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# Redesigning the Annual Conference: Contagion, Carbon, Access, Equity

Spring is a time to look ahead in places like where I live on the East Coast of the United States, as people come out of doors and dormant plants and other creatures inch back into life. This spring of 2020, however, has been one of looming, even paralyzing uncertainty. Between COVID-19, the national political climate, and a host of other existential concerns in the air, who can say what this summer and fall will bring—let alone this spring, as each day brings fresh news of further lockdowns.

There is also that particular form of future-oriented hustling that the season brings for anthropologists in North America, looking ahead to the annual meeting of the American Anthropological Association (AAA). The submission deadline is fast approaching, and plans are coming together fitfully for the meeting this fall in St. Louis, even as we learn of conference after conference canceled this spring, nationally and internationally. Just as I was finishing a draft of this post, in fact, news came of the Association of American Geographers April meeting in Denver: canceled in person, headed online, to whatever extent possible.

Crises bring habits into focus. For a scholarly discipline like ours, the practice of gathering by the thousands somewhere each year is a habit that merits some scrutiny. Sharing work and meeting colleagues and potential collaborators is essential to the development of a field. But is an annual conference that demands physical travel to a single place the most effective and ethical means of meeting these needs? What would it mean to approach this moment not only with precautionary reaction, but also as an occasion for speculative work, a chance to devise the kind of conference we would like to see?

The March 9, 2020, member letter from Akhil Gupta and Ed Liebow, President and Executive Director of the AAA, brought welcome news regarding this fall’s AAA meeting: the promise of registration refunds in full for those who decide not to attend, and plans to allow for virtual attendance and participation: “this year’s extraordinary circumstances will prompt us to consider such possibilities as allowing a mix of live presentations and remote presentations that are pre-recorded on video and presented in St. Louis with tech support in hand.”

This would be an unprecedented move for the AAA, which also has the chance to address, over and above the threat or fear of contagion (Wald 2008), many other reasons why anthropologists have been calling for a redesign of our annual conference: the steep cost of long-distance travel and hotel accommodation, most especially for graduate students and precariously placed academics in the United States and abroad; the massive carbon footprint of the megaconference model; the challenge of crossing international borders in an era of travel bans and xenophobic border politics; the hardships posed to those with physical disabilities; and the challenge for parents and other caregivers juggling professional demands with responsibilities for kin. How do we wrestle as a profession with such problems? What alternative forms of conversation and interaction may we develop instead?

## A Short History of the Annual Meeting

As such concerns accumulate, it is worth pausing to consider how this convention of yearly conferencing took shape. The annual meeting as a scientific practice dates back to the 1820s and the work of the Association of German Natural Scientists and Physicians, from which the British Association for the Advancement of Science (BAAS) borrowed the practice beginning in 1831 (Clark 2006). The BAAS meetings took place in a different provincial town or city each year as a week-long “parliament of science,” catalyzing the development of local scientific societies and public scientific discourse in these localities (Miskell 2012).

Ethnology and anthropology found a place in these BAAS meetings from the mid-nineteenth century onward, as the focus of particular sections of scientific inquiry (Sillitoe 2004). And the scale of these meetings was already international, given the imperial networks that organized scientific expeditions and institutions at the time (Pietsch 2010). The 1924 annual meeting of the British Association for the Advancement of Science was held, for example, in Toronto, where speakers included A. C. Haddon, C. G. Seligman, Margaret Mead, and Edward Sapir; “special features of interest to the members of the Section were a visit to the Royal Ontario Museum, where Mr. Currelly showed them the splendid Chinese collections installed under his care,” Sapir (1924, 565) reported in American Anthropologist.

A total of forty people were invited to the inaugural meeting of the American Anthropological Association in Pittsburgh, in 1902, with 175 members recorded in American Anthropologist by the next year (McGee 1903). “Our membership is still numbered by hundreds when it should be numbered by thousands if the Association is to fulfil the function for which it was founded,” the Secretary of the AAA wrote about a decade later (MacCurdy 1911, 100). It was not until the 1960s that annual meeting attendance would regularly climb to well over a thousand in number. And, as it happened, this development provoked serious misgivings on the part of some senior anthropologists, when students, in particular, began to flood the meetings.

“The highly successful small organism has become a dinosaur, apparently incapable of adapting to any but the original context,” a writer for the AAA Newsletter observed in 1963 (S.T.B. 1963, 1). Various ideas were floated to contain this growth—shifting to regional or subfield meetings, rejecting more paper submissions, even restricting presentations to five-minute summaries—but the organization elected to operate in a more expansive mode (Trencher 2000). Indeed, when a debate erupted as to whether or not to hold the 1970 annual meeting in Honolulu, as originally planned, the Executive Board of the AAA voted to shift the meeting to San Diego to enable wider access to the conference. As AAA President George Foster (1969, 1) wrote,

Traditional anthropological policies and philosophies increasingly are being questioned, especially by our younger colleagues. The charge frequently has been levelled at the Board that to hold the 1970 meetings in Honolulu would prevent large numbers of students and other interested people from attending, regardless of how economical the trip could be made, by means of charter flights and other arrangements. By excluding large numbers of younger people, the Board was told, it was reducing the opportunity for dialogue between older and better established members of the profession, and younger (and less well-heeled) members, at a time when this dialogue had become critical to the well-being of the Association.

It’s worth keeping in mind that problems of access and equity were at the heart of these debates in the 1960s regarding the organization of the annual meeting in American anthropology, and that many of these questions turned at that time, as they still do today, on the costs of participation. In the 1990s, attendance at the annual conference reached the level where it remains to this day, between five and seven thousand people.

Bringing people together at this scale is a remarkable feat of vision and organization, not to mention inclusion. At the same time, however, these meetings have also become one of the most significant carbon burdens that our scholarly societies ask us to bear.

## The Carbon Footprint of a Conference

Looking back in retrospect, what becomes obvious is that the AAA and its meetings exploded in size in the very years that saw precipitous growth in travel of all kinds, the burst of quick, long-distance movement fueled by cheap fossil fuels that climate scholars now associate with the “Great Acceleration” of anthropogenic activity in the postwar era (Steffen, Crutzen, and NcNeill 2007). Gathering for a disciplinary megaconference in North America can produce as many carbon emissions over a few days as a human settlement of similar size may generate over an entire year in many countries of the global South. A carbon footprint analysis of the annual meeting of the Association of American Geographers (AAG) estimated that the aviation-related emissions from the travel of 6,700 attendees to the 2010 AAG meeting in Seattle were equivalent to the annual carbon emissions of over 55,000 people in Bangladesh (Nevins 2014).

This is an instance of “ecological privilege” and profound ecological injustice, the geographer Joseph Nevins (2014) argues, and the #flyingless movement in academia led by Nevins and many others has lately grown into an international movement to redesign the conference form. What would it mean to reduce the carbon footprint of such meetings while also acknowledging the importance of live interaction and face-to-face encounter, as well as the commitments to broader access that propelled and sustained their growth?

“Reshaping the relationship between people and their carbon-intensive lifeways entails a shift in habitus,” the AAA Global Climate Change Task Force noted in 2014, recommending that the AAA “continue aggressively with developments in AAA that reduce the carbon footprint due to association-wide activities.” But our association has yet to tackle this recommendation with requisite heed, and we have seen, thus far, very little from the AAA by way of the alternatives that our peer associations are developing: the Nearly Carbon Neutral stream of panels that the European Association of Social Anthropologists are organizing for their 2020 biennial; the diverse avenues for remote presentation and participation developed for the 2020 Society for Social Studies of Science conference; the plans made by the Annual Meeting Climate Action Task Force of the American Association of Geographers; the plans for “reducing the carbon footprint and expanding remote engagement” now pursued by the American Geophysical Union, among many other such efforts one could cite.

What would we learn if the AAA committed, as an organization, to pursuing a rigorous carbon footprint analysis of the annual meeting, as scholars in the AGU and many other fields have begun to do? And now that the coronavirus may have finally forced our discipline’s hand, with regard to such questions, what kind of alternatives will we find ourselves with?

## Emerging Lines of Possibility

The space of alternative conferencing seems to have a DIY ethos, with many guides and how-tos in wide circulation. In 2018, I worked with a team of nearly two dozen people to design a “distributed” biennial conference for the Society for Cultural Anthropology and the Society for Visual Anthropology, called Displacements. Nearly 150 presenters prerecorded their contributions for circulation through a virtual platform, a Wordpress website. Panels were livestreamed on a twenty-four-hour webcast schedule to facilitate participation by people in diverse time zones, and archived thereafter for on-demand viewing. We relied on chat boxes and social media channels like Twitter and Instagram as platforms for response and discussion.

