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Chemical equation for antacid and stomach acid
Time how long it takes for a burp to occur. Comparing. Measuring acid neutralizing capability. 1 M solution of hydrochloric acid that helps digest foods. Both acids and alkalis are corrosive, but salt and water are, of course, harmless Dec 09, 2012 · Hydrochloric Acid (HCl) Potassium chlorate (KCl) Gastric acid freely sloshes into esophagus. Antacids are a combination of various compounds with various salts of calcium, magnesium, and aluminum as active ingredients. There are two types of pharmaceutical drugs that act indirectly to reduce the amount of stomach acid. As 0. Schreiber Date: April 05, 2022 Antacids contain sodium bicarbonate. It should be used only for Aluminum Hydroxide [Al(OH)3] - Compared to magnesium hydroxide, aluminum hydroxide is a weak, slow-acting antacid, and its acid-neutralizing effect varies among commercial products. Recommended dosages vary, but some manufactures advise mixing 1 / 2 teaspoon (2. The following table contains a list of the active ingredients found in several common commercial antacids, and the reactions by which these antacids neutralize the HCl in stomach acid. 9); GCSE. Malox, an over-the-counter antacid, contains aluminum hydroxide, Al(OH) 3, and magnesium hydroxides, Mg(OH). Method: Remove the lid/thermometer of the calorimeter and add 50 ml of 0. Turn on the stir An antacid tablet can contain sodium bicarbonate and stomach acid is hydrochloric acid. Predict the products, then write the balanced neutralization reaction for the antacid Brioschi in the stomach where the main acid present is hydrochloric acid, HCl. Figure 3: An iron nail in hydrochloric acid. That can cause erosions (ulcers) or inflammation (gastritis or duodenitis). It is a burning or tingling feeling that occurs when the contents of your stomach rise into your food pipe (the oesophagus). Calcium carbonate is used therapeutically as a phosphate buffer in hemodialysis, as an antacid in gastric hyperacidity for temporary relief of indigestion and heartburn, and as a calcium supplement for preventing and treating osteoporosis. 2. Rinse any remaining fragments into the flask with a few cm 3 of Search: Calculate The Number Of Moles Of Hcl Neutralized By An Antacid Tablet CheggThe most common of these bases are hydroxides, carbonates, or bicarbonates. Antacids help people who have or get heartburn. 1-14(above 7). They work by neutralizing stomach acid. the effect of different antacids on gastric acid. In this exploration, we will use simulated stomach acid to pit several antacids against each other to see which is the most potent. Our stomachs contain a solution of roughly 0. 0ml of 0. However, it may not be the right choice for daily use. 6 Quantitative chemistryThe normal volume of the gastric fluid is 20 to 100 mL and its pH is acidic (1. 1 M) approximates the acid conditions of the human stomach, which is typically 0. It is composed of mostly hydrochloric acid (HCl), along with potassium chloride and sodium chloride. For this purpose, the following are used: . Understand the Cause. If a tablet of the antacid neutralized 41. Some antacids contain a buffer that maintains the pH of the stomach. g. 1 mol of each antacid is used. If the body has secreted excess acid, because it is having trouble digesting the food you have eaten, you can get a burning pain in your stomach area. (b) The strong acid is HCl and strong base is KOH. Diarrhea, loose/watery stools and abdominal bloating form when large partially digested food particles ferment and draw extra fluid into the large intestine creating gas and watery stools. One simple treatment for heartburn symptoms is to take a simple antacid – a substance that will reduce the concentration of acid in the stomach by reacting with some of it. Decreased absorption of a variety of Apr 05, 2022 · Water with a small amount of baking soda can help treat heartburn. One way to temporarily reduce the H+ in the stomach is to take an antacid. Antacids, such as Tums are used to neutralize this excess acid. Express your answer as a chemical equation. So for part one here, what's the balance stick equation for calcium carbonates? Plus HCL HCL would be present in stomach acid balanced equation here to me h 20 and Co. Balance the eqaution B. 25g). If you eat or drink too much, you may develop heartburn or indigestion. Crush a tablet using a pestle and mortar and carefully transfer it to a conical flask, using a spatula to ensure complete transfer as far as possible. If you have a weak acid you can eliminate the acidic pH by combining it with a weak alkali. 4 to 0. . In order to do a comparison between the antacids you will need to calculate: 1. Reaction between an antacid and stomach acid is a neutralization reaction. 5% HQ by mass (pH ~ 1). Antacids are basic compounds which neutralize hydrochloric acid in the gastric secretions. Write a balanced equation for this reaction. by. There are other forms of antacid that work by less direct means. Write the equation for the neutralization reaction of this acid/base pair. Weak bases can be used to buffer stomach acid, and are used commonly as OTC medications. This acid provides a medium for the digestion of protein by the enzyme protease. 0. Treatment for Stomach Acid Imbalance. sodium hydrogen carbonate, aluminum hydroxide, aluminum phosphate, algeldrate, calcium carbonate, magnesium (hydr)oxide, magnesium carbonate, and magnesium trisilicate. 10 oct 2015 Antacid Tablets by Using Acid-Base Neutralization Reaction reduce gastric acidity by neutralizing hydrochloric acid tablets. Join Yahoo Answers … What is a balanced chemical equation for this reaction? write the chemical equation for the detonation reaction of this explosive. The specific odor of ginger is related to zingiberene and bisabolene, while the pungent flavor is due to volatile oils of gingerols (23–25%) and shogaols (18–25%). from the stomach lining breaking down and the acid attacking the stomach wall. Expand Section. Exercise 3 Magnesium hydroxide and aluminum hydroxide can act as antacids A) Write an equation for the reaction of hydrochloric acid with each of these antacidsB) Identify which antacid neutralizes the greater amount of acid if 0. Because there is a direct correlation between mass effectiveness and number of moles of HCl neutralized by an antacid, Alka Seltzer will generally have a low mass efficiency as a result of its lack of HCl moles to neutralize stomach acid. Get acid-neutralizing power and heartburn relief with Rolaids® Advanced Antacid plus Anti-Gas Chewable Tablets. Gastric acid is the solution in your stomach responsible for chemical Jul 17, 2020 · Antacids are medications that people can buy over the counter to help relieve heartburn and indigestion. The active ingredient in a product is the ingredient that causes the intended effect. Most home remedies involving baking soda as an antacid recommend dissolving the powder into a glass of water. You will make these two antacids by doing a precipitation reaction (a type of double replacement reaction). Composition of typical brand-name antacids include: Flavorers/sweeteners. The stomach is designed to produce enough hydrochloric acid to transform a large solid meal, as much as 3 litres (>12cups), into a Correct answers: 2 question: Write balanced equations for the reaction of Mg(OH)2 with stomach acid (HCl). The chemical formula for calcium carbonate, which is the active ingredient in Tums, is "CaCO3," according to GlaxoSmithKline. What are balanced equations for the reaction of both with stomach acid (HCl)? Feb 25, 2020 · Just so, what is acid neutralizing capacity of an antacid? Acid neutralizing capacity of an antacid is defined as the number of mEq of 1N HCl that are brought to the pH of 3. Organic chemists hate that. The reaction between the two is as follows: HCl (aq) + NaOH (aq) → H2O (l) + Cl –(aq) + Na +(aq) In this case, Sodium and Chloride act as spectator ions and form into salts in a neutralization Mg (OH) 2 + 2 HCl Mg 2+ + 2 Cl – + 2 H 2 O. Simple subtraction reveals the number of moles of HCl that reacted with the antacid. How does Mg(OH)2 work to relieve the pain caused by excess stomach acid? b. Source: Royal Society of Chemistry. Heartburn. The weaker the acid in your stomach, the less likely it is to give you heartburn. Search: Calculate The Number Of Moles Of Hcl Neutralized By An Antacid Tablet CheggPharmacology. oesophagus and excess acid in the stomach. When an antacid is mixed with an acid the buffer tries to even out the acidity and that is how stomach acid gets neutralized. This virtual lab familiarizes students through the process of acid-base titration. (This is one of several reactions that take place when a type of antacid—a base—is used to treat stomach acid. All antacids have chemical in them called a buffer. 1acid found in the stomach, producing a solution of calcium chloride, converting the stomach acid to water, and releasing carbon dioxide gas (which the person suffering from stomach problems may feel as a "burp"). Acidity is the case where access of hydrochloric acid is released in our stomach. Question 2. Antacids - An Antacid is a substance which neutralizes stomach acidity, which in turn relieves heartburn Learn about the antacids, types of antacids, function of antacids, acid reflux symptoms, antacid examples and more. Pharmacology. Stomach acid is approximately 0. Antacids are medications that people can buy over the counter to help relieve heartburn and indigestion. Okay, so they're also Naji equation. CaCO 3 + 2 HCl Ca 2+ + 2 Cl – + CO 2 (g) + H 2 O. One major side effect of antacids is that gastric acid secretion may rebound after taking this medicine. In all of these reactions the H + ion is converted to either water or hydrogen carbonate. Add a little water if needed or take a vinegar supplement. Wear goggles while handling the concentrated acid and have a box of baking soda handy to neutralize spilled acid. 36 M HCl. They are taken orally to suppress the effects of acidity. DrDAQ is used here with the pH probe to find the pH of various indigestion remedies and the effect of adding dilute Hydrochloric acid. Dr. Stomach acid is neutralized by CaCO 3 The secretion of hydrochloric acid by the stomach plays an important role in protecting the body against pathogens ingested with food or water. Marketed antacids contain salts of aluminum, calcium, magnesium, or sodium. Her drugs I because the carriages from the based and I'm from the acid and also the only different by 100 iron for as it and also by one hydroxide for the base. This problem has been solved! 1. When taken as an antacid, it works to neutralize stomach acid and produce relief from indigestion. If not, you can buy hydrochloric acid at the hardware store as "muriatic acid"; it's used for cleaning bricks. Formulated to neutralize acid and keep it at bay for effective, long-lasting relief from heartburn, indigestion, acid reflux, and upset stomach. They are called histamine H2 antagonists (such as Pepcid, Zantac, and Tagamet) and proton Pharmacology. The . May 25, 2018 · The most common of these bases are hydroxides, carbonates, or bicarbonates. Ghouri’s personal favorite, too. H2 blockers bind to histamine Antacids are medications that help to neutralize stomach acid to cut down on heartburn, sour stomach, stomach upset, and acid indigestion. The balanced chemical equation for the reaction of the main ingredient of the antacid tablet (CaCO 3) with the HCl is as follows. Bitters promote digestion by stimulating the secretion of stomach acid, digestive enzymes, and bile. Another name for an antacid is a ____. The mixture was stirred to facilitate the reaction between the acid and the antacid tablet sample. Two of the more practical methods included the use of plant extracts, commonly known as bitters, and the use of betaine HCL to temporarily increase acid levels with meals. The major function of the antacid is to neutralize excess HCl in gastric juice. Taking an antacid medication may temporarily ease the burning sensation since it reduces stomach acid. Antacids differ greatly in efficacy and side effects. (1) NaHCO3 + HCl → NaCl + H2O + CO2 / HCO3- + H+ → H2O + CO2; States not required for mark. a) State an equation for the reaction of stomach acid with this antacid. 2 HCl (aq) + CaCO 3 (s) -----> CaCl 2 (aq) + H 2 O (l) + CO 2 (g) The mixture was then titrated with 0. Before a meal, take 1 Tbs apple cider vinegar with 8 oz water. Lastly, Alka Seltzer has a low-cost effectiveness because Magnesium Hydroxide Formula: Magnesium Hydroxide or 'Milk of Magnesia' is an inorganic chemical compound with antacid and laxative properties. The antacid was then crushed with the pestle and mortar until it was a fine powder. The effect of antacids on the stomach is due to partial neutralisation of gastric hydrochloric acid and inhibition of the proteolytic enzyme, pepsin. Mar 22, 2017 · Some key symptoms of low stomach acid that you should pay attention to include: Heartburn or GERD. To the left, you can see the covalent bonding of the acid. The following information will help people understand how Pharmacology. Solid calcium carbonate is commonly used in antacids because it reacts with the hydrochloric acid found in the stomach. Nov 19, 2021 · Antacids are a class of medicines that neutralize acid in the stomach. Excess stomach acid can be combated with bases, or "antacids". Notice that the main ingredients are: CaCO 3, NaHCO 3, Mg(OH) 2 and of course HCl. The process of acid reflux & The role of Antacids Chemistry syllabus, specifically acids and bases along with a link to medicine, which is of. The bad effects of stomach acid are not limited to heartburn. The stomach is designed to produce enough hydrochloric acid to transform a large solid meal, as much as 3 litres (>12cups), into a The bad effects of stomach acid are not limited to heartburn. MHCl * VHCL = MNaOH * VNaOH. Balance the eqaution. 7 jul 2011 Acid reflux is due to irritation of the food pipe, heart burn is one is composed of hydrochloric acid (chemical formula, HCl) with large 17 ago 2021 However, while the concept can be applied to chemical reactions between acids and bases, it only complies with aqueous environments. The sodium bicarbonate and citric acid are there mainly to create a pleasant tasting fizzy antacid solution. Antacids raise the pH of the stomach contents toward neutrality. Almost all antacids neutralises the excess stomach acid with weak bases. The reaction of these two substances that have the formula NaHCO3 and HCl produces NaCl plus H2O plus CO2, orThere are usually two compounds used in antacids:- (i) Magnesium hydroxide (Mg (OH)2) (ii) Aluminium hydroxide (Al (OH)3) Antacids are taken in the case of acidity. HCl initial - HCl titrated = HCl neutralized Put on your CHEMICAL SPLASH-PROOF SAFETY GOGGLES! Analytical Procedure 1. < Back to the article list. The longer an antacid stays in the The acid involved is hydrochloric acid. The reaction of these two substances that have the formula NaHCO3 and HCl produces NaCl plus H2O plus CO2 A specific example of this chemical reaction is: Mg (OH) 2 + 2 HCl --> MgCl 2 + 2 H 2 O. You can use it to increase stomach acid in the stomach. 5 produces a 100-fold reduction in the concentration of gastric acid. One of the most familiar and most heavily advertised applications of acid–base chemistry is antacids, which are bases that neutralize stomach acid. Materials: Styrofoam cup and lid to build a calorimeter, two antacid tablets, mortar and pestle, 0. The following information will help people understand how Question: Write the balanced chemical equation for the neutralization reaction of stomach acid HCl with Al (OH)3, an ingredient in some antacids. In most titrations, solutions of the acid and the base are used. Your body also produces enzymes and mucus to help protect itself Antacids are medications that people can buy over the counter to help relieve heartburn and indigestion. Acid reflux disease is battled by a change in diet, or by using antacids, such as Gavison. You can also use it for reducing the levels of phosphate in people suffering from kidney problems. Nov 25, 2021 · When there is too much acid or the protective mechanisms are insufficient, the acid can harm the lining of the stomach, duodenum, or oesophagus, resulting in inflammation and ulcerations, as well as a variety of gastrointestinal symptoms such as: Nausea; Abdominal pain; Heartburn; Antacids are OTC drugs that help to neutralize stomach acid. (Table 4. 5g is a round amount and is relatively easy to measure out, making the method more repeatable. Acid and Bases. Mild heartburn is quite common, and most healthy people will experience it from time to time. Extra strength liquid comes in a pleasant and soothing mint flavor. What is important of this acid is of course the concentration of HCl; where minor changes can cause pain and health issues. 5 in 15 minutes by a unit dose of the antacid preparation. The hydrogen and chlorine atoms are sharing 2 valence electrons, forming a single bond. Write the chemical equation for the reaction of an antacid containing magnesium hydroxide, Mg(OH)2, with stomach acid (hydrochloric acid, HCl) and then Here, the salt is MgCl2. Antacids are actually alkaline ions that directly neutralize the gastric acids of the stomach. This was scaled down by 5 and 0. Magnesium hydroxide and Aluminium hydroxide being bases neutralises the acidic effect. Simethicone is anti- gas medication that works by lowering surface tension of gas bubbles, which gives relief from gas. Tums is one commercially sold antacid that contains CACO3. Biological buffers can be One of the most familiar and most heavily advertised applications of acid–base chemistry is antacids, which are bases that neutralize stomach acid. Bismuth subsalicylate was first approved by the FDA in 1939 and is now mainly used to relieve nausea, diarrhea, and gastrointestinal discomfort. b) Calcium carbonate can also neutralize stomach acid. e. Probiotics for GERD may especially help those with IBS and SIBO. Heartburn that occurs now and then is common. In this demonstration, a 250 mL flask is used to model the stomach and to show how the sodium alginate in the product Gaviscon reacts with the acid in the stomach to form a barrier or “raft” which forms a Other Strategies To Support Stomach Acid. (a) Give Arrhenius definition of an acid and a base. The balanced equations for the neutralization of acid with these active ingredients are:. Some antacids also contain simethicone, an ingredient that helps your body get rid of gas. Sometimes is buffered by bicarbonate produced also by the body. The chemical formula of stomach acid (hydrochloric acid) is HCl. A gastric fluid pH of 1 to 2 is deleterious to many microbial pathogens; however, the neutralization of gastric acid by antacids or the inhibition of acid secretion by various drugs may increase the Investigating the effect of acid on indigestion tablets Introduction. 5. Jpg cacl2 + co2 + h2o 2hcl + mg(oh)2 mr001-3. An acid is any chemical that is capable of donating a hydrogen ion (proton or H+) in a chemical reaction. Uses This medication is used to treat the symptoms of too much stomach acid such as stomach upset, heartburn, and acid indigestion. Stress management, such as breath work, yin yoga, or meditation. The higher the concentration of these hydrogen ions in a solution, the more acidic it is. They may be used to treat these symptoms in patients with peptic ulcer, gastritis, esophagitis, hiatal hernia, or too much acid in the stomach (gastric hyperacidity). It is suitable for treating upset stomach, acid indigestion, heartburn and sour stomach. The present mechanism of hydrochloric acid production in the stomach is demonstrated to be incompatible with measured intracellular or intercellular concentrations of the relevant ions. The traditional approach of treating heartburn is to suppress gastric acid by taking antacids or alkalizers. For many years, physicians have prescribed antacids for symptoms that arise from these problems. Occasional heartburn is annoying but common — in fact, there are some estimates that around 60 million Americans experience heartburn at least once a month. The effects of acidity can majorly suppress by taking antacids orally. They are called histamine H2 antagonists (such as Pepcid, Zantac, and Tagamet) and proton This is called acid reflux, which can cause heartburn and/or inflammation of the gullet (oesophagitis). Rolaids, a commercial antacid tablet, claims to neutralize 47 times its weight in excess acid (i. If you have not burped within five minutes, it may be a sign of insufficient stomach acid. The reaction between the metal hydroxides and the stomach acid is an acid base reaction very similar to that in the previous experiment: Mg(OH) 2 (s) + 2HCl(aq) = MgCl 2 (aq) + 2H 2 O(l) Metal carbonates, which are the most common active component in antacids neutralize the stomach acid by forming a salt, water and a gas. * After comparing the amount of active ingredients in each tablet, which ingredients seem to give the most acid neutralization? Write the chemical formula for the active ingredients in each antacid tablet and show how many H+ ions can displace the cations in each formula by writing a balanced chemical equation for each Most are relatively inexpensive, making antacids a popular product for fast relief. Reduction of stomach acid helps to provide pain relief in patients suffering from stomach Search: Calculate The Number Of Moles Of Hcl Neutralized By An Antacid Tablet CheggAs 0. View the full answer. . The only equation is going to separate each of them into Ryan's. To determine the amount of base in an actual tablet, ideally you would dissolve it in water and titrate with acid. 11. 19 g sample of an antacid tablet was placed in an Erlenmeyer flask containing 20. 13 feb 2019 In your stomach, for example, the primary acid is HCl an acid and an antacid is actually called an acid-base reaction in chemistry. Too much of this acid can cause GERD and other painful conditions. Heartburn is a burning pain that appears in the Neutralization is a chemical reaction through which water and salt are formed as the result of a strong acid and strong base coming together. Neutralization reaction is a chemical reaction in which an acid and a base reacts to form a neutral salt. Since, acid and base reacts they neutralize the affect of each other and no excess of hydroxide ions or hydrogen ions are present in the solution. 111 M NaOH. 2HCl + CaCO3 CaCl2 + CO2 + H2O C. Density: 3-3. 1. Stomach acid is hydrochloric acid that reacts with sodium bicarbonate in a chemical reactionAn antacid neutralizes excess stomach acid (HCl). Citrus fruits: Oranges, lemons, limes, grapefruit, and pineapple can cause acid build-up. Add this volume of ____. 36 M HCl is a good approximation for stomach acid, we will be using this solution as our model. An antacid tablet can contain sodium bicarbonate and stomach acid is hydrochloric acid. Acid reflux is a health condition that causes a wide variety of symptoms. The following information will help people understand how Dec 09, 2012 · Hydrochloric Acid (HCl) Potassium chlorate (KCl) Gastric acid freely sloshes into esophagus. Since 1tx is proportional to the rate constant k a plot of ln 1tx versus 1T should produce a straight line which will have a. a. Molecule. Transcribed image text: Write the balanced chemical equation for the neutralization reaction of stomach acid HCl with Al (OH)3, an ingredient in some antacids. Jan 15, 2001 · A specific example of this chemical reaction is: Mg (OH) 2 + 2 HCl --> MgCl 2 + 2 H 2 O. 37g, Gaviscon = 1. Alka-Seltzers chemical formula is C16H17NaO14. Constipation or loose stools alter the lining of the intestinal tract, compromising its optimal function. They combine with stomach acid and Key takeaways. Cory acid also opium. 01 mol dm−3 hydrochloric acid, Figure 3. 0 grams of Rolaids, you would neutralize 47 This medication is used to treat symptoms caused by too much stomach acid such as heartburn, upset stomach, or indigestion. They contain ingredients such as aluminum, calcium, magnesium, or sodium bicarbonate which act as bases (alkalis) to counteract stomach acid and make its pH more neutral. , nicotinic acid and vitamin A), and minerals are also present in ginger. * After comparing the amount of active ingredients in each tablet, which ingredients seem to give the most acid neutralization? Write the chemical formula for the active ingredients in each antacid tablet and show how many H+ ions can displace the cations in each formula by writing a balanced chemical equation for each Answer (1 of 2): Gastric acid is mainly HCl; NaCl and KCl. When gastric hydrochloric acid reaches the nerves in the gastrointestinal mucosa, they signal pain to the central nervous system. The chemical formula for the substance which are used as antacid Calcium hydroxide Ca (OH)2 is an example of antacid. CaCO3+2HCl(aq)-> CaCl2(aq)+H2O(l)+CO2(g) A. Acids. In an antacid it is not the name brand that tells how well it works it is something called an active ingredient. An alternative set of chemical reactions whereby hydrochloric acid is formed in the stomach is presented. Acidity is measured using the pH scale. 5g of each antacid was weighed out. The balanced equation for the …. Neutralisation. Acid Reactions. The reaction of these two substances that have the formula NaHCO3 and HCl produces NaCl plus H2O plus CO2 This problem has been solved! 1. The human stomach contains an approximately 0. They do this because the chemicals in antacids are bases (alkalis) which are the opposite of acids. Answer (1 of 2): Gastric acid is mainly HCl; NaCl and KCl. Test pH levels in the urine and saliva. If the protective lining of the stomach breaks down, this acid can attack the stomach The balanced chemical equation is as follows: 2CH3CH2CO2H (aq) + Ca (OH)2(aq) → (CH3CH2CO2)2Ca (aq) + 2H2O (l) The reaction of a weak acid and a strong base will go to completion, so it is reasonable to prepare calcium propionate by mixing solutions of propionic acid and calcium hydroxide in a 2:1 mole ratio. Other compounds (for effects aside from pH neutralization) The active So from here, we can deduce that he should be come from Prue. H 2 O is pretty much a main ingredient of everything. Heartburn is a symptom of the stomach producing too much hydrochloric acid, which is one of the substances found in the gastric Chemistry. They consist of calcium carbonate and magnesium and aluminum salts in various compounds or combinations. The reaction of these two substances that have the formula NaHCO3 and HCl produces NaCl plus H2O plus CO2, orThe mixture was stirred to facilitate the reaction between the acid and the antacid tablet sample. Chemical reactions as word equations. Exercise. The Chemical Reaction I chose: I chose to study antacids because i have suffered from heartburn before and it is uncomfortable. An increase in the production of stomach acid also CaCO 3: Chalk is the common name for calcium carbonate and is the most abundantly available antacid. A reaction between an acid and base is called neutralisation. Nov 15, 2013 · In this experiment, the reagents combined are an acid, HCl (aq) and a base, NaOH (aq) where the acid is the analyte and the base is the titrant. For this reason, sodium bicarbonate is commonly used in antacids. There are various signs of excess acid in stomach to watch for and these can be mild to severe. Acid can damage the lining of the stomach or of the adjacent duodenum, the upper part of the small intestine. B. This acidic fluid is composed of hydrochloric acid (chemical formula, HCl) with large quantities of potassium chloride (chemical formula, KCl) and sodium chloride (chemical formula, NaCl). Safety glasses are required for this experiment. It's highly acidic and helps break down food for easier digestion. Controlling Variables. 4 mL of 0. When using PPIs, probiotic supplements can improve symptom control and reduce unwanted side effects. Brands such as Quick-Eze and TUMS have calcium carbonate as the ‘active’ ingredient. The basic chemical reacts with the excess hydrochloric acid (HCl) found in the stomach after over stimulation from stress or overindulgence. 2 The journal Surgical Clinics of North America says that the function of stomach acid is to break down food to be digested. So that would be for part one, uh, for part two. The hydrochloric acid solution used in this experiment (0. Key Points: Probiotics can be effective for acid reflux when used as stand-alone therapy or alongside antacids. 16 M HCl), corresponding to a pH of 0. 8-7. After students understand the concept of neutralization of stomach acid with antacid (base) to maintain the pH, students will be given a virtual lab 21 as home work. When you add an equal amount and strength of an acid substance to an alkali substance, the resulting chemical reaction turns the acid and alkali into salt and water. Textbook Reference: pp 455, 465-469 Introduction: The parietal cells in the stomach secrete hydrochloric acid (HCl) at a concentration of roughly 0. Table of Jan 07, 2016 · Buffer acide. Antacids are chemical substances that neutralize stomach acid that has already been secreted and thereby raise the pH level in the stomach (make it less acidic). Please see our product page. These antacid tablets contain magnesium hydroxide, which is a base, that can react with the excess hydrochloric acid present in the stomach to produce magnesium Antacids are chemical substances that neutralize stomach acid that has already been secreted and thereby raise the pH level in the stomach (make it less The above reactions are all common reactions between an antacid and stomach acid, HCl. Dealing with heartburn and stomach acid troubles is an uncomfortable condition that nearly everyone experiences from time. It is a fact, antacids are reliable for reducing stomach acid, as seen in data tables #4 and #5 when pH of hydrochloric acid was 2 but the antacid with the solution had pH of 8-10 which in the stomach will rapidly increase gastric juice. Dec 09, 2012 · Hydrochloric Acid (HCl) Potassium chlorate (KCl) Gastric acid freely sloshes into esophagus. Hydrochloric acid is the only Introduction: Hydrochloric acid is essential in the stomach for the proper digestion of foods. When sodium bicarbonate and acid meet in the stomach, a chemical reaction occurs that lowers the acidity of the stomach. Multiple food sensitivities. You can even massage peppermint oil on your stomach to get relief from indigestion and nausea. Table of The above reactions are all common reactions between an antacid and stomach acid, HCl. The name antacid means anti-acid (against acid). The burning sensation associated Which is more potent antacid per gram, NaHCO3 or Mg(OH)2 ? 4) The neutralization reaction between baking soda NaHCO3 and HCl in the stomach. The acid in the stomach is hydrochloric Antacids work by counteracting (neutralising) the acid in your stomach. The chemical reaction occurring involves the neutralisation of excess acid with calcium carbonate. Learn the symptoms of acid reflux so you can recognize when it's time to get treatment. The number of moles of acid neutralized per gram of tablet. Acid of pH 2 can be quite corrosive – observe the effect of placing an iron nail in 0. 10 mol/L HCl(aq), which can be nuetralized by one antacid tablet. Gastric acid is the solution in your stomach responsible for chemicalfrom the stomach lining breaking down and the acid attacking the stomach wall. Hydrochloric acid, HCl, is the acid found within the stomach. “antacid testing” consumer chemistry Using an antacid will increase the pH of the stomach, making it less acidic and relieving the pain of heartburn. Below, show the mechanism and products for reaction in which calcium carbonate (the 12 jun 2019 Below is shown the reaction in which calcium carbonate (the active ingredient in Tums) neutralizes HCl in a simple proton transfer reaction. The antacids act by neutralizing the acid in the stomach and by inhibiting pepsin, which is a proteolytic enzyme. This happens when these nerves are exposed, as in peptic ulcers. 5 may 2020 Antacids contain something that interacts with the acid in your stomach, such as sodium bicarbonate, aluminum hydroxide, calcium carbonate, 13 dic 2019 drugs that reduce the release of stomach acid by bonding to a particular receptor on the surface of stomach cells (H2 receptor antagonists); the reaction equation depends on the antacid used. Usually, 20 nov 2018 Stomach has a very strong acid known as hydrochloric acid. CaCO3+2HCl (aq)-> CaCl2 (aq)+H2O (l)+CO2 (g) A. Prepare a solution of a base that is similar in concentration to the acid (0. It depends on what base the antacid contains, but common reaction would be NaHCO3 + HCl ----> NaCl + H2O The general neutralization reaction is: Antacid (weak base) + HCl (stomach acid) —› salts + H2 O + CO2 The hydrochloric acid solution used in this experiment (0. By us: a predominantly over-the-counter consumable drug that aids in the neutralization of the stomach acids. Chemistry My family and 9 nov 2017 Antacids are drugs intended to provide immediate, short term relief for symptoms by neutralising the hydrochloric acid your stomach uses to 23 abr 2018 This is an amazing piece of chemistry and all of it relies on the acid in our stomach to start the reactions. 150 M hydrochloric acid then how many grams of magnesium hydroxide was in the tablet?A specific example of this chemical reaction is: Mg (OH) 2 + 2 HCl --> MgCl 2 + 2 H 2 O. Sodium citrate is an antacid, which means it helps to neutralize stomach acid. Neutralization Neutralization is a chemical reaction, also called a water forming reaction, in which an acid and a base or alkali (soluble base) react and. Heartburn is a burning pain that appears in the Prilosec, or omeprazole, belongs in the proton pump inhibitor category of antacid drugs, which means it reduces the amount of food-digesting acid produced by the cells in your stomach lining. Hydrochloric acid is secreted by the stomach to kill harmful organisms‚ aid digestion and activate digestive enzymes. In the stomach, however, the solution becomes NaHCO 3. A system called the pH (potential of hydrogen) system measures this level on a scale from 0-14. Notice the 2-to-1 mole ratio of HCl-to-base. If the protective lining of the stomach breaks down, this acid can attack the stomach The pH of a base is 7. Acidity in the stomach causes the sensation of heartburn, antacids are taken to relieve this sensation. When there is excess acid in your stomach, the pH One of the most familiar and most heavily advertised applications of acid–base chemistry is antacids, which are bases that neutralize stomach acid. Wear goggles while handling the concentrated acid and have a box of baking soda handy to neutralize spilled acid. Antacids are medications that do not require a prescription; in other words, they are self-prescribed. Solution : Common antacids destroy the excess acid of the stomach by and answers of this Book - CHHAYA PUBLICATION Class 12 CHEMISTRY 19 mar 2017 The substance which is used to relieve indigestion, caused by too much of HCl secretion in the stomach, it is called as Antacid. the effect of different antacids on gastric acid. b. Compound; Chemical Formula; Chemical Reaction; Aluminum hydroxide; Al(OH)3So from here, we can deduce that he should be come from Prue. The most common of these bases are hydroxides, carbonates, or bicarbonates. One dose of each antacid is approximately 2. The chemical formula for calcium carbonate, which is the active ingredient in Tums, is “CaCO3,” according to GlaxoSmithKline. Antacids work by counteracting (neutralising) the acid in your stomach. Colorful demonstration of the fate of "excess stomach acid. Antacid- Magnesium hydroxide is alkaline; therefore, when ingested, it reacts with and neutralizes the hydrochloric acid in the stomach. This means an antacid is a _____. 03 M HCl, which helps us digest the food we eat. The most common of these bases are hydroxides, carbonates or bio carbonates. Both hydrogen and chlorine have full valence shells, showing it is a stable compound. Louise Chang on WebMD says that some foods that can increase stomach acid and cause heartburn symptoms to get worse can include: 18. "This video is part of the Flinn Scientific Best Practices for Teaching Chemistry Answer to: Calcium carbonate (CaCO3) reacts with stomach acid (HCl, hydrochloric acid) according to the following equation: CaCO3(s)+2HCl(aq) =Antacids are a group of substances which neutralizes stomach gastric acid, so are commonly used to relieve heartburn and gastroesophagus reflux disease Chemical Reactions. Which chemical equations show a reaction that occurs when someone takes an antacid? Check all that apply. If you feel relief, you may be producing too little acid. As 0. It also relieves indigestion, sour stomach, and heartburn. ubility makes it an ideal compound to use in commercial antacids since it slowly dissolves as it neutralizes stomach acid rather than dissolving all at once. Dec 16, 2020 · Magnesium hydroxide commonly used as an antacid, for example milk of magnesia, because it reduces stomach acid, and increases water in the intestines which may induce bowel movements. It is an active ingredient found in Pepto-Bismol, a common over-the-counter medication that is used to temporarily treat discomforts of the stomach and gastrointestinal tract. Search: Calculate The Number Of Moles Of Hcl Neutralized By An Antacid Tablet CheggHydrochloric Acid (HCl) Potassium chlorate (KCl) Gastric acid freely sloshes into esophagus. \) Magnesium Hydroxide is also an alkaline earth metal hydroxide and naturally occurs as mineral brucite. * After comparing the amount of active ingredients in each tablet, which ingredients seem to give the most acid neutralization? Write the chemical formula for the active ingredients in each antacid tablet and show how many H+ ions can displace the cations in each formula by writing a balanced chemical equation for each Calcium carbonate reacts w/stomach acid according to the following chemical equation. Vitamin C, also called ascorbic acid, can also improve digestion by increasing your stomach acid. bismuth chemical formulaya book pre order incentives 2022 Velocity Championship ActionAntacids are chemical compounds that can give immediate relief from indigestion or heartburn because they contain carbonate or hydroxide ions that neutralize stomach acids. 27 abr 2018 Double Displacement Reactions Adding Alka Seltzer to hydrochloric acid initiates a chemical reaction known as a double displacement reaction. 1 M HCl. excess stomach acid? 4. 36M HCl. (b) Calculate the number of grams of HCl that can react with 0. Click to see full answer Herein, what is the reaction between calcium carbonate and hydrochloric acid?A 0. It can relieve excess stomach acid and its associated Antacid pills neutralize the hydrochloric acid in your stomach to limit acid reflux. The pH scale ranges from 0 to 14. Liquid antacids usually work faster/better than tablets or capsules. Write the chemical equation for the reaction of an antacid containing magnesium hydroxide, Mg(OH) 2, with stomach acid (hydrochloric acid, HCl) and then balance the equation. The following information will help people understand how One method to relieve these symptoms is to neutralize the excess acid with a non-toxic chemical reagent that maintains the contents of the stomach at an appropriate concentration of acid. What are balanced equations for the reaction of both with stomach acid (HCl)? May 08, 2015 · The pH of a base is 7. Notice that the main ingredients are: CaCO3, NaHCO3, Mg(OH)2 and of So it's just balance it like we would in normal chemical reaction s. Learn More. But by themselves, antacids are not adequate treatment for serious acid-related disorders such as ulcers and severe May 08, 2015 · The pH of a base is 7. Sodium bicarbonate is a very quick-acting antacid. Carbon dioxide, water, and sodium citrate solution Alka Seltzer is a mixture of sodium bicarbonate, citric acid, and acetyl salicylic acid. Common equations would include: Mg(OH)2 + 2HCl --> MgCl2 + 2H2O Al(OH)3 + 3HCl --> AlCl3 + 3H2O NaHCO3 + HCl Equate – Al (OH)3 and Mg (OH)2 Gaviscon – Al (OH)3 Maalox (liquid) – Al (OH)3 and Mg (OH)2 Maalox (tablet) – CaCO3 Milk of Magnesia – Mg (OH)2 Pepto-Bismol – HOC6H4COO Pepto-Bismol Children’s – CaCO3 Rolaids – CaCO3 and Mg (OH)2 Tums – CaCO3 Mylanta DRUG NAMES Some drugs used as antacids are: Aluminium hydroxide Magnesium hydroxide There are usually two compounds used in antacids:- (i) Magnesium hydroxide (Mg (OH)2) (ii) Aluminium hydroxide (Al (OH)3) Antacids are taken in the case of acidity. Other compounds (for effects aside from pH neutralization) The active Pharmacology. If the protective lining of the stomach breaks down, this acid can attack the stomach May 06, 2017 · The antacid was then crushed with the pestle and mortar until it was a fine powder. Calculate the volume of stomach acid, 0. To measure that is interesting to mention the HeiHydrochloric Acid (HCl) Potassium chlorate (KCl) Gastric acid freely sloshes into esophagus. For example, sulfur trioxide reacts with water vapor to form sulfuric acid. Probiotics offer benefits by restoring the gut microbiome. The reaction between the two is as follows: HCl (aq) + NaOH (aq) → H2O (l) + Cl –(aq) + Na +(aq) In this case, Sodium and Chloride act as spectator ions and form into salts in a neutralization Answer (1 of 5): 2HCl(aq) + Mg(OH)2(s) = MgCl2(aq) + 2H2O(l)What type of chemical reaction take place to help remove the excess acid in the stomach whenever antacids are used? Write the NET ionic equation of the reaction between an antacid and stomach acid. Stop Heartburn Instantly:Neutralization of stomach acid. Gastric acid is the solution in your stomach responsible for chemical Apr 03, 2022 · Correct answers: 3 question: The main acid in the stomach is hydrochloric acid (hcl). The main acid in the stomach is hydrochloric acid (HCl). What are balanced equations for the reaction of both with stomach acid (HCl)? May 06, 2017 · The antacid was then crushed with the pestle and mortar until it was a fine powder. Stomach acid, also called gastric acid, is a digestive fluid formed in the stomach. Investigating the effect of acid on indigestion tablets Introduction. Antacids such as Mylanta or Phillips’ milk of magnesia contain bases that neutralize the refluxed stomach acid alleviating heartburn. Dec 05, 2017 · Here’s a look at what causes excess stomach acid, starting with food. 150 M hydrochloric acid then how many grams of magnesium hydroxide was in the tablet? (Show calculation) 3. Two gas. 16 oz of room temperature (mineralized) water with 2 teaspoons of raw organic apple cider vinegar upon waking. However, an increased amount of acid in your stomach can cause much trouble. Antacids are commonly used self-prescribed medications. If Tums is added to 20. Unique formula gives relief extra staying power. Antacids may be used alone for mild symptoms caused by stomach acid. The. Antacids are basic chemicals in a form that is as pleasant to the eye and palate as possible. Each tablet contains 55 milligrams of magnesium plus 270 milligrams of calcium, making Rolaids a one-two punch when it comes to neutralizing and reducing stomach acid on the spot. So We're told that one tablet of Tums, uh, regular strength, contains 500 mg of calcium carbonate. Other compounds (for effects aside from pH neutralization) The active A specific example of this chemical reaction is: Mg (OH) 2 + 2 HCl --> MgCl 2 + 2 H 2 O. Measuring. com Antacids perform a neutralization reaction, i. 2. Other compounds (for effects aside from pH neutralization) The active the effect of different antacids on gastric acid. Write the unbalanced chemical equation for this process. 5g (two tablets – Rennie = 1. B. Too much acid in your stomach can overwhelm the prostaglandins (hormone-like chemicals that influence pain and inflammation) in your stomach and duodenum. Antacids, a class of medication typically bought over the counter, are drugs designed to combat harsh acidic environments in the stomach that are associated with ailments such as heart burn, indigestion, and upset stomach. Antacids are substances that neutralize the acids secreted by the stomach. Jul 21, 2013 · Antacids work based on a very simple principle of basic chemistry: Acid + Alkali = Salt + Water. The chemical formula for ingesting antacid tablets is simply a neutralization reaction. Aluminum may protect the stomach lining from the damaging effects of alcohol and other irritants. 150 M hydrochloric acid then how many grams of magnesium hydroxide was in the tablet? (Show calculation)Sodium hydrogen carbonate is another name for sodium bicarbonate, which has the chemical formula NaHCO3. Chemistry. Find out the symptoms and treatment for excess stomach acid. As you may recall, the stomach contains hydrochloric acid. 1- 14(above 7). The neutralization reaction is the reaction between Mg(OH) 2 (a weak base) and HCl (a strong acid). As an antacid, milk of magnesia is dosed at approximately 0. When one realizes that Fe(OH) 3 (s) is a component of rust, this explains Several brands of antacids use Al(OH)3 to react with stomach acid, which contains primarily HCl: Al(OH)3(s) + HCl(aq)¡AlCl3(aq) + H2O(l) (a) Balance this equation. Acne or eczema. The acidity in the stomach is the root of sensations like irritation and heartburn. The active basic chemical ingredient in TUMS is calcium carbonate (CaCO 3). The overall equation for the reaction is shown in Equation 1 below. Magnesium carbonate, also known as magnesite, is a common over the counter remedy for heartburn and upset stomach caused by overproduction of acid in the stomach. Heartburn, a burning sensation in the chest caused by the regurgitation of bile through the stomach into the lower esophagus, is a frequent symptom of low gastric acid. Calcium carbonate reacts w/stomach acid according to the following chemical equation. Many products designed to treat acid reflux, heartburn, and indigestion contain magnesium, but we like Rolaids Extra Strength Tablets for quick, reliable relief. c. Write the equation for this acid base neutralization chemical reaction. Magnesium hydroxide is also used as a laxative to relieve occasional constipation. The number of moles of HCl neutralized by the antacid (HCl neutralized ) is the difference between the moles of HCl initially present in the excess (HCl initial) and the moles of HCl titrated by the NaOH (HCl titrated ). pH is a measure of the concentration of hydrogen ions in a solution and this determines how acidic or how alkaline that solution is. Acid hydrolysis is the first step in the chemical breakdown The nature of HCl is such that its reaction with water as just described is that take place when a type of antacid—a base—is used to treat stomach acid. One method to relieve these symptoms is to neutralize the excess acid with a non-toxic chemical reagent that maintains the contents of the stomach at an appropriate concentration of acid. Observing. Calcium carbonate, or CaCO3, and magnesium hydroxide, or Mg (OH)2, are basic or alkaline compounds and the active ingredients in Rolaids products. Antacids work based on a very simple principle of basic chemistry: When you add an equal amount and strength of an acid substance to an alkali substance, the resulting chemical reaction turns the acid and alkali into salt and water. Time it for up to 5 minutes. These still-helpful agents have a continuing Apr 14, 2020 · This is called acid reflux, which can cause heartburn and/or inflammation of the gullet (oesophagitis). Drink the baking soda solution. Antacids are drugs capable of buffering stomach acid. The substances which neutralize the acids of the stomach are called antacids. Hyperacidity i. Acid reflux can be an unpleasant condition, but by making a few doctor-approved changes you can often manage your symptoms. Antacids such as Tums are often taken to treat heart burn. Antacids are bases which are generally used to neutralize the acid that causes heartburn. The principle is that the stomach produces hydrochloric acid. If you feel relief, you may be producing too much acid. 1 M HCl, with a pH of around 1. Common equations would include: Mg(OH)2 + 2HCl --> MgCl2 + 2H2O Al(OH)3 + 3HCl --> AlCl3 + 3H2O NaHCO3 + HClAn antacid tablet can contain sodium bicarbonate and stomach acid is hydrochloric acid. Sep 22, 2021 · Neutralization is a type of chemical reaction in which a strong acid and Heartburn, as well as an acidic stomach due to eating too much spicy food, can be relieved by taking an antacid Jun 25, 2013 · Antacid (weak base) + HCl (stomach acid) —> salts + H20 + C02. 36 M HCl, thermometer, stir bar and stir plate. 5g in adults and works by simple neutralization, where the hydroxide ions from the Mg (OH) 2 combine with acidic H+ ions produced in the form of hydrochloric acid by parietal cells in the stomach to produce water. Hcl + naoh mr001-1. Magnesium hydroxide, Mg(OH)2 is the active ingredient of some antacids. People also asked. Calcium carbonate is a common ingredient in over-the-counter antacids, such as TUMS. Constipation or diarrhea. Citrus fruits like oranges and grapefruitsand Acid-Base Titrations: Standardization of NaOH and AntacidAchiever Papers - We help students improve their academic Chemical equation for antacid and stomach acid Sodium bicarbonate (IUPAC name: sodium hydrogencarbonate), commonly known as baking soda or bicarbonate of soda, is a chemical compound with the formula NaHCO 3. It is a salt Stomach acid is vital for your digestion and overall health. 3. if you ate 1. You really want to measure the amount of stomach acid neutralized, not the change in pH. It’s brought on by backflow (reflux) of often acidic stomach contents into the food pipe (esophagus) and is usually felt as a burning sensation behind the breastbone. Antacids are bases used to neutralize the acid that causes heartburn. Bloating and cramping. A pH of 7 is neutral, below 7 is acid and above 7 is alkaline. Alternatively, Make a drink using a drop of peppermint essential oil, one teaspoon of manuka honey and half a teaspoon of apple cider vinegar in a glass of warm water. g The pH of a base is 7. When Antacid tablets are placed in water, they undergo a chemical reaction, where the sodium bicarbonate breaks Magnesium hydroxide commonly used as an antacid, for example milk of magnesia, because it reduces stomach acid, and increases water in the intestines which may induce bowel movements. Calcium carbonate reacts w/stomach acid according to the following chemical equation. Without this strong mineral acid the digestive function of the stomach and intestine would be severely limited. 5). Compare equivalence point to endpoint q1. Nov 30, 2020 · The main symptoms of a base deficiency are upset stomach, acid reflux, nausea, GERD, heartburn, a burning sensation in the chest, burps, indigestion, joint pains, burning sensation while urinating, ulcers, bloating, flatulence, diarrhea, constipation, suppressed white blood cells, and increased outfections (bacteria, yeast and mold being born The general neutralization reaction is: Antacid (weak base) + HCl (stomach acid) —> salts + H20 + C02. Antacids are chemical substances that neutralize stomach acid that has already been secreted and thereby raise the pH level in the stomach (make it less acidic). Sodium hydrogen carbonate is an antacid often used to neutralize excess acid. Acid. Magnesite appears as white, yellowish, grayish-white or brown crystalline solid or crystalline powder. (CBSE 2006) Acid: Acids are those substances which release H + ions when dissolved in water. ALUMINUM HYDROXIDE, CALCIUM CARBONATE, MAGNESIUM HYDROXIDE, SODIUM BICARBONATE. Antacids, as one of the oldest and most effective remedies for indigestion and other stomach acid-related issues, are most commonly weak bases of which are used to affect and influence excess stomach acid, and its unusually low pH, through the chemical process of neutralisation (Eddy, 2016). " The duration of Al(OH)3/Mg(OH)2 action in the stomach was 26 min. But by themselves, antacids are not adequate treatment for serious acid-related disorders such as ulcers and severe Antacids perform a neutralization reaction, i. Q2. ) Nov 20, 2018 · What is the overall chemical equation for the reaction of tums, milk of magnesia and baking soda with stomach acid? - 6741597 Antacids are chemical substances that neutralize stomach acid that has already been secreted and thereby raise the pH level in the stomach (make it less acidic). Acids?? Bases-an acid is a compound that produces hydrogen ions (H+(aq)) when dissolved in water-some acids are safe to eat (citric acid, acetic acid in vinegar), while others aren't-many acids are corrosive and will react with metals-aqueous solutions of acids conduct electricity current, because of the ions present in the solution-In 1. Mar 20, 2020 · The chemical equation representing the partial ionization of a weak electrolyte such as acetic acid would be: As before, by representing hydronium as H + (aq), the ionic equation for acetic acid in water is formally balanced without including a water molecule as a reactant, which is implicit in the following form of the equation: Apr 28, 2022 · A chemical called histamine stimulates cells in the stomach lining to make hydrochloric acid. This sensation relieves by the action of antacids. On this scale Aug 21, 2021 · Antacids are medications that do not require a prescription; in other words, they are self-prescribed. Jun 26, 2018 · To help manage symptoms of excess stomach acid and acid reflux, it is best to avoid some foods that stimulate excessive amounts of gastric juice. It is a chalky material that manufacturers form into tablets or prepare as a liquid suspension. Apples, grapes, bananas, melon Nov 20, 2018 · What is the overall chemical equation for the reaction of tums, milk of magnesia and baking soda with stomach acid? - 6741597 Antacids are chemical substances that neutralize stomach acid that has already been secreted and thereby raise the pH level in the stomach (make it less acidic). They are called histamine H2 antagonists (such as Pepcid, Zantac, and Tagamet) and proton excess stomach acid? 4. We are doing everything we can to provide more of your favorite TUMS fast heartburn relief as quickly as possible. 1 It calls itself the “#1 Doctor Recommended Brand” for heartburn relief, and it’s Dr. How much stomach acid reacts with Mg(OH) 2? Write a chemical equation that represents the reaction of Mg(OH) 2 with this substance. 4 lists the common antacids). It can neutralize acid entirely in the stomach. Heartburn is a burning pain that appears in the from the stomach lining breaking down and the acid attacking the stomach wall. So from here, we can deduce that he should be come from Prue. Aug 01, 2019 · b. This medication works only on existing acid in the stomach. By using antacids to control stomach acid, the stomach compensates by providing more acid. Mg (OH) 2 relieves the pain caused by stomach acid by acting as a strong base to create hydroxide (OH-) ions that will react and bind with the additional HCl present that is able to produce an abundance of hydrogen (H +) ions. Poor digestion leading to allergies, bloating and gas. Some antacids have been used in the treatment of constipation and diarrhea. But by themselves, antacids are not adequate treatment for serious acid-related disorders such as ulcers and severe Dec 01, 2017 · In some people, the flap between the esophagus and the stomach that normally prevents acid reflux becomes damaged, in which case heartburn becomes a regular occurrence. The most common treatment for an imbalance of stomach acid is antacid. Drugstores carry many products that either reduce the secretion of stomach acid or neutralize the acid that is produced. When the acidity of the stomach becomes high enough to cause discomfort, brought about by the ingestion of certain types of food, an antacid preparation can be taken to neutralize the excess stomach acid. Indicator 4 jul 2021 Other antacids, such as Alka Seltzer, work in similar ways. The other examples are sodium bicarbonate (NaHCO 3 ), magnesium hydroxide (Mg (OH) 2) and aluminium hydroxide (Al (OH) 3) which are basic in nature because it neutralizes the excess acid in the stomach which causes acidity. When the high pH antacid meets the low pH acidic conditions in the stomach, the resultant environment is neutral or of balanced pH which is neither high nor low. Heartburn is a symptom of the stomach producing too much hydrochloric acid, which is one of the substances found in the gastric The main symptoms of a base deficiency are upset stomach, acid reflux, nausea, GERD, heartburn, a burning sensation in the chest, burps, indigestion, joint pains, burning sensation while urinating, ulcers, bloating, flatulence, diarrhea, constipation, suppressed white blood cells, and increased outfections (bacteria, yeast and mold being born Search: Calculate The Number Of Moles Of Hcl Neutralized By An Antacid Tablet CheggAntacids are the fastest-acting heartburn relief available because they start to weaken the acid in your stomach the second they reach it. The mineral known as magnesium. Some preparations contain a combination of two salts, such as magnesium carbonate and aluminium hydroxide (e. VOCABULARY. Certain polluntants in the air react with water vapor to form acids. 4. 5-1. When a base is added to an acid, water and salt The general neutralization reaction is: Antacid (weak base) + HCl (stomach acid) iC ACIDS Acids are a group of chemicals, usually in liquid form. Heartburn goes by many names - you might also know it as acid reflux or acid indigestion. Adding a base to an acid neutralizes the acid and produces water and a salt When sodium bicarbonate and acid meet in the stomach, a chemical reaction occurs that lowers the acidity of the stomach. 1. Magnesium hydroxide commonly used as an antacid, for example milk of magnesia, because it reduces stomach acid, and increases water in the intestines which may induce bowel movements. Posted on: March 19, 2019, by : admin Sodium bicarbonate (Alka-Seltzer Heartburn Relief) is an alkalinizing agent ( antacid) that reduces stomach acid. Calculate the volume of stomach acid (___ M ____ (fill in concentration and substance)) that reacts with the mass of CaCO 3 that you made. 15 may 2019 Aluminum Hydroxide, Magnesium Hydroxide are antacids used together to relieve heartburn, acid indigestion, and upset stomach. This neutralisation makes the stomach contents less corrosive. Milk of magnesia, also known as magnesium dihydroxide or magnesium hydroxide, is a chemical compound with the formula Mg (OH)2. This acid and base react as shown in Equation 2 below. HCl catalyzes the formation of pepsin—an enzyme that digests proteins in meats, seeds, eggs, and dairy products. The chemical equation for the reaction is: 3NaHCO3 + C6H8O7 → C6H5Na3O7 + 3CO2 + 3H2O. Jpg nacl + h2o + co2. Watch the video below: Can you answer this? Look at the label on a bottle of Mylanta and identify the bases responsible for the antacid acid? Write the chemical equations showing the reactions of these bases Jun 26, 2018 · To help manage symptoms of excess stomach acid and acid reflux, it is best to avoid some foods that stimulate excessive amounts of gastric juice. The longer an antacid stays in the stomach, the longer it works; and having some food in your stomach may actually prolong an In the stomach, only Al(OH)3/Mg(OH)2 increased gastric pH compared with placebo. The active ingredient in The parietal cells in the stomach secrete hydrochloric acid (HCl) at a concentration of roughly 0. 5 grams) baking soda with 1 / 2 cup (about 118 milliliters) water to get relief from the Acid and Bases. These hormones help protect the lining of your stomach, but if they are overwhelmed, it can cause ulcers as well as a host of other symptoms including: 2. The acetyl salicylic acid is "aspirin", the active ingredient which is a pain killer, and this will only be present in small quantity probably USES: This medication is used to treat the symptoms of too much stomach acid such as stomach upset, heartburn, and acid indigestion. This approach is the opposite of what should often be done, and in Two of the more practical methods included the use of plant extracts, commonly known as bitters, and the use of betaine HCL to temporarily increase acid levels with meals. The flow of HCl increases when food enters the stomach. The neat part is we can When we talk about the chemical formula for Magnesium Hydroxide, is used for treating acid indigestion, heartburn, sour stomach, and constipation. The substances which neutralize the acids of the stomach are called antacids. The reaction between the two is as follows: HCl (aq) + NaOH (aq) → H2O (l) + Cl -(aq) + Na +(aq) In this case, Sodium and Chloride act as spectator ions and form into salts in a neutralization The antacid Brioschi, which has been used to relieve heartburn, is mainly sodium bicarbonate. Answer (1 of 2): Gastric acid is mainly HCl; NaCl and KCl. • Alkalis. Tums is a type of antacid with an active ingredient of . Stomach acid is a highly acidic liquid your body naturally produces to help you digest and absorb nutrients in food. 11 At presently in the market there are many antacid preparations available in different formulations. 400 M HCl, how many grams 59,462 resultsThe acid involved is hydrochloric acid. -However if your lower esophageal sphintcter relaxes or becomes weak stomach acid can flow backwards into the esophagus causing the burning sensation of heartburn. the HCl respectively in the balanced chemical equation. When this is done, improper food digestion occurs, and then ferments. In this experiment, the reagents combined are an acid, HCl (aq) and a base, NaOH (aq) where the acid is the analyte and the base is the titrant. Investigating the effect of acid on indigestion tablets Introduction. a) Complete and balance the following molecular equation: Na_2CO_3 (aq) + HBr (aq) right arrow a) Write the ionic equation for the completed reaction in part (a). The reaction is between an antacid and stomach acid. Practical Skills: • Exploring neutralisation reactions Antacid. A chemical reaction happens if you mix together an acid and a base. Then the whole problem starts all over again. The acid involved is hydrochloric acid. However, it is important to use antacid in moderation as antacids reduce the amount of stomach acid, which can be disastrous if the symptoms are caused by low stomach acid production. The chemical formula for Magnesium Hydroxide is \({\text{Mg}}{\left({{\text{OH}}} \right)_2}. Dry As is known to the majority of individuals, aluminum is a naturally available mineral while Aluminum Hydroxide comes in the form of an antacid. To help manage symptoms of excess stomach acid and acid reflux, it is best to avoid some foods that stimulate excessive amounts of gastric juice. NaHCO 3 (aq) + HCl (aq) -----> NaCl (aq) + H 2 O (l) + CO 2 (g) In this experiment, several brands of antacids will be analyzed to determine the number of moles of acid neutralized per tablet and the cost analysis of each tablet. when stomach produce too much of acid, leads to heartburn. Both acids and alkalis are corrosive, but salt and water are, of course, harmless substances. Stomach acid is HCl, not H2SO4. 5% hydrochloric acid (HCl) by mass, or about 0. Citrus fruits like oranges and grapefruits oesophagus and excess acid in the stomach. Aluminum Hydroxide, Magnesium Hydroxide are antacids used together to relieve heartburn, acid indigestion, and upset stomach. Reaction of tums with HCl is 5 abr 2022 Antacids contain sodium bicarbonate. ' Sometimes the acid escapes from top of the stomach which causes pain in the tube leading to the mouth this is called 'heartburn' The equation of hydrochloric acid being neutralized by sodium bicarbonate looks like this: 2HCl + CaCO3-> CaCl2 Calcium Carbonate is the carbonic salt of calcium (CaCO3). Antacids. Buffer acide. Students then write the balanced chemical equation between the stomach acid and the antacid chosen. Jpg nacl + h2o 2hcl + caco3 mr001-2. 27 ago 2013 This classic demonstration of a chemical reaction is quantified and enhanced Most will assume the pH is low since vinegar is an acid. Write chemical equations showing the reactions of each of the bases in the antacids discussed here with stomach acid (HCl). Stomach acid mostly contains hydrochloric acid (HCl), a very strong acid. HCl + NaOH→ NaCl + H 2O. The active ingredient in many antacids is calcium carbonate (CaCO₃), a base that is actually found in several natural minerals, including limestone, marble, and chalk. Your stomach contains hydrochloric acid, and too much of this causes indigestion. Hydrochloric acid, also known as muriatic acid, is one of the strongest cleaners available to the average homeowner. Aluminum hydroxide and magnesium hydroxide act as antacids by neutralizing stomach acid that result in an increasing pH in the stomach. May 08, 2022 · Stomach acid typically has a pH of 1 and vinegar has a pH of 2 or 3. In this demonstration, a 250 mL flask is used to model the stomach and to show how the sodium alginate in the product Gaviscon reacts with the acid in the stomach to form a barrier or “raft” which forms a Add a drop of peppermint essential oil to your herbal tea. Jpg mgcl2 + 2h2o 6hcl + 2al mr001-4. Rinse any remaining fragments into the flask with a few cm 3 of Search: Calculate The Number Of Moles Of Hcl Neutralized By An Antacid Tablet CheggPharmacology. This is because the reaction between these substances happens […] from the stomach lining breaking down and the acid attacking the stomach wall. Antacids such as Mylanta or Phillips' milk of magnesia contain bases that neutralize the refluxed stomach acid alleviating heartburn. 3 average score. The balanced chemical equation is as follows: 2CH3CH2CO2H (aq) + Ca (OH)2(aq) → (CH3CH2CO2)2Ca (aq) + 2H2O (l) The reaction of a weak acid and a strong base will go to completion, so it is reasonable to prepare calcium propionate by mixing solutions of propionic acid and calcium hydroxide in a 2:1 mole ratio. 400 M HCl, how many grams of carbon dioxide gas are produced?Experiment #11: Titration of a Commercial Antacid Objective: To measure the quantity of stomach acid that can be neutralized by a tablet of Tums. arrow_forward Write an equation for the following reactions and where appropriate, label the conjugate acid-base pairs. These chewable tablets contain a triple-active formula that goes to work instantly * to relieve heartburn, sour stomach, and acid indigestion, and relieve the pressure and bloating commonly referred to as gas associated with these symptoms. ). 400 M HCl, how many grams of carbon dioxide gas are produced?Acid of pH 2 can be quite corrosive – observe the effect of placing an iron nail in 0. This is what I found, hope it helps:) Jul 06, 2016 · How do you write the chemical equation for the reaction of #NaHCO_3# with #HCl#? Malox, an over-the-counter antacid, contains aluminum hydroxide, Al(OH) 3, and magnesium hydroxides, Mg(OH). Jpg 2alcl3 + 3h2 hcl + nahco3 mr001-5. When an antacid is mixed with an acid the buffer tries to even out the iC acidity and that is how stomach acid gets neutralized. 00 mL of 0. they buffer gastric acid, raising the pH to reduce acidity in the stomach. CaCO 3: Chalk is the common name for calcium carbonate and is the most abundantly available antacid. Subsequently, one may also ask, what is the chemical reaction between antacids and stomach acid? Antacids work by Equation 2: Ka=H+ [Cl-] [HCl] The equation is a ratio of products to reactants, whereby the more HCl dissociates into H+ and the conjugate base Cl–, the stronger the acid and thus the closer the value is to one. Learn about the net ionic equation, review examples of If the stomach contains too much acid then it can cause pain and it is called 'INDIGESTION. This problem has been solved! See the answer Show transcribed image text Expert Answer 100% (1 rating) The balanced equation for the … View the full answerPreparing simulated stomach acid. 1 M NaOH would be ideal). Mild Discomfort. It is an antacid that works by lowering the amount of acid in the stomach Antacids-11 Potential problems associated with frequent or long term use of antacids in general include: 1. Which chemical equations show a reaction that occurs when someone takes an antacid? check all that apply. If you're one of those 60 million, you've probably reached for an antacid to relieve that uncomfortable burning sensation, as antacids neutralize excess stomach acids and can usually relieve occasional Neutralization reactions are one type of chemical reaction that proceeds even if one reactant is not in the aqueous phase. What are some reasons you may be struggling with low production of hydrochloric acid, gastric juices and stomach acid? Low stomach acid is a very common problem among people living in Western industrialized nations for reasons including: Regularly taking antacids in order to reduce heartburn symptoms. If you take an antacid, it will buffer the stomach acid. Acid-base reactions are the chemical reactions that occur when acids and bases are mixed together. These compounds react with and neutralize some of the stomach acid in your digestive tract. Step 2. Write the chemical equation for the reaction of an antacid containing magnesium hydroxide, Mg (OH) 2, with stomach acid (hydrochloric acid, HCl) and then balance the equation. Aluminum and magnesium antacids work quickly to lower the acid inAntacid. Both acids and alkalis are corrosive, but salt and water are, of course, harmless Antacids are weak bases. Biological buffers can be5. Two common antacid ingredients are CaCO 3, which is found inTums and Rolaids, and Mg(OH) 2, which is found in Milk of Magnesia. Doctors can prescribe antacids. This acidic fluid is composed of hydrochloric acid (chemical formula, HCl) with large quantities of potassium chloride (chemical formula, KCl) and sodium chloride than other antacids and neutralize stomach acid to a large degree as opposed to its counterparts. 8. There is a certain level of acid in your stomach. Concentrated gastric acid is about 0. Stomach acid, also known as gastric acid, is a digestive fluid formed in the stomach in aid of food digestion. Equipment for illustrating the use of indigestion tablets to neutralise hydrochloric acid. 2HCl + Mg(OH)2 MgCl2 + 2H2O The stomach has an acidic interior generated by dilute HCl, "stomach acid", which insures proper digestion. (a) Write the formula and chemical name of bleaching powder. Antacids are the primary treatment for ailments such as gastric reflux‚ gastritis‚ upset stomach and heartburn. -To neutralize an acid a base needs to be added-Therefore a In determining the efficiency of an antacid tablet, the volume of unreacted HCl in the antacid mixture is titrated with NaOH. Equation two represents the total amount of stomach acid neutralized by the antacid present in solution; equation 3 relates this volume to the actual mass of the Maalox tablet. Everybody has acid in their stomach, so it is a common problem too. Al(OH)3 reacts with H+ in a mole ratio of 1:3; Mg(OH)2 reacts Question 1. Stomach acid is neutralized by CaCO 3 Apr 01, 2019 · First thing in the morning, before eating or drinking anything: Mix ¼ tsp baking soda in 4 to 6 ounces of cold water. b) Write the net ionic equation 1. Antacids. Acids react with carbonate to Calcium carbonate (CaCO3) reacts with stomach acid (HCl, hydrochloric acid) according to the following equation: CaCO3(s)+2HCl(aq)⟶CO2(g)+H2O(l)+CaCl2(aq) Understandings:Non-specific reactions, such as the use of antacids, are those that work to reduce the excess stomach acid. Antacids are a class of medicines that neutralize acid in the stomach. The normal acid level in the stomach is about 2 or 3 on this scale. The reaction between the two is as follows: HCl (aq) + NaOH (aq) → H2O (l) + Cl –(aq) + Na +(aq) In this case, Sodium and Chloride act as spectator ions and form into salts in a neutralization Antacid (weak base) + HCl (stomach acid) —> salts + H2O + CO2. This gives us moles of HCl remaining after the antacid has reacted. Antacid tablets are made of numerous numbers of components, such as sodium bicarbonate (baking powder), magnesium hydroxide, critic acid, and many others. As learned in chemistry, when a base is mixed with an acid a neutralization ( A type of double displacement ) reaction occurs. Freshly secreted gastric juice is 0. Brønsted-Lowry theory of acids and bases discusses them Because it reacts with stomach acid and can produce a significant amount of carbon dioxide gas, sodium bicarbonate may cause people to belch or get flatulence A chemical technique called a 'titration' can be used to see how much acid an antacid tablet can neutralize. Dry This bug suppresses your ability to manufacture hydrochloric acid, in an attempt to survive inside your stomach; Bad breath; After age 50 stomach acid production sharply declines; Antacids and medication for reflux and heartburn suppress stomach acid production, and this has terrible consequences for digestion and overall immune health. 1 g cm-3. This bug suppresses your ability to manufacture hydrochloric acid, in an attempt to survive inside your stomach; Bad breath; After age 50 stomach acid production sharply declines; Antacids and medication for reflux and heartburn suppress stomach acid production, and this has terrible consequences for digestion and overall immune health. They are called histamine H2 antagonists (such as Pepcid, Zantac, and Tagamet) and proton We review their content and use your feedback to keep the quality high. An antacid is a substance which neutralizes stomach acidity and is used to relieve heartburn, indigestion or an upset stomach. Everybody uses antacids. Do not take it straight as it may cause irritation. After ingestion of calcium carbonate, gastric pH usually remained at or below placebo values, a finding consistent with a calcium carbonate-induced "acid rebound. 5 to 3. The byproducts of these reactions are water, magnesium chloride, calcium chloride and carbon dioxide gas. reaction of and antacid tablet within the stomach: B. See full list on ukdiss. Antacid (weak base) + HCl (stomach acid) —> salts + H20 + C02. Equation 1 says that when an acid and a base react together, they produce a salt and water. Jul 17, 2018 · Equation two represents the total amount of stomach acid neutralized by the antacid present in solution; equation 3 relates this volume to the actual mass of the Maalox tablet. b. Take vitamin However, in the reaction between HCl(aq) and Mg(OH) 2 (aq), additional molecules of HCl and H 2 O are required to balance the chemical equation: 2HCl(aq) + Mg(OH) 2 (aq) → 2H 2 O(ℓ) + MgCl 2 (aq) Here, the salt is MgCl 2. 5% HCl by mass (pH ~ 1). Aluminum hydroxide inactivates the gastric digestive enzyme pepsin. The reaction between the two is as follows: HCl (aq) + NaOH (aq) → H2O (l) + Cl –(aq) + Na +(aq) In this case, Sodium and Chloride act as spectator ions and form into salts in a neutralization What type of chemical reaction take place to help remove the excess acid in the stomach whenever antacids are used? Write the NET ionic equation of the reaction between an antacid and stomach acid. Antacids are the fastest-acting heartburn relief available because they start to weaken the acid in your stomach the second they reach it. The main job of stomach acid is to break down food into molecules your body can absorb. Product Availability: Due to high demand some TUMS items are in limited supply. Citrus fruits like oranges and grapefruits What Causes Too Much Acid in Stomach: Signs & Treatments Feb 16, 2017 · With an excess buildup of stomach acid, you can experience symptoms ranging from discomfort to extreme pain. Biological buffers can beWhat type of chemical reaction take place to help remove the excess acid in the stomach whenever antacids are used? Write the NET ionic equation of the reaction between an antacid and stomach acid. PROCESS SKILLS. An antacid is any substance, usually a base or a basic salt (a base or any basic chemical has high pH) which is utilised to neutralize stomach acidity (an acid has very low pH). See if your school's science teacher can provide you with standardized 0. 16 M. 500 g of Al(OH)3. Students then write the balanced chemical equation between the stomach acid and the antacid chosen. Aluminum Hydroxide, Magnesium Hydroxide are antacids used together to relieve heartburn, acid indigestion, and upset stomach. The correct balanced equation between the base Al(OH)₃ and stomach acid HCl will be:First thing in the morning, before eating or drinking anything: Mix ¼ tsp baking soda in 4 to 6 ounces of cold water. Acid-Base Reactions SNC2D. Stomach acid, or gastric acid, is a watery, colorless fluid that's produced by your stomach's lining. Calcium carbonate (CaCO3) reacts with stomach acid (HCl, hydrochloric acid) according to the following equation:CaCO3(s)+2HCl (aq)?CO2 (g)+H2O (l)+CaCl2 (aq)Tums, an antacid, contains CaCO3. One simple treatment for heartburn symptoms is to take a simple antacid - a substance that will reduce the concentration of acid in the stomach by reacting with some of it. For example, the chemical reaction between HCl(aq) and Fe(OH) 3 (s) still proceeds according to the equation 3HCl(aq) + Fe(OH) 3 (s) → 3H 2 O(ℓ) + FeCl 3 (aq) even though Fe(OH) 3 is not soluble. Pepcid Complete Acid Reducer + Antacid Chewable Tablets for Heartburn Relief, Mint Flavor, 50 ct. Equation one represents the calculated volume of excess stomach acid neutralized by the NaOH after the reaction with the antacid tablet. 16 molar in concentration (0. Antacid. Identify all of the phases in your answer. This is because bases are the opposite of acids, when an antacid is consumed it goes into the stomach and creates a chemical reaction lowering the acidity and making stomach acid less corrosive Calcium carbonate antacid tablets. Heartburn is a burning pain that appears in the Dec 05, 2021 · When sodium bicarbonate and acid meet in the stomach, a chemical reaction occurs that lowers the acidity of the stomach. Besides these components, amino acids, raw fiber, ash, protein, phytosterols, vitamins (e. 14 feb 2019 Stomach Antacids. Recent research indicates these drug often . 400 M HCl, how many grams of carbon dioxide gas are produced?Acid of pH 2 can be quite corrosive - observe the effect of placing an iron nail in 0. Sodium hydrogen carbonate is an antacid often used to neutralize excess acid. Excess stomach acid can be combated with bases, or "antacids". 17 reviews submitted with a 8. The stomach acid has a pH of 1 to 2. This is because the reaction between these substances happens […]Alka-Seltzer is used for the relief of heartburn upset stomach acid indigestion with headache and body aches. CCEA Chemistry. In order to neutralise stomach acid and alleviate indigestion and heartburn, milk of magnesia is often sold as an antacid. Search: Calculate The Number Of Moles Of Hcl Neutralized By An Antacid Tablet Cheggbismuth chemical formulaya book pre order incentives 2022 Velocity Championship ActionAntacid (weak base) + HCl (stomach acid) —> salts + H20 + C02. 0 grams of Rolaids, you would neutralize 47 Mg (OH) 2 + 2 HCl Mg 2+ + 2 Cl – + 2 H 2 O. Biological buffers can be Jul 21, 2013 · Antacids work based on a very simple principle of basic chemistry: Acid + Alkali = Salt + Water. An antacid is a substance which neutralizes stomach acidity and is used to relieve heartburn, indigestion or an upset stomach. Mg(OH) 2 (s) + 2H 1. Antacid preparations serve to neutralize gastric acid after it is secreted. Antacids and Heartburn. A substance that neutralises stomach acid. Sodium bicarbonate reduces stomach acid. The chemical equation that describes the reaction between HCl and NaOH is. 1 recall the use of digestion remedies, for example hydroxides and carbonates, to cure excess acid in the stomach (link with Section 1. Ideal pH is between 6. The effectiveness of the calcium carbonate in each tablet was evaluated on a scale of one to ten, with ten neutralizing the full volume of stomach acid. The highly acidic properties of the gastric juice, together with digestive enzymes, help with food breakdown so that the body can extract nutrients from food. In the video, Robert suggests individuals with kidney disease stay away from the use of PPI (proton pump inhibitor Jan 19, 2011 · How Antacids Work. Aluminum hydroxide is an antacid that works quickly to lower the acid in the stomach. Upset stomach, indigestion, and the much publicized "acid reflux" all occur when the body produces an Aluminum and magnesium antacids work quickly to lower the acid in the stomach. The analytical procedure used is known as back titration. The carbonic acid then spontaneously decomposes to form carbon dioxide and water. With proper use, it decreases the pain of acid indigestion and heartburn. In a healthy stomach, pH is regulated naturally and digestion functions properly when the pH is around 3 (recall neutral is pH = 7). For example, HCl(aq) is the acid in your stomach: HCl(aq) → H + (aq) + Cl - (aq). The equation to calculate for the amount of HCl neutralized is. Most people tend to pop an antacid to get relief from the stomach acid pain, but one must know that such chemical compounds weaken your stomach secretion over time or can even increase the production of gastric acid, thus, increasing your trouble. Prilosec, or omeprazole, belongs in the proton pump inhibitor category of antacid drugs, which means it reduces the amount of food-digesting acid produced by the cells in your stomach lining. An antacid that raises the pH from 1. Chemistry. The Effectiveness of Antacid Tablets Introduction: Stomach acid (hydrochloric acid) is vital to human digestion. 150 M hydrochloric acid then how many grams of magnesium hydroxide was in the tablet? It is composed of hydrochloric acid. Search: Calculate The Number Of Moles Of Hcl Neutralized By An Antacid Tablet CheggThe antacid was then crushed with the pestle and mortar until it was a fine powder. Experiment #11: Titration of a Commercial Antacid Objective: To measure the quantity of stomach acid that can be neutralized by a tablet of Tums. Compound; Chemical Formula; Chemical Reaction; Aluminum hydroxide; Al(OH)3 So from here, we can deduce that he should be come from Prue. When sodium bicarbonate and acid meet in the stomach, a chemical reaction occurs that lowers the acidity of This is the reaction that occurs when an antacid containing the active ingredient calcium carbonate (CaCO3) reacts with stomach acid (hydrochloric acid). The overall reaction is shown below: 2 HCl (aq) + CaCO 3 (s) → H 2 O (l) + CaCl 2 (aq) + CO 2 (g) (Equation 2) Stoichiometric Calculations Involving Acid neutralizing capacity of an antacid is defined as the number of mEq of 1N HCl that are brought to the pH of 3. The general neutralization reaction is: Antacid (weak base) + HCl (stomach acid) —> salts + H20 + C02. Antacid pills are composed of calcium carbonate, and react with hydrochloric acid to produce calcium chloride, water and carbon dioxide gas. So When the antacid reaches our stomach, it neutralizes the hydrochloric acid and produces carbonic acid (H 2 CO 3). Antacid (weak base) + HCl (stomach acid) —> salts + H2O + CO2. In medicine, antacids containing small amounts of calcium carbonate are used in the treatment of ‘acid stomach’. It is used as an antacid to treat heartburn, indigestion, and upset stomach. Turn on the stir Jul 20, 2010 · What is a chemical formula for ingesting antacid tablets? Antacid contains a chemical to reduce stomach acid, which is the cause of indigestion. In this demonstration, a 250 mL flask is used to model the stomach and to show how the sodium alginate in the product Gaviscon reacts with the acid in the stomach to form a barrier or “raft” which forms a CaCO 3: Chalk is the common name for calcium carbonate and is the most abundantly available antacid. Antacid tablets are medicines that help neutralize the acid in your stomach. Unit 2: Further Chemical Reactions, Rates and Equilibrium, Calculations and Organic Chemistry. Some antacids contain a base-type chemical compound. Despite the many commercial brand, almost all antacids act on excess stomach acid by in the simulated stomach acid! This is a great demonstration to teach concepts of acids and bases, solubility, Ksp and. The acid reflux which causes a burning sensation in the chest can Feb 22, 2022 · Antacids are bases and most of them react on the excess build up of stomach acid and neutralises the acid. 131 M HCl. Watch the video below: Can you answer this? Look at the label on a bottle of Mylanta and identify the bases responsible for the antacid acid? Write the chemical equations showing the reactions of these bases Antacid. The above reactions are all common reactions between an antacid and stomach acid, HCl. Write a balanced chemical equation for the reaction of $\mathrm{CaCO}_{3}$ and stomach acid $(\mathrm{HCl})$ Plus HCL HCL would be present in stomach acid balanced Too much acid in your stomach can overwhelm the prostaglandins (hormone-like chemicals that influence pain and inflammation) in your stomach and duodenum. Mar 03, 2014 · the reaction equation depends on the antacid used
mdn lnk aaec bfdd gech fc ecgh bh nr vs jf jr bjg lm aaaa dcdb eele mejp bdc hefc jhar ck idd bedg mp aa aaac bika ccdc ce cc
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Question
# A circle touches the side BC of $$\Delta$$ ABC at P and touches AB and AC produced at Q and R respectively.$$If AQ = 5 cm$$, then find the perimeter of$$\Delta$$ ABC
A
5cm
B
10cm
C
25cm
D
50cm
Solution
## The correct option is D $$5 cm$$$$AQ=5$$cmPerimeter of $$\Delta ABC$$$$AQ=AR=5$$cm$$\{$$From a external point if drawn two tangents are equal in length$$\}$$Perimeter of $$\Delta ABC=AB+BC+AC$$ .......$$(1)$$But $$BQ=BP$$ .....$$(2)$$$$CP=CR$$ ......$$(3)$$$$\{$$From a external point if drawn tangents are equal in length$$\}$$$$\Rightarrow BP+PC=BQ+CR=BC$$ ..........$$(4)$$And $$AQ=AB+BQ=AB+BP$$ $$\{$$from equation $$(2)\}$$$$\Rightarrow AB=AQ-BP=5-BP$$$$\Rightarrow AB+BP=5$$and $$AR=AC+CR=AC+CP$$ $$\{$$from equation $$(3)\}$$$$AC=AR-CP=5-CP$$$$AC=CP=5$$From $$(1)$$Perimeter$$=AB+BC+AC$$$$=AB+BP+PC+AC$$ $$\{$$From equation $$(4)\}$$$$=5+5$$$$=10$$cm.Mathematics
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# LuaLaTeX and algorithm2e [closed]
The algorithm2e package seems to be not compatible with LuaLaTeX. For example, compiling the following code produces an error.
\documentclass{article}
\usepackage{fontspec}
\usepackage{algorithm2e}
\begin{document}
foo
\end{document}
Output of lualatex:
...
! String contains an invalid utf-8 sequence.
l.778 \renewcommand{\@algocf@procname}{Proc
�dure}%
?
! Emergency stop.
Has someone an idea how to fix that? I have a lot of algorithms typeset and do not want to switch to another package just because of LuaLaTeX.
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## closed as off-topic by Werner, Kurt, Paul Gaborit, Papiro, JesseNov 25 '15 at 1:37
• This question does not fall within the scope of TeX, LaTeX or related typesetting systems as defined in the help center.
If this question can be reworded to fit the rules in the help center, please edit the question.
The Package is not in UTF-8 format. If you open it and save it back in UTF-8 format it works (for me). To try, please copy algorithm2e.sty in the same directory, open it with an editor that can save it back in UTF-8. – Andy Nov 14 '11 at 15:56
@Andy. That works too. Thanks for your tip! – Peter Nov 14 '11 at 16:38
@Andy: converting to utf8 will help with lualatex but then you will probably get wrong fix names with pdflatex + an 8bit-option of inputenc. Using non-ascii chars in a sty is simply a bad idea. – Ulrike Fischer Nov 14 '11 at 17:33
My version use procédure which is ok for french. A sty should be pure ascii and it doesn't matter how you save it as the result will be the same. ascii chars are encoded identically in utf8, ansinew, latin1 etc. – Ulrike Fischer Nov 14 '11 at 18:06
I'm voting to close this question as off-topic because this problem cannot be reproduced anymore. – Werner Nov 25 '15 at 1:03
algorithm2e.sty contains (at least) two non-ascii chars (é in procédure), but the file is 8bit encoded so it is not a valid utf8 file. You (or the author) should replace the é by \'e.
@Peter: Unfortunately there are several other usages of é in that file, so I would try to use search-and-replace. Please don't forget to post a email to the author and mentioning this. It should be fixed for the next release. – Martin Scharrer Nov 14 '11 at 16:03
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# In the complex ion ${\left[ {{\text{Fe}}\left( {{\text{EDTA}}} \right)} \right]^{\text{ - }}}$ the coordination number and oxidation state of central metal ion is:A) CN = $6$ ON = $+ 3$B) CN = $1$ ON = $- 1$C) CN = $4$ ON = $+ 2$D) CN = $3$ ON = $+ 3$
Last updated date: 29th Mar 2023
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Hint: We need to know that in chemistry three types of chemical bond. There are ionic bonds, covalent bonds and coordinate bonds. The coordination chemistry in one of the major topics in chemistry. The coordination bond plays an important role in coordination chemistry. The complex is formed in nature, basic coordination chemistry. The full form of ${\text{EDTA}}$ is EthyleneDiamineTetraAceticacid.
We also remember that the metal atom present in the complex is called a central metal atom. The atom which donates a lone pair of electrons to the central atom or the coordinate bond with the central atom is known as ligand.
As we know that the oxidation state of the central metal atom is equal to the number of primary valencies. The coordination number of the central metal atom is equal to the secondary valency.
In ${\left[ {{\text{Fe}}\left( {{\text{EDTA}}} \right)} \right]^{\text{ - }}}$
The central atom is ${\text{Fe}}$ and the ligand is ${\text{EDTA}}$.
The number of lone pairs donating atoms in ${\text{EDTA}}$ is $6$.
The oxidation state of${\left[ {{\text{Fe}}\left( {{\text{EDTA}}} \right)} \right]^{\text{ - }}}$ is $+ 3$.
The coordination number and oxidation number of ${\left[ {{\text{Fe}}\left( {{\text{EDTA}}} \right)} \right]^{\text{ - }}}$ is $6$and $+ 3$.
Hence, option A is correct because CN = $6$ ON = $+ 3$
Note:
We also remember that in chemistry, substances are majorly divided into two types. This classification is dependent on the stability of the substance. Compound and complex are the classification of the substance in the chemistry. In coordination chemistry, primary and secondary valency in the complex. The primary valencies are ionic bonds. The primary valencies are non-directional. The secondary valencies are coordinate bonds. The secondary valence is directional. The structure of the complex is dependent on the secondary valence.
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# How to check whether an ideal is a prime (or maximal) ideal?
I have a ring $R$ which is known to be a Dedekind domain, but not necessarily a Euclidian domain, and a nonzero ideal generated by one or two elements in this ring. How can I check if this ideal is a prime ideal?
For ideals generated by one element, this is equivalent to being a prime element in the ring. I programmed a clone of the Erathosthenes sieve for my ring, but this only shows me which elements are irreducible, which does not necessarily imply primality.
To be more concrete, my ring $R$ is the ring of integers in an imaginary quadratic number field $\mathbb{Q}(d)$ (for $d$ a negative squarefree integer).
These rings are of the form $R = \mathbb{Z}[\sqrt{-d}]$ or $R = \mathbb{Z}[\frac{1+\sqrt{-d}}{2}]$, depending on $d$. These are Dedekind domains, and every ideal there is generated by either one or two elements.
For some $d$ (like $-1$, $-2$, $-3$), these are Euclidean domains, where I can use the division with remainder to find the greatest common divisor of two numbers, meaning that each ideal is generated by one element.
For others (like $d = -7$), there is no division with remainder, and we can't use the Euclidean algorithm.
But even here it is not yet clear for me: how do I distinguish irreducible from prime elements? The most famous example: for $d = -5$ we have $R = \mathbb{Z}[\sqrt{-5}]$, and the element $2$ is not prime here, since $2 \cdot 3 = 6 = (1+\sqrt{-5})\cdot(1-\sqrt{-5})$ and 2 is not a factor of either term on the right side.
