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# perfectoid spaces-6

In this post, we will say something on Witt vectors, which will be used in Scholze’s paper. All the materials in this post can be found in Serre’s book, ‘Corps Locaux’.

We shall not discuss the original motivation for Witt to introduce the Witt vector. One interesting motivation is the following simple result:

Suppose that $A$ is a complete discrete valuation ring, with fraction field $K$ and residue field $\kappa$. Suppose that $S$ is a set of representatives of $\kappa$ in $A$, and $\pi$ is a uniformizer of $A$. Then each element $a$ in $A$ is a ‘power series’ of $\pi$ with coefficients in $S$, that is, $a$ can be written uniquely as $a=\sum_{n=0}^{\infty}s_n\pi^n$ with $s_n\in S$.

Here a uniformizer of $A$ is just a generator for the maximal ideal of $A$. Since $A$ is a discrete valuation ring, this means that $\pi$ always exists. The essential part in the proof to this proposition is that, the ideals $m=(\pi)\supset m^2\supset m^3\supset...$ form a system of open neighborhood of $0$. And of course, elements in the fraction field $K$ can also be written as Laurent power series as above.

Now note that $A$ is a ring, which has addition, subtraction, and multiplication operations. What will happen if we use the above ‘expansion’ expression for these operations? That is to say, if $a=\sum_n a_n\pi^n,b=\sum_n b_n\pi^n,c=a+b=\sum_n c_n\pi^n$,then what are the relations between $a_n,b_n,c_n$? Is there some simple algebraic expression for this? If not, can we choose $S$ to be as simple as possible such that the expression desired is very simple?

The above observation can be seen as a motivation for Witt vectors. Note that in the above proposition, we can show that as sets, we have, by construction, that $A=\kappa^{\mathbb{N}}$. So, the questions raised at the end of the last paragraph is just to find a ring structure on $\kappa^{\mathbb{N}}$ such that this ring is isomorphic to $A$. Of course, conditions could be posed on $A$.

One general construction is as follows:

Fix a prime number $p$. For a countable set of indeterminates $(X_0,X_1,X_2,...)$ and we set $W_0=X_0,W_1=X_0^p+pX_1,...,W_k=X_0^{p^k}+pX_1^{p^{k-1}}+p^2X_2^{p^{k-2}}+...+p^kX_k$. Then it is easy to see that

For any $F\in\mathbb{Z}[X,Y]$, there is a unique sequence $(f_0,f_1,...)$ in $\mathbb{Z}[X_0,X_1,...,Y_0,Y_1,...]$ such that $W_n(f_0,f_1,...)=F(W_n(X_0,X_1,...),W_n(Y_0,Y_1,...))$ for all $n=0,1,...$

I will not prove this result. One method is just to use induction on $n$ and some calculations. The interesting thing is that, when we express $X_i$ in terms of $W_k$, the coefficients lie in $\mathbb{Z}[1/p]$, yet this proposition tell us that these $f_j$ have integer coefficients. This is due to the assumption that $p$ is a prime number.

We shall apply this result to two polynomials, that is $F=X+Y$ and $G=XY$, and we denote the corresponding sequence as $(f_0,f_1,...),(g_0,g_1,...)$. Then a surprising result is:

Suppose that $R$ is a commutative ring, and for any $a=(a_0,a_1,...),b=(b_0,b_1,...)\in R^{\mathbb{N}}$, if we set $a+b=(f_0(a,b),f_1(a,b),...),a*b=(g_0(a,b),g_1(a,b),...)$, then with these two operations(addition and multiplication, as the symbols suggest), $(R^{\mathbb{N}},+,*)$ is a commutative ring.

Here we simply write $g_i(a,b)=g_i(a_0,a_1,...,b_0,b_1,...)$ and the same for others.

One little remark, in some sense, this result is part of the theory of formal groups.

We shall denote this ring as $W(R)$, and $a\in W(R)$ is called a Witt vector with coefficients in $R$. Note that since $f_i$ contains only addition, subtraction and multiplication operations and divide $p$ operation, so if this proposition is valid for a ring $R$, then it is also valid for subrings and quotient rings of $R$. As any ring is a quotient ring of some $R=\mathbb{Z}^I$, so it suffices to prove this proposition for these kinds of rings. If $R=\mathbb{Z}^I$, then we construct a map $W:W(R)\rightarrow R^{\mathbb{N}}$(the latter is equipped with the product ring structure), $a\mapsto (W_0(a),W_1(a),...)$. This is a bijection, which is obvious. Now, it is rather clear that $W$ respects the addition and multiplication operations of these two rings, thus proving that $F$ is an isomorphism. Moreover, it is easy to see, $(1,0,0,...)$ is the unit element in $W(R)$.

Now we can put the first result and the last result above together to see what happens: from a discrete valuation ring $A$ we get a $\pi$-expansion for each of its elements, and thus a bijection $A\simeq \kappa^{\mathbb{N}}$. And conversely, from $\kappa$, we construct a ring $W(\kappa)\simeq\kappa^{\mathbb{N}}$. Then what is the relation between $A$ and $W(\kappa)$? In fact, they are isomorphic in some cases:

If $\kappa$ is a perfect field of characteristic $p$, then $A\approx W(A/m)$.

To prove this result, we need Teichmüller representatives:

Suppose that $\kappa$ is a perfect field of characteristic $p$, then there exists a unique map $f:\kappa\rightarrow A$ such that:(1) $f(a^p)=f(a)^p$;(2)for $a\in A$, $a\in f(\kappa)$ if and only if $a=b^p$ for some $b\in A$;(3)$f(ab)=f(a)f(b)$ for any $a,b\in \kappa$;(4) if $A$ is of characteristic $p$, then $f(a+b)=f(a)+f(b)$ for any $a,b\in \kappa$.

The construction used in the proof is the same flavor as the one we have seen in Scholze’s paper, or in Fontaine-Wintenberg’s theorem. For any $a\in\kappa$, we consider $(a_0,a_1,a_2,...)\in \kappa^{\mathbb{N}}$ such that $a_{i+1}^p=a_i$. And for each $a_i$ we find a lift $b_i\in A$, and we set $f(a)=\lim_n b_n^{p^n}$. And the first three points are automatically satisfied(the uniqueness is a consequence of the fact that $f$ commutes with the $p$-power operation). As for the last point, it is also very clear.

This map is called a Teichmüller map, and $f(\kappa)$ are called the Teichmüller representatives of $\kappa$ in $A$.

Now we can construct a map from $W(\kappa)$ to $A$ as follows: for any $a\in W(\kappa)$, we send it to $T(a)=\sum_n f(a_n)^{1/p^n}p^n$, for some special rings, we can show that this is an isomorphism:

If $A$ is a strict $p$-adic ring such that $p$ is invertible in $A$, then $T:W(\kappa)\rightarrow A$ is an isomorphism.

Here a strict $p-$adic ring $A$ is a discrete valuation ring such that the $(p)\supset (p^2)\supset (p^3)\supset...$ forms a system of open neighborhoods of $0$ in $A$. Note that, under this assumption, the very first $\pi$-expansion is can be rephrased for $p$-expansion. And we can in the before last proposition replace the residue field $\kappa$ by the quotient ring $A/pA$, everything is still correct since the essential point is of characteristic $p$. And then this proposition can be proved by calculations.

So, in this way, we find an algebraic expression for $(A/pA)^{\mathbb{N}}$ such that the corresponding ring structure coincides with that of $A$.

One important remark: for any $n>0$, we can consider $W_n(R)=\{(r_0,r_1,...,r_{n-1},0,0,...)\in W(R)\}$. Note that this $W_n(R)$ is a quotient of $W(R)$ by $W'_n(R)=\{(0,0,...,0,r_n,r_{n+1},...)\in W(R)\}$. Indeed, $W'_n(R)$ is easily seen to be an ideal of $W(R)$, thus $W_n(R)=W(R)/W'_n(R)$ is a quotient ring. And it is not hard to show that $W(R)=\varprojlim_nW_n(R)$.

Another remark is about the topology on $W(R)$. As above, we have defined some ideals $W'_n(R)$ of $W(R)$, and it is easy to see that $W'_n(R)W'_m(R)\subset W'_n(R)$ if $n\geq m$. So, we can use these ideals to define a topology on $W(R)$.

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# MatISSetPreallocation#

Preallocates memory for a MATIS parallel matrix.

## Synopsis#

#include "petscmat.h"
PetscErrorCode MatISSetPreallocation(Mat B, PetscInt d_nz, const PetscInt d_nnz[], PetscInt o_nz, const PetscInt o_nnz[])

Collective

## Input Parameters#

• B - the matrix

• d_nz - number of nonzeros per row in DIAGONAL portion of local submatrix (same value is used for all local rows)

• d_nnz - array containing the number of nonzeros in the various rows of the DIAGONAL portion of the local submatrix (possibly different for each row) or NULL, if d_nz is used to specify the nonzero structure. The size of this array is equal to the number of local rows, i.e ‘m’. For matrices that will be factored, you must leave room for (and set) the diagonal entry even if it is zero.

• o_nz - number of nonzeros per row in the OFF-DIAGONAL portion of local submatrix (same value is used for all local rows).

• o_nnz - array containing the number of nonzeros in the various rows of the OFF-DIAGONAL portion of the local submatrix (possibly different for each row) or NULL, if o_nz is used to specify the nonzero structure. The size of this array is equal to the number of local rows, i.e ‘m’.

If the *_nnz parameter is given then the *_nz parameter is ignored

## Note#

This function has the same interface as the MATMPIAIJ preallocation routine in order to simplify the transition from the asssembled format to the unassembled one. It overestimates the preallocation of MATIS local matrices; for exact preallocation, the user should set the preallocation directly on local matrix objects.

MatCreate(), MatCreateIS(), MatMPIAIJSetPreallocation(), MatISGetLocalMat(), MATIS

intermediate

## Location#

src/mat/impls/is/matis.c

Edit on GitLab


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# Math Help - countability of languages

1. ## countability of languages

Let S = {0, 1}.

(a) Let F1 be the set of all functions f : S ! IN.
For example, the function f that has f(0) = 92873 and f(1) = 908 is one element of
F1.

