration levels showed a 42Gpk.
### Observations
Let’s make a table of the results, so we can get the whole picture:
Q Sine (G peak) Random (GRMS) Random (G peak) Predicted (Eqn. 4) (G peak) Control point – 3.5G 1.05G 4.8G 4.2G Ch4 (27Hz resonance) 140 42G 8.35G 28G 30G Ch6 (62Hz resonance) 200 97G 10.9G 42G 37
From these results, we find that at the control point, the random test has higher peak G levels than the sine test. This would lead us to believe that the random test was a more severe test. However, at the resonant points, the sine test has higher peak G levels than the random test. From the product’s perspective, the sine test was the more severe test.
You may also notice that the sine resonance peak values were not as high as would be predicted by the Q factor. By reviewing the recorded time data for Ch4 we are able to determine that, at the 27Hz resonance, the sine sweep passed through the resonance too quickly to fully excite the resonance. Repeating the test using a slower sweep rate or a resonance search-and-dwell feature would allow us to more accurately find the resonance frequency and Q factor. From this, we can conclude that for high Q values, to get the full Q amplification effects of a sine test, you must either sweep slowly or do a resonance dwell at each resonance.
By examining the recorded data for Ch6, we are also able to determine that at the 62Hz resonance, the acceleration levels were so high that they exceeded the accelerometer’s measurement capacity, and therefore the measured waveform was saturated well below the actual acceleration levels. This is an important point because quite often accelerometers are sized based on the test profile’s acceleration level, while the resonances may see 10x or 100x the profile acceleration level. Repeating the test using a higher capacity accelerometer is required to accurately measure the acceleration levels at that resonance.
The actual random peak values are a little different from the predicted values, but this is to be expected due to the random nature of the waveform. Each random test you run will be different from any other random test, so the peak values will vary from test to test, and even over different time intervals within a single test.
### Conclusion
Figure 9: Test setup in the lab at Sperry Marine, Charlottesville, Virginia.
The relative severity of a sine test and a random test will vary depending on your product’s resonant frequencies and Qs. In general, when sine and random tests have the same peak vibration levels at the control point, the product will see higher vibration levels with a sine test than with a random test due to the resonances in the product. Equation (5) gives you a way to convert a random PSD into an approximately equivalent sine peak acceleration, as long as you know the resonant frequencies and Q factors of the product.
However, you must also consider that a sine test only excites a single product resonance at a time, so a sine test will not test the interaction between two resonances in your product. Since a random test excites the full frequency range all at the same time, it can be used to find problems resulting from the interaction between two resonances. | 3,080 | 12,974 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.3125 | 3 | CC-MAIN-2024-18 | latest | en | 0.924723 |
https://mail.haskell.org/pipermail/haskell-cafe/2009-November/068876.html | 1,653,110,399,000,000,000 | text/html | crawl-data/CC-MAIN-2022-21/segments/1652662538646.33/warc/CC-MAIN-20220521045616-20220521075616-00708.warc.gz | 443,082,779 | 1,896 | # [Haskell-cafe] Area from [(x,y)] using foldl
Mon Nov 9 03:49:36 EST 2009
```On Sun, Nov 8, 2009 at 10:30 PM, michael rice <nowgate at yahoo.com> wrote:
>
> This doesn't.
>
> area :: [(Double,Double)] -> Double
> area p = abs \$ (/2) \$ area' (last p):p
>
> where area' [] = 0
> area' ((x0,y0),(x,y):ps) = ((x0-x)*(y0+y)) + area'
> (x,y):ps
>
>
This function is almost correct except you got your priorities wrong :
application priority is always stronger than any operator's so "area' (last
p):p" is read as "(area' (last p)) : p"... Besides your second pattern is
also wrong, the correct code is :
area :: [(Double,Double)] -> Double
area p = abs \$ (/2) \$ area' (last p : p)
where area' ((x0,y0):(x,y):ps) = ((x0-x)*(y0+y)) + area' (x,y):ps
area' _ = 0
--
Jedaï
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https://www.mathwarehouse.com/geometry/triangles/right-triangles/find-the-side-length-of-a-right-triangle.php | 1,713,654,428,000,000,000 | text/html | crawl-data/CC-MAIN-2024-18/segments/1712296817688.24/warc/CC-MAIN-20240420214757-20240421004757-00026.warc.gz | 797,737,839 | 10,003 | Find the Side Length of A Right Triangle
# Find the Side Length of A Right Triangle
Sohcahtoa and the Pythagorean Theorem
There are many ways to find the side length of a right triangle. We are going to focus on two specific cases.
Case I
When we know 2 sides of the right triangle, use the Pythagorean theorem.
Case II
We know 1 side and 1 angle of the right triangle, in which case, use sohcahtoa.
### Practice Problems
Calculate the length of the sides below. In each case, round your answer to the nearest hundredth.
##### Problem 1
Step 1
Since we know 2 sides of this triangle, we will use the Pythagorean theorem to solve for x.
Step 2
Substitute the two known sides into the Pythagorean theorem's formula:
$$a^2 + b^2 = c^2 \\ 8^2 + 6^2 = x^2 \\ 100 = x^2 \\ x = \sqrt{100} \\ x = \boxed{10}$$
##### Problem 2
Step 1
Since we know 1 side and 1 angle of this triangle, we will use sohcahtoa.
Step 2
Set up an equation using a sohcahtoa ratio. Since we know the hypotenuse and want to find the side opposite of the 53° angle, we are dealing with sine
$$sin(53) = \frac{ opposite}{hypotenuse} \\ sin(53) = \frac{ \red x }{ 12 }$$
Now, just solve the Equation:
Step 3
$$sin(53) = \frac{ \red x }{ 12 } \\ \red x = 12 \cdot sin (53) \\ \red x = \boxed{ 11.98}$$
##### Problem 3
Step 1
Since we know 2 sides of this triangle, we will use the Pythagorean theorem to solve for side t.
Step 2
Substitute the two known sides into the Pythagorean theorem's formula:
$$a^2 + b^2 = c^2 \\ \red t^2 + 12^2 = 13^2 \\ \red t^2 + 144 = 169 \\ \red t^2 = 169 - 144 \\ \red t^2 = 25 \\ \red t = \boxed{5}$$
##### Problem 4
Step 1
Since we know 1 side and 1 angle of this triangle, we will use sohcahtoa.
Step 2
Set up an equation using the sine, cosine or tangent ratio Since we want to know the length of the hypotenuse, and we already know the side opposite of the 53° angle, we are dealing with sine.
$$sin(67) = \frac{opp}{hyp} \\ sin(67) = \frac{24}{\red x}$$
Now, just solve the Equation:
Step 3
$$x = \frac{ 24}{ sin(67) } \\ x = 26.07$$
##### Problem 5
Step 1
Since we know 2 sides and 1 angle of this triangle, we can use either the Pythagorean theorem (by making use of the two sides) or use sohcahtoa (by making use of the angle and 1 of the given sides).
Step 2
Chose which way you want to solve this problem. There are several different solutions. The only thing you cannot use is sine, since the sine ratio does not involve the adjacent side, x, which we are trying to find.
Pythagorean Theorem Using Cosine Using Tangent
A² + B² = C²
The answers are slightly different (tangent s 35.34 vs 36 for the others) due to rounding issues. I rounded the angle's measure to 23° for the sake of simplicity of the diagram. A more accurate angle measure would have been 22.61986495°. If you use that value instead of 23°, you will get answers that are more consistent.
Step 3
$$x = \frac{ 24}{ sin(67) } \approx 26.07$$ | 909 | 2,957 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.8125 | 5 | CC-MAIN-2024-18 | latest | en | 0.783801 |
http://www.talkstats.com/showthread.php/56190-Soccer-betting-probability-risk-and-odds-question-help | 1,508,529,107,000,000,000 | text/html | crawl-data/CC-MAIN-2017-43/segments/1508187824325.29/warc/CC-MAIN-20171020192317-20171020212317-00200.warc.gz | 576,311,361 | 10,517 | ## Soccer betting probability, risk and odds question - help
Hello,
Consider two different cases of soccer betting.
1) The first consists of 32 different sets of matches (each consisting of 5 matches with different odds of their own). Some of the individual matches (of 5 matches) in the sets can be the same with another set from time to time, but every single one of 32 sets (32 combinations) is different from each other (a unique set of 5 matches), meaning if one of them wins, the other 31 sets loses automatically.
Lets say one bets 10 dollar for each set, 320 dollars in total of 32 sets. The decimal odds of each set varies from 40 to 80, with an average of 60. So he is expecting to win 10x60=600 dollars on average from the set that wins.
In the end, he expects to get 600 dollars/320 dollars invested on total of 32 sets=1.875dollars per one dollar invested.
2) In the second case, there is only one match with a decimal odd of 1.875. He thinks of investing 320 dollars on this one match, again winning 600 dollars in return.
In both of the cases, the amount invested is the same (320 dollars) and the expected outcome is the same (600 dollars). Which one should he choose?
Does he have better probability of success with betting on 32 different sets, because he only needs only 1 of them to win out of 32 sets?
Or does he have absolutely the same probability of success with betting on one single match in the second case? | 339 | 1,443 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.78125 | 4 | CC-MAIN-2017-43 | latest | en | 0.948239 |
https://www.esaral.com/q/how-many-terms-are-there-in-the-ap-18-72030 | 1,721,426,523,000,000,000 | text/html | crawl-data/CC-MAIN-2024-30/segments/1720763514928.31/warc/CC-MAIN-20240719200730-20240719230730-00890.warc.gz | 667,990,969 | 11,574 | How many terms are there in the AP 18,
Question:
How many terms are there in the AP $18,15 \frac{1}{2}, 13, \ldots,-47 ?$
Solution:
The given $\mathrm{AP}$ is $18,15 \frac{1}{2}, 13, \ldots,-47$.
First term, a = 18
Common difference, $d=15 \frac{1}{2}-18=\frac{31}{2}-18=\frac{31-36}{2}=-\frac{5}{2}$
Suppose there are n terms in the given AP. Then,
$a_{n}=-47$
$\Rightarrow 18+(n-1) \times\left(-\frac{5}{2}\right)=-47 \quad\left[a_{n}=a+(n-1) d\right]$
$\Rightarrow-\frac{5}{2}(n-1)=-47-18=-65$
$\Rightarrow n-1=-65 \times\left(-\frac{2}{5}\right)=26$
$\Rightarrow n=26+1=27$
Hence, there are 27 terms in the given AP. | 256 | 633 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.34375 | 4 | CC-MAIN-2024-30 | latest | en | 0.538013 |
https://byjusexamprep.com/profit-loss--discount-tricks-i | 1,657,082,043,000,000,000 | text/html | crawl-data/CC-MAIN-2022-27/segments/1656104660626.98/warc/CC-MAIN-20220706030209-20220706060209-00779.warc.gz | 195,911,224 | 83,655 | # Profit, Loss & Discount Tricks
By Naveen Singh|Updated : April 29th, 2020
Today we will be covering a very important topic from the quantitative aptitude section that is Profit and loss. These formulas and shortcuts will be helpful for your upcoming Exams like CAPF, CDS, AFCAT, Air Force Group X & Y 2019. If you like it let us know.
Cost Price:
The price, at which an article is purchased, is called its cost price, abbreviated as C.P.
Selling Price:
The price, at which an article is sold, is called its selling prices, abbreviated as S.P.
• Profit/gain = SP – CP
• Profit % = Profit/(CP)×100
• SP = (100+gain % )/100 ×C P
• CP = 100/(100+gain %)×S P
Loss:
If the overall Cost Price exceeds the selling price of the buyer then he is said to have incurred loss.
• Loss = C P – S P
• Loss % = LOSS/(CP)×100
• SP = (100-loss %)/100×C P
• CP = 100/(100-loss %)×S P
Profit and Loss Based on Cost Price
To find the percent gain or loss, divide the amount gained or lost by the cost and multiply it by 100.
Example: A toy that cost 80 rupees is sold at a profit of 20 rupees. Find the percent or rate of profit.
Gain/cost × 100 = % profit.
20/80 × 100 = 25%. - Answer
To find the loss and the selling price when the cost and the percent loss are given, multiply the cost by the percent and subtract the product from the cost.
Example: A damaged chair that cost Rs.110 was sold at a loss of 10%. Find the loss and the selling price.
Cost x percent loss = loss.
110 x 1/10 = 11, loss.
Cost - loss = selling price.
110 - 11 = 99, selling price.
Profit and Loss Based on Selling Price
To find the profit and the cost when the selling price and the percent profit are given, multiply the selling price by the percent profit and subtract the result from the selling price.
Example: A toy is sold for Rs. 6.00 at a profit of 25% of the selling price. Separate this selling price into cost and profit.
Selling price x % profit = profit.
Selling price = profit + cost.
6.00 x .25 = 1.50, profit.
6.00 - 1.50 = 4.50, cost.
To find the loss and the cost when the selling price and the percent loss are given, multiply the selling price by the percent loss and subtract the result from the selling price.
Example: At a sale, neckties selling at Rs. 50.00 are sold at a loss of 60% of selling price. What is the loss and the original cost?
Selling price x % loss = loss.
Selling price + loss = cost.
50.00 x .60 = 30.00, loss.
50.00 - 30.00 = 20.00, cost.
To find the selling price when the cost and the percent loss are given, add the percent loss to 100% and divide the cost by this sum.
Example: Socks that cost 7.00 per pair were sold at a loss of 25% of selling price. What was the selling price?
Answer: Cost / (100% + % loss) = selling price.
7.00 / 1.25 = 5.60, selling price.
To find the selling price when the profit and the percent profit are given, or to find the selling price when the loss and the percent loss are given, divide the profit or loss by the percent profit or loss.
Note: This rule should be compared with the one under Profit and Loss Based on Cost. The two rules are exactly similar except that in one case 100% represents cost while in the other case 100% represents selling price.
Example: A kind of tape is selling at a profit of 12% of selling price, equal to 18 per yard. What is the selling price of the tape?
Answer: Profit / % profit = selling price.
18 /.12 = 1.50 selling price.
To find the percent profit or loss, divide the amount gained or lost by the selling price.
Example: A candy bar sells for 1.30 at a profit of 65. What percent of profit on selling price does this represent?
Answer: Gain / selling price = % profit.
65 / 1.30 = .5 or 50% profit.
Mark-up Price
Generally, the SP is less than the marked price (MP) the difference MP – SP is known as the discount, D.
Discount = M P – S P
Discount %, D% = (Discount) / (MP) ×100
To reduce percent loss on cost to percent loss on selling price, divide percent loss on cost by 100% minus percent loss on cost.
Example: 20% loss on cost is what percent loss on selling price?
% loss on cost / (100% - % loss on cost) = % loss on selling price.
0.20 / 80 = .0025 or 25% loss on selling price
To reduce percent loss on selling price to percent loss on cost, divide percent loss on selling price by 100% plus percent loss on selling price.
Example: 20% loss on selling price is what percent loss on cost?
% loss on selling price / (100% + % loss on selling price) = % loss on cost.
.20 / 1.20 = .16666 or .16.67% loss on cost.
To reduce percent mark-up (percent profit on cost) to percent profit on selling price, divide percent mark-up by 100% plus percent mark-up.
Example: A coat marked up 60% carries what percent of profit on selling price?
Answer : % profit on cost / ( 100% + % profit on cost ) = % profit on selling price.
.60 / 1.60 = .375 or 37.5% on selling price.
### Here we are providing you all the types of questions that have been asked in SSC Exams and How to solve it in an Easy way with Grade Stack methods:-
Type 1:
The cost price of 40 articles is the same as the selling price of 25 articles. Find the gain per cent. (CGL-2012)
(a) 65%
(b) 60%
(c) 15%
(d) 75%
Answer: (b) Gain per cent
=(40-25)/25×100
=15/25×100=60%
BYJU'S Exam Prep method:
In Above question We take x = 40 , y = 25
Then Gain % = (x –y) x 100/ y
Type2:
Bananas are bought at the rate of 6 for Rs. 5 and sold at the rate of 5 for Rs. 6. Profit per cent is: (CGL-2004)
(a) 36%
(b) 42%
(c) 44%
(d) 48%
Answer : (c) To avoid fraction, let the number of bananas bought
LCM of 5 and 6 = 30
CP of 30 bananas
= 5 x 5 = Rs. 25
SP of 30 Bananas = 6 x 6
= Rs. 36
Profit = Rs. (36-25) = Rs. 11
Profit %
= 11/25×100=44%
BYJU'S Exam Prep Method
[(6 x 6 -5x 5)/ (5 x 5)] x 100 = 44%
Type 3:
A man bought oranges at the rate of 8 for Rs 34 and sold them at the rate of 12 for Rs. 57. How many oranges should be sold to earn a net profit of Rs 45? (CGL-2011)
(a) 90
(b) 100
(c) 135
(d) 150
Answers: (a) Let the man buy 24 (LCM of 8 and 12) oranges.
C.P. of 24 oranges = 34/8 ×24 = Rs. 102
S.P. of 24 oranges = 27/12×24= Rs. 114
Gain = 114 – 102 = Rs. 12
Rs. 12 = 24 oranges
Rs. 45 = 24/12×45= 90 oranges
Type 4:
A shopkeeper earns a profit of 12% on selling a book at 10% discount on printed price. The ratio of the cost price to printed price of the book is ? (CGL-2013)
(a) 45 : 56
(b) 50 : 61
(c) 90 : 97
(d) 99 : 125
Answer: (a) C.P. of the book = Rs. x
Printed price = Rs. y
(y×90)/100=x × 112/100
x/y=90/112=45/56
Type 5:
A dealer sold two types of goods for Rs 10,000 each. On one of them, he lost 20% and on the other he gained 20%. His gain or loss per cent in the entire transaction was (CGL-2012)
(a) 2% loss
(b) 2% gain
(c) 4% gain
(d) 4% loss
Answers: (d) Here, S.P. is same, Hence there is always a loss. Loss per cent =(20×20)/100=4%
BYJU'S Exam Prep Trick:
Loss % = (n^2)/100= (20)^2/100= 4%
Where n= 20
Type 6:
On selling an article for Rs170, a shopkeeper loses 15%. In order to gain 20%, he must sell that article at rupees: (CGL-2013)
(a) 215.50
(b) 212.50
(c) 240
(d) 210
Answer ; (c) C.P. of article = (200×120)/100 = Rs. 240
Type 7:
An article is sold at a loss of 10%. Had it been sold for Rs. 9 more, there would have been a gain of 12 1/2% on it. The cost price of the article is (CGL – 2002)
(a) Rs. 40
(b) Rs. 45
(c) Rs. 50
(d) Rs. 35
Answers: (a) Let the cost price of the article = Rs. x
S.P. at 10% loss
= x×90/100= Rs. 9x/10
P. at 12 1/2 % gain
x × (100+12 1/2)/100 = Rs. 225x/200
According to the question
9x/10 + 9 = 225x/200
180x + 1800 = 225x
x = Rs. 40
Type 8:
A sells a suitcase to B at 10% profit. B sells it to C at 30% profit. If C pays Rs 2860 for it, then the price at which a bought it is (CGL-2013)
(a) 1000
(b) 1600
(c) 2000
(d) 2500
Answer: (c) If the C.P. of the suitcase for A be Rs. x, then
x ×110/100×130/100=2860
x=(2860×100×100)/(110×130) = Rs. 2000
Type 9:
Arun marks up the computer he is selling by 20% profit and sells them at a discount of 15%. Arun’s net gain percent is
(a) 4
(b) 2
(c) 3.5
(d) 2.5
BYJU'S Exam Prep method:
r1 = 20 , r2 = 15
Formula = r1 – r2 – (r1 x r2)/100
(20-15-(20×15)/100)
= 20 -18 = 2%
Type10:
A tradesman sold an article at a loss of 20%. If the selling price had been increased by Rs. 100, there would have been a gain of 5%. The cost price of the article was: (CGL-2004)
(a) Rs. 200
(b) Rs. 25
(c) Rs. 400
(d) Rs. 250
Answer (c) Let the C.P. of article be Rs. x.
105% of x - 80% of x = Rx. 100
25% of x = Rx. 100
x = Rs. (100×100)/25
= Rs. 400
That’s how Profit and loss questions are solved easily. Here is a short cut quiz for profit and loss to test your practice.
Below is a PDF for same:
### लाभ, हानि और छूट पर युक्तिया (हिंदी PDF)
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The Most Comprehensive Exam Prep App. | 2,894 | 8,978 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.875 | 4 | CC-MAIN-2022-27 | longest | en | 0.920952 |
https://www.kanopystreaming.com/product/pythagorean-theorem-1 | 1,518,902,354,000,000,000 | text/html | crawl-data/CC-MAIN-2018-09/segments/1518891807825.38/warc/CC-MAIN-20180217204928-20180217224928-00062.warc.gz | 880,673,733 | 12,665 | # The Pythagorean Theorem Episode 5 of Geometry
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Programmer : an Italian Pascal programmer, his name has been forgotten
Tested on TP 6.0 - works correct
Public domain
***************************Hope you'll enjoy******)
Uses Crt, Graph;
Type Matriz = Array [0..21, 0..11] Of Integer;
Type Tipopeca = Array [0..3, 0..3] Of Integer;
Var Matela, Mat1Tela, Mat2Tela, Cima : Matriz;
Next, Pecai, Pecal, Pecaf, Pecat,
Pecao, Pecas, Peca2, Peca, Pecagira : Tipopeca;
Prox, Aux, A, B, C, I, J, Num, Cont, Lin, Speed,
Lines, Nivel, Graphdriver, Graphmode, Con, Bant, Numnex : Integer;
Fim, Turn, Game, Dir, Esq, Giro, Novapeca : Boolean;
Tecla : Char;
Strin : String [6];
Q : String;
Ponto, Old : LongInt;
Procedure Botao (Col, Lin, Col1, Lin1: Integer);
Begin
SetFillStyle (1, 7); Bar (Col, Lin, Col1, Lin1);
SetColor (15); SetLineStyle (0, 1, 1);
Line (Col, Lin, Col1, Lin); Line (Col, Lin, Col, Lin1);
Line (Col, Lin+ 1, Col1, Lin+ 1); Line (Col+ 1, Lin, Col+ 1, Lin1);
Line (Col, Lin+ 2, Col1, Lin+ 2); Line (Col+ 2, Lin, Col+ 2, Lin1);
SetColor (8);
Line (Col, Lin1, Col1, Lin1); Line (Col+ 1, Lin1- 1, Col1, Lin1- 1);
Line (Col+ 2, Lin1- 2, Col1, Lin1- 2); Line (Col1, Lin, Col1, Lin1);
Line (Col1- 1, Lin+ 1, Col1- 1, Lin1); Line (Col1- 2, Lin+ 2, Col1- 2, Lin1);
SetColor (7);
Line (Col, Lin, Col+ 2, Lin+ 2); Line (Col1, Lin1, Col1- 2, Lin1- 2);
End;
Procedure Destela;
Begin
If Old<> Ponto Then Begin
Old:= Ponto;
Bar (1, 1, 100, 98);
SetColor (White);
OutTextXY (520, 85, 'Next');
Str (Ponto, Strin); OutTextXY (5, 10, 'Score:'+ Strin);
Str (Lines, Strin); OutTextXY (5, 30, 'Lines:'+ Strin);
Str (Nivel, Strin); OutTextXY (5, 50, 'Level:'+ Strin);
End;
For I:= 1 To 20 Do
For J:= 1 To 10 Do Begin
If Matela [I, J] = 0 Then Begin
SetFillStyle (1, Black);
Bar ( (J- 1) * 20+ 215, (I- 1) * 20+ 25, (J- 1) * 20+ 19+ 215, (I- 1) * 20+ 19+ 25);
End
Else If Matela [I, J] <> Mat2Tela [I, J] Then Begin
Botao ( (J- 1) * 20+ 215, (I- 1) * 20+ 25, (J- 1) * 20+ 19+ 215, (I- 1) * 20+ 19+ 25);
End;
End;
End;
Procedure Desnext;
Begin
For I:= 0 To 3 Do
For J:= 0 To 3 Do Begin
If Next [I, J] = 0 Then Begin
SetFillStyle (1, Black);
Bar ( (J- 1) * 20+ 515, (I- 1) * 20+ 25, (J- 1) * 20+ 19+ 515, (I- 1) * 20+ 19+ 25);
End
Else Begin
Botao ( (J- 1) * 20+ 515, (I- 1) * 20+ 25, (J- 1) * 20+ 19+ 515, (I- 1) * 20+ 19+ 25);
End;
End;
End;
Procedure Sorteia;
Begin
Numnex:= Random (7);
If Numnex= 0 Then Next:= Pecal
Else If Numnex= 1 Then Next:= Pecaf
Else If Numnex= 2 Then Next:= Pecai
Else If Numnex= 3 Then Next:= Pecao
Else If Numnex= 4 Then Next:= Pecas
Else If Numnex= 5 Then Next:= Peca2
Else If Numnex= 6 Then Next:= Pecat;
End;
Procedure Verlinha;
Begin
Aux:= Lines;
For A:= 1 To 4 Do
For I:= 20 Downto 1 Do Begin
Cont:= 0;
For J:= 1 To 10 Do If Matela [I, J] = 1 Then Cont:= Cont+ 1;
If Cont= 10 Then Begin
For J:= 1 To 10 Do Begin
Matela [I, J] := 0;
End;
Inc (Lines, 1);
For Lin:= 1 To (I- 1) Do
For J:= 1 To 10 Do Begin
Cima [Lin, J] := Matela [Lin, J];
Matela [Lin, J] := 0;
End;
For Lin:= 2 To I Do
For J:= 1 To 10 Do
Matela [Lin, J] := Cima [Lin- 1, J];
End;
End;
Ponto:= Ponto+ ( (Lines- Aux) * (Lines- Aux) * 100);
End;
Procedure Verifica;
Begin
If KeyPressed Then Begin
If Ord (Tecla) = 077 Then Begin
If Dir= True Then Begin
Inc (C, 1);
Inc (Con, 1);
If Con< 4 Then Dec (B, 1);
If Con>= 4 Then Begin
Con:= 0;
Dec (C, 1);
End;
End;
End
Else If Ord (Tecla) = 075 Then Begin
If Esq= True Then Begin
Dec (C, 1);
Inc (Con, 1);
If Con< 4 Then Dec (B, 1);
If Con>= 4 Then Begin
Con:= 0;
Inc (C, 1);
End;
End;
End
Else If Ord (Tecla) = 072 Then Begin
If Giro= True Then Begin
Inc (Con, 1);
If Con< 2 Then Dec (B, 1);
If Con>= 2 Then Con:= 0;
Pecagira:= Peca;
If (Num= 0) Or (Num= 1) Or (Num= 6) Then Begin
For I:= 1 To 3 Do Begin
Peca [3, I] := Pecagira [I, 1];
Peca [2, I] := Pecagira [I, 2];
Peca [1, I] := Pecagira [I, 3];
End;
End
Else If (Num= 4) Or (Num= 5) Then Begin
If Turn= True Then Begin
For I:= 0 To 3 Do Begin
Peca [3, I] := Pecagira [I, 0];
Peca [2, I] := Pecagira [I, 1];
Peca [1, I] := Pecagira [I, 2];
Peca [0, I] := Pecagira [I, 3];
Turn:= False;
End;
End
Else If Turn= False Then Begin
If Num= 4 Then Peca:= Pecas;
If Num= 5 Then Peca:= Peca2;
Turn:= True;
End;
End
Else If Num= 2 Then Begin
For I:= 0 To 3 Do
For J:= 0 To 3 Do
Peca [I, J] := Pecagira [J, I];
End;
End;
End
Else If Ord (Tecla) = 080 Then Speed:= 0;
End;
End;
Begin
DetectGraph (Graphdriver, Graphmode);
InitGraph (Graphdriver, Graphmode, ''); {The path of your BGI driver goes here
or your BGI must be in the current dir}
Randomize;
For I:= 0 To 3 Do
For J:= 0 To 3 Do Begin
Pecai [I, J] := 0;
Pecao [I, J] := 0;
Pecal [I, J] := 0;
Pecaf [I, J] := 0;
Pecat [I, J] := 0;
Pecas [I, J] := 0;
Peca2 [I, J] := 0;
End;
For I:= 0 To 3 Do Pecai [2, I] := 1;
For I:= 1 To 3 Do Pecal [2, I] := 1;
Pecal [1, 3] := 1;
For I:= 1 To 3 Do Pecaf [2, I] := 1;
Pecaf [1, 1] := 1;
For I:= 0 To 1 Do Pecas [I, 1] := 1;
For I:= 1 To 2 Do Pecas [I, 2] := 1;
For I:= 0 To 1 Do Peca2 [I, 2] := 1;
For I:= 1 To 2 Do Peca2 [I, 1] := 1;
For I:= 1 To 3 Do Pecat [2, I] := 1;
Pecat [1, 2] := 1;
For I:= 1 To 2 Do Pecao [1, I] := 1;
For I:= 1 To 2 Do Pecao [2, I] := 1;
Sorteia;
Old:= 0;
Con:= 0;
Ponto:= 0;
Lines:= 0;
Tecla:= '0';
For I:= 1 To 20 Do
For J:= 1 To 10 Do Matela [I, J] := 0;
For I:= 1 To 21 Do Matela [I, 0] := 1;
For I:= 1 To 21 Do Matela [I, 11] := 1;
For J:= 0 To 11 Do Matela [21, J] := 1;
SetBkColor (Black);
SetColor (White);
Line (214, 25, 214, 425);
Line (415, 25, 415, 425);
Line (215, 425, 414, 425);
Fim:= False;
Game:= True;
Repeat
Speed:= 3100;
Nivel:= 1;
Inc (Ponto, 10);
Speed:= Speed- ( (Ponto Div 4000) * 10);
Nivel:= Nivel+ (Ponto Div 4000);
Novapeca:= False;
Peca:= Next;
Num:= Numnex;
Sorteia;
Turn:= True;
C:= 4;
B:= 0;
Desnext;
Repeat
Verifica;
Verifica;
If B= Bant+ 1 Then Con:= 0;
Esq:= True;
Dir:= True;
Giro:= True;
Mat2Tela:= Matela;
Verlinha;
Mat1Tela:= Matela;
For I:= 0 To 2 Do
For J:= 0 To 2 Do Begin
If (Num= 4) Or (Num= 5) Then
If Matela [I+ B, J+ C] = 1 Then Giro:= False;
End;
For I:= 1 To 3 Do
For J:= 1 To 3 Do Begin
If (Num= 6) Or (Num= 0) Or (Num= 1) Then
If Matela [I+ B, J+ C] = 1 Then Giro:= False;
End;
For I:= 0 To 3 Do
For J:= 0 To 3 Do
If Novapeca= False Then Begin
If Num= 3 Then Giro:= False;
If Num= 2 Then
If Matela [I+ B, J+ C] = 1 Then Giro:= False;
If Matela [I+ B, J+ C] <> 1 Then
Begin
Matela [I+ B, J+ C] := Peca [I, J];
If (Matela [I+ B, J+ C+ 1] ) + (Peca [I, J] ) = 2 Then Dir:= False;
If (Mat1Tela [I+ B, J+ C- 1] ) + (Peca [I, J] ) = 2 Then Esq:= False;
If (Matela [I+ B+ 1, J+ C] ) + (Peca [I, J] ) = 2 Then
Begin
For I:= 0 To 3 Do
For J:= 0 To 3 Do
If Matela [I+ B, J+ C] <> 1 Then
Begin
Matela [I+ B, J+ C] := Peca [I, J];
End;
Destela;
Novapeca:= True;
End;
End;
End;
If Novapeca= False Then Begin
Destela;
For I:= 0 To 3 Do
For J:= 0 To 3 Do
If Mat1Tela [I+ B, J+ C] <> 1 Then
Matela [I+ B, J+ C] := 0;
Delay (Speed);
Bant:= B;
Inc (B, 1);
End;
If Ord (Tecla) = 027 Then Fim:= True;
Until (Novapeca= True) Or (Fim= True);
For J:= 4 To 6 Do If Matela [1, J] = 1 Then Game:= False;
Until (Game= False) Or (Fim= True);
CloseGraph;
ClrScr;
End. | 3,215 | 7,086 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.765625 | 3 | CC-MAIN-2019-13 | latest | en | 0.507988 |
https://www.math-only-math.com/worksheet-on-number-10.html | 1,713,845,621,000,000,000 | text/html | crawl-data/CC-MAIN-2024-18/segments/1712296818464.67/warc/CC-MAIN-20240423033153-20240423063153-00088.warc.gz | 795,835,591 | 13,306 | # Worksheet on Number 10
Free printable worksheet on number 10 for preschool kids are perfect for learning numbers. Enjoy the preschool number worksheets that help the kids to recognize number. Practice writing number 10 by tracing the number carefully and then learn to write number 10.
### Trace and learn to write the number 10:
Preschoolers and homeschoolers can practice these printable preschool worksheets on numbers to make the kids handwriting perfect. Parents and teachers can take the printouts of these worksheets on numbers and help the kids to practice these worksheets which are absolutely free. These worksheets can be access by anyone from anywhere. After practicing this worksheet kids can learn to write number 10 on their own.
Math Only Math is based on the premise that children do not make a distinction between play and work and learn best when learning becomes play and play becomes learning.
However, suggestions for further improvement, from all quarters would be greatly appreciated.
Traceable Numbers Worksheets for Kids
Practice tracing the numbers from 1 to 5
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Read More | 791 | 3,515 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.671875 | 4 | CC-MAIN-2024-18 | longest | en | 0.879673 |
https://www.enotes.com/homework-help/ordinate-point-6-distance-from-origin-point-9-220433 | 1,524,263,752,000,000,000 | text/html | crawl-data/CC-MAIN-2018-17/segments/1524125944742.25/warc/CC-MAIN-20180420213743-20180420233743-00390.warc.gz | 780,726,907 | 10,654 | # The ordinate of a point is 6 and the distance from origin to the point is 9. Find the abscissa of the point.
justaguide | Certified Educator
Let the abscissa of the point be x. Therefore the point is (x, 6)
Now the distance of (x, 6) from the origin is given to be 9.
We also know that the distance between (x1, y1) and (x2, y2) is given by sqrt [ (x2- x1)^2 + (y2 - y1)^2]
Therefore here we have 9 = sqrt [ ( x - 0)^2 + ( 6- 0)^2]
=> 9= sqrt ( x^2 + 36)
=> 81 = x^2 + 36
=> x^2 = 45
=> x = sqrt 45 = 3 sqrt 5
or x = -sqrt 45 = -3 sqrt 5
Therefore the abscissa of the point is 3 sqrt 5 or -3 sqrt 5
neela | Student
We know that the distance d between the two points P(x1,y1) and Q(x2, y2) is giben by
d ^2 = PQ^2 = (x2-x1)^2 +(y2-y1)^2.
The given point A has the ordinate 6, d = 9, the abscissa is to be determined. Let the abscissa be x. Therefore the point A is A(x, 6).
So the distance of A(x, 9) from the origin O (0, 0) is given by:
OA^2 = (x-0)^2+(6-0)^2 = 9 ...(1)
We solve the eq (1) for x to get the absissa:
x^2 = 9^2- 6^2
x^2 = 81-36 = 45.
So x = sqrt45 = 3sqrt5 , or x= -sqrt45= -3sqrt5
Therefore the abssisa of A is x = -3sqrt5 or x= - 3sqrt5.
giorgiana1976 | Student
We know that we can find the ordinate and the abscisa of a point, drawing perpendiculars from the given point to the x and y axis.
We'll form a right angle triangle, whose hypotenuse is the distance from origin to the point and cathetus is its abscisa.
We'll note the distance as r:
r = 9 units.
r^2 = 81 square units
We'll note the unknown abscisa as x and the ordinate as y.
y = 6 units
y^2 = 36 square units
We'll calculate x using Pythagorean Theorem:
r^2 = x^2 + y^2
x^2 = r^2 - y^2
x^2 = 81 - 36
x^2 = 45
x1 = sqrt 45
x1 = 3sqrt 5
x2 = - 3 sqrt 5
The ordinate of the point could be x = 3sqrt 5 or x = -3sqrt 5. | 704 | 1,842 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.34375 | 4 | CC-MAIN-2018-17 | latest | en | 0.848289 |
http://yougotmath.com/calculus/Suppose-That-F-x-F-039-x-And-F-quot-x-Are-Continuous-c7447.html | 1,548,336,515,000,000,000 | text/html | crawl-data/CC-MAIN-2019-04/segments/1547584547882.77/warc/CC-MAIN-20190124121622-20190124143622-00343.warc.gz | 402,145,326 | 5,293 | # Suppose That F(x), F'(x) And F"(x) Are Continuous...
AnonymousFrom: -Posts: -Votes: - Suppose that f(x), f'(x) and f"(x) are continuous for real numbersx, and that f has the following properties. i) f is negative on (-∞,6) and positive on (6,∞) ii) f is increasing on (-∞,8) and decreasing on(8,∞) iii) f is concave up on (-∞,3)and concave down on(3,∞) Of the following, which has the smallest numerical value? EXPLAINyour answer. a) f"(3) b) f '(10) c) f '(4) d) f '(1) e) f '(-7)
AnonymousFrom: -Posts: -Votes: - A) should be the largest values its where it goes from concaveup to conave down b) - e) you can see from ii) that f is increasing on(-∞,8) and decreasing on (8,∞) (whichbasically means the slope of f or its derivative) from i)f is negative on (-∞,6) and positive on (6,∞),(-∞,6) would have smaller values than (6,∞) with this information get e) to be the answer I hope this helps | 297 | 900 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.46875 | 3 | CC-MAIN-2019-04 | latest | en | 0.903723 |
http://www.chegg.com/homework-help/questions-and-answers/derive-f-t-e-2t-cos4tu-t-f-t-e-2t-sin4tu-t-q548430 | 1,464,088,653,000,000,000 | text/html | crawl-data/CC-MAIN-2016-22/segments/1464049270527.3/warc/CC-MAIN-20160524002110-00051-ip-10-185-217-139.ec2.internal.warc.gz | 446,736,085 | 12,731 | Derive
f(t)=e^(-2t)*cos4tu(t) and f(t)=e^(-2t)*sin4tu(t) | 33 | 56 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.765625 | 3 | CC-MAIN-2016-22 | latest | en | 0.399532 |
https://de.mathworks.com/matlabcentral/answers/1907420-matrix-addition-according-to-position-vector?s_tid=prof_contriblnk | 1,718,701,379,000,000,000 | text/html | crawl-data/CC-MAIN-2024-26/segments/1718198861747.70/warc/CC-MAIN-20240618073942-20240618103942-00676.warc.gz | 171,357,954 | 26,126 | # matrix addition according to position vector
1 Ansicht (letzte 30 Tage)
Rabb am 6 Feb. 2023
Beantwortet: Voss am 6 Feb. 2023
Hello, i have matrix A wich is 2xn dimension and vector b that is 1xn. I want to sort and sum A acording to vector b. for explamle
A=[1 3 5 7 9 11;
2 4 6 8 10 12]
b=[1 1 3 4 5 3]
C=[4 0 16 7 9
6 0 18 8 10]
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### Akzeptierte Antwort
Voss am 6 Feb. 2023
A=[1 3 5 7 9 11;
2 4 6 8 10 12];
b=[1 1 3 4 5 3];
Maybe something like this:
C = zeros(size(A));
ub = unique(b);
for ii = 1:numel(ub)
C(:,ub(ii)) = sum(A(:,b == ub(ii)),2);
end
disp(C);
4 0 16 7 9 0 6 0 18 8 10 0
Another way:
[bg,gidx] = findgroups(b);
C = zeros(size(A));
C(:,gidx) = splitapply(@(x)sum(x,2),A,bg);
disp(C);
4 0 16 7 9 0 6 0 18 8 10 0
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### Weitere Antworten (1)
Vilém Frynta am 6 Feb. 2023
This looks like homework.
It seems like you know what kind of functions you should work with. I'd recommend to study the documention of these functions and try to think it out. Feel free to share your progress.
If you are beginning with Matlab, it's good idea just to try (and learn from mistakes and experiments).
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Translated by | 571 | 1,690 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.890625 | 3 | CC-MAIN-2024-26 | latest | en | 0.397036 |
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Accounting (51)
ACCTG322 (11)
Chapter 6
# Chapter 6.pdf
7 Pages
79 Views
School
University of Alberta
Department
Accounting
Course
ACCTG322
Professor
Trish Stringer
Semester
Winter
Description
Chapter 6 – Solutions to Recommended Questions Problem 6-14 1. High-lowmethod: Repair Number of Jobs Costs High activity level........................260 \$24,000 Low activity level...........................80 9,600 Change .....................................180.... \$14,400 Variable cost per job: Change in cost = \$14,400 = \$80 per job Change in activity 180 jobs Fixed cost: Total repair cost at high activity level...................\$24,000.. Less variable element: 260 jobs × \$80 per job....................................20,800...... Fixed cost element ........................................\$ 3,200.......... Therefore, the cost formula is: Y = \$3,200 + \$80X. 2. Scattergraph method (see the scattergraph on the following page): (Note: Students’answers will vary due to the inherent imprecision and subjectivity of the scattergraph method of estimating fixed and variable costs.) The line intersects the cost axis at about \$4,250. The variable cost can be estimated as fol- lows: Total cost at 180 jobs (a point that falls on the line)..................\$18,000.... Less the fixed cost element (intersection of the Y axis on the graph)... 4,250 Variable cost element at 180 jobs (total)................................\$13,750........ \$13,750 ÷ 180 jobs = \$76.38 per job. Therefore, the cost formula is: Y = \$4,250 + \$76.38X. Page 1 of 7 Chapter 6 – Solutions to Recommended Questions Problem 6-14 (continued) The completed scattergraph follows: 3. Total predicted repair costs for 200 jobs: Y = \$3,200 + \$80(x) Y = \$3,200 + \$80(200) Y = \$3,200 + \$16,000 \$19,200Y 4. Neither of the formulas developed in parts 1 and 2 should be used to predict costs for a 600-job month because that level of activity appears to be well outside of the relevant range. The next closest activity level is only 260 jobs (May), which is less than half of the number of jobs the manager wants to predict costs for. Both fixed and variable costs could increase if the level of activity is 600 jobs. For example, additional mechanics may need to be hired, more repair equipment may be needed and facilities may need to be ex- panded (even temporarily) to accommodate an increase of that magnitude. Page 2 of 7 Chapter 6 – Solutions to Recommended Questions Problem 6-15 1. Maintenance cost at the 140,000 machine-hour level of activity can be isolated as follows: Level of Activity 80,000 MH 140,000 MH Total factory overhead cost.........................\$340,400 \$483,200 Deduct: Utilities cost @ \$1.30 per MH*.................... 104,000 182,000 Supervisory salaries ..............................120,000. 120,000 Maintenance cost....................................\$116,400.. \$181,200 *\$104,000 ÷ 80,000 MHs = \$1.30 per MH 2. High-low analysis of maintenance cost: Maintenance Machine- Cost Hours High activity level......................\$181,200 140,000 Low activity level.........................116,400 80,000 Change ...................................\$ 64,800. 60,000 Note: in this problem the high level of activity (140,000 hours) does not correspond to the high- est level of total overhead costs, which occurs in November. Variable cost per unit of activity: Change in cost = \$64,800 = \$1.08 per MH Change in activity 60,000 MHs Total fixed cost: Total maintenance cost at the low activity level .......................\$116,400....... Less the variable cost element (80,000 MHs × \$1.08 per MH)..............................................86,400......... Fixed cost element........................................................\$30,000..................... Therefore, the cost formula is \$30,000 per month plus \$1.08 per machine-hour or Y = \$30,000 + \$1.08X, where X represents machine-hours. Page 3 of 7 Chapter 6 – Solutions to Recommended Questions Problem 6-15 (continued) 3. Variable Rate per Ma- chine-HourCo Fsxed Maintenance cost............................ \$1.08 \$ 30,000 Utilities cost: \$104,000/80,000 ........... 1.30 Supervisory salaries cost ................ 120,000 Tota..l.s....................................\$2.38.. \$150,000 Therefore, the cost formula would be \$150,000 plus \$2.38 per machine-hour, or Y = \$150,000 + \$2.38X. 4. Fixedcost...............................................................\$150,000............... Variable co
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So we can recommend you notes for your school. | 1,156 | 4,826 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.15625 | 4 | CC-MAIN-2018-13 | latest | en | 0.783854 |
https://rdrr.io/cran/EnvStats/man/ciTableMean.html | 1,624,066,446,000,000,000 | text/html | crawl-data/CC-MAIN-2021-25/segments/1623487643354.47/warc/CC-MAIN-20210618230338-20210619020338-00296.warc.gz | 446,718,886 | 14,522 | ciTableMean: Table of Confidence Intervals for Mean or Difference Between... In EnvStats: Package for Environmental Statistics, Including US EPA Guidance
Description
Create a table of confidence intervals for the mean of a normal distribution or the difference between two means following Bacchetti (2010), by varying the estimated standard deviation and the estimated mean or differene between the two estimated means given the sample size(s).
Usage
1 2 3 ciTableMean(n1 = 10, n2 = n1, diff.or.mean = 2:0, SD = 1:3, sample.type = "two.sample", ci.type = "two.sided", conf.level = 0.95, digits = 1)
Arguments
n1 positive integer greater than 1 specifying the sample size when sample.type="one.sample" or the sample size for group 1 when sample.type="two.sample". The default value is n1=10. n2 positive integer greater than 1 specifying the sample size for group 2 when sample.type="two.sample". The default value is n2=n1, i.e., equal sample sizes. This argument is ignored when sample.type="one.sample". diff.or.mean numeric vector indicating either the assumed difference between the two sample means when sample.type="two.sample" or the value of the sample mean when sample.type="one.sample". The default value is diff.or.mean=2:0. Missing (NA), undefined (NaN), an infinite (-Inf, Inf) values are not allowed. SD numeric vector of positive values specifying the assumed estimated standard deviation. The default value is SD=1:3. Missing (NA), undefined (NaN), an infinite (-Inf, Inf) values are not allowed. sample.type character string specifying whether to create confidence intervals for the difference between two means (sample.type="two.sample"; the default) or confidence intervals for a single mean (sample.type="one.sample"). ci.type character string indicating what kind of confidence interval to compute. The possible values are "two-sided" (the default), "lower", and "upper". conf.level a scalar between 0 and 1 indicating the confidence level of the confidence interval. The default value is conf.level=0.95. digits positive integer indicating how many decimal places to display in the table. The default value is digits=1.
Details
Following Bacchetti (2010) (see NOTE below), the function ciTableMean allows you to perform sensitivity analyses while planning future studies by producing a table of confidence intervals for the mean or the difference between two means by varying the estimated standard deviation and the estimated mean or differene between the two estimated means given the sample size(s).
One Sample Case (sample.type="one.sample")
Let \underline{x} = (x_1, x_2, …, x_n) be a vector of n observations from an normal (Gaussian) distribution with parameters mean=μ and sd=σ.
The usual confidence interval for μ is constructed as follows. If ci.type="two-sided", the (1-α)100% confidence interval for μ is given by:
[\hat{μ} - t(n-1, 1-α/2) \frac{\hat{σ}}{√{n}}, \, \hat{μ} + t(n-1, 1-α/2) \frac{\hat{σ}}{√{n}}] \;\;\;\;\;\; (1)
where
\hat{μ} = \bar{x} = \frac{1}{n} ∑_{i=1}^n x_i \;\;\;\;\;\; (2)
\hat{σ}^2 = s^2 = \frac{1}{n-1} ∑_{i=1}^n (x_i - \bar{x})^2 \;\;\;\;\;\; (3)
and t(ν, p) is the p'th quantile of Student's t-distribution with ν degrees of freedom (Zar, 2010; Gilbert, 1987; Ott, 1995; Helsel and Hirsch, 1992).
If ci.type="lower", the (1-α)100% confidence interval for μ is given by:
[\hat{μ} - t(n-1, 1-α) \frac{\hat{σ}}{√{n}}, \, ∞] \;\;\;\; (4)
and if ci.type="upper", the confidence interval is given by:
[-∞, \, \hat{μ} + t(n-1, 1-α/2) \frac{\hat{σ}}{√{n}}] \;\;\;\; (5)
For the one-sample case, the argument n1 corresponds to n in Equation (1), the argument
diff.or.mean corresponds to \hat{μ} = \bar{x} in Equation (2), and the argument SD corresponds to \hat{σ} = s in Equation (3).
Two Sample Case (sample.type="two.sample")
Let \underline{x}_1 = (x_{11}, x_{21}, …, x_{n_11}) be a vector of n_1 observations from an normal (Gaussian) distribution with parameters mean=μ_1 and sd=σ, and let \underline{x}_2 = (x_{12}, x_{22}, …, x_{n_22}) be a vector of n_2 observations from an normal (Gaussian) distribution with parameters mean=μ_2 and sd=σ.
The usual confidence interval for the difference between the two population means μ_1 - μ_2 is constructed as follows. If ci.type="two-sided", the (1-α)100% confidence interval for μ_1 - μ_2 is given by:
[(\hat{μ}_1 - \hat{μ}_2) - t(n_1 + n_2 -2, 1-α/2) \hat{σ}√{\frac{1}{n_1} + \frac{1}{n_2}}, \; (\hat{μ}_1 - \hat{μ}_2) + t(n_1 + n_2 -2, 1-α/2) \hat{σ}√{\frac{1}{n_1} + \frac{1}{n_2}}] \;\;\;\;\;\; (6)
where
\hat{μ}_1 = \bar{x}_1 = \frac{1}{n_1} ∑_{i=1}^{n_1} x_{i1} \;\;\;\;\;\; (7)
\hat{μ}_2 = \bar{x}_2 = \frac{1}{n_2} ∑_{i=1}^{n_2} x_{i2} \;\;\;\;\;\; (8)
\hat{σ}^2 = s_p^2 = \frac{(n_1-1) s_1^2 + (n_2-1)s_2^2}{n_1 + n_2 - 2} \;\;\;\;\;\; (9)
s_1^2 = \frac{1}{n_1-1} ∑_{i=1}^{n_1} (x_{i1} - \bar{x}_1)^2 \;\;\;\;\;\; (10)
s_2^2 = \frac{1}{n_2-1} ∑_{i=1}^{n_2} (x_{i2} - \bar{x}_2)^2 \;\;\;\;\;\; (11)
and t(ν, p) is the p'th quantile of Student's t-distribution with ν degrees of freedom (Zar, 2010; Gilbert, 1987; Ott, 1995; Helsel and Hirsch, 1992).
If ci.type="lower", the (1-α)100% confidence interval for μ_1 - μ_2 is given by:
[(\hat{μ}_1 - \hat{μ}_2) - t(n_1 + n_2 -2, 1-α) \hat{σ}√{\frac{1}{n_1} + \frac{1}{n_2}}, \; ∞] \;\;\;\;\;\; (12)
and if ci.type="upper", the confidence interval is given by:
[-∞, \; (\hat{μ}_1 - \hat{μ}_2) - t(n_1 + n_2 -2, 1-α) \hat{σ}√{\frac{1}{n_1} + \frac{1}{n_2}}] \;\;\;\;\;\; (13)
For the two-sample case, the arguments n1 and n2 correspond to n_1 and n_2 in Equation (6), the argument diff.or.mean corresponds to \hat{μ_1} - \hat{μ_2} = \bar{x}_1 - \bar{x}_2 in Equations (7) and (8), and the argument SD corresponds to \hat{σ} = s_p in Equation (9).
Value
a data frame with the rows varying the standard deviation and the columns varying the estimated mean or difference between the means. Elements of the data frame are character strings indicating the confidence intervals.
Note
Bacchetti (2010) presents strong arguments against the current convention in scientific research for computing sample size that is based on formulas that use a fixed Type I error (usually 5%) and a fixed minimal power (often 80%) without regard to costs. He notes that a key input to these formulas is a measure of variability (usually a standard deviation) that is difficult to measure accurately "unless there is so much preliminary data that the study isn't really needed." Also, study designers often avoid defining what a scientifically meaningful difference is by presenting sample size results in terms of the effect size (i.e., the difference of interest divided by the elusive standard deviation). Bacchetti (2010) encourages study designers to use simple tables in a sensitivity analysis to see what results of a study may look like for low, moderate, and high rates of variability and large, intermediate, and no underlying differences in the populations or processes being studied.
Author(s)
Steven P. Millard (EnvStats@ProbStatInfo.com)
References
Bacchetti, P. (2010). Current sample size conventions: Flaws, Harms, and Alternatives. BMC Medicine 8, 17–23.
Berthouex, P.M., and L.C. Brown. (2002). Statistics for Environmental Engineers. Second Edition. Lewis Publishers, Boca Raton, FL.
Gilbert, R.O. (1987). Statistical Methods for Environmental Pollution Monitoring. Van Nostrand Reinhold, New York, NY.
Helsel, D.R., and R.M. Hirsch. (1992). Statistical Methods in Water Resources Research. Elsevier, New York, NY.
Millard, S.P., and N.K. Neerchal. (2001). Environmental Statistics with S-PLUS. CRC Press, Boca Raton, FL.
Ott, W.R. (1995). Environmental Statistics and Data Analysis. Lewis Publishers, Boca Raton, FL.
Zar, J.H. (2010). Biostatistical Analysis. Fifth Edition. Prentice-Hall, Upper Saddle River, NJ.
enorm, t.test, ciTableProp, ciNormHalfWidth, ciNormN, plotCiNormDesign.
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 # Show how potential confidence intervals for the difference between two means # will look assuming standard deviations of 1, 2, or 3, differences between # the two means of 2, 1, or 0, and a sample size of 10 in each group. ciTableMean() # Diff=2 Diff=1 Diff=0 #SD=1 [ 1.1, 2.9] [ 0.1, 1.9] [-0.9, 0.9] #SD=2 [ 0.1, 3.9] [-0.9, 2.9] [-1.9, 1.9] #SD=3 [-0.8, 4.8] [-1.8, 3.8] [-2.8, 2.8] #========== # Show how a potential confidence interval for a mean will look assuming # standard deviations of 1, 2, or 5, a sample mean of 5, 3, or 1, and # a sample size of 15. ciTableMean(n1 = 15, diff.or.mean = c(5, 3, 1), SD = c(1, 2, 5), sample.type = "one") # Mean=5 Mean=3 Mean=1 #SD=1 [ 4.4, 5.6] [ 2.4, 3.6] [ 0.4, 1.6] #SD=2 [ 3.9, 6.1] [ 1.9, 4.1] [-0.1, 2.1] #SD=5 [ 2.2, 7.8] [ 0.2, 5.8] [-1.8, 3.8] #========== # The data frame EPA.09.Ex.16.1.sulfate.df contains sulfate concentrations # (ppm) at one background and one downgradient well. The estimated # mean and standard deviation for the background well are 536 and 27 ppm, # respectively, based on a sample size of n = 8 quarterly samples taken over # 2 years. A two-sided 95% confidence interval for this mean is [514, 559], # which has a half-width of 23 ppm. # # The estimated mean and standard deviation for the downgradient well are # 608 and 18 ppm, respectively, based on a sample size of n = 6 quarterly # samples. A two-sided 95% confidence interval for the difference between # this mean and the background mean is [44, 100] ppm. # # Suppose we want to design a future sampling program and are interested in # the size of the confidence interval for the difference between the two means. # We will use ciTableMean to generate a table of possible confidence intervals # by varying the assumed standard deviation and assumed differences between # the means. # Look at the data #----------------- EPA.09.Ex.16.1.sulfate.df # Month Year Well.type Sulfate.ppm #1 Jan 1995 Background 560 #2 Apr 1995 Background 530 #3 Jul 1995 Background 570 #4 Oct 1995 Background 490 #5 Jan 1996 Background 510 #6 Apr 1996 Background 550 #7 Jul 1996 Background 550 #8 Oct 1996 Background 530 #9 Jan 1995 Downgradient NA #10 Apr 1995 Downgradient NA #11 Jul 1995 Downgradient 600 #12 Oct 1995 Downgradient 590 #13 Jan 1996 Downgradient 590 #14 Apr 1996 Downgradient 630 #15 Jul 1996 Downgradient 610 #16 Oct 1996 Downgradient 630 # Compute the estimated mean and standard deviation for the # background well. #----------------------------------------------------------- Sulfate.back <- with(EPA.09.Ex.16.1.sulfate.df, Sulfate.ppm[Well.type == "Background"]) enorm(Sulfate.back, ci = TRUE) #Results of Distribution Parameter Estimation #-------------------------------------------- # #Assumed Distribution: Normal # #Estimated Parameter(s): mean = 536.2500 # sd = 26.6927 # #Estimation Method: mvue # #Data: Sulfate.back # #Sample Size: 8 # #Confidence Interval for: mean # #Confidence Interval Method: Exact # #Confidence Interval Type: two-sided # #Confidence Level: 95% # #Confidence Interval: LCL = 513.9343 # UCL = 558.5657 # Compute the estimated mean and standard deviation for the # downgradient well. #---------------------------------------------------------- Sulfate.down <- with(EPA.09.Ex.16.1.sulfate.df, Sulfate.ppm[Well.type == "Downgradient"]) enorm(Sulfate.down, ci = TRUE) #Results of Distribution Parameter Estimation #-------------------------------------------- # #Assumed Distribution: Normal # #Estimated Parameter(s): mean = 608.33333 # sd = 18.34848 # #Estimation Method: mvue # #Data: Sulfate.down # #Sample Size: 6 # #Number NA/NaN/Inf's: 2 # #Confidence Interval for: mean # #Confidence Interval Method: Exact # #Confidence Interval Type: two-sided # #Confidence Level: 95% # #Confidence Interval: LCL = 589.0778 # UCL = 627.5889 # Compute the estimated difference between the means and the confidence # interval for the difference: #---------------------------------------------------------------------- t.test(Sulfate.down, Sulfate.back, var.equal = TRUE) #Results of Hypothesis Test #-------------------------- # #Null Hypothesis: difference in means = 0 # #Alternative Hypothesis: True difference in means is not equal to 0 # #Test Name: Two Sample t-test # #Estimated Parameter(s): mean of x = 608.3333 # mean of y = 536.2500 # #Data: Sulfate.down and Sulfate.back # #Test Statistic: t = 5.660985 # #Test Statistic Parameter: df = 12 # #P-value: 0.0001054306 # #95% Confidence Interval: LCL = 44.33974 # UCL = 99.82693 # Use ciTableMean to look how the confidence interval for the difference # between the background and downgradient means in a future study using eight # quarterly samples at each well varies with assumed value of the pooled standard # deviation and the observed difference between the sample means. #-------------------------------------------------------------------------------- # Our current estimate of the pooled standard deviation is 24 ppm: summary(lm(Sulfate.ppm ~ Well.type, data = EPA.09.Ex.16.1.sulfate.df))\$sigma #[1] 23.57759 # We can see that if this is overly optimistic and in our next study the # pooled standard deviation is around 50 ppm, then if the observed difference # between the means is 50 ppm, the lower end of the confidence interval for # the difference between the two means will include 0, so we may want to # increase our sample size. ciTableMean(n1 = 8, n2 = 8, diff = c(100, 50, 0), SD = c(15, 25, 50), digits = 0) # Diff=100 Diff=50 Diff=0 #SD=15 [ 84, 116] [ 34, 66] [-16, 16] #SD=25 [ 73, 127] [ 23, 77] [-27, 27] #SD=50 [ 46, 154] [ -4, 104] [-54, 54] #========== # Clean up #--------- rm(Sulfate.back, Sulfate.down)
EnvStats documentation built on Oct. 23, 2020, 6:41 p.m. | 4,525 | 14,295 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.6875 | 3 | CC-MAIN-2021-25 | longest | en | 0.721471 |
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12-09-2005, 04:03 PM #1 BSOD Join Date: Jul 2005 Posts: 1,724 calculating pi is there a way to have ur comp just like calculate pi to like the end? just like keep calculating it and saving it to a wordpad file or something? __________________
12-09-2005, 04:37 PM #2 BSOD Join Date: Jun 2005 Posts: 2,999 Re: calculating pi There is no end __________________
12-09-2005, 04:49 PM #3
Baseband Member
Join Date: Oct 2005
Posts: 77
Re: calculating pi
Quote:
Originally Posted by MarxSoccer There is no end
No one has yet proven pi to be an irrational number, hence there may or may not be an end: that is the question
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12-09-2005, 05:10 PM #4 Golden Master Join Date: May 2004 Location: No Posts: 5,427 Re: calculating pi well if you got alot of spare times i suppose you could attempt to find an end if there is one
12-09-2005, 05:33 PM #7 Daemon Poster Join Date: Dec 2004 Posts: 1,080 Re: calculating pi Look at my Super Pi thread That does calculate Pi to up to 32million places. You can also apply for a program which will do more
12-09-2005, 05:36 PM #8 BSOD Join Date: Jun 2005 Posts: 2,999 Re: calculating pi That program is stupid. Pi is alot longer than that program computes. Sure if you just want so many digits, but..
12-09-2005, 05:47 PM #9
Daemon Poster
Join Date: Jun 2004
Posts: 838
Re: calculating pi
Quote:
Originally Posted by MarxSoccer That program is stupid. Pi is alot longer than that program computes. Sure if you just want so many digits, but..
its may be lot longer but really, whats the point??
if you have pi to 30 billion places? you can not possibly comprehend the tiny difference between that and *only* 25 billion deciaml places! unless your trying to calculate the size of the universe whats the point exactly?! and what in the end...? you might be a few miles out in millions of light years?!
sorry that sounds like a rant its not really meant to be! lol and yes it is a bit sarcastic...
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12-09-2005, 05:51 PM #10
Daemon Poster
Join Date: Dec 2004
Posts: 1,080
Re: calculating pi
Quote:
Originally Posted by MarxSoccer That program is stupid. Pi is alot longer than that program computes. Sure if you just want so many digits, but..
If you contact the makers, you can apply to have the program which will do Pi to the world record, which is 4.2 billion places Long enough?
__________________ | 702 | 2,642 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.65625 | 3 | CC-MAIN-2016-44 | longest | en | 0.880329 |
https://qna.talkjarvis.com/212985/average-harmonic-components-fundamental-component-average-periodic | 1,713,857,918,000,000,000 | text/html | crawl-data/CC-MAIN-2024-18/segments/1712296818468.34/warc/CC-MAIN-20240423064231-20240423094231-00893.warc.gz | 423,756,023 | 11,001 | For any given signal, average power in its 6 harmonic components as 10 mw each and fundamental component also has 10 mV power. Then, average power in the periodic signal is _______________
+1 vote
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For any given signal, average power in its 6 harmonic components as 10 mw each and fundamental component also has 10 mV power. Then, average power in the periodic signal is _______________
(a) 70
(b) 60
(c) 10
(d) 5
I have been asked this question during an interview for a job.
Question is from Concept of Convolution topic in chapter Signal Transmission Through Linear Systems of Signals and Systems
by (42.1k points)
Correct option is (b) 60
Explanation: We know that according to Parseval’s relation, the average power is equal to the sum of the average powers in all of its harmonic components.
∴ Pavg = 10 × 6 = 60.
+1 vote
+1 vote
+1 vote | 216 | 862 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.21875 | 3 | CC-MAIN-2024-18 | latest | en | 0.949966 |
https://www.numbersaplenty.com/246051191 | 1,701,424,351,000,000,000 | text/html | crawl-data/CC-MAIN-2023-50/segments/1700679100286.10/warc/CC-MAIN-20231201084429-20231201114429-00221.warc.gz | 1,036,196,920 | 3,036 | Search a number
246051191 is a prime number
BaseRepresentation
bin11101010101001…
…11000101110111
3122010222200210002
432222213011313
51000442114231
640225421515
76045254261
oct1652470567
9563880702
10246051191
111169869a1
126a49a89b
133bc8c229
142496cb31
15169040cb
hexeaa7177
246051191 has 2 divisors, whose sum is σ = 246051192. Its totient is φ = 246051190.
The previous prime is 246051173. The next prime is 246051193. The reversal of 246051191 is 191150642.
It is a strong prime.
It is a cyclic number.
It is a de Polignac number, because none of the positive numbers 2k-246051191 is a prime.
Together with 246051193, it forms a pair of twin primes.
It is a Chen prime.
It is a congruent number.
It is not a weakly prime, because it can be changed into another prime (246051193) by changing a digit.
It is a pernicious number, because its binary representation contains a prime number (17) of ones.
It is a polite number, since it can be written as a sum of consecutive naturals, namely, 123025595 + 123025596.
It is an arithmetic number, because the mean of its divisors is an integer number (123025596).
Almost surely, 2246051191 is an apocalyptic number.
246051191 is a deficient number, since it is larger than the sum of its proper divisors (1).
246051191 is an equidigital number, since it uses as much as digits as its factorization.
246051191 is an odious number, because the sum of its binary digits is odd.
The product of its (nonzero) digits is 2160, while the sum is 29.
The square root of 246051191 is about 15686.0189659454. The cubic root of 246051191 is about 626.6261151832.
The spelling of 246051191 in words is "two hundred forty-six million, fifty-one thousand, one hundred ninety-one". | 501 | 1,731 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.171875 | 3 | CC-MAIN-2023-50 | latest | en | 0.851844 |
https://www.daniweb.com/programming/software-development/threads/321927/recursive-function-problem | 1,713,424,395,000,000,000 | text/html | crawl-data/CC-MAIN-2024-18/segments/1712296817200.22/warc/CC-MAIN-20240418061950-20240418091950-00673.warc.gz | 656,779,304 | 21,622 | I dont know how to start. I learn python by myself, hopefully i can solve this problem.
but i think i need your guys help
A palindrome is a sentence that contains the same sequence of letters reading it either forwards or backwards. For example "racecar". Write a recursive function that detects whether a string is a palindrome. The basic idea is to check that the first and last letters of the string are the same letter. If they are, then the entire string is a palindrome if everything between those letters is a palindrome. When you compare letters, ensure you do it in a case-insensitive way. Use your function in a program that prompts the user for a phrase and then tells whether or not it is a palindrome.
## All 17 Replies
Post your code and let us see what you have done up until now.
To help you get started, for recursive function, think of
(1) termination condition
(2) each successive step solves a smaller subset of original problem.
In your case, you can solve the problem by checking the first and last
characters, and passing the shorter substring with first and last characters
removed to the recursive function.
Try this fancy one.
``````def chec(sa):
data=[]; #make a list
for x in sa:
data.append(x.lower()); #pack the result into the list
d1 ,d2 =(data[0], data[-1]);
if d1 == d2: #check up the results
print d1 ,d2 , "are the same";
else:
print d1 , d2 , "are not the same"
chec("racecar")
#============== Reuults=============
r r are the same``````
will do what you wnat i think ;)
And OP must add the recursion?
To only check if things are palindrome is by the way enough to:
``def ispalindrome(x): return x == x[::-1]``
(The recursive version can be written with same amount of lines)
And OP must add the recursion?
To only check if things are palindrome is by the way enough to:
``def ispalindrome(x): return x == x[::-1]``
(The recursive version can be written with same amount of lines)
I like that. It's much shorter than what I was thinking of. However the OP says that palindromes can be sentences as well as single words, so the function perhaps should also remove all punctuation and spaces from the input string before testing it the first time. That way it could handle palindromic sentences such as, "Red Roses run no risk, sir, on nurses order."
Try this fancy stuff:
``````import time # for time
def chec(sa):
fd=sa
for x in range(1, 10): #fancy.... You dont really need this but mmmm
print ".", #
time.sleep(1) #
print '\n' # you can try
data = []; #make a list
try:
for x in sa:
data.append(x.lower()); #pack the result into the list
d1, d2 = (data[0], data[-1]);
except:
print "Values needed"
else:
if d1 == d2: #check up the results
print 'Check Results'
print "-"*30
print d1.upper(), d2.upper(), 'are the same\n';
else:
print 'Check Results'
print "-"*30
print d1.upper(), d2.upper(), 'are not the same\n'
print "You entered:",fd ,'\n\n'
while True: #
choice = raw_input("Please enter choice [Enter] or Q[to quit]: ").lower().strip()#get data
if choice == "q": #check data
break; #action
else:
try: #exception check
palin = raw_input("Please enter a Phrase: ")
chec(palin)
except ValueError: #catch
print "Enter phrase to check";
print "Check finished" #final line``````
Look is fun ok ;)
I like that. It's much shorter than what I was thinking of. However the OP says that palindromes can be sentences as well as single words, so the function perhaps should also remove all punctuation and spaces from the input string before testing it the first time. That way it could handle palindromic sentences such as, "Red Roses run no risk, sir, on nurses order."
