text:
## he66666 5 years ago Trig Identity question? The angle x lies in the interval pi/2≤x≤pi, and sin²x=4/9. Determine cos(x/2). answer: √[(3-√5)/6] How do you solve this question (using trig identities)? It gets confusing because it's x/2, not just x. I keep getting 7/9 as my answer..

1. anonymous

$cos(\frac{x}{2})=\pm \sqrt{\frac{1+cos(x)}{2}}$

2. anonymous

square root should be over whole thing.

3. he66666

How does it have a square root? :S Is it derived from a trig identity?

4. anonymous

$sin^2(x)=\frac{4}{9}$ $sin(x)=\pm \frac{3}{4}$

5. anonymous

derived from "double angle" formula $cos(2x)=2cos^2(x)-1$ replace 2x by x t so x gets replaced by $\frac{x}{2}$ and then solve for $cos(\frac{x}{2})$

6. anonymous

$cos(x)=2cos^2(\frac{x}{2})-1$ $cos(x)+1=2cos^2(\frac{x}{2})$ $\frac{cos(x)-1}{2}=cos^2(\frac{x}{2})$

7. anonymous

typo should be $\frac{cos(x)+1}{2}=cos^2(\frac{x}{2})$

8. anonymous

then take the square root of the whole thing. plus or minus of course. i cannot seem to type set it.

9. anonymous

in case $sin(x)=\frac{3}{4}$ do you know how to find $cos(x)$?

10. he66666

yes, pythagorean theorem?

11. anonymous

whoa hold the phone i am tired. it is $sin(x)=\frac{4}{9}$

12. anonymous

damn $sin^2(x)=\frac{4}{9}$ $sin(x)=\frac{2}{3}$

13. anonymous

draw a triangle opposite side 2 and hypotenuse 3 my mistake sorry

14. anonymous

adjacent side is $\sqrt{3^2-2^2}=\sqrt{9-4}=\sqrt{5}$

15. anonymous

so $cos(x)=\frac{\sqrt{5}}{3}$

16. anonymous

now plug in $\frac{\sqrt{5}}{3}$ in the formula up top to get your answer. i will write it if you like.

17. he66666

no it's alright, I got it. Thanks so much for the help satellite! :)

18. anonymous

oh another mistake i forgot x was in quad II so cosine is negative. it is $-\frac{\sqrt{5}}{3}$

19. anonymous

make sure you use $-\frac{\sqrt{5}}{3}$

20. he66666

alright, I will :) thanks

21. anonymous

welcome


text:
Home > Margin Of > Calculator Error Margin

# Calculator Error Margin

## Contents

However, for customary sample sizes we recommend reporting MoE rounded to the half or whole number, to avoid implying false precision. Note: Calculations of a survey's margin ofsampling error require a probability-based sample, and do not address other potential causes of differences in survey results, such as question wording and noncoverage of A school accountability case study: California API awards and the Orange County Register margin of error folly. Conduct your survey online with Vovici. click site

It can be estimated from just p and the sample size, n, if n is small relative to the population size, using the following formula:[5] Standard error ≈ p ( 1 The true answer is the percentage you would get if you exhaustively interviewed everyone. Margin of Error CalculatorEnter a population size and a sample size to calculate the theoretical margin of error, plus or minus in percentage points, 95% of the time, on questions where This may not be a tenable assumption when there are more than two possible poll responses. http://americanresearchgroup.com/moe.html

## Margin Of Error Formula

Margin of error is often used in non-survey contexts to indicate observational error in reporting measured quantities. In R.P. Thus, the maximum margin of error represents an upper bound to the uncertainty; one is at least 95% certain that the "true" percentage is within the maximum margin of error of According to sampling theory, this assumption is reasonable when the sampling fraction is small.

Toggle navigation Products Pricing Use cases Contact us My Account Create a survey Resources | Tools Resources Defining Scope of the Problem Typing Tools Segmentation Survey Design Mutually Exclusive Collectively Exhaustive To calculate design effects caused by weighting: In samples with the same weighted and unweighted sample size, use the weighted mean of the weights.Or, take the sum of the weights and Design effect = A measure of how much the sampling variability differs from what it would be in a simple random sample (e.g., because of weighting). Standard Deviation Calculator From this information, one can compute the margin of error (MOE): Keep in mind, margin of error only accounts for the errors introduced by random sampling, and does not consider systemic

This makes intuitive sense because when N = n, the sample becomes a census and sampling error becomes moot. Confidence Interval Calculator z-value = The calculated value of the z-testfor statistical significance comparing Sample 1 and Sample 2, based on a formula from this paper. Wiley. http://www.raosoft.com/samplesize.html Please send comments or trouble reports to [email protected]

## Confidence Interval Calculator

presidential campaign will be used to illustrate concepts throughout this article. http://ncalculators.com/statistics/margin-of-error-calculator.htm p-value = The probability that, in multiple tests, you'd see a difference between p1 and p2 as big as the one the survey(s) found, if there were no difference between p1 Margin Of Error Formula The top portion charts probability density against actual percentage, showing the relative probability that the actual percentage is realised, based on the sampled percentage. Sample Size Calculator The margin of error is the range of values below and above the sample statistic in a confidence interval.

Newsweek. 2 October 2004. get redirected here The sample size calculator computes the critical value for the normal distribution. The standard error of a reported proportion or percentage p measures its accuracy, and is the estimated standard deviation of that percentage. In some cases, the margin of error is not expressed as an "absolute" quantity; rather it is expressed as a "relative" quantity. Margin Of Error Calculator Statistics

If we use the "relative" definition, then we express this absolute margin of error as a percent of the true value. Basic concept Polls basically involve taking a sample from a certain population. For example, if the true value is 50 percentage points, and the statistic has a confidence interval radius of 5 percentage points, then we say the margin of error is 5 http://bestwwws.com/margin-of/confidence-level-calculator-margin-of-error.php Therefore we can be 95% confident that the sample result reflects the actual population result to within the margin of error.

Use only when the sample is approximately 5 percent or more of the population (i.e., when the population is particularly small, or the sample size particularly large). Margin Of Error Calculator Without Population Size At X confidence, E m = erf − 1 ( X ) 2 n {\displaystyle E_{m}={\frac {{\text{erf}}^{-1}(X)}{\sqrt {2n}}}} (See Inverse error function) At 99% confidence, E m ≈ 1.29 n {\displaystyle In statistics & probability, the larger & lower ME provides lower & higher confidence intervals.

## In this calculation, "p" is the percentage being tested - that is, whether the p in sample one (let's say, the percentage of women who approve of the president's job performance)

I added an annotation with a correction. See calculation instructions at the bottom of this page. When you survey a sample of the population, you don't know that you've found the correct answer, but you do know that there's a 95% chance that you're within the margin Margin Of Error Calculator Proportion Voila.

p = First percentage being tested. Linearization and resampling are widely used techniques for data from complex sample designs. What is a Survey?. my review here Phelps (Ed.), Defending standardized testing (pp. 205–226).

For example, a 95% confidence interval with a 4 percent margin of error means that your statistic will be within 4 percentage points of the real population value 95% of the Unfortunately, your browser does not support the required technologies. Sample Size: Margin of Error (%) -- *This margin of error calculator uses a normal distribution (50%) to calculate your optimum margin of error. T Score vs.

Leave this as 50% % For each question, what do you expect the results will be? The margin of error of an estimate is the half-width of the confidence interval ... ^ Stokes, Lynne; Tom Belin (2004). "What is a Margin of Error?" (PDF). Let's say the poll was repeated using the same techniques. Home Tables Binomial Distribution Table F Table PPMC Critical Values T-Distribution Table (One Tail) T-Distribution Table (Two Tails) Chi Squared Table (Right Tail) Z-Table (Left of Curve) Z-table (Right of Curve)

format: plain


text:
# Optimizing a Composed Function

Let $f: \mathbb{R}^n \rightarrow \mathbb{R}_{\geq 0}$ be continuous.

Consider $g: \mathbb{R}_{\geq 0} \rightarrow \mathbb{R}_{\geq 0}$ strictly increasing, continuous and such that $g(0)=0$.

I think this is an interesting (maybe trivial) question:

are $f(\cdot)$ and $g(f(\cdot))$ sharing the same minima?

-
For all $x$ and $y$ in $\mathbb R^n$, $f(x) \le f(y)$ if and only if $g(f(x)) \le g(f(y))$, so yes. –  Rahul May 10 '12 at 0:47


text:
# An electron, an a-particle, and a proton have the same kinetic energy. Which of these particles has the shortest de Broglie wavelength?

Apoorva Arora IIT Roorkee
askIITians Faculty 181 Points
8 years ago
We know that,
$\lambda =\frac{h}{P}$
where h is the planck’s constant
in terms of KE,
$\lambda =\frac{h}{\sqrt{2mKE}}$
if the kinetic energy is same,
wavelength is inversely proportional to the root of mass of the particle.
So, out of the three, the heaviest is alpha particle and hence has the shortest de-broglie wavelength.
Thanks and Regards
Apoorva Arora
IIT Roorkee


text:
# Damped Driven Oscillator Dimensional Analysis

So, I am studying the damped driven oscillator with the following drive force:

$$M\ddot{x}+\gamma \dot{x}+kx=F_0 \cos({\omega t})$$ where $M$ is the mass, $\gamma$ is the damping force, $k$ is the spring constant and $\omega$ is constant.

What I am trying to do is find a dimensionless expression of the equation above which can be done by applying the transformation:

\begin{align} & x \to \xi=\frac{x}{x_c} \\ & t \to \tau=\frac{t}{t_c} \end{align} where $x_c, t_c$ are some "x, t characteristic". Now, I found that the expression of the oscillator in those variables would be:

$$\ddot{\xi}+\left( \frac{\gamma t_c}{M} \right) \dot{\xi}+\left( \frac{k t_c^2}{M} \right) \xi=\left( \frac{F_0}{M} \right)\frac{t_c^2}{x_c}\cos({\omega t})$$

and by solving the initial equation I can acquire the analytical solution from which I could deduct that (for the case of $\Delta <0$):

$$t_c=\sqrt{\frac{M}{k-\frac{\gamma^2}{4M}}}$$ which proves that everything is in the right place since it does match the period of the damped oscillator.