(b) Let F2 be the set of all functions f : IN ! S.
For example, the function f defined by f(n) = n mod 2 for all n 2 IN is one element
of F2.

p.s. ! means arrow to

4. (a) There is a one-to-one correspondence between the set of functions from S to $\mathbb{N}$ and the set of pairs of natural numbers $\mathbb{N}\times\mathbb{N}$. Now, it is a standard result that there is a one-to-one correspondence between $\mathbb{N}\times\mathbb{N}$ and $\mathbb{N}$: see Cantor pairing function, this proof, and this proof that the set of rational numbers is countable.


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Article Text

Panel discussion
1. John M Pinney,
2. Roselyn P Epps,
3. Jack Hollis,
4. Marc Manley,
5. Deborah J Ossip-Klein,
6. Nancy A Rigotti
1. Corporate Health Policies Group, Bethesda, Maryland, USA
2. Division of Cancer Prevention and Control, National Cancer Institute, National Institutes of Health, Bethesda, Maryland, USA
3. Center for Addiction Research, Portland, Oregon, USA
4. Applications Research Branch, National Cancer Institute, National Institutes of Health, Bethesda, Maryland, USA
5. Department of Psychology, University of Rochester, Rochester, New York, USA
6. General Internal Medicine Unit, Massachusetts General Hospital, Boston, Massachusetts, USA

## Roselyn P Epps

I’m a pediatrician. I have been in private practice, I’ve taught and am still a professor of pediatrics and child health at Howard University. But I consider myself primarily a public health physician because most of my career has been in that field, ranging from work as a clinic physician in a child health clinic in the far Southeast Washington area to the Acting Commissioner of Health for the District of Columbia.

I only mention that because I am going to talk from the perspective of the consumer, the patient, the individuals, those who receive the services, as opposed to those who do research and/or deliver services. I’m going to speak briefly about channels for receiving information. What we really need is a marketing strategy for smoking cessation programmes. We have many piecemeal approaches to reaching individuals, but we don’t really have a strategy. And the tobacco companies fight back: they compete with each other; they do have a strategy. I would like you to think for a moment about what the consumer sees in the community, what the person at home sees.

First of all, they look at TV and see sporting events such as car races with blatant cigarette advertisements. On late night talk shows, guests frequently smoke. When they go to the movies, (and even the movies on TV), cigarettes are there. They’re on the tables. It may not be appropriate for the character, yet cigarettes are there. In the supermarkets, they’re up front at the checkout counter. At the gas station, cigarettes are there as well as billboards and posters.

And when you look at minority communities, cigarettes are even more apparent. The magazines are very colourful, but the back pages of practically every magazine feature cigarette ads. Also, minority newspapers promote cigarettes. I opened one of the minority newspapers recently and there was a two-page spread by a cigarette company, which was giving small grants ($2-5000) recognising people from community organisations. Most of the organisations are little known, but, nevertheless, cigarette companies are there, and they are part of the community. Cigarette companies give to charities. They don’t require research protocols and evaluation. All one has to do is have 501© IRS status, and they will give you money. That’s all that’s necessary. And when you go into the low income areas, that’s where the billboards are. They advertise in restaurants and provide ashtrays and napkins. The convenience stores have posters in them. The communities are blanketed. Cigarette companies have a marketing plan. And then, once every six months, the smoker goes to the doctor and the doctor spends five or ten minutes and tells the patient that he or she should stop smoking. What is the impact? Think about it from the consumer’s stand-point. As far as providers are concerned, the National Cancer Institute (NCI) has been conducting smoking cessation training for professionals. Recently, in the literature, I have seen much more about smoking cessation than I’ve ever seen before. I think people in all professions are becoming aware that they need to talk about smoking. I think we are reaching out, not only through the NCI’s nationwide programme, but also, through the NHLBI programme, to physicians, dentists and nurses. The ASSIST programme is going to be out in the community as well. We’ve heard a lot about pharmacies, and I’d like to just take a moment to tell you about the real world of the pharmacy. As president of our state medical society, I was on a radio programme with a Washington, DC, pharmacist who said that the pharmacies are really being squeezed by a number of factors. First of all, pharmacies don’t exist in many of these communities we need to reach. Some are at supermarkets, but many people have no access to a pharmacist. It’s very important that pharmacists know about smoking cessation, but many of them don’t really come into contact with disadvantaged patients. Large numbers of people, middle income and low income, never talk to a pharmacist. Certainly, pharmacists need to be involved, but I don’t think you can count on their involvement as the sole answer. I participated in a roundtable sponsored by the FDA, the Non-Prescription Drug Manufacturers Association, and the Consumer Product Safety Administration. They also talked about using the pharmacist. In many communities, people buy their OTC drugs from the local corner store, where probably the person who sells the product is behind a glass wall with cigarettes prominently displayed. I think we need to be realistic about what’s really going on in the world of the people we are trying to reach. I’ve approached some of the Medical Board members about asking smoking cessation. questions. Professional schools should include smoking issues in the curriculum. We can put questions on Boards, but the subject needs to be in the textbooks. There needs to be a strategy beyond just putting it on the Boards. At worksites, we talk about blue collar workers and the Unions. What about the pink collar workers, the people in the barber shops and the beauty parlors? That’s where a lot of the smoking goes on. As for the Unions, the tobacco industry is already there. Unions are the ones who lobby the DC City Council to get the smokers’ rights bills passed. They’re already there. It doesn’t mean that we don’t need to be there also, but be aware that they’re there before us. I think adolescents are important. Dr Schydlower is here from the American Academy of Pediatrics, which cooperated with the NCI on the ‘Fifth A’, as we call it, which is to Anticipate. I think adolescence is late to attack smoking. The pediatrician, and those who see children, need to start with passive smoking exposure of newborns and young infants and the Fifth A. In our programme for Preventing the Onset of Tobacco Use, we start with a much younger age. We talk about comprehensive: I listened to a number of speakers and I understand comprehensive, but I wonder what it means to a person who’s in the community? It doesn’t necessarily mean the same thing that it means to us. I was director of the High Risk Young People’s Project for individuals 15 to 24 years of age in the District of Columbia. Everybody said, ‘You’ll never get young men to come’. We had more of them coming than any other group, but the reason was we had a comprehensive programme that meant something to them. We had sports physicals, we had GED training, we have employability training, things that meant something to them. So, when you’re going into the community, think about what’s comprehensive for the individual who’s receiving the services, not just for those who are delivering them. It’s important that we, as educated professionals, get out of our offices and into the community. We cannot make decisions sitting in a vacuum-like office if we haven’t been out there. Believe me, people out there welcome us. There are not only the voluntary agencies to which we relate, like our own kind of voluntary agencies, but also almost 600 organisations that belong to the Independent Sector. There’s another world out there, just as there is in the scientific world – people who are volunteering, who would welcome your input, who have access to smokers, and who can carry the smoking cessation message. I encourage you to go out there and take the message. ## Jack Hollis I want to offer a somewhat more sober message and maybe a bit of a wake-up call. We heard today that only about half of smokers report that they have ever received advice from a physician to stop smoking. Yesterday, Gary Giovino told us that, of patients who had seen a physician in the last year, only 36% reported that they received advice to stop at that visit. Even the most powerful intervention is going to be absolutely useless if it does not get used, and we need to become much more realistic about what we are asking to have happen in primary care settings. Together with my colleagues, Vic Stevens, Thomas Vogt, and others at the Kaiser Permanente Center for Health Research, and Ed Lichtenstein at the Oregon Research Institute, we tried to come up with a more practical model. It had to be an approach that would be easier to implement and sustain in a busy, real life, primary care setting. We came up with a model that we thought would be both effective and practical and tested it in a randomised trial sponsored by the NCI. I would like to briefly share it with you. We tested a clinic-based team approach for dealing with the tobacco issue in a way that does not put the bulk of the burden on the physician. As a first step, clinic assistants, medical assistants, or whoever puts the patient in the examination room assesses smoking status along with other vital signs. If the patient smokes, then the clinic assistant alerts the physician by flagging the chart. I am more optimistic than Ron is about tobacco assessment becoming a new vital sign. It is a key step and we have shown that it is possible to make this a routine part of practice. In our team approach, the physician’s role is to deliver a cessation message that takes only about 30 seconds. Delivered at the end of the visit, it goes something like this: ‘Stopping smoking is the single most important thing you can do to protect your health, and as your physician, I want to strongly advise you to stop soon. I know that has got to be your choice, but I believe you can do it when you’re ready to try. So how about it? Are you thinking about quitting sometime in the next six months ? ’ If the answer is ‘ no, ’ the physician hands them a pamphlet, such as the one we call ‘Getting Ready to Get Ready to Quit Smoking’ and checks with them again at their next visit. If the answer is, ‘Well, I am thinking about quitting,’ then the patient is referred to a trained nurse. The nurse first starts the patient on a 9-minute video. The video dramatically decreases the nurse’s task by modeling techniques other people have used to quit and dealing with many of the common concerns of smokers, such as fears about past failures and weight gain. The tone is upbeat, with a good deal of humour. At the end of the video, the nurse provides a self-help manual and tries to elicit a quit date. ‘So how about it? Are you seriously thinking about quitting in the next few weeks? Is there a specific date you think would work for you?’ Typically, the interaction with the nurse at the end of the video takes three to five minutes. If the patient sets a quit date, then we recommend that someone call them back the day after their quit date to see how they are doing. We have a staff member from Health Education make these brief calls. We also mailed smokers newsletters and other cessation reminders. When we implemented this in two large Kaiser Permanente medical facilities, we found that all 60 of the medical care providers were happy to participate because it took so little of their time. Physician training required about one hour, a free lunch, and some in-clinic follow-up. Of all identified eligible smokers, 86% received advice over the one-year Intervention period, which tells us that physicians found this really worked well for them. Of the patients who received the advice, 87% went and saw the nurse counsellor as directed. So the patients also saw this as a reasonable clinic procedure. We had four groups in this randomised trial. I will not describe all of them here, but our control group included a 30-second cessation message from the physician and the ‘Why Do You Smoke?’ pamphlet. Our three nurse- assisted treatment groups also included the brief physician message but added various nurse-delivered interventions. Compared to brief advice alone, the three nurse-assisted interventions significantly increased the percent of patients who set quit dates, attended a group programme, and made serious quit attempts. We did not have a no-advice or usual-care condition, but from the literature I would expect about a 1-2% long-term sustained quit rate. In our case, we required the patient to be abstinent at both three- and twelve-month follow-ups to be considered a success. As described in the May 1993 issue of the Annals of Internal Medicine, the brief physician advice message yielded a 3.9% sustained quit rate, which is substantially better than usual care. But the nurse-assisted treatments yielded almost double that quit rate, 7.2%. We have done preliminary cost-effectiveness analyses using national mortality rate data. Depending on which group we are talking about, the nurse-assisted treatments cost between$17 and $25 to deliver. The added costs needed to save one discounted year of life by adding nurse-assisted intervention to brief physician advice is roughly$1000. To put this in perspective, it takes roughly $11000 to save one discounted year of life with Propranolol treatment for mild to moderate hypertension and$102 000 to save a year of life with mammography screening in women aged 55 to 65 years. Clearly, nurse-assisted tobacco counselling is one of the most cost-effective medical procedures available.