By testing multiples, I can find numbers with different decompositions, and then know that those factors can't be prime. But when can I stop searching, if I don't find any?
In this particular ring, the first elements not yet shown as either units, irreducible-not-prime or composite (after checking all elements until about $\pm 50 \pm 50i$) are $\pm \sqrt{-5}$, $\pm 4 \pm 2\sqrt{-5}$, $\pm 6 \pm \sqrt{-5}$. Could I be sure here that there really are prime?
Another example, $d = -7$, $R = \mathbb{Z}[\frac{1+\sqrt{-7}}{2}] = \mathbb{Z}[X]/(X^2+X+2)$: Here I find lots of irreducible-non-prime elements, and the only small "irreducible and not yet shown as non-prime" are $\pm \frac{1-\sqrt{-7}}{2}$. (The principal ideal generated by these elements look quite same as the one created by $\frac{1+\sqrt{-7}}{2}$, though - I think there is simply a glitch in my program.)
This ring is non-Euclidean, and I suppose most (if not all but the zero ideal) prime ideals are generated by two elements here. If I have a candidate pair of elements, how do I find out if it is really a nonzero prime (= maximal) ideal?
Any ideas here would helpful, since I'm a bit stuck here. (Most literature about computational ideal theory I found only works in polynomial rings over fields (and makes heavy use of this fact), thus it does not really help here.)
(I'm writing a program which should then be able to work on any of these rings $R$ (and any ideals there), thus facts that are only valid in a small number of those rings are less helpful. But feel free to mention them nevertheless, maybe some of them can be generalized.)
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To check if an ideal is prime, one way is to look at the quotient $R / I$; the ideal $I$ is prime if and only if $R / I$ is an integral domain.
To expand a bit on that: say you have two elements $(x, y)$, and you want to know if the ideal $I$ they generate is prime. This ideal $I$ certainly contains the elements $xx^*$ and $y y^*$ (where * is the Galois "conjugation" automorphism of R). These are in $\mathbb{Z}$, so they have a highest common factor; let's say that is $k$.
Then $kR$ is an ideal of $R$ contained in $I$. Moreover, the ring $R / k R$ is finite, and you can now describe $R / I$ by a finite computation, because it's a quotient of $R / kR$. In particular, you can check whether or not $R / I$ is a field.
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Looks good. I'll have to see how this fits in my program. – Paŭlo Ebermann Jun 20 '11 at 17:14
This is false for the zero ideal. The correct general statement is that $I$ is a prime ideal if and only if $R/I$ is an integral domain, and $I$ is a maximal ideal if and only if $R/I$ is a field. It just so happens that for number rings, every nonzero ideal $I$ has the property that $R/I$ is finite, hence is an integral domain if and only if it is a field, so every nonzero prime ideal is maximal. – Qiaochu Yuan Jun 20 '11 at 22:35
$\newcommand{\Z}{\mathbb{Z}}$
One way is to translate the problem. You are looking to see if the ideal $I$ is prime in an imaginary quadratic ring. For $d \equiv 1,2$ modulo $4$, this is $\frac{\Z[x]}{x^2+d}$; for $d \equiv 3$ modulo $4$, it's $\frac{\Z[x]}{x^2 + x + \frac{d+1}{4}}$.
The ideal $I$ is prime if $R/I$ is an integral domain (no zero divisors). The trick then is to interchange the quotients of the rings. So for example, in $d=5$, say you're checking to see if $I=(2)$ is prime. Then $R=\frac{\Z[x]}{x^2+5}$. Now by interchanging the quotients this is equivalent to seeing whether $(x^2+5)=(x^2+1)$ is prime in $\frac{\Z[x]}{2}$. In this case it is not, since $(x^2+1) = (x+1)^2$. If you translate this back, since $x$ "represents" $\sqrt{-5}$, you get that the ideal $(2) = (1+\sqrt{-5})^2$.
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# whitespaces in alltt environment get merged
\begin{frame}{Beispiel Mergesort}
\begin{alltt}
mergesort :: (Ord a, Trans a) => [a] -> [a]
mergesort [] = []
mergesort [x] = [x]
mergesort xs = sortmerge (process mergesort \# xs1)
(process mergesort \# xs2)
where (xs1,xs2) = unshuffle xs
\end{alltt}
\end{frame}
I'm doing a beamer presentation and try to display some source code, but I'm loosing all intendation, all whitespaces get merged into a single space. (not only at the beginning of the lines, but also around the '=' characters)
I don't know what I'm doing wrong.
Can someone help?
Cheers,
Lukas
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Welcome to TeX.SX! I guess you want \begin{frame}[fragile]\frametitle{Beispiel Mergesort} – egreg Jul 13 at 14:54
you, sir, are brilliant! thanks! – Whadupapp Jul 13 at 14:59
Frames containing verbatim material should be declared fragile; also you don't really want that dramatic indentation, which will be kept in the listing.
\documentclass{beamer}
\usepackage{alltt}
\begin{document}
\begin{frame}[fragile]
\frametitle{Beispiel Mergesort}
\begin{alltt}
mergesort :: (Ord a, Trans a) => [a] -> [a]
mergesort [] = []
mergesort [x] = [x]
mergesort xs = sortmerge (process mergesort \# xs1)
(process mergesort \# xs2)
where (xs1,xs2) = unshuffle xs
\end{alltt}
\end{frame}
\end{document}
I think it is better to use the \frametitle command rather than an additional argument to \begin{frame}.
Instead of alltt you can use the semiverbatim environment, which doesn't require an additional package, but still requires [fragile].
-
thanks! Actually the tabs in front of the line don't seem to matter, those get killed by tex, just the intendation using spaces is kept. So I keep my tabs and get a nice looking tex code ;-) Thank you =) – Whadupapp Jul 13 at 15:01
@Whadupapp In order my files don't have any TAB character, my editor does exactly nothing when the TAB key is hit. – egreg Jul 13 at 15:03
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Technical Article
# The Interleaved Inverting Charge Pump - Part 1: A Topology for Low Noise Negative Voltage Supplies
March 08, 2022 by Jon Kraft
## Analog Devices offers a wide variety of solutions for producing low noise power. Most of these solutions are designed to produce positive voltage rails, with fewer dedicated ICs for generating negative voltages. This can be particularly limiting when the negative voltage needs to power low noise devices, such as RF amplifiers, switches, and data converters (ADCs and DACs).
### Introduction
Noise must be minimized in precision instrumentation or radio frequency (RF) circuits, but reducing noise comes with a number of challenges due to the nature of these systems. For instance, these systems must often operate over a wide input voltage while meeting strict electromagnetic interference (EMI) and electromagnetic compatibility (EMC) requirements. Furthermore, systems are crowded with electronics, making them space-constrained and heat sensitive. The increasing complexity of integrated circuits (ICs) has led to an increase in the number of power supply voltage rails that these systems require. Generating all these rails, meeting the above requirements, and keeping the entire system low noise can be daunting.
In Part 1 of this article series, we introduce a method to generate this low noise negative rail from a positive supply. It starts with a general understanding of how negative rails are typically generated and where they are used. Then we discuss the standard inverting charge pump before introducing an interleaved inverting charge pump (IICP) topology. A short derivation of the input and output voltage ripple for the IICP emphasizes its unique advantages for low noise systems.
Part 2 of the series gives a practical example of an IICP implementation with Analog Devices’ ADP5600. We first compare this part to a standard inverting charge pump by measuring voltage ripple and radiated emissions. Then we use the equations from Part 1 to optimize the IICP performance and develop a complete solution for powering a low noise RF circuit.
### Traditional Negative Voltage Generation Methods
To create a negative voltage, one of two methods is commonly employed: use an inductive switching regulator or use a charge pump. Inductive switchers use an inductor or transformer to generate the negative voltage. Examples of these magnetic converter topologies are: inverting buck, inverting buck-boost, and Ćuk. Each of these has its own set of advantages and disadvantages regarding solution size, cost, efficiency, noise generation, and control loop complexity.1, 2 In general, the magnetics-based converters are best suited when higher output currents are required (> 100 mA).
For applications requiring less than 100 mA of output current, charge pump positive-to-negative (inverting) dc-to-dc converters can be very small and feature low EMI because no inductors or control loops are required. They simply require moving charge between capacitors via switches—supplying the resulting charge to the output.
Because charge pumps use no magnetics (inductors or transformers), they typically feature lower EMI than inductive switching topologies. Inductors tend to be much larger than capacitors, and unshielded inductors act like antennas by broadcasting radiated emissions. In contrast, the capacitors used in a charge pump do not produce any more EMI than a typical digital output. They can be easily routed in short traces to reduce antenna area and capacitive coupling, resulting in lower EMI.
Table 1 compares inductor-based switching regulator and switched capacitor inverting topologies.
Features Inductor-Based Switching Regulator Switched Capacitor Voltage Converter Design Complexity Moderate to high Low Cost Moderate to high Low to moderate Noise Low to moderate Low Efficiency High Low to moderate Thermal Management Best Moderate to good Output Current High Low Requires Magnetics Yes No Limitations Size and complexity VIN/VOUT ratio
### Traditional Inverting Charge Pump
The configuration of the traditional inverting charge pump is shown in Figure 1.
##### Figure 1. Inverting charge pump schematic. Image used courtesy of Bodo’s Power Systems
The output impedance, ROUT, of the charge pump is defined as the equivalent resistance of the charge pump mechanism from input to output. It is found by measuring the input to output voltage difference and dividing by the load current:
$R_{OUT}=\frac{V_{IN}=GAIN\times V_{OUT}}{I_{LOAD}}$
##### (1)
where GAIN = –1 for an inverting charge pump.
Alternatively, the equivalent output resistance can be calculated as a function of switching frequency, switch resistance, and flyback capacitor size—generally simplified as:
$R_{OUT}=\frac{1}{f_{OSC}\times C_{FLY}}+2\times \Sigma_{1}^4\, R_{ON}$
##### (2)
Where $$\Sigma_{1}^4\, R_{ON}$$ is the summation of the four switches’ resistance.
Each of the four switches operates at the same frequency, fOSC, and they are on for one half of the switching period, T, where T = 1/ fOSC. Operation can be separated into two phases based on the two halves of the switching period, as shown in Figure 2.
##### Figure 3. Timing diagram for inverting charge pump. Image used courtesy of Bodo’s Power Systems
Figure 3 gives the voltages and currents for each phase of the charge pump’s operation. In Phase 1, S1 and S2 are closed and S3 and S4 are open. This charges the flying capacitor (CFLY) to a voltage of +VIN. In Phase 2, the energy from CFLY is discharged into the output by opening S1 and S2 and closing S3 and S4. The two distinct phases of operation means that discontinuous current flows into CFLY from VIN, and discontinuous current flows out of CFLY into COUT. This leads to voltage ripple on CIN and COUT, which can be calculated:
$I_{LOAD}=C_{OUT}\frac{\Delta V_{OUT}}{\Delta t}$
##### (3)
Solving for output voltage ripple gives:
$\Delta V_{OUT} = \frac{I_{LOAD}}{C_{OUT}\times2\,\times f_{OSC}}$
##### (4)
Similarly, the input voltage ripple is:
$\Delta V_{IN} = \frac{I_{LOAD}}{C_{IN}\times2\,\times f_{OSC}}$
##### (5)
Equation 4 and Equation 5 illustrate that, for a standard inverting charge pump, the voltage ripple is a function of switching frequency and input (or output) capacitance. Higher frequency and higher capacitance reduce this ripple in a 1:1 relationship. However, there are practical impediments to increasing frequency: namely increasing current consumption of the chip, which decreases efficiency.
Similarly, cost and PCB area often restrict the maximum input and output capacitance of an inverting charge pump. Also note that the flyback capacitor plays no role in the charge pump’s voltage ripple.
To reduce ripple, input and output filters could be constructed around the charge pump, but this again increases complexity and the charge pump’s output resistance. However, these issues can be addressed with a novel improvement to the standard inverting charge pump inverter: an interleaved inverting charge pump (IICP).
### Interleaved Inverting Charge Pump (IICP)
Phase interleaving is widely used in inductive switching regulators (that is, polyphase operation) to reduce output voltage ripple.3 A 2-phase buck converter interleaved at exactly 50% duty cycle produces, in theory, 0 mV of output voltage ripple. Of course, the duty cycle of a regulated buck converter changes with input and output voltage, so the 50% case is only realized when VIN = 2 VOUT. Charge pumps usually operate at exactly 50% duty cycle, so an interleaved charge pump inverter is interesting to consider.
##### Figure 4. Interleaved inverting charge pump. Image used courtesy of Bodo’s Power Systems
Interleaving charge pumps are sometimes used within ICs when a very low current negative rail is required on the die, but right now there is no commercially available dedicated IICP inverting dc-to-dc converter. The construction of an IICP requires two charge pumps and two flying capacitors. The second charge pump operates the switches 180° out of phase with the first charge pump. Let’s look at the setup and the output ripple of an IICP and highlight how to optimize its performance. The setup is shown in Figure 4 with the timing diagram in Figure 5.
##### Figure 5. Timing diagram for interleaved inverting charge pump. Image used courtesy of Bodo’s Power Systems
In each phase of the oscillator, one of the flying capacitors is connected to VIN and the other is connected to VOUT. At first glance, one might think that the addition of the second capacitor would only reduce the voltage ripple by half. However, this is an inaccurate oversimplification. In fact, the input and output voltage ripple can be far less than a standard inverter, because a capacitor is always charging from the input and discharging to the output. This can be better understood from the derivation of the IICP’s output voltage ripple.
### IICP Output Voltage Ripple Derivation
Since the IICP always has one of the flying capacitors supplying current to the output, its output stage can be simplified, as shown in Figure 6.
##### Figure 6. Simplified IICP output stage. Image used courtesy of Bodo’s Power Systems
Furthermore, the IICP’s output resistance, as defined in Equation 1, can be approximated by:
$R_{OUT}\approx\frac{1}{8\,\times\,f_{OSC}\times C_{FLY}}+0.5\times\Sigma_{1}^{8}R_{ON}$
##### (6)
Where $$\Sigma_{1}^{8}R_{ON}$$ is the summation of the switch resistances. Summing the currents into ILOAD, we arrive at:
$I_{LOAD}=C_{OUT}\frac{dV_{OUT}}{dt}+C_{FLY}\frac{dV_{CFLY(t)}}{dt}$
##### (7)
Where dt is equal to a quarter of the switch period (T/4, or 1/(4 × fOSC)). The output voltage ripple, ∆VOUT, is dVOUT and VCFLY(t) is the voltage difference across CFLY. We can make the reasonable assumption that output voltage ripple is small relative to the flying capacitor voltage ripple. Then to calculate ∆VOUT, we need an understanding of VCFLY(t). From Figure 6, note that IFLY is equal to the current through the two on switches. And each of those switches has a resistance of RON. Therefore:
$C_{FLY}\frac{dV_{CFLY(t)}}{dt}=\frac{V_{CFLY(t)-|V_{OUT}|}}{2\times R_{ON}}$
##### (8)
To solve this differential equation for VCFLY(t), at least one initial condition must be known. This condition can be found via inspection of the timing graphs in Figure 5. Note that from t = 0 to t = T/4, both CFLY capacitors contribute current to ILOAD and charge COUT. Then, from t = T/4 to t = T/2, CFLY and COUT contribute to the output load current. So, right at t = T/4 (and similarly t = 3/4 T), the contribution to ILOAD from COUT is exactly 0. Therefore, at this moment, ILOAD is equal to IFLY, and the voltage of VCFLY is given by:
$V_{CFLY}(t=T/4)=|V_{OUT}|+I_{FLY}\times 2\,\times\,R_{ON}\\where\,V_{OUT}=-V_{IN}+R_{OUT}\times I_{LOAD}$
##### (9)
Using Equation 8 and Equation 9, we can differentially solve for VCFLY(t):
$V_{CFLY}(t)=|V_{OUT}|+|I_{LOAD}|\times (R_{OUT}-2\times R_{ON})\times \beta^{1.5}\\ where\,\beta = e^{1/8fRC}\\where\,f\,is\,f_{OSC},R\,is\,R_{ON}\, and\,C\,is\,C_{FLY}$
##### (10)
To find the delta in VCFLY for Equation 7, take two points (for example, t = 0 and t = T/4), and solve Equation 10 for each of those points. The result simplifies to:
$\Delta V_{CFLY}=I_{LOAD}\times (R_{OUT}-2\times R_{ON})\times\frac{\beta-1}{\sqrt{\beta}}$
##### (11)
Combining Equation 11 and Equation 7, and solving for ∆VOUT gives:
$\Delta V_{OUT}=\frac{I_{LOAD}}{4\times f_{OSC}\times C_{OUT}}-I_{LOAD}\times(R_{OUT}-2\times R_{ON})\times\frac{C_{FLY}}{C_{OUT}}\times\frac{\beta-1}{\sqrt{\beta}}$
##### (12)
The impact of Equation 12 may not be initially obvious. It may help to first simplify it by considering the case of an ideal switch (RON = 0 Ω). Doing so brings the second term to nearly zero, leaving only the first term. That first term is very similar to the standard inverting charge pump ripple (Equation 4), but the dual flying capacitors of the IICP increase the denominator by 2×. Twice the charge pumps yields half the ripple. This result is consistent with intuition.
However, the important part of Equation 12 lies in the second half. Note the minus sign for the second term, meaning that this portion reduces the output voltage ripple. Focus on the switch resistance (RON) and the flying capacitor (CFLY). In a standard inverting charge pump, these terms play no role in reducing the output voltage ripple. But in an IICP, the switch resistance acts to smooth out the charge and discharge current. The dual flying capacitors allow this charge/discharge action to happen uninterrupted.
### Output Voltage Ripple Confirmation
We can use circuit simulation to check the accuracy of Equation 12 and the validity of the assumptions used to derive it. This is easily accomplished using LTspice®. The schematic for this simulation is shown in Figure 7, and the file is available for download.
A comparison was performed for a variety of conditions, with a summary of the results in Table 2.
Table 2 shows that Equation 12 closely matches simulation, validating the assumptions made in simplifying the equations. Now we can use that equation to make trade-offs in the IICP implementation.
VOUT Ripple (mV) VIN (V) ILOAD (mA) fOSC (kHz) COUT (µF) CFLY (µF) RON (Ω) Equation LTspice 10 50 1000 4.7 2.2 2 0.038 0.038 5 100 1000 4.7 2.2 2 0.076 0.075 5 50 1000 1 1 2 0.393 0.390 5 50 1000 1 1 3 0.261 0.260 7.8 37 532 2.4 0.5 4 0.430 0.425 5 100 1000 10 2.2 3 0.024 0.024 5 50 200 4.7 1 10 0.418 0.415 12 50 500 10 1 10 0.031 0.033 12 20 500 4.7 1 3 0.089 0.089
##### Table 2. Comparison of Theoretical vs. LTspice Simulation Results for Various Configurations.
It’s also instructive to compare the voltage ripple between an IICP and a standard charge pump. In Part 2 of this series, we will show bench test data of these differences. But for now, our LTspice model in Figure 8 can illustrate the difference in output voltage ripple.
### Optimization of IICP Topology
Having derived the IICP equations and proved their validity, there are two primary conclusions: For the IICP, the switch resistance (RON) reduces both input and output voltage ripple, a desired result. In contrast, in a standard inverting charge pump, the switch resistance is entirely undesirable, as it increases the ROUT of the charge pump and provides no ripple voltage reduction. In fact, we could further augment the switch resistance by placing a resistor in series with the flyback capacitor. This gives us a knob to reduce input and output voltage ripple at the expense of increased charge pump resistance. We’ll explore this knob further when we discuss use cases of the IICP in Part 2 of this series.
Secondly, the value of the flying capacitors, and their ratio with COUT, can be optimized to further optimize the ripple. For example, a large output capacitor value may be difficult to find in a small package, and subject to a significant capacitance derating at higher voltages. But by reducing COUT, and then increasing CFLY, the same output voltage ripple can be obtained for more attainable values of capacitance. For example, instead of CFLY = 1 µF and COUT = 10 µF, if they were all set to 2.2 µF, then nearly the same output voltage ripple is attained. 2.2 µF/25 V capacitors are more readily available in small packages than 10 µF/25 V capacitors. An example application in Part 2 explores this.
Conclusion
This concludes Part 1 of the 2-part series on the interleaved inverting charge pump topology. This part covers the general concepts behind an IICP topology, including input/output voltage ripple calculations. The derivation of the equations governing input/output ripple yields important insights into how to optimize the performance of an IICP solution.
In Part 2 of the series, we unveil the ADP5600, an integrated solution for the IICP topology. We measure its performance and compare to a standard inverting charge pump. Finally, we’ll put it all together to power a low noise phased array beamforming solution.
About the Authors
Jon Kraft is a senior staff FAE in Colorado and has been with ADI for 13 years. His focus is software-defined radio and aerospace phased array radar. He received his B.S.E.E. from Rose-Hulman and his M.S.E.E. from Arizona State University. He has nine patents issued (six with ADI) and one currently pending.
Steve Knoth is a senior product marketing manager in Analog Devices’ Power Group. He is responsible for all power management integrated circuit (PMIC) products, low dropout (LDO) regulators, battery chargers, charge pumps, charge pump-based LED drivers, supercapacitor chargers, and low voltage monolithic switching regulators. Prior to rejoining Analog Devices in 2004, Steve held various marketing and product engineering positions at Micro Power Systems, Analog Devices, and Micrel Semiconductor. He earned his bachelor’s degree in electrical engineering in 1988 and a master’s degree in physics in 1995, both from San Jose State University. Steve also received an M.B.A. in technology management from the University of Phoenix in 2000. In addition to enjoying time with his kids, Steve is an avid music lover and can be found tinkering with pinball and arcade games or muscle cars, and buying, selling, and collecting vintage toys, movie, sports, and automotive memorabilia.
This article originally appeared in Bodo’s Power Systems magazine.
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# 4.12 Practice 4: geometric distribution
Page 1 / 1
This module provides further practice with topics of Geometric Distribution in Statistics.
## Student learning outcomes
• The student will analyze the properties of a geometric distribution.
## Given:
Use the information from the Binomial Distribution Practice shown below.
The Higher Education Research Institute at UCLA collected data from 203,967 incoming first-time, full-time freshmen from 270 four-year colleges and universities in the U.S. 71.3% of those students replied that, yes, they believe that same-sex couples should have the right to legal marital status. ( Source: http://heri.ucla.edu/PDFs/pubs/TFS/Norms/Monographs/TheAmericanFreshman2011.pdf )
Suppose that you randomly select freshman from the study until you find one who replies “yes.” You are interested in the number of freshmen you must ask.
## Interpret the data
In words, define the Random Variable $X$ .
$X$ ~
G(0.713)
What values does the random variable $X$ take on?
1,2,…
Construct the probability distribution function (PDF). Stop at $x=6$ .
$x$ $\text{P(x)}$
1
2
3
4
5
6
On average( $\mu$ ), how many freshmen would you expect to have to ask until you found one who replies "yes?"
1.4
What is the probability that you will need to ask fewer than 3 freshmen?
0.9176
Construct a histogram or plot a line graph. Label the horizontal and vertical axes with words. Include numerical scaling.
#### Questions & Answers
Do somebody tell me a best nano engineering book for beginners?
what is fullerene does it is used to make bukky balls
are you nano engineer ?
s.
what is the Synthesis, properties,and applications of carbon nano chemistry
so some one know about replacing silicon atom with phosphorous in semiconductors device?
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
how to fabricate graphene ink ?
for screen printed electrodes ?
SUYASH
What is lattice structure?
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
what's the easiest and fastest way to the synthesize AgNP?
China
Cied
types of nano material
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
I'm interested in nanotube
Uday
what is nanomaterials and their applications of sensors.
what is nano technology
what is system testing?
preparation of nanomaterial
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
what is system testing
what is the application of nanotechnology?
Stotaw
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
Prasenjit
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
Azam
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
Prasenjit
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
Damian
silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
Hello
Uday
I'm interested in Nanotube
Uday
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
Prasenjit
can nanotechnology change the direction of the face of the world
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
how did you get the value of 2000N.What calculations are needed to arrive at it
Privacy Information Security Software Version 1.1a
Good
1 It is estimated that 30% of all drivers have some kind of medical aid in South Africa. What is the probability that in a sample of 10 drivers: 3.1.1 Exactly 4 will have a medical aid. (8) 3.1.2 At least 2 will have a medical aid. (8) 3.1.3 More than 9 will have a medical aid.
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# How to Draw a Line Graph? (Definition, Plotting & Examples)
October 21, 2022
This post is also available in: हिन्दी (Hindi)
A graphical representation of data and information offers a quick and simple way to understand the features. It is more effective than presenting the data in the form of tables. A graphic representation of data in the form of a straight line is called a line graph.
Let’s understand what is a line graph and how to draw a line graph and read it using examples.
## What is a Line Graph?
A line graph is a type of chart or graph that is used to show information that changes over time. A line graph is plotted over a Cartesian system with a horizontal axis as $x$-axis and a vertical axis as $y$-axis using several points connected by straight lines. The x-axis usually has a time period over which we would like to measure the quantity of a specific thing or an item in the y-axis.
A line graph helps to analyze the trend of whether the quantity in the y-axis is increasing or decreasing over a period of time. With the help of a line graph, you get a clear picture of an increasing or a decreasing trend.
### Line Graph Examples
Let’s consider a few examples to understand what is a line graph.
Ex 1: A graph showing temperatures of a day.
Note down the temperature at fixed intervals during the day. The following table shows temperatures during a particular day in a city.
The figure below shows a line graph of the given data.
Before moving on to how to draw a line graph, let’s understand the various parts of a line graph.
## Parts of a Line Graph
Line graphs are drawn in an $x-y$ plane, where $x$ is the horizontal axis and $y$ is the vertical axis. A line graph consists of the following parts:
• Title: It tells us about the data for which the graph is drawn and is written at the top of the graph.
• Labels: There are two types of labels in a line graph:
• Horizontal Axis (X-axis): It tells us about the label on the $x$-axis.
• Vertical Axis (Y-axis): It tells us about the label on the $y$-axis.
• Scales: There are two scales that tell us the quantitative value of “how much” or “how many”.
• Horizontal Labels (Labels on X-axis): It tells us about the label on the $x$-axis.
• Vertical Labels (Labels on Y-axis): It tells us about the label on the $y$-axis.
• Points: The points or dots on the graph represent the $\left(x, y \right)$ coordinates. Such pairs of numbers are called ordered pairs. The data represented by $x$ is the independent variable, and the data represented by $y$ is the dependent variable.
• Trend: The consecutive points are joined together to draw a line. The gradient or movement of a line is called the trend. The trend tells whether currently there is an increase or decrease and how fast that increase or decrease is.
• Lines: Straight lines connecting the points give estimated values between the points.
## Properties of a Line Graph
A line graph has the following properties.
• A line graph is drawn using straight line segments between points. By joining all points, we get a resulting line that may be a straight line or a curve.
• It has two variables. One is called the independent variable while the other is called the dependent variable. The value of the dependent variable depends on the independent variable.
• Ideally, the independent variable is exhibited on the horizontal axis, and the dependent variable is shown on the vertical axis.
• A line graph can show the variation of one quantity with another, also known as a variable.
## Types of Line Graphs
There are two main types of line graphs in statistics namely, a simple line graph, and a multiple line graph. Each of these graph types has different uses depending on the kind of data that is being evaluated.
### Simple Line Graph
A simple line graph is a kind of graph that is plotted with only a single line. Like in the diagram above, shows the relationship between two variables.
In most cases, one of these variables is independent, while the other is a dependent variable. The independent variable is usually time, but it can also be any other factor.
In the example above Earnings is the dependent variable while the Year is the independent variable.
### Multiple Line Graph
A multiple-line graph is a line graph that is plotted with two or more lines. It is used to depict two or more variables that change over the same period of time.
The independent variable is usually on the horizontal axis, while the 2 or more dependent variables are on the vertical axis. For example, if you want to compare the number of boys and girls students in a school over a couple of years, you need to visualize it using a multiple-line graph.
The different steps to read and interpret a line graph are given below:
Step 1: Observe the title. It tells about the information presented by the line graph.
Step 2: Observe the labels on the two axes. These figures give information about the data used to draw a line graph.
Step 3: Check out the emerging patterns to understand the trend. A trend can be increasing (line moving upwards when you move from left to right along the $x$-axis) or it can be decreasing (line moving downwards when you move from left to right along the $x$-axis).
Step 4: Observe the data values to get exact figures.
### Examples
Ex 1: The following line graph shows the yearly sales figures for a manufacturing company.
• What were the sales in (a) 2002 (b) 2006?
• Compute the difference between sales in 2002 and 2006.
• In which year was there the greatest difference between the sales as compared to the previous year?
The vertical (y-coordinate) of a point corresponding to the year 2002 is 4. Therefore, sales in 2002 is ₹4,00,00,000.
The vertical (y-coordinate) of a point corresponding to the year 2006 is 8. Therefore, sales in 2006 is ₹8,00,00,000.
Difference between sales in 2002 and 2006 is 8,00,00,000 – 4,00,00,000 = ₹4,00,00,000.
Since the line is steepest between the years 2004 and 2005(the slope of the line is greatest), therefore, in 2005 there is the greatest difference between the sales as compared to the previous year.
## How to Draw a Line Graph?
The different steps to plot the points and draw a line graph are given below:
Step 1: Set Up a Table: Draw the $x$ (horizontal axis) and $y$ (vertical axis) on a page. On the top of the page, write a title that briefly describes the purpose of the chart.
Step 2: Label Each Axis: If one of the elements is time, it goes on the $x$ or the horizontal axis. The other element goes on the $y$ or the vertical axis, the y-axis. Divide and mark the axes as per their individual characteristics.
Step 3: Plot Data: Using the given data, indicate the values on the graph. Join the points. Once you’ve added your data, your line graph will automatically reflect its values.
Step 4: Create a Key: If you are comparing multiple items, you’ll want to create a key that identifies what each line is by its colour.
## Pros and Cons of a Line Graph
##### Pros
• It helps to show small shifts that may be getting hard to spot in other graphs
• It helps show trends for different periods
• They are easy to understand
• To compare data, more than one line can be plotted on the same axis
##### Cons
• If we plot too many lines on the same graph, it can become cluttered and hard to read
• Application is limited to data sets that have numerical and whole values
• When data sets have fractional or decimal values, it becomes difficult to plot them
## Key Takeaways
Following are some of the important points about a line graph.
• A line graph is a graph that is used to display change over time as a series of data points connected by straight-line segments on two axes.
• Line graphs are used to demonstrate information on factors and patterns.
• A line graph is used to determine the relationship between two sets of values, with one data set always being dependent on the other data set. Usually, $x$-points are called independent and $y$-points are called dependent points.
• One important term related to line graphs is the slope. The slope represents how steep a line is. It helps in comparing the magnitude of change between any two consecutive points on the graph.
## Practice Problems
The number of days a hillside city received snow in different years.
Draw a line graph of the above data.
Population (in thousands) of men and women in a village in different years.
Draw a line graph of the above data.
Draw the graph for the following table of values, with suitable scales on the axes.
• Does the graph pass through the origin?
• Use the graph to find the interest on ₹2500 for a year.
• To get an interest of ₹280 per year, how much money should be deposited?
## FAQs
### What is a line graph used for?
Line graphs are used to track changes over short and long periods of time. When smaller changes exist, line graphs are better to use than bar graphs. Line graphs can also be used to compare changes over the same period of time for more than one group.
### What are the different parts of a line graph?
A line graph has six parts. These are
1. Title: It tells us about the data for which the graph is drawn and is written at the top of the graph.
2. Labels: There are two types of labels in a line graph:
2a. Horizontal Axis (X-axis): It tells us about the label on the $x$-axis.
2b. Vertical Axis (Y-axis): It tells us about the label on the $y$-axis.
3. Scales: There are two scales that tell us the quantitative value of “how much” or “how many”.
3a. Horizontal Labels (Labels on X-axis): It tells us about the label on the $x$-axis.
3b. Vertical Labels (Labels on Y-axis): It tells us about the label on the $y$-axis.
4. Points: The points or dots on the graph represent the $\left(x, y \right)$ coordinates. Such pairs of numbers are called ordered pairs. The data represented by $x$ is the independent variable, and the data represented by $y$ is the dependent variable.
5. Trend: The consecutive points are joined together to draw a line. The gradient or movement of a line is called the trend. The trend tells whether currently there is an increase or decrease and how fast that increase or decrease.
6. Lines: Straight lines connecting the points give estimated values between the points.
### Why is it called a line graph?
A line graph is a graph that is used to display change over time as a series of data points connected by straight-line segments on two axes. A line graph is also called a line chart. It helps to determine the relationship between two sets of values, with one data set always being dependent on the other data set.
### How do you analyze a line graph?
The changing slope of the line segments emphasizes changes, trends, and patterns. For a single series of data, assess the changes in the line to identify trends and patterns. When you have multiple metrics, compare their lines to determine whether they have the same trend and patterns.
## Conclusion
A line graph is a type of chart or graph that is used to show information that changes over time. Line graphs can also be used to compare changes over the same period of time for more than one group. Knowing how to draw a line graph helps to determine the relationship between two sets of values, with one data set always being dependent on the other data set.
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# What is distinguish between qualitative and quantitative data?
Question
Describing quantitative data
What is distinguish between qualitative and quantitative data?
2021-02-20
Step 1
The differences between the qualitative and quantitative data.
Step 2
Data refers to the facts and statistics collected together for reference and analysis. There are two types of data called the qualitative data and the quantitative data.
Step 3
Qualitative data is the information about the qualities which cannot be measured. Examples include the colour of the petal, the softness of the fur. Quantitative data is the information about the quantities that can be measured, tabulated or recorded. Examples include the number of sepals in a flower, the volume of nectar produced.
Step 4
The difference between the qualitative data and quantitative data are as follows.
Qualitative data Quantitative data
1. It deals with description. 1. It deals with the numbers.
2. Data can only be observed and not measured. 2. Data can be measured and recorded.
3. It is the classification of samples based on properties. 3. It is the classification of samples on the basis of measurements and numerical expression.
4. It is non-statistical and theoritical. 4. It is statistical.
5. Helps in developing a hypothesis. 5. Helps in concluding a hypothesis with experimentation.
Step 5
Result:
Qualitative data is the non-numerical data and quantitative data is the numerical data.
### Relevant Questions
What is the difference between quantitative and qualitative data.
What is the relationship between a frequency or relativefrequency distribution of a quantitative data set and that of a qualitative data set?
Discuss the differences between quantitative and qualitative data, as well as the advantages and disadvantages of each. As a part of your response, describe one type of quantitative data.
The difference between the qualitative and quantitative data with examples
Determine whether the data described below is quantitative of qualitative variable.
A. The data are quantitative because they don't count nor measure anything.
B. The data are quantitative because they consist of counts or measurements.
C. The data are qualitative because they don't count nor measure anything.
D. The data are qualitative because they consist of counts or measurements.
Show whether the following is quantitative or qualitative data
i) Gender of students at a college
ii) Weight of babies at a hospital
iii) Colour of sweets in a box
iv) Number of students in a class
v) Colour of sweets in a box
In a study, you ask the subjects their gender. Is this data qualitative or quantitative?
In a study, you ask the subjects their age in years. Is this data qualitative or quantitative?
Why do senior executives feel more comfortable relying on quantitative data than qualitative data? How might a qualitative research company lessen the senior-level executive’s skepticism?
A researcher was interested in the effectiveness of a new drug for testosterone replacement in adult men between the ages of 40 and 59 in the U.S. who are experiencing symptoms related to abnormally low testosterone levels. According to the 2010 Census data, there were 36,135,061 men between the ages of 40 and 59 in the U.S. 100 U.S. men participated in a clinical trial of the drug. Those 100 men were classified by race and ethnicity (White, Asian, Black, Hispanic, Native, Islander, Other) and their average testosterone level was 275 $$\displaystyle\frac{{{n}{g}}}{{{d}{L}}}$$. The average testosterone level of all adult men in the U.S. between 40 and 59 is 565 ng/dL. Use this information for problems A-E
A. Describe the population.
B.. What is the sample?
C, Identify the parameter(s) and give their value(s).
D. Identify the statistic(s) and give their value(s).
E. Which of the variable(s) are categorical and which are numerical?
...
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Simplifying Difference Quotient
I was watching lecture 3 from MIT 1801 on single variable calculus, and I am having trouble understanding how the professor simplified the expression for the difference quotient. The original expression for the difference quotient was: $$\frac{\sin(x + \Delta x) - \sin(x)}{\Delta x}$$
and I understand how he simplified it to: $$\frac{\sin(x)\cos(\Delta x) + \cos(x)\sin(\Delta x) - \sin(x)}{\Delta x}$$ I just can't understand the simplification from the above expression to this: $$\sin(x)\biggl (\frac{\cos(\Delta x) - 1}{\Delta x}\biggr) + \cos(x)\biggl(\frac{\sin(\Delta x)}{\Delta x}\biggr)$$
Could someone explain the steps involved to get to this solution? Thanks,
• Factor a $\sin(x)$ out of the first and third terms in the numerator. – N. F. Taussig Oct 31 '17 at 17:02
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main-content
This book systematically addresses the design and analysis of efficient techniques for independent random sampling. Both general-purpose approaches, which can be used to generate samples from arbitrary probability distributions, and tailored techniques, designed to efficiently address common real-world practical problems, are introduced and discussed in detail. In turn, the monograph presents fundamental results and methodologies in the field, elaborating and developing them into the latest techniques. The theory and methods are illustrated with a varied collection of examples, which are discussed in detail in the text and supplemented with ready-to-run computer code.
The main problem addressed in the book is how to generate independent random samples from an arbitrary probability distribution with the weakest possible constraints or assumptions in a form suitable for practical implementation. The authors review the fundamental results and methods in the field, address the latest methods, and emphasize the links and interplay between ostensibly diverse techniques.
### Chapter 1. Introduction
Abstract
This chapter provides an introduction to the different approaches available for sampling from a given probability distribution. We start with a brief history of the Monte Carlo (MC) method, one of the most influential algorithms of the twentieth century and the main driver for the current widespread use of random samples in many scientific fields. Then we discuss the need for MC approaches through a few selected examples, starting with two important classical applications (numerical integration and importance sampling), and finishing with two more recent developments (inverse Monte Carlo and quasi Monte Carlo). This is followed by a review of the three types of “random numbers” which can be generated (“truly” random, pseudo-random, and quasi-random), a brief description of some pseudo-random number generators and an overview of the different classes of random sampling methods available in the literature: direct, accept/reject, MCMC, importance sampling, and hybrid. Finally, the chapter concludes with an exposition of the motivation, goals, and organization of the book.
Luca Martino, David Luengo, Joaquín Míguez
### Chapter 2. Direct Methods
Abstract
In this chapter we look into a collection of direct methods for random sampling. The term direct is used here to indicate that i.i.d. random draws with exactly the desired probability distribution are produced by applying a transformation that maps one (or many) realizations from the available random source into a realization from the target random variable. Most often, this transformation can be described as a deterministic map. However, we also include here techniques that rely on either discrete or continuous mixtures of densities and which can be interpreted as (pseudo)stochastic transformations of the random source.
Furthermore, many of the techniques proposed in the literature are found to be closely related when studied in sufficient detail. We pay here specific attention to some of these links, as they can be later exploited for the design of more efficient samplers, or simply to attain a better understanding of the field.
Luca Martino, David Luengo, Joaquín Míguez
### Chapter 3. Accept–Reject Methods
Abstract
The accept/reject method, also known as rejection sampling (RS), was suggested by John von Neumann in 1951. It is a classical Monte Carlo technique for universal sampling that can be used to generate samples virtually from any target density p o (x) by drawing from a simpler proposal density π(x). The sample is either accepted or rejected by an adequate test of the ratio of the two pdfs, and it can be proved that accepted samples are actually distributed according to the target distribution. Specifically, the RS algorithm can be viewed as choosing a subsequence of i.i.d. realizations from the proposal density π(x) in such a way that the elements of the subsequence have density p o (x).
In this chapter, we present the basic theory of RS as well as different variants found in the literature. Computational cost issues and the range of applications are analyzed in depth. Several combinations with other Monte Carlo techniques are also described.
Luca Martino, David Luengo, Joaquín Míguez
### Chapter 4. Adaptive Rejection Sampling Methods
Abstract
This chapter is devoted to describing the class of the adaptive rejection sampling (ARS) schemes. These (theoretically) universal methods are very efficient samplers that update the proposal density whenever a generated sample is rejected in the RS test. In this way, they can produce i.i.d. samples from the target with an increasing acceptance rate that can converge to 1. As a by-product, these techniques also generate a sequence of proposal pdfs converging to the true shape of the target density. Another advantage of the ARS samplers is that, when they can be applied, the user only has to select a set of initial conditions. After the initialization, they are completely automatic, self-tuning algorithms (i.e., no parameters need to be adjusted by the user) regardless of the specific target density. However, the need to construct a suitable sequence of proposal densities restricts the practical applicability of this methodology. As a consequence, ARS schemes are often tailored to specific classes of target distributions. Indeed, the construction of the proposal is particularly hard in multidimensional spaces. Hence, ARS algorithms are usually designed only for drawing from univariate densities.
In this chapter we discuss the basic adaptive structure shared by all ARS algorithms. Then we look into the performance of the method, characterized by the acceptance probability (which increases as the proposal is adapted), and describe various extensions of the standard ARS approach which are aimed either at improving the efficiency of the method or at covering a broader class of target pdfs. Finally, we consider a hybrid method that combines the ARS and Metropolis-Hastings schemes.
Luca Martino, David Luengo, Joaquín Míguez
### Chapter 5. Ratio of Uniforms
Abstract
This chapter provides a detailed description of the so-called ratio-of-uniforms (RoU) methods. The RoU and the generalized RoU (GRoU) techniques were introduced in Kinderman and Monahan (ACM Trans Math Softw 3(3):257–260, 1977); Wakefield et al. (Stat Comput 1(2):129–133, 1991) as bivariate transformations of the bidimensional region $$\mathcal {A}_0$$ below the target pdf p o (x) ∝ p(x). To be specific, the RoU techniques can be seen as a transformation of a bidimensional uniform random variable, defined over $$\mathcal {A}_0$$, into another two-dimensional random variable defined over an alternative set $$\mathcal {A}$$. RoU schemes also convert samples uniformly distributed on $$\mathcal {A}$$ into samples with density p o (x) ∝ p(x) (which is equivalent to draw uniformly from $$\mathcal {A}_0$$). Therefore, RoU methods are useful when drawing uniformly from the region $$\mathcal {A}$$ is comparatively simpler than drawing from p o (x) itself (i.e., simpler than drawing uniformly from $$\mathcal {A}_0$$). In general, RoU algorithms are applied in combination with the rejection sampling principle and they turn out especially advantageous when $$\mathcal {A}$$ is bounded. In this chapter, we present first the basic theory underlying RoU methods, and then study in depth the connections with other sampling techniques. Several extensions, as well as different variants and point of views, are discussed.
Luca Martino, David Luengo, Joaquín Míguez
### Chapter 6. Independent Sampling for Multivariate Densities
Abstract
In this chapter, we present several techniques for multivariate independent sampling. We recall some techniques introduced in the previous chapters and show how they can be adapted to a multidimensional setup. Additionally, we provide guidelines for their application in higher dimensional spaces. We also consider the problem of drawing uniformly from a measurable set embedded in $$\mathbb {R}^n$$. With this goal, an exhaustive description of transformations of random vectors is given, which extends the study of this approach in the previous chapters.
The problem of sampling a random vector can often be conveniently viewed as generating a (finite) sequence of statistically dependent scalar samples. Thus, in this chapter, we take a slight detour from the main course of the book and show different methods that yield dependent samples, including the use of stochastic processes. Furthermore, a collection of efficient samplers for specific multivariate distributions is described.
Luca Martino, David Luengo, Joaquín Míguez
### Chapter 7. Asymptotically Independent Samplers
Abstract
Markov Chain Monte Carlo (MCMC) methods are possibly the most popular tools for random sampling nowadays. They generate “chains” (sequences) of samples from a target distribution that can be selected with few constraints. However, as highlighted by the term “chain,” the draws output by the MCMC method are statistically dependent (and often highly correlated), which makes such algorithms not directly comparable with the methods in the rest of this monograph. In this chapter, we describe two families of non-standard MCMC techniques that enjoy the property of producing samples that become asymptotically independent as a parameter grows to infinity or the number of random draws in the algorithm is increased. The methods of the first family are based on generating a pool of candidate samples at each iteration of the chain, instead of only one as in conventional procedures. The techniques in the second family rely on an adaptive, non-parametric approximation of the target density, which is improved as new samples are generated. We describe the general methodology for the two families, and provide some specific algorithms as examples.
Luca Martino, David Luengo, Joaquín Míguez
### Chapter 8. Summary and Outlook
Abstract
In this monograph, we have described the theory and practice of pseudo-random variate generation. This is the core of Monte Carlo simulations and, hence, of practical importance for a large number of applications in various fields, including computational statistics, cryptography, computer modeling, games, etc. The focus has been placed on independent and exact sampling methods, as opposed to techniques that produce weighted (e.g., importance sampling) and/or correlated populations (e.g., MCMC).
Luca Martino, David Luengo, Joaquín Míguez
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## FSharp.Compiler.Syntax Namespace
Type/Module Description Represents whether a debug point should be present for a 'let' binding, that is whether the construct corresponds to a debug point in the original source. Represents whether a debug point should be present for the 'finally' in a 'try .. finally', that is whether the construct corresponds to a debug point in the original source. Represents whether a debug point should be present for the 'for' in a 'for...' loop, that is whether the construct corresponds to a debug point in the original source. Represents whether a debug point should be present for the 'in' or 'to' of a 'for...' loop, that is whether the construct corresponds to a debug point in the original source. Represents a debug point at a leaf expression (e.g. an application or constant). Represents whether a debug point should be suppressed for either the first or second part of a sequential execution, that is whether the construct corresponds to a debug point in the original source. Represents whether a debug point should be present for the target of a decision tree, that is whether the construct corresponds to a debug point in the original source. Represents whether a debug point should be present for a 'try', that is whether the construct corresponds to a debug point in the original source. Represents whether a debug point should be present for the 'while' in a 'while...' loop, that is whether the construct corresponds to a debug point in the original source. Represents whether a debug point should be present for the 'with' in a 'try .. with', that is whether the construct corresponds to a debug point in the original source. Indicates if an expression is an atomic expression. An atomic expression has no whitespace unless enclosed in parentheses, e.g. 1, "3", ident, ident.[expr] and (expr). If an atomic expression has type T, then the largest expression ending at the same range as the atomic expression also has type T. Represents an identifier in F# code Represents a parsed hash directive Represents a parsed hash directive argument Represents a parsed implementation file made up of fragments Represents the syntax tree for the contents of a parsed implementation file Represents the full syntax tree, file name and other parsing information for an implementation file Represents the syntax tree for a parsed implementation or signature file Represents a parsed syntax tree for an F# Interactive interaction Represents a parsed signature file made up of fragments Represents the syntax tree for the contents of a parsed signature file Represents the full syntax tree, file name and other parsing information for a signature file Indicates if the construct arises from error recovery Some general F# utilities for mangling / unmangling / manipulating names. Anything to do with special names of identifiers and other lexical rules Represents a qualifying name for anonymous module specifications and implementations, Represents a scoped pragma Indicates if a for loop is 'for x in e1 -> e2', only valid in sequence expressions Represents an accessibility modifier in F# syntax Represents the argument names and other metadata for a parameter for a member or function Represents a syntax tree for arguments patterns Represents an attribute List of attributes enclosed in [< ... >]. Represents a binding for a 'let' or 'member' declaration The kind associated with a binding - "let", "do" or a standalone expression Represents the return information in a binding for a 'let' or 'member' declaration Indicate if the byte string had a special format Represents the syntax tree associated with the name of a type definition or module in signature or implementation. This includes the name, attributes, type parameters, constraints, documentation and accessibility for a type definition or module. For modules, entries such as the type parameters are always empty. The unchecked abstract syntax tree of constants in F# types and expressions. Represents the syntax tree for one case in an enum definition. Represents the right hand side of an exception declaration 'exception E = ... ' plus any member definitions for the exception Represents the right hand side of an exception declaration 'exception E = ... ' Represents the right hand side of an exception definition in a signature file Represents a syntax tree for F# expressions Represents the syntax tree for a field declaration in a record or class Represents an identifier with potentially additional trivia information. Represents a set of bindings that implement an interface Represents a long identifier with possible '.' at end. Typically dotRanges.Length = lid.Length-1, but they may be same if (incomplete) code ends in a dot, e.g. "Foo.Bar." The dots mostly matter for parsing, and are typically ignored by the typechecker, but if dotRanges.Length = lid.Length, then the parser must have reported an error, so the typechecker is allowed more freedom about typechecking these expressions. LongIdent can be empty list - it is used to denote that name of some AST element is absent (i.e. empty type name in inherit) Represents a clause in a 'match' expression Represents an unchecked syntax tree of F# unit of measure annotations. Represents a definition element within a type definition, e.g. 'member ... ' Represents the flags for a 'member' declaration Note the member kind is actually computed partially by a syntax tree transformation in tc.fs Represents the syntax tree for a member signature (used in signature files, abstract member declarations and member constraints) Represents a definition within a module Represents the definition of a module or namespace Represents the kind of a module or namespace definition Represents the definition of a module or namespace in a signature file Represents a definition within a module or namespace in a signature file Represents the target of the open declaration Represents a syntax tree for an F# pattern Represents an unchecked syntax tree of F# unit of measure exponents. Represents the syntactic elements associated with the "return" of a function or method. Represents a syntax tree for simple F# patterns Represents the alternative identifier for a simple pattern Represents a simple set of variable bindings a, (a, b) or (a: Type, b: Type) at a lambda, function definition or other binding point, after the elimination of pattern matching from the construct, e.g. after changing a "function pat1 -> rule1 | ..." to a "fun v -> match v with ..." Represents a syntax tree for a static optimization constraint in the F# core library Indicate if the string had a special format Used to track route during traversal of syntax using SyntaxTraversal.Traverse Represents a syntactic type parameter Represents the explicit declaration of a type parameter List of type parameter declarations with optional type constraints, enclosed in < ... > (postfix) or ( ... ) (prefix), or a single prefix parameter. Represents a syntax tree for F# types The unchecked abstract syntax tree of F# type constraints Represents a type or exception declaration 'type C = ... ' plus any additional member definitions for the type Represents the kind of a type definition whether explicit or inferred Represents the right hand side of a type or exception declaration 'type C = ... ' plus any additional member definitions for the type Represents the syntax tree for a type definition in a signature Represents the syntax tree for the right-hand-side of a type definition in a signature. Note: in practice, using a discriminated union to make a distinction between "simple" types and "object oriented" types is not particularly useful. Represents the syntax tree for the core of a simple type definition, in either signature or implementation. Represents the syntax tree for one case in a union definition. Represents the syntax tree for the right-hand-side of union definition, excluding members, in either a signature or implementation. Represents extra information about the declaration of a value The argument names and other metadata for a member or function Represents the syntax tree for a 'val' definition in an abstract slot or a signature file Represents the names and other metadata for the type parameters for a member or function Represents whether a type parameter has a static requirement or not (^T or 'T)
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# Clojure and jMonkeyEngine Tutorial 4 and 5
And here we go again with the next tutorials. I feel like I should start prefacing these with the following caveat: do not use my code in production unless you have considered alternative code. I've been playing around with these tutorials, last time I questionably used memfn when it wasn't really necessary. Today I'm lifting everything to the global (for the namespace) scope because that makes dynamic manipulation in the REPL very easy.
There was an interesting piece of prose in the very first tutorial which I think bears repeating:
When developing a game application, you want to:
• Initialize the game scene
• Trigger game actions
• Respond to user input.
This is in essence what all video games boil down to. You put some stuff on the screen that does stuff and the player interacts with it in a way that changes stuff. I think it's insightful to keep this broad view in mind and not get too bogged down in the intricacies of your collision system, physics engine, graphics pipeline, AI, or what have you.
Anyway, the code for Tutorial 4:
(ns jme_clj.core
(:import [com.jme3 app.SimpleApplication
material.Material
math.Vector3f
math.ColorRGBA
scene.Geometry
scene.shape.Box
system.AppSettings
system.JmeSystem
]))
(def desktop-cfg (.getResource (.getContextClassLoader (Thread/currentThread))
"com/jme3/asset/Desktop.cfg"))
(def assetManager (JmeSystem/newAssetManager desktop-cfg))
(def ^:dynamic *app-settings* (doto (AppSettings. true)
(.setFullscreen false)
(.setTitle "jme_clj")))
(def b (Box. Vector3f/ZERO 1 1 1))
(def player (Geometry. "blue cube" b))
(def mat (Material. assetManager "Common/MatDefs/Misc/Unshaded.j3md"))
(.setColor mat "Color" ColorRGBA/Blue)
(.setMaterial player mat)
(defn update [tpf]
(.rotate player 0 (* 2 tpf) 0))
(def app (proxy [SimpleApplication] []
(simpleInitApp []
(org.lwjgl.input.Mouse/setGrabbed false)
(.attachChild (.getRootNode this) player))
(simpleUpdate [tpf]
(update tpf))))
(defn -main [& args]
(doto app
(.setShowSettings false)
(.setPauseOnLostFocus false)
(.setSettings *app-settings*)
(.start)))
If you remember my video from one of the previous tutorials, setting the module up this way allows for on-the-fly recoding. Since the true update function is called outside the proxy, in your text editor you can, for instance, change the 2 to a negative 2, and in the REPL enter the new definition for update, and the running game you started earlier by calling -main from the REPL will automatically start using the new function and the cube will rotate in the opposite direction. And as usual you can call arbitrary functions on those objects and watch them update in real-time. I made my cube green. Then I added a simple back and forth movement in the update to watch it oscillate. The world is yours. The tutorial suggests these exercises:
1. What happens if you give the rotate() method negative numbers?
2. Can you create two Geometries next to each other, and make one rotate twice as fast as the other? (use the tpf variable)
3. Can you make a cube that pulsates? (grows and shrinks)
4. Can you make a cube that changes color? (change and set the Material)
5. Can you make a rolling cube? (rotate around the x axis, and translate along the z axis)
These exercises are trivial to do and very fast to do as well because there's no recompile/relaunch step. It's quite fun actually.
The important new concept here is the tpf variable that gets passed into the update function. It stands for "time per frame". It's calculated by JME and allows you to easily make sure certain code runs at the same speed regardless of the true frame rate, an important tool in a game making use of the GPU where the frame rate can be well over 60 fps. How does this variable accomplish the goal?
Suppose our frame rate is 1000 fps. This means the update function gets called 1000 times every second. This corresponds to 2000 "units" of rotation per second, which is very fast. Now suppose we run the same game on another machine that only gets 60 fps. This corresponds to only 120 "units" of rotation per second, which is far slower. What if we really want it to be 2 "units" of rotation per second with a smooth transition that gets smoother if the computer is faster? Multiply by "tps". For the adequate machine that gets 1000 fps, the real time between successive frames is 1/1000 of a second. The multiplication by 2 guarantees that after 1000 frames the cube will be 2 units rotated away from where it started, and it gets there in 1000 sub-steps. Meanwhile the lower end computer has 1/60 of a second between each frame, so it gets to the same position (2 units rotated away from where it started) in 60 sub-steps. An even crappier machine that only gets 2 frames per second will get there in 2 steps, and the rotation will look very blocky. But it will be correct. In Clojure there's some potential to even macro-away this bookkeeping.
Tutorial 5 brings us to an interesting problem. User input, which until now was all handled by the engine, and state management. As you know, Clojure is a functional language and discourages state. Yet here in the example we have a "isRunning" variable that denotes whether the game is paused or not. It's a piece of state we just have to live with, but that's the nature of video games. Is there a way we could factor the state out if we really wanted to? Probably, but I don't think it would be very elegant. So I'll handle that bit of state with an atom.
Here's my code. It's fairly different from the tutorial, but it highlights both the annoyances of interfacing with certain Java code from Clojure but also the ease with which Clojure makes those annoyances disappear. I also cut out the additional handler for mouse controls to simplify my macro, but it shouldn't be too hard to make an even cooler macro that handles any amount of keys and mouse buttons by checking whether the binding identifier begins with KEY or BUTTON. (And remember this check happens at compile time, no efficiency is lost at run time.)
(ns jme_clj.core
(:import [com.jme3 app.SimpleApplication
material.Material
math.Vector3f
math.ColorRGBA
scene.Geometry
scene.shape.Box
input.KeyInput
input.controls.ActionListener
input.controls.AnalogListener
input.controls.KeyTrigger
system.AppSettings
system.JmeSystem
]))
(def desktop-cfg (.getResource (.getContextClassLoader (Thread/currentThread))
"com/jme3/asset/Desktop.cfg"))
(def assetManager (JmeSystem/newAssetManager desktop-cfg))
(def ^:dynamic *app-settings* (doto (AppSettings. true)
(.setFullscreen false)
(.setTitle "jme_clj")))
(def speed 5)
(def is-running? (atom true))
(def b (Box. Vector3f/ZERO 1 1 1))
(def player (Geometry. "blue cube" b))
(def mat (Material. assetManager "Common/MatDefs/Misc/Unshaded.j3md"))
(.setColor mat "Color" ColorRGBA/Blue)
(.setMaterial player mat)
(def action-listener (proxy [ActionListener] []
(onAction [name key-pressed tpf]
(if (and (= name "Pause") (not key-pressed))
(do (swap! is-running? not) (println "State of is-running?:" @is-running?))))))
(def analog-listener (proxy [AnalogListener] []
(onAnalog [name value tpf]
(if @is-running?
(cond
(= name "Rotate") (.rotate player 0 (* value speed) 0)
(= name "Right") (let [v (.getLocalTranslation player)]
(.setLocalTranslation player (+ (.x v) (* value speed))
(.y v) (.z v)))
(= name "Left") (let [v (.getLocalTranslation player)]
(.setLocalTranslation player (- (.x v) (* value speed))
(.y v) (.z v))))))))
(defmacro key-map [manager name key]
(.addMapping ~manager ~name (into-array KeyTrigger [(KeyTrigger. (. KeyInput ~key))])))
(defmacro add-listener [manager listener & names]
(.addListener ~manager ~listener (into-array String '~names)))
(defn init-keys [input-manager]
(doto input-manager
(key-map "Pause" KEY_P)
(key-map "Left" KEY_H)
(key-map "Right" KEY_L)
(key-map "Rotate" KEY_SPACE)
(add-listener action-listener "Pause")
(add-listener analog-listener "Left" "Right" "Rotate")))
(def app (proxy [SimpleApplication] []
(simpleInitApp []
(org.lwjgl.input.Mouse/setGrabbed false)
(.attachChild (.getRootNode this) player)
(init-keys (.getInputManager this)))))
(defn -main [& args]
(doto app
(.setShowSettings false)
(.setPauseOnLostFocus false)
(.setSettings *app-settings*)
(.start)))
The new concept here is the difference in analog and digital input handlers. Analog handlers are for gradually repeating events, and you use them when you want to do something based on whether a key is being continuously pressed rather than toggled. Digital "action" handlers on the other hand are regular toggles on/off, so discrete events like pausing a game would fall under that category. In PyGame, analog would be accessed by getting a list of currently pressed keys, whereas the 'digital' events are accessed in the standard pygame.events.get() loop. The analog events also send a "value" to the handler, which is a measure of its strength, and it's also helpfully pre-multiplied by the tps variable. For a keyboard the "value" will be consistent, but for say a joystick it might range from 0 to 255 depending on how far in some direction it is. It's a nifty feature of the engine.
I want to now draw your attention to the two macros, key-map and add-listener. While programming this I discovered that the input manager's addMapping method is actually variadic. I thought this was strange at first glance, but a second later it made sense. A lot of games have alternate controls for the same action, and so this eases the programming of those games marginally.
Anyway, because of the method declaration, one cannot simply pass a KeyTrigger object by itself from the Clojure end like you can from the Java end. It has to be in an array, and furthermore, it has to be in a Java array rather than a Clojure vector or list. Fortunately Clojure's into-array function takes care of that nicely, and thanks to the macro I don't have to type it in every instance. Similarly with the addListeners method, which is also variadic but the tutorial example indicates it's a regular array--nevertheless Clojure must still cast into an array of Strings.
Additionally I saved myself from an annoying amount of typing by putting the busywork cruft inside the macro. Because really, what's most important in key binding? Associating an action-string (if I didn't have to interface with the game engine, it could be anything, not just a string) with a key on the keyboard. That is the pure data involved. The actual representation of that data in-memory, i.e. with the engine's specific objects, is a secondary concern the programmer shouldn't have to spell out every time. Combined with doto, the savings in typing and increase in readability become even more. This is why I love Clojure.
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# Optimization (mathematics)
In mathematics, the simplest case of optimization, or mathematical programming, refers to the study of problems in which one seeks to minimize or maximize a real function by systematically choosing the values of real or integer variables from within an allowed set. This (a scalar real valued objective function) is actually a small subset of this field which comprises a large area of applied mathematics and generalizes to study of means to obtain "best available" values of some objective function given a defined domain where the elaboration is on the types of functions and the conditions and nature of the objects in the problem domain.
## History
The first optimization technique, which is known as steepest descent, goes back to Gauss. Historically, the first term to be introduced was linear programming, which was invented by George Dantzig in the 1940s. The term programming in this context does not refer to computer programming (although computers are nowadays used extensively to solve mathematical problems). Instead, the term comes from the use of program by the United States military to refer to proposed training and logistics schedules, which were the problems that Dantzig was studying at the time. (Additionally, later on, the use of the term "programming" was apparently important for receiving government funding, as it was associated with high-technology research areas that were considered important.)
Other important mathematicians in the optimization field include:
## Major subfields
In a number of subfields, the techniques are designed primarily for optimization in dynamic contexts (that is, decision making over time):
## Optimization topics
### Optimization problems
An optimization problem can be represented in the following way
Given: a function f : A $\to$ R from some set A to the real numbers
Sought: an element x0 in A such that f(x0) ≤ f(x) for all x in A ("minimization") or such that f(x0) ≥ f(x) for all x in A ("maximization").
Such a formulation is called an optimization problem or a mathematical programming problem (a term not directly related to computer programming, but still in use for example in linear programming - see History above). Many real-world and theoretical problems may be modeled in this general framework. Problems formulated using this technique in the fields of physics and computer vision may refer to the technique as energy minimization, speaking of the value of the function f as representing the energy of the system being modeled.
Typically, A is some subset of the Euclidean space Rn, often specified by a set of constraints, equalities or inequalities that the members of A have to satisfy. The domain A of f is called the search space, while the elements of A are called candidate solutions or feasible solutions.
The function f is called, variously, an objective function, cost function, energy function, or energy functional. A feasible solution that minimizes (or maximizes, if that is the goal) the objective function is called an optimal solution.
Generally, when the feasible region or the objective function of the problem does not present convexity, there may be several local minima and maxima, where a local minimum x* is defined as a point for which there exists some δ > 0 so that for all x such that
$\|\mathbf{x}-\mathbf{x}^*\|\leq\delta;\,$
the expression
$f(\mathbf{x}^*)\leq f(\mathbf{x})$
holds; that is to say, on some region around x* all of the function values are greater than or equal to the value at that point. Local maxima are defined similarly.
A large number of algorithms proposed for solving non-convex problems – including the majority of commercially available solvers – are not capable of making a distinction between local optimal solutions and rigorous optimal solutions, and will treat the former as actual solutions to the original problem. The branch of applied mathematics and numerical analysis that is concerned with the development of deterministic algorithms that are capable of guaranteeing convergence in finite time to the actual optimal solution of a non-convex problem is called global optimization.
### Notation
Optimization problems are often expressed with special notation. Here are some examples.
$\min_{x\in\mathbb R}\; (x^2 + 1)$
This asks for the minimum value for the objective function x2 + 1, where x ranges over the real numbers $\mathbb R$. The minimum value in this case is 1, occurring at x = 0.
$\max_{x\in\mathbb R}\; 2x$
This asks for the maximum value for the objective function 2x, where x ranges over the reals. In this case, there is no such maximum as the objective function is unbounded, so the answer is "infinity" or "undefined".
$\operatorname{argmin}_{x\in]-\infty;-1]}\; x^2 + 1\,$
This asks for the value (or values) of x in the interval $]-\infty;-1]$ that minimizes (or minimize) the objective function x2 + 1 (the actual minimum value of that function does not matter). In this case, the answer is x = -1.
$\operatorname{argmax}_{x\in[-5,5],\;y\in\mathbb R}\; x\cdot\cos(y)\,$
This asks for the (x,y) pair (or pairs) that maximizes (or maximize) the value of the objective function x * cos(y), with the added constraint that x lies in the interval [ − 5;5] (again, the actual maximum value of the expression does not matter). In this case, the solutions are the pairs of the form ( 5 ; 2kπ ) and ( −5 ;(2k+1)π ), where k ranges over all integers.
### Techniques
Crudely all the methods are divided according to variables called:-
SVO:- Single Variable Optimization
MVO:- Multi Variable Optimization
For twice-differentiable functions, unconstrained problems can be solved by finding the points where the gradient of the objective function is zero (that is, the stationary points) and using the Hessian matrix to classify the type of each point. If the Hessian is positive definite, the point is a local minimum, if negative definite, a local maximum, and if indefinite it is some kind of saddle point.
The existence of derivatives is not always assumed and many methods were devised for specific situations. The basic classes of methods, based on smoothness of the objective function, are:
Actual methods falling somewhere among the categories above include:
Should the objective function be convex over the region of interest, then any local minimum will also be a global minimum. There exist robust, fast numerical techniques for optimizing twice differentiable convex functions. This is for your concern.
Constrained problems can often be transformed into unconstrained problems with the help of Lagrange multipliers.
Here are a few other popular methods:
### Multi-objective optimization
Adding more than one objective to an optimization problem adds complexity. For example, if you wanted to optimize a structural design, you would want a design that is both light and rigid. Because these two objectives conflict, a trade-off exists. There will be one lightest design, one stiffest design, and an infinite number of designs that are some compromise of weight and stiffness. This set of trade-off designs is known as a Pareto set. The curve created plotting weight against stiffness of the best designs is known as the Pareto frontier.
A design is judged to be Pareto optimal if it is not dominated by other designs: a Pareto optimal design must be better than another design in at least one aspect. If it is worse than another design in all respects, then it is dominated and is not Pareto optimal.
## Uses
Problems in rigid body dynamics (in particular articulated rigid body dynamics) often require mathematical programming techniques, since you can view rigid body dynamics as attempting to solve an ordinary differential equation on a constraint manifold; the constraints are various nonlinear geometric constraints such as "these two points must always coincide", "this surface must not penetrate any other", or "this point must always lie somewhere on this curve". Also, the problem of computing contact forces can be done by solving a linear complementarity problem, which can also be viewed as a QP (quadratic programming) problem.
Many design problems can also be expressed as optimization programs. This application is called design optimization. One recent and growing subset of this field is multidisciplinary design optimization, which, while useful in many problems, has in particular been applied to aerospace engineering problems.
Mainstream economics also relies heavily on mathematical programming. An often studied problem in microeconomics, the utility maximization problem, and its dual problem the Expenditure minimization problem, are economic optimization problems. Consumers and firms are assumed to maximize their utility/profit. Also, agents are most frequently assumed to be risk-averse thereby wishing to minimize whatever risk they might be exposed to. Asset prices are also explained using optimization though the underlying theory is more complicated than simple utility or profit optimization. Trade theory also uses optimization to explain trade patterns between nations.
Another field that uses optimization techniques extensively is operations research.
## Solvers
• CPLEX
• COMET is a language dedicated to optimization: constraint-based local search, constraint-programming, mathematical programming (free for academic use).
• IMSL Numerical Libraries are collections of math and statistical algorithms available in C/C++, Fortran, Java and C#/.NET. Optimization routines in the IMSL Libraries include unconstrained, linearly and nonlinearly constrained minimizations, and linear programming algorithms.
• IPOPT - an open-source primal-dual interior point method NLP solver which handles sparse matrices
• KNITRO - solver for nonlinear optimization problems
• Mathematica - handles linear programming, integer programming and constrained non-linear optimization problems
• NAG Numerical Libraries-The NAG Library contains a comprehensive collection of Optimization routines, which cover a diverse set of problems and circumstances.http://www.nag.co.uk/optimization/index.asp
• OpenOpt - a free toolbox with connections to lots of solvers, for Python language programmers
• Merlin - A Fortran-77, user friendly open source software package, for non-linear optimization with bound constraints. Available from the URL: http://merlin.cs.uoi.gr
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# Lesson 1
Using Decimals in a Shopping Context
### Problem 1
Mai had $14.50. She spent$4.35 at the snack bar and $5.25 at the arcade. What is the exact amount of money Mai has left? A:$9.60
B:
$10.60 C:$4.90
D:
### Solution
For access, consult one of our IM Certified Partners.
### Problem 4
Chicken costs $3.20 per pound, and beef costs$4.59 per pound. Answer each question and show your reasoning.
1. What is the exact cost of 3 pounds of chicken?
2. What is the exact cost of 3 pound of beef?
3. How much more does 3 pounds of beef cost than 3 pounds of chicken?
### Solution
For access, consult one of our IM Certified Partners.
### Problem 5
1. How many $$\frac15$$-liter glasses can Lin fill with a $$1 \frac12$$-liter bottle of water?
2. How many $$1 \frac12$$-liter bottles of water does it take to fill a 16-liter jug?
### Solution
For access, consult one of our IM Certified Partners.
(From Unit 4, Lesson 16.)
### Problem 6
Let the side length of each small square on the grid represents 1 unit. Draw two different triangles, each with base $$5\frac12$$ units and area $$19\frac14$$ units2.
Why does each of your triangles have area $$19\frac14 \text{ units}^2$$? Explain or show your reasoning.
### Solution
For access, consult one of our IM Certified Partners.
(From Unit 4, Lesson 14.)
### Problem 7
Find each quotient.
1. $$\frac56 \div \frac16$$
2. $$1\frac16 \div \frac{1}{12}$$
3. $$\frac{10}{6 }\div \frac{1}{24}$$
### Solution
For access, consult one of our IM Certified Partners.
(From Unit 4, Lesson 10.)
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Question 113
# Let PQRSTU be a regular hexagon. The ratio of the area of the triangle PRT to that of the hexagon PQRSTU is
Solution
It's given that PQRSTU is a regular hexagon and O is the center of the hexagon.
If we fold $$\triangle$$TSR ,$$\triangle$$PQR ,$$\triangle$$TUP along lines TR, PR, PT respectively then vertices S,Q,U will overlap each other exactly at center of the hexagon.
Hence we can say that Area of hexagon PQRSTU = 2($$\triangle$$PRT)
So Area of $$\triangle$$PRT = 0.5(Area of hexagon PQRSTU)
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# Kristaps Balodis
## Morphisms Of Schemes
Date Thursday, March 14, 2019
Continuing from last week, we develop some basic properties of schemes, and discuss various important types of morphisms between them. If time permits, we will introduce the functor of points, and Grothendieck topologies for categories of schemes.
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# 111 Wiki Sandbox
Jump to: navigation, search
# Use this page for showing examples of problems and trying out features
## Checking equation editing 3/4/13
Equation copied exactly from another wiki page displays correctly:Use $I_{measured}=I_{absolute}(n(E)\frac{\Delta\Omega}{4\pi})$ where n(E) is the intrinsic efficiency and the quantity in brackets (the product of n and the solid angle) is given in the NaI Crystal Information for a distance of d = 15 cm.
Same equation with E changed to pi and 4 changed to 6: Use $I_{measured}=I_{absolute}(n(\pi)\frac{\Delta\Omega}{6\pi})$ where n(E) is the intrinsic efficiency and the quantity in brackets (the product of n and the solid angle) is given in the NaI Crystal Information for a distance of d = 15 cm.
## Uploading a photo 1/14/13
view of optical trap
E. coli is propelled in liquids by a set of four or more helical flagellar filaments that arise from separate positions on the cell surface but intertwine to appear as a single flagellum in forward movement. A cell may lose its flagella under some conditions, and regenerate them under others. Although motile cells on a crowded slide may appear to be moving pretty randomly, a cell actually can modulate its swimmming to follow gradients of chemicals, temperature, or light. It accomplishes this by varying the ratio of two swimming behaviors. The first, called a "run", is swimming forward in a steady, mostly straight path. The second behavior, called a "tumble", is an erratic motion that causes the next run to be in a new direction, pretty much at random. If the cell senses that the environmental gradient is getting worse as it swims, then a tumbles are more frequent; if it is getting better, tumbles are less frequent. So motility of the cell is facultative and under at least crude directional control.
## Checking equation editing 1/14/13
Equation copied exactly from another wiki page displays correctly:Use $I_{measured}=I_{absolute}(n(E)\frac{\Delta\Omega}{4\pi})$ where n(E) is the intrinsic efficiency and the quantity in brackets (the product of n and the solid angle) is given in the NaI Crystal Information for a distance of d = 15 cm.
Same equation with n changed to g, 4 changed to 3:Use $I_{measured}=I_{absolute}(g(E)\frac{\Delta\Omega}{2\pi})$ where n(E) is the intrinsic efficiency and the quantity in brackets (the product of n and the solid angle) is given in the NaI Crystal Information for a distance of d = 15 cm.
Same equation with pi and omega reversed, term 37 added.Use $I_{measured}=I_{absolute}(37n(E)\frac{\Delta\Pi}{4\Omega})$ where n(E) is the intrinsic efficiency and the quantity in brackets (the product of n and the solid angle) is given in the NaI Crystal Information for a distance of d = 15 cm.
## Checking equation editing 9/9/10
Equation copied exactly from another wiki page displays correctly:Use $I_{measured}=I_{absolute}(n(E)\frac{\Delta\Omega}{4\pi})$ where n(E) is the intrinsic efficiency and the quantity in brackets (the product of n and the solid angle) is given in the NaI Crystal Information for a distance of d = 15 cm.
Same equation with n changed to g: Use $I_{measured}=I_{absolute}(g(E)\frac{\Delta\Omega}{4\pi})$ where g(E) is the intrinsic efficiency and the quantity in brackets (the product of n and the solid angle) is given in the NaI Crystal Information for a distance of d = 15 cm.
## Checking equation editing 4/19/10
Equation copied exactly from another wiki page displays correctly:Use $I_{measured}=I_{absolute}(n(E)\frac{\Delta\Omega}{4\pi})$ where n(E) is the intrinsic efficiency and the quantity in brackets (the product of n and the solid angle) is given in the NaI Crystal Information for a distance of d = 15 cm.
Same equation with pi changed to 5 in denominator: Use $I_{measured}=I_{absolute}(n(E)\frac{\Delta\Omega}{4 5})$ where n(E) is the intrinsic efficiency and the quantity in brackets (the product of n and the solid angle) is given in the NaI Crystal Information for a distance of d = 15 cm.
## Equation display problem reported 9/30/09.
This problem seems to be fixed, but equations that displayed improperly need to be changed in some way for the equation image to be replaced. If you make a change, then change it back again, the old incorrect image gets used. Not sure of a workaround here.
-Tom
Equation copied exactly from another wiki page displays correctly:
Use $I_{measured}=I_{absolute}(n(E)\frac{\Delta\Omega}{4\pi})$ where n(E) is the intrinsic efficiency and the quantity in brackets (the product of n and the solid angle) is given in the NaI Crystal Information for a distance of d = 15 cm.
Same equation with pi changed to 2 in denominator displays the edit, but all subscripts are missing:
Use $I_{measured}=I_{absolute}(n(E)\frac{\Delta\Omega}{42})$ where n(E) is the intrinsic efficiency and the quantity in brackets (the product of n and the solid angle) is given in the NaI Crystal Information for a distance of d = 15 cm.
Same as first equation but added alpha square root of 2 to the end. The alpha displays, but square root symbol does not.
Use $I_{measured}=I_{absolute}(n(E)\frac{\Delta\Omega}{4\pi}) \alpha \sqrt{2}$ where n(E) is the intrinsic efficiency and the quantity in brackets (the product of n and the solid angle) is given in the NaI Crystal Information for a distance of d = 15 cm.
Use $I_{measured}=I_{absolute}(n(E)\frac{\Delta\Omega}{2\pi})$ where n(E) is the intrinsic efficiency and the quantity in brackets (the product of n and the solid angle) is given in the NaI Crystal Information for a distance of d = 15 cm.
## How to use the References feature
Here is an example of use of the references tag.[1]
A named reference can be used multiple times[2]
Here is the second time it is used. [2]
## References
1. This is the text of the reference.
2. 2.0 2.1 This reference is referred to multiple times
This item above, which you can not see yet so you must edit this area to see it, is a wiki link in the wiki that automatically indexes the items.
Note that this wiki as of March 12th, 2010 automatically indexes the references for you. So If you want to edit the references go to the up arrow, on the wiki page, just after the number in the reference section, click on it and it will bring you to the sited location for that reference. Then edit that section and you will see the links that correspond to the reference. Don
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# combinatorial
1. ### Combinatorial calculation
I posted this question in the wrong section, so I post it again here, sorry guys! I'm trying to solve a combinatorial problem, more precisely I have the following data: 1) the Italian car number plates are given starting from 1993 in succession according to this criterion, the first plate...
2. ### combinatorial proof
How can I give combinatorial proof to this ?
3. ### Combinatorial proof
Hi guys any idea how I can give combinatorial proof to the given identities? Thanks in advance.
11. ### Chess tournament problem. Combinatorial analysis.
Hi every one. I would like share with you a problem about combinatorial analysis. I can't solve it. In a chess tournament there are n players involved. Assume that every player needs to compete with each of the other players, and assume that there are no ties. how many chess games take...
12. ### Combinatorial Hmk
Hey, I'm taking combinatorics at university in Seoul, Korea. The TA for my class speaks no English so when they do the practice problems I have no idea what the explanation is. I'm a little confused on how to start with these problems and I have no solutions to any of the problems in my book...
13. ### Combinatorial problem
Hi everybody, There are 120 triplets picked out of 10 numbers. 1-2-3,1-2-4,.....8-9-10. What is the minimal number of triplets we can remove from the 120 such as : - no 5-uple could be built using the remaining triplets - only one 5-uple could be built using the remaining triplets -...
14. ### Combinatorial problem
A set has 3^n elements, each of which is either an A or a B. Assume now that this set is divided into three subsets, which in turn is turned into three subsets,etc. At the lowest level, you have sets with three members. Now suppose you have two different decision procedures to determine who...
15. ### Combinatorial identities
Can we express C(n,k) as sum not involving other combinatorials ? Thank you.
16. ### A combinatorial problem
Suppose there are N positions. For each position, one can fill it with S,F or T. There is one constraint that F and T cannot be next to each other. This means that a filling with FT in the sequence or TF in the sequence is not allowed. For example, if N = 5. We have FSSTT, SFSTT are valid...
17. ### Sum of first m terms of a combinatorial number
Dear My Math Forum denizens, I have a tricky problem that I hope one of you can help me with. (It's for a personal project, nothing to do with school.) I'm looking for a closed-form expression for the sum of the first through m-th terms of a combinatorial number. For those of you unfamiliar...
18. ### Help with combinatorial mathematics
This is from my book on discrete and combinatorial mathematics, in the chapter about combinations (just for clarity, this stuff http://en.wikipedia.org/wiki/Combination ). Considering the chapter it is from, simply filling it in shouldn't be the way they expect you to solve it. I probably have...
19. ### Combinatorial proof other than strong induction
Hi guys, I am wondering if there is a way other than strong induction (I already know how to prove it that way for this problem) for this question, " Show that, for any integer n>=4, there exist non-negative integers a,b such that 5n = 10a + 25b" ??? Is there any other way to prove this other...
20. ### 2 combinatorial probability questions
I did my entire assignment and these two are driving me nuts. A comittee of fifty politicians is to be chosen from among our one hundred senators. If the selection is done at random, what is the probability that each state will be represented? For this I thought that it should be (50 choose...
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Properties
Label 2.11.ah_be Base field $\F_{11}$ Dimension $2$ $p$-rank $2$ Ordinary Yes Supersingular No Simple Yes Geometrically simple Yes Primitive Yes Principally polarizable Yes Contains a Jacobian Yes
Invariants
Base field: $\F_{11}$ Dimension: $2$ L-polynomial: $1 - 7 x + 30 x^{2} - 77 x^{3} + 121 x^{4}$ Frobenius angles: $\pm0.183470593443$, $\pm0.430420419745$ Angle rank: $2$ (numerical) Number field: 4.0.39593.1 Galois group: $D_{4}$ Jacobians: 4
This isogeny class is simple and geometrically simple.
Newton polygon
This isogeny class is ordinary.
$p$-rank: $2$ Slopes: $[0, 0, 1, 1]$
Point counts
This isogeny class contains the Jacobians of 4 curves, and hence is principally polarizable:
• $y^2=7x^6+10x^5+3x^4+3x^3+8x^2+5x+8$
• $y^2=x^6+4x^4+x^3+10x^2+10x+2$
• $y^2=6x^6+8x^5+x^4+5x^3+8x+2$
• $y^2=10x^6+6x^5+4x^4+5x^3+x^2+8x+10$
$r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 68 16048 1849328 214465472 25947340108 3144123903232 380029698717212 45951475832008448 5559601338333581552 672737920931822176048
$r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 5 133 1388 14649 161115 1774774 19501529 214367025 2357813684 25936959093
Decomposition and endomorphism algebra
Endomorphism algebra over $\F_{11}$
The endomorphism algebra of this simple isogeny class is 4.0.39593.1.
All geometric endomorphisms are defined over $\F_{11}$.
Base change
This is a primitive isogeny class.
Twists
Below is a list of all twists of this isogeny class.
Twist Extension Degree Common base change 2.11.h_be $2$ 2.121.l_cm
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# teaching machines
## Fabrication Summer Camp: Day 4
May 27, 2021 by . Filed under public, twoville.
Welcome to the fourth day of our summer camp! Laser and vinyl cutters create flat objects. Today we break out of the flat plane into the third dimension. In order to cut these objects with our tools, they must start out flat. But the objects can be folded and assembled into solid shapes. Solid objects that have been laid flat by unfolding them along their edges are sometimes called nets. We’ll make a few nets today.
### Tetrahedron
A tetrahedron is the simplest shape that occupies all three dimensions. It is made of four equilateral triangles. There are several ways to unfold one so that it lies flat. Consider this method:
1. Set the tetrahedron so it’s resting flat on a table.
2. Peel one of the side triangles down so it lies flat.
3. Peel one of the remaining side triangles down so it lies flat.
4. Peel the last side triangle down so it lies flat.
What shape do the flattened triangles form? A bigger equilateral triangle.
We can make this shape in Twoville as a polygon with a bit of turtle geometry:
s = 10
with viewport
size = [s * 4, s * 4]
with polygon()
color = :cornflower
with turtle()
position = [10, 10]
repeat 3
move().distance = s
move().distance = s
turn().degrees = 120
var twovilleDiv = jQuery('#twoville_tetrahedron1');
twovilleDiv.closest('pre').replaceWith(twovilleDiv);
document.getElementById('twoville_form_tetrahedron1').submit();
s = 10
with viewport
size = [s * 4, s * 4]
with polygon()
color = :cornflower
with turtle()
position = [10, 10]
repeat 3
move().distance = s
move().distance = s
turn().degrees = 120
Notice how the internal edges are not visible. We don’t want our cutter to cut through the paper along these edges. However, wouldn’t it be nice if the cutter made a slight cut along them to make the paper easier to fold? Such a cut is called a score. Our cutter can be made to score paper. Let’s trace out these score lines using a path:
s = 10
with viewport
size = [s * 4, s * 4]
with polygon()
color = :cornflower
with turtle()
position = [10, 10]
repeat 3
move().distance = s
move().distance = s
turn().degrees = 120
with path()
with stroke
color = :red
size = 0.1
opacity = 0
with turtle()
position = [10 + s, 10]
repeat 3
move().distance = s
turn().degrees = 120
var twovilleDiv = jQuery('#twoville_tetrahedron2');
twovilleDiv.closest('pre').replaceWith(twovilleDiv);
document.getElementById('twoville_form_tetrahedron2').submit();
s = 10
with viewport
size = [s * 4, s * 4]
with polygon()
color = :cornflower
with turtle()
position = [10, 10]
repeat 3
move().distance = s
move().distance = s
turn().degrees = 120
with path()
with stroke
color = :red
size = 0.1
opacity = 0
with turtle()
position = [10 + s, 10]
repeat 3
move().distance = s
turn().degrees = 120
I’ve colored these lines in red. When I load this design into the cutter, I’ll state that all red lines are scores rather than cuts. I shouldn’t use red for anything else.
