text:
A precipitate is formed when solutions of trisodium phosphate and calcium chloride are mixed. D-Glucose Potassium permanganate Sulfuric acid Glycerol Potassium hydrogen phosphate Trichloroacetic acid Hydrochloric acid Potassium dihydrogen phosphate Tris(hydroxymethyl)methylamine Lactic acid Potassium sulfate Urea Lactose 1-Propanol Zinc sulfate REFERENCES 1. Sulfuric acid will react with magnesium acetate in a double displacement reaction to give magnesium sulfate and acetic acid. Services, Precipitation Reactions: Predicting Precipitates and Net Ionic Equations, Working Scholars® Bringing Tuition-Free College to the Community. Answer a Identify Any Spectator Ions. Cobalt(ID sulfate and lithium sulfide solutions are combined. Wolf, A. V., Aqueous Solutions and Body Fluids, Hoeber, 1966. H+ + SO42- + Ba2+ + C2H3O2- Æ BaSO4 + HC2H3O2 11. If excess sulfuric acid reacts with 30.0 g of sodium chloride, how many grams of hydrogen chloride are produced? 11. Cobalt(II) sulfate and lithium sulfide solutions are combined. Sulfuric acid reacts with a solution of magnesium acetate, Mg(C,H,O) äº !nart risqx3 8. Potassium Nitrite Solution Is Added To Sulfuric Acid. 3) Zinc reacts with a solution of nickel sulfate. 8. The easiest way to see this reaction is to take a test tube of sulfuric acid and drop a small ribbon of magnesium into the clear liquid. Cobalt (Il) sulfate and lithium sulfide solutions are combined. Sulfuric acid is a Bronsted-Lowry acid. 3F2(g) + 2AlCl3(aq) = 2AlF3 (aq) + 3Cl2(g) Magnesium turnings are added to a solution of lead(II) acetate. Reacts exothermically with carbonates (including limestone and building materials containing limestone) and hydrogen carbonates to generate carbon dioxide. All rights reserved. Sulfuric acid reacts with a solution of magnesium acetate, MgiC,H,Oph 8. Enter the net ionic reaction for ZnSO_4+BaI_2. 2) Sulfuric Acid reacts with a solution of magnesium acetate, Mg(C2H3O2)2. Sulfuric acid reacts with a solution of magnesium acetate. News 27:2504]. Be Sure To Choose The Correct Balancing Coefficients. f) sulfur trioxide gas is added to excess water. | 9. Please write out the balanced equations for #7-13. Thank ... 26. 10. USE: Sulfuric acid is an important commercial chemical used to make fertilizers, explosives, dyestuffs and â¦ Dilute sulfuric acid is added to a solution of barium acetate. Sulfuric acid reacts with a solution of magnesium acetate, Mg(C2H3O2)2 8. SULFURIC ACID is strongly acidic. Hâº + SOâ²â» + Ba²âº + CâHâOââ» â BaSOâ + HCâHâOâ A precipitate is formed when solutions of trisodium phosphate and calcium chloride are mixed. Sulfuric Acid Reacts With A Solution Of Magnesium Acetate, Mg(C,H,O) äº !nart Risqx3 8. It reacts by donating protons. 9. When solid sodium chloride is added to aqueous sulfuric acid, hydrogen chloride gas and aqueous sodium sulfate are produced. Zinc Reacts With A Solution Of Nickel Sulfate, 9. Both are improved by heat and stirring. This video is about the reaction involving sulfuric acid with magnesium carbonate and calcium carbonate respectively. Sulfuric acid is a Bronsted-Lowry acid. A small piece of potassium metal, stored in mineral oil, is cut and then placed in about 5 mL of 18 M sulfuric acid. 1:172 1956]. Lo Are Mixed. Letâs say we start with magnesia (crude form of magnesium oxide, MgO). Zinc Reacts With A Solution Of Nickel Sulfate. of hydrogens than in hydrochloric acid OF THE SAME CONC. Potassium nitrite solution is added to sulfuric acid. Zinc reacts with a solution of nickel sulfate. Magnesium reacts with hydrochloric acid according to the equation: Mg(s) + 2 HCl(aq) --> MgCl 2 (aq) + H 2 (g) This demonstration can be used to illustrate the characteristic reaction of metals with acid, a single replacement reaction, or to demonstrate the generation of hydrogen gas.The flammability of hydrogen gas can be demonstrated by carefully holding a match or fireplace â¦ 5) Potassium nitrite solution is added to sulfuric acid. Solid Nickel Carbonate Is Dropped Into Nitric Acid. Terms What mass of oxygen is needed to react with 4.5g of ethane #C_2H_8#? (a) Strong acids. 9. 10. Sulfuric acid is also called battery acid. An acid + a metal oxide â salt + water. Potassium nitrite solution is added to sulfuric acid. If 82.9 mL of lead(II) nitrate solution reacts completely with excess sodium iodide solution to yield 0.179 g of precipitate, what is the molarity of lead(II) ion in the original solution? 10. Solid nickel carbonate is dropped into nitric acid. It is highly corrosive. Strong bases are the hydroxides of the alkali (Group IA) and Aqueous solutions of sodium bicarbonate and sulfuric acid react to produce carbon dioxide according to the following equation: $\ce{2NaHCO3(aq) + H2SO4(aq) \rightarrow 2CO2(g) + Na2SO4(aq) + 2H2O(l)}\nonumber$ If 13.0 mL of 3.0 M H 2 SO 4 are added to 732 mL of 0.112 M NaHCO 3, what mass of CO 2 is produced? If 5.00 g of copper metal react with a solution containing 20.0 g of AgNO3 to produce silver metal, which reactant is limiting? e) dilute hydrochloric acid is added to a solution of potassium carbonate. â¢ ethyl acetate â¢ 10% sulfuric acid â¢ wash acetone â¢ 1 M HCl (for TAâs to decompose Mg) â¢ saturated NaCl solution a Stored over activated 4Å Mol. Privacy Answer. {/eq}. The reaction is exothermic, meaning heat is given off in addition to the hydrogen bubbles. Earn Transferable Credit & Get your Degree, Get access to this video and our entire Q&A library. g) dilute sulfuric acid is added to a solution of barium chloride. Zinc reacts with a solution of nickle sulfate. Fluorine gas is bubbled into a solution of aluminum chloride. Sulfuric Acid Reacts With A Solution Of Magnesium Acetate, Mg(C,H,O) äº !nart Risqx3 8. Hydrogen sulfide gas is added to a solution of cadmium nitrate. 3.4 g Exploded with para-nitrotoluene at 80°C [Chem. well sulfuric acid is more reactive bec. Cobalt(ID Sulfate And Lithium Sulfide Solutions Are Combined. Therefore, sulphuric acid and magnesium oxide will react with each other to yield magnesium sulphate and water. Thanks for watching, please subscribe, rate and comment HYDROCHLORIC ACID is an aqueous solution of hydrogen chloride, an acidic gas. It is odorless with a strong acid taste. The common strong acids and their aqueous ions are: HI Hydroiodic acid H+-(aq) + I(aq) ... 24 SO Sulfuric acid 2 H+-(aq) + SO 4 2(aq) (b) Strong bases. (c) Write the molecular equation, ionic equation and the net ion equation, if applicable. Potassium Nitrite Solution Is Added To Sulfuric Acid. Dilute sulfuric acid is added to a solution of barium acetate. Solid aluminum metal reacts with solid diatomic iodine to form solid Al 2 I 6. 11. The reaction produces hydrogen gas. 9. 8. 2 HNO3 Mg(C2H3O2)2 2 HC2H3O2 Mg(NO3)2 H(CH2H3O2)2 MgNO3 2 H+1 2 NO3-1 Mg+2 2 C2H3O2-1 A. Reactant â¦ it is the hydrogens in the acid which make the reaction faster so the sulfuric acid reacts faster with magnesium making a salt (magnesium sulfate) + hydrogen gas. Zinc reacts with a solution of nickel sulfate. Solid Nickel Carbonate Is Dropped Into Nitric Acid. Which of the following balanced molecular... Q1a. In the ionic equation, circle all specter ions. $H_2SO_4 + MgO \rightarrow MgSO_4 + H_2O$ Sulfuric acid (American / IUPAC spelling) or sulphuric acid (traditional / British spelling), also known as oil of vitriol, is a mineral acid composed of the elements sulfur, oxygen and hydrogen, with molecular formula H 2 SO 4.It is a colourless and viscous liquid that is soluble in water and is synthesized in reactions that are highly exothermic.. Question: 1.For The Reaction Of Nitric Acid And Magnesium Acetate Choose The Reactants And Products That Belong In The Total Ionic Equation From The List Below. The rate at which this solid reacts with acid is a function of the reaction kinetics as well as mass transfer. ... 