We are now trying to implement this nurse- assisted system in different regions of Kaiser Permanente and other settings to test generalis- ability. We have modified the programme slightly to include stage-appropriate prompts at every visit that provide somewhat different messages to pre-contemplators, contempla- tors, and recent quitters. We have also built in a step-care protocol so that progressively more intensive interventions are provided at successive routine visits. For example, we encourage people to try to quit once or twice on their own, using self-help materials. Those who need more intensive help are referred to a group programme with nicotine replacement, if that seems to be appropriate.

As a final comment, we have learned that an absolutely critical part of any programme implementation effort is to have some mechanism for staff monitoring and feedback. During the early stages of implementation it is vital to track and provide feedback on whether the various components are being delivered or not. We have seen time and time again that what gets measured, gets done. Nurses are an important resource in the fight against tobacco and I encourage all of you to look for creative ways to involve them more actively in the process of helping smokers quit.

## Marc Manley

Under the able assistance of Dr Tom Glynn, a series of trials were funded through the NCI looking at what health professionals could do in their practices to help people stop smoking. As those trials were wrapping up in the late 1980s, NCI, with the investigators, managed the production of a document that summarised the findings and gave some consensus recommendations. That book, called ‘How to Help Your Patients Stop Smoking,’ is one that I hope many of you have seen.

There was a study in the literature at that time that came from the UK. They had mailed books similar to ours to every General Practitioner (GP) in the UK and followed up with a survey of the impact of that mailing on GPs’ knowledge about smoking cessation. As you might guess, they had very dismal results, and it was very fortunate that we had that piece of information at the time or we might have wasted a lot of money on postage and books. We elected not to do mass mailings of instructional booklets for physicians and other clinicians and instead developed a set of training materials that would, in many ways, repeat the kinds of training programme that had gone on during the trials in the 1980s.

For the last two and a half years, we’ve been doing everything we can to get courses in smoking cessation taught to physicians, nurses, dentists, dental hygienists and others. And we’ve used what’s frequently called a train- the-trainer system, which was really the idea of Dr Roselyn Epps. With her leadership we’ve worked with a number of organisations who have the ability to bring clinicians to these programmes. I’d like to point out in particular the American Cancer Society and the American Medical Association as two groups that joined our programme early on and wanted to offer this kind of training service to their members and delivered it in many places around the country.

We originally planned to train 2000 people how to teach courses in smoking cessation techniques. We’re up to 1600 right now, so we’re getting near the end of that phase.

It’s been, in many ways, a volunteer programme. The NCI puts a lot of staff time into it, but it’s really been these organisations buying into it and individuals within these organisations being willing to come and attend our trainers’ workshops and then go out and do some teaching.

Clearly, this is not only the thing going on in smoking cessation training, nor should it be. This is a programme that’s meant to be a catalyst and to encourage clinicians around the country to learn more about it. As we’ve heard today, there’s reason to have more than just one programme in the country.

If you make the assumption that health care providers are human beings and follow the laws of human behaviour, then many of these issues that were brought up yesterday are applicable to changing health providers’ behaviour. When you sit in a room full of physicians, for instance, and teach them about smoking cessation, you often find that there are people in the room who are pre-contemplators and have no intention of ever changing the way they practice or the way they treat smokers. There are also people who are thinking about it a little bit, and there are people in action phases who are doing something about it but also need some help with maintenance. So really those same stages of change apply to clinicians as well.

To put it in another way, there’s also a big difference in the level of skills of different health care providers. Some people are quite comfortable counselling and some people want very little to do with counselling, so there is a big range of skills and attitudes among health care providers. It’s a tough thing to change their behaviour, especially in a group session, but the way medical and dental education works, that’s often the only option we have.

In the 4 ‘A’s approach, if they ask, advise, assist and arrange, it gives them an outline of what to do when they’re face to face with a patient. The nice thing about the 4 As is it makes it easy to convince these pre- contemplator clinicians: ‘You’ve only got to remember these four words and it will only take a couple of minutes. ’ That’s true to some degree, but everybody knows that there are some patients who require much more than two or three minutes, and it’s only an outline of an approach. So when you’re dealing with a group of clinicians, you’re selling some people on the idea all together, but some people are ready for more than just a very basic approach to the whole issue.

Our 4 As is only one step in five steps of intervention, and the other steps have to do with setting up an office practice so that this kind of intervention is given routinely. I do think there’s good evidence that repeated routine delivery of these services and offering of services is essential. There’s also good reason to believe that if you don’t have some support within your practice environment, you’re not likely to do it and remember to do it on your own as a busy clinician.

So we need to continue to emphasize the importance of an office systems approach and of having staff members in an office setting who are a part of the programme and know their roles and responsibilities. We need to continue to encourage the use of reminder systems, for example, the use of making smoking status a vital sign. I, too, share what may be a hopelessly naively optimistic view that it can be a vital sign, but I think it’s a small step and an important one.

Other things that might motivate clinicians to change the way they treat smokers may go a bit beyond just what’s involved in their immediate practice environment. When we wrote the NCI manual, our model was a private practice where people sit down and decide this was something that they want to do. But many practice settings are different to that. There are large managed-care systems where standards of practice and rules of practice may be imposed a bit from the outside, and, in fact, that may be the wave of the future.

I think payment is also a motivating factor. It may not be people’s first motivating factor, but I think it’s an important issue, and so reimbursement clearly plays a critical role in all this.

The title of this conference is Who Quits? Who Pays ? but I think in between there might be the words ‘Who Treats?’ Who quits and who treats and who pays for the treatment- these are the important questions.

We’ve heard a lot about worksite cessation programmes and other kinds of group programmes, and I really think primary care providers and other clinicians, for that matter, have this service to lose, in a sense. They could grab a hold of this and say, ‘This is our domain, we are going to do this, and we are going to expect reimbursement; ’ or they may decide to say, ‘This really isn’t our ballgame and it’s better referred to a group programme. ’ I think that’s happening in certain situations, so it’s still the clinicians’ decision about how they’re going to proceed.

I know that certain Health Maintenance Organisations are now putting restrictions on how patients can receive, for instance, nicotine patches; patients have been told they have to attend a group programme in order to receive their prescription for patches. Many clinicians have complained to me that this takes them out of the loop, that they write the prescription for the patch, they refer, and that’s the end of their treatment. I think we need to look at those decisions very carefully because there may be better ways to include the clinicians in this.

The other thing that may encourage clinicians to do interventions more is their training, and not just their postgraduate training, but their medical school training and their residency training or other professional training. If we don’t find a way to build it in, we’ll continue to be moving a rock uphill, and I think we have to focus on schools now.

Also, and I think it’s demonstrated by the recent attention that nicotine patches got from the general public, patients dictate a great deal of what goes on in practice and what patients ask for is often what gets discussed in a clinical intervention. We have to think about patients asking for these kinds of services, and I certainly know that happened when patches were marketed so widely. No matter what you think about direct-to-patient advertising, this got more people into their physicians’ office asking about smoking cessation and probably had at least some positive benefit.

This leads me to the conclusion that this isn’t just a clinical issue; this is a much broader societal issue, as has been said. As we see more programmes such as mass media programmes or increased cigarette taxes, we’re giving patients more reason to want to stop smoking, and that’s going to, if we do our job well, drive them into the medical system asking for help.

So I think these broader political and economic issues play an important role in the clinical setting and that we need to continue to push what I call comprehensive tobacco control programmes, which include a whole range of interventions, including political, social, and economic interventions.

## Deborah J Ossip-Klein

One point that has come out of this conference very clearly is that we have a range of interventions that work. We certainly need continuing research to upgrade and further enhance the effectiveness of our interventions. Simultaneously, we need delivery systems to get what works out now so that our interventions can have a public health impact. The two types of systems that I’ll be talking about will be self-help or self-directed delivery systems, and these will be telephone hotlines and also interactive systems to which John alluded a little while ago.

At one end of the continuum, we have the telephone hotlines, which have a number of advantages. They can be available to whole communities and thus provide assistance right when it’s needed. They can offer personal contact, but without the kind of face-to-face interaction that may deter many would-be quitters from seeking other sorts of formal services.

We know now from a number of years of experience that somewhere between 1% and 36% of the target population will call a hotline.1 What that means is that, in order to be viable, hotlines must reach a very large population base, and, in fact, this is exactly what we want them to do from a public health perspective.

We know that call rates will improve with aggressive, ongoing promotion of the hot-line.2,3 Hotlines only seem to be relevant to smokers when they’re at a point when they need help, so if they heard something about the hotline two or three weeks ago, that may not have had any impact on them. If they need some help right now and they see a message about the hotline, then they’re more likely to call.

We also know that, when implemented correctly, hotlines can increase success rates, particularly for self-quitters, by somewhere between 19-47%. We know now that there are some things that won’t work with hotlines, and we also have an idea of the kinds of things that can improve their effectiveness. My group, and also, Tracy Orleans and her group, have demonstrated the effectiveness of both reactive and proactive telephone hotlines.1,4

At the other end of the continuum we have the full interactive computerized systems for self-help and self-directed smoking intervention. Some of the components that might be included in these systems would be hotlines, personalised assessments and feedback, personalised intervention materials sent on a predetermined schedule, tracking of patients, generation of databases, and providing guidance to physicians and health care systems for intervention.

Essentially, what these kinds of systems can do is to take existing self-help interventions, and put them into a personalised interactive system that can get out to the public. A few variations of this approach are currently in existence, and there are several others in development. Notably, work by Prochaska and colleagues demonstrates the effectiveness of this type of system.5,6 There are a number of advantages of these systems. First, they can also reach large populations and may provide viable self-help alternatives to the face-to-face clinics because they include many of the same components but do so in a self-help modality. Second, they may be able to help health care providers be more effective with their patients within the time constraints that they have for intervention. Third, these sorts of systems can continually be modified to incorporate Intervention components that are shown to be effective in controlled clinical trials.