Suppose we cut this flat and assembled it into a solid tetrahedron again. The triangles would not stick to each other. We could attach them with tape, which would be visible. To attach them invisibly, we could add tabs along the edges that folded under the neighboring triangle. With a little glue, these tabs would hold the tetrahedron together.
In Twoville, we can add tabs by inserting a tab command right before an command that makes a straight line. Here we add a tab to the first triangle along each edge:
s = 10
with viewport
size = [s * 4, s * 4]
with polygon()
color = :cornflower
with turtle()
position = [10, 10]
repeat 3
tab()
move().distance = s
move().distance = s
turn().degrees = 120
with path()
with stroke
color = :red
size = 0.1
opacity = 0
with turtle()
position = [10 + s, 10]
repeat 3
move().distance = s
turn().degrees = 120
var twovilleDiv = jQuery('#twoville_tetrahedron3');
twovilleDiv.closest('pre').replaceWith(twovilleDiv);
document.getElementById('twoville_form_tetrahedron3').submit();
s = 10
with viewport
size = [s * 4, s * 4]
with polygon()
color = :cornflower
with turtle()
position = [10, 10]
repeat 3
tab()
move().distance = s
move().distance = s
turn().degrees = 120
with path()
with stroke
color = :red
size = 0.1
opacity = 0
with turtle()
position = [10 + s, 10]
repeat 3
move().distance = s
turn().degrees = 120
The tabs also need score lines. We add new segments to our path by tracing along the outer edge again. However, this time we use jump to skip over the triangle that doesn’t have a tab:
s = 10
with viewport
size = [s * 4, s * 4]
with polygon()
color = :cornflower
with turtle()
position = [10, 10]
repeat 3
tab()
move().distance = s
move().distance = s
turn().degrees = 120
with path()
with stroke
color = :red
size = 0.1
opacity = 0
with turtle()
position = [10 + s, 10]
repeat 3
move().distance = s
turn().degrees = 120
with turtle()
position = [10, 10]
repeat 3
move().distance = s
jump().distance = s
turn().degrees = 120
var twovilleDiv = jQuery('#twoville_tetrahedron4');
twovilleDiv.closest('pre').replaceWith(twovilleDiv);
document.getElementById('twoville_form_tetrahedron4').submit();
s = 10
with viewport
size = [s * 4, s * 4]
with polygon()
color = :cornflower
with turtle()
position = [10, 10]
repeat 3
tab()
move().distance = s
move().distance = s
turn().degrees = 120
with path()
with stroke
color = :red
size = 0.1
opacity = 0
with turtle()
position = [10 + s, 10]
repeat 3
move().distance = s
turn().degrees = 120
with turtle()
position = [10, 10]
repeat 3
move().distance = s
jump().distance = s
turn().degrees = 120
When we cut this out, we end up with a tetrahedron that almost makes itself. We just apply a little glue.
### Sealed Box
Now it’s your turn design a net that folds into a box. A box has six sides: four walls on the side, one on the top, and one on the bottom. Here’s one possible unfolding with the four walls on the side in a long strip:
Draw your unfolded box on your graph paper. Label the coordinates of all the faces’ corners. Mark the edges where you would like tabs to appear. Not all of them need tabs; you will need to fold this in your brain to identify the ones that do.
Have your drawing checked by a teacher. After any issues are resolved, head to the computer and code it up. Add score lines between the faces and along the tabs in red. Then we’ll cut it.
### Lidded Box
In our remaining time, you challenge is to make a box with a lid. The bottom of the box is made up of its rectangular base and four walls, plus some tabs to make the walls stick together. The top of the box is made up of its rectangular top and four walls, plus some tabs. Both parts look something like this without tabs:
Where do the tabs go?
For the bottom to fit inside the top, the bottom must be slightly smaller than the top. If you use variables, you can save yourself some effort. Design just one piece in terms of a variable. To produce the second piece, change the value of the variable slightly.
As always, start by drawing your design on graph paper. Check in with a teacher. Then code up your design and we’ll get it cut.
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{}
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arrow_back Solve the equation $\sqrt{x+18}=x-2$
32 views
Solve the equation $\sqrt{x+18}=x-2$
1 Answer
Best answer
Best answer
Answer:
$x=7 \quad$ or $\quad x \neq-2$
Explanation:
$\sqrt{x+18}=x-2$
$x+18=x^{2}-4 x+4$
$0=x^{2}-5 x-14$
$(x-7)(x+2)=0$
$x=7 \quad$ or $\quad x \neq-2$
by Gold Status
(30,543 points)
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How to include tables in a post ?
06-02-2016, 07:35 PM
Post: #1
Valentin Albillo Senior Member Posts: 815 Joined: Feb 2015
How to include tables in a post ?
.
Hi, everyone:
I've been doing a number of attempts here in order to get a formatted table of numbers included in a post, where formatted simply means that the numbers appear neatly aligned in columns, like this:
So far I've only succeded if I include the numbers in a CODE section, as the spacing between numbers is kept, but I don't want to use CODE as I don't like it.
I've also attempted to use PSP and LaTeX but surely I'm doing something wrong because I get no decently aligned columns.
Trying to use some TAB tags or similar doesn't work either, so if some kind soul would post here a table example which I could examine to use as a reference I'd be obligued.
Come to that, I'd also welcome tips & tricks on how to upload or include PDF documents and/or images in a post, or if there's some section in the HP Museum for that kind of contents.
Regards.
V.
.
All My Articles & other Materials here: Valentin Albillo's HP Collection
06-02-2016, 09:57 PM
Post: #2
Gerson W. Barbosa Senior Member Posts: 1,465 Joined: Dec 2013
RE: How to include tables in a post ?
Hello Valentin,
http://www.hpmuseum.org/forum/post-1935.html
Best regards,
Gerson.
06-02-2016, 10:22 PM
Post: #3
Valentin Albillo Senior Member Posts: 815 Joined: Feb 2015
RE: How to include tables in a post ?
.
Hi, Gerson:
(06-02-2016 09:57 PM)Gerson W. Barbosa Wrote: There was a thread about this some time ago. I wonder why it is not in this subforum.
Let's see ...
\begin{array}{|c|c|}
\hline n (base) & 2*n+9 (29) & 6*n+9 (69) & sqr(2*n+9) & sqr(6*n+9) \\\hline
0 (*) & 9 & 9 & 3 & 3 \\\hline
36 & 81 & 225 & 9 & 15 \\\hline
540 & 1089 & 3249 & 33 & 57 \\\hline
7560 & 15129 & 45369 & 123 & 213 \\\hline
105336 & 210681 & 632025 & 459 & 795 \\\hline
1467180 & 2934369 & 8803089 & 1713 & 2967 \\\hline
20435220 & 40870449 & 122611329 & 6393 & 11073 \\\hline
284625936 & 569251881 & 1707755625 & 23859 & 41325 \\\hline
\end{array}
Great, it works !
Thanks so much, Gerson ! 8-D
Best regards.
V.
.
All My Articles & other Materials here: Valentin Albillo's HP Collection
06-03-2016, 12:45 AM
Post: #4
rprosperi Super Moderator Posts: 5,286 Joined: Dec 2013
RE: How to include tables in a post ?
(06-02-2016 07:35 PM)Valentin Albillo Wrote: Trying to use some TAB tags or similar doesn't work either, so if some kind soul would post here a table example which I could examine to use as a reference I'd be obligued.
While far from as elegant as Gerson's tip and your pretty darned good first go at Latex, you could just space out the characters and format your table in a fixed-pitch font like Courier. The default font is fairly readable, but the variable-pitch nature of this (and most currently popular fonts) makes aligned output basically impossible.
As noted, it's not nearly as pretty, but it is far simpler and quicker.
--Bob Prosperi
06-03-2016, 02:17 AM
Post: #5
Gerson W. Barbosa Senior Member Posts: 1,465 Joined: Dec 2013
RE: How to include tables in a post ?
(06-03-2016 12:45 AM)rprosperi Wrote: While far from as elegant as Gerson's tip and your pretty darned good first go at Latex,
That was actually Katie's tip. I've only provided the link. I have yet to use it myself.
06-03-2016, 02:42 AM
Post: #6
Joe Horn Senior Member Posts: 1,847 Joined: Dec 2013
RE: How to include tables in a post ?
(06-03-2016 12:45 AM)rprosperi Wrote: While far from as elegant as Gerson's tip and your pretty darned good first go at Latex, you could just space out the characters and format your table in a fixed-pitch font like Courier. The default font is fairly readable, but the variable-pitch nature of this (and most currently popular fonts) makes aligned output basically impossible.
As noted, it's not nearly as pretty, but it is far simpler and quicker.
Unfortunately, using a fixed-pitch font (e.g. Courier) is not enough, because most (if not all) browsers remove extra spaces, as you can see here:
+-----------+-----------+------------+-----------+-----------+
| n(base) | 2n+9(29) | 6n+9(69) | sqr(2n+9) | sqr(6n+9) |
+-----------+-----------+------------+-----------+-----------+
| 0(*) | 9 | 9 | 3 | 3 |
| 36 | 81 | 225 | 9 | 15 |
| 540 | 1089 | 3249 | 33 | 57 |
| 7560 | 15129 | 45369 | 123 | 213 |
| 105336 | 210681 | 632025 | 459 | 795 |
| 1467180 | 2934369 | 8803089 | 1713 | 2967 |
| 20435220 | 40870449 | 122611329 | 6393 | 11073 |
| 284625936 | 569251881 | 1707755625 | 23859 | 41325 |
+-----------+-----------+------------+-----------+-----------+
Here's exactly the same data but inside a "Code" box, which forces browsers to show all spaces:
Code:
+-----------+-----------+------------+-----------+-----------+ | n(base) | 2n+9(29) | 6n+9(69) | sqr(2n+9) | sqr(6n+9) | +-----------+-----------+------------+-----------+-----------+ | 0(*) | 9 | 9 | 3 | 3 | | 36 | 81 | 225 | 9 | 15 | | 540 | 1089 | 3249 | 33 | 57 | | 7560 | 15129 | 45369 | 123 | 213 | | 105336 | 210681 | 632025 | 459 | 795 | | 1467180 | 2934369 | 8803089 | 1713 | 2967 | | 20435220 | 40870449 | 122611329 | 6393 | 11073 | | 284625936 | 569251881 | 1707755625 | 23859 | 41325 | +-----------+-----------+------------+-----------+-----------+
So, theoretically, the following is impossible to do. Discerning how it was done is left as an exercise for the student.
+-----------+-----------+------------+-----------+-----------+
| n(base) | 2n+9(29) | 6n+9(69) | sqr(2n+9) | sqr(6n+9) |
+-----------+-----------+------------+-----------+-----------+
| 0(*) | 9 | 9 | 3 | 3 |
| 36 | 81 | 225 | 9 | 15 |
| 540 | 1089 | 3249 | 33 | 57 |
| 7560 | 15129 | 45369 | 123 | 213 |
| 105336 | 210681 | 632025 | 459 | 795 |
| 1467180 | 2934369 | 8803089 | 1713 | 2967 |
| 20435220 | 40870449 | 122611329 | 6393 | 11073 |
| 284625936 | 569251881 | 1707755625 | 23859 | 41325 |
+-----------+-----------+------------+-----------+-----------+
<0|ɸ|0>
-Joe-
06-03-2016, 03:14 AM
Post: #7
Sylvain Cote Senior Member Posts: 1,784 Joined: Dec 2013
RE: How to include tables in a post ?
Looking at the page source code I see that the MathJax module is being used for LaTeX support
And the supported commands are listed HERE
/*
* /MathJax/config/TeX-AMS-MML_HTMLorMML.js
*
* Copyright (c) 2010-2015 The MathJax Consortium
*
* Part of the MathJax library.
* See http://www.mathjax.org for details.
*
* you may not use this file except in compliance with the License.
*
*/
MathJax.Hub.Config({
delayJaxRegistration: true
});
"[MathJax]/jax/input/TeX/config.js",
"[MathJax]/jax/input/MathML/config.js",
"[MathJax]/jax/output/HTML-CSS/config.js",
"[MathJax]/jax/output/NativeMML/config.js",
"[MathJax]/jax/output/PreviewHTML/config.js",
"[MathJax]/config/MMLorHTML.js",
"[MathJax]/extensions/tex2jax.js",
"[MathJax]/extensions/mml2jax.js",
"[MathJax]/extensions/MathEvents.js",
"[MathJax]/extensions/MathZoom.js",
"[MathJax]/jax/element/mml/jax.js",
"[MathJax]/extensions/toMathML.js",
"[MathJax]/extensions/TeX/noErrors.js",
"[MathJax]/extensions/TeX/noUndefined.js",
"[MathJax]/jax/input/TeX/jax.js",
"[MathJax]/extensions/TeX/AMSmath.js",
"[MathJax]/extensions/TeX/AMSsymbols.js",
"[MathJax]/jax/input/MathML/jax.js",
"[MathJax]/jax/output/PreviewHTML/jax.js",
"[MathJax]/extensions/fast-preview.js",
"[MathJax]/extensions/AssistiveMML.js"
);
MathJax.Hub.Config({
"v1.0-compatible": false
});
06-03-2016, 01:12 PM
Post: #8
rprosperi Super Moderator Posts: 5,286 Joined: Dec 2013
RE: How to include tables in a post ?
(06-03-2016 02:42 AM)Joe Horn Wrote: So, theoretically, the following is impossible to do. Discerning how it was done is left as an exercise for the student.
I did not know browsers removed spaces, how arrogant!
So, maybe use a non-printing (i.e. invisible), non-space character?
--Bob Prosperi
06-03-2016, 06:11 PM
Post: #9
Dieter Senior Member Posts: 2,397 Joined: Dec 2013
RE: How to include tables in a post ?
(06-03-2016 01:12 PM)rprosperi Wrote:
(06-03-2016 02:42 AM)Joe Horn Wrote: So, theoretically, the following is impossible to do. Discerning how it was done is left as an exercise for the student.
I did not know browsers removed spaces, how arrogant!
So, maybe use a non-printing (i.e. invisible), non-space character?
It's a printing space character. ;-) But a special one: the non-breaking space (Alt+0160). You may know it from other software, e.g. in Word it's Ctrl+Shift+Space. That's a very useful character as it will prevent a line break, so you can keep values and units together ("1 m" or "6 km/h") without the risk of line breaks. For our purposes here it's a kind of "hard blank" which - unlinke a regular space - is not removed by your browser:
So you can do things like ...this.
I use non-breaking spaces quite a lot.
BTW, is there a faster way than the Alt+0160 method ?
Dieter
06-03-2016, 06:14 PM
Post: #10
Gerson W. Barbosa Senior Member Posts: 1,465 Joined: Dec 2013
RE: How to include tables in a post ?
(06-03-2016 01:12 PM)rprosperi Wrote: So, maybe use a non-printing (i.e. invisible), non-space character?
Yes, the invisible character under the first Specials, in Katie's Unicode Test does the trick:
π = 3.141592653589793238462643383279503
9 2 3.141574838064079287182344939989334
99 2 3.141592651424974945646180479799372
999 2 3.141592653589572786959492672266442
9999 2 3.141592653589793216377737847078192
99999 2 3.141592653589793238460434495123538
999999 2 3.141592653589793238462643162386710
9999999 2 3.141592653589793238462643383257414
99999999 2 3.141592653589793238462643383279500
06-03-2016, 08:36 PM
Post: #11
rprosperi Super Moderator Posts: 5,286 Joined: Dec 2013
RE: How to include tables in a post ?
(06-03-2016 06:11 PM)Dieter Wrote: It's a printing space character. ;-) But a special one: the non-breaking space (Alt+0160). You may know it from other software, e.g. in Word it's Ctrl+Shift+Space. That's a very useful character as it will prevent a line break, so you can keep values and units together ("1 m" or "6 km/h") without the risk of line breaks. For our purposes here it's a kind of "hard blank" which - unlinke a regular space - is not removed by your browser:
So you can do things like ...this.
This is what I meant, but I did not know there is a special non-breaking space character. Very useful for things like this, thank you sir!.
(06-03-2016 06:14 PM)Gerson W. Barbosa Wrote: Yes, the invisible character under the first Specials, in Katie's Unicode Test does the trick:
That character listing seems to cause havoc under IE11. Here is how the bottom of the list appears:
Attached File(s) Thumbnail(s)
--Bob Prosperi
06-03-2016, 09:06 PM (This post was last modified: 06-22-2016 12:03 PM by striegel.)
Post: #12
striegel Member Posts: 231 Joined: May 2015
Using non-standard blank space character
(06-03-2016 06:11 PM)Dieter Wrote:
(06-03-2016 01:12 PM)rprosperi Wrote: I did not know browsers removed spaces, how arrogant!
So, maybe use a non-printing (i.e. invisible), non-space character?
It's a printing space character. ;-) But a special one: the non-breaking space (Alt+0160). You may know it from other software, e.g. in Word it's Ctrl+Shift+Space. That's a very useful character as it will prevent a line break, so you can keep values and units together ("1 m" or "6 km/h") without the risk of line breaks. For our purposes here it's a kind of "hard blank" which - unlike a regular space - is not removed by your browser:
So you can do things like ...this.
I use non-breaking spaces quite a lot.
BTW, is there a faster way than the Alt+0160 method ?
Dieter
For years, this character was a great help in filling out the 'Name' and 'Company' dialog boxes when installing Microsoft Office.
If I needed to set up MS Office for a business's PC where the name of an individual was not wanted, it would not accept an empty box or the ordinary space character, but Alt+0160 worked fine.
Think of the situation where the employee moves on and the company hires a replacement - forever after it would say 'This product is licensed to" and show the name of the person who no longer works here.
For a home user who wanted their own name but no company name it worked just as well.
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# Fourier coefficients intuition?
I just learned about Fourier series, and this is how I interpreted them: The complex exponentials form a basis for all periodic functions, and the Fourier series essentially decompose the function into a a sum of the basis functions. The Fourier coefficient formula then essentially "projects" the function onto the complex exponential to find how much it "has in common with that exponential". I interpreted the Fourier coefficient formula to be a continuous version of the dot product.
Using this interpretation, shouldn't the formula be as follows (where $T_0$ is the fundamental period) $$a_k = \int_ 0 ^ {T_0}x(t)e^{\frac{2\pi j kt}{T_0}}dt.$$
To me it seems the formula above finds the projection of the function $x(t)$ onto a basis function. The integral is essentially an extension of the dot product (the dot product is a finite sum of the product of the components, the integral above is an infinite sum of the product of the components).
However, the formula above is obviously incorrect. The correct formula is $$a_k = \frac{1}{T_0}\int_ 0 ^ {T_0}x(t)e^{\frac{-2\pi j kt}{T_0}}dt.$$
1) Can someone explain why there is a negative sign in the power? The basis have positive powers (i.e. the exponents in the Fourier sum don't have negative powers) so shouldn't the exponential of the function "dotted with" also have a positive power?
2) Why is it divided by $T_0$?
• To explain the negative power: note that the "dot product" of anything with itself should be a non-negative number. With that in mind, how should we compute $$\langle (1,i),(1,i)\rangle?$$ – Omnomnomnom Jan 19 '15 at 0:47
• As for $T_0$: we want to make sure that out "basis functions" have length $1$, for ease of computation. Dividing the "dot product" by a constant changes lengths while maintaining orthogonality. – Omnomnomnom Jan 19 '15 at 0:51
• @Omnomnomnom For the dot product of the imaginary numbers, could we make it equal to the product of the norms? So 2? But then the usual formula of summing the products of the components wouldn't work... – adfasf Jan 19 '15 at 0:55
• How about take the conjugate of all the elements in the second vector? – Omnomnomnom Jan 19 '15 at 0:56
• @Omnomnomnom That makes sense. We would then get the norm of the vector. But then how do we know the rule we came up with - multiplying by the conjugate- extends to cases where both functions being "dotted" are not the same? – adfasf Jan 19 '15 at 0:59
The definite integral over a fundamental period annihilates all of the complex exponentials except for the constant term. Thus, to determine "how much of $e^{2\pi in t/T}$ is in $f(t)$" you have to do something to $f$ to turn the "$a_\omega e^{2\pi in t/T}$ term" of interest into a constant term; this is achieved by multiplying by the reciprocal of the complex power, namely $e^{-2\pi in t/T}$. Of course integrating a constant over an interval will yield the constant times the interval's length, so for the original constant we need to normalize by the length of the interval.
Note that inner products defined on complex vector spaces incorporate conjugate-linearity in the second argument, so the inner product works like $\langle \vec{a},\vec{b}\rangle=a_1\overline{b_1}+\cdots+a_n\overline{b_n}$, and the negative power of the complex exponential is in keeping with this practice. If we don't have the conjugate part of this definition, then the bilinear form would no longer be quite as useful for linear algebra purposes - for instance you could not use it to "project" and "extract" coefficients of a vector's representation with respect to a given basis, as is being done in this problem.
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## D'Inverno derivation of Schwarzschild solution
If you happen to have D'Inverno's Introducing Einstein's Relativity, this is on page 187. He has reduced the metric to non-zero components:
$g_{00}= e^{h(t)}(1-2m/r)$
$g_{11}=-(1-2m/r)^{-1}$
$g_{22}=-r^2$
$g_{33}=-r^2\sin^2\theta$
The final step is a time coordinate transformation that reduces $g_{00}$ to $1-2m/r$. This is achieved by making $e^{h(t')}=1$, so $h(t')=0$. He does this with the relation
$t'=\int^t_c e^{\frac{1}{2}h(u)}du$, c is an arbitrary constant
I suppose that, since c is arbitrary, I can assign whatever value to c to make $h(t')=0$, but why use this particular integral as the relation between t and t'? Is there something special about this integral?
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Blog Entries: 1 Recognitions: Science Advisor This is pretty easy. You want (1 - 2m/r) dt'2 = eh(t)(1 - 2m/r) dt2, so take dt' = eh(t)/2 dt
Ah, OK...but why would the relation not be $t'=\int e^{h(t)/2}dt$? Instead, they have it as a definite integral from c to t.
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1 2 3 4 ... 252
Grade 7 Algebraic Expressions CCSS: 7.EE.A.1
Simplify the expression $6m + 10 - 10m$
1. $4m + 10$
2. $-4m + 10$
3. $16m + 10$
4. $6m$
Evaluate: $x^{0}$
1. $0$
2. $1$
3. $x$
4. $x^2$
5. None of the above.
The following expression is a....
$-9x^7y^5z^2$
1. monomial
2. binomial
3. trinomial
4. polynomial
Grade 7 Algebraic Expressions CCSS: 7.EE.A.1
Simplify the following:
2y + 9 + 8y + 7
1. 26
2. 10y+16
3. 26y
4. 10y + 9 + 7
simplify -2 (3x + 6)
1. -6x - 12
2. -6x + 12
3. -18x
4. 6x - 12
Grade 6 Algebraic Expressions CCSS: 6.EE.A.2a
3 times, the quantity $m$ minus 7
1. $3(m-7)$
2. $3 xx m-7$
3. $3-m$
4. $3 xx m7$
Grade 7 Algebraic Expressions CCSS: 7.EE.A.1
$-(x-3)$
1. 1x-3
2. 1x-3x
3. -x+3
4. 3-1x
solve
$2x + 6 <= -4$
1. $x <= 1$
2. $x <= 10$
3. $x <= -10$
4. $x >= -10$
Grade 7 Algebraic Expressions CCSS: 7.EE.A.1
Simplify
$2x + 3x^2 - 5x +4 - 7x^2$
1. $7x^2 +4$
2. $7x +10x^2 +4$
3. $-4x^2 -3x +4$
4. $-3x^6$
$(5^2)^3=$
1. $5^5$
2. $5^6$
3. $5^8$
4. 125
Grade 6 Linear Equations CCSS: 6.EE.B.7
What is x in this equation? 8x=48.
1. 8
2. 48
3. 6
4. none of the above
Grade 7 Algebraic Expressions CCSS: 7.EE.A.1
-2(n-6)
1. -2n+12
2. 2n-6
3. -2n-12
4. n-12
Expand and simplify
$(x- 5 ) (x + 6)$
1. $x^2 - 1x + 30$
2. $x^2 +11 x - 30$
3. $x^2 + x - 30$
4. $x^2 - 11x -30$
Grade 6 Algebraic Expressions CCSS: 6.EE.A.2a
Write a verbal expression for the algebraic expression: $4x+8$
1. 4 more than 8 times a number x
2. 8 less than 4 times a number x
3. 8 more than 4 times a number x
4. 4 less than 8 times a number x
1 2 3 4 ... 252
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1. YumYum247
2. YumYum247
3. YumYum247
4. YumYum247
@MAEMAEHOCKEY final got your tagname :D
5. anonymous
give me a couple of mins
6. YumYum247
7. anonymous
i thought it would be simple
8. YumYum247
and i thought ......nvm. i'll just beg at someone's else's door. -_-
9. anonymous
i willl help u i am happy to
10. YumYum247
really?????? :D
11. anonymous
yaaa
12. YumYum247
yuss!!!
13. anonymous
ok i think i got it
14. YumYum247
Hey don't bother, i don't wanna make you go through stress just for a question...leave it, i'll just ask someone else...Chill...:"D
15. anonymous
what .......i am not stressed
16. YumYum247
i'm just saying if your here to be a chill bird, then be a chill bird, i ain't trapping you in a cage. :"D
17. anonymous
i am not
18. YumYum247
Aait then.... i just wanna let you know that i've already done 90% of the question, i just need to find the resultant angle. and Thanks!!!
19. anonymous
ok i think i got it if i am doing it right
20. YumYum247
21. anonymous
24 right ???
22. mathmate
|dw:1442883489245:dw|
23. mathmate
can you confirm if the 24 and 32 degrees as shown in the marked up diagram? |dw:1442883620661:dw|
24. YumYum247
hold up let me attach a picture of the actual question....don't go anywhere...promise me!!! O_O
25. mathmate
ok!
26. YumYum247
27. mathmate
|dw:1442883835366:dw| Yes, this is a little better, with the force magnitudes. One suggestion I make for your future solutions is to draw the forces in the same orientation as the original. This way, there is a lesser chance of making mistakes.
28. YumYum247
ok :)
29. mathmate
|dw:1442883951868:dw| So R^2=15^2+12^2-2(15)(12)cos(124)=23.8812 as you had it.
30. mathmate
|dw:1442884257124:dw| sin($$\theta$$/12=sin(124)/R so sin($$\theta$$=12 sin(124)/23.8812=0.416582 $$\theta$$= asin(0.416582)=24.619 degrees (measured from the 15N force, or 24.619-24=0.619 degrees from the axis of the direction of the vehicle.
31. mathmate
correction: a little confusion for R. Should have written R^2=......., and R=sqrt(...)=23.8812 N
32. mathmate
@YumYum247 Still there? To find the angle, I used the sine rule, but forgot to indicate it.
33. YumYum247
yes i'm still here....!!!
34. YumYum247
0.61deg.....but that's not even a one whole degree tho :O
35. YumYum247
so you used... SineA/a = SineC/c SinA/15 = Sin124/24
36. mathmate
That's with respect to the axis of the vehicle. |dw:1442885722739:dw|
37. mathmate
Yes, but sin(theta)/12 = sin(124)/R. Sine rule sometimes does not give the correct angles when the unknown angle is near 90 degrees (angle or supplement). But here we know the unknown angle is acute, so there's no problem.
38. YumYum247
yah sorry i realized that.... :D
39. YumYum247
Again thank you infinite :"D
40. mathmate
You're welcome! :)
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# zbMATH — the first resource for mathematics
## IMRN. International Mathematics Research Notices
Short Title: Int. Math. Res. Not. Publisher: Oxford University Press, Cary, NC ISSN: 1073-7928; 1687-0247/e Online: https://academic.oup.com/imrn/issue Comments: Indexed cover-to-cover; From 2009, IMRN will incorporate IMRP
Documents Indexed: 4,364 Publications (since 1991) References Indexed: 49 Publications with 1,361 References.
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22 Bourgain, Jean 22 Etingof, Pavel Il’ich 18 Biswas, Indranil 12 Bringmann, Kathrin 12 Ginzburg, David 11 Ghioca, Dragos 10 Cherednik, Ivan V. 10 Kac, Victor G. 10 Katz, Nicholas Michael 10 Volberg, Alexander Lvovich 9 Bobenko, Alexander Ivanovich 9 Gelaki, Shlomo 9 Korotyaev, Evgeny L. 9 Suris, Yuri Borisovich 8 Chen, Xiuxiong 8 Etnyre, John B. 8 Feĭgin, Boris L’vovich 8 Grünbaum, Francisco Alberto 8 Lam, Ching Hung 8 Merle, Frank 8 Nazarov, Fedor L. 8 Varchenko, Alexander Nikolaevich 8 Veselov, Alexander Petrovich 7 Bertola, Marco 7 Bleher, Pavel M. 7 Conrey, John Brian 7 Duke, William Drexel 7 Felder, Giovanni 7 Forrester, Peter J. 7 Frenkel, Igor B. 7 Ginzburg, Victor 7 Ginzburg, Viktor L’vovich 7 Its, Alexander Rudolfovich 7 Kappeler, Thomas 7 Neeb, Karl-Hermann 7 Shparlinski, Igor E. 7 Tataru, Daniel 7 Tzvetkov, Nikolay 7 Van den Bergh, Michel 7 Wooley, Trevor D. 7 Zelditch, Steve 6 Aleman, Alexandru 6 Baik, Jinho 6 Bombieri, Enrico 6 Dong, Chongying 6 Esnault, Hélène 6 Jiang, Dihua 6 Killip, Rowan 6 Klainerman, Sergiu 6 Kuijlaars, Arno B. J. 6 Larsen, Michael Jeffrey 6 Leung, Naichung Conan 6 McLaughlin, Kenneth D. T.-R. 6 Ovsienko, Valentin Yu. 6 Rajan, Conjeeveram S. 6 Sahi, Siddhartha 6 Simon, Barry 6 Tian, Gang 6 Vega, Luis 6 Venkatesh, Akshay 6 Verbitsky, Misha 6 Wang, Weiqiang 6 Yeung, Sai-Kee 6 Zeitouni, Ofer 5 Adamović, Dražen 5 Adler, Mark 5 Baker, Matthew H. 5 Baranovsky, Vladimir 5 Blomer, Valentin 5 Browning, Timothy Daniel 5 Bukhshtaber, Viktor Matveevich 5 Claeys, Tom 5 Deift, Percy A. 5 Dong, Hongjie 5 Ebrahimi-Fard, Kurusch 5 Elkies, Noam David 5 Farmer, David W. 5 Germain, Pierre 5 Grushevsky, Samuel 5 Guillemin, Victor W. 5 Habegger, Philipp 5 Hallnäs, Martin A. 5 Hang, Fengbo 5 He, Weiyong 5 Kajiwara, Kenji 5 Khare, Chandrashekhar 5 Kumar, Shrawan 5 Kurlberg, Pär 5 Lee, Sangyop 5 Lemańczyk, Mariusz 5 Lenart, Cristian 5 Li, Jiayu 5 Li, Tian-Jun 5 Lin, Chang-Shou 5 Liu, Yue 5 Lowen, Wendy 5 Mason, Geoffrey 5 Merkulov, Sergei A. 5 Miranda, Eva 5 Nakanishi, Kenji ...and 5,070 more Authors
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Grothendieck ring of pretriangulated categories. Zbl 1079.18008
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Hingston, Nancy
1993
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1998
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1998
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Kostant, Bertram
1998
Intersecting a curve with algebraic subgroups of multiplicative groups. Zbl 0938.11031
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1999
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2001
Braid group actions and tensor products. Zbl 0990.17009
Chari, Vyjayanthi
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Presenting Schur algebras. Zbl 1059.16015
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2002
Characterization of the spectrum of Schrödinger operators with periodic distributions. Zbl 1104.34059
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Fredholm determinant solutions of the Painlevé. II: Hierarchy and gap probabilities of determinantal point processes. Zbl 07381532
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Quadratic twists of abelian varieties with real multiplication. Zbl 07381559
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Segre indices and Welschinger weights as options for invariant count of real lines. Zbl 07381579
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Regularity properties of free multiplicative convolution on the positive line. Zbl 07381595
Ji, Hong Chang
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Joint eigenfunctions for the relativistic Calogero-Moser Hamiltonians of hyperbolic type. III: Factorized asymptotics. Zbl 07381600
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The $$L^2$$ weak sequential convergence of radial focusing mass critical NLS solutions with mass above the ground state. Zbl 07381607
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Derived functors of differential operators. Zbl 07381609
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Computation of quantum cohomology from Fukaya categories. Zbl 07379771
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Statistical regularity of Apollonian gaskets. Zbl 07379778
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Reflective modular forms: a Jacobi forms approach. Zbl 07379799
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The anomaly flow over Riemann surfaces. Zbl 07379801
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The $$q$$-Hahn PushTASEP. Zbl 07379804
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Semibricks. Zbl 1467.16009
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Large-degree asymptotics of rational Painlevé-IV functions associated to generalized Hermite polynomials. Zbl 1458.35137
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Valuations on Banach lattices. Zbl 07195662
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Dimension formulae in genus zero and uniqueness of vertex operator algebras. Zbl 07195654
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Crystallization of random matrix orbits. Zbl 1447.60021
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Plancherel distribution of Satake parameters of Maass cusp forms on $$\mathrm{GL}_3$$. Zbl 1437.11079
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Off-diagonal asymptotic properties of Bergman kernels associated to analytic Kähler potentials. Zbl 1442.32011
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Ruelle and quantum resonances for open hyperbolic manifolds. Zbl 07188615
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Almost Euclidean isoperimetric inequalities in spaces satisfying local Ricci curvature lower bounds. Zbl 1436.53022
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Continuous cocycle superrigidity for the full shift over a finitely generated torsion group. Zbl 07195636
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Ramsey graphs induce subgraphs of quadratically many sizes. Zbl 1440.05151
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Affine wreath product algebras. Zbl 07217942
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Isomorphisms between big mapping class groups. Zbl 1458.57014
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General variational formulas for abelian differentials. Zbl 1453.30002
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Inhomogeneous dual Diophantine approximation on affine subspaces. Zbl 1454.11128
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Homological projective duality for linear systems with base locus. Zbl 1457.14034
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Imai, Naoki; Tsushima, Takahiro
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Watanabe, Hideya
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Kiem, Young-Hoon; Li, Jun
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Chau, Albert; Weinkove, Ben
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Galois conjugates of entropies of real unimodal maps. Zbl 1444.37015
Tiozzo, Giulio
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Waist of balls in hyperbolic and spherical spaces. Zbl 1446.53033
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Matoušek, Jiří; Nikolov, Aleksandar; Talwar, Kunal
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Miquel dynamics for circle patterns. Zbl 1432.37041
Ramassamy, Sanjay
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Pointwise asymptotics for orthonormal polynomials at the endpoints of the interval via universality. Zbl 1442.42065
Lubinsky, Doron S.
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Formal Abel-Jacobi maps. Zbl 1453.14027
Fiorenza, Domenico; Manetti, Marco
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Model transition for representations of unitary type. Zbl 1440.11084
Morimoto, Kazuki
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Almost positive curvature on an irreducible compact rank 2 symmetric space. Zbl 1455.53077
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Dipierro, Serena; Pinamonti, Andrea; Valdinoci, Enrico
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$$\varepsilon$$-Regularity and structure of four-dimensional shrinking Ricci solitons. Zbl 07188617
Huang, Shaosai
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Hyperbolicity of varieties supporting a variation of Hodge structure. Zbl 1439.32036
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Cho, Peter J.; Kim, Henry H.
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Six-vertex models and the GUE-corners process. Zbl 1439.82025
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Universal Gröbner bases and Cartwright-Sturmfels ideals. Zbl 1439.13075
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Symmetries of projective spaces and spheres. Zbl 1437.81032
Gehér, György Pál
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Conformally covariant bi-differential operators on a simple real Jordan algebra. Zbl 07195657
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Lotay, Jason D.; Schulze, Felix
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Mieda, Yoichi
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Eliashberg, Yakov; Ganatra, Sheel; Lazarev, Oleg
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Xu, Junyan
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Stretching convex domains to capture many lattice points. Zbl 1448.52012
Marshall, Nicholas F.
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The homology class of a Poisson transversal. Zbl 07217941
Frejlich, Pedro; Mărcuţ, Ioan
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New sharp Gagliardo-Nirenberg-Sobolev inequalities and an improved Borell-Brascamp-Lieb inequality. Zbl 1450.26006
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Non-formality of planar configuration spaces in characteristic 2. Zbl 1444.55009
Salvatore, Paolo
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Universal series for Hilbert schemes and strange duality. Zbl 1440.14019
Johnson, Drew
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Strange duality on rational surfaces. II: Higher-rank cases. Zbl 1454.14030
Yuan, Yao
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Species with potential arising from surfaces with orbifold points of order 2. II: arbitrary weights. Zbl 1458.16014
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Cruickshank, James; Guler, Hakan; Jackson, Bill; Nixon, Anthony
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Lattice simplices with a fixed positive number of interior lattice points: a nearly optimal volume bound. Zbl 1455.52010
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Magee, Michael
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Deformation of tilting-type derived equivalences for crepant resolutions. Zbl 1454.14046
Hara, Wahei
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Chen, Po-Ning; Zhang, Xiangwen
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Dependence of the density of states on the probability distribution for discrete random Schrödinger operators. Zbl 1458.82011
Hislop, Peter D.; Marx, Christoph A.
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Frobenius splitting of thick flag manifolds of Kac-Moody algebras. Zbl 07313489
Kato, Syu
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Sharp area bounds for free boundary minimal surfaces in conformally Euclidean balls. Zbl 1458.53065
Freidin, Brian; McGrath, Peter
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Chen, Zhe
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Row contractions annihilated by interpolating vanishing ideals. Zbl 07319799
Clouâtre, Raphaël; Timko, Edward J.
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Product matrix processes as limits of random plane partitions. Zbl 1456.60014
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Decomposition rules for the ring of representations of non-Archimedean $$GL_n$$. Zbl 07319804
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Antisymmetric paramodular forms of weights 2 and 3. Zbl 07319807
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Gromov-Witten theory of toric birational transformations. Zbl 1464.14058
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Exponential sums over finite fields and the large sieve. Zbl 1466.11093
Perret-Gentil, Corentin
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A vanishing associated with irregular MSP fields. Zbl 1467.14130
Chang, Huai-Liang; Li, Jun
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Homology Smale-Barden manifolds with $$K$$-contact but not Sasakian structures. Zbl 1461.57011
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Shifted symplectic Lie algebroids. Zbl 07319823
Pym, Brent; Safronov, Pavel
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$$H^4(\mathrm{Co}_0; Z) = Z/24$$. Zbl 07319833
Johnson-Freyd, Theo; Treumann, David
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Asymptotic stability for some non positive perturbations of the Camassa-Holm peakon with application to the antipeakon-peakon profile. Zbl 1459.35043
Molinet, Luc
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#### Cited by 18,038 Authors
75 Shparlinski, Igor E. 70 Biswas, Indranil 46 Dong, Chongying 45 Korotyaev, Evgeny L. 43 Etingof, Pavel Il’ich 43 Forrester, Peter J. 42 Ruzhansky, Michael V. 40 Kac, Victor G. 39 Borodin, Alexei 39 Kenig, Carlos Eduardo 37 Guo, Boling 35 Wei, Juncheng 34 Tzvetkov, Nikolay 33 Erdős, László 33 Ghioca, Dragos 33 Suciu, Alexander I. 32 Kuijlaars, Arno B. J. 32 Lam, Ching Hung 32 Tao, Terence 31 Bringmann, Kathrin 31 Tabuada, Gonçalo 30 Oh, Tadahiro 29 Bourgain, Jean 29 Chen, Xiuxiong 29 Creutzig, Thomas 29 Milas, Antun 29 Tolsa, Xavier 29 Vega, Luis 28 Bertola, Marco 28 Laterveer, Robert 28 Li, YanYan 28 Varchenko, Alexander Nikolaevich 27 Ionescu, Alexandru D. 27 Liu, Yue 26 Collins, Benoît 26 Duran, Antonio J. 26 Geng, Xianguo 26 Iosevich, Alex 25 Banica, Teodor 25 Feigin, Evgeny 25 Kashiwara, Masaki 25 Lin, Chang-Shou 25 Lu, Guozhen 25 Ol’shanskiĭ, Grigoriĭ Iosifovich 25 Zelditch, Steve 24 Adamović, Dražen 24 Arakawa, Tomoyuki 24 Blomer, Valentin 24 Fourier, Ghislain 24 Ginzburg, David 24 Kappeler, Thomas 24 Li, Haisheng 24 Lubinsky, Doron S. 24 Miao, Changxing 24 Panyushev, Dmitri Ivanovich 24 Scrimshaw, Travis 24 Tataru, Daniel 24 Tian, Gang 24 Wang, Weiqiang 23 Chari, Vyjayanthi 23 Gorin, Vadim 23 Its, Alexander Rudolfovich 23 Ponce, Gustavo 23 Rains, Eric M. 22 Ginzburg, Viktor L’vovich 22 Guo, Li 22 Killip, Rowan 22 Miranda, Eva 22 Morozov, Alexei Yurievich 22 Zaharescu, Alexandru 22 Zheng, Jiqiang 21 Guo, Zihua 21 Molev, Alexander I. 21 Rodnianski, Igor 21 Schilling, Anne 21 Shadrin, Sergey V. 21 Simon, Barry 21 Visan, Monica 21 Yau, Horng-Tzer 21 Zannier, Umberto M. 20 De Sole, Alberto 20 Feĭgin, Boris L’vovich 20 Lu, Guangshi 20 Marcolli, Matilde 20 Mazorchuk, Volodymyr 20 Natale, Sonia 20 Pistoia, Angela 20 Qu, Changzheng 20 Uhlmann, Gunther Alberto 20 Van den Bergh, Michel 20 Vasy, András 20 Verbitsky, Misha 20 Volberg, Alexander Lvovich 19 Burq, Nicolas 19 Cuccagna, Scipio 19 Donninger, Roland 19 Germain, Pierre 19 Grigor’yan, Alexander Asaturovich 19 Himonas, A. Alexandrou 19 Jing, Naihuan ...and 17,938 more Authors
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#### Cited in 670 Journals
1,223 Advances in Mathematics 813 Journal of Algebra 796 Transactions of the American Mathematical Society 792 Communications in Mathematical Physics 598 Proceedings of the American Mathematical Society 554 Journal of Functional Analysis 468 Duke Mathematical Journal 451 Mathematische Zeitschrift 434 Mathematische Annalen 415 Journal of Number Theory 383 Journal of Mathematical Physics 370 Journal of Mathematical Analysis and Applications 352 Journal of Differential Equations 309 Inventiones Mathematicae 289 The Journal of Geometric Analysis 285 Journal of Pure and Applied Algebra 259 Journal of Geometry and Physics 257 Annales de l’Institut Fourier 254 Letters in Mathematical Physics 247 Selecta Mathematica. New Series 222 Calculus of Variations and Partial Differential Equations 212 Israel Journal of Mathematics 193 Compositio Mathematica 192 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 192 Comptes Rendus. Mathématique. Académie des Sciences, Paris 189 Journal of High Energy Physics 186 Journal of the European Mathematical Society (JEMS) 185 Journal für die Reine und Angewandte Mathematik 181 Geometry & Topology 174 Communications in Algebra 174 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 172 Geometriae Dedicata 167 Algebraic & Geometric Topology 159 Communications in Partial Differential Equations 155 Manuscripta Mathematica 152 Journal of Combinatorial Theory. Series A 152 Journal of the American Mathematical Society 152 Annals of Mathematics. Second Series 151 Discrete and Continuous Dynamical Systems 147 Geometric and Functional Analysis. GAFA 143 Journal de Mathématiques Pures et Appliquées. Neuvième Série 141 Journal of Algebraic Combinatorics 137 Transformation Groups 136 International Journal of Mathematics 135 Algebras and Representation Theory 129 International Journal of Number Theory 117 Science China. Mathematics 116 Journal d’Analyse Mathématique 114 Topology and its Applications 111 Bulletin of the American Mathematical Society. New Series 111 The Ramanujan Journal 110 Advances in Applied Mathematics 105 Archive for Rational Mechanics and Analysis 104 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 103 Journal of Approximation Theory 103 Annales Henri Poincaré 101 Memoirs of the American Mathematical Society 100 Communications in Contemporary Mathematics 98 Journal of Statistical Physics 98 Journal de Théorie des Nombres de Bordeaux 96 Probability Theory and Related Fields 96 Revista Matemática Iberoamericana 93 The Annals of Probability 92 Acta Mathematica Sinica. English Series 90 Representation Theory 89 Monatshefte für Mathematik 86 Annals of Global Analysis and Geometry 85 Nuclear Physics. B 85 Forum Mathematicum 85 Journal of Mathematical Sciences (New York) 83 Mathematical Proceedings of the Cambridge Philosophical Society 81 SIAM Journal on Mathematical Analysis 78 Communications on Pure and Applied Mathematics 76 Theoretical and Mathematical Physics 76 Differential Geometry and its Applications 76 The Journal of Fourier Analysis and Applications 75 Archiv der Mathematik 75 Pacific Journal of Mathematics 74 Forum of Mathematics, Sigma 73 Journal of Nonlinear Mathematical Physics 72 Journal of Algebraic Geometry 69 European Journal of Combinatorics 68 Annali di Matematica Pura ed Applicata. Serie Quarta 67 Nonlinearity 67 Documenta Mathematica 67 Séminaire Lotharingien de Combinatoire 67 Journal of the Institute of Mathematics of Jussieu 66 Constructive Approximation 65 Linear Algebra and its Applications 64 Ergodic Theory and Dynamical Systems 63 Michigan Mathematical Journal 63 Kyoto Journal of Mathematics 62 Journal of Knot Theory and its Ramifications 60 Mathematics of Computation 60 Discrete & Computational Geometry 60 St. Petersburg Mathematical Journal 60 Research in the Mathematical Sciences 58 Acta Arithmetica 58 Journal of the Mathematical Society of Japan 58 Algebra & Number Theory ...and 570 more Journals
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#### Cited in 63 Fields
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# Marginal enumeration not in the margins
Based on an answer to one of my previous questions, I implemented the following code which is supposed to enumerate examples discretely in the margins of my document:
\documentclass{memoir}
\usepackage[latin1]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{amsmath,amssymb,geometry,graphicx,amstext}
\usepackage[amsmath]{ntheorem}
% margin theorem
\makeatletter
\newtheoremstyle{mymargin}%
{\item[\theorem@headerfont \llap{##1 ##2}| ##3\theorem@separator\hskip\labelsep]}%
\makeatother
% my example
\theoremstyle{mymargin}
\newtheorem{example}{Example}
\numberwithin{example}{chapter}
\begin{document}
\begin{example}
\centering
\begin{tabular}{cccc}
this & is & a & test\\
table & where & text & goes
\end{tabular}
\end{example}
\end{document}
This produces the following output:
As you see, because the table is centered, the example number is not actually in the margins, which is my major concern. Furthermore, I would like the number to appear aligned with the top of the table and always on the same page as the table (which is not always the case either). Finally, I would like the number always to appear in the outer margin when the two-page option is on. How may this be fixed?
• if you use \begin{tabular}[t] that resolves one of the issues- switching the margins is quite tricky and intricate- see Equation numbers in outer margins on a two-sided document for example – cmhughes Nov 14 '13 at 20:17
• You're not really typesetting the header in the margin, only at the left of the first word in the statement which means, under normal circumstances, in the margin; if the first word (here the tabular) is not at the left margin, also the header won't. – egreg Nov 14 '13 at 20:59
• cmhughes: Thanks, I'll try that out. egreg: Yes, I see your point. Unfortunately, I don't know enough about the ntheorem syntax to change it. – Gaussler Nov 14 '13 at 21:08
\centering is a bit too much here and won't be appropriate if there is following text. Use \begin{center}...\end{center] escaped with a preceeding \leavevmode:
\documentclass{memoir}
\usepackage[latin1]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{amsmath,amssymb,geometry,graphicx,amstext}
\usepackage[amsmath]{ntheorem}
% margin theorem
\makeatletter
\newtheoremstyle{mymargin}%
{\item[\theorem@headerfont \llap{##1 ##2}| ##3\theorem@separator\hskip\labelsep]}%
\makeatother
% my example
\theoremstyle{mymargin}
\newtheorem{example}{Example}
\numberwithin{example}{chapter}
\begin{document}
\begin{example}
Ordinary example.
\end{example}
\begin{example}
\leavevmode\begin{center}
\begin{tabular}{cccc}
this & is & a & test\\
table & where & text & goes
\end{tabular}
\end{center}
And now comes the discussion of the rest of the example.
\end{example}
\begin{example}
\begin{equation*}
x=y
\end{equation*}
\end{example}
\end{document}
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# Computer algebra system for category theory
There are many different computer algebra systems which allows to perform computer aided computation in symbolic object like polynomials and function and also ordinals. Now being a category theory fanatic I'm wondering if there's any such system which can perform calculation in any 2-category. So.......
does anyone know a computer algebra system which can perform calculation with 2-categories and or string diagrams?
-
## 2 Answers
Pretty sure it is not exactly what you're looking for, but Sage is designed in an categorical way (for instance, a group is an instance of the subclass Groups of the class Monoids, which is in turn a subclass of the class Magmas, etc.), and so has some features related to category theory.
-
so does Axiom (FriCAS). Though I doubt if either SAGE or Axiom will do what OP asks. – Yrogirg Jun 30 '13 at 9:27
Maybe it's better that I answer this question, since I posed it to ineff yesterday. I let him ask the question since he is definitely more keen on the subject :) the following explanation is the best I was able to write. Sorry if it seems (and in fact it is) the product of a really simple-minded programmer!
What I had in mind was to write down a simple (?) program helping me to avoid embarassingly elementary questions like this, which turn out to be blatantly trivial once you drew the right diagram.
But now suppose that diagrams can't help you (e.g. suppose they become really huge), and you can only trust bare computations. You have to check whether
{something complicated} = {something even more complicated},
or you wrote "1" in a really complicated fashion and you want to "reduce" it in a suitable sense, with respect to some suitable algebraic laws[2].
Now what I want is to define a "type" Object and a "type" (or a structure? I don't remember almost anything about these topics :) ) Arrow (or 1-cell), where an "arrow" consists of a triple {D,C,f}, where $D,C$ are objects, the domain and codomain of the arrow $f$[3]. The collection of 1-cells come equipped with two (in fact, three) maps Object source(Arrow f), Object target(Arrow f) and int Name(Arrow f), doing what you expect they do. Arrows can be composed if the domain of the one coincides with the codomain of the other (and I think that the problem reduces to the implementation of this operation and the definition of its rules -label a special arrow as the identity, how do you cope with commutative-square-like situations?).
A 2-cell consists now of a square $$\begin{array}{ccc} A &\to&B \\ \downarrow&\alpha&\downarrow\\ C&\to & D \end{array}$$ having horizontal and vertical source and target:
• The horizontal source of $\alpha$ is the arrow $A\to C$;
• The vertical source of $\alpha$ is the arrow $A\to B$;
• ...
• vertical and horizontal source and target are linked by suitable relations: $s(s_v(\alpha))=s(s_h(\alpha))$, $t(s_v(\alpha))=s(t_h(\alpha))$, etc.
Notice that "natural transformations" arise as those 2-cells having identity arrows as horizontal domain and codomain. I think the most naive way to describe a 2-cell is by an inductive argument (exploiting again internalization): $\alpha$ is a structure consisting of a 4-tuple of arrows, such that "they form a square": Arrow Vsource(Nat alpha), Arrow Hsource(Nat alpha), Arrow Vtarget(Nat alpha) and Arrow Htarget(Nat alpha) are given in such a way that the former relations are satisfied.
2-cells can now be composed horizontally ($\boxminus$) and vertically ($\circ$), and I would like to
• Define these compositions and impose the interchange law
• Recover the "whiskering" operation $\alpha*F$ of a 2-cell $\alpha$ and a 1-cell $F$ as horizontal composition of an identity two cell with another composable 2-cell
• Do computations! Suppose now you want to check without any graphical help whether $\theta\circ ((\alpha * F)\boxminus (\gamma\circ \beta)\boxminus (H* \delta))=$something. You feed your program with something like
Vcomp(theta , etc.)
you cross your fingers and then you hopefully get something you can more easily compare with what you desire (the identity 2-cell, an endomorphism of a suitable 1-cell, ...).
====
[2] yup, I know that computationally speaking I'm asking first to run for a km or two and then to climb the Karakorum, but let me get to the point.
[3] which is an element of a suitable alphabet: this is not minimal since I can deduce objects from identity arrows, but I feel more comfortable in this way. Suppose for example you are labeling arrows $A\to B$ with positive-integer labels
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# Q: Will the world end in 2012?
Physicist: Firstly, happy new year!
So, there’s been a lot of hoopla around 2012 doomsday stuff for a while. Maybe not as much fuss as there was over the techno-apocalypse of Y2K, but still. Although there are a variety of cited prophecies, the Mayan calender is arguably the most famous.
I’m not knocking them, but if the Mayans could see the future and understood the nature of the universe so very well, then they should have been able to wipe out the conquistadors with their rail guns and bio-weapons, then nuked Spain from their orbital weapons platform, code-named “Ah Chuy Kak“. That seems like a Mayan response anyway. Those guys were kinda jerks.
Also, and less interestingly, there’s no evidence that the Mayans even made any 2012 predictions in the first place.
So, dismissing out of hand any claims of prognostication (given that those claims don’t tend to pan out), what is the probability that the world will end in 2012?
20th vs. 21st century soothsaying mostly comes down to a difference in print quality.
Back in the day, a statistician (42% of whom are marginally attractive) named Pierre-Simon Laplace (100% French) considered the question “what is the probability that the sun will rise tomorrow?”.
Like most French, Laplace wasn’t entirely ignorant. He knew all about the solar system and whatnot. What he was really getting at was, if you don’t know (or pretend not to know) the underlying probabilities of some phenomena, how do you figure out what those probabilities are?
He figured out that if you see something, that can happen in one of two ways, happen the same way N times in a row, then the probability that it will continue that pattern next time is $\frac{N+1}{N+2}$. There’s a generalization to this, but in the case of sunrises, it’s not needed. Laplace figured, if the Earth is 6 thousand years old (at the time Laplace was living, “young Earth creationist” was essentially the same as “Christian”), then the probability that the sun would rise the next day was around 99.99995%.
One less worry.
Laplace’s “rule of succession“, as the equation is called, assumes a complete lack of knowledge about what the actual probabilities are, but it does require you to know in advance of seeing (or not seeing) an event that either result is possible.
But with the end of the world, we know it’s certainly possible. We know that the Earth has endured environmental catastrophes that any human survivor (if there were survivors) would call “the end of the world”. Looking into the solar system we frequently see impact craters of various sizes on objects, ranging from tiny to very-nearly-large-enough-to-blow that-object apart. (I mean, have you seen Mimas?) Oddly enough, we never see any that are large-enough-to-blow-that-object-apart.
"Meteor Crater" near Flagstaff, AZ. Sometimes these things happen.
So, could the world end any day now? Why not. There’s plenty of stuff that could take us out.
Using only the rule of succession (which basically boils down to “well, it hasn’t happened yet”) we can say that the chance of the entire Earth being destroyed this year is about 1 in 5,000,000,000.
If you define the end of the world as the end of our species, then again using the rule of succession, the probability that we’ll go extinct this year (given no information other than “we’ve made it this far”) is about 1 in 200,000.
It’s kinda comforting to think that the ancient Romans, Mayans, Norse, Indians, freaking everybody, had people running around predicting the end of the world. Throughout all of known human history there have been people deeply concerned with the impending end of everything and, with any luck, they’ll have a chance to make the rest of us nervous for tens or hundreds of thousands of years to come.
This entry was posted in -- By the Physicist, Paranoia, Probability, Skepticism. Bookmark the permalink.
### 12 Responses to Q: Will the world end in 2012?
1. stupidfaceeeeee says:
Ah Chuy Kak is the mayan god of war -__-
2. Gill says:
People are always predicting the world will end and it never happens. Brian Cox definitely does not think it will!!!!
3. Alex says:
How can Laplace possibly make a prediction of the future, simply based on past observations? In other words: How can one determine probabilities of outcomes without having a probability measure?
4. The Physicist says:
The only thing we have access to is the past.
What Laplace did, mathematically speaking, was assume a maximum lack of knowledge about the probability distributions, and then carefully built his knowledge from experience. Mathematically speaking.
5. Thomas says:
There is always this thing with a tree falling in the middle of forest. Isn’t it obvious if you don’t believe in god, when you die, you stop experiencing the world. Therefore not only you cease to exist for the universe (in this case it’s even longer than the other), but universe does the same for you – disappears. This way I have proven that the end of the world happens every day, for many people, and one day it will happen for you. It doesn’t work for everybody, what with all this religions and whatnot, but this is our society – nothing works every time (even stuff like gravity if you have open minded enough scientist ;)).
6. sharafali.a says:
No one knows when the world ends. but the creater know it.
If there is anyone who saying “world will end in 2012” you can ask them to have a bond such that all his properties become yours after 2012…
7. Ron says:
I bet it would be profitable to go into the business of managing post apocalypse assets…does that seem unethical to anyone?? lol
8. lukas says:
Only God know the end and the day be
couse the world was created be him .
9. mohamed says:
I pelieved that the god only know the end of the worid
10. Richardw says:
Thought you’d like an update from the future.
Yes!
🙂
11. Savias says:
Still here in 2016
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# Floating point format: why must 1−emax ≤ q+p−1 ≤ emax?
From the Wikipedia page on the IEEE Standard for Floating-Point Arithmetic,
The possible finite values that can be represented in a format are determined by the base (b), the number of digits in the significand (precision, p), and the exponent (q) parameter emax:
...
q must be an integer such that 1−emax ≤ q+p−1 ≤ emax (e.g., if p=7 and emax=96 then q is −101 through 90).
I can't figure out the reasoning behind the above inequality. I would've thought (in my simplicity) that it would be -emax ≤ q ≤ emax or something similar. What am I missing?
The reason we get a larger range is denormalized numbers. Generally speaking, floating point numbers have three physical parts: sign (1 bit), mantissa $M$ and exponent $e$. Most of the time we think of the number as $\operatorname{sgn} \times 1.M \times 2^{e-e_0}$, where $e_0 = 2^{|e|}-1$ (e.g. for single precision, it's 127, since the exponent is allotted seven bits). Here "$1.M$" means the number you obtain by writing $M$ as a binary string and prefixing $1.$.
For reasons having to do with underflow (non-zero numbers turning to zero), it is important to be able to store numbers very close to zero. These numbers, named denormalized numbers or subnormalized numbers, have $e = 0$ and represent $\operatorname{sgn} \times 0.M \times 2^{1-e_0}$. (This means that normal numbers cannot have $e = 0$.) This explains the extended range mentioned in the Wikipedia page.
Other numbers having special encodings are $\pm \infty$ and NaN (not a number), which represent some illegal operation (division by zero, taking the logarithm of a non-positive number, taking the square root of a negative number, and so on). For more details, consult the Wikipedia page regarding the original standard.
• The exponent is allotted eight* bits IMO . – PleaseHelp Dec 13 '14 at 13:11
I don't think 'subnormality' is at play here. However, 'normality' is!
The Wiki-page you refer to represents a number x to be
x = c . bq with c = 0 ... bp-1 (1)
However, the number we would want to store as an IEEE754 floating point number is represented differently:
x = c' . bq' with c' = 0 ... 1-b-p (2)
This is the 'normalization' I referred to earlier.
We can relate (1) and (2) by reforming (1):
x = c . bq = c . b-p+1 . bp-1 . bq = c' . bp-1 . bq = c' . bq+p-1
Therefore:
q' = q+p-1 (3)
We want to store q' using a limited number range. According to the IEEE 754 standard, we'll do this using 'bias'. Let's define the bias to be emax - 1 (with emax being half the number range we have available. E.g., in the binary32 case we have 8 bits available in the exponent of a float. This leads to an emax = 0.5 . 28 = 128).
In view of this, we can write:
-emax+1 ≤ q' ≤ emax (4)
This ensures that q' plus the bias fully covers the available (but limited) range.
Combining (3) and (4) yields the (at first sight) not so obvious equation of the wiki-page:
-emax+1 ≤ q+p-1 ≤ emax
I hope this helps!
Note: the true IEEE754 binary case also assumes the 'silent leading bit 1' which further complicates the matter and is indeed the root of subnormal numbers.
• Welcome! For future reference, you can use LaTeX to typeset mathematics, which is a good deal easier that coding up all that HTML! We have a short reference that explains the feature. – David Richerby Jan 5 '16 at 20:54
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# Microprocessor Design/Performance
## Clock Cycles
The clock signal is a 1-bit signal that oscillates between a "1" and a "0" with a certain frequency. When the clock transitions from a "0" to a "1" it is called the positive edge, and when the clock transitions from a "1" to a "0" it is called the negative edge.
The time it takes to go from one positive edge to the next positive edge is known as the clock period, and represents one clock cycle.
The number of clock cycles that can fit in 1 second is called the clock frequency. To get the clock frequency, we can use the following formula:
${\displaystyle {\mbox{Clock Frequency}}={\frac {1}{\mbox{Clock Period}}}}$
Clock frequency is measured in units of cycles per second.
## Cycles per Instruction
In many microprocessor designs, it is common for multiple clock cycles to transpire while performing a single instruction. For this reason, it is frequently useful to keep a count of how many cycles are required to perform a single instruction. This number is known as the cycles per instruction, or CPI of the processor.
Because all processors may operate using a different CPI, it is not possible to accurately compare multiple processors simply by comparing the clock frequencies. It is more useful to compare the number of instructions per second, which can be calculated as such:
${\displaystyle {\mbox{Instructions per Second}}={\frac {\mbox{Clock Frequency}}{CPI}}}$
One of the most common units of measure in modern processors is the "MIPS", which stands for millions of instructions per second. A processor with 5 MIPS can perform 5 million instructions every second. Another common metric is "FLOPS", which stands for floating point operations per second. MFLOPS is a million FLOPS, GFLOPS is a billion FLOPS, and TFLOPS is a trillion FLOPS.
## Instruction count
The "instruction count" in microprocessor performance measurement is the number of instructions executed during the run of a program. Typical benchmark programs have instruction counts in the millions or billions -- even though the program itself may be very short, those benchmarks have inner loops that are repeated millions of times.
Some microprocessor designers have the freedom to add instructions to or remove instructions from the instruction set. Typically the only way to reduce the instruction count is to add instructions such that those inner loops can be re-written in a way that does the necessary work using fewer instructions -- those instructions do "more work" per instruction.
Sometimes, counter-intuitively, we can improve overall CPU performance (i.e., reduce CPU time) in a way that increases the instruction count, by using instructions in that inner loop that may do "less work" per instruction, but those instructions finish in less time.
## CPU Time
CPU Time is the amount of time it takes the CPU to complete a particular program. CPU time is a function of the amount of time it takes to complete instructions, and the number of instructions in the program:
${\displaystyle {\mbox{CPU time}}={\mbox{Instruction Count}}\times CPI\times {\mbox{Clock Cycle Time}}}$
Sometimes we can improve one of the 3 components alone, reducing CPU time. But quite often we find a tradeoff -- say, a technique that increases instruction count, but reduces the clock cycle time -- and we have to measure the total CPU time to see if that technique makes the overall performance better or worse.
## Amdahls Law
Amdahl's Law is a law concerned with computer performance and optimization. Amdahl's law states that an improvement in the speed of a single processor component will have a comparatively small effect on the performance of the overall processor unit.
In the most general sense, Amdahl's Law can be stated mathematically as follows:
${\displaystyle \Delta ={\frac {1}{\sum _{k=0}^{n}{{\big (}{\frac {P_{k}}{S_{k}}}{\big )}}}}}$
where:
• Δ is the factor by which the program is sped up or slowed down,
• Pk is a percentage of the instructions that can be improved (or slowed),
• Sk is the speed-up multiplier (where 1 is no speed-up and no slowing),
• k represents a label for each different percentage and speed-up, and
• n is the number of different speed-up/slow-downs resulting from the system change.
For instance, if we make a speed improvement in the memory module, only the instructions that deal directly with the memory module will experience a speedup. In this case, the percentage of load and store instructions in our program will be P0, and the factor by which those instructions are sped up will be S0. All other instructions, which are not affected by the memory unit will be P1, and the speed up will be S1 Where:
${\displaystyle P_{1}=1-P_{0}}$
${\displaystyle S_{1}=1}$
We set S1 to 1 because those instructions are not sped up or slowed down by the change to the memory unit.
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# Math Help - Covergent and Divergent Sequences - Real Analysis
1. ## Covergent and Divergent Sequences - Real Analysis
So I want 2 sequences a and b that are not convergent, but a+b is a convergent sequence.
I can not seem to get this one. I've been thinking about it too long and my brain is fried.
Like could I use (-1)^n for a. My problem is finding a b so that the two added together will converge. Can someone please help me and give me some pointers?
2. Take for example the sequences n and -n.
3. What about $\sum 1/n$and $\sum -1/n$?
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# Exercise 04-8 Using the plantwide overhead rate to assess prices LO P1 Way Cool produces two...
###### Question:
Exercise 04-8 Using the plantwide overhead rate to assess prices LO P1 Way Cool produces two different models of air conditioners. The company produces the mechanical systems in its components department. The mechanical systems are combined with the housing assembly in its finishing department. The activities, costs, and drivers associated with these two manufacturing processes and the production support process follow. (Loss amounts should be indicated with a minus sign. Round your intermediate calculations and round "Cost per unit and OH rate" answers to 2 decimal places.) Process Activity Components Changeover Machining Setups Quantity 750 7,740 200 Finishing Welding Inspecting Rework Overhead Cost Driver $458,500 Number of batches 300, 400 Machine hours 229,000 Number of setups$987,900 $189,800 Welding hours 235,000 Number of inspections 62,000 Rework orders$477,800 $135,500 Purchase orders 32,450 Number of units 60, 050 Number of units 4, 8ee 780 250 Support Purchasing Providing space Providing utilities 525 5, 100 5,100$228,000
additional production information concerning its two product lines follows Units produced Welding hours Batches Number of inspections Machine hours Setups Rework orders Purchase orders Model 145 1,700 2,400 375 480 2,290 100 130 350 Model 212 3,400 2,400 375 300 5,450 100 12e 175 Required: 1. Using a plantwide overhead rate based on machine hours, compute the overhead cost per unit for each product line. 2. Determine the total cost per unit for each product line if the direct labor and direct materials costs per unit are $290 for Model 145 and$150 for Model 212 Activity Activity Driver Plantwide OH rate Total Overgad Cost Units Produced OH Cost per unit Overhead Assigned Model 145 Model 212
1. Using a plantwide overhead rate based on machine hours, compute the overhead cost per unit for each product line. 2. Determine the total cost per unit for each product line if the direct labor and direct materials costs per unit are $290 for Model 145 and$150 for Model 212 Overhead Assigned Activity Driver Plantwide OH rate Total Overhead Cost Units Produced OH Cost per unit Model 145 Model 212 Model 145 Model 212 3. If the market price for Model 145 is 5753 and the market price for Model 212 is $500, determine the profit or loss per unit for each model Model 145 Model 212 Market price ## Answers #### Similar Solved Questions 5 answers ##### ~/6 points LarCAABLS2 2.3.024.SBS,Notes Beton, YOu are given tne 2012 value of product and thc this Intormatlon rate at which tha value Arite Mneet equation A(at expected t0 change during the next gives the Collar value V of the vears Us product tcms the vear: (Let t 2017 Value Ruto 12 represent 2012.) 544,000 52800 decrease year STEP Find the paint 07 the Ilne tat ccrresponds (he Informatlon given abovesteP 2; TndslopoStep Use the polnt-= 0p0 formulaequatlon tne Iine;12$ ( < 17Need Help?Laa
~/6 points LarCAABLS2 2.3.024.SBS, Notes Beton, YOu are given tne 2012 value of product and thc this Intormatlon rate at which tha value Arite Mneet equation A(at expected t0 change during the next gives the Collar value V of the vears Us product tcms the vear: (Let t 2017 Value Ruto 12 represent 20...
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##### FQ3 3. A 240 V DC series motor with 0.1 ohm armature resistance and 0.1 ohm...
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##### For the standard normal distribution, determine the following probabilities: (a) Pr(Z 2 1.25) (b) Pr(1.25 < Z < 1.75)Give your answerto 4 decimalsRound YOur answer [o 4 decimals
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##### QUESTION 11 dissolaing of Jspirin (CoH;oa) 0.79 oxmotic pressure 0/ 4 solution formicd by molar concentration ol the aspirin solutionwatcr ut 37 Cis 2,45 atm_J(2e0
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If G is a simple graph, the complement of G, denoted G', is the simple graph with the same set of nodes as G, where nodes x-y are adjacent in G' if and only if theyare not adjacent in G.a) Given an adjacency matrix A for a simple graph G, describe the adjacency matrix for G'....
##### Real World Financials CODE EDGAR, the Electronic Data Gathering, Analysis, and Retrieval system, performs automated collection,...
Real World Financials CODE EDGAR, the Electronic Data Gathering, Analysis, and Retrieval system, performs automated collection, validation, indexing, and forwarding of submissions by companies and others who are required by law to file forms with the SEC. All publicly traded domestic companies use E...
##### It is sometimes possible to write two inequalities as one inequality, called a ______ inequality.
It is sometimes possible to write two inequalities as one inequality, called a ______ inequality....
##### Factors that shift the AD Curve include A) government purchases B) autonomous investment C) taxes D)...
factors that shift the AD Curve include A) government purchases B) autonomous investment C) taxes D) all of the above E) none of the above 33. If government cuts taxes A) after tax income should increase shifting AD to the left to a lower cu B) after tax income should increase shifting AD to the rig...
##### 6. In a game of billard's a player continues to play until she misses a shot....
6. In a game of billard's a player continues to play until she misses a shot. If a particular player misses any of her shots with probability p-1/6. What is the probability that this players turn will last a) Identify the distribution with the parameters b) exactly 5 shots c) at most 5 shots d) ...
##### Question 22 ptsThe following three solutions are mixed: 100.0 mL of 0.100 M NazSO4: 50.0 mL of 0.300 M ZnClz and 100.0 mL of 0.200 M Ba(CN)z:When the solutions are mixed barium sulfate andprecipitate out of solution: Themolarity of the remaining Na' ions ismolar:The molarity of the remaining CF ionsmolar: The molarity of the remaining CN' ion ismolar: Themolarity of the remaining Ba'* ion ismolar: (3 s.f)
Question 2 2 pts The following three solutions are mixed: 100.0 mL of 0.100 M NazSO4: 50.0 mL of 0.300 M ZnClz and 100.0 mL of 0.200 M Ba(CN)z: When the solutions are mixed barium sulfate and precipitate out of solution: The molarity of the remaining Na' ions is molar:The molarity of the remain...
##### Digestive juice with a pHiof 2 probably came from themouth:pancreas_esophagus:stomach:
digestive juice with a pHiof 2 probably came from the mouth: pancreas_ esophagus: stomach:...
##### 3. Utilizing Ihe following hypothetical cladogram of Ungulates _ answer the following questions.Land Ungulato Arctic Unicom Marsh Unicorn Flying Horso Terrostnal Horsocoloration-hitocoloration-groygrazingwingsfrontal hornpurple eyeshoofed quadriped with turquoise eyesTo distinguish particular clade of Ungulates within the larger clade that corresponds to Superorder Ungulata would hoofs be a useful character? Why or why not? (4 pts)
3. Utilizing Ihe following hypothetical cladogram of Ungulates _ answer the following questions. Land Ungulato Arctic Unicom Marsh Unicorn Flying Horso Terrostnal Horso coloration-hito coloration-groy grazing wings frontal horn purple eyes hoofed quadriped with turquoise eyes To distinguish particul...
##### With what initial velocity must we fire a rocket so it attains a maximum height of $r=20 \mathrm{km}$ above the surface of the earth?
With what initial velocity must we fire a rocket so it attains a maximum height of $r=20 \mathrm{km}$ above the surface of the earth?...
##### Using the power scrics mcthod, solve the second-order ordinary di fferential cquation with variable coefficients y _xy =0, YlO)-k; Y(O)-k; (Compute only thc first coeflicients, ic.a0 through a .)
Using the power scrics mcthod, solve the second-order ordinary di fferential cquation with variable coefficients y _xy =0, YlO)-k; Y(O)-k; (Compute only thc first coeflicients, ic.a0 through a .)...
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# Nines of nines
In the operations business we like to talk about nines of things, especially regarding service levels. If
• “one nine of availability” = available 0.9 of the time,
• “two nines of availability” = available 0.99 of the time,
• and so on…
then generally,
• “$$n$$ nines of availability” = available $$(1 - 10^{-n})$$ of the time,
right?
This works for any whole number n: e.g. 5 nines is \begin{align}1 - 10^{-5} &= 1 - 0.00001 \\ &= 0.99999.\end{align}
There’s a problem with this simple generalisation, and that is, when people say “three and a half nines” the number they actually mean doesn’t fit the pattern. “Three and a half nines” means 0.9995, but
• $$1 - 10^{-3.5} \approx 0.9996838$$, and going the other way,
• $$0.9995 \approx 1 - 10^{-3.30103}$$.
We could resolve this difficulty by saying “3.3ish nines” when we mean 0.9995, or by meaning ~0.9996838 when we say “three and a half nines.” But there’s at least one function that fits the half-nines points as well!
Let’s start with the function above: $$f(n) = 1 - 10^{-n}.$$ For every odd integer, it just has to be lower by a small, correspondingly decreasing amount. We can do this by increasing the exponent of 10 by \begin{align}k &= 0.5 + \log_{10}(0.5) \\ &\approx 0.19897.\end{align}
One function for introducing a perturbation for halfodd integers is $$p(n) = \sin^2(\pi n).$$ When n is a whole integer, $$p(n) = 0$$, and when $$n$$ is half an odd integer, $$p(n) = 1$$. Multiply this function by some constant and you’re in business.
Thus, define a new function $$g(n)$$ for all $$n$$:
$$g(n) := 1 - 10^{-n + k p(n)}$$
i.e.
$$g(n) = 1 - 10^{-n + (0.5 + \log_{10}(0.5))\sin^2(\pi n)}$$
which, when plotted, looks like this:
a negative exponential curve with a negative exponential wiggle. And it has the desired property that at every integer and half-integer it has a value with the traditional number of nines and trailing five (or not).
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# Zener diode makes for a lousy regulator
### Reference and regulation are not the same thing
The Zener diode is often used to create a reference voltage. In tutorials and even college texts, there are mentions of creating a Zener diode based regulator. The idea is that the Zener maintains a known voltage drop. The problem is that current matters. This post looks a quick Zener diode overview and shows what happened when I tried to power a microcontroller using a “Zener diode regulator.”
## Zener diodes overview
Just a brief overview if you are not familiar with Zener diodes. Like typical diodes, Zeners have low forward voltages. Typically you voltages are around 0.7. However, different material sets can offer different forward voltages.
Also like generic diodes, there is a reverse breakdown voltage. If you look at a hefty diode like the 1n4001, you find breakdown voltages starting at 50 volts.
1n4001 Reverse Breakdown Voltage
Zener diodes are unique because their reverse breakdown voltages are relatively low. For example, I have some that are 3.3, 5.0, 9.1, and 12 volts. (Interesting numbers, aren’t they?)
The curve is showing that above the forward voltage and “below” the reverse voltage, the diode conducts. I put below in quotes because it suggests a negative potential. This comment does not mean you need a negative voltage supply, just that the diode is reverse biased. Also known as turned around.
## Zener diode regulator
As mentioned, the idea behind a Zener regulator is that the diode drops a stable voltage when reverse biased. Moreover, with values like the 3.3 and 5.0 I mentioned before, it starts to sound like a good option, doesn’t it?
BZX79C3V3 From Fairchild (On Semi)
Let’s use the BZX79C3V3 as an example Zener diode. Notice in the characteristics table, that the reverse voltage is 3.3 volts at 5.0 milliamps.
The idea is that you pick a resistor value, perhaps even a precision value, to create enough current to reverse bias the Zener diode at 5.0 milliamps.
However, there’s a problem with this basic circuit. The current that flows through the load must also flow through the resistor. Based on Ohm’s law, the resistor’s voltage drop changes based on its current flow.
## Powering ESP8266 with Zener Regulator
Using the above circuit, I tried to power an ESP8266 with a 5.0 volt supply. Before building this circuit, I measured the ESP8266’s current draw to be 60 milliamps when powered by a 3.3 volt supply.
Using a 3.3 volt Zener, the series resistor drops 1.7 volts. With 60 milliamps at the load and 5 milliamps for the Zener, Ohm’s Law tells us we need a 28Ω resistor. The closest value I have is 22 ohms.
$\Huge R = \frac{E}{I} = \frac{1.7V}{60\mathrm{e}{-3}mA} = 28\Omega$
When I hooked the circuit up, nothing happened on the ESP8266. The VOUT node measured around 0.9 volts. What’s worse is that no matter what I made the source voltage, the VOUT node stayed at 0.9 volts.
On a hunch, I dropped resistor value by about 10 ohms.
When I measured with the multimeter, I saw only 1.8 volts at the divider. However, the ESP8266 was operating. After resetting the ESP8266, I saw 2.5 volts. And depending on how much weight was on my left or right foot, any value in between.
So what the heck is happening here? Well, first, thank you for continuing to read before jumping to the comments to say the following statement. You cannot treat a microcontroller, especially a system-on-chip (SOC), as a constant load.
When I press and hold the RESET button, the Vout node jumps to a nice clean 3.4 volts. At that point, most of the active circuits in the chip are turned off.
Since the ESP8266 was a high impedance load, nearly all of the current in this circuit is flowing throw the series resistor and the ESP8266. The amount of current was staggering, almost 200 mA. Well staggering when you might have only expected about sixty.
## More Zener Regulator Problems
This entire exercise was to show why the Zener diode is a lousy regulator. The voltage drop depends too much on the current flowing through the junction. Which means the “regulator circuit,” depends on a constant load. Any active device is going to cause the VOUT node to be unstable.
So what good is this Zener regulator circuit? Well, it is not a regulator. Instead, it is a reference.
For example, you could use a similar circuit on Arduino’s AREF. Let’s say you are using an analog sensor that only outputs 3 volts maximum. Using a Zener reference could give the A/D more resolution.
You could use the Zener circuit as a reference into an op-amp. This circuit is not too different from how linear regulators work.
The lesson here is that if you want to use a Zener diode regulator circuit, you need to reconsider your design. In some very rare or corner cases, it will work fine.
If you have used a Zener as a regulator, and not as a reference, leave a comment below. I would love to hear how you used it.
Long comments, URLs, and code tend to get flagged for spam moderation. No need to resubmit.
ALL comments submitted with fake or throw-away services are deleted, regardless of content.
Don't be a dweeb.
## 28 thoughts on “Zener diode makes for a lousy regulator”
1. Brian Synnott says:
I successfully used a 4.7V zener in series with an R220 resistor to cut a 9-12V p-p square wave down to near-TTL level, by placing the regulator on the square wave output. Since most or all clock inputs on TTL or CMOS chips are high impedance, this worked fine.
2. Peet says:
Hi, can put zener on the base of a high gain transistor. Less current variation and also circuit can supply more current, through transistor
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### Lewin's blog
By Lewin, 3 years ago,
Here's the editorial. Hope you have a happy new year!
Code can be found here: https://www.dropbox.com/sh/i9cxj44tvv5pqvn/AACQs7LLNyTZT-Gt_AMf7UQFa?dl=0
New Year and Counting Cards
New Year and Buggy Bot
New Year and Curling
New Year and Arbitrary Arrangement
New Year and Entity Enumeration
New Year and Original Order
New Year and Boolean Bridges
Tutorial of Good Bye 2017
• +336
» 3 years ago, # | +60 kudos to a lightening fast editorial!
» 3 years ago, # | +11 Is there any way to interpret E as a vector space or group or something like that?
• » » 3 years ago, # ^ | ← Rev. 3 → +8 If I'm not mistaken, E should be related to counting the number of topologies on {1, 2, ..., m} in which the given family of n sets is open.(Not topologies but sigma algebras — lapsus calami)
• » » » 3 years ago, # ^ | +24 It is not a requirement in topological spaces that the complement of an open set is also open (In fact, in spaces like R^n, the complement of an open set is a closed set, and only R^n and the empty set are both open and closed sets). So in this problem, what is asked is exactly to count the number of topological spaces on , such that the complement of any open set is also an open set.Such spaces happen to also be linear subspaces of , since it is easy to write xor using only and, or and not. This observation might or might not help in arriving at the key observation on partitions (it is equivalent to observing than, when performing a careful Gaussian elimination, one can achieve a triangular matrix that has exactly one "1" per column).
• » » » » 3 years ago, # ^ | +8 Continuing with this completely unnecessary abstract translation, the key observation regarding partitions is equivalent to the fact that the Kolmogorov quotient of our space has the discrete topology (Kolmogorov quotient "glues" indistinguishable elements into one new single element).
• » » » 3 years ago, # ^ | +16 I think the term you are looking for is "Sigma Algebra".
• » » » » 3 years ago, # ^ | +3 Indeed! Nice catch. So the key observation can also be stated as "finite sigma algebras are essentially equivalent to partitions". Googling that right now shows a related question here: https://math.stackexchange.com/questions/143796/number-of-sigma-algebra-on-the-finite-set
• » » » » » 3 years ago, # ^ | ← Rev. 2 → +8 Which is how I solved it :DWell, I would have probably figured it out on my own if I had thought about it for a minute or two, but it was too tempting to just google "Number of sigma algebras on a finite set".
• » » » » 3 years ago, # ^ | +21 In fact (to be even more pedantic :D) you don't need the "sigma" part, which refers to countable unions. Since everything is finite it is just an algebra of sets.
• » » » » » 3 years ago, # ^ | ← Rev. 2 → +5 For anyone delighted with the present display of pedantry, a friend of mine just made me notice that finite topologies are equivalent to preorders (a point x is less than another y, if any open set containing y also contains x), which are also essentially just "transitive" directed graphs.So in the finite case:Sigma algebra --> partitionsTopology --> preorder
» 3 years ago, # | +53 maths too hard~~
» 3 years ago, # | +2 Codeforces is becoming awesome day by day :D
» 3 years ago, # | +2 Editorial even before system testing finished, amazing punctuality grandmaster.
» 3 years ago, # | +64 My solution to H is probably equivalent to yours, but it's explained in much simpler terms than Walsh-Hadamard transform :)See "4.2 Inclusion-exclusion" in http://www.wisdom.weizmann.ac.il/~dinuri/courses/11-BoundaryPNP/L01.pdf
• » » 3 years ago, # ^ | +14 Nice solution. I noticed my solution looked like inclusion/exclusion but didn't know how to explain it. I found it easier to explain through walsh hadamard transform since that's how I originally thought of the problem/solution. Glad to know there is a simpler explanation :)
• » » » 3 years ago, # ^ | +44 I actually admire that your knowledge enables you to use Walsh-Hadamard transform in a solution so easily :) I had to Google the paper to make progress.Thanks a lot for the contest!
• » » 3 years ago, # ^ | 0 The O(nk·2.45n) algorithm (dynamic programming, only iterating over maximal independent subsets) also passes in less than 1 second.Unfortunately, too many bugs :(
• » » » 3 years ago, # ^ | +19 We can also all borrow a trick from dotorya: while (clock() - st <= CLOCKS_PER_SEC * 4.5) { random_shuffle(u, u + X); int mx = 0; for (i = 0; i < X; i++) col[i] = 0; for (i = 0; i < X; i++) { int t = u[i]; for (j = 1; j <= X; j++) tchk[j] = false; for (j = 0; j < X; j++) if (conn2[t][j]) tchk[col[j]] = true; for (j = 1;; j++) if (!tchk[j]) break; col[t] = j; mx = max(mx, j); } mn = min(mn, mx); }
• » » » » 3 years ago, # ^ | +3 That should probably fail on a chain of length 23, though?... Or does it have so many attempts that it passes that one as well?
• » » » » » 3 years ago, # ^ | ← Rev. 4 → +18 For a chain of length 23, I think the expected round is at most .I have no time left and implemented a similar solution.And I passed all the system testcases with only 100 iterations and 15ms :)
• » » » » » » 3 years ago, # ^ | 0 At least for a bipartite graph, this solution should work in O(2n).Take one valid coloring, and suppose that there are B black vertices and W white vertices. If dotorya chooses a permutation such that all black vertices come before all white vertices (and vice versa), it works correctly. This happens with probability .Is this O(2n) for general graphs or not?