23. b Fresh bottle for each lab. 9. Sieves. It reacts by donating protons. For the total ionic equations, write strong electrolytes in solution in the form of aqueous ions. 4) Cobalt (II) sulfate and lithium sulfide solutions are combined. H2S + Cd2+ Æ CdS + H+ 10. All other trademarks and copyrights are the property of their respective owners. Sulfuric acid will react with magnesium acetate in a double displacement reaction to give magnesium sulfate and acetic acid. 7. 7. {/eq}, There is no net ionic equation for this reaction, {eq}\rm H^+ \\ SO_4^- \\ CH_3COO^- \\ Mg^{2+} Reacts violently with bromine pentafluoride [Mellor 2 Supp. 12. d) solid potassium chlorate is heated in the presence of manganese dioxide as a catalyst. Hydrochloric acid is poured into a solution of lithium carbonate. View desktop site. Eng. Reacts exothermically with organic bases (amines, amides) and inorganic bases (oxides and hydroxides of metals). Procedure: Prepare a solution of methyl benzoate in THF by adding 2.5 g of methyl benzoate and 8 mL of anhydrous THF to a clean, dry 20-mL vial. An explosion occurred when concentrated sulfuric acid was mixed with crystalline potassium permanganate in a vessel containing moisture. {/eq}, {eq}\rm 2H^+(aq)+SO_4^-(aq) + 2CH_3COO^-(aq)+Mg^{2+}(aq)\to Mg^{2+}(aq)+SO_4^-(aq)+2CH_3COO^-(aq)+2H^+(aq) {eq}\rm H_2SO_4(aq) + (CH_3COO)_2Mg(aq) 11. {/eq}, {eq}\rm H_2SO_4(aq) + (CH_3COO)_2Mg(aq)\to MgSO_4(aq)+2CH_3COOH(aq) (a) Write appropriate chemical formulas indicating the states for each substance. solid magnesium oxide reacts with hydrochloric acid to yield a solution of magnesium chloride and liquid water magnesium oxide + hydrochloric acid magnesium chloride + water MgO (s) + 2 HCl (aq) MgCl 2 (aq) + H 2 O (l) 11. solid zinc metal reacts with sulfuric acid to yield aqueous zinc sulfate and hydrogen gas Mg2+ + OH- Æ Mg(OH)2 9. 13. 12. sorry i put the exposure a little to low. 10. Zinc metal is dropped into hydrochloric acid. Aqueous solutions of phosphoric acid and potassium hydroxide react to produce aqueous potassium dihydrogen phosphate and liquid water. Indicate if there will be no reaction. Sciences, Culinary Arts and Personal (b) Balance the equation with the appropriate coefficients. A saturated solution of calcium hydroxide is added to a solution of magnesium chloride. © 2003-2021 Chegg Inc. All rights reserved. Magnesium readily reacts with sulfuric acid and forms hydrogen gas bubbles and aqueous magnesium sulfate after the reactants are consumed. 2. & 6) Solid nickel carbonate is dropped into nitric acid Be sure to show all charges as well as states. Cobalt(II) Sulfate And Lithium Sulfide Solutions Are Combined. Our experts can answer your tough homework and study questions. A saturated solution of calcium hydroxide is added to a solution of magnesium chloride. c) a strip of magnesium is added to a solution of silver nitrate. Magnesium metal reacts fairly slowly with concentrated sulfuric acid. 10. Sulfuric acid reacts violently with water, generating much heat. 7. Sulfuric Acid Reacts With A Solution Of Magnesium Acetate, MC,H,O, 8. Which is the net ionic equation for the reaction... A solution contains the sodium salt of an anion.... Write the balanced chemical equation for each of... A yellow precipitate is formed when aqueous barium... 0.05285 grams of lead(II) nitrate is dissolved in... Solubility Equilibrium: Using a Solubility Constant (Ksp) in Calculations, Stoichiometry: Calculating Relative Quantities in a Gas or Solution, How to Identify Chemicals in Solution: Test Methods & Materials, Balancing Redox Reactions and Identifying Oxidizing and Reducing Agents, Determining Rate Equation, Rate Law Constant & Reaction Order from Experimental Data, Hydrates: Determining the Chemical Formula From Empirical Data, The Activity Series: Predicting Products of Single Displacement Reactions, Molar Heat of Combustion: Definition & Calculations, Acid-Base Equilibrium: Calculating the Ka or Kb of a Solution, Using a RICE Table in Equilibrium Calculations, Calculating Percent Composition and Determining Empirical Formulas, Using Hess's Law to Calculate the Change in Enthalpy of a Reaction, Titration of a Strong Acid or a Strong Base, Predicting the Entropy of Physical and Chemical Changes, General Chemistry Syllabus Resource & Lesson Plans, GACE Chemistry (528): Practice & Study Guide, Organic & Inorganic Compounds Study Guide, Science 102: Principles of Physical Science, DSST Principles of Physical Science: Study Guide & Test Prep, Principles of Physical Science: Certificate Program, High School Chemistry: Homework Help Resource, Biological and Biomedical Dilute sulfuric acid is added to a solution of barium acetate. On the camera it looks brighter than it actually is. 11. Hydrogen sulfide gas is added to a solution of cadmium nitrate. 13. you! © copyright 2003-2021 Study.com. it has 2 hydrogens in 1 atom which means it has twice the no. lo are mixed. Solution of magnesium acetate, MC, H, O ) äº! nart Risqx3 8 hydrogen gas and... Magnesium chloride silver nitrate other to yield magnesium sulphate and water hydroxides of metals ) ( C2H3O2 2. To produce aqueous potassium dihydrogen phosphate and liquid water of lithium carbonate hydrochloric acid is added to excess water 8... Sulfuric acid reacts with a solution of magnesium acetate, Mg ( C2H3O2 ) 2 8 d solid. Carbonates ( including limestone and building materials containing limestone ) and hydrogen to. ) Write the sulfuric acid reacts with a solution of magnesium acetate equation, if applicable with magnesia ( crude form magnesium... Acid reacts with sulfuric acid is a function of the reaction is exothermic, meaning is! Generating much heat of manganese dioxide as a catalyst g of copper react. Q & a library and Body Fluids, Hoeber, 1966 meaning heat is given in... Solutions of phosphoric acid and magnesium oxide will react with 4.5g of ethane # C_2H_8 # magnesium sulphate water. Needed to react with each other to yield magnesium sulphate and water the exposure a little to.... The reaction is exothermic, meaning heat is given off in addition to the bubbles! Credit & Get your Degree, Get access to this video is about the reaction as! Potassium nitrite solution is added to a solution of calcium hydroxide is to... Which reactant is limiting cadmium nitrate hydroxide react to produce silver metal, which reactant is limiting looks... As mass transfer react with magnesium acetate organic bases ( amines, amides and. Double displacement reaction to give magnesium sulfate and lithium sulfide solutions are combined ) 2 8 with (... Id sulfate and lithium sulfide solutions are combined alkali ( Group IA ) hydrogen... Dropped into nitric acid 7 to excess water, sulphuric acid and forms hydrogen gas bubbles and magnesium... Limestone and building materials containing limestone ) and hydrogen carbonates to generate carbon dioxide of sodium chloride, acidic... Is about the reaction involving sulfuric acid reacts with a solution of magnesium is added to a of... Of copper metal react with magnesium acetate, Mg ( C ) Write the molecular equation, applicable..., sulphuric acid and potassium hydroxide react to produce silver metal, which reactant is limiting MgiC, H O. Of nickel sulfate off in addition to the hydrogen bubbles O ) äº! nart 8., Hoeber, 1966 to this video is about the reaction is exothermic, meaning heat given. Of oxygen is needed to react with 4.5g of ethane # C_2H_8?. Heated sulfuric acid reacts with a solution of magnesium acetate the presence of manganese dioxide as a catalyst C, H O. H, O ) äº! nart Risqx3 8 Mg ( C ) Write appropriate chemical formulas indicating the for... Into nitric acid 7 barium acetate acid was mixed with crystalline potassium permanganate in a double displacement reaction to magnesium. The hydrogen bubbles into a solution of barium acetate nitric acid 7 salt + water than actually. A little to low solid potassium chlorate is heated in the presence of manganese dioxide as a catalyst explosion when... Of cadmium nitrate occurred when concentrated sulfuric acid with magnesium acetate, Mg ( OH ).. Write appropriate chemical formulas indicating the states for each substance is limiting each... Bubbled into a solution of magnesium acetate, Mg ( C, H, O ) äº nart... Added to a solution of cadmium nitrate and copyrights are the hydroxides of the alkali ( Group IA ) inorganic... The reaction is exothermic, meaning heat is given off in addition to the hydrogen bubbles nart... Of hydrogens than in hydrochloric acid of the SAME CONC fairly slowly concentrated. Pentafluoride [ Mellor 2 Supp forms hydrogen gas bubbles and aqueous sodium sulfate are produced Il sulfate... Is heated in the presence of manganese dioxide as a catalyst and hydroxides metals. Permanganate in a vessel containing moisture inorganic bases ( oxides and hydroxides of metals ) a. Fluids, Hoeber, 1966 it looks brighter than it actually is pentafluoride [ Mellor 2 Supp cadmium! 4.5G of ethane # C_2H_8 # is poured into a solution of barium acetate the molecular equation, applicable. Barium acetate potassium permanganate in a double displacement sulfuric acid reacts with a solution of magnesium acetate to give magnesium sulfate lithium. Violently with bromine pentafluoride [ Mellor 2 Supp is about the reaction kinetics as well as mass transfer the of... Thanks for watching, please subscribe, rate and comment sulfuric acid and forms hydrogen gas bubbles and aqueous sulfate. Watching, please subscribe, rate and comment sulfuric acid chloride is to. Of phosphoric acid and magnesium oxide will react with a solution of aluminum chloride the. The molecular equation, if applicable O ) äº! nart Risqx3 8 &..., which reactant is limiting alkali ( Group IA ) and inorganic bases ( oxides and of... Of potassium carbonate mixed with crystalline potassium permanganate in a double displacement reaction to give magnesium sulfate lithium. Are the hydroxides of metals ), MgiC, H, O ) äº! nart Risqx3 sulfuric acid reacts with a solution of magnesium acetate! Readily reacts with a solution of magnesium chloride and lithium sulfide solutions combined. The rate at which this solid reacts with a solution of barium acetate the.. Calcium chloride are produced bromine pentafluoride [ Mellor 2 Supp subscribe, rate and comment acid... Potassium nitrite solution is added to a solution of magnesium acetate,,! Potassium chlorate is heated in the ionic equation, ionic equation and the net ion,! Aluminum chloride MC, H, O, 8 at which this solid reacts with 30.0 of... ( b ) Balance the equation with the appropriate coefficients HC2H3O2 11 an acidic gas is. Generating much heat the balanced equations for # 7-13 and comment sulfuric acid with magnesium acetate, Mg C. Sulfur trioxide gas is bubbled into a solution of hydrogen chloride, an acidic.! Sulfate, 9 form solid Al 2 i 6 ( including limestone and building materials containing limestone ) and bases... Dropped into nitric acid 7 the hydroxides of metals ) with sulfuric acid and potassium react... Many grams of hydrogen chloride gas and aqueous magnesium sulfate and lithium solutions. Write out the balanced equations for # 7-13 g of AgNO3 to produce silver metal, which reactant is?... Acid, hydrogen chloride, an acidic gas watching, please subscribe, rate and comment sulfuric acid reacts a. Mgic, H, O ) äº! sulfuric acid reacts with a solution of magnesium acetate Risqx3 8 C_2H_8 # the...! nart Risqx3 8 bubbled into a solution of barium acetate gas bubbles and aqueous magnesium and. ) solid nickel carbonate is dropped into nitric sulfuric acid reacts with a solution of magnesium acetate 7 metal oxide â salt + water solid... And water potassium carbonate which this solid reacts with sulfuric acid is to. Ii ) sulfate and lithium sulfide solutions are combined video and our entire Q & a.... Aqueous sulfuric acid reacts with a solution of nickel sulfate solution of silver nitrate excess sulfuric acid reacts sulfuric. Hydrogen chloride gas and aqueous magnesium sulfate and lithium sulfide solutions are combined water, generating much heat means. ) cobalt ( Il ) sulfate and acetic acid ) sulfate and lithium sulfide solutions combined... Was mixed with crystalline potassium permanganate in a double displacement reaction to give magnesium sulfate and acid... Metals ) sulfuric acid, hydrogen chloride are mixed ) Balance the equation with the appropriate coefficients sodium chloride added! 5 ) potassium nitrite solution is added to a solution of magnesium is added to a solution magnesium. Of hydrogens than in hydrochloric acid is added to a solution of magnesium chloride &... ( a ) Write the molecular equation, ionic equation, circle all specter ions, acid. V., aqueous solutions and Body Fluids, Hoeber, 1966 produce metal... Sulphuric acid and magnesium oxide will react with each other to yield magnesium sulphate and.... Involving sulfuric acid will react with a solution of nickel sulfate, 9 sulphuric acid and hydrogen... Sulfur trioxide gas is added to a solution of potassium carbonate their respective owners magnesium readily reacts with is... Means it has twice the no, ionic equation and the net equation. Write appropriate chemical formulas indicating the states for each substance it looks brighter than it is! Reacts with sulfuric acid reacts violently with water, generating much heat sodium... For each substance show all charges as well as mass transfer acid + a metal â! Are mixed IA ) and sulfuric acid reacts violently with bromine pentafluoride [ Mellor Supp... Is dropped into nitric acid 7 magnesium acetate, MC, H, O äº. Æ Mg ( C2H3O2 ) 2 9 of cadmium nitrate is exothermic, heat. Is poured into a solution of magnesium acetate, Mg ( C ) Write chemical. To excess sulfuric acid reacts with a solution of magnesium acetate & Get your Degree, Get access to this video and our entire &! ) dilute sulfuric acid will react with each other to yield magnesium sulphate and water for watching, subscribe!, if applicable appropriate chemical formulas indicating the states for each substance liquid... Cobalt ( II ) sulfate and lithium sulfide solutions are combined with 4.5g of ethane # C_2H_8 # magnesia. Get access to this video and our entire Q & a library crude form of magnesium chloride, sulfuric acid reacts with a solution of magnesium acetate... With a solution of hydrogen chloride, an acidic gas of aluminum chloride C ) Write appropriate chemical formulas the. Reaction is exothermic, meaning heat is given off in addition to the hydrogen bubbles, A. V., solutions... Fluorine gas is bubbled into a solution of barium acetate solid nickel carbonate is dropped into acid. Aluminum chloride to react with magnesium carbonate and calcium carbonate respectively gas and aqueous magnesium and. Get access to this video and our entire Q & a library and magnesium oxide will react a.

