# Math Is Fun Forum

Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫  π  -¹ ² ³ °

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## #1701 2023-03-18 19:33:12

ganesh
Registered: 2005-06-28
Posts: 41,269

### Re: Miscellany

1604) Crown glass (Optics)

Summary

Crown glass is a type of optical glass used in lenses and other optical components. It has relatively low refractive index (≈1.52) and low dispersion (with Abbe numbers around 60). Crown glass is produced from alkali-lime silicates containing approximately 10% potassium oxide and is one of the earliest low dispersion glasses.

As well as the specific material named crown glass, there are other optical glasses with similar properties that are also called crown glasses. Generally, this is any glass with Abbe numbers in the range 50 to 85. For example, the borosilicate glass Schott BK7 (Schott designates it as 517642. The first three digits tell you its refractive index (1.517) and the last three tell you its Abbé number (64.2)) is an extremely common crown glass, used in precision lenses. Borosilicates contain about 10% boric oxide, have good optical and mechanical characteristics, and are resistant to chemical and environmental damage. Other additives used in crown glasses include zinc oxide, phosphorus pentoxide, barium oxide, fluorite and lanthanum oxide.

BAK-4 barium crown glass (Schott designates it as 569560. The first three digits tell you its refractive index (1.569) and the last three tell you its Abbé number (56.0)),has a higher index of refraction than BK7, and is used for prisms in high-end binoculars. In that application, it gives better image quality and a round exit pupil.

A concave lens of flint glass is commonly combined with a convex lens of crown glass to produce an achromatic doublet. The dispersions of the glasses partially compensate for each other, producing reduced chromatic aberration compared to a singlet lens with the same focal length.

Details

Crown glass is handmade glass of soda-lime composition for domestic glazing or optical uses. The technique of crown glass remained standard from the earliest times: a bubble of glass, blown into a pear shape and flattened, was transferred to the glassmaker’s pontil (a solid iron rod), reheated and rotated at speed, until centrifugal force formed a large circular plate of up to 60 inches in diameter. The finished “table” of glass was thin, lustrous, highly polished (by “fire-polish”), and had concentric ripple lines, the result of spinning; crown glass was slightly convex, and in the centre of the crown was the bull’s eye, a thickened part where the pontil was attached. This was often cut out as a defect, but later it came to be prized as evidence of antiquity. Nevertheless, and despite the availability of cheaper cylinder glass (cast and rolled glass had been invented in the 17th century), crown glass was particularly popular for its superior quality and clarity. The crown process, which may have been Syrian in origin, was in use in Europe since at least the 14th century, when the industry was centred in Normandy, where a few families of glassblowers monopolized the trade and enjoyed a kind of aristocratic status. From about the mid-17th century the crown glass process was gradually replaced by easier methods of manufacturing larger glass sheets. Window glass of note, however, was made by this method in the U.S. by the Boston Crown Glass Company from 1793 to about 1827.

Crown glass has optical properties that complement those of the denser flint glass when the two kinds are used together to form lenses corrected for chromatic aberration. Special ingredients may be added to crown glass to achieve particular optical qualities.

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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## #1702 2023-03-19 15:16:45

ganesh
Registered: 2005-06-28
Posts: 41,269

### Re: Miscellany

1605) Ferry

Summary

A ferry is a ship, watercraft or amphibious vehicle used to carry passengers, and sometimes vehicles and cargo, across a body of water. A small passenger ferry with many stops, such as in Venice, Italy, is sometimes called a water bus or water taxi.

Ferries form a part of the public transport systems of many waterside cities and islands, allowing direct transit between points at a capital cost much lower than bridges or tunnels. Ship connections of much larger distances (such as over long distances in water bodies like the Mediterranean Sea) may also be called ferry services, and many carry vehicles.