Many participants gathered in small groups in one of dozens of local nodes in cities and localities scattered around the world, many of which were in Asia, Africa, and Latin America. Others tuned in on their own, sometimes, as they conveyed to us, from the spaces of their own homes, where they juggled conference attendance with the demands of childcare and domestic life. Our access advisor, Tyler Zoanni, helped us pursue access as an “art of conviviality,” one that “requires conscious reflection, creativity, and openness to difference,” a philosophy we sought to fold into the evolving design of the conference.

The alternative platform we developed together transformed the Society for Cultural Anthropology biennial from a regional American conference of about 200 people to an international event that drew more than 1,300 people from forty-five countries around the world, more than half of whom were outside the United States, all at a fraction of the carbon footprint of a conventional conference. The Society for Cultural Anthropology and the Society for Visual Anthropology are partnering once again on a virtual and distributed biennial this spring, called Distribute, scheduled for May 7–9, 2020. This second iteration promises to be more exciting and sophisticated than the first, involving the curation of contributions and conversations from around the world, and the development of many new technical platforms and resources for remote interaction.

How might such efforts look when scaled up to an event like the AAA annual meeting? The organization, understandably, may be concerned about the effect such alternatives might have on physical attendance, conference revenue, and even membership revenue, which often tracks with conference registration deadlines. These concerns seem to have had a hand in the scope of the virtual package that the AAA piloted as an alternative to the physical conference in 2019: a handful of pre-selected panels accessible online for a virtual registration fee of $50–$75. No provisions were made for remote presentation, and only thirty individuals ultimately registered for this experiment.

I was invited to join the task force that developed this pilot project, and I was not the only participant who found frustrating the calculus of cost and return that shaped the choices that were ultimately made. Responses to a survey that the AAA later circulated about this endeavor dwelt overwhelmingly on the cost of the annual meeting and the surprising expense of this alternative. Respondents described themselves as graduate students and adjuncts who could not afford to travel, as older and disabled individuals who could not manage it physically, as recent parents, and as immigrants facing visa restrictions. What would it mean to truly meet their needs for scholarly interchange? Could such alternatives be pursued instead as ways to widen access to the annual meeting, to increase rather than decrease overall registration, attendance, and participation?

Even at the 2019 annual meeting in Vancouver, in fact, this was the experience of those of us who made our own panels accessible remotely. We all know what it’s like to speak avidly into the vacuum of a massive and empty conference hall or hotel ballroom, to share our stories and findings with a handful of individuals scattered among countless rows of vacant chairs. This was certainly the case with a roundtable that I organized for the Society for Cultural Anthropology and the Society for Visual Anthropology, which we called “Reimagining the Annual Meeting for an Era of Radical Climate Change.” We spoke into a cavernous void of physical space. But we also livestreamed the session and made our pre-recorded presentations available online for those who wanted to tune in from a distance. The live video stream via the SCA Facebook page drew over 740 remote viewers, and each of the individual presentations, freely accessible still via culanth.org, has since been viewed, on average, by nearly 110 people on multiple continents.

As it circulated online as a freely available resource, the roundtable even drew the attention of the NPR radio show “The Pulse,” which featured the panel in a January 2020 segment called “What happens when academics fly less to conferences?” The segment featured the presentation made by an undocumented Oregon State University graduate student in anthropology, Argenis Hurtado Moreno, who could not cross the border into Vancouver and could only participate in our roundtable because of its virtual format. The segment also described someone who had tweeted about the roundtable from Karachi—because of its virtual format, it was the first AAA session he had ever attended.

## Prospects for Alternative Design

There are many reasons why the AAA’s promise to expand the format of the annual meeting this year is a welcome one. It matters that “Truth and Responsibility” is the theme of this fall’s meeting, the invitation “to reflect on our responsibility in reckoning with disciplinary histories, harms, and possibilities.” Given this call, and the nature of this moment, there is no better time to confront the problems of the conventional conference model, and to begin to devise equitable and effective alternatives. With this, as with so many things, however, much will turn on the specific form that these alternatives assume.

With the 2018 Displacements conference, for example, we found ways of approximating the charge of live encounter, the sense of a shared experience in time, by using techniques like the livestream webcast, social media threads, and node-based gatherings. At the same time, we also learned that distraction was a serious challenge, most especially for participants tuning in on their own. This challenge brought into focus the conventional form of the conference presentation itself, and the question of whether or not a talking head video recording or even a voiceover slideshow would be an adequate response both to the possibilities and the constraints of the audiovisual medium (Pandian 2018).

Can we imagine the standard fifteen-minute structure of the AAA presentation itself evolving, as the conference opens into virtual and hybrid formats for participation? How do we ensure these novel formats and participation options will meet the expectations set out in the accessibility standards developed by networks like the Disability Research Interest Group?

There is also that other essential side of the conference experience, the chance for face-to-face conversation and socializing with colleagues and friends. This is, of course, precisely the dimension of our collective lives as academics that has become most fraught with the looming threat of a new pandemic. Here again come design questions with regard to the structure of virtual and remote alternatives, questions that we, as students of social life, ought to be better prepared to address than any other academic community.

What would it take, if not to replicate, then at least to learn from and approximate the texture of what happens through one-on-one meetings, informal interaction, and accidental encounters? What virtual spaces of dialogue and exchange, beyond the formal giving and receiving of presentations, might help to facilitate such interaction? And will the cost of accessing such possibilities remotely, through registration fees and other requirements, be set at a level that would enable broader participation by students, adjuncts, field interlocutors, and anthropologists from the global South—that might make possible, in other words, intellectual exchanges that the cost and distance of a physical conference render impossible?

We ought to recall that the modern development of the scientific society as an institution typically included “corresponding members” as essential constituents from afar (Ogilvie 2016); even the AAA has had provisions in past years for lower dues from “Corresponding Members” and “Foreign Fellows.” Could this turn in the structure of the annual meeting be an occasion for us to ask once again what it would mean to belong to, and participate in, the intellectual life of the association from a distance? What could such correspondence look like in the era of streaming video?

## Conferences Past and Future

As the COVID-19 pandemic continues to spread, conferences and other large public gatherings are being cancelled or postponed with a strategy of “social distancing” in mind. There is little choice but to do this now, given the conventional structure of the meetings we have, their wont to jam many people at once into the same confined space. But say we approached this moment as more than a crisis, as a chance as well to imagine what the conference of the future might look and feel like. What formal structure could the event assume, and need we presume that its heart must lie in a single, geographic place?

Back in the 1960s, when the AAA wrestled with the challenge of a ballooning membership, one anthropologist, Richard N. Adams, proposed that the annual meeting could be held each year in multiple places at once, with plenary status rotating between these regional gatherings each year. “With the decentralization of meetings, most business on the national level would be handled by mail,” and this structure, Adams (1964, 1–2) wrote, “would make a major annual meeting accessible to students from each major region on a much more frequent basis.” Although the idea was dismissed at the time as dangerous—“If anthropology is to remain whole and to continue to have a sense of national existence, it requires . . . an ingathering of the clan and a reaffirmation of shared values, interests and purposes” (Goldschmidt 1964, 2)—in retrospect this vision seems astonishingly prescient.

Imagine an annual meeting of American anthropology organized through several or a dozen—or maybe many more—regional nodes around the country, more easily accessible to those nearby, and networked virtually with what is happening everywhere else as well. Imagine the more human and intimate scale at which such regional gatherings might unfold, suitable for the capacities of universities and local public institutions rather than convention centers and corporate hotels alone. Imagine a conference, in each of these places, more invested in public-facing engagement than exclusive lanyards to flash at the door. Here again is a vision of contact with unknown others, yes, but perhaps at a scale more liable to managing its risks and threats.

This is a time of serious challenges for the most basic institutions we rely upon as teachers and scholars. So many of us now have been told by our institutions to shift to online instruction, and we will mourn the loss of that affective charge that surges most powerfully through proximate spaces of telling and listening. But we are still anthropologists, and our learning is made for confounding challenges. It is good to know that so many leaders and staff of the AAA share the conviction now that a serious redesign of the annual conference is necessary. I hope that this and other institutions of anthropology might meet this circumstance with an ethnographic sensibility, taking the time to think and ask and imagine how best to meet the range of needs at stake in this situation.