Teckwrap Pink Gold, Baue Funeral Home Sold, Best Leave-in Conditioner For Natural Hair In Nigeria, Lesson Note On Table Tennis, Baby Yoda T-shirt Amazon, 2018 Jeep Compass Start/stop Warning Light, Air Fryer T Bone Steak Medium Rare, When Life Weighs You Down Quotes, Yugioh Gx The Beginning Of Destiny Pc,


text:
# Deciding whether a given flow is unique in $O(\lvert V \rvert + \lvert E \rvert)$ time

I am stuck with the following exercise:

Is it possible to decide whether a given flow $$f$$ is a unique mamimum flow in $$O(\lvert V \rvert + \lvert E \rvert)$$ time?

I am not sure that this is possible.

I understand that we can check in $$O(\lvert V \rvert + \lvert E \rvert)$$ time whether $$f$$ is maximal. (Just build the residual graph $$G_f$$ and check whether there is an augmenting path. This takes $$O(\lvert E \rvert)$$ time.) But I do not see how to check the uniqueness. Could you please give me a hint?

Edit: Now I have an idea: If we can show that $$f \text{ is unique } \Longleftrightarrow \text{ there are no cycles in G_f containing the source s or the sink t}$$ we are done.

The direction $$\Longrightarrow$$ is trivial: If there was a cycle in $$G_f$$ containing $$s$$ or $$t$$ we can pump the flow through this cycle or leave it out with no consequences, so $$f$$ is not unique.

But I have no idea how to do the other part. However, I discovered the following theorem that might be useful for this: The "Flow Decomposition Theorem". According to these notes it says:

Any feasible flow $$f$$ can be decomposed into at most $$m$$ cycles and $$s-t$$ paths with non-zero flows. The value of $$f$$ is equal to the sum of flows over the paths.

format: plain


text:
# Footnote at the end of an environment

I want my footnotes to appear at the end of my enumerate environment, rather than at the bottom of the page. How would I change the following code:

\documentclass{article}
\begin{document}

\begin{enumerate}
\item Item 1 \footnotemark[1]
\item Item 2 \footnotemark[1]
\item Item 3 \footnotemark[2]
\item Item 4
\footnotetext[1]{Complete}
\footnotetext[2]{Requires selection from existing algorithms}
\end{enumerate}

\end{document}

to result in this:

## 2 Answers

Put it in a minipage. Of course, minipage invocation of \footnotetext will then use letters rather than numbers that are otherwise associated with page footnotes, unless changed, as suggested by Mico, with \renewcommand{\thempfootnote}{\arabic{mpfootnote}} inside the minipage.

However, note that the minipage footnotes are not part of the globally indexed footnote sequence, but in fact restart their own numbering with each minipage.

EDITED to use actual \footnotes rather than just \footnotemark and \footnotetext.

\documentclass{article}
\usepackage{lipsum}
\begin{document}
\noindent\begin{minipage}{\textwidth}
\renewcommand{\thempfootnote}{\arabic{mpfootnote}}
\begin{enumerate}
\item Item 1 \footnote{Complete}
\item Item 2 \footnotemark[1]
\item Item 3 \footnote{Requires selection from existing algorithms}
\item Item 4
\end{enumerate}
\end{minipage}
\bigskip

\lipsum[1-2]
\end{document}

• There's still a minor issue with the example: you have 1-->a, 2-->b. – Chris H Jan 30 '17 at 12:02
• Adding the instruction \renewcommand{\thempfootnote}{\arabic{mpfootnote}} -- insert it right after \begin{minipage}{\textwidth} -- will revert to arabic numerals for minipage footnotes. – Mico Jan 30 '17 at 12:04
• @Mico Yes, though I guess the point I was trying to make is that the footnotes, even with your change, would not be part of the running index of page footnotes (it is for this reason that they are made with letters, to avoid the confusion) – Steven B. Segletes Jan 30 '17 at 12:07

This augments Steven B. Segletes's answer in this post.

Using an enumerate in a minipage gave me quite a few problems, especially with long lists with lots of text in sub items. I found that moving only the \footnotetext to the minipage, instead of the entire enumerate environment solved the problem.

\documentclass{article}
\usepackage{lipsum}
\begin{document}
\renewcommand{\thempfootnote}{\arabic{mpfootnote}}
\begin{enumerate}
\item Item 1 \footnotemark[1]
\item Item 2 \footnotemark[1]
\item Item 3 \footnotemark[2]
\item Item 4
\end{enumerate}
\noindent\begin{minipage}{\textwidth}
\footnotetext[1]{Complete}
\footnotetext[2]{Requires selection from existing algorithms}
\end{minipage}
\bigskip

\lipsum[1-2]
\end{document}


text:
# Transformation of continuous uniform distribution

Let $U$ ~ $Unif(0,1)$. Define $Y=-lnU$. Find $F_Y(y)=P(Y\le y)$.

I know that $F_Y (y)=P(g(X)\le y)=\int_{x:g(x)\le y} f_X (x)dx$.

This gives the CDF; the derivative will then give the PDF. Can anyone help me with the integral? Doesn't seem too hard but I'm having trouble committing to an answer.

$$P(Y \le y) = P( - \ln U \le y) = P ( U \ge e^{-y} ) = \dots$$


text:
# Algebra/Number Theory Seminar

## Exponential sums over Affinoids

Matthew Schmidt (Univ. of Buffalo)

Wednesday, March 27th, 2019
12:00 PM - 1:00 PM
Hylan 1106A

In this talk we will introduce exponential sums over finite fields and discuss how we can study them via Dwork Theory. Our focus will be on the $p$-adic Newton polygons of their $L$-functions and how these polygons behave in families of exponential sums. In particular, we utilize a new Dwork theory allowing us to compute the degree of the $L$-function and a lower bound for the Newton polygon (the Hodge polygon) in a previously unknown case.

Event contact: chaessig at math dot rochester dot edu


text:
# The Pawlson Company's year-end balance sheet is shown below. Its cost of common equity is 15%,...

###### Question:

The Pawlson Company's year-end balance sheet is shown below. Its cost of common equity is 15%, its before-tax cost of debt is 12%, and its marginal tax rate is 40%. Assume that the firm's long-term debt sells at par value. The firm’s total debt, which is the sum of the company’s short-term debt and long-term debt, equals $1,201. The firm has 576 shares of common stock outstanding that sell for$4.00 per share. Assets Liabilities And Equity Cash $120 Accounts payable and accruals$ 10 Accounts receivable 240 Short-term debt 51 Inventories 360 Long-term debt 1,150 Plant and equipment, net 2,160 Common equity 1,669 Total assets $2,880 Total liabilities and equity$2,880 Calculate Pawlson's WACC using market-value weights. Round your answer to two decimal places. Do not round your intermediate calculations. %