Details

A ferry is a place where passengers, freight, or vehicles are carried by boat across a river, lake, arm of the sea, or other body of water. The term applies both to the place where the crossing is made and to the boat used for the purpose. By extension of the original meaning, ferry also denotes a short overwater flight by an airplane carrying passengers or freight or the flying of planes from one point to another as a means of delivering them.

Perhaps the most prominent early use of the term appears in Greek mythology, where Charon the ferryman carried the souls of the dead across the River Styx. Ferries were of great importance in ancient and medieval history, and their importance has persisted into the modern era. Before engineers learned to build permanent bridges over large bodies of water or construct tunnels under them, ferries offered the only means of crossing. Ferries include a wide variety of vessels, from the simplest canoes or rafts to large motor-driven ferries capable of carrying trucks and railway cars across vast expanses of water. The term is frequently used in combination with other words, as in the expressions train ferry, car ferry, and channel ferry.

In the early history of the United States, the colonists found that the coasts of the New World were broken by great bays and inlets and that the interior of the continent was divided by rivers that defied bridging for many generations. Crossing these rivers and bays was a necessity, however. At first, small boats propelled by oars or poles were the most common form of ferry. They were replaced later by large flatboats propelled by a form of long oar called a sweep. Sails were used when conditions were favourable and in some rivers the current itself provided the means of propulsion.

Horses were used on some ferries to walk a treadmill geared to paddle wheels; in others, horses were driven in a circle around a capstan that hauled in ropes and towed the ferry along its route. The first steam ferryboat in the United States was operated by John Fitch on the Delaware River in 1790, but it was not financially successful. The advent of steam power greatly improved ferryboats; they became larger, faster, and more reliable and began to take on a design different from other steamers. At cities divided by a river and where hundreds of people and many horse-drawn wagons had to cross the river daily, the typical U.S. ferryboat took shape. It was a double-ended vessel with side paddle wheels and a rudder and pilothouse on both ends. The pilothouses were on an upper deck, and the lower deck was arranged to hold as many vehicles as possible. A narrow passageway ran along each side of the lower deck with stairways to give passengers access to the upper deck. The engine was of the walking beam type with the beam mounted on a pedestal so high that it was visible above the upper deck.

Terminals to accommodate such ferries were built at each end of their routes. In order to dock promptly and permit wheeled vehicles to move on and off quickly, a platform with one end supported by a pivot on land and the other end supported by floats in the water was sometimes provided. As roads improved and the use of automobiles and large motor trucks increased, ferries became larger and faster, but the hull arrangement remained the same. High-speed steam engines with propellers on both ends of the ferry were used. Steam engines gave way to diesel engines, diesel-electric drives, and, in some cases, hovercraft. Several states organized commissions which took over ferries from private ownership and operated them for the public; these commissions frequently also operated bridges, public roads, and vehicular tunnels. Increase in the use of motor vehicles so overtaxed many ferries that they could not handle the load. As a result, more bridges and tunnels were built, and ferries began to disappear, but their use on some inland rivers and lakes still continues. Commuter ferries remained popular in densely populated coastal communities.

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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## #1703 2023-03-20 14:22:23

ganesh
Registered: 2005-06-28
Posts: 41,269

### Re: Miscellany

1606) Scholarship

Summary

Scholarship: learning; knowledge acquired by study; the academic attainments of a scholar.
2. a sum of money or other aid granted to a student, because of merit, need, etc., to pursue his or her studies.
3. the position or status of such a student.
4. a foundation to provide financial assistance to students.

Details

A scholarship is a form of financial aid awarded to students for further education. Generally, scholarships are awarded based on a set of criteria such as academic merit, diversity and inclusion, athletic skill, and financial need.

Scholarship criteria usually reflect the values and goals of the donor of the award, and while scholarship recipients are not required to repay scholarships, the awards may require that the recipient continue to meet certain requirements during their period of support, such maintaining a minimum grade point average or engaging in a certain activity (e.g., playing on a school sports team for athletic scholarship holders).