Yes unfortunately it takes two lines without being too hackish (replacing assignment with single item loop):
``````sentence = "Red Roses run no risk, sir, on nurses order."
sentence_clean = ''.join(c.lower() for c in sentence if c.isalpha())
print '%r %s palindrome.' % (sentence, 'is' if sentence_clean == sentence_clean[::-1] else 'is not')``````
Not recursion, but proof of concept only (and done quickly). Returns zero if it is a palindrome.
``````def ispalindrome(pal): return sum([0 if x == pal[(ctr+1)*-1] else 1 for ctr, x in enumerate(pal) if ctr < len(pal)/2])
sentence = "Red Roses run no risk, sir, on nurses order."
sentence_clean = ''.join(c.lower() for c in sentence if c.isalpha())
print ispalindrome(sentence_clean)
print ispalindrome("abcdef")``````
zero is False so may I kindly suggest that you wooee replace sum with not any which has short cut logic. Using generator instead of producing list would be also nicer.
Have to say that your algorithm looks little too FORTRANish for my taste ;)
How do you guys expert a newbie to understand short algorithm like this.????
Are you helping or showing off???
;)
qingmui does not get you guys ;)
We are just entertaining ourself while not giving the answer.
OK, OP:
consider these candidates from simpler to more difficult for recursive algorithm base case:
ispalindrome('')
ispalindrome('a')
ispalindrome('aa')
ispalindrome('ab')
ispalindrome('aba')
ispalindrome('abc')
and consider that
'aa' = 'a'+''+'a'
'ab' = 'a'+''+'b'
means 'aa'[1:-1] = '', which is valid input for ispalindrome function.
There are literally hundreds of palindrome examples on the web, most using "standard" methods, and some of which I have posted myself. Solutions using recursion are posted in many places on Daniweb as well, for anyone who looks. I am not going to reward the lazy.
There are literally hundreds of palindrome examples on the web, most using "standard" methods, and some of which I have posted myself. Solutions using recursion are posted in many places on Daniweb as well, for anyone who looks. I am not going to reward the lazy.
Your recursive solution link is luckily the Vegaseat solution that I gave in this thread for the very reason it is not recursive. We are trying to make one guy to understand recursion, not to learn copy-paste, I think!
The recursive solution is very simple one liner, I do not think it is necessary to mislead the OP nor to give the solution. If he gets it we can show our cards.
This is also usefull fact for super simplicity of the recursive solution:
``````>>> 'a'[1:-1]
''``````
can you help me!!
I have assignment that told me to write a function 'CheckSmaller' that takes two linked list as input arguments. These linked list contain numbers like this:
num1->3->5->2->NULL (assuming that num1 is pointing to number 352)
num2->4->3->9->1->NULL (assuming that num2 is pointing to number 4391)
The function CheckSmaller should return 1 if num1 points to a linked list which represents a smaller number than the number pointed to by num2 linked list. Otherwise, it returns -1. If both linked list point to exactly the same number, CheckSmaller returns a 0.
int CheckSmaller(Node* num1, Node* num2);
Notice that if two linked lists are:
num1->8->4->2->NULL (assuming that number 1 is 842) and
num2->8->4->3->NULL (assuming that number 2 is 843)
then your function should return 1 since 842 is smaller than 843.
and I want to use Recursion for this function
THANK YOU
Notice:
Hijacking older threads with an unrelated problem is considered bad manners!
Please start your own thread and show some coding effort!
Please i want it today or tomorrow >__<
I am showing this only as a basic example of a recursive function ...
``````# a typical example of a recursive function
# there is a limit to recursions in Python
# sys.getrecursionlimit() --> usually 1000
# can be changed with
# sys.setrecursionlimit(new_limit)
def palindrome_recursive(s):
# slicing gets the first and last letter
first = s[:1]
last = s[-1:]
print(first, last, s[1:-1]) # for testing only
if first != last:
return False
# exit condition
if len(s) < 2:
return True
# recursion calls the function from within the function
# with an adjusted parameter, first and last letter sliced off
return palindrome_recursive(s[1:-1])
s = "racecar"
print(palindrome_recursive(s))``````
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We're a friendly, industry-focused community of developers, IT pros, digital marketers, and technology enthusiasts meeting, networking, learning, and sharing knowledge. | 2,036 | 8,234 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.3125 | 3 | CC-MAIN-2024-18 | latest | en | 0.880055 |
https://study-assistantph.com/filipino/question2388104 | 1,669,960,352,000,000,000 | text/html | crawl-data/CC-MAIN-2022-49/segments/1669446710898.93/warc/CC-MAIN-20221202050510-20221202080510-00483.warc.gz | 544,223,585 | 61,071 | # Chunye euch set of dissimilar fractions into similar fractions usindenominator.2 13 210 39 182 5 109'15'545145/453'8'123 5 43.10 3 49'18'622' 4'1113 6 128 1 1216'12'2421²1472 8 44 8 93'12 '1446'92'232 5210 2 43 1619'4'76think ahead
Changing Dissimilar Fractions to Similar
6/16, 4/16, 10/16
Step-by-step explanation:
Find the least common denominator of 8, 4, and 16 which is 16.
Use 16 as the denominator for the similar fractions such that (3)(2)/16, (1)(4)/16, and 10/16.
Simplify the fractions, 6/16, 4/16, and 10/16.
Connaissez-vous la bonne réponse?
Chunye euch set of dissimilar fractions into similar fractions usindenominator.2 13 210 39 182 5 109... | 250 | 669 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.796875 | 4 | CC-MAIN-2022-49 | latest | en | 0.681947 |
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- OpenFOAM (http://www.cfd-online.com/Forums/openfoam/)
- - p relaxationFactor in twoPhaseEulerFoam (http://www.cfd-online.com/Forums/openfoam/91927-p-relaxationfactor-twophaseeulerfoam.html)
hkhosravi August 26, 2011 11:42
p relaxationFactor in twoPhaseEulerFoam
dear foamers
i`m using twoPhaseEulerFoam for my simuation.
relaxationfactor for my simulation is:
relaxationFactors
{
Ua 0.7;
Ub 0.7;
p 0.3;
alpha 0.2;
beta 0.2;
Theta 0.2;
k 0.4;
epsilon 0.4;
}
but an error was occure only for p (pressure relaxation factor) !!
the error is:
Courant Number mean: 0.00035655 max: 0.0004
Max Ur Courant Number = 0.0004
deltaT = 1.1999e-05
Time = 1.1999e-05
PIMPLE: iteration 1
DILUPBiCG: Solving for alpha, Initial residual = 1.08695e-06, Final residual = 1.52185e-22, No Iterations 1
Dispersed phase volume fraction = 0.11 Min(alpha) = 0 Max(alpha) = 0.55
DILUPBiCG: Solving for alpha, Initial residual = 8.6948e-07, Final residual = 1.52191e-22, No Iterations 1
Dispersed phase volume fraction = 0.11 Min(alpha) = 0 Max(alpha) = 0.55
kinTheory: max(Theta) = 1e-05
kinTheory: min(nua) = 2.94999e-08, max(nua) = 2.97152e-06
kinTheory: min(pa) = 0, max(pa) = 1.20197e-10
GAMG: Solving for p, Initial residual = 1, Final residual = 0.0810062, No Iterations 4
--> FOAM FATAL ERROR:
previous iteration field
IOobject: volScalarField p "/home/hamed/OpenFOAM/hamed-2.0.0/mycase/al96-H0=10-03/0"
not stored. Use field.storePrevIter() at start of iteration.
From function GeometricField<Type, PatchField, GeoMesh>::prevIter() const
in file /home/hamed/OpenFOAM/OpenFOAM-2.0.0/src/OpenFOAM/lnInclude/GeometricField.C at line 844.
FOAM aborting
#0 Foam::error::printStack(Foam::Ostream&) in "/home/hamed/OpenFOAM/OpenFOAM-2.0.0/platforms/linuxGccDPOpt/lib/libOpenFOAM.so"
#1 Foam::error::abort() in "/home/hamed/OpenFOAM/OpenFOAM-2.0.0/platforms/linuxGccDPOpt/lib/libOpenFOAM.so"
#2
in "/home/hamed/OpenFOAM/OpenFOAM-2.0.0/platforms/linuxGccDPOpt/bin/twoPhaseEulerFoam"
#3
in "/home/hamed/OpenFOAM/OpenFOAM-2.0.0/platforms/linuxGccDPOpt/bin/twoPhaseEulerFoam"
#4
in "/home/hamed/OpenFOAM/OpenFOAM-2.0.0/platforms/linuxGccDPOpt/bin/twoPhaseEulerFoam"
#5
in "/home/hamed/OpenFOAM/OpenFOAM-2.0.0/platforms/linuxGccDPOpt/bin/twoPhaseEulerFoam"
#6 __libc_start_main in "/lib/tls/i686/cmov/libc.so.6"
#7
in "/home/hamed/OpenFOAM/OpenFOAM-2.0.0/platforms/linuxGccDPOpt/bin/twoPhaseEulerFoam"
Aborted
any solution or idea??? :confused:
wyldckat August 26, 2011 12:51
Greetings hkhosravi,
OpenFOAM's take on folder and file names is that the file system reflects the program variables... with the exception of time folders which should be properly formatted numbers.
Therefore "al96-H0=10-03" is a very bad folder name! I'm stuned how OpenFOAM didn't stop right at the beginning telling you that the name "al96-H0=10-03" is invalid...
Try again with another folder name for your case! Something more... simple! You could try with "al96_H0__10_03".
Best regards,
Bruno
hkhosravi August 26, 2011 14:16
Hi Bruno
I changed the folder name to "al96_03" also "al96", but there are the same error.
i`m sure the problem relate to "p" relaxation factor, because when i delete it, everything is correct !!
wyldckat August 26, 2011 14:39
Quote:
Originally Posted by hkhosravi (Post 321822) I changed the folder name to "al96_03" also "al96", but there are the same error.
Well, at least that's a relief... it would be very annoying that one's liberty to create crazy folder names (programmatically-wise) would be restricted as well ;)
Quote:
Originally Posted by hkhosravi (Post 321822) i`m sure the problem relate to "p" relaxation factor, because when i delete it, everything is correct !!
:eek: How could I have not spotted this before... Does the file "0/p" exist and have the necessary boundaries and field? That's what the error message is talking about!
In case you can't define it yourself, I think you can use the following instructions to write the p field: http://openfoamwiki.net/index.php/Ti...gisteredObject
hkhosravi August 26, 2011 15:53
:eek: How could I have not spotted this before... Does the file "0/p" exist and have the necessary boundaries and field? That's what the error message is talking about![/QUOTE]
The file "0/p" exist and have the correct BC, because I can run the case without using relaxation factor for "p".
also, In the stored time directory, "p" field exist and I can see pressure field in paraview.
wyldckat August 26, 2011 16:11
After googling it a bit... :eek: It's a bug! See http://www.openfoam.com/mantisbt/view.php?id=245
It should be fixed in OpenFOAM 2.0.1, so you should upgrade!
Best regards,
Bruno
hkhosravi August 27, 2011 02:18
yes, it`s a bug and solved in OF 2.0.1.
thanks Bruno
Regards
All times are GMT -4. The time now is 09:02. | 1,594 | 4,870 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.734375 | 3 | CC-MAIN-2016-36 | latest | en | 0.577284 |
https://www.codeavail.com/you-will-create-a-PowerPoint-presentation-that-contains-the- | 1,716,583,000,000,000,000 | text/html | crawl-data/CC-MAIN-2024-22/segments/1715971058736.10/warc/CC-MAIN-20240524183358-20240524213358-00546.warc.gz | 614,494,668 | 13,951 | # you will create a PowerPoint presentation that contains the various heat transfer mechanisms,
INSTRUCTIONS TO CANDIDATES
For Unit VII assignment, you will create a PowerPoint presentation that contains the various heat transfer mechanisms, some applications of ideal gas law, and the kinetic theory. In your presentation, be sure to include the following: 1.
Compare and contrast the three heat transfer methods(conduction, convection, and radiation) with examples. 2.Describe the relationship between temperature, pressure, and volume in the ideal gas law with examples. 3.
Explain the concept of the kinetic theory of gases For addition information you can click PowerPoint Basics link. Your PowerPoint presentation must contain the following components: (1) title slide, (2) at least ten slides explaining the bullet points listed above, (3) presenter notes for every slide except the title and reference slide, (4) a reference from the CSU Library Database and other references including our textbook, (5) at least five images/diagrams/tables.
PowerPoint slides should not contain a lot of text; •Use presenter notes to provide the details of your presentation. The general best practice is to use no more than 5-6 bullet points per slide
. •Your PowerPoint must be a minimum of 10 slides not including the title and reference slide. •You also need to utilize presenter notes to provide a detailed description of your content. •You are required to insert appropriate images, diagrams, and tables to enhance your content.
•In addition, you must use at least two scholarly references in your presentation. Use the CSU Online Library and Writing Center for assistance with the research and proper formatting. Im thinking 13 slides (not counting title and references) due date in about 14 days there about.
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Hire Me
Hire Me | 712 | 3,473 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.71875 | 3 | CC-MAIN-2024-22 | latest | en | 0.863829 |
http://www.cheresources.com/content/articles/safety/rupture-disks-for-process-engineers-part-4?pg=2 | 1,547,937,196,000,000,000 | text/html | crawl-data/CC-MAIN-2019-04/segments/1547583684033.26/warc/CC-MAIN-20190119221320-20190120003320-00243.warc.gz | 287,918,099 | 16,622 | ## Rupture Disks for Process Engineers - Part 4
Nov 08 2010 01:30 PM | pleckner in Safety and Pressure Relief
Backpressure
A rupture disk is actually a differential pressure device where the specified burst pressure is equal to the difference between the desired upstream pressure (vessel) at the time of rupture disk burst and the downstream pressure (backpressure):
Pburst = Pvessel - Pbackpressure
Or alternately the desired upstream pressure (vessel) at the time of rupture disk burst is equal to the sum of the specified burst pressure and the downstream pressure (backpressure):
Pvessel = Pburst + Pbackpressure
Either way, it is apparent that the vessel pressure at the time the rupture disk bursts (commonly called the relief pressure) is directly dependent on backpressure.
When discussing relief systems, three types of backpressure are considered, these being constant, built-up and superimposed.
Figure 1A: Single Vessel, Single Rupture Disk Protection, Expected Constant Back pressure = 0 psig
Figure 1A shows a system comprised of a single vessel protected by a single rupture disk with a specified burst pressure of 100 psig. The relief pipe discharges a few inches below the liquid surface in a knockout drum, which is held at a constant 0-psig pressure. Therefore, the rupture disk sees a constant (fixed) backpressure of 0 psig. If the vessel were to go into relief, this disk will burst at 100 psig and the vessel relief pressure will be 100 psig (100 + 0 = 100).
Figure 1B: Single Vessel, Single Rupture Disk Protection, Actual Constant Back pressure >Â Expected
Figure 1B is the same system however for some reason the pressure in the knockout drum is to be maintained at 5 psig instead of 0 psig. The constant (fixed) backpressure against the rupture disk is now 5 psig. If the vessel were to go into relief, the rupture disk would still burst at 100 psig but the vessel relief pressure would now be 105 psig (100 + 5 = 105) rather than the 100 psig expected. This situation could result in a violation of code3.
Figure 1C: Single Vessel, Single Rupture Disk Protection, Actual Constant Back pressure <Â Expected
Figure 1C is again the system however for some reason the pressure in the knockout drum is to be maintained at -5 psig instead of 0 psig. The constant (fixed) backpressure against the rupture disk is now -5 psig. If the vessel were to go into relief, the rupture disk would still burst at 100 psig but the vessel relief pressure would now be only 95 psig (100 + (- 5) = 95) rather than the 100 psig expected. There is no particular safety concern here because the vessel can't over pressure. However, the Operating Ratio is affected, which can result in a very premature bursting of the rupture disk.
For the vessel relief pressure to be specified correctly, the rupture disk vendor must be told the constant back pressure so that the rupture disk can be designed accordingly. And, if you truly want the vessel relief pressure to be at a specific value then the "constant" backpressure given to the vendor must be maintained at all times.
The key point is that during design, be aware of the constant backpressure and ensure that the vessel relief pressure will not violate code or affect normal operation.
Â
Figure 2A: Two Vessel System - Common Discharge Built-up and Superimposed Back Pressures
Now let's look at the system shown in Figure 2A. A second vessel with a single rupture disk also specified to burst at 100 psig is added in close proximity to the first vessel. The relief piping from the two vessels is tied into a common header before discharging into a knockout drum in the same manner as before, the tie-in occurs near the vessels. At the exact moment Vessel No. 2 goes into relief and its rupture disk bursts, Vessel No. 2's relief pressure is 100 psig due to the constant 0-psig backpressure as described above. After the disk bursts, flow is established causing pressure to build up in the piping system (built-up backpressure). The amount of built-up backpressure is dependent on the system pressure drop and possibly even the phenomenon of choked flow. For the purpose of this discussion, assume total built-up backpressure is 10 psig after rupture disk No. 2 bursts and the pressure in Vessel No. 2 is about 110 psig. Because of the proximity of the two discharge pipes and vessels, the pressure near vessel No. 1 will also be at about 110 psig. This pressure, which is exerted or imposed onto rupture disk No. 1, is called the superimposed backpressure with respect to rupture disk No. 1. If vessel No. 1 were to go into relief shortly afterwards, then for rupture disk No. 1 to burst, the pressure in vessel No. 1 would have to build to about 210 psig (100 + 110)!  This is clearly unacceptable!!
One solution to this potentially catastrophic condition is to separate the two relief lines so that one cannot directly affect the other (see Figure 2B below). Of course the answer may very well be that this is not an application for rupture disks but for relief valves! The key point is, avoid combining multiple rupture disk piping into a common relief header.
Figure 2B: Two Vessel System - Common Discharge Built-up and Superimposed Back Pressures
Note that built-up backpressure is variable and depends on the relieving rate, which is a function of the relieving scenario. Also, built-up backpressure has no affect on the vessel's relief pressure for systems such as those shown in Figure 1 above. Built-up backpressure is the result of fluid flow only and there is no fluid flow before the rupture disk bursts.
Therefore, along with the Manufacturing Range (MR), Operating Ratio (OR) and Burst Tolerance (BT) that were discussed in Part 3, the process design engineer must also strongly consider the backpressure (especially superimposed backpressure) when specifying the rupture disk.
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### Producer theory, average, marginal, fixed, total costs… oh my!
There are a lot of costs that you have to memorize (scratch that) LEARN in microeconomics. Here is a list of the costs, followed by their equation and definition with some explanation.
Total Cost (TC): (FC+VC) or AC*Q. Total cost is the cost of everything used by the firm in production, it is the total of all the costs (sorry, I can’t think of another way to say it J).
Fixed Costs(FC), also known as Total Fixed Costs (TFC): (TC-VC) or AC*Q-VC. Fixed costs are the easiest to remember because they are fixed. This is the cost associated with expenses that you can’t change, and only occur in the short run. Common fixed costs are rent, electricity, or other contractual obligations.
Variable Costs (VC), also known as Total Variable Costs (TVC): (TC-FC) or AC*Q-VC. Variables costs are the costs that change as you produce more. For example, if you want to make more burritos, your need more tortillas, so the money you spend on tortillas is a variable cost because it changes with the amount of burritos you make.
The above costs are the ones present in our check book or accounting software. They represent the amounts that we are actually paying to keep our company running. However, in order to make economic decisions, we also need to consider the following costs, which require a bit of calculation:
Average Cost (AC): TC/Q. To get this just divide your total cost by the quantity produced.
Average Fixed Cost (AFC): FC/Q. This is easy to calculate, just take your fixed costs and divide by the number of units produced. Since your fixed costs don’t change, as you produce more and more output, you will see your average fixed costs go down.
Average Variable Cost (AVC): VC/Q. This one is also easy to calculate, but a little tricky to interpret. Just divide your total variable costs by your quantity produced. Since variable costs vary with the amount produced, you won’t see a definite relationship with average variable cost, as you would with average fixed cost.
Marginal Cost (MC): (difference between TC). To get your marginal cost you will have to look at the difference between your total costs at different quantities. For example, if your TC was 50, and then went to 55 with one more unit of production, than your MC is 5. Marginal cost is the most important of the costs because as economists, we analyze everything on the margin.
Future posts will go through the graphical representation of these costs for a typical firm, as well as some guided solution examples. | 594 | 2,592 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.484375 | 3 | CC-MAIN-2018-05 | latest | en | 0.950512 |
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# The Values of K for Which the Quadratic Equation 16 X 2 + 4 K X + 9 = 0 Has Real and Equal Roots Are - Mathematics
Course
#### Question
The values of k for which the quadratic equation $16 x^2 + 4kx + 9 = 0$ has real and equal roots are
##### Options
• $6, - \frac{1}{6}$
• 36, −36
• 6, −6
• $\frac{3}{4}, - \frac{3}{4}$
#### Solution
The given quadratic equation $16 x^2 + 4kx + 9 = 0$
has equal roots.
Here,
$a = 16, b = 4k \text { and } c = 9$ .
As we know that
$D = b^2 - 4ac$
Putting the values of $a = 16, b = 4k \text { and } c = 9$.
$D = \left( 4k \right)^2 - 4\left( 16 \right)\left( 9 \right)$
$= 16 k^2 - 576$
The given equation will have real and equal roots, if D = 0
Thus,
$16 k^2 - 576 = 0$
$\Rightarrow k^2 - 36 = 0$
$\Rightarrow (k + 6)(k - 6) = 0$
$\Rightarrow k + 6 = 0 \text { or } k - 6 = 0$
$\Rightarrow k = - 6 \text { or } k = 6$
Therefore, the value of k is 6, −6.
Is there an error in this question or solution? | 391 | 976 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.3125 | 4 | CC-MAIN-2020-34 | latest | en | 0.596429 |
http://nrich.maths.org/6144/index?nomenu=1 | 1,386,637,621,000,000,000 | text/html | crawl-data/CC-MAIN-2013-48/segments/1386164003799/warc/CC-MAIN-20131204133323-00086-ip-10-33-133-15.ec2.internal.warc.gz | 132,645,658 | 3,385 | The rate of an enzyme-catalysed reaction depends on the temperature of its solution. The reaction activates at $20^\circ C$, at a rate of zero mol/l/min, and deactivates at $80^\circ C$. For each degree increase in temperature between $20^\circ C$ and $60^\circ C$ the rate of reaction increases by 0.1 mol/l/min and for each degree increment between $60^\circ C$ and $80^\circ C$ the rate reduces by 0.2 mol/l/min.
10 litres of the solution is prepared at a temperature of $20^\circ C$ and then placed immediately into an oven. Assume that the oven heats the solution at a fixed rate of $R^\circ C$ per minute. Consider these questions
1. What rate of heating would give rise to exactly 100 mol being catalysed?
2. For heating at a rate of 1 degree per minute, after how long will exactly 100 mol been catalysed?
3. (Hard numerical extension) What rate of heating would lead to exactly 100 mol being catalysed in the shortest time?
Consider an alternative problem: if the solution is prepared at boiling point: at what rate must 1 litre be cooled to end up with exactly 3 mol having been catalysed?
Hard extension: In reality, the temperature of the oven would probably be fixed and the rate of increase in temperature of the solution would be proportional to the difference in temperature between the oven and the solution. How far are you able to analyse this situation (note: you need to use differential equations)?
Notes and background
Whilst the chemistry of certain processes might seem reasonably straightforward, to implement reactions on an industrial scale requires very precise levels of timing, heating and so on. Since a human is unable carefully to watch a reaction progress in many cases, checking mechanisms must be automated. Scaling up reactions to large volumes can introduce many engineering complications not seen in the laboratory.
Furthermore, many chemical and biological reactions will naturally activate once certain temperatures are reached. Measuring a specific quantity of reactants in these cases might be tricky, and the amount taken out of the freezer, for example, might need to be smaller than the amount required for an experiment so as to take into account this (inevitable) continuous growth.
More realistically, heating does not typically occur at a fixed rate. Newton's Law of Cooling tells us that the rate of change in temperature is proportional to the difference in the temperature between the body and the heat source. | 517 | 2,469 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.078125 | 3 | CC-MAIN-2013-48 | longest | en | 0.936547 |
www.wikiboardgames.com | 1,726,135,144,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725700651440.11/warc/CC-MAIN-20240912074814-20240912104814-00392.warc.gz | 990,518,554 | 43,776 | # The Sudoku rules
Sudoku is a logic game that is played solo. It consists of completing a grid of 81 cells with numbers from 1 to 9. Be careful! The same number appears only once in a row, once in a column and once in a zone. Sudoku exists in a giant version, but also in a version for children.
## The grid
• The grid of a classic sudoku consists of 81 cells, 9 columns and 9 rows.
• The grid is then divided into 9 zones.
• A zone consists of 3 rows and 3 columns.
• An area, a column and a row contain numbers from 1 to 9.
• A number does not appear twice in the same area, column and row.
## How do you play?
• At the beginning of the game, the grid is partially filled.
• Proceed by elimination.
Example:
It already appears in rows 2 and 3.
It can therefore only appear in row 1.
It already appears in fields 1 and 2.
It can therefore only appear in field 3
• Look at the rows or columns where only one digit is missing.
Example:
The blue column is missing only one number, which is “3”.
If there are several possibilities, you can write the numbers in the corner of the box and eliminate them as you go along.
Example:
The last column is missing 2 numbers: 1 and 7.
The red lines mark the boxes where the number 1 cannot appear.
The blue lines mark the cells where the number 7 cannot appear.
By elimination, the number 1 occupies the entire second row.
The number 7 will naturally occupy the last free square and complete the column.
## End of the game
• The game ends when all the squares are completed.
## Variant
• There is a 16 square sudoku for children.
• There is a giant 256-square sudoku for adults. | 398 | 1,640 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.3125 | 3 | CC-MAIN-2024-38 | latest | en | 0.91786 |
https://math.stackexchange.com/users/505611/arsenberk?tab=topactivity | 1,624,260,749,000,000,000 | text/html | crawl-data/CC-MAIN-2021-25/segments/1623488268274.66/warc/CC-MAIN-20210621055537-20210621085537-00127.warc.gz | 347,557,599 | 27,725 | ArsenBerk
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5 Putting $m$ distinct balls to $n$ identical boxes with each box has at least $2$ balls 4 Short way for upper triangularization 2 contour integral on a line segment 1 Is there any impredicative definition or axiom which has no predicative counterpart? 1 Existence of limit of a function from existence of another limit of a function
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### Bookmarks (14)
1403 Visually stunning math concepts which are easy to explain 237 What are some examples of when Mathematics 'accidentally' discovered something about the world? 101 Can we remove any prime number with this strange process? 81 $6!\cdot 7!=10!$. Is there a natural bijection between $S_6\times S_7$ and $S_{10}$? 76 Conjectures (or intuitions) that turned out wrong in an interesting or useful way | 427 | 1,673 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.546875 | 3 | CC-MAIN-2021-25 | latest | en | 0.827204 |
https://convertilo.com/411-megabits-to-gigabits | 1,590,571,913,000,000,000 | text/html | crawl-data/CC-MAIN-2020-24/segments/1590347392142.20/warc/CC-MAIN-20200527075559-20200527105559-00371.warc.gz | 307,459,258 | 8,290 | ## How to convert 411 Megabits to Gigabits
To convert 411 Megabits to Gigabits you have to multiply 411 by 0.001, since 1 Megabit is 0.001 Gigabits. The result is the following:
411 Mb × 0.001 = 0.411 Gb
411 Mb = 0.411 Gb
We conclude that four hundred eleven Megabits is equivalent to zero point four one one Gigabits:
411 Megabits is equal to 0.411 Gigabits.
Therefore, if you want to calculate how many Gigabits are in 411 Megabits you can do so by using the conversion formula above.
## Definition of units
Let's see how both units in this conversion are defined, in this case Megabits and Gigabits:
### Megabit (Mb)
The megabit is a multiple of the unit bit for digital information. The prefix mega (symbol M) is defined in the International System of Units (SI) as a multiplier of 106 (1 million), and therefore 1 megabit = 106 bits = 1000000 bits = 1000 kilobits. The megabit has the unit symbo l Mb or Mbit. The megabit is closely related to the mebibit, a unit multiple derived from the binary prefix mebi (symbol Mi) of the same order of magnitude, which is equal to 220 bits = 1048576 bits, or approximately 5% larger than the megabit. Despite the definitions of these new prefixes for binary-based quantities of storage by international standards organizations, memory semiconductor chips are still marketed using the metric prefix names to designate binary multiples. Using the common byte size of eight bits and the standardized metric definition of megabit and kilobyte, 1 megabit is equal to 125 kilobytes (kB) or approximately 122 kibibytes (KiB). The megabit is widely used when referring to data transfer rates of computer networks or telecommunications systems. Network transfer rates and download speeds often use the megabit as the amount transferred per time unit, e.g., a 100 Mbit/s (megabit per second) Fast-Ethernet connection, or a 10 Mbit/s Internet access service, whereas the sizes of data units (files) transferred over these networks are often measured in megabytes. To achieve a transfer rate of one megabyte per second one needs a network connection with a transfer rate of eight megabits per second.
### Gigabit (Gb)
The gigabit is a multiple of the unit bit for digital information or computer storage. The prefix giga (symbol G) is defined in the International System of Units (SI) as a multiplier of 109 (1 billion, short scale), and therefore 1 gigabit = 109 bits = 1000000000 bits. The gigabit has the unit symbol Gbit or Gb. Using the common byte size of 8 bits, 1 Gbit is equal to 125 megabytes (MB) or approximately 119 mebibytes (MiB).
## Megabits to Gigabits conversion table
Below is the conversion table you can use to convert from Megabits to Gigabits
Megabits (Mb) Gigabits (Gb)
412 Megabits 0.412 Gigabits
413 Megabits 0.413 Gigabits
414 Megabits 0.414 Gigabits
415 Megabits 0.415 Gigabits
416 Megabits 0.416 Gigabits
417 Megabits 0.417 Gigabits
418 Megabits 0.418 Gigabits
419 Megabits 0.419 Gigabits
420 Megabits 0.42 Gigabits
421 Megabits 0.421 Gigabits
## Frequently asked questions to convert 411 Megabits into Gigabits
• How many Gigabits are in 411 Megabits?
• 411 Megabits equals how many Gigabits?
• How many is 411 Megabits in Gigabits?
• What is 411 Megabits in Gigabits?
• How much is 411 Megabits in Gigabits?
• How many Gb are in 411 Mb?
• 411 Mb is equal to how many Gb?
• How many is 411 Mb in Gb?
• What is 411 Mb in Gb?
• How much is 411 Mb in Gb? | 945 | 3,431 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.84375 | 4 | CC-MAIN-2020-24 | latest | en | 0.888784 |
https://thestemlaboratory.com/number-sense-mystery-puzzles/ | 1,680,224,570,000,000,000 | text/html | crawl-data/CC-MAIN-2023-14/segments/1679296949506.62/warc/CC-MAIN-20230330225648-20230331015648-00044.warc.gz | 643,884,777 | 104,082 | # Number Sense Mystery Puzzles
Developing number sense is something that takes kids time and a lot of effort. But this number sense activity makes it both exciting and challenging!
Add them to your math centers or morning work! For more number work, head over to our shop and grab our Place Value Cover Up!
This post contains Amazon affiliate links.
Prepping this number sense activity was quick and easy!
I started by printing out a few copies of the 100 chart and the matching mystery number cards (below).
I printed everything on Astrobrights cardstock to give this activity a POP of color and some extra durability, then laminated them.
It was obvious this math center would be a hit and my kiddos would want to do it over and over again!
I cut out the mystery number cards so they would easily fit right on top of the 100 chart.
I put each “set” in a gallon-sized Ziploc baggie with a dry erase marker.
## Number Sense Mystery Puzzles
Since this number sense activity takes some brain power, I decided to use it in a small group setting.
While my class was working on various math centers like Skip Counting Puzzles and Flip Flop Measuring to review previously taught skills, I called over five of my students to my small group table.
To spark their thinking, I started out by showing them a single mystery number card and asking them what I should write in the blanks. It was a tricky concept at first, but once I showed them that the mystery number card was a section of the 100 chart, I could see their eyes lighting up.
I passed out a Ziploc baggies full of materials to each child and let them start exploring.
Most of my students started out by setting the mystery number cards directly on top of the 100 chart. They were counting across the chart to fill in the blanks.
This was great for some of my students, but some were ready for a challenge. So, I challenged a few children who were ready to flip the 100 chart over and only use it when they were stuck.
I let them work and I supported each child as they needed it through the number sense activity.
To wrap up, we discussed the strategies we used to fill in the blanks and compared answers.
My students loved trying something challenging and new, and I loved that they had to think critically! | 489 | 2,285 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.484375 | 3 | CC-MAIN-2023-14 | longest | en | 0.970539 |
https://www.motilaloswal.com/blog-details/How-do-investors-judge-if-a-stock-is-overpriced/1968 | 1,660,613,731,000,000,000 | text/html | crawl-data/CC-MAIN-2022-33/segments/1659882572215.27/warc/CC-MAIN-20220815235954-20220816025954-00302.warc.gz | 783,222,262 | 36,549 | How do investors judge if a stock is overpriced - Motilal Oswal
# How do investors judge if a stock is overpriced?
We all like to talk about undervalued stocks but rarely do we venture to talk about a stock that is overpriced or overvalued. That is because most investors have a natural tendency to buy stocks rather than to sell stocks. Valuation metrics are fine but there are companies and sectors in India that are appreciating for many years without any let-up in the P/E ratio. Take FMCG as a classic example in India. So what exactly are overvalued or undervalued stocks? How to determine if a stock is overpriced and how to find overvalued stocks in the stock market? Stock valuation is as much an art as it is a science. However, there are 5 key factors you can use to judge if the stock is underpriced or it is overpriced.
1. P/E ratio may be misleading at times, but the PEG givers a clearer picture
Before we get into the finer points, let us first understand what the PEG is all about. It is nothing but the P/E Ratio adjusted for growth. For example, P/E ratio of 25 with 20% growth may be acceptable but P/E ratio of 15% with 5% growth is not acceptable. That is where PEG creates a standardized matrix.
PEG Ratio = PE Ratio / company's earnings growth rate
Ideally, you must look at the prospective P/E ratio based on estimated earnings and the prospective growth rate. At the end of the day, the stock price of the company factors the future performance and not the past performance. Hence a futuristic approach to PEG can work better from an analytical standpoint.
You can also use a slightly modified version of the formula PEG which is called the dividend adjusted PEG. Let us look at this concept. A company rewards its shareholders in the form of dividends and by capital appreciation. When you add dividend to growth, you are not being unfair to higher dividend yield companies.
Dividend-adjusted PEG ratio = PE ratio / (earnings growth + dividend yield)
In this case, the lower the number the better, with anything at 1 or below considered a good deal. The level of 2 is considered the upper limit of overpricing. Beyond that the stock is truly overpriced and calls for action.
2. Examine the Likelihood of a Cyclical Industry
Certain sectors such as homebuilders, automobile manufacturers, and steel mills have unique characteristics. These businesses tend to experience sharp drops in profit during periods of economic decline, and large spikes in profit during periods of economic expansion. When the latter happens, some investors are enticed by what appear to be fast-growing earnings, low P/E ratios, and, in some cases, large dividends. This is popularly called a value trap. This is true of commodity companies and capital goods companies that are subject to regular cycles. If your cyclical companies trade at up cycle values during down cycles then it is a clear case of overvaluation.
3. Compare the earnings yield with the bond yield
There is a very smart logic to this argument. The earnings yield is the inverse of the P/E ratio. So a company with a P/E ratio of 20 has an earnings yield of 20%. It is measured as under:
Earnings Yield = Earnings per share (EPS) / Market price of the stock
Earnings yield in isolation does not mean anything. It has to be seen in conjunction with the yield on government securities or safe bonds. For example, if the earnings yield is 6% and the bond yields are 4% then the situation is normal as you are getting more on equities than on bonds due to the higher risk entailed. But if the earnings yield is 3.5% and bonds are yielding 6.5% then it is a clear case of overvaluation of equities. This is the time to make your move out of equities.
4. Too much dependence on one product line
This is a slightly more qualitative factor for company valuation. But always remember the story of the Forbes cover story of Nokia in 2007 calling it an invincible company. The company was almost entirely bankrupt within 4 years due to the onslaught of smart phones. Nokia’s profits were unsustainably high but the stock market had priced in that the current level of profits is sustainable. When economic conditions change or a key product falls out of favour there tends to be downside to both the company’s profits and valuation, leading to a significant share price fall. That is exactly what happened to companies like Kodak, Nokia, MTNL, PSU banks etc who got prised out of the market even as they lived on their past glory.
5. Beware of management sweet talk and accounting jugglery
This is again a qualitative factor and relies more on judgement than on hard facts. But the signals are there for all to pick up. If you look at cases like Enron, Lehman Brothers, Deccan Chronicle, Satyam or Kingfisher Airlines it was an eclectic mix of management bravado and accounting jugglery at its worst. This is where a business’s management, sell-side analysts or others stop focusing on traditional metrics, such as earnings, and come up with their own.
As John Templeton rightly said, “The most dangerous argument in financial markets is that this time it is different”. Be cautious of valuations when the company starts talking about metrics like EV / EBITDA, Price per eyeball, Value per footfall etc. In some cases, the accounting issues may be hiding that a company is in financial difficulty or even insolvent. Whenever you find the managements and accountants getting too aggressive, it is time to be cautious about valuations.
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https://www.plati.market/itm/2-1-13-the-solution-of-the-problem-of-the-collection-of/2048432?lang=en-US | 1,585,671,943,000,000,000 | text/html | crawl-data/CC-MAIN-2020-16/segments/1585370502513.35/warc/CC-MAIN-20200331150854-20200331180854-00085.warc.gz | 1,129,723,419 | 12,993 | # 2.1.13 The solution of the problem of the collection of
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## Description
A lever having a fixed axis O, forces F1 = F2 and 6 h. Identify Module force F2, in which the lever is at rest, if the angle a = 70 °, the length AD = 0.3 m, VO = 0.4 m. | 171 | 510 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.78125 | 3 | CC-MAIN-2020-16 | latest | en | 0.718401 |
https://solvedlib.com/n/a-polynomial-is-factorable-but-it-is-not-a-perfect-square,18040955 | 1,696,340,527,000,000,000 | text/html | crawl-data/CC-MAIN-2023-40/segments/1695233511106.1/warc/CC-MAIN-20231003124522-20231003154522-00851.warc.gz | 569,639,450 | 18,932 | # A polynomial is factorable, but it is not a perfect square trinomial or a difference of two squares. Canyou factor
###### Question:
A polynomial is factorable, but it is not a perfect square trinomial or a difference of two squares. Can you factor the polynomial without finding the GCF?
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##### Pbys 333 Assignment 7 Due Tuesday, November 5, 2019Retinders: Sbow your workl Include references On your subritted version, Write legiblyl 7.1 This problem is similar to Wangsness 6-1, but different. Suppose that the two conductors shown Figurc 6-8 are originally uncharged. charge Q is then placed on the inner conductor of radius Find tbe final static charge distribution, giving Q on cach gurface Find the surface charge density & On each surface Find the electric field and potential for a
Pbys 333 Assignment 7 Due Tuesday, November 5, 2019 Retinders: Sbow your workl Include references On your subritted version, Write legiblyl 7.1 This problem is similar to Wangsness 6-1, but different. Suppose that the two conductors shown Figurc 6-8 are originally uncharged. charge Q is then place...
##### 40) Lyroroma A)help digest wom dumaged egeneDet B) myce material within the ch Oandetroy harmful bacteria engulled [ by white blood cells: 6uaa hydrolytic = enryme with food vaquole expose nutrient E) All of the choices arE contecl 31) Tha Etorn the milochondrion: spacr brtwcen thc inncr and outcr mcmbranes of = milochondrion: walery Quid cnclosed by the inner membrane of C) Ouid within the grana. D) thick Juid cnclosed by thc inner chloroplast membrane E) space between the inner und ouler membr
40) Lyroroma A)help digest wom dumaged egeneDet B) myce material within the ch Oandetroy harmful bacteria engulled [ by white blood cells: 6uaa hydrolytic = enryme with food vaquole expose nutrient E) All of the choices arE contecl 31) Tha Etorn the milochondrion: spacr brtwcen thc inncr and outcr m...
##### View FUNCIES Current Attempt in Progress Ivanhoe, Inc., is a fast-growing technology company. Management projects rapid...
View FUNCIES Current Attempt in Progress Ivanhoe, Inc., is a fast-growing technology company. Management projects rapid growth of 30 percent for the next two years, then a growth rate of 17 percent for the following two years. After that, a constant-growth rate of 8 percent is expected. The firm exp...
##### Joni Winters, a 64-year-old female client, is admitted with a fractured hip. She has chronic renal...
Joni Winters, a 64-year-old female client, is admitted with a fractured hip. She has chronic renal failure and has continuous peritoneal dialysis (CAPD) exchanges every 6 hours. The Tenckhoft peritoneal catheter site has redness, which goes across the abdomen. The client states that her abdomen is t...
##### JI "9lim f (x) cos(2)thcn wc know that(B) f(c) cas(r) (C) = 2 and (r)J(A) f(r) is continous at I f(r) cos(r)cos(r) (D)None of the above
JI "9 lim f (x) cos(2) thcn wc know that (B) f(c) cas(r) (C) = 2 and (r)J (A) f(r) is continous at I f(r) cos(r) cos(r) (D) None of the above...
##### Weak property rights encourage faster extraction than would otherwise maximize the long-term stream of profits. True...
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##### 2. Let f(€,y) = 31V r3_y Find all critical points of f and state whether each is & local maximum local minimum or saddle point_ Give reasons for your answers_ (There are two such points
2. Let f(€,y) = 31V r3_y Find all critical points of f and state whether each is & local maximum local minimum or saddle point_ Give reasons for your answers_ (There are two such points... | 1,587 | 5,864 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.828125 | 3 | CC-MAIN-2023-40 | latest | en | 0.840168 |
https://hackernoon.com/sharf-create-a-3d-model-of-an-object-using-just-a-single-image-ot4933xq | 1,716,611,114,000,000,000 | text/html | crawl-data/CC-MAIN-2024-22/segments/1715971058773.28/warc/CC-MAIN-20240525035213-20240525065213-00636.warc.gz | 236,930,658 | 54,904 | ShaRF: Create a 3D Model of an Object Using Just a Single Imageby@whatsai
# ShaRF: Create a 3D Model of an Object Using Just a Single Image
February 20th, 2021
ShaRF stands for Shape-conditioned Radiance Fields from a Single View. The goal is to take a picture of a real-life object, and translate this into a 3D scene.
Neural scene representation from a single image is a really complex problem. The "end goal" is to be able to take a picture of a real-life object, and translate this picture into a 3D scene. It implies that the model understands a whole 3-dimensional scene, or real-life scene, using information from a single picture.
## References:
[1] Rematas, K., Martin-Brualla, R., and Ferrari, V., "ShaRF: Shape-conditioned Radiance Fields from a Single View", (2021), https://arxiv.org/abs/2102.08860
[2] Project website and link to code for ShaRF: http://www.krematas.com/sharf/index.html
[3] Mildenhall et al., NeRF: Representing Scenes as Neural Radiance Fields for View Synthesis, (2020), https://www.matthewtancik.com/nerf
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## Chapters:
0:00 - Hey! Tap the Thumbs Up button and Subscribe. You'll learn a lot of cool stuff, I promise.
0:28 - Paper explanation & examples
4:42 - Conclusion
## Video Transcript:
(this has been auto-generated by YouTube and may have inaccuracies)
00:00
just imagine how cool it will be to just
00:02
take a picture of an object and have it
00:04
in
00:05
3d to insert in the movie or video game
00:07
you are creating
00:08
this is what google is working on
00:17
this is what's ai and i share artificial
00:20
intelligence news every week
00:21
if you are new to the channel and want
00:23
to stay up to date please consider
00:25
subscribing to not miss any further news
00:28
neural scene representation from a
00:30
single image is a really complex problem
00:33
the end goal is to be able to take a
00:35
picture from a real life object
00:37
and translate this picture into a 3d
00:39
scene
00:40
it implies that the model understands a
00:42
whole three-dimensional
00:44
scene or real-life scene using
00:46
information from a single picture
00:48
and this is sometimes hard even for
00:51
humans
00:52
where the colors or shadows tricks our
00:54
eyes
00:55
oh and not only that it needs to
00:56
understand the depth
00:58
in the image which is already a
01:00
challenging task to do but it also needs
01:02
to reconstruct the objects with the
01:04
right materials and texture
01:06
so it can look real you can just imagine
01:08
how cool it will be to just take a
01:10
picture of an
01:11
object and have it in 3d to insert in
01:14
the movie or video game you are creating
01:16
or in a 3d scene for an illustration
01:19
well
01:19
i am not the only one thinking about all
01:21
the possibilities this type of model
01:23
could create
01:24
01:26
into this in their new paper
01:28
sherf shape condition regions field
01:31
from a single view and you're seeing the
01:33
results they could produce since the
01:35
start of the video
01:36
note that for each of these results you
01:38
saw they only used one picture
01:40
taken from any angle it was then sent to
01:43
the model in order to produce these
01:45
results
01:46
which are incredible to me when you
01:48
think of the complexity of the task in
01:50
all the possible parameters to take into
01:52
consideration
01:53
just regarding the initial picture such
01:55
as the lighting
01:56
the resolution the size the angle or
01:58
viewpoint the location of the object in
02:00
the image
02:01
and etc if you're like me you may be
02:04
wondering
02:04
how are they doing that okay so i lied a
02:07
little
02:08
they do not only take the image as
02:10
inputs to the network
02:11
but they also take the camera parameters
02:13
to help the process
02:15
the algorithm learn the function that
02:17
converts
02:18
these 3d points and 3d viewpoints into
02:21
an
02:22
rgb color as well as a density value for
02:24
each of this point
02:26
providing enough information to render
02:28
the scene from any viewpoints
02:29
later on this is called a radiance field
02:33
taking positions in its viewing
02:34
direction as inputs to output this color
02:37
and volume density value
02:39
for each of these points it's very
02:41
similar to what nerf does
02:43
which is a paper i already covered on my
02:46
channel
02:46
basically in the nerf case the regions
02:49
field function
02:50
is done using a neural network trained
02:52
on images and the internet output
02:55
this implies that they need a large
02:56
number of images for each scene
02:59
as well as training a different network
03:01
for each of these scenes
03:03
making the process very costly and
03:04
inefficient so the goal is to find a
03:07
better way to have this needed radiance
03:09
field
03:10
composed of rgb and density values to
03:12
then
03:13
render the object in 3d in novel views
03:16
in order to have the needed information
03:18
to create such a radiance field
03:20
they used what they call a shape network
03:23
that maps a latent code of the image
03:25
into a 3d
03:26
shape made of voxels voxels are just the
03:29
same as pixels but in three dimensional
03:32
space
03:32
and the latent code in question is
03:34
basically all the useful information for
03:37
the shape of the object in the image
03:39
this condensed shape information is
03:41
found using a neural network composed of
03:43
fully connected layers
03:45
and followed by convolutions which are
03:47
powerful architectures for computer
03:49
vision applications
03:50
since convolutions have two main
03:52
properties
03:54
they are invariant to translations and
03:56
use the local properties of the images
03:59
then it takes this latent code to
04:01
produce this first
04:02
3d shape estimation you will think that
04:05
we are done here
04:06
but it's not the case this is just the
04:08
first step
04:09
then as we discussed we need the
04:11
04:13
of this representation using here an
04:15
appearance network
04:16
here again it uses a similar latent code
04:19
but for the appearance
04:20
as well as the 3d shapes we just found
04:23
as inputs
04:24
to produce this regions field using
04:26
another network
04:27
referred here as f then this radians
04:31
field
04:31
can finally be used with the camera
04:33
parameters information
04:35
to produce this final render of the
04:38
object
04:38
in novel views
04:42
this was just an overview of this new
04:44
paper i strongly recommend reading the
04:46
paper
04:47
linked in the description below the code
04:49
is unfortunately
04:50
not available right now but i contacted
04:53
one of the authors
04:54
and he said that it will be available in
04:56
a couple of weeks
04:57
so stay tuned for that please leave a
05:01
like if you went this far in the video
05:03
and since there are over 80 percent of
05:05
you guys that are not subscribed yet
05:07
05:08
channel to not miss any further news
05:11
thank you for watching
L O A D I N G
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Geometry Level 4
The median drawn to the hypotenuse of a right triangle divides the right angle in the ratio $$1:2$$ and it is equal to $$2015$$. Find the perimeter of the triangle.
If your answer comes as $$a+b\sqrt{c}$$ then submit it as $$a+b+c$$.
× | 77 | 274 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.625 | 3 | CC-MAIN-2018-26 | latest | en | 0.843931 |
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GMAT 1: 710 Q49 V40 | 956 | 2,754 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.546875 | 3 | CC-MAIN-2022-27 | latest | en | 0.832613 |
abstractalgo.com | 1,627,420,522,000,000,000 | text/html | crawl-data/CC-MAIN-2021-31/segments/1627046153491.18/warc/CC-MAIN-20210727202227-20210727232227-00231.warc.gz | 101,325,054 | 5,993 | # "Relativity" in complex systems
March 28, 2018
## :: relativity in complex systems
Let me tell you about two examples that I noticed were sharing a same pattern and could easily extended to other cases as well.
I wondered how in movies all those celestial beings big as tens of Suns were slow. They always had deep voice and slow but calculated moves that crushed entire worlds. You'd then have some type of Avengers flying around it and killing it bit by bit. They'd fire thousands of bullets and missiles at that titan while titan would for that time only manage to do one swing of the hand because it was so damn slow. But here's where the pattern kicks in. Let's say that titan has nervous system and other senses, as we do. It's eyes would capture incoming light and send signal to the brain which would then be processed and sent to the muscles to react. But the distance that electric signals need to travel across titan's body is huge, it's tens of thousands of kilometers. But when titan finally moves, it's doesn't do it slowly, it may only be perceived as such. But his absolute position of moves is huge. Being that large moves its parts of body in the least time possible, but it has also huge muscles and huge amounts of energy stored in entirety of its body. So it has enough energy to move large masses at big speed. So in its coordinate space, moving hand from the height of its head to the height of its chest is perceived to be as fast in its subjective time space and conscious mind as it would be in a case of a mere human that is only 1.8m tall. Yes, the human took an absolute 0.4s to move its hand, and titan took 40s to move its hand, but amounts of energy exchanged, and impact on the change of the entire system remains proportional. Human only exchanged E amount of energy and disturbed volume of couple of cubic decimeters of particles. But titan exchanged 1000x E amount of energy and disturbed a full two planets of volume of particles while it made that move.
So it seems that:
titan's resources spent / titan's impact achieved = human's resources spent / human's impact achieved
Absolute time passed is different, but so are consequences.
It also looks like titan has some sort of delay in his actions. Say that Avenger attacked him and hit him in the eye. The titan would still need to wait all those signals to travel along its body and reach the muscles eventually before being able to respond to that. It seems that Avenger by that time would be able to escape easily. But here's also another thing - the distance that Avenger needs to travel before being safe and out of titan's reach is huge and it would take him a lot of time to reach it. And guess what, titan has that approximately same amount of time to activate muscles and swing its hand at the avenged that attacked him. So after all, it is a fair fight.
And it also seems that titan has some kind of "delay" in its actions, because its body is waiting for all those signals to travel across the body. But its body is still reacting to previous signals that were sensed. So its body is always "active" and is actively responding to the environment. And energy exchanged while those signals are traveling is still the proportional to titan's size. So, in a unit of time, there are billions of signals firing and re-firing across the titan's body, while human only has say thousands of signals. And let's say that each signal can be represented by the same amount of energy. So even the titan is larger, it has proportionally larger amount of signals. So, the amount of system's changes within titan's body per unit time is about the same as in human's. It has perceived delay in actions but actually looking at the derivatives of the change of the system - they are the same.
Another example is also concerned about amounts of change in the system versus size/complexity of the system.
I was doing startup at the moment of writing this, and so we were concerned about some big company trying to copy us and just ditching our product off the market because big company can make a huge impact and achieve huge results.
In a startup, you have only a few people, in our case only two. From idea to realization we only have a couple of minutes of discussion and the rest of the time goes onto realization.
In big company, to go from idea to realization, it takes discussion between board members. Then meetings with managers of managers. Then organizing hierarchy and job split between the teams. Than manager of each team needs to delegate jobs to its members, but only after briefing them and explaining them the project and what other teams are working on and how it all fits in one big picture. And only then can the workers do their job. And each worker has only a "small" part of the entire thing, so they also spend equally the same amount of time programming as we in startup did. But entire process took much more time for reasons of hierarchy existing.
And while at startup, we only took 2 days to develop a feature, and the company took 6 months to create that same feature, the impact is also proportional. Out area of effect is very small and affects only few people, but big company is big because in the past it affected a lot of people so it has many resources, and now it has the ability to disrupt larger quantities of the global system.
In both cases, per-person's impact on the system in comparison to amount of work invested is the same. Two people at startup work 8h/day for two days and develop a feature that changed their product, but the product is small so absolute amount of change is small, and so it the area of effect. And in the big company, thousands of people work 8h/day for 6 months are develop a feature that changes their company's entire product, and that product was/is big, so amount of change is huge, and so it would be the area of effect. Each person did the same amount of work (energy of one electric signal in the body ^), but system that it's part of is changing environment as a whole.
And again, it looks like big company has a delay in actions, but watching at the amount of workhours spent in comparison to the scale of the system making those changes, that remains the same.
thousands of employees * 8h / thousands of employees
=
2 employees * 8h / 2 employees
$\text{size of the system} : \text{resources spent} : \text{impact} = \text{const}$
It seems like some sort of rule. It seems that systems are bound to do not less than that amount of work, and can't do more than that. The impact of the big system is only relative to its size, while its units are still at the constant rate of work done.
It seems intuitive to me for physical systems to be bound by this, because of transfer of energy. But from the startup/company example it looks like this law of constant derivative of change is not present in physical systems. It sure is dictated by the different rules and might not have to do anything with physical energy, but it exhibits that behavior nevertheless.
Is this applicable to finances, where amount of impact (resources earned) could be related and is proportional to the resources spent? But finances use statistics to find best returns for resources invested, but maybe then entire financial world is bound by the amount of change that can happen during a unit of time. Yes, local inhomogeneities mean that somebody earned more money, and somebody earned less money than that constant factor, but overall the system's change could be constant.
In science, could it be that progress of science is also constant? If each scientist progresses the science by fixed amount of progress, the next week, entire science is bigger thanks to things discovered previous week, so now the science progress is slowing when talking about relative comparison of amount of progress vs size of science?
I guess there are more examples of this pattern and is very interesting. | 1,669 | 7,943 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 1, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.1875 | 3 | CC-MAIN-2021-31 | longest | en | 0.984828 |
https://developer.aliyun.com/article/652756 | 1,590,967,626,000,000,000 | text/html | crawl-data/CC-MAIN-2020-24/segments/1590347413786.46/warc/CC-MAIN-20200531213917-20200601003917-00146.warc.gz | 319,777,207 | 12,786 | Python科学恋爱大法
“你肿么啦？”我仔细地掰开蟹壳，问道。
“十一假期好多朋友办婚礼，可我男票一点要求婚的意思都没有，我都想考虑备胎了。”
“你自己和他说嘛！”我放下了金黄的大闸蟹。
“我可是个妹子，这样多不好。”学姐叹了口气。
1)参加求婚的男女数量保持一致
2)每个男子都按喜爱程度对女子进行排序，比如最爱a，其次爱b，再次爱c
3)每个女子也同样给每个男子排序
*此方法名为Gale-Shapley算法。优点如下：1. 总有大家都订了婚的一天，不可能无限循环2. 中止后所有的婚姻是稳定婚姻（不稳定婚姻：比如有两对夫妇M1&F1和M2&F2, M1的老婆是F1，但他更爱F2；而F2的老公虽说是M2，但她更爱M1。这样的婚姻就是不稳定婚姻）有兴趣的读者可以自行搜索证明过程。
（此处展示部分代码，完整源文件请看文末）
#设置男女生喜好样本
print('==============================生成样本数据==============================')
man = pd.DataFrame( [['w'+str(i) for i in random.sample(range(1,women_num+1),women_num)] \
for i in range(man_num)],
index = ['m'+str(i) for i in range(1,man_num+1)],
columns = ['level'+str(i) for i in range(1,women_num+1)]
)
women = pd.DataFrame( [['m'+str(i) for i in random.sample(range(1,man_num+1),man_num)] \
for i in range(women_num)],
index = ['w'+str(i) for i in range(1,women_num+1)],
columns = ['level'+str(i) for i in range(1,man_num+1)]
)
return (man,women)
print('==============================测试集{}模拟开始=============================='.format(i))
print('==============================开始模拟求婚过程==============================')
level_num = 0
while man_ismapping['love_level'].min() == 0:
level_num += 1
print('==============================开始第{}天婚姻配对=============================='.format(level_num))
u_mapping_man = man_ismapping[man_ismapping.target == 'n'].index.tolist()
if level_num < 2:
level_col = 'level' + str(level_num)
man_choose = man[man.index.isin(u_mapping_man)][level_col].to_frame().reset_index()
man_choose.columns = ['man_id', 'women_id']
man_choose['range'] = 1
else:
m_id = u_mapping_man
l = []
for man_id in m_id:
col_n = int(man_ismapping[man_ismapping.index == man_id].range[0])
level_col = 'level' + str(col_n + 1)
women_id = man[man.index == man_id][level_col][0]
rg = col_n + 1
l.append([man_id, women_id, rg])
man_choose = pd.DataFrame(l, columns=['man_id', 'women_id', 'range'])
for r in range(0, len(man_choose)):
relationship = man_choose[man_choose.index == r]
m = [i for i in relationship['man_id']][0]
w = [i for i in relationship['women_id']][0]
find = women[women.index == w].unstack().reset_index()
find.columns = ['level', 'women_id', 'man_id']
find = int([i for i in find[find['man_id'] == m]['level']][0].split('level')[1])
o_love_level = [i for i in women_ismapping[women_ismapping.index == w]['love_level']][0]
rg = [i for i in relationship['range']][0]
if o_love_level == 0:
women_ismapping.loc[w, 'love_level'] = find
women_ismapping.loc[w, 'target'] = m
women_ismapping.loc[w, 'range'] = level_num
man_ismapping.loc[m, 'love_level'] = rg
man_ismapping.loc[m, 'target'] = w
man_ismapping.loc[m, 'range'] = rg
elif o_love_level > find:
m_o = women_ismapping.loc[w, 'target']
man_ismapping.loc[m_o, 'love_level'] = 0
man_ismapping.loc[m_o, 'target'] = 'n'
man_ismapping.loc[m, 'love_level'] = rg
man_ismapping.loc[m, 'target'] = w
man_ismapping.loc[m, 'range'] = rg
women_ismapping.loc[w, 'love_level'] = find
women_ismapping.loc[w, 'target'] = m
women_ismapping.loc[w, 'range'] = level_num
else:
man_ismapping.loc[m, 'range'] = rg
pass
*纵轴代表其中一次模拟中，男性/女性的平均伴侣喜爱排名均值，即：匹配到的伴侣是他们/她们第X喜欢的异性。
Python中文社区
+ 订阅 | 1,241 | 3,318 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.234375 | 3 | CC-MAIN-2020-24 | latest | en | 0.226761 |
https://howard-bison.com/fluff-wordle-more-details-about-wordle/ | 1,726,493,196,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725700651697.32/warc/CC-MAIN-20240916112213-20240916142213-00294.warc.gz | 273,039,893 | 18,737 | # Fluff Wordle More details about Wordle
Are you a Wordle fan? Are you a Wordle fan? Do you eagerly wait for new puzzles to be released each day? If you answered yes, then you’d know that wordle puzzles are getting increasingly difficult. Wordle has a large fan base World. Today we will discuss the current plight, which was released on 06/07/2022.
Research shows that many people found the puzzle difficult and complicated. In the following sections, we’ll discuss Fluff Wordle, and why it is in the news.
## Why is Fluff in the News?
Wordle, an online English puzzle-game, has been praised Worldwide. It was created by Josh Wardle and is growing in popularity every day. The 382 puzzle was the wordle puzzle that was released on 06/07/2022. There are two “Fs” at the beginning and end of the answer.
The word also contains one vowel. It can be difficult to guess a word that starts with F. Research shows that the word contains one vowel as well as three Fs. This makes FLUFF the word of today.
We will be discussing Fluff Wordle in the next section.
• Wordle is an online puzzle that Josh Wardle developed.
• This includes guessing a five letter word in six attempts
• The players will however be given hints to help them make the right guess
• If you enter the correct letter, the tile should turn green.
• However, if the letter was incorrectly placed on the wrong tile it will turn yellow
• The tile will also glow grey for any incorrect answers
• Once the answer is correct, the player can share the information on social media with his or her friends.
## Fluff WordleWhat is the word for the day?
Wordle answers are not always easy to figure out. Similar results were seen with the 382 Wordle puzzle, which was released on 06/07/2022.
There are spoilers ahead. Combinations and permutations include adding vowels to every word and removing a few letters such as j, y and z. The word had 3 Fs and 1 vowel. Therefore, FLUFF is the word of today.
But what does Fluff Wordle actually mean? It is a soft fibre found in fabrics such as wool and cotton that accumulates as light clumps. It can also be used to refer to writing, which is considered superficial.
### Final Conclusion
Fluff is one the most difficult words to guess because it contains duplicate Fs that players often don’t consider. It is even more difficult because it contains three Fs. | 561 | 2,368 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.53125 | 3 | CC-MAIN-2024-38 | latest | en | 0.964416 |
http://savannah.gnu.org/file/zplane.m?file_id=43432 | 1,571,038,012,000,000,000 | text/plain | crawl-data/CC-MAIN-2019-43/segments/1570986649232.14/warc/CC-MAIN-20191014052140-20191014075140-00418.warc.gz | 241,191,513 | 2,948 | ## Copyright (C) 1999, 2001 Paul Kienzle ## Copyright (C) 2004 Stefan van der Walt ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {} zplane (@var{z}, @var{p}) ## @deftypefnx {Function File} {} zplane (@var{b}, @var{a}) ## @deftypefnx {Function File} {} zplane (..., nods) ## ## Plot the poles and zeros. If the arguments are row vectors then they ## represent filter coefficients (numerator polynomial b and denominator ## polynomial a), but if they are column vectors or matrices then they ## represent poles and zeros. ## ## This is a horrid interface, but I didn't choose it; better would be ## to accept b,a or z,p,g like other functions. The saving grace is ## that poly(x) always returns a row vector and roots(x) always returns ## a column vector, so it is usually right. You must only be careful ## when you are creating filters by hand. ## ## Note that due to the nature of the roots() function, poles and zeros ## may be displayed as occurring around a circle rather than at a single ## point. ## ## The transfer function is ## ## @example ## @group ## B(z) b0 + b1 z^(-1) + b2 z^(-2) + ... + bM z^(-M) ## H(z) = ---- = -------------------------------------------- ## A(z) a0 + a1 z^(-1) + a2 z^(-2) + ... + aN z^(-N) ## ## b0 (z - z1) (z - z2) ... (z - zM) ## = -- z^(-M+N) ------------------------------ ## a0 (z - p1) (z - p2) ... (z - pN) ## @end group ## @end example ## ## The denominator a defaults to 1, and the poles p defaults to []. ## @end deftypefn ## 2/3/2018 modifications by Dr. Brian M. Reeder ## changes colour for each system plotted ## correctly marks multiple poles / zeros function zplane (z, p = []) if (nargin<1 || nargin>2) print_usage; endif if (columns (z)>1 || columns (p)>1) if (rows (z)<=1 || rows (p)<=1) if (isempty (z)) z = 1; endif # convert to poles / zeros if (isempty (p)) p = 1; endif M = length (z) - 1; N = length (p) - 1; z = [roots(z); zeros(N - M, 1)]; p = [roots(p); zeros(M - N, 1)]; endif endif a = axis; # plot range xmin = min ([a(1)/1.1; -1; real(z(:)); real(p(:))]); xmax = max ([a(2)/1.1; 1; real(z(:)); real(p(:))]); ymin = min ([a(3)/1.1; -1; imag(z(:)); imag(p(:))]); ymax = max ([a(4)/1.1; 1; imag(z(:)); imag(p(:))]); r = exp (2i*pi*[0:100]/100); # draw unit circle plot (real (r), imag (r), "k"); grid on; hold on; colororder = get (gca (), "colororder"); for c = 1:columns (z) # for every system ci = get (gca (), "colororderindex"); # get plot colour for zeros col = colororder (ci, :); plot_with_labels (c, z, col, "o"); set (gca (), "colororderindex", ci); # use same colour for poles plot_with_labels (c, p, col, "x"); endfor axis equal; axis (1.1*[xmin, xmax, ymin, ymax]); hold off endfunction function plot_with_labels (c, x, col, symbol) # plot poles or zeros if (! isempty (x)) x_u = unique (x(:,c)); plot (real (x_u), imag (x_u), symbol, "color", col); for i = 1:length (x_u) n = sum (x_u(i) == x(:,c)); if (n > 1) text (real (x_u(i)), imag (x_u(i)), [" " num2str(n)], "color", col); endif endfor endif endfunction %!demo %! ## construct target system: %! ## symmetric zero-pole pairs at r*exp(iw),r*exp(-iw) %! ## zero-pole singletons at s %! pw=[0.2, 0.4, 0.45, 0.95]; #pw = [0.4]; %! pr=[0.98, 0.98, 0.98, 0.96]; #pr = [0.85]; %! ps=[]; %! zw=[0.3]; # zw=[]; %! zr=[0.95]; # zr=[]; %! zs=[]; %! %! ## system function for target system %! p=[[pr, pr].*exp(1i*pi*[pw, -pw]), ps]'; %! z=[[zr, zr].*exp(1i*pi*[zw, -zw]), zs]'; %! M = length(z); N = length(p); %! sys_a = [ zeros(1, M-N), real(poly(p)) ]; %! sys_b = [ zeros(1, N-M), real(poly(z)) ]; %! disp("The first two graphs should be identical, with poles at (r,w)="); %! disp(sprintf(" (%.2f,%.2f)", [pr ; pw])); %! disp("and zeros at (r,w)="); %! disp(sprintf(" (%.2f,%.2f)", [zr ; zw])); %! disp("with reflection across the horizontal plane"); %! subplot(231); %! zplane(sys_b, sys_a); %! title("transfer function form"); %! subplot(232); %! zplane(z,p); %! title("pole-zero form"); %! subplot(233); %! zplane(z); %! title("empty p"); %! subplot(234); %! zplane(sys_b); %! title("empty a"); %! disp("The matrix plot has 2 sets of points, one inside the other"); %! subplot(235); %! zplane([z, 0.7*z], [p, 0.7*p]); %! title("matrix"); | 1,555 | 4,788 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.515625 | 3 | CC-MAIN-2019-43 | latest | en | 0.694494 |
https://gis.stackexchange.com/questions/459966/arcgis-pro-raster-percentiles | 1,717,101,256,000,000,000 | text/html | crawl-data/CC-MAIN-2024-22/segments/1715971670239.98/warc/CC-MAIN-20240530180105-20240530210105-00110.warc.gz | 237,587,583 | 38,190 | # ArcGIS Pro - Raster percentiles
In ArcGIS Pro I have a continuous raster.
I want to calculate an upper and lower percentile value and apply to smooth out the range of values. For example applying the 90th percentile value to the top end, reducing the effects of extreme outlier values.
I have the below code in a Python notebook within ArcGIS Pro to determine percentiles:
``````import numpy as np
arr = arcpy.RasterToNumPyArray('raster_raste')
print(arr.max())
print(arr.min())
print(arr.mean())
p1 = np.percentile(arr,10)
p2 = np.percentile(arr,90)
p3 = np.percentile(arr,100)
``````
The values I got for p1, p2 and p3 were 0, 0 and 83 respectively. The mean of the raster was 0.025. This indicated there could have been many zero's or noData values, so I used 'Extract by Attributes' to select all values above 1.
However applying the same code to the new filtered raster layer I still get the same percentiles and mean values.
How do I get the actual percentiles and apply them to the raster layer?