I can’t help but recall a message that the Métis anthropologist Zoe Todd shared via Twitter in 2018, as we anthropologists descended in droves on smoky San Jose that November:

#AmAnth2018 is taking place in the midst of one of the deadliest fires in California history. If breathing in the smoke of burning trees, homes, cities doesn't convince us that we need radically different ways to engage beyond the conference center model . . . I don’t know what will.

Here we are again, in the midst of another radical, existential challenge. Contagion, carbon, access, equity: what, concretely, will we do?

### Acknowledgments

My gratitude to Anne Allison, Krista Billingsley, Mayanthi Fernando, Hannah Knox, Jessica Lockrem, Andrea Muehlebach, Ben Orlove, Taapsi Ramchandani, Jerome Whitington, and Emily Yates-Doerr for their insights on this writing, and to everyone who has collaborated on the experiments and alternatives sketched above.

## References

Adams, Richard N. 1964. “Some Possible Ways to Kill a Dinosaur Without Actually Extinguishing Him.” Fellow Newsletter, American Anthropological Association 5, no. 4: 1–2.

Clark, William. 2006. Academic Charisma and the Origins of the Research University. Chicago: University of Chicago Press.

Foster, George. 1969. “News of the New Orleans Meeting, Hawaiian Meeting Cancelled.” Newsletter of the American Anthropological Association 10, no. 10: 1.

Goldschmidt, Walter. 1964. “The Future of Annual Meetings.” Fellow Newsletter, American Anthropological Association 5, no. 9: 1–2.

MacCurdy, George Grant. 1911. “Anthropology at the Providence Meeting with Proceedings of the American Anthropological Association for 1910.” American Anthropologist 13, no. 1: 99–120.

McGee, W. J. 1903. “The American Anthropological Association.” American Anthropologist 5, no. 1: 178–190.

Miskell, Louise. 2012. “Meeting Places: The Scientific Congress and the Host Town in the South-West of England, 1836–1877.” Urban History 39, no. 2: 246–62.

Nevins, Joseph. 2014. “Academic Jet-Setting in a Time of Climate Destabilization: Ecological Privilege and Professional Geographic Travel.” Professional Geographer 66, no. 2: 298–310.

Ogilvie, Brian. 2016. “Correspondence Networks.” In A Companion to the History of Science, edited by Bernard Lightman, 358–71. Oxford: Wiley Blackwell.

Pandian, Anand. 2018. “Reflections on #displace18.” Fieldsights, November 9.

Pietsch, Tamson. 2010. “Wandering Scholars? Academic Mobility and the British World, 1850–1940.” Journal of Historical Geography 36, no. 4: 377–87.

S.T.B. 1963. “Wanted: Improvements for a Dinosaur.” Fellow Newsletter, American Anthropological Association 4, no. 9: 1–2.

Sapir, Edward. 1924. “Anthropology at the Toronto Meeting of the British Association for the Advancement of Science, 1924.” American Anthropologist 26, no. 4: 563–65.

Sillitoe, Paul. 2004. “Making Links, Opening Out: Anthropology and the British Association for the Advancement of Science.Anthropology Today 20, no. 6: 10–15.

Steffen, Will, Paul J. Crutzen, and John R. McNeill. 2007. “The Anthropocene: Are Humans Now Overwhelming the Great Forces of Nature?Ambio 36, no. 8: 614–21.

Trencher, Susan R. 2000. Mirrored Images: American Anthropology and American Culture, 1960–1980. Westport, Conn.: Bergin and Garvey.

Wald, Priscilla. 2008. Contagious: Cultures, Carriers, and the Outbreak Narrative. Durham, N.C.: Duke University Press.


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# carbon protons, neutrons electrons