My question is the following

What about $x_c$? I am not able to find an expression for it, and I can see that it is directly involved in the ODE.

Thank you all!

• Is $\Delta$ the discriminant which indicates that the damping is small, i.e. $\gamma^2/4-k/M$? Oct 12, 2015 at 22:46
• Also, shouldn't there in the formula for $t_c$ be $\gamma^2$ instead of $\gamma$? Oct 12, 2015 at 22:57
• Set $x_c=\frac{M}{F_0t_c^2}$ then see what you can do with $t_c$. Oct 12, 2015 at 23:16
• @Sobanoodles yeap its $\gamma ^2$ :) And $\Delta$ is the discriminant of the characteristic polynomial for the initial equation. (I also studied the overdamped and the critical case but only the underdamped case has appears to have oscillations obviously) Oct 13, 2015 at 8:19
• @David Are you sure I should do that? Why would you do that? Oct 13, 2015 at 8:20

For the dimensionless expression, the constant coefficient $\frac{F_0 t_c^2}{Mx_c}$ of the drive force $\cos({\omega t})$, stands for the oscillation length. Taking that into account, along with the fact that we do demand $x_c$ to be dimensionless, one could think:
$$\frac{F_0 t_c^2}{Mx_c}=\lambda \Leftrightarrow x_c=\frac{F_0 t_c^2}{M \lambda}$$ where $\lambda$ of course is a dimensionless constant.
Next, something that did not occure to me while posting this question, is that $t_c$ could be expressed either on terms of the system's own period like above: $$t_c=\sqrt{\frac{M}{k-\frac{\gamma^2}{4M}}}$$ or on terms of the frequency applied to the system by the drive force, therefore: $$t_c=\frac{1}{\omega}$$ One can use both, and I gave to myself a treat by using the second (and simpler) to reach the final result:
$$x_c=\frac{F_0}{\lambda M \omega^2}, \quad t_c=\frac{1}{\omega}$$


text:
# What is the PDF of the Square Length of a Normally-Generated Vector?

Consider a vector $\mathbf{x}\in\mathbb{R}^n$, where each element in $\mathbf{x}$ is sampled independently from a normal distribution $\mathcal{N}(0,\sigma^2)$.

What is the probability density function of $||\mathbf{x}||_2^2$?

-

## 1 Answer

Note that $$\frac{1}{\sigma^2}\|\mathbf{x}\|_2^2=\frac{1}{\sigma^2}(x_1^2+\cdots+x_n^2)=z_1^2+\cdots+z_n^2,$$ where $z_i\sim \mathcal{N}(0,1)$ and hence $\frac{1}{\sigma^2}\|x\|_2^2$ follows a $\chi^2(n)$-distribution.

-
That's great, thanks a lot. –  M.G Dec 14 '12 at 4:02
+1 but calling that a "hint" is a bit of an understatement. –  guy Dec 14 '12 at 4:14
@guy: Hehe, I guess you're right :) –  Stefan Hansen Dec 14 '12 at 6:25


text:
What Types of Radiation Emanate in the Future and are Perceived in the Present?

We are searching data for your request:

Forums and discussions:
Manuals and reference books:
Data from registers:
Wait the end of the search in all databases.
Upon completion, a link will appear to access the found materials.

Years ago I came upon a scientific text which mentioned different types of radiation and how they are perceived. One such form of radiation was described (from our perspective and understanding of space-time) to originate from the future and travel backwards through time.

I cannot for the life of me remember what this type of radiation was called and I would love to know it.

One concept of antiparticles (see Feynman) is that they're regular particles travelling backward in time. If you go with that, then by extending the meaning of "radiation" to include physical particles -- which is common usage, e.g. $alpha$ and $eta$ particles -- then antiparticles such as positrons came from the future.

Nothing that is known to exist

Relativity does not allow for a massive particle to travel at the speed of light, but it doesn't prevent a particle from travelling faster than light. Such a particle has been called a Tachyon. No such particle has ever been observed. There are good reasons for believing that they don't exist.

Such a particle would be extremely strange. The mass of such a particle would not be positive, it would be imaginary! However you could not use such a particle to send a message to the past. The particles can't be localised, which means that you can't detect them as being "at" a particular place at a particular time.

In conclusion, such particles have never been detected, probably don't exist, and couldn't be used to send messages.

read more at http://math.ucr.edu/home/baez/physics/ParticleAndNuclear/tachyons.html

Long-term health effects of Hiroshima and Nagasaki atomic bombs not as dire as perceived

The detonation of atomic bombs over the Japanese cities of Hiroshima and Nagasaki in August 1945 resulted in horrific casualties and devastation. The long-term effects of radiation exposure also increased cancer rates in the survivors. But public perception of the rates of cancer and birth defects among survivors and their children is in fact greatly exaggerated when compared to the reality revealed by comprehensive follow-up studies. The reasons for this mismatch and its implications are discussed in a Perspectives review of the Hiroshima/Nagasaki survivor studies published in the August issue of the journal GENETICS, a publication of the Genetics Society of America.

"Most people, including many scientists, are under the impression that the survivors faced debilitating health effects and very high rates of cancer, and that their children had high rates of genetic disease," says Bertrand Jordan, an author and a molecular biologist at UMR 7268 ADÉS, Aix-Marseille Université/EFS/CNRS, in France. "There's an enormous gap between that belief and what has actually been found by researchers."

Dr. Jordan's article contains no new data, but summarizes over 60 years of medical research on the Hiroshima/Nagasaki survivors and their children and discusses reasons for the persistent misconceptions. The studies have clearly demonstrated that radiation exposure increases cancer risk, but also show that the average lifespan of survivors was reduced by only a few months compared to those not exposed to radiation. No health effects of any sort have so far been detected in children of the survivors.

Approximately 200,000 people died in the bombings and their immediate aftermath, mainly from the explosive blast, the firestorm it sparked, and from acute radiation poisoning. Around half of the those who survived subsequently took part in studies tracking their health over their entire lifespan. These studies began in 1947 and are now conducted by a dedicated agency, the Radiation Effects Research Foundation (RERF), with funding from the Japanese and U.S. governments. The project has followed approximately 100,000 survivors, 77,000 of their children, plus 20,000 people who were not exposed to radiation.

This massive data set has been uniquely useful for quantifying the risks of radiation because the bombs served as a single, well-defined exposure source, and because the relative exposure of each individual can be reliably estimated using the person's distance from the detonation site. The data has been particularly invaluable in setting acceptable radiation exposure limits for nuclear industry workers and the general public.

Cancer rates among survivors was higher compared to rates in those who had been out of town at the time. The relative risk increased according to how close the person was to the detonation site, their age (younger people faced a greater lifetime risk), and their sex (greater risk for women than men). However, most survivors did not develop cancer. Incidence of solid cancers between 1958 and 1998 among the survivors were 10% higher, which corresponds to approximately 848 additional cases among 44,635 survivors in this part of the study. However, most of the survivors received a relatively modest dose of radiation. In contrast, those exposed to a higher radiation dose of 1 Gray (approximately 1000 times higher than current safety limits for the general public) bore a 44% greater risk of cancer over the same time span (1958-1998). Taking into consideration all causes of death, this relatively high dose reduced average lifespan by approximately 1.3 years.

Although no differences in health or mutations rates have yet been detected among children of survivors, Jordan suggests that subtle effects might one day become evident, perhaps through more detailed sequencing analysis of their genomes. But it is now clear that even if the children of survivors do in fact face additional health risks, those risks must be very small.

Jordan attributes the difference between the results of these studies and public perception of the long-term effects of the bombs to a variety of possible factors, including historical context.

"People are always more afraid of new dangers than familiar ones," says Jordan. "For example, people tend to disregard the dangers of coal, both to people who mine it, and to the public exposed to atmospheric pollution. Radiation is also much easier to detect than many chemical hazards. With a hand-held geiger counter, you can sensitively detect tiny amounts of radiation that pose no health risk at all."

Jordan cautions that the results should not be used to foster complacency about the effects of nuclear accidents or the threat of nuclear war. "I used to support nuclear power until Fukushima happened," he says. "Fukushima showed disasters can occur even in a country like Japan that has strict regulations. However, I think it's important that the debate be rational, and I would prefer that people look at the scientific data, rather than gross exaggerations of the danger."

Contents

Since the earliest days of radio communications, the negative effects of interference from both intentional and unintentional transmissions have been felt and the need to manage the radio frequency spectrum became apparent.

In 1933, a meeting of the International Electrotechnical Commission (IEC) in Paris recommended the International Special Committee on Radio Interference (CISPR) be set up to deal with the emerging problem of EMI. CISPR subsequently produced technical publications covering measurement and test techniques and recommended emission and immunity limits. These have evolved over the decades and form the basis of much of the world's EMC regulations today.

In 1979, legal limits were imposed on electromagnetic emissions from all digital equipment by the FCC in the US in response to the increased number of digital systems that were interfering with wired and radio communications. Test methods and limits were based on CISPR publications, although similar limits were already enforced in parts of Europe.

In the mid 1980s, the European Union member states adopted a number of "new approach" directives with the intention of standardizing technical requirements for products so that they do not become a barrier to trade within the EC. One of these was the EMC Directive (89/336/EC) [3] and it applies to all equipment placed on the market or taken into service. Its scope covers all apparatus "liable to cause electromagnetic disturbance or the performance of which is liable to be affected by such disturbance".

This was the first time there was a legal requirement on immunity, as well as emissions on apparatus intended for the general population. Although there may be additional costs involved for some products to give them a known level of immunity, it increases their perceived quality as they are able to co-exist with apparatus in the active EM environment of modern times and with fewer problems.

Many countries now have similar requirements for products to meet some level of electromagnetic compatibility (EMC) regulation.

Electromagnetic interference can be categorized as follows:

EMI or RFI , which typically emanates from intended transmissions such as radio and TV stations or mobile phones EMI or RFI , which is unintentional radiation from sources such as electric power transmission lines. [4][5][6]

Conducted electromagnetic interference is caused by the physical contact of the conductors as opposed to radiated EMI, which is caused by induction (without physical contact of the conductors). Electromagnetic disturbances in the EM field of a conductor will no longer be confined to the surface of the conductor and will radiate away from it. This persists in all conductors and mutual inductance between two radiated electromagnetic fields will result in EMI.