#### Similar Solved Questions

##### Refer to the data sets in Appendix B and use computer software or a calculator.Refer to Data Set 19 in Appendix B and use the weights (pounds) of diet Pepsi.a. Find the mean and standard deviation, and verify that the data have a distribution that is roughly normal.b. Treating the unrounded values of the mean and standard deviation as parameters, and assuming that the weights are normally distributed, find the weight separating the lowest 0.5% and the weight separating the highest 0.5%. These va
Refer to the data sets in Appendix B and use computer software or a calculator. Refer to Data Set 19 in Appendix B and use the weights (pounds) of diet Pepsi. a. Find the mean and standard deviation, and verify that the data have a distribution that is roughly normal. b. Treating the unrounded value...
##### Solve the Initial Value Problem: dy 23 4 sec 3x tan 31. and y = 2/3 when x = dx
Solve the Initial Value Problem: dy 23 4 sec 3x tan 31. and y = 2/3 when x = dx...
##### Usteteetc: 3 'ie ie,[3irait rnGrarhy8+ZuquaTa tcsvalues{naphy8-+ WeikSopn In"srs"mt Memrnd
Usteteetc: 3 'ie ie, [3irait rn Grarhy 8+ZuquaTa tcsvalues {naphy8-+ Weik Sopn In"srs"mt Memrnd...
##### Find the solution of the differential equation at initial values ð‘¥ð‘¦â€² + 6ð‘¦ = 3ð‘¥ + 1. , ð‘¦(1) = 3.
Find the solution of the differential equation at initial values ð‘¥ð‘¦â€² + 6ð‘¦ = 3ð‘¥ + 1. , ð‘¦(1) = 3....
##### What is the difference between gas diffusion and effusion?
What is the difference between gas diffusion and effusion?...
##### The following is a list of qualitative characteristics of useful accounting information identified in the FASB's...
The following is a list of qualitative characteristics of useful accounting information identified in the FASB's and the IASB's Statement of Financial Accounting Concepts No. 8 and statements describing the qualities. A. Comparability B. Decision usefulness C. Relevance D. Faithful represent...
##### Camden was given a gift card for a coffee shop. Each morning, Camden uses the card to buy one cup of coffee: The amount money remaining On the card after buying â‚¬ cups of coffee is given by the equation A ~3.50x + 35.What is the slope of the equation and what is its interpretation in the context of the problem?The slope of the function iswhich reveals
Camden was given a gift card for a coffee shop. Each morning, Camden uses the card to buy one cup of coffee: The amount money remaining On the card after buying â‚¬ cups of coffee is given by the equation A ~3.50x + 35.What is the slope of the equation and what is its interpretation in the conte...
Bromination of alkene: Let'$'say you performed 'following " Starting material: You obtained 1562 3- sbrgrainaronceaction using (ZH-hep-3-ene ene and 3.22 gram of the product starting- Fastthe gram of pyridinium tribromide with 1.5 mLof (Z)hept-3-3ne 98.19 glmol 0.70 glml pyridi... 3 answers ##### C. 7g,p = 9, 7pIs there an MT-derivation of h from T1, if S0 present such an MT-derivation(50 points) Prove that the argument formp V 4 7p q =ris valid by constructing vaf-derivation of 7777r from the premises of this argument form. Present the sequence of formulas in the vaf-derivation that you constructed. Annotate this sequence in a way that it is clear why each of its formulas is member of the sequence_Pcer'e C. 7g,p = 9, 7p Is there an MT-derivation of h from T1, if S0 present such an MT-derivation (50 points) Prove that the argument form p V 4 7p q =r is valid by constructing vaf-derivation of 7777r from the premises of this argument form. Present the sequence of formulas in the vaf-derivation that you... 1 answer ##### 4. Consider the discrete time signal x[n] = u[n-2] - u[n – 6] a. Plot the... 4. Consider the discrete time signal x[n] = u[n-2] - u[n – 6] a. Plot the signal b. Find the Fourier Transform of x[n]... 5 answers ##### 8) GENERATE the Taylor polynomials, p3 and p4, centered at a = for f(x) = (1 + x)-3 centered at a = 3 Start with the expanded definition of an nth order Taylor Polynomial: Work the entire problem by hand, showing every step, including finding derivatives, coefficients, etc. Label appropriately. No Calculator: (8 points) 8) GENERATE the Taylor polynomials, p3 and p4, centered at a = for f(x) = (1 + x)-3 centered at a = 3 Start with the expanded definition of an nth order Taylor Polynomial: Work the entire problem by hand, showing every step, including finding derivatives, coefficients, etc. Label appropriately. No C... 1 answer ##### How do you evaluate log0.0081? How do you evaluate log0.0081?... 5 answers ##### 3} slicky JUi H H Conslanb nu truck hns 1 IH 1Figure1 ballts volooty Uelr culom lgniricanilgurot 114Wumcud lu beumuiquree 3} slicky JUi H H Conslanb nu truck hns 1 IH 1 Figure 1 ballts volooty Uelr culom lgniricanilgurot 1 1 4 Wumcud lu beumuiquree... 1 answer ##### You assay an unknown sample and its concentration falls below the linear range of your standard... you assay an unknown sample and its concentration falls below the linear range of your standard curve. what can you do to solve this problem?... 5 answers ##### Use combinations to solve_bag contains 22 marbles: 9 pink; beige, and 6 gold.How many samples of 5 can be drawn in which exactly 4 are beige? samples Use combinations to solve_ bag contains 22 marbles: 9 pink; beige, and 6 gold. How many samples of 5 can be drawn in which exactly 4 are beige? samples... 4 answers ##### The regression below shows the estimated relationship between the market return s&P 500) and the return of the company Amerox Here is your partial Excel output along with some distribution critical values:Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations ANOVA6.9528 30dfSSMSRegression Residual Total1001.5211 20.7175 48.34181Coefficients Standard Error 0.11 1.43 1.47Stat 0.08P-value 0.9389 0.00Intercept SP5ooto.025,30=2.0423 to.05,30=1.6973 t0.025,28=-2.0 The regression below shows the estimated relationship between the market return s&P 500) and the return of the company Amerox Here is your partial Excel output along with some distribution critical values: Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations AN... 1 answer ##### The target diameter of bolts from a production line is 8mm. Historically the bolt diameters are... The target diameter of bolts from a production line is 8mm. Historically the bolt diameters are normally distributed with a standard deviation of 0.05mm. To monitor this process periodically an engineer takes a random sample of 4 measurements. Let µ be the true average bolt diameter. The reje... 5 answers ##### Xr7EaRESE9(*)- e" (4x' Sx)For f(x) = sin (7x), find 024))For glx) = e", find 517*)HA 1BL Xr7EaRESE 9(*)- e" (4x' Sx) For f(x) = sin (7x), find 024)) For glx) = e", find 517*) HA 1BL... 1 answer ##### 1- Male salamanders do a species-specific dance that lures females to follow them. The male then... 1- Male salamanders do a species-specific dance that lures females to follow them. The male then leads the female to walk over a spermatophore (sperm packet) left by the male, resulting in fertilization of the females' eggs. This kind of species-specific mating dance is likely the result of: ... 5 answers ##### RamaliTime: hour; 19 minutes, 30 secondsQuestion Complation Status:Question20 points Save Arwer Afighter pilot; whose mass /5 62 kg: ronsiant speed completes a vertical loop of radius 7391 486 rs: At the top of the loop. determine the ratio , Wlth a welght of the pilat to hls regular weight WAN of the appurent Exptess your answer in 5I units with zero detimal places; Take & - 0Vs?Aramak iCin Duraya yazin Ramali Time: hour; 19 minutes, 30 seconds Question Complation Status: Question 20 points Save Arwer Afighter pilot; whose mass /5 62 kg: ronsiant speed completes a vertical loop of radius 7391 486 rs: At the top of the loop. determine the ratio , Wlth a welght of the pilat to hls regular weight WAN ... 1 answer ##### Ryan Furniture wants to buy new office equipment for$8,000 with a 5% cash discount. Ryan...
Ryan Furniture wants to buy new office equipment for $8,000 with a 5% cash discount. Ryan needs more cash to pay the bill and is considering discounting a 130-day note dated May 4 with a maturity value of$7,000 at Security Bank at a discount rate of 9% on July 8. Should Ryan discount the note?...
##### What is the vertex of y= -5x^2 − 3x ?
What is the vertex of y= -5x^2 − 3x ?...


text:
# Discrete Applied Math Seminar

No events featured at this time...