• » » » » » » » 3 years ago, # ^ | ← Rev. 6 → 0 What about complement of complete tripartite graph (so? Growth rate of is around O(33n).UPD: I misunderstood algorithm, sorry for many updates.However, it seems like it might be more difficult to bound this runtime.
• » » » » » » » » 3 years ago, # ^ | 0 Doesn't it always handle complete tripartite graphs correctly?
• » » » » » » » 3 years ago, # ^ | 0 What do you think about the graph on n vertices where vertex i is connected to vertices in interval [i - k, i + k] with chromatic number k + 1?
• » » » » » 3 years ago, # ^ | +31 Actually I didn't compute probability at all. I just wrote general time-cutting method and prayed this would pass. Sorry :( After the conteat, I thought that the worst case is a chain with 23 vertices, which makes 10^-6 probability, which can pass this within time limit. But I was not sure whether this is the worst case...
• » » » » » » 3 years ago, # ^ | +31 There's nothing to be sorry about, I meant it when I said we should borrow a trick from you — you got the problem accepted quicker, and that is good!
• » » 3 years ago, # ^ | 0 I imagine that the number of k-colourings can get quite big though (n! for a complete graph, and I'm not sure if that's the worst case). I see you used a randomly selected prime modulus to get a solution that is right with high probability (and which is hack-resistant), but would a solution that's guaranteed correct (presumably using bignums) run fast enough?
• » » » 3 years ago, # ^ | 0 Well, the probability of error is at most 23*1e-9, so I would say that there's not much difference — i.e., in my mind it's like quicksort working in O(nlogn).But I don't know a deterministic fast enough version of my solution.
• » » » » 3 years ago, # ^ | 0 I managed to add an extra O(logk) factor, and I had to use modulo 232 hash to fit into TL. Luckily it passes.
» 3 years ago, # | 0 Really nice problems! I kept thinking about how to handle the infinitely large case in D, but couldn't figure it out at last :( And also, F is a really cool problem I think :D
» 3 years ago, # | 0 WOW! Thank you so much for super fast Editorial and also for the awesome problems !
» 3 years ago, # | 0 Whoohh such a fast editorial!!!!!!!!
» 3 years ago, # | +11 F was a Div2C question. I wonder why the authors kept it at F :(
» 3 years ago, # | ← Rev. 2 → -90 What's wrong with my code for problem B? #include #include #include using namespace std; int main() { string s="lrud"; int n,m; cin>>n>>m; char a[n][m]; int x,y,p,q; for(int i=0;i>c; sort(s.begin(),s.end()); for(int i=0;i0 && a[x-1][y]!='#') { x--; k=1; } if(ch=='r' && x0 && a[x][y-1]!='#') { y--; k=1; } if(ch=='d' && y
• » » 3 years ago, # ^ | +3 Use the spoiler tag to share code or put your submission link, please.
• » » » 3 years ago, # ^ | -18
• » » 3 years ago, # ^ | +5 next_permutation STL function only permutes according to the lexicographically greater comparator...hence in our case, it does consider all the 24 cases needed.
• » » » 3 years ago, # ^ | -21
» 3 years ago, # | 0 can anyone please help in understanding the dp transition in D.
» 3 years ago, # | +21 goodbye rating
• » » 3 years ago, # ^ | ← Rev. 2 → 0 dude you solved 4 question on one go. you shouldn't be saying this :P
• » » » 3 years ago, # ^ | 0 but the problem D had cost most of my time during the contest. :( Anyway the problems are good, yet I'm foolish.
» 3 years ago, # | 0 Problems blew my mind, great contest-great problems.
» 3 years ago, # | 0 For C, do we need to compute dy for all discs that can possibly touch (i.e. all discs in the ≤ 2r range), or can we just compute it for the disc with the highest y coordinate of these?
• » » 3 years ago, # ^ | +1 You want to find the highest y+dy overall, not the highest y (and then + the dy of that).
• » » » 3 years ago, # ^ | ← Rev. 2 → 0 My question is:Suppose a disc X is within the +/- 2r range. That means, if the disc currently being processed keeps dropping, it will eventually touch this disc X, unless it first touches some disc Z.The question is whether we can conclude such disc Z must have a higher Y coordinate than disc X.I.E. for N discs in the range, the dropping disc must touch the one with the highest Y coordinate.
• » » » » 3 years ago, # ^ | ← Rev. 3 → +1 No, that's not true in general. You can try this case for example: 5 1 2 1 4 4 2 For the last disk, the highest y-coordinate disk wihtin range is the fourth one, but it will touch the second disk first.
• » » » » 3 years ago, # ^ | +6 No, that's false. if the highest-y disc is far away, and an almost-as-high-y disc is very close, it can touch the almost-as-high disc before the highest disc.For concreteness, consider R=2, discs at (0, 2), (2, 1), and a new disc dropping at x=2. Then it will touch the (2,1) disc first.
• » » » 3 years ago, # ^ | 0 That is where I fell :( I found the highest y colliding with a circle and then found the dy of that. :/Great question btw!
» 3 years ago, # | +6 Light-speed Tutorial,Light-speed System Test! I like it!
» 3 years ago, # | +6 Editorial before Final testing. So fast. (y)
» 3 years ago, # | +1 Editorials before system testing. That's a perfect goodbye to 2017 (*-*)
» 3 years ago, # | +4 Great problems and a fast, nice, and concise editorial. Great Job!
» 3 years ago, # | 0 There is a slight formatting error with the bell number link. (Extra right bracket at the end)
» 3 years ago, # | 0 Thanks for good contest!
» 3 years ago, # | 0 In Problem D Can somebody please explain why infinite length sequence is not necessary for "exact answer" ?
• » » 3 years ago, # ^ | +3 Didn't solve it, but I'm guessing it's because you can find the expected value of the amount of trials until first success with a closed form formula: https://www.cut-the-knot.org/Probability/LengthToFirstSuccess.shtmlJust 1/p.
• » » 3 years ago, # ^ | ← Rev. 2 → +18 At some point adding only one 'b' will satisfy the condition k. The probability of adding n 'a's then one 'b' at this point is: (1 - p)n × p where p is the probability of putting a 'b' (e.g: ).Hence the expected value of the sequence's length is: which is finite.
• » » » 3 years ago, # ^ | ← Rev. 4 → +3 I know i am wrong,but i don't know whywhy cant i say thatE = (1 — p)(E + 1) + pbecause it has probability p of ending here,taking one step,or it has 1 — p of continuing,which takes one extra stepthenE = E(1 — p) + 1 — p + pE * p = 1E = 1 / p LE:this would give me the average number of steps untill i stop,but i should subtract 1 from it because i am interested in the average numbers of ab,not the avreage length. So 1/p — 1 = (1-p) / p
• » » » » 3 years ago, # ^ | 0 This is correct!!
• » » » » » 3 years ago, # ^ | -7 yeah but i didn't realise for a long time that i need to subtract 1 :))).But yeah,now it's corect :))
• » » » » 3 years ago, # ^ | 0 can you please help me in understanding the solution. I didn't understand : "because it has probability p of ending here,taking one step,or it has 1 — p of continuing,which takes one extra step" please elaborate it a little and if possible please explain it with an example.
• » » » » » 3 years ago, # ^ | +3 So lets say 2 events could happen:-a succes with probability of p-a failure with probabilty of 1 — p we are at the first step,and we ant to see the expected number of steps untill the first succeswell if you have a succes(with probability p),then you only take one step. so E = p * 1 + the other caseif you have a failure(with probability 1 — p),then imagine that the next step is exactly like step 1,so the expected from that point would be the same. But,because you already had a failure,you must add one to it.so E = p * 1 + (1 — p) * (E + 1)if you do a bit of math this meansE = 1 / pNow,back to our original problem,this is the expected length of a string untill we put a b.this would give us length — 1 more ab's.So the real expected value is E — 1 = (1 / p) — 1 = (1 — p) / p
• » » » » » » 3 years ago, # ^ | 0 here p is probability to get 'ab' ?
• » » » » » » » 3 years ago, # ^ | ← Rev. 2 → 0 no,p is probability to put bso pb/(pa + pb)
• » » » 3 years ago, # ^ | 0 I wonder how to prove this formula..
• » » » » 3 years ago, # ^ | +3
• » » » » » 3 years ago, # ^ | 0 Thanks
• » » » 3 years ago, # ^ | 0 Why we need to use DP if the answer to the problem is (1-p)/p? I can not understand it at all.
• » » » » 3 years ago, # ^ | 0 The condition for applying the formula is when adding only one ‘b’ is enough to satisfy the condition ‘k’. This means that we have constructed a prefix of ‘a’s and ‘b’s, and that appending one ‘b’ to our prefix is enough to satisfy our condition.To construct that prefix we use DP. The formula is applied when we hit a base case.
» 3 years ago, # | ← Rev. 2 → +5 For problem D, I managed to get the formula but then I did not know how to make sure P and Q to be coprime. It turned out that I did not have to do anything and it would still pass. Can someone explain to me please why. (I used the same formula in the editorial)
• » » 3 years ago, # ^ | +11 Say you have integers p = p'g and q = q'g where g = gcd(p, q).Then pq - 1 = p'g(q'g) - 1 = p'gg - 1q' - 1 = p'q' - 1.
• » » » 3 years ago, # ^ | 0 Makes sense, thanks.
» 3 years ago, # | 0 What is wrong with my approach to problem C ? Approach — for any circle- check all the points in the range c-r to c+r (c is center). find which previous circle(if any) in that range has the largest height. so it will touch that circle. then find the height as per the formula in the editorial. and update the range with the new circle.My solution link http://codeforces.com/contest/908/submission/33786083
• » » 3 years ago, # ^ | 0 I haven't seen ur code but you have to check from c-r-r to c+r+r
• » » » 3 years ago, # ^ | 0 why is it? range of the outermost points of the circle colliding should be [c-r,c+r] right?
• » » » » 3 years ago, # ^ | 0 The center of the circle it collides with is another r distance away
• » » » » » 3 years ago, # ^ | 0 I mark the range of each circle, so it will encounter the circle whose center is r distance away from its circumference. The reason I got wa was the thing that bmerry explained below.
• » » 3 years ago, # ^ | +16 I think you made a mistake that I hacked a few other solutions on too: you've assumed that the disk you hit first will be the one that stopped with greatest y, but that's not necessarily true if there is one with a slightly lower y but much closer x.
• » » » 3 years ago, # ^ | 0 yes, that might be the case. I should have taken the max over all. :( Thanks.
» 3 years ago, # | 0 Will there be an editorial in Russian?
• » » 3 years ago, # ^ | +2 You can use Chrome and then translate automaticaly all the page
» 3 years ago, # | 0 It should be noted for problem F that, if there are no green points, you do not have to connect the red points and the blue points. In every other case, the optimal solution must involve connecting all points to each other, but, in this case, none of the red points have to be connected to the blue points. The problem may be a little misleading in this regard, as it says that Roy and Biv want all the points to be connected; however, later on, it does specify that they only want all the points they can see to be connected.
» 3 years ago, # | ← Rev. 2 → +10 In H, I've picked random number and calculated result modulo this number, hopeing, that when number of colorings will be greater than zero, then it will also after moduling be greater than zero. Can you prove, that we don't have to use any modulo (so use 2^64), and it'll still be ok?
» 3 years ago, # | +10 Thanks for the contest :) was really fun ^^ and thank you for the fast editorial! srsly.
• » » 3 years ago, # ^ | 0 And wow kudos for the solution in multiple language!!
» 3 years ago, # | 0 what is wrong in my solution for problem C the link is here.
• » » 3 years ago, # ^ | 0 Figured out :D Thanx for the comment bmerry
» 3 years ago, # | 0 Editorial has appear faster than ratings. Hm....
» 3 years ago, # | +14 I can't get D solution. Could somebody explain the solution with more detail?
• » » 3 years ago, # ^ | 0 Finally I've got it! solution coded directly from formula 33810491
» 3 years ago, # | 0 What is wrong with this solution for Problem C http://codeforces.com/contest/908/submission/33779874 . It is giving WA for Test Case 7.
• » » 3 years ago, # ^ | 0 Got it.
» 3 years ago, # | ← Rev. 4 → +4 Why is the formula for D not dp[i][j] = (pa * dp[i minus 1][j] + pb * dp[i][i minus j]) / (pa + pb) ?As in to reach current state with i a's we can only arrive here from having i-1 a'sand to reach current state having j ab subsequences we can add b to prefix with i-j a's and get a prefix with j ab's Thanks :)EDIT(for those who clicked pluses): Okay, so it seems we are working backwards, because our base cases are when j >= k, it means that at (i,j) we are ending our algorithm, so expected value of 'ab' subsequences is j. Because of that our answer should be dp[0][0]we also have the i + j >= k condition, to ensure that a's in our prefix doesn't exceed b's so that out count of a's are bounded by k.Therefore our answer is dp[1][0], because there has to be atleast one 'a' to form some amount of 'ab' subsequences
• » » 3 years ago, # ^ | 0 Thank you your comment helped to understand the way the editorial thinks.The key is that you start the algorithm from a fixed state and it only matters the amount of a's and ab's sub-sequences to compute the expected ab's when the algorithm finishes
» 3 years ago, # | +20 dotorya solved G at 00:49:58 before bmerry
• » » 3 years ago, # ^ | +20 Oops, thanks for catching this.
» 3 years ago, # | ← Rev. 2 → 0 Didn't understand some moments in explanation of problem F. Firstly, outer points = the leftmost and the rightmost points on the line ? Assuming that let's consider the first case: the outer green points are not directly connected, in which case, we must connect all the red/blue points in the line. Okay, look at the test: 1 G 3 B 5 G 7 B 9 G Firstly, doing the second observation I should connect 3 — 5 and 5 — 7. Okay, what's next? I guess I should connect 7 — 9 and 1 — 3 ? Just can't see something like that in editorial. Secondly, let's consider the second case: the outer green points are directly connected, in which case, we can omit the heaviest red and blue segment. Word "directly" seems very strange to me there. I really can't imagine that case not counting variant when we have only two adjacent green points. For example: 1 G 3 G 5 G Are x = 1 and x = 5 points directly connected if they linked through the point with x = 3 ? Need more detailed explanation, please.
• » » 3 years ago, # ^ | +3 I think you may be misinterpreting what the observations give you. The main point is that there can be no edge that "skips" a green point, thus, we can split the problem into sections which are each independent so that we only need to solve the case where the only green points could be first and last points.For the second case, I should have clarified that a "red" edge is an edge that connects (red/green) to (red/green), and a "blue" edge is an edge that connects (blue/green) to (blue/green).
» 3 years ago, # | +1 In D why "The second is that any 'b's that we get before any occurrences of 'a' can essentially be ignored. To fix this, we can adjust our answer to be dp[1][0]."Why just ignore it? Why doesn't it change the answer?
• » » 3 years ago, # ^ | +3 Those b's can't be part of any subsequence that forms 'ab', since there's no 'a' before them, and we're only interested in expected amount of times 'ab' occurs.
• » » » 3 years ago, # ^ | 0 So what happens with sequences like "bab.." or "bbbaab.."? Don't we count them in the answer?
• » » » » 3 years ago, # ^ | ← Rev. 3 → +3 The reasoning is this way. With no loss of generality every case we run the algorithm start with a finite amount of b's and then an a. In all the cases so we finish with 1 a and 0 ab's, thus, by definition the answer is dp[1][0].
» 3 years ago, # | 0 In problem D, I didn't understand the meaning of this statement.You stop once there are at least k subsequences that form 'ab'.We can have infinite bs then an ab, can this be the case?Please help me understand the problem.
» 3 years ago, # | +6 The second is that any 'b's that we get before any occurrences of 'a' can essentially be ignored.Shouldn't we multiply by 1 + p + p2 + .. where p = pb / (pa + pb) instead of ignoring?
• » » 3 years ago, # ^ | ← Rev. 2 → +3 dp[i][j] = (pa * dp[i + 1][j] + pb * dp[i][i + j]) / (pa + pb)When i = j = 0, dp[0][0] = (pa * dp[1][0] + pb * dp[0][ 0]) / (pa + pb)bring pb/(pa+pb) to the left and it becomes (1-pb)/(pa+pb) = pa/(pa+pb) which cancels on both sides, so we getdp[0][0] = dp[1][0]
• » » » 3 years ago, # ^ | +6 Ah, or continuing from what I said, the answer is (1 + p + p2 + ...) * pa / (pa + pb) * dp[1][0] = dp[1][0]. In either your derivation or what I wrote above, the initial 'b's cannot be "ignored", they simply cancel out with the leading a. Is there any intuitive explanation of this fact, or is lewin's editorial misleading in using the word "ignored"?
• » » » » 3 years ago, # ^ | ← Rev. 2 → +8 The number of 'ab' subsequences in a string s is the same as if there was an extra 'b' in the beginning of s (or two b's, three, etc).Maybe it gets intuitive if you think that the distribution is constant for every "pattern" (I mean, s, s and an extra 'b', two extra b's, etc), and the expected value of a constant distribution is the value of the constant. It's like you could just get the value for s rather than the "average" of all these cases, since all their values are equal.
• » » » 3 years ago, # ^ | +13 Logically, (pa+pb)/pa * dp[0][0] is the answer. Which is also equivalent to dp[1][0] by calculation. But how are they equivalent intuitively?
» 3 years ago, # | +5 When will the ratings be updated ?
» 3 years ago, # | ← Rev. 3 → 0 In solution code of D- why have you kept if (ab >= k) ? if we already have this check - if (a + ab >= k) ? First one will never be encountered.
• » » 3 years ago, # ^ | 0 Keep this if (ab >= k) condition above second one so that it is checked earlier
• » » » 3 years ago, # ^ | 0 But its useless. if you have ab>=k then a+ab>=k is already satisfied. so it never executes.
• » » » » 3 years ago, # ^ | 0 Yes we can avoid that
» 3 years ago, # | ← Rev. 2 → +19 Problem G can be solved in O(102n).
• » » 3 years ago, # ^ | 0 Well what do one and cnt mean in your code? Would you please explain it a little bit? Thanks a lot.
• » » » 3 years ago, # ^ | +18 For fixed d, we would like to add o(x) = 111...1 (x's ones) to the answer if the number contains x digits not less than d.To maintain when we find a new digits not less than d, .
• » » » » 3 years ago, # ^ | 0 Got it. Thanks. But what does means? Is it a typo?
» 3 years ago, # | ← Rev. 4 → 0 My approach to F(New Year and Rainbow Roads) is to connect all green points where the cost = (last green - first green). And then considering all green points a single one, connect it with the red ones using mst and do the same with blue ones. If there is no green point then ans should be (last red - first red + last blue - first blue). Can someone tell me where I am wrong...please
• » » 3 years ago, # ^ | +3 The issue is that green points don't need to be directly connected: it is also valid to connect two green points using two different paths, one going over all the red points in between and one going over all blue points in between. It is easy to verify that this satisfies the constraints of the problem.The following should be a breaking case that tests this case: 7 1 G 2 R 3 B 4 R 5 B 6 R 7 G The correct answer for this case is 12, but it seems like your solution would output 14.
• » » » 3 years ago, # ^ | 0 Understood..Thanks a lot!!
» 3 years ago, # | ← Rev. 4 → 0 Can someone help where I am going wrong in finding closed-form condition for Problem DImageUPD : The derivation is actually correct we can put (1-a)=b then cancel out b and the ans will finally be x+b/a = done+f+(b/a)
• » » 3 years ago, # ^ | ← Rev. 2 → 0 https://imagebin.ca/v/3mS1m1CZVCff You mean this?
• » » » 3 years ago, # ^ | ← Rev. 2 → 0 Yes, it is similar but i is varying from 0 to inf but I wonder what about that constant factor x(=done + f) Why it is not added later?
• » » » » 3 years ago, # ^ | ← Rev. 7 → 0 I think you are having trouble with the base case.The formula you wrote there in the image is wrong. You are not considering all the cases. (a+ab >= k) is just the marker. here we know one b has to come to satisfy the min k ab's constraint.In base case we have to consider three things - expectation(of already present ab) it will simply 1*ab = ab expectation(ab's formed with already present a's and coming one b) it will be equal to 1*a = a expectation(of ab's formed with, one coming b and number of a's it brings with it). For the calculation of 3. we consider say it brings 0 a or 1 a with it or 2 a or n a, upto inf a's. we consider all these cases by the summation formula in my image. As 1 and 2 will always be the same irrespective of the number of a's the coming one b brings with it.summation formula = Here if the coming number of extra ab's formed will be equal to number of a's it brings with it.So, P(ab) = Pa*Pb and E(ab) = P(ab)*1 ,as 1 ab is formedP(aab) = Pa2*Pb and E(ab) = P(aab)*2 ,as 2 ab's are formed.similary you can compute upto inf and get the summation formula to generalize. Here, Pa = a/(a+b) , Pb = b/(a+b) , Pa = 1 — Pb
• » » » » » 3 years ago, # ^ | 0 Thanks :) Got it!
» 3 years ago, # | +5 Can someone please provide a good explanation of problem E?
» 3 years ago, # | 0 In problem D, in second base case, i + j ≥ k, can some one explain the closed form of expectation?
• » » 3 years ago, # ^ | 0 Check http://codeforces.com/blog/entry/56713?#comment-404349 and the image I posted in that thread above.
• » » » 3 years ago, # ^ | ← Rev. 2 → 0 Nevermind, got it!
• » » » » 3 years ago, # ^ | 0 Look at my comment and think carefully. Its in the same form.
• » » 3 years ago, # ^ | ← Rev. 2 → +4 I will try to explain it:i => number of a's in the prefix,j => number of ab's in the prefix.and i+j >= K,so we can do like this:1) put 1 b in the end => number of ab is now (i+j) which is >= K so we stop and probability is (Pb/(Pa+Pb)) so we add (i+j)*(Pb/(Pa+Pb)) .2) put 1 a and then 1 b in the end => number of ab is now (i+j+1) which is >= K , so we stop and probability is (Pa/(Pa+Pb))*(Pb/(Pa+Pb)) so we add (i+j+1)*(Pa/(Pa+Pb))*(Pb/(Pa+Pb)).3)put 2 a and then 1 b in the end => number of ab is now (i+j+2) which is >= K , so we stop and probability is ((Pa/(Pa+Pb))^2)*(Pb/(Pa+Pb)) so we add (i+j+2)*((Pa/(Pa+Pb))^2)*(Pb/(Pa+Pb)).and so on..Now if we add these it becomes =>(i+j)*(Pb/(Pa+Pb)) + (i+j+1)*(Pa/(Pa+Pb))*Pb/(Pa+Pb)) + (i+j+2)*((Pa/(Pa+Pb))^2)*(Pb/(Pa+Pb)) + ...Let's leave as an exercise for you to solve this. Spoiler: answer is => i+j+Pa/Pb Hope this helps :)
• » » » 3 years ago, # ^ | 0 Thanks, I got it from the picture and comment described in http://codeforces.com/blog/entry/56713?#comment-404349
• » » » 3 years ago, # ^ | 0 Hi faceless_man =))) Can you explain me more about the line : "1) put 1 b in the end => number of ab is now (i+j) which is >= K so we stop and probability is (Pb/(Pa+Pb)) so we add (i+j)*(Pb/(Pa+Pb)) " Why when put 1b in the end => we add (i+j) * (Pb / (Pa+Pb)) instead of adding Pb / (Pa + Pb) . I can't find the reason for why (i+j) * ... ?? =))) Sory for my bad English =))
• » » » 3 years ago, # ^ | 0 i have a question for i+j>=k if i=k and j=0 is this like aaaaaa(k times) and 0 'ab' if we put 1 'b' at the end it become aaaaa(k times)b why we can stop this if we only get one 'ab' but not at least k 'ab'?
» 3 years ago, # | 0 Can anyone explain paragraph 5th of D'solution? I couldn't get it's idea
• » » 3 years ago, # ^ | 0
• » » » 3 years ago, # ^ | 0 This is how i understand: we consider all satisfied subsequence, for each of them, calculate p = probality and x = number of 'ab' sequence, then our excepted number equal sum of product of all pair (p, x). So why can we ignore subsequences which is large or have 'b' continuously at the beginning?
• » » » » 3 years ago, # ^ | 0 we are not ignoring the large subsequences. we are including that in the summation formula. also if you have b's in the beginning then number of ab's formed is zero since no a's are prior to those b's. so expectation = (probab of those b)*0 = 0, so we ignore that case.
• » » » » » 3 years ago, # ^ | ← Rev. 2 → 0 I was wrong when asking ignore subsequences which have 'b' continuously at the beginning. i mean why can we ignore all continuously 'b' at the beginning of every sequence, as the editorial said that we can ignore them, or did i misunderstood the editorial?For example, probality of adding 'a' is 0.3, adding 'b' is 0.7, then for subsequence 'bab', p = 0.147 and x = 1. But if we ignore first 'b', we get p = 0,21, which change the anwser.
• » » » » » » 3 years ago, # ^ | +7 Oh you are confused over the word "ignored"our answer has to be Pbn * Pa * dp[1][0] for lets say n b's occurred before the first a.so generalizing this case for we can get 0 to inf number of b's before first a.we get ans = (Pb0 + Pb1 + Pb2 + ..) * Pa * dp[1][0]= = dp[1][0]
• » » » » » » » 3 years ago, # ^ | ← Rev. 2 → 0 I don't know why they didn't explain in the editorial like what you did. Ignore few explanations could make the editorial harder, when they can add them easily.
• » » » » » » » » 3 years ago, # ^ | 0 Maybe because It was div1+div2 combined that's why.
• » » » » » » » » » 3 years ago, # ^ | 0 Yeah, but at least D is still for div 2
• » » » » » » » 3 years ago, # ^ | 0 Also, intuitively you can think that if you start the algorithm from beginning in all cases you will expect to have n b's and one a in some moment, thus the expected answer in all cases is dp[1][0], thus ans=dp[1][0] no matter how we weigh the cases.
» 3 years ago, # | 0 Looking at number of solutions passed each task we could notice that A,B,C and too far from D,E,F. I think difficulty should reduce more.. gradually.
» 3 years ago, # | 0 Can't Understand G. Anyone?
» 3 years ago, # | 0 In Problem E, can someone explain me — by taking f(i) as a partitioning factor how can we get a partition of the bit positions?
• » » 3 years ago, # ^ | 0 Elements with the same f value will belong in the same set in a particular partition.
» 3 years ago, # | 0 Problem D.-Let dp[i][j] be the expected answer given that there are i subsequences of the form 'a' in the prefix and j subsequences of the form 'ab' in the prefix.-The answer should be dp[0][0].These two statements seem contradicting to me.
• » » 3 years ago, # ^ | +7 We are working backwards. We start our dp from known values which are dp[i][j] where i + j >= k, and the answer is in dp[1][0]. In state dp[i][j] we can add a letter 'a' with probability p and have expected value which is in dp[i + 1][j] or 'b' with probability (1 — p) and have expected value from dp[i][i + j].
• » » 3 years ago, # ^ | ← Rev. 3 → +7 You start with an empty string (that does not have any 'a' nor 'ab' occurrence)I think what may be troubling you is that the "base case" of this dynamic programming approach is not in the beginning, but in the end. (Sometimes the base case is i == 0 or j == 0, but here we have i+j >= k)
• » » » 3 years ago, # ^ | +1 Ok, I got it now.But still I think the definition of dp in the editorial is quite confusing. I suppose it would be more clear if explained as "answer we get if we start with a sequence containing i subsequences of the form 'a' and j of the form 'ab'". But maybe that's just my dullness.
» 3 years ago, # | 0 Didn't know cards can have same indentity, which pay me 1 hack!
» 3 years ago, # | 0 I have a solution to G with higher time complexity and I don't know how to make it better.Supposed X have len digit, we enumerate the first different digit i with X (notice the case that the first element is 0) , then we can use any number in the last len-i digit. It can be solved with f[a][b],g[a][b] which means we have filled the first b digit using 0~a,the sum and the count of it(Remember to consider the number we filled in fist i-1 digit).I have to pay len*10 in the part of enumerate , and used len^2*10 in dp , so the general time complexity is len^3*100 that can't pass the test cases :(Can anyone help me?My English isn't good and I may have many mistakes in my expreesion , sorry for it.
» 3 years ago, # | 0 Problem H was nice and hard!
» 3 years ago, # | +3 in problem E, can someone explain to me what is the relation between: 1- when f(x) != f(y) therefore f(x) & f(y) will be 0. and 2- the good sets S correspond to the partitions of {1,2,...,m} ??
• » » 3 years ago, # ^ | 0 Elements with the same f value belong in the same set in a particular partition
» 3 years ago, # | +1 I think I'm missing some concepts in order to fully understand problem D. Can anyone point me out where to look?In the first example, if we stop when we get the first 'ab' sub-sequence, how is it possible for expected value of the number of such sub-sequences be greater than 1 in the end?Thank you.
• » » 3 years ago, # ^ | 0 For the first example, we could make a sequence like "aaab", which has 3 occurences of the subsequence "ab".
• » » » 3 years ago, # ^ | 0 Ah, that's what message was about. Are these three exactly: "a**b", "*a*b" and "**ab"?Anyway, I think I've got it now. Thanks :)
» 3 years ago, # | 0 Can someone give a brief description on solution of D. I read the editorial, but couldn't understand it....
• » » 3 years ago, # ^ | ← Rev. 4 → 0 Define dp[i][j] as they expected answer of se start problem algoritm with Amy position that has i a's and j ab's subsequences. Imagine you start the algorithm from one of these positions. In one case worth pa a's are incremented and in the other case worth pb ab's are incremented by i. So we know in both cases the new state thus the expected answer in them (asumming we have already computed dp with higher i,j) We just make a weigthed average of expected answer in both cases to reach dp[i][j] formula (case a worths pa, expected answer dp[i+1][j], case b worths pb, expected answer dp[i][i+j]. (See Wikipedia for weigthed average, it is an easy formula ) Base case and final case are very hard. Try to think them and ask if you are lost
• » » » 3 years ago, # ^ | ← Rev. 2 → 0 thanks a lot..... i understood it a bit now. One query, why the final answer is dp[1][0] and not dp[0][0]??
• » » » » 3 years ago, # ^ | ← Rev. 2 → 0 dp[0][0] is defines as any starting position with only b's. dp[1][0] is any starting positions with a finite amount of b's and then an a. It can be proved mathematically dp[0][0]=dp[1][0] but I used intuitive aproach. When you start algorithm you have 0 b's thus expected answer must be dp[0][0]. However no matter your luck when you the algorithm in all scenarios you end in a moment with a finite amount of b's and an a (could be 0 b's). Thus in all cases expected answer should be dp[1][0]
• » » » » » 3 years ago, # ^ | 0 okay... understood it now.. thanks
» 3 years ago, # | ← Rev. 2 → 0 Hi! and Happy new Year to all. In problem E, I think to understand the editorial (most of it) but I don't get how all hypothesis claimed there implies a solution for the given problem. If someone would give me an example where this hypothesis are used. thanks
» 3 years ago, # | 0 Can anyone please explain Problem G in details ? Codeforces editorial was a bit difficult to understand. Something about dynamic programming on digits...... I watched Endagorion's screencast of the same, but I couldn't understand properly.
» 3 years ago, # | 0 for those who are having problem in understanding D : https://discuss.codechef.com/questions/120548/help-in-understanding-expectationAll the credits to John_smith :)
• » » 3 years ago, # ^ | 0 Thanks, E(aaa)=E(aaaa)/2+E(aaab)/2 nice example explanation for understanding dp
• » » » 3 years ago, # ^ | 0 yaah it's awesome ! ALl thanks to JOHN :)
• » » » 3 years ago, # ^ | 0 btw did you have any good tutorial for centroid decomposition? If you have then please share!Happy coding :)
• » » » » 3 years ago, # ^ | 0 currently don't have enough EXP to unlock that skill :(
» 3 years ago, # | 0 Need some help for problem E. I understood it as letting fi=fj or fi*fj=0 for all i,j, thus counting the number of ways of partitioning {1,2...m}. But how are we take into account set T?
• » » 3 years ago, # ^ | ← Rev. 3 → +17 so, basically, T is describing whether 2 elements can stay in the same set in the partition or not.for example, you are given T as (the same format as problem input): 01234567 -------- 11100000 10100111 10011111 01101111 And for example, you are now checking whether element 0 and 2 can be in the same set, then you retrieve their bits (just take the corresponding columns of the input matrix): 02 -- 11 11 10 01 now the third row is 1 and 0, meaning if 0 is taken, don't take 2 in the final partition.you will see that 2 elements can be in the same set iff their bits (columns) are the same.So you can group the elements with same bits together and calculate how many ways you can partition them.
» 3 years ago, # | 0 Thank you for the great problems and quality editorials!Since I still have difficulty in understanding editorial of problem D, can I add one more question? Can you explain how i+j >= k can contribute to make sequence space closed ? For example, with k = 3, there are infinite i, j pairs. (3,0), (4, 0), (5, 0), and so on.
• » » 3 years ago, # ^ | +3 So for i + j >= k, if you get another 'b', you will stop. Now ignore the i and j.Suppose you get a 'b' with probability p each time, which corresponds to pb/(pa+pb) in the problem. Then the expected number of experiments you have to do to get a 'b' is 1/p.So i + j >= k the case where you can calculate the exact expected number.
• » » » 3 years ago, # ^ | 0 To be honest, I am not clear with your statement "i + j >= k the case where you can calculate the exact expected number." Could you elaborate a little further on that point?
• » » 3 years ago, # ^ | +3 Let me answer my previous question as I understood. If i + j >= k, E(i, j) = i + j + Pa/Pb <== faceless_man showed how it is calculated. Though infinite i/j pairs satisfies i+j>=k, we want to have smaller number of base cases for the efficiency (which means smaller DP states to be calculated.) So, with k=3, (3,0), (2,1), (1, 2) are considered as the base cases, but (4,0), (2,2), (3,1), (1,3) are not.
» 3 years ago, # | +1 That D has to be one of the coolest DP problems I've seen. Seriously, compressing an infinitely long memoization matrix into finite size is sweet.
» 3 years ago, # | -8 I can't get G solution.Can somebody explain me the solution with more details?
• » » 3 years ago, # ^ | ← Rev. 4 → +3 You need to calculate this subproblem: solve n[i][j], which means the number of integers that is <= X and when sorted, has i-th digit >= j. (say, i starting from 0 and counting from the least significant digit)For example, let X = 22, and let's sort the numbers: 1 2 3 4 5 6 7 8 9 01 11 12 13 14 15 16 17 18 19 02 12 22 You will see that, n[1][1] = 10 {11,12,...,19, 12} and n[1][2] = 1 {22}.Suppose you have this subproblem solved, you can get the final answer by doing sum for i to be the length of the sequence and for j to be 1 to 9: (n[i][j] - n[i][j + 1]) * 10^(i) * j i.e. you reformulate the sum of the original problem, by doing it digit by digit.However, to calculate n[i][j] is not easy (I'm not sure). (this is similar to calculating bell numbers directly is not easy, you need a O(n^2) dp).So, you now turn to calculate dp[a][b][c] for a fixed digit j. The state represents that you have considered a digits, how many intergers <= X, when not sorted, have equal to or more than b occurrence of j, given that integer is still equal to X or not (c). (the same defined in the official solution)After solving that dp, n[i][j] = dp[0][i + 1][0]. (Since you have a number >= j on i-th index, then you must have at least i+1 digits that are >= j for that number)And to calculate dp[a][b][c], you will need: dp[a+1][b/b-1][0/1]. The boundary cases are when b = 0/ a = |len(X)|.Also, you must be careful about the multiplication and modulo.So you see this problem is not so direct. If this is your first-ish digit dp problem, don't worry. It is not easy to understand and you may want to first do some easier digit dp first. Also, you may notice that there is a common strategy for solving dp[a][b][c] (like, assuming whether you are getting a number < or == the given upperbound or so...).
» 3 years ago, # | 0 Can someone read my solution of problem H and tell me the complexity? http://codeforces.com/contest/908/submission/33975786
» 3 years ago, # | +3 Can somebody explain me, how in problem D do we get 370000006 from 341/100 and 1e9+7? ... как взять дробь по модулю целого числа?
• » » 3 years ago, # ^ | +5 a / b = a * b^-1 ≡(mod m) a * b^-1 * b^φ(m) = a * b^(φ(m) - 1)For prime m latter is equal to a * b^(m - 2). It can be calculated using binary exponentiation.φ is called Euler function, b^-1 ≡(mod m) b^(φ(m) - 1) is called modular (multiplicative) inverse.
• » » » 3 years ago, # ^ | 0 Thank you very much
» 3 years ago, # | 0 What is the meaning of "the expected number of times 'ab' is a subsequence in the resulting sequence" in D?
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# 5th Class Mathematics Mensuration
Mensuration
Category : 5th Class
Mensuration
• Perimeter:
The total boundary length of a closed figure is called its perimeter. It is expressed in usual units of measurement of length.
• Area:
The amount of surface enclosed by a closed figure is called its area.
(a) Area is measured in square units.
(b) 1 m = 100 cm; 1 sq. m = 10000 sq. cm;
(c) 1 cm = 10 mm; 1 sq. cm = 100 sq. mm
• Volume:
The space occupied by an object is called its volume.
(a) Volume is measured in cubic units.
(b) 1 cu m = 1000000 cu cm;
(c) 1 cu cm = 1000 cu mm
• Cube:
It is a solid figure with 6 square surfaces.
• Volume of a cube = edge x edge x edge cu units.
• Cuboid:
It is a solid figure with 6 rectangular surfaces.
• Volume of a cuboid = length × breadth × height cubic units.
V =$l$ × b × h
$\therefore l=\frac{\text{V}}{\text{bh}};$ $b=\frac{\text{V}}{l\text{h}};$ $\text{h}=\frac{\text{V}}{l\text{b}};$
• The shape obtained on opening a solid shape is called a net.
• A net can be folded back or closed into form a solid.
• Net of a cube :
The net of a cube has 6 squares.
• Net of a cuboid :
The net of a cuboid has 6 rectangles.
#### Other Topics
##### Notes - Mensuration
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Two parallel plate capacitors A and B having capacitance $1 \mu F$ and $5 \mu F$ are charged separately to the same potential of $100\; volt$. Now the positive plate of A is connected to the negative plate of B and negative plate of A to the positive plate of B.Find the final charge on each capacitors and total loss of electrical energy in the given system.
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Planet dgplug
A (Corona) walk in the park
lone strollers with dogs and bottles of wine
going out for walks under basswood and pine
children singing and whirling around
playin' their favorite games on a crowded playground
an army of joggers on bouncing feet
elderly people tryin' to cross the street
the twilight sky, dipped in orange and blue
the silvery loom of the crescent moon
more faces than I have seen in weeks
November wind gives them rosy cheeks
from football games and from jam sessions
engrossed in music engrossed in sports
engrossed in coffee, talks and thoughts
a spirit of life and truth and hope
and the occasional smell of dope
like collecting pieces to make me whole
like an emergency bandage for my soul
Putting Emacs Backup Files in a Separate Location
Whenever Emacs saves a file, it makes a backup of the original.
So if I had a file.txt and I make changes and save it, Emacs firsts backs up the original to file.txt~.
While I love this functionality, and it has saved me from a pickle more than once, I don’t love the way my folders get polluted with ~ files all over the place.
My blog’s drafts folder had hundreds of these.
Mercifully, Emacs offers a way to stow all these files in one central folder of your choosing.
All I did was add this little snippet to my init.el
;; Set the folder for backup files to a subfolder in the
;;.emacs.d folder of the user.
(setq backup-directory-alist
'(("." . "~/.emacs.d/file-backups")))
Emacs now stops littering all over the place and saves the backups it creates, to a file-backups folder in my .emacs.d folder.
You can choose a location, you like better :)
P.S. Subscribe to my mailing list!
P.P.S. Feed my insatiable reading habit.
Jason Braganza (Work)
Could not focus much on programming today.
So decided on doing things with Python programs.
I use Nikola to generate both my websites.
It is an extremely easy to use, no fuss static site generator, which is easy on my server’s resources.
Version 8.1.2 was released a few hours ago and I hopped on and installed it.
I follow a slightly unconventional upgrade path, because I was terrified of breaking my server in the early days, when I was still learning about how to go about installing things on servers.
• I have Miniconda installed.
• I use that to generate a conda environment, which I then installed Nikola into.
• When a new release drops, I create a new conda environment, install the new release in there and run them against my source folders (after backing them up).
• This lets me revert very quickly to the old data and the older version of Nikola, in case I do something boneheaded and screw things up.
• If all works fine for a month, I delete the older conda environment along with the old Nikola release.
• I have been doing this for quite a while now, and while it may be overkill, it gives me peace of mind.
• As usual, Nikola upgraded with no issues at all.
Pleroma Bot
I always wanted to understand what bots do.
Now I realise they are athromorphic programs that (with the right permissions and the right credentials) look like actual users of a service, doing sets of activities they are programmed to do.
Like your banking app has set of solutions to common queries that it shows you, before it hands off to an actual human, if those solutions don’t fit your needs.
They feel like supercharged scripts to me.
So I decided to see if I could install one.
Since I am learning Python, I love reading the low volume Daily Python Tip Twitter account.
It has surprising, handy, funny, interesting tips and tricks about the Python language and the massive ecosystem around it.
But, I have weaned myself off Twitter for my own sanity.
I only use it sparingly once a day.
And going back to that noise and tumult no longer interests me.
I saw a bot that mirrored tech news accounts to Mastodon and wondered if a bot could get Daily Python Tip to me on my Pleroma timeline.
A quick search led me to Pleroma Bot.
A couple of struggling hours later, (creating a twitter developer account, creating a pleroma account for the bot, figuring out how to get bearer tokens for said accounts) and tada, I got the bot to come alive!
It checks the Twitter account once a day, and mirrors the tweets to the bot account.
You’re most welcome to follow it for a Python tip, daily.
The next thing to do, is to see if I can get a bot to post a tagged pleroma status to my twitter account.
But that is something for another day …
Update, 2020/11/17: figured out how to use the bot to mirror multiple accounts. It now mirrors, Daily Python Tip, RegexTip, and CompSciFact.
P.S. Subscribe to my mailing list!
P.P.S. Feed my insatiable reading habit.
How to use Hugo Modules
I use Hugo for this site. I migrated to Hugo from WordPress a year ago. Hugo is a static site generator written in Go. Hugo project has frequent releases, so I usually update the version once in a few months. This involves reading all the release notes and making any changes to the theme if required. The theme changes are required rarely though. While going through the release notes of v0.
What I Learnt from Antifragile (III)
This post was sent to my newsletter on October 25th, 2020.
You really ought to subscribe :)
What I Learnt from Antifragile (III)
What Does Not Kill Me … Antifragility for the Collective
What does not kill me makes me stronger.
— Friedrich Nietzsche, Maxims and Arrows
The world breaks everyone and afterward many are strong at the broken places.
But those that will not break it kills.
It kills the very good and the very gentle and the very brave impartially.
If you are none of these you can be sure it will kill you too but there will be no special hurry.
— Ernest Hemingway, A Farewell to Arms
That, in a nutshell, explains my learning today.
To become Antifragile, we need to understand be aware of what we do, our actions and then see who it ultimately benefits.
Antifragility, like I imagined in my head, was me getting stronger with every blow that life dealt me, Hydra like.
If you cut off one head, I would just grow another one.
But I realised that everything comes at the expense of something.
If I am growing Antifragile, something else has to give.
If there’s just nature on the otherside, we’re fine. But if there are people, then we better be careful about how we get Antifragile.
There’s also the notion of scale. Something small, dying to make the bigger collective stronger.
So there’s always a balancing act and a constant need to be observant.
This is how I imagine it, in a few scenarios in my life.
My cells need to die, my muscles need to tear in order that I build up my strength.
Here the individual is nature (my cells), dying in order to make me (my body, the collective) much stronger.
Imagine if that did not happen, if each cell decided, why should I die?
Actually, you don’t have to imagine.
That’s what cancer is.
If I die this year, I am insured. My folks get a hefty payout. (Antifragility for my family’s finances)
But the insurance company can only afford to do this, because they have money from a ton of folks placing the same bet as I did. That we would croak this year.
This is again the individual (me) benefiting the collective (the vast pool of people, who do not have enough saved, yet want to provide for their loved ones).
A nasty one is when someone uses this for their own benefit.
They win, but the collective loses.
Scams of various sorts come to mind here, where an unscrupulous person, takes advantage and become antifragile at the benefit of other people.
The flip side is the hero, where the individual takes risks and sacrifices to benefit the collective
Soldiers, Teachers, Firefighters, Tinkerers, Entrepreneurs are all examples of folks who sacrifice individually so that society as a whole benefits.
So this is what I learnt. To see how actions towards antifragility (mine or others) have ramifications on my life.
To always see if I or society benefit. Not someone else taking undue advantage.
P.S. Subscribe to my mailing list!
Forward these to your friends and get them to subscribe!
P.P.S. Feed my insatiable reading habit.
How to use Yubikey or any GPG smartcard in Thunderbird 78
Thunderbird is the free and open source email client by Mozilla Foundation. I have been using it for some years now. Till now the Thunderbird users had to use an extension Enigmail to use GnuPG. Thunderbird 78 now uses a different implementation of OpenPGP called RNP.
Since RNP library still does not support the use of secret key on smartcards, to use Yubikey or any other GnuPG enabled smartcards, we need manually configure Thunderbird with GnuPG. The steps as said are the following :
Install GPGME
dnf install GPGME
GPGME, GnuPG Made Easy library makes the GnuPG easily accessible by providing a high level crypto API for encrypt, decrypt, sign, verify and key management. I already have GnuPG installed in my Fedora 33 machine and my Yubikey ready.
Modify Thunderbird configuration
Go to the Preferences menu then click on the config editor button at the very end.
Click on the I accept the risk.
Search for mail.openpgp.allow_external_gnupg and switch to true.
Remember to restart the Thunderbird after that.
Configure the secret key usage form Yubikey
Now go to the Account Settings and then go to the End-To-End-Encryption at the sidebar. Select the Use your external key through GnuPG(e.g. from a smartcard) option and click on continue.
Type your Secret Key ID in the box and click on Save key ID.
Now open the OpenPGP Key Manager and import your public key and then verify.
Now you can start using your hardware token in Thunderbird.
In this case we have to use 2 keyrings - GnuPG and RNP’s keyring (internal in Thunderbird). This is an extra step, which I hope in future can be avoided.
Using Mailvelope with Yubikey in Linux
Mailvelope is an extension on web browsers to send end to end encrypted emails. This is a good option available to the users to send end to end encrypted without changing the email service they use. It is licensed under AGPL v3, making it Free and Open Source software. The code is there in Github for the community to have a look. This can be added as an extension to the - Chrome, Firefox and Edge browsers to securely encrypt emails with PGP using your email providers.
Mailvelope does provide end to end encryption for the email content but does not protect the metadata (subject, IP address of the sender) from third parties. As most of the email encryption tools, it does not work on the mobile browser. There is a detailed user guide on Mailvelope from the Freedom of the Press Foundation, which is really helpful for the new users.
By default, Mailvelope uses its own keyring. To use my Yubikey along with GnuPG keyring, I had to take the following steps:
Install gpgme
We need gpgme installed. On my Fedora 33 I did
$sudo dnf install gpgme -y For Chrome browser We have to create gpgmejson.json .json file in the ~/.config/google-chrome/NativeMessagingHosts directory write the following json in there. { "name": "gpgmejson", "description": "Integration with GnuPG", "path": "/usr/bin/gpgme-json", "type": "stdio", "allowed_origins": [ "chrome-extension://kajibbejlbohfaggdiogboambcijhkke/" ] } For Firefox mkdir -p ~/.mozilla/native-messaging-hosts After creating the native-messaging-hosts directory inside the Mozilla directory, add gpgmejson.json file there with the following content. vim ~/.mozilla/native-messaging-hosts/gpgmejson.json { "name": "gpgmejson", "description": "Integration with GnuPG", "path": "/usr/bin/gpgme-json", "type": "stdio", "allowed_extensions": [ "jid1-AQqSMBYb0a8ADg@jetpack" ] } Remember to restart the respective browser after you add the .json file. Then go to the Mailvelope extension to select the GnuPG keyring. November 02, 2020 Kushal Das Johnnycanencrypt 0.4.0 released Last night I released 0.4.0 of johnnycanencrypt module for OpenPGP in Python. This release has one update in the creating new key API. Now, we can pass one single UID as a string, or multiple in a list, or even pass None to the key creation method. This means we can have User ID-less certificates, which sequoia-pgp allows. I also managed to fix the bug so that users can use pip to install the latest release from https://pypi.org. You will need the rust toolchain, I generally install from https://rustup.rs. For Fedora sudo dnf install nettle clang clang-devel nettle-devel python3-devel For Debian/Ubuntu sudo apt install -y python3-dev libnettle6 nettle-dev libhogweed4 python3-pip python3-venv clang Remember to upgrade your pip version inside of the virtual environment if you are in Buster. For macOS Install nettle via brew. Installing the package ❯ python3 -m pip install johnnycanencrypt Collecting johnnycanencrypt Downloading https://files.pythonhosted.org/packages/50/98/53ae56eb208ebcc6288397a66cf8ac9af5de53b8bbae5fd27be7cd8bb9d7/johnnycanencrypt-0.4.0.tar.gz (128kB) |████████████████████████████████| 133kB 6.4MB/s Installing build dependencies ... done Getting requirements to build wheel ... done Preparing wheel metadata ... done Building wheels for collected packages: johnnycanencrypt Building wheel for johnnycanencrypt (PEP 517) ... done Created wheel for johnnycanencrypt: filename=johnnycanencrypt-0.4.0-cp37-cp37m-macosx_10_7_x86_64.whl size=1586569 sha256=41ab04d3758479a063a6c42d07a15684beb21b1f305d2f8b02e820cb15853ae1 Stored in directory: /Users/kdas/Library/Caches/pip/wheels/3f/63/03/8afa8176c89b9afefc11f48c3b3867cd6dcc82e865c310c90d Successfully built johnnycanencrypt Installing collected packages: johnnycanencrypt Successfully installed johnnycanencrypt-0.4.0 WARNING: You are using pip version 19.2.3, however version 20.2.4 is available. You should consider upgrading via the 'pip install --upgrade pip' command. Now, you can import the module inside of your virtual environment :) Note: In the future, I may change the name of the module to something more meaningful :) November 01, 2020 Kushal Das High load average while package building on Fedora 33 Enabling Link time optimization (LTO) with rpmbuild is one of the new features of Fedora 33. I read the changeset page once and went back only after I did the Tor package builds locally. While building the package, I noticed that suddenly there are many processes with /usr/libexec/gcc/x86_64-redhat-linux/10/lto1 and my load average reached 55+. Here is a screenshot I managed to take in between. Jason Braganza (Personal) What I Learnt from Antifragile (II) This post was sent to my newsletter on October 18th, 2020 You really ought to subscribe :) What I Learnt from Antifragile (II) I fell sick and missed writing last week. I have to live up the name of the news letter, anyhoo. It would not be erratic without me whiffing once in a while, non? Apologies all around, anyway! The Barbell Heuristic to Taking Risks Basically a shortcut to figuring out whether you ought to do something or not, based on the risks it entails. How do we take a decision, when we don’t know all the pros and cons? How do we decide in an uncertain world? Simply put, What kind / amount of loss am I willing to accept, to gain some reward? Life basically consists of three outcomes: 1. The safe outcome, with little to no success, but you don’t lose anything 2. The normal outcome, with some middling success, but you stand to lose some. • But here’s the kicker. You might stand to lose everything, if you don’t understand the risks you take, or if the risk is unknowable. (Blow ups due to these unknown risks are what are now popularly called, thanks to Taleb’s earlier book, Black Swans) 3. High Risk, high reward! You know you will lose, but if you win, you win Big! It helps if you take risks with a domain that you have deep expertise in. Taleb suggests that the best and safest way, to make decisions that propel your forward with minimal risk, is to ignore point 2 altogether. Most of your daily life decisions ought to be with point 1. Some of your decisions you, go to point 3. Your strategy is to be as hyper-conservative and hyper-aggressive as you can be, instead of being mildly aggressive or conservative. — Taleb, The Black Swan And that is the barbell strategy. It looks like an unbalanced barbell actually, like the one on the cover of his next book, Skin in the Game. This is what will give you maximum peace of mind. Risk taking also becomes easier, if you have options like I pointed out last week. The best worst case scenario, is one that you have the option to reverse. (like buying something you need, but uncertain about how it’ll be? Easy to buy it, if the thing comes with an option to return it if you don’t like it.) Three personal life cases, Money I don’t understand investing. I do know, that I need a nest egg for when Abby & I are old :) Ergo, barbell strategy. Most of our money is parked in safe investments like the Provident Fund and fixed deposits. And some of it, in risky stuff like stocks and equity mutual funds. (since this is not my domain of expertise, I pay someone trustworthy to help me out.) So if the market crashes like it did earlier this year, I was not as worried as other folk. I did not lose my shirt. I could follow, what the given advice at the time was (Stay Invested) with a clear, calm mind. And I am confident, compounding will work its magic over time over both sets of investments. Work Let’s put the barbell, to work here too. Your safe, boring job is one end of the spectrum. Your risky side projects, hustles, are the other. You need both. You could either do both together, or serially. Work a safe job for a few years, then take up a risky moonshot, and if it doesn’t pan out, go back to another safe job. While right now, I am in between jobs, due to health reasons, in my earlier lives, I had pretty boring jobs. But, I write a lot. I teach a lot. And that brought me a lot of opportunities that helped me through really trying times in the past two decades. Health This is relevant to me, because it helped me get fit over the past year. I have three slipped discs. Do I have surgery? The docs are undecided. Or rather they are, but are unwilling to guarantee, how long the surgery would help me. And I had bloated to 98 odd kgs at my worst. What do I do? So, the safe thing to do was to lose weight. And the hard thing to do was to get strong. Both of which, are progressing along nicely. I lost 30 kgs and am doing aggressive physio to build up my back muscles, so that my poor vertebrae don’t have to do all the heavy lifting by themselves. I feel much better today, better than I did in my twenties! And that about does it for using barbells to help make decisions. That’s all we have for you this week :) I really do hope, this little heuristic, changes your life as much as it did mine :) P.S. Subscribe to my mailing list! Forward these to your friends and get them to subscribe! P.P.S. Feed my insatiable reading habit. October 04, 2020 Armageddon Dotfiles with /Chezmoi/ A few months ago, I went on a search for a solution for my dotfiles. I tried projects likes GNU Stow, dotbot and a bare git repository. Each one of these solutions has its advantages and its advantages, but I found mine in Chezmoi. Chezmoi ? That's French right ? How is learning French going to help me ? Introduction On a *nix system, whether Linux, BSD or even Mac OS now, the applications one uses have their configuration saved in the user's home directory. These files are called configuration files. Usually, these configuration files start with a . which on these systems designate hidden files (they do not show up with a simple ls). Due their names, these configuration files are also referred to as dotfiles. Note I will be using dotfiles and configuration files interchangeably in this article, and they can be thought as such. One example of such files is the .bashrc file found in the user's home directory. It allows the user to configure bash and change some behaviours. Now that we understand what dotfiles are, let's talk a little bit about the previously mentioned solutions. They deserve mentioning, especially if you're looking for such solution. GNU Stow GNU Stow leverages the power of symlinks to keep your configuration in a centralized location. Wherever your repository lives, GNU Stow will mimic the internal structure of said repository in your home directory by smartly symlinking everything. I said smartly because it tries to minimize the amount of symlinks created by symlinking to common root directories if possible. By having all your configuration files under one directory structure, it is easier to push it to any public repository and share it with others. The downsize is, you end-up with a lot of symlinks. It is also worth mentioning that not all applications behave well when their configuration directories are symlinked. Otherwise, GNU Stow is a great project. Dotbot Dotbot is a Python project that aims at automating your dotfiles. It gives you great control over what and how to manage your dotfiles. Having it written in Python means it is very easy to install; pip. It also means that it should be easy to migrate it to different systems. Dotbot has a lot going for it. If the idea of having control over every aspect of your dotfiles, including the possibility of the setup of the environment along with it, then dotbot is for you. Well, it's not for me. Bare Git Repository This is arguably the most elegant solution of them all. The nice thing about this solution is its simplicity and cleanliness. It is essentially creating a bare git repository somewhere in your home directory specifying the home directory itself to be the working directory. If you are wondering where one would use a bare git repository in real life other than this use case. Well, you have no other place to turn than any git server. On the server, Gitea for example, your repository is only a bare repository. One has to clone it to get the working directory along with it. Anyway, back to our topic. This is a great solution if you don't have to worry about things you would like to hide. By hide, I mean things like credentials, keys or passwords which never belong in a repository. You will need to find solutions for these types of files. I was looking for something less involving and more involved. Chezmoi to the rescue ? Isn't that what they all say ? I like how the creator(s) defines Chezmoi Manage your dotfiles across multiple machines, securely. Pretty basic, straight to the point. Unfortunately, it's a little bit harder to grasp the concept of how it works. Chezmoi basically generates the dotfiles from the local repository. These dotfiles are saved in different forms in the repository but they always generate the same output; the dotfiles. Think of Chezmoi as a dotfiles templating engine, at its basic form it saves your dotfiles as is and deploys them in any machine. Working with Chezmoi I think we should take a quick look at Chezmoi to see how it works. Chezmoi is written Golang making it fairly easy to install so I will forgo that boring part. First run To start using Chezmoi, one has to initialize a new Chezmoi repository. chezmoi init This will create a new git repository in ~/.local/share/chezmoi. This is now the source state, where Chezmoi will get your dotfiles. Plain dotfiles management with Chezmoi Now that we have a Chezmoi repository. We can start to populate it with dotfiles. Let's assume that we would like to start managing one of our dotfiles with Chezmoi. I'm going with an imaginary application's configuration directory. This directory will hold different files with versatile content types. This is going to showcase some of Chezmoi's capabilities. Note This is how I use Chezmoi. If you have a better way to do things, I'd like to hear about it! Adding a dotfile This DS9 application has its directory configuration in ~/.ds9/ where we find the config. The configuration looks like any generic ini configuration. [character/sisko] Name = Benjamin Rank = Captain Credentials = sisko-creds.cred Mastodon = sisko-api.mastodon Nothing special about this file, let's add it to Chezmoi chezmoi add ~/.ds9/config Listing dotfiles And nothing happened… Hmm… chezmoi managed /home/user/.ds9 /home/user/.ds9/config Okay, it seems that it is being managed. Diffing dotfiles We can test it out by doing something like this. mv ~/.ds9/config ~/.ds9/config.old chezmoi diff install -m 644 /dev/null /home/user/.ds9/config --- a/home/user/.ds9/config +++ b/home/user/.ds9/config @@ -0,0 +1,5 @@ +[character/sisko] +Name = Benjamin +Rank = Captain +Credentials = sisko-creds.cred +Mastodon = sisko-api.mastodon Alright, everything looks as it should be. Apply dotfiles But that's only a diff, how do I make Chezmoi apply the changes because my dotfile is still config.old. Okay, we can actually get rid of the config.old file and make Chezmoi regenerate the configuration. rm ~/.ds9/config ~/.ds9/config.old chezmoi -v apply Note I like to use the -v flag to check what is actually being applied. install -m 644 /dev/null /home/user/.ds9/config --- a/home/user/.ds9/config +++ b/home/user/.ds9/config @@ -0,0 +1,5 @@ +[character/sisko] +Name = Benjamin +Rank = Captain +Credentials = sisko-creds.cred +Mastodon = sisko-api.mastodon And we get the same output as the diff. Nice! The configuration file was also recreated, that's awesome. Editing dotfiles If you've followed so far, you might have wondered… If I edit ~/.ds9/config, then Chezmoi is going to override it! YES, yes it will. warning Always use Chezmoi to edit your managed dotfiles. Do NOT edit them directly. ALWAYS use chezmoi diff before every applying. To edit your managed dotfile, simply tell Chezmoi about it. chezmoi edit ~/.ds9/config Chezmoi will use your $EDITOR to open the file for you to edit. Once saved, it's saved in the repository database.
Be aware, at this point the changes are not reflected in your home directory, only in the Chezmoi source state. Make sure you diff and then apply to make the changes in your home.
Chezmoi repository management
As mentioned previously, the repository is found in ~/.local/share/chezmoi. I always forget where it is, luckily Chezmoi has a solution for that.
chezmoi cd
Now, we are in the repository. We can work with it as a regultar git repository. When you're done, don't forget to exit.
Other features
It is worth mentioning at this point that Chezmoi offers a few more integrations.
Templating
Due to the fact that Chezmoi is written in Golang, it can leverage the power of the Golang templating system. One can replace repeatable values like email or name with a template like {{ .email }} or {{ .name }}.
This will result in a replacement of these templated variables with their real values in the resulting dotfile. This is another reason why you should always edit your managed dotfiles through Chezmoi.
Our previous example would look a bit different.
[character/sisko]
Name = {{ .sisko.name }}
Rank = {{ .sisko.rank }}
Credentials = sisko-creds.cred
Mastodon = sisko-api.mastodon
And we would add it a bit differently now.
chezmoi add --template ~/.ds9/config
warning
Follow the documentation to configure the values.
Once you have the power of templating on your side, you can always take it one step further. Chezmoi has integration with a big list of password managers. These can be used directly into the configuration files.
In our hypothetical example, we can think of the credentials file (~/.ds9/sisko-creds.cred).
Name = {{ (keepassxc "sisko.ds9").Name }}
Rank = {{ (keepassxc "sisko.ds9").Rank }}
Access_Code = {{ (keepassxc "sisko.ds9").AccessCode }}
Do not forget that this is also using the templating engine. So you need to add as a template.
chezmoi add --template ~/.ds9/sisko-creds.cred
File encryption
Wait, what ! You almost slipped away right there old fellow.
We have our Mastodon API key in the sisko-api.mastodon file. The whole file cannot be pushed to a repository. It turns out that Chezmoi can use gpg to encrypt your files making it possible for you to push them.
To add a file encrypted to the Chezmoi repository, use the following command.
chezmoi add --encrypt ~/.ds9/sisko-api.mastodon
Misc
There is a list of other features that Chezmoi supports that I did not mention. I did not use all the features offered yet. You should check the website for the full documentation.
Conclusion
I am fully migrated into Chezmoi so far. I have used all the features above, and it has worked flawlessly so far.
I like the idea that it offers all the features I need while at the same time staying out of the way. I find myself, often, editing the dotfiles in my home directory as a dev version. Once I get to a configuration I like, I add it to Chezmoi. If I ever mess up badly, I ask Chezmoi to override my changes.
I understand it adds a little bit of overhead with the use of chezmoi commands, which I aliased to cm. But the end result is a home directory which seems untouched by any tools (no symlinks, no copies, etc…) making it easier to migrate out of Chezmoi as a solution and into another one if I ever choose in the future.
Bookmark with Org-capture
I was reading, and watching, Mike Zamansky's blog post series about org-capture and how he manages his bookmarks. His blog and video series are a big recommendation from me, he is teaching me tons every time I watch his videos. His inspirational videos were what made me dig down on how I could do what he's doing but… my way…
I stumbled across this blog post that describes the process of using org-cliplink to insert the title of the post into an org-mode link. Basically, what I wanted to do is provide a link and get an org-mode link. Sounds simple enough. Let's dig in.
Org Capture Templates
I will assume that you went through Mike's part 1 and part 2 posts to understand what org-capture-templates are and how they work. I essentially learned it from him and I do not think I can do a better job than a teacher.
Now that we understand where we need to start from, let's explain the situation. We need to find a way to call org-capture and provide it with a template. This template will need to take a url and add an org-mode url in our bookmarks. It will look something like the following.
(setq org-capture-templates
'(("b" "Bookmark (Clipboard)" entry (file+headline "~/path/to/bookmarks.org" "Bookmarks")
"** %(some-function-here-to-call)\n:PROPERTIES:\n:TIMESTAMP: %t\n:END:%?\n" :empty-lines 1 :prepend t)))
I formatted it a bit so it would have some properties. I simply used the %t to put the timestamp of when I took the bookmark. I used the %? to drop me at the end for editing. Then some-function-here-to-call a function to call to generate our bookmark section with a title.
The blog post I eluded to earlier solved it by using org-cliplink. While org-cliplink is great for getting titles and manipulating them, I don't really need that functionality. I can do it manually. Sometimes, though, I would like to copy a page… Maybe if there is a project that could attempt to do someth… Got it… org-web-tools.
Configuring org-capture with org-web-tools
You would assume that you would be able to just pop (org-web-tools-insert-link-for-url) in the previous block and you're all done. But uhhh….
Wrong number of arguments: (1 . 1), 0
No dice. What would seem to be the problem ?
We look at the definition and we find this.
(defun org-web-tools-insert-link-for-url (url)
"Insert Org link to URL using title of HTML page at URL.
If URL is not given, look for first URL in kill-ring'."
(interactive (list (org-web-tools--get-first-url)))
I don't know why, exactly, it doesn't work by calling it straight away because I do not know emacs-lisp at all. If you do, let me know. I suspect it has something to do with (interactive) and the list provided to it as arguments.
Anyway, I can see it is using org-web-tools--org-link-for-url, which the documentation suggests does the same thing as org-web-tools-insert-link-for-url, but is not exposed with (interactive). Okay, we have bits and pieces of the puzzle. Let's put it together.
First, we create the function.
(defun org-web-tools-insert-link-for-clipboard-url ()
"Extend =org-web-tools-inster-link-for-url= to take URL from clipboard or kill-ring"
(interactive)
Then, we set our org-capture-templates variable to the list of our only item.
(setq org-capture-templates
'(("b" "Bookmark (Clipboard)" entry (file+headline "~/path/to/bookmarks.org" "Bookmarks")
"** %(org-web-tools-insert-link-for-clipboard-url)\n:PROPERTIES:\n:TIMESTAMP: %t\n:END:%?\n" :empty-lines 1 :prepend t)))
Now if we copy a link into the clipboard and then call org-capture with the option b, we get prompted to edit the following before adding it to our bookmarks.
** [[https://cestlaz.github.io/stories/emacs/][Using Emacs Series - C'est la Z]]
:PROPERTIES:
:TIMESTAMP: <2020-09-17 do>
:END:
Works like a charm.
Custom URL
What if we need to modify the url in some way before providing it. I have that use case. All I needed to do is create a function that takes input from the user and provide it to org-web-tools--org-link-for-url. How hard can that be ?! uhoh! I said the curse phrase didn't I ?
(defun org-web-tools-insert-link-for-given-url ()
"Extend =org-web-tools-inster-link-for-url= to take a user given URL"
(interactive)
We can, then, hook the whole thing up to our org-capture-templates and we get.
(setq org-capture-templates
'(("b" "Bookmark (Clipboard)" entry (file+headline "~/path/to/bookmarks.org" "Bookmarks")
"** %(org-web-tools-insert-link-for-clipboard-url)\n:PROPERTIES:\n:TIMESTAMP: %t\n:END:%?\n" :empty-lines 1 :prepend t)
("B" "Bookmark (Paste)" entry (file+headline "~/path/to/bookmarks.org" "Bookmarks")
"** %(org-web-tools-insert-link-for-given-url)\n:PROPERTIES:\n:TIMESTAMP: %t\n:END:%?\n" :empty-lines 1 :prepend t)))
if we use the B, this time, it will prompt us for input.
Conclusion
I thought this was going to be harder to pull off but, alas, it was simple, even for someone who doesn't know emacs-lisp, to figure out. I hope I'd get more familiar with emacs-lisp with time and be able to do more. Until next time, I recommend you hook org-capture into your workflow. Make sure it fits your work style, otherwise you will not use it, and make your path a more productive one.
My journey in the Kubernetes Release Team
My learnings from working on the Kubernetes Release Team and leading the enhancements vertical
Concurrency bugs in Go
I recently read this paper titled, Understanding Real-World Concurrency Bugs in Go (PDF), that studies concurrency bugs in Golang and comments on the new primitives for messages passing that the language is often known for.
I am not a very good Go programmer, so this was an informative lesson in various ways to achieve concurrency and synchronization between different threads of execution. It is also a good read for experienced Go developers as it points out some important gotchas to look out for when writing Go code. The fact that it uses real world examples from well known projects like Docker, Kubernetes, gRPC-Go, CockroachDB, BoltDB etc. makes it even more fun to read!
The authors analyzed a total of 171 concurrency bugs from several prominent Go open source projects and categorized them in two orthogonal dimensions, one each for the cause of the bug and the behavior. The cause is split between two major schools of concurrency
Along the cause dimension, we categorize bugs into those that are caused by misuse of shared memory and those caused by misuse of message passing
and the behavior dimension is similarly split into
we separate bugs into those that involve (any number of ) goroutines that cannot proceed (we call themblocking bugs) and those that do not involve any blocking (non-blocking bugs)
Interestingly, they chose the behavior to be blocking instead of deadlock since the former implies that atleast one thread of execution is blocked due to some concurrency bug, but the rest of them might continue execution, so it is not a deadlock situation.
Go has primitive shared memory protection mechanisms like Mutex, RWMutex etc. with a caveat
Write lock requests in Go have ahigher privilege than read lock requests.
as compared to pthread in C. Go also has a new primitive called sync.Once that can be used to guarantee that a function is executed only once. This can be useful in situations where some callable is shared across multiple threads of execution but it shouldn't be called more than once. Go also has sync.WaitGroups , which is similar to pthread_join to wait for various threads of executioun to finish executing.
Go also uses channels for the message passing between different threads of executions called Goroutunes. Channels can be buffered on un-buffered (default), the difference between them being that in a buffered channel the sender and receiver don't block on each other (until the buffered channel is full).
The study of the usage patterns of these concurrency primitives in various code bases along with the occurence of bugs in the codebase concluded that even though message passing was used at fewer places, it accounted for a larger number of bugs(58%).
Implication 1:With heavier usages of goroutines and newtypes of concurrency primitives, Go programs may potentiallyintroduce more concurrency bugs
Also, interesting to note is this observation in tha paper
Observation 5:All blocking bugs caused by message passing are related to Go’s new message passing semantics like channel. They can be difficult to detect especially when message passing operations are used together with other synchronization mechanisms
The authors also talk about various ways in which Go runtime can detect some of these concurrency bugs. Go runtime includes a deadlock detector which can detect when there are no goroutunes running in a thread, although, it cannot detect all the blocking bugs that authors found by manual inspection.
For shared memory bugs, Go also includes a data race detector which can be enbaled by adding -race option when building the program. It can find races in memory/data shared between multiple threads of execution and uses happened-before algorithm underneath to track objects and their lifecycle. Although, it can only detect a part of the bugs discovered by the authors, the patterns and classification in the paper can be leveraged to improve the detection and build more sophisticated checkers.
My Rubber Ducks
There are times when I find myself stuck when solving any problem. This deadlock can arise due to several factors. Somet...
Url Shortner in Golang
TLDR; Trying to learn new things I tried writing a URL shortner called shorty. This is a first draft and I am trying to approach it from first principle basis. Trying to break down everything to the simplest component.
I decided to write my own URL shortner and the reason for doing that was to dive a little more into golang and to learn more about systems. I have planned to not only document my learning but also find and point our different ways in which this application can be made scalable, resilient and robust.
A high level idea is to write a server which takes the big url and return me a short url for the same. I have one more requirement where I do want to provide a slug i.e a custom short url path for the same. So for some links like https://play.google.com/store/apps/details?id=me.farhaan.bubblefeed, I want to have a url like url.farhaan.me/linktray which is easy to remember and distribute.
The way I am thinking to implement this is by having two components, I want a CLI interface which talks to my Server. I don’t want a fancy UI for now because I want it to be exclusively be used through terminal. A Client-Server architecture, where my CLI client sends a request to the server with a URL and an optional slug. If a slug is present URL will have that slug in it and if it doesn’t it generates a random string and make the URL small. If you see from a higher level it’s not just a URL shortner but also a URL tagger.
The way a simple url shortner works:
A client makes a request to make a given URL short, server takes the URL and stores it to the database, server then generates a random string and maps the URL to the string and returns a URL like url.farhaan.me/<randomstring>.
Now when a client requests to url.farhaan.me/<randomstring>, it goest to the same server, it searches the original URL and redirects the request to a different website.
The slug implementation part is very straightforward, where given a word, I might have to search the database and if it is already present we raise an error but if it isn’t we add it in the database and return back the URL.
One optimization, since it’s just me who is going to use this, I can optimize my database to see if the long URL already exists and if it does then no need to create a new entry. But this should only happen in case of random string and not in case of slugs. Also this is a trade off between reducing the redundancy and latency of a request.
But when it comes to generating a random string, things get a tiny bit complicated. This generation of random strings, decides how many URLs you can store. There are various hashing algorithms that I can use to generate a string I can use md5, base10 or base64. I also need to make sure that it gives a unique hash and not repeated ones.
Unique hash can be maintained using a counter, the count either can be supplied from a different service which can help us to scale the system better or it can be internally generated, I have used database record number for the same.
If you look at this on a system design front. We are using the same Server to take the request and generate the URL and to redirect the request. This can be separated into two services where one service is required to generate the URL and the other just to redirect the URL. This way we increase the availability of the system. If one of the service goes down the other will still function.
The next step is to write and integrate a CLI system to talk to the server and fetch the URL. A client that can be used for an end user. I am also planning to integrate a caching mechanism in this but not something out of the shelf rather write a simple caching system with some cache eviction policy and use it.
Till then I will be waiting for the feedback. Happy Hacking.
I now have a Patreon open so that you folks can support me to do this stuff for longer time and sustain myself too. So feel free to subscribe to me and help me keeping doing this with added benefits.
Farhaan Bukhsh
TLDR; Link Tray is a utility we recently wrote to curate links from different places and share it with your friends. The blogpost has technical details and probably some productivity tips.
Link Bubble got my total attention when I got to know about it, I felt it’s a very novel idea, it helps to save time and helps you to curate the websites you visited. So on the whole, and believe me I am downplaying it when I say Link Bubble does two things:
1. Saves time by pre-opening the pages
2. Helps you to keep a track of pages you want to visit
It’s a better tab management system, what I felt weird was building a whole browser to do that. Obviously, I am being extremely naive when I am saying it because I don’t know what it takes to build a utility like that.
Now, since they discontinued it for a while and I never got a chance to use it. I thought let me try building something very similar, but my use case was totally different. Generally when I go through blogs or articles, I open the links mentioned in a different tab to come back to them later. This has back bitten me a lot of time because I just get lost in so many links.
I thought if there is a utility which could just capture the links on the fly and then I could quickly go through them looking at the title, it might ease out my job. I bounced off the same idea across to Abhishek and we ended up prototyping LinkTray.
Our first design was highly inspired by facebook messenger but instead of chatheads we have links opened. If you think about it the idea feels very beautiful but the design is “highly” not scalable. For example if you have as many as 10 links opened we had trouble in finding our links of interest which was a beautiful design problems we faced.
We quickly went to the whiteboard and put up a list of requirements, first principles; The ask was simple:
1. To share multiple links with multiple people with least transitions
2. To be able to see what you are sharing
We took inspiration from an actual Drawer where we flick out a bunch of links and go through them. In a serendipitous moment the design came to us and that’s how link tray looks like the way it looks now.
Link Tray was a technical challenge as well. There is a plethora of things I learnt about the Android ecosystem and application development that I knew existed but never ventured into exploring it.
Link Tray is written in Java, and I was using a very loosely maintained library to get the overlay activity to work. Yes, the floating activity or application that we see is called an overlay activity, this allows the application to be opened over an already running application.
The library that I was using doesn’t have support for Android O and above. To figure that out it took me a few nights , also because I was hacking on the project during nights . After reading a lot of GitHub issues I figured out the problem and put in the support for the required operating system.
One of the really exciting features that I explored about Android is Services. I think I might have read most of the blogs out there and all the documentation available and I know that I still don't know enough. I was able to pick enough pointers to make my utility to work.
Just like Uncle Bob says make it work and then make it better. There was a persistent problem, the service needs to keep running in the background for it to work. This was not a functional issue but it was a performance issue for sure and our user of version 1.0 did have a problem with it. People got mislead because there was constant notification that LinkTray is running and it was annoying. This looked like a simple problem on the face but was a monster in the depth.
The solution to the problem was simple stop the service when the tray is closed, and start the service when the link is shared back to link tray. Tried, the service did stop but when a new link was shared the application kept crashing. Later I figured out the bound service that is started by the library I am using is setting a bound flag to True but when they are trying to reset this flag , they were doing at the wrong place, this prompted me to write this StackOverflow answer to help people understand the lifecycle of service. Finally after a lot of logs and debugging session I found the issue and fixed it. It was one of the most exciting moment and it help me learn a lot of key concepts.
The other key learning, I got while developing Link Tray was about multi threading, what we are doing here is when a link is shared to link tray, we need the title of the page if it has and favicon for the website. Initially I was doing this on the main UI thread which is not only an anti-pattern but also a usability hazard. It was a network call which blocks the application till it was completed, I learnt how to make a network call on a different thread, and keep the application smooth.
Initially approach was to get a webview to work and we were literally opening the links in a browser and getting the title and favicon out, this was a very heavy process. Because we were literally spawning a browser to get information about links, in the initial design it made sense because we were giving an option to consume the links. Over time our design improved and we came to a point where we don’t give the option to consume but to curate. Hence we opted for web scraping, I used custom headers so that we don’t get caught by robot.txt. And after so much of effort it got to a place where it is stable and it is performing great.
It did take quite some time to reach a point where it is right now, it is full functional and stable. Do give it a go if you haven’t, you can shoot any queries to me.
Happy Hacking!
GNU Emacs pretest builds for Fedora
I have been following GNU Emacs development through Debbugs and Sacha Chua’s newsletter. I always felt that I should use the latest development version of Emacs, instead of sticking to stable release. That way I get to use the latest improvements and also help in testing the changes. If I find any bugs, I can report those. The motivation for building pretests I was planning to build RPM packages for Fedora from master branch.
Holiday Greetings
I'm on vacation at the North Sea with my family, and like exactly one year ago I was facing the problem of having too many postcards to write. Last year, I had written a small Python script that would take a yaml file and compile it to an HTML postcard.
The yaml describes all adjustable parts of the postcard, like the content and address, but also a title, stamp and front image. A jinja2 template, a bit of CSS and javascript create a flipable postcard that can be sent via email - which is very convenient if you, like me, are too lazy to buy postcards and stamps, and have more email addresses in your address book than physical addresses.
A postcard yaml could look like this (click the card to flip it around):
---
- name: Holiday Status 2020
front_image: 'private_images/ninja.jpg'
Schubisu's Blog
World Wide Web
title: I'm fine, thanks :)
content: |
Hey there!
I'm currently on vacation and was stumbling over the same problem I had last year; writing greeting cards for friends and family. Luckily I've solved that issue last year, I simply had totally forgotten about it.
This is an electronic postcard, made of HTML, CSS and a tiny bit of javascript, compiling my private photos and messages to a nice looking card.
Feel free to fork, use and add whatever you like!
Greets,
Schubisu
stamp: 'private_images/leuchtturm_2020.jpg'
and will be rendered by the script to this:
I was curious anyway, how this would be rendered on my blog. I've added a small adjustment to my CSS to scale the iframe tag by 0.75% and I'm okay with the result ;)
Write your own postcard or add some features! You can find the repository here: https://gitlab.com/schubisu/postcard.
Transitioning to Windows
So, recently I started using windows for work. Why? There are a couple of reasons, one that I needed to use MSVC, that is the Microsoft Visual C++ toolchain and the other being, I wasn’t quite comfortable to ifdef stuff for making it work on GCC aka, the GNU counterpart of MSVC.
Krita Weekly #14
After an anxious month, I am writing a Krita Weekly again and probably this would be my last one too, though I hope not. Let’s start by talking about bugs. Unlike the trend going about the last couple of months, the numbers have taken a serious dip.
Bikeshedding
http://bikeshed.org/
What color should I paint the bike-shed?
Handling nested serializer validations in Django Rest Framework
I understand that the title of this post is a little confusing. Recently, while working on the Projects API in Weblate, I came across an interesting issue. The Projects API in Weblate allowed you to get an attribute called source_language. Every project has only one source_language and in the API, it was a read-only property.
{
"name": "master_locales",
"slug": "master_locales",
"web": "https://example.site",
"source_language": {
"code": "en",
"name": "English",
"direction": "ltr",
"web_url": "http:/example.site/languages/en/",
"url": "http://example.site/api/languages/en/"
},
"web_url": "http://example.site/projects/master_locales/",
"url": "http://example.site/api/projects/master_locales/",
"components_list_url": "http://example.site/api/projects/master_locales/components/",
"repository_url": "http://example.site/api/projects/master_locales/repository/",
"statistics_url": "http://example.site/api/projects/master_locales/statistics/",
"changes_list_url": "http://example.site/api/projects/master_locales/changes/",
"languages_url": "http://example.site/api/projects/master_locales/languages/"
}
As you can see, unlike the other relational fields, it's not a HyperLinkedIdentityField. It uses the nested language serializer to show all the attributes of the source_language.
Now, previously, when a project was created via API, a default language was always assigned to the project and there was no way to define the source_language while creating the project via API.
Problem?
Doing GET on Language Serializer when sending POST on Project Serializer
So we needed to add the feature to define the source_language of the project when we send a POST request to the Project API. And also edit the project via API to update the source_language. So, to use the same serializer, the request body for the POST request would look something like this:
{
"name": "master_locales",
"slug": "master_locales",
"web": "https://example.site",
"source_language": {
"code": "ru",
"name": "Russian",
"direction": "ltr",
}
}
Now, in general, we would have a python serializer like this:
class LanguageSerializer(serializers.ModelSerializer):
class Meta:
model = Language
fields = ("code", "name", "direction", "web_url", "url")
extra_kwargs = {
"url": {"view_name": "api:language-detail", "lookup_field": "code"}
}
class ProjectSerializer(serializers.ModelSerializer):
source_language = LanguageSerializer(required=False)
# ...
# Other parts of the serializer
The problem with having code like this is, when the ProjectSerializer gets a request like shown above and tries to validate the data in the request, it also validates the LanguageSerializer part. The LanguageSerializer part whenever it gets data, it will automatically try to validate the data. The code property of Language model has a unique constraint. So, when LanguageSerializer tries to validate
{
"code": "ru",
"name": "Russian",
"direction": "ltr",
}
it will throw an error "This field must be unique" for code property in case a language with codename ru already exists in the database.
Solution
So there are few steps to get this done.
Remove validators from code field
extra_kwargs = {
"url": {"view_name": "api:language-detail", "lookup_field": "code"},
"code": {"validators": []},
}
Add "code": {"validators": []} to the extra_kwargs to remove the validator from the LanguageSerializer on every data request it receives.
Add manual validation for code field
Removing validator will also remove the validation while doing POST request. Now, the LanguageSerializer in Weblate specifically doesn't support POST, but in any case, you would manually need to add a validation function to the LanguageSerializer so if someone checks for validity before adding language, it throws an error. To do that, add a function validate_code like this:
def validate_code(self, value):
check_query = Language.objects.filter(code=value)
if check_query.exists() and not (
isinstance(self.parent, ProjectSerializer)
and self.field_name == "source_language"
):
raise serializers.ValidationError(
"Language with this Language code already exists."
)
if not check_query.exists():
raise serializers.ValidationError(
)
return value
Note: The name of the function must be validate_{field_name} when you are trying to validate a field based on how DRF handles validation.
Overwrite create() in ProjectSerializer
Finally, we would want to overwrite the create() function of ProjectSerializer to:
• Validate source_language data using the above validation to check if the language with that code exists
• Modify source_language key of the validated_data to have the Language model object rather than the dictionary, so it can be used to create a project with the foreign key.
• Lastly, create a project with the new validata_data
The code would look something like this:
def create(self, validated_data):
source_language_validated = validated_data.get("source_language")
if source_language_validated:
validated_data["source_language"] = Language.objects.get(
code=source_language_validated.get("code")
)
project = Project.objects.create(**validated_data)
return project
And now, if you create a project, using the source_language key, you can define the source language for the project while using the Project API. There might be several other ways to go about it. But this is one of the ways I found works.
Also, this feature is now live in Weblate 4.* versions which allows you to define the source_language via the API.
git config
Git comes with this handy tool that let’s you manage your Git configuration with ease. Configuration Levels --local (Default) Local configuration values are stored and managed at the repository level. The values are stored in a file found in the repo’s .git directory: .git/config If you are planning to set some configuration only to be used by the specific repo you are in, then go ahead with using --local.
Creating Custom Whoosh Plugin
Recently, while trying to work on a query parser feature in Weblate, I came across this search engine library called Whoosh. It provides certain nice features like indexing of text, parsing of search queries, scoring algorithms, etc. One good thing about this library is most of these features are customizable and extensible.