Interference with the meaning of electromagnetic interference, also radio-frequency interference (EMI or RFI) is – according to Article 1.166 of the International Telecommunication Union ' s (ITU) Radio Regulations (RR) [7] – defined as "The effect of unwanted energy due to one or a combination of emissions, radiations, or inductions upon reception in a radiocommunication system, manifested by any performance degradation, misinterpretation, or loss of information which could be extracted in the absence of such unwanted energy".

This is also a definition used by the frequency administration to provide frequency assignments and assignment of frequency channels to radio stations or systems, as well as to analyze electromagnetic compatibility between radiocommunication services.

In accordance with ITU RR (article 1) variations of interference are classified as follows:

Conducted EMI is caused by the physical contact of the conductors as opposed to radiated EMI which is caused by induction (without physical contact of the conductors).

For lower frequencies, EMI is caused by conduction and, for higher frequencies, by radiation.

EMI through the ground wire is also very common in an electrical facility.

Interference tends to be more troublesome with older radio technologies such as analogue amplitude modulation, which have no way of distinguishing unwanted in-band signals from the intended signal, and the omnidirectional antennas used with broadcast systems. Newer radio systems incorporate several improvements that enhance the selectivity. In digital radio systems, such as Wi-Fi, error-correction techniques can be used. Spread-spectrum and frequency-hopping techniques can be used with both analogue and digital signalling to improve resistance to interference. A highly directional receiver, such as a parabolic antenna or a diversity receiver, can be used to select one signal in space to the exclusion of others.

The most extreme example of digital spread-spectrum signalling to date is ultra-wideband (UWB), which proposes the use of large sections of the radio spectrum at low amplitudes to transmit high-bandwidth digital data. UWB, if used exclusively, would enable very efficient use of the spectrum, but users of non-UWB technology are not yet prepared to share the spectrum with the new system because of the interference it would cause to their receivers (the regulatory implications of UWB are discussed in the ultra-wideband article).

In the United States, the 1982 Public Law 97-259 allowed the Federal Communications Commission (FCC) to regulate the susceptibility of consumer electronic equipment. [8] [9]

Potential sources of RFI and EMI include: [10] various types of transmitters, doorbell transformers, toaster ovens, electric blankets, ultrasonic pest control devices, electric bug zappers, heating pads, and touch controlled lamps. Multiple CRT computer monitors or televisions sitting too close to one another can sometimes cause a "shimmy" effect in each other, due to the electromagnetic nature of their picture tubes, especially when one of their de-gaussing coils is activated.

Switching loads (inductive, capacitive, and resistive), such as electric motors, transformers, heaters, lamps, ballast, power supplies, etc., all cause electromagnetic interference especially at currents above 2 A. The usual method used for suppressing EMI is by connecting a snubber network, a resistor in series with a capacitor, across a pair of contacts. While this may offer modest EMI reduction at very low currents, snubbers do not work at currents over 2 A with electromechanical contacts. [11] [12]

Another method for suppressing EMI is the use of ferrite core noise suppressors (or ferrite beads), which are inexpensive and which clip on to the power lead of the offending device or the compromised device.

Switched-mode power supplies can be a source of EMI, but have become less of a problem as design techniques have improved, such as integrated power factor correction.

Most countries have legal requirements that mandate electromagnetic compatibility: electronic and electrical hardware must still work correctly when subjected to certain amounts of EMI, and should not emit EMI, which could interfere with other equipment (such as radios).

Radio frequency signal quality has declined throughout the 21st century by roughly one decibel per year as the spectrum becomes increasingly crowded. [ additional citation(s) needed ] This has inflicted a Red Queen's race on the mobile phone industry as companies have been forced to put up more cellular towers (at new frequencies) that then cause more interference thereby requiring more investment by the providers and frequent upgrades of mobile phones to match. [13]

The International Special Committee for Radio Interference or CISPR (French acronym for "Comité International Spécial des Perturbations Radioélectriques"), which is a committee of the International Electrotechnical Commission (IEC) sets international standards for radiated and conducted electromagnetic interference. These are civilian standards for domestic, commercial, industrial and automotive sectors. These standards form the basis of other national or regional standards, most notably the European Norms (EN) written by CENELEC (European committee for electrotechnical standardisation). US organizations include the Institute of Electrical and Electronics Engineers (IEEE), the American National Standards Institute (ANSI), and the US Military (MILSTD).

Integrated circuits are often a source of EMI, but they must usually couple their energy to larger objects such as heatsinks, circuit board planes and cables to radiate significantly. [14]

On integrated circuits, important means of reducing EMI are: the use of bypass or decoupling capacitors on each active device (connected across the power supply, as close to the device as possible), rise time control of high-speed signals using series resistors, [15] and IC power supply pin filtering. Shielding is usually a last resort after other techniques have failed, because of the added expense of shielding components such as conductive gaskets.

The efficiency of the radiation depends on the height above the ground plane or power plane (at RF, one is as good as the other) and the length of the conductor in relation to the wavelength of the signal component (fundamental frequency, harmonic or transient such as overshoot, undershoot or ringing). At lower frequencies, such as 133 MHz, radiation is almost exclusively via I/O cables RF noise gets onto the power planes and is coupled to the line drivers via the VCC and GND pins. The RF is then coupled to the cable through the line driver as common-mode noise. Since the noise is common-mode, shielding has very little effect, even with differential pairs. The RF energy is capacitively coupled from the signal pair to the shield and the shield itself does the radiating. One cure for this is to use a braid-breaker or choke to reduce the common-mode signal.

At higher frequencies, usually above 500 MHz, traces get electrically longer and higher above the plane. Two techniques are used at these frequencies: wave shaping with series resistors and embedding the traces between the two planes. If all these measures still leave too much EMI, shielding such as RF gaskets and copper tape can be used. Most digital equipment is designed with metal or conductive-coated plastic cases.

RF immunity and testing Edit

Any unshielded semiconductor (e.g. an integrated circuit) will tend to act as a detector for those radio signals commonly found in the domestic environment (e.g. mobile phones). [16] Such a detector can demodulate the high frequency mobile phone carrier (e.g., GSM850 and GSM1900, GSM900 and GSM1800) and produce low-frequency (e.g., 217 Hz) demodulated signals. [17] This demodulation manifests itself as unwanted audible buzz in audio appliances such as microphone amplifier, speaker amplifier, car radio, telephones etc. Adding onboard EMI filters or special layout techniques can help in bypassing EMI or improving RF immunity. [18] Some ICs are designed (e.g., LMV831-LMV834, [19] MAX9724 [20] ) to have integrated RF filters or a special design that helps reduce any demodulation of high-frequency carrier.

Designers often need to carry out special tests for RF immunity of parts to be used in a system. These tests are often done in an anechoic chamber with a controlled RF environment where the test vectors produce a RF field similar to that produced in an actual environment. [17]

Interference in radio astronomy, where it is commonly referred to as radio-frequency interference (RFI), is any source of transmission that is within the observed frequency band other than the celestial sources themselves. Because transmitters on and around the Earth can be many times stronger than the astronomical signal of interest, RFI is a major concern for performing radio astronomy. Natural sources of interference, such as lightning and the Sun, are also often referred to as RFI.

Some of the frequency bands that are very important for radio astronomy, such as the 21-cm HI line at 1420 MHz, are protected by regulation. This is called spectrum management. However, modern radio-astronomical observatories such as VLA, LOFAR, and ALMA have a very large bandwidth over which they can observe. Because of the limited spectral space at radio frequencies, these frequency bands cannot be completely allocated to radio astronomy. Therefore, observatories need to deal with RFI in their observations.

Techniques to deal with RFI range from filters in hardware to advanced algorithms in software. One way to deal with strong transmitters is to filter out the frequency of the source completely. This is for example the case for the LOFAR observatory, which filters out the FM radio stations between 90-110 MHz. It is important to remove such strong sources of interference as soon as possible, because they might "saturate" the highly sensitive receivers (amplifiers and analog-to-digital converters), which means that the received signal is stronger than the receiver can handle. However, filtering out a frequency band implies that these frequencies can never be observed with the instrument.

A common technique to deal with RFI within the observed frequency bandwidth, is to employ RFI detection in software. Such software can find samples in time, frequency or time-frequency space that are contaminated by an interfering source. These samples are subsequently ignored in further analysis of the observed data. This process is often referred to as data flagging. Because most transmitters have a small bandwidth and are not continuously present such as lightning or citizens' band (CB) radio devices, most of the data remains available for the astronomical analysis. However, data flagging can not solve issues with continuous broad-band transmitters, such as windmills, digital video or digital audio transmitters.

Another way to manage RFI is to establish a radio quiet zone (RQZ). RQZ is a well-defined area surrounding receivers that has special regulations to reduce RFI in favor of radio astronomy observations within the zone. The regulations may include special management of spectrum and power flux or power flux-density limitations. The controls within the zone may cover elements other than radio transmitters or radio devices. These include aircraft controls and control of unintentional radiators such as industrial, scientific and medical devices, vehicles, and power lines. The first RQZ for radio astronomy is United States National Radio Quiet Zone (NRQZ), established in 1958. [21]

Prior to the introduction of Wi-Fi, one of the biggest applications of 5 GHz band is the Terminal Doppler Weather Radar. [22] [23] The decision to use 5 GHz spectrum for Wi-Fi was finalized in World Radiocommunication Conference in 2003 however, meteorological community was not involved in the process. [24] [25] The subsequent lax implementation and misconfiguration of DFS had caused significant disruption in weather radar operations in a number of countries around the world. In Hungary, the weather radar system was declared non-operational for more than a month. Due to the severity of interference, South African weather services ended up abandoning C band operation, switching their radar network to S band. [23] [26]

Transmissions on adjacent bands to those used by passive remote sensing, such as weather satellites, have caused interference, sometimes significant. [27] There is concern that adoption of insufficiently regulated 5G could produce major interference issues. Significant interference can significantly impair numerical weather prediction performance and incur substantially negative economic and public safety impacts. [28] [29] [30] These concerns led US Secretary of Commerce Wilbur Ross and NASA Administrator Jim Bridenstine in February 2019 to urge the FCC to cancel proposed spectrum auctioning, which was rejected. [31]

What Types of Radiation Emanate in the Future and are Perceived in the Present? - Astronomy

All articles published by MDPI are made immediately available worldwide under an open access license. No special permission is required to reuse all or part of the article published by MDPI, including figures and tables. For articles published under an open access Creative Common CC BY license, any part of the article may be reused without permission provided that the original article is clearly cited.