Ideally I would like something like below for rasters but I'm not sure the right code/tool to apply:
``````#use cursor to update the new rank field
with arcpy.da.UpdateCursor(input , ['population_density','PerRank']) as cursor:
for row in cursor:
if row[0] < p1:
row[1] = 0 #rank 0
elif p1 <= row[0] and row[0] < p2:
row[1] = 1
else:
row[1] = 2
cursor.updateRow(row)
``````
Doesn't really matter what you do to the raster, NoData will be included in the numpy array. Just filter it out. Either work out what the NoData value is or tell `RasterToNumPyArray` to set the NoData elements to a specific value, e.g.
``````## Either figure out NoData value
nodata = arcpy.da.Describe(your_raster)["noDataValue"]
# or
nodata = arcpy.Raster(your_raster).noDataValue
arr = arcpy.RasterToNumPyArray('raster')
## Or specify a NoData value
nodata = -9999
arr = arcpy.RasterToNumPyArray('raster', nodata_to_value=nodata)
## Then filter your array for that nodata value
arr = arr[arr<nodata] | 547 | 1,997 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.5625 | 3 | CC-MAIN-2024-22 | latest | en | 0.784464 |
https://www.chegg.com/homework-help/elementary-survey-sampling-7th-edition-solutions-9781133420569 | 1,529,523,685,000,000,000 | text/html | crawl-data/CC-MAIN-2018-26/segments/1529267863834.46/warc/CC-MAIN-20180620182802-20180620202802-00380.warc.gz | 815,483,868 | 15,294 | # Elementary Survey Sampling (7th Edition) View more editions 79% (328 ratings) for this book
• 344 step-by-step solutions
• Solved by professors & experts
• iOS, Android, & web
Chapter: Problem:
An experimenter wants to estimate the average water consumption per family in a city. Discuss the relative merits of choosing individual families, dwelling units (single-family houses, apartment buildings, and so on), and city blocks as sampling units. What would you use as a frame in each case?
Sample Solution
Chapter: Problem:
• Step 1 of 1
An experimenter wants to estimate the average water consumption per family in a city.
If individual families are used as the sampling units, a frame could be using census data or a telephone book.
If dwelling units are used as the sampling units, a frame could be using an address book or city directory.
If city blocks are used as the sampling units, a frame could be using a city directory.
• Anonymous
What are the merits of choosing a given sampling unit?
Corresponding Textbook
Elementary Survey Sampling | 7th Edition
9781133420569ISBN-13: 1133420567ISBN: Authors:
This is an alternate ISBN. View the primary ISBN for: Elementary Survey Sampling 7th Edition Textbook Solutions
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The best part? As a Chegg Study subscriber, you can view available interactive solutions manuals for each of your classes for one low monthly price. Why buy extra books when you can get all the homework help you need in one place?
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You bet! Chegg Study Expert Q&A is a great place to find help on problem sets and 1 study guides. Just post a question you need help with, and one of our experts will provide a custom solution. You can also find solutions immediately by searching the millions of fully answered study questions in our archive.
### How do I view solution manuals on my smartphone?
You can download our homework help app on iOS or Android to access solutions manuals on your mobile device. Asking a study question in a snap - just take a pic. | 757 | 3,713 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.78125 | 3 | CC-MAIN-2018-26 | latest | en | 0.895976 |
https://slideum.com/doc/109613/chapter-9-review-ii | 1,591,298,653,000,000,000 | text/html | crawl-data/CC-MAIN-2020-24/segments/1590347458095.68/warc/CC-MAIN-20200604192256-20200604222256-00354.warc.gz | 520,690,339 | 8,818 | #### Transcript Chapter 9 Review II
For
f(x)
=
x
2 – 3
x
– 15 find
f(
-2
)
-5
Determine the vertex, axis of symmetry and graph.
y
x
2 3 Vertex:
(0, 3)
Axis of symmetry:
x = 0
x
-2 -1 0 1 2 7 4 3 4 7
y
Find the vertex and axes intercepts.
y
x
2
x
### (-2, 0) & (0, 0)
Find the coordinates of the points of intersection of the graphs with equations
y
=
x
2 – 5
x
+ 10 and
y
=
x
+ 5
## (1, 6) and (5, 10)
A skateboard manufacturer finds that the cost \$C of making x skateboards per day is given by
C(x)
=
x
2 – 24
x
+ 244 a) How many skateboards should be made per day to minimize the cost of production?
12 b) What is the minimum cost?
\$100
A rectangular has a perimeter of 200cm. Let
x
be the width of the rectangle. Find the maximum area for the rectangle.
Area =
x
(100 –
x
) P=2L+ 2w 200 = 2L + 2x Area = 100
x
x
2 100 – x = L The vertex is: (50, 2500) 100 – x x The maximum area is 2500cm 2 .
Find the minimum of
f(x)
= 2
x
2 – 6
x
+ 5
x
b
2
a
6 2 ( 2 ) 6 2 3 2
f
3 2 2 3 2 2 6 3 2 5 1 2 3 2 , 1 2
State the vertex, equation for the axis of symmetry,
y
-intercept.
y
2 (
x
1 ) 2 3 Vertex:
(1, -3)
Axis of symmetry:
x = 1
y-intercept:
(0, -1)
Determine the axis of symmetry and vertex.
y
=
x
2 – 4
x
+ 7 Vertex:
(2, 3)
Axis of symmetry:
x = 2
For
y
=
x
2 – 2
x
• axes intercepts find the • direction the parabola opens • equation of the axis of symmetry and graph Opens up
y
-intercept:
(0, 0)
x
-intercepts:
(0, 0) & (2, 0)
Vertex:
(1, -1)
Axis of symmetry:
x = 1
Name the vertex and axis of symmetry. Graph.
y
x
2
x
### + 11
Vertex:
(-4, -5)
Axis of symmetry:
x = -4
x
-6 -5 -4 -3 -2 -1 -4 -5 -4 -1
y
Name the vertex and axis of symmetry.
y
x
2
### – 7
Vertex:
(0, -7)
Axis of symmetry:
x = 0
A manufacturer of barbeques knows that if
x
of them are made each week then the total cost will be (60
x
+ 800) dollars and the total receipts per week will be (1000
x
– 3
x
2 ) dollars. How many barbeques should be made per week for maximum profits?
157
t
The height 0.
H
meters, of a rocket
t
seconds after it is fired vertically upwards is given by
H
(
t
) = 100
t
– 5
t
2 , a) How long does it take for the rocket to reach its maximum height?
t = 10 seconds
b) What is the maximum height reached by the rocket?
H(10) = 500 meters
c) How long does it take for the rocket to fall back to earth?
20 seconds
A manufacturer finds that the profit \$P from assembling
x
bicycles per day is given by P(
x
) = -
x
2 + 50
x
– 200.
a) How many bicycles should be assembled per day to maximize the profit?
25 bicycles
b) What is the maximum profit?
\$425
c) What is the loss made if no bicycles are assembled in a day?
\$200
Find the coordinates of the points of intersection of the graphs with equations
y
x
2
x
y
x | 1,084 | 2,941 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.984375 | 4 | CC-MAIN-2020-24 | latest | en | 0.746412 |
https://cs.stackexchange.com/questions/59429/efficient-algorithm-for-getting-from-1-to-n-with-3-specific-operations | 1,726,406,592,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725700651630.14/warc/CC-MAIN-20240915120545-20240915150545-00104.warc.gz | 174,081,046 | 44,486 | # Efficient algorithm for getting from 1 to n with 3 specific operations
The question:
Given those 3 valid operations over numbers and an integer $n$:
• add $1$ to the number
• multiply the number by $2$
• multiply the number by $3$
describe an efficient algorithm for the minimal number of operations of getting from $1$ to $n$ with the 3 operations mentioned above.
For example for $n=28$ the answer is $4$ : $1\times 3\times 3\times 3+1=27+1=28$.
My approach:
I noticed that there is a recursive algorithm that will provide the answer but even when I used memoization the algorithm took a lot of time to end with $n\geq 1000$. I thought of a way to start with $n$ instead and try to reduce it to $1$ with the inverse operations of subtracting $1$ dividing by $2$ or by $3$ and trying to get it to be devisible by $3$ or by $2$ by subtracting $1$'s and checking the mod. But my second approach had some (more than some) mistakes where It stated that the smallest number of operations is more than it is. Please help or give a hint I clearly missing some kay fact about the nature of such operations.
Edit:
def ToN(n):
d=dict()
def to(x,num,di):
if (num==x):
return 0
elif (num>x):
return num
elif num in di:
return di[num]
else:
if num+1 not in di:
di[num+1]=to(x,num+1,di)
if num*2 not in di:
di[num*2]=to(x,num*2,di)
if num*3 not in di:
di[num*3]=to(x,num*3,di)
di[num]=min(di[num+1],di[num*2],di[num*3])+1
return di[num]
I wrote the code above in python and it takes a lot of time to end for num=1000. Can you help me understand what is wrong w.r.t. efficiency.
• Hint: Use dynamic programming to get an $O(n)$ algorithm. I'll let you fill in the details. Commented Jun 9, 2016 at 8:08
• What specifically did you try? "took a lot of time" is not a lot to go on. Commented Jun 9, 2016 at 9:52
• Your first approach should have worked, and should have been really fast. You must have programmed it inefficiently somehow. Commented Jun 9, 2016 at 12:22
• This isn't the right stackexchange for debugging code. But where's the memoization? Commented Jun 9, 2016 at 16:32
• Your code is wrong. Think again. Commented Jun 9, 2016 at 20:27
Find the shortest path from $1$ to $n$ on an appropriate graph on vertices $\{1, \dots, n\}$. This approach will work whenever it's guaranteed that intermediate values in the calculations will lie within some bounded range.
An optimal solution will start with x = 1 and repeatedly replace x with 2x (1 step), 2x+1 (2 steps), 3x (1 step), 3x+1 (2 steps) or 3x+2 (3 steps).
I'd attack the problem from both ends: Find the shortest way from 1 to x, and how many steps it takes, for every x ≤ $n^{1/2}$ , and find the ways back from n to a number x ≤ $n^{1/2}$, then combine both. That should work in $O (n^{1/2})$.
For example n = 196 (just a random number)
1. 0 steps
2. 1 step
3. 1 step
4. 2 steps
5. 3 steps
6. 2 steps
7. 3 steps
8. 3 steps
9. 2 steps
10. 3 steps
11. 4 steps
12. 3 steps
13. 4 steps
14. 4 steps
From 196: 0 steps From 98: 1 step From 65: 2 steps From 49: 2 steps From 32: 4 steps From 24: 4 steps From 21: 5 steps From 16: 4 steps From 12: 5 steps From 10: 7 steps From 8: 5 steps From 7: 6 steps From 5: 6 steps
So there are two ways to get there in 8 steps. 1 -> 8 -> 98, and 1 -> 12 -> 98. The calculation was much quicker than O (n).
If you needed to solve this for multiple values n, I'd probably make the table of small values larger. For example, 100 values n around 1 million, I'd start with a table up to 10,000.
Edit about comments: In an optimal chain, x2 cannot be followed by +1, +1 because adding one before the multiplication would be shorter. And x3 cannot be followed by +1, +1, +1 because adding one before the multiplication would again be shorter. At the start with x = 1, we may assume that we don't add +1 once or twice because we can multiply by 2 or 3 instead. So there is always an optimal chain that consists of x2 possibly followed by +1, or x3 possibly followed by +1 or +2.
Finding all optimal solutions up to some k can clearly be done in a total of k steps. k = n^(1/2) means n^(1/2) steps. I assumed going backwards from to some x ≤ n^(1/2) would divide n by some k not much larger than n^(1/2) so could also be done in n^(1/2).
BUT you can actually do much better. By working your way backward, if the number of steps needed is S (n), then S (n) = min (S (floor (n/2)) + 1 + (n modulo 2), S (floor (n/3)) + 1 + (n modulo 3)). You either subtract 1 as long as the number is not divisible by 2, then divide by 2, or you subtract 1 as longas the number is not divisible by 3, then divide by 3.
One step back divides quite exactly by 2 or 3. There are only about log (n) steps going backwards. There are only about (log (n))^2 combinations of divisions by 2 or 3, because you end up at the same number no matter in which order you make steps dividing be 2 or 3. So you can easily find an optimal chain in O ((log (n))^2).
For example, if n = 1234567, then you can easily find the optimal chain 1 -> 2 -> 4 -> 5 -> 15 -> 45 -> 46 -> 47 -> 141 -> 423 -> 1269 -> 1270 -> 3810 -> 11430 -> 11431 -> 22862 -> 68586 -> 68587 -> 137174 -> 411522 -> 1234566 -> 1234567 (21 steps).
• So you will have two optimal chains, but is it globally optimal?
– Evil
Commented Jun 10, 2016 at 13:40
• Why will every solution have the form you claim? What's special about $\sqrt{n}$ that allows you to find out the answer by looking at the shortest route from $1$ to $x\in\{1, \dots, \lceil \sqrt{n}\rceil\}$ and then from $x$ to $n$? Why can't you get an $O(\sqrt[3]{n})$ algorithm by just considering intermediates up to $\lceil\sqrt[3]{n}\rceil$? Commented Jun 10, 2016 at 14:20
• Actually, the real killer: Why do you feel that you can find the number of steps from $1$ to $\sqrt{n}$ in constant time but finding the number of steps from $1$ to $n$ takes more-than-constant time? Commented Jun 10, 2016 at 14:22
• The longest chain (hailstone?) is at most $2\lceil log_2(N)\rceil$ and the shortest is exactly $log_3(N)$. If you take $3^{20}$ it has $20$ numbers in the chain. $sqrt(3^{20}) = 531441$, so what it represents?
– Evil
Commented Jun 10, 2016 at 16:25
• The fact you can reach $1234567$ in 21 steps does not prove your algorithm is $O((\log n)^2)$. To find that you'd have to make much more recursive backward steps, according to your equation for $S(n) = \min (S (\lfloor n/2 \rfloor) +...)$, since you fork each $n$ into (approx.) $n/3$ and $n/2$ and solve the problem for 2 (smaller) cases now, which looks like $O(n)$. Commented Jun 11, 2016 at 8:53 | 2,043 | 6,558 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.03125 | 4 | CC-MAIN-2024-38 | latest | en | 0.913737 |
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Solving Linear Equations - Fractions Objective: Solve linear equations with rational coefficients by multi-plying by the least common denominator to clear the fractions. Often when solving linear equations we will need to work with an equation with fraction coefficients. We can solve these problems as we have in the past. This is
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Linear algebra provides a way of compactly representing and operating on sets of linear equations. For example, consider the following system of equations: 4x 1 − 5x 2 = −13 −2x 1 + 3x 2 = 9. This is two equations and two variables, so as you know from high school algebra, you can find a unique solution for x 1 and x
Preface Linear Algebra deals with the most fundamental ideas of mathematics in an abstract but easily understood form. The notions and techniques employed in Linear Algebra are widely spread across various topics and are found in almost every branch of mathematics, more prominently, in Differential Equations, Functional Analysis, and Optimization, which have wide applications in science and ...
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• Numerical Linear Algebra From a practical standpoint numerical linear algebra is without a doubt the single most important topic in numerical analysis. Nearly all other problems ultimately can be reduced to problems in numerical linear algebra; e.g., solution of systems of ordinary differential equation initial value
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Linear Algebra I Sets & Functions Applying a row operation to a linear system (De nition 1.2) corresponds to the same row operation (De nition 2.6) on the corresponding augmented matrix of this linear system. De nition 2.7. Two matrices Aand Bare called row equivalent, if Bcan be obtained from Aby elementary row operations. In this case we ...
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1 Introduction 1.1 Reference Material Main resources Algebra textbook Howard Anton and Chris Rorres, Elementary Linear Algebra : Applications Version (10th or 11th edition). Also available as an e-text from Wiley Direct Wattle On Wattle you will find lecture recordings, notes, assignments, sample exercises. On WebAssign you will find a diagnostic test. WebAssign will also be used to grade some ...
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Functions and Relations – Graphing using a table of values Class: Pre-Algebra. Complete the table for and graph the resulting line. x. y-5 . 0 . 4 . Complete the table for and graph the resulting line. x. y-3 . 0 . 2 . Complete the table for and graph the resulting line. x. y-4 . 0 . 3 . Complete the table for and graph the resulting line. x ...
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Lecture notes on linear algebra by David Lerner Department of Mathematics University of Kansas and The students of Math 291 (Fall, 2007) These are notes of a course given in Fall, 2007 to the Honors section of our elementary linear algebra course. The lectures were distributed to the students before class, then posted on a
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7 Projection of a vector onto linear constraints 12 8 Minimization of a linear function subject to elliptical constraints 12 9 KL Divergence for Gaussian distributions 13 1 Householder Transformations Much of this section was copied and paraphrased from Heath’s Scientific Computing. Anyways.
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Simple Linear Regression An analysis appropriate for a quantitative outcome and a single quantitative ex-planatory variable. 9.1 The model behind linear regression When we are examining the relationship between a quantitative outcome and a single quantitative explanatory variable, simple linear regression is the most com-
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Abstract Linear Algebra M416 notes Zhao Yang Department of Mathematics University of Illinois at Urbana-Champaign This note will collect key ingredients taught in class. It cannot be used as a substitute of your textbook. December 2, 2019 Zhao Yang M416 notes
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5. Test of consistency of linear equations. If A is the coefficient matrix, X is the variable matrix and B be the constant matrix, then the system of equations is represented as AX=B. If , then the system has a unique solution. If and (a) there is no solution (b) there are infinite or no solutions. 6. Solution of Linear equations 6.1 Cramer’s ...
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These lecture notes do not replace a proper textbook in Linear Algebra. Since Linear Algebra appears in almost every area in Mathematics a slightly more advanced textbook which complements the lecture notes will be a good companion throughout your mathematics courses. There is a wide choice of books in the library you can consult. 1
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Computational Linear Algebra: A First Course. To Eileen, my wife for the last forty-three years. My thanks to David Einstein, who read most of an earlier version of this book and made many helpful suggestions. Contents Preface xxiii I Preliminaries 1 1 Introduction 1
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Lecture Notes. Below are links to rough lecture notes. They are meant to be convenient, but not definitive. In particular, there may be (lots of!) typos. Please inform your instructor of typos and other errors. Karp Lectures. Lecture 1: Vectors and the Dot Product Lecture 2: Projections and Planes Lecture 3: Systems of Linear Equations
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Apr 06, 2011 · Tutorial 49: Solving Systems of Linear Equations in Two Variables. Tutorial 50: Solving Systems of Linear Equations in Three Variables. Tutorial 51: Systems of Linear Equations and Problem Solving. Tutorial 52: Solving Systems of Nonlinear Equations in Two Variables. Tutorial 53: Practice Test on Tutorials 49 - 52
Numerical Linear Algebra From a practical standpoint numerical linear algebra is without a doubt the single most important topic in numerical analysis. Nearly all other problems ultimately can be reduced to problems in numerical linear algebra; e.g., solution of systems of ordinary differential equation initial value | 4,185 | 17,480 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.265625 | 3 | CC-MAIN-2021-25 | latest | en | 0.899901 |
http://nbviewer.jupyter.org/github/jiffyclub/ipythonblocks/blob/master/demos/Firework.ipynb | 1,495,544,115,000,000,000 | text/html | crawl-data/CC-MAIN-2017-22/segments/1495463607636.66/warc/CC-MAIN-20170523122457-20170523142457-00174.warc.gz | 247,313,077 | 12,912 | A simple firework animation with ipythonblocks.
In [1]:
from ipythonblocks import BlockGrid
In [2]:
import math
import itertools
In [3]:
def dist(p1, p2):
return math.sqrt((p1[0] - p2[0]) ** 2 + (p1[1] - p2[1]) ** 2)
In [4]:
grid = BlockGrid(41, 41, block_size=8, lines_on=False)
red = (255, 43, 43)
orange = (255, 142, 43)
yellow = (248, 255, 43)
black = (0, 0, 0)
gray = (188, 188, 188)
blue = (15, 183, 255)
pink = (255, 79, 249)
green = (76, 224, 133)
# launch explosion
launch_center = (40, 20)
for i in (1, 2, 3, 2, 1):
for block in grid:
if dist((block.row, block.col), launch_center) < i*3:
block.rgb = yellow
else:
block.rgb = black
if dist((block.row, block.col), launch_center) < i*2:
block.rgb = orange
if dist((block.row, block.col), launch_center) < i:
block.rgb = red
grid.flash()
# ascent
for i in range(17):
grid[:, :] = black
row = 36 - i
grid[row:row + 2, 20] = gray
grid.flash()
# firework
firework_center = (20, 20)
colors = itertools.cycle((blue, pink, green))
for i in range(0, 20):
grid[:, :] = black
for j in range(0, i, 2):
color = colors.next()
for block in grid:
if round(dist((block.row, block.col), firework_center)) == j:
block.rgb = color
grid.flash()
grid.show()
In [4]: | 441 | 1,218 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.578125 | 3 | CC-MAIN-2017-22 | longest | en | 0.474615 |
https://owlcalculator.com/Area/Square-Centimeter | 1,638,265,325,000,000,000 | text/html | crawl-data/CC-MAIN-2021-49/segments/1637964358966.62/warc/CC-MAIN-20211130080511-20211130110511-00188.warc.gz | 512,881,370 | 13,588 | # Area - Convert From Square Centimeter
## Area
Using our calculator, you can easily convert units of area from one dimension to another.
Area is a numerical characteristic of a two-dimensional (flat or curved) geometric figure, informally speaking, showing the size of this figure. Historically, the calculation of the area was called quadrature.
## Tags
Square Centimeter Square Centimeter conversion Square Centimeter definition Convert Square Centimeter
1 Hectare (ha) =
### Convert From Square Centimeter
1 Square Centimeter (cm²) =
### Convert From Square Feet
1 Square Feet (ft²) =
### Convert From Square Kilometer
1 Square Kilometer (km²) =
### Convert From Square Meter
1 Square Meter (m²) =
### Convert From Square Miles
1 Square Miles (mi²) =
### Convert From Square Yards
1 Square Yards (yd²) =
### Convert From Square decimeter
1 Square decimeter (dm²) =
1 Decar (daa) = | 212 | 904 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.59375 | 3 | CC-MAIN-2021-49 | latest | en | 0.767694 |
https://quant.stackexchange.com/questions/tagged/time-series?sort=active&pageSize=50 | 1,566,530,007,000,000,000 | text/html | crawl-data/CC-MAIN-2019-35/segments/1566027317817.76/warc/CC-MAIN-20190823020039-20190823042039-00474.warc.gz | 603,754,206 | 40,002 | # Questions tagged [time-series]
A temporal sequence of events measured at discrete points in time.
537 questions
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7 views
### how to model NGARCH using 5min frequency data?
NGARCH model using 5-min High-frequency data in R I wanted to analyze some 5 minute frequency data of stock market. My teacher asked me to use NGARCH to model, but I didn't know how to program.Here ...
22 views
### Serial Correlation in Rolling Change Linear Regression Models
1.) Lets say I have two time series GDP, BUSINV from (1948, 2019); Frequency of Data is Quarterly. 2.) Say I want to predict GDP i.e. GDP ~ BUSINV 3.) Since GDP is not stationary (i.e. level) and ...
47 views
### Difference between Predicting stock returns and Forecasting stock Returns?
The data that is used are either Technical Indicators, Fundamentals Indicators or Macro Indicators which is time series in nature. Given, if we are estimating one-period ahead returns(t+1), is there a ...
76 views
### Fama French Three Factor Model: How do I get the risk premia?
I try to calculate the cost of equity with the FF3 model and already estimated the beta factors for the market, size and value risk premia by using regressions and the data provided on the Kenneth ...
12 views
### How to implement Time varying EWMA cross correlation in STATA?
I have read this question, I know about lambda, demeaned subindexes. But not able to implement in STATA?
2k views
### Estimating correlation using EWMA
I am using an EWMA model to evaluate the correlation between yearly time series. I know Riskmetrics uses $\lambda=0.94$ for daily data and $\lambda=0.97$ for monthly data. Is there a value ...
387 views
### Block bootstrap to synthesize asset prices
I have a few basic questions on block bootstrapping on a financial time series ('TS'). Assuming my trade universe consists of 10 stocks, I would like to create a set of synthetic prices for all 10 ...
400 views
### How to synchronize put and call option-data?
I recently retrieved a large amount of European option data, for call and put prices, from OptionMetrics. Doing so for the same time period I get a file consisting of 62558 rows of call prices & ...
157 views
### Multivariate Markov Regime switching GARCH
I have a regression with 4 independent variables and a dependent variable. I want to implement a Regime switching GARCH model but have been unable to find a package in R,Python or Matlab. MSGARCH ...
123 views
### Absorption Ratio
I'm actually trying to implement Mark Kritzman's absorption ratio (Principal Components as a Measure of Systemic Risk by Kritzmam, Li, Page and Rigobon, 2010, SSRN 1633027) using Python, but I'm not ...
15 views
### Bloomberg tick data timezone offset because mismatch in bloomberg api and excel bloomberg
i am trying to fetch intraday tick data for security->C Z9 COMB Comdty,startdatetime:2019-08-05 15:30:00 Enddatetime:2019-08-05 15:35:00 from excel and bloomberg Api but response is mismatching can ...
252 views
### Generating surface of Kernel Density Estimates over time
I have a 1-minutely OHLC dataset indexed by time as follows: ...
43 views
### modelling known regime shifts
I wish to model a price time series with a known regime shift: electricity price before during and after the introduction of a carbon price. The time series looks like this: you can see the jump in ...
147 views
### Can you use GARCH-MIDAS for intraday data?
I'm working on a project to forecast volatility and I'm using intraday data (1 min). I want to include exogenous variables to the model that have daily frequency. I was wondering if GARCH-MIDAS can be ...
54 views
### Can MACD be calculated for values other than 12 and 26?
I am working on time-series classification problem using Convolutional Neural Networks in Python. The data-set used is financial stock market data (like yahoo finance). I am using some technical ...
101 views
### Why do we need event-driven backtesters?
I am reading this article at quantstart regarding event-driven backtesters. It seems to me that the main advantage of using an event-driven backtesters is that it avoids look-ahead bias. Usually I ...
80 views
### Trading 3 stocks X Y Z where X cointegrated to Y, Y to Z, but no other cointegration is available
Suppose you have 3 stocks, say X Y Z. You also know that X is cointegrated to Y using some test (say ADF) and Y is cointegrated to Z. However, no transitivity, and no threesome cointegration ...
91 views
### How to handle Holidays in Time-Series Datasets?
Im currently analyzing a Dataset of the German Stock market. While Holidays like Christmas or New Year aren't a problem for Return Calculation or Portfolio Performance, im testing some regressions and ...
72 views
### What does A(B) mean in time series
So I have been reading some papers regarding time series, mainly from Granger and Engle. I am a bachelor econometrics student, but I have never seen such notation before. For example, A(B)(1-B)x(t) = -...
1k views
### Why quants think that the risk-neutral measure should not be used for financial forecasting?
In posts regarding the $\mathbb{P}$ vs $\mathbb{Q}$ debate (see 1, 2, 3 or 4), most answers conclude that historical-based methods are better suited than risk-neutral models for financial predictions. ...
2k views
### How to forecast high-frequency data?
Introduction: I have seen a plenty of articles/books regarding volatility forecasting applied to high frequency data, but none of them were dedicated to forecasting the actual prices (for example bid/...
64 views
### generalisation of cointegrated stock pair strategies to multiple cointegration
Question: as it is well known, there are strategies to trade pairs of stocks which are known to be co-integrated. See for instance here: https://medium.com/auquan/pairs-trading-data-science-...
54 views
### Cross Effect in OLS
I am using cross effect in OLS regression for a time series problem for a multivariate regression. I want to quote reference for use of cross effect. Secondly, I want to explain why better to use ...
86 views
### linear model of price changes
I came across the below equation for linear model of price changes in E.Chan book Algorithmic Trading which is the base for a strategy. ...
90 views
### How can stationary time series data be used as input in an ML model?
I am halfway through "Advances in Financial Machine Learning" by Marcos Lopez de Prado. I understand that a time series like stock prices can be transformed to make it sufficiently stationary. ...
79 views
### Exponential Smoothing - Alpha greater than 1
Simple stats question. I'm having trouble finding anything in the literature as to why the smoothing coefficient can never be greater than 1. This question was started by me doing time series ARIMA ...
170 views
### Filling a few missing data in time series?
I'm writing a paper about Uncertainty indices like VIX, etc. I already collected all data but it seems that some of the variables got a few or a little more missing data. I have daily and monthly data ...
41 views
### Brownian motion from price-series, what is the time step?
If I assume a given empirical price-series is a brownian motion, I can estimate the drift and standard deviation as long as I know what the time step was when the process was 'generated'. But since ...
64 views
### Forecasting a seasonal series with R
I am working with the program "R". I used the command "seas (X-13)" to deseasonalize my quarterly series, then I did the forecast with it. Therefore my forecast is in deseasonalized terms. Now, I was ...
587 views
### Up and Down days in GBPUSD and a Filter
I want to study if the odds of an up or down day in a forex pairs is 50-50. I just count the total number of up and down days in X years and compare it with the total days. The results are very ...
20 views
### Pricing a transfer option for oil
Need some input in how to attack this problem. Given are 8 timeseries: UK Oil price, Delivery Quarter 1 2020 UK Oil price, Delivery Quarter 2 2020 UK Oil price, Delivery Quarter 3 2020 UK Oil price, ...
231 views
### Reverse chronological time-series / inverse time-series
If a timeseries follows a BM, is it true that the inverse ts and reverse chronological ts is also a BM? What if the ts exhibits mean reversion tendencies? Would these tendencies become a momentum ...
49 views
### Log transformation of TS-stationary time series
I usually see the $log$ transformation of prices: $$p_{new}\left(t\right) = ln\left(\frac{p_t}{p_{t-1}}\right), t \in [2...N]$$. Let's our series be a trend stationary time series like: p\left(t\...
33 views
### Auto-covariance function of station time series
How to show that for any stationary time series its auto-covariance function is symmetric about the origin, that is $\gamma_{k}=\gamma_{-k}$ where, $\gamma_k=cov(z_t,z_{t-k})$
46 views
### Is this a good (partial) autocorrelation or bad?
I was playing with some data on deviation of close prices from its smoothed estimated and got these ACF and partial ACFs: I still struggle to get proper intuition to the ACF plots. What do the plots ...
65 views
### Misunderstanding of time series autocovariance
I'm reading the "Time Series: Theory and Methods (2nd ed.)" by P.J.Brockwell and R.A.Davis. I've stopped at the one moment at pp.218-219 (Chapter 7 "Estimation of the mean and the Autocovariance ...
45 views
### Significance Of Missing Data for RMSE Estimation
I have a time series covering ten years of daily close prices, which I compare to a theoretical time series generated by a model. The original series has a handful of missing data points (~2%), some ...
53 views
### Fama-French 3, Carhart 4, Fama-French 5 Factor models return borderline 0% R2 (max. 6.6%). Time series regression
I am currently working on an industry specific time series analysis of European Equities between 201001 and 201812. I use the European Fama French factor returns (plus the momentum factor return) that ...
94 views
### when a co-integrated times series pair has broken the leash
I have two times series, say $T_i$ and $S_i$ over a reasonably large time window, and I have calculated their cointegration (using python's OLS and Adfuller) . Say that the test has passed with high ...
35 views
### Problem with Hurst exponent estimation for ARFIMA models
guys. I try to realize my ARFIMA model identification script in R. I try to find the best method for unbiased Hurst exponent estimation (fractional difference parameter could be found as Hurst - 0.5) ...
175 views
### Volume or Dollar bars vs. volatility normalized and demeaned financial time series
In his book - Advances in Financial Machine Learning, Marcos Lopez de Prado familiarises the reader with a number of ways of normalizing our financial time series data. Below I provide a couple of ...
908 views
### Fitting Copula and Simulation
I would greatly appreciate any insights into the problem described below, regarding using the data obtained from applying the functions of the rugarch package ...
27 views
### Tools related to Granger Causality
I would like to know if there are some tools that can measure that one time series is "faster" than the second one. I talk about really similar time series related to high frequency trading (hundreds ...
74 views
### Is there such a thing as resonance in economic underliers?
In physics the occurence of resonance is explained and widely understood in its linear form and subject to research in nonlinear resonance. Example for instance are resonant frequencies of objects. ...
46 views
### serial correlation and CUSUM results
I have the following CUSUM test resulted from autoregressive distributed lag models (ARDL). Does the CUSUM results show that the model is stable? I am a bit confused because the red line in CUSUM ...
66 views
### Calculating Ex-ante Sharpe Ratio in multi-period setting
I have built a return process $\{x_t, t = 1,\dots,T\}$ for an asset. Suppose I have generated $K$ sample paths $\{x_t^j, t=1,\dots,T\}, j=1,\dots,K$. I think of two ways to compute the Sharpe ratio. ...
185 views
### what are the criteria to select pairs?
I'm new to this forum, this is the first question I posted. I have many candidate pairs and I've used ADF test to make a first selection. There are more than 800 selected. The pairs are absolutely too ...
151 views
### R Equilibrium FX using VEC or Behavioural Equilibrium Exchange Rate (BEER)
I dont have much experience with R. I would like to do create model for FX Equlibrium using VEC or BEER. I already know what variables I want to use in model: trade differential between UK and the ... | 2,950 | 12,710 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.828125 | 3 | CC-MAIN-2019-35 | latest | en | 0.888478 |
https://docslib.org/doc/3572645/work-and-energy-x | 1,708,535,910,000,000,000 | text/html | crawl-data/CC-MAIN-2024-10/segments/1707947473524.88/warc/CC-MAIN-20240221170215-20240221200215-00298.warc.gz | 227,378,261 | 8,634 | <<
Done by a Constant
FF
Work and Δx
The work done, W, by a constant , F, causing an object to move by a , d, is: W = F·d SI unit: 1 N·m = 1 (J) 1 2
Work Done by a Constant Force Negative Work Done
F F Negative work done occurs when the force and θ θ displacement vectors are in opposite directions. A typical example for such a force is .
vi vf = 0 d
In general, if the net force, F, makes an θ, fk with the displacement vector, d, the work done W d by F is:
Net Work Done = (– fk)d = -fkd W = F·dcosθ Negative work done 3 4
Work Done and Kinetic Energy Consider the work done by a constant force, F, on an object with , m. The kinetic energy K of an object with mass m and W = F⋅d= ma⋅d= m(a⋅d) ……… (1) v is defined as:
The a brought about by the force would cause the velocity of the object to change from v to v , following 0 f K = ½ mv2 2 2 2 2 the relation, vf = v0 + 2a ⋅d, implying ad = ½ (vf –v0 ). Substitute this in eqn. (1), we get:
2 2 W = ½ m(vf –v0 ) ……. (2)
The RHS represents a change in the , ½ mv2, between the initial (o) and final state (f). What is ½ mv2? Notice that it must be an energy since the LHS is an energy. 5 6 Net Work done by multiple Work-Kinetic Energy Theorem Acting on an Object Given the definition of K, we can rewrite eqn. (2) as: The work done, Wi by a particular force, Fi, on an object is given by: 2 2 W = ½ m(vf –v0 ) = ΔK W = (F cosθ )d Or, ΔK = W = Fdcosθ i i i
ΔK = W If there are multiple forces, F1, F2, … acting on an object, the net work done on the object is the sum of the work This is the work-kinetic energy theorem. The RHS is the done by all the forces F , F , …. net work. It is: 1 2
-zero when the net force is perpendicular to the Wnet = Σ[(Ficosθi)d] = (Fnetcosθ)d, displacement. - positive when the net force has a component in the where θ is the angle Fnet makes with d. This expression of direction of the displacement (or velocity). Wnet is the same as what we had before. This shows that - negative when the net force has a component opposite the net work done is just that by the net force acting on to the direction of the displacement (or velocity). 7 the object. 8
The net force vs. graph Two disks Given the relation: Two disks are initially at rest. The mass of disk B is two larger than that of disk A. The two disks then experience ΔK = W = Fnet,//⋅d(Fnet,// = Fcosθ) equal net forces F. These net forces are applied for the same Work-KE Theorem amount of . After the net forces are removed: 1. The disks have the same and kinetic energy. 2. The disks have equal momentum; disk A has more kinetic Change in KE is the under the net force vs. energy. position graph. 3. The disks have equal momentum; disk B has more kinetic energy. This should be contrasted with the use of the net force 4. The disks have equal kinetic energy; disk A has more vs. time graph, where change in momentum is the area momentum. under the net force vs. time graph. 5. The disks have equal kinetic energy; disk B has more 9 momentum. 10
Momentum and Kinetic Energy
Two disks -- scenario 2 Momentum Kinetic Energy
SI unit: kgm/s SI unit: J Two disks are initially at rest. The mass of disk B is two times larger than that of disk A. The two disks then experience equal net forces F. These net forces are applied over equal vector displacements. After the net forces are removed: 2 2 1. The disks have the same momentum and kinetic energy. p = mv KE = mv /2 = p /(2m) 2. The disks have equal momentum; disk A has more kinetic energy. p2 = 2m(KE) 3. The disks have equal momentum; disk B has more kinetic energy. If two objects have the same momentum, the object 4. The disks have equal kinetic energy; disk A has more with smaller mass will have bigger kinetic energy. momentum. If two objects have the same kinetic energy, the object 5. The disks have equal kinetic energy; disk B has more 11 with smaller mass will have smaller momentum. 12 momentum. Work -- example 1 Work -- example 2
You hold an object that weighs 10 N at a You raise a 10 N object up by a vertical fixed, elevated height for 15 minutes. How of 0.5 m. You maintain a constant much work do you do to the object? acceleration of 1 m/s2 throughout the process. The net work you do to the object is … 1. Zero. 1. 5 J 2. Positive. 2. More than 5 J 3. Negative. 3. Less than 5 J
The net force, F required to move the 10 N object vertically up The displacement is zero. So W = Fs = 0. at a constant acceleration of 1 m/s2 is +11 N (up). So W = Fd = 13 (11N)(0.5m) = 5.5 J 14
Work -- example 3 You lower a 10 N object at a constant by a vertical distance of 0.5 m. The net work done on the object is …
1. 5 J 2. More than 5 J 3. Less than 5 J
The net force, F required to move the 10 N object vertically down at a constant speed is 10 N (up). So W = Fd = (10N)(- 15 0.5m) = -5 J | 1,398 | 4,816 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.28125 | 4 | CC-MAIN-2024-10 | latest | en | 0.905102 |
https://citizenmaths.com/frequency/cycles-per-nanosecond-converter | 1,713,435,878,000,000,000 | text/html | crawl-data/CC-MAIN-2024-18/segments/1712296817206.28/warc/CC-MAIN-20240418093630-20240418123630-00167.warc.gz | 155,277,746 | 13,804 | # Cycle per Nanosecond Conversion Calculators
From
Cycle per Nanosecond
• Action per Minute
• Attohertz
• Centihertz
• Cycle per Day
• Cycle per Hour
• Cycle per Microsecond
• Cycle per Millisecond
• Cycle per Minute
• Cycle per Month
• Cycle per Nanosecond
• Cycle per Picosecond
• Cycle per Second
• Cycle per Year
• Decahertz
• Decihertz
• Degree per Hour
• Degree per Millisecond
• Degree per Minute
• Degree per Second
• Exahertz
• Femtohertz
• Frame per Second
• Fresnel
• Gigahertz
• Hectohertz
• Hertz
• Kilohertz
• Megahertz
• Microhertz
• Millihertz
• Nanohertz
• Petahertz
• Picohertz
• Revolution per Minute
• Terahertz
• Yoctohertz
• Yottahertz
• Zeptohertz
• Zettahertz
To
Attohertz
• Action per Minute
• Attohertz
• Centihertz
• Cycle per Day
• Cycle per Hour
• Cycle per Microsecond
• Cycle per Millisecond
• Cycle per Minute
• Cycle per Month
• Cycle per Nanosecond
• Cycle per Picosecond
• Cycle per Second
• Cycle per Year
• Decahertz
• Decihertz
• Degree per Hour
• Degree per Millisecond
• Degree per Minute
• Degree per Second
• Exahertz
• Femtohertz
• Frame per Second
• Fresnel
• Gigahertz
• Hectohertz
• Hertz
• Kilohertz
• Megahertz
• Microhertz
• Millihertz
• Nanohertz
• Petahertz
• Picohertz
• Revolution per Minute
• Terahertz
• Yoctohertz
• Yottahertz
• Zeptohertz
• Zettahertz
Formula 19,878 cpns = 19878 x 1e+27 aHz = 2.0e+31 aHz
## Cycle per Nanosecond Conversion Charts
This chart provides a summary of Cycle per Nanosecond conversions to different Frequency units.
Units 1 5
Zeptohertz 1 cpns = 1.0e+30 zHz 5 cpns = 5.0e+30 zHz
Yoctohertz 1 cpns = 1.0e+33 yHz 5 cpns = 5.0e+33 yHz
Terahertz 1 cpns = 0.001 THz 5 cpns = 0.005 THz
Revolution per Minute 1 cpns = 6.0e+10 RPM 5 cpns = 3.0e+11 RPM
Picohertz 1 cpns = 1.0e+21 pHz 5 cpns = 5.0e+21 pHz
Hectohertz 1 cpns = 10,000,000 hHz 5 cpns = 50,000,000 hHz
Gigahertz 1 cpns = 1 GHz 5 cpns = 5 GHz
Fresnel 1 cpns = 0.001 fresnel 5 cpns = 0.005 fresnel
Frame per Second 1 cpns = 1.0e+09 FPS 5 cpns = 5.0e+09 FPS
Femtohertz 1 cpns = 1.0e+24 fHz 5 cpns = 5.0e+24 fHz
Degree per Second 1 cpns = 3.6e+11 deg/s 5 cpns = 1.8e+12 deg/s
Degree per Minute 1 cpns = 2.2e+13 deg/m 5 cpns = 1.1e+14 deg/m
Degree per Millisecond 1 cpns = 3.6e+08 deg/ms 5 cpns = 1.8e+09 deg/ms
Degree per Hour 1 cpns = 1.3e+15 deg/h 5 cpns = 6.5e+15 deg/h
Decihertz 1 cpns = 1.0e+10 dHz 5 cpns = 5.0e+10 dHz
Decahertz 1 cpns = 100,000,000.0 daHz 5 cpns = 5.0e+08 daHz
Cycle per Year 1 cpns = 3.2e+16 cpy 5 cpns = 1.6e+17 cpy
Cycle per Second 1 cpns = 1.0e+09 cps 5 cpns = 5.0e+09 cps
Cycle per Picosecond 1 cpns = 0.001 cpps 5 cpns = 0.005 cpps
Kilohertz 1 cpns = 1,000,000 kHz 5 cpns = 5,000,000 kHz
Megahertz 1 cpns = 1,000 MHz 5 cpns = 5,000 MHz
Microhertz 1 cpns = 1.0e+15 µHz 5 cpns = 5.0e+15 µHz
Millihertz 1 cpns = 1.0e+12 mHz 5 cpns = 5.0e+12 mHz
Nanohertz 1 cpns = 1.0e+18 nHz 5 cpns = 5.0e+18 nHz
Attohertz 1 cpns = 1.0e+27 aHz 5 cpns = 5.0e+27 aHz
Action per Minute 1 cpns = 6.0e+10 APM 5 cpns = 3.0e+11 APM
Centihertz 1 cpns = 1.0e+11 cHz 5 cpns = 5.0e+11 cHz
Cycle per Day 1 cpns = 8.6e+13 cpd 5 cpns = 4.3e+14 cpd
Cycle per Hour 1 cpns = 3.6e+12 cph 5 cpns = 1.8e+13 cph
Cycle per Microsecond 1 cpns = 1,000 cpµs 5 cpns = 5,000 cpµs
Cycle per Millisecond 1 cpns = 1,000,000 cpms 5 cpns = 5,000,000 cpms
Cycle per Minute 1 cpns = 6.0e+10 cpm 5 cpns = 3.0e+11 cpm
Cycle per Month 1 cpns = 2.6e+15 cpmo 5 cpns = 1.3e+16 cpmo
Hertz 1 cpns = 1.0e+09 Hz 5 cpns = 5.0e+09 Hz | 1,548 | 3,436 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.0625 | 3 | CC-MAIN-2024-18 | latest | en | 0.339678 |
http://www.governmentadda.com/daily-ibps-po-knowledge-booster-magic-box-day-3-13th-september-2018/ | 1,537,692,821,000,000,000 | text/html | crawl-data/CC-MAIN-2018-39/segments/1537267159165.63/warc/CC-MAIN-20180923075529-20180923095929-00148.warc.gz | 339,589,873 | 32,949 | Daily IBPS PO Knowledge Booster Magic Box : Day 3 (13th September 2018) | | GovernmentAdda
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Daily IBPS PO Knowledge Booster Magic Box : Day 3 (13th September 2018)
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S No All Material For Daily Current Affairs Knowledge Booster Magic Box Link For Material 1. Daily Current Affairs Learn Now 2. Daily Current Affairs Free Quiz Attempt Now | 818 | 3,832 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.53125 | 3 | CC-MAIN-2018-39 | longest | en | 0.647577 |
http://web2.0calc.com/questions/i-know-i-don-t-ask-questions-but | 1,508,351,371,000,000,000 | text/html | crawl-data/CC-MAIN-2017-43/segments/1508187823067.51/warc/CC-MAIN-20171018180631-20171018200631-00248.warc.gz | 357,856,852 | 6,483 | +0
# I know I don't ask questions, but...
+2
271
3
+1221
Find the diameter of a right cone with a slant height of $$18cm$$ and a surface area of $$208\pi cm^2$$.
TheXSquaredFactor May 22, 2017
Sort:
#1
+8768
+3
Find the diameter of a right cone with a slant height 18cm of and a surface area of 208 pi cm2.
Omi67 May 22, 2017
#3
+1221
0
Thank you. I knew that the surface area equals the circumference of the base multiplied by the slant height and then add the area of the base. I didn't realize that I could setup an equation with that information, though...
TheXSquaredFactor May 22, 2017
#1
+18610
0
Find the diameter of a right cone with a slant height of $$18\ cm$$ and a surface area of $$208 \pi \ cm^2$$.
Surface area of cone $$A = \pi r^2+\pi rl$$
$$\begin{array}{|rcll|} \hline \pi r^2+ \pi rl &=& A \quad & | \quad : \pi \\ r^2+rl &=& \frac{A}{\pi} \\ r^2+rl -\frac{A}{\pi} &=& 0 \\ r &=& \frac{-l\pm \sqrt{l^2-4\cdot (-\frac{A}{\pi}) } } {2} \\ r &=& \frac{-l\pm \sqrt{l^2+ \frac{4A}{\pi} } } {2} \\ 2r = d &=& -l\pm \sqrt{l^2+ \frac{4A}{\pi} } \quad & | \quad A = 280\pi \qquad l = 18 \\ d &=& -18\pm \sqrt{18^2+ 4\cdot 208 } \\ d &=& -18\pm \sqrt{1156 } \\ d &=& -18\pm 34 \\ d &=& -18 + 34 \\ d &=& 16 \\ \hline \end{array}$$
The diameter is 16 cm
heureka May 22, 2017
#3
+1221
0
Thank you. I knew that the surface area equals the circumference of the base multiplied by the slant height and then add the area of the base. I didn't realize that I could setup an equation with that information, though...
TheXSquaredFactor May 22, 2017
### 24 Online Users
We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners. See details | 652 | 1,829 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.03125 | 4 | CC-MAIN-2017-43 | longest | en | 0.752349 |
http://support.hfm.io/1.6/api/stringsearch-0.3.6.6/Data-ByteString-Lazy-Search-KarpRabin.html | 1,722,999,325,000,000,000 | text/html | crawl-data/CC-MAIN-2024-33/segments/1722640667712.32/warc/CC-MAIN-20240807015121-20240807045121-00347.warc.gz | 27,280,886 | 3,490 | stringsearch-0.3.6.6: Fast searching, splitting and replacing of ByteStrings
Copyright (c) 2010 Daniel Fischer BSD3 Daniel Fischer Provisional non-portable (BangPatterns) None Haskell98
Data.ByteString.Lazy.Search.KarpRabin
Contents
Description
Simultaneous search for multiple patterns in a lazy ByteString using the Karp-Rabin algorithm.
A description of the algorithm for a single pattern can be found at http://www-igm.univ-mlv.fr/~lecroq/string/node5.html#SECTION0050.
Synopsis
# Overview
The Karp-Rabin algorithm works by calculating a hash of the pattern and comparing that hash with the hash of a slice of the target string with the same length as the pattern. If the hashes are equal, the slice of the target is compared to the pattern character by character (since the hash function generally isn't injective).
For a single pattern, this tends to be more efficient than the naïve algorithm, but it cannot compete with algorithms like Knuth-Morris-Pratt or Boyer-Moore.
However, the algorithm can be generalised to search for multiple patterns simultaneously. If the shortest pattern has length k, hash the prefix of length k of all patterns and compare the hash of the target's slices of length k to them. If there's a match, check whether the slice is part of an occurrence of the corresponding pattern.
With a hash-function that
• allows to compute the hash of one slice in constant time from the hash of the previous slice, the new and the dropped character, and
• produces few spurious matches,
searching for occurrences of any of n patterns has a best-case complexity of O(targetLength * lookup n). The worst-case complexity is O(targetLength * lookup n * sum patternLengths), the average is not much worse than the best case.
The functions in this module store the hashes of the patterns in an IntMap, so the lookup is O(log n). Re-hashing is done in constant time and spurious matches of the hashes should be sufficiently rare. The maximal length of the prefixes to be hashed is 32.
## Caution
Unfortunately, the constant factors are high, so these functions are slow. Unless the number of patterns to search for is high (larger than 50 at least), repeated search for single patterns using Boyer-Moore or DFA and manual merging of the indices is faster. Much faster for less than 40 or so patterns.
indicesOfAny has the advantage over multiple single-pattern searches that it doesn't hold on to large parts of the string (which is likely to happen for multiple searches), however, so in contrast to the strict version, it may be useful for relatively few patterns already.
Nevertheless, this module seems more of an interesting curiosity than anything else.
# Function
Arguments
:: [ByteString] List of non-empty patterns -> ByteString String to search -> [(Int64, [Int])] List of matches
indicesOfAny finds all occurrences of any of several non-empty strict patterns in a lazy target string. If no non-empty patterns are given, the result is an empty list. Otherwise the result list contains the pairs of all indices where any of the (non-empty) patterns start and the list of all patterns starting at that index, the patterns being represented by their (zero-based) position in the pattern list. Empty patterns are filtered out before processing begins. | 703 | 3,296 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.640625 | 3 | CC-MAIN-2024-33 | latest | en | 0.84706 |
http://ballistipedia.com/index.php?title=Fliers_vs._Outliers | 1,579,308,221,000,000,000 | text/html | crawl-data/CC-MAIN-2020-05/segments/1579250591431.4/warc/CC-MAIN-20200117234621-20200118022621-00121.warc.gz | 16,803,539 | 11,131 | # Fliers vs. Outliers
Title page "Fliers" to replace existing page of that name
# Fliers - Defects or Outliers?
To target shooters a shot is colloquially labeled as a "flier" if the shot flies wide of the target, or if has a POI too far from the COI of the other shots on the target. Every shooter experiences fliers. The shooter may, or may not know the cause of the flier.
# Definitions
In using statistics to analyze target precision it is very necessary to formalize the definition of a "flier" and to separate fliers into two types.
Definitions:
Flier
A shot which is either a defective shot or an outlier.
Defect
A shot that is the result of an atypical factor, the defect, that affects one or more of the shooting processes. The shooter may or may not be aware of the atypical factor.
Outlier
A shot that is at an extreme value for the distribution. In other words a shot with such a large position difference from the average of the other shots that it seems improbable.
Thus there is a subtle but significant difference between formal definitions of defect and outlier. The gist is that there is no way to guarantee that a defect can be modeled since we don't know all of the atypical factors that might cause a defect, or what sort of distribution most of those aberrations would create even if we could identify them. Worse given the nature shooting, we might not be able to directly measure the factor which is atypical. In that case the only objective evidence would be from the target analysis. However outliers can be readily mathematically modeled using target analysis.
# Defects
In essence a defective shot is a shot which has a different distribution than "regular" shots. For the purposes of this discussion let's define the distribution of shots by their Center Of Impact (COI) and their Mean Radius (MR). So for regular shots assume:
$$COI_{reg}, MR_{reg}$$
but let's assume that we have 6 different possible defects each with its own different distribution:
$$COI_{defect(1)}, MR_{defect(1)}$$
$$COI_{defect(2)}, MR_{defect(2)}$$
...
$$COI_{defect(6)}, MR_{defect(6)}$$
When we were considering the overall system error we added the various error sources as:
$$\sigma_{System}^2 = \sigma_{Weapon}^2 + \sigma_{Ammunition}^2 + \sigma_{Shooter}^2$$
because the weapon contributes some error, then the ammunition contributes some more error, and the shooter even more. However defects are handled differently.
you and buddy...
Let's simulate what happens with defects. Consider that 1/6 of the shots are fliers. Get a blank regular d6 die from the hobby store and mark one face with a black circle, the other faces being plain. When you roll the die, you get a regular shot if you roll a plain face, and a flier if you roll the face with the black spot. Now for the nasty rub. A hole is a hole is a hole. There is no way to tell if a hole is a "true flier shot" or a "true regular shot"!
Remember that we have used infinite distributions to model the shot distribution. So if we are given the parameters for the horizontal and vertical normal distributions, then we can readily calculate a pistol shot being 5 miles wide even though that is impossible by physics. Consider being able to "fairly" flip a coin heads a thousand times in a row. It is so impossible that you'd have to suspect cheating, but it is possible. So to a statistician improbable certainly does not mean impossible. To prove that a pistol shot won't travel 5 miles we couldn't use the probability models, but rather external ballistics using muzzle velocity and a drag coefficient for the projectile. This of course requires a more sophisticated distribution model, and more assumptions.
You might think that we might be able to get the fliers to go to one group and the regular shots to another. It might work for different ammunition types, but there is no guarantee. It could be that $$COI_{reg} = COI_{flier}$$ but that $$MeanRadius_{flier} \gg MeanRadius_{reg}$$ in which case the fliers would be sprayed all around the COI.
Obviously another problem with trying to "pattern" the two types is sampling. With 1/6 fliers (an appalling bad defect probability!) to get 5 flier shots we'd shoot on average 30 shots. To most shooters that is an exorbitant amount of shooting.
A flier might have a known cause before the target is examined, for example:
• Benchrest-level shooters traditionally discard the first round(s) after cleaning a barrel as a "fouling" shot(s). The friction difference between a clean and a fouled bore are enough to significantly alter the point of impact.
• A shooter may "call a flier" if he knows he committed an error that is not characteristic of his shooting.
• If the shots are being chronographed, then the shooter might "call a flier" on any shot that chronographs outside of the 95% confidence interval around the mean muzzle velocity.
However a defect (or fliers) might have an unknown cause, and might not be suspected until the shot pattern on the target is observed.
• If the shots are not being chronographed, but one shot is very low, then the shooter would suspect an excessive muzzle velocity variation.
So to obtain objective evidence that muzzle velocity variation is the problem, the shooter would need to design an experiment to test for that process difference - for instance using a chronograph. In this situation the chronograph adds objective evidence which is not available looking at the bullet holes alone.
• A projectile might be off-balance in the distribution of mass.
So in this case the shot is a true defect, but the shooter doesn't have any means to measure the mass balance of a spinning projectile. So there would be now way to know that the projectile was a defect. (Making an example, rather than challenging experimentalists!) The only objective evidence is the bullet hole such a projectile makes - and a bullet hole is a bullet hole is a bullet hole.
The salient point is that some objective evidence of process variation must exist to be able to label a shot a defect. If the only evidence is the position of the holes in the target, then a shot can't be labeled a defect. The only way to analyze a flyer on the target when just the relative holes positions of the shots are known, is through the consideration of outliers. An outlier just being an improbable shot given the target analysis model.
## Outliers
Not every outlier is a defect.
Unbounded distributions have been accepted as models for the shooting process, and so outliers are part of both the model and real world, and that our model can correctly account for them if they are part of the modeled process. Granted, if I had a rail gun on an indoor range and had triple-checked every component of every round I sent downrange I may not accept an unbounded normal distribution as a model of my shot dispersion. But once we allow for outdoor conditions and normal ammunition, not to mention a shooter operating the gun, then in the normal course of events we will get outliers, and they are representative of the underlying normally-distributed process.
It is not unreasonable to accept a model that says 1 round in 100 is going to miss the target entirely. If we are recording statistically significant samples and using robust estimators then including such outliers will not ruin our estimates. And in a way our metrics for "statistical significance" will tell us whether an outlier is valid. E.g., if in my first three shots after sighting in one shot nicks the edge of the target backer then I know right away I need more samples because so far my confidence interval is wider than my target! If I take another 20 shots and they cluster into a single hole then perhaps I can decide whether to exclude the outlier as a "flier" or incorporate it as a sample from the "true" model of my precision.
Ideally maybe we do want to clip our unbounded distribution models, or maybe we want to overlay our shot distribution model with a Poisson dispersion model that allows us to exclude samples that may be due to a defective round, wind gust, etc. But practically we are already pushing the bounds on the sample size needed just to determine covariance for a general bivariate normal model, so adding a fourth parameter to the models of dispersion may be a bridge too far.
# Counting Fliers
A caveat - This section isn't meant to give a detailed or reasonable statistical analysis design model, but rather is a contrived situation to illustrate some points about what in process control is called "Acceptance Testing."
Consider two different types of ammunition, A and B, which you want to use to hunt. So you decide to test 25 shots of each on the range using the mean radius measurement. Obviously one characteristic to compare would be the precision of the two types of ammunition. When measuring precision we decided to set a clip level at the 95th percentile of the mean radius. So we are going to, on average, throw out the worst 5% of the shots.
But here is perhaps a unknown twist. You can also measure a quality factor based on what percentage of the shots are fliers due to the ammunition. In the above sections we took great care to separate fliers into defects and outliers and here we've combined the two again, but notice the very important qualification phrase due to the ammunition. So if type B ammunition has a muzzle velocity problem where some shots will have a abnormally low velocity, then such a shot is a defect. The shot would be low compared to the COI for type B ammo, so that shout wouldn't be counted in measuring the precision of B. But it is a flier due to the ammunition.
Labeling a shot a flier due to the ammunition is a non-parametric measurement. You just get a count. But that count can be useful as a quality factor. There are two problems with statistical tests based on non-parametric measurements. First, in general they aren't as precise as parametric measurements which means that larger samples are needed. Second we'd expect commercial ammunition to have a relatively low percentage of fliers. So to use non-parametric methods will probably require a lot of shooting.
Type A has 2 fliers. One was a called flier due to shooter error. The other was an outlier. So overall Type A has 24 shots in the sample with 1 shot being a flier flier due to the ammunition.
Type B has 3 fliers, 2 outliers and 1 defect due to low muzzle velocity. The parametric measurement (radial distance for the shot to the center) of the 2 bad shots in B radius distance allowed them to be labeled defects. So overall Type B has 25 shots in the sample with 3 shots being a flier flier due to the ammunition.
wiki table...
Based on this data (admittedly small sample) you can statistically compare the flier count of the two types of ammunition. (Based on our clip level we expect a 5% defect rate.) Type A has an expected rate of 4.2%, and type B has an expected rate of 12%. For full details details on the statistical procedure see: yada yada.
# Examples
To perhaps belabor the difference between defects and outliers consider the following examples.
Example 1 - Ten shots are shot at a paper target with ten bulls-eyes. The cartridge cases are lined after each is shot. After shooting it is discovered that nine of the shots are ammunition type-A and one is type-B. Shot 7 is the type-B ammunition shot.
Shot 7 is a defect and should be ignored in the measurement(s). Note here that it doesn't matter where the shot hit. The only reason to allow type-A ammunition and type-B ammunition to mix would be if the two types had already been comparatively tested and found to have the same performance. Here performance doesn't just mean the same precision since the two types of ammunition could have the same precision, but have different average COI positions.
Example 2 - Ten shots are shot at a target (single bulls-eye). After shooting it is discovered that nine of the shots are ammunition type-A and one is type-B. It is unknown which shot used the type-B ammunition. There is one shot which is wide of the group of the other nine.
In this situation the shot with the type-B ammunition is a really defect since it isn't of the same type as the other shots. Since it is unknown which shot used the type-B ammunition, it is invalid to just throw out "wide" shot and assumed it was the shot with type-B ammunition. The shot with the type-B ammunition may in fact be the closet shot to the center of the group!
The wide shot can only be labeled as an "outlier" if it falls outside of some set confidence interval. Ideally the confidence interval for acceptance should be decided upon before the experiment, and then data outside of the confidence interval would be properly rejected.
So here some ad hoc judgment may be required. The best option is probably to throw out the group/measurement entirely. This would be especially true if using the measurement Extreme Spread. However if we're using the mean radius measurement then the one Type-B shot probably won't perturb the mean radius measurement too much. Thus for the mean radius measurement the solution to the predicament might be to consider the confidence interval about the measurement to decide if the wide shot should be thrown out as an outlier, and use the resulting 9 or 10 shot measurement. Such a group measure gets "an asterisk", but it would be very useful to estimate the sample size needed to get a mean radius measurement of specific precision.
Example 3 - Ten shots are shot at a target (single bulls-eye). There is one shot which is wide of the group of the other nine. The shooter has no idea why there is one wide shot.
In this case the wide shot would be an outlier if it was rejected based on some confidence limit.
The nasty part here is that the wide shot might, unknown to the shooter, truly be a defect. For example in the manufacture of the cartridge, this particular cartridge might have had bad primer which was outside of the normal process variations. After shooting this would of course be impossible to determine. Even if this sort of quality problem had been suspected, it would be virtually impossible to measure for a commercial cartridge. So some ammunition manufacturing problems can not be isolated by independent measurement, but rather only a nebulous judgement is possible that the "quality" of the ammunition is "poor" based on the fact that the system variance was much larger than for other ammunition types, or the particular ammunition had a large number of outliers.
Note on spelling: Flier vs flyer has not been well established. We use the former spelling here because flyer seems to be more commonly used to refer to leaflets and architectural features, as opposed to "things that fly". | 3,149 | 14,776 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.171875 | 3 | CC-MAIN-2020-05 | longest | en | 0.945432 |
http://thatlogicblog.blogspot.com/2005/05/doing-proofs.html | 1,519,459,155,000,000,000 | text/html | crawl-data/CC-MAIN-2018-09/segments/1518891815500.61/warc/CC-MAIN-20180224073111-20180224093111-00612.warc.gz | 336,562,400 | 7,745 | # That Logic Blog
## May 02, 2005
### Doing Proofs
Casually reading through Greg Restall's book on substructural logics, I came across a curious line:
"However, proofs are not so easy to construct in tree form - often it is easier to construct proofs writing the consecutions in a list."
Personally, I have always found the "list" way of constructung proofs to be rather arbitrary and nonintuitive. If I have access to a sequent(esque) system, then I invariably construct the proof by doing a backwards "proof search". But maybe that is because I cut my (logical) teeth by working on theorem proving software.
I'm interested in seeing what method other people prefer, so leave a comment if you have a preference!
Anonymous said...
Yes, I'm not sure if I agree with me either. I think that if you're constructing proofs from premises to a conclusion, the benefit of a list is that you can start with your premises before worrying about how they're going to be used. In Gentzen/Prawitz-style natural deduction, where the premises actually end up depends on how they're used. In Lemmon-style natural deduction, any proof from a premise set X can start with each premise in X as the first steps in the proof, before you worry about making other assumptions or anything else.
I think that is what I was thinking back then.
I am still trying to articulate my views on the tactics of proof-search. (It becomes even more fun in multiple-premise, multiple-conclusion natural deduction, but that's another matter entirely...)
Posted by Greg Restall
11:31 AM
Anonymous said...
I agree that "list" style may be better if one is starting from premises. Obviously though, the problem then is "guiding" the proof properly. I have some frivolous ideas related to generating random "proofs" thoughs. One example of this is, I guess, generating random sentences based on a Lambek calculus, which would then come equipped with a proof of their "grammaticality". The dynamics could be interesting because there are lots of "proofs" starting from "s" (for example), corresponding to different correct sentence structures.
Being a lazy programmer, however, I haven't gotten around to hacking something like that up yet.
Posted by Jon
3:18 PM
Anonymous said...
I learned logic the list-way, and thought that was easier. Then I used theorem proving tools for a while with Gentzen-style sequents, and now I can't understand why I ever liked list-proofs.
Posted by Z (just a random reader)
4:59 PM
Anonymous said...
Until teaching logic this fall, I was almost incapable of doing proofs more than four lines or so long by hand - I was content to prove metatheorems and let them do all the work. I do seem to remember trees being easier to actually use to construct proofs, though the lists are more natural to think of as a representation, at least when you first come to formal proofs.
Posted by Kenny Easwaran
12:03 PM | 639 | 2,917 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.125 | 3 | CC-MAIN-2018-09 | latest | en | 0.963282 |
http://www.tankspot.com/printthread.php?t=77916&pp=20&page=1 | 1,416,587,969,000,000,000 | text/html | crawl-data/CC-MAIN-2014-49/segments/1416400372999.9/warc/CC-MAIN-20141119123252-00009-ip-10-235-23-156.ec2.internal.warc.gz | 793,705,065 | 4,171 | # Warrior Tank - Dodge vs Parry
• 10-26-2011, 11:02 AM
lunateth
Warrior Tank - Dodge vs Parry
With current mechanics, I see every reason to reforge dodge into mastery > parry > threat stats but I see posts here saying parry should be only be 2.5% greater than dodge to get maximum benefit from Hold the Line (HtL). What information determines that percentage and how is the talent mechanics such that this would be the case?
In the Rawr app, I see it recommends reforging some parry to dodge as well (although I see the model status is "Mostly" ready for Cata)
Since dodge and parry are subject to the same diminishing returns, why would you ever choose dodge over parry? I get that some dodge enchants are just better for certain slots where there is no better alternative, but I see no reason to ever choose dodge over mastery or parry.
School me.
• 10-26-2011, 11:57 AM
sifuedition
Warrior Tank - Dodge vs Parry
Fictional example to illustrate:
If you have 5000 ratings points...
5000 dodge = 25% dodge
5000 parry = 25% parry because the dr is the same for each if you have the same amount of ratings points in each. The more you add, the more you lose to dr.
The catch is all 5000 in one or the other is much deeper into dr so...
2500 dodge + 2500 parry = 14% of each. Total of 28% avoid with the same amount of ratings. You are only half as deep into the dr.
A perfect balance will get the most combined effective avoidance because you are losing the least to dr.
For warrior and HtL, however, crit block changes the equation. If you search this site a bit, there is a graph running around that shows you how much higher parry can be and still get more damage reduction despite losing parry to dr.
• 10-26-2011, 05:59 PM
kopcap
• 10-26-2011, 11:42 PM
sifuedition
Another way to demostrate what Diminishing Returns (dr) is doing (still fictional numbers to demonstrate):
If you have 0 of any rating; add 100 dodge
1% dodge (100 rating you got 1% for 100)
0% parry
1.95% dodge (200 rating..you only got 0.95% for that next 100 rating)
0% parry
You can see here, you now have 1.95% avoidance for your 200 rating. If you had added 100 parry the second time, the parry is not into the dr yet so
1% dodge (100 rating)
1% parry (100 rating)
You have 2% avoidance for the same amount of rating.
The more of a stat you add that is affected by dr, the less actual effective percent of that stat you get from the rating.
100 dodge = 1% Gained 1%
+100 dodge = 1.95% Gained 0.95%
+100 dodge = 2.75% Gained 0.8%
+100 dodge = 3.45% Gained 0.7%
You get the idea.
Saying that parry and dodge have the same diminishing returns just means that the curve of how much it is diminished at the same amount of ratings is the exact same for both. In wotlk, parry suffered a much harsher curve at the same amount of rating points.
• 10-27-2011, 07:45 AM
lunateth
Thanks for the replies, I guess my misunderstanding was that parry and dodge don't share DR as in combined avoidance DR like I hoped, instead they share the same RATE of DR. I guess playing a druid all these years shielded (look ma I made a pun) from the whole parry stat.
• 10-28-2011, 10:26 PM
Kahmal
Not trying to sound lazy but that chart gave me a headache. And despite being in Calculus I've never understood Ratio's lol. Can the spreadsheet or rawr do this for you?
• 10-29-2011, 06:37 AM
Tengenstein
AFAIK No they can't. Sorry if the following sounds patronizing.
okay here's what you need to know from you character sheet your dodge rating, your parry rating and your mastery
First off, add your parry and dodge rating together, mark where this is on the X axis (along the bottom). Next trace a line upwards from the the mark till you hit the coloured mastery line closest the amount of mastery rating you have (so if we had say 3400 wed mark halfways between the magenta and the babyblue curves)now trance a line across to the Y axis. mark where you cross it. that mark is your ideal parry to dodge ratio.