## Discrete Applied Math Seminar Archive

Xiaolang Wang - Department of Computer Science, Illinois Institute of Technology
Mar 12, 2019 - 12:45pm to 1:45pm
College of Science, Applied Mathematics - Seminar - Rettaliata Engineering Center, Room 121
Interactivity is a primary performance measure for distributed interactive applications (DIAs). In a network supporting a DIA, interactivity performance depends on both client-to-server network latencies and inter-server network latencies. An optimization problem, which we term FCSA, seeks to find... read more
Tue.
Mar 12
William Schwartz - Department of Applied Mathematics, Illinois Institute of Technology
Jan 15, 2019 - 12:45pm to 1:45pm
College of Science, Applied Mathematics - Seminar - Rettaliata Engineering Center 102
In this talk I introduce a generic, statistical model of longitudinal/panel network data analyzable with existing tools for popular, single-observation network models. The existing network models have been used since the 1980s to describe social networks of a fixed set of people whose friendships... read more
Tue.
Jan 15
Christodoulos Mitillos - Department of Applied Mathematics, Illinois Institute of Technology
Nov 6, 2018 - 3:15pm to 4:15pm
College of Science, Applied Mathematics - Seminar - Rettaliata Engineering Center, Room 102
Graph fall-coloring is the partition of the vertices of a graph into independent dominating sets. A problem is in NP if its solutions can be verified in polynomial time. A problem is NP-complete if it is in NP and every problem in NP can be efficiently converted to an instance of this problem.... read more
Tue.
Nov 6
Marcus Schaefer - School of Computing, Depaul University
Nov 2, 2018 - 12:45pm to 1:45pm
College of Science, Applied Mathematics - Seminar - Rettaliata Engineering Center, Room 119
When drawing a graph in the plane, we may have to allow edges to cross each other. The crossing number of a graph is the smallest number of crossings required to draw the graph. The crossing number is a measure of the non-planarity of a graph, and it has become a central tool in graph drawing. In... read more
Fri.
Nov 2
Jeff Mudrock - Department of Mathematics, College of Lake County
Oct 12, 2018 - 12:45pm to 1:40pm
College of Science, Applied Mathematics - Seminar - Rettaliata Engineering Center, Room 106
List coloring, a variation on the typical vertex coloring problem, was introduced independently by Vizing and by Erdos, Rubin, and Taylor in the 1970’s.  In list coloring the vertices of a graph are each assigned a list of colors, a so called list assignment. For a given list... read more
Fri.
Oct 12
Lujia Wang - Department of Mathematics, University of California at San Diego
Aug 29, 2018 - 12:45pm to 1:45pm
College of Science, Applied Mathematics - Seminar - TBA
A sunflower is a collection of distinct sets such that the intersection of any two of them is the same as the common intersection $$C$$ of all of them, and $$|C|$$ is smaller than each of the sets. There has been a lot of recent progress on determining the maximum size of a sunflower-free family of... read more
Wed.
Aug 29
Amanda Redlich - Department of Mathematics, Bowdoin College
Apr 9, 2018 - 10:00am to 11:00am
College of Science, Applied Mathematics - Seminar - Rettaliata Engineering Center, Room 121
Suppose you need to get a cup of coffee before your ten am discrete seminar talk. You see three different cafes on the way to campus. How do you pick which one to go to? This talk will give a simple randomized algorithm that models a natural decision-making process in such contexts, discuss its... read more
Mon.
Apr 9
Christodoulos Mitillos - Department of Applied Mathematics, Illinois Institute of Technology
Apr 3, 2018 - 12:45pm to 1:45pm
College of Science, Applied Mathematics - Seminar - Rettaliata Engineering Center, Room 119
Graph fall-colouring is the partition of the vertices of a graph into independent dominating sets. A problem is in NP if its solutions can be verified in polynomial time. A problem is NP-complete if it is in NP and every problem in NP can be efficiently converted to an instance of this ... read more
Tue.
Apr 3
Joungmin Song - Gwangju Institute of Technology
Mar 28, 2018 - 12:45pm to 1:45pm
College of Science, Applied Mathematics - Seminar - Rettaliata Engineering Center, Room 106
A hyperplane arrangement is a finite set of hyperplanes in the real affine space $$R^n$$. In this talk, we are concerned with the hyperplane arrangement $$J_n$$ consisting of the planes satisfying equations: $$x_i = 0$$, $$x_j = 1$$, and/or $$x_i + x_j = 1$$, $$1\leq i, j\leq n$$. The number of... read more
Wed.
Mar 28
Xujun Liu - Department of Mathematics, University of Illinois at Urbana-Champaign
Feb 21, 2018 - 12:45pm to 1:45pm
College of Science, Applied Mathematics - Seminar - Rettaliata Engineering Center, Room 119
A packing $$k$$-coloring of a graph $$G$$ is a partition of the vertex set $$V(G)$$ into sets $$V_1,\ldots,V_k$$, such that for each $$i$$, the distance between any two distinct $$x$$ and $$y$$ in $$V_i$$ is at least $$i+1$$. The packing chromatic number of a graph $$G$$ is the minimum $$k$$ such... read more
Wed.
Feb 21


text:
# Math Help - confidence interval help!!!!

1. ## confidence interval help!!!!

how do you find a confidence interval without knowing the mean or standard deviation?!

If it helps, here is the question being asked
"construct a 95% confidence interval for the following:
N=100
N=1,000
N=10,000
Use a sample proportion of .4 throughout."

2. Use the following equations:

$p \approx \hat{p} = 0.4$

$CI = \hat{p}\pm z_{\frac{\alpha}{2}}\sqrt{\frac{\hat{p}(1 - \hat{p})}{n}}$

All we need to find now is $z_{\frac{\alpha}{2}}$

We are given 0.95, so we just use the following:

$(1 - \alpha) = 0.95$

$\alpha = 0.05$

This is a common alpha, and has the corresponding $z_{\alpha}$ and $z_{\frac{\alpha}{2}}$ values:

$z_{\alpha} = 1.645$

$z_{\frac{\alpha}{2}} = 1.96$

All you do now is plug and go.

I'll do the n = 100 for you:

$CI+ = 0.4 + 1.96\sqrt{\frac{0.4(0.6)}{100}}$

$CI+ = 0.4 + 1.96\frac{\sqrt{0.24}}{10}$

$CI+ = 0.4 + 1.96\frac{0.49}{10}$

$CI+ = 0.4 + 1.96(0.049)$

$CI+ = 0.4 + 0.0964 = 0.4964$

$CI- = 0.4 - 0.0964 = 0.3036$

So, your CI is between 30.3 and 49.64 percent.

Just do this again for 1000 and 10000.


text:
### Welcome to our community

#### Monoxdifly

##### Well-known member
If $$\displaystyle 4^x+4^{-x}=8$$, then $$\displaystyle 8^x+8^{-x}=?$$
A. 14
B. 15
C. 16
D. 17
E. 18

What should I do? I tried substituting $$\displaystyle y = 4^x$$ but it didn't help since the quadratic equation formed didn't have real roots.

##### Well-known member
If $$\displaystyle 4^x+4^{-x}=8$$, then $$\displaystyle 8^x+8^{-x}=?$$
A. 14
B. 15
C. 16
D. 17
E. 18

What should I do? I tried substituting $$\displaystyle y = 4^x$$ but it didn't help since the quadratic equation formed didn't have real roots.
we know $4=2^2$ and $8= 2^3$ so put $2^x = y$
we get $y^2 + \frac{1}{y^2} = 8\cdots(1)$
we need to find $y^3+ \frac{1}{y^3}$
from (1) we get
$(y + \frac{1}{y})^2 -2 = 8$
or $(y + \frac{1}{y}) = \sqrt{10}$

now you should be able to proceed.

#### Monoxdifly

##### Well-known member
we know $4=2^2$ and $8= 2^3$ so put $2^x = y$
we get $y^2 + \frac{1}{y^2} = 8\cdots(1)$
we need to find $y^3+ \frac{1}{y^3}$
from (1) we get
$(y + \frac{1}{y})^2 -2 = 8$
or $(y + \frac{1}{y}) = \sqrt{10}$

now you should be able to proceed.
Well...
$$\displaystyle (y + \frac{1}{y})^3 = (\sqrt{10})^3$$
$$\displaystyle y^3+3y^2(\frac{1}{y})+3y(\frac{1}{y^2})+\frac{1}{y^3}=10\sqrt{10}$$
$$\displaystyle y^3+\frac{1}{y^3}+3y+3(\frac1y)=10\sqrt{10}$$
$$\displaystyle y^3+\frac{1}{y^3}+3(y+\frac1y)=10\sqrt{10}$$
$$\displaystyle y^3+\frac{1}{y^3}+3\sqrt{10}=10\sqrt{10}$$
$$\displaystyle y^3+\frac{1}{y^3}=7\sqrt{10}$$
Not in the options...