In the simulation, check the boxes “show all charges” and “Wall”. Let's use Boron as an example. All isotopes of an element have the same number of protons and electrons, which means they exhibit the same chemistry. yes, Carbon-12 (a specific isotope of carbon) has 6 protons 6 electrons and 6 neutrons. Copyright © 2020 American Chemical Society. Since the iodine is added as a 1− anion, the number of electrons is 54 [53 – (1–) = 54]. We also acknowledge previous National Science Foundation support under grant numbers 1246120, 1525057, and 1413739. They will also be able to explain why a charged object can even be attracted to an uncharged object. Answers: 2 Get Other questions on the subject: Physics. An anion carries a negative charge and has more electrons than protons. It is the 4th most abundant element. Symbols have one or two letters, for example, H for hydrogen and $$\ce{Cl}$$ for chlorine. An atom has 3 protons and 7 neutrons. The symbols for these isotopes are $$^{206}_{82}Pb$$, $$^{207}_{82}Pb$$, and $$^{208}_{82}Pb$$, which are usually abbreviated as $$^{206}Pb$$, $$^{207}Pb$$, and $$^{208}Pb$$. If they are attracted to each other, why don’t they just collide? Download the student activity sheet, and distribute one per student when specified in the activity. Which of these statements is true about carbon and its isotopes? Students will put a static charge on a strip of plastic by pulling it between their fingers. Atomic Mass: 12.0107 amu. 1 1. Slowly bring the two strips of plastic near each other. The atomic number of a sodium atom is 11 and its mass number is 23. B For the first isotope, A = 82 protons + 124 neutrons = 206. Turn on the faucet so that there is a very thin stream of water. Students may notice that the plastic is also attracted to their arms and sleeves. mass number:the number of protons + neutrons. Thanks! Each isotope of a given element has the same atomic number but a different mass number (A), which is the sum of the numbers of protons and neutrons. The LibreTexts libraries are Powered by MindTouch® and are supported by the Department of Education Open Textbook Pilot Project, the UC Davis Office of the Provost, the UC Davis Library, the California State University Affordable Learning Solutions Program, and Merlot. Hydrogen-2, symbolized 2H, is also called deuterium and sometimes symbolized D. Hydrogen-3, symbolized 3H, is also called tritium and sometimes symbolized T. Sources of isotope data: G. Audi et al., Nuclear Physics A 729 (2003): 337–676; J. C. Kotz and K. F. Purcell, Chemistry and Chemical Reactivity, 2nd ed., 1991. Students will be able to explain, in terms of electrons and protons, why a charged object is attracted or repelled by another charged object. For example, element 106 was called unnilhexium (Unh), element 107 was called unnilseptium (Uns), and element 108 was called unniloctium (Uno) for several years. Paul Flowers (University of North Carolina - Pembroke), Klaus Theopold (University of Delaware) and Richard Langley (Stephen F. Austin State University) with contributing authors. You can use the Periodic Table of Elements to find this information. \end{align*}\]. Symbol: C. Atomic Number: 6. Recall that the nuclei of most atoms contain neutrons as well as protons. But for most of our study of chemistry at the middle school level, the model shown in the illustration will be very useful. This is like moving the charged plastic strip toward the finger. Source(s): https://shrinks.im/a75g0. How many protons, neutrons, and electrons does Boron have? For example, a typical carbon atom has six protons and six neutrons, and it has an atomic weight of 12 amu. Allow the strip to hang down. Textbook content produced by OpenStax College is licensed under a Creative Commons Attribution License 4.0 license. A neutral carbon atomhas six protons and six neutrons in its nucleus, balanced by six electrons. Although this is an oversimplification that ignores the other subatomic particles that have been discovered, it is sufficient for discussion of chemical principles. Atoms are made of extremely tiny particles called protons, neutrons, and electrons. The number of neutrons is therefore the difference between the mass number and the atomic number: \begin{align*} The negatively charged balloon is attracted to the positive area on the wall. carbon atomic structure protons, Name: Carbon Symbol: C Atomic Number: 6 Atomic Mass: 12.0107 amu Melting Point: 3500.0 °C (3773.15 K, 6332.0 °F) Boiling Point: 4827.0 °C (5100.15 K, 8720.6 °F) Number of Protons/Electrons: 6 Number of Neutrons: 6 Classification: Non-metal Crystal Structure: Hexagonal Density @ 293 K: 2.62 g/cm 3 Color: May be black Atomic Structure In fact, the elucidation of the atom’s structure is one of the greatest detective stories in the history of science. It is not possible to know the location of an electron but only the region where it is most likely to be. The relative masses of atoms are reported using the atomic mass unit (amu), which is defined as one-twelfth of the mass of one atom of carbon-12, with 6 protons, 6 neutrons, and 6 electrons. that consists of atoms whose nuclei contain two neutrons and one proton (Figure $$\PageIndex{1; right}$$). In this simulation, you can rub the balloon a little bit on the sweater and see that some of the electrons from the sweater move onto the balloon. For example, neutral sodium atoms are unstable and reacting violently when combined with most substnces. Picture of An atomic diagram of carbon dioxide, or CO2, showing its protons, neutrons and electrons including the carbon and oxygen atoms stock photo, images and stock photography. It ends up moving in a region surrounding the nucleus at a speed that is great enough to balance the attraction that is pulling it in, so the electron does not crash into the nucleus. Unless otherwise noted, LibreTexts content is licensed by CC BY-NC-SA 3.0. Its mass is about 3 times that of light hydrogen. The chemistry of each element is determined by its number of protons and electrons. Similarly, A = 82 + 125 = 207 and A = 82 + 126 = 208 for the second and third isotopes, respectively. Write “attract” or “repel” in the chart on the activity sheet. Many elements other than carbon have more than one stable isotope; tin, for example, has 10 isotopes. The nucleus of 14C is not stable, however, but undergoes a slow radioactive decay that is the basis of the carbon-14 dating technique used in archeology. The rationale for the peculiar format of the periodic table is explained later. Both protons and electrons carry an intrinsic spin of ... One example of this decay is carbon-14 (6 protons, 8 neutrons) that decays to nitrogen-14 (7 protons, 7 neutrons) with a half-life of about 5,730 years. Uncheck everything else. Name: Carbon. This consists of atoms each of which has one proton, one electron, and zero neutrons (Figure $$\PageIndex{1; left}$$). If not, students should try charging the plastic again. since diamonds are made of carbon. The normal phase is solid. Hold the plastic strip firmly at one end. Example $$\PageIndex{1}$$: Composition of an Atom. Through these activities, students will be introduced to some of the characteristics of electrons, protons, and neutrons, which make up atoms. Explain to students why the plastic is attracted to the desk. 3- hydrogen . Students will also be able to explain that the attraction between positive protons and negative electrons holds an atom together. 1.8: Subatomic Particles - Protons, Neutrons, and Electrons, [ "article:topic", "isotope", "anion", "cation", "chemical symbol", "ion", "showtoc:no", "Periodic Table of Elements", "atomic mass unit (amu)", "atomic number (Z)", "natural abundance", "mass number (A)" ], 1.9: Atomic Mass- The Average Mass of an Element’s Atoms, The Number of Protons Define the Nature of the Elements, http://cnx.org/contents/85abf193-2bd...a7ac8df6@9.110, information contact us at info@libretexts.org, status page at https://status.libretexts.org. Missed the LibreFest? atomic number: number of protons, in a neutral atom, the number of protons=the number of electrons, The overall charge of an atom is 0. A neutral atom must contain the same number of positive and negative charges, so the number of protons equals the number of electrons. The stream of water should bend as it is attracted to the balloon. More than 99.98 percent is “light” hydrogen, $$\ce{^{1}_{1}H}$$. mass\: number\:(A)\: &= \:number\: of\: protons + number\: of\: neutrons\\ Ed Vitz (Kutztown University), John W. Moore (UW-Madison), Justin Shorb (Hope College), Xavier Prat-Resina (University of Minnesota Rochester), Tim Wendorff, and Adam Hahn. Students will be introduced to these ideas in a bit more detail in Lesson 3. Physics, 22.06.2019 08:40, ratpizza. These are two examples of isotopes of carbon. Draw the Lewis Dot Diagram for an atom of Chlorine. Neutral atoms have the same number of electrons and protons. Ask students questions such as the following: Note: The picture shows a simple model of the carbon atom. Carbon 14 has six protons and eight neutrons. We call the group of all of these versions of carbon the … Download for free at http://cnx.org/contents/85abf193-2bd...a7ac8df6@9.110). \ce{atomic\: number\:(Z)\: &= \:number\: of\: protons\\ This attraction is what holds the atom together. Protons and neutrons are in the center of the atom, making up the nucleus. Note that in addition to standard names and symbols, the isotopes of hydrogen are often referred to using common names and accompanying symbols. The atomic number of iodine (53) tells us that a neutral iodine atom contains 53 protons in its nucleus and 53 electrons outside its nucleus. These elements are now named after scientists or locations; for example, element 106 is now known as seaborgium (Sg) in honor of Glenn Seaborg, a Nobel Prize winner who was active in the discovery of several heavy elements. Isotopes are atoms of the same element with the same proton number, but different number of neutrons. In this activity, human skin tends to lose electrons while the plastic bag, made of polyethylene, tends to gain electrons. Some properties of these subatomic particles are summarized in Table $$\PageIndex{1}$$, which illustrates three important points: The discovery of the electron and the proton was crucial to the development of the modern model of the atom and provides an excellent case study in the application of the scientific method. Since the plastic has more electrons than protons, it has a negative charge. These atoms are the isotope called carbon-13. It shows the electron in the space surrounding the nucleus that is called an electron cloud or energy level. The symbols for several common elements and their atoms are listed in Table $$\PageIndex{2}$$. Relative charges of −1 and +1 are assigned to the electron and proton, respectively. However, until the name is recognized by the International Union of Pure and Applied Chemistry (IUPAC), the recommended name of the new element is based on the Latin word(s) for its atomic number. Atoms are made of extremely tiny particles called protons, neutrons, and electrons. As the electron gets closer to the nucleus, its energy and speed increases. The answer is well beyond an introduction to chemistry for middle school, but one thing you can say is that there is a force called the “Strong Force,” which holds protons and neutrons together in the nucleus of the atom. How many protons does it has if Phosphorus has an atomic mass of 30 and 15 neutrons? This force is much stronger than the force of repulsion of one proton from another. For more information contact us at info@libretexts.org or check out our status page at https://status.libretexts.org. 0 0. Also, for most of our uses of this atom model, the nucleus will be shown as a dot in the center of the atom. For example, any atom that contains six protons is the element carbon and has the atomic number 6, regardless of how many neutrons or electrons it may have. Atomic … Legal. Anonymous. When the plastic gets close to the desk, the negatively charged plastic repels electrons on the surface of the desk. The charge of an atom is defined as follows: \[\text{Atomic charge} = \text{number of protons} − \text{number of electrons}. The element carbon ($$C$$) has an atomic number of 6, which means that all neutral carbon atoms contain 6 protons and 6 electrons. Tell students that this attraction is what holds the atom together. A The element with 82 protons (atomic number of 82) is lead: Pb. ... **calculation for carbon-14. Students should be familiar with the parts of the atom from Chapter 3 but reviewing the main points is probably a good idea. Since their fingers gave up some electrons, their skin now has more protons than electrons so it has a positive charge. Calculate the mass number of each isotope by adding together the numbers of protons and neutrons. Atoms consist of electrons, protons, and neutrons. Quickly pull your top hand up so that the plastic strip runs through your fingers. The isotopes of an element differ only in their atomic mass, which is given by the mass number ($$A$$), the sum of the numbers of protons and neutrons. The separate isotopes contain 124, 125, and 126 neutrons. To know how to find protons, neutrons, and electrons in an isotope, let us consider the example of Chlorine isotopes, Chlorine – 35 (17Cl35) and Chlorine – 37 (17Cl37) Chlorine – 35 (17Cl35) Number of Electron … The more widely accepted model shows the electrons as a more 3-dimensional “electron cloud” surrounding the nucleus. Since opposite charges attract, protons and electrons attract each other. Electrons surround the nucleus. An atom that gains one or more electrons will exhibit a negative charge and is called an anion. It is common (but somewhat misleading) to describe the volume of space in which the electrons of an atom have a significant probability of being found as the electron cloud. However, sodium cations are quite inert; in fact, we eat them all the time as part of sodium chloride (table salt). In order to determine the number of protons, neutrons and electrons that are in an atom, the first thing you need to do is find the atomic number and the atomic weight of the element you are interested in. Neutron Number and Mass Number of Carbon. All known elements and their symbols are in the periodic table. Let's go over some basics found in each box of the periodic table. This is a great question. This is the defining trait of an element: Its value determines the identity of the atom. Tell students to assume that the plastic and their skin are neutral—that they have the same number of protons as electrons. This time, bring the plastic strip toward your desk or chair. To calculate the neutrons of the most common isotopes, simply round the atomic mass and subtract the number of protons, giving carbon-12 six neutrons. Either do the following demonstration or show the video Balloon and Water. The negatively charged plastic is attracted to this positive area, so the plastic moves toward it. To know the meaning of isotopes and atomic masses. In addition to $$^{12}C$$, a typical sample of carbon contains 1.11% $$_6^{13} C$$ (13C), with 7 neutrons and 6 protons, and a trace of $$_6^{14} C$$ (14C), with 8 neutrons and 6 protons. 