Ratios are fairly simple, if we had hit the y axis at 1.2, it would mean that we had a parry/didge ratio of 1.2:1 this basically means for every 1.2 parry rating we had we would want 1 dodge rating as well, or approximately 20% more parry rating than dodge rating. From there its simple reforging, if you had 1800 dodge rating, you'd want 2100 parry rating. If you had 2000 dodge rating.
• 11-14-2011, 12:01 AM
Kahmal
Quote:
Originally Posted by Tengenstein
AFAIK No they can't. Sorry if the following sounds patronizing.
okay here's what you need to know from you character sheet your dodge rating, your parry rating and your mastery
First off, add your parry and dodge rating together, mark where this is on the X axis (along the bottom). Next trace a line upwards from the the mark till you hit the coloured mastery line closest the amount of mastery rating you have (so if we had say 3400 wed mark halfways between the magenta and the babyblue curves)now trance a line across to the Y axis. mark where you cross it. that mark is your ideal parry to dodge ratio.
Ratios are fairly simple, if we had hit the y axis at 1.2, it would mean that we had a parry/didge ratio of 1.2:1 this basically means for every 1.2 parry rating we had we would want 1 dodge rating as well, or approximately 20% more parry rating than dodge rating. From there its simple reforging, if you had 1800 dodge rating, you'd want 2100 parry rating. If you had 2000 dodge rating.
Are you supposed to go by your buffed parry rating btw? I just realized how much higher it gets raid buffed
• 11-14-2011, 12:09 AM
Tengenstein
well, yes. unless you usually fight unbuffed.
• 11-14-2011, 05:51 PM
edeesis
If you go to the last page of WarTotem's spreadsheet (he goes under a different name now, like A-something) there's a EHP value for Dodge and Parry. If Dodge is higher than Parry, reforge to Dodge, and vice versa.
• 11-15-2011, 01:49 AM
Airowird
Quote:
Originally Posted by edeesis
If you go to the last page of WarTotem's spreadsheet (he goes under a different name now, like A-something) there's a EHP value for Dodge and Parry. If Dodge is higher than Parry, reforge to Dodge, and vice versa. | 1,678 | 6,155 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.5625 | 3 | CC-MAIN-2014-49 | latest | en | 0.916629 |
https://zbmath.org/?q=an%3A1437.92081 | 1,660,521,612,000,000,000 | text/html | crawl-data/CC-MAIN-2022-33/segments/1659882572089.53/warc/CC-MAIN-20220814234405-20220815024405-00093.warc.gz | 935,335,561 | 11,475 | ## A mathematical model of malaria transmission with structured vector population and seasonality.(English)Zbl 1437.92081
Summary: In this paper, we formulate a mathematical model of nonautonomous ordinary differential equations describing the dynamics of malaria transmission with age structure for the vector population. The biting rate of mosquitoes is considered as a positive periodic function which depends on climatic factors. The basic reproduction ratio of the model is obtained and we show that it is the threshold parameter between the extinction and the persistence of the disease. Thus, by applying the theorem of comparison and the theory of uniform persistence, we prove that if the basic reproduction ratio is less than 1, then the disease-free equilibrium is globally asymptotically stable and if it is greater than 1, then there exists at least one positive periodic solution. Finally, numerical simulations are carried out to illustrate our analytical results.
### MSC:
92C60 Medical epidemiology 92-10 Mathematical modeling or simulation for problems pertaining to biology
Full Text:
### References:
[1] Ross, R., The prevention of malaria, (1911), John Murray: London, John Murray [2] Macdonald, G., The epidemiology and control of malaria, (1957), London: Oxford University press, London [3] Chiyaka, C.; Tchuenche, J. M.; Garira, W.; Dube, S., A mathematical analysis of the effects of control strategies on the transmission dynamics of malaria, Applied Mathematics and Computation, 195, 2, 641-662, (2008) · Zbl 1128.92022 [4] Ngwa, G. A.; Shu, W. S., A mathematical model for endemic malaria with variable human and mosquito populations, Mathematical and Computer Modelling, 32, 7-8, 747-763, (2000) · Zbl 0998.92035 [5] Beck-Johnson, L. M.; Nelson, W. A.; Paaijmans, K. P.; Read, A. F.; Thomas, M. B.; Bjørnstad, O. N., The effect of temperature on Anopheles mosquito population dynamics and the potential for malaria transmission, PLoS ONE, 8, 11, (2013) [6] Moulay, D.; Aziz-Alaoui, M. A.; Cadivel, M., The chikungunya disease: modeling, vector and transmission global dynamics, Mathematical Biosciences, 229, 1, 50-63, (2011) · Zbl 1208.92044 [7] Chukwu, E. N., On the boundedness and stability properties of solutions of some differential equations of the fifth order, Annali di Matematica Pura ed Applicata. Serie Quarta, 106, 245-258, (1975) · Zbl 0341.34038 [8] Sinha, A. S., Stability result of a sixth order non-linear system, 7, 641-643, (1971) · Zbl 0228.34031 [9] Tunç, C., On the stability and boundedness of solutions in a class of nonlinear differential equations of fourth order with constant delay, Vietnam Journal of Mathematics, 38, 4, 453-466, (2010) · Zbl 1226.34072 [10] Tunç, C., New results on the stability and boundedness of nonlinear differential equations of fifth order with multiple deviating arguments, Bulletin of the Malaysian Mathematical Sciences Society, 36, 3, 671-682, (2013) · Zbl 1275.34095 [11] Lou, Y.; Zhao, X.-Q., A climate-based malaria transmission model with structured vector population, SIAM Journal on Applied Mathematics, 70, 6, 2023-2044, (2010) · Zbl 1221.34224 [12] Wang, W.; Zhao, X., Threshold dynamics for compartmental epidemic models in periodic environments, Journal of Dynamics and Differential Equations, 20, 3, 699-717, (2008) · Zbl 1157.34041 [13] Wang, J.; Gao, S.; Luo, Y.; Xie, D., Threshold dynamics of a huanglongbing model with logistic growth in periodic environments, Abstract and Applied Analysis, 2014, (2014) · Zbl 1474.34360 [14] Xiao-Qiang, Z., CMS Books in mathematics/Ouvrages de mathématiques de la SMC, (2003), New York, NY, USA: Springer Verlag, New York, NY, USA [15] Magal, P.; Zhao, X.-Q., Global attractors and steady states for uniformly persistent dynamical systems, SIAM Journal on Mathematical Analysis, 37, 1, 251-275, (2005) · Zbl 1128.37016 [16] Ouedraogo, W.; Sangaré, B.; Traoré, S., Some mathematical problems arising in biological models: a predator-prey model fish-plankton, Journal of Applied Mathematics and Bioinformatics, 5, 4, 1-27, (2015) · Zbl 1377.92075 [17] Chitnis, N.; Hyman, J. M.; Cushing, J. M., Determining important parameters in the spread of malaria through the sensitivity analysis of a mathematical model, Bulletin of Mathematical Biology, 70, 5, 1272-1296, (2008) · Zbl 1142.92025
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching. | 1,254 | 4,704 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.671875 | 3 | CC-MAIN-2022-33 | latest | en | 0.782583 |
http://math.stackexchange.com/questions/449069/why-does-a-fractional-differential-equation-have-a-unique-solution | 1,469,357,824,000,000,000 | text/html | crawl-data/CC-MAIN-2016-30/segments/1469257823996.40/warc/CC-MAIN-20160723071023-00213-ip-10-185-27-174.ec2.internal.warc.gz | 153,390,588 | 16,163 | # why does a fractional differential equation have a unique solution?
Why must there be a unique solution to a linear constant-coefficient fractional differential equation of order $(n,q)$ with $\lceil\frac{n}{q}\rceil$ initial conditions? (All notation is as in Miller & Ross, An Introduction to the Fractional Calculus and Fractional DEs.)
More specifically, if $n$ and $q$ are positive integers and $v=\frac{1}{q}$ and $N=\lceil nv\rceil$ and $P(x)$ is a monic polynomial of degree $n$, consider the fractional DE $$P(_0D_t^v)y(t)=x(t)$$ $$y(0)=y'(0)=\dots=y^{(N-1)}(0)=0.$$ I can prove that $y(t)=\int_0^tK(t-\xi)x(\xi)d\xi$ is a solution, where $K$ is the fractional Green's function (inverse Laplace transform of $\frac{1}{P(s^v)}$), but Miller & Ross say it's the unique solution, and I can't see why!
I've been thinking of a proof along the lines of:
Assume there are 2 solutions, say $y_1(t)$ and $y_2(t)$. Then $y_1-y_2$ must satisfy the corresponding homogeneous DE, with the same initial conditions. But why does this mean $y_1-y_2\equiv0$? Is there some theorem from ODE theory about the dimension of the solution space which extends to cover fractional DEs - and if so, why does it extend?
Many thanks for any help with this!
- | 356 | 1,247 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.3125 | 3 | CC-MAIN-2016-30 | latest | en | 0.872544 |
https://sites.google.com/site/numeropedia2/numbers410m | 1,488,194,035,000,000,000 | text/html | crawl-data/CC-MAIN-2017-09/segments/1487501172783.57/warc/CC-MAIN-20170219104612-00279-ip-10-171-10-108.ec2.internal.warc.gz | 755,926,335 | 7,806 | Numbers 410,000,000s
A page of the Numeropedia - the Special Encyclopedia of Numbers
410,000,000420,000,000430,000,000 – 440,000,000
450,000,000460,000,000470,000,000480,000,000 – 490,000,000
[1M] & [10M] & [100M- [200M] - [300M] - [400M] - [500M] - [600M] - [700M] - [800M] - [900M] & [1B]
1 - 10 - 100 - 1000 - 10,000 - 100,000 - 1M - 10M - 100M1B10B - 100B - 1T - 10T - 100T - 1Q ...
412,130,601
[Math.] Sum of the first 201 cube numbers:
13+23+…+2013 = 412,130,601 = (1+2+…+201)2 = 20,3012.
412,739,856
[Math.] 203162 = 412,739,856, one of thirty 9-digit square numbers using all 9 digits 1-9 once.
415,329,070
[Math.] 415,329,070 = 21+32+53+74+115+136+177.
418,195,493
[Math.] 418,195,493 = (4+18+1+9+5+4+9+3)5 = 535.
419,753,086
[Math.] Multiples of 012345679 by 7, 16, 25, 34, 43, 52, 61, 70 and 79 will yield all 9 rotations of 086419753: 086419753, 197530864, 308641975, 419753086, 530864197, 641975308, 753086419, 864197530 and 975308641. All numbers are missing digit 2.
xyz,abc,def
[Math.] For any xyz = 100 to 999, there are always six 6-digit numbers abc,edf such that the sum (xyz+abc,def) is equal to one of 6 digit-rotations of 142,857 and the number xyz,abc,def is a multiple of 142,857.
For any xyz = 100 to 999, there are always twelve 6-digit numbers abc,edf such that the sum (xyz+abc,def) is equal to one of 12 digit-rotations of 076,923 or 153,846 and the number xyz,abc,def is a multiple of 76,923. | 614 | 1,454 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.625 | 4 | CC-MAIN-2017-09 | latest | en | 0.526618 |
http://stackoverflow.com/questions/9287351/while-loop-acting-up-not-doing-what-it-should-for-some-reason | 1,462,494,306,000,000,000 | text/html | crawl-data/CC-MAIN-2016-18/segments/1461861700245.92/warc/CC-MAIN-20160428164140-00051-ip-10-239-7-51.ec2.internal.warc.gz | 271,467,342 | 20,794 | # while loop acting up… not doing what it should for some reason
I have this code for a simple Dice throwing program with betting units and everything... you bet, if you get it right you get the amount u bet times the amount of dice you chose... if you're wrong but by a little (in the range of the number you picked +- the number of dice u picked) you don't lose anything, and if you're really off you lose...
I have a while loop that basically keeps 2 things in mind: as long as the user either has BUs or if they didn't type "no" or "No" for the try again... but for some reason it just doesn't work... lol. any ideas why? the betting system works, it recognizes that betting.currentBU == 0, but the while loop just won't react lol.
``````#include <iostream>
#include <string>
#include <cstdlib>
#include <time.h>
#include <limits>
using namespace std;
struct Dices{ // structure containing all the dice related integers
int dice;
int total;
int choice;
} Dices = {0,0,0};
struct betting{ // structure containing all the betting integers
int currentBU;
int bettedBU;
} betting = {100, 0};
int DiceThrow(int dicechoice, int totalnum){ // a method for the dice being rolled
for(int i=1; i <= dicechoice;i++){
totalnum = totalnum + (rand() % 6 + 1); //total number, repeated by the loop for every dice
}
}
int winningbet(int dicea, int cBU, int bBU){ // in case the user guesses it right
std::cout << "Congratulations, you got it right! \n";
cBU = cBU + (dicea * bBU); // give him money...
return(cBU);
}
int losingbet(int dicen, int totaln, int choicen, int cBU2, int bBU2){ //in case the user guesses wrong
if(choicen > (totaln+dicen) || choicen < (totaln+dicen)) // checks how wrong he is, if he's too off, he loses BUs
cBU2 = cBU2-bBU2;
else
std::cout << "you we're so close, you don't lose any BUs! \n"; //if he was really close, just let him know he was close
return(cBU2);
}
int main(){
string decision; // decision if they want to keep playing or not
srand ( (unsigned int)time(NULL) );
while(decision != "no" || decision != "No" || betting.currentBU != 0) // makes sure of the decision AND that he still has BUs
{
Dices.total = 0;
std::cout << "how many dice would you like to use? ";
std::cin >> Dices.dice;
std::cout << "how many How many BUs are you betting?(" << betting.currentBU << " BUs left) ";
std::cin >> betting.bettedBU;
if(betting.bettedBU > betting.currentBU){ // if he doesn't have enough BUs
std::cout << "Sorry, you don't have that many BUs...";
std::cout << "Want to try again with a different amount?(Yes/No) ";
std::cin >> decision;
}
else{
std::cout << "guess what number was thrown: ";
std::cin >> Dices.choice;
Dices.total = DiceThrow(Dices.dice, Dices.total);
if(Dices.choice == Dices.total){
betting.currentBU = winningbet(Dices.dice, betting.currentBU, betting.bettedBU);
std::cout << "Want to try again?(Yes/No) ";
std::cin >> decision;
} else{
std::cout << "Sorry, the number was " << Dices.total << "... better luck next time \n" ;
betting.currentBU = losingbet(Dices.dice, Dices.total, Dices.choice, betting.currentBU, betting.bettedBU);
if(betting.currentBU > 0){
std::cout << "Want to try again?(Yes/No) ";
std::cin >> decision;
}
}
}
}
if(betting.currentBU == 0){
std:cout << "sorry, you ran out of BUs...";
std::cin.ignore( std::numeric_limits<std::streamsize>::max(), '\n' );
}
else{
std::cout << "your final BU count is: " << betting.currentBU << "\n";
std::cout << "Thanks for playing, see you next time! (Press ENTER to terminate...)";
std::cin.ignore( std::numeric_limits<std::streamsize>::max(), '\n' );
}
return 0;
}
``````
-
What exactly is your problem? Does it not recognize your input? You don't really define the issue you're having, just that you have one. – Pochi Feb 15 '12 at 3:11
isn't it supposed to be:
``````while(decision != "no" && decision != "No" && betting.currentBU != 0)
``````
We need to check if decision not equal to "no" AND not equal to "No" AND the currentBU not equal to 0
-
yessir... I confused the logic of || with &&... thanks ;) – Gal Appelbaum Feb 15 '12 at 3:41
Your test is `while (A || B || C)`, which will loop as long as ANY of those three things are true. Since `decision` can't be equal to both `"no"` and `"No"` at the same time, at least one of those two not-equals tests will always be true, so the loop will loop forever...
-
thanks for the answer ;) yea I definitely confused the logic of || with &&... smdh. – Gal Appelbaum Feb 15 '12 at 3:41 | 1,269 | 4,456 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.546875 | 3 | CC-MAIN-2016-18 | latest | en | 0.873965 |
https://www.physicsforums.com/threads/read-somewhere-about-polarization.100101/ | 1,547,948,152,000,000,000 | text/html | crawl-data/CC-MAIN-2019-04/segments/1547583688396.58/warc/CC-MAIN-20190120001524-20190120023524-00327.warc.gz | 899,676,603 | 13,639 | 1. Nov 16, 2005
### dervast
Hi i need to read somewhere about polarization. What polariation is.. Why we need it? What types of polarization exist and what are the differences.. and so on
2. Nov 16, 2005
### marlon
Here and here you go...
feel free to ask more clarification, if you need.
marlon
3. Nov 16, 2005
### marlon
using a simple vocabularium, one could define polarization as the "way" a material reacts when you apply an incident electric field onto it.
Reacts means (and this is the clue) the change in charge distribution. Like for example the way the electron cloud will change its structure because of this incident E-field.
this E-field has a frequency and depending on that value, you get different contributions to the polarization. Ie, different mechanism react to the incident E-field like dipoles, ionic contribution, electronic contribution...
Another classical example is this : suppose you have 5 + charges and 5 - charges that are randomly distributed in a medium. the net charge is zero. If you apply a voltage onto this medium, the - charges will go to the positive side (electrode) and the + charges wil go to the negative side. Now you do have a net charge in the medium, you see ?
marlon
4. Nov 16, 2005
### dervast
Thx i ll read your interesting links.. I am asking because we are using polarization in wireless communications.. and he polarization seems to be a factor that alters somehow the attributes of the signals/
5. Nov 16, 2005
### Ouabache
Polarization is important in wireless communications. This technology comes from one that has been developed since 19th century, radio communications. When radio waves are generated, the polarity of the electric field defines the polarity of the antenna. The electric field is perpendicular (orthogonal) to the magnetic field in a linearly polarized antenna.
Here is a http://www.hp.com/rnd/images/pdf_html/antennas_figure7.jpg [Broken] example of horizontal versus vertical linear polarization (They are showing the orientation of the electric field). A recieving antenna ought to be of the same polarity as the transmitting antenna to recieve the maximum signal. That does not mean you cannot use a horizontal antenna to recieve a vertically polarized radio wave or vice versa. I've done it.. However it is not as efficient as the signal is attenuated. Both of these antennas radiate linearly polarized waves.
Other kinds of polarization are circular or more generally elliptical. In circular polarization, the orientation of both the electric field and magnetic field rotate through 360 degrees. Depending on which way the field rotates, a circularly polarized wave may be clockwise or counterclockwise. marlon's second ref is a good technical discussion of what I have given.
[edited by Russ on request]
Last edited by a moderator: May 2, 2017 | 631 | 2,851 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.59375 | 3 | CC-MAIN-2019-04 | latest | en | 0.891943 |
https://gis.stackexchange.com/questions/69131/calculating-area-of-multipolygons-within-250m-buffer-of-points | 1,720,831,512,000,000,000 | text/html | crawl-data/CC-MAIN-2024-30/segments/1720763514459.28/warc/CC-MAIN-20240712224556-20240713014556-00301.warc.gz | 233,362,833 | 38,948 | # Calculating area of MultiPolygons within 250m buffer of points
I am using using PostgreSQL 9.2 and PostGIS 2.0. I have two tables: 1) a geocoded table of home addresses (address_list) and 2) a table containing data on tree density in the same geographical area. I have included examples of the relevant columns in each table below.
``````house_id (serial) | geom(Point, 4283)
------------------+-----------------------
1 |
2 |
``````
tree_density:
`````` gid (serial) | tree_dens | geom(MultiPolygon, 4283)
------------+------------+----------------------------
1 | scattered |
2 | medium |
3 | dense |
``````
What I would like to do is compute the area of forest (m2) by tree_density categories within 250m of each home address for my whole address table (approx 6,000 entries). (E.g for house_id = 1: area_scattered_within250m = 50m2, area_med_within250m = 0m2, area_dense_within250m = 20m2)
Can this be done easily? Even if in 3 or more seperate queries? Does anyone have a moment to assist me with the syntax? I guess I need to combine ST_Area, ST_Buffer and perhaps ST_Contains or St_Within, but I'm new to PostGIS and although I've been ok with other (simpler) spatial joins, I'm lost here and haven't found any similar examples. For the area of my study I transform to SRID 3112 (meters) for measurements.
Many thanks Mike
EDIT: This gives you bulk area for each of the tree density categories:
``````SELECT SUM(ST_Area(ST_Intersection(sq.house_aoi, tree_density.geom))), tree_dens
FROM tree_density,
-- Assuming the linear unit in your projection is meters
GROUP BY tree_density.tree_dens;
``````
This, instead, should give you the area of each unique house-tree density pair after a spatial intersection:
``````SELECT aoi.house_id, t.tree_dens, SUM(ST_Area(ST_Intersection(aoi.house_aoi, t.geom))) AS area
FROM
(SELECT a.house_id, ST_Buffer(a.geom, 250) AS house_aoi
tree_density t
WHERE ST_Intersects(house_aoi, t.geom)
GROUP BY aoi.house_id, t.tree_dens
``````
If I'm right, it wasn't as complicated as I initially thought. My test set of geometries is totally contrived, so this may not make sense for your application.
• Thanks so much Arthur. That's very close, but I really need the result to list all house_ids, and then summarise the area of scattered, the area of medium & and the area of dense forest within 250m of each house rather than giving me the sum of the total area of each category of tree density within 250m across all houses in the sample. Does that make sense? I'm down on myself that I can't work this out. I'll keep trying.
– Mike
Commented Aug 21, 2013 at 2:21
• Yes, that makes sense. I think you will need to join multiple subqueries together on the house_id field. Each subquery would calculate the total area in one of the tree density (tree_dens) categories for each house. I'll try this out later and get back to you. Commented Aug 21, 2013 at 12:23
• Edited my original answer. Commented Aug 21, 2013 at 17:29
• Arthur, thank you very much. For anyone else who reads this in the future, I can confirm that Arthur's syntax works beautifully.
– Mike
Commented Sep 14, 2013 at 10:26
• @Mike You should mark the answer as correct then. Commented Sep 27, 2013 at 12:07 | 868 | 3,266 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.796875 | 3 | CC-MAIN-2024-30 | latest | en | 0.806005 |
https://www-history.mcs.st-andrews.ac.uk/Search/historysearch.cgi?SUGGESTION=simple&CONTEXT=1 | 1,571,865,303,000,000,000 | text/html | crawl-data/CC-MAIN-2019-43/segments/1570987836295.98/warc/CC-MAIN-20191023201520-20191023225020-00341.warc.gz | 779,926,776 | 155,287 | # Search Results for simple
## Biographies
1. John Thompson (1932-)
• The reason was that suddenly progress began to be made on one of the main problems of finite group theory, namely the classification of finite simple groups.
• Every finite group can be viewed as built from a finite collection of finite simple groups.
• The finite simple groups are therefore the building blocks from which finite groups are built.
• To classify finite groups therefore reduces to two problems, namely the classification of finite simple groups and the solution of the extension problem, that is the problem of how to fit the building blocks together.
• Claude Chevalley showed in 1955 that the Lie groups have finite analogues which are finite simple groups.
• M Suzuki in 1960 discovered new infinite families of finite simple groups.
• Thompson, working with Walter Feit, proved in 1963 that all nonabelian finite simple groups were of even order.
• This result stunned the world of mathematics but it also led mathematicians to believe that a classification of finite simple groups might prove possible.
• Another major early step by Thompson towards the classification of finite simple groups was his classification of those finite simple groups in which every soluble subgroup has a soluble normaliser.
• Here, the authors proved a famous conjecture, to the effect that all non-cyclic finite simple groups have even order.
• In it he determined the minimal simple finite groups, this is to say, the simple groups whose proper subgroups are solvable.
• These results are the first substantial results achieved concerning simple groups.
• The nonabelian finite simple groups fall into a small number of infinite series and 26 sporadic groups.
• I like to say that I would like to see the solution of the problem of the finite simple groups and the part I expect Thompson's work to play in it.
• Thompson revolutionised the theory of finite groups by proving extraordinarily deep theorems that laid the foundation for the complete classification of finite simple groups, one of the greatest achievements of twentieth century mathematics.
• Simple groups are atoms from which all finite groups are built.
• In a major breakthrough, Feit and Thompson proved that every non-elementary simple group has an even number of elements.
• Later Thompson extended this result to establish a classification of an important kind of finite simple group called an N-group.
• Its almost incredible conclusion is that all finite simple groups belong to certain standard families, except for 26 sporadic groups.
• AMS (Classification of finite simple groups) .
2. Michio Suzuki (1926-1998)
• During this period he published a series of excellent papers: The lattice of subgroups of a finite group (in Japanese) (1950); On the finite group with a complete partition (1950); On the lattice of subgroups of finite groups (1951); On the L-homomorphisms of finite groups (1951); and A characterization of simple groups LF(2,p) (1951).
• As usual, we denote by LF(2,p) the simple group of order p(p-1)(p+1)/2, (p > 3 a prime number).
• If all proper subgroups of a non-cyclic simple group G are of one of these four types, then G is isomorphic to a group LF(2,p).
• Then in 1960 he discovered a new class of finite simple groups, something which stunned the world of mathematics.
• A simple group is one which has no normal subgroups other than the identity subgroup and the group itself.
• Simple groups are the building blocks from which any group is made up.
• Cyclic groups of prime order are simple, but the interesting problem with simple groups is investigating non-abelian finite simple groups.
• Burnside had conjectured that there did not exist non-abelian finite simple groups of odd order.
• Up to the early 1960s, really nothing of real interest was known about general simple groups of finite order.
• In his paper The nonexistence of a certain type of simple groups of odd order he showed exactly what the title indicates.
• For those who know some group theory, we note that Suzuki proved that a finite group of odd order cannot be simple if the centraliser of every non-identity element is abelian.
• Suzuki's discovery of a new class of finite simple groups in 1960 shook mathematics.
• No new finite simple groups had been discovered since Emile Mathieu discovered five such groups in 1860 and 1873.
• In 1967 Suzuki discovered another new finite simple group.
• His work was a major factor in inspiring the remarkable combined effort by a large number of outstanding mathematicians on the classification of finite simple groups which many regard as the most important mathematical achievement of the 20th century.
• We believe that his work in the 1950's ignited work on the classification of finite simple groups, and in the 1960's and 70's he led its development.
• for his achievements in the domain of group theory, above all in recognition of his path-breaking works on the classification of finite simple groups as well as for his fundamental work on lattices of subgroups and his contributions to the theory of permutation groups.
• He continued to work on this final paper during his final days in Japan and the paper On the prime graph of a finite simple group - an application of the method of Feit-Thompson-Bender-Glauberman was published in [',' E Bannai, H Suzuki, H Yamaki and T Yoshida (eds.), Groups and combinatorics - in memory of Michio Suzuki (Mathematical Society of Japan, Tokyo, 2001).','1].
3. Rimhak Ree (1922-2005)
• In 1957 Ree published his first paper on finite simple groups, the topic for which he is best known today.
• In this paper On some simple groups defined by C Chevalley, Ree identifies many classes of finite simple groups defined by Claude Chevalley in his ground-breaking 1955 paper, with classes of classical simple groups.
• Ree's most famous papers were A family of simple groups associated with the simple Lie algebra of type G2 (1960) and A family of simple groups associated with the simple Lie algebra of type F4 (1961) in which he announced the construction of new families of finite simple groups.
• Joseph Gallian writes [',' J A Gallian, The Search for Finite Simple Groups, Mathematics Magazine 49 (4) (1976), 163-180.','3]:- .
• Michio Suzuki [in 'A new type of simple groups of finite order' (1960)], while in the process of classifying a certain type of doubly transitive permutation groups, discovered another new infinite family.
• This in turn led him to investigate two other similar situations and eventually discover his two families of simple groups.
• The Suzuki and Ree groups together with those of Chevalley and Steinberg are collectively referred to as the simple groups of Lie type.
• In fact these were the final two families of finite simple groups of Lie type to be discovered, bringing the total to sixteen classes.
• His achievements of research in some 29 simple groups including the two found in 1960s made him a gigantic figure in world mathematic circles and remain as important accomplishments in the world history of mathematics.
4. Daniel Gorenstein (1923-1992)
• His involvement in the classification of finite simple groups began in the year 1960-61 when he attended the Group Theory Year at the University of Chicago.
• My first foray into simple group theory dated from the famous 1960-61 group theory year at the University of Chicago, during which Walter Feit and John Thompson settled the solvability of groups of odd order.
• The classification of finite simple groups involved contributions by a host of mathematicians world wide.
• It is for the classification of finite simple groups that his name will always be remembered, certainly the mathematical achievement of the 20th century.
• Conway in England, and Fischer in Germany, each discovering three new sporadic groups, stimulated considerable additional interest, leading to an intensification of the search for further simple groups.
• But it was Aschbacher's entry into the field in the early 1970s that irrevocably altered the simple group landscape.
• Simultaneously with this burgeoning research effort, finite simple group theory was establishing a well-deserved reputation for inaccessibility because of the inordinate lengths of the papers pouring out.
• No mathematical theorem could require the number of pages these fellows were taking! Surely they were missing some geometric interpretation of the simple groups that would lead to a substantially shorter classification proof.
• Gorenstein's books on finite groups and the classification of finite simple groups are Finite groups (1968), Finite simple groups : an introduction to their classification (1982), The local structure of finite groups of characteristic 2 type (jointly written with Richard Lyons) (1983) and The classification of the finite simple groups (jointly written with Richard Lyons and Ronald Solomon) (1994).
• AMS (Classification of finite simple groups) .
5. Richard Brauer (1901-1977)
• This was the time when Brauer made his fundamental contribution to the algebraic theory of simple algebras.
• a theory of central division algebras over a given perfect field, and showed that the isomorphism classes of these algebras can be used to form a commutative group whose properties gave great insight into the structure of simple algebras.
• This he used to obtain results on finite groups, particularly finite simple groups, and the theory of blocks would play a big part in much of Brauer's later work.
• He began to formulate a method to classify all finite simple groups and his first step on this road was a group-theoretical characterisation of the simple groups PSL(2,q) in 1951 (although for a complicated number of reasons explained in [',' J A Green, Richard Dagobert Brauer, Bull.
• The paper was On groups of even order and it provided the key to the major breakthrough by Walter Feit and John Thompson when they proved that every finite simple group has even order.
• Brauer was to spend the rest of his life working on the problem of classifying the finite simple groups.
• (See the biography of Gorenstein for further details on the programme to classify finite simple groups.) Most important was Brauer's vital step in setting the direction for the whole classification programme in the paper On groups of even order where it is shown that there are only finitely many finite simple groups containing an involution whose centraliser is a given finite group.
• Brauer had announced these results and his programme for classifying finite simple groups at the International Congress of Mathematicians in Amsterdam in 1954.
• AMS (Classification of finite simple groups) .
6. John Conway (1937-)
• Knowing that he did not have the group theory skills necessary to prove his conjectures he tried to interest others, see [',' T M Thompson, From error-correcting codes through sphere packings to simple groups (Washington, 1983).
• A detailed description of this discovery is given in [',' T M Thompson, From error-correcting codes through sphere packings to simple groups (Washington, 1983).
• He showed that the symmetry group G of the Leech lattice, when factored by a central subgroup of order 2, was a previously undiscovered finite simple group of order 8,315,553,613,086,720,000.
• It had a great number of very interesting subgroups, including two more previously unknown simple groups, as well as groups having as homomorphic images almost all the finite sporadic simple groups known at that time.
• A finite sporadic simple group is a finite simple group which is not a member of one of the standard infinite families.
• I [EFR] cannot vouch for this change in confidence since I did not hear Conway lecture before his discovery of new simple groups.
7. Charles Sims (1937-2017)
• In 1967 Sims made a major breakthrough when, working with Donald Higman, he discovered the previously unknown sporadic simple group now known as the Higman-Sims group.
• They described the group in the paper A simple group of order 44n352n000 which appeared in Mathematische Zeitschrift in 1968.
• I think that Charles silently followed the good old saying that the proof of a pudding is in its eating and that similarly the proof of an algorithm is in its use and he did indeed prove the existence of three sporadic simple groups by constructing them as permutation groups using his 'Schreier-Sims' method.
• At the conference Computational methods for representations of groups and algebras at the University of Essen, Essen, 1-5 April 1997, Sims and George Havas gave a presentation for this Lyons finite simple sporadic group.
• We give a presentation of the Lyons simple group together with information on a complete computational proof that the presentation is correct.
• This fills a long-standing gap in the literature on the sporadic simple groups.
• In 1977, in collaboration with Jeffrey Leon, Sims proved the existence and uniqueness of a simple group generated by {3, 4}-transpositions.
• His name is attached to two sporadic simple groups; the one I know best, the Higman-Sims group, was found without any recourse to computation at all.
8. Wilhelm Killing (1847-1923)
• They discussed the simple Lie algebras which they knew about and Killing conjectured (wrongly) on 12 April 1886 that the only simple algebras were those related to the special linear group and orthogonal groups.
• By the time he wrote to Engel on 23 May Killing had discovered that his conjecture about simple algebras was wrong, for he had discovered G, and by 18 October he had discovered the complete list of simple algebras.
• The most remarkable part of this work is his discovery of the exceptional simple Lie algebras.
• The exceptional simple Lie algebras are the subject of the final Section 18 of Killing's paper.
• It was Cartan, in his doctoral thesis submitted in 1894, who found concrete representations of all the exceptional simple Lie algebras (although he did not work out all the details in his thesis).
9. Marshall Hall Jr (1910-1990)
• It was at this time that he was able to confirm the existence of a simple group of order 604,800 which had been predicted by Zvoninir Janko.
• He published his findings in the paper A search for simple groups of order less than one million presented to the conference 'Computational Problems in Abstract Algebra' held in Oxford 29 August to 2 September 1967.
• Very recently Z Janko announced that a simple group with certain properties would have order 604,800 and have a specific character table.
• The construction of a simple group of order 604,800 is given for the first time in this paper.
• The construction of the simple group of order 604,800 was carried out in August 1967 at the University of Warwick and at Cambridge University.
• The uniqueness of the simple group of this order was proved in Hall's paper, written jointly with David Wales, The simple group of order 604,800 (1968).
10. Maryam Mirzakhani (1977-2017)
• She also published A small non-4-choosable planar graph in 1996 and A simple proof of a theorem of Schur in 1998.
• Mirzakhani looked at what happens to the "prime number theorem for geodesics" when one considers only the closed geodesics that are simple, meaning that they do not intersect themselves.
• She was awarded her doctorate in 2004 for her 130-page thesis Simple Geodesics on Hyperbolic Surfaces and Volume of the Moduli Space of Curves.
• These results include a recursive formula for Weil-Petersson volumes of moduli spaces of Riemann surfaces, a determination of the asymptotics of the number of simple closed geodesics on a hyperbolic surface in terms of length, and a new proof of Witten's Conjecture (originally established by Kontsevich) establishing the KdV recursion for the intersection numbers on moduli space.
• These papers were: Weil-Petersson volumes and intersection theory on the moduli space of curves (2007); Simple geodesics and Weil-Petersson volumes of moduli spaces of bordered Riemann surfaces (2007); Random hyperbolic surfaces and measured laminations (2007); Growth of the number of simple closed geodesics on hyperbolic surfaces (2008); Ergodic theory of the earthquake flow (2008); and (with Elon Lindenstrauss) Ergodic theory of the space of measured laminations (2008).
11. Ottó Steinfeld (1924-1990)
• Other topics on which Steinfeld undertook research included the structure of simple artinian rings, for example in Some characterizations of semisimple rings with minimum condition on principal left ideals, and analogues in other algebraic systems.
• His article Uber die Verallgemeinerungen und Analoga der Wedderburn-Artinschen und Noetherschen Struktursatze Ⓣ (1967) discussed generalizations of the Noether and Wedderburn-Artin characterizations of the semi-simple and simple Artinian rings to F-rings, to the MHL-rings, for semi-simple linear compact rings, for semirings, for semi-simple near-rings, and for semi-groups which are unions of completely 0-simple.
12. Aleksei Kostrikin (1929-2000)
• This text, intended for 19- or 20-year old students, includes such topics as: general properties of mappings and of binary relations; some properties of simple groups; theory of representations; elements of the theory of finite fields; fields of algebraic numbers; as well as traditional subjects in a first course in algebra.
• In the 1960's, Kostrikin studied infinite-dimensional Lie algebras of Cartan type for finite characteristic and, with Shafarevich, formulated a conjecture describing all simple Lie p-algebras for characteristic p > 5.
• In the 1990's, Kostrikin discovered, with many young mathematicians, a theory of integral lattices in simple Lie algebras which are invariant under the Killing form.
• These had unexpectedly rich applications to other areas such as representations of certain finite simple groups.
• The book deals with certain "concrete" aspects of the representation theory of finite (almost) simple groups, namely with the realization of certain classes of these groups as automorphism groups of integral lattices and of related algebraic and combinatorial objects (root systems, symplectic spreads).
• The lattices are of a particular kind, embedded into a simple Lie algebra over C and endowed with the Killing form.
13. Edith Hirsch Luchins (1921-2002)
• In 1958 her fifth child was born and in the following year the two papers On radicals and continuity of homomorphisms into Banach algebras and On strictly semi-simple Banach algebras appeared, both in the Pacific Journal of Mathematics.
• A Banach algebra is said to be absolute if every homomorphism of a Banach algebra into it is continuous, and is said to be strictly semi-simple if its two-sided regular maximal right ideals have zero intersection.
• It is proved that an absolute Banach algebra contains no non-zero nilpotent elements, and that a strictly semi-simple Banach algebra is absolute.
• For certain special Banach algebras (including semi-simple annihilator algebras) it is proved that if B contains no non-zero nilpotent elements, then B is strictly semi-simple (and hence absolute).
• If the strict radical is zero, the algebra is called strictly semi-simple (sss).
14. Jacques Tits (1930-)
• This paper is an essay on how the development of group theory led to the discovery of various families of simple groups, and how these in turn led to the theory of buildings.
• Galois first used the term 'group' in the technical sense, and found the first simple groups.
• Killing came to such groups independently, and in 1888 found the classification of the simple Lie groups, using semisimple complex Lie algebras (families A through G).
• (2) Schemas en groupes a fibre generique simple sur les anneaux d'entiers Ⓣ; .
• The theory of buildings is a central unifying principle with an amazing range of applications, for example to the classification of algebraic and Lie groups as well as finite simple groups, to Kac-Moody groups (used by theoretical physicists), to combinatorial geometry (used in computer science), and to the study of rigidity phenomena in negatively curved spaces.
15. François Bruhat (1929-2007)
• This paper considered induced representations which Bruhat then applied in his next paper Representations induites des groupes de Lie semi-simples complexes Ⓣ (1954) to a complex semi-simple Lie group none of whose simple factor groups is one of the exceptional simple Lie groups.
• In the same year his paper Representations induites des groupes de Lie semi-simples reels Ⓣ appeared which dealt with the case of a real semi-simple Lie group.
• Together with Jacques Tits, Bruhat developed the theory of simple algebraic groups over local fields.
16. Michael Stifel (1487-1567)
• These productive years at Holzdorf ended when religious wars broke out in 1546 but these were far from simple Catholic versus Protestant affairs.
• At this time he produced a new edition of Rudolff's Coss (1552-1553) but this was certainly not a simple editing exercise but rather he more than doubled its length by adding much material of his own.
• But if one places this sign before a simple number which has not the root which the sign indicates, then from that simple number arises a surd number.
• In other words √4 is a simple number but √2 is a surd.
17. Robert May (1936-)
• What makes populations stabilise? What makes them fluctuate? Are populations in complex ecosystems more stable than populations in simple ecosystems? In 1973, Robert May addressed these questions in this classic book.
• He published highly significant papers such as Biological populations with nonoverlapping generations: stable points, stable cycles, and chaos (1974), Simple mathematical models with very complicated dynamics (1976), Bifurcations and dynamic complexity in simple ecological models (1976), and Thresholds and breakpoints in ecosystems with a multiplicity of stable states (1977).
• The 'Simple mathematical models' paper has been cited an incredible number of times.
• Such equations, even though simple and deterministic, can exhibit a surprising array of dynamical behaviour, from stable points, to bifurcating hierarchy of stable cycles, to apparently random fluctuations.
18. Alfred Hoblitzelle Clifford (1908-1992)
• as an assistant professor, a paper famous in the semigroup community about union of groups semigroups, that Clifford learned about Rees's Theorem determining the structure of completely 0-simple semigroups, generalizing the Wedderburn theory of rings.
• The impact was profound, first because [Clifford's first paper] was a special case (in fact of the Suschkiewitsch paper), second, its application to paper 'Semigroups admitting relative inverses' in hand, where Clifford proved S is a union of groups if and only if S is a semilattice of completely simple semigroups (to which Rees structure theorem applies), and finally because of its intrinsic beauty and importance.
• Clifford's 1953 paper 'A class of d-simple semigroups' on d-simple semigroups was his first reaction to Green and was really about inverse d-simple (one D class, and remember Green introduced D) semigroups.
19. Akos Seress (1958-2013)
• He continued his work in computational group theory with a series of important papers on the statistical theory of finite simple groups with Bill Kantor and others; this line of work contributed to a recent definitive result on the complexity of algorithms for matrix groups over finite fields by Seress and coauthors.
• They played an indispensable role in the proof of many deep results, including the construction and study of sporadic finite simple groups.
• This book describes the theory behind permutation group algorithms, up to the most recent developments based on the classification of finite simple groups.
• on Symbolic and Algebraic Manipulation) and was hailed as "a groundbreaking work" that "marks a turning point in Majorana Theory." His most recent work, with Harald Helfgott, under publication in the Annals of Mathematics, gives a long-sought bound on the diameter of the alternating and symmetric groups and represents a tour de force in the study of the geometry of finite simple groups.
• After some discussion, I suggested that Graham Higman's finitely presented simple group should give him the example he was seeking and pointed him towards a reference.
20. Élie Cartan (1869-1951)
• However, although Killing had shown that only certain exceptional simple algebras were possible, he had not proved that in fact these algebras exist.
• This was shown by Cartan in his thesis when he constructed each of the exceptional simple Lie algebras over the complex field.
• His first papers, published in 1893, were two notes stating his results on simple Lie groups.
• After the work of his thesis on finite continuous Lie groups, he later classified the semisimple Lie algebras over the real field and found all the irreducible linear representations of the simple Lie algebras.
• M Cartan points out that, in their most general mathematical form, spinors were discovered by him in 1913 in his work on linear representations of simple groups, and he emphasises their connection ..
21. Alan Day (1941-1990)
• One of the first was in the paper A simple solution to the word problem for lattices (1970) where he gave a simple solution to the word problem in free lattices.
• Alan once told me that he really liked elegant mathematics: simple ideas that give profound insights.
• It is a method which is simultaneously powerful and simple, with subtleties that go beyond the surface.
• His proofs involved a subtle manipulation of terms and, when asked by a colleague about how he found one particularly hard proof, he replied "Simple.
22. Walter Feit (1930-2004)
• Solomon, in [',' R Solomon, A brief history of the classification of the finite simple groups, Bull.
• It defined the monumental scale of the classification project for finite simple groups and threw down a gauntlet to other researchers in the field.
• It resolved a seemingly intractable case of the problem and offered entirely new and powerful ways of thinking about finite simple groups - ways of thinking that proved powerful enough to complete the entire project.
• He addressed the International Congresses of Mathematicians in Nice in 1970 on The Current Situation in the Theory of Finite Simple Groups.
23. Philip Hall (1904-1982)
• Hall offered parts of that book for examination in the Tripos and gave a proof that no group of order pn, n > 1, can be simple.
• In On non-strictly simple groups published in 1963 Hall established the existence of simple groups which were the infinite union of a chain of subgroups, each normal in the next.
• Besides containing a discussion of the possible order types of abelian series in simple groups, the paper also presents an extremely informative survey of the inter-relations that are known or conjectured to exist between the various classes of generalized soluble groups.
24. Ivor Etherington (1908-1994)
• Although he was working on general relativity, he published the following two papers in 1932: On errors in determinants and A simple method of finding sums of powers of the natural numbers.
• Combination of distributions by random mating is usually symbolised by the mathematical sign for multiplication; but this sign is not taken literally for the simple reason that the genetical laws connecting the distributions of progenitors and progeny are inconsistent with the laws governing multiplication in ordinary algebra.
• Here I propose to consider the symbolism more from the geneticist's point of view, applying it to some simple population problems, without going into the details of the mathematical background.
• I wish that this thesis may not be judged as a finished achievement in biological investigations but may be judged primarily as a contribution to algebra, suggested by biological problems, and perhaps having possibilities of applications beyond the simple ones so far demonstrated.
25. Graham Higman (1917-2008)
• Higman published further important papers in 1951 when he gave an example of a finitely presented group which is isomorphic to a proper factor of itself, and Higman's famous example of a finitely generated infinite simple group.
• After working on finitely generated nilpotent groups and infinite simple permutation groups, Higman, together with Philip Hall, produced another of his landmark papers in 1956 On the p-length of p-soluble groups and reduction theorems for Burnside's problem.
• Then in 1967 Higman became interested in the sporadic finite simple groups being discovered at this time and played an important role in constructing certain of these groups from a knowledge of their character tables.
• He published papers on the Higman-Sims simple group (named after D G Higman and not Graham Higman) and on Janko's group of order 50232960.
26. Wendelin Werner (1968-)
• In an interview after being awarded the Fields Medal, Werner was asked if he could explain, in simple terms, one of the problems he worked on.
• Understanding the behaviour of certain natural very long random curves in the plane is a seemingly simple question that has turned out to raise deep questions, some of which remain unsolved.
• have made predictions concerning the existence and values of critical exponents for various two-dimensional systems in statistical physics (such as self-avoiding walks, critical percolation, intersections of simple random walk) using considerations related to several branches of mathematics (probability theory, complex variables, representation theory of infinite-dimensional Lie algebras).
• One simple but important example is percolation ..
27. John Leech (1926-1992)
• Leech is, however, best known for the Leech lattice which gives rise to three sporadic simple groups.
• Knowing that he did not have the group theory skills necessary to prove his conjectures he tried to interest others, see [',' T M Thompson, From error-correcting codes through sphere packings to simple groups (Washington, 1983).','1]:- .
• A detailed description of this discovery is given in [',' T M Thompson, From error-correcting codes through sphere packings to simple groups (Washington, 1983).','1].
• Leech died almost exactly one month after Gorenstein who had overseen the classification of finite simple groups.
28. William Burnside (1852-1927)
• However it was in 1893 that he published his first paper on finite simple groups, showing that the alternating group A5 is the only finite simple group whose order is the product of four (not necessarily distinct) primes.
• They are concerned chiefly with the proof of certain tests that may be applied in particular cases to determine whether it is possible for a simple group of a given order to exist.
• For example he proved in a paper published in 1895 that if a group of even order has a cyclic Sylow 2-subgroup then the group cannot be simple.
29. Donald Higman (1928-2006)
• In 1967 Higman made a major breakthrough when, working with Charles Sims, he discovered the previously unknown sporadic simple group now known as the Higman-Sims group.
• At the conference Marshall Hall lectured on the construction of the Hall-Janko sporadic simple group as a rank-3 permutation group on 100 points and this prompted a discussion.
• Higman and Sims described the group in the paper A simple group of order 44,352,000 which appeared in Mathematische Zeitschrift in 1968.
• In June 1966 he was in Japan and, in that month, gave the lecture 'Remarks on Finite Permutation Groups' at the University of Tokyo in which he described the discovery of Janko's simple group and discussed Donald Livingstone's construction of it.
30. Emil Artin (1898-1962)
• He presented new insight into semi-simple algebras over the rationals.
• In 1955 he produced two important papers on finite simple groups, proving that the only coincidences in orders of the known (in 1955) finite simple groups were those given by Dickson in his Linear groups.
• This important piece of work is one of a number of results leading to the intense interest in finite simple groups which eventually led to their classification.
31. Marion Walter (1928-)
• This book has many mirror tricks in it that are simple enough for a 41/2 year old to enjoy.
• This is the most entertaining book ever! Simple yet dynamic.
• "Can you make this shape bigger? Can you make this shape smaller?" Simple and inexpensive.
32. Jakob Steiner (1796-1863)
• There exist a limited number of very simple fundamental relationships that together constitute the schema by means of which the remaining theorems can be developed logically and without difficulty.
• Here the main thing is neither the synthetic nor the analytic method, but the discovery of the mutual dependence of the figures and of the way in which their properties are carried over from the simple to the more complex ones.
• Starting from a few spatial properties Steiner attempted, by means of simple schema, to attain a comprehensive view of the multitude of geometric theorems that had been rent asunder.
33. Doris Schattschneider (1939-)
• for her 45-page thesis Restricted roots of a semi-simple algebraic group.
• A paper giving the main results of her thesis appeared in 1969 with the title On restricted roots of semi-simple algebraic groups.
• The second contribution was his deformation of Polya's simple motifs (bounded by line segments or arcs of circles) into recognizable birds, lizards, fishes, etc.
34. Claude Chevalley (1909-1984)
• Chevalley groups play a central role in the classification of finite simple groups.
• His name is also attached to Chevalley decompositions and to a Chevalley type of semi-simple algebraic group.
• The basic definitions are chosen deftly, and each topic is developed with simple directness.
35. Richard Borcherds (1959-)
• From the automorphism group of this lattice, Conway had discovered three previously unknown finite simple groups in 1968.
• In the classification of finite simple groups, one of the most mysterious objects found was the monster group.
• The concept was used extensively by Frenkel, Lepowski and Meurman in their work on the Monster simple group, and very recently it has been an essential tool in the progress made by E Frenkel on a conjecture of Drinfeld about the Langlands correspondence for representations of loop groups.
36. James McConnell (1915-1999)
• The next five chapters contain a simple, readable account on the general notions concerning semi-simple Lie algebras, their root diagrams, weight diagrams, and the reduction of product representations.
• The first half of this brochure is devoted to a detailed and elaborate discussion of the weight diagrams of representations of the simple Lie groups of rank two: A2, B2 and G2.
37. Christian Kramp (1760-1826)
• I use the very simple notation n! to designate the product of numbers decreasing from n to unity, i.e.
• Kramp went further than simple factorials, however, in his article Memoire sur les facultes numeriques Ⓣ published in Gergonne's Annales de Mathematiques in 1812.
• I note that any numerical faculty whatever is always reduced to the very simple form .
38. Jules Bienaymé (1796-1878)
• Bienayme published the Bienayme-Chebyshev inequality, which was used to give a very simple and precise demonstration of the generalised law of large numbers, in his important paper Considerations a l'appui de la decouverte de Laplace sur la loi de probabilite dans la methode des moindres carres Ⓣ (1853).
• Bienayme also worked on independent binomial trials and his most important contribution was his statement of the criticality theorem for simple branching processes which he gave in 1845 - eventual extinction of a family name has probability one if and only if the mean number of male children is one or less.
• He also gave a simple test for randomness of observations on a continuously varying quantity.
39. Abraham Wald (1902-1950)
• points out that the two major problems of statistical theory at that time, testing hypotheses and estimation, can both be regarded as simple special cases of a more general problem - known nowadays as a "statistical decision problem".
• The idea here is a simple one yet Wald was the first to build it into a statistical theory.
• He was a master at deriving complicated results in amazingly simple ways.
40. Thomas Graham (1905-1974)
• Tommy Graham wanted to go to the University of Cambridge to undertake research in mathematics for his doctorate but obtaining the necessary funding was not simple.
• Returning to Cambridge in 1932, Graham submitted his thesis On the Structure of Simple and Semi-Simple Groups and, after being examined, was awarded a Ph.D.
41. Ludwig Wittgenstein (1889-1951)
• This is essentially an atomic theory with the world built from simple objects.
• Why is philosophy so complicated? It ought to be entirely simple.
• Although the result of philosophy is simple, its method cannot be if it is to succeed.
42. Edward Lorenz (1917-2008)
• It was a simple event in 1961 which led Lorenz to results which brought him worldwide fame.
• Another account of aperiodic behaviour in ordinary differential equations, and difference equations, in which Lorenz describes how he arrived, starting from the description of convection in meteorology, at the Lorenz equations is contained in his paper On the prevalence of aperiodicity in simple systems delivered at the Biennial Seminar of the Canadian Mathematical Congress in Calgary, Canada, in 1978.
• The primary purpose of this study is to find out what the attractor set looks like for some simple atmospheric model.
43. Benoit Mandelbrot (1924-2010)
• Despite their pathological qualities, their extraordinary complexity, especially when viewed in greater and greater detail, they were often very simple to describe in the sense that the rules which generated them were absurdly simple to state.
• They occur in physics in the description of the extraordinarily complex behaviour of some simple physical systems like the forced pendulum and in the hugely complex behaviour of turbulence and phase transition.
44. Clarence Lewis (1883-1964)
• My mother was a vital young woman - nineteen when I was born - of simple faith and with the love of life.
• These studies are of so recent an origin that there has been till now no opportunity to consolidate into a single treatise anything but their most simple and primitive aspects.
• Accordingly the student, after leaving the almost childishly simple Boolean algebra as presented in the writings of Couturat and del Re, is immediately confronted with that forbidding monument of patience and research, the 'Principia Mathematica' of Whitehead and Russell.
45. Bill Boone (1920-1983)
• His thesis was entitled Several Simple, Unsolvable Problems of Group Theory Related to the Word Problem.
• He wrote up the results of his thesis in four parts under the title Certain simple, unsolvable problems of group theory; two parts appeared in 1954, and two more in 1955.
• It gives an algebraic characterisation of groups with soluble word problem connecting this property with embeddability in a simple group.
46. Atle Selberg (1917-2007)
• the basic ideas were rather simple always, and could be explained in rather simple terms ..
• His breakthroughs on long-standing problems were based on imaginative and novel ideas which, once digested, were appreciated as simple and decisive.
• The finite control was programmable with very simple instructions, and one could easily write a program that would read a string of A, T, C and G on the input tape and write the Watson-Crick complementary string on the output tape.
• But there was one important piece of information that made this similarity truly striking: Turing's toy computer had turned out to be universal - simple as it was, it could be programmed to compute anything that was computable at all.
• Theoretically, only two things were needed to build a computer capable of computing anything computable - a method by which information was stored and simple operations which acted on it.
48. Eduard Stiefel (1909-1978)
• Following earlier work of H Cartan and H Weyl, he introduced the so-called Stiefel Diagram for continuous groups, relating closed semi-simple groups and discontinuous reflection groups.
• Accordingly he was looking for a way to gain access to computing power beyond the level that could be performed by simple desktop calculators.
• However, we tried to use simple and transparent proofs, presented in detail.
• The rapid extension during recent years of the ideas of simple correlation has imposed their use upon many scientists not trained in the mathematical theory underlying them.
• One object of this bulletin is to present in simple un-technical language some explanation of the meaning and uses of the various correlation coefficients, simple partial and multiple.
50. Hans Samelson (1916-2005)
• My aim has been to follow as direct a path to these topics as I could, avoiding detours and side trips, and to keep all arguments as simple as possible.
• deals with the structure and representation theory of semi-simple Lie algebras and succeeds in covering a good deal of material.
• The purpose, as before, is to present a simple straightforward introduction, for the general mathematical reader, to the theory of Lie algebras, specifically to the structure and the (finite dimensional) representations of the semisimple Lie algebras.
51. Lyudmila Vsevolodovna Keldysh (1904-1976)
• It was in 1934 that her first papers were published: On the Homeomorphism of Canonical Elements of the 3rd Class; On Simple Functions of Class a; and On the Structure of B Measurable Functions of Class a.
• [She and her husband Petr Sergeevich Novikov] had a very simple lifestyle in the family, no excesses, simple furniture, only interesting pictures on the walls, and warm human relations.
52. Robert Boyle (1627-1691)
• He did follow Descartes in his overall belief that the world was basically a complex system governed by a small number of simple mathematical laws.
• Although others before him had applied mathematics to physics, Boyle was one of the first to extend the application of mathematics to chemistry which he tried to develop as a science whose complex appearance was merely the result on simple mathematical laws applied to simple fundamental particles.
53. Alexander Animalu (1938-)
• We list most of these in the following list: The spin-orbit interaction in metals and semiconductors (1966); (with F Bonsignori and V Bortolani) Electron-phonon contribution to the specific heat of alkalines (1966); (with F Bonsignori and V Bortolani) The phonon spectra of alkali metals and aluminium (1966); Optical conductivity of simple metals (1967); Self-consistent theory of optical transitions in simple metals (1967); The pressure dependence of the electrical resistivity thermopower and phonon dispersion in liquid mercury (1967); (with B Vasvari and V Heine) Electronic structure of Ca, Sr, and Ba under pressure (1967) [Note: Vasvari was a Hungarian who worked at Cambridge, England, while in receipt of a scholarship.
• Animalu writes, "This work was completed, supported in part by the Advanced Research Projects Agency through the Center for Materials Research, Stanford University, Stanford, California]; Many-electron effects in the optical conductivity of simple metals by Kubo formula (1970); General theory of magnetic-field-induced surface states (1970); Mass ratio of quarks (1971); Charge spectrum of four-component fields with O(4, 2) symmetry (1971); Bound states and mass spectra of hadrons in the quark model (1971); Scale symmetry (1972); Lepton and hadron currents in O(4, 2) current algebra (1972); High-field magnetoresistance of metals by Kubo-Mott formula (1972); Pseudopotential approach to magnetic energy bandstructure and magnetic breakdown in metals (1972); Josephson current in tunneling between coupled superconductors (1973); A relativistic model of quark-quark strong interactions (1973); Electronic structure of transition metals.
54. Émile Mathieu (1835-1890)
• Emile Mathieu is remembered especially for his discovery (in 1860 and 1873) of five sporadic simple groups named after him.
• By March 1859 he had been awarded his Docteur es Sciences by the Faculty of Science in Paris for his thesis Sur le nombre de valeurs que peut acquerir une fonction quand on y permute ses lettres de toutes les manieres possibles Ⓣ on transitive functions, the work which led to his initial discovery of sporadic simple groups.
• He lived in simple style dividing his time between his lectures and his mathematical researches.
55. Charles Fefferman (1949-)
• When I was a little boy I was interested in children's science: how rockets work and things like that, but I wasn't satisfied with simple explanations, so I checked a Physics textbook out of the public library and I couldn't understand anything.
• Fourier analysis is the study of how complicated vibrations break up into simple ones.
• A photograph is a two-dimensional image, also built up from simple pieces analogous to the fundamental note and overtones of a string.
56. Mark Aronovich Naimark (1909-1978)
• This is a fairly comprehensive account of the irreducible continuous unitary representations of the classical simple (complex) Lie groups, and of related aspects of harmonic analysis on such groups.
• (The title is somewhat misleading in that partial differential operators are not analysed.) Starting from simple facts about boundary-value problems, the author develops the theory of expansion by eigenfunctions, and the spectra of ordinary differential operators, including many of the results obtained recently by Russian mathematicians.
• The style is simple and lucid.
57. Øystein Ore (1899-1968)
• An effort has been made to present the subject matter in the book in as simple a form as possible.
• Many of these are quite simple; others are more in the nature of proposed research problems; these have been marked with an asterisk.
58. Johannes Robert Rydberg (1854-1919)
• Rydberg's most important work is on spectroscopy where he found a relatively simple expression relating the various lines in the spectra of the elements.
• Some of the features noted by Rydberg were observed about the same time by Kayser and Runge, but his work had the special merit of connecting different series in the spectrum of the same element into one system, which could be represented by a set of simple formulae having but few adjustable constants.
59. Isaac Todhunter (1820-1884)
• His habits and tastes were singularly simple; and to a gentle kindly disposition he united a high sense of honour, a warm sympathy with all that was calculated to advance the cause of genuinely scientific study in the university, and considerable humour.
• From the majority of the papers in our few mathematical journals, one would almost be led to fancy that British mathematicians have too much pride to use a simple method, while an unnecessarily complex one be had.
60. James Hutton (1726-1797)
• His simple and eloquent style consisted of a series of chapters clearly stating the Huttonian theory, giving the facts to support it, and the arguments given against it.
• But it is impossible by words to convey any idea of the effect of his conversation, and of the impression made by so much philosophy, gaiety nd humour, accompanied by a manner at once so animated and simple.
61. David Mumford (1937-)
• Klein studied infinitely repeated reflections and was led to forms with multiple co-existing symmetries, each simple in itself, but whose interactions produce fractals on the edge of chaos.
• I will try to explain what this means, using simple examples and then go on show why it is proposed as a new tool in the diagnosis of medical conditions.
62. Jan Tinbergen (1903-1994)
• The ability of a planning expert to communicate with politicians and with citizens constitutes an important element in any type of democratic or semi-democratic planning and such communication can be enhanced by relatively simple models.
• In a neat, simple house, virtually indistinguishable from others on his block in the middle class neighbourhood of The Haviklaan, The Hague, lives one of the world's most distinguished economists, a co-winner of the first Nobel Prize in Economics in 1969, and a man who is known for his gentleness, his modesty, and his selfless dedication to the cause of human welfare.
63. Raphael Robinson (1911-1995)
• The book gives an introductory account of the methods introduced by Tarski for establishing the undecidability of several fairly simple branches of mathematics (group theory, lattices, abstract projective geometry, closure algebras and others).
• In each of them he takes a problem, old or new, which can be stated in simple and intelligible terms, and either solves it, or at least adds much that is new.
64. Charles-Marie de La Condamine (1701-1774)
• There was never any discussion of constructing a fancy edifice, but rather a simple and durable monument appropriate for showing clearly the two endpoints of our base.
• widely known in every society, possessing the art of persuading the ignorant people to whom he had listened, bringing back singular observations to pique the frivolous curiosity of the people of the world, writing with enough charm to have people read his work, with enough neglect and too simple a tone to foster envy or threaten the self-esteem of others, interesting for his bravery and piquant for his faults.
65. Bronius Grigelionis (1935-2014)
• As an application, the problem of testing a simple hypothesis against a simple alternative in a Poisson process is considered.
66. Lazar Matveevich Gluskin (1922-1985)
• His other early papers included Homomorphisms of unilaterally simple semigroups on groups (Russian) (1955), Simple semigroups with zero (Russian) (1955), and Elementary generalized groups (Russian) (1957).
67. Pedro Abellanas (1914-1999)
• In particular, it is shown that the geometric definition of a simple point of a surface (in terms of the multiplicity of the intersection with two generic primes) is equivalent to the arithmetic definition [O Zariski, (1939)].
• According to the author's preface, this book is devoted to the study of the basic spaces (vectorial, affine, euclidean and projective) and the maps among them, especially the linear ones and also the differential functions in simple cases.
68. John Carr (1948-2016)
• He readily explained his insights in patient and simple terms both to students and to many others who approached him for help.
• He readily explained his insights in patient and simple terms both to students and to many others who approached him for help.
69. Wanda Szmielew (1918-1976)
• Why did Maria [Tarski's wife] put up with this? The simple answer is: She did not think she had much choice.
• Every movement seems simple, natural, the way it has to be.
70. Jean Richer (1630-1696)
• Again we do not know the date of his birth; in fact the year of 1630 that we give, although generally accepted by most historians, is simple a guess based on the fact he joined the Academie as a junior astronomer in 1666.
• The vibrations of the simple pendulum which was used were very short and remained quite perceptible up to 52 minutes, and were compared with those of an extremely good clock whose vibrations indicated seconds.
71. James Whitbread Lee Glaisher (1848-1928)
• Their fundamental principles are derived from observations so simple as to be almost axiomatic.
• There was no shred of pomposity in his bearing, which was frank and simple.
72. Bruce Kellogg (1930-2012)
• He summarises Some simple boundary value problems with corner singularities and boundary layers (2006) as follows:- .
• He co-authored several papers with Martin Stynes as, for example, Sharpened bounds for corner singularities and boundary layers in a simple convection-diffusion problem (2007).
73. Joseph Wedderburn (1882-1948)
• In this paper On hypercomplex numbers which appeared in the Proceedings of the London Mathematical Society, he showed that every semisimple algebra is a direct sum of simple algebras and that a simple algebra was a matrix algebra over a division ring.
74. Paul Painlevé (1863-1933)
• brought up in the simple democratic atmosphere of French skilled artisan family life.
• Painleve had a naturally simple and unaffected manner, and was possessed of a singular charm that few persons, even among his opponents, were able to resist.
75. Isaac Newton (1643-1727)
• Taking differentiation as the basic operation, Newton produced simple analytical methods that unified many separate techniques previously developed to solve apparently unrelated problems such as finding areas, tangents, the lengths of curves and the maxima and minima of functions.
• He had reached the conclusion during the two plague years that white light is not a simple entity.
76. Étienne Bézout (1730-1783)
• Of course on the face of it this does not help solve the equation but Bezout made the simplifying assumption that one of the two equations was of a particularly simple form.
• One has to understand the problems that faced Bezout for he did not have our simple suffix notation to denote the unknowns by x1, x2, x3, ..
77. Kathleen McNulty Antonelli (1921-2006)
• We did have desk calculators at that time, mechanical and driven with electric motors, that could do simple arithmetic.
• We were preparing a firing table for each gun, with maybe 1,800 simple trajectories.
78. Evangelista Torricelli (1608-1647)
• This theory allowed Cavalieri to find, in a simple and rapid way, the area and volume of various geometric figures.
• He was a skilled lens grinder, making excellent telescopes and small, short focus, simple microscopes, and he seems to have learnt these techniques during the time he lived with Galileo.
79. Karl Gräffe (1799-1873)
• The law by which the new equations are constructed is exceedingly simple.
• A simple notion, but effective and it is just what everyone does today.
80. Boris Yakovlevic Bukreev (1859-1962)
• The basic principles Bukreev adopted as a teacher included ensuring completeness of coverage of the topic under discussion, accuracy and clarity of presentation, and presenting his material in simple language.
• These books are written at a high scientific level, yet in simple and clear language.
81. George Greenhill (1847-1927)
• There, with his books around him, his tables covered in neat disorder with innumerable scraps of material and apparatus to be used as dynamical models, his walls festooned with every variety of pendulum, simple or compound, contrived from articles purchased below a prescribed limit of cost at the local stores, upon his floor the treasured roll of Turkish carpet from his room of long ago at St John's, and above the mantelpiece the portrait of his beloved teacher, Clerk Maxwell, smiling approval - with all these and the precious memories they recalled, the scholar was content.
• To the question of whether he would take tea or coffee his reply was a simple affirmative ..
82. Geoffrey Bennett (1868-1943)
• In the simple cases, when the modulus is a real number which is an odd prime, a power of an odd prime, or double the power of an odd prime, we know that there exist primitive roots of the modulus: that is, that there are numbers whose successive powers have for their rests the complete set of numbers less than, and prime to, the modulus.
• Many of these are authors giving their thanks to Bennett with words such as: "G T Bennett, of Emmanuel College, Cambridge, sent the author the following simple construction in August, 1902..
83. Georges Darmois (1888-1960)
• Distribution functions, mean values, characteristic functions with their various properties, and moments are presented in a very simple manner.
• Equally simple is the presentation of pairs of variables with the corresponding Laplace-Gauss law, convergence theorems, domains of attraction of the Laplace-Gauss law, with elements of the theory of errors and the influence of dependence on random quantities.
84. David Enskog (1884-1947)
• A simple theory does not predict this behaviour.
• He derived general formulas for the viscosity, conduction, and diffusion in simple and mixed gases, and also determined the pressure-tensor to a third approximation.
85. Ismael Boulliau (1605-1694)
• The simple suggestion I put to him should make him wiser and more reserved in making injurious statements against someone who has never made such cruel remarks, and who has never offended him.
• There is one aspect of Boulliau's philosophy which is well worth commenting on - namely the fact that he believed in simple explanations and moreover he wanted many different observed properties to result from a single cause.
86. Florence Nightingale David (1909-1993)
• the ideas are simple and easy to understand, but the manipulative procedures are discouraging in that they depend on mathematical tricks which have to be learnt.
• The book is written with care but without pedantry, and takes the reader from deceivingly simple problems to serious and sometimes quite involved mathematical theory.
87. Yitz Herstein (1923-1988)
• Before being appointed to Chicago he had published papers such as A proof of a conjecture of Vandiver (1950), On a conjecture on simple groups (1950), and Group-rings as *-algebras (1950).
• The book largely concerns Herstein's work on Lie and Jordan structure of simple associative rings which he published in various papers in the early 1950s.