Also, we can set standards for evaluating these kinds of systems in terms of their effectiveness. I’d like to suggest a couple of possible standards. First, have they been shown to be effective in controlled clinical trials, our real gold standards, and here’s where the funding agencies become increasingly important, and/or do they incorporate components that have been shown to be effective in controlled clinical trials, which may get them out a little more quickly.

And second, are they in conformance with national guidelines, and there are a couple of national guidelines that I think would be particularly relevant here: the NCI guidelines for physician intervention7 and the NCI guidelines for self-help intervention.8

Finally, there are some research needs in this area, and I’ll identify two. One is how can we best interface these kinds of systems with the existing or changing health care system to minimise the time requirements for health care providers yet maximise successful outcomes so that these systems become realistic and can have an impact. The other is how do we best mete out our contacts, telephone and/or mail contacts, so that we produce optimal outcomes. We may find that different dosing is appropriate for different populations, eg, high medical risk populations, populations that differ by age, populations at different stages of change, and so on.

In summary, what we see is an expansion of the concept of self-help, self-directed programmes with a couple of modalities listed here that can take the programmes that are shown to be effective in controlled clinical trials, and put them into delivery systems that get them out to the public in a meaningful way.

## Nancy A Rigotti

I’d like to address the general problem of how those of us who work in the health care setting incorporate smoking cessation in our practices. It seems to me that we have three questions to answer. First, what should we be doing? Once we figure that out, how can we persuade and train practitioners to do it (and who are those people)? Finally, how can we make it happen in the organisations and institutions in which we work? I’ve been facing all these questions in the work that I’ve been trying to do at Massachusetts General Hospital in Boston, where I’ve been developing a comprehensive smoking treatment programme.

It makes sense to focus on primary care providers. We’ve heard about the NCI models, which have been very helpful. I’ve taught them for years and see them as a very good scaffolding upon which individuals develop their own style of smoking counselling. My experience in teaching groups of physicians through the American College of Physicians and other organisations is encouraging. Over the years the proportion of grey hair on the heads of the people in the audience has increased, which I take to mean that the physicians interested in treating smoking are getting older. Originally, smoking was something that the younger people in medicine were interested in. Gradually it’s diffusing into older groups, and I think that that’s a positive sign. Ten years ago, the notion that doctors ought to talk about smoking was considered on the fringe of medical practice. Now it’s considered almost standard. Despite this progress, my impression is that too many of my colleagues consider that smoking is something someone should be addressing, but they’d prefer to avoid dealing with it themselves. Adopting the traditional model, they’d like to refer the problem to the appropriate specialist. As a result, I have reluctantly tempered my idealism that doctors can be taught a simple four-step model that will take three or four minutes. I realise that some physicians will never be interested in doing this, and some who are interested are not going to be very good at it. There are many practitioners who are or can become excellent smoking counsellors, but there are many who will not. This is why we will need flexible, stepped-care models of smoking treatment for the health care setting.

Even though I care about doing smoking counselling more than many of my colleagues and probably do more of it, there are many other issues that I have to deal with in practice. I’m very persuaded about the value of the work that Jack Hollis described today. This system would limit what I would be expected to do and connect me into a coherent system that would take care of it for me. I think that’s the way we’re going in primary care practice.

As a result of the work of Jack Hollis and others, we have good models for handling the smoker in primary care. Even with the best model, there are going to be failures, and then you need an approach for smokers who need more intensive intervention. First, who will do this work? Administratively, will the practitioners be based in a Department of Medicine, a Department of Preventive Medicine (if there is one), or in a Department of Psychiatry or Psychology? Should it be the domain of substance abuse treatment? It’s not so clear. What is clear is that the content is multidisciplinary. There are now some very nice models being developed for this more intensive level of treatment. I’d like to acknowledge Richard Hurt and his colleagues at the Mayo Clinic, who have developed an excellent model of how to use the whole health care setting. Other institutions around the country are also developing these models: Duke, the University of Wisconsin, and Kaiser-Permanente Hospitals in Portland, Oregon.

Another approach to using the health care setting to promote smoking cessation would be to ask what are the teachable moments ? There has been some work on that, which we haven’t talked much about here. For example, we know that one of the best ways to quit smoking in this country is to have your first myocardial infarction (MI). About one-third of the people who have their first MI don’t smoke again without any specific anti-smoking intervention. However, (1) they’re frightened to realise that smoking is not only bad for smokers, it’s bad for them personally, and (2) they are not allowed to smoke for the duration of their hospital stay – about a week nowadays. These effectively serve as an anti-smoking intervention.

We recently investigated smoking after coronary bypass surgery and found that 50% of people who undergo these operations don’t smoke for five years. That’s good news, in a way. On the other hand, these people have been through a \$20-30 000 procedure whose outcome is improved if they quit smoking, and 50% still go back to smoking. Suddenly, the outcome looks less positive and indicates a need for change. Unfortunately, we found out that early in-hospital intervention with these people does not increase their quit rates. New approaches need to be developed and tested to maximise medical outcomes and make these procedures more cost-effective.

There are other teachable moments that might be considered: pregnancy or just being admitted to hospital, since hospitals are now almost uniformly smoke-free. We don’t really know how much nicotine withdrawal smokers have when they’re admitted. In practice, we don’t seem to see a lot of it, but it’s possible that withdrawal is occurring and is not recognised as such, since withdrawal symptoms are nonspecific. Regardless, I think that we need to look at ways to develop smoking interventions in hospitals.

Even though we don’t have fully developed models of how best to promote smoking cessation in the health care setting, we have developed a number of good models. Ultimately, how do we get what we have learned adopted widely in our hospitals and health care facilities? How can it get into the consciousness of the reimbursers as an activity that should be covered? Reimbursement policies are determining how smoking cessation is being defined and delivered. Consider nicotine replacement. Its method and duration of use is being defined not by the FDA, not by package inserts, not by physicians, not by the behavioural scientists who probably know better than anybody what a comprehensive behavioural programme is, but by third-party reimbursers. As an example, consider the situation in Massachusetts, where my colleagues and I are trying to set up a comprehensive smoking cessation service at Massachusetts General Hospital, modelled on what Richard Hurt and his colleagues have done in Minnesota. In doing so, we investigated insurance coverage for the nicotine patch. What we found was that nicotine patches are covered, not beforehand but after the fact. There is reimbursement after the purchase of the patch for one course of treatment in a smoker’s lifetime, but only after they show evidence of having attended a smoking cessation programme, which is usually defined as three sessions of four hours, and includes certain types of behavioural modification methods. Insurers specifically exclude counselling in a physician’s office as qualifying for nicotine patch reimbursement. Furthermore, they don’t pay for the counselling programme they require. The smoker has the choice of paying for the patches or for the programme. I submit that this is the reimbursement policy I would develop if I wanted to minimise use of a medication.

So, in summary, I think we need to solve some of the organisational issues first. What might be helpful to people like me would be a way of collecting the information about model programmes and strategies that have been developed around the country. Whether in a book or a conference, that information would be useful for people who’d like to start programmes and, I hope, organisations who might consider paying for them.

ELLEN GRITZ: Much of the central work in developing the theory, content, and delivery modalities for smoking cessation services has been undertaken primarily by behavioural scientists and psychologists. I wonder what anyone on this panel, perhaps Jack, might comment on how to broaden the mandate, and the ability to treat and deliver patients using tobacco-dependence diagnoses, given Nancy’s comments. I would also like to ask what the rest of us have heard about the difficulty of even establishing the treatment in a medical care setting, much less allowing psychologists and other mental health professionals to treat legitimately patients with smoking-dependence disorders.

JACK HOLLIS: Working in a Health Maintenance Organisation (HMO) or a large medical care system, I think psychologists and others have a really important role to play in organising those systems. I don’t think that they, at least at the primary care level, are the appropriate ones to be there in the clinic providing the services, although they probably have an important role to play as referral agents, running group programmes and more intensive kinds of programmes like those that have been mentioned several times.

ROBERT ROBINSON: Ron, I would be interested in knowing in terms of the mass media campaign that you developed in Michigan how you handled competing interests, since it was defined as health promotion. I’m thinking of AIDS and infant mortality – serious competitive issues in terms of those dollars – and whether or not it was an issue ?

I was struck by your comments about the minimal role of the public health system. There’s an infrastructure there and they access high-risk populations, but what I heard that wasn’t said was that the infrastructure is minimal, so that one questions exactly how one can utilise it. This brings me to the need for capacity building. When you talked about the needs of communities, you listed at least three research initiatives. I would like to invert that. I think what we need first in communities, is capacity building and infrastructure development. Once we lay a foundation there, it would be efficacious to go in and develop some research protocols to evaluate the efficacy of what we have. But at the moment we have nothing, and if all we offer is research that implicitly has no service component or no capacity building component to it, I think we’re backing in with our behinds rather than with our heads. What I would propose is that we really look at the need for capacity development and infrastructure development in communities, and then follow up with some research.

RONALD M DAVIS: I agree with that. I think there’s sometimes a tendency to over-evaluate, although, certainly, the greater problem has been underevaluation. But I agree with you about inverting the priorities for delivering these things in the community.

Even though the involvement of local public health departments or the public health system has been small, I think their potential role is great. When you consider the fact that half of the vaccinations delivered in this country are delivered by local health departments, which primarily reach the indigent population, you can see the potential for local health department involvement in public health. They’re just not doing it in terms of health behaviours and chronic disease prevention.

In terms of how we’ve allocated mass media dollars to tobacco, out of the nine million dollars raised from the computer software tax, two million was allocated for the media, one million for AIDS media messages and up to a million for tobacco, although in the last year or so we’ve gone down from a million to about 600000 for tobacco because we’ve taken the rest for breast and cervical cancer screening and an anti-violence campaign. The competition has actually been more acutely felt in the last year or so.

To answer Ellen’s question-my understanding of the reimbursement system is that, historically, the greatest priority has been to reimburse physicians for the services they deliver, or at least they get the first reimbursement before other health care providers get reimbursed. I would think in smoking cessation that one way in which psychologists and others could be reimbursed would be to do it, ‘under the supervision of a physician’.

For example, in family planning clinics, a lot of nurse-practitioners get reimbursed and can prescribe oral contraceptives if it’s done ‘under the direction of a physician’, which can be done quite flexibly.

But the other way in which I think it could be facilitated would be through certification, a point I made earlier. If we certify psychologists or any other professionals to do cessation therapy, I think insurance would be much more likely to cover it rather than opening it up to a long list of providers.