Now, the feature I was trying to implement is an exact search query. An exact search query would behave in a way such that the backend would search for an exact match of any query text provided to it instead of the normal substring search. Whoosh provides a plugin for regex, which can be accessed via whoosh.qparser.RegexPlugin(). So we can technically go about writing a regex to do the exact match. But a regex search will have worse performance than a simple string comparison.
So, one of the ways of doing a new kind of query parsing is creating a custom whoosh plugin. And that's what this blog is going to be about.
Simple Whoosh Plugin
In some cases, you will probably not need a complicated plugin, but just want to extend the feature of an existing plugin to match a different kind of query. For example, let's say you want to extend the ability of SingleQuotePlugin to parse queries wrapped in either single-quotes or double-quotes.
class QuotePlugin(whoosh.qparser.SingleQuotePlugin):
"""Single and double quotes to specify a term."""
expr = r"(^|(?<=\W))['\"](?P<text>.*?)['\"](?=\s|\]|[)}]|$)" In the above example, QuotePlugin extends the already existing SingleQuotePlugin class. It just overrides the expression to parse the query. The expression, mentioned in the variable expr is usually a regex expression with ?P<text> part denoting the TermQuery. A TermQuery is the final term/terms searched for in the database. So in the above regex, we say to parse any query such that the TermQuery is wrapped in between single-quotes or double-quotes. Query Class A query class is the class, whose instance the final parsed term will be. Unless otherwise mentioned, it's usually <Term>. So if we want our plugin to parse the query and show it as an instance of a custom class, we need to define a custom query class. class Exact(whoosh.query.Term): """Class for queries with exact operator.""" pass So, as you can say, we can just have a simple class just extending whoosh.query.Term so that while checking the parsed terms, we can get is as an instance of Exact. That will help us differentiate the query from a normal Term instance. Custom Whoosh Plugin After writing the query class, we will need to write the custom plugin class. class ExactPlugin(whoosh.qparser.TaggingPlugin): """Exact match plugin with quotes to specify an exact term.""" class ExactNode(whoosh.qparser.syntax.TextNode): qclass = Exact def r(self): return "Exact %r" % self.text expr = r"\=(^|(?<=\W))(['\"]?)(?P<text>.*?)\2(?=\s|\]|[)}]|$)"
nodetype = ExactNode
In the above example, unlike the simple case, we extend TaggingPlugin instead of any other pre-defined plugin. Most of the pre-defined plugins in whoosh also extend TaggingPlugin. So it is a good fit as a parent class.
Then, we create a ExactNode class. This we will assign to the node type for the custom plugin. A node type class basically defines the query class to be used in this custom plugin, along with various representations and properties of the parsed node. qclass will have the query class created before to denote the Exact instance to the final parsed term.
Apart from that, we have the expr which contains the regex just like in the simple example to parse the query term.
Finally...
After creating the custom plugin, you can:
• add this plugin to the list of plugins defined in the whoosh query parser class
• use the query class to make an isinstance() check when making database queries
• check for the node type in the different nodes used by the parser
Using Docker with Ansible
[Published in Open Source For You (OSFY) magazine, October 2017 edition.]
This article is the eighth in the DevOps series. In this issue, we shall learn to set up Docker in the host system and use it with Ansible.
Introduction
Docker provides operating system level virtualisation in the form of containers. These containers allow you to run standalone applications in an isolated environment. The three important features of Docker containers are isolation, portability and repeatability. All along we have used Parabola GNU/Linux-libre as the host system, and executed Ansible scripts on target Virtual Machines (VM) such as CentOS and Ubuntu.
Docker containers are extremely lightweight and fast to launch. You can also specify the amount of resources that you need such as CPU, memory and network. The Docker technology was launched in 2013, and released under the Apache 2.0 license. It is implemented using the Go programming language. A number of frameworks have been built on top of Docker for managing these cluster of servers. The Apache Mesos project, Google’s Kubernetes, and the Docker Swarm project are popular examples. These are ideal for running stateless applications and help you to easily scale them horizontally.
Setup
The Ansible version used on the host system (Parabola GNU/Linux-libre x86_64) is 2.3.0.0. Internet access should be available on the host system. The ansible/ folder contains the following file:
ansible/playbooks/configuration/docker.yml
Installation
The following playbook is used to install Docker on the host system:
---
- name: Setup Docker
hosts: localhost
gather_facts: true
become: true
tags: [setup]
- name: Update the software package repository
pacman:
update_cache: yes
- name: Install dependencies
package:
name: "{{ item }}"
state: latest
with_items:
- python2-docker
- docker
- service:
name: docker
state: started
- name: Run the hello-world container
docker_container:
name: hello-world
image: library/hello-world
The Parabola package repository is updated before proceeding to install the dependencies. The python2-docker package is required for use with Ansible. Hence, it is installed along with the docker package. The Docker daemon service is then started and the library/hello-world container is fetched and executed. A sample invocation and execution of the above playbook is shown below:
$ansible-playbook playbooks/configuration/docker.yml -K --tags=setup SUDO password: PLAY [Setup Docker] ************************************************************* TASK [Gathering Facts] ********************************************************** ok: [localhost] TASK [Update the software package repository] *********************************** changed: [localhost] TASK [Install dependencies] ***************************************************** ok: [localhost] => (item=python2-docker) ok: [localhost] => (item=docker) TASK [service] ****************************************************************** ok: [localhost] TASK [Run the hello-world container] ******************************************** changed: [localhost] PLAY RECAP ********************************************************************** localhost : ok=5 changed=2 unreachable=0 failed=0 With verbose ’-v’ option to ansible-playbook, you will see an entry for LogPath, such as /var/lib/docker/containers//-json.log. In this log file you will see the output of the execution of the hello-world container. This output is the same when you run the container manually as shown below: $ sudo docker run hello-world
Hello from Docker!
This message shows that your installation appears to be working correctly.
To generate this message, Docker took the following steps:
1. The Docker client contacted the Docker daemon.
2. The Docker daemon pulled the "hello-world" image from the Docker Hub.
3. The Docker daemon created a new container from that image which runs the
executable that produces the output you are currently reading.
4. The Docker daemon streamed that output to the Docker client, which sent it
To try something more ambitious, you can run an Ubuntu container with:
$docker run -it ubuntu bash Share images, automate workflows, and more with a free Docker ID: https://cloud.docker.com/ For more examples and ideas, visit: https://docs.docker.com/engine/userguide/ Example A Deep Learning (DL) Docker project is available (https://github.com/floydhub/dl-docker) with support for frameworks, libraries and software tools. We can use Ansible to build the entire DL container from the source code of the tools. The base OS of the container is Ubuntu 14.04, and will include the following software packages: • Tensorflow • Caffe • Theano • Keras • Lasagne • Torch • iPython/Jupyter Notebook • Numpy • SciPy • Pandas • Scikit Learn • Matplotlib • OpenCV The playbook to build the DL Docker image is given below: - name: Build the dl-docker image hosts: localhost gather_facts: true become: true tags: [deep-learning] vars: DL_BUILD_DIR: "/tmp/dl-docker" DL_DOCKER_NAME: "floydhub/dl-docker" tasks: - name: Download dl-docker git: repo: https://github.com/saiprashanths/dl-docker.git dest: "{{ DL_BUILD_DIR }}" - name: Build image and with buildargs docker_image: path: "{{ DL_BUILD_DIR }}" name: "{{ DL_DOCKER_NAME }}" dockerfile: Dockerfile.cpu buildargs: tag: "{{ DL_DOCKER_NAME }}:cpu" We first clone the Deep Learning docker project sources. The docker_image module in Ansible helps us to build, load and pull images. We then use the Dockerfile.cpu file to build a Docker image targeting the CPU. If you have a GPU in your system, you can use the Dockerfile.gpu file. The above playbook can be invoked using the following command: $ ansible-playbook playbooks/configuration/docker.yml -K --tags=deep-learning
Depending on the CPU and RAM you have, it will take considerable amount of time to build the image with all the software. So be patient!
Jupyter Notebook
The built dl-docker image contains Jupyter notebook which can be launched when you start the container. An Ansible playbook for the same is provided below:
- name: Start Jupyter notebook
hosts: localhost
gather_facts: true
become: true
tags: [notebook]
vars:
DL_DOCKER_NAME: "floydhub/dl-docker"
- name: Run container for Jupyter notebook
docker_container:
name: "dl-docker-notebook"
image: "{{ DL_DOCKER_NAME }}:cpu"
state: started
command: sh run_jupyter.sh
You can invoke the playbook using the following command:
$ansible-playbook playbooks/configuration/docker.yml -K --tags=notebook The Dockerfile already exposes the port 8888, and hence you do not need to specify the same in the above docker_container configuration. After you run the playbook, using the ‘docker ps’ command on the host system, you can obtain the container ID as indicated below: $ sudo docker ps
CONTAINER ID IMAGE COMMAND CREATED STATUS PORTS NAMES
a876ad5af751 floydhub/dl-docker:cpu "sh run_jupyter.sh" 11 minutes ago Up 4 minutes 6006/tcp, 8888/tcp dl-docker-notebook
You can now login to the running container using the following command:
$sudo docker exec -it a876 /bin/bash You can then run an ‘ifconfig’ command to find the local IP address (“172.17.0.2” in this case), and then open http://172.17.0.2:8888 in a browser on your host system to see the Jupyter Notebook. A screenshot is shown in Figure 1: TensorBoard TensorBoard consists of a suite of visualization tools to understand the TensorFlow programs. It is installed and available inside the Docker container. After you login to the Docker container, at the root prompt, you can start Tensorboard by passing it a log directory as shown below: # tensorboard --logdir=./log You can then open http://172.17.0.2:6006/ in a browser on your host system to see the Tensorboard dashboard as shown in Figure 2: Docker Image Facts The docker_image_facts Ansible module provides useful information about a Docker image. We can use it to obtain the image facts for our dl-docker container as shown below: - name: Get Docker image facts hosts: localhost gather_facts: true become: true tags: [facts] vars: DL_DOCKER_NAME: "floydhub/dl-docker" tasks: - name: Get image facts docker_image_facts: name: "{{ DL_DOCKER_NAME }}:cpu" The above playbook can be invoked as follows: $ ANSIBLE_STDOUT_CALLBACK=json ansible-playbook playbooks/configuration/docker.yml -K --tags=facts
The ANSIBLE_STDOUT_CALLBACK environment variable is set to ‘json’ to produce a JSON output for readability. Some important image facts from the invocation of the above playbook are shown below:
"Architecture": "amd64",
"Author": "Sai Soundararaj <saip@outlook.com>",
"Config": {
"Cmd": [
"/bin/bash"
],
"Env": [
"PATH=/root/torch/install/bin:/root/caffe/build/tools:/root/caffe/python:/usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/sbin:/bin",
"CAFFE_ROOT=/root/caffe",
"PYCAFFE_ROOT=/root/caffe/python",
"PYTHONPATH=/root/caffe/python:",
"LUA_PATH=/root/.luarocks/share/lua/5.1/?.lua;/root/.luarocks/share/lua/5.1/?/init.lua;/root/torch/install/share/lua/5.1/?.lua;/root/torch/install/share/lua/5.1/?/init.lua;./?.lua;/root/torch/install/share/luajit-2.1.0-beta1/?.lua;/usr/local/share/lua/5.1/?.lua;/usr/local/share/lua/5.1/?/init.lua",
"LD_LIBRARY_PATH=/root/torch/install/lib:",
"DYLD_LIBRARY_PATH=/root/torch/install/lib:"
],
"ExposedPorts": {
"6006/tcp": {},
"8888/tcp": {}
},
"Created": "2016-06-13T18:13:17.247218209Z",
"DockerVersion": "1.11.1",
"Os": "linux",
"task": { "name": "Get image facts" }
You are encouraged to read the ‘Getting Started with Docker’ user guide available at http://docs.ansible.com/ansible/latest/guide_docker.html to know more about using Docker with Ansible.
Testing the next-gen pip dependency resolver
This is an attempt to summarize the broader software architecture around dependency resolution in pip and how testing is being done around this area.
The motivation behind writing this, is to make sure all the developers working on this project are on the same page, and to have a written record about the state of affairs.
Architecture
The “legacy” resolver in pip, is implemented as part of pip’s codebase and has been a part of it for many years. It’s very tightly coupled with the existing code, isn’t easy to work with and has severe backward compatibility concerns with modifying directly – which is why we’re implementing a separate “new” resolver in this project, instead of trying to improve the existing one.
The “new” resolver that is under development, is not implemented as part of pip’s codebase; not completely anyway. We’re using an abstraction that separates all the metadata-generation-and-handling stuff vs the core algorithm. This allows us to work on the core algorithm logic (i.e. the NP-hard search problem) separately from pip-specific logic (eg. download, building etc). The abstraction and core algorithm are written/maintained in https://github.com/sarugaku/resolvelib right now. The pip-specific logic for implementing the “other side” of the abstraction is in https://github.com/pypa/pip/tree/master/src/pip/_internal/resolution/resolvelib.
Testing
In terms of testing, we have dependency-resolution-related tests in both resolvelib and pip.
resolvelib
The tests in resolvelib are intended more as “check if the algorithm does things correctly” and even contains tests that are agnostic to the Python ecosystem (eg. we’ve borrowed tests from Ruby, Swift etc). The goal here is to make sure that the core algorithm we implement is capable of generating correct answers (for example: not getting stuck in looping on the same “requirement”, not revisiting rejected nodes etc).
pip
The tests in pip is where I’ll start needing more words to explain what’s happening. :)
YAML-based tests
We have “YAML” tests which I’d written back in 2017, as a format to easily write tests for pip’s new resolver when we implement it. However, since we didn’t have a need for it to be working completely back then (there wasn’t a new resolver to test with it!), the “harness” for running these tests isn’t complete and would likely need some work to be as feature complete as we’d want it to be, for writing good tests.
“new” resolver tests
unit tests
We have some unit tests for the new resolver implementation. These cover very basic “sanity checks” to ensure it follows the “contract” of the abstraction, like “do the candidates returned by a requirement actually satisfy that requirement?”. These likely don’t need to be touched, since they’re fairly well scoped and test fairly low-level details (i.e. ideal for unit tests).
New resolver unit tests: https://github.com/pypa/pip/tree/master/tests/unit/resolution_resolvelib
functional tests
We also have “new resolver functional tests”, which are written as part of the current work. These exist since how-to-work-with-YAML-tests was not an easy question to answer and there needs to be work done (both on the YAML format, as well as the YAML test harness) to flag which tests should run with which resolver (both, only legacy, only new) and make it possible to put run these tests in CI easily.
New resolver functional tests: https://github.com/pypa/pip/blob/master/tests/functional/test_new_resolver.py
test_install*.py
These files test all the functionality of the install command (like: does it use the right build dependencies, does it download the correct files, does it write the correct metadata etc). There might be some dependency-resolution-related tests in test_install*.py files.
These files contain a lot of tests so, ideally, at some point, someone would go through and de-duplicate tests from this as well.
How can you help?
If you use pip, there are a multiple ways that you can help us!
• First and most fundamentally, please help us understand how you use pip by talking with our user experience researchers. You can do this right now! You can take a survey, or have a researcher interview you over a video call. Please sign up and spread the word to anyone who uses pip (even a little bit).
• Right now, even before we release the new resolver as a beta, you can help by running pip check on your current environment. This will report if you have any inconsistencies in your set of installed packages. Having a clean installation will make it much less likely that you will hit issues when the new resolver is released (and may address hidden problems in your current environment!). If you run pip check and run into stuff you can’t figure out, please ask for help in our issue tracker or chat.
Thanks to Paul Moore and Tzu-Ping for help in reviewing and writing this post, as well as Sumana Harihareswara for suggesting to put this up on my blog!
OSS Work update #8
I’m trying to post these roughly once a month. Here’s the January post.
I am working on open source projects, as part of an internship at FOSSEE and as a part of grant-funded work on pip’s dependency resolver.
Work I did (Jan 6 - Feb 5)
Technical
• Co-worked with another developer, in person, for 1 week, on pip!
• Triaged pip’s issue tracker (a lot).
• Spend some time improving pip’s test suite infrastructure.
• Investigated Python 2 usage, to identify anomalies.
• Helped with virtualenv 20.0 release (kinda!).
• Invested effort to improve pip’s test suite
• Helped aggregate test cases for pip’s next generation resolver.
Communication
• Managed the pip 20.0 release fiasco.
• Helped the UX folks get started with working on pip.
January has been a very productive month.
Most of the challenges have been the logistics around work, not the work as such.
My health has been pretty good and there’s a certain flow to my work that I’m enjoying now. Turns out, if you like what you’re doing, you tend to be pretty productive! :)
As long as I remember to push my blog posts to the repository, they’ll actually go live on the day they’re supposed to.
Goals for February 2020
Technical
• Internal Cleansing: AKA Technical debt down payment.
• Issue triage: Triage a fair number of issues on pip’s issue tracker.
• Technical Documentation: improving pip’s technical documentation, for contributors and developers
Communication
• Help all the other contractors to get up to “full speed” for working on pip
• Get PyPA to participate in GSoC 2020
• Python Packaging Summit at PyCon US 2020: help organization.
• Move forward on Python Packaging Governance
None.
Help us
How can you help us?
• provide test cases where the latest released version of pip (19.3.1, at the time of writing) fails to resolve dependencies properly (on zazo’s issue tracker). They will help us design and test the new resolver.
• talk with your company about becoming a PSF sponsor. The Fundable Packaging Improvements page lists fairly well-scoped projects that would happen much faster if we get funding to achieve them.
• Have an interview with our UX expert, who is working to improve usability of Python Packaging tooling.
"isn't a title of this post" isn't a title of this post
[NOTE: This post originally appeared on deepsource.io, and has been posted here with due permission.]
In the early part of the last century, when David Hilbert was working on stricter formalization of geometry than Euclid, Georg Cantor had worked out a theory of different types of infinities, the theory of sets. This theory would soon unveil a series of confusing paradoxes, leading to a crisis in the Mathematics community regarding the stability of the foundational principles of the math of that time.
Central to these paradoxes was the Russell’s paradox (or more generally, as we’d talk about later, the Epimenides Paradox). Let’s see what it is.
In those simpler times, you were allowed to define a set if you could describe it in English. And, owing to mathematicians’ predilection for self-reference, sets could contain other sets.
Russell then, came up with this:
$$R$$ is a set of all the sets which do not contain themselves.
The question was "Does $$R$$ contain itself?" If it doesn’t, then according to the second half of the definition it should. But if it does, then it no longer meets the definition.
The same can symbolically be represented as:
Let $$R = \{ x \mid x \not \in x \}$$, then $$R \in R \iff R \not \in R$$
Cue mind exploding.
“Grelling’s paradox” is a startling variant which uses adjectives instead of sets. If adjectives are divided into two classes, autological (self-descriptive) and heterological (non-self-descriptive), then, is ‘heterological’ heterological? Try it!
Or, the so-called Liar Paradox was another such paradox which shred apart whatever concept of ‘computability’ was, at that time - the notion that things could either be true or false.
Epimenides was a Cretan, who made one immortal statement:
“All Cretans are liars.”
If all Cretans are liars, and Epimenides was a Cretan, then he was lying when he said that “All Cretans are liars”. But wait, if he was lying then, how can we ‘prove’ that he wasn’t lying about lying? Ein?
This is what makes it a paradox: A statement so rudely violating the assumed dichotomy of statements into true and false, because if you tentatively think it’s true, it backfires on you and make you think that it is false. And a similar backfire occurs if you assume that the statement is false. Go ahead, try it!
If you look closely, there is one common culprit in all of these paradoxes, namely ‘self-reference’. Let’s look at it more closely.
Strange Loopiness
If self-reference, or what Douglas Hofstadter - whose prolific work on the subject matter has inspired this blog post - calls ‘Strange Loopiness’ was the source of all these paradoxes, it made perfect sense to just banish self-reference, or anything which allowed it to occur. Russell and Whitehead, two rebel mathematicians of the time, who subscribed to this point of view, set forward and undertook the mammoth exercise, namely “Principia Mathematica”, which we as we will see in a little while, was utterly demolished by Gödel’s findings.
The main thing which made it difficult to ban self-reference was that it was hard to pin point where exactly did the self-reference occur. It may as well be spread out over several steps, as in this ‘expanded’ version of Epimenides:
The next statement is a lie.
The previous statement is true.
Russell and Whitehead, in P.M. then, came up with a multi-hierarchy set theory to deal with this. The basic idea was that a set of the lowest ‘type’ could only contain ‘objects’ as members (not sets). A set of the next type could then only either contain objects, or sets of lower types. This, implicitly banished self-reference.
Since, all sets must have a type, a set ‘which contains all sets which are not members of themselves’ is not a set at all, and thus you can say that Russell’s paradox was dealt with.
Similarly, if an attempt is made towards applying the expanded Epimenides to this theory, it must fail as well, for the first sentence to make a reference to the second one, it has to be hierarchically above it - in which case, the second one can’t loop back to the first one.
Thirty one years after David Hilbert set before the academia to rigorously demonstrate that the system defined in Principia Mathematica was both consistent (contradiction-free) and complete (i.e. every true statement could be evaluated to true within the methods provided by P.M.), Gödel published his famous Incompleteness Theorem. By importing the Epimenides Paradox right into the heart of P.M., he proved that not just the axiomatic system developed by Russell and Whitehead, but none of the axiomatic systems whatsoever were complete without being inconsistent.
Clear enough, P.M. lost it’s charm in the realm of academics.
Before Gödel’s work too, P.M. wasn’t particularly loved as well.
Why?
It isn’t just limited to this blog post, but we humans, in general, have a diet for self-reference - and this quirky theory severely limits our ability to abstract away details - something which we love, not only as programmers, but as linguists too - so much so, that the preceding paragraph, “It isn’t … this blog … we humans …” would be doubly forbidden because the ‘right’ to mention ‘this blog post’ is limited only to something which is hierarchically above blog posts, ‘metablog-posts’. Secondly, me (presumably a human) belonging to the class ‘we’ can’t mention ‘we’ either.
Since, we humans, love self-reference so much, let’s discuss some ways in which it can be expressed in written form.
One way of making such a strange loop, and perhaps the ‘simplest’ is using the word ‘this’. Here:
• This sentence is made up of eight words.
• This sentence refers to itself, and is therefore useless.
• This blog post is so good.
• This sentence conveys you the meaning of ‘this’.
• This sentence is a lie. (Epimenides Paradox)
Another amusing trick for creating a self-reference without using the word ‘this sentence’ is to quote the sentence inside itself.
Someone may come up with:
The sentence ‘The sentence contains five words’ contains five words.
But, such an attempt must fail, for to quote a finite sentence inside itself would mean that the sentence is smaller than itself. However, infinite sentences can be self-referenced this way.
The sentence
"The sentence
"The sentence
...etc
...etc
is infinitely long"
is infinitely long"
is infinitely long"
There’s a third method as well, which you already saw in the title - the Quine method. The term ‘Quine’ was coined by Douglas Hofstadter in his book “Gödel Escher, Bach” (which heavily inspires this blog post). When using this, the self-reference is ‘generated’ by describing a typographical entity, isomorphic to the quine sentence itself. This description is carried in two parts - one is a set of ‘instructions’ about how to ‘build’ the sentence, and the other, the ‘template’ contains information about the construction materials required.
The Quine version of Epimenides would be:
“yields falsehood when preceded by it’s quotation” yields falsehood when preceded by it’s quotation
Before going on with ‘quining’, let’s take a moment and realize how awfully powerful our cognitive capacities are, and what goes in our head when a cognitive payload full of self-references is delivered - in order to decipher it, we not only need to know the language, but also need to work out the referent of the phrase analogous to ‘this sentence’ in that language. This parsing depends on our complex, yet totally assimilated ability to handle the language.
The idea of referring to itself is quite mind-blowing, and we keep doing it all the time — perhaps, why it feels so ‘easy’ for us to do so. But, we aren’t born that way, we grow that way. This could better be realized by telling someone much younger “This sentence is wrong.”. They’d probably be confused - What sentence is wrong?. The reason why it’s so simple for self-reference to occur, and hence allow paradoxes, in our language, is well, our language. It allows our brain to do the heavy lifting of what the author is trying to get through us, without being verbose.
Back to Quines.
Reproducing itself
Now, that we are aware of how ‘quines’ can manifest as self-reference, it would be interesting to see how the same technique can be used by a computer program to ‘reproduce’ itself.
To make it further interesting, we shall choose the language most apt for the purpose - brainfuck:
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Running that program above produces itself as the output. I agree, it isn’t the most descriptive program in the world, so written in Python below, is the nearest we can go to describe what’s happening inside those horrible chains of +’s and >’s:
THREE_QUOTES = '"' * 3
def eniuq(template): print(
f'{template}({THREE_QUOTES}{template}{THREE_QUOTES})')
eniuq("""THREE_QUOTES = '"' * 3
def eniuq(template): print(
f'{template}({THREE_QUOTES}{template}{THREE_QUOTES})')
eniuq""")
The first line generates """ on the fly, which marks multiline strings in Python.
Next two lines define the eniuq function, which prints the argument template twice - once, plain and then surrounded with triple quotes.
The last 4 lines cleverly call this function so that the output of the program is the source code itself.
Since we are printing in an order opposite of quining, the name of the function is ‘quine’ reversed -> eniuq (name stolen from Hofstadter again)
Remember the discussion about how self-reference capitalizes on the processor? What if ‘quining’ was a built-in feature of the language, providing what we in programmer lingo call ‘syntactic sugar’?
Let’s assume that an asterisk, * in the brainfuck interpreter would copy the instructions before executing them, what would then be the output of the following program?
*
It’d be an asterisk again. You could make an argument that this is silly, and should be counted as ‘cheating’. But, it’s the same as relying on the processor, like using “this sentence” to refer to this sentence - you rely on your brain to do the inference for you.
What if eniuq was a builtin keyword in Python? A perfect self-rep was then just be a call away:
eniuq('eniuq')
What if quine was a verb in the English language? We could reduce a lot of explicit cognitive processes required for inference. The Epimenides paradox would then be:
“yields falsehood if quined” yields falsehood if quined
Now, that we are talking about self-rep, here’s one last piece of entertainment for you.
The Tupper’s self-referential formula
This formula is defined through an inequality:
$${1 \over 2} < \left\lfloor \mathrm{mod}\left(\left\lfloor {y \over 17} \right\rfloor 2^{-17 \lfloor x \rfloor - \mathrm{mod}(\lfloor y\rfloor, 17)},2\right)\right\rfloor$$
If you take that absurd thing above, and move around in the cartesian plane for the coordinates $$0 \le x \le 106, k \le y \le k + 17$$, where $$k$$ is a 544 digit integer (just hold on with me here), color every pixel black for True, and white otherwise, you'd get:
This doesn't end here. If $$k$$ is now replaced with another integer containing 291 digits, we get yours truly:
TeX User Group Conference 2019, Palo Alto
The Tex User Group 2019 conference was held between August 9-11, 2019 at Sheraton Palo Alto Hotel, in Palo Alto, California.
I wanted to attend TUG 2019 for two main reasons - to present my work on the “XeTeX Book Template”, and also to meet my favourite computer scientist, Prof. Donald Knuth. He does not travel much, so, it was one of those rare opportunities for me to meet him in person. His creation of the TeX computer typesetting system, where you can represent any character mathematically, and also be able to program and transform it is beautiful, powerful and the best typesetting software in the world. I have been using TeX extensively for my documentation and presentations over the years.
Day I
I reached the hotel venue only in the afternoon of Friday, August 9, 2019, as I was also visiting Mountain View/San Jose on official work. I quickly checked into the hotel and completed my conference registration formalities. When I entered the hall, Rishi T from STM Document Engineering Private Limited, Thiruvananthapuram was presenting a talk on “Neptune - a proofing framework for LaTeX authors”. His talk was followed by an excellent poetic narration by Pavneet Arora, who happened to be a Vim user, but, also mentioned that he was eager to listen to my talk on XeTeX and GNU Emacs.
After a short break, Shreevatsa R, shared his experiences on trying to understand the TeX source code, and the lessons learnt in the process. It was a very informative, user experience report on the challenges he faced in navigating and learning the TeX code. Petr Sojka, from Masaryk University, Czech Republic, shared his students’ experience in using TeX with a detailed field report. I then proceeded to give my talk on the “XeTeX Book Template” on creating multi-lingual books using GNU Emacs and XeTeX. It was well received by the audience. The final talk of the day was by Jim Hefferon, who analysed different LaTeX group questions from newbies and in StackExchange, and gave a wonderful summary of what newbies want. He is a professor of Mathematics at Saint Michael’s College, and is well-known for his book on Linear Algebra, prepared using LaTeX. It was good to meet him, as he is also a Free Software contributor.
The TUG Annual General Meeting followed with discussions on how to grow the TeX community, the challenges faced, membership fees, financial reports, and plan for the next TeX user group conference.
Day II
The second day of the conference began with Petr Sojka and Ondřej Sojka presenting on “The unreasonable effectiveness of pattern generation”. They discussed the Czech hyphenation patterns along with a pattern generation case study. This talk was followed by Arthur Reutenauer presenting on “Hyphenation patterns in TeX Live and beyond”. David Fuchs, a student who worked with Prof. Donald Knuth on the TeX project in 1978, then presented on “What six orders of magnitude of space-time buys you”, where he discussed the design trade-offs in TeX implementation between olden days and present day hardware.
After a short break, Tom Rokicki, who was also a student at Stanford and worked with Donald Knuth on TeX, gave an excellent presentation on searching and copying text in PDF documents generated by TeX for Type-3 bitmap fonts. This session was followed by Martin Ruckert’s talk on “The design of the HINT file format”, which is intended as a replacement of the DVI or PDF file format for on-screen reading of TeX output. He has also authored a book on the subject - “HINT: The File Format: Reflowable Output for TeX”. Doug McKenna had implemented an interactive iOS math book with his own TeX interpreter library. This allows you to dynamically interact with the typeset document in a PDF-free ebook format, and also export the same. We then took a group photo:
I then had to go to Stanford, so missed the post-lunch sessions, but, returned for the banquet dinner in the evening. I was able to meet and talk with Prof. Donald E. Knuth in person. Here is a memorable photo!
He was given a few gifts at the dinner, and he stood up and thanked everyone and said that “He stood on the shoulders of giants like Isaac Newton and Albert Einstein.”
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I had a chance to meet a number of other people who valued the beauty, precision and usefulness of TeX. Douglas Johnson had come to the conference from Savannah, Georgia and is involved in the publishing industry. Rohit Khare, from Google, who is active in the Representational State Transfer (ReST) community shared his experiences with typesetting. Nathaniel Stemen is a software developer at Overleaf, which is used by a number of university students as an online, collaborative LaTeX editor. Joseph Weening, who was also once a student to Prof. Donald Knuth, and is at present a Research Staff member at the Institute for Defense Analyses Center for Communications Research in La Jolla, California (IDA/CCR-L) shared his experiences in working with the TeX project.
Day III
The final day of the event began with Antoine Bossard talking on “A glance at CJK support with XeTeX and LuaTeX”. He is an Associate Professor of the Graduate School of Science, Kanagawa University, Japan. He has been conducting research regarding Japanese characters and their memorisation. This session was followed by a talk by Jaeyoung Choi on “FreeType MF Module 2: Integration of Metafont and TeX-oriented bitmap fonts inside FreeType”. Jennifer Claudio then presented the challenges in improving Hangul to English translation.
After a short break, Rishi T presented “TeXFolio - a framework to typeset XML documents using TeX”. Boris Veytsman then presented the findings on research done at the College of Information and Computer Science, University of Massachusetts, Amherst on “BibTeX-based dataset generation for training citation parsers”. The last talk before lunch was by Didier Verna on “Quickref: A stress test for Texinfo”. He teaches at École Pour l’Informatique et les Techniques Avancées, and is a maintainer of XEmacs, Gnus and BBDB. He also an avid Lisper and one of the organizers of the European Lisp Symposium!
After lunch, Uwe Ziegenhagen demonstrated on using LaTeX to prepare and automate exams. This was followed by a field report by Yusuke Terada, on how they use TeX to develop a digital exam grading system at large scale in Japan. Chris Rowley, from the LaTeX project, then spoke on “Accessibility in the LaTeX kernel - experiments in tagged PDF”. Ross Moore joined remotely for the final session of the day to present on “LaTeX 508 - creating accessible PDFs”. The videos of both of these last two talks are available online.
A number of TeX books were made available for free for the participants, and I grabbed quite a few, including a LaTeX manual written by Leslie Lamport. Overall, it was a wonderful event, and it was nice to meet so many like-minded Free Software people.
A special thanks to Karl Berry, who put in a lot of effort in organizing the conference, but, could not make it to due to a car accident.
The TeX User Group Conference in 2020 is scheduled to be held at my alma mater, Rochester Institute of Technology.
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Happy Birthday Dear me!
A panegyric about my mentor, Omar Bhai
I was still up at this unearthly hour, thinking about life for a while now - fumbled thoughts about where I had come, where I started, and quite expectedly, Omar Bhai, your name popped in.
The stream continued. I started thinking about everything I’ve learned from you and was surprised with merely the sheer volume of thoughts that followed. I felt nostalgic!
I made a mental note to type this out the next day.
I wanted to do this when we said our final goodbyes and you left for the States, but thank God, I didn’t - I knew that I would miss you, but never could I have guessed that it would be so overwhelming - I would’ve never written it as passionately as I do today.
For those of you who don’t already know him, here’s a picture:
I’m a little emotional right now, so please bear with me.
You have been warned - the words “thank you” and “thanks” appear irritatingly often below. I tried changing, but none other has quite the same essence.
How do I begin thanking you?
Well, let’s start with this - thank you for kicking me on my behind, albeit civilly, whenever I would speak nuisance (read chauvinism). I can’t thank you enough for that!
I still can’t quite get how you tolerated the bigot I was and managed to be calm and polite. Thank You for teaching me what tolerance is!
Another thing which I learnt from you was what it meant to be privileged. I can no longer see things the way I used to, and this has made a huge difference. Thank You!
I saw you through your bad times and your good. The way you tackled problems, and how easy you made it look. Well, it taught me [drum roll] how to think (before acting and not the other way round). Thank You for that too!
And, thank you for buying me books, and even more so, lending away so many of them! and even more so, educating me about why to read books and how to read them. I love your collection.
You showed all of us, young folks, how powerful effective communication is. Thank You again for that! I know, you never agree on this, but you are one hell of a speaker. I’ve always been a fan of you and your puns.
I wasn’t preparing for the GRE, but I sat in your sessions anyways, just to see you speak. The way you connect with the audience is just brilliant.
For all the advice you gave me on my relationships with people - telling me to back off when I was being toxic and dragging me off when I was on the receiving side - I owe you big time. Thank You!
Also, a hearty thank you for making me taste the best thing ever - yes, fried cheese it is. :D
Thank You for putting your trust and confidence in me!
Thank you for all of this, and much more!
Yours Truly, Rahul
Some pending logs!
September 11, 2019
It’s been a very long time since I wrote here for the last.
The reason is nothing big but mainly because:
1. Apparently, I was not able to finish some tasks in time that I used to write about.
2. I was not well for a long time that could be an another reason .
3. Besides, life happened in many ways which ultimately left me working on some other things first, because they seemed to be *important* for the time.
And, yes, there is no denying the fact that I was procastinating too because writing seems to be really hard at most times.
Though I had worked on many things throughout the time and I’ll try to write them here as short and quick logs below.
• Around the second last week of august, I worked on setting up a self-hosted OpenVPN server which supported client scalability. The infrastructure required two servers/VMs, each having a basic firewall setup and a non-root “sudo” priviliged user. One among them was to host the OpenVPN service and another one was to serve as a Certificate Authority (CA). You can refer the following links to check for the related process.
• In the last week of August, I worked on another task i.e to read about Syslogs and figure out how each of the systems can email the root mails to a certain email address for log collection. Thus, I read about Syslogs, how it works, its format and various Syslogs message levels. The latter part of the task was accomplished using ssmtp as mail program & writing cron jobs to actually send them to the intended email addresses. Check the following links for resources.
This one question always came up, many times, the students managed to destroy their systems by doing random things. rm -rf is always one of the various commands in this regard.
Kushal Das
• While I was doing the above task, at one time I ruined my local system’s mail server configs and actually ended up doing something which kushal writes about in one of his recent post (quoted above). I was using the command rm -rf to clean some of the left-over dependencies of some mail packages, but that eventually resulted into machine being crashed. It was not the end of the mess this time. I made an another extremely big mistake meanwhile. I was trying to back up the crashed system, into an external hard disk using dd. But because I had never used dd before, so again I did something wrong and this time, I ended up losing ~500 GBs of backed up data. This is “the biggest mistake” and “the biggest lesson” I have learnt so far. (now I know why one should have multiple backups) And as there was absolutely no way of getting that much data back, the last thing I did was, formatting the hard-disk into 2 partitions, one with ext4 file system for linux backup and the other one as ntfs for everything else.
Thank you so much jasonbraganza for all the help and extremely useful suggestions during the time.
• Okay, now after all the hassle bustle above, I got something really nice. This time, I received the “Raspberry Pi 4, 4GB, Complete Kit ” from kushal.
Thank you very much kushal for the RPi and an another huge thanks for providing me with all the guidance and support that made me reach to even what I am today.
• During the same time, I attended a dgplug guest session from utkarsh2102. This session gave me a “really” good beginner’s insight of how things actually work in Debian Project. I owe a big thanks to utkarsh2102 as well, for he so nicely voluteered me from there onwards, to actually start with Debian project. I have started with DPMT and have done packaging 4 python modules so far. And now, I am looking forward to start contributing to Debian Ruby Team as well.
• With the start of september, I spent some time solving some basic Python problems from kushal’s lymworkbook. Those issues were related to some really simply sys-admins work. But for me, working around and wrapping them in Python was a whole lot of learning. I hope I will continue to solve some more problems/issues from the lab.
• And lastly (and currently), I am back to reading and implementing concepts from Ops School curriculum.
Voila, finally, I finish compiling up the logs from some last 20 days of work and other stuffs. (and thus, I am eventually finishing my long pending task of writing this post here as well).
I will definitely try to be more consistent with my writing from now onwards.
That’s all for now. o/
Why I prefer SSH for Git?
In my last blog, I quoted
I'm an advocate of using SSH authentication and connecting to services like Github, Gitlab, and many others.
On this, I received a bunch of messages over IRC asking why do I prefer SSH for Git over HTTPS.
I find the Github documentation quite helpful when it comes down to learning the basic operation of using Git and Github. So, what has Github to say about "SSH v/s HTTPS"?
Github earlier used to recommend using SSH, but they later changed it to HTTPS. The reason for the Github's current recommendation could be:
• Easily accessible: HTTPS in comparison to SSH is easily accessible. Why? You may ask. The reason is a lot of times SSH ports are blocked behind a firewall and the only option left for you might be HTTPS. This is a very common scenario I've seen in the Indian colleges and a few IT companies.
Why do I recommend SSH-way?
SSH keys provide Github with a way to trust a computer. For every machine that I have, I maintain a separate set of keys. I upload the public keys to Github or whichever Git-forge I'm using. I also maintain a separate set of keys for the websites. So, for example, if I have 2 machines and I use Github and Pagure then I end up maintaining 4 keys. This is like a 1-to-1 connection of the website and the machine.
SSH is secure until you end up losing your private key. If you do end up losing your key, even then you can just login using your username/password and delete the particular key from Github. I agree, that the attacker can do nasty things but that would be limited to repositories and you would have control of your account to quickly mitigate the problem.
On the other side, if you end up losing your Github username/password to an attacker, you lose everything.
I also once benefitted from using SSH with Github, but IMO, exposing that also exposes a vulnerability so I'll just keep it a secret :)
Also, if you are on a network that has SSH blocked, you can always tunnel it over HTTPS.
But, above all, do use 2-factor authentication that Github provides. It's an extra layer of security to your account.
If you have other thoughts on the topic, do let me know over twitter @yudocaa, or drop me an email.
Photo by Christian Wiediger on Unsplash
Increasing Postgres column name length
This blog is more like a bookmark for me, the solution was scavenged from internet. Recently I have been working on an analytics project where I had to generate pivot transpose tables from the data. Now this is the first time I faced the limitations set on postgres database. Since its a pivot, one of my column would be transposed and used as column names here, this is where things started breaking. Writing to postgres failed with error stating column names are not unique. After some digging I realized Postgres has a column name limitation of 63 bytes and anything more than that will be truncated hence post truncate multiple keys became the same causing this issue.
Next step was to look at the data in my column, it ranged from 20-300 characters long. I checked with redshift and Bigquery they had similar limitations too, 128 bytes. After looking for sometime found a solution, downloaded the postgres source, changed NAMEDATALEN to 301(remember column name length is always NAMEDATALEN – 1) src/include/pg_config_manual.h`, followed the steps from postgres docs to compile the source and install and run postgres. This has been tested on Postgres 9.6 as of now and it works.
Next up I faced issues with maximum number columns, my pivot table had 1968 columns and postgres has a limitation of 1600 total columns. According to this answer I looked into the source comments and that looked quite overwhelming . Also I do not have a control over how many columns will be there post pivot so no matter whatever value i set , in future i might need more columns, so instead I handled the scenario in my application code to split the data across multiple tables and store them.
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# Why would a random forest model be biased towards sensitivity/specificity?
I am training a random forest model using the sk-learn library, for a binary classification task. For some reason, when I set the max_depth parameter to 1, the model has an average 90% accuracy on predicting positive labels (sensitivity), but only around 30% when predicting negative class labels (specificity). When I increase max_depth, these two (sensitivity and specificity) begin to even out. I am unsure of the cause behind the skewed sensitivity, does anyone know of a possible explanation?
Note: My train and test data sets both have relatively even number of positive and negative examples
• When you adjust the max_depth parameter, you actually adjust the size of the trees. With a value of 1 you grow decision stumps (trees with only 2 leaves) which will always lead to poor performance, because RF trees need to be grown as deep as possible, see stats.stackexchange.com/questions/169357/… and stats.stackexchange.com/questions/173390/…). When you increase max_depth, I guess that not only pos/neg balances out but also that performance increases, right? Jul 18 '16 at 10:04
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ere le 60106 Call Toll Free: 800 -323 -2272 Illinois Call 312 -595 -0461 www. 657-660, 15-18 May 2011. Increased intracellular levels of α-synuclein are implicated in Parkinson's disease and related disorders and may be caused by alterations in the ubiquitin–proteasome system (UPS) or the autophagy–lysosomal pathway (ALP). Il est inhumain de se souvenir du codage de chacune des instructions d'un micro-processeur même simplifié à l'extrême comme le LC-3 et a fortiori encore plus pour un micro-processeur réel. Upon autophagy induction, LC3-I is sequentially modified by the E1-like enzyme Atg7 and the E2-like enzyme Atg3 to form LC3-II after the conjugation of LC3-I to. In animals, the contribution of autophagy and the UPS to antibacterial immunity is well documented and several bacteria have evolved measures to target and exploit these systems to the benefit of infection. Besides several theoretical concepts, brain circuits that. It all depends on: * The CPU architecture you're targeting, because each CPU family has its own set of mnemonic assembly language instructions, addressing modes, etc. LC3 Assembly Friday, 20 December 2013 use the stack to build a single-digit RPN (Reverse Polish Notation) multiplier: this is a very useful method of calculation in which the operands are pushed onto the stack first, followed by the operation to be performed on them. (IN LC3, Assmbly) Vector multiply: multiplies a number in one vector with the corresponding number in another vector. We found that JUNV infection induces an increment of the LC3-II/LC3-I ratio. LC3 assembly-how to count string length. org, a friendly and active Linux Community. 3, the amounts of LC3-II protein in the heart, caecal tonsil and bursa at different time points were analyzed by Western blotting. Finally, Salmonella and TRIM21 colocalise with the autophagosomal marker LC3, and intracellular defence is enhanced in starved cells suggesting an involvement of the autophagocytic pathway. If the condition is met, PC is updated as PC += immediate << 2. PC is the address of the conditional jump. dimanche 26 février 2017 Anyone know if there were any great differences between the Leyland 4/98 engine in my TLB and the 4/98 engines used the Leyland farm tractors like the 270? According to the specs I can find they are both the 4/98 NT. phage display to isolate peptides that possess bona fide LIR (LC3-interacting region) properties and are selective for individual mATG8 isoforms. If we are multipling two BCD numbers the Result is saved in AX register in HEXadecimal form. Assembly Language shift and rotate instructions summary. Autophagy and the ubiquitin-proteasome system (UPS) are two major protein degradation pathways implicated in the response to microbial infections in eukaryotes. Financial/Operational: Lockheed/General Electric contract October 16 1992 $165 million for 2 units- potential 5 units. causes LC3-II-conversion that reflects an induction of autophagy and that 1 and 10 mM of 2dG induced apoptosis associated with caspase-4 activation. Caching — algorithms with sequential comparisons take advantage of spatial locality and prefetching, which is good for caching. This is a nice example of a divide and conquer strategy – multiplication is repeated addition. Apply the algorithm described in Note 17 on the class page. Another approach: Add 100 to itself times. & 4'b1001 = 0 & 4'bx111 = x & 4'bz111 = x ~& 4'b1001 = 1 ~& 4'bx001 = 1. Division (input 1 in R0, input2 in R1, for division keep subtracting input1 with input2 and print out the remainder) 3. Provide details and share your research! But avoid … Asking for help, clarification, or responding to other answers. Practice: Associative property of multiplication. I'm sure that you recognize the first four operations as addition, subtraction, multiplication and division, but that the fifth one may be unfamiliar. Problem: multiply the value stored in R2 by 15 Fig 1. The immediate is a two complement value (to jump back eventually), so the range is from PC-2^17 to PC+2^17-4 or PC-40000h to PC+3fffch. So I have an LC3 coding assignment where we have to implement and test user subroutines for input and output of unsigned integers in decimal format. This example finishes after 8. Finally the factorial result is stored into memory location x4001 b. web; books; video; audio; software; images; Toggle navigation. The array in question is just a table holding the double–precision floating–point values equivalent to the first ten non–negative integers (0 through 9), as well as the value 10. Asm x86 segmentation fault in reading from file. Associative property of multiplication review. ENVIRONMENTAL PROTECTION AGENCY Office of Air and Waste Management Office of Air Quality Planning and Standards Research Triangle Park, North Carolina 27711. For this assignment you must implement the multiplication algorithm for the LC-3. You can also think of this theorem as the hypotenuse formula. Many microprocessors don't have a multiplication instruction, including the 6502. 40 Après la Terreur, le clergé français, toujours divisé depuis 1790, se rétablit avec, selon la formule de l’historien Paul Christophe, la volonté « de survivre34 ». The four ASCII adjust instructions, AAA, AAS, AAM, and AAD, can also be used with unpacked BCD representation. In LC3 program how to change operation (e. We found that JUNV infection induces an increment of the LC3-II/LC3-I ratio, an accumulation of punctate pattern in RFP-LC3-transfected cells and the colocalisation of viral nucleoprotein and LC3 protein, suggesting. In this study, we investigated the role of autophagy during Junín virus (JUNV) multiplication using human A549 cells. platelet derived growth factor Self proteins, such as interferon and interleukins, that induce fever are called ___ pyrogens. phagocytophilum is a Gram-negative obligate intracellular bacterium that causes human granulocytic anaplasmosis. Key enhancements to the previous generation include a twofold increase in DSP multiplication capacity, significantly higher. 35 BnF, Lc3 10, Annales de la religion, prospectus, mai 1795, p. • The feedback path comes from the Q output of the leftmost FF. 6 billion), to the multiplication by 1. Output Forming Logic. 15, open dinner in Friendship Room, 5:30-6:15pm; Session for outreach and encouragement, from 6:30-8:00pm. Dr Wagner's Animations of steps of HSV Infection and Replication. In ordinary mathematics, we sometimes express numbers in "scientific notation such as: 0. Inhibition of NOX2 and ROS enhances the conventional. fsubp %st, %st(7). Multiplying unsigned numbers in binary is quite easy. b = de2bi (d) converts a nonnegative decimal integer d to a binary row vector. It can really be viewed as 5 + 5 + 5 + 5. 2007 ) and acidify, thereby activating the. Group A Streptococcus Induces LAPosomes via SLO/β1 Integrin/NOX2/ROS Pathway in Endothelial Cells That Are Ineffective in Bacterial Killing and Suppress Xenophagy. Start studying Java An Introduction to Problem Solving and Programming Chapter 4 (PROGRAMMING PROJECTS). Skills: C Programming See more: i have 36 statements that i need entered into excel the maximum number of entries per statement is 86 rows and two columns one c, i need a c programmer, i need a c++ programmer, i need a matlab and c code is to be written, i need a matlab and c++ code is to be written, i need a programmer that knows c 11, i need an. Then the result holds since the function is then the constant function 0 and by L1, its limit is zero, which gives the required limit, since also. Multiplication In LC3 (input 1 In R0, Input 2 In R1) 2. After internalization of L. in transgenic mice because multiplication of the α-synuclein gene locus is known to increase α-synuclein Knockdown of LC3 or Atg7, two. Then we would like to make a combination of load cases LC1 +1. LC3-II (phosphatidyl ethanolamine-modified form of LC3) is stably associated with autophagosomal membranes and is therefore considered an autophagy-specific marker. For example, if the number was 12, you would end up with 10 and 2. ORIG x3000 mul10 ADD R0,R1,R1 ; R0 == 2*R1 ADD R0,R0,R0 ; R0 == 4*R1 ADD R0,R0,R1 ; R0 == 5*R1 ADD R0,R0,R0 ; R0 == 10*R1 HALT XOR registers R1 and R2. The Reduced Instruction Set of all chips in the ARM family - from the ARM2 to the StrongARM - includes weird and wonderful instructions like MLA (Multiply with Accumulate: multiply two registers and add the contents of a third to the result) and ASL (Arithmetic Shift Left: absolutely identical to the Logical Shift Left instruction). This suggests having a loop that repeats b times. Very late to this I realize, but if I was doing this in 16 bit x86 ASM, it would look something like this: softwareMultiply: ; INPUT CX,BX ; OUTPUT DX:AX - 32 bits ; CLOBBERS BX,CX,DI xor ax,ax ; cheap way to zero a reg mov dx,ax ; 1 clock faster than xor mov di,cx or di,bx ; cheap way to test for zero on both regs jz @done mov di,ax ; DI used for reg,reg adc @loop: shr cx,1 ; divide by two. In fact, ACC used to get zeroed out too at first, when I had my counter set to 16 - this was because the multiplication loop is supposed to iterate N times, where N is the number of bits that make up the numbers you're multiplying, and since the LC-3 is 16-bit addressable, I thought I'd set the counter to 16 bits. Easily share your publications and get them in front of Issuu’s. Precision. Practice. Hence there is a different letters for different Number Systems. Counting bits and printing result LC3 Assembly Tag: assembly , output , bit-shift , bits , lc3 I'm trying to write a simple program that takes a 16-bit integer from Data1, counts how many bits are 1-bits, and then prints the result to the screen. LC3 Assembly Friday, 20 December 2013 use the stack to build a single-digit RPN (Reverse Polish Notation) multiplier: this is a very useful method of calculation in which the operands are pushed onto the stack first, followed by the operation to be performed on them. These virus-induced compartments promote highly efficient genome replication, allow spatiotemporal coordination of the different steps of the viral. As an example, Fig 1 below represents multiplication at the level of register assignments as presented in class. Sign up or log in to view additional materials. Shift and Rotate Instructions Shifting means to move bits right and left inside an operand. In this lesson, you will learn to multiply. 7 times of MMS sent (43. B LC3 puncta were observed under the fluorescence microscope. 111110001001110010010110100000101100100000011011000 101000101100011111110110111101010001100101111000000 010001001000011101000010. You need to implement Booth's multiplication algorithm in LC-3 machine language or in LC-3 assembly language. Includes: - Intel i7 multi-core processor, 8 GB memory. LC3 Tutor is designed to help you get started quickly with the LC-3 (Little Computer 3) Assembly Language. Epub 2019 Dec 23. ” We have explained, small groups are the place where the rest of Christianity takes place – outside the walls of the weekend gatherings. 2-liter compression ignition engine operated with natural gas and diesel pilot" published at International Journal of Engineering Research and Development, Volume 10, Issue 3 (March 2014). A language called LC3 is a great tool for students wishing to learn assembly and wish to see what is actually in the RAM space. Modify the implementation to take into account a carry produced at the addition step of the algorithm. Requirement: Finished Part 1 Hints: Read input from memory stored in Part 1, one character each Convert eachh d lh character to decimal: xIf (intput from '0' to '9'). bss num1 resb 2 num2 resb 2 res resb 1 section. The degradation of undesirable cellular components or organelles, including invading microbes, by autophagy is crucial for cell survival. Role of 5-HT5A and 5-HT1B/1D receptors in the antinociception produced by ergotamine and valerenic acid in the rat formalin test. By joining our community you will have the ability to post topics, receive our newsletter, use the advanced search, subscribe to threads and access many other special features. 0523 when multiplication is set 1x, PRI = 0. PC is the address of the conditional jump. The LC-3 computer does not have instructions (opcodes) for subtraction, multiplication, division and modulo operations. 1 Passing Arguments in Registers. Assembler for Little Computer 3 (LC-3) in Python Home. Exploring bacterial infections: theoretical and experimental studies of the bacterial population dynamics and antibiotic treatment. This is the currently selected item. BASEX is computationally cheap and only requires matrix multiplication once the basis sets have been generated and saved to disk. & Assembly. Background : Bubble Sort is the simplest sorting algorithm that works by repeatedly swapping the adjacent elements if they are in wrong order. Question: Code A Calculator Using LC3 Assembly Coding. You'll gain access to interventions, extensions, task implementation guides, and more for this instructional video. La multiplication des usages est incitée par d’autres facteurs, comme la chute des prix des imprimantes 3D, la disponibilité des matériaux de qualité médicale, mais aussi l’amélioration des vitesses d’impression 3D. LC-3 Assembly Examples Multiply by 10;; Set R0 to 10*R1. In this assignment, you are asked to implement a function to. GFP-LC3 BMDM were cultured with apoptotic thymocytes (UV-irradiation) labeled with Cell Trace Violet (CTV) cells, then treated with digitonin and analyzed by flow cytometry. txt) or read book online for free. 35 BnF, Lc3 10, Annales de la religion, prospectus, mai 1795, p. Similarly, to improve the binding affinity of fluorescence‐based LC3/GABARAP‐specific sensors to the LC3/GABARAP protein, multiplication of the LIR motif itself or the addition of a PI3P binding motif to increase the membrane association or PB domain to induce oligomerization can be applied (Stolz et al, 2017). Exploring bacterial infections: theoretical and experimental studies of the bacterial population dynamics and antibiotic treatment. 9 Ways Board Members can Raise Money without Fundraising! So good to see the points put across so well. Assembly Language binary integer arithmetic summary. A Simple Solution is to repeatedly add n to result. Taken together, it suggests that the S. It means, the result is PRI = 0. 1 Displacements Contents Index 4. To do long multiplication quickly, start by splitting up the tens and ones place in the smaller number. Irvine, Kip R. division and 'performs the desired functions on each memory. Data are expressed as mean of triplicate BMDM samples ± SEM. Infection-induced change in the expression of autophagy markers like LC3 and LAMP-1 were analyzed by RT-PCR, q-PCR, Western blot, immunofluorescence and transmission electron microscopy (TEM) studies were carried out to ascertain the localization of autophagosomes. write a code so that the program ask for an input and then ask for another. AAM Instruction has NO Operands or values attached to it. I'm working on an assignment for a computer science course. Most of these subtle differences lie in the way memory is addressed, exceptions are handled, branches are executed etc. Re: Prompt the user to enter two numbers to add and display the sum Posted 27 January 2010 - 02:00 PM Right, you have declared the num1, num2 and sum values as db which is a single 8-bit values:. ) Since we have a small range of numbers (0-9), use number as an index into a lookup table. Input: 7 Output: 49 Input: n = 12 Output: 144. Yersinia pseudotuberculosis is able to replicate inside macrophages. \$\begingroup\$@HC_ The inc function tests its argument to see if the lowest bit is 1; if so, it calls itself on the remaining upper bits of the argument and returns the result with the same low bit that was checked being set to 0, while if not (i. They will make you ♥ Physics. About the Decimal to Floating-Point Converter. and then output it onto the console For example: Convert 0001001010000011 into "ADD R1 R2 R3". Issues with byte order are sometimes called the NUXI problem: UNIX stored on a big-endian machine can show up as NUXI on a little-endian one. Inhibiting angiogenesis of tumours. LC3 Assembly. LC3 is regarded as a molecular marker of autophagosomes. The C program is successfully compiled and run on a Linux system. • The feedback path comes from the Q output of the leftmost FF. data msg1 db "Enter a digit ", 0xA,0xD len1 equ$- msg1 msg2 db "Please enter a second digit", 0xA,0xD len2 equ $- msg2 msg3 db "The sum is: " len3 equ$- msg3 segment. We therefore investigated whether 2dG-induced autophagy or apoptosis suppresses the replication of inhibition of intracellular multiplication of Lp-1 in A/J M. The multiplication of two numbers in A(a, b) and A(c, d) formats results in a product in A( a+c+1, b+d) format. LCM stands for Lowest Common Multiple. Th brokers was extremely economical in triggering Jolkinolide B Biological Activity autophagy in vivo (Fig. Mehul has 7 jobs listed on their profile. For the Love of Physics - Walter Lewin - May 16, 2011 - Duration: 1:01:26. Multiplication. 2*5 = 2 + 2 + 2 + 2 + 2 Division: through iterative subtraction e. Here we demonstrate that the Drosophila membrane protein Ema is required for the growth of autophagosomes. 760 Maple Lane Benses. You will find lots of easy to understand tutorials, articles, code, example for Assembly Language. Take a binary number as input. Summing the numbers when two dice are rolled. LC3 is predominantly pres-ent in cells in its nonlipidated form, i. LC3 microtubule-associated protein light chain 3 AcKnowLedgeMents We thank Noboru Mizushima for the gift of anti-LC3 antibody, GFP-LC3 expression vector and Atg5-/-and wild-type control MEFs, Darren E. Assume that in reality the load on the floor of the room is always present (LC3), but 1. We used phage display to isolate peptides that possess bona fide LIR (LC3-interacting region) properties and are selective for individual mATG8 isoforms. ” We have explained, small groups are the place where the rest of Christianity takes place – outside the walls of the weekend gatherings. With most of the components going obsolete, it is a quick fix project. Have beeen on courses and heard all of the points, but not all at the same time. The main difference between 1′ s complement and. ORIG x3000 mul10 ADD R0,R1,R1 ; R0 == 2*R1 ADD R0,R0,R0 ; R0 == 4*R1 ADD R0,R0,R1 ; R0 == 5*R1 ADD R0,R0,R0 ; R0 == 10*R1 HALT XOR registers R1 and R2. Réparer plutôt que de jeter est une idée dans l’air du temps qui ne cesse de prendre de l’ampleur chez les consommateurs. Lab 4 Multiplication, Division, and Data Conversion Objectives. LC3 Register Transfer Descriptions and Control Signals - Duration: 1:21:20. The 6th prime number is 13 An array 1: first 2: second 3: third Some primes 1: 2 2: 3 3: 5 4: 7 5: 11 6: 13 7: 17 8: 19 9: 23 10: 29 A list of cities 1: Ottawa 2: Washington DC 3: Mexico City 4: New York. 2020 Feb;97:375-381. Multiplication is achieved by addition as in: X. LC3 Multiplication. fsub %st(7), %st Subtract Real (fsubp) fsubp Example. Making statements based on opinion; back them up with references or personal experience. To understand this example, you should have the knowledge of the following C programming topics: The LCM of two integers n1 and n2 is the smallest positive integer that is perfectly divisible by both n1 and n2 (without a remainder). The NUXI Problem. 5人 寝椅子 カウチソファー 2人掛け 3人掛け ソファー 合皮 合成皮革 三人掛け ニ人掛け 2. GFP-LC3 punctate structures were observed under a fluorescence microscope. Western blotting also showed that expression of the. ” We have called them “church families on a mission. LC3 is regarded as a molecular marker of autophagosomes. To explore the significance of the exosome pathway on prion infectivity and release, we investigated the role of the endosomal sorting complex required for transport (ESCRT. It's best to complete each step and test before moving onto the next. Best How To : Conditional branches are I type instructions, they have 16 bit immediate field. Write a LC-3 assembly language program to compute + - * / of complex numbers input form keyboard with the requirement below: number/ real parts / imaginary parts are signed integers give all prompts b4 inputting. Take for example 5 x 4. Identifying the autophagy genes in yeast and finding orthologs in other organisms reveals the conservation of the mechanism of autophagy in eukaryotes and allows the use of. 3 MUL Examples 100h * 2000h, using 16-bit operands:. To enhance our security here on the site, we have stopped accepting any. You will find lots of easy to understand tutorials, articles, code, example for Assembly Language. LC-3 assembly language. 40 Après la Terreur, le clergé français, toujours divisé depuis 1790, se rétablit avec, selon la formule de l’historien Paul Christophe, la volonté « de survivre34 ». The increase in LC3-II in the absence of TBK-1 cannot be explained by derepression of autophagy initiation given that the amounts of LC3-II protected from degradation by bafilomycin A1 were slightly lower in or equal to Tbk1 −/− cells (Figures 2F, 2G, and S2A). Like subtraction, LC-3 does not natively support multiplication. Inverse property of addition. We've added multiplication to the LC-3 using the "reserved" 1101 opcode. LC-3 Datapath. Using the NOT instruction, we are able to achieve this in LC-3. This suggests having a loop that repeats b times. Associative property of multiplication review. STACK 100H 51. Introduction. write a code so that the program ask for an input and then ask for another input and print out a result after an operation (subtraction. "LD" in LC3 "LDI" in LC3 "LDR" in LC3. LC3-I is cytosolic, whereas LC3-II is membrane-bound. The Coxiella -containing vacuoles then merge with late endosomes recruiting markers such as Rab7 ( Romano et al. La multiplication des usages est incitée par d’autres facteurs, comme la chute des prix des imprimantes 3D, la disponibilité des matériaux de qualité médicale, mais aussi l’amélioration des vitesses d’impression 3D. 56 x 10 kg/kkg 2. You may enter between two and ten non-zero integers between -2147483648 and 2147483647. We therefore investigated whether 2dG-induced autophagy or apoptosis suppresses the replication of inhibition of intracellular multiplication of Lp-1 in A/J M. After internalization of L. outputting / 16 bits faceing to zero /mistakes. July 25, 2013. Then we would like to make a combination of load cases LC1 +1. Inhibition of NOX2 and ROS enhances the conventional. No credit if you write code in assembly. GFP-LC3 punctate structures were observed under a fluorescence microscope. In response to infection with flagellate. Both operands have the same precedence and are left-to-right associative. Assembly Language - Division. shift is a shell builtin that operates on the positional parameters. Shift Right Arithmetic. 1, x'' is a name for the address of a memory location that was initialized to 23. g if we put 2 different number, how do we tell it to perform a subtraction/division. You should use BRNZP because the assembler apparently doesn't like BRZNP. Tutorial Week 6 LC3 and Assembly 1 Today we will cover some exercises and questions regarding assembly and the LC-3. Autophagy is now being recognized as an essential component of innate immunity; i. The NUXI Problem. g If We Put 2 Different Number, How Do We Tell It To Perform A Subtraction/division/multiplication Etc). The LC-3 computer does not have instructions (opcodes) for subtraction, multiplication, division and modulo operations. Derm_GFP-LC3 cells stably expressing a heterologous GFP-LC3 fusion protein were generated. Autophagy is a self-degradative process in which cellular material is enclosed within autophagosomes and trafficked to lysosomes for degradation. 3 MUL Examples 100h * 2000h, using 16-bit operands:. Baxt LA, Goldberg MB. + X Y times. Division (input 1 in R0, input2 in R1, for division keep subtracting input1 with input2 and print out the remainder). 781 * 10^-3. flexneri effector IcsB modulates LC3 recruitment around intracellular bacteria at the early stage of infection and inhibits autophagy late during infection (11, 18). La multiplication des usages est incitée par d’autres facteurs, comme la chute des prix des imprimantes 3D, la disponibilité des matériaux de qualité médicale, mais aussi l’amélioration des vitesses d’impression 3D. phage display to isolate peptides that possess bona fide LIR (LC3-interacting region) properties and are selective for individual mATG8 isoforms. vicinity of the bacterium. 1, x'' is a name for the address of a memory location that was initialized to 23. So if a program reads user input as, say, 123 10, that input is read as the characters '1', '2', and '3' ', but the value used in the program is. Intracellular bacterial have a smaller genome, compared to the host cell, thus requiring. The multiplication of two numbers in U(a, b) and U(c, d) formats results in a product in U( a+c, b+d) format. LRRK2 is a large protein containing a small GTPase domain and a kinase domain, but its physiological role is unknown. Example conversions from signed 8-bit binary to hexadecimal and to decimal. Use MathJax to format equations. Tutorial Week 6 LC3 and Assembly 1 Today we will cover some exercises and questions regarding assembly and the LC-3. Embedded systems; machine language execution; assembly and C language programming; local variables and subroutines; input/output synchronization; analog to digital conversion and digital to analog conversion; debugging; and interrupts. Programmation du LC-3 Programmation en assembleur. In this lab, you will write an assembly language program to multiply two 16-bit integers for the LC-3 computer. So the integer division result is 70 (throw out anything after the decimal point). Introduction. Since LC-3 has a limited number of instructions, many basic logical and mathematical features are left out from the ISA, therefore you must hand-write a lot of code to perform simple tasks. discover that the influenza A virus M2 protein contains a cytoplasmic LC3-interacting region (LIR) motif that binds to the autophagy protein LC3 and diverts it to the plasma membrane during virus budding. In an assembly language program, a label is simply a name for an address. CS270 Recitation 8 “LC-3 Programming Practice” we have seen the multiplication but limited to unsigned numbers. Assume that in reality the load on the floor of the room is always present (LC3), but 1. Properties of addition. MicroprocessorMicrocontroller8086. By showing that the knockdown of RAB25 promoted autophagy, inhibited cell. Booth's multiplication algorithm You need to implement Booth's multiplication algorithm in LC-3 machine language or in LC-3 assembly language. During their development within the vertebrate host, Plasmodium parasites infect hepatocytes and red blood cells. causes LC3-II-conversion that reflects an induction of autophagy and that 1 and 10 mM of 2dG induced apoptosis associated with caspase-4 activation. (E) LC3 lipidation increases in CHCHD2 T61I neurons. The current basis set is composed of the modified Gaussian functions which are highly localized, uniform in coverage, and sufficiently narrow. Group A Streptococcus Induces LAPosomes via SLO/β1 Integrin/NOX2/ROS Pathway in Endothelial Cells That Are Ineffective in Bacterial Killing and Suppress Xenophagy. When microbes contaminate the macrophage cytoplasm, leukocytes undergo a proinflammatory death that is initiated by nucleotide-binding-domain-, leucine-rich-repeat-containing proteins (NLR proteins) that bind and activate caspase-1. • For any degree, there exists at. The administrators of LC-3Help are committed to stopping these attacks once and for all. Normalization of the GFP/mCherry-LC3 puncta (%) were presented in C. To further confirm the evidence of SVCV‐G protein‐induced autophagosome formation, microscopy was used to detect GFP. LC-3 Datapath. In row-major order, the consecutive elements of a row reside next to each other, whereas the same holds true for consecutive elements of a column in. Th brokers was extremely economical in triggering Jolkinolide B Biological Activity autophagy in vivo (Fig. Symptomatique du mouvement makers, la multiplication des fablabs et autres espaces de fabrication comme les repairs cafés ou les cliniques des objets, traduit une volonté de plus en plus forte de consommer de façon plus durable. For example, given the declarations shown in Example 2. To know more about Assembly language, such Shift, Rotate, Multiplication and Division Instructions. GAS infection induces LAP formation for GAS multiplication. Structure and conventions. 03 Max Benzo(a)pyrene » 2. The multiples of 6 are : 6, 12, 18, 24, 30,. This is cleaved in its C‐terminal region to generate LC3I that is lipidated on its C‐terminal glycine to yield a membrane‐bound form, LC3II by the E1/E2‐like enzymes that are homologues of Atg7 and Atg3 (Kabeya et al. And when used with two integers, the / operator in C/C++ causes the fractional part to be lost. and ROS downregulates GAS multiplication by enhancing acidification of LC3-positive GAS-containing vacuoles which fuse with lysosomes. Easily share your publications and get them in front of Issuu’s. REMAINDER (in HEXADECIMAL) Start by dividing the number by 16, that is (1128/16). LC3-II is the form of LC3 that is localized to the autophagosome and is essential for autophagosomal maturation. Recommended for you. Welcome to LinuxQuestions. ADD takes in two numbers and stores their. , 2000 ; Tanida et. Modifications to LC3 Arithmetic & Control Instructions Based on slides by Amir Roth Modified by Diana Palsetia(2009-2010) Opcode for NOT AblM iAssembly Mnemonic NOT R2, R6 ; R2 = ~R6 Assembly compatible with LC3 i. phagocytophilum replicates in a membrane-bound compartment contains autophagy-related proteins LC3 and Beclin1 but is endosomal or lysosomal markers are absent. We found that JUNV infection induces an increment of the LC3-II/LC3-I ratio. Cell death occurs spontaneously in normally involuting tissues such as the thymus. Another approach: Add 100 to itself times. 1 Displacements Contents Index 1. Shift,Rotate,Multiplication and Division Instruction. Bài giảng môn Assembly 47. ADD takes in two numbers and stores their sum in the Destination register. We saw in Section 3. LC3 recruitment occurs upon fungal cell wall swelling and subsequent presentation of immunostimulatory β-glucans on the surface of conidia (Hohl et al. Example: First Pass: ( 5 1 4 2 8 ) -> ( 1 5 4 2 8 ), Here, algorithm compares the first two elements, and swaps since 5 > 1. We found that JUNV infection induces an increment of the LC3-II/LC3-I ratio, an accumulation of punctate pattern in RFP-LC3-transfected cells and the colocalisation of viral nucleoprotein and LC3 protein, suggesting. END 3) The following LC-3 program is assembled. Maximum for nickel equals 2. Is the resulting pattern the correct representation for -16/4? No. To shift left (in this case by eight): shl EAX,8 To shift right (in this case by eight): shr EAX,8 You simply provide the two operands: 1) the register […]. But to do math, to efficiently handle tables, or even to input a multidigit number, a program must be fruitful, and multiply. ) The American Standard Code for Information Interchange, or ASCII code, was created in 1963 by the "American Standards Association" Committee or "ASA", the agency changed its name in 1969 by "American National Standards Institute" or "ANSI" as it is known since. Your code will read two 16-bit numbers (in the range -128 to 127) from predetermined memory locations, multiply those two numbers using Booth's multiplication algorithm, and save the result as a 16-bit. Very similar outcomes ended up attained when these brokers were injected into WT mice, as revealed by way of LC3 lipidation and p62 degradation (Fig. LC3-II can also be generated on the limiting membrane of endosomes during processes such as LC3-associated phagocytosis (LAP) (Sanjuan et al, 2007; Florey et al, 2011). In this project, you will be tested on recently covered material including loops, conditionals, and the basic structure of a low-level (machine or assembly language) program. You need to implement Booth's multiplication algorithm in LC-3 machine language or in LC-3 assembly language. By joining our community you will have the ability to post topics, receive our newsletter, use the advanced search, subscribe to threads and access many other special features. IcsB did not. Loops - Add only positive numbers. They will make you ♥ Physics. So, the Lowest Common Multiple is 24. Finally the factorial result is stored into memory location x4001 b. We found that JUNV infection induces an increment of the LC3-II/LC3-I ratio, an. The professor did not give very good instruction, and I can't find very much information about the subject online. LC3 is regarded as a molecular marker of autophagosomes. info email addresses. Induction of autophagy facilitates Anaplasma infection. The recognition of microbes in selective autophagy is mediated by proteins that bind to LC3 in a process called xenoautophagy. Topic: Family – From Hell To Eternity: Strengthening Marriages through Men’s Mentorship/Discipleship. Winning a lottery, being hit by a stray bullet, or surviving a plane crash, all are instances of a mundane phenomenon: luck. Have beeen on courses and heard all of the points, but not all at the same time. miR-155: It was reported that live and virulent M. CODE MOV AX,@DATA MOV DS,AX MAIN PROC MOV AX,20 MOV BX,3 MUL BX MOV M,AX. It states that the sum of the squares of the sides of a right triangle equals the square of the hypotenuse. As far a multiplication is concerned, the key is to go through the bits of one number and it is 1 , then we add the other number to the sum. ↑ The operand of prefix ++ and -- can't be a type cast. g if we put 2 different number, how do we tell it to perform a subtraction/division. in this video i described how to do Division in assembly language !!! so stay tuned with me and subscribe to my channel thank you!!!. We saw in Section 3. Perform an 8-bit unsigned divide of the AX register by the contents of the effective address (addressed by the ESI register plus an offset of 1) and store the quotient in the AL register, and the remainder in AH: Perform a 16-bit unsigned divide of the DX:AX register by the contents of the effective address (addressed by the EDI register plus. Hence there is a different letters for different Number Systems. To do long multiplication quickly, start by splitting up the tens and ones place in the smaller number. STRINGZ "EVEN " ODD. Biotin concentrations in culture media correlated negatively with. Irvine, Kip R. The numbers must be separated by commas, spaces or tabs or may be entered on separate lines. Réparer plutôt que de jeter est une idée dans l’air du temps qui ne cesse de prendre de l’ampleur chez les consommateurs. In this lab exercise you will develop functions which multiply and divide numbers, using nested subroutine calls. ”); scanf(“%d”,&n); sqt=n/2; temp=0; while(sqt!=temp) { temp. Comment each line of the source code and submit the binary code to dropbox. The fundamental unit of computer storage is a bit; it could. What is nice about binary representation of powers of two? What about exponentiation? (This is a very similar process. What you will do in lab today. Group A Streptococcus Induces LAPosomes via SLO/β1 Integrin/NOX2/ROS Pathway in Endothelial Cells That Are Ineffective in Bacterial Killing and Suppress Xenophagy. Réparer plutôt que de jeter est une idée dans l’air du temps qui ne cesse de prendre de l’ampleur chez les consommateurs. 2*5 = 2 + 2 + 2 + 2 + 2 Division: through iterative subtraction e. PC is the address of the conditional jump. For example, the number 1234 is stored as − There are two instructions for processing these numbers −. These results indicate that inhibition of NOX2 and ROS downregulates GAS multiplication by enhancing acidification of LC3-positive. What is subtraction? It is simply adding the negative value of a number. However, the impact of the autophagy machinery on bovine ephemeral fever virus (BEFV) infection is not yet determined. Data manipulation L2a. Although both NZ131 and its nga mutant were trapped by LC3-positive vacuoles, only nga mutant vacuoles were highly co-localized with acidified lysosomes. Elle aurait dû disposer d'un système d'exploitation multi-tâches et d'une interface graphique utilisant des fenêtres. Question: Help With LC3 I Already Have The Code For Multiplication And Division I Just Need To Merge It Together To Make Them Subroutines, Just Like It Says On The Assignment Here Is My Code For Multiplication And Division: MULTIPLICATION:. 8% in 2005, partly due to an 18% increase in text messaging (SMS) sent by SFR customers (1. A shell script is a file that contains ASCII text. LC3-I is the cytoplasmic form and translate into LC3-II, which is autophagosome membrane form. Identity property of 0. (B) MNT-1 cells ended up taken care of. This suggests having a loop that repeats b times. (D) The relative band intensities of LC3-I and LC3-II were measured by densitometry analysis using ImageJ software and expressed as the ratio of LC3-II/LC3-I. A - B is the same as A + (-B). – Multiplication factor applied to threshold – Adjusts threshold stringency/leniency – Setting this factor is empirical • Upper/lower bounds – Set safety limits on automatic threshold to guards against false positives – Helpful for unexpected images: Empty wells, images with dramatic artifacts, etc. 2007 ) and acidify, thereby activating the. Lectures by Walter Lewin. division and 'performs the desired functions on each memory. Code for An Assembly Language Program to check for Palindrome string in Assembly Language Data Segment str1 db 'MADAM', '$' strlen1 dw$-str1 strrev db 20 dup(' ') str_palin db 'String is Palindrome. 3 MUL Examples 100h * 2000h, using 16-bit operands:. Phage display allowed isolation of peptides with LIR (LC3‐interacting region) properties that are selective for individual mATG8 family members. Jump to the LC3 simulator by clicking on the simulator icon. and ROS downregulates GAS multiplication by enhancing acidification of LC3-positive GAS-containing vacuoles which fuse with lysosomes. In addition to the full length 60kDa ATG6/Beclin 1 [ 21 ], its 50kDa cleavage proteolytic fragment appears in all three groups of cells. Rip3 Knockdown sauve la mort de cellules photoréceptrices dans le poisson zèbre aveugle pde6c. Programming Forum """ Assembler for teaching processor LC3 (original version) Tools exist to do same job, but check how much effort it is to do in Python. In packed BCD representation, each digit is stored using four bits. Learn vocabulary, terms, and more with flashcards, games, and other study tools. Home > By Subject > Place value > Comparing Numbers: Greater Than & Less Than; Numbers are used to show how many there are of something. phage display to isolate peptides that possess bona fide LIR (LC3-interacting region) properties and are selective for individual mATG8 isoforms. Since LC-3 has a limited number of instructions, many basic logical and mathematical features are left out from the ISA, therefore you must hand-write a lot of code to perform simple tasks. The elegant thing about this kind of multiplication is that the answer is correct over several bytes. LC3 Assembly Friday, 20 December 2013. LC3-I is cytosolic, whereas LC3-II is membrane-bound. The Reduced Instruction Set of all chips in the ARM family - from the ARM2 to the StrongARM - includes weird and wonderful instructions like MLA (Multiply with Accumulate: multiply two registers and add the contents of a third to the result) and ASL (Arithmetic Shift Left: absolutely identical to the Logical Shift Left instruction). ORIG x3000 ST R0,#7 LEA R0,LABEL TRAP x22 TRAP x25 LABEL. 28 x 10 kg/kkg 2. Host and bacterial proteins that repress recruitment of LC3 to Shigella early during infection. Hyperosmotic worry activates LC3 but does not enhance the degradation of melanogenesis-related proteins. Derm_GFP-LC3 cells stably expressing a heterologous GFP-LC3 fusion protein were generated. Multiplication Factors A. Machine language to add two numbers. Problem 1 (5 points): Warm-up. 25 times the average values. 657-660, 15-18 May 2011. Both references are invaluable resources for the cytogenetics laboratory. Examples : Input: n = 5 Output: 25. None, do not go to lab. (C) The LC3 conversion of GAS-infected HMEC-1 cells under NAM treatment were analyzed by Western blotting. If there is a carry, set the high-bit of the shifted ACC. © Bucknell University 2014. The sum of two identically-signed numbers may very well exceed the range of the bit field of those two numbers, and so in this case overflow is a possibility. Also it's not clear to me why you skip the first 3 bits, that makes even your best estimates off by a factor of 2. The program should load numbers from x3100, x3101. 28 x 10 kg/kkg 2. Multiplication is achieved by addition as in: X. 4 Postprocessing Previous: 4. model small. Being able to read and write code in low-level assembly language is a powerful skill to have. phage display to isolate peptides that possess bona fide LIR (LC3-interacting region) properties and are selective for individual mATG8 isoforms. , for inputs N and K, your program will return the number (N Modulo K). "Aliens love underpants, in every shape and size, But there are no underpants in space, so here's a big surprise-" You probably thought aliens came down to Earth with a view to taking over the planet - but, no, they simply want to steal your pants! Investigate the rhyming in the story? look at the spelling patterns for each pair of rhyming words. The fluorescent images were displayed in a 10× multiplication. What AAM exactly does is it converts the result into BCD form and first digit is saved in AH register and second digit is saved in AL register. When BHK/Tecpr1-3Myc/GFP-LC3 or HeLa/Tecpr1-3Myc/GFP-LC3 cells were infected with Shigella Cell Host & Microbe Tecpr1 in Selective Autophagy Cell Host & Microbe 9, 376–389, May 19, 2011 ª2011 Elsevier Inc. This program takes a binary number as input and converts it into decimal number. Similarly, to improve the binding affinity of fluorescence‐based LC3/GABARAP‐specific sensors to the LC3/GABARAP protein, multiplication of the LIR motif itself or the addition of a PI3P binding motif to increase the membrane association or PB domain to induce oligomerization can be applied (Stolz et al, 2017). PubFacts seeks to make the world's scientific research easy to locate, access, and collaborate on. The program output is also shown below. $2 becomes$1, $3 becomes$2, $4 becomes$3, and so on. We have a good board and they have been of great support especially in the hard times we are all experiencing at the presently. BASEX is computationally cheap and only requires matrix multiplication once the basis sets have been generated and saved to disk. This is a decimal to binary floating-point converter. In this study, we have used well-characterized biomechanically active scaffolds in which cultured cells can perceive and distinguish different magnitudes of dynamic compressive forces, and can respond to them accordingly. assembly binary lc3 disassembler this question edited Apr 28 '15 at 22:03 Jester 39. The human opportunistic pathogen, Pseudomonas aeruginosa (P. , 2000 ; Tanida et. In row-major order, the consecutive elements of a row reside next to each other, whereas the same holds true for consecutive elements of a column in. The program should load numbers from x3100, x3101. Counting bits and printing result LC3 Assembly Tag: assembly , output , bit-shift , bits , lc3 I'm trying to write a simple program that takes a 16-bit integer from Data1, counts how many bits are 1-bits, and then prints the result to the screen. , the recognition, selective targeting, and elimination of microbes. It means, the result is PRI = 0. Apply the algorithm described in Note 17 on the class page. White arrow represents GFP-LC3 punctate structure. With all the hoopla and headlines surrounding 3D printing innovation, it’s also good to get back to basics and focus on the major impact this technology can have in the classrooms–especially. You are currently viewing LQ as a guest. How do I make it so it will divide negative numbers also? (Don't worry about dividing by zero). SYS_EXIT equ 1 SYS_READ equ 3 SYS_WRITE equ 4 STDIN equ 0 STDOUT equ 1 segment. i can get it to work for numbers 0-9 however any numbers above that i get weird letters or symbols. The Grievance Redress Committee at the district will at a minimum comprise the LC3 representative, representatives of vulnerable groups, District Land Officer/Surveyor, District Community Development Officer and a Grievance Officer from the implementing agency who will oversee and coordinate grievance issues at the village level including. To reference any memory location in a segment, the processor combines the segment address in the segment register with the offset value of the location. The Components of the CPU · Figure 7. Multiplication is for obtaining the multiplied results. The following table lists the precedence and associativity of C operators. b = de2bi (d,n) has an output with n columns. Institute for Medical Microbiology, Virology and Hygiene, University, Medical Center Eppendorf, Hamburg, Germany. DA neuron pathologies in these transgenic models are very mild even at the oldest age, which is likely due to the relatively low transgenic α-synuclein expression in DA neurons. Assume that in reality the load on the floor of the room is always present (LC3), but 1. com - id: 6f5f46-NDQ0O. Email all professors and TAs ([email protected] Sign up or log in to view additional materials. But an operating system is a collection of programs that coordinate all the activities of the hardware, and they expect that register usage will follow specific rules. Now for our input we have to do a sequence of keystrokes to construct a single integer. write a code so that the program ask for an input and then ask for another input and print out a result after an operation (subtraction. Subtract stack element 7 from stack element 0 and return the difference to stack element 7, then pop the stack. 3 CSE240 5-9 ADD (Immediate) this one means "immediate mode" 1514131211109 8 7 6 5 4 3 2 1 0 AD0001 DR SR11 imm5 Register File R7 R6 R5 R4 R3 R2 R1 R0 01 01 ALU B A 16 16 ADD AD R3 5 -1 IR0001011101111111 SEXT 5 16 1 1 0. Prints EVEN if the number stored in NUM is even, otherwise ODD. Upon uptake, Coxiella is found in a tight-fitting vacuole positive for early endosomal and autophagy markers (Rab5 and LC3, respectively) (Gutierrez et al. For practical purposes, though, multiplying and dividing are much more easily. You need to implement Booth's multiplication algorithm in LC-3 machine language or in LC-3 assembly language. If there were no other programs running on your Raspberry Pi, you could use most of the registers any way you like. In addition to the full length 60kDa ATG6/Beclin 1 [ 21 ], its 50kDa cleavage proteolytic fragment appears in all three groups of cells. 2011 IEEE International Symposium on Circuits and Systems (ISCAS-2011), Rio de Janeiro, Brazil, pp. pose a risk to human and animal populations worldwide. CS270 Recitation 8 “LC-3 Programming Practice” we have seen the multiplication but limited to unsigned numbers. 2005; Romano et al. To understand this example, you should have the knowledge of the following C programming topics: The LCM of two integers n1 and n2 is the smallest positive integer that is perfectly divisible by both n1 and n2 (without a remainder). Associative property of multiplication review. One compromise is to use a different sorting method. and ROS downregulates GAS multiplication by enhancing acidification of LC3-positive GAS-containing vacuoles which fuse with lysosomes. 24 When auto-phagy is induced, a series of conjugation reactions mediated by a specific set of autophagy-related (ATG) proteins leads to the covalent linkage of LC3 to the phosphatidylethanolamine pres-ent on autophagosomal membranes. The following table lists the precedence and associativity of C operators. Use MathJax to format equations. You will find lots of easy to understand tutorials, articles, code, example for Assembly Language. Once the addition is done, multiplication is just repeated addition. In contrast, the implication of intestinal Afa/Dr DAEC in diarrhea is still under debate. Clear R6 to hold result of multiplication. To multiply two numbers by paper and pencil, the algorithm is to. In a concerted fashion, viral and cellular factors generate distinct organelle-like structures, designated viral replication factories. It means, the result is PRI = 0. LC3 conjugation system in mammalian autophagy: Int J Biochem Cell Biol: 2004 : CORD-19: 30209: First-in-human clinical trials with vaccines-what regulators want: Nat Biotechnol: 2010 : CORD-19: 30210: The multifaceted exosome: Biogenesis, role in normal and aberrant cellular function, and frontiers for pharmacological and biomarker opportunities. Helicobacter pylori is a Gram-negative, spiral-shaped bacterium that infects more than 50% of the human population and can cause gastritis, peptic ulcer, or gastric malignancies. BRnzp multiplication OUTSIDE LEA R0,changeLine PUTS AND R0,R0,#0 ADD R0,R3,0 OUT LC3的输出都是用ASCII的，譬如说0～9都要加48才是它们的ascii. Non-Confidential PDF versionARM DUI0379H ARM® Compiler v5. Example: Multiplication •Problem: –Design a multiplier program in LC-3 binary. 3 Max Benzene - 6. For example, x1A2B 3C4D is stored as 2) Implement the unsigned multiplication subroutine UNSMUL. The immediate is a two complement value (to jump back eventually), so the range is from PC-2^17 to PC+2^17-4 or PC-40000h to PC+3fffch. Merge (search also class N7) L2e. ', '$' str_not_palin db 'String is not Palindrome. Hyperosmotic worry activates LC3 but does not enhance the degradation of melanogenesis-related proteins. Sensitivity of the developed sensors was optimized by multiplication, charge distribution, and fusion with a membrane recruitment (FYVE) or an oligomerization (PB1) domain. If one of the operands is a memory address, then the operation has an. There are many, many text editors available for your Linux system, both for the command line environment and the GUI environment. 16/05/10, 7 e dim. Japanese encephalitis virus (JEV) is a mosquito-borne flavivirus from the family Flaviviridae. com - id: 6f5f46-NDQ0O. I am supposed to write code for the LC-3 to perform multiplication. In this study, we investigated the role of autophagy during Junín virus (JUNV) multiplication using human A549 cells. B16F10 cells transfected with GFP-LC3 were infected with VNP20009 at the multiplicity of infection (MOI) of 1:1 for one hour. javascript. The LC-3 has no multiply instruction. WUTDO11231235. The 6th prime number is 13 An array 1: first 2: second 3: third Some primes 1: 2 2: 3 3: 5 4: 7 5: 11 6: 13 7: 17 8: 19 9: 23 10: 29 A list of cities 1: Ottawa 2: Washington DC 3: Mexico City 4: New York. Viewed 3k times 0. (LC3)-I to LC3-II protein, a marker of autophagy, was observed in IPNV-infected cells using confocal fluorescence microscopy and western blot analysis. The Bitwise Calculator is used to perform bitwise AND, bitwise OR, bitwise XOR (bitwise exclusive or) operations on two integers. Take for example 5 x 4. The main difference between 1′ s complement and. In fact, ACC used to get zeroed out too at first, when I had my counter set to 16 - this was because the multiplication loop is supposed to iterate N times, where N is the number of bits that make up the numbers you're multiplying, and since the LC-3 is 16-bit addressable, I thought I'd set the counter to 16 bits. FIX-LC3-1 PDF - Documentation langue en dimension 0. Institute for Medical Microbiology, Virology and Hygiene, University, Medical Center Eppendorf, Hamburg, Germany. division and 'performs the desired functions on each memory. Taken together, it suggests that the S. GFP-LC3 lipidation is show as the ratio between GFP-LC3 MFI of deficient/wild-type in CTV + BMDM. Below is the implementation of this idea. 25 times the average values. A complete 8-bit Microcontroller in VHDL In this VHDL project , VHDL code for a microcontroller is presented. Procedure: This lab was a little easier to begin since there was some code that has been given to use from the instructor. Host and bacterial proteins that repress recruitment of LC3 to Shigella early during infection. By continuing to use this site you consent to the use of cookies on your device as described in our cookie policy unless you have disabled them. flexneri (18). Two decimal digits are packed into a byte. Embedded systems; machine language execution; assembly and C language programming; local variables and subroutines; input/output synchronization; analog to digital conversion and digital to analog conversion; debugging; and interrupts. Dihydroartemisinin inhibits multiplication of Brucella suis vaccine strain 2 in murine microglia BV2 cells via stimulation of caspase‑dependent apoptosis: Link: 11/09/2019: Effect of electroacupuncture at the ST36 and GB39 acupoints on apoptosis by regulating the p53 signaling pathway in adjuvant arthritis rats: Link: 11/09/2019. STACK 100H 51. We found that JUNV infection induces an increment of the LC3-II/LC3-I ratio, an accumulation of punctate pattern in RFP-LC3-transfected cells and the colocalisation of viral nucleoprotein and LC3 protein, suggesting. Identity property of 0. In LC3 Program How To Change Operation (e. Next, we invoke the read command with "text" as its argument. Autophagy-mediated Reentry of Francisella Tularensis Into the Endocytic Compartment After Cytoplasmic Replication - Free download as PDF File (. BRp AGAIN. There are less rules when multiplying positive and negative numbers than in adding and subtracting positive and negative numbers. MODEL SMALL. code for program to convert decimal number to binary in assembly language dis macro str mov ah,09h lea dx,str int 21h endm data segment msg2 db "binary number is :$" str1 db 20 dup('$') str2 db 20 dup('$') no dw 100 line db 10,13, '$' data ends code segment assume ds:data,cs:code start: mov ax,data mov ds,ax lea si,str1 mov ax,no mov bh,00 mov bl,2 l1:div bl add ah, '0' mov byte ptr[si],ah. C64 (the 'kernal') consisted of machine code routines, stored in ROM, that can be called directly from BASIC or machine code. 19x 10 kg/kkg O Max Hienol - 6. Asm x86 segmentation fault in reading from file. LC3/4 Implementing Functions Based on slides by Amir Roth Modified by Diana Palsetia (2009-2010) Recap Functions A function is a program fragment that. Non-Confidential PDF versionARM DUI0379H ARM® Compiler v5. Faust and C. Financial/Operational: Lockheed/General Electric contract October 16 1992$ 165 million for 2 units- potential 5 units. 56 x 10 kg/kkg 2. They perform a bit-wise operation on a single operand to produce a single bit result. Two LC3 homologs, GABARAPL1 and GATE16, also accumulated during HCMV infection and were associated with the vAC, in proximity with fragmented Golgi stacks. Subtraction Instructions Subtract Real and Pop (fsub) fsub{ls} Example. data val1 WORD 2000h val2 WORD 100h. Try this:. , the recognition, selective targeting, and elimination of microbes. TRAP vectors. Exploring bacterial infections: theoretical and experimental studies of the bacterial population dynamics and antibiotic treatment. This is a nice example of a divide and conquer strategy - multiplication is repeated addition. Multiplication in LC3 (input 1 in R0, input 2 in R1) 2. 2fwbi0nnvorqzl, qnhe7f4u1h3, c0ha6z4b39, 287egjmf89d0, wn6797jc3hvg, p3qkekf2ingdwzk, 7xw1ha6z3d, 1fiiiavana, 7g0yqvm2m1t8, ib5bgqyjv8as96, 5n8jzlg2wpia, wtv85e90l2ib, bll1ozyogqf, kg06udge4l33ze1, gvi06fn5u55, wjvw94h91ycs1n1, 5xwv4m12oybjkh, lja9117xgawj, 6eslxftndjys, 0e49h0ufgqv16h, uf3kllk1tc3b91, zeax38dxcqidg, ef1f4j5tljrl, 5kdx75htv439o, ehunybik3kvlpm, z8kduhcukgc, ojcqy1qokk9h, pjkmpuf0wbudqd, hrauc44keg4htu8
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# Special Characters of HTML5
HTML5, Web Development / Monday, July 30th, 2018
# HTML5 Special Characters:
Here we will learn about HTML5 Special Characters. You have seen that there are certain characters that have special meaning in HTML code. For example, the “<” and “>” characters delimit tags. If you want to display such characters on the web page, you have to take care that the characters are not interpreted and are displayed literally. To display the “<” character, it can be specified as “<”. The “&” interprets the “lt” as the “<” symbol and displays it. But now what if you want to display the & symbol itself? Simply writing “&” in the code will not display it. But first, let us see how to display some special characters.