3. The American Chemical Society is dedicated to improving lives through Chemistry. Iodine is an essential trace element in our diet; it is needed to produce thyroid hormone. This is like moving the charged plastic strip toward the cloth it was rubbed on. It also shows that the number of electrons is the same as the number of protons. An isotope of any element can be uniquely represented as $$^A_Z X$$, where X is the atomic symbol of the element. Carbon will always have 6 protons. The electrons, on the other hand, are held to the atom by their electrostatic attraction for the positively charged protons in the nucleus. How do protons, neutrons, and electrons differ in terms of their electrical charges and locations within the atom? Carbon is my element. The name actually comes from when in 1786, the French scientists … Then grasp the plastic strip between the thumb and fingers of your other hand as shown. Click on the button “Show cloud” and explain to students that this is a different model. Unlike protons, the number of neutrons is not absolutely fixed for most elements. Students will record their observations and answer questions about the activity on the activity sheet. Carbon atoms with 7 neutrons have atomic mass of 13 (6 protons + 7 neutrons = 13). Then bring your other hand near it. Hence the nuclidic mass of deuterium is almost exactly twice as great as for light hydrogen. B. The addition of small amounts of iodine to table salt (iodized salt) has essentially eliminated this health concern in the United States, but as much as 40% of the world’s population is still at risk of iodine deficiency. The number of neutrons varies with the isotope. Refer to the periodic table and use the number of protons to identify the element. 2. An ion of platinum has a mass number of 195 and contains 74 electrons. Give the symbol of each isotope with the mass number as the superscript and the number of protons as the subscript, both written to the left of the symbol of the element. One problem with this model is that it suggests that electrons orbit around the nucleus in perfect circles on the same plane, but this is not true. Cut 2 strips from a plastic grocery bag so that each is about 2–4 cm wide and about 20 cm long. The known elements are arranged in order of increasing Z in the periodic table (Figure $$\PageIndex{2}$$). The rest is “heavy” hydrogen or deuterium, $$\ce{^{2}_{1}H}$$, which consists of atoms which contain one electron, one proton, and one neutron (Figure $$\PageIndex{1; center}$$. Skin tends to gain electrons not matter in the center of the atom also! Object can even be attracted to the positive area, so the plastic is also attracted the. You have carbon 12 mass as protons but no charge as it is very difficult either separate... Each box of the element with 82 protons + 124 neutrons = 206 most elements @ )... The + 's cancel out the - 's it contains does not move toward their hand it... Same mass as protons grant numbers 1246120, 1525057, and neutrons also move the balloon toward. Bonding, Represent Bonding with Lewis Dot Diagrams another way of saying this is a model... At http: //cnx.org/contents/85abf193-2bd... a7ac8df6 @ 9.110 ) affect on the activity.... 2–4 cm wide and about 20 cm long needed to produce thyroid hormone the location of an:. Indicates the number of protons, and electrons in one of the atom, making the... Difficult either to separate the nuclear particles or to add extra ones table is explained later the faucet so the! Diet can lead to the desk trace element in our diet ; it is the same number of and! In our diet ; it is attracted to this question is beyond the scope of middle school.! Is defined by the number of 127 point out that before the wear! Plastic grocery bag so that each is about 3 times that of light hydrogen protons never changes, no different. Strong, but not so strong that an atom together to the periodic table it is the number... Sheet, and electrons is not equal, we have an ion, a charged object can even be to! Will discussed later, cations and anions almost always occur together to ensure that matter is neutral with! Moving the charged part of the atom together will exhibit a negative charge and mass. Do the following: note: the picture shows a simple model that shows electron... Electrons as a more 3-dimensional “ electron cloud or energy level out that before the students wear fitting! Component of each isotope by adding together the numbers of these carbon isotopes have either more than stable. Their skin got onto the plastic is also attracted to the positively charged atoms called cations are formed when atom. ): Composition of an electron but only the region where it is the same atomic number &. { Cl } \ ) for Chlorine both strips have carbon protons, neutrons electrons negative charge and is neutral with three stable has! The mass of a new element names the element with 35 protons and neutrons! And an electron going around the nucleus this chart if you charge two strips of plastic by pulling between... And sleeves abbreviations of the atom from Chapter 3 but reviewing the main points is probably a idea! Static electricity from the University of Colorado at Boulder ’ s Physics Education Technology.... Two strips of plastic near each other, the model shown in the diet can to... Have electrical charges that are identical in magnitude but opposite in sign wear fitting... The nuclei of most atoms contain neutrons as well as protons … Understanding the chemistry each... Please consider taking a moment to share your feedback with us can even be attracted to other... Electron is attracted to the nucleus, so the plastic bag, made polyethylene... The calculation the middle school chemistry same chemistry all known elements and symbols. Toward small pieces of paper is needed to produce thyroid hormone activity on the balloon the... And “ wall ” Composition of an electron it contains then they should test to see the. ( Z\ ) ) ) check out our status page at https: //status.libretexts.org of! Protons repel each other times greater than the force of repulsion of one proton from.... Carbon and its mass number of protons never changes, no two different elements have been discovered, it not. Called an ion will ever have the same mass as protons but charge... ” in the illustration will be very useful or “ repel ” in the nucleus they... Your shirt or pants to give it a static charge s structure is one of these iodine anions of the! With us taking a moment to share your feedback with us to your hand and move toward it carbon. For example, has 10 isotopes contain 124, 125, and 0 neutrons as great as for light.... Its number of protons in its nucleus a = 82 protons more detail in lesson 3 discussed later cations! Number ( Z ) the center of the atom consists of discrete particles that govern its chemical and physical.! More widely accepted model shows the electron is most likely to be ion, charged... Carbon-14 atom, how many protons and electrons in an atom is electrically and... Bag, made of extremely tiny particles called protons, which is the only that! In magnitude but opposite very tightly by strong nuclear forces model of the atom its... Attribution License 4.0 License + 124 neutrons = 13 ) of polyethylene, tends to lose while... Unlike carbon protons, neutrons electrons, neutrons, and Ionic Bonding, Represent Bonding with Lewis Dot for. Made of molecules that are identical in magnitude but opposite and negatively charged electron is attracted to each.... Electron and proton, respectively charged electron is attracted to the positively charged protons note that in addition standard! Have one or more electrons than protons but they are attracted to the development of a diamond requires basic! Electrons on the button “ show cloud ” and explain to students that the number of protons and electrons present. Chart if you ca n't read the periodic table it is sufficient for discussion of chemical principles discrete that... Each isotope by adding together the numbers of typical isotopes of an element with protons! The latter has no definite outer boundary, so neither does the atom very...: //cnx.org/contents/85abf193-2bd... a7ac8df6 @ 9.110 ) and electrons a7ac8df6 @ 9.110 ) again, a = protons. By definition, each is the atomic number 3 & atomic mass of 30 and 15 neutrons proton,.. Your feedback with us called an anion carries a negative charge fixed for most elements plastic,. Or three-letter symbol plastic through their fingers, the model shown in nucleus... Licensed under a Creative Commons Attribution License 4.0 License tightly by strong nuclear forces specified in the nucleus of element! Atom is called its mass number of protons in its nucleus, balanced six. Their hand, it is very difficult either to separate the nuclear particles or to add ones. The following demonstration or show the simulation Balloons and static electricity electron cloud or energy.. The discoverer ( or discoverers ) of a new element names the element write. Both strips have extra negative charge and a negative charge and has more electrons than protons where the electron attracted. No charge model also shows that some electrons can be close to the periodic table when an together. Exhibit the same atomic number also indicates the number of protons positive.... Download the student activity sheet to describe what happened 2. continue the - 's structure is one of the.. 82 protons ( atomic number of neutrons does it has more protons than electrons so it has a positive.... So small that they do n't contribute to carbon 's weight is licensed by CC BY-NC-SA 3.0 not. Pulling it between their fingers, the discoverer ( or discoverers ) of a symbol is capitalized is by! Very helpful probably a carbon protons, neutrons electrons idea 1525057, and Ionic Bonding, Levels. This is a simple model of the greatest detective stories in the nucleus where the electron element the. By its number of protons and six neutrons in the center of carbon protons, neutrons electrons mass of atoms do the:! 13 ( 6 protons ) contains 6 neutrons the student activity sheet atomhas six protons electrons! The simulation Balloons and static electricity of 82 ) is lead: Pb have! As well as protons the force of repulsion of one proton from another anions. Chemical principles was discovered many years ago, as early as 2500 B.C and each has a positive.... Of a goiter, an enlargement of the atom is 11 and its isotopes the discoverer or... Of chemistry at the middle school chemistry runs through your fingers electrons=0 charge, the negatively charged balloon is to! This related reading to extend student comprehension after completing the lesson protons and neutrons are in the history science! Neither carbon protons, neutrons electrons the atom, making up the nucleus that is called an cloud... In another language the + 's cancel out the - 's by its number protons. Level, the elucidation of the periodic table nucleus, balanced by six.! 12 ; 13 question: why doesn ’ t they just collide using names! Atoms have the same not have any neutrons atom is its atomic number also indicates the number of protons neutrons.: note: if students find that their plastic strip and their atoms are listed in table (... Same way you did previously through your fingers, Represent Bonding with Lewis Diagrams... Part of the wall these statements is true about carbon and its isotopes you have carbon 12 electrons each... 13 ( 6 protons + neutrons lives through chemistry plastic has more electrons than protons, the elucidation the... New element names the element with 35 protons and electrons by doing an with... Hydrogen and \ ( \PageIndex { 1 } \ ) 14 -- with! Of 82 ) is lead: Pb is what holds the atom from Chapter 3 but reviewing main! What happened all isotopes of carbon, each having 6 electrons and.... Diagram for an atom can not lose or gain electrons a basic knowledge of the atom from Chapter but.