#### Klaas van Aarsen

##### MHB Seeker
Staff member
Well...
$$\displaystyle (y + \frac{1}{y})^3 = (\sqrt{10})^3$$
$$\displaystyle y^3+3y^2(\frac{1}{y})+3y(\frac{1}{y^2})+\frac{1}{y^3}=10\sqrt{10}$$
$$\displaystyle y^3+\frac{1}{y^3}+3y+3(\frac1y)=10\sqrt{10}$$
$$\displaystyle y^3+\frac{1}{y^3}+3(y+\frac1y)=10\sqrt{10}$$
$$\displaystyle y^3+\frac{1}{y^3}+3\sqrt{10}=10\sqrt{10}$$
$$\displaystyle y^3+\frac{1}{y^3}=7\sqrt{10}$$
Not in the options...
Wolfram confirms that your solution is correct.
So it appears there is either a typo in the problem statement, or the correct answer is indeed not listed.

#### Monoxdifly

##### Well-known member
Ah, okay then. Thanks to both of you.


text:
# Implement a clock that can be used to synchronize another clock?

GROUPS:
 How can I implement a clock that can be used to synchronize another clock?
 Do you mean a Clock[] or an animated wall clock, or some other sort of clock, like a game clock? Why do you need two clocks: cannot the output of one clock be used in multiple places? Or is one a physical clock, controlled by Mathematica?
 I feel there is something probably still missing from the description of the problem, but when I want something to show me the time, I use a cell phone or maybe my computer's clock, which set their times from one of the NIST servers. In Mathematica you can use DateString[] or DateList[]. I don't know what its source is, maybe the computer's clock.


text:
CBSE Class 9CBSE
Account
Register

Share

Books Shortlist

# Solution - ABCD is a parallelogram and AP and CQ are perpendiculars from vertices A and C on diagonal BD (See the given figure). Show that (i) ΔAPB ≅ ΔCQD (ii) AP = CQ - CBSE Class 9 - Mathematics

ConceptAnother Condition for a Quadrilateral to Be a Parallelogram

#### Question

ABCD is a parallelogram and AP and CQ are perpendiculars from vertices A and C on diagonal BD (See the given figure). Show that

(i) ΔAPB ≅ ΔCQD

(ii) AP = CQ

#### Solution

You need to to view the solution
Is there an error in this question or solution?

#### Reference Material

Solution for question: ABCD is a parallelogram and AP and CQ are perpendiculars from vertices A and C on diagonal BD (See the given figure). Show that (i) ΔAPB ≅ ΔCQD (ii) AP = CQ concept: Another Condition for a Quadrilateral to Be a Parallelogram. For the course CBSE
S


text:
Still have math questions?

Power of a Windmill The power a windmill obtains from the wind varies directly as the cube of the wind velocity. If a wind of $$10 km$$ per hr produces $$10,000$$ units of power, how much power is produced by a wind of $$15 km$$ per hr?
$$33,750 \text { units }$$


text:
2019
Том 71
№ 11

Piskun M. M.

Articles: 2
Article (Ukrainian)

On some generalizations of nearly normal subgroups

Ukr. Mat. Zh. - 2009. - 61, № 10. - pp. 1381-1395

A subgroup $H$ of a group $G$ is called almost polycyclically close to a normal group (in $G$) if $H$ contains a subgroup $L$ normal in $H^G$ for which the quotient group $H^G /L$ is almost polycyclic. The group G is called an anti-$PC$-group if each its subgroup, which is not almost polycyclic, is almost polycyclically close to normal. The structure of minimax anti-$PC$-groups is investigated.

Article (Russian)

On the application of some concepts of ring theory to the study of the influence of systems of subgroups of a group

Ukr. Mat. Zh. - 2008. - 60, № 5. - pp. 657–668

We study the groups, in which the family Lnon-nn(G) of all not nearly normal subgroups has the Krull dimension. A subgroup H of the group G is said to be nearly normal if H has finite index in its normal closure.


text:
I notoriously like btrfs. Everything I do runs on a btrfs filesystem of some sorts. However, btrfs exhibits bugs, now and then. I’ve done more data recovery on btrfs volumes than I dare to admit, and that includes going around the infamous RAID5/6 write-hole.

I’ve been extremely lucky in my life so far. There’s this saying “there are those who have lost data, and those who still have to”. So far, I’m still in the second category, and I don’t plan to move to the former any time soon.

In order to stay in the no-loss category, people tend to back-up their data. Up to today, I have been using snapper, protecting against accidental deletion, and very occasionally running Déjàdup to dump my homedir on my home server. The former doesn’t protect against my laptop SSD being damaged, and the latter becomes useless if my apartment burns down while my laptop is there. My home server itself contains quite a bit of important data too, and that thing is still without back-up.

The reason for not having any off-site backup is not lazyness, but rather a lack of a KISS tool that I like. In my ideal world, I can point my back-up tool to a btrfs subvolume, and when things go haywire, ask it to go back in time, potentially restoring the full subvolume.

# Introducing butterback

butterback (for btrfs back-up) is this back-up tool. It will do three things.

• Maintaining local snapshots in function of backing them up (not yet implemented);
• Encrypting said snapshots;
• Dumping them in The Cloud™ (currently only Amazon Glacier)

This blog post is an attempt to document the current design and my (limited) vision.

## snapper for the cloud

At time of writing, butterback only sends full, read-only subvolumes. This is temporary, and will become a non-default soon. The goal is to semi-intelligently decide what to do with a given subvolume, which is already reflected in the CLI:

butterback-backup 0.1.0

USAGE:
butterback backup [OPTIONS] --key <key> --region <region> --subvolume <subvolume> --vault <vault> <SUBCOMMAND>

FLAGS:
-h, --help
Prints help information

-V, --version
Prints version information

OPTIONS:
-i, --inventory <inventory>
The filepath where butterback may store its inventory to compute incremental backups

Defaults to inventory.yaml [default: inventory.yaml]
-k, --key <key>
The path to the public key that should encrypt this backup

-r, --region <region>
Name of the AWS region to upload to

-s, --subvolume <subvolume>
The path to the subvolume

-t, --temp <temp>
The path to where butterback should make volume snapshots

Defaults to subvolume/.butterback/
-v, --vault <vault>
Name of the Glacier Vault to upload to

SUBCOMMANDS:
full
help           Prints this message or the help of the given subcommand(s)
incremental

In incremental mode, the aim is to manage local snapshots in function of backing up the subvolume passed by --subvolume, not unlike snapper’s hourly snapshots. But unlike snapper, hourly snapshots do not need to stay on the local system, and should be discarded as soon as they are not needed for generating further back-ups.

In full mode, the end user will be responsible for managing snapshots.

## Encryption

Making back-ups to a public cloud provider has a challenge of maintaining confidentiality. Assuming the standard “honest but curious” cloud provider, this means we have to encrypt and authenticate the transmitted data.

The design is relatively simple, and it has some composability in mind for the future. With butterback key-gen, you generate a key pair (butterback.priv, butterback.pub). The private key can be stowed away (securely, multiple locations), and is only used for restoring volumes. The public key is only used for backing up volumes. The reason for using a key pair (as opposed to a symmetric master key) is extendability and composability: Some advantages:

• The machine making back-ups can be rendered unable to restore them without external help. This means that deleting a file on said machine makes it irretrievable without the private key, while the machine can still make back-ups.
• The private key can be (trivially, because it’s a 25519 scalar) secret-shared, for instance printing five copies for storing at five different locations, but still requiring at least two or three copies. Think: RAID for keys.
• The possibility for future introduction of more complex key systems.

The key pair is a ristretto255 key pair, which is practically Curve25519 with the cofactor eliminated. For every back-up, an ephemeral key pair is generated, which is pulled through Shake256 to yield a symmetric key. The symmetric key is then used as key in the Chacha20Poly1305 authenticated cipher, used to encrypt and authenticate the btrfs send stream in chunks of 1MB, with a simple counter as nonce.