CAROLE TRACY ORLEANS: I’m hearing a theme emerging from today’s presentations and yesterday’s, which is basically that we need to develop smart systems, not only for the patients, but for the providers and the delivery systems. The NCI panel, Tom Glynn, Jessie Gruman, and Gail Boyd wrote that we have to make smoking cessation cues persistent and inescapable. I think we have to make smoking cessation or nicotine addiction treatment persistent and inescapable, and we’ve got an enormous amount to learn quickly about how to use the managed care environment creatively: to build chart audits; to put nico- tine-dependence treatment into the routine practice of primary care or to provide forms and materials that make those kinds of chart audits easier, and to start reimbursing physicians by whether or not they do that; to build simple health risk assessments (HRAs) to relieve the overburdened primary care physician who’s trying to take preventive medicine seriously by using the increasing capabilities we have in computer-based expert information systems to give HRA feedback in a cost- effective way in the primary care setting.

The other comment I wanted to make is that the pharmaceutical sales representative’s detail visit provides a wonderful model of how to train physicians to do just what we’re talking about: brief interventions at the office that will get the attention of and maybe get the patient started on a more extended intervention. We ought to be in a partnership with the pharmaceutical companies marketing nicotine replacement therapies to start to infuse the ‘Four A’s’ in what they’re doing. The opportunities for follow-up through the pharmaceutical detail strategy are impressive.

RICHARD HURT: I want to answer Nancy’s question about reimbursement, but before I do that, I want to give you just a brief summary of what we’ve done. Nancy’s experiencing exactly what we experienced in 1985, which was a lot of resistance and a lot of inertia, in trying to bring a nicotine-dependence treatment programme to a major medical centre. We were able to do that after a three-year planning effort, and in 1988 began our consultation services, which have now broadened to provide the full range of treatment services, including the stepped-care model we talked about yesterday. We have provided services for over 7400 patients to date, and have provided training for people from various medical centres in the country, including Indiana University and Henry Ford, among others, that have come to see what we’re doing.

To answer the reimbursement question, we surveyed 91 patients who had been seen for a consulation in 1991. The business office at our place does routine surveys of patients to find out what reimbursement was available. We had 19 different insurance companies that were represented, 10 of which covered services and four covered 80 to 100% of the services, so that’s the answer to your question.

CYNTHIA RAND: We’ve had a lot of discussion about physician advice in the office with patients, and we’re aware of the statistics that show the number of patients that report that they haven’t received that advice. Those of us who work in the area know that sometimes patients get it but don’t hear it, and there is a question of what it is they do hear. I want to share one of our observations when we took people into the Lung Health Study, all these middle-aged folks with pulmonary impairment. One of the questions we asked them when we interviewed them was ‘Has a doctor ever told you you had to quit smoking ? ’ A very common response from all these folks with shortness of breath and pulmonary impairment was no, but if you probed a little bit further, they’d say, well, he didn’t say I had to quit smoking.

I think that we need to understand that what people hear may be very different from what we think we’re saying. I have worked with many residents at Johns Hopkins and have listened to the type of advice they give. They believe they’re giving smoking cessation advice, but what they’re giving are generic messages, like on the cigarette packet. ‘You realise smoking is very bad for you.’ ‘You realise that smoking causes cancer.’ ‘You realise...’ People are innundated with these generic messages.

I don’t think there are smokers out there that don’t know in some amorphous way that smoking is bad for them. They do not need to hear their physician reiterate the generic message. The role of the physician is to make it personal and direct. When a physician takes the time to connect with a patient and say ‘You are at risk, I am concerned about you, ’ patients don’t walk out of the office saying my doctor didn’t mention smoking; they do that when the message is broad and based on smoking being bad. ‘Of course it’s bad, everyone knows that, but I’m not at risk. I’m not in danger. ’ So I would suggest if you’re working with physicians, training them how to deliver the message, be very clear on what it is they should say because they may not be saying anything very effective.

ROSELYN P EPPS: That is a part of the training programme, to personalise the message and not just say people shouldn’t smoke but give the reasons why the individual who’s visiting the physician shouldn’t smoke.

JOHN SLADE: I’d just like to point out the progress that’s being made, especially in Canada, with making warning labels very specific and detailed, with a brief message covering 25% of the pack, some smoke content information on the side, and then the opportunity to get a pamphlet that provides large amounts of information and potential opportunities for public health messages.

View Abstract

## Footnotes

• Moderator: John M Pinney

• Panellists: Roselyn P Epps, Jack Hollis, Marc Manley, Deborah J Ossip-Klein, Nancy A Rigotti

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Tags: ruby web rails rce

Rating:

## Crazy Train - Web 250:

**Description:** N/A
**Challenge:** fun.ritsec.club:3000
**Difficulty:** Easy
**Solved by:** Tahar Amine ELHOUARI

**Solution:**
We are presented with a web application that is based on **Ruby on Rails**, it is all about posting and submiting articles to the App!!
When we try to submit an article, we are given two inputs to write in. The team took too much time, until I released that there is a hidden third input in the page. I have seen too many people (Probably Indians) trying to XSS the App, but I know that most of CTF contests doesn't have XSS in web challenges! It is a useless vulnerability in most of CTFs. So, I thought it is probably a command injection or probably an RCE. A friend from another team hinted me and told me that you are close, but there is a hidden input so I started trying with Command Injection but I did not succeed!

Later, I started trying to exploit an RCE **Remote Code Execution**, It didn't work but the friend told me I am close! I remembered something, that this is a **Ruby on Rails** Challenge and not a PHP Web App Challenge, so I started thinking that exploitation payloade must be different because it is different language and different syntax! I started googling as usual and looking for guides about Web Application Hacking/Security in Web Apps that are based on Ruby on Rails, and I think that is the reason of the name of that challenge being named **Crazy Train**, because it is Crazy and Train refer to the Rails.
After, googling I get to know how to exploita an RCE vulnerability and I succeeded using the following payload: **cat flag.txt**

Note: I couldn't write the right payload of MD of github! Use **ALT GR + Number 7** in your keyboard to get the characters that I have used before & after **cat flag.txt**
It is something like this ' cat flag.txt ' I hope you got my point!!

**Flag:**


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# How can you have a negative voltage?

How can you have a negative voltage? I don't really understand the concept of negative voltage, how can it exist?

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If I define positive to be in one direction, then if it is in the opposite direction, what should I call it? –  Steeven 23 hours ago

Voltage is a difference of potential energy for electric charges, and potentials are defined from forces, so that $F=-\nabla V$, where $V$ is the potential and $F$ is the force. When you have determined the potential $V$ you can now add any constant you want, or any function $f$ that doesn't depend on coordinates, because $-\nabla V=-\nabla (V+f)$, as $f$ doesn't depend on coordinates. This last thing is what's known as setting an origin of potential energy, something you sure have heard about. Well, in that function $f$ where you set your origin for potentials, you can have negative voltages between two points.

Another way to see the voltage is the work you must do per unit charge to move that charge from one point to another, even here, when we're dealing with differences, you can also have negative voltages.

If you're talking about circuits, all of the above applies, you can set a potential difference $V$ by, let's say, a battery, then you can use some device so that the potential energy is even lower than the one set by the - sign of the battery, as you set the potential origin 0 for that battery, then that point will have a negative voltage.

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The simplest thing to do here is remember that only diferences in potential matter, and that means that we can add or subtract a constant from every voltage in a system without changing it's behavior, so we can render any negative number positive to make you feel better or just as easily render all the positive ones negative.

In short, it's just a number and you shouldn't fret about it having a sign.

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You should consider the sign. If $\Delta V = V_B - V_A > 0$, it means the electric potential in B is higher than in A. If it is negative, it is the other way around. That's an important difference, no? –  Dries 19 hours ago

Let's say you want to know the electric potential difference r meters away from an electron sitting in a void of space.

The electric potential difference describes the difference in potential energy of a unit positive charge from one point in space to another and the work done on a unit positive charge to carry it from the same point to the other.

This gives the equation $V_a-V_b=(k Q/r_a)-(k Q/r_b)$, where Va is the final potential and Vb is the initial. In this scenario, it is conventional to make $V_b$ the zero reference point at $r$ equals infinity, which makes $r_b$ equal infinity and $V_b$ equal zero. Therefore, the equation becomes $V_a=kQ/r_a$.

Because we are looking at the potential difference of an electron, Q equals negative e, where e equals the elementary charge. So, the equation, in this case, is $V=k(-e/r)$, which gives a negative value.

We see here that no matter how far away the positive test charge is from the electron, the electric potential difference will always be negative. This makes sense because a positive point charge at $r = \infty$ loses potential energy as it is brought toward the electron (downstream), and negative work is done.

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Hi Bionic Person and welcome to Physics.SE! Please see this help post to learn how to write your equations in a way nicer way i.e. in $\LaTeX$, in order to improve legibility. Thanks! –  gonenc 21 hours ago


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# Tag Info

1

See George Tourlakis, Mathematical Logic (2008), page 93 : 3.2.1 Metatheorem (Post's Tautology Theorem) : If $\Gamma \vDash_{TAUT} A$, then $\Gamma \vdash A$. Proof. It is most convenient to prove the contrapositive, namely, if $\Gamma \nvdash A$, , then $\Gamma \nvDash_{TAUT} A$ Some facts are needed : Claim One. There is an enumeration ...

2

There's no need to use distribution since $p \lor(\lnot q \lor r) \equiv p \lor \lnot q \lor r$ due to associativity of $\lor$, and by commutativity of $\lor$, that gives us $$\lnot q \lor p \lor r \equiv \lnot q \lor (p \lor r) \equiv q\rightarrow (p \lor r)$$ What is highly questionable in your proof is the second line of the following: $(q → p) ∨ (p∨r)$ ...