Consider the example shown in below and also look at Table.
<!DOCTYPE html>
<html>
<title>HTML5 Special Characters</title>
<body>
This is
Used for blank space.
<BR>
< is the Less Than symbol <BR>
> is the Greater Than symbol <BR>
& is the ampersand symbol <BR>
" is the quotation mark symbol <BR>
à is small a, grave accent symbol <BR>
À is capital a, grave accent symbol <BR>
ñ is small n, tilde symbol <BR>
Ñ is capital n, tilde symbol <BR>
ü is the umlaut small u symbol <BR>
Ü is the umlaut <BR>
 is the symbol Delta<BR>
¼ is the quarter symbol <BR>
½ is the hay symbol <BR>
</body>
</html>
The special characters shown in the example are some of the most frequently used characters displayed on web pages. Each of the special characters can be displayed by using its character sequence after the “&”. These can be seen in the following Table.
Special Character Character Symbol Description < < Less-than symbol > > Greater-than symbol & & Ampersand “ " Quotation Mark Blank space à à small a, grave accent À À capital A, grave accent Ñ Ñ capital N, tilde ü ü umlaut small u Ü Ü umlaut capital U ∆ Delta ¼ ¼ One Fourth ½ ½ Half
The browser will display your text in a steady stream unless you tell it to do so otherwise with line breaks. It will reduce any amount of white space to a single space. If you want more spaces, you must use the space character ( ). If you hit Return (or Enter) while you are typing, the browser will interpret that as a space unless there is already a space there.
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# How do you solve the system 2x+7y=3 and x = 1-4y by substitution?
May 24, 2015
Try this:
May 24, 2015
Substitute the formula for $x$ from the second equation into the first equation as follows:
$3 = 2 x + 7 y = 2 \left(1 - 4 y\right) + 7 y = 2 - 8 y + 7 y = 2 - y$
Add $y$ to both ends to get:
$y + 3 = 2$
Subtract #3 from both sides to get:
$y = - 1$
Substitute this value for $y$ into the original second equation to find $x$:
$x = 1 - 4 y = 1 - 4 \left(- 1\right) = 1 + 4 = 5$
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# Why is this let expression not working in TikZ (calculating a midpoint)?
I have a rectangle in TikZ and the top left and bottom right corners are called (topleft) and (bottomright) respectively. I wanted to have a label midway down the left hand side of the rectangle, so I tried the following, both of which failed with cryptic error messages:
\draw let \p1 = (topleft), \p2 = (bottomright)
in (\x1,\pgfmathparse{0.5*(\y1 + \y2)}\pgfmathresult) node[right]{6 metres};
and
\draw let \p1 = (topleft), \p2 = (bottomright)
in (\x1,{0.5*(\y1 + \y2)}) node[right]{6 metres};
I got the desired result in a roundabout way:
\draw let \p1 = (topleft), \p2 = (bottomright)
in ($(\x1,\y1)!.5!(\x1,\y2)$) node[right]{6 metres};
But why did the first two attempts not work?
EDIT (in response to request for more detail): If it helps, you can assume that the context of the command above is something like:
\usetikzlibrary{calc}
\begin{tikzpicture}
\draw (0,10) coordinate (topleft) rectangle (6,0) coordinate (bottomright);
%% relevant let statement would go just below here
\end{tikzpicture}
but I do not want a solution that uses the knowledge that the coordinates are (0,10) and (6,0).
-
I think we can be more help if you include a full example that we can compile (and therefore see the errors) – Joseph Wright Aug 23 '10 at 7:01
@Joseph, I've now done this but I can't help suspecting that a tikz user who doesn't know how to define coordinates probably won't be able to explain why the let statements above don't work... – bryn Aug 23 '10 at 12:11
Rather than doing "all that arithmetic", I'd let Tikz do it for me. Try something like this:
\begin{tikzpicture}[scale=1,>=stealth]
\draw(-10,0) node (topleft) {TL};
\draw(0,-10) node (bottomright) {BR};
\draw (topleft) rectangle (bottomright);
\path (topleft) edge node (here) {Here} (topleft |- bottomright);
\end{tikzpicture}
The two secrets are these: node will draw at the midpoint of a path, and |- (or -|) represents a vertical/horizontal point of intersection (ie, in the example, "drop a line vertically from (topleft) until it meets a horizontal line through (bottomright). Try swapping -| for |- and you'll see what I'm getting at.
You can also refine things, like this:
\path (topleft) edge[draw opacity=0]
node [right,pos=0.25] (here) {Here}
(topleft |- bottomright);
draw opacity=0 suppresses the line that \path normally draws
right places the text to the right
pos=0.25 places the node 1/4 of the way along the path (and so on), saving your arithmetic for better things...
-
Working with \pgfmathparse inside a path
If you need to do a calculation inside a path, I recommend to suspend this path, do the calculation, then resume the path. That "escaping" could be done by using the \pgfextra{code} macro executing code.
In your example, \pgfextra may contain the \pgfmathparse calculation, \pgfmathresult may be used later on in the path.
Here's the modification for your first example:
\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{calc}
\begin{document}
\begin{tikzpicture}
\draw (0,10) coordinate (topleft) rectangle (6,0) coordinate (bottomright);
\draw let \p1 = (topleft), \p2 = (bottomright)
in \pgfextra{\pgfmathparse{0.5*(\y1 + \y2)}}
(\x1,\pgfmathresult pt) node[right]{6 metres};
\end{tikzpicture}
\end{document}
Output:
This advice is for the case that you need to do more complex calculation not easily done by simple expressions or perhaps intersections.
-
I ran into a similar problem. I am not sure, but it seems as if TikZ has some problems with evaluating nested expressions. So, instead of calulating
0.5*(\y1 + \y2)
I would suggest to calculate
0.5*\y1+0.5*\y2
This worked for me.
-
The problem with ( ) inside outer ( ) is that the first opening ( is matched to to first closing ) found. This is because of the way TeX parses things. For the same reason you can't use [] inside an optional argument directly. Try to hide these things from the TeX parser by placing them in { }: 0.5*{(\y1 + \y2)}. However, this works only on places where an argument (or PGF expression) is awaited so that the {}` are stripped again. – Martin Scharrer Apr 6 '11 at 8:53
Your second example does work in TikZ v2.10. So I suspect it is a bug in the math parser of version 2.00.
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# Very simple
## Main Question or Discussion Point
suppose p and q are positive rational numbers with the condition : 0<x<Pi/2
find the minimum y=Tan(x)^p+Cot(x)^q
arildno
Homework Helper
Gold Member
Dearly Missed
Well set u=Tan(x),
Hence, y=u(x)^p+(1/u)^q, along with $$\frac{dy}{dx}=\frac{dy}{du}\frac{du}{dx}$$
should settle it nicely.
you did not use the condition
tiny-tim
Homework Helper
you did not use the condition
arildno left that to you!
If 0 < x < π/2, and u = tanx, then the condition on u is … ?
i found this problems in a book which was just talking about trigonometry and that book was empty of calculus
tiny-tim
Homework Helper
i found this problems in a book which was just talking about trigonometry and that book was empty of calculus
ah … you put this in the Calculus & Analysis sub-forum, so we assumed you wanted a calculus answer!
I really have no idea how to do this with trignonometry.
you are right
please tell me where is the appropriate sub-forum
HallsofIvy
Homework Helper
$$tan(x)= \frac{sin(x)}{cos(x)}$$
and
$$cot(x)= \frac{cos(x)}{sin(x)}$$
so
$$tan^p(x)+ cot^q(x)= \frac{sin^p(x)}{cos^p(x)}+ \frac{cos^q(x)}{sin^q(x)}= \frac{sin^{p+q}(x)+ cos^{p+q}(x)}{sin^q(x)cos^p(x)}$$
Are you sure that you have found the minimum of this problem?
or changing tan to sin/cos and .....
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# The class of the locus of intermediate Jacobians of cubic threefolds
@article{Grushevsky2012TheCO,
title={The class of the locus of intermediate Jacobians of cubic threefolds},
author={Samuel Grushevsky and Klaus Hulek},
journal={Inventiones mathematicae},
year={2012},
volume={190},
pages={119-168}
}
We study the locus of intermediate Jacobians of cubic threefolds within the moduli space $\mathcal{A}_{5}$ of complex principally polarized abelian fivefolds, and its generalization to arbitrary genus—the locus of abelian varieties with a singular odd two-torsion point on the theta divisor. Assuming that this locus has expected codimension g (which we show to be true for g≤5, and conjecturally for any g), we compute the class of this locus, and of its closure in the perfect cone toroidal… CONTINUE READING
#### Citations
##### Publications citing this paper.
SHOWING 1-6 OF 6 CITATIONS
## Stable cohomology of the perfect cone toroidal compactification of g
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CITES METHODS
HIGHLY INFLUENCED
## The locus of plane quartics with a hyperflex
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CITES BACKGROUND & METHODS
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CITES RESULTS
## Geometry of theta divisors --- a survey
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## The moduli space of cubic threefolds via degenerations of the intermediate Jacobian
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## Singularities of theta divisors in algebraic geometry
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## Principally polarized semiabelic varieties of torus rank up to 3
S. Grushevsky, K. Hulek
• and the Andreotti-Mayer loci. Pure and Applied Mathematics Quarterly, special issue in memory of Eckart Viehweg, to appear,
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## Dedicata
S. Grushevsky, R. Salvati Manni. The loci of abelian varieties with divisor.Geom
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## Perfect forms and the moduli space of abelian varieties
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G. van der Geer. The Chow ring of the moduli space of threefolds
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In thermodynamics, ideal gas refers to a body of particles (atoms or molecules) in a state of gas particles, which are said to abide by the Boltzmann chaos assumption, i.e. have non-correlations of velocities, and to obey the ideal gas law:
$PV = nRT\,$
where P is the pressure, V the volume, n the number of particles , R the gas constant, and T the temperature of the body of gas. [1] Deviations in the behavior of gases, from the ideal gas law, occur at extreme pressures and temperatures, at which point the gas no longer is considered "ideal".
Perfect gas | Ideal perfect gas
The prefix term "ideal" is a modern etymological evolution stemming from the phrase "perfect gas" in the context of making a "perfect" vacuum via explosion in early gunpowder engine and other vacuum engine prototypes, such as is found in the works of Denis Papin and Christiaan Huygens.
In the early 20th century, terms such as “ideal perfect gas” (Preston, 1904) (Ѻ), were being employed.
References
1. Perrot, Pierre. (1988). A to Z of Thermodynamics (section: Ideal gas, pgs. 144-48). Oxford University Press.
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Tag Info
Write $A = [A_1 ~~ A_2]$ with $A_1 \in \mathbb{Z}_q^{n\times m'}$ and $A_2 \in \mathbb{Z}_q^{n\times (m-m')}$. Likewise, $e = (e_1 ~~ e_2)$ with $e_1 \in \mathbb{Z}_q^{m'}$ and $e_2 \in \mathbb{Z}_q^{m-m'}$. Then, $$Ae = 0 \bmod q \iff A_2e_2 = -A_1e_1 \bmod q.$$ So, given an instance of SIS, that is, an $n\times m$ matrix $A$, if you have an oracle to solve ...
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Chapter 10 - Section 10.2 - Multiplication Properties of Exponents - Practice: 1
$z^{11}$
Work Step by Step
Use the product property for exponents $(a^{m} \times a^{n}=a^{m+n})$ to simplify $z^{5}\times z^{6}$: $z^{5}\times z^{6}$ =$z^{5+6}$ =$z^{11}$
After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.
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## The universal tRNA modification t6A is available at position 37 of
The universal tRNA modification t6A is available at position 37 of nearly all tRNAs decoding ANN codons. prospects to protein folding defects and show that this absence of t6A led to stress sensitivities (warmth ethanol salt) and sensitivity to TOR pathway inhibitors. Additionally L-homoserine suppressed the slow growth phenotype seen in t6A-deficient strains and proteins aggregates and Advanced Glycation End-products (AGEs) were increased in the mutants. The global effects on translation caused by t6A Rabbit polyclonal to AP4E1. absence were examined by ribosome profiling. Interestingly the absence of t6A did not lead to global translation defects but did Carnosic Acid increase translation initiation at upstream non-AUG codons and increased frame-shifting in specific genes. Analysis of codon occupancy rates Carnosic Acid suggests that Carnosic Acid one of the major functions of t6A is usually to homogenize the process of elongation by slowing the elongation rate at codons decoded by high large quantity tRNAs and I34:C3 pairs while increasing the elongation rate of rare tRNAs and G34:U3 pairs. This work reveals that the consequences of t6A absence are complex and multilayered and offers arranged the stage to elucidate the molecular basis of the observed phenotypes. contributions of many Carnosic Acid ASL modifications to translational robustness are still poorly recognized [6]. Number 1 (A) Complex modifications found in the anticodon stem loop (ASL) of tRNA. (B) Codon table with decoding tRNAs based on Johansson mutant when the gene was found out [34] the deletion of the and results in an increase in +1 and ?1 frameshifts as well as to mis-initiation at CUG codons of specific reporter genes [20 23 Further studies linked loss of with raises in leaky scanning bypass of start codons 1 frameshifts read-through of UAG UAA and UGA quit codons and an increase in internal ribosome access site translation (IRES-dependent initiation of translation) [33]. Polysome profiles of prospects to increased levels of the transcriptional activator is definitely a positive regulator of genes indicated during amino-acid starvation Carnosic Acid and is dependent on eIF2α phosphorylation by Gcn2 which screens uncharged tRNAs [35 36 Over-expression of tRNAiMet or deletion of did not reduce the high levels of inside a induction in the translation [38]. Evidence has surfaced that some tRNA adjustments can become determinants of following tRNA adjustment enzymes. Recently certain requirements of 2’-[38 54 which regulates > 1500 genes in response to dietary cues [35] and Focus on of Rapamycin Organic (TORC) through modifications in Tor kinase activity [55-58] (analyzed in Thiaville and de Crécy-Lagard [59]). Modulating the degrees of t6A in through appearance of the unmodifiable tRNAiMet or overexpression of resulted in modifications of Tor activity and adjustments entirely organism development [56]. Additionally knock-down of Tcs3 (Kae1) or Tcs5 (Bud32) in larvae turned on the Unfolded Proteins Response (UPR) [55]. Latest ribosome profiling research of mutations in the mcm5s2U pathway ([61]. These outcomes indicate that mcm5s2U34 and t6A37 usually do not need one another because of their synthesis although getting rid of t6A did boost degrees of mcm5s2U. Overexpression of tRNAs or Ternary Organic (TC) usually do not suppress the development flaws of (Amount S2B). Amount 3 Appearance of tRNALysUUU will not suppress gradual development of mutants without t6A Therefore unlike the suppression of mcm5s2U by tRNALysUUU neither the overexpression of every ANN-tRNA nor the overexpression of TC elements could suppress the fitness flaws seen in mutants from the t6A biosynthesis pathway. The consequences of the increased loss of t6A hence seem to be more technical than those of the loss of mcm5s2U. t6A-deficient strains are sensitive to warmth and inhibitors of TOR but growth can be partially rescued by L-homoserine To better characterize how the absence of t6A was influencing cellular function growth on several carbon sources and under different stress conditions was tested (Number 4). t6A-deficient strains were found to be sensitive to warmth stress with and exposed that AGEs become more abundant when t6A levels are reduced [61 66 To assess levels of AGEs in our context equal amounts of total and insoluble proteins from BY4742 = 0.049 with five genes recognized. None of the arginine catabolism pathways were.
## Background In Duchenne muscular dystrophy (DMD) abnormal cardiac function is typically
Background In Duchenne muscular dystrophy (DMD) abnormal cardiac function is typically preceded by a decade of skeletal muscle disease. BDNF was elevated in cardiac muscle of younger GRMD but was unaltered in skeletal muscle while SPP1 was increased only in GRMD skeletal muscle. In human DMD circulating levels of BDNF were inversely correlated with ventricular function and fibrosis while SPP1 levels correlated with skeletal muscle function. Conclusion These results highlight gene expression patterns that could account for differences in cardiac and skeletal disease in GRMD. Most notably animal model-derived data were translated to DMD and support use of BDNF and SPP1 as biomarkers for cardiac and skeletal muscle involvement respectively. INTRODUCTION Duchenne muscular dystrophy (DMD) is caused WIN 55,212-2 mesylate by mutations in the gene resulting in severely reduced or absent dystrophin protein which primarily affects striated muscle function (1). DMD natural history involves progressive skeletal muscle weakness leading to loss of ambulation respiratory failure and death in the second to third decade of life (2 3 Although progressive respiratory failure was long the primary cause of DMD mortality the advent of corticosteroid therapy and non-invasive ventilatory support has increased overall survival (4) such that cardiomyopathy is now the leading cause of death (5). This has heightened the importance of early identification of cardiomyopathy. Currently prediction models incorporating advanced imaging can define abnormalities but identifying which patients will exhibit the earliest onset and rapid progression has been elusive (6-8). Despite tremendous progress in defining the WIN 55,212-2 mesylate molecular basis and pathogenesis of DMD since the identification of dystrophin (9) major gaps remain in our understanding of factors that contribute to disease progression. Animal models have been useful in studying the pathophysiologic mechanisms of DMD. The mouse the most widely used animal model of muscular dystrophy has proven invaluable in a range of pre-clinical studies. However the subtle nature of cardiac abnormalities (10) limits extrapolation to human disease (11-13). The golden retriever muscular dystrophy (GRMD) model closely approximates the progressive skeletal muscle involvement WIN 55,212-2 mesylate of human disease (12-14). Moreover onset and progression of cardiac involvement in GRMD is delayed compared with skeletal muscle (12 13 and follows a course more in line with that of human DMD (11 15 (reviewed in reference (16)). Importantly the severity of the cardiac and skeletal phenotypes varies markedly among dogs similar to humans (12 13 We used gene expression studies of GRMD cardiac and skeletal muscle to gain insights into the WIN 55,212-2 mesylate molecular pathways that might contribute to differences in onset and progression of cardiac versus skeletal muscle dysfunction. Because the GRMD model closely approximates human disease we sought to identify biomarkers of dystrophin-associated cardiomyopathy in this model and then translate our findings by studying sera from adolescent patients with DMD. Rabbit Polyclonal to RGAG1. RESULTS GRMD gene expression profiles are age-dependent and tissue-specific A total of 30 tissues (LV and MHG) from WIN 55,212-2 mesylate 15 dogs (6 normal and 9 GRMD) were grouped and analyzed according to age disease and tissue type (Table 1). For GRMD dogs versus age-matched controls there were 4 873 probes detected at disparate levels between dystrophic and wild type MHG. The vast majority (~80%) were detected for the younger animals only as shown by hierarchical clustering in Figure 1A with only 466 probes altered in GRMD dogs of both ages (Figure 1B). These results suggest that age strongly influences the transcriptional processes that drive disease progression in dystrophic skeletal muscle which is not surprising given that the clinical course of disease is strongly age-dependent. Figure 1 Microarray analysis of GRMD skeletal muscle Table 1 Overview of Gene Expression Analysis Results Dogs with GRMD typically do not have impaired ventricular function detectable by imaging or symptoms of heart failure until 2 years of age or considerably later (16) well beyond the onset of skeletal muscle involvement and consistent with the relatively delayed onset of cardiomyopathy in human DMD. Accordingly cardiac function was not assessed for the 6-12 month-old GRMD dogs. No animal had overt evidence of clinical cardiac disease. Of the three oldest.
## Objectives Small cigars and cigarillos are gaining in popularity as cigarette
Objectives Small cigars and cigarillos are gaining in popularity as cigarette use wanes mainly due to relaxed regulatory standards that make them cheaper easier to buy individually and available in a variety Rabbit polyclonal to TXLNA. of flavors not allowed in cigarettes. is at least equal to that Bedaquiline (TMC-207) resulting from similar levels of cigarette SHS. Our findings support the need to prevent even brief exposure to little cigar SHS and support tobacco control policies that regulate little cigars as strictly as smoking. Keywords: small cigars filtered cigars cigarillos secondhand smoke cigarettes vascular endothelial function flow-mediated dilation Small cigars (ie filtered cigars) and cigarillos have already been rising in popularity for at least 2 years 1 counteracting the achievement of Bedaquiline (TMC-207) cigarette control initiatives on using tobacco. As of Oct 2015 small cigars and cigarillos aren’t at the mercy of the same item regulations as smoking including warning brands on packages minimal pack size and prohibition of advertising using characterizing tastes apart from menthol and they’re frequently taxed at a lesser rate.1 2 Small cigars are regarded as getting much less harmful than smoking also.3 Filtered little cigars specifically are practically identical to smoking in size form and filter design4 5 (Body 1). In order to avoid getting regulated as smoking the tiny cigar products contain cigarette wrapped within a cigarette leaf or in paper formulated with cigarette (smoking do not include cigarette within their wrapper) and cigarillos are heavier compared to the pounds range that defines smoking. Furthermore the cigarette is certainly of different pH and mix than that in smoking.6 7 Nonetheless unlike conventional cigars the smoke from little cigars and cigarillos is often inhaled as in cigarette smoking and secondhand smoke (SHS) poses hazards to bystanders regardless of smoking technique.8 Regulating little cigars as strictly as smokes would arguably prevent them from simply replacing smokes 9 but the relative lack of knowledge about Bedaquiline (TMC-207) their smoke composition and their health effects1 makes such regulatory expansion difficult to achieve. Figure 1 Smokes and Little Cigars Used for this Study Like smokes little cigar smoke contains nicotine and the thousands of chemicals that result from tobacco combustion and is particularly rich in carbon monoxide nitrosamines nitrogen oxides and ammonia.5-8 Cigar smoke is associated with elevated risk of oral lung and esophageal cancers.8 The risk of coronary heart disease is 30% higher for cigar smokers than non-smokers and doubles for those who inhale the smoke.13 These effects demonstrate the risks associated with long-term use of these products but the case for regulating them as equivalents of smokes would be strengthened by evidence that their immediate health consequences are comparable to those of smokes. One of the most acute health effects of exposure to cigarette smoke is the immediate impairment of vascular endothelial function measured as arterial flow-mediated dilation (FMD). FMD is usually a well-validated marker of cardiovascular risk that is chronically impaired in humans by both active smoking Bedaquiline (TMC-207) of smokes and standard cigars and by cigarette SHS exposure.14-16 FMD is temporarily impaired in humans by 30 minutes of exposure to SHS or aged sidestream smoke at real-world SHS levels.17-19 Sidestream smoke is smoke from your smoldering tip that comprises ~85% of SHS with the rest being exhaled mainstream smoke.20 Because the sidestream smoke ages in the exposure chamber prior to exposure like real SHS does in real exposure scenarios we refer to it here as SHS. Our micro-ultrasound-based approach to measure FMD in living rats yields results whose pharmacological and biophysical effects are similar to those observed in humans.21 22 This rat model showed that impairment of FMD occurred with one minute of exposure to cigarette SHS.23 We statement here that brief exposure to little cigar SHS impairs vascular function in rats as least as much as exposure to cigarette SHS. METHODS Animals We used male Sprague-Dawley rats 10 weeks aged N = 8 or 9 rats/group. Rats continued to be anesthetized (ketamine 100 mg/kg xylazine 5 mg/kg) through the entire experiment and had been euthanized Bedaquiline (TMC-207) instantly afterward. All techniques were accepted by the UCSF Institutional Pet Use and Treatment Committee. Dimension of Endothelial Function Flow-mediated.
## Rhabdomyosarcoma (RMS) may be the most frequent soft tissue sarcoma in
Rhabdomyosarcoma (RMS) may be the most frequent soft tissue sarcoma in children that shares many features of developing skeletal muscle. and we establish that suppression of PTEN is a frequent event in both subtypes of RMS. TBX2 represses PTEN by binding to the promoter and recruiting the histone deacetylase HDAC1 directly. RMS cells possess high degrees of triggered AKT because of the deregulation of PI3K signaling and depletion or disturbance with TBX2 which up regulates PTEN leads to a reduced amount of phospho-AKT. We’ve also discovered that the extremely related T-box relative TBX3 will not repress PTEN in the Rabbit Polyclonal to GATA6. muscle tissue lineage. This function shows that TBX2 can be a central element of the PTEN/PI3K/AKT signaling pathway deregulation in RMS cells which focusing on TBX2 in RMS tumors may provide a book therapeutic strategy for RMS. causes embryonic lethality recommending that PTEN is vital for embryonic advancement 8. Heterozygous deletion of promotes tumorigenesis of many malignancies including medulloblastoma 3 intestinal tumors 41 and prostate tumor 9. In medulloblastoma individuals whose tumor communicate a minimal to absent degree of PTEN display a worse success percentage 3 and in prostate tumor PTEN level inversely correlates with event of intrusive prostate tumor 9. Germline mutation of causes multiple disease syndromes including Cowden disease Bannayan-Riley-Ruvalcaba Lhermitte-Duclos and symptoms symptoms 4. PTEN may function in the cytoplasmic membrane to antagonize the PI3K signaling pathway by dephosphorylating phosphatidylinositol-3 4 5 PIP3 the key secondary-messenger molecule of PI3K pathways 16. Inactivation of PTEN leads to activation from the PI3K/AKT pathway and following upsurge in cell routine development migration and success 5 17 PTEN also features in the nucleus where PTEN is usually indicated to have multiple roles including cell cycle control 52 51 and stabilizing chromosomes 42. In the cytoplasm PTEN prefers PIP3 as the major biological phosphoprotein substrate for dephosphorylation and converts PIP3 to PIP2 25. PIP3 is usually absent or very low in Otamixaban (FXV 673) Otamixaban (FXV 673) quiescent cells but is usually rapidly up regulated by PI3K in response to growth factors or extracellular signaling. PIP3 Otamixaban (FXV 673) is the major activator of AKT. AKT is usually recruited via PIP3 to the plasma membrane where AKT can then be fully activated by phosphorylation. In muscle activation of PI3K/AKT pathway induced by Otamixaban (FXV 673) serum starvation is crucial for myoblast differentiation driven by muscle creatine kinase (MCK) promoter was found to protect mice from insulin resistance and did not grossly affect muscle histology or induce tumor development 53. In the nucleus PTEN regulates cell cycle progression by down regulating transcriptional expression and protein stability of cyclin D1 as well as inhibiting its nuclear localization 32. Besides cyclin D1 PTEN also is shown to potentially repress cyclin D2 13 and cyclin D3 55 to arrest the cell cycle at G1. PTEN is also been shown to modulate the cell cycle by up regulating the CDK inhibitor p27 46. The status of PTEN in rhabdomyosarcoma has not been extensively studied. A recent genome wide mutational analysis revealed that mutations in the receptor tyrosine kinase/RAS/PIK3CA genetic Otamixaban (FXV 673) axis are common in RMS 43. In 147 human tumors analyzed in this study only one homozygous mutation in PTEN was identified 43. This work established that mutation of PTEN is not a frequent event in RMS cells but the expression of PTEN in clinical RMS samples has not been characterized. In RMS cells the fusion protein PAX3-FOXO1 has been proven to donate to repression of PTEN 18. Depletion of PAX3-FOXO1 in RMS cells up governed PTEN and exogenous appearance of PAX3 in C2C12 cells down governed PTEN 18. In both C2C12 regular myoblasts and RMS cells the amount of PTEN has been proven to become inversely correlated with AKT serine 473 phosphorylation 50 which is certainly mediated with the rapamycin-insensitive mTOR complicated (mTORC2) 39 and necessary for complete activation of AKT Otamixaban (FXV 673) 47. It has also been shown that microRNA miR-183 functions as an oncogene in RMS cells by targeting the transcription factor EGR1 which is an activator of PTEN 40. Here we show that TBX2 directly represses PTEN in RMS cells. The repression is usually mediated at least in part through recruitment of the histone deacetylase HDAC1 to the promoter. TBX2 expression and PTEN expression are inversely correlated in both RMS cell lines and human RMS tumor samples representing both ERMS and ARMS cells. We.
## Survival for glioblastoma (GBM) patients with an unmethyated promoter in their
Survival for glioblastoma (GBM) patients with an unmethyated promoter in their tumor is generally worse than methylated tumors as temozolomide (TMZ) response is limited. every 2 weeks until progression. Imaging evaluations occurred every 8 weeks. The primary endpoint was overall survival. Of the 48 unmethylated patients enrolled 46 were evaluable (29 men and 17 women); median age was 55.5 years (29-75) and median KPS was 90 (70-100). All patients completed RT with Daidzein TMZ. The median number of cycles (1 cycle was 4 weeks) was 8 (2-47). Forty-one patients either progressed or died with a median progression free survival of 9.2 months. At a follow up of 33 months the median overall survival was 13.2 months. There were no unexpected toxicities and most observed toxicities were categorized as CTC grade 1 or 2 2. The combination of erlotinib and bevacizumab is tolerable but did not meet our primary endpoint of increasing survival. Daidzein Importantly more trials are needed to find better therapies for GBM patients with an unmethylated promoter. promoter survive on average twice as long as those with unmethylated promoters when treated with TMZ [2 3 5 The efficacy of concurrent and adjuvant TMZ in Daidzein the unmethylated patient population is quite limited. Unfortunately only one-third of patients have tumors with methylated promoter creating a significant unmet need for improved therapies for the remainder and majority of patients with GBM [5]. Vascular proliferation is one of Pfkp the hallmarks of GBM that is most commonly associated with an increase in production of vascular endothelial growth factor (VEGF) subtype A [6 7 VEGF blockade can potentially decrease tumor growth by inhibiting pathway activation thereby preventing neoangiogenesis. Several anti-angiogenic agents targeting the VEGF pathway in recurrent GBM have been tried in clinical trials [8-11]. Only bevacizumab had positive data leading to an accelerated FDA approval in 2009 2009 based on data from two trials [8 9 Two confirma-tory trials in newly diagnosed patients failed to show a survival benefit with bevacizumab [3 12 Prominent abnormalities in signal transduction pathways are also characteristic of GBM. Based on the data from the TCGA Epidermal Growth Factor is one of the most overexpressed or mutated abnormalities in GBM [13]. EGF is mitogenic an effect mediated by the binding of EGF to a cell surface EGF receptor (EGFR). To date single agents targeting EGFR such as erlotinib gefitinib or afatinib have Daidzein not been successful in the treatment of recurrent glioblastoma [14-19]. The efficacy of single agent targeted therapies in malignant gliomas has been poor. However pre-clinical data suggest that a multi-targeted approach may be more efficacious than single target inhibition [20-24]. Given the poor outcome of GBM patients with unmethylated promoter methylation status was assessed by a central laboratory (Lab Corp NC). Unmethylated patients then moved onto to the second step of the trial after completion of RT; methylated patients were not enrolled. Consent had to be signed before the onset of radiation. A 1 cm3 block of tissue was required for analysis thereby excluding biopsy only patients. For eligibility patients had to be ≥18 years of age with a Karnofsky performance status (KPS) ≥70. Tumor was required to be supratentorial and a post operative MRI was required no more than 72 h after Daidzein surgery or >4 weeks (±7 days) after surgery. Evaluable or measurable disease following resection of tumor was not mandated. No prior treatment was allowed including the use of carmustine implant (Gliadel? Wafer) or radiosurgery. All patients were treated with 60 Gy of radiation with concomitant TMZ at 75 mg/m2/day × 42 days (±3 days). Eligible patients started the experimental regimen of bevacizumab and erlotinib 4 weeks (±7 days) after the completion of RT + TMZ. Eligibility was reassessed as step 2 2 of sign up prior to initiation of the experimental treatment. Within 7 days of sign up individuals were required to have adequate bone marrow liver and renal function a prothrombin time/international normalized percentage (PT/INR) <1.4 for individuals not on warfarin and they could not possess proteinuria as demonstrated by a urine protein: creatinine (UPC) percentage ≥1.0 or urine dipstick for protein-uria ≥2+ (if ≥2+.
## Glioblastoma multiforme (GBM) is the most common principal human brain tumor
Glioblastoma multiforme (GBM) is the most common principal human brain tumor in adults using a median success of 16. needle shall penetrate. Lift the needle such Rilmenidine that it will not obstruct the certain area. Drill a little burr gap using a 0.6 mm bit for mice and 1.75 mm bit for rats using wide circular drill motions. The burr gap ought to be wide to provide a large open area for the insertion of the needle. Drilling into the skull produces considerable heat so it is definitely advisable to drill in short bursts while intermittently bathing the skull with snow cold saline remedy which can be removed using a cotton swab. Avoid severing any blood vessels during drilling. In the event of bleeding clean the burr opening to prevent the blood clot from obstructing the needle access and retraction (observe Notice 5 and 6). Weight the Hamilton syringe (33G needle for mice 26 for rats) with the proper dose of cells (observe Note 7). Lower the needle such that it is definitely leveled with the dura. Read the dorsoventral coordinates and lower the needle to 0.5 mm plus the right Rilmenidine coordinates depending on the GBM model. Pull the needle up toward the dura 0.5 mm and wait for 2 minutes. The extra 0.5 mm provides a pocket for the cells at Rilmenidine the time of injection. Administer the injection slowly over the course of 0.5 μl/min. Keep the needle in place for 5 minutes post injection to allow tumor cells to settle before slowly withdrawing the needle from the brain. Clean the syringe thoroughly by flushing 3 times with saline (see Note 8). Flush the skull with sterile saline 3 times to remove any residual cells from the brain surface and dry the area with a cotton swab. Remove the skin retractor and close the incision using 3-0 nylon suture. Resuscitate the animal by i.p injection of atipamazole. Administer buprenorphine subcutaneously. Monitor the animal until it fully recovers from anesthesia and return them to their cage. Provide the animals with water soaked chow in a petri dish and monitor for any surgical complications. Remove any staying sutures at 10-14 times post medical procedures. 3.2 Adenoviral gene therapy 1 Dilute the adenovirus preparation in sterile PBS in a way that the required amount of infectious devices can be given in the correct volume (discover Notice 9). 2 Anesthetize tumor bearing pets with an i.p shot of dexdomitor and ketamine. Ensure that the pet is fully anesthetized by checking for having less reactions to tail and footpad pinching. Place the anesthetized mice inside a stereotactic equipment. 3 Right now the sutures through the operation for tumor implantation could have dropped off as well as the older pores and skin incision could have healed. Utilizing a scalpel make a 1.5 cm midline incision in to the pores and skin at the same location as before. Utilize the scalpel cutting tool to split up the healed pores and skin through the underlying cells gently. 4 Make use of pores and skin retractors RCBTB1 to attend your skin on either family member part from the incision. 5 Take away the fibrous tissue covering the site of the tumor injection by gently scraping with the scalpel blade. Wash the area with cold saline to stop any bleeding and clean with ethanol swab. 6 The Rilmenidine old burr hole should now be clearly visible. At this point it is not required to drill again through the bone to provide access to the needle into the site of tumor implantation. Use a bent 26G needle to remove the scar tissue that forms at the burr hole. Use ethanol swabs to clean the burr hole to remove any clotted blood. 7 Lower the needle into the brain to the dorsoventral coordinate of tumor injection plus 0.5 mm ventrally and wait for 2 minutes before slowly injecting 1/3rd of the vector suspension. Wait for 1 minute for the vector solution to infuse into the tissue. Move 0.5 mm up dorsally and inject another 1/3rd of the vector and wait an additional minute. Do it again for 1 last time for you to inject the rest of the vector suspension. Wait around for five minutes following the last administration and slowly pull the needle out then. 8 Beginning a day gene therapy administer 25 mg/kg of Ganciclovir i post.p double daily for 7 days for mice or 10 days for rats (see Note 10). Monitor the animals for signs of moribund behavior (hunched posture lack of grooming porphyrin staining around the eyes) and euthanize when their health status reaches the criteria established by the institutional animal care guidelines. Animals will be humanely killed by terminal perfusion with oxygenated heparinized Tyrode’s solution under deep.
## The Institute of Medicine’s National Cancer Policy Panel report warns how
The Institute of Medicine’s National Cancer Policy Panel report warns how the healthcare workforce is inadequate to meet up the rising demand for cancer care. with many adverse results including work Rabbit Polyclonal to BMP8B. dissatisfaction purpose to keep current placement and increased unintentional exposure to dangerous drugs.3 4 While variation in operating conditions are documented across institutions zero scholarly research to day possess analyzed variation institutions. Such an strategy would enable organizations to improve deficiencies and study from guidelines within healthcare organizations. Likewise the perspectives of medical market leaders and advanced practice nurses such as for example nurse professionals and medical nurse specialists never have been researched. The Dana-Farber Tumor Institute (DFCI) utilizes approximately 329 authorized nurses and 76 nurse professionals. Ambulatory care quantity at DFCI and three satellites was 216 150 individual appointments in fiscal season 2014. DFCI is among the few ambulatory care-based services that is recognized by the American Nurses’ Hydrochlorothiazide Credentialing Center Magnet Recognition Program? for nursing excellence.5 The DFCI Nursing and Patient Care Services (NPCS) department leadership team supports the measurement and improvement of practice environments to support the delivery of excellent patient care. The institution collects and submits data to the National Database of Nursing Quality Indicators.6 However these measures focus on acute care indicators and many measures do not apply directly to ambulatory oncology settings. Therefore the NPCS department launched a one-year project to assess the nursing practice environments and overall performance of behaviors that support patient safety and several nursing outcomes including nurse satisfaction and intention to leave. The leadership team plans to use the data to identify and prioritize interventions to strengthen the practice environments within specific models. The methods and study findings have great relevance to the large number of ambulatory oncology settings in the United States where the bulk of malignancy care is usually delivered. The objective of this paper is usually to examine the patterns and correlates of the work environment for nurses and nurse practitioners working in a National Cancer Institute-designated Comprehensive Cancer. METHODS This descriptive study employed a web-based survey of registered nurses and advanced practice nurses employed by DFCI to address three research objectives: (1) To examine nurse-reported outcomes throughout the institution (2) to examine how the practice environment of registered nurses in our institution correlates with these outcomes and (3) to identify variation in practice environments and the presence or absence of behaviors congruent with individual safety across models. Provided the project’s impetus to motivate quality improvement and our omission of personal identifiers in the study the institutional review plank deemed the analysis exempt from review and waived the necessity for signed up to date consent. Test and Setting People utilized or contracted by DFCI and functioning within the primary campus in Boston or among three off-site satellite television locations who keep a rn license were asked to take part in Hydrochlorothiazide the study. The institution’s recruiting database discovered 403 people with an active rn permit. These nurses had been utilized across 13 systems including the three satellite Hydrochlorothiazide television locations. Study and Methods Qualtrics (Provo UT) an encrypted protected cloud-based study management system was utilized to conduct Hydrochlorothiazide the analysis. Dillman’s Tailored Style technique7 guided the questionnaire style introductory cover reminder and notice scripts to potential individuals. Because all methods have been previously evaluated for Hydrochlorothiazide validity and dependability graduate students executed pilot testing to assure items could be completed with simplicity within the web-based platform; these tests confirmed the survey required approximately ten minutes to total. To encourage participation all devices received snack baskets and a authorized card from the Chief Nurse Executive and one of the investigators with no direct management obligations. Participation rates were monitored by the study staff and unit directors with low participation rates were urged to remind staff to total the.
## effect of a potential global influenza pandemic calls for the development
effect of a potential global influenza pandemic calls for the development and delivery of effective antiviral therapeutics [1]. the neuraminidase inhibitors (the focus of this commentary) and the adamantanes which block the M2 protein ion channel [6]. Neuraminidase is an influenza membrane glycoprotein responsible for cleaving sialic acid from host cell membranes and therefore potentiating viral launch [7 8 Phylogenetic analyses and high-resolution crystal constructions of influenza neuraminidase in complicated using the enzyme’s organic substrate sialic acidity exposed that residues in immediate connection with the substrate are Folinic acid calcium salt (Leucovorin) extremely conserved among influenza strains (Shape 1A) [9 10 Info from these high-resolution constructions thus provided understanding towards the logical style of neuraminidase inhibitors with nanomolar strength and high dental bioactivity [11]. Oseltamivir (Shape 1B) can be an Folinic acid calcium salt (Leucovorin) optimized substance produced from these research that is presently a respected anti-influenza medications [5 12 13 Nevertheless oseltamivir shows a C6-pentyloxy group that interacts having a hydrophobic site in neuraminidase whereas the indigenous substrate sialic Folinic acid calcium salt (Leucovorin) acidity consists of a glycerol moiety at C6 that will not interact significantly with the hydrophobic site [10 14 15 This distinction has assisted the acquisition of drug-resistant mutations by enabling neuraminidase variants to exclude oseltamivir from the active site while continuing to process sialic acid with high efficiency in the presence of the drug [14 15 Alternatively oseltamivir resistance-conferring mutations have also been observed in hemagglutinin that weaken binding to sialic acid receptors alleviating the pressure on neuraminidase to cleave sialic acid for virion budding [16]. Physique 1 (A) Structure of N1 neuraminidase with sialic acid bound in the active site. Sialic acid is shown in Folinic acid calcium salt (Leucovorin) cyan functional residues are shown in blue and framework residues are shown in magenta (PDB 2BAT) [10]. (B) Structure of oseltamivir [12]. A commonly observed amino acid substitution in neuraminidase that confers oseltamivir resistance H275Y also results in decreased neuraminidase stability and surface expression relative to wild-type N1 neuraminidase [17]. The associated fitness costs of the H275Y substitution for influenza prevented this variant from circulating prior to 2008 after which permissive secondary mutations that rescue H275Y neuraminidase surface expression appeared [2 18 19 Significant progress has been made in identifying these compensatory mutations and characterizing their mechanisms of action [18-20]. Beyond the H275Y substitution it is now known that this I223R/K/T N295S and several other amino acid substitutions can also confer oseltamivir resistance although they simultaneously reduce neuraminidase activity for various reasons [21-24]. Interestingly reported neuraminidase amino acid substitutions that engender oseltamivir resistance in influenza strains most often occur at active site framework residues which are residues that interact with functional residues but are not directly involved in the catalytic mechanism of action (Physique 1 [23-25]. While mutation of Folinic acid calcium salt (Leucovorin) functional residues generally abrogates protein function mutation of framework residues is usually less detrimental to protein function but can still have significant associated fitness costs. Indeed prior to the work of Jiang et al. [26] the reported oseltamivir-resistant mutations in neuraminidase had associated fitness costs that often required compensatory fitness-enhancing mutations for efficient viral Mouse monoclonal to CTCF propagation. Although computational methods have had success in specific cases [18] the diverse structural locales of oseltamivir-resistance mutations and the associated permissive secondary mutations question the feasibility of using purely theoretical methods to predict amino acid substitutions that could donate to antiviral medication level of resistance. Rationally designing medications that are much less vunerable to antiviral medication level of resistance mechanisms is rather likely to need extremely integrated experimental and theoretical research. With advancements in next-generation sequencing technology the field provides as a result shifted toward high-throughput testing to systematically recognize potential resistance-conferring mutations at one nucleotide resolution. Many research have used a number of experimental solutions to bring in mutations execute selection and evaluate results [27]. An average strategy involves arbitrary mutagenesis of codons or specific nucleotides of influenza genes appealing.
## Cocaine affects neuronal activity and constricts cerebral blood vessels making it
Cocaine affects neuronal activity and constricts cerebral blood vessels making it difficult to determine whether cocaine-induced changes in cerebral blood flow (CBF) reflect neuronal activation or its vasoactive effects. EEG recordings and CBF with TDZD-8 laser Doppler flowmetry in the rat’s somatosensory cortex for both resting state and forepaw stimulation prior to and following cocaine administration (1mg/kg resting state) was used to quantify the relative flow change to brain activation. For field potential detection a pair of ?0.3mm EEG electrodes (EL450 Biopac) – with one affixed on the thinned skull in the cranial window one on the thinned skull on the contralateral side of the brain and a third ground electrode (Biopac EL452) inserted under the neck skin (Fig.1a) were connected to a multi-channel EEG amplifier (Biopac MP150/EEG100C). The signal was digitized at 2kHz bandpass filtered (0.1–35 Hz) amplified and then interfaced to PC for recording and real-time display (Fig.2a). To optimize the signal TDZD-8 recordings the LDF probe was slightly adjusted in the cortical area until the maximal response was reached (i.e. the location at peak ?CBFp shown in Fig.1b). Then the signal electrode was positioned on the skull next to the LDF probe for EEG recording above the somatosensory cortex (AP ?0.25; LR +3.0). Measurement on the thinned skull maintains the integrity of the cortex environment. Fig.2 Field potential (a) and CBF (b) traces measured before and after cocaine administration (1mg/kg i.v. at t=0min) during which forepaw stimulation was performed every 3min from ?9min (baseline period) to 30min after cocaine injection. Panels (c … Electrical forepaw stimulation Two needle electrodes inserted under the skin of contralateral forepaws of the rat were connected to an electrical stimulator (A–M System 2100) for forepaw stimulation. Synchronized with PC each forepaw stimulation epoch lasted 10s during which 30 bipolar rectangular electrical pulses (0.3ms pulse width 2 peak-to-peak amplitude) were delivered at 3Hz (Fig.1c and Suppl. Fig.s1B0). Prior to forepaw stimulation and drug administration the rat was kept in the resting state for >15min to minimize physiological fluctuations. Moreover rat was in the resting state for 3min between 2 adjacent forepaw stimulations to reduce baseline drift. Briefly the whole experiment procedure included 3 forepaw stimulation epochs during the baseline period (e.g. 9 followed by 10 forepaw stimulation epochs following cocaine or saline administration (30min) thus totaling 13 stimulation epochs (i.e. 40 including 1min for cocaine administration) for each rat (Figs.1b & 1c). Data analysis for field potential TDZD-8 and CBF As shown in Suppl. Fig.s1B1 the electrical forepaw TDZD-8 stimulation evoked field potential referred to as stimulation evoked potentials (SEP) was quantified by the average peak-to-peak intensity TDZD-8 VSEP over all of the spikes within a pulse epoch i.e.
$VSEP=1NSEP∑i=1NSEPVi$
(1) where Vi (i=1 2 … NSEP) denotes the amplitudes of forepaw stimulation evoked SEP spikes and NSEP is the total number Rabbit Polyclonal to DOCK1. of spikes within the pulse epoch. Meanwhile spontaneous field potential spikes between two adjacent forepaw stimulations that reflect resting-state neuronal activity were evaluated by the field potential spike counts per minute
$nrest=1Δt∑Δti$
(2) where Δt is the time duration to count field potential spikes. Δt=1min before each forepaw simulation was used in the study. For simplicity resting-state spontaneous neuronal.
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The crisis of commodities for the concept of capitalism
Capital today pursues the goal of its own accumulation through a bizarre inversion of its materials. On the one had, what Karl Polanyi dubbed “fictitious commodities” – namely money, land, and labour1 – are increasingly commodified by modern law and fiscal policy (a topic beyond the scope of this essay). Yet on the other, those objects that another Karl would have readily recognised in his day as commodities (Waren)2, have been subjected over the past century to a process of rapid decommodification.
The capitalism of old relied on the notion of Homo economicus, a rational individual who sought out largely homogenous commodities at the best available price, as and when they needed them. But the all-pervading advertising industry developed by capital (through the vehicle of Sigmund Freud’s nephew, Edward Bernays) in the early twentieth century to accelerate accumulation now does all it can to encourage individuals to behave irrationally. Advertising plus prosperity shifted the economies of advanced Western nations from economies of need to economies of want. No longer did the interests of capital lie in the utilitarian consumer: instead, the consumer had to be reprogrammed to behave irrationally, buying things they didn’t need at uncompetitive prices. In short, they had to be trained to stop buying commodities, and start buying post-commodities.
Consumers today increasingly buy not use values (Gebrauchswert)3, but stories (what Guy Debord calls “star commodities”, vedettes-marchandise)4: this car will take you on adventures, this deodorant will make you irresistible to women, this handbag will make people like you more. The transition from industrial capitalism to consumerism has produced a peculiar fusion of commodity fetishism with pre-capitalist mythical society.
During the earlier stages of capitalism, as Debord points out in The Society of the Spectacle, exchange value – though distorted by market forces – maintained an essential link with use value, because the consumption of goods in society was still largely determined by utility. In the age of advertising and designer brands however, that link has been all but severed5. Two products with exactly the same propensity to fulfill exactly the same function can sell at radically different price points to radically different consumers, simply because of a logo. This not only lulls us into a manifold of artifice (le spectacle)6, but undermines the very effectiveness of the capitalist system, because market saturation no longer induces price competition which forces capitalists to switch to the production of things that society actually needs in order to make a profit.
In their paper, The Economic Life of Things7, Luc Boltanski and Arnaud Esquerre divide “things” into three categories: commodities, as conventionally understood, and two categories of post-commodity, collectibles – broadly analogous to Debord’s vedettes-marchandise – and assets. Like advertising before it, finance has fundamentally revolutionised the mechanics of capitalism and brought about a modern economy in which speculative investment – investment in assets – competes with productive investment for the affections of capital, thus supplanting the production of genuine commodities.
The failure of the tax system to discriminate effectively against returns on productive and speculative investments – erroneously lumped together under the misnomer “capital gains” – only exacerbates this. Attempts to stimulate productive investment by cutting capital gains tax only serve to increase the relative attractiveness of speculative investments.8 Fixing this is not straightforward: a simple new-issue shares/bonds equals productive investment, “assets” equals speculative investment formula is vulnerable to exploitation via new companies being set up who issue new shares, but derive all or most of their profits from speculative activities. But if we are to find a solution to this crisis of value9 – whereby the production of actual use values (in the form of genuine commodities) is supplanted by a virtual economy of speculative gambling – then CGT must be replaced with a smarter framework for the taxation of profit.
Having just emerged from a seemingly fundamental crisis, the vague notion of “capitalism” is still the only game in town. Though flawed, I will not venture here to suggest there is an obviously better alternative. But everyone, those who critique and those who proselytise for capitalism alike, must accept that the economic system that is dominant today is unrecognisable from that of the late nineteenth century, and thus the term “capitalism” – originally predicated on the formula M‑C‑M’ 10– is fundamentally meaningless.
Footnotes:
[1] Polanyi, Karl; The Great Transformation, 1944
[2] Marx, Karl; Das Kapital, Buch I: Der Produktionsprocess des Kapitals, 1867
[3] Marx, ibid.
[4] Debord, Guy; La Société du spectacle, 1967
[5] Debord, ibid.: “Exchange value could arise only as a representative of use value, but the victory it eventually won with its own weapons created the conditions for its own autonomous power. By mobilizing all human use value and monopolizing its fulfillment, exchange value ultimately succeeded in controlling use. Use has come to be seen purely in terms of exchange value, and is now completely at its mercy. Starting out like a condottiere in the service of use value, exchange value has ended up waging the war for its own sake.” (translated by Ken Knabb)
[6] Debord, ibid.
[7] Boltanski, Luc; Esquerre, Arnaud; The Economic Life of Things, New Left Review vol. 98 (March-April 2016) pp. 31-56
[8] If Y is the yield on a particular investment, and T is the rate of capital gains tax, the ratio between the return on two investments – and thus the relative attractiveness of the juicier over the drier – is: ${{1 + Y_1 (1-T)}\over{1 + Y_2 (1-T)}},Y_1 >= Y_2$ , which increases as T decreases.
[9] Westra, Richard; Unleashing Usury: How Finance Opened the Door for Capitalism then Swallowed it Whole, 2016
[10] Marx, ibid.
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Van der Pol and the history of relaxation oscillations: \\ toward the emergence of a concept - Archive ouverte HAL Access content directly
Journal Articles Chaos: An Interdisciplinary Journal of Nonlinear Science Year : 2012
## Van der Pol and the history of relaxation oscillations: \\ toward the emergence of a concept
(1) , (2)
1
2
Jean-Marc Ginoux
Christophe Letellier
#### Abstract
Relaxation oscillations are commonly associated with the name of Balthazar van der Pol via his eponymous paper (Philosophical Magazine, 1926) in which he apparently introduced this terminology to describe the nonlinear oscillations produced by self-sustained oscillating systems such as a triode circuit. Our aim is to investigate how relaxation oscillations were actually discovered. Browsing the literature from the late 19th century, we identified four self-oscillating systems in which relaxation oscillations have been observed: i) the series dynamo machine conducted by Gérard-Lescuyer (1880), ii) the musical arc discovered by Duddell (1901) and investigated by Blondel (1905), iii) the triode invented by de Forest (1907) and, iv) the multivibrator elaborated by Abraham and Bloch (1917). The differential equation describing such a self-oscillating system was proposed by Poincaré for the musical arc (1908), by Janet for the series dynamo machine (1919), and by Blondel for the triode (1919). Once Janet (1919) established that these three self-oscillating systems can be described by the same equation, van der Pol proposed (1926) a generic dimensionless equation which captures the relevant dynamical properties shared by these systems. Van der Pol's contributions during the period of 1926-1930 were investigated to show how, with Le Corbeiller's help, he popularized the "relaxation oscillations" using the previous experiments as examples and, turned them into a concept.
### Dates and versions
hal-01056923 , version 1 (20-08-2014)
### Identifiers
• HAL Id : hal-01056923 , version 1
• ARXIV :
• DOI :
### Cite
Jean-Marc Ginoux, Christophe Letellier. Van der Pol and the history of relaxation oscillations: \\ toward the emergence of a concept. Chaos: An Interdisciplinary Journal of Nonlinear Science, 2012, 22, pp.023120. ⟨10.1063/1.3670008⟩. ⟨hal-01056923⟩
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[–]Algebra 4 points5 points ago
sorry, this has been archived and can no longer be voted on
Perhaps I'm missing something, but I thought vector spaces were modules over fields.... F[x] is, in general, not a field.
[–] 7 points8 points ago
sorry, this has been archived and can no longer be voted on
A linear transformation T on a finite dimensional vector space over F actually determines an F[x]-module structure on that vector space by setting f(x)·v = f(T)·v (so for example (x2+x+2)·v = T(T(v))+T(v)+2v). This allows us to use the decomposition theorem for finitely generated modules over PIDs to study T. For example, two transformations are similar if and only if they induce the same decomposition.
(F[x] is never a field, btw)
[–]Algebra 5 points6 points ago
sorry, this has been archived and can no longer be voted on
Somehow I've never seen this. Thanks
And thanks for the correction
[–] 2 points3 points ago
sorry, this has been archived and can no longer be voted on
A given vector space can frequently be a module, and indeed a vector space, over many rings. For example, every complex vector space can be considered as a R-module (where R is the real numbers), and then of course because R is a field, it is actually also a vector space over the reals. Another instructive example would be to consider the reals as a vector space over the rationals - what dimension would it have then? And of course there is the F[x]-module structure mentioned by talkloud, where it is important to note that there are many non-module-isomorphic F[x]-module structures for the vector space (which is not the case for turning a complex vector space into a real vector space - every way to do it is isomorphic).
This then leads to the theory of tensor products of modules, as all of these constructions can be unified in the language of tensor products.
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# Tag Info
1
So we ended up calling this quantity the $\alpha$th moment of information and proving some inequalities about it: https://arxiv.org/abs/2004.12680 (paper to appear in the NIPS 2021 conference).
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# Why do high frequencies have a larger deflection through a prism than smaller frequencies? [duplicate]
The following is a proof that higher (angular) frequencies have a greater deflection than lower frequencies through a glass prism:
It was omitted in the image above, but $n_{\text{air}}$ is taken to be unity, which is the reason for the $1$ in Snell's law.
My problem is as follows; in a general dielectric (such as a glass prism) we have the following dispersion relation:
$$v_{\text{phase}}=\frac{\omega}{k}=\frac{1}{\sqrt{\mu_0\,\epsilon}}=\frac{c}{{\epsilon_r}^{1/2}}=\frac{c}{n}\tag{1}$$
so in short $$\frac{\omega}{k}=\frac{c}{n}$$
or $$n=\frac{k\,c}{\omega}$$
therefore $$n\propto \frac{1}{\omega}\tag{2}$$
Now looking at the writing in the image it says:
$v_{\text{phase}}$ decreases with $\omega$
According to $(1)$ $v_{\text{phase}}$ increases with $\omega$; since $v_{\text{phase}}\propto\omega$.
But that's not the only problem the text also says:
$n_{\text{glass}}$ increases with $\omega$
According to $(2)$ $n$ decreases with $\omega$. Another contradiction.
Is there anyone that can explain why $v_{\text{phase}}$ decreases with $\omega$ and why $n_{\text{glass}}$ increases with $\omega$?
## EDIT:
I'm voting to close this question now since I no longer care whether or not it it is a duplicate of this question as I already have accepted an answer to my question.
• There is no proof in general, since it all depends on the dispersion relationship of the particular glass used to make the prism. But, in general the index of refraction will change with frequency, so the matching conditions at the boundary change, requiring some angle of deflection. – Jon Custer Aug 9 '17 at 22:09
• You have implicitly assumed that the wave-number remains the same when crossing a boundary; only it doesn't. Understanding the relationship between $n$ and $\omega$ requires you to look at the microscopic physics on the wave interacting with the atoms of the material. A basic treatment can be found in any upper-division E&M text, where it makes up roughly a semester's worth of work. Treatments at the graduate level are both faster and more detailed. – dmckee --- ex-moderator kitten Aug 9 '17 at 22:24
• @JonCuster Okay then, I have edited my question. All I would like to know at this point is why those quotations in my question are correct. Could you please explain? – BLAZE Aug 9 '17 at 22:31
• Possible duplicate of Why do prisms work (why is refraction frequency dependent)? – Floris Aug 10 '17 at 0:44
• @BLAZE - see my updated answer. I think I should have cleared up your confusion. – Floris Aug 10 '17 at 1:24
higher (angular) frequencies have a greater deflection than lower frequencies through a glass prism
is false - materials have a refractive index that trends lower at higher frequencies (for X rays the refractive index is almost 1.0). But it is true for the limited frequencies that correspond to visible light, for a transparent glass prism (no absorption bands, i.e. colorless glass).
Considering a dielectric as made up from different damped harmonic oscillators, as you approach resonance you will initially get an increase in response amplitude and then a decrease, as you pass through resonance. This means that the refractive index as a function of frequency tends to follow a curve like this (after Hecht and Zajak, "Optics" (1973), figure 3.14)
If you have a material that has a positive slope in the range of frequencies of interest, your relationship holds - this is the "normal dispersion" range. But in general it doesn't (because of the "anomalous dispersion" that occurs around regions of resonance).
In general, the refractive index follows an equation of the form
$$\frac{n^2(\omega)-1}{n^2(\omega)+2} = \frac{Nq_e^2}{3\epsilon_0 m_e} \sum_j \frac{F_j}{\omega_{0j}^2 - \omega^2+i\gamma_j \omega}$$
(equation 3.38 from Hecht and Zajac (1973) "Optics"). You can see there are terms related to the individual resonances, $\omega_{0j}$, that correspond to absorption modes of the molecules that make up your medium. As the frequency increases, fewer and fewer of these modes will be excited, which is why the large scale trend is for the refractive index to decrease; but on a smaller scale, between characteristic frequencies, the trend is reversed. And it so happens that for a clear material like glass, the fact it is colorless implies that there can be no absorption in the visible range, and that therefore the entire visible range must have "normal" dispersion.
UPDATE
I was too hasty in my reply; from the comments, I realize there are specific parts of the derivation you are struggling with. Let's take these two in turn.
$v_{phase}$ decreases with $\omega$
This seems to be contradicted by the equation $v_{phase}=\frac{\omega}{k}$ which suggests that $v_{phase}$ should increase with frequency. But that ignores the fact that the wave number $k$ is also changing with frequency. That is why the more sensible expression is $v_{phase}=\frac{c}{n}$ - we know that $c$ is constant so we only have to worry about the effect of frequency on $n$. And we know that, over the range of visible light frequencies, the refractive index increases with frequency (decreases with wavelength, which is how it's shown in the image I reproduced from the answer to the duplicate question I marked).
The second statement,
$n_{glass}$ increases with $\omega$
is again not contradicted by your expression (2), because once again it contains $k(\omega)$ so you can't just state it will be proportional to $\frac{1}{\omega}$.
• @BLAZE I have edited my answer - hope this is clearer now, and more to the point of your question. – Floris Aug 10 '17 at 1:23
• @Floris Hi again, I have fixed errors in the quotations of your post (under the update) so that it matches the quotes in my question. Could you please revise your answer to see if your argument is still valid? Many thanks. – BLAZE Aug 10 '17 at 12:59
• @BLAZE sorry yes I don't know how I ended up writing $n$ instead of $\omega$ there... the argument I made only makes sense with $\omega$... – Floris Aug 10 '17 at 13:35
The phase velocity equation (1) is not relevant here. Yes, it relates all these properties at fixed frequency, but it ignores the fact that n is a function of frequency: $n(\omega)$, and hence, leads to confusion.
The index of refraction of any material is of course a material property--and in the prism, it increases with frequency. Generally, this is a result of the Kramer-Kronig relation, which relates the real part of the index of refraction (propagation) with the complex part (absorption). As you approach the absorption frequency from below, the index of refraction increases, and voila: dispersion.
Of course, now you can ask why there is absorption in the ultraviolet.
In the case of linear dispersive materials, two processes can lead to deviation of a composite light from its actual path- refraction, which leads to a change in phase velocity, and dispersion, which leads to frequency-dependent refractive index. The change in the magnitude of wavevector for a light in such a case is given by
$$k(\omega)=\frac{n(\omega)\omega}{c}=\frac{\omega}{v_p(\omega)}$$
Going with the proof given in the book, as frequency $\omega$ increases, the refractive index, $n(\omega)$, increases (Why?). This will naturally lead to a decrease in phase velocity, since
$$v_p(\omega)=\frac{c}{n(\omega)}$$
Now, for a given frequency $\omega$, the wavenumber decreases from the free-space value, when it undergoes refraction ($k(\omega)<k_0(\omega))$:
$$k(\omega)=\frac{2\pi}{\lambda(\omega)}=\frac{2\pi n(\omega)}{\lambda_0(\omega)}$$
Increasing the frequency will hence lead to an increase in refractive index as well as a decrease in wavelength. This will lead to an overall increase in $k$ with increase in $\omega$. This is what you are missing. You treated $k$ as a constant in saying $n\propto\omega^{-1}$, which is not true: $k(\omega)\propto\omega^2\implies n(\omega)\propto\omega$.
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# Elleana is planning to join a DVD club and is investigating the options for membership. Option 1 is a $20 membership fee and$1.25 rental charge for each DVD rented. Option 2 has no rental fee and charges $2.50 for each DVD rented. How many DVDs would Elleanna have to rent in order for the total cost of Option 1 to be equal to Option 2? Question Linear equations and graphs asked 2021-01-17 Elleana is planning to join a DVD club and is investigating the options for membership. Option 1 is a$20 membership fee and $1.25 rental charge for each DVD rented. Option 2 has no rental fee and charges$2.50 for each DVD rented. How many DVDs would Elleanna have to rent in order for the total cost of Option 1 to be equal to Option 2?
2021-01-18
Let y be the total cost and x be the DVD's rented. Option 1 has a total cost of:
y=20+1.25x
Option 2 has a total cost of:
y=2.50x
Equate the two costs and solve for x:
2.50x=20+1.25x
1.25x=20
x=16
So, Elleana has to rent 16 DVD's in order for the total cost of Option 1 to be equal to Option 2.
### Relevant Questions
To print his first novel, Shane can use a print-on-demand book printer or he can buy a printer. The book printer charges a setup fee of $150 plus$6 per copy of the book. The printer he would need costs $750, and it would cost$2 per copy to print the book. For how many copies are the costs the same?
A yoga studio charges a $36 membership fee and a$20.60 per month for 10 classes. A Martial Arts studio charges a $20 membership fee and$22.20 per month for 10 classes. Your friend belongs to the yoga studio the same month you belong to the Martial Arts studio. After how many months is your friend's total cost the same as your total cost?
The mill Mountain Coffee shop blends coffee on the premises for its customers. it sells three basic blends in 1- pound bags, Special , Mountain dark, and Mill regular. It uses four different types of coffee to produce the blends- Brazilian, mocha,Columbian, and mild. The shop used the following blend recipe requirements :
$$\displaystyle{b}{e}{g}\in{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}{\left\lbrace{\left|{l}\right|}{l}{\left|{l}\right|}\right\rbrace}{h}{l}\in{e}\text{Blend}&\text{Mix requirement}&\text{Selling price/lb(\\)}\backslash{h}{l}\in{e}\text{special}&\text{at least 40% columbian,}&{6.50}\backslash&\text{at least 30% mocha}\backslash{h}{l}\in{e}\text{Dartk}&\text{at least 60% Brazillian}&{5.25}\backslash&\text{no more than 10% mid}\backslash{h}{l}\in{e}\text{Regular}&\text{no more than 60% mid}&{3.75}\backslash&\text{at least 30% Brazillian}\backslash{h}{l}\in{e}{e}{n}{d}{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}$$
The cost of Brazilian coffee is 2.00 per pound, the cost of mocha is $2.75 per pound, the cost of Columbian is$2.90 per pound,and the cost of mild is $1.70 per pound. The shop has 110 pounds of Brazilan coffee. 70 pounds of mocha, 80 pounds of Columbian, and 150 pounds of mild coffee available per week. The shop wants to know the amount of each blend it should prepare each week to maximize profit. a. Formulate a linear programming model b. Solve this model asked 2020-10-23 1. Find each of the requested values for a population with a mean of $$? = 40$$, and a standard deviation of $$? = 8$$ A. What is the z-score corresponding to $$X = 52?$$ B. What is the X value corresponding to $$z = - 0.50?$$ C. If all of the scores in the population are transformed into z-scores, what will be the values for the mean and standard deviation for the complete set of z-scores? D. What is the z-score corresponding to a sample mean of $$M=42$$ for a sample of $$n = 4$$ scores? E. What is the z-scores corresponding to a sample mean of $$M= 42$$ for a sample of $$n = 6$$ scores? 2. True or false: a. All normal distributions are symmetrical b. All normal distributions have a mean of 1.0 c. All normal distributions have a standard deviation of 1.0 d. The total area under the curve of all normal distributions is equal to 1 3. Interpret the location, direction, and distance (near or far) of the following zscores: $$a. -2.00 b. 1.25 c. 3.50 d. -0.34$$ 4. You are part of a trivia team and have tracked your team’s performance since you started playing, so you know that your scores are normally distributed with $$\mu = 78$$ and $$\sigma = 12$$. Recently, a new person joined the team, and you think the scores have gotten better. Use hypothesis testing to see if the average score has improved based on the following 8 weeks’ worth of score data: $$82, 74, 62, 68, 79, 94, 90, 81, 80$$. 5. You get hired as a server at a local restaurant, and the manager tells you that servers’ tips are$42 on average but vary about $$12 (\mu = 42, \sigma = 12)$$. You decide to track your tips to see if you make a different amount, but because this is your first job as a server, you don’t know if you will make more or less in tips. After working 16 shifts, you find that your average nightly amount is $44.50 from tips. Test for a difference between this value and the population mean at the $$\alpha = 0.05$$ level of significance. asked 2021-03-02 Adult tickets to a play cost$22. Tickets for children cost $15. Tickets for a group of 11 people cost a total of$228. Write and solve a system of equations to find how many children and how many adults were in the group.
A small drugstore orders copies of a certain magazine for it magazine rack each week. Let X=demand for the magazine, with pmf
$$\displaystyle{b}{e}{g}\in{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}{\left\lbrace{\left|{l}\right|}{l}{\mid}\right\rbrace}{h}{l}\in{e}{x}&{1}&{2}&{3}&{4}&{5}&{6}\backslash{h}{l}\in{e}{p}{\left({x}\right)}&{\frac{{{1}}}{{{15}}}}&{\frac{{{2}}}{{{15}}}}&{\frac{{{3}}}{{{15}}}}&{\frac{{{4}}}{{{15}}}}&{\frac{{{5}}}{{{15}}}}&{\frac{{{6}}}{{{15}}}}\backslash{h}{l}\in{e}{e}{n}{d}{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}$$
Suppose the store owner actually pays $1.00 for each copy of the magazine and the price to customers is$2.00. If magazines left at the end of the week have no salvage value, is it better to order three or four copies of the magazine?
The owner of a large equipment rental company wants to make a rather quick estimate of the average number of days a piece of ditch-digging equipment is rented out per person per time. The company has records of all rentals, but the amount of time required to conduct an audit of all accounts would be prohibitive. The owner decides to take a random sample of rental invoices. Fourteen different rentals of ditch-diggers are selected randomly from the files, yielding the following data. She wants to use these data to construct a $$99\%$$ confidence interval to estimate the average number of days that a ditch-digger is rented and assumes that the number of days per rental is normally distributed in the population. Use only the appropriate formula and/or statistical table in your textbook to answer this question. Report your answer to 2 decimal places, using conventional rounding rules.
DATA: 3 1 3 2 5 1 2 1 4 2 1 3 1 1
A concert promoter produces two kinds of souvenir shirt, one kind sells for $18 ad the other for$25. The company determines, the total cost, in thousands of dollars, of producting x thousand of the $18 shirt and y thousand of the$25 shirt is given by
$$\displaystyle{C}{\left({x},{y}\right)}={4}{x}^{{2}}-{6}{x}{y}+{3}{y}^{{2}}+{20}{x}+{19}{y}-{12}.$$
How many of each type of shirt must be produced and sold in order to maximize profit?
Looking around in your own country, discuss one practical application in which “piecewise functions” are used either explicitly or implicitly.
Example to be used- A paid parking lot based on length of time stayed, up to half an hour cost $1, over half an hour up to an hour cost$2.50 and over an hour and up to 15 hours cost \$20.
The table below shows the number of people for three different race groups who were shot by police that were either armed or unarmed. These values are very close to the exact numbers. They have been changed slightly for each student to get a unique problem.
Suspect was Armed:
Black - 543
White - 1176
Hispanic - 378
Total - 2097
Suspect was unarmed:
Black - 60
White - 67
Hispanic - 38
Total - 165
Total:
Black - 603
White - 1243
Hispanic - 416
Total - 2262
Give your answer as a decimal to at least three decimal places.
a) What percent are Black?
b) What percent are Unarmed?
c) In order for two variables to be Independent of each other, the P $$(A and B) = P(A) \cdot P(B) P(A and B) = P(A) \cdot P(B).$$
This just means that the percentage of times that both things happen equals the individual percentages multiplied together (Only if they are Independent of each other).
Therefore, if a person's race is independent of whether they were killed being unarmed then the percentage of black people that are killed while being unarmed should equal the percentage of blacks times the percentage of Unarmed. Let's check this. Multiply your answer to part a (percentage of blacks) by your answer to part b (percentage of unarmed).
Remember, the previous answer is only correct if the variables are Independent.
d) Now let's get the real percent that are Black and Unarmed by using the table?
If answer c is "significantly different" than answer d, then that means that there could be a different percentage of unarmed people being shot based on race. We will check this out later in the course.
Let's compare the percentage of unarmed shot for each race.
e) What percent are White and Unarmed?
f) What percent are Hispanic and Unarmed?
If you compare answers d, e and f it shows the highest percentage of unarmed people being shot is most likely white.
Why is that?
This is because there are more white people in the United States than any other race and therefore there are likely to be more white people in the table. Since there are more white people in the table, there most likely would be more white and unarmed people shot by police than any other race. This pulls the percentage of white and unarmed up. In addition, there most likely would be more white and armed shot by police. All the percentages for white people would be higher, because there are more white people. For example, the table contains very few Hispanic people, and the percentage of people in the table that were Hispanic and unarmed is the lowest percentage.
Think of it this way. If you went to a college that was 90% female and 10% male, then females would most likely have the highest percentage of A grades. They would also most likely have the highest percentage of B, C, D and F grades
The correct way to compare is "conditional probability". Conditional probability is getting the probability of something happening, given we are dealing with just the people in a particular group.
g) What percent of blacks shot and killed by police were unarmed?
h) What percent of whites shot and killed by police were unarmed?
i) What percent of Hispanics shot and killed by police were unarmed?
You can see by the answers to part g and h, that the percentage of blacks that were unarmed and killed by police is approximately twice that of whites that were unarmed and killed by police.
j) Why do you believe this is happening?
Do a search on the internet for reasons why blacks are more likely to be killed by police. Read a few articles on the topic. Write your response using the articles as references. Give the websites used in your response. Your answer should be several sentences long with at least one website listed. This part of this problem will be graded after the due date.
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# Thread: Techniques For Solving Equations and Inequalities
1. ## Techniques For Solving Equations and Inequalities
Okay, so im facing a little difficulty with some of this, for example:
$5secx=-x^2, 0
So you have to make LS=RS using trial and error. Now thats all find and dandy except that the answer is 2.5. For this, one side is positive the other is negative...
Another question is for the x must be between o and pi, does that mean I can only use numbers between 0 and 3.14 or is that some sort of radian measure?
$cosx=1/x, -4
The answer is -2.1???? Wouldn't -1 make much more sense?
Im probably missing something simple here, but im going crazy nonetheless.
2. Originally Posted by abc10
Okay, so im facing a little difficulty with some of this, for example:
$5secx=-x^2, 0
So you have to make LS=RS using trial and error. Now thats all find and dandy except that the answer is 2.5. For this, one side is positive the other is negative...
Another question is for the x must be between o and pi, does that mean I can only use numbers between 0 and 3.14 or is that some sort of radian measure?
$cosx=1/x, -4
The answer is -2.1???? Wouldn't -1 make much more sense?
Im probably missing something simple here, but im going crazy nonetheless.
you'll have to solve these using technology (a calculator) ... there is no elementary method to do so by hand.
graph $y = 5\sec{x} + x^2$ and look for the zero(s) of y for x-values between 0 and $\pi$
same for the second ...
graph $\displaystyle y = \cos{x} - \frac{1}{x}$ and look for zero(s) in the given interval for x.
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# A Note on Rectangular Morrey-Campanato Spaces
### New Zealand Journal of Mathematics
Vol. 47, (2017), Pages 111-119
Carolina Espinoza-Villalva
Departamento de Matematicas,
Rosales y Luis Encinas,
Hermosillo, Sonora, 83000,
Mexico.
Abstract We define rectangular central versions of the Campanato and Morrey spaces in $\mathbb{R}^2$ and consider the commutator operator of the rectangular 2-dimensional Hardy operator and a locally integrable function b acting on these Morrey spaces. We prove continuity of this operator when b belongs to a rectangular central Campanato space.
Keywords Rectangular Morrey-Campanato spaces, commutators, Hardy operator
Classification (MSC2000) Primary 47B47; Secondary 42B35.
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# The graph of $f$ is given. State, with reasons, the numbers at which $f$ is $not$ differentiable.
Limits
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### Discussion
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##### Kristen K.