Feature Papers represent the most advanced research with significant potential for high impact in the field. Feature Papers are submitted upon individual invitation or recommendation by the scientific editors and undergo peer review prior to publication.

The Feature Paper can be either an original research article, a substantial novel research study that often involves several techniques or approaches, or a comprehensive review paper with concise and precise updates on the latest progress in the field that systematically reviews the most exciting advances in scientific literature. This type of paper provides an outlook on future directions of research or possible applications.

Editor’s Choice articles are based on recommendations by the scientific editors of MDPI journals from around the world. Editors select a small number of articles recently published in the journal that they believe will be particularly interesting to authors, or important in this field. The aim is to provide a snapshot of some of the most exciting work published in the various research areas of the journal.

Present

Refinements to the definition of the candela came with advances in radiometry (the measurement of optical radiation) and to accommodate easier methods of creating light that did not rely on a platinum “artifact,” but they continued to reference the amount of light a traditional candle would generate. In 1979, the General Conference on Weights and Measures (CGPM) adopted a new definition: “The candela (cd) is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540 × 10 12 hertz and that has a radiant intensity in that direction of 1/683 watt per steradian.” Technical though this language may be, it remains an attempt to match our modern understanding of the human eye with what we still perceive to be a candle’s brightness.

The 1979 definition narrowed the previous formulation in one notable respect: It specified one particular frequency of light, not the entire visible spectrum. This change acknowledges a particularity of human vision. Though we can see colors from red to violet, our eyes—in the daytime at least—are most sensitive to greenish-yellow light. The frequency 540 × 10 12 hertz is a hue of green.

Most lightbulbs are not green, however. For light of another color, or a broad spectrum of colors such as the light from a white LED bulb, the International Commission on Illumination (CIE) has created a method of accounting for the eye’s greater sensitivity to certain hues. Akin to the idea of placing weights on a scale, the method grants more influence to those colors the eye registers more strongly. Taking into account each color’s respective influence gives you the light source’s overall luminous intensity.

Speaking of intensity, there are also two distinct references to it in the definition: luminous intensity and radiant intensity. This distinction relates to human perception as well. While “radiant intensity” is the intensity of light without adjustments for human vision, luminous intensity is a “photometric” unit that compensates for human visual sensitivity.

To convey the idea of light radiating into three-dimensional space, scientists employ the idea of a solid angle. Where a two-dimensional flat angle carves out a piece of a circle looking like a slice of pie, a three-dimensional solid angle is a section of a sphere shaped like a cone. This three-dimensional angle stretching out from the center to the surface is measured in steradians, the unit of solid angle. If you had a sphere whose radius was one meter, a one-steradian section’s base would be a circle marking out an area of one square meter of its surface. (Regardless of its size, the solid angle of a sphere is 4π steradians.)

Using solid angles as part of the candela definition specifies light that shines in a particular direction. When you purchase a lightbulb, its brightness is given not in candelas but in lumens, which tells you how much light it puts out in total—telling you its brightness in all directions. (This makes sense because you want to figure out how well it will illuminate your entire room.) The candela, on the other hand, is a measure of how brightly the light source will appear to your eye if you look directly at it.

This understanding of the human vision has led to the creation of one of the seven defining constants for the SI base units. This constant, Kcd, is equal to 683 lumens per watt—a value that makes the modern candela roughly equivalent to the previously defined candela. Roughly speaking, 1/683 watt per steradian is the amount of power needed to generate a candle’s brightness. (This value of 1/683 watt per steradian is not tied to any particular fundamental physical effect separate from human perception, any more than the previous definition’s 1/600,000 square meter of a black body was. In both cases, scientists were literally eyeballing it.)

All this attention on human sense is striking when Kcd is compared with the other fundamental constants. Many of the others—such as the speed of light in a vacuum or the charge of an electron—are properties of the universe. Kcd is universal in that it is green everywhere in the cosmos, but to an alien—or a creature from our planet that has different visual sensitivity—its selection as a definitive constant would seem highly arbitrary. It is simply convenient for human perception.

As of May 20, 2019, the definition of the candela has changed to a far more complicated wording than the 1979 definition. The actual value of the candela will not appreciably change, though because it is tied to the other SI units, which in some cases have been redefined themselves, there will be an imperceptible difference. The language of the candela’s definition is now primarily aimed at technical experts:

“The candela is defined by taking the fixed numerical value of the luminous efficacy of monochromatic radiation of frequency 540×10 12 Hz, Kcd, to be 683 when expressed in the unit lm⋅W −1 , which is equal to cd⋅sr⋅W −1 , or cd⋅sr⋅kg −1 ⋅m −2 ⋅s 3 , where the kilogram, meter and second are defined in terms of h, c and ΔνCs.”

The candela is now linked closely to the other units and constants of the new SI. A one-candela light source, though, will still appear to the human eye to be as bright as a wax candle of yesteryear.

Indices of environmental temperatures for primates in open habitats

Studies of thermoregulation in primates are under-represented in the literature, although there is sufficient evidence to suggest that temperature represents an important ecological constraint. One of the problems in examining thermoregulation in primates, however, is the difficulty in quantifying the thermal environment, since shade temperatures, solar radiation, humidity and wind speed all serve to alter an animal's 'perceived' temperature. Since animals respond to their perceived temperature, we need methods to account for each of these factors, both individually and collectively, if we are to understand the integrated impact of the thermal environment on primates. Here, we present a review of some thermal indices currently available. Black bulb temperatures can account for the effect of solar radiation, with wind chill equivalent temperatures and the heat index providing quantifiable estimates of the relative impact of wind speed and humidity, respectively. We present three potential indices of the 'perceived environmental temperature' (PET) that account for the combined impact of solar radiation, humidity and wind speed on temperature, and perform a preliminary test of all of the climatic indices against behavioural data from a field study of chacma baboons ( Papio cynocephalus ursinus) at De Hoop Nature Reserve, South Africa. One measure of the perceived environmental temperature, PET2, is an effective thermal index, since it enters the models for feeding and resting behaviour, and also accounts for levels of allogrooming. Solar radiation intensity is an important factor underlying these relationships, although the wind chill equivalent temperature and humidity enter the models for other behaviours. Future studies should thus be mindful of the impact of each of these elements of the thermal environment. A detailed understanding of primate thermoregulation will only come with the development of biophysical models of the thermal characteristics of the species and its environment. Until such developments, however, the indices presented here should permit a more detailed examination of the thermal environment, allowing thermoregulation to be given greater precedence in future studies of primate behaviour.

Particles of information

This experiment was part of a larger pilot study that tutored participants in the basics of radiation science to test whether greater knowledge might lessen the gap between expert and lay perceptions. The study produced mixed results (MacGregor, 2002), but pre- and post-tutorial testing showed that educated laypersons could significantly increase their knowledge of radiation science. Increased knowledge led to increased concerns about radiation exposure from x-rays and other medical applications, air travel, cosmic radiation, natural background radiation, and radon. Risk perception decreased for hospital waste, nuclear waste, and nuclear power plants. Attitudes toward the adequacy of radiation risk-management policies were slightly more favorable after exposure to the tutorial. More studies of this nature should be conducted to determine the effects of education on radiation risk perceptions and attitudes.

Calculated Risks: How Radiation Rules Manned Mars Exploration

Nearly everything we know about the radiation exposure on a trip to Mars we have learned in the past 200 days.

For much longer, we have known that space is a risky place to be, radiation being one of many reasons. We believed that once our explorers safely landed on the surface of Mars, the planet would provide shielding from the ravages of radiation. We didn’t how much, or how little, until very recently. Radiation and its variations impact not only the planning of human and robotic missions, but also the search for life taking place right now.

The first-ever radiation readings from the surface of another planet were published last month in the journal Science. The take-home lesson, as well as the getting-there lesson and the staying-there lesson, is this: don’t forget to pack your shielding. [Mars Radiation Threat to Astronauts Explained (Infographic)]

"Radiation is the one environmental characteristic that we don’t have a lot of experience with on Earth because we’re protected by our magnetosphere and relatively thick atmosphere. But it’s a daily fact of life on Mars," said Don Hassler, the lead author on the paper, "Mars’ Surface Radiation Environment Measured with the Mars Science Laboratory’s Curiosity Rover."

Measuring radiation on Mars

On Earth, we often associate radiation exposure with fallout from catastrophes such as Chernobyl and Fukushima. We sometimes worry over CAT scans, chest X-rays or transcontinental flights. However, according to the Health Physics Society, the biggest source of radiation for most of us, by far, is inhaled radon. The sky above our heads and the earth beneath our feet are typically the least of our worries.

In open space, human beings continuously contend with intense solar and cosmic background radiation. Solar energetic particles (SEPs) and galactic cosmic rays (GCRs) turn a trip to Mars into a six-month radiation shower.

The Mars rover Curiosity has allowed us to finally calculate an average dose over the 180-day journey. It is approximately 300 mSv, the equivalent of 24 CAT scans. In just getting to Mars, an explorer would be exposed to more than 15 times an annual radiation limit for a worker in a nuclear power plant.

Data from Curiosity also demonstrated that landing only partially solves the problem. Once on the Martian surface, cosmic radiation coming from the far side of the planet is blocked. This cuts down detected GCRs by half. The protection from strong solar particles, though, is shoddy and inconsistent. Substantial variations in SEPs occur as the meager Martian atmosphere is tussled by solar wind.

"The variability [in radiation levels] was much larger than expected," Hassler said. "[This creates] variability in weekly and monthly dose rates. There are also seasonal variations in radiation."