Scholarships also range in generosity; some range from covering partial tuition ranging all the way to a 'full-ride', covering all tuition, accommodation, housing and others.

Some prestigious, highly competitive scholarships are well-known even outside the academic community, such as Fulbright Scholarship and the Rhodes Scholarships at the graduate level, and the Robertson, Morehead-Cain and Jefferson Scholarships at the undergraduate level.

Scholarships vs. grants

While the terms scholarship and grant are frequently used interchangeably, they are distinctly different. Where grants are offered based exclusively on financial need, scholarships may have a financial need component but rely on other criteria as well.

* Academic scholarships typically use a minimum grade-point average or standardized test score such as the ACT or SAT to narrow down awardees.
* Athletic scholarships are generally based on athletic performance of a student and used as a tool to recruit high-performing athletes for their school's athletic teams.
* Merit scholarships can be based on a number of criteria, including performance in a particular school subject or club participation or community service.

A federal Pell Grant can be awarded to someone planning to receive their undergraduate degree and is solely based on their financial needs.

Types

A Navy Rear Admiral presents a Midshipman with a ceremonial cheque symbolizing her \$180,000 Navy Reserve Officers Training Candidate scholarship.

The most common scholarships may be classified as:

* Merit-based: These awards are based on a student's academic, artistic, athletic, or other abilities, and often a factor in an applicant's extracurricular activities and community service record. Most such merit-based scholarships are paid directly by the institution the student attends, rather than issued directly to the student.
* Need-based: Some private need-based awards are confusingly called scholarships, and require the results of a FAFSA (the family's expected family contribution). However, scholarships are often merit-based, while grants tend to be need-based.
* Student-specific: These are scholarships for which applicants must initially qualify based upon gender, race, religion, family, and medical history, or many other student-specific factors. Minority scholarships are the most common awards in this category.[citation needed] For example, students in Canada may qualify for a number of Indigenous scholarships, whether they study at home or abroad. The Gates Millennium Scholars Program is another minority scholarship funded by Bill and Melinda Gates for excellent African American, American Indian, Asian Pacific Islander American, and Latino students who enroll in college.
* Career-specific: These are scholarships a college or university awards to students who plan to pursue a specific field of study. Often, the most generous awards go to students who pursue careers in high-need areas, such as education or nursing. Many schools in the United States give future nurses full scholarships to enter the field, especially if the student intends to work in a high-need community.
* College-specific: College-specific scholarships are offered by individual colleges and universities to highly qualified applicants. These scholarships are given on the basis of academic and personal achievement. Some scholarships have a "bond" requirement. Recipients may be required to work for a particular employer for a specified period of time or to work in rural or remote areas; otherwise, they may be required to repay the value of the support they received from the scholarship. This is particularly the case with education and nursing scholarships for people prepared to work in rural and remote areas. The programs offered by the uniformed services of the United States (Army, Navy, Marine Corps, Air Force, Coast Guard, National Oceanic and Atmospheric Administration Commissioned Officer Corps, and Public Health Service Commissioned Corps) sometimes resemble such scholarships.
* Athletic: Awarded to students with exceptional skill in a sport. Often this is so that the student will be available to attend the school or college and play the sport on their team, although in some countries government funded sports scholarships are available, allowing scholarship holders to train for international representation. School-based athletics scholarships can be controversial, as some believe that awarding scholarship money for athletic rather than academic or intellectual purposes is not in the institution's best interest.
* Brand: These scholarships are sponsored by a corporation that is trying to gain attention to their brand, or a cause. Sometimes these scholarships are referred to as branded scholarships. The Miss America beauty pageant is a famous example of a brand scholarship.
* Creative contest: These scholarships are awarded to students based on a creative submission. Contest scholarships are also called mini project-based scholarships, where students can submit entries based on unique and innovative ideas.
* "Last dollar": can be provided by private and government-based institutions, and are intended to cover the remaining fees charged to a student after the various grants are taken into account. To prohibit institutions from taking last dollar scholarships into account, and thereby removing other sources of funding, these scholarships are not offered until after financial aid has been offered in the form of a letter. Furthermore, last dollar scholarships may require families to have filed taxes for the most recent year, received their other sources of financial aid, and not yet received loans.