University of Michigan - Ann Arbor
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### Video Transcript
in this problem, It is given that the graph of F is given stayed with reasons, the number at which F is not different shape. So for the first card we can see here the F is not that is function F is not differentiable. It X is equal to -4. Okay, see them, you can right here at is equal to You can see your -40. Great boy, because open point is senior at X is equal to zero. Can you see here? Yes. So, this this shows that this is an undefined point. So when the graph breaks then it is not different shape letter right? And there becomes a discontinuity on stop. Mm Has this continued to this continuously? Right. All right. So now we can say at X equals two minus for a sharp turn is present. Right? So for the sharp turn we cannot differentiate it. Oh right, so now for this second part second graph we can see here, F is not differentiable at X is equal to minus one and FZ equals 2 -2. I'm sorry. Uh X equals two minus two minus one and ex Z equals two. Two. So, similarly from here, we can see this was -4. Right, this was zero. Similarly here, we can see a Sharpton, Right? At XX equals to two. So this is not different tables. Right? So this is the reason for the xxi, closer to it is not different people again At x equals 2 -1, X equals 2 -1. Here. They graph is breaking, you can you can see here like this, this is not a point right here, like you can in first year as you can see this is a point filled with and this is not a bank point. This is a break off the point, right? So we cannot say this is this is also breaking, this is also breaking, right? This is also breaking. So we cannot say this is a point. So that's why this is not a different shape right now. Moving ahead, we can see Now for the 3rd graf. So it is no different table at x equals two. So I'm sorry x is equal to one. So this is not differentiable again, this is a sharp gun, this is a sharp turn. So this is not the friendship. I'm jane. And also the graph breaks. Uh and we can say this is uh this graph is also spread it over minus infinity to infinity. We cannot different the points here. So that's why this is not different. She able right? No, for the 4th and the last what we can see here it will be. This is the graph. Okay, so f is not different shape. X is equal to -2, one and three. So minus two, one and three. Mhm. So bad. Ever A sharp turn is seen. So that is not the friendship. So we can see in -2 -2 and -3 -2 and three. It's it's equals two minus two. And ecstasy Question my three. We can see here the Sharpton. So that's why this is not different people. And here if we solve this graph we can see in your like this that this is this is open point and this is also open point, right? This is open, this is open, this is open. So the points are open here, right? So they can say they they start graph breaks which represents the undefined value. So if the value is not defined, right? So if any of the graph is breaking order, you can see if the value is not defined uh or you can say this is a spread it over minus infinity to infinity. You cannot define the function. So this is how we solve this problem. I hope you understood this concept. Thank you for watching.
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# Practice on Toph
Participate in exhilarating programming contests, solve unique algorithm and data structure challenges and be a part of an awesome community.
# Himi's Negligence
By msabeer · Limits 4s, 512 MB
Himi is a very nice girl but also very lazy and inattentive to her studies. So, her tutor decided to teach her a lesson. Each time Himi misses her homework for her laziness, she’ll have to do the following task:
Himi will need to build exactly $N$ strings, each containing exactly $M$ characters. The valid alphabets are ‘a’, ‘b’, ‘c’ (all lowercase) or if she wants to leave it empty, she can use ’#’. Finally, she has to tell her tutor how many ways she can build such strings.
Here’s the catch: each consecutive strings must follow the given rule:
* Let’s assume i-th string is $X$ and (i + 1)-th string is $Y$ and each index is denoted by j. Then, for each alphabet $X[j]$, $Y[j-1]$ and $Y[j+1]$ must be different from $X[j]$. If j - 1 or j + 1 is out of bound, you can ignore that condition. She is allowed to leave $Y[j-1]$ and/or $Y[j+1]$ empty (using the ’#’ character) and the conditions will not apply then.
Also, there can not be more than 2 unique alphabets in any string. i.e: “aaba” is a valid string but “aabc” is not.
Himi may be lazy but she’s smart. You are the best programmer Himi knows and asked you to write her a program that can do this tiresome work easily.
For your ease, Himi will construct the first string for you following the above mentioned rule. You must not change the first (line number = 1) string.
## Input
The first line of the input will be an integer $T$, the number of test cases.
Each test case will contain two integers $N, M$ and the first string $S$ of length $M$.
### Constraints
#### Subtask 1: (5 Points)
$1 \leq T \leq 50$
$1 \leq M \leq 1$
$1 \leq N \leq 10^7$
#### Subtask 2: (15 Points)
$1 \leq T \leq 50$
$1 \leq M \leq 3$
$1 \leq N \leq 5$
#### Subtask 3: (upto 30 Points)
$1 \leq T \leq 10$
$1 \leq M \leq 4$
$1 \leq N \leq 10^4$
#### Subtask 4: (upto 50 Points)
$1 \leq T \leq 4$
$1 \leq M \leq 4$
$1 \leq N \leq 10^9$
50% test cases on Subtask 3 and 4 will have $M \leq 3$
## Output
For each test case, you have to output “Case #X: Y” (without the quotes), where $X$ is the case number and $Y$ is the result modulo $1000000007 \, \, (10^9+7)$.
## Samples
InputOutput
2
1 1 a
4 1 #
Case #1: 1
Case #2: 64
InputOutput
2
2 2 aa
2 3 aaa
Case #1: 9
Case #2: 27
### Statistics
100% Solution Ratio
YouKnowWhoEarliest, 3w ago
YouKnowWhoFastest, 1.8s
YouKnowWhoLightest, 864 kB
YouKnowWhoShortest, 3218B
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# 7.3 - The Cumulative Distribution Function (CDF)
7.3 - The Cumulative Distribution Function (CDF)
The cumulative distribution function (CDF or cdf) of the random variable $$X$$ has the following definition:
$$F_X(t)=P(X\le t)$$
The cdf is discussed in the text as well as in the notes but I wanted to point out a few things about this function. The cdf is not discussed in detail until section 2.4 but I feel that introducing it earlier is better. The notation sometimes confuses students. The notation $$F_X(t)$$ means that $$F$$ is the cdf for the random variable $$X$$ but it is a function of $$t$$.
We do not focus too much on the cdf for a discrete random variable but we will use them very often when we study continuous random variables. It does not mean that the cdf is not important for discrete random variables. They are just not always used since there are tables and software that help us to find these probabilities for common distributions.
The cdf of random variable $$X$$ has the following properties:
1. $$F_X(t)$$ is a nondecreasing function of $$t$$, for $$-\infty<t<\infty$$.
2. The cdf, $$F_X(t)$$, ranges from 0 to 1. This makes sense since $$F_X(t)$$ is a probability.
3. If $$X$$ is a discrete random variable whose minimum value is $$a$$, then $$F_X(a)=P(X\le a)=P(X=a)=f_X(a)$$. If $$c$$ is less than $$a$$, then $$F_X(c)=0$$.
4. If the maximum value of $$X$$ is $$b$$, then $$F_X(b)=1$$.
5. Also called the distribution function.
6. All probabilities concerning $$X$$ can be stated in terms of $$F$$.
I have provided a few very brief examples using the cdf. We will be looking at these functions in more detail in the future.
Suppose $$X$$ is a discrete random variable. Let the pmf of $$X$$ be equal to
$$f(x)=\dfrac{5-x}{10}, \;\; x=1,2,3,4.$$
Suppose we want to find the cdf of $$X$$. The cdf is $$F_X(t)=P(X\le t)$$.
• For $$t=1$$, $$P(X\le 1)=P(X=1)=f(1)=\dfrac{5-1}{10}=\dfrac{4}{10}$$.
• For $$t=2$$, $$P(X\le 2)=P(X=1 \text{ or } X=2)=P(X=1)+P(X=2)=\dfrac{5-1}{10}+\dfrac{5-2}{10}=\dfrac{4+3}{10}=\dfrac{7}{10}$$
• For $$t=3$$, $$P(X\le 3)=\dfrac{5-1}{10}+\dfrac{5-2}{10}+\dfrac{5-3}{10}=\dfrac{4+3+1}{10}=\dfrac{9}{10}$$.
• For $$t=4$$, $$P(X\le 4)=\dfrac{5-1}{10}+\dfrac{5-2}{10}+\dfrac{5-3}{10}+\dfrac{5-4}{10}=\dfrac{10}{10}=1$$.
It is worth noting that $$P(X\le 2)$$ does not equal $$P(X<2)$$; $$P(X\le 2)=P(X=1, 2)$$ and $$P(X<2)=P(X=1)$$. It is very important for you to carefully read the problems in order to correctly set up the probabilities. You should also look carefully at the notation if a problem provides it.
Consider $$X$$ to be a random variable (a binomial random variable) with the following pmf
$$f(x)=P(X=x)={n\choose x}p^x(1-p)^{n-x}, \;\; \text{for } x=0, 1, \cdots , n.$$
The cdf of $$X$$ evaluated at $$t$$, denoted $$F_X(t)$$, is
$$F_X(t)=\sum_{x=0}^t {n\choose x}p^x(1-p)^{n-x}, \;\; \text{for } 0\le t\le n.$$
• When $$t=0$$, we have $$F_X(0)={n\choose 0}p^0(1-p)^{n-0}$$.
• When $$t=1$$, we have $$F_X(1)={n\choose 0}p^0(1-p)^{n-0}+{n\choose 1}p^1(1-p)^{n-1}$$.
• When $$t=2$$, we have $$F_X(2)={n\choose 0}p^0(1-p)^{n-0}+{n\choose 1}p^1(1-p)^{n-1}+ {n\choose 2}p^2(1-p)^{n-2}$$.
And so on and so forth.
One last example. Suppose we have a family with three children. The sample space for this situation is
$$\mathbf{S}= \left \{ BBB, BBG, BGB, GBB, GGG, GGB, GBG, BGG \right \}$$
where $$B$$ = boy and $$G$$ = girl and suppose the probability of having a boy is the same as the probability of having a girl. Let the random variable $$X$$ be the number of boys. Then $$X$$ will have the following pmf:
t 0 1 2 3 $$P(X=t)$$ $$\dfrac{1}{8}$$ $$\dfrac{3}{8}$$ $$\dfrac{3}{8}$$ $$\dfrac{1}{8}$$
Then, we can use the pmf to find the cdf.
t 0 1 2 3 $$F_X(t)=P(X\le t)$$ $$\dfrac{1}{8}$$ $$\dfrac{1}{8}+\dfrac{3}{8}=\dfrac{4}{8}$$ $$\dfrac{4}{8}+\dfrac{3}{8}=\dfrac{7}{8}$$ $$\dfrac{7}{8}+\dfrac{1}{8}=1$$
## Additional Practice Problem
These are some theoretical problems for the CDF and for expectations. Work these problems out on your own and then click on the link to view the solution.
1. Express the following probabilities in terms of the cdf, $$F_X(t)$$, if $$X$$ is a discrete random variable with support such that $$x$$ being any integer from 0 to $$b$$ and $$0\le a\le b$$:
1. $$P(X\le a)$$
$$P(X\le a)=F_X(a)$$ by definition of cdf
2. $$f_X(a)=P(X=a)$$, where $$f_X(x)$$ is the pmf of $$X$$
$$P(X=a)=P(X\le a)-P(X\le a-1)=F_X(a)-F_X(a-1)$$
3. $$P(X<a)$$
$$P(X<a)=P(X\le a)-P(X=a)=P(X\le a-1)=F_X(a-1)$$
4. $$P(X\ge a)$$
$$P(X\ge a)=1-P(X\le a-1)=1-F_X(a-1)$$
2. Let $$X$$ have distribution function $$F$$. What is the distribution function and expectation of $$\dfrac{X - \mu}{\sigma}$$? In other words, find the distribution function in terms of $$F_X$$ and the expectation in terms of $$E(X)$$.
Let $$Y=\dfrac{X-\mu}{\sigma}$$. We want $$F_Y(t)$$ and $$E(Y)$$.
\begin{align*} & F_Y(y)=P(Y\le y), \text{ by definition of cdf of Y}\\ & F_Y(y)=P(Y\le y)=P\left(\dfrac{X-\mu}{\sigma}\le y\right)=P\left(X\le y\sigma+\mu\right)\\ & F_Y(y)= F_X(t\sigma+\mu) \end{align*}
Now, to find the expectation, we can do this in two ways. One way is to find it using the definition of expectation, $$E(Y)=\sum_y yf_Y(y)$$. In order to do this though, we would need to find $$f_Y(y)$$, which we can find using the CDF if $$F_X$$ was given.
The other way to approach this is to use the properties of expectation.
$$E(Y)=E\left(\dfrac{X-\mu}{\sigma}\right)=\dfrac{1}{\sigma}E(X-\mu)=\dfrac{E(X)-\mu}{\sigma}$$
[1] Link ↥ Has Tooltip/Popover Toggleable Visibility
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# Physics Publications of the ALICE Collaboration in Refereed Journals
#### Numerical values for all ALICE results can be found in the Durham Reaction Database
Total: 114
Measurement of jet quenching with semi-inclusive hadron-jet distributions in central Pb-Pb collisions at ${\sqrt{\bf{s}_{\mathrm {\bf{NN}}}}}$ = 2.76 TeV
Measurement of jet quenching with semi-inclusive hadron-jet distributions in central Pb-Pb collisios at sqrt(NN)=2.76 TeV
Measurement of charm and beauty production at central rapidity versus charged-particle multiplicity in proton-proton collisions at $\mathbf{\sqrt{\textit s}}=7$ TeV
Measurement of charm and beauty production as a function of charged particle multiplicity in proton–proton collisions at sqrt(s) = 7 TeV
Coherent $ρ^0$ photoproduction in ultra-peripheral Pb--Pb collisions at $\mathbf{\sqrt{\textit{s}_{\rm NN}}} = 2.76$ TeV
Coherent rho0 production in ultra-peripheral Pb-Pb collisions at sqrt{s_NN} = 2.76 TeV
Precision measurement of the mass difference between light nuclei and anti-nuclei
Precision measurement of the mass difference between light nuclei and anti-nuclei
Measurement of charged jet production cross sections and nuclear modification in p-Pb collisions at $\sqrt{s_\rm{NN}} = 5.02$ TeV
Measurement of charged jet production cross sections and nuclear modification in p-Pb collisions at sqrt(sNN) = 5.02 TeV
Inclusive, prompt and non-prompt J/$ψ$ production at mid-rapidity in Pb-Pb collisions at $\sqrt{s_{\rm NN}}$ = 2.76 TeV
Inclusive, prompt and non-prompt J/psi production at mid-rapidity in Pb-Pb collisions at sqrt(sNN) = 2.76 TeV
Elliptic flow of identified hadrons in Pb-Pb collisions at $\sqrt{s_{\rm{NN}}}$ = 2.76 TeV
Elliptic flow of identified hadrons in Pb-Pb collisions at sqrt(sNN) = 2.76 TeV
Charged jet cross sections and properties in proton-proton collisions at $\sqrt{s}=7$ TeV
Charged jet production cross sections and properties in proton-proton collisions at sqrt{s} = 7 TeV
Rapidity and transverse-momentum dependence of the inclusive J/$\mathbfψ$ nuclear modification factor in p-Pb collisions at $\mathbf{\sqrt{\textit{s}_{NN}}}=5.02$ TeV
Transverse momentum dependence of the inclusive J/psi nuclear modification factor in p-Pb collisions at the LHC
Centrality dependence of particle production in p-Pb collisions at $\sqrt{s_{\rm NN} }$= 5.02 TeV
Centrality determination of pPb collisions at sqrt(sNN) = 5 TeV in the ALICE experiment
Measurement of pion, kaon and proton production in proton-proton collisions at $\sqrt{s}=7$ TeV
Production of pions, kaons and protons in pp collisions at sqrt(s) = 7 TeV
Forward-backward multiplicity correlations in pp collisions at $\sqrt{s}$=0.9, 2.76 and 7 TeV
Forward-backward multiplicity correlations in pp collisions at sqrt(s)=0.9, 2.76 and 7 TeV
Measurement of dijet $\mathbf{\textit{k}_{T}}$ in p-Pb collisions at $\mathbf{\sqrt{\textit{s}_{NN}}=5.02}$ TeV
Measurement of dijet kT in p-Pb collisions at sqrt(sNN)=5.02 TeV
Measurement of jet suppression in central Pb-Pb collisions at $\sqrt{s_{\rm NN}}$ = 2.76 TeV
Measurement of jet suppression
Inclusive photon production at forward rapidities in proton-proton collisions at $\sqrt{s}$ = 0.9, 2.76 and 7 TeV
Inclusive photon production at forward rapidities for proton-proton collisions in sqrt(s) = 0.9, 2.76 and 7 TeV
Two-pion femtoscopy in p-Pb collisions at $\sqrt{s_{\rm NN}}=5.02$ TeV
Charged pion femtoscopy correlations in pPb collisions
K*(892)$^{0}$ and $Φ$(1020) production in Pb-Pb collisions at $\sqrt{s_{\rm NN}}$ = 2.76 TeV
K*(892)0 and phi(1020) production in Pb-Pb collisions at sqrt(s_NN) = 2.76 TeV
Production of $Σ(1385)^{\pm}$ and $Ξ(1530)^{0}$ in proton-proton collisions at $\sqrt{s}=$ 7 TeV
Production of Σ(1385)± and Ξ(1530)0 in proton-proton collisions at √s = 7 TeV
Measurement of electrons from semileptonic heavy-flavor hadron decays in pp collisions at $\sqrt{s} = 2.76$ TeV
Measurement of electrons from semi-leptonic heavy-flavour hadron decays in proton-proton collisions at sqrt(s) = 2.76 TeV with ALICE
Multiplicity dependence of jet-like two-particle correlations in p-Pb collisions at $\sqrt{s_{NN}}$ = 5.02 TeV
Multiplicity dependence of jet-like two-particle correlations in pPb collisions at sqrt(sNN) = 5.02 TeV with ALICE at LHC
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# “maximizing” logistic regression
Suppose I have some simple data for when someone buys or not buys something at a certain price, looking something like this:
1 1 11
2 1 14
3 0 20
4 1 13
5 1 19
6 0 16
. . .
. . .
. . .
10000 1 14
Where 1 would mean buying and 0 not buying at that certain price, the numbers are just made up. I would like to fit a logistic regression to this data, dont really care in what software/language but this example is in python with the result:
Logit Regression Results
==============================================================================
Dep. Variable: dependent No. Observations: 306
Model: Logit Df Residuals: 304
Method: MLE Df Model: 1
Date: Fri, 15 Apr 2016 Pseudo R-squ.: 0.01063
Time: 09:40:27 Log-Likelihood: -200.91
converged: True LL-Null: -203.07
LLR p-value: 0.03773
==============================================================================
coef std err z P>|z| [95.0% Conf. Int.]
------------------------------------------------------------------------------
price -0.2341 0.114 -2.058 0.040 -0.457 -0.011
intercept 2.4598 1.436 1.712 0.087 -0.356 5.275
==============================================================================
I'm not sure if a logistic regression would be the correct way to do this, but how would I maximize (not sure if im supposed to maximize anything though) the logistic function to determine what price would be the best price?
The optimal price would be defined where the total revenue is maximized, thus $E[R_i]=R_i⋅Pr(R_i)$ where $R_i$ would be the expected revenue of individ $i$ and $Pr(R_i)$ would be the probability of purchasing at that price. What would be the optimal price here?
• This is not exactly what you want, but maybe closed enough. You could look at it as if you have run an A/B test with your customers, let's say for one of the groups you've kept the prices as they are, for others you've offered a discount. Then, you could use uplift modeling to predict the effect on lowering the price. From the results, you could do a cost/benefit analysis. You can use logistic regression for fitting the uplift. It is not even closed to what you want, but anyway, in case it helps. – lrnzcig Apr 21 '16 at 17:46
• @lrnzcig thanks for your comment, not exactly what I was after but still it is a good way to go and worth trying – destinychoice Apr 26 '16 at 10:56
Let $$p$$ be the price of the item and let $$Q$$ be the corresponding indicator of a sale (your quantity variable). Then your logistic regression can be specified as:
$$\mathbb{E}(Q) = \text{logistic}(\beta_0 + \beta_1 p).$$
Hence, the expected revenue at price $$p$$ is the unknown quantity:
\begin{aligned} \bar{R}(p) \equiv \mathbb{E}(\text{Revenue}) &= p \cdot \mathbb{E}(Q) \\[6pt] &= p \cdot \text{logistic}(\beta_0 + \beta_1 p) \\[6pt] &= \frac{p}{1 + e^{-\beta_0 - \beta_1 p}}. \\[6pt] \end{aligned}
Note that this function involves unknown parameters $$\beta_0$$ and $$\beta_1$$ and so you cannot maximise it. Substituting the parameter estimates gives the predicted revenue:
\begin{aligned} \hat{R}(p) \equiv \hat{\mathbb{E}}(\text{Revenue}) &= \frac{p}{1 + e^{-\hat{\beta}_0 - \hat{\beta}_1 p}}. \\[6pt] \end{aligned}
This latter function is known and can therefore be maximised via standard calculus techniques. In particular, it has first derivative:
$$\frac{d \hat{R}}{dp}(p) = \frac{1 + (1+\hat{\beta}_1 p) e^{-\hat{\beta}_0 - \hat{\beta}_1 p}}{(1 + e^{-\hat{\beta}_0 - \hat{\beta}_1 p})^2},$$
which leads to the critical point equation $$1 + \hat{\beta}_1 \hat{p} = - e^{\hat{\beta}_0 + \hat{\beta}_1 \hat{p}}$$. As Ingolifs correctly points out in another answer, solving this critical point equation uses the Lambert W function.
So you have the following functions describing your data:
And you want the maximum of GLM result * price.
You have two approaches: 1. Solve analytically. You have an equation of the form $$\frac{x}{1+e^{-(ax+b)}}$$ where $$a$$ and $$b$$, according to your model, are -0.2341 and 2.45, respectively.
You can use calculus to find the optimum. It is a bit involved, however, as you will (I'm pretty sure, but could be wrong) need to use the Lambert W function.
The other alternative is to plot the values of $$\frac{x}{1+e^{-(ax+b)}}$$ from some range that contains the maximum, say, 1:100, and find the maximum value, and the price that gives the maximum value that way. It won't be exact, but you probably don't need exact.
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Math Help - Irreducible Polynomials:
1. Irreducible Polynomials:
(1):
Find all irreducible polynomials of the form $x^2 + ax +b$, where a,b belong to the field $\mathbb{F}_3$ with 3 elements.
Show explicitly that $\mathbb{F}_3(x)/(x^2 + x + 2)$ is a field by computing its multiplicative monoid.
Identify [ $\mathbb{F}_3(x)/(x^2 + x + 2)$]* as an abstract group.
Find all irreducible polynomials of the form $x^2 + ax +b$, where a,b belong to the field $\mathbb{F}_3$ with 3 elements.
Just list all of them $x^2 + x+1,x^2+x+2,...$ there are only $9$ or them. Now, just check which ones have zeros (there are only three zeros to check). And this tells you which are irreducible and which are not.
Show explicitly that $\mathbb{F}_3(x)/(x^2 + x + 2)$ is a field by computing its multiplicative monoid.
Identify [ $\mathbb{F}_3(x)/(x^2 + x + 2)$]* as an abstract group.
Any element in $\mathbb{F}_3[x]/(x^2+x+2)$ has form $a+bx+(x^2+x+2)$. Now show that these elements form a field.
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## Introduction
Neuropathic pain is a debilitating condition arising from injury to the somatosensory neurons which triggers the development of allodynia and hyperalgesia1. Several conditions such as traumatic accidents, surgery and diseases affecting peripheral and central nervous systems contribute to etiopathogenesis of the neuropathic pain. Experimental studies reveal inflammation is the main cause of neuropathic pain. The inflammatory cytokines and oxidative stress along with allogeneic mediators released subsequent to a nerve injury induce neuropathic pain through sensitization of the nociceptive receptors2,3. The palliative treatment of neuropathic pain include the use of gabapentin, tricyclic antidepressants, α2-δ calcium channel ligands, slow serotonin reuptake inhibitors and local aesthetics4. Gabapentin is recommended as the standard of care in the neuropathic pain5. However, the absorption of gabapentin follows saturation kinetics upon oral administration and even at higher doses its bioavailability does not improve. This renders a need for dose-titration to achieve the expected therapeutic effects6. Other antineuropathic drugs including anticonvulsants, tricyclic antidepressants and opioids have a limited effect and possess abuse liabilities or intolerable side-effects. Thus, there is a continuous demand for novel antineuropathic drugs which could be more safe and effective. The recent approach of repositioning of therapeutic agents for discrete indications may prove to be useful in the exploration of certain neuroprotective, anti-inflammatory and antioxidant agents to be added as an add-on therapy to the primary recommended therapy for neuropathy and associated pain.
In preview of such repositioning approach, many recent preclinical and clinical evaluations have highlighted diverse effects of omeprazole other than its proton pump inhibitory actions. Omeprazole is a proton pump inhibitor that is widely used in the treatment of peptic ulcer7. In vitro and and in vivo evaluations have proved omeprazole have carbonic anhydrase inhibitory8, anti-inflammatory9 and antioxidant10 activities. Omeprazole following in vitro co-incubation with isolated human neutrophils showed to reduce hemotaxis and oxidative radical production induced by bacterial chemotactic tetrapeptide, N-formyl-Met-Leu-Phe (fMLP)11. Additionally, omeprazole also antagonizes the inflammatory response of mouse macrophages infected with salmonella enterica. In this in vitro study, it delayed the IκB degradation, blocked nitric oxide production and reduced the secretion of proinflammatory cytokines from the infected macrophages12. The anti-inflammatory activity of omeprazole and other proton pump inhibitors (PPIs) in a murine model of asthma through IL-4 and IL-13 signalling STAT-6 (signal transducer and activator of transcription-6) activation were also reported13. On the other hand, omeprazole also reduces the LPS-induced release of TNF-α and IL-6 from the human microglial cell culture and human monocytes culture in vitro. This effect is proposed to contribute to the neuroprotective effect of omeprazole against the microglial and monocytic toxicity14. Further, it has also been revealed to reduce the IFN-γ induced astrocyte toxicity and phosphorylation of STAT314. Moreover, it also inhibits the carrageenan-induced acute paw inflammation in rats10,15. Considering these findings, we hypothesized that omeprazole should reduce the post-injury nerve damage and inhibit the development of nerve injury-related neuroinflammation and neuropathic pain. The present study was designed to investigate the effects of chronic oral administration of omeprazole employing the CCI-induced neuropathic pain in rats.
## Results
### Effect of omeprazole on cold, warm & mechanical allodynia in CCI-induced neuropathic pain
Figure 1A–C illustrates the effects of omeprazole on cold, warm & mechanical allodynia during CCI-induced neuropathic pain in rats. In the plantar test to determine cold allodynia, the paw withdrawal latency (PWL) was significantly increased as compared to sham group (14.4 ± 1.17 sec Vs. 3.86 ± 1.16 sec, P < 0.001). Oral treatment with omeprazole (50 mg/kg/day) for 14 days significantly increased the PWL as compared to the CCI-control animals [9.37 ± 0.56 sec Vs. 3.86 ± 1.16 sec; F (117.3) DF = 4, P < 0.001]. Similar effect was observed in GP treated group when compared with their respective control group (7.62 ± 0.34 sec Vs. 3.86 ± 1.16 sec; P < 0.001; Fig. 1A).
Figure 1B shows the effect of omeprazole on warm allodynia after CCI surgery. The baseline level of PWL of the CCI-induced hind paw was 2.610 ± 0.94 sec, when challenged with warm water, whereas the sham operated rats didn’t show any change in the warm allodynia. Omeprazole (50 mg/kg/day/oral) for 14 days treatment significantly increased the PWL as compared to the CCI-control group (8.82 ± 0.57 sec Vs. 2.610 ± 0.94 sec; [F (42.74) DF = 4, P < 0.001]).
The paw withdrawal pressure threshold (PWT) was estimated using the electronic von Frey apparatus. The CCI-control group shows significant decreased in PWT as compared to sham operated animals (6.103 ± 0.86 g Vs. 18.7 ± 0.19 g, P < 0.001, Fig. 1C). The omeprazole treatment significantly increased the PWT as compared to respective control group (13.31 ± 1.27 g Vs. 6.103 ± 0.86 g; [F(17.23) DF = 4, P < 0.001]).
### Effect of omeprazole on motor nerve conduction velocity in CCI-induced neuropathic pain
MNCV was evaluated on the day 14th after the respective treatments. There was a significant reduction (17.68 ± 1.01 mm/sec; P < 0.001) in the MNCV in the CCI-control group. The rats treated with omeprazole 50 mg/kg/day/oral for 14 days showed significant increase (30.50 ± 0.91 mm/sec) in the MNCV as compared to the CCI-control group [F (15.62) DF = 4, P < 0.001]. It is noteworthy that the alleviative effect of omeprazole on the MNCV was comparable to the gabapentin (Fig. 2).
### Effect of omeprazole on biochemical parameters in CCI-induced neuropathic pain
Oxidative stress status was evaluated by the measurement of MDA as a marker of lipid peroxidation, GSH as well as SOD and catalase as markers of enzymatic and non-enzymatic antioxidant defence systems. CCI induced a state of marked oxidative stress as demonstrated by a significant increase (405.4 ± 55.97 μg/mg of protein) in the MDA level and a significant decrease in the GSH (18.45 ± 2.59 μg/mg of protein), activity of SOD (7.613 ± 1.77 U/mg of protein) and catalase (7.84 ± 1.32 U/mg of protein) levels in sciatic nerve homogenates as compared to control group. The treatment with omeprazole 50 mg/kg/day/oral for 14 days alleviated the effect CCI-induced oxidative stress on the levels of MDA, GSH. It also had significant restorative effect on the activities of SOD and catalase enzymes as compared to CCI-control group (Fig. 3).
### Effect of omeprazole on proinflammatory cytokines in CCI-induced neuropathic pain
To further define the mechanisms by which cytokine signalling may be associated with CCI induced neuropathic pain, we examined the effect of omeprazole on release of pro-inflammatory cytokine expression of TNF-α, IL-1β and IL-6 in the nerve tissue homogenate. A significant increase in the cytokine levels in the CCI-control group (TNF-α [38.8 ± 1 Vs. 23.2 ± 0.9 pg/mg of protein respectively]), IL-6 [761.7 ± 1.8 Vs. 675.5 ± 0.7 pg/mg of protein respectively] and IL-1β [859 ± 0.7 Vs. 656.4 ± 1.2 pg/mg of protein respectively]) compared to normal group. The groups treated with omeprazole (50 mg/kg/day/oral) for 14 days showed a significant reduction in these elevated cytokines (TNF-α [25.5 ± 0.8 Vs. 23.2 ± 0.9 pg/mg of protein respectively], IL-6 [676.2 ± 1.0 Vs. 656.4 ± 1.2 pg/mg of protein respectively] and IL-1β [666.5 ± 1.1 Vs. 656.4 ± 1.2 pg/mg of protein respectively]) almost to the normal levels indicating that omeprazole exerts a consistent inhibitory effect on the cytokine release (Fig. 4).
### Effect of omeprazole on tissue architecture of sciatic nerve in CCI-induced neuropathic pain
The CCI induced a noticeable histological perturbation as revealed in the longitudinal nerve sections including axonal swelling, neutrophil migration and an increase in the number of Schwann satellite cells and derangement in the nerve architecture. Omeprazole 50 mg/kg/day/oral for 14 days treatment protected the sciatic nerve from the CCI-induced structural damage and inflammatory changes (Fig. 5; Table 1).
### Effect of omeprazole on LPS-induced oxidative stress in primary glioblastoma U-87cells
To study the impact of omeprazole in vitro, we first induced ROS by LPS treatment (500 ng/ml for 20 min) in primary glioblastoma U-87cells. After LPS stimulation, we treated the cells with graded concentrations of omeprazole and carried out a series of cell based assays. To check the anti-cell proliferative activity of omeprazole on LPS-induced cells, an MTT cell viability assay was performed. Figure 6A revealed that omeprazole decreased LPS-mediated ROS induced cell viability dose dependently with an IC50 of 100 μM. However, no appreciable cytotxicity was observed when cells were treated with omeprazole (0–200 μM) without LPS stimulation (data not shown). Interestingly, no cytotoxicity was also noted after treatment of LPS alone for 20 min (data not shown). Flow cytometric analysis of ROS production by DCFH-DA staining revealed a 25% ROS positive population after LPS induction which reduced to 15% after 50 μM of omeprazole treatment. Complete diminished (less than1%) ROS positive population was noted at 100 μM omeprazole exposure in LPS pre-treated cells (Fig. 6B). H2O2 is used as positive control for ROS generation. LPS treated cells displayed reduced activities of SOD and catalase which was alleviated after omeprazole exposure (Fig. 6C,D). Omeprazole alleviated the SOD and catalase even more than basal level at 100 μM (Fig. 6C,D).
Next, we measured the cytokine profile (TNF-α, IL-6 and IL-1β) after omeprazole exposure in LPS pre-treated cells. LPS increased cytokines level compared to untreated cells. Interestingly, omeprazole dose dependently decreased the LPS-induced cytokines level in cells. Omeprazole treatment almost brings down the cytokines level to basal level at 200 Μm (Fig. 6E–G).
## Discussion
The present study demonstrated that in addition to its PPI effect, omeprazole exhibits a protective effect by improving nerve conduction velocity and PWL; restoring the endogenous antioxidant system; preventing the increased level of inflammatory cytokines such as TNF-α, IL-1β and IL-6; reducing lipid peroxide metabolism; and preserving the structure and morphology of sciatic nerve via inhibiting proinflammatory cytokines. The present study shows for the first time that omeprazole exerts its neuroprotective effect not only through its antioxidant effect but also in part by inhibiting cytokines release. Therefore, our study provides direct evidence that the cytokines signaling pathway plays a key role in regulating oxidative stress and subsequent nerve injury in CCI-induced neuropathic pain. To the best of our knowledge, this is the first study to describe the neuroprotective effect of omeprazole through inhibiting cytokines release in CCI-induced model of neuropathic pain in rats.
Several other drugs like minocycline16 and atorvastatin3 are reported to attenuate the CCI-induced neuropathic pain through anti-inflammatory and antioxidant actions. Omeprazole is previously reported as an anti-inflammatory13,17, antioxidant18, carbonic anhydrase and cytokine release inhibitor8,19 and neuroprotective agent14. Recently, there is an increased interest in the repositioning of the proton pump inhibitors as anticancer agents through targeting the thioesterase domain of the fatty acid synthase20. In light of these preclinical studies, we evaluated omeprazole for its antineuropathic efficacy in the CCI induced neuropathy model in rats and ROS induced model of U-87 human neuronal cell line. We selected the oral dose of 50 mg/kg of omeprazole for evaluation of the antineuropathic efficacy. At this dose it significantly inhibits the carrageenan induced acute paw inflammation. Such efficacy of omeprazole is reported earlier by El-Nezhawy10. The oral dose of 50 mg/kg/day of gabapentin was similarly selected dependent upon a prior report on its antineuropathic effect in CCI rat model21. CCI of the sciatic nerve in rats is the most commonly used model to induce neuropathic pain in rats and it mimics the pathophysiology of neuropathic pain in human22. In CCI model, the loose ligation compresses the nerve fibres and induces nerve damage, a consequent release of various inflammatory mediators from the mast cells, neutrophils and macrophage. CCI induces a persistent neuropathic pain state characterized by spontaneous pain, allodynia and hyperalgesia3,22. The causative factors of neuroinflammation induced by CCI include pro-inflammatory cytokines, prostaglandins and reactive oxygen species. In addition to the inflammatory mediators, an increased concentration of extracellular H + ions at the site of injury lowers the pH of the extracellular fluid. This acidic pH activates the TRPV1 (transient receptor potential vanilloid receptor 1- an acid sensitive ion channel) which serves as a sole sensor for the protons23. Activated TRPV1 alters calcium levels in the sensory neurons and sensitizes the capsaicin-sensitive neurons24. The peripheral injury induced by CCI also leads to the release of tachykinins and neurotransmitters such as glutamate, calcitonin gene-related peptide and γ-amino butyric acid. Prolonged release and binding of these substances to neural receptors activates the N-methyl-D-aspartate receptors, which causes an increase in the intracellular calcium levels25. Increased intracellular calcium through N-type calcium channels in the central nervous system plays an important role in the maintenance of the pain sensation in the central nervous system26.
The other remarkable observation obtained in the present study was the ability of omeprazole to reduce the cytokine levels in CCI injury in rats. The pathogenesis of CCI-induced neuropathic pain and hyperalgesia involves a role of the immune cells that infiltrate the damaged nerve27 and the inflammatory immune mediators like IL-628, IL-1β29 and TNF-α30. Damage to the nerve activates neurons and glial cells and releases pro inflammatory mediators like TNF-α, IL-1β and IL-6. In the present study, it was found that CCI control animals showed a significant rise in the levels of these cytokines, whereas, omeprazole significantly decreased the increased levels of cytokines. Other studies suggesting that omeprazole possesses anti-inflammatory activity, reported to reduce vascular permeability and experimentally induced colitis by suppressing elevated level of inflammatory mediators such as neutrophils IL-1β, TNF-α and IFN-γ14,28. An in vitro investigation on the stimulated mouse macrophages has shown that omeprazole reduces the release of inflammatory cytokines. Omeprazole and other proton pump inhibitors are also known to inhibit IL-4 and IL-13 signalling STAT6 activation and thereby exert anti-inflammatory effects13. LPS induced ROS in U-87 human glioma cells which allevated pro-inflammatory cytokines (TNF-α, IL-6 and IL-1β). Omeprazole suppressed the elevated inflammatory cytokines, restoring the normal profile which revealed antineuropathic efficacy of omeprazole via reduction of ROS in vitro. Hence, the antineuropathic efficacy of omeprazole may involve its inhibitory effects on the release of these inflammatory cytokines. Omeprazole reduces the chemotaxis of neutrophils11, which also might contribute to the decreased amounts of cytokines in the nerve homogenates. Omeprazole is also known to protect the astrocytes from IFN-γ induced toxicity. In vitro study has proved its neuroprotective effects against monocytic and microglial damage14. In addition to reduction in chemotaxis of neutrophils, omeprazole reduces the oxidative stress through scavenging hydroxyl radicals and also inhibits the oxidative stress induced DNA damage related apoptosis18. The CCI-induced ischemic hypoxia causes disturbance in the secondary metabolites in the afflicted nerve fibres and induces oxidative stress. Further, the decreased nerve energy and degeneration of the nerve fibres due to neuronal ischemia reduces the MNCV31,32. In present study, omeprazole inhibited the decrease in the MNCV. It was observed in present study, that there was a significant increase in the PWT and PWL in the mechanical and thermal allodynia tests in omeprazole treated rats. This effect may be attributed to the antioxidant and anti-inflammatory property of omeprazole. Omeprazole reduced the oxidative stress induced by CCI and this was evident from the reduced malondialdehyde and restoration of the depleted GSH, catalase and SOD. Thus, the antioxidative effect of omeprazole may be considered as one of the mechanisms of its antineuropathic effect.
Considering the time tested safety profile of omeprazole and its antineuropathic efficacy observed in this study, it is suggested that omeprazole may be considered for further evaluation in preclinical and clinical studies against painful neuropathic conditions. Further investigation in this direction may lead to the repositioning of omeprazole in treatment of inflammatory and painful disease conditions. Whether the present conclusions can be extrapolated to a clinical scenario remains to be determined in clinical studies.
## Methods
### Animals
Adult male Wistar rats (180–250 g) were procured from the laboratory animal facility of our Institute. They were housed in standard temperature/humidity conditions and environment (12 h light/dark cycle). All animals were provided standard pellet diet and water ad libitum all time except during the estimation of the behavioural parameters. The animals were maintained in conformity with the regulations laid down by the Committee for the Purpose of Control and Supervision of the Experiments on Animals (CPCSEA) constituted under the Prevention of the cruelty to animals Act, 1960, Ministry of Environment and Forests, Government of India. The experimental protocols were approved by the Institutional Animal Ethics Committee of R. C. Patel Institute of Pharmaceutical Education and Research, Shirpur, Dist-Dhule, Maharashtra, India (Protocol approval # IAEC/RCPIPER/2014-15/09). All the tests complied with the recommendations of the International Association for the Study of Pain.
### Chemicals
Omeprazole was obtained from Pharmachem R&D Laboratories, India. Gabapentin was gifted by Mylan laboratories, India. Cytokine ELISA Ready SET-Go kits for mouse IL-1β (Cat: 887013-22; Batch No. E09323-1645), IL-6 (Cat: 837064-22: Batch No. E09358-1645) and TNF-α (Cat: 837324-22: Batch No. E09479-1645) were procured from e-Biosciences Incorporation, USA. Freshly prepared drug suspensions in 0.5% carboxymethyl cellulose were used for oral administration to rats. LPS (Cat: L2880; Lot No. 025M4040V) was purchased from Sigma-Aldrich, St. Louis, Missouri, USA.
### Induction of CCI in rats
The CCI surgery was performed as described by Aswar et al.22. The rats were anaesthetized under pentobarbital sodium (60 mg/kg, intraperitoneal). The common sciatic nerve of the right hind limb was exposed at the middle of the thigh by a blunt dissection through biceps femoris. Proximal to the trifurcation of sciatic nerve, about 5–7 mm of the nerve was freed off the adhering tissue and four loose ligatures (4.0 silk) were put around it approximately 1 mm apart. After performing nerve ligation, muscular and skin layers were immediately sutured and povidone-iodine solution was applied externally. After the surgery, the rats were kept in individual cages and were allowed to recover. The respective drugs treatments were initiated on the next day after the surgery.
### Cell culture and treatment
The human glioma cell line; U-87 was grown and cultured in DMEM containing 10% FBS, 100 U/ml penicillin, 100 μg/ml of streptomycin, 1.5 mM L-Glutamine in a humidified atmosphere of 5% CO2 at 37 °C. After confirming that the cells attained 80% confluence, the media was replaced with fresh media containing 500 ng/ml LPS for 20 min for ROS induction. Various concentrations of omeprazole were added in LPS pre-treated cells for another 24 h prior to perform other experiments. A fixed concentration (10 μM) of H2O2 was treated for 30 min to produce ROS and used as positive control.
### MTT cell viability assay
To check the cytotoxicity of omeprazole in LPS mediated ROS-induced U-87 cells, we have performed an MTT cell viability assay according to the protocol referred earlier33. Briefly, 8000–10,000 cells were seeded in triplicate in 96 well plate and grown to 80% confluence. Then, cells were treated with 500 ng/ml LPS for 20 min for ROS induction. LPS containing media was aspirated and the cells were further treated with a varied concentration of omeprazole for another 24 h. Then, 0.05% MTT reagent was added to each well and incubated overnight for the formation of formazan crystal. The colour intensity was spectrophotometrically (Berthold, Germany) measured at 570 nm after dissolving the formazan crystals in DMSO. Data was calculated and represented as percent viability against omeprazole concentrations.
### Experimental design
The anti-inflammatory activity of orally administered omeprazole at 10, 30 and 50 mg/kg dose was measured in rat model of carrageenan-induced paw edema (data not shown). At the dose of 50 mg/kg, omeprazole significantly inhibited the induction of carrageenan-induced paw edema. Therefore, the dose of 50 mg/kg was chosen further to investigate the efficacy of omeprazole against CCI induced neuropathy and was compared with well reported anti-neuropathic dose of gabapentin (50 mg/kg p.o.).
After CCI induction, the rats were allowed to habituate for 3 days. Treatment of omeprazole was initiated on the next day of CCI surgery. The thermal and mechanical allodynia were measured as described by Demir2 on 3rd, 7th, 11th and 14th days after surgery. The paw withdrawal latency (PWL) was observed with a maximum cut off time of 20 sec. For the determination of the thermal allodynia, the right paw of each rat up to the ankle joint was immersed in warm water (40 ± 1 °C) and cold water (12 ± 1 °C). The mechanical allodynia was measured using electronic Von-Frey apparatus using super-tips probes (2390 series, IITC Life Sciences Incorporation) and paw withdrawal threshold (PWT) was observed with cut-off pressure at 30 gm.
On the 14th day post-surgery, the rats were anesthetized with pentobarbital sodium (60 mg/kg, intraperitoneal) in the temperature controlled atmosphere (25 °C). Sciatic-tibial motor MNCV was measured by stimulating proximally at the sciatic notch and distally at the knee via bipolar needle electrodes (Power Lab/ML856; AD Instruments, Australia; frequency 0.10 Hz, duration 0.1 ms, amplitude 1.5 V). After single stimulus the compound muscle action potential was recorded from the first interosseous muscle of the hind-paw by unipolar pin electrodes. The recording was a typical biphasic response with an initial M-wave which is a direct motor response due to stimulation of motor fibers. The MNCV was calculated as the ratio of the distance (mm) between both sites of stimulation divided by the difference between proximal and distal latencies measured in ms31.
After recording of MNCV, the rats were sacrificed using overdose of pentobarbital sodium (intraperitoneal) and the injured right sciatic nerve was isolated along with 1 cm segments on proximal and distal side of the CCI injury. A 5 mm central portion of the isolated nerve segment was further processed for histological examination. The sections of 4 μm thickness were obtained and were stained with haematoxylin and eosin. The stained sections were examined under the light microscope for structural alterations including fibre derangement, swelling of nerve fibre and presence of activated satellite cells and Schwann cells.
A 10% homogenate of the remaining segments of sciatic nerve from each rat was prepared in ice chilled phosphate buffer (50 mM, pH 7.4). The homogenate was centrifuged at 2000 g for 20 min at 4 °C and the aliquots of the supernatant were used to estimate the content of lipid peroxidation measures as malondialdehyde (MDA), reduced glutathione (GSH), catalase and superoxide dismutase (SOD) as follows.
Lipid peroxidation in the nerve tissue was determined by measuring MDA content as described by Ohkawa et al.34. Briefly, 0.2 ml of the tissue homogenate was mixed with 0.2 ml of 8.1% sodium dodecyl sulphate, 1.5 ml of 30% acetic acid (pH 3.5) and 1.5 ml of 0.8% thiobarbituric acid. The reaction mixture was heated for 60 min at 95 °C and then cooled on ice. After cooling, 1.0 ml of distilled water and 5.0 ml of n-butanol: pyridine (15:1 v/v) solution were added and centrifuged at 5000 rpm for 20 min. The absorbance of the generated pink colour in organic layer was measured at 532 nm. The reagent; 1,1,3,3-tetraethoxypropane (Sigma Chemicals, USA) was used as the standard MDA and the levels were expressed as μg/mg of protein.
The neuronal GSH was estimated by the method of Moron et al.35. Briefly, 100 μl of tissue homogenate was mixed with 100 μl of 10% trichloro acetic acid and vortexed. The contents were then centrifuged at 5000 rpm for 10 min. Subsequently 0.05 ml of supernatant was mixed with a reaction mixture containing 3.0 ml 0.3 M phosphate buffer (pH 8.4) and 0.5 ml of DTNB. Within 10 min, the absorbance was measured spectrophotometrically at 412 nm. The concentration of GSH was determined from a standard curve produced using commercially available standard GSH (Sigma Chemicals, USA). The levels of GSH were expressed as μg/mg of protein.
Catalase activity was estimated by the method described by Aebi36. Briefly, to 50 μl of tissue supernatant a cocktail of 1.0 ml of 50 mM phosphate buffer (pH 7) and 0.1 ml of 30 mM hydrogen peroxide was added. The absorbance which read as reduction in optical density was measured spectrophotometrically on every 5 sec for 30 sec at 240 nm. The activity of catalase was expressed as U/mg protein.
SOD activity was determined by the method described by Marklund and Marklund37. Briefly, to 25 μl of tissue supernatant a cocktail of 100 μl of 500 mM Na2CO3, 100 μl of 1 mM EDTA, 100 μl of 240 μM/ NBT, 640 μl of distilled water, 10 μl of 0.3% Triton x 100 and 25 μl of 10 mM Hydroxylamine was added. The readings were recorded spectrophotometrically in kinetic mode at interval of 1 min up to 3 min at 560 nm. The enzyme activity was expressed as U/mg protein.
As the IC50 of omeprazole treated LPS stimulated U-87 cells was 100 μM with no detectable cytotoxicity on the non-induced cells, so, for other in-vitro experimentation, LPS mediated ROS induced U-87 cells were treated with 50, 100 and 200 μM of omeprazole. Total cellular lysate was prepared using modified RIPA lysis buffer and 50 μg of protein was used to determine the activity of SOD and catalase. The quantification of TNF- α, IL-1β and IL-6 was performed both in homogenate and cell culture supernatant using 50 μg of protein by the commercially procured ELISA kits37.
### Statistical analysis
The statistical analysis was performed using Graph Pad Prism version 6.0 software, USA. The results are expressed as mean ± S.E.M. The data from the behavioural parameters were analysed by repeated measure one-way analysis of variance (ANOVA). The data sets of the biochemical parameters are analysed using one-way ANOVA followed by Dennett’s post-hoc test and Bonferroni’s multiple comparison test for cytokine analysis. The results are expressed as F (DFn, DFd). The statistical significance of difference in the central tendencies of treatment groups as compared to CCI group was designated as **p < 0.005 and ***p < 0.001. Whereas, the significance of difference of CCI and LPS group compared to control group was shown as ###p < 0.001. The significance of difference of H2O2 (positive control of ROS in in-vitro experiments) compared to control was designated as \$p < 0.001.
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Derivatives and Integrals of Power Series
Applications and Examples
Taylor and Maclaurin Series
The Formula for Taylor Series
Taylor Series for Common Functions
Adding, Multiplying, and Dividing Power Series
Miscellaneous Useful Facts
Applications of Taylor Polynomials
Taylor Polynomials
When Functions Are Equal to Their Taylor Series
When a Function Does Not Equal Its Taylor Series
Other Uses of Taylor Polynomials
Partial Derivatives
Visualizing Functions in 3 Dimensions
Definitions and Examples
An Example from DNA
Geometry of Partial Derivatives
Higher Order Derivatives
Differentials and Taylor Expansions
Multiple Integrals
Background
What is a Double Integral?
Volumes as Double Integrals
Iterated Integrals over Rectangles
How To Compute Iterated Integrals
Examples of Iterated Integrals
Cavalieri's Principle
Fubini's Theorem
Summary and an Important Example
Double Integrals over General Regions
Type I and Type II regions
Examples 1-4
Examples 5-7
Order of Integration
Logistic Growth
In an epidemic, whether of the flu, AIDS, or a zombie apocalype, people become sick from contact between sick and healthy people. This means that $\frac{dy}{dt}$ is proportional to the product of the number of sick and healthy people. The standard form of the equation, which is called logistic, is
$$\frac{dy}{dt} = k y \left ( 1 - \frac{y}{M} \right )$$
where $M$ is the total number of people who could get sick. Being a separable equation, we can solve it by separation of variables. This gives us the integral $$\int \frac{M\,dy}{y(M-y)},$$ which can then be solved by partial fractions. The end result is an S-shaped curve that starts by growing exponentially and then levels off, approaching $M$ exponentially.
The same equation can be used to model the dynamics of a population with limited resources. Here $M$ represents the "carrying capacity" of the ecosystem, that is the maximum population that can live sustainably.
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Sorry, because I think it's a many times asked topic. But I don't find an example which help me to understand how to create a white space between paragraphs. I think parskip is the package I need to ...
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In LaTeX I'm using memoir class. I want to break long passages into logical units with some white inter-paragraph space. \medskip etc. indents the first subsequent paragraph - I want it unindented, as ...
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Rest On The Flight Into Egypt Joachim, Product Key Finder Windows 10, Trader Joe's Carnitas Stovetop, Silicon Nitride Kischkat, Courts Air Fryer, Chefman Rj50-m Recipes, Best Grill Pans For Outdoor Grill, Jamaica National Bank Swift Code, Words Of Encouragement For Youth Workers, Phenyl Trimethyl Ammonium Uses, " /> , Product Key Finder Windows 10 The value of Oxidation state of an element is sum of all contributions due to all other elements/bonds. Covalent bonds are formed by the overlapping of atomic orbitals. What kind of intermolecular forces are present in the following compounds: #C Cl_4#, #CH_2Cl_2#,... What are the molecular orbital configurations for #N_2^+#, #N_2 ^(2+)#, #N_2#, #N_2^-#, and #N_2^(2-)#? HCN is produced on an industrial scale and is a highly valuable precursor to many chemical compounds ranging from polymers to pharmaceuticals. a year ago. b) How many sigma bonds are present? 1 sigma and 3 pi bonds. Sciences, Culinary Arts and Personal 2 3 C. 2 2 D. 3 1 21. How many sigma (σ) and pi (π) bonds are present in the structure of HCN? Which of the following contain a bond angle of 90°? 2 sigma bonds. Here is the simple structure And here is the structure made on the basis of valence bond theory you can refer to them to understand the structure in detail. SURVEY . There should be at least one bond each that makes four electrons. Usually, all bonds between atoms in most organic compounds contain one sigma bond each. Ethene (C 2 H 4) contains a double covalent bond between the two carbon atoms and single bonds between the carbon atoms and the hydrogen atoms. σ π A. An sp3 hybridised carbon can form 4 sigma bonds and 0 pi bonds … A triple bond consists of a sigma bond and two pi bonds. You can find out that Hydrogen brings 1, Carbon brings 4, and Nitrogen carries five each, which means there are 10 electrons in total. Answer and Explanation: To answer this question, we first need to draw the Lewis structure for HCN, so that we can determine the bonding. What mode of hybridization is associated with each of the five common electron domain geometries? In Valence Bond Theory we described the $$\pi$$ bonding in ethylene (C 2 H 4) as the result of overlapping parallel 2p atomic orbitals (e.g. ... HCN. Hence, 2 sigma bonds and 2 pi bonds are present in the HCN molecule. One difference between single and multiple bonds is that single bonds only have a sigma bond, whereas multiple bonds have both sigma and pi bonds. See all questions in Molecular Orbitals and Hybridizations. In your question, due to C-H bond, carbon gets -1 and hydrogen +1. How many lone pairs and bonding pairs of electrons surround xenon in the XeF 4 molecule? What is the number of sigma and pi bonds and the hybridization of the carbon atom in Sigma Pi Hybridization A. One with a triple bond between C and N. sigma and pi bonds there are two sigma bonds H-C and C-N and additionally two pi bonds between C and N. Hydrogen can make 1 bond since it is in Group 1A. AP Chemistry-Bonding DRAFT. All other trademarks and copyrights are the property of their respective owners. And $$2xxC-N$$ $$pi$$ bonds. If there is a sigma bond: c) What type of orbital on the carbon is involved in sigma bonding? Write them down on the paper with probably the least electronegative atom in the center and draw the bonds, then put some electrons in the bond. Answer: Molecule sigma bonds pi bonds … 4 sigma bonds. And #2xxC-N# #pi# bonds. Therefore, in HCN we find two sigma bonds and two pi bonds. Nitrogen is in Group 5A and and can make 3 bonds. 2 sigma and 2 pi bonds. Sigma and pi bonds are types of covalent bonds that differ in the overlapping of atomic orbitals. Hydrogen cyanide, sometimes called prussic acid, is a chemical compound with the chemical formula HCN. How many single bonds are in HCN molecule? 4 1 sp3 C. 3 2 sp3 D. 3 1 sp2. 2 A. 0 8 C. 0 4 D. 2 4 Revision 1 4 Lone pairs Bonding pairs A. How many sigma bonds are in HCN? To complete the valence shells, carbon will make a single bond with hydrogen and a triple bond with nitrogen as shown below: Our experts can answer your tough homework and study questions. #H-C-=N# formally possesses #1xxC-H# and #1xxC-N# #sigma# bonds. 2. 12th grade. Within #H-C-=N#? The bond energy of a C-C single bond averages 347... Glyphosate (below) is a common herbicide that is... How many sp^2 centres does cyclohexane have? Edit. How many sigma and pi bonds are in HC2H3O2? Edit. HCN thus has one single and one triple bond. 2 sigma and 2 pi bonds. How does a molecular orbital differ from an atomic orbital? 3. Who created the molecular orbital theory? 16 times. by kemilyh. In the molecule HCN, characterize the bond between carbon and nitrogen: (assume the internuclear axis is the x-axis) a) The bonding between carbon and nitrogen is a _____ bond. How many sp centres does cyclohexene have? The pi bond: 2 pi bonds are formed. How Many Electrons Does The Carbon Atom Have? Which of the following species does not contain a pi bond? © copyright 2003-2020 Study.com. You can get assistance with the Lewis dot structures from your textbook if necessary. HCN sp NCl3 sp 3 BrF5 sp 3d2 XeF2 sp 3d 2. 300 seconds . 15596 views It is a colorless, extremely poisonous and flammable liquid that boils slightly above room temperature, at 25.6 °C (78.1 °F). Non-singular Bonding. Save. How many single bonds are in HCN molecule? Question: For The Lewis Structure Of CH3-, What Is The Central Atom. Explanation: $$H-C-=N$$ formally possesses $$1xxC-H$$ and $$1xxC-N$$ $$sigma$$ bonds. Multiple bonds (double and triple), however, contains sigma and pi bonds. Choose the selection which gives the correct... Diatomic nitrogen (N2) is the abundant gas in the... What happens when two nitrogen atoms bond? Summing all, Oxidation state of hydrogen is +1 A triple bond is made of 1 sigma and 2 pi bonds. These are the sigma ({eq}\rm \sigma{/eq}) and pi ({eq}\rm \pi{/eq}) bonds present in single, double and triple bonds: To answer this question, we first need to draw the Lewis structure for HCN, so that we can determine the bonding. This chemistry video tutorial provides a basic introduction into sigma and pi bonds. As carbon is in Group 4A it can make 4 bonds. Previous question Next question Get more help from Chegg. ... How many sigma (σ) and pi (π) bonds are present in the structure of HCN? 2. a year ago. Two #sigma# and 2 #pi# bonds. 5.To these 4 steps for each and every bond. Within $$H-C-=N$$? 1 sigma and 3 pi bonds. The molecule HCN (C is the central atom) has 1. Two $$sigma$$ and 2 $$pi$$ bonds. 2 sigma bonds. 2 pi bonds. 4. d) How many pi bonds are present? 4 sigma bonds. 5. Services, Working Scholars® Bringing Tuition-Free College to the Community. 4 8 B. The molecule HCN (C is the central atom) has 1. What are the steps associated with the process of constructing a hybrid orbital diagram? If it is a single bond, it contains only sigma bond. Tags: Question 19 . How many sp centres does cyclohexane have? Two pi bonds between C and N are formed. How many sigma and pi bonds are in one molecule of benzene (C6H6), acetone (CH3COCH3) and acetic acid (CH3COOH)? The hybridization model helps explain molecules with double or triple bonds (see Figure 1 below). Earn Transferable Credit & Get your Degree, Get access to this video and our entire Q&A library. A double bond is made of 1 sigma and 1 pi bond. 75% average accuracy. How many individual sigma bonds and individual pi bonds are in HCN pi bonds: sigma bonds: Expert Answer . As a result of all this, an sp hybridised carbon for example can form 2 sigma bonds (because it has to hybridised orbitals, the s and the p) and 2 pi bonds (because it has to p orbitals). Sigma and Pi Bonds. Q. This organic chemistry video tutorial explains the hybridization of atomic orbitals. kemilyh. A triple bond is made of 1 sigma and 2 pi bonds. The latter consists of a sigma bond from the overlap of a C atom sp hybrid orbital with a N atom p orbital, and two mutually perpendicular pi bonds are formed from parallel atomic p orbitals of carbon and nitrogen atoms. 0. AP Chemistry-Bonding DRAFT. Determine the number of sigma bonds in CH3OCH3 and the hybridization of Carbon (hint- both carbons have the same hybridization) One with a triple bond between C and N. sigma and pi bonds there are two sigma bonds H-C and C-N and additionally two pi bonds between C and N. around the world, Hybridization and Atomic and Molecular Orbitals. So in total, the … Okay, so see on nitrogen has a triple bomb on the carbon, and hydrogen has a single bond. 7 sigma bonds, 1 pi bond. Pi bonds can only be formed between two p orbitals. Carbon will therefore be the central atom as it can make the most bonds. So the single bond between carbon and hydrogen is one Sigma bond on the triple bond between carbon and nitrogen should be one sigma bone and two pi bonds. 3. And What Is The Hybridization Of Carbon In CH3-? Like a double bond contains 1 sigma and 1 pi bond whereas a triple bond contains 1 sigma and 2 pi bonds. How many pi bonds are in C2H2? 1 3 B. A single bond is a sigma bond. Due to the triple bond between C and N, N gets -3 and C gets +3. All rights reserved. The entire molecule is planar. 4 1 sp2 B. Sigma bonds are a result of the head-to-head overlapping of atomic orbitals whereas pi bonds are formed by the lateral overlap of two atomic orbitals.Various bond parameters such as bond length, bond angle, and bond enthalpy depend on the way the overlapping of atomic orbital takes place. Many covalent compounds contain multiple bonds (double or triple bonds). Chemistry. Single Covalent Bond: Definition & Examples, Double Bond: Definition, Formation & Example, Coordinate Covalent Bond: Definition & Examples, Monatomic Ions: Definition & Naming Convention, Lewis Structures: Single, Double & Triple Bonds, Substitution Reaction Examples in Organic Chemistry, Tetrahedral in Molecular Geometry: Definition, Structure & Examples, Metal Reactions: Dilute Acids, Water & Oxygen, Alkanes: Definition, Properties, Formula & Examples, Alkynes: Properties, Uses, Formula & Examples, Butene: Structural Formula, Boiling Point & Isomers, Alkenes: Definition, Properties & Examples, Valence Electron: Definition, Configuration & Example, Bronsted-Lowry Acid: Definition & Examples, Comparing Compounds Based on Boiling Point, Structural Isomers: Definition & Examples, Dipole Moment: Definition, Equation & Examples, UExcel Anatomy & Physiology: Study Guide & Test Prep, Praxis Middle School Science (5440): Practice & Study Guide, MTTC Chemistry (018): Practice & Study Guide, TExMaT Master Science Teacher 4-8 (091): Study Guide & Test Prep, Human Anatomy & Physiology: Help and Review, Holt Physical Science: Online Textbook Help, Praxis Chemistry (5245): Practice & Study Guide, Biological and Biomedical How many molecular orbitals are in #O_2#? How Many Sigma And Pi Bonds In HCN?
how many pi bonds in hcn
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## Proving the Formula for the Kinetic Energy of a Body
If a resultant force acts on a body initially at rest, the speed of the body will increase. The force will do work on the body. If there is no resistance to motion, all the work done by the force will be expressed in an increase of kinetic energy of the body.
If the forceis constant then Newton's Second Law of motion,tells us that the acceleration will be constant. The work done is the force mult0lied by the distance moved,
Using Newtons second law in this equation for the work done gives
Now we can use one of the equations of motion,Since the body starts from rest, so
Substitute this expression into the formula for the work done to give
Problems can often be solved using either the equations of motion for uniform acceleration or by assuming energy is conserved and equation the initial to the final energy. Suppose for example that a ball is thrown up in the air with a speed of 20 m/s. . We want to find the maximum height of the ball. Gravity will cause it to decelerate down with an acceleration of -9.8 m/s 2 (negative since down). Using SUVAT gives
Equating the initial kinetic energy to the graviational potential energy at the maximum height gives
as before.
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## Sunday, December 8, 2013
### Homotopy type theory on Images des mathématiques
This post will be a short advertisement to a longer general audience text about homotopy type theory that I published on the website Images des mathématiques.
In this text, I try to convey my excitement at the reading of the book published by the participants of last year's IAS program, under direction of Steve Awoodey, Thierry Coquand and Vladimir Voevodsky. As I write there (this is the title of this article), this remarkable work is at the crossroads of foundations of mathematics, topology and computer science. Indeed, the new foundational setup for mathematics provided by type theory may not only replace set theory; it is also at the heart of the systems for computer proof checking, and gave birth to a new kind of synthetic homotopy theory'' which is totally freed of the general topology framework.
Also remarkable is the way this book was produced: written collaboratively, using technology well known in open source software's development, then published under a Creative commons's license, and printed on demand.
This is not the only general audience paper on this subject, probably not the last one neither. Here are links to those I know of:
Once more, here is the link towards my article on Images des mathématiques and that towards the HoTT Book!
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GA Search for stable FCC alloys¶
In this tutorial we will emulate an older paper [Johannesson] and determine the most stable FCC alloy using the genetic algorithm. Since the purpose is only the tutorial we will limit the phase space to the elements supported by the EMT potential. The search is also equivalent to the recent search for mixed metal ammines with superior properties for ammonia storage described here:
P. B. Jensen, S. Lysgaard, U. J. Quaade and T. Vegge
Physical Chemistry Chemical Physics, Vol 16, No. 36, pp. 19732-19740, (2014)
Setting up reference database¶
Now we need to set up a database in which reference calculations can be stored. This can either be in a central database server where keywords distinguish between different references or dedicated separate databases for each different type of reference calculations.
In the following script, ga_fcc_references.py, we put the references in the database file refs.db. Our model structure is fcc which is loaded with ase.lattice.cubic.FaceCenteredCubic(). We perform a volume relaxation to find the optimal lattice constant and lowest energy, which we save in the database as key-value pairs for quick retrieval.
import numpy as np
from ase.lattice.cubic import FaceCenteredCubic
from ase.calculators.emt import EMT
from ase.eos import EquationOfState
from ase.db import connect
db = connect('refs.db')
metals = ['Al', 'Au', 'Cu', 'Ag', 'Pd', 'Pt', 'Ni']
for m in metals:
atoms = FaceCenteredCubic(m)
atoms.set_calculator(EMT())
e0 = atoms.get_potential_energy()
a = atoms.cell[0][0]
eps = 0.05
volumes = (a * np.linspace(1 - eps, 1 + eps, 9))**3
energies = []
for v in volumes:
atoms.set_cell([v**(1. / 3)] * 3, scale_atoms=True)
energies.append(atoms.get_potential_energy())
eos = EquationOfState(volumes, energies)
v1, e1, B = eos.fit()
atoms.set_cell([v1**(1. / 3)] * 3, scale_atoms=True)
ef = atoms.get_potential_energy()
db.write(atoms, metal=m,
latticeconstant=v1**(1. / 3),
energy_per_atom=ef / len(atoms))
Initial population¶
We choose a population size of 10 individuals and create the initial population by randomly selecting four elements for each starting individual.
import random
from ase import Atoms
from ase.ga.data import PrepareDB
metals = ['Al', 'Au', 'Cu', 'Ag', 'Pd', 'Pt', 'Ni']
population_size = 10
# Create database
db = PrepareDB('fcc_alloys.db',
population_size=population_size,
metals=metals)
# Create starting population
for i in range(population_size):
atoms_string = [random.choice(metals) for _ in range(4)]
atoms_string=''.join(atoms_string))
Note how we add the population size and metals as extra key-value pairs when we create the database fcc_alloys.db. We can then retrieve these parameters later when running the main script to avoid having to input the same parameters twice.
We can study our initial population by doing (on the command-line):
$ase db fcc_alloys.db -c +atoms_string the term atoms_string determines the order in which the elements are put into the model structure. So it is possible to fully describe an individual by just providing the atoms_string. Run the algorithm¶ The following script runs the algorithm, also find it here: ga_fcc_alloys_main.py. Note that the relaxation script is imported from an external file ga_fcc_alloys_relax.py. from ase.ga.data import DataConnection from ase.ga.element_mutations import RandomElementMutation from ase.ga.element_crossovers import OnePointElementCrossover from ase.ga.offspring_creator import OperationSelector from ase.ga.population import Population from ase.ga.convergence import GenerationRepetitionConvergence from ga_fcc_alloys_relax import relax # Specify the number of generations this script will run num_gens = 40 db = DataConnection('fcc_alloys.db') ref_db = 'refs.db' # Retrieve saved parameters population_size = db.get_param('population_size') metals = db.get_param('metals') # Specify the procreation operators for the algorithm # Try and play with the mutation operators that move to nearby # places in the periodic table oclist = ([1, 1], [RandomElementMutation(metals), OnePointElementCrossover(metals)]) operation_selector = OperationSelector(*oclist) # Pass parameters to the population instance pop = Population(data_connection=db, population_size=population_size) # We form generations in this algorithm run and can therefore set # a convergence criteria based on generations cc = GenerationRepetitionConvergence(pop, 3) # Relax the starting population while db.get_number_of_unrelaxed_candidates() > 0: a = db.get_an_unrelaxed_candidate() relax(a, ref_db) db.add_relaxed_step(a) pop.update() # Run the algorithm for _ in range(num_gens): if cc.converged(): print('converged') break for i in range(population_size): a1, a2 = pop.get_two_candidates(with_history=False) op = operation_selector.get_operator() a3, desc = op.get_new_individual([a1, a2]) db.add_unrelaxed_candidate(a3, description=desc) relax(a3, ref_db) db.add_relaxed_step(a3) pop.update() # Print the current population to monitor the evolution print(['-'.join(p.get_chemical_symbols()) for p in pop.pop]) In this script we run a generational GA as opposed to the pool GA outlined in Optimization with a Genetic Algorithm. This is achieved by having two for-loops; the innermost loop runs the number of times specified by the population size it corresponds to one generation. The outermost loop runs as many generations as specified in num_gens. The function pop.update() is called after the innermost loop has finished thereby only adding individuals to the population after a whole generation is calculated. After each generation is finished the population is printed to the screen so we can follow the evolution. The calculated individuals are continuously added to fcc_alloys.db, we can evaluate them directly by doing from the command line (in another shell instance if the GA is still running): $ ase db fcc_alloys.db -c +atoms_string,raw_score,generation,hof -s raw_score
Note: When reading the database using ase db, it might be necessary to increase the number of shown entries, e.g. ase db fcc-alloys.db --limit N, where N is the number of entries to show (as default only the first 20 entries are shown, --limit 0 will show all. For further info use ase db --help, or consult the ase db manual).
To prevent clutter we import the relax function from the following script:
import numpy as np
from ase.lattice.cubic import FaceCenteredCubic
from ase.calculators.emt import EMT
from ase.eos import EquationOfState
from ase.db import connect
def relax(input_atoms, ref_db):
atoms_string = input_atoms.get_chemical_symbols()
# Open connection to the database with reference data
db = connect(ref_db)
# Load our model structure which is just FCC
atoms = FaceCenteredCubic('X', latticeconstant=1.)
atoms.set_chemical_symbols(atoms_string)
# Compute the average lattice constant of the metals in this individual
# and the sum of energies of the constituent metals in the fcc lattice
# we will need this for calculating the heat of formation
a = 0
ei = 0
for m in set(atoms_string):
dct = db.get(metal=m)
count = atoms_string.count(m)
a += count * dct.latticeconstant
ei += count * dct.energy_per_atom
a /= len(atoms_string)
atoms.set_cell([a, a, a], scale_atoms=True)
# Since calculations are extremely fast with EMT we can also do a volume
# relaxation
atoms.set_calculator(EMT())
eps = 0.05
volumes = (a * np.linspace(1 - eps, 1 + eps, 9))**3
energies = []
for v in volumes:
atoms.set_cell([v**(1. / 3)] * 3, scale_atoms=True)
energies.append(atoms.get_potential_energy())
eos = EquationOfState(volumes, energies)
v1, ef, B = eos.fit()
latticeconstant = v1**(1. / 3)
# Calculate the heat of formation by subtracting ef with ei
hof = (ef - ei) / len(atoms)
# Place the calculated parameters in the info dictionary of the
# input_atoms object
input_atoms.info['key_value_pairs']['hof'] = hof
# Raw score must always be set
# Use one of the following two; they are equivalent
input_atoms.info['key_value_pairs']['raw_score'] = -hof
# set_raw_score(input_atoms, -hof)
input_atoms.info['key_value_pairs']['latticeconstant'] = latticeconstant
# Setting the atoms_string directly for easier analysis
atoms_string = ''.join(input_atoms.get_chemical_symbols())
input_atoms.info['key_value_pairs']['atoms_string'] = atoms_string
The relaxation script is naturally similar to the script we used to calculate the references.
Note that the global optimum is PtNi3 with a -0.12 eV heat of formation, whereas the second worst alloy is AlNi3 heat of formation 0.26 eV. This result is in complete contrast to the conclusion obtained in [Johannesson], where AlNi3 is the most stable alloy within the phase space chosen here. Obviously there is a limit to the predictive power of EMT!
Extending the algorithm¶
There are different ways one can extend the algorithm and make it more complex and sophisticated, all employed in [Jensen]:
Extra mutation operators¶
Instead of only using random operations we can include some that mutates elements to other elements nearby in the periodic table:
from ase.ga.element_mutations import RandomElementMutation
from ase.ga.element_mutations import MoveDownMutation
from ase.ga.element_mutations import MoveUpMutation
from ase.ga.element_mutations import MoveLeftMutation
from ase.ga.element_mutations import MoveRightMutation
from ase.ga.element_crossovers import OnePointElementCrossover
...
oclist = ([4,1,1,1,1,8], [RandomElementMutation([metals]),
MoveDownMutation([metals]),
MoveUpMutation([metals]),
MoveLeftMutation([metals]),
MoveRightMutation([metals]),
OnePointElementCrossover([metals])])
operation_selector = OperationSelector(*oclist)
These operators takes advantage of the fact that chemically like elements (close in the periodic table) exhibit similar properties and the substitution of one to a chemically similar elements could refine the properties of an alloy in the population. A natural extension of these operators would be to use a different ordering of the elements than the periodic table; e.g. Pettifor chemical scale, electronegativity, etc.
Note how we have set the probabilities for selecting operators differently. The probability for RandomElementMutation is equal to the sum of the move mutations. Similarly the probability of OnePointElementCrossover is equal to the sum of all the mutation operators. This is to prevent the search from being purely local.
Prevent identical calculations from being performed¶
In the current main script there is no check to determine whether an identical calculation has been performed, this is easy to check in this regime where model structures are used and we can just use the atoms_string. We insert the following in the inner loop:
for i in range(population_size):
dup = True
while dup:
a1, a2 = pop.get_two_candidates(with_history=False)
op = operation_selector.get_operator()
a3, desc = op.get_new_individual([a1, a2])
dup = db.is_duplicate(atoms_string=''.join(a3.get_chemical_symbols()))
Since the fcc model structure is completely symmetric we could compare sorted versions of the atoms_string, thereby ruling out individuals containing the same elements in different order.
Reuse of calculations between algorithm runs¶
Since genetic algorithms are inherently random in nature one can never be sure to obtain the global minimum with only one algorithm run, it is customary to perform more runs and check that the results agree. In this case it is vital to be able to reuse identical calculations between runs.
We do the following from the command line to create a new database file containing only the relaxed structures:
\$ ase db fcc_alloys.db relaxed=1 -i all_relaxed.db
We subsequently add this to the relaxation script:
def relax(input_atoms, ref_db):
atoms_string = input_atoms.get_chemical_symbols()
relaxed_db = connect('all_relaxed.db')
save_relax = True
try:
dct = relaxed_db.get(atoms_string=''.join(atoms_string))
except KeyError:
# Open connection to the database with reference data
db = connect(ref_db)
# Omitting lines up to the point where hof has been calculated
...
else:
hof = dct.hof
latticeconstant = dct.latticeconstant
save_relax = False
# Place the calculated parameters in the info dictionary of the
# input_atoms object
...
# Put this at the very end
if save_relax:
relaxed_db.write(input_atoms,relaxed=1,
key_value_pairs=input_atoms.info['key_value_pairs'])
Before the actual calculation is performed all_relaxed.db is checked to see if it has been calculated before; if so we just collect the heat of formation, but if not we do the calculation and save it directly to all_relaxed.db. Note: this addition assumes that Prevent identical calculations from being performed.
[Johannesson] (1, 2) G. Jóhannesson, T. Bligaard, A. Ruban, H. Skriver, K. Jacobsen and J. Nørskov. Combined Electronic Structure and Evolutionary Search Approach to Materials Design, Phys. Rev. Lett., Vol 88, No. 25, pp. 1-5 (2002)
[Jensen] P. B. Jensen, S. Lysgaard, U. J. Quaade and T. Vegge. Designing Mixed Metal Halide Ammines for Ammonia Storage Using Density Functional Theory and Genetic Algorithms Phys. Chem. Chem. Phys., Vol 16, No. 36, pp. 19732-19740, (2014)
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# contingencies after changing switching states
2 posts / 0 new
Dr. Stephen Elbert
contingencies after changing switching states
In the case of a contingency K defined by the outage of a grid element J that was already disconnected in the base case, all of the general rules apply:
• A contingency K solution file needs to be written.
• Element J should not be included in the contingency K solution file.
• The constraints on the contingency K solution are those listed in the formulation. In particular, the contingency K solution need not be the same as the base case solution.
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Topic Name Description
Course Introduction Course Syllabus
1.1: Preview of Calculus Preview of Calculus
Read this section for an introduction to calculus.
Derivatives and Tangent Lines
Watch this video (until 8:12) on how to find the slopes of tangent lines from a graph.
Find the Area of an Irregular Shape
Watch this video on how to find the area of an irregular shape.
Practice Problems
Work through the odd-numbered problems 1-7. Once you have completed the problem set, check your answers.
1.2: Lines in the Plane Lines in the Plane
Read this section and work through practice problems 1-9.
Find a Slope Given Two Points
Watch this video on how to find the slope of a line given two points on a graph.
Find the Equation of a Line Given Two Points
Watch this video on how to write the equation of a line through two points using the slope-point formula, and converting the equation to slope-intersect form.
Equations of Circles: Radius and Center
Watch this video on how to write an equation of a circle with the given center and radius.
How to Find the Equation of a Line from a Slope and Point
Watch this video on how to write an equation of a line through a point given the slope.
Determine the Equation of a Line Parallel to a Line in General Form
Watch this video on how to find the equation of a line going through a point and parallel to another line.
Determine the Equation of a Line Perpendicular to a Line in Slope-Intercept Form
Watch this video on how to find the equation of a line going through a point and perpendicular to another line.
Practice Problems
Work through the odd-numbered problems 1-29. Once you have completed the problem set, check your answers.
1.3: Functions and Their Graphs Functions and Their Graphs
Read this section for an introduction to functions and their graphs. Work through practice problems 1-5.
Evaluate Function at a Point
Watch this video on evaluating function at a point.
Practice Problems
Work through the odd-numbered problems 1-23. Once you have completed the problem set, check your answers.
1.4: Combinations of Functions Combinations of Functions
Read this section for an introduction to combinations of functions, then work through practice problems 1-9.
More on the Composition of Functions
Watch the first 16 minutes of this video on evaluating composition of functions.
Combine Functions using Algebraic Operations
Watch this video on combining functions using algebraic operations.
Evaluating Functions Given Equations, Graphs, and Tables
Watch this video on evaluating functions given equations, graphs and tables.
Practice Problems
Work through the odd-numbered problems 1-31. Once you have completed the problem set, check your answers.
1.5: Mathematical Language Mathematical Language
Read this section for an introduction to mathematical language, then work through practice problems 1-4.
Negating Quantified Statements
Watch this video on how to negate a quantified statement.
Converse and Contrapositive
Watch this video on converse and contrapositive of a conditional statement and how to write them.
Practice Problems
Work through the odd-numbered problems 1-25. Once you have completed the problem set, check your answers for the odd-numbered questions.
2.1: Tangent Lines, Velocities, and Growth Tangent Lines, Velocities, and Growth
Read this section for an introduction to connecting derivatives to quantities we can see in the real world. Work through practice problems 1-4.
Slope of a Function at a Point
Watch this video on how to find the slope of the line tangent to the graph of a function at a point.
Practice Problems
Work through the odd-numbered problems 1-9. Once you have completed the problem set, check your answers for the odd-numbered questions.
2.2: The Limit of a Function The Limit of a Function
Read this section for an introduction to connecting derivatives to quantities we can see in the real world. Work through practice problems 1-4.
Evaluating Limits Using a Graph
Watch this video on evaluating limits using a graph.
More on the Limit of a Function
Watch this video on how to evaluate limit of a function.
The Limit of Laws
Practice Problems
Work through the odd-numbered problems 1-19. Once you have completed the problem set, check your answers.
2.3: Properties of Limits Properties of Limits
Read this section to learn about the properties of limits. Work through practice problems 1-6.
Solving Limits (Rationalization)
Watch this video on finding limits algebraically. Be warned that removing $x-4$ from the numerator and denominator in Step 4 of this video is only legal inside this limit. The function $\frac{x - 4}{x - 4}$ is not defined at $x = 4$; however, when $x$ is not 4, it simplifies to 1. Because the limit as $x$ approaches 4 depends only on values of $x$ different from 4, inside that limit $\frac{x - 4}{x - 4}$ and 1 are interchangeable. Outside that limit, they are not! However, this kind of cancellation is a key technique for finding limits of algebraically complicated functions.
Calculating Slope of Tangent Line Using the Definition of a Derivative
Watch this video on limits as the slopes of tangent lines.
Before you watch, know that, for this problem, the limit that gives the slope of the tangent line to a curve is $y = f(x)$ at a point $x = a$, which is the derivative of $f(x)$ at $a$. We will talk about this more in Unit 3.
Practice Problems
Work through the odd-numbered problems 1-21. Once you have completed the problem set, check your answers.
2.4: Continuous Functions Continuous Functions
Read this section for an introduction to what we mean when we say a function is continuous. Work through practice problems 1 and 2.
More on Continuous Functions
Watch this video on continuous functions.
Intermediate Value Theorem
Watch this video on the Intermediate Value Theorem.
Practice Problems
Work through the odd-numbered problems 1-23. Once you have completed the problem set, check your answers.
2.5: Definition of a Limit Definition of a Limit
Read this section to learn how a limit is defined. Work through practice problems 1-6.
Epsilon-Delta Limits
Watch this video to learn the epsilon-delta definition of a limit.
Practice Problems
Work through the odd-numbered problems 1-23. Once you have completed the problem set, check your answers.
3.1: Introduction to Derivatives Introduction to Derivatives
Read this section to lay the groundwork for introducing the concept of a derivative. Work through practice problems 1-5.
The Tangent Line
Watch this video on the slope of secant lines converging to tangent line slopes.
Practice Problems
Work through the odd-numbered problems 1-17. Once you have completed the problem set, check your answers.
3.2: The Definition of a Derivative The Definition of a Derivative
Read this section to understand the definition of a derivative. Work through practice problems 1-8.
Derivatives from the Definition
Watch this video on how to find a derivative from the definition.
Practice Problems
Work through the odd-numbered problems 1-37. Once you have completed the problem set, check your answers.
3.3: Derivatives, Properties, and Formulas Derivatives, Properties, and Formulas
Read this section to understand the properties of derivatives. Work through practice problems 1-11.
Applying the Product Rule for Derivatives
Watch this video on the product rule for differentiation.
Practice Problems
Work through the odd-numbered problems 1-55. Once you have completed the problem set, check your answers.
3.4: Derivative Patterns Derivative Patterns
Read this section to learn about patterns of derivatives. Work through practice problems 1-8.
The Power Rule for Polynomials
Watch this video on how to find derivatives of polynomial functions using the power rule.
Derivatives of Exponential Functions
Watch this video on derivatives of exponential functions.
Derivatives of Trigonometric Functions
Watch this video on how to find the derivatives of trig functions.
Higher-Ordered Derivatives
Watch this video on how to calculate and intepret higher ordered derivatives.
Practice Problems
Work through the odd-numbered problems 1-47. Once you have completed the problem set, check your answers.
3.5: The Chain Rule The Chain Rule
Read this section to learn about the Chain Rule. Work through practice problems 1-8.
Chain Rule Examples
Watch these videos for an introduction to the chain rule for differentiation and examples of the chain rule for differentiation.
Practice Problems
Work through the odd-numbered problems 1-83. Once you have completed the problem set, check your answers.
3.6: Some Applications of the Chain Rule Some Applications of the Chain Rule
Read this section to learn how to apply the Chain Rule. Work through practice problems 1-8.
Solving a Related Rates Problem
Watch this video on using the chain rule to solve rates problems.
Practice Problems
Work through the odd-numbered problems 1-49. Once you have completed the problem set, check your answers.
3.7: Related Rates Related Rates
Read this section to learn to connect derivatives to the concept of the rate at which things change. Work through practice problems 1-3.
Derivatives as Rates of Change
Watch this video on application of derivatives
Differentiating Parametric Functions
Watch this video on differentiating parametric functions.
Practice Problems
Work through the odd-numbered problems 1-21. Once you have completed the problem set, check your answers.
3.8: Newton's Method for Finding Roots Newton's Method for Finding Roots
Read this section. Work through practice problems 1-6.
Using Newton's Method
Watch this video on Newton's method.
Determining Differentiability Graphically
Watch this video on how to determine differentiability graphically.
Continuity on Intervals
Watch this video on continuity of intervals and continuous functions.
Practice Problems
Work through the odd-numbered problems 1-21. Once you have completed the problem set, check your answers.
3.9: Linear Approximation and Differentials Linear Approximation and Differentials
Read this section to learn how linear approximation and differentials are connected. Work through practice problems 1-10.
More on Linear Approximation
Watch this video on linear approximation and differentials.
The Properties of a Differential of a Function
Watch this video on how to calculate the differential of a function using derivatives.
Practice Problems
Work through the odd-numbered problems 1-19. Once you have completed the problem set, check your answers.
3.10: Implicit and Logarithmic Differentiation Implicit and Logarithmic Differentiation
Read this section to learn about implicit and logarithmic differentiation. Work through practice problems 1-6.
Implicit Differentiation and the Derivative of x^(x^x)
Watch these videos on implicit and logarithmic differentiation.
Practice Problems
Work through the odd-numbered problems 1-55. Once you have completed the problem set, check your answers.
4.1: Finding Maximums and Minimums Finding Maximums and Minimums
Read this section to learn about maximums, minimums, and extreme values for functions. Work through practice problems 1-5.