Study co-author Jennifer Eigenbrode, from the Goddard Institute of Space Studies, described how fluxes in radiation are critical in determining the possibility of life on the Red Planet.

"Radiation is probably the key parameter in determining how much alteration organics are experiencing in the rocks on the surface," Eigenbrode said.

Eigenbrode said this is because the most powerful particles in the air also penetrate the Martian soil. On impacting the surface, the GCRs and strong SEPs from space produce gamma rays and neutrons easily capable of breaking molecular bonds in the soil.

These events may have obliterated all evidence of life close to the surface. The new study estimates that finding intact organic molecules means digging deeper, down a meter or so, and digging for newer evidence, near impact sites where rock has spent less time exposed to the elements. [The Search for Life on Mars (A Photo Timeline)]

"If we find organics on Mars, the circumstance in which we find them [the context of the rocks], the history of the rocks, and the chemistry that we find, will help guide our mission strategy," Eigenbrode said.

Radiation levels measured by Curiosity have given us a better guide on how and where to look for former or current life. Future life, specifically the lives of our astronauts, also hinges upon these radiation measurements.

Fundamentally, "situational awareness is the strategy we have to use going forward," Hassler said. "We can design shelters on the surface to protect the astronauts."

Deep space, the place of greatest exposure, remains an issue.

"Perhaps one of the areas they would be most vulnerable would be during a spacewalk [on the way] to Mars."

Predicting space weather

In transit and on the planet, surviving space means predicting space weather. Space weather forecasting is a relatively new field, but one that's proving to be critical to all space missions.

Space weather prediction involves forecasting solar flares, coronal mass ejections, and geomagnetic storms. These highly energetic events emanate from the sun. When they cross the orbit of a planet, the same SEPs attacking organics can spell disaster for satellites, space stations, astronauts and the communication systems they all depend upon.

"To protect our satellites is becoming more and more important here on Earth," Hassler said.

Protecting satellites and people around Earth and Mars likely involves setting up two separate systems. Using Earth-based technologies to predict the radiation levels on Mars isn’t the best choice. The distance and opposition of the planets compounds the problem. When Mars is on the far side of the sun, it isn’t even an option.

"When we send astronauts to Mars, we will have to do our own space weather monitoring from [Mars]," Hassler said.

From beneath the shelter of Earth’s ample atmosphere, we continue to receive daily updates from Curiosity. Its 3-pound Radiation Assessment Detector (RAD) instrument informs us about surface radiation events, particle type and relative frequencies. For now, RAD is the only way that we can study Martian radiation and make plans for the future.

In the future, what we’ve learned from RAD will be used to better look for life on the surface, to design suits and habitats, to plan extravehicular activities. Because of what we have learned, we can begin to establish weather prediction systems. We can tell explorers that there is an increased risk of cancer associated with a trip to Mars (approximately 5 percent over a lifetime).

In these ways, radiation rules the past, present and future of effective planetary exploration. Thanks to RAD measurements and the resulting analysis, we can begin to write a survival guide for life on Mars.

People In The U.S. And The U.K. Show Strong Similarities In Their Attitudes Toward Nanotechnologies

The results of a new U.S.&ndashU.K. study published in the journal Nature Nanotechnology show that ordinary people in both countries hold very positive views of nanotechnologies and what the future of these technologies might bring. Participants in both countries indicated a significantly higher comfort level with energy applications of nanotechnologies than with applications used in health treatments.

Nanotechnology &ndash&ndash the science and technology of exceptionally small materials and processes &ndash&ndash is among the latest new technologies to raise public concerns about health and environmental risks.

The article reports on the first study of its kind. It involved four workshops, held at the same time in Santa Barbara and Cardiff, Wales. Workshop participants deliberated about two broad types of nanotechnology applications &ndash&ndash energy and health.

The study was carried out in the United States by the NSF Center for Nanotechnology in Society at the University of California, Santa Barbara, and in the United Kingdom by a collaborating research team from the School of Psychology at Cardiff University.

Barbara Herr Harthorn, director of the UCSB Center, led the interdisciplinary, international research team. She noted that one of the unexpectedly strong findings of the study was that the type of nanotechnology mattered greatly to the participants. She said participants in both countries viewed energy applications of nanotechnology more positively than health technologies, in terms of risks and benefits.

"Much of the public perception research on nanotechnology in the U.S. and abroad has focused on a generic 'nanotechnology' risk object," said Harthorn. "This work moves to a higher level of specificity and in doing so finds striking differences in views of benefit depending on application context.

"More specifically, perceived urgency of need for new energy technologies is strongly associated with high perceived benefit and lower risk perception, regardless of what materials, processes, or environmental risks are associated," she said.

Nick Pidgeon, who led the research team at the School of Psychology at Cardiff University, explained, "The Royal Society's 2004 report on nanotechnologies recommended public engagement and deliberation on nanotechnology risks and benefits. This study represents the first ever such public engagement exercise to be simultaneously conducted in two different countries."

The results include the following key findings:

• Overall participants in both countries focused on the benefits rather than the risks of nanotechnologies, and also exhibited a high degree of optimism regarding the future contribution of new technologies to society. This pattern was very similar in the workshops in both the United States and Britain.
• Some small cross-country differences were present. U.K. participants were generally more aware of recent technological controversies and risk governance failures (examples include genetically modified organisms, bovine spongiform encephalopathy (BSE), and foot and mouth disease), leading some to voice specific concerns about future nanotechnology risks.
• Greater differences were observed when participants (irrespective of their country) discussed the different applications. In particular, new technology developments for energy applications were seen as unproblematic, while questions of human health were felt to raise moral and ethical dilemmas. As was found by the U.K. Royal Society in 2004 for Britain, in the current study participants in both the U.K. and U.S. questioned whether those responsible (governments, industry, scientists) could be fully trusted to control nanotechnologies in the future.

The research was funded primarily by the National Science Foundation with additional support to Cardiff University provided by the Leverhulme Trust.

What Types of Radiation Emanate in the Future and are Perceived in the Present? - Astronomy

All articles published by MDPI are made immediately available worldwide under an open access license. No special permission is required to reuse all or part of the article published by MDPI, including figures and tables. For articles published under an open access Creative Common CC BY license, any part of the article may be reused without permission provided that the original article is clearly cited.

Feature Papers represent the most advanced research with significant potential for high impact in the field. Feature Papers are submitted upon individual invitation or recommendation by the scientific editors and undergo peer review prior to publication.

The Feature Paper can be either an original research article, a substantial novel research study that often involves several techniques or approaches, or a comprehensive review paper with concise and precise updates on the latest progress in the field that systematically reviews the most exciting advances in scientific literature. This type of paper provides an outlook on future directions of research or possible applications.

Editor’s Choice articles are based on recommendations by the scientific editors of MDPI journals from around the world. Editors select a small number of articles recently published in the journal that they believe will be particularly interesting to authors, or important in this field. The aim is to provide a snapshot of some of the most exciting work published in the various research areas of the journal.


text:
### Some(?) of the Parts

A circle touches the lines OA, OB and AB where OA and OB are perpendicular. Show that the diameter of the circle is equal to the perimeter of the triangle

### Just Rolling Round

P is a point on the circumference of a circle radius r which rolls, without slipping, inside a circle of radius 2r. What is the locus of P?

### Medallions

I keep three circular medallions in a rectangular box in which they just fit with each one touching the other two. The smallest one has radius 4 cm and touches one side of the box, the middle sized one has radius 9 cm and touches two sides of the box and the largest one touches three sides of the box. What is the radius of the largest one?

# Arrh!

##### Stage: 4 Challenge Level:

This is really an aha' problem: the sort that has a very short and sweet solution, if you look at it the right way. We leave this as a further challenge for you to think about and send your ideas to Further Inspirations'. We give the solution sent by David of Madras College, St Andrews which depends on splitting the equilateral triangle into four smaller equilateral triangles.

Since a straight line touching the circumference of a circle will unavoidably find itself at right angles to the radius it touches'' - in this case line DE - we know angle DEC to be a right angle. As the whole thing is an equilateral triangle, angle ACB must be 60 degrees. The missing angle'' in triangle ECD (angle CDE) must therefore be 30 degrees.

Triangle ECD can be reflected along line DE to produce the equilateral triangle FCD. Triangle FCD is similar to the whole triangle but with sides half the length, therefore 4 FCDs'' can fit into ABC in the well known pattern:

The height of triangle FCD (or any of the other congruent triangles) is R and the height of triangle ABC is twice the height of triangle FCD, that is 2 R .

The upper section of the upper triangle (from the middle of the small circle upwards - AHJ) can be analysed similarly to the semi-circle below, so we find the height of triangle AHJ is 2 r . Therefore the height of triangle AFG = the height of triangle AHJ + r = 3 r . Therefore R = 3 r so the ratio R : r = 3 : 1.


text:
# 看绝望的主妇学英语地道表达:I take it that…

I take it that…: You can say ‘I take it’ to check with someone that what you believe to be the case or what you understand them to mean is in fact the case, or is in fact what they mean; I imagine this is the case; I presume it to be true (that); it is my understanding (that).

#### 看绝望的主妇学英语

error: Content is protected !!


text:
<img src="https://d5nxst8fruw4z.cloudfront.net/atrk.gif?account=iA1Pi1a8Dy00ym" style="display:none" height="1" width="1" alt="" />

# Composition of Inverse Reciprocal Trig Functions

## Application of one of six trigonometric functions or inverses and then another.

0%
Progress
Practice Composition of Inverse Reciprocal Trig Functions
Progress
0%
Hard Trig Inverse Composition Problems
Gives examples of solving the composition of a trigonometric function with a different inverse trigonometric function.


text:
Home » ECEA-4 » Section f: Astrophysics and Cosmology » Paper

# [] Boltzmann entropy, the holographic bound and Newtonian cosmology

* Author to whom correspondence should be addressed.
20 November 2017
186 views
0/5 rated ( 0 ratings )

## Abstract

The holographic principle sets an upper bound on the total (Boltzmann) entropy content of the Universe at around $10^{123}k_B$ ($k_B$ being Boltzmann's constant). In this work we point out the existence of a remarkable duality between nonrelativistic quantum mechanics on the one hand, and Newtonian cosmology on the other. Specifically, nonrelativistic quantum mechanics has a quantum probability fluid that exactly mimics the behaviour of the cosmological fluid, the latter considered in the Newtonian approximation. One proves that the equations governing the cosmological fluid (the Euler equation and the continuity equation) become the very equations that govern the quantum probability fluid after applying the Madelung transformation to the Schroedinger wavefunction. Under the assumption that gravitational equipotential surfaces can be identified with isoentropic surfaces, this model allows for a simple computation of the gravitational entropy of the Universe.