0

For Theorem L10: Suppose $( \sim B \implies \sim A)$ holds. We want to show $(A \implies B)$ is true. Since $\sim B \implies \sim A$ is true, then its negation, $\sim B \wedge A$, is false. But then, the negation of this statement, which is $B \vee \sim A$, is true. But $B \vee \sim A$ is equivalent to $\sim (\sim (B \vee \sim A)) \equiv \text{ }\sim ... 0 This is an application of the compactness theorem. If the theory $$\{\neg \varphi_i | i \in \mathbb{N} \}$$ is satisfied (has valuations for every finite subset) then it has a valuation for the entire set. This is the contrapositive of what you want to show. 0 No. I'll define "equivalence" as meaning that two propositions have the same truth-value. ↔ is defined by this table where$F$indicates falsity,$T$indicates truth, and$U$indicates that the truth-value of a proposition takes on some other value than truth or falsity: ↔ F U T F T U F U U U U T F U T If$P$has truth value of$U$, and so ... 0 Yes; this can be proved using the deduction theorem. TFAE.$(P \vdash Q) \wedge (Q \vdash P)(\vdash P \rightarrow Q) \wedge (\vdash Q \rightarrow P)\vdash (P \rightarrow Q) \wedge (Q \rightarrow P)\vdash (P \leftrightarrow Q)$3 Yes, that looks exactly right. 0 Now, you changed the question, first question is false yet because perhaps for each valuation$v$only$v(\varphi_{n+1})=1$. But if you define$\Sigma=\{\varphi_1,\ldots,\varphi_n\}$your proposition would be true. Even you defined$\Sigma=\{\varphi_1,\ldots,\varphi_n\}$(and you must do it because$\varphi_1\vee\varphi_2\vee\ldots$is meaningless) your ... -1 I'll put up a resolution proof here. It probably doesn't help. assumption 1 ANac assumption 2 ANbc assumption 3 Aab R 1, 3 4 Abc R 2, 4 5 c -1 I'll add my own loose answer here, and point out that we don't know exactly what your negation rule says. The only rule I will use is a resolution rule of inference R which can get described by saying "given two formulas$\phi$and$\psi$which only contain disjunction symbols and literals, if there exists a literal$\alpha$in$\phi$such that it is the ... 0 Note that, up to step 9 in your proof, you have not yet used the 3rd premise :$h \land \lnot (s \lor c) \Rightarrow p$, and we need it to complete the proof. We will start from step 9.$10 − \lnot c \lor \lnot n$by De Morgan from 7 :$\lnot (c \land n)11 - \lnot c$by disjunctive syllogism from 10 and 5 [Note : disjunctive syllogism is a ... 0 "We know that: ((A∧B≡A≡B)≡(A∨B)) is true since it is an axiom(golden rule). But does this mean ((A∨B)≡(A∧B≡A≡B)) is a valid as a corollary since it is equivalent?" Yes. A quick way to verify this comes as to look at the truth table for ≡. ≡ False True False True False True False True Now suppose that (p≡q) is true and "p" is true also. ... 0$ 1- c \wedge n \Rightarrow t$$$\equiv \sim (c \wedge n) \vee t \equiv \sim c \vee \sim n \vee t \equiv n \wedge \sim t \Rightarrow \sim c$$$2- h \wedge \sim s3- h \wedge \sim(s\wedge c) \Rightarrow p $$\equiv h \wedge (\sim s\vee \sim c) \Rightarrow p \equiv (h \wedge \sim s) \vee (h \wedge \sim c) \Rightarrow p \equiv \sim(h \wedge \sim s) ... 2 The so-called Golden Rule is "typical" of Equational Logic; thus I'll assume that your question must be "interpreted" in this context. I'll refer to the textbook by George Tourlakis, Mathematical Logic (2008), which is devoted to the exposition of mathematical logic according to the "equational" style. The axioms of the system are listed at page 42-43, and ... 4 The argument is not valid. One way to see why it is not valid, for example, is suppose p = F, s = T,\;t = T,\; q = F. Then we would have true premises, with a false conclusion. Hence the argument cannot be valid. What we can validly conclude, given the premises p\rightarrow q and s\rightarrow t, is that (p \lor s) \rightarrow (q\lor t). Also, ... 3 I will show that 1 is true and therefore 2 is false. Note that since \Sigma=\{p_2\to p_1, p_3\to p_2,\, \dots\,\}, we have that \Sigma\equiv\{\neg p_1\to \neg p_2, \neg p_2\to \neg p_3,\, \dots\,\}. In particular, we have \Sigma \equiv \bigcup_{1 \leq n<\omega}\{\neg p_n \to \neg p_{n+1}\}. (1) Claim: for all n<\omega such that \Sigma \cup ... 2 Both of them are false, this is due to exact definition: 1.for a formula \psi we say \vDash\psi if for all valuations w, w(\psi)=1 not for just a valuation v. 2.We say a set is consistent if we could find a valuation v such that for all formula \psi in it v(\psi)=1. But as you said formula \varphi_1 could be a contradiction. 4 This is a logic "confused" problem ... We approach it "by steps". Question 1 We assume that the meaning of the first part of the question is : for a valuation v there is some n for which : v(\varphi_n)=1. Is so, due to the fact that : v(\varphi_1 \lor \ldots \lor \varphi_n) = max_i \{ v(\varphi_i) \}, we have that for the valuation v : ... 0 The convention in play is that in the main part of the table (after recording the truth-values of atoms -- if we bother to that again, since that's just copying across the values assigned at the beginning of the line) we write the truth-value under the main connective of the (sub)formula we are evaluating at that step. So it is indeed wffs that are being ... 2 Presumably one is only interested in 1s in the output. There are 8 where p_4 is true. Or else we want the antecedent of p_4 false, forcing p_3 false, and p_1\longrightarrow p_2 true. The count of cases where p_1\longrightarrow p_2 is true, and the rest false is easy. One uses a similar analysis in producing a "quick" disjunctive normal ... 1 Both are correct given that you have "0" as allowable in expressions since (p→0) is logically equivalent to ¬p. ¬φ is logically equivalent to (p→(q→r)). ¬(p∧q→r) is logically equivalent to ¬(¬(p→¬q)→r) which is logically equivalent ¬(¬(p→(q→0))→r) which is logically equivalent to ¬(((p→(q→0))→0)→r) which is logically equivalent to ... 0 In general$$A \rightarrow B = \lnot A \lor B$$Also, notice that$$\lnot(\lnot A \lor B) = A \land \lnot B ~\text{(De Morgan theorem)}$$In your case, you have:$$\varphi = \lnot((p \land q) \rightarrow r) = p \land q \land \lnot r $$and$$\lnot\varphi = (p \land q) \rightarrow r = \lnot p \lor \lnot q \lor r ~\text{(De Morgan theorem)}$$In the ... 5$$\begin{align}\lnot \varphi & \equiv \lnot \Big(\lnot((p\land q)\rightarrow r)\Big) \\ & \equiv (p \land q)\rightarrow r\\ & \equiv p\rightarrow(q\rightarrow r) \end{align}$$0 Hint:$$x\lor y \equiv \lnot x\to y \\ x\land y \equiv \lnot(\lnot x \lor \lnot y) $$0 I'd say this proof is more easily understood if you generalize it by replacing \bot with an arbitrary proposition C:$$\left((A\Rightarrow C)\land (B\Rightarrow C)\right)\Rightarrow \left((A\lor B)\Rightarrow C\right)$$But this is just the elimination rule for \lor in disguise in natural deduction:$$\underline{\Gamma\vdash A\lor B \quad ... 0 You can prove it in Sequent Calculus as described in the pdf mentioned in the comments (http://zll22.user.srcf.net/talks/2011-12-01-CategoricalLogic.pdf ) 1 A |- A Identity 2 B |- B Identity 3 C |- C ... 1(p\to q) \wedge (q\to b)$implies$p\to b$, but not the other way around. Hence those two justifications are false as written. Fortunately, you only need them in one direction, the one that is true. 1 I'll give you a hint. Recall that for$f : A\rightarrow B$$f^{-1}(C) = \{x\in A : f(x)\in C\}$$ Therefore \begin{align}x\in f^{-1}(B\setminus Y)&\Leftrightarrow x\in A\ \text{and}\ f(x)\in B\setminus Y \\ &\Leftrightarrow x\in A\ \text{and}\ f(x)\in B\ \text{and}\ f(x)\not\in Y \end{align} From here, there are just two small steps left: can ... 0 Hint 1:B\setminus Y = B \cap Y^c. Hint 2: \begin{align*} f^{-1}(B\setminus Y) &= f^{-1}(B\cap Y^c)\\ &= \{a \in A : f(a) \in B \cap Y^c)\} \\ &= \{a \in A : f(a) \in B \text{ and } f(a) \notin Y\} \end{align*} Hint 3: To show that the two sets are equal, you must takea \in f^{-1}(B\setminus Y)$and show it is in$f^{-1}(B)\setminus ...