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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## #1704 Today 21:14:42

ganesh
Registered: 2005-06-28
Posts: 41,269

### Re: Miscellany

1607) Sepsis

Summary

Sepsis, formerly known as septicemia (septicaemia in British English) or blood poisoning, is a life-threatening condition that arises when the body's response to infection causes injury to its own tissues and organs.

This initial stage of sepsis is followed by suppression of the immune system. Common signs and symptoms include fever, increased heart rate, increased breathing rate, and confusion. There may also be symptoms related to a specific infection, such as a cough with pneumonia, or painful urination with a kidney infection. The very young, old, and people with a weakened immune system may have no symptoms of a specific infection, and the body temperature may be low or normal instead of having a fever. Severe sepsis causes poor organ function or blood flow. The presence of low blood pressure, high blood lactate, or low urine output may suggest poor blood flow. Septic shock is low blood pressure due to sepsis that does not improve after fluid replacement.

Sepsis is caused by many organisms including bacteria, viruses and fungi. Common locations for the primary infection include the lungs, brain, urinary tract, skin, and abdominal organs. Risk factors include being very young or old, a weakened immune system from conditions such as cancer or diabetes, major trauma, and burns. Previously, a sepsis diagnosis required the presence of at least two systemic inflammatory response syndrome (SIRS) criteria in the setting of presumed infection. In 2016, a shortened sequential organ failure assessment score (SOFA score), known as the quick SOFA score (qSOFA), replaced the SIRS system of diagnosis. qSOFA criteria for sepsis include at least two of the following three: increased breathing rate, change in the level of consciousness, and low blood pressure. Sepsis guidelines recommend obtaining blood cultures before starting antibiotics; however, the diagnosis does not require the blood to be infected. Medical imaging is helpful when looking for the possible location of the infection. Other potential causes of similar signs and symptoms include anaphylaxis, adrenal insufficiency, low blood volume, heart failure, and pulmonary embolism.

Sepsis requires immediate treatment with intravenous fluids and antimicrobials. Ongoing care often continues in an intensive care unit. If an adequate trial of fluid replacement is not enough to maintain blood pressure, then the use of medications that raise blood pressure becomes necessary. Mechanical ventilation and dialysis may be needed to support the function of the lungs and kidneys, respectively. A central venous catheter and an arterial catheter may be placed for access to the bloodstream and to guide treatment. Other helpful measurements include cardiac output and superior vena cava oxygen saturation. People with sepsis need preventive measures for deep vein thrombosis, stress ulcers, and pressure ulcers unless other conditions prevent such interventions. Some people might benefit from tight control of blood sugar levels with insulin. The use of corticosteroids is controversial, with some reviews finding benefit, and others not.

Disease severity partly determines the outcome. The risk of death from sepsis is as high as 30%, while for severe sepsis it is as high as 50%, and septic shock 80%. Sepsis affected about 49 million people in 2017, with 11 million deaths (1 in 5 deaths worldwide). In the developed world, approximately 0.2 to 3 people per 1000 are affected by sepsis yearly, resulting in about a million cases per year in the United States. Rates of disease have been increasing. Some data indicate that sepsis is more common among males than females, however, other data show a greater prevalence of the disease among women. Descriptions of sepsis date back to the time of Hippocrates.

Details

What is Sepsis?

What is sepsis?
Is sepsis contagious?
What causes sepsis?
Who is at risk?
What are the signs & symptoms?
What should I do if I think I might have sepsis?