In a first approximation we model the cosmological fluid as the quantum probability fluid of free Schroedinger waves. We find that this model Universe saturates the holographic bound. As a second approximation we include the Hubble expansion of the galaxies. The corresponding Schroedinger waves lead to a value of the entropy lying three orders of magnitude below the holographic bound. Although a considerable improvement, this still lies above existing phenomenological estimates of the entropy of the Universe. Current work on a fully relativistic extension of our present model can be expected to yield results in even better agreement with empirical estimates of the entropy of the Universe.

## Keywords

Newtonian cosmology, holographic principle, quantum mechanics


text:
# Nice NSL problem w/ calculus

1. Aug 7, 2004

### abercrombiems02

A block rests on a horizontal surface with a rope attached. Assume the block is a pointlike particle in order that any moments on the box can be neglected. If kinetic friction opposes the motion of the block as it is dragged by a tensile force induced on the block by the rope, then what angle above the horizontal should the rope be pulled if the acceleration of the box is to be maximized for any given mass and tension? Hint: the solution is quite a simple answer

2. Aug 7, 2004

### vsage

Hoo boy. I thought I did well in physics but I question for the first time how I pulled off doing well ever, oops. No matter what the mass is, the tension must be greater than the original static friction, then we also know that the tension in the rope must be greater than the kinetic friction. Now my memory is getting fuzzy. Ok so here's my final answer then I guess in my stupor having just woken up from a nap: If k > 1, the angle should be 90 degrees, if k < 1, it should be 0 degrees. If k = 1, it doesn't really matter perpendicular or parallel. Any other angle I can only see it maximize the friction + gravity components. Oh and k is the coefficient of kinetic friction. I remember seeing in a book there was some substance with a coefficient of like 1.2 but feel free to correct me, I really am drawing a blank and my grasp of physics on fundamental levels like this is laughable.

Last edited by a moderator: Aug 8, 2004
3. Aug 8, 2004

### Galileo

The horizontal component of the net force is:
$$F\cos\theta - F_r$$
Where $F_r$ is the frictional force.

$$F_r=\mu N$$
Where N is the (magnitude of the) normal force.
$$N=mg-F\sin\theta$$

Therefore:

$$F\cos\theta-\mu(mg-F\sin\theta)=ma$$

Which gives for the acceleration:

$$a=\frac{F}{m}(\cos\theta+\mu\sin\theta)-\mu g$$

You can work out the angle $\theta_m$ for which this is a maximum and you'll find:

$$\theta_m=\arctan(\mu)$$

It seems the answer is dependent on the coefficient of friction alone.
If there is alot of friction, the angle higher. If there is no friction you should pull horizontally.

So if you want to drag along a heavy object by a rope, you should first
pull more or less vertically (high angle) to overcome the static friction, then
when it moves you should pull more horizontally.
I don't know what a typical coefficient of friction is (for stone for example),
but it may yield some practical information for when you're moving out of the house .

4. Aug 8, 2004

### abercrombiems02

typically coefficients of friction lie between 0 and 1, a very very rough surface would have a coefficient of friction of 1, if the coefficient was one, then in order to push a 100kg block on the ground you would need to exert a force of 9800 N

5. Aug 8, 2004

### thermodynamicaldude

Galileo is correct with his answer (isn't he always correct...i mean...about moons and Jupiter...acceleration on Earth independent of mass.....except maybe for his non-relativistic work on motion for frame of references). Anyways, the answer to the problem is that the angle = arctan u. If the coeficient were 0, then the angle would be 0, which makes sense. If the coefficient were 1, then the angle would be 45 degress, which also makes sense.


text:
# crash of tikz-uml and pgf-umlcd

I am stuck with inheritance diagram using pgf-umlcd. I am using both pgf-umlcd and tikz-uml. There is no error but the inherited line is not showing.

\documentclass[a4paper,10pt]{book}
\usepackage{tikz-uml}
\usepackage{pgf-umlcd}
\begin{document}
\begin{figure}[H]
\centering

\begin{tikzpicture}
\begin{abstractclass}[text width=5cm]{Shape}{0,0}
\end{abstractclass}

\begin{class}[text width=4cm]{Rectangle}{-3,-3}
\inherit{Shape}
\end{class}

\begin{class}[text width=4cm]{Ellipse}{3,-3}
\inherit{Shape}
\end{class}
\begin{class}[text width=4cm]{Circle}{3,-6}
\inherit{Ellipse}
\end{class}

\end{tikzpicture}
\end{figure}
\end{document}

• Are you using an up-to-date distribution? – user11232 Aug 26 '13 at 6:44
• Dear harish i am using up-to date one. problem is that if i interchange the packages then one of them is not working correctly – NARAYAN CHANGDER Aug 26 '13 at 11:30

The error message explains things fully:

! LaTeX Error: Command \umlnote already defined.
Or name \end... illegal, see p.192 of the manual.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.

Both packages attempt to define the command \umlnote. There can only be one! – Highlander

You can work around this by choosing which package should maintain normal functionality of \umlnote and loading that one last. Then, between loading the two packages, use something like

\let\umlnoteold\umlnote
\let\umlnote\relax

The first line is optional, and is used to store the first package's version of \umlnote for later use if needed. This might involve patching the first package to use this saved command instead of the original \umlnote. The second line "erases" the definition of \umlnote so that when the second package tries to create the command, \newcommand doesn't throw an error.

\documentclass[a4paper,10pt]{book}
\usepackage{tikz-uml}
\let\umlnotetikzuml\umlnote
\let\umlnote\relax
\usepackage{pgf-umlcd}
\begin{document}
\begin{figure}[H]
\centering

\begin{tikzpicture}
\begin{abstractclass}[text width=5cm]{Shape}{0,0}
\end{abstractclass}

\begin{class}[text width=4cm]{Rectangle}{-3,-3}
\inherit{Shape}
\end{class}

\begin{class}[text width=4cm]{Ellipse}{3,-3}
\inherit{Shape}
\end{class}
\begin{class}[text width=4cm]{Circle}{3,-6}
\inherit{Ellipse}
\end{class}

\end{tikzpicture}
\end{figure}
\end{document}


text:
# Why is it hard to give a lattice definition of string theory?

In Polyakov's book, he explains that one possible way to compute the propagator for a point particle is to compute the lattice sum $\sum_{P_{x,x'}}\exp(-m_0L[P_{x,x'}])$, where the sum goes over all paths between $x$ and $x'$. One then needs to compute this sum and choose the bare mass so that there's a good continuum limit.

Polyakov then goes on to say that this doesn't work for string theory. I skimmed the literature and couldn't find any explanation of this fact. Naively I would think that in order to find the propagator, you could just compute the sum $\sum_{W_{C,C'}}\exp(-T_0 A[W_{C,C'}])$, where the sum is over worldsheets that end on the curves $C$ and $C'$. What goes wrong? Is this just a hard sum to do?

-


text:
Thornton & Marion (Fifth Edition), Chapter 01, Exercise Problem 03 Solution

Chapter 01. Matrices, Vectors, and Vector Calculus

Problem 03. Transformation Matrix

The problem asks you to
find a transformation matrix that satisfying some condition.
This problem gives (or assumes)
This matrix rotates a rectangular coordinate through an angle of 120 degrees about an axis making equal angles with the original one.
You should know about
1) Direction cosine $\lambda_{ij} = cos(x'_i, x_j)$$\lambda_{ij} = cos(x'_i, x_j)$
2) Transformation matrix
Solution

We can see the relation between the rotated and the original coordinates system. This picture shows that

$\vec{e_1}' = \vec{e_2}$
$\vec{e_2}' = \vec{e_3}$
$\vec{e_3}' = \vec{e_1}$

So, the transformation matrix is

$\lambda = \left( \begin{array}{ccc} \lambda_{11} & \lambda_{12} & \lambda_{13} \\ \lambda_{21} & \lambda_{22} & \lambda_{23} \\ \lambda_{31} & \lambda_{32} & \lambda_{33} \\ \end{array} \right)$
$\lambda = \left( \begin{array}{ccc} \cos 90^\circ & \cos 0^\circ & \cos 90^\circ \\ \cos 90^\circ & \cos 90^\circ & \cos 0^\circ \\ \cos 0^\circ & \cos 90^\circ & \cos 90^\circ \\ \end{array} \right)$

Therefore,

$\lambda = \left( \begin{array}{ccc} 0 & 1 & 0 \\ 0 & 0 & 1 \\ 1 & 0 & 0 \\ \end{array} \right)$

Reference
https://math.stackexchange.com/questions/1599561/determining-the-transformation-matrix-r?newreg=f85754c5968d4b7fae383aabe7bfd2a5


text:
# Mac – Copy Excel worksheet and maintain relative cell reference in formulas

macrosmicrosoft excelmicrosoft-excel-2007microsoft-excel-2010vba

Another copy problem in Excel:

How can I copy a Worksheet from WorkbookA.xlsx into WorkbookB.xlsx without the copied Worksheet still referencing WorkbookA.xlsx e.g. the formula =B!23 becomes =[WorkbookA.xlsx]!B!23 when copied over.

I want to maintain "relative" cell references instead of "absolute" cell references (i shall invent this terminology in Excel world if it does not yet exists).

Another possible alternative that I cannot get it to work is the option to paste cell "values" only. Excel treats "values" as calculated values rather than the actual formulas in the cell. If I choose paste formula, it still gives absolute references.