Maxima and Minima
Watch this video on how to identify minimum/maximum points of a function.
Practice Problems
Work through the odd-numbered problems 1-43. Once you have completed the problem set, check your answers.
4.2: The Mean Value Theorem and Its Consequences The Mean Value Theorem and Its Consequences
Read this section to learn about the Mean Value Theorem and its consequences. Work through practice problems 1-3.
Critical Points and the Mean Value Theorem
Watch this video on local maximums/minimums and proves Rolle's Theorem and the Mean Value Theorem.
Practice Problems
Work through the odd-numbered problems 1-35. Once you have completed the problem set, check your answers.
4.3: The First Derivative and the Shape of a Function f(x) The First Derivative and the Shape of a Function f(x)
Read this section to learn how the first derivative is used to determine the shape of functions. Work through practice problems 1-9.
Examples of the First Derivative Test
Watch both parts of this video on the first derivative test.
Practice Problems
Work through the odd-numbered problems 1-29. Once you have completed the problem set, check your answers.
4.4: The Second Derivative and the Shape of a Function f(x) The Second Derivative and the Shape of a Function f(x)
Read this section to learn how the second derivative is used to determine the shape of functions. Work through practice problems 1-9.
Concavity Across Intervals
Watch this video on the second derivative test. This video describes a way to identify critical points as minima or maxima other than the first derivative test, using the second derivative.
Concavity and the Second Derivative
Watch this video, which works through an example of the second derivative test.
Practice Problems
Work through the odd-numbered problems 1-17. Once you have completed the problem set, check your answers.
4.5: Applied Maximum and Minimum Problems Applied Maximum and Minimum Problems
Read this section to learn how to apply previously learned principles to maximum and minimum problems. Work through practice problems 1-3. There is no review for this section; instead, make sure to study the problems carefully to become familiar with applied maximum and minimum problems.
Minimizing Sum of Squares
Watch this video on optimization.
Minimum Triangle Area
Watch this video on optimization.
Practice Problems
Work through the odd-numbered problems 1-33. Once you have completed the problem set, check your answers.
4.6: Infinite Limits and Asymptotes Infinite Limits and Asymptotes
Read this section to learn how to use and apply infinite limits to asymptotes. Work through practice problems 1-8.
Limits at Infinity and Asymptotes
Watch this video on finding limits at infinite, and graphing using first and second derivative tests.
Practice Problems
Work through the odd-numbered problems 1-59. Once you have completed the problem set, check your answer
4.7: L'Hopital's Rule L'Hopital's Rule
Read this section to learn how to use and apply L'Hopital's Rule. Work through practice problems 1-3.
Introduction to L'Hopital's Rule
Watch this video for an introduction to L'Hopital's Rule.
Practice Problems
Work through the odd-numbered problems 1-29. Once you have completed the problem set, check your answers.
5.1: Introduction to Integration Introduction to Integration
Read this section to learn about area. Work through practice problems 1-9.
Find the Exact and Approximate Area of a Region
Watch this video on finding the exact and approximate area of a region.
Practice Problems
Work through the odd-numbered problems 1-15. Once you have completed the problem set, check your answers.
5.2: Sigma Notation and Riemann Sums Sigma Notation and Riemann Sums
Read this section to learn about area. Work through practice problems 1-9.
Riemann Sums in Summation Notation
Watch this video on riemann sums in summation notation.
Practice Problems
Work through the odd-numbered problems 1-61. Once you have completed the problem set, check your answers.
5.3: The Definite Integral The Definite Integral
Read this section to learn about the definite integral and its applications. Work through practice problems 1-6.
Find the Area between Two Curves Using Definite Integrals
Watch this video on how to find the area between two curves using definite integrals.
Practice Problems
Work through the odd-numbered problems 1-29. Once you have completed the problem set, check your answers.
5.4: Properties of the Definite Integral Properties of the Definite Integral
Read this section to learn about properties of definite integrals and how functions can be defined using definite integrals. Work through practice problems 1-5.
Integrals and the Graph of a Function
Watch this video on definite integral and a function's graph.
Practice Problems
Work through the odd-numbered problems 1-51. Once you have completed the problem set, check your answers for the odd-numbered questions against here.
5.5: Areas, Integrals, and Antiderivatives Areas, Integrals, and Antiderivatives
Read this section to learn about the relationship among areas, integrals, and antiderivatives. Work through practice problems 1-5.
Integration and Antiderivatives
Watch this video on Power Rule of Integration, Antiderivative of Polynomial Functions, Integrating Square Root Functions, and Antiderivatives of Rational Functions.
Practice Problems
Work through the odd-numbered problems 1-25. Once you have completed the problem set, check your answers.
5.6: The Fundamental Theorem of Calculus The Fundamental Theorem of Calculus
Read this section to see the connection between derivatives and integrals. Work through practice problems 1-5.
Integrals and the Fundamental Theorem of Calculus
Watch this video on Integrals and Fundamental theorem of calculus.
Differentiating an Integral Function
Watch this video on differentiating integral functions.
Practice Problems
Work through the odd-numbered problems 1-67. Once you have completed the problem set, check your answers.
5.7: Finding Antiderivatives Finding Antiderivatives
Read this section to see how you can (sometimes) find an antiderivative. In particular, we will discuss the change of variable technique. Change of variable, also called substitution or u-substitution (for the most commonly-used variable), is a powerful technique that you will use time and again in integration. It allows you to simplify a complicated function to show how basic rules of integration apply to the function. Work through practice problems 1-4.
Integrating with U-Substitution
Watch these videos on change of variable, also called substitution or U-substitution.
Practice Problems
Work through the odd-numbered problems 1-69. Once you have completed the problem set, check your answers.
5.8: First Application of Definite Integral First Application of Definite Integral
Read this section to see how some applied problems can be reformulated as integration problems. Work through practice problems 1-4.
Practice Problems
Work through the odd-numbered problems 1-41. Once you have completed the problem set, check your answers.
5.9: Using Tables to Find Antiderivatives Using Tables to Find Antiderivatives
Read this section to learn how to use tables to find antiderivatives. See the Calculus Reference Facts for the table of integrals. Work through practice problems 1-5.
Practice Problems
Work through the odd-numbered problems 1-55. Once you have completed the problem set, check your answers.
Study Guide MA005 Study Guide
Course Feedback Survey Course Feedback Survey
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## Penumbra: An Eclipse Plugin for Introductory Programming
#### Abstract
Eclipse is a full-featured and easily extensible integrated development environment. As such, it has grown to include a large degree of functionality that may be overwhelming to the novice programmer. Nevertheless, we believe Eclipse is an environment that students of programming will come to find useful and empowering once they become familiar with it. The trick is easing them into using Eclipse without them feeling overwhelmed at the outset. Penumbra is an Eclipse plug-in developed at Purdue University for use in our introductory programming classes. It is intended to ease the transition to use of the full-featured functionality of Eclipse. Penumbra presents an Eclipse perspective that hides all but the basic actions of Eclipse’s existing Java perspective, while packaging elements of other perspectives (e.g., the CVS perspective) into simpler actions that ease the downloading and turn-in of programming assignments, and adding new code views inspired by other environments for introductory programmers. Our experiences using Eclipse with a small group of introductory programming students in the Spring of 2003 have guided the development of Penumbra, which is now being rolled out for general use by the full class of 230 students in the Fall of 2003.
@inproceedings{Mueller+2003ETX,
author = {Mueller, Frank and Hosking, Antony L.},
title = {Penumbra: An {E}clipse Plugin for Introductory Programming},
booktitle = {OOPSLA Workshop on {E}clipse {T}echnology e{X}change},
series = {eTX},
year = {2003},
pages = {65--68},
month = {October},
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Top
LC Resonance Calculator
Top
An electrical circuit is said to undergo resonance when the net current is in phase with the applied voltage. A circuit at resonance exhibits certain characteristics such as maximum current or minimum current. The resonance frequency fo is given by
fo =$\frac{1}{2 \pi \sqrt{LC}}$
Where L and C are inductance and capacitance value.
LC resonance Calculator is a online tool to calculate the resonance frequency fo. You just have to enter the inductance L and capacitance C value and get the answer instantly.
Steps for L-C Resonance Calculator
Step 1 :
Read the given problem and observe the given quanities.
Step 2 :
The resonant frequency is given by
fo = $\frac{1}{2 \pi \sqrt{LC}}$
Here L is inductance and C is capacitance value. Substitute the given values and get the unknown quantity.
Problems on L-C Resonance Calculator
1. A coil having an inductance of 50 mH and resistance of 100 ohms is connected in series with a capacitor and a 100 V, 1 KHz source. Obtain the value of capacitance that will cause a resonance on the circuit.
Step 1 :
Given: Inductance L = 50 mH, Capacitance C = 100 $\Omega$
Step 2 :
The resonance frequency is
fo = $\frac{1}{2 \pi \sqrt{LC}}$
1000 = $\frac{1}{2 \times 3.142 \times \sqrt{50 \times 10^-3 \times C}}$
Capacitance C = 0.5 $\mu$ F
The Capacitance is C = 0.5 $\mu$ F
2. A circuit has L = 50 mH and C = 70 $\mu$ F. Calculate its resonant frequency.
Step 1 :
Given: Inductance L = 50 mH, Capacitance C = 70 $\mu$ F
Step 2 :
The resonance frequency is
fo = $\frac{1}{2 \pi \sqrt{50 \times 10^{-3} \times 70 \times 10 ^{-6}}}$
= 85.07 Hz.
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# Ring of integers modulo $n$ with a property for the zero divisors.
This is a follow-up of Is $a+b$ a unit if $a,b,a-b$ are zero divisors?
Let $n$ be a natural number such that the ring $R:=\mathbb{Z}/(n \mathbb{Z})$ has the following property: $$a,b,a-b\in Z \implies a+b \in Z$$ where $Z$ are the zero-divisors of $\mathbb{Z}/(n \mathbb{Z})$.
User @lhf made the observation that $R$ seems to have this property exactly when $n$ has less than three prime divisors. I am interested if this can be made into a proof.
Edit: Here is a partial result if $\omega(n)=1$, hence $n=p^\alpha$ is a prime power: If $a,b,a-b\in Z$ then we must have: $p^{a_0} = \gcd(a,n)>1$,$p^{b_0} = \gcd(b,n)>1$,$p^{c_0} = \gcd(a-b,n)>1$ for $a_0,b_0,c_0\ge 1$. From this it follows that: $$a = x p^{a_0}, b = y p^{b_0}, a-b=zp^{c_0}$$ and we get: $$a+b = (a-b)+2b = zp^{c_0} + 2yp^{b_0} = p^{d_0}(zp^{c_0-d_0}+2yp^{b_0-d_0})$$ with $d_0 = \min(c_0,b_0) \ge 1$ since $b_0,c_0 \ge 1$. Hence $\gcd(a+b,n)>1$ and $a+b \in Z$.
• What is the source of the original problem? – lhf Jun 2 '18 at 12:25
• @lhf: I am trying to collect examples for "graph algebras". See this question, example g) : math.stackexchange.com/questions/2805133/… – orgesleka Jun 2 '18 at 12:27
• @lhf: If you have an idea for a graph algebra, feel free to add it, to the linked question. – orgesleka Jun 2 '18 at 12:29
• I found this while researching your question: math.lsu.edu/system/files/BeamerPresentation3.pdf – lhf Jun 2 '18 at 12:30
• @lhf: thank you, that is very useful! – orgesleka Jun 2 '18 at 12:32
Theorem. There exist $a,b\in\mathbb{Z}/n\mathbb{Z}$ for which $a,b,a-b$ are zero divisors but $a+b$ isn't if and only if $n$ has at least $3$ distinct prime factors.
Proof. First assume $n$ has only $1$ or $2$ prime factors. If $a,b,a-b$ are each zero divisors, then they are each divisible by one of these one or two primes, so a pair of them share a prime divisor by the pigeonhole principle. If $a,b$ share it, then $a+b$ is a zero divisor, but if $a,a-b$ or $b,a-b$ share it then so does the third since $b=a-(a-b)$ and $a=(a-b)+b$, so same conclusion.
Now assume $n$ has at least $3$ distinct prime factors. Then we can write $n=ABC$ where $A,B,C$ are pairwise coprime and $C$ is odd. Since the Chinese Remainder Theorem says
$$\mathbb{Z}/n\mathbb{Z}\cong (\mathbb{Z}/A\mathbb{Z})\times(\mathbb{Z}/B\mathbb{Z})\times(\mathbb{Z}/C\mathbb{Z}),$$
so we can work in this ring instead. Then set $a=(0,1,-1)$ and $b=(1,0,-1)$, which are both nonunits since they have a coordinate $0$, then verify $a-b=(-1,1,0)$ is also a nonunit for the same reason, but $a+b=(1,1,-2)$ is a unit since it is a unit in each coordinate.
I got this example from looking at the case $(A,B,C)=(3,4,5)$. The first example I found were the numbers $a=9$ and $b=4$, with $a-b=5$ and $a+b=13$. I took both of these values and found they corresponded to $(0,1,-1)$ and $(1,0,-1)$ mod $3,4,5$ and noticed that would always work as long as $A,B,C$ were pairwise coprime and $C$ was odd.
• I don't understand your argument in the case when where $n$ has only $1$ or $2$ prime factors. Why does the same argument not apply when $n$ has more than $3$ prime factors? – orgesleka Jun 3 '18 at 5:05
• @stackExchangeUser If there are at most two primes and each of $a,b,a-b$ is divisible by one of them, then a pair of them share a prime factor. Pigeonhole principle. That doesn't work with three or more primes. – anon Jun 3 '18 at 5:30
• thank you for your answer – orgesleka Jun 3 '18 at 6:42
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# Density operators and separable states
I know that a density operator is separable if it can be written in the form:
$$\rho =\sum_k a_k \rho^A_k \otimes \rho^B_k\tag{1}$$ where
$$a_k \ge 0,\quad \sum_k a_k=1\tag{2}$$
My question is will any set of $\rho_k^A \otimes \rho_k^B$ work? I.e. I am asking if the following statement is true (if so how do we prove it and if not - why not):
A density matrix $\rho$ is separable if and only if when written as the sum of "factorized" states $\rho_K^A \otimes \rho_k^B$ (independent of which factorized states are used) the relations (1) and (2) hold.
This is clearly a stronger statement then saying it can be written as (1) and (2) - and if true leads to a quick way to test entanglement.
$\rho$ is separable if and only if there exist $\rho_i^A\ge0$, $\rho_i^B\ge0$, and $p_i\ge0$ such that $$\rho = \sum_i p_i \rho_i^A\otimes \rho_i^B\ .$$
All other properties (that the $\rho_i^\bullet$ have trace 1 and the $p_i$ sum to $1$) follow automatically.
If your possible set of states is infinitely large (every possible pure state of 1 qubit), you can always do it, of course. But, worse, it has to be this large. Imagine you have a finite set $\{\rho^A_i\}$ and you want to describe a pure single-qubit state $|\psi\rangle\langle\psi|$ that is not one of the $\rho^A_i$. Clearly, there is no choice of $\{p_i\}$ such that $\sum_ip_i\rho^A_i=|\psi\rangle\langle\psi|$ because you must sum at least two terms, and hence will have a state with at least rank 2, while the pure state has rank 1.
A good way to visualise this is with the Bloch sphere. Imagine a sphere. Every possible pure state corresponds to a point on the surface. The set $\{\rho^A_i\}$ form a set of points on, or in, the sphere. The set of possible states that you can make via the term $\sum_ip_i\rho^A_i$ is given by the convex hull of the points. You can't reconstruct the surface of the sphere from a convex hull (the shape has flat sides!) unless you have infinitely many points.
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Jan van Dijk 2007-12-12 10:33:50 UTC In our plasma modelling group we have been happy doxygen users for a long time now. After all these years of using doxygen, we feel that one feature is still missing: LaTeX-style bibliography support (a \cite command). In my (C++) code, I would like to be able to write: /** Nifty class implements the Nifty algorithm that has been * discussed in \cite{Dijk2007/1}. */ struct NiftyClass { // ... }; Dijk2007/1 would be a BibTeX entry, declared in a bibtex file myrefs.bib, say. (The fact that Doxygen uses this file, and perhaps others as well, could be configured in the .doxy file, or somewhere else.) The idea is that doxygen compiles a bibliographic reference from the .bib files and the\cite commands. That would be a separate HTML page, similar to those generated by the \todo and \bug tags. Then, in the doxygen-output (in particular the HTML-docs) for the NiftyClass we would see something like: Nifty class implements the Nifty algorithm that has been discussed in [42]. Where [42] would be a clickable reference to the appropriate anchor on the generated bibliography page. Could such feature be considered? We would welcome it very much! Dimitri van Heesch 2007-12-12 19:16:02 UTC *** Bug 503235 has been marked as a duplicate of this bug. *** Dimitri van Heesch 2007-12-12 19:16:38 UTC *** Bug 503237 has been marked as a duplicate of this bug. *** Jan van Dijk 2011-03-01 13:31:42 UTC I spotted two more duplicates: 317328 and 635562. (The former is older, but seems to refer to Latex output only.) That adds up to four, indicating that this feature is desired for real. I really hope somebody with knowledge of Doxygen's internals will pick this up. Thanks. BTW: I seem to recall that Dimitri has responded to this enhancement request, and confirmed it. Now It appears that the bug is unconfirmed ... and those comments are nowhere to be seen. David Munger 2011-07-25 01:53:33 UTC I proposed a patch for BibTeX support here: https://bugzilla.gnome.org/show_bug.cgi?id=635562#c1 Dimitri van Heesch 2011-07-28 18:45:37 UTC Thanks David, a variant of your patch has been included in the latest subversion update. Dimitri van Heesch 2011-07-28 18:46:53 UTC *** Bug 635562 has been marked as a duplicate of this bug. *** Dimitri van Heesch 2011-07-28 18:47:43 UTC *** Bug 317328 has been marked as a duplicate of this bug. *** Jan van Dijk 2011-08-08 12:36:29 UTC I have just started to play with this. Thanks a lot, this is what we have been wishing for for a long time! I have a few comments, though. They look like simple issues to fix for somebody who knows what he is doing: * Specifying an absolute path as argument of CITE_BIB_FILES results in problems. As an example, "CITE_BIB_FILES = /home/jan/src/gum-cvs/doc/refs/plreflst.bib" resulted in: "error: could not write to file /home/jan/src/test_doxygen/bib/doxygen_bibtex_28135_/home/jan/src/gum-cvs/doc/refs/plreflst.bib" and similar errors. * Something like \cite VanDijk2011/2 will not work, since the argument of \cite is parsed as a LABELID, it will stop parsing at the '/' character. It would be nice if this were changed, since using '/' (or ':', for that matter), followed by an index is quite common among BibTex users. Otherwise, would it be possible to allow \cite "VanDijk2011/2" instead? It would not be nice if users have to modify all their .bib files to use (e.g.) VanDijk2011_2 instead. * url={blabla} lines in bibtex files are not handled correctly. They result in the message "citelist:4: warning: Found unknown command \rev'". Indeed, in the files doxygen.bst and doxygen_bst.h (line 156) I see that \rev is emitted. Should that have been \ref? I blindly tried that change, but this results in other errors: "citelist:4: warning: unable to resolve reference to CITEREF_' for \ref command". Thanks again, With kind regards, Jan. Dimitri van Heesch 2011-08-14 14:05:28 UTC This bug was previously marked ASSIGNED, which means it should be fixed in doxygen version 1.7.5. Please verify if this is indeed the case. Reopen the bug if you think it is not fixed and please include any additional information that you think can be relevant. Jan van Dijk 2011-08-14 14:31:27 UTC I just checked with trunk (revision 773) and I still observe the three issues that I mentioned in comment #8. Therefore, I reopened this bug. Dimitri van Heesch 2011-10-01 21:42:41 UTC Confirmed. Should be fixed in the next subversion update. Dimitri van Heesch 2011-12-03 18:22:57 UTC This bug was previously marked ASSIGNED, which means it should be fixed in doxygen version 1.7.6. Please verify if this is indeed the case. Reopen the bug if you think it is not fixed and please include any additional information that you think can be relevant. david.coeurjolly 2012-02-20 13:32:11 UTC Hi all, I'm still having issues with cite command (svn doxygen release 1.7.6.1-20120122): - my cite commands and the bibtex file are correctly parsed/handled in the latex output (result is perfect) - in the HTML output * \cite generates correct links (e.g. html/citelist.html#CITEREF_MyKey) * however, the citelist.html page is empty (header/footer but no "content") When I look at the doxygen outputs, nothing special appears (hop.txt is std output and hop2.txt is std:cerr) : %%%> grep cite hop.txt hop2.txt hop.txt:Generating docs for page citelist... hop2.txt:citelist:3: warning: expected
instead! hop2.txt:citelist:4: warning: unexpected end of comment while looking for a html description title Nothing appears if I "grep" on "bib". Any idea ? Guillaume Lazzara 2013-03-07 13:44:49 UTC Thanks for this feature. I encounter two problems though: - Something like \cite sauvola.00.pr will not work, only the first word will be taken into account. - citelist pages wont be generated when a tag file is used. The tagfile usually already specifies a page citelist Bibliographic References citelist and this prevents the new citelist from being written. The result are broken links in the documentation.
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## What does it mean for a reaction to be "thermodynamically favored?"
$\Delta G^{\circ}= \Delta H^{\circ} - T \Delta S^{\circ}$
$\Delta G^{\circ}= -RT\ln K$
$\Delta G^{\circ}= \sum \Delta G_{f}^{\circ}(products) - \sum \Delta G_{f}^{\circ}(reactants)$
Posts: 96
Joined: Fri Sep 29, 2017 7:04 am
### What does it mean for a reaction to be "thermodynamically favored?"
I saw somewhere that reactions with a negative enthalpy change are exothermic and thus more favorable than reactions with a positive enthalpy change (endothermic).
But according to the 2nd Law of Thermodynamics (states that reactions tend to go from low to high entropy) then why is a reaction with a negative enthalpy change favorable?
Ishita Monga 1B
Posts: 31
Joined: Thu Jul 27, 2017 3:00 am
### Re: What does it mean for a reaction to be "thermodynamically favored?"
Whether or not a reaction is favored is determined by deltaG. You have to use the relation deltaG=deltaH - TdeltaS in order to determine favorability. If a reaction has a negative enthalpy and entropy increases over the course of the reaction, then a negative minus a positive is still negative. Thus, deltaG would be negative which means that the reaction is favorable.
Cristina Sarmiento 1E
Posts: 52
Joined: Wed Nov 16, 2016 3:02 am
### Re: What does it mean for a reaction to be "thermodynamically favored?"
Reactions that do not require energy are seen as more favorable. Since exothermic reactions release energy and endothermic reactions require energy, exothermic reactions are more favorable.
Angela G 2K
Posts: 30
Joined: Fri Sep 29, 2017 7:06 am
### Re: What does it mean for a reaction to be "thermodynamically favored?"
Enthalpy tends to go from high enthalpy to low enthalpy, whereas entropy tends to go from low entropy to high entropy.
Delta H -, Delta S + = favored
Delta H -, Delta S - = favored at low temperatures only
Delta H +, Delta S + = favored at high temperatures only
Delta H +, Delta S - = not favored (reverse reaction is thermodynamically favored)
Shreya Ramineni 2L
Posts: 50
Joined: Fri Sep 29, 2017 7:07 am
### Re: What does it mean for a reaction to be "thermodynamically favored?"
Thermodynamically favorable means spontaneous, or that the reaction does not require energy in order to happen.
Phillip Winters 2F
Posts: 50
Joined: Fri Sep 29, 2017 7:05 am
### Re: What does it mean for a reaction to be "thermodynamically favored?"
A reaction if thermodynamically favorable if delta G is negative, which means that the reaction is spontaneous and thus doesn't require energy to occur
Kevin Tabibian 1A
Posts: 42
Joined: Fri Sep 29, 2017 7:06 am
### Re: What does it mean for a reaction to be "thermodynamically favored?"
It means that it is energetically favorable and naturally occurring ( spontaneous). This is represented by a negative delta G
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# How to show that $\mathcal{O}(1)$ is generated by the global sections $x_1, \ldots, x_n$?
On page 150 of Algebraic Geometry by Hartshorne, line 4 of paragraph 2, it is said that $\mathcal{O}(1)$ is generated by the global sections $x_1, \ldots, x_n$. How to show that $\mathcal{O}(1)$ is generated by the global sections $x_1, \ldots, x_n$?
By definition, $\mathcal{O}(1) = \widetilde{S(1)}$, $S=k[x_0, \ldots, x_n]$. Let $U_i=\{(x_0, \ldots, x_n): x_i \neq 0\}$ be the open covering of $\mathbb{P}^{n}_k$. Then $\mathcal{O}(1)(U_i)$ is the set of functions $s: U_i \to \sqcup_{p \in U_i} S(1)_{p}$ such that $s(p) \in S(1)_p$ and $s$ satisfies some properties. I think that $S(1)_n = S_{n+1}$. Therefore $S(1)_0 = S_1 = \sum_{i=0}^{n} k x_i$. But how to show that $\mathcal{O}(1)$ is generated by the global sections $x_1, \ldots, x_n$? Thank you very much.
To say that $\mathcal{O}(1)$ is generated by the global sections $x_0,\ldots,x_n$ means we have a surjective morphism of $\mathcal{O}_X$-modules
$$\mathcal{O}_X^{\oplus(n+1)} \to \mathcal{O}(1) \to 0$$ where the global section $e_i$ of $\mathcal{O}_X(X)^{\oplus( n+1)}$ maps to $x_i\in \mathcal{O}(1)(X)$. Thus it is enough to compute global sections of $\mathcal{O}(1)$. Do you know how to do this?
The answer is: $$\mathcal{O}(1)(X) = \{\text{linear polynomials in x_0,\ldots,x_n}\}.$$
How to compute this
Use the standard affine open cover of $\Bbb{P}^n_k$ by $U_0,\ldots,U_n$. Recall that $\mathcal{O}(1)(U_i) = k[x_0,\ldots,x_n]_{(x_i)}$ where $(x_i)$ means the degree zero component of the localization at $\{1,x_i,x_i^2,\ldots\}$.
Now say you had a global section $s$. What does $s_i:= s|_{U_i}$ look like? Say it is $f_i(x_0,\ldots,x_n)/x_i^{k_i}$ where $f_i$ is homogeneous of degree $k_i$. Since the polynomial ring over a field is a UFD we may assume the denominator and numerator for every $i$ have no common factor. Now what does it mean to now say $$s_i|_{U_i \cap U_j} = s_j|_{U_i \cap U_j}?$$
Can you deduce your original $f_i$'s had to be linear? If you're confused then just do the case of $X =\Bbb{P}^1$; I have always found that very illuminating.
• thank you very much. How to show that $f_i$'s are linear? I think that in line 7 you mean $$\mathcal{O}(1) (\mathbb{P}^n)= \{\text{linear polynomials in }x_0, \ldots, x_n\}.$$ – LJR Dec 25 '13 at 16:40
• @LJR Try doing it yourself first (if you're stuck do $\Bbb{P}^1$) and if all else doesn't work ping me and i'll edit my answer. – user38268 Dec 25 '13 at 23:34
• Let $s \in \mathcal{O}(1)(\mathbb{P}^1)$. Then $s|_{U_0}=g/x_0^d$, $s|_{U_1}=g'/x_1^{\ell}$ for some $g, g'$, $\deg g = d+1, \deg g' = \ell+1$. Let $(1: x_1)\in U_0 \cap U_1$. Suppose that $g(x_0, x_1) = \sum_{i+j=d+1} k_{ij} x_0^i x_1^j$ and $g'(x_0, x_1) = \sum_{i+j=\ell+1}k'_{ij}x_0^i x_1^j$. Then $s(1, x_1) = g(1, x_1)=\sum_{i+j=d+1}k_{ij}x_1^j$ and $s(1, x_1)=g'(1,x_1)/x_1^\ell=\sum_{i+j=d+1}k'_{ij} x_1^j/x_1^\ell=\sum_{i+j=\ell+1}k'_{ij}x_1^{j-\ell}$. Therefore the degree of $x_1$ in $s(1, x_1)$ is less or equal to $1$ and greater or equal to $0$. – LJR Jan 5 '14 at 10:25
• Similarly, the degree of $x_0$ in $s(x_0,1)$ is less or equal to 1 and greater or equal to $0$. Since $s(x_0, x_1)$ is of degree 1, $s(x_0, x_1)$ is a linear combination of $x_0, x_1$. – LJR Jan 5 '14 at 10:27
• $s(1, x_1), s(x_0, 1)$ are polynomials of degree less or equal to 1. Therefore $s(x_0, x_1)$ is a polynomial. Since $s \in \mathcal{O}(1)(\mathbb{P}^1)$, $s$ is of degree 1. – LJR Jan 5 '14 at 14:58
Just in case there is someone who wants to think about it in another way. (This is how I thought about it.)
The situation is the following. Let $A$ be a ring, $\mathbb{P}^n_A= \text{Proj}(S)$ with $S=A[x_0,\dots,x_n]=\bigoplus_{d\geq 0}S_d$ (standard grading) be the $n$-th projective space over $A$ and let us for short denote by $\mathscr{O}=\mathscr{O}_{\mathbb{P}^n_A}$ the structure sheaf of $\mathbb{P}^n_A$.
What is meant by "$\mathscr{O}(1)$ is generated by the global sections $\{x_i\}_i$" is that for every point $P \in \mathbb{P}^n_A$, the stalk $\mathscr{O}(1)_P$ is generated over $\mathscr{O}_P$ by the germs $\{{x_i}_P \}_i$ of the global sections at $P$. But here one has to be carefully (at least at the first attempt): the $x_i$ are not "really" global sections of the twist $\mathscr{O}(1)$. At first we have to clarify how they give rise to global sections of $\mathscr{O}(1)$.
By definition, \begin{align*} \mathscr{O}(1)=S(1)^{\sim}=(\bigoplus_{d\geq 0}S_{d+1})^{\sim}=(S_+)^{\sim}. \end{align*} Then $x_i$ gives a map \begin{align*} X_i \colon \mathbb{P}^n_A &\longrightarrow \coprod_{P \in \mathbb{P}^n_A} (S_+)_{(P)}, \\ P & \longmapsto \big(\frac{x_i}{1},P\big), \end{align*} (here note that $\frac{x_i}{1}$ is a degree zero element in the localization $(S_+)_P$, since $x_i$ is a degree zero element in the grading of $S_+$) which is a global section of $\mathscr{O}(1)$.
Now using the natural isomorphisms \begin{align*} (\mathscr{O}(1))_P \cong (S_+)_{(P)} \;\;\; \text{and} \;\;\; \mathscr{O}_P \cong S_{(P)}, \end{align*} we see that it is enough to show that the elements $\frac{x_i}{1} \in (S_+)_{(P)}$ (corresponding to the germs of the $X_i$ at $P$) generate $(S_+)_{(P)}$ over $S_{(P)}$.
But $\{ x_i \}_i$ generates $S_+$ over $S$, hence we get that $\{ \frac{x_i}{1} \}_i$ generates $(S_+)_{(P)}$ over $S_{(P)}$ as desired.
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# Function space
In mathematics, a function space is a set of functions between two fixed sets. Often, the domain and/or codomain will have additional structure which is inherited by the function space. For example, the set of functions from any set X into a vector space have a natural vector space structure given by pointwise addition and scalar multiplication. In other scenarios, the function space might inherit a topological or metric structure, hence the name function space.
## In linear algebra
Let V be a vector space over a field F and let X be any set. The functions XV can be given the structure of a vector space over F where the operations are defined pointwise, that is, for any f, g : XV, any x in X, and any c in F, define
{\displaystyle {\begin{aligned}(f+g)(x)&=f(x)+g(x)\\(c\cdot f)(x)&=c\cdot f(x)\end{aligned}}}
When the domain X has additional structure, one might consider instead the subset (or subspace) of all such functions which respect that structure. For example, if X is also vector space over F, the set of linear maps XV form a vector space over F with pointwise operations (often denoted Hom(X,V)). One such space is the dual space of V: the set of linear functionals VF with addition and scalar multiplication defined pointwise.
## Examples
Function spaces appear in various areas of mathematics:
## Functional analysis
Functional analysis is organized around adequate techniques to bring function spaces as topological vector spaces within reach of the ideas that would apply to normed spaces of finite dimension.
• Schwartz space of smooth functions of rapid decrease and its dual, tempered distributions
• Lp space
• ${\displaystyle C(\mathbf {R} )}$ continuous functions endowed with the uniform norm topology
• ${\displaystyle C_{c}(\mathbf {R} )}$ continuous functions with compact support
• ${\displaystyle B(\mathbf {R} )}$ bounded functions
• ${\displaystyle C_{0}(\mathbf {R} )}$ continuous functions which vanish at infinity
• ${\displaystyle C^{r}(\mathbf {R} )}$ continuous functions that have continuous first r derivatives.
• ${\displaystyle C^{\infty }(\mathbf {R} )}$ smooth functions
• ${\displaystyle C_{c}^{\infty }(\mathbf {R} )}$ smooth functions with compact support
• ${\displaystyle D(\mathbf {R} )}$ compact support in limit topology
• ${\displaystyle W^{k,p}}$ Sobolev space
• ${\displaystyle {\mathcal {O}}_{U}}$ holomorphic functions
• linear functions
• piecewise linear functions
• continuous functions, compact open topology
• all functions, space of pointwise convergence
• Hardy space
• Hölder space
• Càdlàg functions, also known as the Skorokhod space
## Norm
If y is an element of the function space ${\displaystyle {\mathcal {C}}(a,b)}$ of all continuous functions that are defined on a closed interval [a,b], the norm ${\displaystyle \|y\|_{\infty }}$ defined on ${\displaystyle {\mathcal {C}}(a,b)}$ is the maximum absolute value of y (x) for axb,[2]
${\displaystyle \|y\|\equiv \max _{a\leq x\leq b}|y(x)|\qquad {\text{where}}\ \ y\in {\mathcal {C}}(a,b)\,.}$
## Bibliography
• Kolmogorov, A. N., & Fomin, S. V. (1967). Elements of the theory of functions and functional analysis. Courier Dover Publications.
• Stein, Elias; Shakarchi, R. (2011). Functional Analysis: An Introduction to Further Topics in Analysis. Princeton University Press.
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# Dirac delta an even function?
Hi this is my first post here so I'm sorry if my question seems trivial.
I haven't worked a lot with the dirac delta function before, so i always thought that the shifting property would only work as:
$$\int\delta(x-h)\;f(x)\;dx=f(h)$$
Now I've been reading some articles and I came across expressions like:
$$\int\delta(h-x)\;f(x)\;dx=f(h)$$
which didn't make sense to me so I checked on the internet and saw that the delta function is supposed to be an even function.
Now I know it is not entirely a true function, but still the only description I know is that it's zero everywhere except for x. If I can give values to x other than zero, than
$$\delta(x)=\delta(-x)$$ means for example
$$\delta(5)=\delta(-5)$$ which doesn't make sense to me.
So I'll be very glad if someone can explain to me why it's an even function.
Thanks!
Hurkyl
Staff Emeritus
Gold Member
To a great extent, the kind of object the dirac delta function is plays well with changes of variable. The simplest case is when f is an invertible, differentiable, increasing function, $\varphi$ is a distribution, and both g(x) and g(f(x)) f'(x) are test functions, then
$$\int_{-\infty}^{+\infty} \varphi(x) g(x) \, dx = \int_{-\infty}^{+\infty} \varphi(f(x)) g(f(x)) f'(x) \, dx$$
This equation can be taken as the very definition of $\varphi(f(x))$ -- although some effort must be taken to show this definition is well-defined.
For other f, things are a little trickier. f(x) = -x isn't so bad, since it's still differentiable and invertible. Other f simply won't make sense all, such as when f(x) = 0 in the case where $\varphi = \delta$.
I should point out that there is an ambiguity in notation. When we have expressions involving a variable, such as sin(x) or x + 3, sometimes we mean for that expression to represent the (undetermined) real number that is the result of the computation involving the (undetermined) real number x. Other times, we mean for that expression to represent a function of a single variable, which we have named x.
The latter kind of notation is often applied to distributions like the Dirac delta, since it is rather convenient to write.
Now I know it is not entirely a true function, but still the only description I know is that it's zero everywhere except for x.
x being which number, exactly?
The delta function is, roughly, zero everywhere except for 0, and as such is obviously even - delta(0) = +infinity (metaphorically speaking), delta(non-zero) = 0. To say that it's zero everywhere except for "x" doesn't even make sense.
yes ok i see your point.
no need to be hostile, what i meant to ask was why it's an even function in general. so i could also phrase it like
$$\delta (x-h) = \delta (-x+h)$$
or just give a number
$$\delta (x-5) = \delta (-x+5)$$
In this case I just felt like the "spike" formed by the delta function would be on the other side of the axis, but the distribution argument makes sense.
Thanks for the replies!
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# Graphicspath for MikTeX
Is there a way to specify a `\graphicspath` that includes all sub-directories? I know I could put all my graphics in a texmf tree, but I'd like to have them in another directory tree. As far as I can tell, `\graphicspath` won't include sub-directories.
I'm using MikTeX 2.8.
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You marked Trevor's answer as correct: did this work for you, and if so how? I'm trying to track down some information one whether this really works, and if so the detailed requirements (TeX system, etc.). – Joseph Wright Sep 14 '11 at 20:33
I think it used to work, but I actually just ended up putting my images into a texmf root so I didn't use it. In any case, it doesn't work now. I'm using MikTeX 2.9 on Windows 7 64bit. – Rob Hyndman Sep 15 '11 at 4:23
Nope. (Not as far as I know.) The way `\graphicspath` works is simply to iterate over each directory specified and ask the equivalent of `\IfFileExists{<thepath><thegraphic>.pdf}` when you try to `\includegraphics{<thegraphic>}`. Since you can't specify wildcards when asking TeX to input a file, similarly you can't specify wildcards when asking it to insert a graphic.
One small caveat: with `-shell-escape` you could run a batch script (or, better, a Lua script) that iteratively listed the subdirectories of a given path and then inserted them back into the document for `\graphicspath`. But there's nothing around currently that will do that. (Again, as far as I know. I don't use Windows these days so I'm a bit out of the loop with MiKTeX.)
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Has this changed at all (It's been 6 years)? Do want. – kando May 13 at 15:59
For me `\graphicspath{{Figures//}}` seems to work with miktex. Note the extra slash.
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using this will be very very usefull, but I've tried to use `\graphicspath{{Figures//}}` on windows7, texmaker, and it doesn't work. Why? . Can you include and example document? Thank you – Daniteba Jan 16 '13 at 13:39
Sorry for the extremely late reply. I haven't logged into tex.stackexchange for a long time. This method worked for me or used to work (I haven't tried it recently) but judging by more recent comments it no longer does. From the dates I can only assume something must have changed some time in 2011 since all references of this working for me and others are from 2010 or earlier sometimes with a warning against its use. eg latex-community.org/viewtopic.php?f=5&t=3205 – cue Feb 5 '13 at 16:50
You could add the relevant directory to your `TEXINPUTS` environment variable. If you end with a double-slash (eg, `TEXINPUTS=.:/home/me/images//` on a unix system) TeX should search recursively (I haven't tested personally). This is much more efficient than having latex macros do the searching.
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I tried using texlive2012 on Windows and for me it works, but with usual windows paths ( ; and \ instead of : and ) Thanks! – Marco van de Voort Oct 2 '13 at 8:03
Sure, it is possible. E.g.
``````\usepackage{graphicx}
\graphicspath{{}{eps/}{eps/seminar/}{png/}}
``````
if the eps, png folders are placed at same level as your source file. A more sophisticated version allows importing graphics from the parent folder:
``````\usepackage{graphicx}
\graphicspath{{}{../eps/}{../eps/seminar/}{../png/}}
``````
With this settings, you don't need (althoug you can!) to indicate path to graphics file from within `\includegraphics`.
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It sounds like what you want is to specify one folder using \graphicspath and then recursively use all the subfolders as part of the graphics path.
If this is what you need, then you can easily do that by doing the following (from wikibooks Latex):
``````\graphicspath{{images//}}
``````
Explanation of the above command:
• The root folder is "images". But you could replace that with any path.
• The more important part of this code is the double slash "//". The double slash "//" tells graphicspath to recursively include all the subfolders.
• There is a caveat that using this recursive search may hog memory, please keep this in mind.
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Can you point to a system where this actually works? At the LaTeX level, recursion is not possible, so this would have to use modified binaries. For me, both TeX Live 2011 (Mac, Ubuntu, Windows) and MiKTeX 2.9 (Windows) do not do this. – Joseph Wright Sep 14 '11 at 20:13
hm... well... i don't know what to say. Other than i didn't test it. the person asking the question accepted it... so i assumed he tested. but i guess not??? AND i got the answer from wikibooks... so i guess they are also wrong. – Trevor Boyd Smith Sep 14 '11 at 20:30
cue also answered... below mine... he says it works on miktek. – Trevor Boyd Smith Sep 14 '11 at 20:31
What I've seen is that various people say 'it is in the wikibook', but I'm yet to find someone who has actually done this! It certainly does not work at a LaTeX package level, so it would have to be engine dependent, hence asking about it. Thanks for the quick response: I'll ask the questioner! – Joseph Wright Sep 14 '11 at 20:32
@Joseph I was under the impression that double-slash for recursive search was only for paths in `TEXINPUTS` env variable. – Lev Bishop Sep 14 '11 at 21:06
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# How much work would it take to push a 12 kg weight up a 9 m plane that is at an incline of pi / 3 ?
Apr 29, 2016
$917.54 J$
$\text{Work done = change in potential energy }$
Now, change in potential energy = $m g h = m g l \sin \theta = 12 k g \times 9.81 m {s}^{-} 2 \times 9 m \times \sin \left(\frac{\pi}{3}\right) \approx 917.54 J$
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### hmehta's blog
By hmehta, history, 9 days ago, ,
Hey All!
Topcoder SRM 774 is scheduled to start at 12:00 UTC -5, Jan 11, 2020. Registration is now open in the Web Arena or Applet and will close 5 minutes before the match begins.
Thanks to lg5293 and misof for writing the problems and coordinating the round.
This is the first SRM of Stage 2 of TCO20 Algorithm Tournament and TCO20 Regional Events Qualification
Match Results (To access match results, rating changes, challenges, failure test cases)
Problem Archive (Top access previous problems with their categories and success rates)
Problem Writing (To access everything related to problem writing at Topcoder)
Algorithm Rankings (To access Algorithm Rankings)
Editorials (To access recent Editorials)
Good luck to everyone!
• +43
» 8 days ago, # | ← Rev. 3 → +15 Happy new year! The first SRM in 2020 :) It's nice to see lewin / lg5293 as writer of SRM! Last time was about 2 years ago, but it's still one of my favorite.
» 8 days ago, # | +12 Gentle Reminder: The match begins in 1hr 30mins
» 8 days ago, # | 0 How to solve land splitter?:(
• » » 8 days ago, # ^ | +6 The cost is (sum of squares of starting sizes — sum of squares of goal sizes) / 2. You just need to find the maximum of $\sum x_i^2$ for any $A \le x_i \le B$, $\sum x_i = N$.
• » » » 8 days ago, # ^ | +20 Oh, right. Thank you.So, how to solve landsplitter? :-)
• » » » » 8 days ago, # ^ | +8 You've got a hint, you could try finishing it yourself.Next hint: you never want two $x_i$ in the interval $(A, B)$ because moving them away from each other improves the sum of squares. Now there are several $O(N)$ solutions.
• » » » » » 7 days ago, # ^ | 0 Is there a book or set of tutorials to help you prepare for such problems or is this supposed to be basic stuff?
• » » » » » » 7 days ago, # ^ | +13 Subtract x from one element, add x to another, see how the optimised function changes is supposed to be basic stuff. It works for a lot of problems.For continuous variables and arbitrary conditions, there's something called Lagrange multipliers that gives you a set of equations that any extremum point (that isn't on the border of the allowed region) must satisfy.
• » » » » » » 7 days ago, # ^ | 0 As Xellos is telling us, it does involve basic stuff. For example, if you break it into two pieces then they have to be equal like he said, as moving them apart increases the cost.I had to prove that differently, if we break N into two pieces N = X + (N-X), then the cost is X*(N-X) = N*X-X^2. You can take derivative: N-2*X and set that to zero to minimize, solving that gives us X = N/2 as the lowest cost if you split into two pieces. That too is basic calculus.The difficulty I have is that these tasks are a linked series of basic facts and it's hard to know how to link them together to solve the whole problem. Anyway, that's where the learning comes in, so it's good. Thanks for the hints, Xellos!
• » » » 7 days ago, # ^ | 0 Thank you, but why is that the cost?
• » » » » 6 days ago, # ^ | +3 An insight for LandSplitter: Imagine that the land you are dividing is a complete graph on N vertices. The tax you pay when you cut into pieces is equal to the number of edges you cut. Thus, minimizing the total cost is the same as maximizing the number of edges that remain uncut in the end.
• » » 5 days ago, # ^ | +3 Can anyone tell how this problem could be solved in O(1). This has done that.
» 8 days ago, # | 0 Why topcoder doesn't allow people with the non-positive score to hack?
• » » 8 days ago, # ^ | +3 Probably so that you couldn't have a random new account (totally not a smurf) who challenges everyone in the room on 100 tests.
• » » 8 days ago, # ^ | 0 Really? I thought it's "negative" instead. We are able to challenge (we don't say "hack" in topcoder) for having 0.00 pts, I guess.
• » » » 8 days ago, # ^ | -39 Do we say "f*ck you moron" in topcoder?
• » » » » 8 days ago, # ^ | +83 ...what?
• » » » 8 days ago, # ^ | +16 My score was -25pts and I got this popup. I was denied hacks. Spoiler
• » » 6 days ago, # ^ | 0 Possibly how many failed challenge attempts for a user is mistakenly stored in an integer. If somebody failed for 1 << 31 times, they would get positive score :-p
» 8 days ago, # | +34 Lol Jatana got more points from 250 by challenging than by solving but got challenged on it too.
» 8 days ago, # | 0 How to solve Div1 1000? I did something like "repeatedly get the non-decided longest path and assign values of arithmetic progression", but it failed in system test.
• » » 8 days ago, # ^ | ← Rev. 2 → +13 Here's a simple counter case 0 3 3 4 4 5 0 1 1 2 2 5 1 4 Answer should be {0, 1/4, 5/8, 1/4, 1/2, 3/4, 1}, but yours gives {0, 1/3, 2/3, 1/4, 1/2, 3/4, 1} instead. how to fixInstead of longest path, choose a path where (difference in endpoints) / (length of path) is minimized. We can show that this quantity only increases at each iteration which helps prove correctness.
» 7 days ago, # | -8 Hi, is the editorial from this SRM will be publish? ( Cuz in the link you provided the last editorial is from SRM 771 ). Thanks.
» 7 days ago, # | 0 What was the intended solution for Div2 500 points? Thanks.
• » » 6 days ago, # ^ | +4 Primes are quite dense, so anything reasonable that goes through all possibilities will work. (I.e., iterate over all possibilities of how many digits you add, where you add them and what they are. Stop once you find a prime.)For a short correct solution, special-case N=0 and N=10^9, and for any other input N check the numbers N000 through N999. (The first sequence of 1000+ consecutive numbers occurs only somewhere after 10^15. Our numbers are smaller than 10^12, so there is certainly at least one prime among them. See Prime gap (Wikipedia))
» 7 days ago, # | 0 The last editorial is for SRM 771. What about editorials for 772, 773 and 774 — are they going to be made available?
• » » 4 days ago, # ^ | +2 We are working on it. Should have them up within a week.
• » » » 4 days ago, # ^ | 0 Great, thanks!
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# How to set combined stop condition in AMPL/CPLEX?
I would like to set a stop condition combined of a timelimit and a relative MIP gap. So I would like AMPL/CPLEX to look for the solution of my LP for an hour and if there isn't a solution stop if or as soon as a relative MIP gap of X percent has been reached.
For clarification, could you try to explain to me the exact meaning of a MIP gap? I was looking for a second stop condition to get at least somewhat close to a solution and not randomly stopping after time X has passed. I understand the relative MIP gap as an educated guess on how much the currently found solution is distant from the best possible solution therefore
$$\frac{\text{current objective function result}}{\text{best possible objective function result}}$$
but the actual relative MIP gap seems to be a little bit more complicated
Relative tolerance for optimizing integer variables: stop if
$$\text{abs}((\text{best bound}) - (\text{best integer})) < \text{mipgap} \times (1 + \text{abs}(\text{best bound})).$$
$$\text{Default} = 1\cdot 10^{-4}$$ must be between $$1\cdot 10^{-9}$$ and $$1$$.
I am not sure how exactly best bound and best integer is defined, on the other hand I am not even close to an expert in optimisation stuff.
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## Differential Equations and Linear Algebra (4th Edition)
In a row-echelon form, the columns that contain the leading $1$s correspond the leading variables whereas the columns that do not contain the leading $1$s represents the free variables.
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# public gastlygem /lsqlthw-cn
### Subversion checkout URL
You can clone with HTTPS or Subversion.
Fetching contributors…
Cannot retrieve contributors at this time
file 73 lines (58 sloc) 3.537 kb
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 \chapter{Exercise 14: Basic Transactions}Imagine if the SQL in your last exercise had an error half-way through it's runand it aborted. You may have even ran into this problem, and then you see thatyour database is not seriously broken. You've been getting away with thisbecause you have a big \file{code.sql} file that rebuilds your database, but ina real situation you can't trash your whole database when you mess up.What you need to make your script safer is the \ident{BEGIN}, \ident{COMMIT},and \ident{ROLLBACK} commands. These start a transaction, which creates a"boundary" around a group of SQL statements so you can abort them if they havean error. You start the transaction with \ident{BEGIN}, do your SQL, and thenwhen everything's good end the transaction with \ident{COMMIT}. If you havean error then you just issue \ident{ROLLBACK} to abort what you did.For this exercise I want you to do the following:\begin{enumerate}\item Take your \file{ex13.sql} and copy it to \file{ex14.sql} so you can modify it.\item Once you have that, put a \ident{BEGIN} at the top and a \ident{ROLLBACK}. At the bottom.\item Now run it and you'll see that it's as if your script didn't do anything.\item Next, change the \ident{ROLLBACK} to be \ident{COMMIT} and run it again, and you'll see it works like normal.\item Get rid of the \ident{BEGIN} and \ident{COMMIT} from your \file{ex14.sql} so it's back the way it was.\item Now create an error by removing one of the \ident{TABLE} keywords from one of the lines. This is so you can make it have an error and recover.\end{enumerate}Once you have this broken \file{ex14.sql} you'll play with it in the \program{sqlite3}console to do a recovery:\begin{code}{ex14 Session Output}<< d['code/ex14.sqlite3-console|pyg|l'] >>\end{code}This one's long so I'm going to break it down so you can track what's going on:\begin{description}\item[1] I start up \program{sqlite3} so I can get into the console with \file{ex14.db}.\item[7] I then \ident{.read} the \file{code.sql} file to setup the database like normal but doing it from within sqlite3.\item[11] I enter \ident{BEGIN} so I can start a transaction boundary.\item[12] I run \ident{.read ex14.sql} to run it, but remember it has an error so it aborts. My error was on line 5 but yours could be anywhere else.\item[14] I then run \ident{.schema} so you can see that some of the changes actually were made, and I'll want to undo them.\item[16] Since the last command had an error I run \ident{ROLLBACK} here to abort all the things I did since the \ident{BEGIN} on line 11.\item[18] To show that the database is back the way it should be, I do another \ident{.schema} and you can see all that junk is now gone.\end{description} \section{Extra Credit}\begin{enumerate}\item Read the instructions on \href{http://www.sqlite.org/lang_transaction.html}{SQLite3 transactions} to get an idea of what's possible.\item Use transactions to bound some example UPDATES and INSERTS to see how those work too.\item Try using the alternative syntax of \ident{BEGIN TRANSACTION}, \ident{COMMIT TRANSACTION}, and \ident{ROLLBACK TRANSACTION}.\end{enumerate}\section{Portability Notes}Some databases don't have the same rollback and commit semantics as other databases.Some also don't understand the syntax with the word \ident{TRANSACTION}. They shoulduniversally abort everything you did, but again look at your manual to confirmthis is true.
Something went wrong with that request. Please try again.
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Math Help - A set of parametric equations
1. A set of parametric equations
Find a set of parametric equations for the line through the point
P(2,1, 0) which is perpendicular
to the plane described by the general equation
x + z = 2.
ok so that's how i did
-1i + 0j + 1k = 2
x = 2 - k
y = -1
z = k
Is it correct?
Thank you
2. Yes that is correct.
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## Annuity:
In the context of Finance, an annuity is a streak of periodic investments or payments made for a given investment horizon. The mechanism of annuity is generally resorted to when one has to accumulate significant retirement fund by making relatively small and regular annual investments.
The calculated value of the annual investment to be made every year for 20 years is option (c) $2,185. The value of the annual investment amount is given by: • {eq}P = F * \dfrac{i}{(1 + i)^ {n} - 1} {/eq} where; F = future value of the annuity =$100,000
P = annual investment amount
i = interest rate = 8% (or 0.08)
n = number of years = 20 years
{eq}P = 100,000 * \dfrac{0.08}{(1 + 0.08)^ {20} - 1} {/eq}
{eq}P = \$2,185.22 {/eq}
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# Talk:Catalan number
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This article is within the scope of WikiProject Mathematics, a collaborative effort to improve the coverage of Mathematics on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.
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## Untitled
Need to get page number, ISBN for reference to enumerative combinatorics vol 2, and perhaps write up some more examples from there. Dmharvey 19:07, 31 May 2005 (UTC)
The first formula accompanying the quadruple factorial discussion might be made more clear with some parentheses- i.e., (2n)!/n! rather than 2n!/n!. I know that with just a little thought it is obvious, but since factorial has precedence over multiplication it caught me for a moment. By the way, this is a very nice article. :)
• The generating function actually yields the formula for C_n pretty easily, using the binomial formula for the square root term. This should really be described somewhere as the "generating function proof of the formula"; then the "Proof of the formula" section should be relabelled "Bijective proofs of the formula".
• Need to mention the Ballot problem somewhere, which is a generalisation of many of the ideas in this article.
• What was Andre's first name? I can't seem to work this out.
• Need to add this reference:
D. Andre, Note: Calcul des probabilites. Solution directe du probleme resolu par M. Bertrand, Comptes Rendus de l’Academie des Sciences, Paris, vol 105(1887), p. 436., where the reflection principle was first used (I think?)
• I recall reading a long time ago (can't remember where) that the first disucssion of "exceedance" was in a probability setting. Consider a coin tossing game between A and B. They toss a coin 2n times. Heads gives A a point, tails gives B a point. Now, given that they each win n tosses, what is the probability that A is not ahead of B at any point of the game? You could also ask, for any k between 0 and n inclusive, what is the probability that A is ahead of B for precisely k turns? (you need to be a bit careful about how exactly you define when A is ahead.) The point is that it was shown that the answer does not depend on k, and so must be equal to 1/(n+1), which a priori is quite a surprising result. Would be nice to mention this in the History section, but the details need to be found.
• My explanations of the two bijective proofs are a little wordy. Someone please write them better. Thanks.
• Give C_3 examples/pictures for some of the other combinatorial interpretations listed.
• Add more combinatorial interpretations; there are plenty of interesting and accessible ones still left. I don't have a copy of EC vol 2 handy.
Dmharvey 12:07, 1 Jun 2005 (UTC)
## "prepositional groups"
I have deleted the following from the "history" section.
It has been shown that the number of possible interpretations of a sentence, function of the number of prepositional groups ("he saw a man on the hill with a telescope"), is the Catalan number series.
It doesn't belong under History. Perhaps it belongs in the list of combinatorial applications. But the text quality needs to be improved, and I don't really know what it's about. Dmharvey Talk 17:11, 6 Jun 2005 (UTC)
That's just the number of binary parse trees. Not particularly interesting, seeing as equiparseable sentences with distinct meanings are highly artificial anyway. EdC 10:41, 21 July 2006 (UTC)
## History
Ming An-tu discovered them before but they were published in 1839. 24.203.251.69 03:27, 31 October 2005 (UTC)
## 3x3 grid image in SVG
I've created the 3x3 grid image in SVG for the article in the spanish wikipedia:
http://es.wikipedia.org/wiki/Imagen:Catalan_number_3x3_grid_example.svg
I don't know about licensing, but I want to release it on the public domain as a trivial work. I hope it will be useful. Thank you.
## Graphical relation between Catalan numbers, stairs with slope<45°, triangulated polygons
As an architect I try to understand things with graphics. See: http://home.versateladsl.be/vt649464/TrapVeelhNummering.PDF If someone wants to use it I can give a version without text.--Bleuprint (talk) 05:12, 8 February 2008 (UTC)
## Ballot problem
Dmharvey wrote in the TODO list above:
Need to mention the Ballot problem somewhere, which is a generalisation of many of the ideas in this article.
I've added Bertrand's ballot theorem to the See also section, of course, some more details are worth including. --Kompik 11:28, 11 March 2006 (UTC)
## hankel matrix stuff
Does anyone have any references for this hankel matrices stuff? Thanks. Dmharvey 11:15, 31 May 2006 (UTC)
Yes. Firstly, let me say that I'll don't know anything about uniqueness of such a series, only that this series have an all ones Hankel-transform. I'll only talk about why the Hankel-transform of this sequence is all ones.
I've read of this property in the OEIS entry of Catalan numbers. I became curious and started to look for a proof. This entry refers to the article J. W. Layman, The Hankel Transform and Some of its Properties, J. Integer Sequences, 4 (2001), #01.1.5. That article also states that the Catalan sequence has this property, and while it doesn't give a full proof, it does give a valueable hint to find it.
I've given this property as a task on a course, so I had to derive the complete proof, but I've never written the proof down completely, so it took me a while to reconstruct the proof from my old notebook and memory. As I think this is a notable property and proof, I'm glad you've asked about it so I'll finally write the proof down. Btw, the problem lists for that course are available on my homepage: this one is problem number 5 on series 7 of term 4 (automn term 2005/2006).
Now I'll draft the proof. The basic idea (from the article) is that we will find the LU decomposition of the Hankel matrix as it's easy to calculate the determinant from them. If you do the decomposition with a computer for some matrices, it's easy to guess the general statement.
Let ${\displaystyle \mathbf {H} }$ be the Hankel-matrix formed fromed by the Catalan-numbers: ${\displaystyle h_{k,l}=C_{k+l}}$ (note that we are numbering rows and columns from 0 here). This matrix is this:
1 1 2 5 14 42 132
1 2 5 14 42 132 429
2 5 14 42 132 429 1430
5 14 42 132 429 1430 4862
14 42 132 429 1430 4862 16796
42 132 429 1430 4862 16796 58786
132 429 1430 4862 16796 58786 208012
Now let's define the Catalan triangle like this: ${\displaystyle c_{k,l}}$ is the number of paths of ${\displaystyle k}$ right and ${\displaystyle l}$ upwards segments that always stay below the diagonal from the starting point (i.e. no prefix of the path has more upwards segments then right ones). Then, clearly, ${\displaystyle C_{n}=c_{n,n}}$. The Catalan triangle has some interesting properties, one of which I should write about later. The triangle looks like this:
1 0 0 0 0 0 0 0 0 0
1 1 0 0 0 0 0 0 0 0
1 2 2 0 0 0 0 0 0 0
1 3 5 5 0 0 0 0 0 0
1 4 9 14 14 0 0 0 0 0
1 5 14 28 42 42 0 0 0 0
1 6 20 48 90 132 132 0 0 0
1 7 27 75 165 297 429 429 0 0
1 8 35 110 275 572 1001 1430 1430 0
1 9 44 154 429 1001 2002 3432 4862 4862
Now let ${\displaystyle \mathbf {S} }$ be a matrix we get from half of the elements from the Catalan-triangle like this: ${\displaystyle s_{u,w}=c_{u+w,u-w}}$. ${\displaystyle \mathbf {S} }$ looks like this:
1 0 0 0 0 0 0
1 1 0 0 0 0 0
2 3 1 0 0 0 0
5 9 5 1 0 0 0
14 28 20 7 1 0 0
42 90 75 35 9 1 0
132 297 275 154 54 11 1
I state that ${\displaystyle \mathbf {S} \mathbf {S} ^{\textrm {T}}=\mathbf {H} }$. For this, we need to prove that ${\displaystyle C_{u+v}=\sum _{w}s_{u,w}s_{v,w}=\sum _{0\leq w\leq \max(u,v)}c_{u+w,u-w}c_{v+w,v-w}}$. Now ${\displaystyle C_{u+v}}$ is, by definition, the number of paths of ${\displaystyle u+v}$ right and ${\displaystyle u+v}$ upwards segments which are under the main diagonal, which means that none of its prefixes have more up then right segments, and also that none of its suffixes have more right than up segments. Let's split this path to a first part that's ${\displaystyle 2u}$ long and a second one that's ${\displaystyle 2v}$ long. Let ${\displaystyle u+w}$ be the number of right segments in the first part of the path. Then, clearly, ${\displaystyle w}$ is positive because this part is a prefix, and this part has ${\displaystyle u-w}$ up segments. Also, the second part of the path has ${\displaystyle v-w}$ right segments and ${\displaystyle v+w}$ up segments, and all suffixes of this part has at most the same number of up segments then right pointing ones. It's also easy to see that if the first part of the path has no more up segments than right in any of its prefixes, and the second part of the path has no more right than up segments in any of its suffixes, we can combine these two parts to a valid path which stays under the diagonal. Thus, we can calculate ${\displaystyle C_{u+v}}$ by multiplying the number of valid first parts and the number of valid second parts, and summing this product for every ${\displaystyle w}$. The number of valid first parts is, by definition ${\displaystyle c_{u+w,u-w}}$. To calculate the number of second parts, we have to mirror them, so reverse the order of paths in it and replace up paths with right ones and vice versa. Then we have a path which has ${\displaystyle v+w}$ right pointing segments and ${\displaystyle v-w}$ upward pointing ones, and each of whose prefixes have no less right segments then up segments. The number of such paths is ${\displaystyle c_{v+w,v-w}}$ so the matrix equation is indeed true.
Now observe that ${\displaystyle s_{u,v}=0}$ if ${\displaystyle u and ${\displaystyle s_{u,u}=1}$, so ${\displaystyle \mathbf {S} }$ is a triangular matrix with all ones in its diagonal. Thus, ${\displaystyle \det(\mathbf {S} )=1}$, thus indeed ${\displaystyle \det(\mathbf {H} )=\det(\mathbf {S} )\det(\mathbf {S} ^{\textrm {T}})=1}$ which is what we wanted to prove.
The proof of that the determinant of the Hankel matrix starting with ${\displaystyle C_{1}}$,
1 2 5 14 42
2 5 14 42 132
5 14 42 132 429
14 42 132 429 1430
42 132 429 1430 4862
is also one is almost the same as above. The difference is that instead of ${\displaystyle \mathbf {S} }$ we use the matrix ${\displaystyle \mathbf {T} }$ defined by ${\displaystyle t_{u,w}=c_{u+w+1,u-w}}$ . This matrix contains the other half of the elements of ${\displaystyle \mathbf {C} }$ like this.
1 0 0 0 0 0 0
2 1 0 0 0 0 0
5 4 1 0 0 0 0
14 14 6 1 0 0 0
42 48 27 8 1 0 0
132 165 110 44 10 1 0
429 572 429 208 65 12 1
Finally, let me ask you or anyone else reading this to feel free correcting errors or anything you don't like in this proof inline (unlike normal posts on talk pages). Thanks. – b_jonas 23:03, 31 July 2006 (UTC)
I'm reacting to this sentence: "The Catalan numbers form the unique sequence with this property." This cannot be true, as the Hankel transform is invariant under the binomial transform (see the article on the binomial transform). —Preceding unsigned comment added by 84.215.177.45 (talk) 15:46, 26 January 2011 (UTC)
## RE: Catalan Recurrence
The Catalan Recurrence
C(x)=SIGMA C(i) C(n-1)
has not been solved properly. A Quadratic eqn. appears out of nowhere. Can someone explain where it came from?
It's not "out of nowhere", although the explanation is not very explicit. It comes from realizing that the sum defines a Cauchy product. I'll see if I can add something on this. Michael Hardy 20:43, 20 August 2006 (UTC)
OK, I've expanded that section, adding a more leisurely derivation of the quadratic equation. Michael Hardy 21:07, 20 August 2006 (UTC)
Is it possible to explain why a particular root of the Quadratic equation is used instead of the another one? In the expanded presentation that is no justification on that. —Preceding unsigned comment added by 207.46.55.31 (talkcontribs)
I've added an explicit explanation of that. Michael Hardy 02:07, 22 June 2007 (UTC)
## Two more Catalan problems
Perhaps these two problems with Catalan solutions are already in the harder stuff in the article. If not, do they belong?
1. How many ways can 2n ordered objects be arranged in a 2 x n matrix so that the elements are strictly increasing left to right and top down? (sometimes posed as a photographer arranging 2n people in 2 rows so that the heights increase left to right and front to back)
2. How many ways can n non-intersecting diagonals be drawn in a 2n-gon? (How many ways can 2n people seated at a circular table shake hands with no one's arms crossing) Jd2718 18:00, 5 November 2006 (UTC)
These have been added.--RDBury (talk) 17:53, 8 February 2009 (UTC)
## Catalan numbers
${\displaystyle a\,}$
${\displaystyle a(a+b)=\,}$
${\displaystyle a(a+b)(a+b+c)=\,}$
${\displaystyle a(a+b)(a+b+c)(a+b+c+d)=\,}$
${\displaystyle a\,}$
${\displaystyle ab+a^{2}\,}$
${\displaystyle abc+ab^{2}+ca^{2}+2ba^{2}+a^{3}\,}$
${\displaystyle a^{2}c^{2}+abcd+abc^{2}+adb^{2}+cda^{2}+ab^{3}+da^{3}+2acb^{2}+2bda^{2}+4bca^{2}+3a^{2}b^{2}+2ca^{3}+3ba^{3}+a^{4}\,}$
The sum of the entries of every row is ${\displaystyle n!\,}$ Twentythreethousand (talk) 16:36, 31 May 2008 (UTC)
More relevantly, the number of terms is Cn. Similarly, the number of terms in the expansion of (a1+a2+...+ak)n is ${\displaystyle {n+k-1 \choose n}}$. Both of these can be proven by mapping the terms to lattice paths.--RDBury (talk) 18:28, 8 February 2009 (UTC)
vvvv a shape or a patern numbers take.the knowledge of God whether you think he is dead or not.v
'''''''''''''''
,,,,,,,,,,,, —Preceding unsigned comment added by 74.198.10.74 (talk) 11:17, 28 August 2009 (UTC)
## Other kind of Catalan numbers?
Where should we send the reader who typed "Catalan numbers" into the search box, looking for how to count to ten in Catalan? --Damian Yerrick (talk | stalk) 21:31, 23 August 2008 (UTC)
That would probably be Catalan language#Numerals but it doesn't exist yet.--RDBury (talk) 06:25, 4 January 2012 (UTC)
## Ballot problem/second proof
The reflection method is described both here and in Bertrand's ballot theorem. I added a more obvious link in the article; should there be an attempt to merge? Also, it's not entirely incorrect to call it André's reflection method, he had the basic idea but without the reflection part. The reflections are essentially only a way of giving a one-one proof that ${\displaystyle {2n \choose n-1}={2n \choose n+1}}$.--RDBury (talk) 17:11, 8 February 2009 (UTC)
## Is the definition of Dyck's word correct?
The article says that "A Dyck word is a string .. such that no initial segment of the string has more Y's than X's" then it lists several examples including XXXYYY. But: X, XX, XXX, XXXY are all initial segments of XXXYYY and each of them has more X's than Y's.--Jirka6 (talk) 00:25, 10 April 2009 (UTC)
My fault, sorry. Of course it is correct. I switched X and Y.--Jirka6 (talk) 22:18, 13 April 2009 (UTC)
## Trees and catalan numbers
The nice picture with green trees is correct, the description was not. There is an infinite number of binary trees (not necessarily full) with n leaves. Also, "ordered" is already implied by "binary". The picture actually belongs to (what used to be) the next item, I fixed that. --Ikska (talk)
## As a binomial coefficent
What do you think? Is it worthy of inclusion in the article that a Catalan number can be written in terms of a generalized binomial coefficient?:
{\displaystyle {\begin{aligned}C_{n}&={\frac {2n!}{n!(n+1)!}}={\frac {(1\cdot 3\cdot \ldots \cdot (2n-1))(2\cdot 4\cdot \ldots \cdot 2n)}{n!(n+1)!}}=2^{2n}{\frac {({\frac {1}{2}}\cdot {\frac {3}{2}}\cdot \ldots \cdot {\frac {2n-1}{2}})({\frac {2}{2}}\cdot {\frac {4}{2}}\cdot \ldots \cdot {\frac {2n}{2}})}{n!(n+1)!}}\\&=2^{2n}{\frac {\left({\frac {\Gamma (n+1/2)}{\Gamma (1/2)}}\right)(n!)}{n!(n+1)!}}=2^{2n}{\frac {\left({\frac {\Gamma (n+1/2)}{(-1/2)\Gamma (-1/2)}}\right)}{(n+1)!}}=-2^{2n+1}{\frac {\left({\frac {\Gamma (n+1/2)}{\Gamma (-1/2)}}\right)}{(n+1)!}}=-2^{2n+1}{\binom {n-{\frac {1}{2}}}{-{\frac {3}{2}}}}\,,\end{aligned}}}
using the Gamma function. Thanks -- Quantling (talk) 17:01, 21 April 2010 (UTC)
## New non-geometric bijective proof
I have added a new bijective proof aimed to directly derive the fascinating ${\displaystyle {\tfrac {1}{n+1}}}$ factor in the formula. I think it makes a nice complement to the existing bijective proofs as it is not based on a geometric interpretation but instead uses Dyke words and calculates the factor algebraically by comparing coefficients.
I tried several approaches and found this to be the most economical. I made this proof up myself as I could not find a similar one with the same features on the web. Still it should be simple and straightforward enough to be immediately obvious and verifiable by anyone with basic math skills in order to justify its inclusion into wikipedia. If it has been done before (which seems likely), please feel free to add a reference.
Bernhard Oemer (talk) 16:02, 10 January 2011 (UTC)
What the heck is this section refering to? Where does the name "quadruple factorial" come from? Is it notable at all? Right now I'm inclined to delete it because I can't figure out what it's about, but if someone can tell me what it means, then I'd be happy to reverse my position. (Maybe it would be better as a subsection somewhere?) --JBL (talk) 13:32, 17 September 2012 (UTC)
Hearing nothing after one year, I've removed mentions of the "quadruple factorial". --JBL (talk) 03:10, 16 September 2013 (UTC)
## Second proof
I have just finished some copyediting of the second proof to improve the English and flow of the proof. I tried to preserve as much of the section as I could, but it did require some significant changes to increase clarity and deal with some of the harder parts of the proof. I did not, at this time, put back the historical sentence concerning Andre's reflection method, since there is an editor who objects to that, and so, it should be discussed here. My feeling is that it should be returned since it has encyclopedic value and we are writing an encyclopedia, not a textbook. The statement is of interest and I should point out a comment concerning it made above on this talk page. Bill Cherowitzo (talk) 06:41, 8 January 2015 (UTC)
I would accept one sentence about the author if it provided some new information in addition to the reflection article. The point to discuss the authorship of reflection method, whenever you apply it is stupid verbosity and as any verbosity it was confusing: I could not even understand who is author of what. Encyclopedia does not mean that you copy-paste referred material under every reference. Which encyclopedic standard tells you that you must copy only the historic sections but not the whole referenced articles every time you use/refer them? Finally, sane people can distinguish Andreas reflection from Schwarz reflection without notice. Only dumb ones will follow the hyperlink and confuse it with Schwarz reflection. For them, you should notice that Andre's reflection principle is different from both electricity, economics, computer manufactoring, psychology and everything we have in the world (there are 20 reflection principles that you had to enumerate in your article at least). It seems that your purpose was to draw the proof into the stupid verbosity. I do not understand which fluence you are talking about. --Javalenok (talk) 13:09, 11 January 2015 (UTC)
## Incorrect Equation
The last formula in the first equation of the page:
${\displaystyle C_{n}=\prod \limits _{k=2}^{n}{\frac {n+k}{k}}\qquad {\mbox{ for }}n\geq 0.}$
Is incorrect (or at least gives inconsistent answers with the other formulas), for example for
n = 0, 1, 2, 3, 4, 5
this gives:
1, 1, 2, 4, 14, 36
but should be:
1, 1, 2, 5, 14, 42
— Preceding unsigned comment added by Agold1982 (talkcontribs)
(3+2)/2 * (3+3)/3 = 5. (5+2)/2 * (5+3)/3 * (5+4)/4 * (5+5)/5 = 42. It is also easy to check that this formula agrees with the factorial formula. --JBL (talk) 14:55, 27 November 2015 (UTC)
You are completely right, this was my mistake. (Agold1982)
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# Chemistry Class 12 NCERT Solutions: Chapter 12 Aldehydes Ketones and Carboxylic Acids Part 6 (For CBSE, ICSE, IAS, NET, NRA 2022)
Get top class preparation for CBSE/Class-12 right from your home: get questions, notes, tests, video lectures and more- for all subjects of CBSE/Class-12.
Q: 9. Write structural formulas and names of four possible aldol condensation products from propanal and butanal. In each case, indicate which aldehyde acts as nucleophile and which as electrophile.
(i) Taking two molecules of propanal, one which acts as a nucleophile and the other as an electrophile.
(ii) Taking two molecules of butanal, one which acts as a nucleophile and the other as an electrophile.
(iii) Taking one molecule each of propanal and butanal in which propanal acts as a nucleophile and butanal acts as an electrophile.
(iv) Taking one molecule each of propanal and butanal in which propanal acts as an electrophile and butanal acts as a nucleophile.
Q: 10. An organic compound with the molecular formula forms 2,4-DNP derivative, reduces Tollens՚ reagent and undergoes Cannizzaro reaction. On vigorous oxidation, it gives 1,2-benzenedicarboxylic acid. Identify the compound.
It is given that the compound (with molecular formula ) forms 2,4-DNP derivative and reduces Tollen՚s reagent. Therefore, the given compound must be an aldehyde. Again, the compound undergoes cannizzaro reaction and on oxidation gives 1,2- benzenedicarboxylic acid. Therefore, the group is directly attached to benzene ring and this benzaldehyde is ortho-substituted. Hence, the compound is 2-ethylbenzaldehyde.
The given reactions can be explained by the following equations.
Q: 11. An organic compound (A) (molecular formula ) was hydrolysed with dilute sulphuric acid to give a carboxylic acid (B) and an alcohol (C) . Oxidation of (C) with chromic acid produced (B) . (C) on dehydration gives but-1-ene. Write equations for the reactions involved.
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Outlook: NightDragon Acquisition Corp. Warrants to purchase Class A common stock is assigned short-term Ba1 & long-term Ba1 estimated rating.
Dominant Strategy : Sell
Time series to forecast n: 22 Jan 2023 for (n+16 weeks)
Methodology : Deductive Inference (ML)
## Abstract
NightDragon Acquisition Corp. Warrants to purchase Class A common stock prediction model is evaluated with Deductive Inference (ML) and Pearson Correlation1,2,3,4 and it is concluded that the NDACW stock is predictable in the short/long term. According to price forecasts for (n+16 weeks) period, the dominant strategy among neural network is: Sell
## Key Points
1. What is neural prediction?
2. Which neural network is best for prediction?
3. What is a prediction confidence?
## NDACW Target Price Prediction Modeling Methodology
We consider NightDragon Acquisition Corp. Warrants to purchase Class A common stock Decision Process with Deductive Inference (ML) where A is the set of discrete actions of NDACW stock holders, F is the set of discrete states, P : S × F × S → R is the transition probability distribution, R : S × F → R is the reaction function, and γ ∈ [0, 1] is a move factor for expectation.1,2,3,4
F(Pearson Correlation)5,6,7= $\begin{array}{cccc}{p}_{a1}& {p}_{a2}& \dots & {p}_{1n}\\ & ⋮\\ {p}_{j1}& {p}_{j2}& \dots & {p}_{jn}\\ & ⋮\\ {p}_{k1}& {p}_{k2}& \dots & {p}_{kn}\\ & ⋮\\ {p}_{n1}& {p}_{n2}& \dots & {p}_{nn}\end{array}$ X R(Deductive Inference (ML)) X S(n):→ (n+16 weeks) $\stackrel{\to }{S}=\left({s}_{1},{s}_{2},{s}_{3}\right)$
n:Time series to forecast
p:Price signals of NDACW stock
j:Nash equilibria (Neural Network)
k:Dominated move
a:Best response for target price
For further technical information as per how our model work we invite you to visit the article below:
How do AC Investment Research machine learning (predictive) algorithms actually work?
## NDACW Stock Forecast (Buy or Sell) for (n+16 weeks)
Sample Set: Neural Network
Stock/Index: NDACW NightDragon Acquisition Corp. Warrants to purchase Class A common stock
Time series to forecast n: 22 Jan 2023 for (n+16 weeks)
According to price forecasts for (n+16 weeks) period, the dominant strategy among neural network is: Sell
X axis: *Likelihood% (The higher the percentage value, the more likely the event will occur.)
Y axis: *Potential Impact% (The higher the percentage value, the more likely the price will deviate.)
Z axis (Grey to Black): *Technical Analysis%
## IFRS Reconciliation Adjustments for NightDragon Acquisition Corp. Warrants to purchase Class A common stock
1. When designating a risk component as a hedged item, the hedge accounting requirements apply to that risk component in the same way as they apply to other hedged items that are not risk components. For example, the qualifying criteria apply, including that the hedging relationship must meet the hedge effectiveness requirements, and any hedge ineffectiveness must be measured and recognised.
2. Time value of money is the element of interest that provides consideration for only the passage of time. That is, the time value of money element does not provide consideration for other risks or costs associated with holding the financial asset. In order to assess whether the element provides consideration for only the passage of time, an entity applies judgement and considers relevant factors such as the currency in which the financial asset is denominated and the period for which the interest rate is set.
3. Expected credit losses shall be discounted to the reporting date, not to the expected default or some other date, using the effective interest rate determined at initial recognition or an approximation thereof. If a financial instrument has a variable interest rate, expected credit losses shall be discounted using the current effective interest rate determined in accordance with paragraph B5.4.5.
4. If items are hedged together as a group in a cash flow hedge, they might affect different line items in the statement of profit or loss and other comprehensive income. The presentation of hedging gains or losses in that statement depends on the group of items
*International Financial Reporting Standards (IFRS) adjustment process involves reviewing the company's financial statements and identifying any differences between the company's current accounting practices and the requirements of the IFRS. If there are any such differences, neural network makes adjustments to financial statements to bring them into compliance with the IFRS.
## Conclusions
NightDragon Acquisition Corp. Warrants to purchase Class A common stock is assigned short-term Ba1 & long-term Ba1 estimated rating. NightDragon Acquisition Corp. Warrants to purchase Class A common stock prediction model is evaluated with Deductive Inference (ML) and Pearson Correlation1,2,3,4 and it is concluded that the NDACW stock is predictable in the short/long term. According to price forecasts for (n+16 weeks) period, the dominant strategy among neural network is: Sell
### NDACW NightDragon Acquisition Corp. Warrants to purchase Class A common stock Financial Analysis*
Rating Short-Term Long-Term Senior
Outlook*Ba1Ba1
Income StatementBaa2Caa2
Balance SheetBaa2B3
Leverage RatiosCB2
Cash FlowB1Baa2
Rates of Return and ProfitabilityBa1Baa2
*Financial analysis is the process of evaluating a company's financial performance and position by neural network. It involves reviewing the company's financial statements, including the balance sheet, income statement, and cash flow statement, as well as other financial reports and documents.
How does neural network examine financial reports and understand financial state of the company?
### Prediction Confidence Score
Trust metric by Neural Network: 82 out of 100 with 645 signals.
## References
1. K. Boda and J. Filar. Time consistent dynamic risk measures. Mathematical Methods of Operations Research, 63(1):169–186, 2006
2. Miller A. 2002. Subset Selection in Regression. New York: CRC Press
3. Byron, R. P. O. Ashenfelter (1995), "Predicting the quality of an unborn grange," Economic Record, 71, 40–53.
4. Candès EJ, Recht B. 2009. Exact matrix completion via convex optimization. Found. Comput. Math. 9:717
5. Chernozhukov V, Chetverikov D, Demirer M, Duflo E, Hansen C, et al. 2018a. Double/debiased machine learning for treatment and structural parameters. Econom. J. 21:C1–68
6. M. Colby, T. Duchow-Pressley, J. J. Chung, and K. Tumer. Local approximation of difference evaluation functions. In Proceedings of the Fifteenth International Joint Conference on Autonomous Agents and Multiagent Systems, Singapore, May 2016
7. Abadie A, Diamond A, Hainmueller J. 2010. Synthetic control methods for comparative case studies: estimat- ing the effect of California's tobacco control program. J. Am. Stat. Assoc. 105:493–505
Frequently Asked QuestionsQ: What is the prediction methodology for NDACW stock?
A: NDACW stock prediction methodology: We evaluate the prediction models Deductive Inference (ML) and Pearson Correlation
Q: Is NDACW stock a buy or sell?
A: The dominant strategy among neural network is to Sell NDACW Stock.
Q: Is NightDragon Acquisition Corp. Warrants to purchase Class A common stock stock a good investment?
A: The consensus rating for NightDragon Acquisition Corp. Warrants to purchase Class A common stock is Sell and is assigned short-term Ba1 & long-term Ba1 estimated rating.
Q: What is the consensus rating of NDACW stock?
A: The consensus rating for NDACW is Sell.
Q: What is the prediction period for NDACW stock?
A: The prediction period for NDACW is (n+16 weeks)
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Eszti Gál
### Eszti Gál
További ötletek tőle: Eszti
*pardon the cussword*
RA - Highfive! by BIazeRod.deviantart.com on @DeviantArt
And then I'm thinking "Halt, you can definitely see a resemblance between you and Will. You just asked two questions at once." And then Selethen said pretty much said the exact thing I was thinking. Though I'm exactly like Will in that sense, I ask a TON of questions. I like the fact that me and Will (and Halt) have some things in common. Or at least, I think we do.
Ranger's Apprentice
.....
Just Keep Walking, Horace... ( an RA tektek comic) by Lil-Treaty.deviantart.com on @deviantART
It Was For Your Own Good! (an RA tektek comic) by Lil-Treaty.deviantart.com on @deviantART
Ranger's Apprentice
Rangers by SixofClovers.deviantart.com on @DeviantArt
RA: I've been thinking ... by BIazeRod.deviantart.com on @DeviantArt
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Infoscience
Journal article
# Low-Power and Widely-Tunable Linearized Biquadratic Low-Pass Transconductor-C Filter
A sixth-order low-pass $g_m$-C filter with a very wide tuning range ($f_c$ = 100 Hz to 10 MHz) is presented. The wide tuning range has been achieved without using switchable components or programmable building blocks. A single stage folded-cascode transconductor is employed to implement the proposed filter. A modified biquadratic topology is introduced to improve the linearity performance of the filter over its tuning range. The power consumption of the filter scales linearly with the cutoff frequency (60 pW/Hz/pole). Implemented in 0.18 $\mu$m CMOS technology, the filter exhibits a relatively constant noise and linearity performance over its entire tuning range and occupies 0.16 mm$^2$ (0.027 mm$^2$/pole) silicon area.
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## Loser66 one year ago For what value of b is the line y = 10x tangent to the curve $$y= e^{bx}$$ at some point in the xy plane? Please, help
1. Loser66
Options: 1) 10/e 2) 10 3) 10e 4) $$e^{10}$$ 5) e brb
2. freckles
$y=10x \\ \text{ means } y'=10 \text{ at some point } (m,n) \\ \text{ so we have the following } \\ n=10m \\ 10=be^{bm} \\ n=e^{bm} \\ \\ \text{ multiplying } n=e^{bm} \text{ on both sides by b gives us } bn=be^{bm} \\ \implies nb=10 \implies b=\frac{10}{n} \implies b=\frac{10}{10m}=\frac{1}{m} \\ \text{ going back to } n=e^{bm} \text{ we have} n=e \\ \text{ so } m=\frac{n}{10}=\frac{e}{10} \text{ and so } b=\frac{1}{m}$ one last thing to do and I leave it to you
3. freckles
http://www.ets.org/gre/subject/about/content/mathematics if anyone is curious these are gre practice questions loser got me wanting to take this practice test buy I kind of got bored with them :p
4. freckles
Not trying to imply they are easy just got bored testing myself :p
5. Loser66
Thanks a lot. :)
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