Anyone can get an infection, and almost any infection, including COVID-19, can lead to sepsis. In a typical year:

* At least 1.7 million adults in America develop sepsis.
* At least 350,000 adults who develop sepsis die during their hospitalization or are discharged to hospice.
* 1 in 3 people who dies in a hospital had sepsis during that hospitalization
* Sepsis, or the infection causing sepsis, starts before a patient goes to the hospital in nearly 87% of cases.

Sepsis is the body’s extreme response to an infection. It is a life-threatening medical emergency.  Sepsis happens when an infection you already have triggers a chain reaction throughout your body.  Infections that lead to sepsis most often start in the lung, urinary tract, skin, or gastrointestinal tract. Without timely treatment, sepsis can rapidly lead to tissue damage, organ failure, and death.

Is sepsis contagious?

You can’t spread sepsis to other people. However, an infection can lead to sepsis, and you can spread some infections to other people.

Sepsis happens when…

What causes sepsis?

Infections can put you or your loved one at risk for sepsis. When germs get into a person’s body, they can cause an infection. If you don’t stop that infection, it can cause sepsis. Bacterial infections cause most cases of sepsis. Sepsis can also be a result of other infections, including viral infections, such as COVID-19 or influenza, or fungal infections.

Who is at risk?

Anyone can develop sepsis, but some people are at higher risk for sepsis:

People with weakened immune systems

People with chronic medical conditions, such as diabetes, lung disease, cancer, and kidney disease

People with recent severe illness or hospitalization

What are the signs & symptoms?

A person with sepsis might have one or more of the following signs or symptoms:

High heart rate or weak pulse

Confusion or disorientation

Extreme pain or discomfort

Fever, shivering, or feeling very cold

Shortness of breath

Clammy or sweaty skin

A medical assessment by a healthcare professional is needed to confirm sepsis.

What should I do if I think I might have sepsis?

Sepsis is a medical emergency. If you or your loved one has an infection that’s not getting better or is getting worse, ACT FAST.

Get medical care IMMEDIATELY. Ask your healthcare professional, “Could this infection be leading to sepsis?” and if you should go to the emergency room.

If you have a medical emergency, call 911. If you have or think you have sepsis, tell the operator. If you have or think you have COVID-19, tell the operator this as well. If possible, put on a mask before medical help arrives.

With fast recognition and treatment, most people survive.  Treatment requires urgent medical care, usually in an intensive care unit in a hospital, and includes careful monitoring of vital signs and often antibiotics.

Sepsis is systemic inflammatory condition that occurs as a complication of infection and in severe cases may be associated with acute and life-threatening organ dysfunction. Worldwide, sepsis has long been a common cause of illness and mortality in hospitals, intensive care units, and emergency departments. In 2017 alone, an estimated 11 million people worldwide died from sepsis, accounting for nearly one-fifth of all deaths globally that year. Nonetheless, this number marked a decrease in sepsis death rates from the last part of the 20th century. Improvements in health care, including better sanitation and the development of more effective treatments, were thought to have contributed to the decline.

Populations most susceptible to sepsis include the elderly and persons who are severely ill and hospitalized. In the early 21st century, other factors, including increased life expectancy for persons with immunodeficiency disorders (e.g., HIV/AIDS), increased incidence of antibiotic resistance, and increased use of anticancer chemotherapy and immunosuppressive drugs (e.g., for organ transplantation), have emerged as important risk factors of sepsis.