More About Why I Need This:
I have a production xlsx in use for daily operations. We constantly need to make "upgrades" to this xlsx and so one person may create a copy and his changes there for a single sheet. Concurrently, another person may also be making changes to another sheet. Given that these sheets have no dependant cells on other sheets, like a summary report, it is desirable for us to just copy and merge the sheets back into the original xlsx. But the "absolute" referencing is giving a lot of trouble.


text:
# Effusion of particles from one box to another - pressure calculation

1. Jun 15, 2014

### unscientific

1. The problem statement, all variables and given/known data

Suppose we have a container divided into equal halves. Right half is fixed at temperature $T$, volume $V_2$.

Initially it has pressure $P_0$, a hole of area $A$ is opened between them.

Part (a): Show that the pressure in the right half is:

$$p = \frac{p_0}{2} \left[ 1 + exp \left(-\langle v \rangle\frac{A}{V}t \right) \right]$$

Part (b): Vessel has total volume $10^{-4} m^3$, area of $7.9 \times 10^{-9} m^2$, $T = 290 K$. Find the time taken for the pressure on the left half to become half that in the right part.

2. Relevant equations

3. The attempt at a solution

Part (a)

$$dN = -A\phi_{(t)} dt$$
Using flux as $\phi = \frac{1}{4} n\langle v \rangle$:
$$dN = - \frac{A}{4} n \langle v \rangle dt = -\frac{A}{4}\left( \frac{N}{V/2} \right) \langle v \rangle dt = -\frac{NA}{2V} \langle v \rangle dt$$

The graph looks like:

We solve for the dotted graph, then translate upwards by $\frac{N_0}{2}$. Integrating, and translating upwards i get: $p = \frac{p_0}{2} \left[ 1 + exp \left(-\langle v \rangle\frac{A}{2V}t \right) \right]$. Not sure why I'm missing a factor of $2$..

Part (b)

I know the way to solve this question is to find the pressure on the left half as a function of time, using a process similar to part (a). The graph we want to solve for is (L):

But I'm not sure how to begin..

2. Jun 15, 2014

### TSny

The hole is not a one-way passage. Particles can pass through the hole from either side.

3. Jun 16, 2014

### unscientific

Yes but I think that makes the problem insanely difficult. I think we can assume molecules only go from right to left.

Part (a): Any idea why I'm missing by a factor of 2?

Part (b): I don't even know how to start..

4. Jun 16, 2014

### TSny

Surely particles will need to come back through the hole from left to right. Otherwise, the entire gas would eventually end up in the left half.

I get the correct factor of 2 if I account for particles passing back through the hole from left to right. However, I did assume that the gas in the left side is always in thermal equilibrium with the gas in the right side. That would be the case if the wall separating the two halves is a good diathermal (heat conducting) wall.

I think part (b) is just a fairly direct application of the result from part (a). But I haven't worked out the numerical answer.

[EDIT: It seems to me you need to know the molecular mass to answer (b).]

Last edited: Jun 16, 2014
5. Jun 16, 2014

### unscientific

Part (a)

$$dN_r = -A\phi_r dt + A \phi_l dt$$
$$= -\frac{AN_r \langle v \rangle}{2V} dt + \frac{AN_l \langle v_l \rangle }{2V} dt$$
$$= -\frac{AN_r \langle v \rangle}{2V} dt + \frac{A(N_0 - N_r) \langle v_l \rangle }{2V} dt$$

Assuming $\langle v \rangle_l = \langle v \rangle_r$ here (If not, $T_r = \frac{4}{3} T_l$, so $\langle v \rangle_l = \frac{2}{\sqrt 3} \langle v \rangle_r$):

$$dN = -\frac{A \langle v \rangle}{V} \left(\frac{N_0}{2} - N \right) dt$$

Integrating, I get $N = \frac{N_0}{2} \left( 1 + e^{-\frac{A \langle v \rangle t}{V}} \right)$. Assuming temperature in the right side stays constant throughout,

$$p = \frac{p_0}{2} \left[ 1 + exp \left(-\langle v \rangle\frac{A}{V}t \right) \right]$$

Part(b)

I can say $N_{left} = N_0 - N_{right} = \frac{N_0}{2} \left( 1 - e^{-\frac{A\langle v \rangle}{V} t} \right)$.

Thus,

$$\frac{P_{left}}{T_{left}} = \frac{P_0}{2T_0}\left( 1 - e^{-\frac{A\langle v \rangle}{V} t} \right)$$

Now, $T_{left} = T_{right}$ (Assumption made in part (a))

$$P_{left} = \frac{P_0}{2} \left( 1 - e^{-\frac{A\langle v \rangle}{V} t} \right)$$

Mass of nitrogen molecule is $4.65 \times 10^{-26} kg$
Average speed is $468 ms^{-1}$
I get an answer of $29.7 s$

Last edited: Jun 16, 2014
6. Jun 16, 2014

### TSny

That all looks good.


text:
# How do rescale a Grid (with other grids and plots as elements) for printing?

I have a created a grid, as shown below,

   PowerLawPlottingGrid = Grid[{
{PowerLawLinearPlotGrids, PowerLawCompiledPlots}
}, Alignment -> Top]

where PowerLawLinearPlotGrids and PowerLawCompiledPlots are TabView[] functions containing more grids and/or plots as shown below:

PowerLawLinearPlotGrids = TabView[
{
"PVT" ->
Grid[{{ PowerLawLinearPVTInputGrid1,
PowerLawLinearPVTInputGrid2}}, Alignment -> Top],
"Reservoir" -> PowerLawLinearRESInputGrid,
"Model" ->
Grid[{{PowerLawLinearpDInputGrid1, PowerLawLinearpDInputGrid2}},
Alignment -> Top]
},
Background -> BCTV,
Alignment -> Left

]

PowerLawCompiledPlots = TabView[{
"Typecurve" -> CompiledPLPlots,
"Perm Distribution (SRV)" -> PowerLawKwdPlot

}, Alignment -> Center];

I want to be able to print my notebook to a PDF. I have tried converting my main grid to GraphicsGrid and implementing the following option with little success (x = 0.5, 0.7, etc)

ImageSize->Scaled[x]

When I review my PDF from "Save As", I usually get some sort of truncated image as shown below.

Ideally, I would prefer to see the entire output seen here. I can sacrifice some readability of the text/labels.


text:
MILP-Based Automatic Differential Searches for LEA and HIGHT

Abstract

In this paper we use MILP technique for automatic search for differential characteristics of ARX ciphers LEA and HIGHT. We show that the MILP model of the differential property of modular addition with one constant input can be represented with a much less number of linear inequalities compared to the general case. Benefiting from this new developed model for HIGHT block cipher, we can achieve a reduction of 112r out of 480r in the total number of linear constraints for MILP model of r-round of HIGHT. This saving accelerates the searching process of HIGHT about twice as fast. We enjoy the MILP model to investigate the differential effect of these ciphers and provide a more accurate estimation for the differential probability, as well. Our observations show that despite HIGHT, LEA exhibits a strong differential effect. The details of differential effects are reflected in a more compact manner using the newly defined notion of probability polynomial. The results gained by this method improve or extend the previous results as follows. For LEA block cipher, we found more efficient 12 and 13-round differentials whose probabilities are better than the best previous 12 and 13-round differentials for a factor of about 2^6 and 2^7, respectively. In the case of HIGHT block cipher, we found two new 12 and 13-round differentials, though with the same best reported probabilities.

Available format(s)
Category
Secret-key cryptography
Publication info
Preprint. MINOR revision.
Keywords
MILP modelDifferential AttackARX ciphers
Contact author(s)
History
Short URL
https://ia.cr/2018/948

CC BY

BibTeX

@misc{cryptoeprint:2018/948,


text:
# Which one of the following complexes is an outer orbital complex

$\begin{array}{1 1}(a)\;[Fe(CN)_6]^{4-}&(b)\;[Ni(NH_3)_6]^{2-}\\(c)\;[CO(NH_3)_6]^{2-}&(d)\;[Mn(CN)_6]^{4-}\end{array}$

Solution :
Complexion Hybridization of central atom
edited Nov 20, 2017 by meena.p


text:
#### Archived

This topic is now archived and is closed to further replies.

# Phasers on Shields effect?

This topic is 5160 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic.

## Recommended Posts

Can anyone give me some tips on getting that "phasers on shields" effect in a 3d game? What I have so far is a transparent sphere that I fade in then out. This is almost right, but it looks like the shot is hitting and enveloping the entire ship. I want only a part of the shield''s sphere to light up where the shot is hitting. Does that make sense? If not I can make some images of what I''m talking about.

##### Share on other sites
Try using only parts of textured spheres where each impact happens, if blended right it should look fine.

[edited by - Shane I am on October 16, 2003 5:23:20 PM]

##### Share on other sites
You could also fake it by turning off all lights except a point light at the spot where the phaser hits it, render the shield sphere, then do your normal rendering afterwards. Crank up the specular values REAL high to whatever color you want the glow to be on the light and use a blended texture.

---
http://www.gapingwolf.com

##### Share on other sites
Shane: Duh... Ok, now I feel so stupid! I made a "partial sphere" mesh and then just rotated it to the right position.

Thanks... I''ll be sure to post binaries asap (3d space shooter).

##### Share on other sites
Projected textures might look better.

##### Share on other sites
I did think about more "elegant" solutions, however we''re talking something that''s probably going to be no larger than 10-20 pixels on the screen. At the most, 40-50 pixels.

##### Share on other sites
quote:

Projected textures might look better.

Are you recommending using a textured QUAD rendered as a billboard at the point where the phaser intersection with the shield? If this is not the case, can you explain your implementation of a projected texture?

Understanding is a three edged sword...

[edited by - Sean Doherty on October 17, 2003 8:28:21 PM]

##### Share on other sites
Projective textures can be projected onto curved surfaces as well as quads. But, yeah, that would be overkill for this. Can''t wait to see the game!

##### Share on other sites
A spherical mesh with a funky texture on it. Make it dynamic, and when hit, modify the alpha values on the vertices to be opaque-ish near where it''s hit, and then fade off. Stronger hits would wrap more than tiny ones. Of course this might be overkill, but it''d look cool.

Stay Casual,

Ken
Drunken Hyena

##### Share on other sites
This is really easy to do, on your sphere the intensity of the effect is simply the dot product of the normal at that particular point and the vector of the phaser beam and clamp it at zero, if you want to concentrate it more square it or cube it.