• Columella was a Roman soldier and farmer who wrote extensively on agriculture and similar subjects, hoping to foster in people a love for farming and a liking for the simple life.
• They give methods of lifting heavy weights and describe simple mechanical machines.
89. Helmut Hasse (1898-1979)
• At Halle Hasse obtained fundamental results on the structure of central simple algebras over local fields.
• While in Marburg he began joint work with Brauer and Emmy Noether on simple algebras, culminating in the complete determination of what is today called the Brauer group of an algebraic number field.
90. Donald Knuth (1938-)
• There has been much recent interest in languages whose grammar is sufficiently simple that an efficient left-to-right parsing algorithm can be mechanically produced from the grammar.
• In this paper, we define LR(k) grammars, which are perhaps the most general ones of this type, and they provide the basis for understanding all of the special tricks which have been used in the construction of parsing algorithms for languages with simple structure, e.g., algebraic languages.
91. Giorgio Bidone (1781-1839)
• Simple and modest in his desires, he loved science for its own sake, and he never used it to pursue dreams of ambition and wealth.
• I entered into this clean apartment which was so simple and austere; exact and precisely ordered like a page of calculations.
92. Charles René Reyneau (1656-1728)
• Fortunately, in the last century, the lines and figures were expressed by the familiar characters of the alphabet, and these expressions were reduced to an easy calculus, which also expresses all the simple and compound relations which these lines and figures can have.
• He added to it the excellent method of employing indeterminate expressions, which, however simple they were, represented an infinity of magnitudes; and to determine from all of them the particular magnitudes which they may satisfy.
93. John Crank (1916-2006)
• In the 1940s such calculations were carried out on simple mechanical desk machines.
• Crank and Nicolson's method, which is numerically stable, requires the solution of a very simple system of linear equations (a tridiagonal system) at each time level.
94. R H Bing (1914-1986)
• Bing worked for his doctorate under R L Moore's supervision, undertaking research on simple plane webs.
• He worked on topological classification of the 2-sphere, the 3-sphere, pseudo arcs, simple closed curves and Hilbert space.
95. Lyman Spitzer (1914-1997)
• This approach is necessary in discussing containment by magnetic mirrors and the lack of it in a simple torus.
• This is joined with Maxwell's equations, and the simple limits of high and low magnetic fields are briefly considered.
96. Matyá Lerch (1860-1922)
• However, things are not quite so simple since his given name (the one that appears on his birth certificate) is Matěj.
• He attended courses on the theory of elliptic functions by Weierstrass, and courses on the theory of algebraic equations and on simple and multiple integrals by Kronecker.
97. Gaetano Fichera (1922-1996)
• In pure mathematics Gaetano Fichera achieved considerable results in the following fields: mixed boundary value problems of elliptic equations; generalized potential of a simple layer; second order elliptic-parabolic equations; well posed problems; weak solutions; semicontinuity of quasi-regular integrals of the calculus of variations; two-sided approximation of the eigenvalues of a certain type of positive operators and computation of their multiplicity; uniform approximation of a complex function f(z); extension and generalization of the theory for potentials of simple and double layer; specification of the necessary and sufficient conditions for the passage to the limit under integral sign for an arbitrary set; analytic functions of several complex variables; solution of the Dirichlet problem for a holomorphic function in a bounded domain with a connected boundary, without the strong conditions assumed by Francesco Severi in a former study; construction of a general abstract axiomatic theory of differential forms; convergence proof of an approximating method in numerical analysis and explicit bounds for the error.
98. Efim Zelmanov (1955-)
• The Schreier conjecture, that the outer automorphism groups of finite simple groups are soluble, was shown to be true as a consequence of the classification of finite simple groups.
99. William Edge (1904-1997)
• He also used geometrical configurations to investigate groups and, although his work was out of fashion at a time when group theorists were moving towards the classification of finite simple groups, his work did provide a deeper understanding of some of these groups, for example Conway's simple groups.
100. Wolfgang Gaschütz (1920-2016)
• The effects that this simple exchange of books had on the development of the mathematical seminar in Kiel can arguably still be perceived today.
• After completion of the classification of simple groups the main problem in the theory of finite groups remains the problem of mastering mechanisms of their interaction in arbitrary groups.
101. Jacob Levitzki (1904-1956)
• In it he showed that every semisimple algebra is a direct sum of simple algebras and that a simple algebra was a matrix algebra over a division ring.
102. Shiing-shen Chern (1911-2004)
• He knew all these papers on simple Lie groups, Lie algebras, all by heart.
• Through war and peace and through bad and good times we have shared a life for forty years, which is both simple and rich.
103. Hubert Wall (1902-1971)
• Over less than two hundred pages the reader travels from elementary number theory to simple graphs, from integrals and surfaces to linear spaces of simple graphs.
104. Leo Moser (1921-1970)
• a simple, courteous and soft spoken person full of anecdotes, humour and problems.
• He had an infinite stock of amusing stories, and a huge storehouse of simple puzzles of both a mathematical and a non-mathematical nature.
105. Oded Schramm (1961-2008)
• (The spheres must have disjoint interiors, but they don't have to be the same size.) It's a standard theorem in classical geometry, also related to important work in hyperbolic geometry and complex analysis, that you can realize any planar simple graph by kissing circles in R2, i.e., the circles are the vertices and the kissing pairs are the edges.
• The simple random walk on the square grid in the plane converges to Brownian motion under appropriate scaling.
106. Hans Zassenhaus (1912-1991)
• During this time he proved the Zassenhaus (butterfly) lemma, a beautiful result on subgroups which can be used to give a simple, and very beautiful, proof of the Jordan-Holder theorem.
• These groups play an important role in the classification of finite simple groups coordinated by Daniel Gorenstein.
107. Guido Grandi (1671-1742)
• The Accademia Arcadia was a literary academy which was founded in Rome in 1690 to promote a more natural, simple poetic style and around 1700 Grandi attended this Academy.
• However, he lived a simple retiring life among a small circle of friends.
108. Robert Edward Bowen (1947-1978)
• This three page paper gives simple bounds (using Euler's polyhedron formula) for the number of edges in the sets obtained when the vertices of a planar graph are partitioned into two sets.
• life was simple and unpretentious, punctuated by occasional parties full of noise and dancing.
109. Raymond Brink (1890-1973)
• Such tests are interesting not only because they can be used for testing types of series which are very difficult to examine by other methods, but also because, through the natural connection between integration and summation, they offer a simple and attractive means of unifying and establishing many tests of other kinds.
• Its statement and proof are simple for convergence, but rather awkward for the divergence test.
110. Herman Hollerith (1860-1929)
• The punch was constructed in a similar way to a typewriter having a simple keyboard.
• By this time he had added a mechanism to feed the cards automatically and other automatic sorting procedures which added sophistication to the original simple mechanical counting process.
111. Leonid Vital'evich Kantorovich (1912-1986)
• The method of successive approximations is often applied to proving existence of solutions to various classes of functional equations; moreover, the proof of convergence of these approximations leans on the fact that the equation under study may be majorised by another equation of a simple kind.
• The basic principle of their effective use was the paralleling of similar calculations, which made it possible to introduce simple program changes on the plugboard (of course, by hand).
112. Leslie Valiant (1949-)
• His results here range from simple, but powerful and elegant, insights to reexamining the very foundations.
• An example of a simple insight is his parallel routing scheme, described in the paper "A scheme for fast parallel communication" (1982).
113. Jan A Schouten (1883-1971)
• For example in 1924 he published Uber die Geometrie der halb-symmetrischen Ubertragungen Ⓣ jointly with Alexander Friedmann, and in 1926 he published two papers written jointly with Elie Cartan: On Riemaniann geometries admitting an absolute parallelism, and On the Geometry of the Group-manifold of Simple and Semi-simple Groups.
• J-P Serre showed with simple examples that no such functorial theory exists for abstract algebraic varieties which reflects the usual (singular) integral cohomology of spaces.
• I will describe a simple model which is useful for the study of the relationship between the history of a population and its genetic properties.
115. Aleksei Alekseevich Dezin (1923-2008)
• The potential reader is transported from very simple systems of linear equations to concepts as complex as that of linear space, invertible operator, eigenvalue and eigenvector, norm, adjoint, unitary and selfadjoint operator.
• He shows a special gift for making complicated facts look simple.
116. John Charles Fields (1863-1932)
• This long period of study, which exercised a decisive influence on his life and outlook, was rendered possible by a modest private income, combined with simple living and abstemious habits.
• The machinery, which he had to invent for the purpose, is simple, and its parts are beautifully coordinated.
117. Olabisi Ugbebor (1951-)
• We did some simple ones.
• Then, I showed them why if we were using that simple method for a larger collection, we would be there all day.
118. Ernst Witt (1911-1991)
• Having seen a remarkably simple proof by Witt of Wedderburn's theorem that every finite skew field is commutative, Herglotz encouraged him to submit it for publication and it became Witt's first paper appearing in 1931.
• joined the SA, urged on by the simple wish ..
119. Józeph Petzval (1807-1891)
• Petzval produced an achromatic portrait lens that was vastly superior to the simple meniscus lens then in use.
• His attack was based on the fact that Doppler derived the principle in a few lines using only simple equations.
120. Hermann von Helmholtz (1821-1894)
• Theoretical natural science must, therefore, if it is not to rest content with a partial view of the nature of things, take a position in harmony with the present conception of the nature of simple forces and the consequences of this conception.
• Its task will be completed when the reduction of phenomena to simple forces is completed, and when it can at the same time be proved that the reduction given is the only one possible which the phenomena will permit.
121. Timothy Pedley (1942-)
• Section 2 outlines the simple one-dimensional theory of pulse propagation in distended vessels, based on a 'tube law' to describe the elastic properties, and points out that there are a number of features (involving (a) wave attenuation and (b) localized constraints) that the simple theory still cannot explain.
• While an undergraduate he had already published some important papers (all in Russian): Simple examples of unsolvable canonical calculi (1967), Simple examples of unsolvable associative calculi (1967), Arithmetic representations of powers (1968), A connection between systems of word and length equations and Hilbert's tenth problem (1968), and Two reductions of Hilbert's tenth problem (1968).
123. Bella Abramovna Subbotovskaya (1938-1982)
• "A problem cannot be uninteresting, it can only be simple or complicated" - this was her saying.
• Bella Abramovna's and her like-minded people's idea was humane and simple: attempt to at least partially restore fairness by offering students who were seriously interested in mathematics the possibility of receiving that fundamental mathematical education which the administrators of Mekh-Mat deprived them.
124. Charles Noble (1867-1962)
• On 14 August 1907 Noble was in Zurich when he submitted his paper Singular points of a simple kind of differential equation of the second order to the Bulletin of the American Mathematical Society.
• In a series of four memoirs in the 'Journal de Mathematiques', Poincare has, among other things, discussed the topology of curves defined by ordinary differential equations of a simple character.
125. Herbert Pahlings (1939-2012)
• At that time the classification of finite simple groups had just been finished and the preparation of the 'Atlas of Finite Groups' was on the way.
• Character tables of simple and related groups are a dominant feature of the Atlas and programs such as the ones of CAS were welcome in particular for interactive handling the character tables of groups which were far too big to be worked with from their elements.
126. John Playfair (1748-1819)
• Playfair's simple and eloquent style consisted of a series of chapters clearly stating the Huttonian theory, giving the facts to support it, and the arguments given against it.
• He was, according to one of his many illustrious pupils, 'a charming teacher, so simple, unaffected and sincere in manner, so chaste in style, so clear in demonstration'.
127. Mineo Chini (1866-1933)
• Chini examined one of the writings of Eugenio Beltrami, Sulla flessione delle superfici rigate Ⓣ, in which the author studied the deformation of such surfaces; Chini was able to reduce to the minimum the number of possible elements that identifies the shape of a ruled surface, he researched the formulae - rather simple in this case - that gave all the bump-shaped surfaces and applied these formulae to treat some problems of the same type, but less simple, than those tackled by Beltrami in his essay.
128. Francesco Faà di Bruno (1825-1888)
• The subject is thoroughly and brilliantly set out, the exposition is simple, clear and, in several places, elegant.
• Faa di Bruno was tall and not always well dressed, but he was simple and good natured.
129. D'Arcy Thompson (1860-1948)
• It behoves us always to remember that in physics it has taken great men to discover simple things.
• When he meets with a simple geometrical construction, for instance in the honeycomb, he would fain refer it to psychical instinct, or to skill and ingenuity, rather than to the operation of physical forces or mathematical laws; when he sees in snail, or nautilus, or tiny foraminiferal or radiolarian shell a close approach to sphere or spiral, he is prone of old habit to believe that after all it is something more than a spiral or a sphere, and that in this 'something more' there lies what neither mathematics nor physics can explain.
130. Francesco Severi (1879-1961)
• His lectures on his own work were unforgettable, the style was beautifully simple ..
• Personal relationships with Severi, however complicated in appearance, were always reducible to two basically simple situations: either he had just taken offence or else he was in the process of giving it - and quite often genuinely unaware that he was doing so.
131. Ingrid Daubechies (1954-)
• But I also was interested in seeing how machinery worked, or in why certain mathematical things were true (like the fact that a number is divisible by nine if, when you add all its digits together, you get another number divisible by 9 - try it with 73512 and 8577, both multiples of 9; there is no rule that is quite as simple for divisibility by 7, say).
• The use of wavelets as an analytical tool is like Fourier analysis - simple and yet very powerful.
132. Ernst Jacobsthal (1882-1965)
• Indeed, he was so humanly simple and natural, that you had to be fond of him.
• He also showed that it is possible to find a solution p = x2 + y2 where x and y can be expressed with simple sums over Legendre symbols.
133. Jan Mikusiski (1913-1987)
• It introduces natural numbers through a new mathematical approach; replaces the Riemann integral with the more general Lebesgue integral; and rigorously develops the real number system from four simple axioms of natural numbers.
• Additional features include a wider range of problems than other texts - including simple and routine as well as problems requiring more in depth creativity, answers to common questions, a new approach to the concept of equivalence relation which simplifies the construction of real numbers, and a large number of computational applications.
134. Johannes de Groot (1914-1972)
• As is well known, any field can be obtained from its prime field by a succession of simple transcendental extensions followed by a succession of algebraic extensions.
• This trait was his strength, where the riches came from his grasp of simple ideas without much background knowledge, which made it possible for him to lead others to work together and to encourage them.
135. Philip Maini (1959-)
• Now, when kicking a football about, I dream of solving maths problems instead! I first saw the power and beauty of mathematics when, in the first year of A levels, my teacher wrote down the equation for simple harmonic motion for a swinging pendulum and I saw how this simple equation could describe everything about the motion of the pendulum.
• It, like the ideas of Pythagoras, tried to explain the multitude of complexity seen in the world as being the consequence of a small number of simple underlying properties.
• Although we no longer believe in Empedocles' four element theory, we do still look for simple mathematics which will explain the complex phenomena that surround us.
137. Sydney Chapman (1888-1970)
• There was a simple directness about his mode of expression, which often concealed deep thought.
• Chapman's mild manner veiled a strong will and great determination; his tastes and habits were simple.
138. Jean d'Alembert (1717-1783)
• Rational mechanics was a science based on simple necessary principles from which all particular phenomenon could be deduced by rigorous mathematical methods.
• In order to avoid delicate experiments or long tedious calculations, in order to substitute analytical methods which cost them less trouble, they often make hypotheses which have no place in nature; they pursue theories that are foreign to their object, whereas a little constancy in the execution of a perfectly simple method would have surely brought them to their goal.
139. Charles Augustin Coulomb (1736-1806)
• his simple, elegant solution to the problem of torsion in cylinders and his use of the torsion balance in physical applications were important to numerous physicists in succeeding years.
• Viewing fortresses as nothing more than immense permanent batteries designed to pour overwhelming fire on attacking armies, Montalembert simplified the intricate geometric designs of Vauban and relied on simple polygonal structures, often with detached peripheral forts instead of projecting bastions.
140. Christian Heinrich von Nagel (1803-1882)
• to expose the ideas laid down in nature: the simple pure utterances of the deity.
• This is constructed in a simple way.
141. Max Dehn (1878-1952)
• Written in 1914, not long after the discovery of the fundamental group of a topological space, it tackles a simple and beautiful problem: to confirm a property of the simplest knot which is suggested by five minutes of experimentation: that the right and left trefoil knots are not isotopic.
• before 1984 we really didn't have any simple tests for non-amphicheirality, so that Dehn's work (which at first glance looks like the use of a cannon to kill a sparrow) remained central to the subject for nearly 70 years.
142. Otto Hölder (1859-1937)
• He searched for finite simple groups and in the 1892 paper Die einfachen Gruppen im ersten und zweiten Hundert der Ordnungszahlen Ⓣ in Mathematische Annalen he showed that all simple groups up to order 200 are already known.
143. Ali Moustafa Mosharrafa (1898-1950)
• Mosharrafa's next paper, On the quantum theory of the simple Zeeman effect was submitted for publication on 1 September 1922 and published in February 1923.
• The aim of this paper is to put forward a theory of the simple Zeeman effect which possesses the same general features as those of the corresponding theory in the case of the Stark effect already developed by Epstein and Schwarzschild.
144. James Murray (1931-)
• For example A theoretical study of the effect of impulse on the human torso (1966), A simple method for obtaining approximate solutions for a class of diffusion-kinetic enzyme problems (Part I, 1968; Part II, 1968), and On the molecular mechanism of facilitated oxygen diffusion by haemoglobin and myoglobin (1971) are on mathematical biology while A simple method for determining asymptotic forms of Navier-Stokes solutions for a class of large Reynolds number flows (1967), Singular perturbations of a class of nonlinear hyperbolic and parabolic equations (1968) and On Burgers' model equations for turbulence (1973) are on fluid dynamics.
145. Herbert Richmond (1863-1948)
• It is true that the scope of these methods is restricted, but there is compensation in the fact that when geometry is successful in solving a problem the solution is almost invariably both simple and beautiful.
• A result already known is obtained in a simple manner.
146. Otto Szász (1884-1952)
• In fact Szasz worked on problems associated with both Riesz brothers, and he gave a very simple proof a theorem by Marcel Riesz on rational functions with given bounds on the unit circle.
• His life and energy were dedicated to the promotion of simple and beautiful problems of mathematics, in particular of the classical analysis.
147. Maurits Escher (1898-1972)
• After all his efforts, how far short of the originally so lucid and misleading simple idea did this result fall! .
• Circle Limit III was created using only simple drawing instruments and Escher's great intuition, but Coxeter proved that [',' D Schattschneider, Escher: A mathematician in spite of himself, in R K Guy and R E Woodrow (eds), The Lighter Side of Mathematics (Washington, 1994), 91-100.','8]:- .
• Zeno's challenge to simple pluralism is successful, in that he forces anti-Parmenideans to go beyond common sense.
• Zeno bases both the dichotomy paradox and the attack on simple pluralism on the fact that once a thing is divisible, then it is infinitely divisible.
149. Gregori Margulis (1946-)
• However, PSL2(R) was for a long time the only simple Lie group which was known to contain non-arithmetic discrete subgroups of finite covolume, and further examples discovered in 1965 by Makarov and Vinberg involved only few other Lie groups, thus adding credit to conjectures of Selberg and Pyatetski-Shapiro to the effect that "for most semisimple Lie groups" discrete subgroups of finite covolume are necessarily arithmetic.
• for his monumental contributions to algebra, in particular to the theory of lattices in semi-simple Lie groups, and striking applications of this to ergodic theory, representation theory, number theory, combinatorics and measure theory.
150. Raymond Wilder (1896-1982)
• The best known example of such a positional invariant is embodied in the Jordan curve theorem: A simple closed curve in the 2-sphere has precisely two complementary domains and is the boundary of each of them.
• A converse to the Jordan curve theorem, proved by Schonflies, states that a subset of the 2-sphere is a simple closed curve if it has two complementary domains, is the boundary of each of them, and is accessible from each of these domains.
151. Bertrand Russell (1872-1970)
• Thus, in its details, the theory admits of two versions, the "simple theory" and the "ramified theory".
152. Volker Strassen (1936-)
• It is an intricate yet simple algorithm that remains the method of choice for multiplying dense matrices of size 30 by 30 or more on machines today.
153. Wilhelm Ackermann (1896-1962)
• A remarkably simple axiomatization of a system of set theory is presented which the reviewer feels deserves serious consideration.
154. Bernhard Neumann (1909-2002)
• The present note, written in gratitude, affection and esteem, in Bernhard Neumann's honour, comprises some simple variations on the themes of that paper.
155. Paul Ehrenfest (1880-1933)
• Although he knew mathematics it was not simple for him.
156. Alfred Kempe (1849-1922)
• Hence many problems - such as, for example, the trisection of an angle - which can readily be effected by employing other simple means, are said to have no geometrical solution, since they cannot be achieved by straight lines and circles only.
157. Nikolai Luzin (1883-1950)
• His presentation was always very elegant and at first sight apparently unnecessarily simple - the result of his great pedagogic talent.
158. Kurt Mahler (1903-1988)
• His attitude to mathematics was like his attitude to life: he liked things as simple as possible and usually eschewed abstraction, but with his direct methods was often able to go surprisingly far.
159. Herbert Dingle (1890-1978)
• He wrote Relativity for All in 1922, in which he explained the subject (which was considered highly specialised at the time) in simple terms.
160. Charles Hermite (1822-1901)
• What radiates from the text is [Hermite's] humility, his Catholicism, his concern for his (very extended) family, his willingness to fight for colleagues whose merit he discerns, and his devotion to family, merit, and principle rather than simple influence.
161. John Colenso (1814-1883)
• "a simple-minded, but intelligent, native" asked him if he truly believed the story of Noah and a worldwide flood.
162. Agner Erlang (1878-1929)
• However, Magdalene and Hans Nielsen made a happy if simple home for their family making sure that they had sufficient food prepared which they prepared in the most hygienic manner possible.
163. Tom Whiteside (1932-2008)
• He held the most august and the most lowly colleagues to the same simple intellectual standards and judged - and treated - each only in terms of their intellectual integrity.
164. Paul Dirac (1902-1984)
• reflects Dirac's very characteristic approach: abstract but simple, always selecting the important points and arguing with unbeatable logic.
165. Pierre-Simon Laplace (1749-1827)
• The book continues with methods of finding probabilities of compound events when the probabilities of their simple components are known, then a discussion of the method of least squares, Buffon's needle problem, and inverse probability.
166. Andor Kertész (1929-1974)
• Kertesz defended his thesis entitled Operator modules and semi-simple rings in 1954.
167. Kollagunta Ramanathan (1920-1992)
• Simple proofs are given of a number of known theorems, such as the one that asserts that the product of 2sin π( n/m) taken over all n less than and prime to m has the value p or 1 according as m is or is not a power of the prime p.
168. Theodor Estermann (1902-1991)
• Until I read this book I would not have believed it possible to give so lucid and simple an account of the proofs of these three difficult and important theorems.
169. Tosio Kato (1917-1999)
• emphasizes clear and simple explanations of the fundamental notions of functional analysis.
170. Werner Rogosinski (1894-1964)
• The so-called Lindelof principle is nothing more than a transformation and systematic application of the simple Schwarz lemma.
171. Mikhail Yakovlevich Suslin (1894-1919)
• He had plenty of time to do this since he found his school work rather simple.
172. Anton Kazimirovich Suschkevich (1889-1961)
• In this Chapter there is an excellent contribution to the major structure theorem for algebraic semigroup theory which today is known as the Rees Theorem (named after David Rees) which classifies completely 0-simple semigroups.
173. John Stallings (1935-2008)
• This simple sounding theorem proves to be very powerful, implying (with a little work) the following two theorems: .
174. Gilles Pisier (1950-)
• Pisier's unique and clear way of presenting the material might even surprise researchers in the field: complicated results look very natural and simple in Pisier's presentation.
175. Sophus Lie (1842-1899)
• I have found it, it is quite simple! .
176. John Kemeny (1926-1992)
• Just as von Neumann realised that a computer that did only ordinary arithmetic operations could have extraordinary power, Kemeny realised that to make this power available to everyone, a programming language could and should be exceedingly simple.
177. Piers Bohl (1865-1921)
• There are many seemingly simple questions in this area which still seem to be open.
178. Francisco José Duarte (1883-1972)
• He published papers on the general solution of a diophantine equation of the third degree x3 + y3 + z3 - 3xyz = v3, simplified Kummer's criterion and gave a simple proof of the impossibility of solving the Fermat equation x3 + y3 + z3 = 0 in nonzero integers.
• Rogers in [',' Biography by C Ambrose Rogers, in Dictionary of National Biography (Oxford, 2004).','2] illustrates this with a simple example:- .
180. Raoul Bott (1923-2005)
• Usually he likes to discuss a simple key example that encapsulates the essence of the problem.
181. Dmitrii Matveevich Sintsov (1867-1946)
• in 1903) elementary simple proofs of its general real solutions.
182. Alexander Ostrowski (1893-1986)
• Life is often not that simple, however, since there was a quota on the number of Jewish students allowed into the university and entrance was decided by a lottery rather than on merit.
183. Charles Hutton (1737-1823)
• In 1776 he published A new and general method of finding simple and quickly converging series and two year later, in the same Transactions he published The force of fired gunpowder and the velocity of cannon balls.
184. Paul Erds (1913-1996)
• He posed and solved problems that were beautiful, simple to understand, but notoriously difficult to solve.
185. Ernesto Pascal (1865-1940)
• The chief fault of the book, from our point of view, is that it sacrifices simple and natural discussion to the pursuit of the end so dear to Italian mathematicians, the greatest possible generality.
186. Julius Gysel (1851-1935)
• In his obituary, his parents' home is described as a place with 'simple living, hard work, and a lot of music' [',' Obituary: Julius Gysel (1881-1972), Verhandlungen der Schweizerischen Naturforschenden Gesellschaft 153, 1973, 264-265','9].
187. Étienne Bobillier (1798-1840)
• He first set up a problem in the form of an equation in a particular case, simple enough so that the analytic geometry of his time could deal with it.
188. Ivan Georgievich Petrovsky (1901-1973)
• In art, as in science, he values depth, simplicity and clarity; in painting he likes Rembrandt, Serov, Nesterov, in music, Bach, Vivaldi, in architecture, simple and severe forms.
189. Vaughan Jones (1952-)
• These included (in addition to knots and links) that part of statistical mechanics having to do with exactly solvable models, the very new area of quantum groups, and also Dynkin diagrams and the representation theory of simple Lie algebras.
190. Tobias Mayer (1723-1762)
• The celebrate Tobias Mayer contrived, however, a method to determine, at one reading, instead of the simple angle observed, a multiple of the same angle; and, by this means, the instrument became, in practice, capable of any degree of accuracy, as far as regards the above mentioned errors.
191. Gabriel Mouton (1618-1694)
• He conducted experiments which led him to the conclusion that a simple pendulum of length one virgula would oscillate 3959.2 times in 30 minutes.
192. Lois Griffiths (1899-1981)
• Even moderately elaborate theorems are resolved into simple elements; illustrative examples and particular cases are introduced to pave the way for the formal proofs which follow; and there is much restatement.
193. Irving John Good (1916-2009)
• He was awarded a Smith's Prize in 1940 for his essay on fractional dimensions of sets of simple continued fractions, and he received his doctorate in 1941 for his thesis The topological concept of partial dimension based on the ideas of Henri Lebesgue.
194. Max Born (1882-1970)
• He was widely known for his exposition of the ideas of physics to the layman, and he was held in affection by his many colleagues and pupils for the warmth and simple directness of his personality.
195. Francesco Cecioni (1884-1968)
• A master of life, nobody failed to take his precious advice; he helped everyone with detached disinterest; he was paternal and understanding, simple, patient, humble, generously charitable, particularly with the young.
196. Mikhael Leonidovich Gromov (1943-)
• His work is unique through the abundance and the force of the concepts he has created, as well as through the new techniques he has devised and applied to solve problems, often simple to state and to understand, and which seem, at first sight, inaccessible.
197. Daniel Pedoe (1910-1998)
• However, it is not that simple; for his father, who was a Polish Jew from the priestly tribe of Kohanim, changed his name to Cohen when he arrived in Britain in the 1890s.
198. Alan Mercer (1931-2014)
• Mercer published Some simple duration-dependent stochastic processes (1959) and A queueing problem in which the arrival times of the customers are scheduled (1960) giving his address in both as Birkbeck College, University of London and Atomic Weapons Research Establishment at Aldermaston.
199. François-Joseph Servois (1768-1847)
• I confess that I do not yet see in this notation anything but a geometric mask applied to analytic forms the direct use of which seems to me simple and more expeditious.
200. Onorato Nicoletti (1872-1929)
• He had great power of analysis; examining questions dealt with by others, even the most extreme, he often succeeded in overcoming large-scale hypotheses and unnecessary conditions, thus reducing his treatment to a very simple logical scheme, which allowed him, sometimes overcoming serious difficulties with uncommon abilities and deductive force, to obtain far more general results than those already known.
201. John von Neumann (1903-1957)
• After a talk with him one always came away with a feeling that the problem was really simple and transparent.
• that a scholion replaced, perhaps in a damaged copy, the first of four proofs by a simple reference to generally known theorems.
203. Fatma Moalla (1939-)
• And I hope that one day one will stop making such a fuss, largely for a simple chronological chance ..
204. Hector Macdonald (1865-1935)
• The problem was simple.
205. James Booth (1806-1878)
• I was then led to the discovery of a simple method and compact notation from the following considerations.
206. Lóránd Eötvös (1848-1919)
• He discovered Eotvos's law of surface tension which states that the temperature coefficient of the molecular surface energy of a liquid is independent of the nature of simple unassociated liquids.
207. Hendrik de Vries (1867-1954)
• He knew how to give fascinating talks about the origins of Analytical Geometry, the misunderstood 'Rough draft for an essay on the results of taking plane sections of a cone' of Desargues, the brilliant young man Blaise Pascal, and especially about Gaspard Monge, who as a student at the Ecole Militaire, using some simple constructions, solved an important problem ..
208. F F P Bisacre (1885-1954)
• In §1 a simple test, using polarized light, for the best setting of a diffraction grating is described.
209. Kenneth Appel (1932-2013)
• I cannot believe that most mathematicians could have accepted our announcement as utterly convincing, although later work in the classification of simple groups showed it to be correct.
210. Mary Somerville (1780-1872)
• Her conversation very simple and pleasing.
211. Bernard de Fontenelle (1657-1757)
• Simple, exact, unaffected, and as varied in their scientific content as the sixty-nine astronomers, chemists, physicists, anatomists and others whom they commemorated, the Eloges exemplify a new literary form, moulded and created by Fontenelle, peculiarly French and still neither easily nor very successfully imitated in other languages ..
212. Richard Fuchs (1873-1944)
• During these years, busy with the release of the publications of his father, he promoted his life's work, the theory of linear differential equations in the complex domain, through its own investigations, and a wide readership benefited from his ability present a clear presentation and a simple argument.
213. Wim Cohen (1923-2000)
• It is an excellent introduction to the power of the regenerative-process approach to queueing theory, especially when it comes to providing simple, intuitively based arguments for well-known results in a general setting.
214. Leone Battista Alberti (1404-1472)
• Polyalphabetic substitution was introduced into diplomatic practice by Alberti, who also invented a simple mechanical device to speed up coding and decoding, consisting of a fixed and a movable ring.
• It appears both as al-Karaji and as al-Karkhi but this is not a simple matter of two different transliterations of the same Arabic name.
216. Julius Plücker (1801-1868)
• Things were not so simple, however, for the chair of mathematics in Berlin had just been filled by Jakob Steiner.
217. Tom Cowling (1906-1990)
• In the important chapter on the non-uniform state for a simple gas, use is made of Enskog's method of solving the integral equation and of Burnett's calculation of certain quantities A and B with the aid of Sonine's polynomials.
218. Eliakim Moore (1862-1932)
• He also studied infinite series of finite simple groups.
219. Irmgard Flügge-Lotz (1903-1974)
• The purpose of this book is to acquaint the reader with the problem of discontinuous control by presenting the essential phenomena in simple examples before guiding him to an understanding of systems of higher order.
220. Édouard Goursat (1858-1936)
• The Cauchy-Goursat theorem states the integral of a function round a simple closed contour is zero if the function is analytic inside the contour.
221. Carlos Benjamin de Lyra (1927-1974)
• From 1956 on he directed a weekly seminar on the subject covering the most important topics of the field as for instance: simple homotopy type, topological localization, homology of fibre spaces, cohomological operations, applications of cohomological operations, Postnikov systems, localization and applications.
222. Augustin Fresnel (1788-1827)
• It was a great chance for Fresnel to put his revolutionary work before the world and he was very confident of his theory since his mathematical deductions from the one simple hypothesis led to results which he had verified experimentally giving a highly accurate agreement between theory and experimental evidence.
223. Pierre-Louis Moreau de Maupertuis (1698-1759)
• These laws, so beautiful and so simple, are perhaps the only ones which the Creator and Organizer of things has established in matter in order to effect all the phenomena of the visible world ..
224. Endre Szemerédi (1940-)
• Of course quite often the proofs using only elementary methods are not simple because one may have to put together basic ingredients in extremely complicated and sophisticated ways.
225. Sigekatu Kuroda (1905-1972)
• Therefore, in formulating these systems, some special conditions to restrict the free application of logic are needed, for instance, simple or ramified type theory, introduced to logic first by Russell, or the restriction of the comprehension axiom of set theory.
226. Jacob Wolfowitz (1910-1981)
• It is also a handy introductory text because of its brief and simple formulations of problems and estimates.
227. Karl Reinhardt (1895-1941)
• The choice of material includes not only the integration of the ordinary simple functions, but contains also the derivation of the fundamental rules for manipulating integrals, such as the methods for introducing new variables and for integrating a product of two functions.
228. Emil Grosswald (1912-1989)
• He also wrote two papers which were published in 1950, the first being On a simple property of the derivatives of Legendre's polynomials while the second was Functions of bounded variation.
• The topics are: positive and negative numbers; zero; the unknown; surds; the kuttaka; indeterminate quadratic equations; simple equations; quadratic equations; equations with more than one unknown; quadratic equations with more than one unknown; operations with products of several unknowns; and the author and his work.
230. Emanuels Grinbergs (1911-1982)
• By 1954 he was allowed to lecture at the University of Latvia and in 1956 he defended a second thesis (to replace the one declared void by the authorities) Problems of analysis and synthesis of simple linear circuits.
231. Giuseppe Biancani (1566-1624)
• Before the work could be published, Biancani had to remove the description of Galileo's work on floating bodies, and replace it with a simple reference indicating where Galileo's theory could be found.
232. Willem 'sGravesande (1688-1742)
• the theory of matter, elementary mechanics, the five simple machines, Newton's laws of motion, gravity, central forces, hydrostatics, hydraulics, sound, and wave motion.
233. Hermann Grassmann (1809-1877)
• By this demonstration Grassmann also undermined the notion that language developed from an analytic to a synthetic structure through [combining simple words without changing their form to make new words].
234. Alicia Boole Stott (1860-1940)
• She then produced three-dimensional central cross-sections of all the six regular polytopes by purely Euclidean constructions and synthetic methods for the simple reason that she had never learned any analytic geometry.
235. Yves Rocard (1903-1992)
• It is assumed that the reader has some facility in mathematics and thus is familiar with the common vector operations, simple manipulations with complex variables, linear differential equations, and series expansions.
236. Pierre Fatou (1878-1929)
• I had during those years a simple and modest pupil, who was a mathematical genius.
237. Oscar Zariski (1899-1986)
• His use of the notions of integral independence, valuation rings, and regular local rings, in algebraic geometry proved particularly fruitful and led him to such high points as the resolution of singularities for threefolds in characteristic 0 in 1944, the clarification of the notion of simple point in 1947, and the theory of holomorphic functions on algebraic varieties over arbitrary ground fields.
238. Guido Fubini (1879-1943)
• In addition to the areas of analysis detailed above, he worked on the calculus of variations where he studied reducing Weierstrass's integral to a Lebesgue integral and also he worked on the expression of surface integrals in terms of two simple integrations.
239. François Budan (1761-1840)
• He did not appeal to the theory of finite differences or to the calculus of these coefficients, preferring to give them "by means of simple additions and subtractions".
240. Yakov Grigorevich Sinai (1935-)
• Sinai's work centres round the grand aim of deriving the basic physical laws which describe the behaviour of many particle systems as a direct consequence of simple rules governing the interaction of individual particles.
241. John Polkinghorne (1930-)
• In particular, the author gives a simple motivation for the complicated definition of the transformation used by the reviewer.
242. Jean-Louis Koszul (1921-2018)
• The first was Sur le troisieme nombre de Betti des espaces de groupes de Lie compacts Ⓣ in which he completed the proof that the third Betti number of a simple compact Lie group is one by studying certain of the exceptional groups.
243. Mario Fiorentini (1918-)
• However [',' E Sernesi, A simple article, in Commutative algebra and algebraic geometry, Ferrara (Dekker, New York, 1999), x-xiii.
244. Jacopo Riccati (1676-1754)
• His way of life was a very simple one, and he travelled very little.
245. Dimitrei D Stancu (1927-2014)
• In some of them, only the cases of 2 or 3 variables are worked out, in order to keep notations reasonably simple.
246. Sheila Power Tinney (1918-2010)
• It is shown that among the cubic Bravais lattices contained in this group the face and body centred ones correspond to a minimum of potential energy, but the simple cubic lattice to a maximum.
247. Virgil Snyder (1869-1950)
• Simple, forceful language is employed throughout, the theorems are models of clear expression and, when a paragraph is completed, its connection with the rest of the subject is apparent.
248. André Weil (1906-1998)
• He didn't want to return to France to avoid being forced into the army, but it was not a simple matter to escape from the war in Europe at this time.
249. Vilhelm Bjerknes (1862-1951)
• The next step forward in the mathematical approach was due to Richardson in 1922 when he reduced the complicated equations produced by Bjerknes's Bergen School to long series of simple arithmetic operations.
250. Fritz Ursell (1923-2012)
• A critical estimate is only possible when the meteorological conditions are sufficiently simple, but in one selected example it appears that the velocity of propagation is within 5% of the value prescribed by hydrodynamical theory.
• Vladimirov was assigned to assist Leonid Vitalevich Kantorovich calculating critical parameters of certain simple nuclear systems.
252. Edwin Spanier (1921-1996)
• No matter how complex the subject, at the end the reader feels the theorems are the right ones, the hypotheses natural, and the methods as simple as possible.
• For the present it is not known how to obtain simple and geometrically clear theorems on the distribution of the lattice points on the sphere by other methods.
254. Diederik Korteweg (1848-1941)
• The reason is simple, he did not have the necessary qualifications to enter a university even though he had already begun to publish papers while he worked as a school teacher.
255. Norman Ferrers (1829-1903)
• is so simple and instructive, that I am sure every logician will be delighted to meet with it here or elsewhere.
256. George Mackey (1916-2006)
• Of course, in order to avoid excessive pedantry I left many simple arguments to the imagination of the student - especially after the first few chapters.
257. Jean Dieudonné (1906-1992)
• Well the Bourbaki method is very simple-we cut the threads.
258. George Boole (1815-1864)
• Boole approached logic in a new way reducing it to a simple algebra, incorporating logic into mathematics.
259. André Bloch (1893-1948)
• Although there is a simple classification of Riemann surfaces (hyperbolic, elliptic, parabolic), any specific Riemann surface can be a nasty, brutish, intricate object.
260. Michelangelo Ricci (1619-1682)
• However, this is not quite as simple as it might at first appear since, when the Pope informed him that he would be made a cardinal, Ricci politely and humbly replied to the Pope in a long letter refusing to accept the position:- .
261. Jeremiah Horrocks (1618-1641)
• Horrocks purchased a simple telescope which he set up to project an image of the sun onto a graduated circle six inches in diameter.
262. Dimitri Fedorovich Egorov (1869-1931)
• In this paper, in addition to the independent, very elegant and simple solution of the problem proposed, the originality and logical rigour of the exposition of the basic general geometrical principles deserve special mention, as does also the very successful working out of many details.
263. Wolfgang Pauli (1900-1958)
• he had a genius of fastening on some one point which could be made simple, and so presented was seen at once to be important.
264. Solomon Grigoryevich Mikhlin (1908-1990)
• Its essence relies on the possibility of substituting the kernel of the integral operator by its variational-difference approximation, so that the resolvent of the new kernel can be expressed by simple recurrence formulae.
265. Edwin Olds (1898-1961)
• Finally a third test procedure is developed by using the Neyman-Pearson Lemma for testing simple hypotheses.
266. Maria Agnesi (1718-1799)
• She is a girl of about twenty years of age, neither ugly nor pretty, with a very simple and very sweet manner.
267. Jérôme Franel (1859-1939)
• That the relationship between a series of fractions so simple can be connected to a mathematical hypothesis so profound with such economy is the mark of a teacher of mathematics of the very highest order.
268. Tommaso Ceva (1648-1737)
• This academy was founded in Rome in 1690 to promote a more natural, simple poetic style.
269. David Spence (1926-2003)
• The second extension appeared in his paper Some simple results for two-dimensional jet-flap aerofoils which was also published in 1958.
270. Joseph Raabe (1801-1859)
• This test, which is an extension of d'Alembert's ratio test, often succeeds for series in which the terms contain factorials, where d'Alembert's simple ratio test is inconclusive.
271. Simon Stevin (1548-1620)
• Before presenting the numerical tables, Stevin gave rules for simple and compound interest and also gave many examples of their use.
272. Stanisaw wierczkowski (1932-2015)
• Although the discipline was congenial, its methods were not! He writes [',' S Świerczkowski, Looking Astern autobiography.','1]: "Mathematically the work was simple.
273. Georges Buffon (1707-1788)
• Voltaire did not appreciate his style, and d'Alembert called him "the great phrasemonger." According to the writer J-F Marmontel, Buffon had to put up with snubs from the mathematicians, chemists, and astronomers, while the naturalists themselves gave him little support and some even reproached him for writing ostentatiously in a subject that required a simple and natural style.
274. Niels Abel (1802-1829)
• It was a monument resplendent in its simple lines - the main theorem from his Paris memoir, formulated in few words.
275. Wilhelm Lexis (1837-1914)
• It posed the question of whether an empirical index of dispersion is consistent with the assumption that sex is governed by a simple chance mechanism.
276. Oliver Byrne (1810-1880)
• He published A Treatise on Diophantine Algebra in 1831 but he referred to this work as "A Treatise on Algebra" in the 35-page pamphlet A Short Practical Treatise on Spherical Trigonometry: Containing a Few Simple Rules, by which the Great Difficulties to be Encountered by the Student in this Branch of Mathematics are Effectually Obviated which he published in 1835.
• There is no simple relation between the length of these two types of years hence they were to be calculated as exactly as possible.
278. Paul Cohen (1934-2007)
• He made mathematics look simple and unified.
279. Avicenna (980-1037)
• In his work Mi'yar al-'aqul ibn Sina defines simple machines and combinations of them which involve rollers, levers, windlasses, pulleys, and many others.
280. Brian Hartley (1939-1994)
• Although in a different area of group theory from Hartley, John Thompson was also at Chicago and had just gained world fame with his 1963 paper, written with Walter Feit, proving all nonabelian finite simple groups were of even order.
281. Archimedes (287 BC-212 BC)
• It is not possible to find in all geometry more difficult and intricate questions, or more simple and lucid explanations.
• The exercises are deliberately not "graded" - after all the problems we meet in mathematical "real life" do not come in order of difficulty; some of them are very simple illustrative examples; others are in the nature of tutorial problems for a conventional course, while others are quite difficult results.
283. Frank Cole (1861-1926)
• He published The linear functions of a complex variable in the Annals of Mathematics in 1890 then, between the years 1891 to 1893, he found the complete list of simple groups with orders between 200 and 600.
284. William Whewell (1794-1866)
• It secures me a comfortable establishment for life at least so long as my life is a simple one.
285. Agnes Mary Clerke (1842-1907)
• It has thus become practicable to describe in simple language the most essential parts of recent astronomical discoveries.
• Clearly this simple device was not understood at the time.
287. Evgeny Sergeevich Lyapin (1914-2005)
• His classes were always full of deep concepts and new ideas expressed in a simple, rigorous, and crisp form.
288. Henri Poincaré (1854-1912)
• remainder of the thesis is a little confused and shows that the author was still unable to express his ideas in a clear and simple manner.
289. Leone Burton (1936-2007)
• A simple grouping of these words and phrases characterizes Leone for us very effectively: (i) Leone was a sensitive and caring friend, good company, generous, kind, warm, honest, wise and supportive.
290. Aleksei Krylov (1863-1945)
• is to present simple methods of composition of the secular equation in the developed form, after which, its solution, i.e.
291. Robert Fricke (1861-1930)
• Fricke's long experience with the latter subject made it easy for him to give a simple authoritative exposition of those portions of it which suffice for the transcendental solutions of equations of low degrees.
292. Sergei Novikov (1938-)
• simple, elegant and natural.
293. Frank Harary (1921-2005)
• As a rule the theory is presented as a sequence of simple theorems, each with a clear and precise proof.
294. Bent Christiansen (1921-1996)
• Yet his great integrity led him to be intolerant of injustice, of those who were rude, self-seeking, inefficient and not disposed to think, and of those who peddled simple solutions to complex problems.
295. Giuseppe Veronese (1854-1917)
• He illustrated the fact that difficulties arose when a simple surface in high dimension was projected onto 3-space.
296. Thomas Hirst (1830-1892)
• Yet with all his aloofness of manner he could be very simple, very patient, and extremely kind.
297. Athanase Dupré (1808-1869)
• In 1866 Athanase and Paul Dupre jointly published the article On the law of the union of simple substances, and on attractions at small distances.
298. Witold Hurewicz (1904-1956)
• In this book it has been the aim of the authors to give a connected and simple account of the most essential parts of dimension theory.
299. Henry More (1614-1687)
• More does not deny this fact which any simple experiment will verify, but he claimed that the motion of the second ball is from an internal property of its own, awakened by the impact of the first ball.
300. Yozo Matsushima (1921-1983)
• Zassenhaus had conjectured that every semisimple Lie algebra L over a field of prime characteristic, with [L, L] = L, is the direct sum of simple ideal and Matsushima was able to construct a counterexample.
301. Charles-François Sturm (1803-1855)
• Sturm achieved fame with his paper which, using ideas of Fourier, gave a simple solution.
302. Leopold Löwenheim (1878-1957)
• Simple devices, some of which may be useful in investigating the intuitionistic validity of propositions.
303. Dmitry Aleksandrovich Grave (1863-1939)
• He could explain deep mathematical ideas in a remarkably clear and simple way, and this talent led to a large number of students attending his lectures.
304. Tommaso Boggio (1877-1963)
• He was a modest man, with simple ways and needs, yet he was strong and decent, friendly towards his colleagues and kind to his students.
305. George E Andrews (1938-)
• His list of publications continued to grow with the paper A simple proof of Jacobi's triple product identity (1965) appearing before three papers were published in the following year based on the work of his doctoral thesis on mock theta functions and partitions.
306. David Rittenhouse (1732-1796)
• He published A method of finding the sum of several powers of the sines in 1793 and in a paper of 12 August 1795 he gave an expansion of log10 n, where n a positive number, as a simple continued fraction and then computed log10 99 to nine decimal places.
307. Bernard Lamy (1640-1715)
• The fourth part examines style in a larger sense: imagination, memory, and judgment as the basis of good style; the three levels of style; the lofty, the simple, and the middle; and the differences between styles of an orator or preacher, a historian, and a poet.
308. Edmund Landau (1877-1938)
• Written with the greatest care, Landau's books are characterised by argumentation which is complete, and as simple as possible.
309. John Maynard Keynes (1883-1946)
• his axioms are good; they are simple and few and by the aid of the symbolism he deduces the whole subject from them by rigid reasoning.
310. Brooke Benjamin (1929-1995)
• a careful and thorough analysis of the flows over a simple harmonic wavy boundary which is either (a) rigid (b) a flexible solid or (c) completely mobile, as if it were the interface with a second fluid.
311. George Atwood (1745-1807)
• Atwood is best known for a work A Treatise on the Rectilinear Motion and Rotation of Bodies (published by Cambridge University Press in 1784) which is a textbook on Newtonian mechanics describing impact and simple harmonic motion.
312. Gaston Darboux (1842-1917)
• are as pure as they are simple and beautiful.
313. Eugenio Levi (1883-1917)
• The work of E E Levi almost always deal with issues of fundamental importance: he was not discouraged by the difficulties, even major ones, encountered by other mathematicians, and with a more profound analysis, often very simple and ingenious, was able to clarify and overcome them.
314. Carlo Bonferroni (1892-1960)
• To indicate the interest in this area we note that an generalisation of Bonferroni's inequalities by S Holm in the paper A simple sequentially rejective multiple test procedure published in the Scandinavian Journal of Statistics 6 (1979), 65-70, has received around 2000 citations.
315. Andrew Wiles (1953-)
• it was so indescribably beautiful, it was so simple and so elegant, and I just stared in disbelief for twenty minutes, then during the day I walked round the department.
316. Henry Scheffé (1907-1977)
• For models possessing this property, it turns out that both testing and estimation become particularly simple.
317. Walter Shewhart (1891-1967)
• About a third of that page was given over to a simple diagram which we would all recognize today as a schematic control chart.
318. Guido Stampacchia (1922-1978)
• The personality of Stampacchia was both strong and simple, open and helpful.
319. Gottfried Köthe (1905-1989)
• Linear functionals are of course studied intensively here; while the standard simple Banach spaces ..
320. Martin Gardner (1914-2010)
• I think of myself as like a person who loves classical music, but whose talents never advanced beyond playing simple tunes on a musical saw.
321. Olli Lehto (1925-)
• It led in due time to a simple solution of the geometric problem of moduli, and there are encouraging signs of a fruitful theory in several dimensions.
322. Paul Bachmann (1837-1920)
• The author is usually scrupulous in crediting even simple and commonly current results to their original publisher.
323. Udita Narayana Singh (1920-1989)
• We have given a simple overview of Udita Narayana Singh's career, but a detailed account is given in [',' B S Yadav, U N Singh: His life and Work, Indian Journal of Mathematics 33 (1991), i-xxiv.','1].
324. Gaspard de Prony (1755-1839)
• The present generation would never have witnessed the end of this monumental work if M de Prony had not had the fortunate idea of applying the powerful method of division of labour, conceiving methods to reduce the long and laborious part of the production of the tables to simple additions and subtractions..
325. Félix Savart (1791-1841)
• For example, he would use, in combination, wheels with numbers of teeth which bore a simple relationship to each other.
326. Gilbert Hunt (1916-2008)
• "Two maximal abelian subgroups of a compact connected Lie group G are conjugate within G." I present a simple metric proof.
327. Alonzo Church (1903-1995)
• He published A formulation of the simple theory of types in 1940 in which he attempted to give a system related to that of Whitehead and Russell's Principia Mathematica which was designed to avoid the paradoxes of naive set theory.
328. Victor Amédée Lebesgue (1791-1875)
• Very simple manners, of a character full of frankness, and independence, virtuous at every test, never seeking the opportunities of putting himself to the fore, Lebesgue lived a very solitary life, constantly occupied with his favourite studies.
329. Ernest Esclangon (1876-1954)
• The method, so simple in principle, was not made a practical success without several years of experimenting.
330. Robert Recorde (1510-1558)
• He therefore wrote all his books in English and, in addition, he tried to use clear and simple expressions.
331. Hans Wussing (1927-2011)
• the lively, clear, and simple style nicely conveys its main message: that mathematics is a human pursuit whose aims and motivations can be understood by everyone.
332. Euphemia Lofton Haynes (1890-1980)
• I give and devise unto my son, Joseph William Lofton, and unto my daughter, Martha Euphemia Haynes, in fee simple, as tenants in common, Lots Twenty Three (23) and Twenty Four (24), in Square One Hundred and ninety six (196), improved by premises No.
333. Hermann Weyl (1885-1955)
• There I attended his lectures on the Elie Cartan calculus of differential forms and their application to electromagnetism - eloquent, simple, full of insights.
334. Otto Schreier (1901-1929)
• His first paper in 1924 On the groups AaBb = 1 gave a simple algebraic proof of a theorem on knot groups, which generalised a theorem given by Max Dehn ten years earlier that the trefoil knot and its mirror image are not equivalent.
335. Beno Eckmann (1917-2008)
• Peter Hilton, who had been a personal friend of Eckmann's for many years spoke in detail of Eckmann's research in topology: continuous solutions of systems of linear equations, a group-theoretical proof of the Hurwitz-Radon theorem, complexes with operators, spaces with means, simple homotopy type.
• Difficult modern theories become quite clear and simple in his exposition.
337. R A Fisher (1890-1962)
• In fact the reasons for the feud were not nearly as simple as those usually given.
338. Donald Eperson (1904-2001)
• This was probably because they were a kind of word puzzle whose solution depended upon finding words with simple rhythms that fitted into a musical framework of pentameters and hexameters.
339. William Threlfall (1888-1949)
• In our conception of space a simple-minded idea of continuity comes before everything else.
340. Robert Carmichael (1879-1967)
• This simple and logical account will serve a useful purpose by showing what assumptions we are in the habit of making, and wherein these admit of modification without contradicting the evidence of our senses.
341. Attia Ashour (1924-2017)
• Simple explanations are suggested for some known features of micropulsations, and for some well-known phenomena of magnetic disturbance, including Sangster's rotating disturbance vector.
342. John Semple (1904-1985)
• Projective geometry is a subject that lends itself naturally to algebraic treatment, and we have had no hesitation in developing it in this way - both because to do so affords a simple means of giving mathematical precision to intuitive geometrical concepts and arguments, and also because the extent to which algebra is now used in almost all branches of mathematics makes it reasonable to assume that the reader already possesses a working knowledge of its methods.
343. André Lichnerowicz (1915-1998)
• Apart from its intrinsic merits, not the least of which is its simple and clear style, the book therefore provides a good introduction to the works of Cartan ..
344. Hans Hahn (1879-1934)
• He wrote papers on the theory of curves including one which gave a rigorous proof of the Jordan's theorem for simple closed polygons which he based on Veblen's geometrical axioms.
345. Ernst Öpik (1893-1985)
• He steered me towards planets and satellites, and taught me to use simple physical principles in place of more obscure mathematical approaches.
346. Edwin Pitman (1897-1993)
• Using the familiar fact that two simple linear combinations of two normally correlated variates are independently and normally distributed, an exact test is derived for the significance of the ratio of sample variances in samples from a normal bivariate population.
347. Bibhutibhushan Datta (1888-1958)
• He lived a simple itinerant life over the following years, drifting from place to place.
348. Nathan Jacobson (1910-1999)
• Florie did not give up mathematics for she was a joint author with her husband on their 1949 paper Classification and representation of semi-simple Jordan algebras.
349. Carl Neumann (1832-1925)
• with one and the same relatively simple mathematical expression." He noted with satisfaction that Neumann had required many hypotheses to reach a similar result.
350. Pierre Humbert (1891-1953)
• Moreover, he was unsatisfied with the simple juxtaposition of knowledge and religious faith.
351. Enzo Martinelli (1911-1999)
• For example, in order to be able to provide simple and interesting examples, I soon adopted cellular cross-links, while postponing the justification of their use until later.
352. Paul Guldin (1577-1643)
• A rotation is a simple and perfectly circular motion, around a fixed centre, or an unmoved axis, which is called the 'axis of rotation', turning around either a point, or a line, or a plane surface, which, almost as leaving a trace behind it, describes or generates a circular quantity, either a line, or a surface, or a body.
• he discussed for instance the difference between the broader meaning of the word element (in which any proposition leading to another may be said to be an element of it) and the stricter meaning of something simple and fundamental standing to consequences drawn from it in the relation of a principle, which is capable of being universally applied and enters into the proof of all manner of propositions.
354. Karl Sundman (1873-1949)
• Its adaptation for these other aims will be relatively simple to achieve.
355. Arthur Schönflies (1853-1928)
• He introduced the topological notions of accessible point, closed curve and simple closed curve.
356. Sharaf al-Din al-Tusi (about 1135-1213)
• a simple wooden rod with graduated markings but without sights.
357. William Berwick (1888-1944)
• Berwick was an algebraist who worked on the problem of computing an integral basis for the algebraic integers in a simple algebraic extension of the rationals.
358. James Clerk Maxwell (1831-1879)
• Maxwell showed that a few relatively simple mathematical equations could express the behaviour of electric and magnetic fields and their interrelation.
• He discovered many propositions himself, and instructed his successors in the principles underlying many others, his method of attacking problems had greater generality in some cases and was more in the nature of simple inspection and observation in other cases.
360. Rudolf Kalman (1930-)
• Randomness does, and to capture it better he proposes a new definition: random is not uniquely determined by simple classical rules.
361. Gerbert of Aurillac (946-1003)
• So astonishing was his skill, that the simple folk of his day, in sheer bewilderment, accepted without question the belief that his knowledge was universal ..
362. Heisuke Hironaka (1931-)
• Some fundamental theorems in the theory of several complex variables and of the geometry of complex manifolds are proved in a simple but rigorous form.
363. Lothar Collatz (1910-1990)
• The Collatz problem is simple to state.
364. Erland Bring (1736-1798)
• The coefficient of y2 is rather simple, m2 - mb - 2n + 3a, but the next coefficient has degree three and nine terms.
365. Johann Franz Encke (1791-1865)
• They bear strong and uniform testimony to his eminent frankness and truthfulness; his labours, they say, were incessant, his recreations few; he was simple in his manners, and in all his habits temperate.
366. Dorothea Beale (1831-1906)
• She also suggests that girls aged sixteen to eighteen should study advanced pure and applied mathematics, which is quite different to the simple arithmetic previously thought acceptable.
367. Arnold Sommerfeld (1868-1951)
• In the evenings, when the simple meal was cooked, the dishes were washed, the weather and snow properly discussed, the talk invariably turned to mathematical physics, and this was the occasion for the receptive students to learn the master's inner thoughts.
368. Benjamin Moiseiwitsch (1927-2016)
• It begins with a straightforward account, accompanied by simple examples of a variety of integral equations and the methods of their solution.
369. Shreeram Shankar Abhyankar (1930-2012)
• He broke this rule the first time when he used the classification of finite simple groups.
370. Jean-Baptiste Bélanger (1790-1874)
• Belanger provided a stepwise integration of this equation in the simple case of the horizontal aqueduct that had been built recently to bring the waters of the Ourcq River into Paris.
371. Urbain Le Verrier (1811-1877)
• One should have seen M Lescarbault, so small, so simple, so modest, and so timid, in order to understand the emotion with which he was seized, when Le Verrier, from his great height, and with that blunt intonation which he can command, thus addressed him: "It is then you, Sir, who pretend to have observed the intra-Mercurial planet, and who have committed the grave offence of keeping your observation secret for nine months.
372. Rajeev Motwani (1962-2009)
• His lectures were so perfectly crafted, from the progression of describing a simple approach providing the intuition to generalizing it, to doing an impeccable formal analysis, to the perfect board technique, that I left every lecture excited about a new powerful topic that I have just learned and understood.
373. Krystyna Kuperberg (1944-)
• The paper is an important contribution to the theory of dynamical systems, and it solves in a simple but elegant way the long-standing Seifert conjecture.
374. Leslie Woods (1922-2007)
• If F is harmonic or is a solution to Poisson's equation, it may have singular points in the field or on the boundary at which it (a) has finite values, but has infinite derivatives, (b) has logarithmic infinities, or (c) has simple discontinuities.
375. Albert Einstein (1879-1955)
• said hardly anything beyond presenting a very simple objection to the probability interpretation ..
376. John Aitchison (1926-2016)
• Recognition that the study of compositions must satisfy simple principles has led recently to the advocacy of new forms of analysis of compositional data.
377. Roberto Frucht (1906-1997)
• Our object in this note is to construct a new and simple operation on two graphs G1 and G2, called their corona, with the property that the group of the new graph is in general isomorphic with the wreath product of the groups of G1 and G2.
378. Sixto Ríos (1913-2008)
• One day Rios placed on the chalkboard, before Barinaga arrived, an easy and simple solution he had found to one of the difficult problems.
379. Hanno Rund (1925-1993)
• The theoretical physicist is shown how the theory of non-homogeneous single integral problems give rise to relativistic particle mechanics, in which the special invariant Hamiltonian function permits a particularly simple method of quantization, from which the relativistic wave equations (Dirac, Kemmer, etc.) may be obtained directly.
380. Gordon Whyburn (1904-1969)
• The theory was based on cyclic elements, that is a region C such that any two points of C are contained in a simple closed curve of C.
381. Josip Plemelj (1873-1967)
• Another contribution that we should mention was Plemelj's simple proof of the n = 5 case of Fermat's Last Theorem which he published in 1912.
382. Charles Chree (1860-1928)
• etc.; there are thus enormous obvious differences between the simple mathematical problems of my papers and the actual state of matters on the earth; and if there is any resemblance between the results in the papers and actualities, it may quite as likely be a pure accident as not.
383. Lejeune Dirichlet (1805-1859)
• His proofs characteristically started with surprisingly simple observations, followed by extremely sharp analysis of the remaining problem.
384. James Alexander (1888-1971)
• He returned to Princeton where he submitted his dissertation Functions which map the interior of the unit circle upon simple regions and, in 1915, was awarded his Ph.D.
385. Dimitrie Pompeiu (1873-1954)
• This simple remark has led to many interesting problems in analysis known as the problem of Pompeiu.
386. Chukwuka Okonjo (1928-)
• The concepts of growth, population and simple growth; III.
387. Hugh Dowker (1912-1982)
• This first step is here reduced to a simple algorithm suitable for computer use.
388. Thomas Flett (1923-1976)
• Mean value theorems of differential and integral calculus provide a relatively simple, but very powerful tool of mathematical analysis suitable for solving many diverse problems.
389. Alfred Goldie (1920-2005)
• In fact Goldie's first paper in this area Decompositions of semi-simple rings (1956) made an immediate impact since Jacobson included one of Goldie's theorems in his classic monograph Structure of Rings of 1956, acknowledging that it had been communicated by Goldie.
390. Pieter Hendrik Schoute (1846-1913)
• This paper may be regarded as a continuation of [On the Angles of the Regular Polytopes of Four-Dimensional Space]; it is concerned with polytopes of S4 characterized by the property of admitting one kind of vertex and one length of edge, which polytopes will be called "semiregular." These polytopes, corresponding to the Archimedian semiregular polyhedra of ordinary space, have been deduced from the regular ones by very simple geometrical operations called "expansions" and "contractions" in a masterly memoir of A Boole Stott; they will be indicated here by the symbols introduced in that memoir.
391. Guido Ascoli (1887-1957)
• Ascoli does not limit himself to dryly following the guidelines for university courses, but attempts to "discern in the admirable edifice of concepts and results that small bit that is essential in the very first study from what would otherwise be destined to remain a lifeless and inexpressive knowledge; to present to young people a simple and harmonic organism of fundamental ideas that contribute effectively towards their intellectual formation" (Preface).
392. Ron Book (1937-1997)
• [He] did not like large towns, he did not like the sophistication of the traditional elite, he liked simple people working day after day to grow crops.
393. Gustav Elfving (1908-1984)
• The results had a simple geometric interpretation and were computationally easy before computer technology was highly developed.
394. Roger Cotes (1682-1716)
• a new sort of construction in geometry which appear to me very easy, simple and general.
395. William Jones (1675-1749)
• An obvious question would be: why was his father not named 'Jones'? The answer is simple, he was named Jones since this is the English version of the Welsh Sion.
396. René Eugène Gateaux (1889-1914)
• Gateaux's body was buried near the St Anne Chapel in Rouvroy, a simple cross without inscription marking the place.
397. Charles Graves (1812-1899)
• This is a simple error arising from the fact that, as Bishop of Limerick, Graves would sign himself Charles Limerick or C Limerick.
398. Gilbert Bliss (1876-1951)
• The book starts with a typical simple problem, the non-parametric problem in 3-space with fixed end-points.
399. Andre-Louis Cholesky (1875-1918)
• The problem of adjusting the grid greatly worried officers in the Geographical Service, who were anxious to find a method which was simple, fast and precise.
400. Abigail Thompson (1958-)
• Surprisingly, any closed orientable 3-manifold can be split into two simple pieces, called handlebodies.
401. Heinz Prüfer (1896-1934)
• In it Prufer gives a very simple proof of an expansion theorem for a particular second order linear homogeneous differential equation coming from the oscillation and evolution theorem.
402. Rudolf Peierls (1907-1995)
• Surprises in theoretical physics are either theoretical results in disagreement with naive physical intuition, or simple solutions to apparently unmanageable problems.
403. Alfred Pringsheim (1850-1941)
• He gave a very simple proof of Cauchy's integral theorem.
404. Girolamo Cardano (1501-1576)
• In the same year, Cardan's first two mathematical books were published, the second The Practice of Arithmetic and Simple Mensuration was a sign of greater things to come.
405. Petre Sergescu (1893-1954)
• They were exceedingly hospitable to friends, and it was my privilege to enjoy their simple but gallant welcome when I visited them in their little home in the rue Daubenton no.
406. Grace Alele-Williams (1932-)
• Teaching the teachers mathematics is a relatively simple task but changing their attitude and practice is harder.
407. Judita Cofman (1936-2001)
• There she continued her work on finite geometries and published papers such as: On a characterization of finite desarguesian projective planes (1966); Double transitivity in finite affine planes (1967); Triple transitivity in finite Mobius planes (1967); Translations in finite Mobius planes (1968); On Baer involutions of finite projective planes (1970); and Simple groups and Mobius planes of even order.
408. al-Kashi (1390-1450)
• Al-Kashi can no longer be considered as the inventor of decimal fractions; it remains nonetheless, that in his exposition the mathematician, far from being a simple compiler, went one step beyond al-Samawal and represents an important dimension in the history of decimal fractions.
409. Samarendra Nath Roy (1906-1964)
• He was a man who practiced simple living and high thinking.
410. Mikhail Egorovich Vashchenko-Zakharchenko (1825-1912)
• That a man so well acquainted with modern investigations of the principles of the science of space as Mr Vashchenko-Zakharchenko (a bibliography of this subject is also appended to the volume) should prove such an ardent adherent of Euclid, pure and simple, for the schools, is a truly remarkable fact.
411. Lazarus Fuchs (1833-1902)
• They lived in a great number of different houses, forced to live a very simple and modest life-style since, especially in the first few years, they lived off the income that Fuchs made through giving private lessons.
412. Charles Weatherburn (1884-1974)
• I cannot agree with those who would make nature more akin to the complex than to the simple.
413. Charles Coulson (1910-1974)
• From this simple experimental fact has developed the whole science of electrostatics, that is the properties of electricity at rest.
414. Louis de Branges (1932-)
• The proof is now available in a form that can be verified by any experienced mathematician as analysis that is "hard" in the original aesthetic sense of Hardy - simple algebraic manipulations linked by difficult inequalities.
415. Karl Aubert (1924-1990)
• The most important aspect of Aubert's research was the basic ideas, the simple and general concepts, that he introduced.
416. Duilio Gigli (1878-1933)
• How many of the combinations of n integers from 1 to m have the same sum s, and how many have a sum ≤ L? With the help of a generating function, the author solves these problems in a simple way.
417. Wilhelm Meyer (1856-1934)
• gave lectures discussing the essential aspects of mathematical research in the spirit of Klein's Erlangen programme, and gave lectures discussing the essential aspects of mathematical research in the spirit of the time and emphasizing the importance of simple algebraic identities, the symmetries of group theory, and transformation principles as a source of geometric theorems.
418. William Wager Cooper (1914-2012)
• In sum, most of the features of linear programming are illuminated by a deceptively simple example.
419. Derrick Norman Lehmer (1867-1938)
• The following course is intended to give, in as simple a way as possible, the essentials of synthetic projective geometry.
420. Daniel Bernoulli (1700-1782)
• While in St Petersburg he made one of his most famous discoveries when he defined the simple nodes and the frequencies of oscillation of a system.
• Based on his observations of solstices and equinoxes, Ptolemy found the lengths of the seasons and, based on these, he proposed a simple model for the sun which was a circular motion of uniform angular velocity, but the earth was not at the centre of the circle but at a distance called the eccentricity from this centre.
422. John Backus (1924-2007)
• I remember doing relatively simple calculations to get a few points on a curve for an amplifier.
423. Giacinto Morera (1856-1907)
• He developed the study of the harmonic functions, applying results due to Pizzetti, finding a simple expression for the inner and outer gravitational field of an ellipsoid, solving the Dirichlet problem.