Risk factors, symptoms, and diagnosis

In addition to the elderly and to persons with weak immune systems, newborns, pregnant women, and individuals affected by chronic diseases such as diabetes mellitus are also highly susceptible to sepsis. Other risk factors include hospitalization and the introduction of medical devices (e.g., surgical instruments) into the body. Early symptoms of sepsis include increased heart rate, increased respiratory rate, suspected or confirmed infection, and increased or decreased body temperature (i.e., greater than 101.3 °F [38.5 °C] or lower than 95 °F [35 °C]). Diagnosis is based on the presence of at least two of these symptoms. In many instances, however, the condition is not diagnosed until it has progressed to severe sepsis, which is characterized by symptoms of organ dysfunction, including irregular heartbeat, laboured breathing, confusion, dizziness, decreased urinary output, and skin discoloration. The condition may then progress to septic shock, which occurs when the above symptoms are accompanied by a marked drop in blood pressure. Severe sepsis and septic shock may also involve the failure of two or more organ systems, at which point the condition may be described as multiple organ dysfunction syndrome (MODS). The condition may progress through these stages in a matter of hours, days, or weeks, depending on treatment and other factors.

Treatment and complications

Prompt treatment is required in order to decrease the risk of progression to septic shock or MODS. Initial treatment includes the emergency intravenous administration of fluids and antibiotics. Vasoconstrictor drugs also may be given intravenously to raise blood pressure, and patients who experience breathing difficulties sometimes require mechanical ventilation. Dialysis, which helps clear the blood of infectious agents, is initiated when kidney failure is evident, and surgery may be used to drain an infection.

Many patients experience a decrease in quality of life following sepsis, particularly if the patient is older or the attack severe. Acute lung injury and neuronal injury resulting from sepsis, for example, have been associated with long-term cognitive impairment. Older persons who suffer from such complications may not be able to live independently following their recovery from sepsis and often require long-term treatment with medication.

Pathophysiology

At the cellular level, sepsis is characterized by changes in the function of endothelial tissue (the endothelium forms the inner surface of blood vessels), in the coagulation (blood clotting) process, and in blood flow. These changes appear to be initiated by the cellular release of pro-inflammatory substances in response to the presence of infectious microorganisms. The substances, which include short-lived regulatory proteins known as cytokines, in turn interact with endothelial cells and thereby cause injury to the endothelium and possibly the death (apoptosis) of endothelial cells. These interactions lead to the activation of coagulation factors. In very small blood vessels (microvessels), the coagulation response, in combination with endothelial damage, may impede blood flow and cause the vessels to become leaky. As fluid and microorganisms escape into the surrounding tissues, the tissues begin to swell (edema); in the lungs this leads to pulmonary edema, which manifests as shortness of breath. If the supply of coagulation proteins becomes exhausted, bleeding may ensue. Cytokines also cause blood vessels to dilate (widen), producing a decrease in blood pressure. The damage incited by the inflammatory response is widespread and has been described as a “pan-endothelial” effect because of the distribution of endothelial tissue in blood vessels throughout the body; this effect appears to explain the systemic nature of sepsis.

The existence of multiple conditions that are characterized by similar symptoms complicates the clinical picture of sepsis. For example, sepsis is closely related to bacteremia, which is the infection of blood with bacteria, and septicemia, which is a systemic inflammatory condition caused specifically by bacteria and typically associated with bacteremia. Sepsis differs from these conditions in that it may arise in response to infection with any of a variety of microorganisms, including bacteria, viruses, protozoans, and fungi. However, the occasional progression of septicemia to more-advanced stages of sepsis and the frequent involvement of bacterial infection in sepsis preclude clear clinical distinction between these conditions. Sepsis is also distinguished from systemic inflammatory response syndrome (SIRS), a condition that can arise independent of infection (e.g., from factors such as burns or trauma).

Sepsis through history

One of the first medical descriptions of putrefaction and a sepsislike condition was provided in the 5th and 4th centuries BCE in works attributed to the ancient Greek physician Hippocrates (the Greek word sepsis means “putrefaction”). With no knowledge of infectious microorganisms, the ancient Greeks and the physicians who came after them variably associated the condition with digestive illness, miasma (infection by bad air), and spontaneous generation. These apocryphal associations persisted until the 19th century, when infection finally was discovered to be the underlying cause of sepsis, a realization that emerged from the work of British surgeon and medical scientist Sir Joseph Lister and French chemist and microbiologist Louis Pasteur.

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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