This can be done the easiest in a vertex shader and a nicely tesseslated mesh

##### Share on other sites
quote:

A spherical mesh with a funky texture on it. Make it dynamic, and when hit, modify the alpha values on the vertices to be opaque-ish near where it's hit, and then fade off. Stronger hits would wrap more than tiny ones. Of course this might be overkill, but it'd look cool.

I have this solution implemented, but it is not quite working the way I would have expected. So far I have a target being enveloped by a sphere; and the D3DXVec3Dot product is being calculated for the vertices using the normalized laser vector and the each of the vertex normal. Using the output of the D3DXVec3Dot product I am able to calculate and set an opaque-ish color and alpha values where the laser hits the target, and then fade off. That said; I have two remaining problems to solve:

1) When the sphere that is enveloping the target is rotated, you can that there are actually two impact points being generated. The first point is at 0 degrees and the second is at 180 degrees. I have tried using the absolute values of the vectors to eliminate the second impact point with little no success thus far.

2) The target in the center of the sphere is not visible unless I render the target before the sphere or turn off the z-buffer? Maybe this is normal; or I could have something wrong with the alpha blending and alpha testing?

(Edit: It would seem that as long as the target is render prior to the sphere; and the sphere is rendered with D3DRS_ZENABLE state set to false then you are able to see the target properly through the sphere. Does it have to be this way?)

Any advice would be much appreciated.

// Phaser vector.D3DXVec3Normalize(&vecDotSource, &vecDotSource);// Vertice Normal.vecNormal = D3DXVECTOR3(vertices[count].fNormalX, vertices[count].fNormalY, vertices[count].fNormalZ);D3DXVec3Normalize(&vecNormal, &vecNormal);// Output used to set the color and the alpha of the vertex.fDotOutput = (float) D3DXVec3Dot(&vecDotSource, &vecNormal);

Understanding is a three edged sword...

[edited by - Sean Doherty on October 18, 2003 6:40:26 PM]

##### Share on other sites
quote:

When the sphere that is enveloping the target is rotated, you can that there are actually two impact points being generated. The first point is at 0 degrees and the second is at 180 degrees. I have tried using the absolute values of the vectors to eliminate the second impact point with little no success thus far.

1) The problem was caused by using the power of a negative Dot Product to calculate the color of the vertex.

2) Still experiencing some issues with the proper rendering order of 3D objects; especially objects where the state of D3DRS_ALPHABLENDENABLE is set to true? Would someone explain the proper rendering order?

Understanding is a three edged sword...

##### Share on other sites
I wouldn''t say that I am entirely happy with my Phaser implementation. That said; I would appreciate any advice on how I can improve the effect; or on an algorithm to automate the rendering order?

_______________________________________
Understanding is a three edged sword...

##### Share on other sites
Wow, game looks cool even from one screenshot The smaller sphear idea might look better for white star. This some alternate universe thing star trek vs b5? I''d like beta

Heh see why you have your sig as u do...

Who are you...What do you want...Who do you trust...

##### Share on other sites

I started this project as a top view shooter that I was planning to release as soon as possible. Since then, the project has started to evolve into a fully featured third person real time strategy game. At the present time, there is no schedule release date and many of the ideas and features are still being formed and tweaked. In fact lately it seems as though I have been removing more code than I have been writing in order to concentrate on certain effects; such as the phaser on shield effect and rendering. That said, perhaps I will post an updated screen shot when I am able to solve my some of these problems and reintegrate explosions, tweaked lighting, and the skybox.

Again, thank for your comments, and if anyone has any advice technical advice; especially in the area of lighting, the rendering order of objects, or ways to improve the special; it would be very much apprenticed.

_______________________________________
Understanding is a three edged sword...

##### Share on other sites
hmm, were did you get that whitestaar?

Bobboau, bringing you products that work... in theory

• ### Forum Statistics

• Total Topics
628682
• Total Posts
2984213

• 11
• 13
• 13
• 9
• 10


text:
# Proth number

(Redirected from Proth prime)
Jump to: navigation, search

In number theory, a Proth number, named after the mathematician François Proth, is a number of the form

${\displaystyle N=k\cdot 2^{n}+1}$

where ${\displaystyle k}$ is an odd positive integer and ${\displaystyle n}$ is a positive integer such that ${\displaystyle 2^{n}>k}$. Without the latter condition, all odd integers greater than 1 would be Proth numbers.[1]

The first few Proth numbers are (sequence A080075 in the OEIS):

3, 5, 9, 13, 17, 25, 33, 41, 49, 57, 65, 81, 97, 113, 129, 145, 161, 177, 193, 209, 225, 241, etc.

The Cullen numbers (n·2n+1) and Fermat numbers (22n+1) are special cases of Proth numbers.

## Proth primes

A Proth prime is a Proth number which is prime. The first few Proth primes are ():

3, 5, 13, 17, 41, 97, 113, 193, 241, 257, 353, 449, 577, 641, 673, 769, 929, 1153, 1217, 1409, 1601, 2113, 2689, 2753, 3137, 3329, 3457, 4481, 4993, 6529, 7297, 7681, 7937, 9473, 9601, 9857.

The primality of a Proth number can be tested with Proth's theorem which states[2] that a Proth number ${\displaystyle p}$ is prime if and only if there exists an integer ${\displaystyle a}$ for which the following is true:

${\displaystyle a^{\frac {p-1}{2}}\equiv -1\ {\pmod {p}}.}$

The largest known Proth prime as of 2016 is ${\displaystyle 10223\cdot 2^{31172165}+1}$, and is 9,383,761 digits long.[3] It was found by Szabolcs Peter in the PrimeGrid distributed computing project which announced it on 6 November 2016.[4] It is also the largest known non-Mersenne prime.[5]

## References

1. ^
2. ^
3. ^ Chris Caldwell, The Top Twenty: Proth, from The Prime Pages.
4. ^
5. ^ Chris Caldwell, The Top Twenty: Largest Known Primes, from The Prime Pages.


text:
15
May

## Gerhard Rosenberger (Hamburg): On the surface group conjecture and embeddings of surface groups into one-relator groups

Academic or specialist Colloquium / Congress / Forum
15.05.2012 17:15
Onsite

Let $F$ be a finitely generated free group, $\bar{F}$ an isomorphic
copy of $F$, $W$ a word in $F$ and $\bar{W}$ its copy in $\bar{F}$.
A Baumslag double is a free product of $F$ and $\bar{F}$ amalgamated
via $\bar{W}=W$. For example, an orientable surface group of genus 2
is a Baumslag double, and it is known that a Baumslag double is a
hyperbolic group if and only if $W$ is not a proper power of in F.

We will discuss what conditions make fundamental groups of orientable
and nonorientable surfaces of finite genus embed into Baumslag
doubles, and also present recent results concerning the Surface Group
Conjecture, which states: Suppose that G is a non-free, non-solvable
one-relator group such that every subgroup of finite index is again a
one-relator group and every subgroup of infinite index is a free
group. Then G is a surface group.

When? 15.05.2012 17:15 PER 08 Phys 2.52Chemin du Musée 31700 Fribourg Department of Mathematicsisabella.schmutz@unifr.ch
backtolist


text:
# Also in the Article

Measurement of residual water and crystallinity in dry samples
This protocol is extracted from research article:
Anti-fatigue-fracture hydrogels
Sci Adv, Jan 25, 2019;

Procedure

We measured the crystallinities of the resultant PVA hydrogels in their dry state by DSC (DSC/cell: RCS1-3277 Cooling System: DSC1-0107). For as-prepared chemically cross-linked PVA and freeze-thawed PVA, we used excess chemical cross-links to fix the amorphous polymer chains before air-drying, minimizing the formation of further crystalline domains during the air-drying process. We first soaked the samples (thickness of 1 mm) in the aqueous solution consisting of 10 ml of glutaraldehyde (25 volume %; Sigma-Aldrich, G6257), 500 μl of hydrochloric acid (36.5 to 38 wt %; J.T. Baker, 9535-02), and 50 ml of DI water for 2 hours. Thereafter, we soaked the samples in a DI water bath for 2 hours to remove the residual hydrochloric acid. The samples were further dried in an incubator (New Brunswick Scientific, C25) at 37°C for 2 hours.

Thereafter, we measured the mass of residual water mresidual, the mass of crystalline domains mcrystalline, and the total mass of the dry samples (with residual water) m using DSC. In a typical DSC measurement, we first weighed the total mass of the dry sample (with residual water) m. The sample was thereafter placed in a Tzero Pan and heated up from 50° to 250°C at a rate of 20°C/min under a nitrogen atmosphere with a flow rate of 30 ml/min. The curve of heat flow shows a broad peak from 60° to 180°C, indicating that the sample contains a small amount of residual water. The integration of the endothermic transition ranging from 60° to 180°C gives the enthalpy for evaporation of the residual water per unit mass of the dry sample (with residual water) Hresidual. Therefore, the mass of the residual water mresidual can be calculated as$mresidual=m⋅HresidualHwater0$(3)where $Hwater0=2260J/g$ is the latent heat of water evaporation. The curve of heat flow shows another narrow peak ranging from 200° to 250°C, corresponding to melting of the crystalline domains. The integration of the endothermic transition ranging from 200° to 250°C gives the enthalpy for melting the crystalline domains per unit mass of the dry sample (with residual water) Hcrystalline. Therefore, the mass of the crystalline domains mcrystalline can be calculated as$mcrystalline=m⋅HcrystallineHcrystalline0$(4)where $Hcrystalline0=138.6J/g$ is the enthalpy of fusion of 100 wt % crystalline PVA measured at the equilibrium melting point $Tm0$ (30). Therefore, the crystallinity in the ideally dry sample Xdry (without residual water) can be calculated as$Xdry=mcrystallinem−mresidual$(5)

Note: The content above has been extracted from a research article, so it may not display correctly.

# Also in the Article

Q&A
Please log in to submit your questions online.
Your question will be posted on the Bio-101 website. We will send your questions to the authors of this protocol and Bio-protocol community members who are experienced with this method. you will be informed using the email address associated with your Bio-protocol account.

We use cookies on this site to enhance your user experience. By using our website, you are agreeing to allow the storage of cookies on your computer.