424. Elizabeth Fennema (1928-)
• However, things were not so simple.
425. Pietro Cataldi (1548-1626)
• We note that he does not use what are called today 'simple continued fractions' and his method will always give a continued fraction for a square root which has period 1.
426. Carl Johannes Thomae (1840-1921)
• The rules of chess are arbitrary; the system of rules for arithmetic is such that by means of simple axioms the numbers can be related to intuitive manifolds, so that they are of essential service in the knowledge of nature.
427. Joan Sylvia Lyttle Birman (1927-)
• A third will be the unifying principles provided by representations of simple Lie algebras and their universal enveloping algebras.
428. Roger Godement (1921-2016)
• Resume de lecons Ⓣ (1959); Cours d'Algebre Ⓣ (1963); (with Herve Jacquet) Zeta functions of simple algebras Ⓣ (1972); Introduction a la theorie des groupes de Lie Ⓣ (1982); Analyse Mathematique I.
429. Georg Simon Ohm (1789-1854)
• This may have no simple explanation but rather be the result of a number of different contributary factors.
430. Paul Mansion (1844-1919)
• studied, by a particularly simple original method, the multiplication and transformation of elliptic functions.
431. James Wiegold (1934-2009)
• In the first of these two papers he proved that a group G has the property that every normal subgroup is a direct factor if and only if G is a restricted direct product of simple groups, while the second paper extended the results of his earlier paper Nilpotent products of groups with amalgamations.
432. Félix Savary (1797-1841)
• Although this might appear to be a fairly simple consequence of Newton's law of gravitation, nevertheless it was important for it was the first verification of the laws for objects outside the solar system.
433. John Bell (1928-1990)
• As a simple example, the state-vector above might apply to an ensemble of many systems, but in addition a hidden variable for each system might say what the actual value of sz might be.
434. Hyman Bass (1932-)
• The (J H C) Whitehead torsion, introduced in order to study the topological notion of simple homotopy type, leads to the groups K1.
435. Georgios Remoundos (1878-1928)
• He considered his teaching work, according to his own words, "as a sacred duty of utmost importance." Cyparissos Stephanos, who taught Remoundos said that, "Remoundos is so clear and simple in his teaching, and so effective that one can say that he opens the head of the student, puts the mathematics in, then locks the head and takes the key, and leaves reassured!" .
436. Anneli Lax (1922-1999)
• When I think of that day I carry in my heart many of the things I loved about Anneli - her quiet determination, her openness and acceptance of the weaknesses of others and her joy in simple pleasures.
437. Hideo Tanaka (1938-2012)
• Possibility data analysis offers not only the general methodology to analyze and model the uncertainty in operations research but also the common and simple way to solve the problems.
438. Heraclides (387 BC-312 BC)
• It is an unconvincing article and it seems to only repeat van der Waerden's earlier hypothesis without making any attempt to counter the rather simple and totally convincing argument by Neugebauer.
439. Cyrus Colton MacDuffee (1895-1961)
• He continued to publish on rings and algebras with papers such as A correspondence between matrices and quadratic ideals (1927), An introduction to the theory of ideals in linear associative algebras (1929), The discriminant matrix of a semi-simple algebra (1931), and Matrices with elements in a principal ideal ring (1933).
440. Oskar Bolza (1857-1942)
• Papers which appeared in the Transactions of the American Mathematical Society over the next few years were: New proof of a theorem of Osgood's in the calculus of variations (1901); Proof of the sufficiency of Jacobi's condition for a permanent sign of the second variation in the so-called isoperimetric problems (1902); Weierstrass' theorem and Kneser's theorem on transversals for the most general case of an extremum of a simple definite integral (1906); and Existence proof for a field of extremals tangent to a given curve (1907).
441. John Pople (1925-2004)
• is devoted to theoretical principles and experimental methods and the authors have achieved a comprehensive and yet simple account of what can be a difficult subject.
• In it he presented a very simple algebraic approach but was aware of its limitations writing:- .
443. Phyllis Nicolson (1917-1968)
• Crank and Nicolson's method, which is numerically stable, requires the solution of a very simple system of linear equations (a tridiagonal system) at each time level.
444. John Dougall (1867-1960)
• By regarding Q as a 4-sphere in complex Euclidean 5-space, and making some projections, he relates this to a simple theorem of plane geometry: .
445. Alan Turing (1912-1954)
• In one sense 'decidability' was a simple question, namely given a mathematical proposition could one find an algorithm which would decide if the proposition was true of false.
446. Harald Cramér (1893-1985)
• ','1] sums up Cramer's contribution with simple but effective words:- .
447. Klaus Fuchs (1911-1988)
• For the symmetric group on n symbols, there is a procedure for constructing the simple matrix representation corresponding to a given partition of n [cf.
448. Annibale Giordano (1769-1835)
• Mathematics being of this kind, is not in effect, having the development of simple ideas constituting the ideas of different magnitudes we know, and of some of our primitive conventions above them.
449. Kunihiko Kodaira (1915-1997)
• Thus, Cauchy's integral formula is first proved in a topologically simple case from which the author deduces the basic properties of holomorphic functions.
• It was not a simple modification that al-Farisi made.
451. Louis Antoine (1888-1971)
• Antoine was trying to prove a three-dimensional analogue of the Jordan-Schonflies theorem, which says that, given a simple closed curve in the plane, there exists a homeomorphism of the plane that takes the curve into the standard circle.
452. Thoralf Skolem (1887-1963)
• It characterizes the automorphisms of simple algebras and was later rediscovered by Emmy Noether.
453. Barnabé Brisson (1777-1828)
• [They] applied descriptive geometry to the actual geography of France [discovering] a way to find the lowest points in the watersheds between basins by a simple examination of existing topographical maps, which lacked contour lines and all but a few isolated points of altitude.
454. William Clifford (1845-1879)
• If you can say a few more words about my husband I would love it - how brilliant he was, how witty and what an adorable nature he had: he was so gay and simple and light-hearted, and had an indescribable charm.
455. Friedrich Engel (1861-1941)
• But, now, Lie decided to tackle a major piece on transformation groups, which was certainly intended to be much more than a simple introduction to the elements of the theory.
456. Reinhold Baer (1902-1979)
• Baer also had a very positive effect on the development of the Mathematics Department: in particular he was responsible for Michio Suzuki coming to Illinois - a crucial event that led to the Department becoming a centre of research in finite simple group theory.
457. Giovanni Poleni (1683-1761)
• Poleni actually built this machine which was reportedly very simple and easy to operate; but when he heard of another machine presented to the Emperor by the Viennese mechanician Brauer, he destroyed his own and never rebuilt it.
• Peter's appointment at Rutgers University was not a simple move of a professor from one institution to another.
459. Gerard Murphy (1948-2006)
• This association helps in the study of Lie ideals, and is especially useful for studying simple algebras.
460. Wilhelm Fiedler (1832-1912)
• Fiedler never mentions Cremona in his paper, but in a letter to Cremona, at the beginning of 1873, he praises his book and the simple way in which Cremona introduces the topics.
461. Phillip Griffiths (1938-)
• Some of the author's most enduring results come from simple such calculations which show how different higher-dimensional variations of cycles or Hodge structures are, often referred to as Griffiths transversality.
• The powerful, yet simple, Platonic theism and morality which shines out of the De consolatione philosophiae made it extremely popular during the Middle Ages and the Renaissance.
463. Fabian Franklin (1853-1939)
• His simple demeanour and dignity of person commanded the instant respect of his students, a respect which was never lost.
464. Stephen C Kleene (1909-1994)
• Difficult proofs are broken down into a large number of simple cases; some of these cases are usually left to the reader.
465. Olinthus Gregory (1774-1841)
• We do not deny that the scheme of revelation has its difficulties: for if the things of nature are often difficult to comprehend, it would be strange indeed if supernatural matters were so simple, and obvious, and suited to finite capacities, as never to startle or puzzle us at all.
466. Hermann Schubert (1848-1911)
• In all these essays, which are of a simple and popular character, and designed for the general public, Professor Schubert has incorporated much of his original research.
467. Pavel Tichy (1936-1994)
• He was awarded his doctorate in 1959 for his thesis An Exposition of Godel's Incompleteness Theorem in the Simple Theory of Types (Czech).
468. Luigi Fantappiè (1901-1956)
• For example in Deduzione autonoma dell'equazione generalizzata di Schrodinger, nella teoria di relativita finale Ⓣ (1955) Fantappie deduces the Klein-Gordan equation in quantum mechanics as a limit, as the radius of the universe tends to infinity, of a classical (non-quantized) equation in his extension of relativity based on a simple (pseudo-orthogonal) group having the Lorentz group as a type of limit.
469. Karl Menger (1902-1985)
• There is an important phase in the development of modern point set theoretical geometry which has been closely associated with the concept of dimensionality, - we refer to the attempt to create precise mathematical meaning for the simple geometric spaces of our intuition in terms of primitive non-arithmetical concepts.
470. Richard Tapia (1939-)
• It is also shown that this procedure can be applied to a class of two point boundary value problems containing the Euler-Lagrange equation for simple variational problems and most second order ordinary differential equations.
471. Jan Stampioen (1610-1690)
• If this sounds like a particularly modern approach to selling, then let us simple say that human nature does not seem to have changed much over the centuries! .
472. Georges de Rham (1903-1990)
• Formes, courants, formes harmoniques Ⓣ (1955); (with S Maumary and M A Kervaire) Torsion et type simple d'homotopie Ⓣ (1967); and Lectures on introduction to algebraic topology (1969).
473. Jerzy o (1920-1998)
• For example he published A simple proof of the existence of equilibrium in a von Neumann model and some of its consequences (1971), Extended von Neumann models and game theory (1976), and Mathematical theory of von Neumann economic models.
474. Hans Meinhardt (1938-2016)
• It will be shown that a relatively simple set of interactions can explain seemingly complex experimental observations in a quantitative manner.
475. Valentina Mikhailovna Borok (1931-2004)
• In the same period she obtained formulae that made it possible to compute in simple algebraic terms the numerical parameters that determine classes of uniqueness and well-posedness of the Cauchy problem for systems of linear partial differential equations with constant coefficients.
476. Felix Behrend (1911-1962)
• In the same year in Note on the compactification of separated uniform spaces he gave a simple method of obtaining, for any uniform space S, a uniform structure which is totally bounded and compatible with the topology of S.
477. Raymond Smullyan (1919-2017)
• Before the class began, he tried to warm up the group, tossing out some simple puzzles ..
478. Charles Fox (1897-1977)
• The methods of contour integration, however, give extremely simple proofs of these results, and also give rise to many interesting results which, I believe, are new.
479. Roger Apéry (1916-1994)
• It has been my good fortune to find a very simple version of the proof a few months after Apery's announcement.
480. Pascual Jordan (1902-1980)
• Things, however, are not quite as simple as they might appear and one must not think that because Jordan was a staunch and enthusiastic Nazi supporter, he believed in all the Nazi policies.
481. Alexis Clairaut (1713-1765)
• In order to avoid delicate experiments or long tedious calculations, in order to substitute analytical methods which cost them less trouble, they often make hypotheses which have no place in nature; they pursue theories that are foreign to their object, whereas a little constancy in the execution of a perfectly simple method would have surely brought them to their goal.
482. Piero della Francesca (1420-1492)
• Also it is clear that Piero's Italian writing lacked style, and was rather simple and elementary.
483. Gustav Kirchhoff (1824-1887)
• In all his work he strove for clarity and rigour in the quantitative statement of experience, using a direct and straightforward approach and simple ideas.
484. Giovanni Vailati (1863-1909)
• I saw him universally celebrated and requested from all intervening scholars; in the streets, in the pubs, in gatherings and meetings he was always in the middle of a group which he fascinated with his simple, whole-hearted, and nonetheless interesting, informative conversation.
485. Vincenzo Riccati (1707-1775)
• Vincenzo Riccati, somehow, put an end to this trend by showing that one could construct in a simple continuous way all transcendental curves from the differential equations that define them.
486. Gheorghe Calugrenu (1902-1976)
• As a lecturer, Calugăreănu gave simple, clear explanations.
487. Monteiro da Rocha (1734-1819)
• He gave a simple method of calculating a parabolic orbit given three observations which he presented to the Academy of Sciences of Lisbon in 1782.
488. Jorgen Gram (1850-1916)
• This work provided a simple and natural framework for invariant theory.
489. Willem de Sitter (1872-1934)
• This is a particularly simple solution of the field equations of general relativity for an expanding universe.
490. Charlotte Angas Scott (1858-1931)
• When retiring for study after an extremely simple 'tea' in the Common Room, they would pick up three things en route to their rooms ..
• Kuku's first three papers were (i) Some algebraic K-theoretic applications of the LF and NF functors (1973), (ii) Whitehead group of orders in p-adic semi-simple algebras (1973) and (iii) Some finiteness theorems in the K-theory of orders in p-adic algebras (1976).
492. Victor Puiseux (1820-1883)
• His kindness, his charity, and above all his simple, unaffected modesty overshadowed even his talents.
493. Pierre Rémond de Montmort (1678-1719)
• The simple fact that Remond de Montmort and Taylor felt compelled to debate the physics of universal gravitation was an important marker of the changing intellectual climate of the time, yet the appearance of their thoroughly exchange within a journal self-consciously devoted to promoting and provoking public, critical debate of philosophical matters was even more catalysing.
494. Thomas Allen (1540-1632)
• He had a great many mathematical instruments and glasses in his chamber, which did also confirm the ignorant in their opinion; and his servitor [servant] (to impose on Freshmen and simple people) would tell them that sometimes he should meet the spirits coming up his stairs like bees.
495. Alice T Schafer (1915-2009)
• Choice of the proper projective coordinate system permits the reduction of these power series to simple canonical forms.
496. Benjamin Bramer (1588-1652)
• One must not think that the fighting was a simple conflict between Protestant and Roman Catholic forces.
497. Gustav Roch (1839-1866)
• This was not a simple matter, for Roch did not have a particularly strong background in either mathematics or physics, so in order to prepare himself for advanced study he took courses at a private institute as well as at the Polytechnic Institute.
498. Karl Schwarzschild (1873-1916)
• I had not expected that one could formulate the exact solution of the problem in such a simple way.
499. Hans Schubert (1908-1987)
• In Uber die Potentiale der auf dem Mantel eines Kreiszylinders ausgebreiteten einfachen und doppelten Belegung Ⓣ (1952) he derives a Fourier integral representation containing Bessel functions for the axially symmetric potential induced by a simple and double layer on the surface of a circular cylinder.
500. August Crelle (1780-1855)
• The solution was simple, even if it required a change in policy, and that was to have a second journal for more practical mathematics and this he moved to a second journal which he started in 1829, the Journal fur die Baukunst.
501. Herbert Robbins (1915-2001)
• From a level approximately that of a sound high-school training, the development proceeds by direct paths to some of the best content of mathematics; and fundamental ideas are made strikingly clear by well-chosen, simple examples.
502. Gordon Preston (1925-2015)
• He published papers over the next years such as Chains of congruences on a completely 0-simple semigroup (1965), Matrix representations of inverse semigroups (1969) and Free inverse semigroups (1973).
503. Jean-Pierre Serre (1926-)
• The events started in bright sunshine in Oslo on Sunday, 1 June 2003, with a simple ceremony at the Abel Monument in Slottsparken.
504. Winifred Sargent (1905-1979)
• provided a simple and direct proof for a theorem which is fundamental in the development of the Cesaro-Perron scale of integration.
505. Gaston Julia (1893-1978)
• This book presents a continuation of the first volume of the author dealing with those aspects of the modern theory of functions of a complex variable which are derivable from simple geometrical principles.
506. Lipót Fejér (1880-1959)
• Fejer's theorem is a simple, beautiful theorem, and, in the opinion of Jean-Pierre Kahane [',' J-P Kahane, Leopold Fejer et l’analyse mathematique au debut du XXe siecle, Cahiers du Seminaire d’Histoire des Mathematiques 2 (Inst.
507. Ernest Wilczynski (1876-1932)
• in the midst of a lecture [in 1923] he finally realised that he could go no further and, with a simple statement to that effect, walked from his classroom never to return, leaving his students amazed by the classic self-restraint with which he accepted his tragic fate.
508. Robert Hooke (1635-1703)
• He failed to develop major theories from his inspired ideas for the simple reason that he did not really have the technical ability to develop such comprehensive theories as some of his contemporaries like Newton and Huygens.
509. Angelo Genocchi (1817-1889)
• His explanations were calm, with no repetitions, and he aimed at rigorously presenting the fundamental concepts and studying them so as to arrive at simple procedures and clear exposition.
510. Hans Lewy (1904-1988)
• His paper An example of a smooth linear partial differential equation without solution (1957) gave a simple partial differential equation which has no solution, a result which had a substantial impact on the area.
511. Paul Kelly (1915-1995)
• The book is easy to read, notation is kept simple, and the proofs are clear and complete.
512. Elemér Kiss (1929-2006)
• Their family, as many families at that time, led a very simple life, but they brought up their three children with great love, all of them graduating from university.
513. Ilya Iosifovich Piatetski-Shapiro (1929-2009)
• Among his main achievements are: the solution of Salem's problem about the uniqueness of the expansion of a function into a trigonometric series; the example of a non symmetric homogeneous domain in dimension 4 answering Cartan's question, and the complete classification (with E Vinberg and G Gindikin) of all bounded homogeneous domains; the solution of Torelli's problem for K3 surfaces (with I Shafarevich); a solution of a special case of Selberg's conjecture on unipotent elements, which paved the way for important advances in the theory of discrete groups, and many important results in the theory of automorphic functions, e.g., the extension of the theory to the general context of semi-simple Lie groups (with I Gelfand), the general theory of arithmetic groups operating on bounded symmetric domains, the first 'converse theorem' for GL(3), the construction of L-functions for automorphic representations for all the classical groups (with S Rallis) and the proof of the existence of non arithmetic lattices in hyperbolic spaces of arbitrary large dimension (with M Gromov).
514. Marius Lacombe (1862-1938)
• He is not one of those who consider mathematics to be simple gymnastics or an adornment of the mind.
515. Louis Arbogast (1759-1803)
• Do the arbitrary functions introduced when differential equations are integrated belong to any curves or surfaces either algebraic, transcendental, or mechanical, either discontinuous or produced by a simple movement of the hand? Or should they legitimately be applied only to continuous curves susceptible of being expressed by algebraic or transcendental equations? .
516. Max Zorn (1906-1993)
• He studied the structure of semisimple alternative rings in 1932, proving that such a ring is a direct sum of simple alternative algebras which he classified.
517. Elliott Montroll (1916-1983)
• At the Third Berkeley Symposium on Mathematical Statistics and Probability 1954-1955, Montroll gave a paper Theory of the vibration of simple cubic lattices with nearest neighbor interactions in which described vibrations of a cubic lattice with 1, 2, 3, and n dimensions where n is large.
518. Henrietta Swan Leavitt (1868-1921)
• A straight line can readily be drawn among each of the two series of points corresponding to maxima and minima, thus showing that there is a simple relation between the brightness of the variables and their periods.
519. Max Newman (1897-1984)
• At a time when the study of manifolds was based on a number of different combinatory concepts, he established a simple combinatory system of simplicial complexes with an equivalence relation based on elementary moves.
520. David Rees (1918-2013)
• They contain the concept known today as a Rees matrix semigroup which Rees defines and uses to classify completely 0-simple semigroups.
521. Floyd Burton Jones (1910-1999)
• Although one can see how this might have led him to mathematics the route was not as simple as that for the topic which he decided to take up instead of law was chemistry.
522. Maurice d'Ocagne (1862-1938)
• The purpose of Nomography is to reduce to simple readings on graphical charts, constructed once for all, the computations which necessarily intervene in the practice of various technical arts.
• He gives a wide variety of applications including problems involving ratios, barter, simple interest, mixtures, purchase and sale, rates of travel, wages, and filling of cisterns.
524. Herbert Wilf (1931-2012)
• The remarkably simple idea of the work of Wilf and Zeilberger has already changed a part of mathematics for the experts, for the high-level users outside the area, and the area itself.
525. Michael Freedman (1951-)
• The simple nature of his results in the topological case must be contrasted with the extreme complications which are now known to occur in the study of differentiable and piecewise linear 4-manifolds.
526. George Stokes (1819-1903)
• Though he was never narrow in his faith and religious sympathies, he always held fast by the simple evangelical truths he learnt from his father..
527. David Gale (1921-2008)
• We mention one further paper which in many ways is typical of the delightfully simple yet deep questions that Gale often investigated.
528. Maria Winckelmann (1670-1720)
• Her argument was simple: her husband had been ill for some time and she had actually been doing the job herself for that period, and after his death she had continued to produce the Kirch calendars.
529. Crispin Nash-Williams (1932-2001)
• of developing nontrivial and fairly deep mathematics from a very simple initial concept.
530. Samuel Haughton (1821-1897)
• The personal charm of Dr Haughton's character was something which cannot be expressed in words, while to the outside public he was a brilliant speaker, a racy raconteur, a versatile genius, and a sagacious man of affairs; to the inner circle of his friends he was a wise and willing advisor, one ever ready to help and to guide, affectionate, sincere, and intensely sympathetic, a calm and simple Christian who in all his work ever kept clearly before him his responsibilities as a Christian teacher.
531. Mitchell Feigenbaum (1944-)
• When Feigenbaum first found 4.669 in August 1975, which he only found to three places due to the limit of the accuracy of his HP65, he spend some time trying to see if it was a simple combination of 'well-known' numbers.
• In "Elements" Legendre gave a simple proof that π is irrational, as well as the first proof that π2 is irrational, and conjectured that π is not the root of any algebraic equation of finite degree with rational coefficients.
533. Nathan Divinsky (1925-2012)
• For example, he published On commuting automorphisms of rings (1955), Commutative subdirectly irreducible rings (1957), On simple, semi-radical and radical algebras (1959) and General radicals that coincide with the classical radical on rings with D.C.C.
534. David Eisenbud (1947-)
• Thus this book introduces big ideas with seemingly simple, concrete examples, generalizes from them to an appropriate abstract formulation, and then applies the concept to interesting classical problems in a meaningful way.
535. Richard Delamain (1600-1644)
• In Delamain's we have two (or three) flat brass rings, of the same thickness, graduated and grooved on the edges, one moving within, and in contact with, the other: Oughtred's instrument consists of one round plate, divided into several concentric circles, on which are laid down the logarithms of numbers, sines and tangents, and all operations are performed by means of two indices, radiating from a pin at the centre, like the legs of a sector; this mode of operation, it must be obvious, is far more complex, more inconvenient, and more liable to derangement, than the simple movement first proposed by Delamain.
536. Edwin Hubble (1889-1953)
• The explanation is simple, but revolutionary: the Universe is expanding.
537. Demetrios Kappos (1904-1985)
• It is doubtful whether anyone else could have been such a support to the young Kappos who later said, "I learned how to work because of Caratheodory." The relationship between the two Greeks was more than a simple professor-student relationship for Kappos was a frequent guest at the Caratheodory home, and also a companion of the professor at the park in the area known as the English garden.
## History Topics
1. Word problems
• Notice that there is a simple connection between the Conjugacy Problem and the Word Problem.
• He published these results in 1927 and at the same time gave a simple rigorous proof of the solution of the word problem in a free group.
• These functions were built up from simple functions.
• (x) simple.
• We note that although given a finite group presentation we cannot recursively recognisable whether the group is simple, if we know that a given presentation defines a simple group then that group has soluble word problem.
2. Physical world
• If we deduce results about mechanics from these laws, are we discovering properties of the physical world, or are we simply proving results in an abstract mathematical system? Does a mathematical model, no matter how good, only predict behaviour of the physical world or does it give us insight into the nature of that world? Does the belief that the world functions through simple mathematical relationships tell us something about the world, or does it only tell us something about the way humans think.
• Music, perhaps strangely, was the motivating factor for the Pythagoreans realised that musical harmonies were related to simple ratios.
• Moreover the same simple ratios hold for vibrating strings and for vibrating columns of air.
• It was a belief that a simple mathematical relationship must be physically significant which led Kepler to discover his third law of planetary motion.
• He set up an axiom system consisting of hard particles which were at rest or in motion, obeying three simple laws concerning motion and forces, and a universal law of gravitation.
• As we have suggested there were problems with Newton's system despite the fact that it appeared to reduce the whole of nature to consequences of simple mathematical laws.
3. Gravitation
• the simple bodies such as earth, fire, air and water; for we say that these things and things of this sort are natural.
• As well as giving a simple mathematical model for planetary motion, these laws were highly significant since they stated for the first time that the motions of the heavenly bodies are not composed of circular motion.
• Comets, he showed, were subject to the same gravitational forces and these forces gave a simple explanation of tides.
• It was a devastating attack on Descartes' vortex theory of gravitation and put forward a brilliantly simple theory from which so much could be explained.
• There was no simple solution to the problems that the different theories posed.
4. African women 1
• Biographical Data: Abstract of the thesis: "This research aims to study the conceptions expressed by Moroccan students and teachers at the end of secondary school about the notion of (simple) continuity of a function.
• Accordingly, their physical occurrences and phenomena, and simple solutions are discussed in chapter one, with derivation of conservation conditions given therein in chapter two, a theoretical study of methods is considered and sufficient conditions for stability and convergence results are presented.
• Given the means (or the totals) of auxiliary variables positively correlated with the character of interest, we construct a multivariate estimator for the population mean/total to be used with simple random sampling (srs) or with any probability proportional to size (pps) design.
• She has published The two-dimensional stability of a viscous fluid between rotating cylinders (1996), Symmetric simple map for a single-null divertor tokamak (1997), The principle of exchange of stabilities for Couette flow (2003), Derivation of the dipole map (2004), and Symplectic mappings for divertor tokamaks (2005).
• After a review of the various models described in the literature, our study deals with the simple zero-equation model and the more complex two-equation model of the k-e kind.
5. Kepler's Laws
• (Moreover, the same principle is invoked in relation to planetary motion when Kepler based his investigation on what Aristotle had specified as the only two simple motions, circular and rectilinear, discussed in Section 9.) This principle has far-reaching ramifications, as we will demonstrate in connection with the complementary pairings that recur in Kepler's mature work in Epitome Ⓣ Book V (1621) - where the term 'complementary' is used in the everyday sense that the pair complete one another, and also with the mathematical connotation of being at right angles.
• He adopted the traditional mechanism of deferent, epicycle, and eccentric, being aware, as the Ancients had been, that motion in the circle of radius a centred on A, when combined with motion in the epicyclet of radius ZQ = AB = ae (whose centre Z lies on the deferent), together produce a motion of Q equivalent to a simple motion of Q round the eccentric circle centre B radius a.
• The mathematical treatment carried out in Planetary motion tackled kinematically demonstrates that this angle is the uniquely appropriate foundation for a structure which is simple because it depends on orthogonality and therefore is the only workable basis for Kepler's astronomy.
• In De Caelo Ⓣ I, 3, Aristotle had declared that there were only two simple motions, circular and linear.
• This is the process that was described (in Section 4) as idealization because it ensured an exact solution (of the one-body problem) which was uniquely simple.
6. African men 1
• He has published around 70 papers including A class of algebraically special perfect fluid space-times (1970), Geometric properties of neutrino fields in curved spacetime (1971), Some exact cosmological models with gravitational waves (1979), Power law singularities in orthogonal spatially homogeneous cosmologies (1984), Mathematical cosmology (1990), Introduction to dynamical systems (1994), Cosmological models from a dynamical systems perspective (2005), The dynamics of Lemaitre-Tolman cosmologies (2009), and Simple expressions for second order density perturbations in standard cosmology (2014).
• He has published over 150 papers on Finite Groups, Simple Groups and Sporadic Simple Groups, Representation Theory of Finite Groups, Character Tables of Extension Groups, Cliûord-Fischer Matrices, Presentations of Group Extensions, Application of Finite Groups to Combinatorial Designs and Finite Geometries.
• Here are a few examples of Moori's papers: On certain groups associated with the smallest Fischer group (1981); Subgroups of 3-transposition groups generated by four 3-transpositions (1994); (p, q, r)-Generations of the Smallest Conway Group Co_3 (1997); Codes, Designs and Graphs from the Janko Groups J_1 and J_2 (2002); Permutation decoding for the binary codes from triangular graphs (2004); Some designs and codes invariant under the simple group Co_2 (2007); Codes associated with triangular graphs and permutation decoding (2010); and A survey on Clifford-Fischer Theory (2015).
7. Greek astronomy
• On the other side there is an important idea in the Pythagorean philosophy which had a lasting impact, namely the idea that all complex phenomena must reduce to simple ones.
• Another important philosophical idea which had important consequences from the time of Pythagoras, and was emphasised by Plato, was that complex phenomena must be consequences of basic simple phenomena.
• 45">The changing aspects of the revolution of the planets is because, being fixed in their own circles or in their own shperes whose movements they follow, they are carried across the zodiac, just as Pythagoras had first understood it, by a regulated simple and equal revolution but which results by combination in a movement that appears variable and unequal.
• Eudoxus was the first to propose a model whereby the apparently complex motions of the heavenly bodies did indeed result from simple circular motion.
8. Abstract linear spaces
• He starts with undefined elements which he calls 'simple quantities' and generates more complex quantities using specified rules.
• I go further, since I call these not just quantities but simple quantities.
• There are other quantities which are themselves compounded quantities and whose characteristics are as distinct relative to each other as the characteristics of the different simple quantities are to each other.
9. African women I
• This research aims to study the conceptions expressed by Moroccan students and teachers at the end of secondary school about the notion of (simple) continuity of a function.
• Has published The two-dimensional stability of a viscous fluid between rotating cylinders (1996), Symmetric simple map for a single-null divertor tokamak (1997), The principle of exchange of stabilities for Couette flow (2003), Derivation of the dipole map (2004), and Symplectic mappings for divertor tokamaks (2005).
• After a review of the various models described in the literature, our study deals with the simple zero-equation model and the more complex two-equation model of the k-e kind.
10. Burnside problem
• There are finitely many finite simple groups of exponent n, .
• The outer automorphism group Out(G) = Aut(G)/Inn(G) is soluble for any finite simple group of exponent n.
• Now (moving ahead), the classification of finite simple groups in the 1980's shows that ii.
11. Weather forecasting
• However, as the article should provide only an overview of the mathematical methods used in current forecasting models, I have chosen to include only simple equations and explain some mathematical symbols in order to make understanding the methods easier.
• The approximations described above are very simple examples illustrating the general idea of finite differences.
• A simple example that can be solved in terms of a Fourier series illustrates the idea of the spectral method: One of the processes described by the primitive equations is advection (which is the transport of for instance heat in the atmosphere), and the non-linear advection equation is given by .
12. Newton's bucket
• The experiment is quite simple and any reader of this article can try the experiment for themselves.
• What is the problem? Is this not precisely what we would expect to happen? Newton asked the simple question: why does the surface of the water become concave? One is inclined to reply to Newton: that is an easy question - the surface becomes concave since the water is spinning.
• Why should that be? Well in simple terms, in a universe with no matter there is no gravity.
13. Elliptic functions
• For example the period of a simple pendulum was found to be related to an integral which expressed arc length but no form could be found in terms of 'simple' functions.
• This is a particularly simple case of an elliptic integral.
14. Chandrasekhar Eddington
• He reinforced the established idea of a simple model for the evolution of the stars (in which they all eventually become white dwarfs).
• He brought the matter to Bohr's attention and reported back to Chandrasekhar that they were "absolutely unable to see any meaning in Eddington's statements" but that the question seemed to be "quite simple." In the hopes of getting them to settle the controversy, Chandrasekhar sent Eddington's manuscript to Rosenfeld and Bohr, who then in turn sent it to Wolfgang Pauli.
• His ideas involved the seven primitive constants of physics which Eddington sought to relate in simple numerical ways.
15. Special relativity
• The simultaneity of two events or the order of their succession, as well as the equality of two time intervals, must be defined in such a way that the statements of the natural laws be as simple as possible.
• The conception of an ether absolutely at rest is the most simple and the most natural - at least if the ether is conceived to be not a substance but merely space endowed with certain physical properties.
• While Lorentz must be considered as the first to have found the mathematical content of the relativity principle, Einstein succeeded in reducing it to a simple principle.
16. Mathematics and Architecture
• But the first gardener in history to lay out a perfect ellipse with three stakes and a length of string certainly held no degree in the theory of cones! Nor did Egyptian architects have anything more than simple devices -- "tricks", "knacks" and methods of an entirely empirical kind, no doubt discovered by trial and error -- for laying out their ground plans.
• He made an art out of structural purity, using simple geometric forms for aesthetic as well as functional purposes.
17. Ring Theory
• In 1908 Wedderburn had the important idea of splitting the study of a ring into two parts, one part he called the radical, the part which was left being called semi-simple.
• He used matrix rings to classify the semi-simple part.
18. Fair book
• Walker uses six figure logs to do the simple multiplications.
• This must be a simple miscopying.
19. Infinity
• His argument is a simple one.
• Why does defining a set make the actual infinite a reality? The answer is simple.
20. Topology history
• It is interesting to realise that this, really rather simple, formula seems to have been missed by Archimedes and Descartes although both wrote extensively on polyhedra.
Go directly to this paragraph
• He called a simple closed curve on a surface which does not intersect itself an irreducible circuit if it cannot be continuously transformed into a point.
Go directly to this paragraph
21. Black holes
• I had not expected that one could formulate the exact solution of the problem in such a simple way.
• Israel, using general relativity, showed that non-rotating black holes had to be very simple; they were perfectly spherical, their size depended upon their mass only, and any two such black holes with the same mass must be identical.
22. Indian mathematics
• The idea seems so simple nowadays that its significance and profound importance is no longer appreciated.
• The main topics of Jaina mathematics in around 150 BC were: the theory of numbers, arithmetical operations, geometry, operations with fractions, simple equations, cubic equations, quartic equations, and permutations and combinations.
23. Mental arithmetic
• This may be due to the simple fact that such calculating abilities require continual practice for many hours each day and education occupies too much time to allow this to continue.
• My aim has been to demonstrate, in these various rather simple examples, some part of the repertoire, the armoury of resource upon which a mental calculator may draw, and in regard to the choice of which he must make instantaneous decisions, and keep to them.
24. African men 2
• Thesis title: Analyse sur les algebres de Jordan simples reelles [Analysis on real simple Jordan algebras].
• Thesis title: 2-Generations of the Sporadic Simple Groups.
25. Indian numerals
• The idea seems so simple nowadays that its significance and profound importance is no longer appreciated.
• The second aspect of the Indian number system which we want to investigate here is the place value system which, as Laplace comments in the quote which we gave at the beginning of this article, seems "so simple that its significance and profound importance is no longer appreciated." We should also note the fact, which is important to both aspects, that the Indian number systems are almost exclusively base 10, as opposed to the Babylonian base 60 systems.
26. Newton poetry
• Clouded in dust, from motion's simple laws, .
• From laws sublimely simple, speak thy fame .
27. Chinese overview
• The method of calculation is very simple to explain but has wide application.
• After having understood how to make use of the golden section, I began to believe that the different geometrical methods could be understood and that neither the missionaries attitude of considering this simple technique as a divine gift, nor the Chinese attitude of rejecting it as heresy is correct.
28. Planetary motion
• Therefore it is clear that this expression for the radius vector of a circle with its origin at an eccentric point is much less simple than that for the radius vector of the ellipse with the same origin when that point is its focus, as set out in (5) just above.
29. Real numbers 2
• In order to complete the connection presented in this section of the domains of the quantities defined [his determinate limits] with the geometry of the straight line, one must add an axiom which simple says that every numerical quantity also has a determined point on the straight line whose coordinate is equal to that quantity, indeed, equal in the sense in which this is explained in this section.
30. Mathematical games
• Mathematical puzzles vary from the simple to deep problems which are still unsolved.
31. Fractal Geometry
• Equally, no simple shape from Euclidean geometry comes to mind when contemplating things such as the path of a river.
32. Bourbaki 2
• Clearly this powerful mathematical team did not see their task simple to push the last of the chapters through the publishing process.
33. Nine chapters
• Many of the problems seem simple an excuse to give the reader practice at handling difficult calculations with fractions.
34. Alcuin's book
• This is not a simple copying error in the manuscript since 32788 is multiplied by 8 to get the final number.
35. Jaina mathematics
• the theory of numbers, arithmetical operations, geometry, operations with fractions, simple equations, cubic equations, quartic equations, and permutations and combinations.
36. Real numbers 3
• A simple code will let us translate these into letters, 00 become a, 01 become b, ..
37. Squaring the circle
• It neither prevented the stream of publications claiming that π had some simple rational value, nor did it prevent the stream of publications of quite correct constructions to approximately square the circle with ruler and compass.
38. References for Egyptian mathematics
• M Guillemot, Les methodes de simple fausse position dans les mathematiques egyptiennes et les mathematiques arabes, in Histoire des mathematiques arabes, Vol.
39. Greek numbers
• We have omitted the symbol for 'one', a simple '|', which was an obvious notation not coming from the initial letter of a number.
40. Copernicus autograph
• There is no simple progression so the idea that first he used C, moving on to D, then E and finally F is just not born out by the way the quires are made up of the papers.
41. Group theory
42. Wave versus matrix
• All that Foucault had shown is that the simple corpuscular model is not an accurate model to predict all the properties of light.
43. Neptune and Pluto
• if a simple study of its physical appearance can replace the rigorous determination of the positions of all the stars, the search will proceed much more rapidly.
44. The four colour theorem
• If you retort with some very simple case which makes me out a stupid animal, I think I must do as the Sphynx did..
45. Egyptian Papyri
• This is discussed in detail in [',' M Guillemot, Les methodes de simple fausse position dans les mathematiques egyptiennes et les mathematiques arabes, in Histoire des mathematiques arabes, Vol.
46. Perfect numbers
• 44">Among simple even numbers, some are superabundant, others are deficient: these two classes are as two extremes opposed to one another; as for those that occupy the middle position between the two, they are said to be perfect.
47. Golden ratio
• Of course if AB has length 1 and AC = x where C divides AB in the golden ratio, then we can use simple algebra to find x.
48. Braids arithmetic
• Simple proportion.
• To reduce a compound fraction to an equivalent simple fraction.
49. Fair book insert
• Part of the difficulty is that the material in the Fair Book itself does not always advance in difficulty, and sometimes after quite hard problems, simple ones of the same type will appear.
50. Orbits
• Even if the Earth - Moon system were considered as a two body problem, theoretically solved in the Principia, the orbits would not be simple ellipses.
51. Arabic numerals
• The story of this transmission is not, however, a simple one.
52. Babylonian mathematics
• From the mathematical point of view these problems are comparatively simple ..
53. General relativity
• in all my life I have not laboured nearly so hard, and I have become imbued with great respect for mathematics, the subtler part of which I had in my simple-mindedness regarded as pure luxury until now.
54. Pell's equation
• The method relies on a simple observation, namely that, for any m, (1, m) satisfies the 'Pell type equation' .
55. Brachistochrone problem
• Even so, while the method is ingenious and rich, one must admit that it is not as simple as one might hope in a work of pure analysis ..
56. Classical light
• Newton carried out a very simple experiment.
57. Tartaglia versus Cardan
• Ferrari to Tartaglia: You have the infamy to say that Cardano is ignorant in mathematics, and you call him uncultured and simple-minded, a man of low standing and coarse talk and other similar offending words too tedious to repeat.
58. The Scottish Book
• As the reader will see, this general rule could not guarantee against an occasional question to which the answer was quite simple or even trivial.
59. Voting
• The simple system in which each voter gives a single vote to their favourite candidate can also lead to tactical voting.
60. Christianity and Mathematics
• The Creator is the great architect of all things; in the cognition of the mathematically simple structure of the universe man will become united with Him.
61. 20th century time
• The foundations on which the theory is based are remarkably simple.
62. Zero
• How could the brilliant mathematical advances of the Greeks not see them adopt a number system with all the advantages that the Babylonian place-value system possessed? The real answer to this question is more subtle than the simple answer that we are about to give, but basically the Greek mathematical achievements were based on geometry.
63. Greek sources I
• The truth, however, is not nearly so simple and we will illustrate the way that Greek mathematical texts have come down to us by looking first at perhaps the most famous example, namely Euclid's Elements.
Go directly to this paragraph
64. References for Egyptian Papyri
• M Guillemot, Les methodes de simple fausse position dans les mathematiques egyptiennes et les mathematiques arabes, in Histoire des mathematiques arabes, Vol.
## Societies etc
1. Trinity Cambridge Mathematical Society
• The second symbol, which is the official logo of the Society, is the unique smallest simple squared square.
• That it is simple means that no proper subset of the squares of size at least 2 forms a rectangle and smallest in that no square can be so divided with fewer squares.
• This squared square was discovered in March 1978 by A J W Duijvestijn using a computer search and published in his paper Simple perfect squared square of lowest order (1978) which contained the order 21 simple perfect squared square (see [',' A J W Duijvestijn, Simple perfect squared square of lowest order, J.
• However, these solutions were not simple in the sense defined above.
• Ten years later Tutte found a simple squared square with 69 different size squares in the dissection which he published in Squaring the square (1950), see [',' W T Tutte, Squaring the square, Canadian J.
• the logo of the Society shall be the (unique) smallest simple squared square, with the largest partitioning square in the top left corner and the largest of the squares adjacent to this to its right (rather than below it).
• "Everything is voluntary in our general Swiss society," it said, and the study of nature should be "for the greater part of its members their only love, everything else being incidental." Therefore, "only a very simple, unpretentious organization" should be established.
• The Academy began as a "very simple, unpretentious organization" but as it grew it became a complex, well-organised body.
3. References for Trinity Cambridge
• A J W Duijvestijn, Simple perfect squared square of lowest order, J.
4. Max Planck Society for Advancement of Science
• The changeover from the Kaiser Wilhelm Society, however, was not as simple as all that for the two Societies both continued to exist side by side for twelve years with the Kaiser Wilhelm Society only completing its dissolution following its last Annual General Meeting on 21 June 1960.
5. German Mathematical Society
• The potencies represent the simple and important generalisation of the finite cardinal numbers.
## Honours
1. Groups St Andrews.html
• Finite simple groups: a survey .
• Finite regularity of locally finite simple groups .
• Economical generating sets for finite simple groups .
• Width questions for finite simple groups .
• Finite simple groups and fusion systems .
• On characters and p-blocks of finite simple groups .
• Simple groups, generation and probabilistic methods .
• Representations and subgroup structure of simple algebraic groups .
2. Galway Group Theory.html
• T J Laffey (University College Dublin) On finite simple groups .
• M Liebeck (Cambridge) Some applications of the classification of finite simple groups to permutation group theory .
• B Hartley (Manchester) Simple locally finite groups .
• O Puglisi (Florence) Group algebras of locally finite simple groups .
• G Hiss (Aachen) Low dimensional representations of quasi-simple groups .
• Inna (Korchagina) Capdeboscq (University of Warwick) Finite simple groups with double life .
• Radu Stancu (Picardie - Jules Verne) Evaluations of simple biset functors .
3. AMS Steele Prize
• for his book "Finite Simple Groups, An Introduction to their Classification", and his two survey articles "The Classification of Finite Simple Groups" and "Classifying the Finite Simple Groups".
• for his construction of the "Monster" sporadic finite simple group.
• for their work, "The classification of finite simple groups: groups of characteristic 2 type" .
4. International Congress Speaker
• John Griggs Thompson, Characterizations of Finite Simple Groups.
• Walter Feit, The Current Situation in the Theory of Finite Simple Groups.
• Elias M Stein, Some Problems in Harmonic Analysis Suggested by Symmetric Spaces and Semi-Simple Groups.
• Daniel Gorenstein, The Classification of Finite Simple Groups.
5. AMS Cole Prize in Algebra
• for his groundbreaking research on representation theory, cohomology, and subgroup structure of finite quasi-simple groups, and the wide-ranging applications of this work to other areas of mathematics.
6. Wolf Prize
• for his monumental contributions to algebra, in particular to the theory of lattices in semi-simple Lie groups, and striking applications of this to ergodic theory, representation theory, number theory, combinatorics, and measure theory.
7. MAA Chauvenet Prize
• The Simple Continued Fraction Expansion of e, Amer.
• Odd characterisations of finite simple groups.
9. Gibbs Lectures.html
• December 1955; Houston, Texas; Joseph E Meyer; The structure of simple fields.
10. Sylvester Medal
• for his fundamental contributions leading to the complete classification of all finite simple groups.
11. AMS Conant Prize
• for his article "A Brief History of the Classification of the Finite Simple Groups".
12. Rolf Schock Prize
• for his fundamental contributions to one of the largest mathematical projects ever, the classification of finite simple groups, notably his contribution to the quasi-thin case.
## References
1. References for John Conway
• T M Thompson, From error-correcting codes through sphere packings to simple groups (Washington, 1983).
2. References for Georges de Rham
• J Milnor and O Burlet, Torsion et type simple d'homotopie, in A Haefliger and R Narasimhan (eds.), Essays on Topology and Related Topics : Memoires dedies a Georges de Rham (Springer, Berlin - Heidelberg - New York, 1970), 12-17.
3. References for Subrahmanyan Chandrasekhar
• N Panchapakesan, Seeing beauty in the simple and the complex : Chandrasekhar and general relativity, in Classical and quantum aspects of gravitation and cosmology, Madras, 1996 (Madras, 1998), 1-10.
4. References for Galileo Galilei
• R Naylor, Galileo's simple pendulum, Physis 16 (1974), 23-46.
5. References for Walter Feit
• R Solomon, A brief history of the classification of the finite simple groups, Bull.
6. References for Jules Bienaymé
• C C Heyde and E Seneta, The simple branching process, a turning point test and a fundamental inequality : A historical note on I-J Bienayme, Biometrica 59 (3) (1972), 680-683.
7. References for John Leech
• T M Thompson, From error-correcting codes through sphere packings to simple groups (Washington, 1983).
8. References for Mario Fiorentini
• E Sernesi, A simple article, in Commutative algebra and algebraic geometry, Ferrara (Dekker, New York, 1999), x-xiii.
9. References for Paul Dubreil
• C Hollings, Embedding semigroups in groups: not as simple as it might seem, Arch.
10. References for Rimhak Ree
• J A Gallian, The Search for Finite Simple Groups, Mathematics Magazine 49 (4) (1976), 163-180.
11. References for Émile Mathieu
• R Silvestri, Simple groups of finite order in the nineteenth century, Arch.
12. References for Levi ben Gerson
• R Glasner, Gersonides on simple and composite movements, Stud.
13. References for Fischer Black
• (1988c), A Simple Discounting Rule, Financial Management, 17(2), 7-11.
1. Hardy Inaugural Lecture
• There is nothing in the least popular about its methods, as to its votaries it is the most beautiful, so by common consent it is the most difficult of all branches of a difficult science; but many of the actual results are such as can be stated in a simple and striking form.
• There are various ways of solving this extremely simple problem.
• And even this problem, simple as it is, has sufficient content to bring out clearly certain principles of cardinal importance.
• It is easy to see this by considering a simple example.
• If s, the number of squares, is even and less than 10, the number of representations may be expressed in a very simple form by means of the divisors of n.
• When s is 3, 5, or 7, the number of representations can also be found in a simple form, though one of a very different character.
• Liouville's proof, which was first published in 1859, is quite simple and, as the simplest example of an important type of argument, is worth reproducing here.
• Thus G(4) ≥ 15; and Kempner, by a slight elaboration of this simple argument, has proved that G(4) ≥ 16.
• In the second row I have shown the best known lower bounds, which are given by the simple general formula [(3/2)k] + 2k - 2, in which [(3/2)k] denotes the integral part of (3/2)k.
• All this is simple enough; but the further study of the integral is very intricate and difficult, and I cannot attempt to do more than to give a rough idea of the obstacles that have to be surmounted.
• In the present case we have no such simple recourse; for every point of the unit circle is a singularity of an exceedingly complicated kind, and the circle as a whole is a barrier across which it is impossible to deform the contour.
• (sum is over n) which (a) is as simple and natural as we can make it, and (b) behaves perfectly regularly at all points of the unit circle except at the one point with which we are particularly concerned.
• The process is, at bottom, one of 'decomposition into simple elements', applied in an unusual way.
• It will be seen that these numbers conform to a simple law, and that is the third advantage of the method, that it is not a mere existence proof, but gives us a definite upper bound for G(k) for all values of k, viz.
2. Élie Cartan reviews
• This book begins with very simple and familiar ideas of vectors in Euclidean space in rectangular Cartesian coordinates and gradually arrives at the notion of a tensor and the algebraic and differential operations with tensors.
• After two chapters on the generalities of the theory there is a chapter on closed groups and one on closed simple groups.
• There follows a chapter on open groups, containing the theorem that the first Betti number of an open simple group is 0 or 1.
• The book concludes with a statement of all known theorems on the Betti numbers of closed simple groups - among others the results of L Pontrjagin and R Brauer, who have calculated them for the four main types of simple group.
• In the preface to the two volumes under review M Cartan points out that, in their most general mathematical form, spinors were discovered by him in 1913 in his work on linear representations of simple groups, and he emphasises their connection, shown in Vol.
• For example, he completed the work of Killing and Lie on the classification of simple Lie algebras.
• It was first published in 1966, when the work of Killing and Cartan on the classification of simple Lie groups was beginning to be applied in elementary particle physics.
• In terms of contemporary Lie group theory, it deals with the B and D series of simple Lie algebras and the Lie groups which go along with them, i.e., the orthogonal matrix groups over the real and complex numbers and their simply connected covering groups.
• Clearly, he is presenting a "vulgarization" of the general theory of semi-simple Lie algebras and groups, which he developed almost single-handedly (with the help of Hermann Weyl!) in the period 1893-1930.
3. German syllabus
• Simple equations of first degree with one unknown, in connection with operations with rational numbers.
• Equations of first degree with one or more unknowns; simple applications, especially from everyday life.
• Simple masses of shrubbery and borders of garden paths.
• Simple integral and rational functions.
• Simple equations, and systems of equations which c an be solved by quadratic equations - numerical and graphical treatment.
• Simple triangle calculations.
• Simple exercises in surveying and levelling.
• Simple representations by means of functions of a complex variable.
• Simple astronomical observations with measurements and calculations.
4. ELOGIUM OF EULER
• Taylor was made into an important branch of integral calculus by assigning a simple and workable notation which was found to apply successfully to the theory of series.
• This was done by searching for the sums or the expression of their general terms and to those of the roots or determinant equations, by which to obtain with a simple calculation the approximate value of the products or the indefinite sums of certain numbers.
• He abandoned his first ideas and submitted new ones to proof by experiments and enriched Dioptics with analytical formulas which were simple, useful, general and applicable for every instrument that could be built.
• At other times it would be a problem that appeared insurmountable that he resolved in an instant by a very simple method or an elementary problem with a very difficult solution that could only be overcome with the greatest efforts.
• At other times simple numbers, or a new series presented questions novel by their uniqueness which took him to unexpected proofs.
• Euler's work due to the telling of the very simple and unvaried events of his life.
• Euler's name, so highly regarded in the Sciences and the imposing way in which his insights reveal the most thorny and abstract ideas, reveals in these simple and easily readable Letters and unique charm and those who have not studied Mathematics, are astonished and flattered to be able to understand a work by Euler and are grateful that his message has been placed within their grasp.
• Euler's simple modesty felt his force and on more than on occasion used it to good purpose.
• For most of the Northern aristocracy to whom he was personally known, they had already provided him with marks of their esteem, or more like veneration that one can hardly deny when one sees the uniting of such simple virtues to such vast heightened genius.
5. Value of Mathematics
• Simple generalisation to others of a demand of their own allows us to see the impossibility of a desire that our blind selfishness imposed on us with a pressing imperative.
• It is, in short, to make use of the faculty which in Mathematics we call intuition (to look inside ourselves) and that should not be confused with the faculty called intuition by some psychologists and pedagogues that hardly differs from simple perception.
• If the student were accustomed to constantly project the data and results of the problems into the realm of reality, absurdities of this nature would be avoided, the pupil would become accustomed to keep in mind this simple and yet so often forgotten truth that all data translating a measure of the physical world is necessarily approximate, and that, therefore, the alleged accuracy in the results is not only a pure chimera but a grotesque falsification of reality.
• These simple laws serve, for example, to justify the implantation of the cyclical methods that establish the continuity in the study of the topic without breaking them up into separate areas; justify the introduction of intuitive methods in the first years of high school to fill the gap that existed between the empiricism of primary education and the rationalism of university education, and the progressive evolution of methods that without discontinuity or sudden jumps allow one to develop the psychological activities of the child gradually from early childhood to university.
• - Simple analysis, observation of the facts and points surrounding the child.
• But it is necessary in such a case that the technique of handling the book is adequate so that this management is not converted into simple memory exercises.
• How can we combine the two utilitarian and formative tendencies without reloading the programmes with the overwhelming and unbearable weight they suffer today? I propose a very simple formula.
• If the educational efficacy of mathematical teaching lies mainly in methods, respecting them, we will have the freedom to select the knowledge that will be most useful and thus arouse greatest interest, and thus the two utilitarian and educational points of view, which have so often been presented as opposed to one another, will be joined in a simple harmonizing formula: Teaching useful knowledge with educational methods.
6. A A Albert: 'Structure of Algebras
• It has been most fortunately possible at this time to give a new treatment of the early parts of our subject simplifying not only the proofs in the theory of normal simple algebras but even the exposition of the structure theorems of Wedderburn.
• Their exposition is begun in Chapter IV which contains the theory of the commutator subalgebra of a simple subalgebra of a normal simple algebra, the study of automorphisms of a simple algebra, splitting fields, and the index reduction factor theory.
• This is believed to be the first time the extension has been made in a really simple fashion.
• The theory of involutorial simple algebras arose in connection with the study of Riemann matrices but is now a separate branch of the theory of simple algebras with structure theorems on approximately the same level as those on arbitrary simple algebras.
7. Kelvin on the sun, Part 2
• The continually repeated blows upon any part of the walls or ceiling will in the aggregate be equivalent to a continuous pressure which will be in simple proportion to the average density of the crowd at the place.
• One very remarkable and important result which be finds is, that the density at the centre is about twenty times the mean density; and this, whether the mass be large or small, and whether of oxygen, nitrogen, or hydrogen, or other substance; provided only it be of one kind of gas throughout, and that the density in the central parts is not too great to allow the condensation to take place, according to the ordinary gaseous law of density, in simple proportion to pressure for the same temperatures.
• But when the compressing force is sufficiently increased, they all show greater resistance to condensation than according to the law of simple proportion, and it seems most probable that there is for every gas a limit beyond which the density cannot be increased by any pressure however great.
• Lane remarks that the density at the centre of the sun would be "nearly one-third greater than that of the metal platinum," if the gaseous law held up to so great a degree of condensation for the ingredients of the sun's mass; but he does not suggest this supposition as probable, and he no doubt agrees with the general opinion that in all probability the ingredients of the sun's mass, at the actual temperatures corresponding to their positions in his interior, obey the simple gaseous law through but a comparatively small space inwards from the surface; and that in the central regions they are much less condensed than according to that law.
• According to the simple gaseous law, the sun's central density would be thirty-one times that of water; we may assume that it is in all probability much less than this, though considerably greater than the mean density, 1.4.
• If we ask, How does the temperature of equi-dense portions of the sun vary from age to age? the answer certainly is that the matter of the sun of which the density has any stated value, for example, the ordinary density of our atmosphere, becomes always less and less hot, whatever be its place in the fluid, and whatever be the law of compression of the fluid, whether the simple gaseous law or anything from that to absolute incompressibility.
• But at a certain time in the history of a wholly fluid globe, primitively rare enough throughout to be gaseous, shrinking under the influence of its own gravitation and its radiation of heat outwards into cold surrounding space, when the central parts have become so much condensed as to resist further condensation greatly more than according to the gaseous law of simple proportions, it seems to me certain that the early process of becoming warmer, which has been demonstrated by Lane, and Newcomb, and Ball, must cease, and that the central temperature must begin to diminish on account of the cooling by radiation from the surface, and the mixing of the cooled fluid throughout the interior.
• If the substance were oxygen, or nitrogen, or other gas or mixture of gases simple or compound, of specific density equal to the specific density of our air, the central temperature would be 51,200° C, and the average translational velocity of the molecules 6.66 kilometres per second, being √(3/7) of 10.2, the velocity acquired by a heavy body falling unresisted from the outer boundary (of 40 times the radius of the earth's orbit) to the centre of the nebulous mass.
8. Max Planck: 'Quantum Theory
• This exceedingly simple relation is a complete and adequate expression of Wien's law of distribution of energy; for the dependence upon wave-length is always given immediately as well as the dependence upon energy by Wien's generally accepted law of displacements.
• Finally, the observations made by G Rubens and F Kurlbaum, with infra-red rays after transmission through fluorspar and rock salt, showed a totally different relation, which, under certain conditions, was still very simple.
• Thus, by direct experiment, two simple limits have been fixed for the function R, i.e.
• (It would be better to substitute temperature for energy here.) On this basis a comparatively simple combinatory method was derived for calculating the physical probability of a certain distribution of energy in a system of resonators.
• The interpretation of the second universal constant of the radiation formula was much less simple.
• The first advance in this work was made by A Einstein, who proved, on the one hand, that the introduction of the energy quanta, required by the quantum of action, appeared suitable for deriving a simple explanation for a series of remarkable observations of light effects, such as Stokes's rule, emission of electrons, and ionization of gases.
• By greatly simplifying the assumptions regarding the nature of the oscillations, P Debye obtained a comparatively simple formula for the specific heat of a solid body.
• Proceeding further along the same lines, P Epstein succeeded in giving a complete explanation of the Stark effect of the electrical separation of the spectral lines, and P Debye in giving a simple meaning to the K-series of the Rontgen spectrum, investigated by Manne Siegbahn.
9. Jacobson: 'Structure of Rings
• These are: the structure theory of rings without finiteness assumptions, cohomology of algebras, and structure and representation theory of non-semi-simple rings (Frobenius algebras, quasi-Frobenius rings).
• Thus the present volume includes virtually all the results on semi-simple rings which can be found in the two books cited before.
• For example, the theory of centralizers of finite dimensional simple subalgebras of simple rings with minimum condition appears as a special case of the Galois theory of the complete ring of linear transformations of a vector space over a division ring.
• A semi-simple ring is one which has enough irreducible representations to distinguish elements.
• In the first part we consider the theory of semi-simple rings with minimum condition.
• In Chapter V we define Kronecker products of modules and algebras and we reduce the problems of determining the structure of Kronecker products of simple algebras to the case of division algebras and fields.
10. D'Arcy Thompson on Greek irrationals
• Aristotle gives us the following statement of Plato's concept of the 'genesis of number': [Number is derived from Unity and the indeterminate dyad]; but this apparently simple statement has never been satisfactorily explained.
• In short if we keep to this restricted definition of our problem, and if we then go a step or two farther in its interpretation than Prof Taylor has gone, we come to a very simple understanding of what [the one/unity] and the [infinite/indeterminate dyad] are; and of how, between them both, such a 'number' as √2 is generated.
• The continued fraction is an elegant arithmetical device, and the mathematician calls it a simplified expression; but it does not follow that it is simple to work with.
• This point, this precise nature of the agency of the 'One', and the simple explanation which it involves of the precise meaning of [to define] or [to equal], both seem to me to be made clear by our study of the Greek side-and-diagonal series; but the point is lost as soon as we replace that formula by the continued fractions of our modem arithmetic.
• All this arithmetic is so simple that it can hardly have escaped the notice of any calculator who pondered over the elementary table with which we began.
• It is inconceivable that the Greeks should have been familiarly acquainted with the one and yet unacquainted with the other of these two series, so simple, so interesting and so important, so similar in their properties and so closely connected with one another.
• All this is a beautifully simple illustration of a principle recognized in modern mathematics, that you may immensely extend the efficiency (so to speak) of the series of natural numbers if only you can add one other number to it.
11. Aitken: 'Statistical Mathematics
• What is the axiomatic basis of the science of statistics, and what are the facts upon which the inductive synthesis is based? The facts are certain regularities which have been observed in the proportionate frequency with which certain simple events happen or do not happen, when the circumstances under which they may occur are reconstructed again and again in repeated trials; and the axioms, and the structure of theorems founded upon them, constitute the subject called mathematical probability.
• The reader is recommended to experiment with simple repeated trials of this kind, and for future reference to record the results in sequence, in the order in which they occur.
• Simple ideas such as these suggest by generalization and abstraction the axioms of probability; but the choice of axioms may be made in various ways, which lead to different formulations of the theory of probability.
• As our simple illustrations of the coin and the die have suggested, the crude intuition of probability rests on the observation that when a given set of circumstances S, such as a symmetrical coin spun rapidly, has been present on numerous occasions in the past, it has been associated in a nearly constant proportion of those occasions with some event E, such as the fall of "heads." .
• To take a classical example, in the sequence defining a certain simple geometric series, .
• Let us examine more closely the system S, keeping some simple system such as a coin or die in mind.
• Now the question of assigning a measure to such aggregates has been deeply studied in modern pure mathematics, the guiding idea being that of extending as widely as possible the scope of a concept familiar in simple cases, namely the cardinal number of a finite set of objects, the length of a line, the area of a surface, the volume of a solid.
12. Maini papers
• A non-linear bifurcation analysis is presented for a simple version of the field equations: a non-standard element is required.
• A nonlinear bifurcation analysis is presented for a simple version of the governing field equations.
• Simple analytical solutions are obtained when the reaction rates and the initial substrate concentration satisfy a certain condition.
• Here we examine a simple one-dimensional caricature of their model which exhibits similar linear behaviour and present a nonlinear analysis which shows the possibility of superposition of modes subject to appropriate parameter values and initial conditions.
• We propose a simple partial differential equation model for a chemotactic system of two species, a population of cells and a chemo-attractant to which cells respond.
• By using mode selection from the linear analysis we produce simple pattern elements such as stripes and regular spots.
• More complex patterns evolve from these simple solutions as parameter values or domain shape change continuously.
13. Cheney books
• The usual questions from classical approximation theory can be posed for these approximating subspaces, such as (i) Do best approximations exist? (ii) Are best approximations unique? (iii) How are best approximations characterized? (iv) What algorithms can be devised for computing best approximations? (v) Do there exist simple procedures which provide "good" approximations, in contrast to "best" approximations? (vi) What are the projections of least norm on these subspaces? and (vii) what are the projection constants of these subspaces? This volume surveys only a part of this growing field of research.
• First we ask, "What subclasses of functions are suitable for approximating other functions?" Here interest focuses naturally on functions that are simple combinations of univariate functions.
• The important tensor-product subspaces play the principal role here because of their simple linear structure.
• In other cases, the reverse is true, and the students learn much from programming simple algorithms themselves and experimenting with them - although we offer a blanket admonition to use well-tested software.
• In style, we have tried to make the exposition as simple and clear as possible, electing to furnish proofs that are complete and relatively easy to read without the reader needing to resort to pencil and paper.
• To paraphrase Shaw: We have done our best to avoid conciseness! We have also made considerable efforts to find simple ways to introduce and explain each topic.
14. Truesdell's books
• With this tractate I aim to provide a simple logical structure for the classical thermodynamics of homogeneous fluid bodies.
• I think it is as simple and pretty as can be.
• That this tractate is a long one, results from its triple scope: (1) Conceptual: for those already expert in thermodynamics, to show how all the concepts of the traditional, elementary theory can be derived from simple and natural assumptions about heat engines, developed by simple and rigorous mathematics.
• For this reason I have included detailed proofs of propositions which to physicists and engineers may seem so obvious as to need no proof, to mathematicians so simple that anyone can prove them.
• (with R G Muncaster) Fundamentals of Maxwell's kinetic theory of a simple monatomic gas.
15. Raphson books
• Moreover, Mr Raphson explains his Method after the very same manner as he invented it, and to show the large Extent and Certainty thereof, he propounds a general Theorem, which he afterwards resolves more particularly in Two Propositions: Then he proceeds to illustrate his Method by Examples, in 32 Problems; wherein is exhibited the Resolution of Equations, of all manners of Dimensions, taken from the Resolution of a Simple Equations: Whereunto he adds Examples of Quadratic Equations, All his Operations are described at large; and to render the Practice more plain and obvious, the Author hath taken the Pains to compose certain Tables, which are inserted at the End; insomuch that if he continues to prosecute these Studies, as he hath begun, it is not to be doubted but that he will become one of the most skilful Mathematicians that are now living; since at the Age of 22 Years, he hath already attained to so great a Knowledge in those abstruse and difficult Sciences: Wherefore what improvement may we from not expect from the extraordinary Judgement of his riper Years? .
• First, that we admit of nothing as a first Principle, but what appears to be certain and most evidently true even to the meanest Capacity; such a Principle he reckons a Simple Idea to be, an Attribute Essential to the thing to which it belongs: That it may be certain tis requisite it should the first and undoubted Truth; and that it be evidently True, a clear and distinct Perception is Necessary.
• The other sort of Arguments for the Proof of real Space distinct from Matter, Mr Raphson in a Geometrical Way deduces from the Necessary and Natural Concatenation and Consequences of simple Ideas.
• Sixthly, That a Self-existent Being is in its own Nature a most simple Being.
• In the Conclusion of the first Part Mr Raphson observes, That as the Self-existent Being necessarily exists, so such Beings as are not self-existent owe their Being to something extraneous to themselves: That as the former is what it is of it self, so the later receive all that they are and have, from something else: That as the former is in its own Nature eternal, so the later are in the same manner temporal: As the one is infinite, the other are finite: As the one is necessarily and of it self one, the other owe their Unity not to themselves, but to what made them such: As the one is a most absolutely simple Being, so the other are either compounded, and so resolvable into the Principles of which they consist; or if they are in their Nature simple, as they were made, so they may be unmade; or, as far as they were produced, so far also are they capable of being destroyed by the Being that produced them: As the one is immutable, the other are mutable: And as the one is all that is or can be, in an absolute and infinitely perfect Sense, the other are of restrained and limited Essences, which is the Reason that there are many of them, for Finiteness is the natural Root of Plurality.
16. Moran reviews
• In fact, Chapter II of this monograph consists of an analysis of several simple inventory models.
• Simple ideas of linkage, cross-over, recombination fraction and so on must be familiar.
• For example, the untutored reader might imagine from the discussion here that the Canadian lynx data was an example of a simple sinusoidal regression with an added random error.
• Simple calculations are usually left to the reader and for difficult proofs the reader is often referred to the literature.
• Among stochastic processes considered, apart from simple Markov chains and processes, are less common models like Daniels's stiff chains and Hammersley's self-avoiding random walks.
17. Marion Walter's books
• This book will have great appeal, for it invites the young mathematician to explore, to discover, and to learn by doing as he uses the safe metal mirror that is provided with the book to answer the stimulating questions or to follow the simple directions.
• While having much fun, the child will grasp simple mathematical concepts.
• The young reader will have fun seeing, doing, thinking, and imagining as he uses the safe, metal mirror, which comes with the book, to follow the simple suggestions and to answer the intriguing questions.
• Simple mathematical concepts will be developed while the child is having fun.
• The puzzles move from simple to more challenging, along with some impossible puzzles.
18. Von Neumann: 'The Mathematician' Part 2
• This means that the criterion of success for such a theory is simply whether it can, by a simple and elegant classifying and correlating scheme, cover very many phenomena, which without this scheme would seem complicated and heterogeneous, and whether the scheme even covers phenomena which were not considered or even not known at the time when the scheme was evolved.
• One expects a mathematical theorem or a mathematical theory not only to describe and to classify in a simple and elegant way numerous and a priori disparate special cases.
• Also, if the deductions are lengthy or complicated, there should be some simple general principle involved, which "'explains" the complications and detours, reduces the apparent arbitrariness to a few simple guiding motivations, etc.
• These criteria are clearly those of any creative art, and the existence of some underlying empirical, worldly motif in the background - often in a very remote background - overgrown by aestheticizing developments and followed into a multitude of labyrinthine variants - all this is much more akin to the atmosphere of art pure and simple than to that of the empirical sciences.
19. Valiant Turing Award
• However, his model was so simple and compelling that it immediately captured the imagination of the community and led to widespread agreement that this was indeed the right approach.
• His results here range from simple, but powerful and elegant, insights to reexamining the very foundations.
• An example of a simple insight is his parallel routing scheme, described in the paper "A scheme for fast parallel communication" (SIAM J.
• Using simple greedy schemes to route the data can often lead to congestion - too many data paths may end up using the same link in the network at once.
• Valiant discovered a brilliant and simple randomized solution to the problem.