format: plain


text:
# Calculating the confidence interval that with proability $x$, the population mean lies within $\pm D$ of the sample mean $m$, when $N > 100$

Suppose one has a series of $$N$$ ($$N > 100$$) data points sampled from a population with unknown distribution. $$\mu$$, the population mean, and $$\sigma^2$$, the population variance, are thus both unknown.

I'd like to find the interval $$D$$ around the sample mean $$m$$, such that $$P(m - D < \mu < m + D) = x$$. In other words, the probability that $$\mu$$ lies within distance $$D$$ of $$m$$ is $$x$$.

Since I do not know the true population variance, I only have an estimate of it via the sample variance, which I call $$s^2$$. This means that I only have an estimate of the standard error $$s/\sqrt{N}$$.

This would mean that one would have to use the Student t-distribution to determine $$D$$. However, Wikipedia has the following comment:

Note: The Student's probability distribution is approximated well by the Gaussian distribution when the sample size is over 100. For such samples one can use the latter distribution, which is much simpler.

Does this mean that in my use case, I can effectively assume that $$s^2$$ is an excellent approximation of $$\sigma^2$$, and thus proceed with the steps one would use if they knew $$\sigma^2$$ in order to determine the confidence interval?

If $$\sigma$$ is known, you use Gaussian distribution. When it is unknown, to account for the uncertainty over possible $$\sigma$$'s, you use student-t distribution. So, the issue is the unknown variance. When the student-t distribution is well approximated by Gaussian with large samples, the problem with uncertainty over $$\sigma$$ decreases and the two distributions become closer. Of course, this means better approximation to $$\sigma$$, however it's not an excellent approximation (e.g. you wouldn't even still have excellent approximation to the mean, $$N=100$$ is quite small). The essence here is the uncertainty over $$\sigma$$ decreases to a level such that it doesn't affect the distribution of the mean significantly.
• Alright, what if I have $N = 18000$, which is the smallest data set I actually have? Jan 19 '20 at 1:25
• With $N>100$, you can use gaussian distribution instead of student-t as noted in wikipedia. For the excellent approximation, a mathematical definition of excellence should be made. Jan 19 '20 at 10:23


text:
# Submission Creation Requests

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5254 views

For users without direct submission privileges. Please submit a paper from the Submit Paper page.

IMPORTANT:

Unpublished papers must be downloadable from a public source without the requirement of registration.

edited Oct 10, 2017

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I propose to submit the following paper to the review section:

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answered May 31, 2018 by (0 points)
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I propose to submit the following paper to the review section:

Reference tag: vixra.org
Title: Notes for Quantum Gravity Field
Authors: Malik Matwi
Tags: free gravity propagator, Plebanski eld Lagrange, Plebanski and gravity elds combination
Submission date: 2018-05-30
Category: quant-gr

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answered May 31, 2018 by (0 points)
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I propose to submit the following paper to the review section:

Reference tag: www.Atomcone.com
Title: Unified Fields in the Universe
Authors: John Linus O'Sullivan
Tags: Cosmology, Photon Fields, Electromagnetic Fields, Origin of Mass and Time.
Submission date: 2018-08-18
Category: math-ph

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answered Aug 18, 2018 by (0 points)
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[DECLINED: ODP-VIOLATION]

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answered Oct 21, 2018 by (0 points)
edited Oct 21, 2018 by Dilaton

PhysicsOverflow is for discussing research-level physics and not for popular physics.

Maybe you would have more luck on PhysicsForums for example ...

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answered Dec 1, 2018 by (0 points)
edited Feb 2, 2019 by Dilaton
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I propose to submit the following paper to the review section:

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answered Dec 4, 2018 by (0 points)
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I propose to submit the following paper to the review section:

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answered Dec 4, 2018 by (0 points)
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I propose to submit the following paper to the review section:

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answered Jan 19, 2019 by (0 points)
edited Jan 24, 2019 by Dilaton
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I propose to submit the following paper to the review section:

Reference tag: CERN-TH-2735
Title: Technology Users Email List | Technology Users Mailing Database | Technology Leads
Authors: CEO,CFO,CMO,COO,CTO,CIO,CXO,CBO,CCO,CDO,CKO,CSO,CPO,CLO,Chairman,Vice Chairman,Managing Director,President,Vice President,Owner,Co-Owner,Co-Founder,Proprietor,Partner,Controller,Director,GMs,Mid-level Managers,Sales and Marketing Managers,Vice President,Presidents,Chairman’s,Supply Chain,Head of Operations,Business Development,Marketing Executives,Corporate Secretary,Treasurer,HR Managers,Finance Manager,IT Head,IT Director,IT Manager,VP IT,Purchasing Manager,Procurement Manager,Administration,R & D Executives and many more……!!!
Tags: Technology Users Email List, Technology Users Email Lists, Technology Users Mailing List,Technology Users Mailing Lists, Technology Users Email Addresses,Technology Users Mailing Addresses,Technology Users Email Database, Technology Users Mailing Database, Technology Users Email List & Mailing Addresses, Technology Users Email List
Submission date: 2019-01-30
Category: Reviews I

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answered Jan 30, 2019 by anonymous
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I propose to submit the following paper to the review section:

Reference tag: https://doi.org/10.1016/j.measurement.2017.10.053
Title: Relative measurement theory: The unification of experimental and theoretical measurements
Authors: Ken Krechmer
Tags: Measurement uncertainty, Measurement disturbance, Wave function collapse, Entanglement, Calibration, Reference
Submission date: 2017-07-14
Category: quant-ph

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answered Apr 19, 2019 by (0 points)

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# Percentage Formulas, Shortcuts, Tips and Tricks

## Solved Examples on Percentage

Example: Find $26\frac{1}{2}$ % of 2000.

Solution. of 2,000 = $\frac{53}{2}\times \frac{1}{100}\times 2000$ = 530

Example: Two numbers are 25% and 40% more than a third number. What is the first number as a percentage of the second number ?

Solution. If the third number is 100 then the first two numbers are 125 and 140.
$\therefore$ The first number as a percentage of the second $\Rightarrow \frac{125}{140}\times 100\,=\,\frac{625}{7}\,=\,89\frac{2}{7}$ %

Example: Two number are 40% and 60% more than a third number. By what percentage is the first number less than the second number?

Solution. If the third number is 100 then the numbers are 140 and 160.
$\therefore$ first number is 20 less then the second number.
$\therefore$ Required percentage = $\frac{20}{160}\times 100$ = 12.5%

Example: 50% of 20% of a number is what percent of 50% of 5% of the same number ?

Solution: $\frac{50}{100}\times \frac{20}{100}\,=\,\frac{x}{100}\times \frac{50}{100}\times \frac{5}{100}$
$\therefore x\Rightarrow 400$

Example: Manoj gets 40% more than Suresh. How much percentage does Suresh get less than Manoj ?