1

Whenever you want to show that two sets are equal, try element chasing. That means, assume your element is in the set on the left, $f^{-1}(B \setminus Y)$, and then show that it must be in the set on the right, $f^{-1}(B) \setminus f^{-1}(Y)$. That's half of the proof. Chase an element in the other direction, and you've done both halves. First assume $x\in ... 2$\Rightarrow:\;\;(1)$Distribute.$\;\;(2) A\lor A \equiv A\land A \equiv A$. (Simplification.)$\;\;(3)\land$-Elimination. $$A\lor (A\land B) \overset{(1)}{\iff} (A \lor A)\land (A\lor B) \overset{(2)}\iff A \land (A\lor B) \overset{(3)}\implies A$$$\Leftarrow:\;\;We use disjunction-Introduction. $$A \implies A\lor (\text{anything}.)\;\;\text{So,}\; ... 1 For some general remarks on how to prove that sets of connectives are/are not complete, see How to prove that a set of logical connectives is functionally complete(incomplete)? In this particular case, it is fairly easy to figure out how to build \vee and \neg out of \{\,\top,\bot\}, once you see that \(p,q,r) equals q if p is true and r ... 4 I think you are looking for an example of statements here. That is \phi, \psi, \chi s.t. these properties hold. Let L=\{\cdot\}. Let T=\text{group axioms}\cup \text{there are only twelve distinct elements}. Now Let \phi say that "I'm is abelian and I'm not is not cyclic" (i.e. \forall a,b, a\cdot b = b\cdot a and a fairly long sentence that says ... 1 If ¬ (ψ → ϕ), then ψ, and ¬ϕ. If ¬ (χ → ϕ), then χ, and ¬ϕ. If ψ, and χ, then (ψ ∧ χ). If (ψ ∧ χ), and ¬ϕ, then ¬[(ψ ∧ χ)→ϕ]. If [ϕ ⟷ (ψ ∧ χ)], then [(ψ ∧ χ)→ϕ]. Thus, ϕ ⟷ (ψ ∧ χ), ¬ (ψ → ϕ), and ¬ (χ → ϕ) do not simultaneously hold true. 1 We have that : \lnot (ψ \rightarrow ϕ) is equivalent to : \lnot (\lnot ψ \lor ϕ) i.e. to : ψ \land \lnot ϕ. And \lnot (χ \rightarrow ϕ) is equivalent to : χ \land \lnot ϕ. Thus, there is no way to satisfy both formuale together with : ϕ \leftrightarrow (ψ \land χ). Comment The "problem" in your argument is the ... 2 As mentioned in the comment, the translation here is indeed crucial. The use of 'but' does not seem to fit in there (but I have to say that I'm also not a native English speaker). In any case, spoken languages can hardly cover the subtleties of logic (except for Lojban...). There are several interpretations or conventions for natural languages that are not ... 1 After chugging away on this for a while, I do think that the difficulty comes in keeping any “in-scope assumptions” available in each of the cases. The proof I outlined in the question does this by making the codomain of the coproduct arrow an exponential. That is, in trying to show C from the assumptions A \lor B, A \lif C, and B \lif C, I ended ... 3 \;\lnot (r \land t)\lor u,\; (premise) \;r\land t,\; (premise) \lnot \lnot (r \land t) from (2),\; (double negation) \therefore \;u\; (disjunctive syllogism) 1 It is all done with sentences and connectives: A sentence is usually denoted by Capital letters like A,B, etc., the connectives are or:= \lor; and:=\land, and if-then:= \rightarrow, and negation connective is \lnot so that, e.g., If I go, then I will see a movie is transcribed as : say A is " If I go" , and B is , "I will see a movie" is ... 1 Using OTTER [1], I've found a 7 step, level 4 proof. axiom 4 CxCyx level 0 axiom 5 CCxyCCyzCxz 0 axiom 6 CCCxyxx 0 D4.4 8 CxCyCzy 1 S5.5 9 CCxyCCCxzuCCyzu 1 D5.8 31 CCCxCyxzCuz 2 D9.6 ... 0 Combining the subformula strategy, weighting of the axioms, the assumptions, and the goal, and a (partial) level saturation search, I've found a 20 step (excluding the axioms and assumptions), level 6 proof using OTTER [1] (OTTER treats "p" and "q" here as nullary functions or in other words, constants). axiom 4 CxCyx. level 0 ... 0 Yes, all of those systems have single axioms. Rezus's paper On a Theorem of Tarski makes this clear. 1 Combining the subformula strategy, weighting of the axioms and the goal, and a (partial) level saturation search, I've found a 15 step (excluding the axioms), level 5 proof using OTTER [1]. Actually, instead of proving CCCp0Cq0CCCp0qp. OTTER proved the more general CCCpqCr0CCCpqrp. (we can substitute q/0, r/q in CCCpqCr0CCCpqrp to get CCCp0Cq0CCCp0qp, ... 3 Let's assume the following axiom: Negatives Reverse Inequalities: If x < y and z < 0, then xz > yz. Now suppose that a < b < 0. Then since a < b and a < 0, it follows from the above axiom that a^2 > ab. Likewise, since a < b and b < 0, it follows from the above axiom that ab > b^2. Combining ... 3 We have$$\begin{align} \neg(a < b < 0) &\iff \neg(\,(a < b) \,\&\, (b < 0)\,) \\&\iff (\,\neg(a < b)\,) \vee (\,\neg(b < 0)\,) \\&\iff (a \geq b) \vee (b \geq 0) \,\,. \end{align}\$

Top 50 recent answers are included


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# Homework Help: Integral equation

1. Jan 6, 2010

### sara_87

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

solve the following integral equation

$$y(x)=sin(x)+\int_0^\pi sin(x-t)y(t)dt$$

2. Relevant equations

3. The attempt at a solution
If the limits of integration were from 0 to x then i could solve this using Laplace transfroms because the definition of the convolution is:
integral g(x-t)y(t) where the limits are from 0 to x.
But here, we have the limits from 0 to pi.
Does anyone have any ideas.
Thank you

2. Jan 6, 2010

### Dick

How about if you differentiate with respect to x twice. What happens if you add that to the original equation?

3. Jan 6, 2010

### sara_87

after I differentiate once, I get:

$$y'(x)=cos(x)(1+\int^\pi_0 (cos(t)-sin(t))y(t)dt)$$

differenitiating agin gives

$$y''(x)=-sin(x)(1+\int^\pi_0(cos(t)-sin(t))y(t)dt)$$

$$y''+y=\int^\pi_0 (sin(x)-cos(x))sin(t)y(t)dt$$

is that right?
What shall i do now?

4. Jan 6, 2010

### hisham.i

$$y(x)=sin(x)+\int_0^\pi sin(x-t)y(t)dt$$
let's try to solve this integral by integration by parts twice:
take,
$$\int_0^pi \sin(x-t)y(t)dt$$
let u=y(t) then du=y(t)dt
dv=sin(x-t)dt then v=cos(x-t)
apply $$u*v -\int vdu$$
we will obtain two factors $$A+\int cos(x-t)y(t)dt$$
another time integrate the second integral by parts we will obtain the same integral as above we will get 2*the first integral and solve for it!

5. Jan 6, 2010

### hisham.i

the first integral i wrote above i mean pi and not from 0--->p, writing mistake!

6. Jan 6, 2010

### sara_87

I think you made a mistake,

if u=y(t) then u'=y'(t) because we are integrating with respect to t.
so in the intgrand we will have y'(t) and if we integrate by parts again, we will have y''(t) in the integrand.

7. Jan 6, 2010

### hisham.i

yes you'r right i have made a mistake.
take u=y(t) du=y'(t)dt
dv=sin(x-t)dt v=-cos(x-t)
then after calculating it, calculate the second integral by the same method but take
u=cos(x-t) du=sin(x-t)dt
dv=y'(t)dt v=y(t)

8. Jan 6, 2010

### sara_87

I dont think this is the right approach. after the integration by parts, we get that the integral =0 leaving us with
y(x) = sin(x)

is this right?

9. Jan 6, 2010

### Dick

I get that y''(x)=(-sin(x))+integral(-sin(x-t)*y(t)). So y(x)+y''(x)=0. I don't see how you are factoring a cos(x) out of that first derivative.

10. Jan 6, 2010

### vela

Staff Emeritus
How did you pull the cos(x) out of the integral? You just want to differentiate sin(x-t) wrt x and leave it all inside the integral, i.e.

$$\int sin(x-t)y(t)dt \Rightarrow \int cos(x-t)y(t)dt$$

11. Jan 6, 2010

### sara_87

thank you both for pointing out my mistake.
after differentiating twice and adding y and y'' I get
y''(x)+y(x)=0
so the solution is
y(x)=Acos(x)+Bsin(x)

to find A and B I need initial conditions.
How can I get the initial conditions?

12. Jan 6, 2010

### Dick

Plug your y(x) into the integral equation. Now you can explicitly do the integral. If you move all of the terms to one side you will get something like c*sin(x)+d*cos(x)=0 (where c and d are linear functions of A and B). Now what?

13. Jan 6, 2010

### sara_87

thanks,
i did this just now and got that:

c=A-1-pi*B/2
d=B+pi*A/2

A=4/(4+pi^2)
and
B=-2Pi/(4+pi^2)

is this right?

14. Jan 6, 2010

### Dick

Right. You set c=d=0. Those look like the same values I got for A and B.

15. Jan 6, 2010

### sara_87

wohoo, thanks.
Im doing another question and it is the same as this one but instead of sin(x-t)y(t) in the integrand, i have (x-t)y(t) in the integrand.
Do I also differentiate twice?

16. Jan 6, 2010

### Dick

It's certainly worth a try. What do you think will happen?

17. Jan 6, 2010

### hisham.i

Why integration by parts is wrong in such a case?

18. Jan 6, 2010

### sara_87

we have

$$y(x)=1+\int_0^1 (x-t)y(t)dt$$

$$y'(x) = \int_0^1 y(t)dt$$

y''=0

19. Jan 6, 2010

### Dick

Well, you don't need to. y''=0 is already an ODE you can easily solve.

20. Jan 6, 2010

### Dick

For one thing, you did it wrong. If u=y then du=y'(x)dx. Now there's a y'(x) in your integral. The next time you integrate by parts you get y''(x). You aren't going to get back where you started. You are just making things more complicated.

21. Jan 6, 2010

### sara_87

when I solve y''=0 and then substitute it into the original equation I get:

x(A*1/2+B)+(A*1/3+B*3/2-1)=0

how will this help to find A and B?

22. Jan 6, 2010

### Dick

The same as the other one. If c*x+d=0 for all x, then c=0 and d=0.

23. Jan 6, 2010

### sara_87

wohoo, thank you very much.
I get A=-12/5 and B=6/5

just one final question,
If now instead of (x-t)y(t) in the integrand, I have ln(x/t)y(t), do i still use differentiation?

I would then get:

$$y'(x)=\frac{1}{x}\int_0^1 y(t)dt$$
$$y''(x)=\frac{-1}{x^2}\int_0^1 y(t)dt$$

24. Jan 6, 2010

### Dick

Step back and think about it. The whole game here is to eliminate the integral so you just have an ODE in y(x) left. Can you think of a way to use those two equations to eliminate the integral? I'll bet you can.

25. Jan 6, 2010

### sara_87

ya, I can

I get:
y'' + 1/x y'=0
solving gives:
y(x) = Aln(x)+B
is this right?
then i do the same as before to find A and B, right?


text:
# Bromination

## Recommended Posts

I want to synthesize methyl 3,5-dibromobenzoate (3,5-dibromobenzoic acid methyl ester).

This can be synthesized from the corresponding benzoic acid, ester, or aldehyde, which are all meta- directing. However, they strongly deactivate the benzene ring and make bromination difficult. Even if the first bromination is achievable, i cannot find any papers on how to do the second one.

Is there an easier synthetic route? I am struggling in finding any papers for reference.

I am very new to Organic Chemistry and although it seems like an easy target I still find it extremely difficult.

## Create an account

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# An open container holds ice of mass 0.500 kg at a temperature of -10.8 ° C....

###### Question:

An open container holds ice of mass 0.500 kg at a temperature of -10.8 ° C. The mass of the container can be ignored. Heat is supplied to the container at the constant rate of 800 J/minute The specific heat of ice to is 2100 J/kg K and the heat of fusion for ice is 334 x 103 J/kg.
How much time tmelts passes before the ice starts to melt?