20. G H Hardy addresses the British Association in 1922
• They are seemingly simple questions, and it is not necessary to be anything of a mathematician to understand them; and I have chosen them for no better reason than that I happen to be interested in them myself.
• Is there, I am asking, any simple criterion by which such numbers can be distinguished? .
• Then, if it is of the form 4m + 1, it is a sum of squares, and in one way only, while if it is of the form 4m + 3 it is not so expressible; and this simple rule may readily be generalised so as to apply to numbers of any form.
• There is no case, except the simple case of squares, in which the solution is in any sense complete.
• There are no simple general tests by which the primality of a number chosen at random can be determined, and the amount of computation required in any particular case may be quite appalling.
21. Gordon Preston on semigroups
• What he gave was the structure, in terms of its maximal subgroups, of a completely 0-simple inverse semigroup.
• 1037-1049) showed that semigroups which are unions of groups are disjoint unions of completely simple semigroups, an important early structure theorem, emphasising also the importance of completely simple semigroups, introduced by Rees in his 1940 paper.
• It was said that semigroups were objects that were too simple to be interesting, and that useful mathematics would not stem from their study.
• It was an attempt at giving an integrated account of the Green relations, the Schutzenberger group and representations (we had just had what we called a "Schutzenberger week" at which Schutzenberger had lectured each day on his representations and associated matters), completely 0-simple semigroups, 0-minimal ideals, etc.
22. Mathematicians and Music 3
• The great feature of this work is the formulation and proof of the laws by which the ear bears musical sounds from one or more distinct sources; how the theory of combined musical sounds is reduced to the theory of combined simple sounds.
• From these laws we learn the nature of consonance and dissonance, knowledge so necessary for building up a system of harmony; we learn the principles which determined those degrees of musical sound selected by various nations at various times; we understand the reasons for the simple ratios of the lengths of strings producing consonant tones and the limitation of the numbers of these ratios; and we appreciate the value of temperaments for different instruments.
• Or, if we have a graph of the vibrations corresponding to such tones, the series may also be calculated, various terms in the series corresponding to simple elements compounded in the tone or tones.
• That is, a tone made up of 30 simple tones can be analyzed and the coefficients of the corresponding number of terms in the Fourier series written down.
• In concluding references to activities of the past one hundred years, I should, however, take time to recall that when, in these latest days, there arose a question as to the manner in which our present musical notation for equal temperament scales could best be simplified, it was a former president of this Association who brought forward a scheme so beautifully simple that further advance in this regard cannot be imagined.
23. Hilbert reviews
• (3) the principle of not merely proving a proposition in the most simple way but indicating precisely what axioms are necessary and sufficient for the proof; .
• The many-mansioned discipline known as "symbolic logic" has for a long time ceased to be a simple affair, and introductions to it vary according to the special interests to which they cater.
• The paradoxes are presented, and Russell's simple theory of types is adopted for their avoidance.
• Six chapters (Simple curves and surfaces, regular systems of points, configurations, differential geometry, kinematics, topology) serve to lead the average reader to a number of vantage points from which large domains can be surveyed.
• Thus although the primary object is to present proofs of consistency (Widerspruchsfreiheit) of mathematical systems, no such proof appears in the first volume, whose 468 pages are occupied by preliminary considerations, such as the possibility of transforming formulae in the propositional calculus into a standard form, the extent to which logical quantifiers can be eliminated from an axiom system, the exact specification of the rules for the use of recursive definitions, and proofs of categoricity (Entscheidungsbarkeit) and completeness (Vollstandigkeit) for simple systems.
• The analogy is drawn with a simple model of frequency conversion.
• For a general class of two-mode, simple analytic expressions are derived for the evolution of the field quantum entropy in the bimodal field interacting with an effective two-level atom via the Raman transition, with an additional Kerr-like medium.
• Simple expressions for the atomic populations, the cavity photon statistics, and the reflection and transmission probabilities are given for any initial state of the atom-field system.
• We propose a generation of Bell-type states having a simple initial state preparation of the present system.
• We propose a method of generating Bell-type states from a simple initial state preparation of two different modes of electromagnetic field.
25. De Montmort: 'Essai d'Analyse
• The life of Pierre-Remond de Montmort, after a stormy start, was a simple, happy one.
• He discusses such simple games as Pharaoh, Bassette, Lansquenet and Treize, and then, not so fully or successfully, Ombre and Picquet.
• Having set down the rules, he solves simple cases in a method somewhat reminiscent of Huygens, and then takes a plunge into a general solution which appears to be correct but is not always demonstrably so.
• the Arithmetic Triangle) in the perpendicular column which corresponds to p, beginning with p, and the denominator the series of products p × p - 1 × p - 2 × p - 3 × p - 4 × p - 5; so that, cancelling out the common terms, we have for Pierre's chance the very simple .
• He doesn't bother with the rules (they must have been entirely established by this time) and he calculates several simple chances but remarks that in the majority of situations the solution cannot be found.
26. Slaught's books
• These exercises are for the most part very simple, but by bringing into play a large number of straight lines and circle arcs in a single problem, they are a valuable aid in the development of geometric imagination.
• The new Algebra contains numerous attractive features, all aiming to make the subject more simple and interesting and therefore more valuable to first year pupils.
• Among these features the most distinctive are perhaps the following four: (i) The presentation of the subject is as simple as it can be made.
• Like previous books by these authors there is great emphasis on simple presentation and easy gradation in each topic, and on the side of concrete applications.
• While recognizing the increased maturity of the pupils, the authors nevertheless maintain in this present text that simple and interesting form of presentation which characterizes the earlier book.
27. Craig books
• Perhaps the only division of the subject - omitting the simple case of perspective projection - that has ever been fully treated is that of projection by similarity of infinitely small areas.
• A few of the solutions of simple problems in the paper, it is believed by the author, are new and simpler than any he was able to find in the writings of others.
• With these few exceptions there is no claim of originality in what follows: the attempt having simply been made to present in as simple and natural form as possible what others have done.
• The object of that chapter is only to give in a simple manner some of the more important and elementary properties of the curves of the second order, so that convenient reference could be made in the subsequent part of the paper to the various formulas connected with these curves, and also simple means given for constructing them.
28. Halmos books 2
• The rules are simple and the advantages of following them to the conscientious and diligent reader are surely obvious and incalculable.
• What makes a problem interesting? Its statement should be simple, not requiring excessive explanations, and the solution should be readily understandable by the intended audience.
• Understanding simple things such as basic linear algebra does not seem to be an easy task.
• As to the form, the style is vivid and clear, using simple words, and free of long and complex technicalities.
• The text is rich in brief comments explaining the ideas behind the reasoning and calculations, and frequently refers to simple examples and to the basic notions of universal algebra.
29. Loney CUP
• We have been particularly struck with the manner in which the author combines perspicuity with brevity in his short chapter on "units and dimensions," a subject which, though apparently very simple, often presents considerable difficulties to a beginner.
• Mr Loney may be congratulated on the production of a most valuable text-book, at once simple and complete.
• We are glad to see that the method of the hodograph is used in treating of normal acceleration, and that cycloidal motion is considered as a case of simple harmonic motion.
• The author has succeeded in his purpose to produce "a fairly complete elementary text-book on Plane Trigonometry." The faithful student of this treatise "will have little to unlearn when he commences to read treatises of a more difficult character." The style is clear and simple; even when it is diffuse, the author never hides his thoughts with words either large or small.
30. D'Arcy Thompson on Plato and Planets
• Without recapitulating further details for Sun and Moon, we come to a very great difficulty in the case of the planets, namely to explain, by any simple imaginary mechanism, what are known as their stations and retrogradations.
• But the fourth sphere was not coaxial with the third, but was set somewhat obliquely to it (just as the first sphere was to the second), and thus introduced another component in the form of a simple harmonic motion, causing the planet to perform apparently a pendulum-like vibration in the plane of the ecliptic, while all the while it was being carried around that circle by the proper motion of the second sphere.
• The calculation, a very simple one, has been performed by Schiaparelli, who shows the angles to be as follows: .
• A chief source of obscurity in the whole passage is the simple circumstance that Plato was talking in riddles and in allegory, after the fashion of antiquity and the East, and therefore did not choose to tell us many things which he must have known.
31. Berge books
• In what are called simple graphs, the vertices are divided into two sets such that all arcs connect only members of one set with points of the other.
• Matching on a simple graph (assignment problem, Latin squares); 11.
• The Preface tells us that it "aims to demonstrate that a large part of these mathematical programming problems can be solved in a simple and elegant manner using ..
• Surprisingly, Vajda's excellent 'Mathematical Programming' (1961) [Steven Vajda (1901-1995)] is not mentioned, though in that book all the essential ideas of the present one are explained in simple numerical terms so that this one could almost have been subtitled "A Mathematical Gloss on a Text by Vajda".
32. Apostol Project
• Simple applications, Archimedes' discovery, computation, and extensions (lattices, random numbers, Buffon needle).
• This leads to elegant derivations of addition formulas, with applications to simple harmonic motion.
• Intrigue and drama are injected into the story when alternative theories are pro posed, for example, Did Eupalinos physically measure around the mountain or over the mountain? Site exploration, simple mathematics, and common sense sup ply the answer.
• After an introduction and a brief survey of mathematical events up to the seventeenth century, the units describe topics in or about numeration systems, number theory, the Pythagorean theorem, irrational numbers, pi, the evolution of trigonometry from astronomy, simple analytic geometry, and some fundamental calculus.
33. Didactics of Mathematics
• Geometry consists of a set of definitions of geometric figures and calculation of perimeters of polygons, and areas of the same in simple cases.
• Geometry is practically reduced to applying formulas for the areas of simple polygons, of circles and some circular figures.
• The first course includes: natural number, fractions, decimal numbers, simple rule of three, elementary geometric figures, some geometric constructions and area calculation.
• It is possible that, in addition to the reasons just mentioned, there is a more powerful one that is really that it has reduced the teaching of mathematics, in its elementary phase, to a simple calculator, but with the aggravating aspect of automatism.
34. Piaggio Reviews
• The object of this book is to give an account of the central parts of the subject in as simple a form as possible, suitable for those with no previous knowledge of it, and yet at the same time to point out the different directions in which it may be developed.
• In devoting an early chapter to some simple partial differential equations, Prof Piaggio has put teachers and students alike under a debt which the latter cannot realise.
• Is it credible that some of us became acquainted with the equations of wave motion and with their simpler solutions surreptitiously in treatises on sound, because in pure mathematics a partial differential equation of the second order, however simple, was expected to yield precedence to the twenty-four solutions of the hypergeometric equation and to an abstract discrimination between general integrals, complete primitives, and the like? .
• "The object of this book is to give an account of the central parts of the subject in as simple a form as possible, suitable for those with no previous knowledge of it, and yet at the same time to point out the different directions in which it may be developed." The only previous knowledge assumed is that of the differential and integral calculus.
35. Orr Stability
• An explanation of the difficulty was given by showing that it is necessary to push Lord Rayleigh's investigations a step farther by resolving a disturbance into its constituent fundamental ones by quasi-Fourier analysis, and that, when this is done for disturbances of initially simple type in some of the most important and simplest cases of flow, it is found that the disturbance will, for suitable values of the constants, increase very much, so that the motion is practically unstable.
• As the fundamental modes of disturbance do, as is shown in Chapter II., possess stability of the simple exponential character, the "special" solution is, I believe, as a matter of fact, the solution for a given initial disturbance; if this be a simple trigonometrical function of the coordinates, the form of v is simple; but that of the "forced" disturbance in no case appears capable of being readily calculated.
36. Coulson: 'Electricity
• From this simple experimental fact has developed the whole science of electrostatics, that is, the properties of electricity at rest.
• First, the microscopic viewpoint throws light on the fundamental physical processes; this enables us to view our subject as one whole and means that we shall not have to introduce from time to time apparently unrelated physical assumptions, for we shall see how our macroscopic equations arise quite naturally from simple microscopic properties of the atom and the electron.
• The explanation is simple, for in these substances all the negative charges (or electrons) are firmly attached to corresponding positive charges.
• Thus the difference between substances which are or are not permanent magnets is not that they are made of essentially different material, but rather that with permanent magnets we have no way (or at any rate no simple way) of destroying the co-operative effect of the separate atoms, whereas with non-permanent magnets this co-operation is solely the result of forces exerted from outside, and automatically disappears when the force is removed.
37. Semple and Kneebone: 'Algebraic Projective Geometry
• Projective geometry is a subject that lends itself naturally to algebraic treatment, and we have had no hesitation in developing it in this way - both because to do so affords a simple means of giving mathematical precision to intuitive geometrical concepts and arguments, and also because the extent to which algebra is now used in almost all branches of mathematics makes it reasonable to assume that the reader already possesses a working knowledge of its methods.
• Our first rudimentary idea of number is arrived at by simple abstraction from the processes of counting and measuring ordinary objects, and this idea is adequate at the level of school arithmetic.
• In this book we shall study the structure of projective geometry which, as is well known, is closely associated with certain simple algebraic structures, and with linear algebra particularly.
• Finally, the essentials of euclidean geometry may be treated projectively by the simple artifice of introducing the line at infinity and the circular points.
38. H L F Helmholtz: 'Theory of Music' Introduction
• Later physics has extended the law of Pythagoras by passing from the lengths of strings to the number of vibrations, and thus making it applicable to the tones of all musical instruments, and the numerical relations 4 to 5 and 5 to 6 have been added to the above for the less perfect consonances of the major and minor Thirds, but I am not aware that any real step was ever made towards answering the question: What have musical consonances to do with the ratios of the first six numbers? Musicians, as well as philosophers and physicists, have generally contented themselves with saying in effect that human minds were in some unknown manner so constituted as to discover the numerical relations of musical vibrations, and to have a peculiar pleasure in contemplating, simple ratios which are readily comprehensible.
• E Hanslick, in his book On the Beautiful in Music (Ueber das musikalisch Schone), triumphantly attacked the false standpoint of exaggerated sentimentality, from which it was fashionable to theorise on music, and referred the critic to the simple elements of melodic movement.
• The question of how the ear is able to perceive these harmonic upper partial tones then leads to an hypothesis respecting the mode in which the auditory nerves are excited, which is well fitted to reduce all the facts and laws in this department to a relatively simple mechanical conception.
• 5a), but that I was unwilling to omit that hypothesis because it is so well suited to furnish an extremely simple connection between all the very various and very complicated phenomena which present themselves in the course of this investigation.
39. Max Planck and the quanta of energy
• The noteworthy result was found that this connection was in no way dependent upon the nature of the resonator, particularly its attenuation constants - a circumstance which I welcomed happily since the whole problem thus became simpler, for instead of the energy of radiation, the energy of the resonator could be taken and, thereby, a complex system, composed of many degrees of freedom, could be replaced by a simple system of one degree of freedom.
• This extremely simple relationship can be considered as the completely adequate expression of Wien's energy distribution law; for with the dependence upon the energy, the dependence upon the wavelength is always directly given through the general, well-established displacement law by Wien.
• Whilst for small values of the energy and for short waves, Wien's law was satisfactorily confirmed, noteworthy deviations for larger wavelengths were found, first by O Lummer and E Pringsheim, and finally by H Rubens and F Kurlbaum, whose measurements on the infrared residual rays of fluorite and rock salt revealed a totally different, though still extremely simple relationship, characterized by the fact that the quantity R is not proportional to the energy, but to the square of the energy, and in fact this holds with increasing accuracy for greater energies and wavelengths.
• So, through direct experiment, two simple limits were determined for the function R: for small energies, proportionality with the energy; for greater energies, proportionality with the square of the energy.
40. Teixeira on Rocha
• The solution thus obtained is more closely approximate than those given previously, but less simple.
• Analysis and geometry help each other, but there are questions in the domain of the latter science to which the mathematician, without consideration, throws himself on the wings of the first, and, by flying, seeks to find by complicated formulas results to which the latter leads by a simple path.
• Anastacio da Cunha gave two very simple geometric demonstrations of this formula, and he censured the Academy of Sciences not only for posing such a simple question, but also for having rewarded such a mediocre memoir.
41. A N Whitehead addresses the British Association in 1916, Part 2
• The theory of the interconnection between the truth-values of the general propositions arising from any such aggregate of propositional functions forms a simple and elegant chapter of mathematical logic.
• But it is objected that this process and its consequences are so simple that an elaborate science is out of place.
• What, then, is the use of an elaborate chemical analysis of sea-water? There is the general answer, that you cannot know too much of methods which you always employ; and there is the special answer, that logical forms and logical implications are not so very simple, and that the whole of mathematics is evidence to this effect.
• Another example of this law is the way physicists and chemists have dissolved the simple idea of an extended body, say of a chair, which a child understands, into a bewildering notion of a complex dance of molecules and atoms and electrons and waves of light.
42. Born on wave mechanics
• Frequency and wave-number, on the other hand, are properties of simple harmonic waves, whose definition implies that they extend indefinitely in time and space.
• Nevertheless, modern physics declares that the matter is not so simple as this, whenever we have to deal with the restless universe of atoms and electrons.
• But the position of a physicist who wishes to observe an electron in its path is not so simple.
• Physically there is no meaning in regarding this wave as a simple harmonic wave of infinite extent; we must, on the contrary, regard it as a wave packet consisting of a small group of indefinitely close wave-numbers, that is, of great extent in space.
43. Smith's Teaching Books
• It is believed that teachers will welcome the logical, and at the same time simple, presentation of subjects like evolution, factoring, the theory of indices, and the treatment of the quadratic as set forth in this work.
• The noteworthy features of the book are the early and simple introduction of graphs with a table of squares and cubes at the end of the book to facilitate computation, the large number of oral problems under each topic and the cumulative reviews at the end of the book.
• Every important magazine such as well informed persons read uses graphs, formulas, and simple equations.
• that the work should proceed from the simple to the complex" and that "..
44. Gyula König Prize
• Here he gives very simple numerical expressions for Lebesgue constants whose properties were previously studied by Lipot Fejer and Thomas Gronwall.
• The expansions studied by Szego have an interesting and very simple relationship with the conformal mapping of the finite and infinite domains bounded by the given curve onto the unit disk.
• In this area, where the first classical results are linked with the names of Laplace and Darboux, Szego not only obtains very general results, far overshadowing anything known previously, but he obtains these results exactly because he examines these questions, considered very difficult, using a simple, one can say elementary, method.
• The main point of his method is that he squeezes the weight function P(x) between two functions of a very simple structure that have the form √(1 - x2)/P(x) where P(x) is a polynomial.
45. Vector calculus problems
• The method of exposition adopted by Grassmann is exceedingly abstract and this fact has stood stubbornly in the way of the general adoption of the Ausdehnungslehre to such an extent that we use today the barycentric calculus, the theory of equipollences, quaternions, or the Cartesian geometry, for the resolution of geometric questions which are capable of much more simple resolution by the methods of Grassmann.
• In ordinary differential geometry simple properties most frequently yield themselves only after very complicated calculations.
• On the other hand the geometrical calculus makes no use whatever of coordinates; it operates directly on the geometric elements; each formula which it produces is an invariant, capable of a simple geometric interpretation and leading directly to the graphic representation of the elements considered.
• What advantage has this circuitous definition with its adventitious vectors which in no way affect the value of a × b - what advantage has this over the simple statement, let a × b = ab cos q? By the non-quaternionic approach, some definition must be given - why not choose the simplest? .
46. de Montessus publications
• Quelques statistiques reductibles et non reductibles a la loi de probabilite simple, Annales Societe sc.
• (with F J Duarte), Determination de la mode, ou ecart le plus probable dans les courbes de probabilite simple, Annales Societe sc.
• Les phenomenes de physique et la loi de probabilite simple.
• Determination rigoureuse de la frequence moyenne et de la mode dans les courbes de probabilite simple - Application a un exemple, La Meteorologie (1928), 241-250.
47. Basset prefaces
• I have devoted Chapter IX to the flexion and vibrations of naturally straight wires and rods; whilst an entirely new chapter has been added on the finite deformation of naturally straight and curved wires, in which I have discussed a variety of questions which admit of fairly simple mathematical treatment.
• I have accordingly included Plucker's equations, which determine the number and the species of the simple singularities of any algebraic curve; and have also considered all the compound singularities which a quartic curve can possess.
• I have therefore confined the discussion to the simple and compound singularities of curves of this degree, together with a few miscellaneous propositions; and in Chapter IX, I proceed to investigate the theory of bicircular quartics and cartesians, concluding with the general theory of circular cubics, which is better treated as a particular case of bicircular quartics than as a special case of cubic curves.
• Simple Consequences and Extensions .
• Simple Properties of the Elementary Functions.
• Simple Non-Linear Mapping Problems.
49. Hardy on the Tripos
• It seems to me also that, if I wish afterwards to be certain that they have understood me, the obviously sensible way of finding out is to ask them to reproduce the substance of what I said or to apply the theorems which I proved to simple examples.
• We have not to undertake a general defence of mathematics and the position which is at present allowed to it in education, or to repel the very formidable onslaught which might be directed against it by Philistinism pure and simple.
• We may ask in the first place, if it be granted that what I have said about the past is roughly true, how far have things improved? Is it not true already that the Tripos means a great deal less, and English mathematics appreciably more, than forty years ago, and is it not extremely likely that, even if there be no further radical changes, this process will continue? Then, if we are not content to answer this question by a simple affirmative and leave it there, we may ask what really are the fundamental faults of an examination on the Tripos model, and whether it is not possible to make less drastic suggestions model, and whether it is not possible to make less drastic suggestions for its improvement.
50. Edmund Landau: 'Foundations of Analysis' Prefaces
• The complex numbers, incidentally, are not needed by the student in his first semester, but their introduction, being quite simple, can be made without difficulty.
• The matter now looks so simple and the proof so similar to the other proofs in the first chapter, that not even the expert might have noticed this point had I not given above a detailed confession of crime and punishment.
• For x.y the same simple type of proof applies; however, ∑ xn and ∏ xn are possible only with the Dedekind procedure.
51. Hart books
• The application of the higher branches of mathematical analysis to the solution of mechanical problems has been so perfectly successful as to procure its universal adoption, not only in the treatment of abstruse and difficult questions, but also of the most simple and elementary parts of the science.
• In the hope of contributing to its removal, he has been induced to publish the following treatise, in which he has endeavoured, by means of simple geometrical constructions, to render the most important fundamental propositions easily understood by all classes of students.
• In this manner the fundamental propositions of Hydrostatics are demonstrated; but as this is the only part of the subject in which accurate results have been obtained, so it is the only part which appears capable of such simple and elementary demonstration.
52. James Jeans: 'Physics and Philosophy' I
• To take a simple illustration, the physicist finds that the spectrum of atomic hydrogen contains the line Ha which we have already mentioned, and also a very great number of other lines which are usually designated as Hb, Hg, Hd, etc.
• The wave-lengths of these lines can be measured, and are found to be related with one another in a very simple way which can be expressed by a quite simple mathematical formula.
53. Born Inaugural
• Relativity gave the first example in which the intrusion of the observer into the description of facts is not so simple, and leads to a new conception to conserve the idea of an objective world Einstein has acknowledged that his studies on this problem were deeply influenced by the ideas of Ernst Mach, a Viennese physicist who developed more and more into a philosopher.
• But if we take into account the simple quantitative law relating energy and frequency already discovered by Planck, the case becomes very serious.
• This is indeed the case, and the connecting law is extremely simple when all the particles of the beam have exactly the same velocity.
54. Cariolaro's papers
• In particular, we give generalizations of Vizing's Theorem, Shannon's Theorem and Vizing's Adjacency Lemma, and an extension to multigraphs of the simple graph version of Vizing's Theorem which is obtained by proving that the chromatic index of an arbitrary multigraph must assume one of only two possible values.
• Star multigraphs turn out to be useful tools in the study of the chromatic index of simple graphs.
• We show that the following fundamental edge-colouring problem can be solved in polynomial time for any given constant B: given a simple graph G, find an edge-colouring of G where each colour is assigned to at most B edges and which, subject to this condition, has the fewest number of colour classes.
55. Fejer descriptions
• It is due to such care spent on the elaboration of the solution that Fejer's papers are very clearly written, and easy to read and most of his proofs appear very clear and simple.
• Yet only the very naive may think that it is easy to write a paper that is easy to read, or that it is a simple thing to point out a significant problem that is capable of a simple solution.
56. Dahlin Extracts
• To begin with he defines a star as a simple, ethereal, shining and essentially spherical body, which, through an intrinsic divine force rotates around the axis mundi, completes its orbit in a fixed time and has been created by God for the sake of mankind.
• It was split into two classes: pure or simple and impure or mixed.
• Dahlin describes some of the calculations, which, except for a few trigonometric, mainly make use of simple numeric operations.
57. Wolfgang Pauli and the Exclusion Principle
• giving the lengths of the periods in the natural system of chemical elements, was zealously discussed in Munich, including the remark of the Swedish physicist, Rydberg, that these numbers are of the simple form 2n2 if n takes on all integer values.
• On the one hand, the anomalous type of splitting exhibited beautiful and simple laws and Lande had already succeeded to find the simpler splitting of the spectroscopic terms from the observed splitting of the lines.
• The fundamental idea can be stated in the following way: The complicated numbers of electrons in closed subgroups are reduced to the simple number one if the division of the groups by giving the values of the four quantum numbers of an electron is carried so far that every degeneracy is removed.
58. E W Hobson: 'Mathematical Education
• I do not of course contemplate the introduction into such a course of artificial problems on scales of notation; only the fundamental principles should be explained, with such quite simple illustrations as may be found necessary for their complete elucidation.
• I do not know to what extent some rudimentary and informal treatment of the properties of simple figures in three-dimensional space has at the present time become part of the normal instruction in Geometry in our schools.
• It is unnecessary to insist upon the importance of an endeavour to uproot ignorance of this kind, due as it is to lack of stimulation of the power of observing simple spatial properties.
59. Serre reviews
• In Chapter III, the author conjectures that every rational semi-simple abelian l-adic representation ..
• In particular, if these stabilizers are trivial, G is free so obtaining a simple proof of the theorem of Otto Schreier stating that any subgroup of a free group is free.
• After an overview of the main theorems on NX(p), the book offers simple, illustrative examples and discusses the Chebotarev density theorem, which is essential in studying frobenian functions and frobenian sets.
60. Menger on teaching
• (d) The symbol x, because of its equivocal use, is unfit to express in a simple way some of the most important properties of the identity function.
• But although these ideas can be presented in the form of deductive systems they deprive the student of the experience of developing such a theory from assumptions about really simple and purely geometric concepts such as points, lines, and incidence.
• The way to achieve these aims is to abandon the idea of teaching Euclidean geometry in its entirety and to present only a part or an aspect of Euclidean geometry - but that part or aspect with absolute rigour - as well as some simple related theories which, from the points of view of various students, are "relevant".
61. Max Planck: 'The Nature of Light
• What is this something which spreads through empty space and moves through the atmosphere at the enormous, speed of 300,000 kilometres per second? Isaac Newton, the founder of classical mechanics, made the most simple and obvious assumption that there are certain infinitesimally small corpuscles which are sent out in all directions with that velocity from a source of light, e.g.
• Instead of collecting as many as possible of the multifarious facts available, I shall simple examine one of them in detail.
• For we have long known that the chemical atom is not by any means the simple invariable element of which all matter is constituted, but rather that every single atom, particularly one of a heavy metal, must be considered as a world in itself, and the farther one penetrates, the richer and more varied the structure appears.
62. Newcomb Elements of Geometry
• The author has considered it more important to base the subject on natural and customary modes of thought than to adopt a system simple and rigorous, but not so based.
• The mode in which he has endeavoured to avoid the difficulty, and to render the natural system as rigorous and nearly as simple as the other, will be seen by an examination of the chapter on Proportion.
• From the fourth book onward a knowledge of simple equations is sometimes presupposed.
63. Ernest Hobson addresses the British Association in 1910, Part 3
• Here we have a case in which an enumeration, which appears to be not amenable to direct treatment, can actually be carried out in a simple manner when the underlying identity of the operation is recognised with that involved in certain operations due to differential operators, the calculus of which belongs superficially to a wholly different region of thought from that relating to Latin squares.
• One of the most general mathematical conceptions is that of functional relationship, or 'functionality.' Starting originally from simple cases such as a function represented by a power of a variable, this conception has, under the pressure of the needs of expanding mathematical theories, gradually attained the completeness of generality which, it possesses at the present time.
• But, in the schemes of purely deductive geometry, the systems of axioms and postulates are far from being of a very simple character; their real nature, and the necessity for many of them, can only be appreciated at a much later stage in mathematical education than the one of which I am speaking.
64. Mary Boole writing
• There seems to be evidence that in ancient times all people in good society were expected to know simple truths about geometric forms in the same way as we all know simple facts in natural history.
• The question asked by a parent should be, 'At what age would you recommend me to let my child begin learning such portions of Algebra (or Trigonometry) as can only be learned by the aid of complicated devices invented, centuries after the science itself was an actual working possession of our race, for the sake of projecting its action into fields which would be inaccessible to it if only natural and simple tools were used?' The answer should be, 'When the process of learning by the more direct means has become so familiar as to be performed sub-consciously.' .
65. Kingman autobiography
• After a couple of weeks, I graduated to some simple modelling the group was doing of the demand for telephone cable pairs to homes.
• Our models were very simple, and involved probability calculations little more advanced than those in Lindley's lectures.
• So I tried to solve simple queues with service in random order, and eventually found a formal solution for M/G/1 for this discipline.
66. Douglas Jones's books
• On the other hand, much attention is given to simple numerical processes, which provide excellent illustrations of the uses of analysis in a field of general importance.
• The concept of an antenna as a piece of wire or portion of dielectric which radiates electromagnetic energy is simple enough in principle, but the derivation of quantitative results of value for design purposes is fraught with difficulties.
• It would have been interesting to see an example of some simple problem being worked by both 'standard' and 'non-standard' processes, so that the reader may compare the two methods.
67. Marshall Hall books
• Here, the specific nature of the rule of combination did not matter as long as it satisfied certain simple properties (closure, associativity, possession of inverse), i.e., the collection with its rule of combination formed a group.
• If the specified rules are very simple, then the chief emphasis is on the enumeration of the number of ways in which the arrangement may be made.
• Combinatorial theory encompasses a wide variety of topics, from simple counting of permutations and use of the pigeonhole principle to partitions, map colourings, latin squares, rook polynomials, design of experiments and Ramsey theory.
68. Menger on the Calculus of Variations
• A simple but interesting example, due to the economist H Hotelling (Columbia University), is to find the most economic way of production in a mine.
• For example, we consider the two following extremely simple problems: two given points may be joined by all possible curves; which of them has the shortest length, and which of them has the greatest length? The first problem is soluble: The straight line segment joining the two points is the shortest line joining them.
• The most simple example of this theory, which calculates the number of minimizing and maximizing curves as well as of stationary curves, is the following "geographical" theorem quoted by Morse: If we add the number of peaks and the number of pits on the surface of the earth, and subtract the number of passes, then the result will be the number 2, whatever the shape of the mountains may be (highlands excluded).
69. Pólya on Fejér
• It is due to such care spent on the elaboration of the solution that Fejer's papers are very clearly written, and easy to read and most of his proofs appear very clear and simple.
• Yet only the very naive may think that it is easy to write a paper that is easy to read, or that it is a simple thing to point out a significant problem that is capable of a simple solution.
70. Geary's books
• It is nowhere clearly stated that each tableau is a representation of the original problem with the equations solved for the basic variables in terms of the non-basic variables, so that only a simple change of variable (Jordan elimination) is involved in progressing from one tableau to the next.
• Rather crucial in such an elementary work on linear programming is to explain the Simplex Method by means of a simple example.
• Part I, "Theory", begins by considering a simple example which is solved graphically and by a labored use of a simplex method.
71. R A Fisher: 'Statistical Methods' Introduction
• If an observation, such as a simple measurement, be repeated indefinitely, the aggregate of the results is a population of measurements.
• In all cases, perhaps, it is possible to reduce to a simple numerical form the main issues which the investigator has in view, in so far as the data are competent to throw light on such issues.
• Some simple examples of the application of the method of maximum likelihood, and other methods, to genetical problems are developed in the final chapter.
72. Segel books
• Part B (Some fundamental procedures illustrated on ordinary differential equations) contains chapters entitled: Simplification, dimensional analysis, and scaling; Regular perturbation theory; Illustration of techniques on a physiological flow problem; Introduction to singular perturbation theory; Singular perturbation theory applied to a problem in biochemical kinetics; Three techniques applied to the simple pendulum.
• Chapter 7: Regular Perturbation Theory; The series method applied to the simple pendulum; Projectile problem solved by perturbation theory; .
• Chapter 11: Three Techniques Applied to the Simple Pendulum; Stability of normal and inverted equilibrium of the pendulum; A multiple scale expansion; The phase plane; .
73. Mirsky books
• This work provides an elementary and easily readable account of linear algebra, in which the exposition is sufficiently simple to make it equally useful to readers whose principal interests lie in the fields of physics or technology.
• The book is intended mainly for students pursuing an honours course in mathematics, but I hope that the exposition is sufficiently simple to make it equally useful to readers whose principal interests lie in the fields of physics or technology.
• The proofs of these are generally very simple, but are widely scattered throughout the literature and are often not easily accessible.
74. Gender and Mathematics
• (See for example, [',' L O Adetula, Solution of simple word problems by Nigerian children: Language and schooling factors, Journal for Research in Mathematics Education 20 (1989), 489-497.
• Nothing appears to be simple and listing what I really know is difficult.
• But a closer examination reveals that nothing to do with gender is simple.
75. Newton by his contemporaries
• These indeed derive the causes of all things from the most simple principles possible; but then they assume nothing as a principle that is not proved by phenomena.
• From some select phenomena they deduce by analysis the forces of nature, and the more simple laws of forces; and from thence by synthesis show the constitution of the rest.
• Therefore that we may begin our reasoning from what is most simple and nearest to us, let us consider a little what is the nature of gravity with us on Earth, that we may proceed the more safely when we come to consider it in the heavenly bodies that lie at so vast a distance from us.
76. Biography of Mathematics
• For a very simple reason: because Geometry is a living subject and therefore changing.
• This simple fact produces an extraordinary simplification, because when forgetting the quantities, which were vectors, and that could not be multiplied as numbers, what required one to resort to introducing a multiplication of the tensor product, considering the symbol having empty content and operating with it as if it were a number, we immediately obtain a set, whose elements we now call polynomials, with which we operate as with integers.
• The new foundation of Mathematics is based on a very simple principle, which can be stated as follows: "In order to be able to demonstrate the propositions with rigour, it is necessary to empty the concepts of primitive content, limited to establishing the allowed logical mechanism and the fundamental relations between such concepts." .
77. Mathematicians and Music 2.2
• In the early part of the third period in the development of music, namely, the period of Harmonic or Modern Music, we have the first opera and the first oratorio, and, as I have already said, the discovery by Galileo that the simple ratios of the lengths of strings existed also for the pitch numbers of the tones they produced, an observation later generalized by Newton.
• when a string is plucked or struck, or, as we may add 'bowed' at any point in its length which is the node of any of its so-called harmonics those simple vibrational forms of the string which have a node in that point are not contained in the compound vibrational form.
• Hence if we attack at its middle point, all the simple vibrations due to the even numbered partials, each of which has a node at that point, will be absent.
78. Skolem: 'Abstract Set Theory
• However, the simple theory of types, Quine's theory and the ramified theory of types are treated to a certain extent.
• The simple infinite sequence.
• The simple theory of types .
79. Bratteli publications
• Ola Bratteli, George A Elliott, David E Evans and Akitaka Kishimoto, Homotopy of a pair of approximately commuting unitaries in a simple C*-algebra, J.
• Ola Bratteli, Palle E T Jorgensen, Ki Hang Kim and Fred Roush, Decidability of the isomorphism problem for stationary AF-algebras and the associated ordered simple dimension groups, Ergodic Theory Dynam.
• Ola Bratteli, Palle E T Jorgensen, Ki Hang Kim and Fred Roush, Corrigendum to the paper: "Decidability of the isomorphism problem for stationary AF-algebras and the associated ordered simple dimension groups'' [Ergodic Theory Dynam.
80. Poincaré on the future of mathematics
• An algebraical formula which gives us the solution of a type of numerical problems, if we finally replace the letters by numbers, is the simple example which occurs to one's mind at once.
• It is for the same reason that, when a somewhat lengthy calculation has conducted us to some simple and striking result, we are not satisfied until we have shown that we might have foreseen, if not the whole result, at least its most characteristic features.
• And since it enables us to foresee whether the solution of these problems will be simple, it shows us at least whether the calculation is worth undertaking.
81. Senechal on Delone
• But on the basis of his papers and through my friendship with Ravil V Galiulin (1940-2010), Nikolai P Dolbilin, and Mikhail I Shtogrin, I became and remain his disciple, trying always to emulate his clear and simple approach to crystallographic problems and his informal, lucid writing style.
• From these simple hardcore and homogeneity axioms they drew a surprising amount of information about the geometry of the distribution of these points in space.
• Not only is this approach simple and elegant, it has turned out to be useful.
82. Sigmund books
• What does one learn from this book? The biologists will learn of the mathematical unity of seemingly distinct biological problems, of the wealth of mathematical complexity hidden behind even relatively simple biological models, and of the mathematical rigour that can be usefully applied in the analysis of such models.
• He is the only mathematician about whom I dare make this assertion." This book wants to give a simple, intuitive and easily digestible introduction to Godel's life and work, meant for readers interested in the human and cultural aspects of science.
• Karl Sigmund, a pioneer in evolutionary game theory, uses simple and well-known game theory models to examine the foundations of collective action and the effects of reciprocity and reputation.
83. Rudio's Euler talk
• The humble rural conditions of Leonhard Euler's upbringing surely contributed to his simple, modest attitude, as well as his impartiality, which he managed to preserve up to old age.
• Since the natural phenomena are dependent on each other in the most varied ways, there are infinitely many mathematical functions -- but please do not believe that these dependencies and hence the corresponding functions are always as simple as in the examples I mentioned above.
• As an example, it would not be possible to describe the motions of Earth around the Sun in a more simple and comprehensive manner than by Kepler's laws.
84. Heath: Everyman's Library 'Euclid' Introduction
• The simple truth is that it was not written for schoolboys or schoolgirls, but for the grown man who would have the necessary knowledge and judgment to appreciate the highly contentious matters which have to be grappled with in any attempt to set out the essentials of Euclidean geometry as a strictly logical system, and, in particular, the difficulty of making the best selection of unproved postulates or axioms to form the foundation of the subject.
• Simson had, it is true, a "bee in his bonnet." The title-page of his first editions says that "in this edition the errors by which Theon or others have long ago vitiated these Books are corrected, and some of Euclid's Demonstrations are restored." Simson, however, was not in any real sense a competent textual critic; he acted on the simple but uncritical principle that whatever he found in the text which fell short of perfection, whether of form or content, must have been due to alterations made by Theon or "some unskilful editor.
• The simplest case of "application of areas," which is equivalent to the solution for x of the simple equation ax = S, can be read in this volume (Eucl.
85. Peter's books
• The illustrations are simple and interesting.
• Next follows fractions and how they do not fill the number line and a beautifully simple sketch of Cantor's proof that, contrary to appearances, there are as many positive integers as there are rational numbers (fractions).
• The objective of this book is principally to show that many of the definitional structures used in programming languages can be expressed formally as partial recursive functions and that these partial recursive functions can be implemented by straightforward techniques on a random access machine with a simple assembly language instruction set.
86. Feller Prefaces
• Some of them are simple exercises, but most of them serve as additional illustrative material to the text or contain various complements.
• In the resulting confusion closely related problems are not recognized as such and simple things are obscured by complicated methods.
• Some theorems which were considered strikingly original and deep now appear with simple proofs among more refined results.
87. Halmos popular papers
• A public lecture should be simple and elementary; it should not be complicated and technical.
• If you believe and can act on this injunction ("be simple"), you can stop reading here; the rest of what I have to say is, in comparison, just a matter of minor detail.
• My test for what makes a good teacher is very simple: it is the pragmatic one of judging the performance by the product.
88. Tverberg Bergen institute
• (It is quite interesting comparing the various proofs of Ramsey's theorem: Ramsey's original proof is an excellent instance of how one can refine the structure of a result so as to be able to prove it in many small steps; but Skolem's proof is simpler; and subsequent proofs of Erdos and Szekeres and Erdos and Rado illustrate how a simple change in strategy can effect a reduction in numerical bounds by several orders of magnitude.) But Skolem had an early, substantial interest in combinatorial problems per se, publishing a lengthy account Untersuchungen Ouber einige Klassen kombinatorischer Probleme in 1917; for example, Skolem includes a catalogue of connected graphs on up to 8 vertices, each of degree at most 3, clearly with an eye to what we would recognise as design-theoretic properties.
• Fundamental to Skolem's approach is the simple idea of partitioning the set of integers {1, 2, ..
89. E C Titchmarsh: 'Aftermath
• An analyst should be able to handle such things as integrals and infinite series just as well as if they were the simple expressions of elementary algebra.
• But essentially their patterns are of the same sort as the simple ones of which we have given some examples here.
90. Edward Sang on his tables
• Accident brought it again before me, and this time, considering not the relations of the lines connected with it, but the relations of the areas concerned, an exceedingly simple solution was found.
• The mean anomaly of a planet may be deduced from its angle of position, or as it is generally called, its excentric anomaly, by simple additions and subtractions of these circular segments.
91. Godement's reviews
• Zeta functions of simple algebras (1972), by Roger Godement and Herve Jacquet.
• The aim of the authors is to define the Hecke zeta-functions for all simple algebras over algebraic number fields and to prove a functional equation for them.
92. Rudio's talk
• I do not even wish to remind you that this simple assumption, which forms the basis of our calculation today, has escaped a mathematically gifted people such as the Greeks.
• Children in public schools were not even taught simple calculations with digits.
93. Chrystal: 'Algebra' Preface
• I suppose that the student has gone in this way the length of, say, the solution of problems by means of simple or perhaps even quadratic equations, and that he is more or less familiar with the construction of literal formulae, such, for example, as that for the amount of a sum of money during a given term at simple interest.
94. Mercer's papers
• Some simple duration-dependent stochastic processes, J.
• Some simple wear-dependent renewal processes, J.
95. W Burnside: 'Theory of Groups of Finite Order
• Galois introduced into the theory the exceedingly important idea of a self-conjugate sub-group, and the corresponding division of groups into simple and composite.
• The last Chapter contains a series of results in connection with the classification of groups as simple, composite, or soluble.
96. Burton papers
• Conclusions: The key themes identified in the literature were: (i) the conceptualisation of management as masculine, to which we would add 'white'; (ii) discrimination in promotion; (iii) women's career patterns; (iv) domestic responsibilities, to which we would add responsibilities to their communities; (v) mentoring, which is clearly neither singular nor simple; and (vi) management styles.
• Although untangling the inter-relationships between these three is no simple matter, they make effective starting points in order to ask similar questions of mathematics to those asked by our colleagues in science.
97. Feller Reviews 1
• Starting with some rather simple problems of combinatorial analysis, the text then goes on to such advanced topics as Markov chains, recurrent events, random walks, waiting time, trunking problems, and time-dependent stochastic processes.
• To avoid advanced mathematical concepts (measure theory, etc.) and to make the work useful to beginners, the author limits it to questions which involve only a countable sample space; but about these simple questions it addresses the most advanced problems of probability theory, many of which have not until now been exposed in a book, so that the work is of the highest interest for specialists.
98. Loney reviews
• The author has succeeded in his purpose to produce "a fairly complete elementary text-book on Plane Trigonometry." The faithful student of this treatise "will have little to unlearn when he commences to read treatises of a more difficult character." The style is clear and simple; even when it is diffuse, the author never hides his thoughts with words either large or small.
• The sections dealing with curves of buoyancy and tensions of vessels are as simple as is necessary for ordinary students.
99. Wussing Reviews
• The virtues of this volume are simple.
• the lively, clear, and simple style nicely conveys its main message: that mathematics is a human pursuit whose aims and motivations can be understood by everyone.
100. Eddington: 'Mathematical Theory of Relativity' Introduction
• Or again, instead of cutting short the astronomical calculations when we reach the parallax, we might go on to take the cube of the result, and so obtain another manufactured quantity, a "cubic parallax." For some obscure reason we expect to see distance appearing plainly as a gulf in the true world-picture; parallax does not appear directly, though it can be exhibited as an angle by a comparatively simple construction; and cubic parallax is not in the picture at all The physicist would say that he finds a length, and manufactures a cubic parallax; but it is only because he has inherited a preconceived theory of the world that he makes the distinction.
• But to catalogue all the precautions and provisos in the operation of determining even so simple a thing as length, is a task which we shirk.
101. St Andrews Physics Examinations
• Define a simple pendulum and a compound pendulum.
• How may the length of a simple pendulum and its time of vibration be determined by observations made with a compound pendulum? (Kater's method.) .
102. Feller Reviews 2
• Most of the chapters, include numerous problems, ranging from simple exercises to applications and extensions of the text.
• He restricts himself to a discussion of enumerably infinite simple events.
103. Hamming's Reviews
• The algorithms are explained geometrically and often illustrated by a simple numerical example, sometimes showing the limitations of the algorithm.
• I have no hesitation in recommending the book as a simple introduction to computers and their uses.
104. Heinrich Weber's books
• Our admiration is no less excited by its pedagogic excellencies ; Weber's German is simple and concise, the demonstrations are clear and rigorous, and many of them are of extreme elegance.
• The theory of interest is based upon compound interest, in the sense that simple interest is looked upon as an annuity in perpetuity.
105. Pedoe's books
• The inclusion of unfamiliar, yet conceptually relatively simple, phenomena associated with circles furnishes examples that should be both interesting and challenging to students.
• It is, in essence, a pictorial essay requiring a persistent intense concentration on the simple and subtle beauty inherent in the plethora of diagrams.
106. Dehn on Aristotle
• And finally, it gives the mature mathematician great satisfaction to methodically examine large systems of propositions, to see the wonderful architecture of entire disciplines rise as a result of stringent combination from simple fundamentals to heights inaccessible to direct observation.
• Pre-Greek mathematics had primitive knowledge about integers and simple geometrical forms like points, straight lines, planes, etc.
107. Edinburgh Physics Examinations
• Define Simple Harmonic Motion; and show that the resultant of two S.H.M: of the same period, in one line, is another of the same period.
• Explain the action of a convex lens of short focus when employed as a simple microscope.
108. Peacock Treatise
• If the first principles of Algebra had been consistent with themselves, or had led to no difficulties either in the reasoning immediately connected with them, or in their remote consequences, which did not admit of a simple and uniform explanation, we should very properly hesitate before we acceded to any innovations in those principles or in their exposition; for under such circumstances, the perfect union and attachment of the parts of the fabric would furnish the best evidence of the sufficiency of the foundations: but it is the admitted existence of difficulties in the consequences of the principles of Algebra, as they are commonly stated, both immediate and remote, which naturally, and indeed necessarily, induces us to suspect the existence likewise of imperfections or inaccuracies in the principles themselves: a suspicion which becomes confirmed when it appears, after the most careful examination of them, that the difficulties in question are not referable to their imperfect development.
• Algebra has always been considered as merely such a modification of Arithmetic as arose from the use of symbolic language, and the operations of one science have been transferred to the other without any statement of an extension of their meaning and application: thus symbols are assumed to be the general and unlimited representatives of every species of quantity: the operations of Addition and Subtraction in their simple arithmetical sense, are assumed to be denoted by the signs + and -, and to be used in connecting such symbols with each other: Multiplication and Division, two inverse operations in Arithmetic, are supposed to be equally applicable to all quantities which symbols may denote, without any necessary modification of their meaning: but at the same time that the primitive assumption of such signs and operations is thus carefully limited in the extent of their signification, there is no such limitation imposed upon the extent of their application: thus it is not considered necessary that the operations of Addition and Subtraction should be confined to quantities of the same kind, or that the quantities subtracted should be less than the quantities from which they are subtracted: and when the violation of this restriction, which would appear to be rendered necessary by the primitive meaning of those operation, has led to the independent existence of the signs + and -, as an assumption which is also necessary in order to preserve the assumed universality of the values of the symbols and of the possibility of the operations which they designate, it is not considered that by this additional usage of them, we have altogether abandoned the definitions of those operations in practice, though we have retained them in name: for the consequences of those operations, and the assumptions connected with them, must be determined by the fundamental rules for performing them, which are independent of each other, or whose necessary connection is dependent upon their assumed universality only: and the imposition of the names Addition and Subtraction upon such operations, and even their immediate derivation from a science in which their meaning and applications are perfectly understood and strictly limited, can exercise no influence upon the results of a science, which regards the combinations of signs and symbols only, according to determinate laws, which are altogether independent of the specific values of the symbols themselves.
109. Recollections of Mary Somerville
• A still smaller number of her own letters have been added, either as illustrating her opinions on events she witnessed, or else as affording some slight idea of her simple and loving disposition.
• Nor is her simple account of her early days without interest, when, as a lonely child, she wandered by the seashore, and on the links of Burntisland, collecting shells and flowers; or spent the clear cold nights at her window, watching the starlit heavens, whose mysteries she was destined one day to penetrate in all their profound and sublime laws, making clear to others that knowledge which she herself had acquired, at the cost of so hard a struggle.
110. Weyl on Hilbert
• His optimism, his spiritual passion, his unshakable faith in the supreme value of science, and his firm confidence in the power of reason to find simple and clear answers to simple and clear questions were irresistibly contagious.
111. Plucker Copley medal
• He has succeeded in obtaining the mathematical definition of these curved lines or surfaces, by a simple application of the known laws of electromagnetic action, regarding an element of the discharge as the element of an electric current.
• In a recent memoir, which has only just been published in the Philosophical Transactions, Professor Plucker has investigated the two totally different spectra frequently afforded by the same elementary substance according as it is submitted to the instantaneous discharge of a Leyden jar charged by an induction-coil, or rendered incandescent by the simple discharge of the coil, or else, in some cases, by ordinary flames.
112. James Jeans: 'Physics and Philosophy' II
• A simple specific example of this general argument will be found below.
• For suppose - to imagine a simple although not very likely possibility - that it had been found that the pattern of events could be fully explained by assuming that matter consisted of hard spherical atoms, and that each of these behaved like a minute billiard-ball.
113. Rhode Island College
• The work in algebra consists of a systematic drill in the fundamental operations, leading up to a study of the equation, both simple and quadratic, the theory of exponents, radicals, the progressions, the binomial formula, and the graphic representation of equations.
• It includes the differentiation of algebraic, trigonometric, anti-trigonometric, exponential and logarithmic functions, successive differentiation and the integration of simple forms, illustrated by applications to the rectification of plane curves, the areas of plane curves and the surface and volume of solids of revolution.
114. Whyburn's books
• Though the treatment is not difficult, it is likely to be more readily intelligible to those with some mathematical training who are seeking knowledge of economics than for economists without any initial facility in manipulating simple mathematics.
• The volume in question seems particularly interesting for Italian students of Economics; in fact, it constitutes a clear and elementary introduction to traditional mathematics, the introduction is presented in a very simple way but not without rigour, and therefore fills a gap in the range of books, because every argument put forward is always illustrated by examples with elementary mathematics drawn from economics.
115. W H Young addresses ICM 1928 Part 2
• And yet, these also deserve their place of honour, if only for services like that rendered by Sir Ronald Ross in utilising the simple idea that it is on the percentage of mosquitoes to the individual, not on their mere presence, or even their number, that depends the epidemic of malaria, thereby creating anew the science of tropical medicine.
• The necessity for the recognition of the region of validity may be illustrated by the following simple fable: .
116. Shepherdson Tribute
• The first I found, connected to Heilbronn, is on simple additive combinatorics (and was reviewed by Erdos).
• He used Tarski's work on real-closed fields, in a simple but brilliant way (and elsewhere alludes to doing things with open induction for exponentiation).
117. Reviews of Shafarevich's books
• Groups are illustrated by simple examples, the symmetry groups of polyhedra and various crystals, but also by more abstract cases such as the Brauer group.
• To help the reader grasp the material, simple problems are given to be solved.
118. Enciclopedia delle Matematiche
• The treatment is simple, interesting and in connection with topics treated reasonably comprehensive.
• But throughout the presentation is scholarly, the emphasis welt-placed , and the language simple, connected and interesting.
119. Magnus books
• The authors of the present volume have overcome this obstacle by leading the reader slowly from the concrete to the abstract, from the simple to the complex, employing effectively graphs or Cayley diagrams to help the student visualize some of the structural properties of groups.
• It may be appropriate to remark here that the theory of Hill's equation reveals the occurrence of a surprising phenomenon which can be described in rather simple terms.
120. H F Baker: 'A locus with 25920 linear self-transformations' Introduction
• The geometrical properties of this primal are very interesting; and they form a vivid and simple concrete representation of the group of the lines of a cubic surface, and its more important subgroups; and incidentally illustrate the elements of the theory of the substitutions of five and six objects.
• One remark should perhaps be added here to make the general statements of this introduction more precise: The group of the lines of a cubic surface is of order 24× 34× 40; this group has a subgroup of order 1/2 (24× 34× 40) or 23× 34× 40, which, as Jordan proved, is simple [it is PSp(4,3), the projective symplectic group of 4 × 4 matrices over the field of 3 elements].
121. André Weil: 'Algebraic Geometry
• for instance, one will find here all that is needed for the proof of Bertini's theorems, for a detailed ideal-theoretic study (by geometric means) of the quotient-ring of a simple point, for the elementary part of the theory of linear series, and for a rigorous definition of the various concepts of equivalence.
• V deals with the intersections of an arbitrary variety and of a linear variety in an affine space, first (in § 1) when these varieties have complementary dimensions, then (in § 2) in general; § 3 contains some applications of these results to the theory of simple points.
122. Bell books
• Dr Bell, incidentally a successful novelist, has written in simple style, mathematically unconventional perhaps, but not flippant.
• [The reader] must on occasion be content to have some historical claim substantiated by simple repetition; he should remember his Undergraduate Society debating the eternal "Hen-or-Egg" Priority problem; but before all else he must be mature enough not to be muddled, as so many of us are, by irony and sarcasm - and he must certainly not be pedantic about detail.
123. Mordell reminiscences
• The reason is a very simple and natural one.
• So as I have said in the beginning of my talk, there was a very simple explanation of why I went to Cambridge.
124. Santalo honorary doctorate
• The first systematic work of pure geometry was the Euclid's Elements (3rd century BC) whose purity refers both to its constituent elements (points, lines, planes) that are simple and perfect, obtained by idealization of visual forms discernible by the senses, to the axiomatic construction, which served as a model for all subsequent mathematics, and also to the common notions with which the congruence of figures is introduced through the movements of the plane.
• We have tried to make it clear with a simple and very limited example, but surely an analogous evolution can be found in many other chapters of that science.
125. A N Whitehead: 'Autobiographical Notes
• Such Scripture lessons, on each Sunday afternoon and Monday morning, were popular, because the authors did not seem to know much more Greek than we did, and so kept their grammar simple.
• The only point on which I feel certain is that there is no widespread, simple solution.
126. Kepler's Planetary Laws
• (Moreover, the same principle is invoked in relation to planetary motion when Kepler based his investigation on what Aristotle had specified as the only two simple motions, circular and rectilinear, discussed in Section 9.) This principle has far-reaching ramifications, as we will demonstrate in connection with the complementary pairings that recur in Kepler's mature work in Epitome Book V (1621) - where the term 'complementary' is used in the everyday sense that the pair complete one another, and also with the mathematical connotation of being at right angles.
• He adopted the traditional mechanism of deferent, epicycle, and eccentric, being aware, as the Ancients had been, that motion in the circle of radius a centred on A, when combined with motion in the epicyclet of radius ZQ = AB = ae (whose centre Z lies on the deferent), together produce a motion of Q equivalent to a simple motion of Q round the eccentric circle centre B radius a.
127. David Hilbert: 'Mathematical Problems
• By the examples of the simple and double integral I will show briefly, at the close of my lecture, how this way leads at once to a surprising simplification of the calculus of variations.
• But what an important nerve, vital to mathematical science, would be cut by the extirpation of geometry and mathematical physics! On the contrary I think that wherever, from the side of the theory of knowledge or in geometry, or from the theories of natural or physical science, mathematical ideas come up, the problem arises for mathematical science to investigate the principles underlying these ideas and so to establish them upon a simple and complete system of axioms, that the exactness of the new ideas and their applicability to deduction shall be in no respect inferior to those of the old arithmetical concepts.
• But all this ingenuity, all this jovial character, would remain as a simple anecdote if it were not united to an impressive capacity to transmit ideas; and this ability he develops using the most diverse of strategies: "I wanted to keep this operation intact on the board - he tells his students one day, showing them the remains of a polynomial multiplication operation - but the janitor has come and erased almost all of it; I just arrived in time to stop him deleting the multiplicand and the product.
• Emphatic truth that, although simple enough, many teachers have not yet assimilated.
129. Gibson History 4 - John Napier
• But between Michael and Napier we can name no Scot whose interest lay specially in the domain of science, and the explanation is simple.
• It is quite obvious that the logarithm as thus defined is not so simple in actual work as the logarithm we now use.
130. Thomas Bromwich: 'Infinite Series
• 44 is not strictly historical, but is intended to emphasise the similarity between the tests for uniform convergence and for simple convergence (Arts.
• To illustrate the general theory, a short discussion of Dirichlet's integrals and of the Gamma integrals is given; it is hoped that these proofs will be found both simple and rigorous.
131. J A Schouten's Opening Address to ICM 1954
• The faculty of deduction belongs more to the conscious mind, the subconscious being in general only able to perform very simple and trivial deductions.
• In fact, there are machines, effecting a few simple logical deductions, and other machines, especially constructed for the investigation of big molecules, which are able to pass in a short time over say a million possible combinations of phases in order to single out some twenty five most suitable ones for a more detailed examination.
132. Frank Harary's books
• On the whole the book is clearly written with plenty of simple exercises, but Professor Harary's boundless enthusiasm makes rather extravagant calls on the reader's attention; he is so anxious that nothing be left out.
• Even at the simple level of drawing pictures and looking at them there is ample scope for experiment and investigation, since the number of distinct graphs increases so rapidly even with only a few vertices.
133. Carathéodory: 'Conformal representation
• In the proof of this theorem, which forms the foundation of the whole theory, he assumes as obvious that a certain problem in the calculus of variations possesses a solution, and this assumption, as Weierstrass (1815-1897) first pointed out, invalidates his proof Quite simple, analytic, and in every way regular problems in the calculus of variations axe now known which do not always possess solutions.
• During the present century the work of a number of mathematicians has created new methods which make possible a very simple treatment of our problem; it is the purpose of the following pages to give an account of these methods which, while as short as possible, shall yet be essentially complete.
134. Levitzki's papers
• A Galois theory in semi-simple rings, Bull.
• On the equivalence of the nilpotent elements of a semi simple ring, Compositio Math.
135. Bell papers
• The old assurances and arrogances are gone; the universe is not a book to be read in a cloister, nor is the solar system the simple parish it was in the middle ages.
• A typical simple specimen, which has passed unaltered into current usage, is his postulational definition of an ideal, and there are many others.
136. Charles Bossut on Leibniz and Newton Part 2
• At the same time Johann Bernoulli gave another method which, to the advantage of being incomparablely more simple, added that of embracing all the geometrical curves, all the mechanical curves completely similar, and lastly a great number of mechanical curves incompletely similar.
• Newton had determined the curve described by a projectile in a medium resisting in the ratio of the simple velocity: but had not touched on the case, at that time more difficult, where the resistance of the medium is as the square of the velocity.
137. L R Ford - Differential Equations
• It is unusual to find Clairaut's equation and simple examples of solution in series in the first chapter of a text-book on differential equations, but the idea is a good one.
• General solutions of simple types of partial differential equations are obtained before separation of variables is used to solve problems of vibration and the Laplace equation in two dimensions.
138. Samarskii's books
• The author gives a systematic exposition of the foundations of the theory of difference schemes and applications of this theory to the solution of simple typical problems of mathematical physics.
• The author has attempted to make his presentation understandable on the first reading, paying attention to the basic concepts of the theory of numerical methods and illustrating them by very simple examples.
139. Jordan algebras
• In a fundamental 1934 paper, Jordan, John von Neumann, and Eugene Wigner showed that every finite-dimensional formally real Jordan algebra is a direct sum of a finite number of simple ideals, and that there are only five basic types of simple building blocks ..
140. Byrne: Doctrine of Proportion
• Professor Young will not deny (for they are his own words) that "the term in reality denotes the quotient arising from the division of one magnitude or quantity by another of the same kind (or the multiple or submultiple which an antecedent is of its consequent); it is accurately assignable (in numbers) when the magnitudes are commensurable, but unassignable (in numbers) when they are incommensurable." When this simple fact is known, what is to be understood by the term cannot be misconstrued, although we do allow that in many cases the exact ratio of one magnitude to another of the same kind cannot be expressed by numbers; this may be a fault in our present system of notation, or in the plan adopted for finding a common measure, and not in our geometrical notion of that which is to be conveyed by the term.
• The student will readily perceive that the term ratio is not intended to convey a real and substantial essence, but merely a simple conception of the mind, which can be well defined, and not, as some writers would have it, an ill defined or unknown term.
141. M Bôcher: 'Integral equations
• Mathematicians have so far devoted their attention mainly to two peculiarly simple types of integral equations, - the linear equations of the first and second kinds, - and we shall not in this tract attempt to go beyond these cases.
• We shall also restrict ourselves to equations in which only simple (as distinguished from multiple) integrals occur.
142. Groups St Andrews proceedings
• Computational methods are surveyed in several articles in particular the major survey by Joachim Neubuser and find application in papers on Burnside groups and finite simple groups.
• The Theory of Groups continues to move forward on many fronts, and twenty years on from the announcement of the classification of the finite simple groups, it prospers perhaps surprisingly well (rather like Mark Twain).
143. E C Titchmarsh on Counting
• Number must have a meaning such that it is true that I have the same number of fingers on each hand, and the same number of buttons as buttonholes on my waistcoat (with coats the situation does not seem to be so simple).
• The conclusion of all this seems to be that we must do without a simple and direct answer to the question, "What is a number?" This will not prevent us from doing mathematics.
144. Rios Honorary Degree
• This has contributed to considering Monte Carlo simulation as more than a simple complement to modelling, because of the basic advantages of understanding, implementation, execution and memory requirements, etc.
• The extraordinary similarity of the structure of all parts of the human cortex to each other and of human cortex with the cortex of the most primitive mammals suggests that a relatively simple universal principle governs its operation, even in complex processes like language." .
145. Atiyah reviews
• Our philosophy has been to build up to the main theorems in a succession of simple steps and to omit routine verifications.
• Some of them are simple and others are rather difficult.
146. Jacobson: 'Theory of Rings
• That this has been possible in a book dealing with results of the significance of Wedderburn's theorems, the Albert-Brauer-Noether [A Adrain Albert, Richard Brauer, Emmy Noether] theory of simple algebras and the arithmetic ideal theory is another demonstration of one of the most remarkable characteristics of modern algebra, namely, the simplicity of its logical structure.
• In the first part of this chapter we consider the theory of simple algebras over a general field.
147. Michell Twisted Rings
• The problem is simple to state: "If a wire of isotropic section and naturally straight be twisted, and the ends joined so as to form a continuous curve, the circle will be a stable form of equilibrium for less than a certain amount of twist." In other words, consider an isotropic elastic rod (the rod has no preferred bending direction) that is stress-free when held straight.
• Apparently, Michell realized that when these frequencies become imaginary the equilibrium shape loses its stability and he applied this idea to derive a simple criterion for the instability of a twisted elastic ring.
148. Edinburgh Mathematics Examinations
• Show that their resultant may be treated as simple harmonic motion, in a direction which rotates slowly.
• (b) the other is forced to execute transverse simple harmonic motions of given period and range.
149. Rios's books
• Ten chapters take you in logical steps from "individual decisions in a probabilistic environment" up to "utility in a multistage environment" and "collective decisions." It includes also a reasonably full treatment of Bayesian methods and is illustrated with simple examples.
• This is an excellent simple introduction to decision theory.
150. James Jeans addresses the British Association in 1934, Part 2
• It may seem strange, and almost too good to be true, that nature should in the last resort consist of something we can really understand; but there is always the simple solution available that the external world is essentially of the same nature as mental ideas.
• Let me digress again to remind you of two simple instances of such conflicts and of the verdicts which observation has pronounced upon them.
151. Kurosh: 'The theory of groups' 1st edition
• Moreover, from the point of view of algebra itself - of which the theory of groups is a part - a situation could hardly be regarded as normal in which such very simple and important groups as, for example, the additive group of integers remained outside the limits of the theory.
• Furthermore, very often a problem that is simple and completely solved in the case of finite groups changes to a broad theory, yet far from complete, this happens, for example, in the theory of abelian groups, one of the most important parts of contemporary group theory.
152. Harold Jeffreys on Logic and Scientific Inference
• But the importance of simple laws in inference leads us to concentrate on those properties of sensations that actually satisfy simple laws as far as they have been tested.
153. Halsted Beltrami
• In the exordium of a memoir dated Pisa, 31 May 1866, Beltrami remarks that in treating of a map destined to serve for measurements of distance it would be most convenient to determine, that to the geodetics of the surface should correspond the straights of the plane, because, such a representation accomplished, the questions concerning geodetic triangles would be reduced to simple questions of plane trigonometry.
• At least it seems that to such attempts we owe a memoir where is studied with scrupulous care the surface generated by the rotation of the tractrix about its asymptote with the aim of deducing the elements by a construction simple and exact of the surface itself.
154. Bolyai house and grave
• Thanks to his tireless diligence and procurement, a campaign started in the capital city circles and the Mathematics and Physics Society marked the grave of the author of "Appendix" with a simple, pretty tacky gravestone.
• I was hoping, that even a simple gravestone would be given to him, rather to his grave, for the occasion of the marking of his father's gravestone, but the Committee was not willing to do that - the remaining 100 forints from the collected money they wished to use as a scholarship called "Bolyai-fund", whose interest would be distributed as a reward for the best mathematics students of the last 4 classes of secondary school.
155. Halmos books 1
• The idea is to emphasize the simple geometric notions common to many parts of mathematics and its applications, and to do so in a language that gives away the trade secrets and tells the student what is in the back of the minds of people proving theorems about integral equations and Hilbert spaces.
• Mathematical logic has been intertwined with algebra from its beginnings, through Boole's discovery that simple laws of logic can be expressed symbolically as algebraic equations.
156. Vanstone obituary
• With Ray even a simple conversation would almost always turn into a serious discussion of non-trivial matters.
• Their many acts of kindness to visitors and colleagues, and their families, went far beyond simple human civility.
157. Boas books
• The text is a valuable contribution to mathematical literature in that it sets forth in simple language and in short space the parts of the real variable theory that are essential to further study in the various fields of mathematics.
• His prose is simple and direct, and at the same time, elegant and witty ..
158. Centenary of John Leslie
• His wants, however, were simple, and he managed to support himself in comfort by his pen and by tutoring little Colin Maclaurin; and he combined these with travel and study.
• In character Leslie was simple, good-natured and straightforward, free from jealousy and ready in his appreciation of the work of others.
159. Ahrens book of quotes
• For a scientist, explaining is analogous to tracing something back to a handful of desirably simple fundamental laws, which cannot be overcome, but must simply be taken for granted, in order to exhaustively explain a phenomenon.
• During a conversation with the writer in the last weeks of his life, Sylvester remarked as curious that notwithstanding he had always considered the bent of his mind to be rather analytical than geometrical, he found in nearly every case that the solution of an analytical problem turned upon some quite simple geometrical notion, and that he was never satisfied until he could present the argument in geometrical language.
160. Primes abstract
• How can one predict when the next prime number will occur? Is there a formula which could generate primes? These apparently simple questions have confounded mathematicians ever since the Ancient Greeks.
161. Ramchundra Preface
• This is a method which appears extremely simple and easy, though it baffled all my endeavours for the space of three years.
162. Gregory's Astronomical Clock
• The movement of the clock is of simple construction and contains only three wheels with an ordinary tick-tack escapement driven by a weight, suspended on a slender chain, which requires to be pulled up every twenty-four hours.
163. NAS Memoir of Chauvenet
• At the time of its publication trigonometry in many of our colleges was restricted to the simple cases of plane and spherical triangles, by the trammelling geometric processes.