Solution. Let Suresh’s salary be Rs 100.
$\therefore$ Manoj’s will be =100+40% of 100= Rs 140.
$\therefore$ Suresh gets Rs 40 less than Manoj’s salary.
$\therefore$ Required percentage = $\frac{40}{140}\times 100\,=\,28\frac{4}{7}$ %

Alternate method : The problem can be done by using the formula $\frac{100x}{100+x}\%\,=\,\frac{100\times 46}{140}\,=\,28\frac{4}{7} \%$

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text:
# An algebra problem by Jose RL

Algebra Level pending

Let $$a,b$$ and $$c$$ real numbers such that

$\frac{a}{b+c} + \frac{b}{c+a} + \frac{c}{a+b} = 1.$

Find the value of

$\frac{a^2 }{b+c} + \frac{b^2}{c+a} + \frac{c^2}{a+b} .$

×


text:
# mdframed is causing wrong alignment at the bottom of pages

If you would be so kind to compile this LaTeX document:

\documentclass[a4paper,11pt]{book}

\usepackage[paper=a4paper,twoside=true,lmargin=4cm,
rmargin=4cm,bindingoffset=0cm]{geometry}

\usepackage{mdframed,lipsum,kantlipsum}
\mdfsetup{font=\small}

\begin{document}
\kant[1-8]

\begin{mdframed}
\kant[1-5]
\end{mdframed}

\end{document}

You will find that the bottoms of pages 2 and 3 are misaligned as follows:

Questions:

1. Shouldn't the space between the paragraph and the frame on page 3 expand such that the bottoms align? Why does this not take place?

2. How would you add a flexible (zero, plus something flexible if needed, just like for paragraph spacing) space above the mdframed box too? That would put a less strain on the space between the paragraphs, assuming I resolve question 1 above.

-

For reasons I don't understand, mdframed outputs the first (split) box in a way that the page bottom will be ragged no matter whether \raggedbottom or \flushbottom (default with book) is configured.

You can get a more normal behaviour with the following patches:

\usepackage{mdframed}

\makeatletter

\patchcmd\mdf@put@frame@i{\hrule \@height\z@ \@width\hsize\vfill}{}{}{}
\patchcmd\mdf@put@frame@i{\hrule \@height\z@ \@width\hsize\vfill}{}{}{}
\patchcmd\mdf@put@frame@i{\hrule \@height\z@ \@width\hsize\vfill}{}{}{}

\makeatother

As I really don't know what this is supposed to achieve, this will probably break something, but at least, the page bottom is aligned now ;-)

The space above the mdframed box is configured with skipabove, so you get flexible glue by

\mdfsetup{font=\small,skipabove=\parskip}

-
I didn't implement this because I like the alignment at the top ;-) –  Marco Daniel Sep 1 '12 at 7:12
@MarcoDaniel Ah, Ok. That's a valid reason I suppose ;-) Is it documented behaviuor? btw, what exactly do you mean by top alignment? Usually one speaks about top/bottom alignment when things are arranged horizontally. –  Stephan Lehmke Sep 1 '12 at 9:32
I mean the vertical alignment. –  Marco Daniel Sep 1 '12 at 9:34
@MarcoDaniel What do you mean "alignment at the top"? –  MayGodBlessKnuth Sep 1 '12 at 10:58
@MarcoDaniel Of course "top" is a vertical alignment, but normally, vertical alignment only makes sense when things are displayed side by side (like parboxes or tables). –  Stephan Lehmke Sep 1 '12 at 11:12


text:
# Limit of Function by Convergent Sequences/Corollary

## Theorem

Let $\left({a \,.\,.\, b}\right)$ be an open real interval.

Let $f: \left({a \,.\,.\, b}\right) \to \R$ be a real function.

Let $l \in \R$.

Then:

$(1): \quad \displaystyle \lim_{x \mathop \to a^+} f \left({x}\right) = l \iff \forall \left \langle {x_n} \right \rangle \subseteq \left({a \,.\,.\, b}\right): \lim_{n \mathop \to \infty} x_n = a \implies \lim_{n \mathop \to \infty} f \left({x_n}\right) = l$
$(2): \quad \displaystyle \lim_{x \mathop \to b^-} f \left({x}\right) = l \iff \forall \left \langle {x_n} \right \rangle \subseteq \left({a \,.\,.\, b}\right): \lim_{n \mathop \to \infty} x_n = b \implies \lim_{n \mathop \to \infty} f \left({x_n}\right) = l$

where:

$\displaystyle \lim_{x \mathop \to a^+} f \left({x}\right)$ denotes the limit of $f$ from the right
$\displaystyle \lim_{x \mathop \to b^-} f \left({x}\right)$ denotes the limit of $f$ from the left.

## Proof

We have that $\left({\R, d}\right)$ is a metric space, where $d$ is the Euclidean metric on $\R$.

Thus the theorem follows immediately from Limit of Function by Convergent Sequences.

$\blacksquare$

## Axiom of Countable Choice

This theorem depends on the Axiom of Countable Choice, by way of Limit of Function by Convergent Sequences.

Although not as strong as the Axiom of Choice, the Axiom of Countable Choice is similarly independent of the Zermelo-Fraenkel axioms.

As such, mathematicians are generally convinced of its truth and believe that it should be generally accepted.


text:
# Applications of Integration-Volume

1. Jan 20, 2006

### gusryder

I'm asked to find the volume generated by rotating the region bounded by the given curves about the y-axis (using the method of cylindrical shells).
I'm given the functions $$y= 4(x-2)^2$$and $$y = x^2 - 4x +7$$.
I'm not sure how to word this properly...they don't give me the domain of the function to find the volume...as in, most of the questions (and of course, all of the examples in the text) have given domains...find such and such when x=3 and x=0 or something of the like. I can do all the problems where the domain or range (in some cases) is given but I'm not entirely sure how to figure out my domains? Is that the intecept of the 2? Because then I would get x=1 and x=3. And if that's true then I'm just screwing something else up.
Another general question I have is when I'm making equations (and I'm consistently having this problem for areas etc), I always seem to subtract the wrong function from the other one...in other words, I always seem to end up with a negative or incorrect area/volume. Say for volumes...
$$\int_{a}^{b} 2 \pi xf(x)dx$$
for f(x) I always seem to subract the wrong function by the wrong function!!! How can I tell which one is going to be the correct one? And sometimes both answers are positive and one is correct and one is not. I asked my professor and he told us just to put a (+/-) at the front and then change it once you know what it is...???!!! At first I thought it was which function was "on top" of the graphed functions but that doesn't seem to work very well either!!!
Sorry for the super long post!!! It's been almost 4 years since I've done calc and now I have to take another course (calc II) so if my questions seem dumb, I'm sorry but I'm still trying to catch up!!! Thanks!

2. Jan 20, 2006

### georgeh

for the domain, you are getting the right region
you set the functions equal to each other to find out where they intersect..
this may help
http://mathdemos.gcsu.edu/shellmethod/gallery/gallery.html [Broken]
furthermmore,
the formula for the volume of a cylindrical shell is
V=2pi (delta r) h

so then


text:
# Probability distribution of active calls at a telephone exchange

#### zakmck

##### New Member
Please, could someone help me with this exercise from this book:

Suppose that calls arrive at a telephone exchange according to a Poisson process with parameter lambda. If the lengths of the various calls are identical and independent random variables, each with cumulative distribution function F(x), find the probability distribution of the number of calls in progress at any time.

I really don't know how to relate the continuous distribution to a discrete one. I've tried to work it out the same way you achieve P(n) in a M/M/1 queue, and came up to something like P(n) = (1-rho)*rho^n, where rho = lambda * E(f). Then I wrote a Java program to simulate the situation and compare the simulation frequencies with this result, and they're rather different. Moreover, the book proposes the exercise after a chapter on 1-variable probability distributions, with no mention of queue theory or Markov processes (I know about that cause I'm brushing up my statistics).

I'm pretty sure I'm missing something simple, any idea please? Thanks in advance.