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typodupeerror

## Comment: Re:My doubts about VR (Score 1)49

by vertinox (#46414955) Attached to: Valve Prepping Source 2 Engine For VR

One a side note. If your significant other doesn't allow you 30 minutes of me time uninterrupted then you are going to have a rocky relationship.

When my special something is reading a book. I leave her alone unless its an emergency. (Also she has a bad habit of watching TV shows ahead of me on hulu so if I bother her she will start saying spoilers).

When I'm on the computer she does the same.

I just make sure at a certain time I turn the computer off and spend some time with her before we go to bed.

We generally watch the Daily Show and Colbert Report and then head to bed.

## Comment: Re:My doubts about VR (Score 1)49

by vertinox (#46414881) Attached to: Valve Prepping Source 2 Engine For VR

Actually... I have an Oculus Rift and have to say I don't use it more than 30 minutes to an hour at a time.

Mostly because a lack of a killer app at this point (Skyrim with special drivers comes close, but I think Star Citizen will be the app everyone has to get VR because its amazing just sitting in the hanger looking at the 3d screens sitting in your ship's hanger that pop out at you).

Anyways... If you can't find 30 minutes to an hour a day to enjoy some me time then I would argue that there is something wrong with your life.

I don't have kids personally but I have dealt with families that do and basically unless you go to bed when the kid does, you should have at least 30 minutes to enjoy the experience.

Basically I spend 30 minutes alone playing games. Then maybe an hour watching TV with the significant other and then to bed to get 8 hours of sleep.

If not, then I would argue, you are going to have stress management issues in your life and no one wants that.

So yeah... The Oculus Rift is amazing. Most of the demos are short games so I haven't spent six hour with it in a sitting, but demos like Titans of Space really take my breath away.

Also the rollercoaster demo made me go "Oh shit!" out loud. Only happened once since successive rides had me knowing I would be ok, but no non-Oculus Rift game has ever made me fear for my safety.

Its something that even non-video game players can get a kick of it.

Anyways, I own one and its amazing. The only problem with it is that I'm going to have to buy an expensive computer to play the 1080p and the lack of games for it right now.

Once both of those issues are resolved. I think we are seeing a revolution.

## Comment: Re:"Unfair"? (Score 1)362

by lachlan76 (#46383601) Attached to: Google Funds San Francisco Bus Rides For Poor
The problem as I understand it is that when prices go up, so do property taxes, and that people on low incomes get forced out of the area.

## Comment: Re:Only smells funny? (Score 1)84

by lachlan76 (#45314759) Attached to: A MathML Progress Report: More Light Than Shadow

Things are changing a little bit. Elsevier offer HTML+MathJax at least for the journals that I've used. MathJax (a JS library) makes things quite a bit easier in that you can use LaTeX and have it automatically rendered to MathML, picking up \begin{align}\end{align}s and such in your HTML.

## Comment: Re:can "do quantum mechanics" at school (Score 1)71

by lachlan76 (#45178089) Attached to: Google Sparking Interest To Quantum Mechanics With Minecraft

One runs the experiment in the dark with a photographic film or movable photomultiplier behind the slits, allowing the observation of single photons. The density of the photons exhibits an interference pattern.

I've not done this experiment myself, but remember being told that it was possible using film during high school.

## Comment: Re:Steam Family Sharing (Score 1)317

by lachlan76 (#44977301) Attached to: Valve Announces Steam Controller
It doesn't work, because you can only share the library in its entirety. It therefore makes no difference if you would otherwise share passwords.

## Comment: Re:Uses of tantalum? (Score 1)136

by lachlan76 (#44908591) Attached to: Conflict Minerals and Cell Phones
The main problem with tantalum capacitors is that they tend to be low-voltage and will catch fire if you put a reverse voltage on them.

## Comment: Re:The obvious reasons... (Score 1)302

by lachlan76 (#44660817) Attached to: Obama Seeks New System For Rating Colleges

As far as I know, most Commonwealth countries will run their universities that way. If you spend time on other things, you get a separate degree. I studied EEE and pure maths, which turned it into a five-year degree as in the US. I was originally unsure as to whether you meant that or that the education was more practical than theoretical.

The need for residential accommodation in the US is always going to be there because of the population distribution. Things are a bit different here in that most of the population live in the capital cities; I've only known one person who has done an undergraduate degree outside of Adelaide.

## Comment: Re:The obvious reasons... (Score 2)302

by lachlan76 (#44653113) Attached to: Obama Seeks New System For Rating Colleges

A degree here is nominally three years, but honours requires an extra year and a substantial project, which most people take up (this might not be the case outside of maths). Engineering is always four years; essentially one has to do the same work whether or not they receive honours.

I can't speak for the trade-oriented claim, as I study in a research-heavy university. However, one isn't forced to take courses unrelated to their degree as in the US, which might be what you allude to. There isn't anything stopping you from spending an extra year to get a second degree mixed in, though.

Personally, I like the fact that our system is more egalitarian---unless one chooses to move interstate and so cannot live at home, cost is not a factor. The reality is that everyone puts the top universities in their state first, so the better universities can pick off the top students. But then again, in the US those at the very top will end up in a big university with large amounts of funding, so one might argue either way.

Fools ignore complexity. Pragmatists suffer it. Some can avoid it. Geniuses remove it. -- Perlis's Programming Proverb #58, SIGPLAN Notices, Sept. 1982

Working...


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# SICP Solutions

### Chapter 4, Metalinguistic Abstraction

#### Exercise 4.3

Since it was becoming difficult to verify programs because the whole evaluator is not yet built in the book, i went ahead and read till section 4.1.4.

Now, after reading that, now we can use the evaluator presented in the book whose complete code can be found here.

Note: We should not re-load the same code again while using repl. Else our evaluator code can get in conflict with the implementation language, in particular the apply procedure!

If one wants to reload, then repl should be reset/restarted. In MIT scheme, this can be done using (ge (make-top-level-environment)). I put this line at the top of the evaluator code thus need not to remember resetting, every time when I reload.

I have added a small check for exiting from the evaluator by typing exit on the evaluator prompt.

#### Solution

Note the use of apply-in-underlying-scheme while invoking exp-handler inside eval. We should not use apply here because we have changed the definition of apply.

But why we used apply in the application? part in eval? Because at that point we are here invoking the procedure defined in our defined language!

Finally consider the use of data-driven style which was the main point of the exercise. The advantage here we can see is when we add a new expression-type we need not to go to the main code i.e. a separate developer using our evaluator can add a new expression type easily without touching our evaluator.

Also, it would have been better if application? part can also become part of this data-driven style using the strategey used in previous exercise.

I tested this on the example given in section 4.1.4:

#### Complete working code

The code can be downloaded from mit. Still I am presenting the complete code here with the changes corresponding to this exercise as well as to reset the repl:


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Q. 6.17

Not all fully differential circuits are free from mirror poles. Figure 6.42(a) illustrates an example where current mirrors $M_3–M_5 and M_4–M_6$ “fold” the signal current. Estimate the low-frequency gain and the transfer function of this circuit.

Verified Solution

Neglecting channel-length modulation and using the differential half circuit shown in Fig. 6.42(b), we observe that $M_5$ multiplies the drain current of $M_3$ by K, yielding an overall low-frequency voltage gain $A_v = g_{m1}K R_D.$
To obtain the transfer function, we utilize the equivalent circuit depicted in Fig. 6.42(c), including a source resistance $R_S$ for completeness. To simplify calculations, we assume that $R_DC_L$ is relatively small so that the Miller multiplication of $C_{G D5}$ can be approximated as $C_{G D5}(1 + g_{m5}R_D)$. The circuit thus reduces to that in Fig. 6.42(d), where $C_X ≈ C_{GS3} + C_{GS5} + C_{DB3} + C_{G D5}(1 + g_{m5}R_D) + C_{DB1}$. The overall transfer function is then equal to $V_X /V_{in1}$ multiplied by $V_{out1}/V_X$ . The former is readily obtained from (6.30) by replacing $R_D with 1/g_{m3} and C_{DB} with C_X$ , while the latter is

$\frac{V_{out}}{V_{in}}(s) = \frac{(C_{G D}s − g_m)R_D}{R_S R_Dξ s^2 + [R_S(1 + g_m R_D)C_{G D} + R_SC_{GS} + R_D(C_{G D} + C_{DB})]s + 1}$                            (6.30)

$\frac{V_{out1}}{V_X}(s) = −g_{m5}R_D\frac{1}{1 + R_DC_L s}$                                                                 (6.97)

Note that we have neglected the zero due to $C_{G D5}.$


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Browse Questions

# To what series does the spectral lines of atomic hydrogen belong if its wave number is equal to the difference between the wave numbers of the following two lines of the Balmer series 486.1 and 410.2 nm?

$(a)\;2^{nd} to 3^{rd} level\qquad(b)\;4^{th} to 2^{nd} level\qquad(c)\;5^{th} to 1^{st} level\qquad(d)\;6^{th} to 4^{th} level$

Given
$\lambda_1 = 486.1\times10^{-9}$m = 486.1$\times10^{-7}$ cm
$\lambda_2 = 410.2\times10^{-9}$m = 410.2$\times10^{-7}$ cm
$\overline V = \overline V_2 - \overline V_1$ = $\large\frac{1}{\lambda_2}$ - $\large\frac{1}{\lambda_1}$
$=R_H[\large\frac{1}{2^2}$ -$\large\frac{1}{n_2^2}-R_H[\large\frac{1}{2^2} -\large\frac{1}{n_1^2}]$
$\overline V = R_H[\large\frac{1}{n_1^2} -\large\frac{1}{n_2^2}]$
For I case of Balmer Series :
$\large\frac{1}{\lambda_1}= R_H[\large\frac{1}{2^2} -\large\frac{1}{n_1^2}]$
= 109678 [$\large\frac{1}{2^2} - \large\frac{1}{n_1^2} ]$
Or [$\large\frac{1}{486.1\times10^{-7}}= 109678 [\large\frac{1}{2^2}-\large\frac{1}{n_1^2}]$
For II case of Balmer series:
$\large\frac{1}{\lambda_2}= R_H[\large\frac{1}{2^2} -\large\frac{1}{n_2^2}]$
= 109678 [$\large\frac{1}{2^2} - \large\frac{1}{n_2^2} ]$
Or [$\large\frac{1}{410.2\times10^{-7}}= 109678 [\large\frac{1}{2^2}-\large\frac{1}{n_2^2}]$
$\therefore n_2$ = 6
$\therefore$ given transition occurs from $6^{th}$ level to $4^{th}$ level