164. Schrödinger: 'Statistical Thermodynamics
• The object of this seminar is to develop briefly one simple, unified standard method, capable of dealing, without changing the fundamental attitude, with all cases (classical, quantum, Bose-Einstein, Fermi-Dirac, etc.) and with every new problem that may arise.
165. Netto books
• The simple fact that the able and fairly complete treatise now under review hardly mentions the work of Hindenburg shows that what are now considered the substantial parts of combinatoric have been developed outside of the German Combinatorial School.
• Be simple.
167. Practical Logical Beautiful
• Then there is percentages, and estimating various quantities with simple calculations (Chapter 4), some knowledge of graphs, some probability and statistics.
168. Kepler's 'Foundations of modern optics' Preface to a translation
• But Kepler's text is not only a Latin text of the late sixteenth century written by an author from the Germanic cultural sphere, it is a technical text in which numerous passages - notably Chapter IV - testify more to a pure and simple transcription of personal notes than to a patiently executed draft.
169. Hans Hahn: 'The crisis in intuition
• Again and again we have found that, even in simple and elementary geometric questions, intuition is a wholly unreliable guide.
170. Moiseiwitsch Variational Principles
• Variational principles have long played two major roles in mathematical physics; one as great unifying principles through which the different equations can be ex- pressed in elegantly simple form, and the other as remarkably useful computational tools for the accurate determination of discrete eigenvalues such as the vibration frequencies of classical systems and the bound state energies of quantum mechanical systems.
171. H F Baker: 'A locus with 25920 linear self-transformations' Preface
• This volume, is concerned with a locus - itself very interesting to explore geometrically - which exhibits in a simple way the structure of the group of the lines of a cubic surface in ordinary space, regarded as the group of the tritangent planes of the surface.
172. Feller Reviews 4
• And just as in volume one the author delights in giving many deceptively simple results which tease the probabilistic intuition or which would require sophisticated proof if viewed outside their natural probabilistic context.
173. System Reliability Theory
• For this purpose we treat simple situations first.
174. Gattegno reflections
• These words came to me in 1960 when I was interviewed for the Christchurch Daily (New Zealand), and was asked to characterize my work in a few simple words.
• It is the successful organisation of multitudinous sounds of words, associations of words, pictorial memories of diverse events and feelings ordinarily occurring in life, combined with a special narrative of great events: the whole so disposed to excite emotions which, as defined by Milton, are simple, sensuous, and passionate.
176. Kuku interview
• I came from a very simple background.
177. Newcomb School Algebra
• The First Course, which extends to Simple Equations, is intended to drill the student in all the fundamental processes by exercises which are, for the most part, of the simplest character.
178. Ernest Hobson addresses the British Association in 1910, Part 2
• Except in certain very simple cases no process of measurement, such as the determination of an area or a volume, can be carried out with exactitude by a finite number of applications of the operations of arithmetic.
179. Landau and Lifshitz Prefaces
• For similar reasons, the microscopic theory of superconductivity is described with the simple model od an isotropic Fermi gas with weak interaction, disregarding the complications due to the presence of the crystal lattice and the Coulomb interaction.
180. A I Khinchin on Information Theory
• On the whole, I follow the path indicated in the works of McMillan and Feinstein, deviating from them only in the comparatively few cases when I see a gap in their explanation, or when another explanation seems to me more complete and convincing (and sometimes, more simple).
181. Segel Asymptotic analysis
• To do this we shall briefly examine (i) certain basic theorems connected with asymptotic expansions, (ii) a differential equation in the neighbourhood of an essential singularity, (iii) a very simple singular perturbation problem, and (iv) the lack of genuine distinction between a large variable and a small one - all in order to emphasize the connection between asymptotic approximations and essential singularities.
182. Ahrens book reviews
• We do not find much of value in the story of the boys who convinced a simple old man that in their use of logarithm tables they were mastering the house numbers of Europe.
183. Closing Gap abstract
• Prime numbers have intrigued, inspired and infuriated mathematicians for millennia, and yet mathematicians' difficulty with answering simple questions about them reveals their depth and subtlety.
184. Laplace: 'Méchanique Céleste
• I hope, in consideration of the difficulty and importance of the subject, that mathematicians and astronomers will receive it with indulgence, and that they will find the results sufficiently simple to be used in their researches.
185. Noether's students
• Thesis title: Nichtgaloissche Zerfallungskorper einfacher Systeme (Non-Galois splitting fields of simple systems).
186. Karl Menger on Hans Hahn
• No one knew as well as he how to present those leading ideas in such a simple as well as thorough way, in such a logical as well as suggestive form." .
187. Galois Sainte Pelagie preface
• Long algebraic calculations were at first hardly necessary for progress in Mathematics; the very simple theorems hardly gained from being translated into the language of analysis.
188. Catalan manifesto
• If my name was not heard in the political assemblies, there is a very simple reason: in the oligarchic regime that you just reversed, I was not a voter, and I would never become a voter! But ask those whom I dare to call my illustrious friends: Dupont (de l'Eure), Arago, Ledru-Rollin, Louis Blanc, Garnier-Pages; ask the young people who left the Ecole Polytechnique the previous eight years; invoke memories of my old comrades of the eleventh legion: they will all tell you that I was always seen at the breach, and that my well known republican views prevented me from making the progress that I was legitimately due.
189. Champernowne reviews
• Those already familiar with the field will find Champernowne's book generally fascinating because of the many novel simple models developed in the book.
190. Kantorovich books
• The first chapter deals with simple cases of short-run planning of production.
191. Analysis of Variance
• An agricultural experiment of a relatively simple structure to which the analysis of variance would be applicable would be the following: In each of three localities four varieties of tomatoes are grown in tanks containing chemical solutions.
• I was fortunate enough to communicate with Nikolai Ivanovich many times - a refined intellectual, an unusually simple, benevolent person with a great sense of humour.
193. William and Grace Young: 'Sets of Points
• The present volume is an attempt at a simple presentation of one of the most recent branches of mathematical science.
194. Stringham books
• Starting with the theory of proportion as stated by Euclid, the author builds upon this the algebra of real quantities and establishes the laws of combination of such quantities by simple geometrical constructions.
195. Taleb reviews
• Non-technically written and built on episodes, stories and simple visualisations; the book is easy to read.
196. Dingle books
• "Into this simple unison of thought there broke with the Renaissance the discordant note of modern science," with its independent direct appeal to experience.
197. R A Fisher: 'History of Statistics
• Gauss, further, perfected the systematic fitting of regression formulae, simple and multiple, by the method of least squares, which, in the cases to which it is appropriate, is a particular example of the method of maximum likelihood.
198. Collected Papers of Paul Ehrenfest' Preface
• He has a great preference for the use of simple models that show the essential traits of a problem - and is a master at inventing them; this is a common feature of his lectures and his writings.
199. H L F Helmholtz: 'Theory of music' Prefaces
• Again, it appears that the peculiar articulation between the auditory ossicles called -hammer' and 'anvil' might easily cause within the ear itself the formation of harmonic upper partial tones for simple tones which are sounded loudly.
200. Klein Elementary Mathematics
• I shall endeavor to put before the teacher, as well as the maturing student, from the view-point of modern science, but in a manner as simple, stimulating, and convincing as possible, both the can lent and the foundations of the topics of instruction, with due regard for the current methods of teaching.
201. Kurosh: 'The theory of groups' 2nd edition
• Of course, even now the classification of extensions is far from having reached that degree of perfection which would allow the solving of any problem on extensions by a simple reference to this classification; but the whole position cannot be compared to what it was twelve years ago.
202. Knorr's books
• The implications of this simple conception struck me, as I was completing a paper on Apollonius' construction of the hyperbola (1980; published in Centaurus, 1982), for it served to unify a diverse range of geometric materials I had then been collecting for some five years.
203. Max Born's matrices
• A student occasionally goes to lectures about abstruse subjects just for fun and speedily forgets all about them This is what happened to me with a lecture on higher algebra, of which I recollected little more than the word "matrix" and a few simple theorems about these matrices.
204. Catalan retirement
• It would not be the same, I am convinced, that if I give my dear students, old and new, not a dissertation on the delights of mathematics (this would lead us too far afield), but a few simple thoughts relating to intellectual work.
205. Gibson History 7 - Robert Simson
• His method of teaching was simple and perspicuous, his elocution clear, and his manner easy and impressive.
206. J L Synge: 'Geometrical Optics
• A "perfect" scientific theory may be described as one which proceeds logically from a few simple hypotheses to conclusions which are in complete agreement with observation, to within the limits of accuracy of observation.
207. Henry Baker addresses the British Association in 1913
• And, alas! to deal only with one of the earliest problems of the subject, though the finally sufficient conditions for a minimum of a simple integral seemed settled long ago, and could be applied, for example, to Newton's celebrated problem of the solid of least resistance, it has since been shown to be a general fact that such a problem cannot have any definite solution at all.
208. J J Nassau - Practical Astronomy
• The most complex of them are remarkably clear as a result of the simple device of heavy-lining the principal parts so that they stand out from the background of reference circles.
209. L'Hôpital: 'Analyse des infiniment petits' Preface
• At the time, however, this method was not as simple as M Barrow has since made it, by having paid closer attention to the properties of polygons, which naturally suggest that one consider the small triangles each made up of a part of the curve cut off between two infinitely close ordinates, the difference between these ordinates and the difference between the corresponding abscissae.
210. Harold Jeffreys: 'Scientific Inference' Preface
• It is found to lead to an explanation and a justification of the high probabilities attached in practice to simple quantitative laws, and thereby to a recasting of the processes involved in description.
211. Halmos: creative art
• Even that can be done, and I could show you a perfectly simple method in one minute and convince you that it works in two more minutes.
212. George Temple's Inaugural Lecture I
• Many of these primers of natural philosophy give the impression that the various divisions of this great subject are mainly and essentially deductive systems, each solidly based on a few general principles, which themselves are almost immediate inferences from a few simple and unequivocal experiments or observations.
213. Sims computation
• While the author's presentation neatly embeds the Todd-Coxeter method into the general context of his automaton theoretic set up, it has to be said that the rather simple basic idea that the Todd-Coxeter method is trying to construct a transitive permutation representation by a backtrack method is not very easily understood coming in the guise of dealing with automata.
214. Comments by Charlotte Angas Scott
• In reviewing a book, one of the canons of fair criticism is to regard its adaptation to the readers for whom the author himself designs it; but as a preliminary to this notice, we must object to the selection implied in the preface, where Professor Smith describes his book as intended "to present in simple and intelligible form a body of geometric doctrine acquaintance with which may fairly be demanded of candidates for the Freshman class," and then points out that one year's study of geometry is about as much as can be expected in schools.
215. Finlay Freundlich's Inaugural Address, Part 2
• The spherical geometry is the most simple case of a non-Euclidean geometry.
216. Percy MacMahon addresses the British Association in 1901, Part 2
• In the case of simple unrestricted partition it gives directly the composition by rows of units which is in fact carried out by the Ferrers-Sylvester graphical representation, and led in the hands of the latter to important results connection with algebraical series which present themselves in elliptic functions and in other departments of mathematics.
217. Loney Prefaces
• In order to deal as fully as possible with the less elementary processes of Arithmetic, and at the same time to keep the book within a reasonable size, it is assumed that the student already knows the four "Simple" Rules and the "Compound" Rules.
218. Women mathematics teachers
• [','','8, page 72] The 1870 Education Act introduced a curriculum focused on the three Rs; reading, writing and arithmetic, thus women began to learn simple arithmetic with an aim to improve domestic skills.
219. Isaacs' Differential Games
• The theory is illustrated throughout by applications to deceptively simple pursuit games.
220. O'Brien Calculus
• XV contains a very simple method of tracing curves.
221. Bartlett reviews
• With a few notable exceptions, biologists have tended to avoid anything but the most trivial uses of mathematics, partly because of a lack of mathematical training, partly because of a feeling that the complexities of living organisms cannot be reduced to a few simple equations.
222. Ball papers
• Here I will assume that we allow the use of brackets and the symbols for square roots, decimals (simple and repeating), factorials, and subfactorials [this is n!(1 - 1/1! + 1/2! - 1/3! + ..
223. Dubreil Books
• This lucid and simple introduction to abstract algebra approaches the subject from an extremely general point of view.
224. Wall's Creative mathematics
• Thus in calculus the simple graph rather than the concept of variable is taken as fundamental.
225. Boyer's books
• One's envy that there are places of higher learning where such textbooks are widely wanted is somewhat modified when one sees the drudgery of a set of exercises at the end of each chapter; they contain, however, not only the usual essay-type revision questions, but also simple sums to test whether the plain mathematical content has been assimilated.
226. Santalo quotes
• Tycho Brahe could scarcely suspect that all his tables of observations could be condensed into the simple mathematical formula of Newton's universal law of attraction.
227. George William Hill's new theory of Jupiter and Saturn
• Later the terms factored by the simple power of the eccentricities were added by himself, Lalande, Lagrange, Bailly and Lambert.
228. Rydberg's application
• They can in the main be expressed through a few and simple propositions, but their importance becomes evident only, when we compare the state before and after the publication of his treatise and when we consider the labour it has cost to attain this, whereof the memoir of Docent Rydberg of 1890 bears sufficient witness.
• I was fortunate enough to communicate with Nikolai Ivanovich many times - a refined intellectual, an unusually simple, benevolent person with a great sense of humour.
230. Mary Boole Darwin
• But I cannot see how the belief that all organic beings including man have been genetically derived from some simple being, instead of having been separately created bears on your difficulties.
231. Heinrich Tietze on Numbers, Part 2
• Compare the time required to do a simple problem in addition in the decimal system with that required by the same problem using Roman numerals: .
232. University of Glasgow Examinations
• Investigate the relation between the length of a simple pendulum and the time of oscillation.
233. Atiyah on beauty
• But of course with a beautiful result it can be very simple to state yet proving it can be very complicated like Fermat's Last Theorem.
234. AMS war appeal.html
• In the cause of simple humanity and in the interests of the unborn generations for whom science can prepare benefits as yet but dimly descried, the American Mathematical Society now appeals to its sister-societies in every land - and most particularly to those in lands which are at war with one another - to exert all possible effort towards the conservation of the scientific resources of the world against the day when peace shall reign once more.
235. Burali-Forti Russell letter
• It will not have the importance that you would like and that I wish it would have; but it will have the sole merit of showing how both simple and precise is the notation of your great Hamilton, of whom I am ardent admirer.
236. Cofman books
• There are many collections of mathematical problems for various ages and levels of ability so why commend another? The answer is simple.
237. Encke Obituary
• They bear strong and uniform testimony to his eminent frankness and truthfulness; his labours, they say, were incessant, his recreations few; he was simple in his manners, and in all his habits temperate.
238. Charles Bossut on Leibniz and Newton
• In the piece entitled De Analysi per Aequationes Numero Terminorum infinitas besides the method for resolving equations by approximation, which has nothing to do with us here, Newton teaches how to square curves, the ordinates of which are expressed by monomials or sums of monomials; and when the ordinates contain complex radicals, he reduces the question to the former case by evolving the ordinate into an infinite series of simple terms by means of the binomial theorem, which no one had done before.
239. Zehfuss publications
• Georg Zehfuss, Deduction simple de l'Expression Γ(x) de Gauss, Nouvelles annales de mathematiques (1) 18 (1859), 356.
• And the reason is simple enough.
241. Ahlfors' Complex analysis
• Many situations which seem intuitively simple are logically quite involved and must be avoided.
242. Dehn on Mathematical abilities
• One-dimensional rhythm (simple music).
243. A I Khinchin: 'Statistical Mechanics' Introduction
• Darwin and Fowler also created a simple, convenient, and mathematically rigorous apparatus for the computation of asymptotic formulas.
244. Erdos document
• Number theory is full of incredibly simple, and seemingly almost unsolvable problems, Edmund Landau listed four of these in the international conference in Cambridge in 1912, whose solutions are "unreachable with our current scientific knowledge".
245. Von Neumann: 'The Mathematician
• Euclid's postulational treatment represents a great step away from empiricism, but it is not at all simple to defend the position that this was the decisive and final step, producing an absolute separation.
246. James Jeans addresses the British Association in 1934
• Yet a simple argument will show that he can never get beyond x, y and z.
247. Gender and Mathematics refs
• L O Adetula, Solution of simple word problems by Nigerian children: Language and schooling factors, Journal for Research in Mathematics Education 20 (1989), 489-497.
248. Valdivia Infinity
• The infinitesimal calculus, differential equations and even the calculus of probabilities and mathematical statistics are presented in a very simple way in non-standard analysis, but in return the meanings are not as clear as in classical mathematical analysis.
249. Napier Tercentenary
• Mr H S Gay gave some simple and for practical purposes sufficiently accurate formula for determining the trigonometrical functions when the angle is given and conversely, without the use of elaborate tables.
250. Binet Papers
• Note sur le mouvement du pendule simple en ayant egard a l'influence de la rotation diurne de la Terre, Comptes Rendus des Seances de l'Academie des Sciences 32 (1851), 157-159; 160; 197-205.
251. Kuku Representation Theory
• Profinite K-theory of p-adic orders and semi-simple algebras .
252. Solve Applied Problems
• All the problems can be solved in closed analytical forms in terms of elementary functions or simple integrals.
253. Descartes' 'La Geometrie'
• Perceiving that in order to understand these relations I should sometimes have to consider them one by one, and sometimes only to bear them in mind, or embrace them in the aggregate, I thought that, in order the better to consider them individually, I should view them as subsisting between straight lines, than which I could find no objects more simple, or capable of being more distinctly represented to my imagination and senses; and on the other hand that in order to retain them in the memory, or embrace an aggregate of many, I should express them by certain characters, the briefest possible.
254. Mannheim publications
• A Mannheim, Determination simple et rapide d'une equation des surfaces du second ordre contenant six points donnes, Bulletin des Sciences Mathematiques et astronomiques (I) II (1871), 125-127.
255. Thomson on 'ether
• I feel that I have a right to drop the adjective luminiferous, because the medium, far above the earth's surface, through which we receive sun-heat (or light), and through which the planets move, was called ether 2000 years before chemists usurped the name for "sulphuric ether," "muriatic ether," and other compounds, fancifully supposed to be peculiarly ethereal; and I trust that chemists of the present day will not be angry with me if I use the word ether, pure and simple, to denote the medium whose undulatory motions constitute radiant heat (or light).
256. Ernesto Pascal's books
• The chief fault of the book, from our point of view, is that it sacrifices simple and natural discussion to the pursuit of the end so dear to Italian mathematicians, the greatest possible generality.
257. Etherington papers
• I M H Etherington, A simple method of finding sums of powers of the natural numbers, Edinburgh Math.
258. V Lebesgue books
• The work of Legendre is no longer sufficient in spite of its extent, and by this very fact the author has not been willing to confine himself to the simple role of translator.
259. Felix Klein on intuition
• [If a work like] Cours d'analyse of Camille Jordan is placed in the hands of a beginner a large part of the subject will remain unintelligible, and at a later stage, the student will not have gained the power of making use of the principles in the simple cases occurring in the applied sciences ..
260. Johnson pre1900 books
• The investigation thus initiated resulted in a satisfactory method of obtaining the differentials of the simple functions, which was embodied in a paper communicated to the American Academy of Arts and Sciences, January 14, 1873, by Professor J M Peirce, and published in the Proceedings of the Society.
261. Eulogy to Euler by Fuss
• His mood was always on an even-keel, a sweet, natural happiness, a good-natured sarcasm; a story-teller both innocent and simple made his conversation pleasant and coveted.
262. Descartes' Method
• The long chains of simple and easy reasonings by means of which geometers are accustomed to reach the conclusions of their most difficult demonstrations led me to imagine that all things, to the knowledge of which man is competent, are mutually connected in the same way, and that there is nothing so far removed from us as to be beyond our reach, or so hidden that we cannot discover it, provided only we abstain from accepting the false for the true, and always preserve in our thoughts the order necessary for the deduction of one truth from another.
263. Aitchison books
• It presents an elementary introduction to the ideas of statistical decision making, with little mathematical prerequisite or formal demand on the reader, and with the material firmly tied to an extensive framework of simple but realistic examples.
264. John Walsh's delusions
• He will find in it geometry more deep and subtle, and at the same time more simple and elegant, than it was ever contemplated human genius could invent.
265. Edwin Elliot: 'Algebra of Quantics
• In endeavouring to improve this second edition, which is the last I shall live to produce, and is probably definitive, I have continued to think mainly for him, and to picture him as one better prepared for being led on from the simple - it may be the crude -to the elaborate, than for first receiving, and then applying, comprehensive theory.
266. Franklin's textbooks
• He gives the most important results, with proofs where they are simple, and references to original papers where they are long and tedious; so that the brochure is very readable.
267. A N Whitehead: 'Mathematics in the History of Thought
• Suppose we project our imagination backwards through many thousands of years, and endeavour to realise the simple-mindedness of even the greatest intellects in those early societies.
268. Mac Lane books
• Throughout the book, the author's style is simple and direct, as one would expect.
269. L E Dickson: 'Linear algebras
• The remarkable properties of Cayley's algebra of eight units are here obtained for the first time in a simple manner, without computations.
270. Weatherburn books
• The book should serve as a simple introduction to these subjects treated by way of the vector methods, and for the purposes in view is admirably adapted to the student's needs.
271. Eperson contributions
• Ask a friend to choose a number with two digits, which you will endeavour to discover if he/she tells you the answer to some simple calculations.
272. McBride equal bisectors
• But, alas! a simple case of Euclid I.
273. R L Wilder: 'Cultural Basis of Mathematics III
• Without a symbolic apparatus to convey our ideas to one another, and to pass on our results to future generations, there wouldn't be any such thing as mathematics - indeed, there would be essentially no culture at all, since, with the possible exception of a few simple tools, culture is based on the use of symbols.
274. Fatou Fonctions Automorphes
• Fatou uses Montel's theory of normal families of functions to obtain a new and very simple proof of the theorem that a group of real linear transformations which has no infinitesimal transformation is properly discontinuous.
275. Cafaro's papers
• Very often, self-similarity of intermediate asymptotics can be derived from simple dimensional-analysis arguments.
276. Simplicius on astronomy and physics
• But he must go to the physicist for his first principles, namely, that the movements of the stars are simple, uniform, and ordered, and by means of these principles he will then prove that the rhythmic motion of all alike is in circles, some being turned in parallel circles, others in oblique circles.
277. Kelvin on the sun
• To advance another step, still through impracticable mechanism, towards the practical method by which the sun's heat is produced, let the thread of the screw be of uniformly decreasing steepness from the surface downwards, so that the velocity of the weight, as it is allowed to descend by the turning of the screw, shall be in simple proportion to distance from the sun's centre.
278. Gibson History 5 - James Gregory
• Later, after seeing one of Newton's series, he developed many series and for the inspiration, though not for the methods, he was in these cases indebted, I think, to the simple statement (without explanations of any kind) of the Newtonian series.
279. Mitchell Feigenbaum: the interviewer
• Briefly, he discovered a universal quantitative solution characterized by specific measurable constants that describes the crossover from simple to chaotic behaviors in many complex systems.
280. Bronowski and retrodigitisation
• Based on the fact that 7 is a divisor of 1001, it provides a simple way to compute remainders on division by 7.
• To illustrate by a very simple example, the function x2 has for its graph a parabola with its principal vertex at the origin of coordinates, and its principal diameter coincident with the y-axis.
282. Sikorski books
• There is no high points or climaxes, no broad over-view, no explanation of a simple illustration before meeting the full treatment.
283. Einstein NY Times
• Public interest in Albert Einstein's relativity theory had become so great in 1929 that, when he presented to the Prussian Academy his comprehensive theory fusing electromagnetism and gravitation in a single law, the New York Times urged him to prepare an explanation of his new work in terms as simple as the subject would allow.
284. Payne-Gaposchkin introduction
• Most of its concepts can be expressed in simple, everyday language.
285. Poincaré on non-Euclidean geometry
• Further, this interpretation is not unique, and several dictionaries may be constructed analogous to that above, which will enable us by a simple translation to convert Lobachevsky's theorems into the theorems of ordinary geometry.
286. Algebraic Triplets
• Mr Charles Graves stated that Sir Wm Hamilton had been the first to announce that if the real unit line, the factors, and the product line, be projected upon the symmetric axis, the projections will form a proportion in the simple sense of that term ..
287. Young Researchers
• Title: Decompositions of graphs: splitting huge structures into simple pieces .
288. Helmholtz on Thomas Young
• I include myself among the number; for I long toiled at the task, without getting any nearer my object, until I at last discovered that a wonderfully simple solution had been discovered at the beginning of this [nineteenth] century, and had been in print for any one to read who chose.
289. H Weyl: 'Theory of groups and quantum mechanics' Introduction
• In this chapter many details will be introduced with an eye to future use in the applications; it is to be hoped that in spite of this the simple thread of the argument has remained plainly visible.
290. What do mathematicians do?
• Nowadays quite simple proofs exist, but they use sophisticated new tools such as group theory and field theory.
291. Cardan: autobiography
• He confesses it without impudence and without feigned contrition, without even wishing to make himself an object of interest, but with the same simple and sincere love of fact which guided him in his scientific researches.
292. Kerr: 'Technical Education
• As confirmatory evidence of the volume and importance of the work done it is interesting to find in 1824 an eminent mechanical engineer, M Dupin, calling the attention of France to the Andersonian College, "a school for teaching the theory of the mechanical and chemical arts - intended not only for the directors of the workshops but particularly for the simple working man." He attributes the industrial supremacy of this country to the cultivation of science, and he calls upon Frenchmen "not to remain behind in this immense progress but to proceed on the same lines in order to outstrip, if possible, a people whom Nature has made our rival in every kind of glory." .
293. George Gibson: 'Calculus
• Simple exercises are attached to many of the sections; in the formal sets will be found several theorems and results for which room could not be made in the text, and which are yet of sufficient importance to be explicitly stated.
294. Plato on Mathematics
• 'Think a little,' I told him, 'and you will see that what has preceded will supply the answer; for if simple unity could be adequately perceived by the sight or by any other sense, then, there would be nothing to attract the mind towards reality any more than in the case of the finger we discussed.
295. Carol R Karp: 'Languages with expressions of infinite length
• My interest in infinitary logic dates back to a February day in 1956 when I remarked to my thesis supervisor, Professor Leon Henkin, that a particularly vexing problem would be so simple if only I could write a formula that would say x = 0 or x = 1 or x = 2 etc.
296. Ptolemy's hypotheses of astronomy
• The ground for this conviction which is readiest to hand, seeing that the earth has been proved to be spherical and situated in the middle of the universe, is this simple fact: in all parts of the earth without exception the tendencies and the motions of bodies which have weight - I mean their own proper motions - always and everywhere operate at right angles to the (tangent) plane drawn evenly through the point of contact where the object falls.
297. Turnbull lectures on Colin Maclaurin
• We may pause for a moment to consider what a boon this interval of unhampered leisure would bring to the lad upon the threshold of manhood: the simple life in the manse of Kilfinan upon the open easterly shore of Loch Fyne, but a few miles over the hill from Glendaruel, the home of his childhood: the opportunity for his thoughts upon geometry to ripen, the fruit of the teaching that he received from Robert Simson, his Professor at college.
298. Louis Auslander books
• In each chapter basic notions are introduced after illustrating and discussing simple cases of the objects, and almost all sections end with a set of exercises which facilitate the understanding of the subject.
299. Howie Thanksgiving Service
• Those of us who had the good fortune to enjoy John's friendship and hospitality, equally don't need reminding of his simple human qualities - devotion to family, enjoyment of good company and conversation, multitude of interests, including of course his love of music, and his service to the community.
300. Apostol books
• The presentation is simple and clear.
301. Malcev: 'Foundations of Linear Algebra' Introduction
• For example, the fundamental idea behind the solution of a system of linear equations in several unknowns is that of replacing such a system by a chain of these simple equations.
302. Lewis's papers
• I can only put forward certain statements intended to formulate attributes which are essential to mind; to point to phenomena of which we can say, "Whatever else is or is not comprehended under 'mind,' at least it is intended to include these." In particular, I shall wish to emphasize that whatever is called "content of consciousness" is so included, and to consider certain consequences of that simple fact.
303. Peres publications
• Joseph Peres, Action sur un obstacle d'un fluide visqueux; demonstration simple de formules de Faxen, Comptes Rendus Acad.
304. Arvesen publications
• Ole Peder Arvesen, Sur certaines surfaces algebriques, parmi lesquelles la surface de Steiner constitue le cas le plus simple, Norske Vid.
305. Kuratowski: 'Introduction to Topology
• and Frechet), and the space of continuous functions are metric spaces; at the same time, the very concept of a metric space is especially simple and geometrically clear.
306. A D Aleksandrov's view of Mathematics
• Of course, the rules here are very simple, but we should remember that in some period of antiquity they represented the most advanced mathematical achievements of the age.
307. William Herschel discoveries
• Herschel began to examine stellar spectra using a simple prism in 1798.
308. Gerard Murphy papers
• G J Murphy, Simple C*-algebras and subgroups of Q, Proc.
309. Weil on history
• ultimately upon the values, for suitable values of the arguments, of the simple series discussed above in our Chapter 7.
310. Perron books
• The style is simple and precise and presents no difficulties to a reader having a firm grasp of the fundamental principles of elementary analysis.
311. Green's students
• Thesis title: A Sporadic Simple Group of B Fischer of Order 64,561,751,654,400.
312. Mathematicians and Music 2.1
• Pythagoras proposed to find in the order of the universe, where whole numbers and simple ratios prevail, an answer to the question: Why is consonance (the beautiful in sound) determined by the ratio of small whole numbers? The correct numerical ratios existing between the seven tones of the diatonic scale corresponded, according to Pythagoras, to the sun, moon and five planets, and the distances of the celestial bodies from the central fire, etc.
313. Lorch books
• Chapter VI expounds the Gel_fand representation of semi-simple commutative Banach algebras.
314. Vajda books
• Linear programming computations consist of simple arithmetic processes, although the mathematical proofs and problems of formulation are sometimes quite deep and technical.
315. Leslie Origins Number
• These simple arrangements would, on their first application, carry the power of reckoning but a very little way.
316. De Rham books
• Torsion et type simple d'homotopie (1967), by G de Rham, S Maumary and M A Kervaire.
317. Douglas Jones publications
• D S Jones, The scattering of sound by a simple shear layer, Phil.
318. Survey of Modern Algebra
• Then the abstract definition appears simple, and the theoretical properties which are deduced from the definition exhibit the power of the concept.
319. Richard Courant: 'Differential and Integral calculus' English edition
• I felt that owing to the difference between the methods of teaching the calculus in Germany and in Britain and America a simple translation was out of the question, and that fundamental changes would be required in order to meet the needs of English-speaking students.
320. Krejci's book
• There is no simple and satisfactory explanation of this fact.
321. Groups in Galway
• Finite simple groups.
322. Ernest Hobson addresses the British Association in 1910
• These times must have been preceded by still earlier ages in which the mental evolution of man led him to the use of the tally, and of simple modes of measurement, long before the notions of number and of magnitude appeared in an explicit form.
323. Todd: 'Basic Numerical Mathematics
• However, most of the problems in Volume 1 can be dealt with using simple programmable hand calculators, but many of these in Volume 2 require the more sophisticated hand calculators (i.e., those with replaceable programs).
324. Cajori: 'A history of mathematics' Introduction
• After the pupils have learned how to bisect a given angle, surprise them by telling of the many futile attempts which have been made to solve, by elementary geometry, the apparently very simple problem of the trisection of an angle.
325. Gentry Berlin
• Berlin was chosen as place of residence for the first few weeks or months, as the case might be, for the simple reason that I knew of people here who would kindly take me in charge till I should have learned to take care of myself in a foreign land.
326. Hormander books
• A brief chapter on differential equations with no solutions is followed by chapters on operators of constant strength, operators with simple characteristics, the Cauchy problem, and a concluding chapter on elliptic boundary value problems.
327. Zwicky books
• In simple terms, morphological research is a method of ensuring "unbias" (a word coined by Zwicky for the purpose) by the systematic listing of all conceivable alternatives in a given complex situation.
328. Cheltenham exams
• This simple sum is made more difficult by the need to understand the definition of an improper fraction and the wordy nature of the question.
329. Borali-Forti preface
• Leibniz was the first to conceive the grand plan to create a universal writing system, by which every idea could be expressed by means composed of simple ideas, each represented by a special sign.
330. Horace Lamb addresses the British Association in 1904, Part 2
• The investigators of the classical school, as it may perhaps be styled, were animated by a simple and vigorous faith; they sought as a matter of course for a mechanical explanation of phenomena, and had no misgivings as to the trustiness of the analytical weapons which they wielded.
331. Einar Hille: 'Analytic Function Theory
• These general considerations have led to the following arrangement of the subject matter of Volume I: After a preliminary study of number systems, the geometry of the complex plane is developed, and simple functions such as linear fractions, powers, and roots are studied.
332. More Smith History books
• To cover the ground of whole numbers so completely in thirty-four pages is a masterpiece of condensation, more noticeable because the matter is given in simple words and explained as to a beginner.
333. Leslie works
• The first portion deals with the more simple properties of conics, while the higher part treats chiefly of the construction of conics to satisfy all sorts of conditions.
334. Peirce publications
• A simple device for measuring the deflections of a mirror galvanometer, Proc.
335. Galileo: 'Dialogue
• Salviatus: So that its motion should be compounded of two; from this it would follow that the stone would no longer describe that simple straight and perpendicular line but one transverse and perhaps not straight.
336. John Collins by Wood
• (4) 'The Doctrine of Decimal Arithmetic, simple Interest, etc.
337. Ahlfors' reviews
• The book contains several of the author's results; the style is clear; the proofs are simple; we find several examples and problems; but there is no index or references.
338. Einstein: 'Ether and Relativity
• The laws were clear and simple, the mechanical interpretations clumsy and contradictory.
339. Clifford's books
• It is therefore very refreshing to find someone who reminds us that in spite of all these learned trappings the basic rules of arithmetic and algebra are nothing more and nothing else but "common sense"; especially if this is done in as simple and as convincing a manner as in the book under review.
340. Heinrich Tietze on Numbers
• system is simple, compared to the strange and complicated duodecimal system.
341. Scholar and the World.html
• The point that I wish to make is a simple - even a trite - one.
342. Venice and statistics
• The towns, on the other hand, throughout the West must from very early times have treated production, which with them depended on industry and commerce, as exceedingly variable; but, even in the most flourishing times of the Hanseatic League, they never got beyond a simple commercial balance sheet.
343. Percy MacMahon addresses the British Association in 1901
• The gravitation formula has been recognised from the time of Newton as ruling the dynamics of the heavens, and the exact agreement of the facts derived from observation with the simple theory has established astronomy as the most exact of all the departments of applied science.
344. Coxeter and Moser: 'Generators and Relations
• Some of them play an essential role in the theory of simple Lie groups.
345. Weil reviews
• In the second part - Chapters III and IV - the author studies the zeta function of division algebras and central simple algebras and then uses the Poisson summation formula to calculate the Tamagawa numbers of "most" classical groups .
346. Twenty-Five Years of Groups St Andrews Conferences
• The twenty-five years since 1981 have been an important period in the development of group theory following the classification of finite simple groups.
347. Founding the Indian Mathematical Society
• I shall soon be submitting to members proposals for a simple constitution for the Society according to which the affairs of the Society will be managed by a committee consisting of a President, a few office bearers and some additional members.
348. Booth Analytic Method
• Among other applications of the method, I trust that to the theory of reciprocal polars will be found simple and satisfactory.
349. Keynes: 'Probability' Introduction Ch II
• All it can do is so to arrange the reasoning that the logical relations, which have to be perceived directly, are made explicit and are of a simple kind.
350. Gaschutz's My Path
• The effects that this simple exchange of books had on the development of the mathematical seminar in Kiel can arguably still be perceived today.
351. Catalan manifesto
• Si mon nom n'a pas retenti dans les Assemblees politiques, c'est par une raison bien simple: sous la regime oligarchique que vous venez de renverser, je n'etais pas electeur, et je ne serais jamais devenu electeur! Mais consultez ceux que j'ose appeler mes illustres amis: Dupont (de l'Eure), Arago, Ledru-Rollin, Louis Blanc, Garnier-Pages; interrogez les jeunes gens sortis de l'Ecole Polytechnique depuis huit ans; invoquez les souvenirs de mes anciens camarades de la XIe legion: tous vous diront qu'ils m'ont constamment vu sur la breche, et que mes opinions republicaines bien connues m'ont empeche d'obtenir l'avancement qui m'etait legitimement du.
352. Valdivia aspects of maths
• It can be said that Euclid was the systematiser of almost all the mathematical results known in his time, ordering them in a masterly way in a deductive system, demonstrating from a few simple geometric properties, self-evident and not requiring proof, according to the spirit of the time, all that follows as logical consequences of the former.
353. Science at St Andrews
• With a simple diagram Gregory explained how the light rays on passing along the cylindrical tube would strike a large parabolic mirror and be reflected through a focus to a small concave mirror standing on the central axis of the tube, from which by a second reflexion they resume their course and pass out at a central aperture in the first mirror to an eye-piece.
354. Andrew Forsyth addresses the British Association in 1905
• The simple laws of planetary motion were not formulated, for Kepler had them only in the making.
355. Mathematics at Aberdeen 4
• In Mathematics the minimum required was on the first six books of Euclid, plane trigonometry and algebra as far as simple and quadratic equations.
356. Alfred Tarski: 'Cardinal Algebras
• The derivations are not simple but, in general, are not more involved than direct proofs carried through by the method indicated above.
357. Kline's books
• His writing is clear and simple, though somewhat repetitious.
## Quotations
1. Quotations by Ampere
• By combining at random simple truths with each other, more complicated ones are deduced from them.
• [Ampere gives this example drawn from geometry to illustrate his meaning for direct synthesis when deductions following from more simple, already-known theorems leads to a new discovery.] .
• There is analysis when from a complicated truth one deduces more simple truths.
2. Quotations by Bronowski
• Einstein was a man who could ask immensely simple questions.
• And what his work showed is that when the answers are simple too, then you can hear God thinking.
3. Quotations by Einstein
• Everything should be made as simple as possible, but not simpler.
• Most of the fundamental ideas of science are essentially simple, and may, as a rule, be expressed in a language comprehensible to everyone.
4. Quotations by Kepler
• My aim is to say that the machinery of the heavens is not like a divine animal but like a clock (and anyone who believes a clock has a soul gives the work the honour due to its maker) and that in it almost all the varety of motions is from one very simple magnetic force acting on bodies, as in the clock all motions are from a very simple weight.
5. Quotations by Brahe
• So Mathematical Truth prefers simple words since the language of Truth is itself simple.
6. Quotations by Weyl
• A modern mathematical proof is not very different from a modern machine, or a modern test setup: the simple fundamental principles are hidden and almost invisible under a mass of technical details.
• They are nothing but marks, and all that is in them we have put into them by the simple rule of straight succession.
7. Quotations by Hilbert
• Mathematics is a game played according to certain simple rules with meaningless marks on paper.
8. A quotation by Davenport
• A peculiarity of the higher arithmetic is the great difficulty which has often been experienced in proving simple general theorems which had been suggested quite naturally by numerical evidence.
9. A quotation by Maseres
• Negative numbers darken the very whole doctrines of the equations and make dark of the things which are in their nature excessively obvious and simple.
10. Quotations by Russell
• The point of philosophy is to start with something so simple as not to seem worth stating, and to end with something so paradoxical that no one will believe it.
11. Quotations by Laplace
• It is India that gave us the ingenious method of expressing all numbers by means of ten symbols, each symbol receiving a value of position as well as an absolute value; a profound and important idea which appears so simple to us now that we ignore its true merit.
12. Quotations by Sylvester
• During a conversation with the writer in the last weeks of his life, Sylvester remarked as curious that notwithstanding he had always considered the bent of his mind to be rather analytical than geometrical, he found in nearly every case that the solution of an analytical problem turned upon some quite simple geometrical notion, and that he was never satisfied until he could present the argument in geometrical language.
13. Quotations by Schrodinger
• The idea of the continuum seems simple to us.
14. Quotations by Born
• The problem of physics is how the actual phenomena, as observed with the help of our sense organs aided by instruments, can be reduced to simple notions which are suited for precise measurement and used of the formulation of quantitative laws.
15. Quotations by Von Neumann
• If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is.
16. A quotation by Chasles
• The doctrines of pure geometry often, and in many questions, give a simple and natural way to penetrate the origin of truths, to lay bare the mysterious chain which unites them, and to make them known individually, luminously and completely.
17. Quotations by Hawking
• My goal is simple.
18. Quotations by Condorcet
• uniformity of measures can only displease those lawyers who fear to see the number of lawsuits diminished, and those traders who fear a loss of profit from anything which renders commercial transactions easy and simple ..
19. A quotation by Lemoine
• A mathematical truth is neither simple nor complicated in itself, it is.
20. Quotations by Dantzig
• The two relatively simple problems -- the determination of the diagonal of a square and that of the circumference of a circle -- revealed the existence of new mathematical beings for which no place could be found within the rational domain.
21. A quotation by MacMahon
• During a conversation with the writer in the last weeks of his life, Sylvester remarked as curious that notwithstanding he had always considered the bent of his mind to be rather analytical than geometrical, he found in nearly every case that the solution of an analytical problem turned upon some quite simple geometrical notion, and that he was never satisfied until he could present the argument in geometrical language.
22. Quotations by Anaxagoras
• Anyhow we take in nourishment which is simple and homogeneous, such as bread or water, and by this are nourished hair, veins, arteries, flesh, sinews, bones and all the other parts of the body.
23. Quotations by Atiyah
• The most useful piece of advice I would give to a mathematics student is always to suspect an impressive sounding Theorem if it does not have a special case which is both simple and non-trivial.
24. Quotations by Dee
• A marveilous newtrality have these things mathematicall, and also a strange participation between things supernaturall, immortall, intellectuall, simple and indivisible, and things naturall, mortall, sensible, componded and divisible.
25. Quotations by Gauss
• A great part of its [higher arithmetic] theories derives an additional charm from the peculiarity that important propositions, with the impress of simplicity on them, are often easily discovered by induction, and yet are of so profound a character that we cannot find the demonstrations till after many vain attempts; and even then, when we do succeed, it is often by some tedious and artificial process, while the simple methods may long remain concealed.
26. Quotations by Descartes
• These long chains of perfectly simple and easy reasonings by means of which geometers are accustomed to carry out their most difficult demonstrations had led me to fancy that everything that can fall under human knowledge forms a similar sequence; and that so long as we avoid accepting as true what is not so, and always preserve the right order of deduction of one thing from another, there can be nothing too remote to be reached in the end, or to well hidden to be discovered.
27. Quotations by Turnbull
• A simple instance of failing in this is provided by the poll-man at Cambridge, who learned perfectly how to factorize a2 - b2 but was floored because the examiner unkindly asked for the factors of p2 - q2 .
28. A quotation by Mazur Barry
• In the history of the concept of number has been adjective (three cows, three monads) and noun (three, pure and simple), and now .
## Famous Curves
1. Folium
• There are three special forms of the folium, the simple folium, the double folium and the trifolium.
• The graph plotted above is the simple folium.
• The simple folium is the pedal curve of the tricuspoid where the pedal point is one of the cusps.
2. Double
• There are three special forms of the folium, the simple folium, the double folium and the trifolium.
• There are separate entries for the simple folium and the trifolium.
3. Trifolium
• There are three special forms of the folium, the simple folium, the double folium and the trifolium.
• There are separate entries for the simple folium and the double folium.
4. Cycloid
• The cycloid has the property that a particle P sliding on a cycloid will exhibit simple harmonic motion and the period will be independent of the starting point.
5. Tricuspoid
• The pedal of the tricuspoid, where the pedal point is the cusp, is a simple folium.
## Chronology
1. Mathematical Chronology
• The first symbols for numbers, simple straight lines, are used in Egypt.
• Maxwell publishes On Faraday's lines of force showing that a few relatively simple mathematical equations could express the behaviour of electric and magnetic fields and their interrelation.
• Cartan, in his doctoral dissertation, classifies all finite dimensional simple Lie algebras over the complex numbers.
• Russell discovers "Russell's paradox" which illustrates in a simple fashion the problems inherent in naive set theory.
• M Suzuki discovers new infinite families of finite simple groups.
• Edward Lorenz discovers a simple mathematical system with chaotic behaviour.
• John Thompson and Feit publish Solvability of Groups of Odd Order which proves that all nonabelian finite simple groups are of even order.
• Conway publishes details of his discovery of new sporadic finite simple groups.
• The classification of finite simple groups is complete.
2. Chronology for 1960 to 1970
• M Suzuki discovers new infinite families of finite simple groups.
• Edward Lorenz discovers a simple mathematical system with chaotic behaviour.
• John Thompson and Feit publish Solvability of Groups of Odd Order which proves that all nonabelian finite simple groups are of even order.
• Conway publishes details of his discovery of new sporadic finite simple groups.
3. Chronology for 1900 to 1910
• Russell discovers "Russell's paradox" which illustrates in a simple fashion the problems inherent in naive set theory.
4. Chronology for 1970 to 1980
• The classification of finite simple groups is complete.
5. Chronology for 1890 to 1900
• Cartan, in his doctoral dissertation, classifies all finite dimensional simple Lie algebras over the complex numbers.
6. Chronology for 1850 to 1860
• Maxwell publishes On Faraday's lines of force showing that a few relatively simple mathematical equations could express the behaviour of electric and magnetic fields and their interrelation.
7. Chronology for 1950 to 1960
• M Suzuki discovers new infinite families of finite simple groups.
8. Chronology for 30000BC to 500BC
• The first symbols for numbers, simple straight lines, are used in Egypt.
9. Chronology for 1980 to 1990
• The classification of finite simple groups is complete.
## EMS Archive
1. Edinburgh Mathematical Society Lecturers 1883-2016
• A simple method of finding any number of square numbers whose sum is a square .
• (Provincial Training College, Glasgow) On a simple theodolite suitable for use in schools .
• (Glasgow) Elementary methods for calculating first and second moments of simple configurations .
• (lived in Glasgow) A simple theodolite: A teaching appliance .
• (Edinburgh) A simple linkage for describing equal areas .
• (Glasgow) A simple link apparatus for the mechanical solution of quadratic equations .
• (Edinburgh) Exhibition of two simple nomograms .
• (Edinburgh) A simple form of integrometer .
• (Syracuse University, New York) A generalisation and simple proof of Kronecker's theorem concerning the minors of a compound determinant, {Communicated by David Gibb} .
• On the teaching of simple mathematical astronomy in schools; .
• (Cambridge) Some advances and retreats in the study of simple groups .
• (Warwick) Geometrical structures associated with simple groups of Lie type .
• (Cambridge) Finite simple groups - some special cases .
• (Oxford) Infinite simple groups .
• (University College, Cardiff) Problems about generating simple groups .
• (Leeds) Projective modules and simple rings .
• (Birmingham) Characterizations of simple groups .
• (Warwick) A simple partial differential equation with surprising behaviour .
2. EMS Proceedings papers
• A simple linkage for describing equal areas .
• A simple form of integrometer .
3. EMS 1930 Colloquium
• Simple rational curves in a plane: rational curves in space (cubics, quartics): general rational curves: conditions for a curve to be rational: simple rational surfaces (quadrics, cubics): general notions as to rational surfaces: conditions for a surface to be rational.
4. EMS Proceedings papers
• Elementary methods for calculating first and second moments of simple configurations .
• Common logarithms calculated by simple multiplication .
5. 1908-09 Jan meeting
• Miller, William: "A simple theodolite: A teaching appliance", [Title] .
6. 1883 Mar meeting
• A simple majority shall decide all questions not otherwise provided for in the Rules, the Chairman having in all cases both a deliberative and a casting vote .
7. 1905-06 Mar meeting
• Arneil, Loudon: "On a simple theodolite suitable for use in schools", [Title] .
8. 1906-07 Jun meeting
• Muirhead, Robert Franklin: "Elementary methods for calculating first and second moments of simple configurations" .
9. 1895-96 Feb meeting
• Martin, Artemas: "A simple method of finding any number of square numbers whose sum is a square" .
10. 1930-31 Rules meeting
• 16: A simple majority shall decide all questions not otherwise provided for in the Rules, the Chairman having in all cases a deliberative and a casting vote.
11. 1914-15 May meeting
• Whittaker, Edmund Taylor: "Exhibition of two simple nomograms", [Title] .
12. 1930-31 meeting
• 16: A simple majority shall decide all questions not otherwise provided for in the Rules, the Chairman having in all cases a deliberative and a casting vote.
13. EMS Proceedings papers
• A simple nomogram for the solution of quadratic equations .
14. EMS Proceedings papers
• A simple method of finding any number of square numbers whose sum is a square .
15. EMS 1938 Colloquium
• An analytic deformation of a function f(x) in the neighbourhood of x = infinity means replacing the independent variable by an analytic function of itself, x' = f(x), which has a simple pole at infinity.
16. EMS honours James Leslie
• His wants were simple, and he was able to travel widely.
17. EMS Freundlich
• Theoretical prediction and observational evidence as to the divergence from a simple Kepler orbit were compared and applied to test the accuracy of models of the constitution of stars.
18. EMS school mathematics
• (2) Encourage study on simple lines of the nature of mathematical reasoning.
19. 1923-24 May meeting
• Metzler, W H: "A generalisation and simple proof of Kronecker's theorem concerning the minors of a compound determinant", [Proceedings, session 43] {Communicated by David Gibb} .
20. 1914-15 Mar meeting
• Stokes, George D C: "A simple link apparatus for the mechanical solution of quadratic equations", [Title] .
21. 1915-16 Feb meeting
• Horsburgh, Ellice Martin: "A simple form of integrometer", [Title] .
22. 1912-13 Jun meeting
• Horsburgh, E M: "A simple linkage for describing equal areas" .
23. Napier Tercentenary
• Mr H S Gay gave some simple and for practical purposes sufficiently accurate formula for determining the trigonometrical functions when the angle is given and conversely, without the use of elaborate tables.
24. EMS 1980 Colloquium
• I had the privilege of attending these lectures which were extremely successful in meeting Nash-Williams' aim "of developing nontrivial and fairly deep mathematics from a very simple initial concept." .
25. Solution5.1.html
• By the way, by varying the coefficients in the recursion for the tn one can replace the above (E, P) by essentially any elliptic curve over Q and any rational point on it, so that in an elementary course in number theory one could develop (or at least introduce) the entire theory of elliptic curves just by starting with these simple recursions! .
## BMC Archive
1. BMC 2016
• Pyber, LHow to avoid the Classification Theorem of Finite Simple Groups in Asymptotic Group Theory .
• Malcolm, AThe involution width of a finite simple group .
2. BMC 1970
• Macdonald, I GRepresentation of semi-simple Lie groups .
3. BMC 1963
• Carter, R WSimple groups and simple Lie algebras .
4. BMC 1982
• Gorenstein, D Reworking the classification of finite simple groups .
5. BMC 2003
• Bavula, V Maximal commutative subalgebras of simple infinite-dimensional algebras .
6. BMC 1999
• Shalev, A Simple groups, Cayley groups and probability .
7. BMC 1976
• Aschbacher, MThin finite simple groups .
8. BMC 1977
• Collins, M JThe identification problem for finite simple groups .
9. BMC 1996
• Holland, M P Grothendieck groups of primitive factors of enveloping algebras of semi-simple Lie algebras .
10. BMC 1998
• Premet, A A Recent progress in the classification of finite-dimensonal simple Lie algebras in prime characteristic .
11. BMC 1987
• Wilson, R A Subgroups of simple groups .
12. BMC 2007
• Vassiliev, D Teleparallelism: difficult word but simple way of reinterpreting the Dirac equation .
13. BMC 1993
• Curtis, R T Symmetric generation of sporadic simple groups .
14. BMC 2018
• Grazian, VThe classification of simple fusion systems .
15. BMC 1969
• Thompson, J GFinite simple groups .
## Gazetteer of the British Isles
1. London individuals H-M
• First to observe that falling barometer indicates bad weather, to build a Gregorian telescope, to show that Mars and Jupiter rotated (being the first to observe the Great Red Spot of Jupiter), to observe that the tail of a comet was repelled by the sun, to invent the iris diaphragm, to note that movement where the restoring force is proportional to the displacement gives simple harmonic motion, to observe Chladni figures.
• However, he also produced a simple adding machine at the same time and Pepys disparaged it: 'very pretty, but not very useful' [The Diary of Samuel Pepys M.A., F.R.S; Clerk of the Acts and Secretary to the Admiralty Transcribed by the late Rev.
2. Oxford Institutions and Colleges
• 53-54',55)">Gunther] - I recall this is a rather simple adding device of 1666 which was rightly disparaged by Pepys, but Morland produced, at the same time, the first successful multiplying calculator).
• The Museum has the fine late 16C Flemish painting The Measurers depicting a mathematical instrument maker and numerous applications of simple measuring instruments.
3. London Museums
• Toward the left end are several diagrams of triangles which are area problems and at the left end are diagrams of pyramids where simple computations involving the slope are done.
4. Oxford individuals
• He has a floor slab in the middle of the north floor with the simple inscription 'Henricus Briggius' [Early Science in Oxford: Vol.
5. Exeter, Devon
• The Royal Albert Museum, Queen Street, Exeter, contains the Exeter Puzzle Jug, probably made in the Saintonge region of western France, c1300, perhaps the finest example of medieval pottery imported to England and the earliest extant example in England of a puzzle jug, though the puzzle aspect is quite simple.
6. Harpenden, Hertfordshire
• During this time he formally developed analysis of variance, he introduced the word variance and found the distribution of the correlation coefficient, the correct chi-squared distribution for contingency tables (Pearson failed to get the right number of degrees of freedom) and the distributions of the simple and multiple correlation coefficients.
7. Dorchester
• a simple adding machine (British Calculator, Model B, probably early 20C); .
## Astronomy section
No matches from this section
This search was performed by Kevin Hughes' SWISH and Ben Soares' HistorySearch Perl script
JOC/BS August 2001 | 82,888 | 384,401 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.578125 | 3 | CC-MAIN-2019-43 | latest | en | 0.938349 |
http://mail.scipy.org/pipermail/numpy-discussion/2008-March/031936.html | 1,438,272,698,000,000,000 | text/html | crawl-data/CC-MAIN-2015-32/segments/1438042987402.78/warc/CC-MAIN-20150728002307-00034-ip-10-236-191-2.ec2.internal.warc.gz | 148,507,122 | 1,926 | # [Numpy-discussion] View ND Homogeneous Record Array as (N+1)D Array?
Robert Kern robert.kern@gmail....
Mon Mar 17 15:55:10 CDT 2008
```On Mon, Mar 17, 2008 at 3:44 PM, Alexander Michael <lxander.m@gmail.com> wrote:
> Is there a way to view an N-dimensional array with a *homogeneous*
> record dtype as an array of N+1 dimensions? An example will make it
> clear:
>
> import numpy
> a = numpy.array([(1.0,2.0), (3.0,4.0)], dtype=[('A',float),('B',float)])
> b = a.view(...) # do something magical
> print b
> array([[ 1., 2.],
> [ 3., 4.]])
> b[0,0] = 0.0
> print a
> [(0.0, 2.0) (3.0, 4.0)]
Just use a.view(float) and then reshape as appropriate.
In [1]: import numpy
In [2]: a = numpy.array([(1.0,2.0), (3.0,4.0)], dtype=[('A',float),('B',float)])
In [3]: a.view(float)
Out[3]: array([ 1., 2., 3., 4.])
In [4]: b = _
In [5]: b.shape = a.shape + (-1,)
In [6]: b
Out[6]:
array([[ 1., 2.],
[ 3., 4.]])
In [7]: b[0,0] = 0.0
In [8]: a
Out[8]:
array([(0.0, 2.0), (3.0, 4.0)],
dtype=[('A', '<f8'), ('B', '<f8')])
--
Robert Kern
"I have come to believe that the whole world is an enigma, a harmless
enigma that is made terrible by our own mad attempt to interpret it as
though it had an underlying truth."
-- Umberto Eco
``` | 489 | 1,256 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.8125 | 3 | CC-MAIN-2015-32 | longest | en | 0.616264 |
http://www.chegg.com/homework-help/automotive-electrical-and-electronic-systems-classroom-manual-5th-edition-chapter-5-solutions-9780132388832 | 1,436,313,948,000,000,000 | text/html | crawl-data/CC-MAIN-2015-27/segments/1435375635143.91/warc/CC-MAIN-20150627032715-00085-ip-10-179-60-89.ec2.internal.warc.gz | 404,514,240 | 14,074 | View more editions
Automotive Electrical and Electronic Systems Classroom Manual
# TEXTBOOK SOLUTIONS FOR Automotive Electrical and Electronic Systems Classroom Manual 5th Edition
• 277 step-by-step solutions
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SAMPLE SOLUTION
Chapter: Problem:
• Step 1 of 4
The total resistance is equal to the sum of all the resistance is always true for series circuits.
Thus, the option is correct.
• Step 2 of 4
In parallel circuits, the total resistance is always less than resistance of its smallest resistor. So total resistance is equal to the sum of all the resistance is not possible for parallel circuits. Therefore option ‘b’ is incorrect.
• Step 3 of 4
As in series-parallel circuits, the total resistance is a combination of resistance of series and parallel resistor and in is known that in parallel circuits the total resistances of a parallel circuit are always less than resistance of its smallest resistor.
Therefore, total resistance is equal to the sum of all the resistance is not possible for series-parallel circuits. So, option ‘c’ is incorrect.
• Step 4 of 4
In series circuits the total resistance is equal to the sum of all the resistance, but in parallel circuits it is not possible. So option ‘d’ is incorrect.
Corresponding Textbook
Automotive Electrical and Electronic Systems Classroom Manual | 5th Edition
9780132388832ISBN-13: 0132388839ISBN: Authors: | 337 | 1,545 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.40625 | 3 | CC-MAIN-2015-27 | latest | en | 0.879183 |
https://www.studypool.com/discuss/19840001/engineering-maths | 1,606,689,935,000,000,000 | text/html | crawl-data/CC-MAIN-2020-50/segments/1606141203418.47/warc/CC-MAIN-20201129214615-20201130004615-00404.warc.gz | 869,925,980 | 32,737 | Mathematics
TEE 2003 Engineering Maths Questions
TEE 2003
TEE
### Question Description
Help me study for my Mathematics class. I’m stuck and don’t understand.
answer the 3 questions in the attached. Pls bid if you know the answers correctly only else will request for redu
### Unformatted Attachment Preview
TE/TEE2003 Advanced Mathematics for Engineers Graded Assignment 2 • • • Answer all the questions and show your working Total marks: 50 Deadline: March 25, 2020 (hardcopy submission in class or softcopy submission online via LumiNUS) Q1 A supermarket has 60 customers, each showing up at the counter for check-out with probability p=0.2 in a given interval. Assume all customers check out independently. (a) Calculate the probability that there is only one customer at the counter during this interval. [5 marks] (b) Using Poisson distribution, find an approximate value for the probability in (a). [5 marks] Q2 Let Y=10X+1, where X~N(0,1). Express your answers using the Q(·) function. (a) Calculate P(Y<10). [5 marks] (b) Calculate P(-5≤Y<5). [5 marks] (c) Calculate P(Y≥10 | Y ≥5). [5 marks] Q3 Let X~fX(x), where 𝑥𝑥 𝑓𝑓𝑋𝑋 (𝑥𝑥) = �2 − 𝑥𝑥 0 (a) Find the CDF of X. [10 marks] 0 ≤ 𝑥𝑥 < 1 1 ≤ 𝑥𝑥 ≤ 2 otherwise (b) Calculate the mean and the variance of X. [10 marks] 1 (c) Let 𝑌𝑌 = 𝑋𝑋. Find the CDF of Y. [5 marks] ...
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Find the attached solution....I am here for any edits/revision
1. There are 60 customers, that may come to supermarket.
a. Considering the binomial probability distribution
Probability of success is 𝑝 = 0.2
Probability of failure is 𝑞 = 1 − 𝑝 = 1 − 0.2 = 0.8
Probability of having exactly one customer in a time...
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4.4 | 656 | 2,266 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.375 | 3 | CC-MAIN-2020-50 | latest | en | 0.858944 |
https://bowdenc.com/tag/palindromic-numbers/ | 1,680,137,618,000,000,000 | text/html | crawl-data/CC-MAIN-2023-14/segments/1679296949093.14/warc/CC-MAIN-20230330004340-20230330034340-00109.warc.gz | 183,659,241 | 19,563 | Projects
## Project Euler Problem #4 – Palindromic Numbers
Problem 4 asks us to “Find the largest palindrome made from the product of two 3-digit numbers.” First we know our maximum factor is 999, which safely puts our possible palindromes in the 6 digit range. This is important because of the proof that all even-digit palindromes have 11 as a factor. I use this to reduce the possible numbers to check.
Rather than checking all the possible products for palindrome-ness, I decided to start from the largest possible number (999*999), working backward. At each multiple of 11, the number is tested for palindrome, and if found, tested for the existence of two 3-digit factors.
In retrospect, this method required ~91k iterations to determine palindrome-ocity, and another ~82k iterations to test each palindrome’s factors’ lengths (173k total!). In comparison, a factor-first approach starting with 990 (90*11) and working backward by 11 would have only required 7 factor testing loops with a max bound of 899 possibilities each – yielding only 6293 iterations total. | 240 | 1,073 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.671875 | 3 | CC-MAIN-2023-14 | latest | en | 0.889253 |
http://cboard.cprogramming.com/c-programming/130483-output-piecewise-defined-function.html | 1,472,429,304,000,000,000 | text/html | crawl-data/CC-MAIN-2016-36/segments/1471982949773.64/warc/CC-MAIN-20160823200909-00282-ip-10-153-172-175.ec2.internal.warc.gz | 39,934,826 | 12,235 | # Thread: Output of a piecewise defined function
1. ## Output of a piecewise defined function
Hi all, I'm having trouble printing the output of a piecewise defined function
the function is f(x)= 1 for x=0,1,2
f(x-2) + f(x-3) for x>2
so the user will enter a value for x and I have to print all of the values of the function up to x. I'm trying to do this with loops, I'm not sure if recursion can be used but I would like to do it with loops/if statements only. I can obviously print the first 3 values of x. Can anyone add any tips? Thanks
2. Post what you've got so far and let the gang have a look...
I'm sure you'll get plenty of helpful hints and tips.
3. Okay, with this I'm actually having a bit of trouble even starting it. I use the obvious if (x<=2) then it will go into the block of the if statement and print either 1, 1 1, or 1 1 1 for the first three values.
For x>2, I don't even know how to get started. I'll think I have an idea, like adding two numbers and putting it into a variable and looping it somehow, but it just turns into a bunch of garble. What I'm looking for here is some way to start this program, like what the fundamental idea is behind it, or just to be thrown a bone.
4. recursion would be the way to go
5. No recursion please, only methods with loops and if statements.
6. So, the fact is you're waiting for one of us to write you your program?
7. No not at all, I was hoping for a one or two-liner hint that might be able to point me in the right direction because I am stuck.
8. Never mind, I got it. | 409 | 1,551 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.78125 | 3 | CC-MAIN-2016-36 | latest | en | 0.946982 |
https://docs.go101.org/std/src/math/sqrt.go.html | 1,653,214,983,000,000,000 | text/html | crawl-data/CC-MAIN-2022-21/segments/1652662545326.51/warc/CC-MAIN-20220522094818-20220522124818-00449.warc.gz | 262,659,169 | 4,920 | ````// Copyright 2009 The Go Authors. All rights reserved.`
`// Use of this source code is governed by a BSD-style`
`// license that can be found in the LICENSE file.`
`package math`
`// The original C code and the long comment below are`
`// from FreeBSD's /usr/src/lib/msun/src/e_sqrt.c and`
`// came with this notice. The go code is a simplified`
`// version of the original C.`
`//`
`// ====================================================`
`// Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.`
`//`
`// Developed at SunPro, a Sun Microsystems, Inc. business.`
`// Permission to use, copy, modify, and distribute this`
`// software is freely granted, provided that this notice`
`// is preserved.`
`// ====================================================`
`//`
`// __ieee754_sqrt(x)`
`// Return correctly rounded sqrt.`
`// -----------------------------------------`
`// | Use the hardware sqrt if you have one |`
`// -----------------------------------------`
`// Method:`
`// Bit by bit method using integer arithmetic. (Slow, but portable)`
`// 1. Normalization`
`// Scale x to y in [1,4) with even powers of 2:`
`// find an integer k such that 1 <= (y=x*2**(2k)) < 4, then`
`// sqrt(x) = 2**k * sqrt(y)`
`// 2. Bit by bit computation`
`// Let q = sqrt(y) truncated to i bit after binary point (q = 1),`
`// i 0`
`// i+1 2`
`// s = 2*q , and y = 2 * ( y - q ). (1)`
`// i i i i`
`//`
`// To compute q from q , one checks whether`
`// i+1 i`
`//`
`// -(i+1) 2`
`// (q + 2 ) <= y. (2)`
`// i`
`// -(i+1)`
`// If (2) is false, then q = q ; otherwise q = q + 2 .`
`// i+1 i i+1 i`
`//`
`// With some algebraic manipulation, it is not difficult to see`
`// that (2) is equivalent to`
`// -(i+1)`
`// s + 2 <= y (3)`
`// i i`
`//`
`// The advantage of (3) is that s and y can be computed by`
`// i i`
`// the following recurrence formula:`
`// if (3) is false`
`//`
`// s = s , y = y ; (4)`
`// i+1 i i+1 i`
`//`
`// otherwise,`
`// -i -(i+1)`
`// s = s + 2 , y = y - s - 2 (5)`
`// i+1 i i+1 i i`
`//`
`// One may easily use induction to prove (4) and (5).`
`// Note. Since the left hand side of (3) contain only i+2 bits,`
`// it is not necessary to do a full (53-bit) comparison`
`// in (3).`
`// 3. Final rounding`
`// After generating the 53 bits result, we compute one more bit.`
`// Together with the remainder, we can decide whether the`
`// result is exact, bigger than 1/2ulp, or less than 1/2ulp`
`// (it will never equal to 1/2ulp).`
`// The rounding mode can be detected by checking whether`
`// huge + tiny is equal to huge, and whether huge - tiny is`
`// equal to huge for some floating point number "huge" and "tiny".`
`//`
`//`
`// Notes: Rounding mode detection omitted. The constants "mask", "shift",`
`// and "bias" are found in src/math/bits.go`
`// Sqrt returns the square root of x.`
`//`
`// Special cases are:`
`// Sqrt(+Inf) = +Inf`
`// Sqrt(±0) = ±0`
`// Sqrt(x < 0) = NaN`
`// Sqrt(NaN) = NaN`
`func Sqrt(x float64) float64 {`
` if haveArchSqrt {`
` return archSqrt(x)`
` }`
` return sqrt(x)`
`}`
`// Note: Sqrt is implemented in assembly on some systems.`
`// Others have assembly stubs that jump to func sqrt below.`
`// On systems where Sqrt is a single instruction, the compiler`
`// may turn a direct call into a direct use of that instruction instead.`
`func sqrt(x float64) float64 {`
` // special cases`
` switch {`
` case x == 0 || IsNaN(x) || IsInf(x, 1):`
` return x`
` case x < 0:`
` return NaN()`
` }`
` ix := Float64bits(x)`
` // normalize x`
` exp := int((ix >> shift) & mask)`
` if exp == 0 { // subnormal x`
` for ix&(1<<shift) == 0 {`
` ix <<= 1`
` exp--`
` }`
` exp++`
` }`
` exp -= bias // unbias exponent`
` ix &^= mask << shift`
` ix |= 1 << shift`
` if exp&1 == 1 { // odd exp, double x to make it even`
` ix <<= 1`
` }`
` exp >>= 1 // exp = exp/2, exponent of square root`
` // generate sqrt(x) bit by bit`
` ix <<= 1`
` var q, s uint64 // q = sqrt(x)`
` r := uint64(1 << (shift + 1)) // r = moving bit from MSB to LSB`
` for r != 0 {`
` t := s + r`
` if t <= ix {`
` s = t + r`
` ix -= t`
` q += r`
` }`
` ix <<= 1`
` r >>= 1`
` }`
` // final rounding`
` if ix != 0 { // remainder, result not exact`
` q += q & 1 // round according to extra bit`
` }`
` ix = q>>1 + uint64(exp-1+bias)<<shift // significand + biased exponent`
` return Float64frombits(ix)`
`}`
``` | 1,573 | 5,309 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.234375 | 3 | CC-MAIN-2022-21 | latest | en | 0.593535 |
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