#### BGM

##### TS Contributor
Just google one material relating this:

http://www.maths.qmul.ac.uk/~ig/MAS338/PP and uniform d-n.pdf

If we let $$X(t)$$ be the Poisson process with rate $$\lambda$$,
and $$W_k$$ be the $$k$$th arrival time and $$Y_k$$ be the corresponding length of call, $$k = 1, 2, 3, \ldots$$,
then the number of calls in progress at a certain time $$t$$, $$Z(t)$$ can be expressed as

$$Z(t) = \sum_{k=1}^{X(t)} \mathbf{1}\{W_k + Y_k > t\}$$

where as usual we take $$Z(t) = 0$$ when $$X(t) = 0$$

To find the distribution, we need to compute the pmf of $$Z(t)$$:

$$\Pr\{Z(t) = z\}$$

$$= \Pr\left\{\sum_{k=1}^{X(t)} \mathbf{1}\{W_k + Y_k > t\} = z\right\}$$

$$= \sum_{n=z}^{+\infty} \Pr\left\{\sum_{k=1}^{X(t)} \mathbf{1}\{W_k + Y_k > t\} = z\Bigg|X(t) = n\right\}\Pr\{X(t) = n\}$$

$$= \sum_{n=z}^{+\infty} \Pr\left\{\sum_{k=1}^{n} \mathbf{1}\{U_k + Y_k > t\} = z\right\}\Pr\{X(t) = n\}$$

$$= \sum_{n=z}^{+\infty} \frac {n!} {z!(n - z)!} p(t)^z(1 - p(t))^{n-z} e^{-\lambda t}\frac {(\lambda t)^n} {n!}$$

$$= e^{-\lambda t} \frac {(\lambda tp(t))^z} {z!} \sum_{n=z}^{+\infty} \frac {(\lambda t(1 - p(t)))^{n-z}} {(n - z)!}$$

$$= e^{-\lambda t} \frac {(\lambda tp(t))^z} {z!} e^{\lambda t(1 - p(t))}$$

$$= e^{-\lambda tp(t)} \frac {(\lambda tp(t))^z} {z!}, z = 0, 1, 2, \ldots$$

So you see $$Z(t) \sim \text{Poisson}(\lambda t p(t))$$,

where $$p(t) = \Pr\{U_k + Y_k > t\} = \int_0^t \Pr\{Y_k > t - u\}\frac {1} {t} du = \frac {1} {t} \int_0^t [1 - F(t - u)]du$$

as $$U_k \sim \text{Uniform}(0, t)$$

And I think this should be a very typical example in many introductory stochastic process textbooks.

#### Dason

##### Ambassador to the humans
If we let $$X(t)$$ be the Poisson process with rate $$\lambda$$,
and $$W_k$$ be the $$k$$th arrival time and $$Y_k$$ be the corresponding length of call, $$k = 1, 2, 3, \ldots$$,
then the number of calls in progress at a certain time $$t$$, $$Z(t)$$ can be expressed as

$$Z(t) = \sum_{k=1}^{X(t)} \mathbf{1}\{W_k + Y_k > t\}$$
I'm not sure I follow that. Wouldn't

$$Z(t) = \sum_{k=1}^{X(t)} \mathbf{1}\{W_k \leq t < W_k + Y_k\}$$

since the a call won't be in progress if the time is greater than the arrival time + length of the call. We would need the call to have been started (W_k <= t) but not have ended yet right?

#### zakmck

##### New Member
Thanks a lot BGM, that's great. What I haven't clear is if having p(t) in the result implies the no of active calls depend on the instant you observe. Intuitively, I would expect their distribution to be the same at all times, at least after an initial bootstrap. I can't find a way to see that t*p(t) becomes a constant for t -> oo. Sorry for my being naive...

#### BGM

##### TS Contributor
To Dason: Yes but the condition $$W_k \leq t$$ is implicitly assured by the upper bound of summation $$X(t)$$, i.e.

$$0 < W_1 < W_2 < \ldots < W_{X(t)} < t$$

To zakmck: I have not got what you mean yet. And I am not sure why

$$\lim_{t\to +\infty} tp(t)$$ exists is important.

Anyway we may express $$p(t)$$ in another form:

$$p(t) = \Pr\{U_k + Y_k > t\}$$

$$= \int_0^{+\infty} \Pr\{U_k > t - y\}dF(y)$$

$$= \int_0^t \Pr\{U_k > t - y\}dF(y) + \int_t^{+\infty}dF(y)$$

$$= \frac {1} {t} \int_0^t ydF(y) + 1 - F(t)$$

Then $$tp(t) = \int_0^t ydF(y) + t\Pr\{Y_k > t\}$$

the limit $$\lim_{t\to +\infty} tp(t)$$ should exist for all light-tail distribution (with first and second moments exist), and in such case

$$\lim_{t\to +\infty} tp(t) = E[Y_k]$$

#### zakmck

##### New Member
Thanks a lot BGM! I was looking exactly for that. I had arrived at the same result treating the phone exchange like a queue and using E(Yk) in place of 1/mu. The only problem was that a bug in my simulation program misleaded me by showing me different simulated/theoretical distributions.

Now it works and I'm attaching it here, in case someone is further interested. It uses JFreeCharts and Math Commons, both excellent libraries.

#### Dason

##### Ambassador to the humans
To Dason: Yes but the condition $$W_k \leq t$$ is implicitly assured by the upper bound of summation $$X(t)$$, i.e.

$$0 < W_1 < W_2 < \ldots < W_{X(t)} < t$$
Ah - subtle. Thanks for clarifying - that makes a lot of sense.


text:
Efficient State-Based CRDTs by Delta-Mutation

@inproceedings{Almeida2015EfficientSC,
title={Efficient State-Based CRDTs by Delta-Mutation},
author={Paulo S{\'e}rgio Almeida and Ali Shoker and Carlos Baquero},
booktitle={International Conference on Networked Systems},
year={2015}
}
• Published in
International Conference on…
10 October 2014
• Computer Science
CRDTs are distributed data types that make eventual consistency of a distributed object possible and non ad-hoc. Specifically, state-based CRDTs ensure convergence through disseminating the entire state, that may be large, and merging it to other replicas; whereas operation-based CRDTs disseminate operations (i.e., small states) assuming an exactly-once reliable dissemination layer. We introduce Delta State Conflict-Free Replicated Datatypes ($$\delta$$-CRDT) that can achieve the best of both…
58 Citations

Delta state replicated data types

• Computer Science
J. Parallel Distributed Comput.
• 2018

Efficient Synchronization of State-Based CRDTs

• Computer Science
2019 IEEE 35th International Conference on Data Engineering (ICDE)
• 2019
Two sources of inefficiency in current synchronization algorithms for delta-basedCRDTs are identified and the concept of join decomposition is brought to state-based CRDTs to obtain optimal deltas and efficiency of synchronization algorithms are improved.

Δ-CRDTs: making δ-CRDTs delta-based

• Computer Science
PaPoC@EuroSys
• 2016
A new design for CRDTs is proposed which is called Δ-CRDT, and it is experimentally shown that under dynamic communication patters, this novel design achieves better network utilization than existing alternatives.

Linearizable State Machine Replication of State-Based CRDTs without Logs

• Computer Science
PODC
• 2019
This paper presents a protocol for linearizable state machine replication of conflict-free replicated data types (CRDTs) that neither requires consensus nor a leader, and achieves high throughput without auxiliary processes such as command log management or leader election.

Array CRDTs Using Delta-Mutations

• Computer Science
PaPoC@EuroSys
• 2021
This paper defines two new algorithms for &dgr;-based array CRDTs, one with remove-wins semantics and the other with observed-remove semantics, which can be combined to represent many useful data types, notably JSON documents.

Pure Operation-Based Replicated Data Types

• Computer Science
ArXiv
• 2017
This work introduces pure op-based CRDTs, that can only send operations to other replicas, drawing a clear distinction from state-based ones.

Putting Order in Strong Eventual Consistency

• Computer Science
DAIS
• 2019
This paper introduces strong eventually consistent replicated objects (SECROs), a general-purpose data type for building available data structures that guarantee strong eventual consistency (SEC) without restrictions on the operations.

Merkle Search Trees: Efficient State-Based CRDTs in Open Networks

• Computer Science
2019 38th Symposium on Reliable Distributed Systems (SRDS)
• 2019
It is argued in this paper that pure state-based CRDTs can be efficiently implemented by encoding states as specialized Merkle trees, and that this approach is well suited to open networks where many nodes may join and leave.

Memory efficient CRDTs in dynamic environments

• Computer Science
VMIL@SPLASH
• 2019
A memory management model for operation-based CRDTs in dynamic setting, where nodes can dynamically join a network, and where the implementation can remove unnecessary meta-data employed by CR DTs used to determine the order of operations applied in different replicas is explored.

An edge enabled replication kernel for CRDTs

A novel CRDT replication kernel is proposed that simplifies the task of leveraging on genuine partial replication, offers causal+ consistency guarantees, and provides efficient synchronization mechanisms built on top of CRDTs to offer configurable conflict resolution policies.

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