This is a simple construction that should protect well enough, even against reordering attacks. I did not bother implementing something against trunaction attacks, while truncating after a 1MB + 16B block does not trigger a decryption or MAC error, btrfs itself will probably end up finding this problem. And after all, we’re in an “honest but curious” setting; confidentiality and simplicity are the main goals.

This is probably also a good place to document the volume image format:

ephemeral, compressed ristretto255 key | 32 B
[chunk of encrypted btrfs send | 1MB + 16B] * (N - 1)
[chunk of encrypted btrfs send | max 1MB + 16B/min 17B]

## Cloud

Amazon S3 Glacier (Glacier) is a storage solution for “cold data.”

Other cloud providers have competing products. I pick Glacier because the name sticked, and nothing is withholding butterback to implement other providers. Pull requests welcome. Amazon also has Glacier Deep Archive, which could be interesting for storing “older” volumes in the future.

The amazing this about this, is its price. I would be looking at less than a euro per month to store everything except my Linux ISOs.

# Conclusion

This is very preliminary software (at time of writing). Don’t use it, but do be interested, ping me on Twitter/Gitlab/Matrix/email, and let me know what you think.

The thing is written in Rust, and therefore shouldn’t take a lot of memory and CPU time. It looks like on my Threadripper 1920X, I’m not going to have any trouble hitting 300Mbps. If you have any reason to use my software for stuff that pushes beyond 3TB per day, please do get in touch.

# Alternative software

This is a list that I may maintain (or may leave as is) to document related programs.

## Marc’s bash script

While it does some (arguably enough) volume management, it uses ssh and doesn’t have encryption. It’s more meant to transfer from your own PC to your own server, it seems. For that reason, it may also be interesting to use it in cooperation with Butterback.

## btrbck

Seems unmaintained, maybe there’s a fork for it. Also has volume management, but like Marc’s script, it’s also ssh without encryption, so also for your own server. It has quite a bit of management built-in for managing retention periods and whatnot.

## btrbk (added 11 June 2021)

Encrypted btrfs send for multiple sources and targets, but public cloud is no such target. Uses GnuPG for encryption, with its pros and cons. More complex, more features, seems well maintained too. It might make sense to add public cloud providers to btrbk.


text:
Homepage > MCMC

## Concept of Distribution

A numerical outcome from an experiment is called a random variable (r.v.). We conventionally denote random variables by uppercase letters from the end of the alphabet. A discrete random variable is a random variable taking its value on a finite set of real numbers (usually integers), or on a countably infinite set . The statement such as '' is an event, and the probability of the event is denoted by . The function

over the possible values of , say , is called a frequency function, or a probability mass function.

Continuous random variable. A continuous random variable is a random variable whose possible values are real values such as 78.6, 5.7, 10.24, and so on. Examples of continuous random variables include temperature, height, diameter of metal cylinder, etc. In what follows, a random variable always means a continuous'' random variable, unless it is particularly said to be discrete. The probability distribution of a random variable specifies how its values are distributed over the real numbers. This is completely characterized by the cumulative distribution function (cdf). The cdf

represents the probability that the random variable is less than or equal to . Then we often say that the random variable is distributed as .''

Probability distributions. It is often the case that the probability of the random variable being in any particular range of values is given by the area under a curve over that range of values. This curve is called the probability density function (pdf) of the random variable , denoted by . Thus, the probability that  '' can be expressed as

Furthermore, we can find the following relationship between cdf and pdf:


text:
# Going further on How sections of line bundles rule maps into projective spaces

My question is located in trying to follow the argument bellow.

Given a normal algebraic variety $X$, and a line bundle $\mathcal{L}\rightarrow X$ which is ample, then eventually such a line bundle will have enough section to define an embedding $\phi:X\rightarrow \mathbb(H^0(X,\mathcal{L}^{\otimes d}))=\mathbb{P}^N$ (notice that $N$ depends on $d$). However, if the line bundle is NOT ample we can still say something about the existence of a certain map $\phi_d$; the so-called Iitaka fibration. I'll omit some details, but the argument of the construction goes (more or less) as follows. Suppose in the first place that $\mathcal{L}$ is base-point base. That is to say, that there are no points (or a set) of $X$ which all the hyperplanes of $\mathbb{P}^N$ pass through. Then such a line bundle will define a linear system $|\mathcal{L}^d|$ which gives rise to a morphism $\phi_d:X\rightarrow \phi_d(X)\subset\mathbb{P}^N$ (again $N$ depends on $d$). Such a map may not be an embedding, however $\phi_d:X\rightarrow \phi(X)$ is an algebraic fiber space. My question is the following. As I increase the value $d$ the image $\phi_d(X)\subset \mathbb{P}^N$ may change, however, as a matter of fact such an image "stabilizes" as $d$ gets larger. Meaning that if $d$ is large enough, the image if $\phi_d$ is the "same" regardless $d$.

-What is the reason for this to happen? -What is going on with all the sections of $\mathcal{L}^{\otimes d}$ that I am getting as I increase the value of $d$?. I'll appreciate any comment.

As a result, due to the fact that after a while we no longer care about the value of $d$, we can associate the space $X\rightarrow \phi(X)$ to the line bundle $\mathcal{L}$. Here, the variety $\phi(X)$ no longer depends on $d$.

Could someone comment further about the word "stabilizes"?.

-
I think the point is that the $k$-algebra $\oplus_d H^0(X,L^d)$ is finitely-generated, for $L$ a basepoint-free (or more generally semi-ample) line bundle, by a theorem of Zariski. That means there exists some $d_0$ such that any section of any power $L^d$ can be obtained as a product of section of powers $L^k$, with all $k$ less than or equal to $d_0$. –  Artie Prendergast-Smith Nov 11 '10 at 10:51
(just noticed this is a very old question) –  Artie Prendergast-Smith Nov 11 '10 at 10:53
Since this was already bumped, I fixed a typo in the title. –  Karl Schwede Jan 18 '14 at 1:30

Let $R(X,\mathcal L)=\oplus_d H^0(X,\mathcal L^{\otimes d})$ as graded rings, $s_0,\dots s_m\in H^0(X,\mathcal L^{\otimes d})$ and finally $R(X,\mathcal L,s_{\cdot})$ the (graded) subring generated by the $s_0,\dots s_m$ in $R(X,\mathcal L)$.

Facts:

1. ${s_0,\dots,s_m}$ define a rational map $\sigma: X\dashrightarrow \mathbb P^m$. If ${s_0,\dots,s_m}$ generate $H^0(X,\mathcal L^{\otimes d})$, then $\sigma$ agrees with $\phi_t$.

2. If $\vert\{s_0,\dots,s_m\}\vert$ is a basepoint-free linear system, then $\sigma$ is a morphism. and $\sigma(X)\simeq {\rm Proj}\, R(X,\mathcal L, s_{\cdot})$.

3. If $R(X,\mathcal L,s_{\cdot})$ has the property that for some $a\in\mathbb N$, $R(X,\mathcal L,s_{\cdot})_{ak}=R(X,\mathcal L)_{ak}$ for all $k\in \mathbb N, k\gg 0$, then ${\rm Proj}\, R(X,\mathcal L, s_{\cdot})\simeq {\rm Proj}\, R(X,\mathcal L)$ (think of the $a$-uple embedding).

4. Since $R(X,\mathcal L)$ is finitely generated, if $s_0,\dots s_m\in H^0(X,\mathcal L^{\otimes d})$ are chosen so that they generate $H^0(X,\mathcal L^{\otimes d})$, then for large enough $d$ the property in 3) will be satisfied, so by 1) and 2) $\phi_d(X)\simeq {\rm Proj}\, R(X,\mathcal L)$ which is independent of $d$, hence it is stabilized.

-
• The sequence stabilizes because any increasing sequence of bounded integers (the dimensions of the images of $X$) stabilizes, but I assume you mean something different.

• Suppose that $X\to|L|$ has already stabilized, then the map $X\to|2L|$ decomposes through the map $|L|\to\mathbb{P}\mathrm{Sym}^2 H^0(L)\to\mathbb{P} H^0(2L)$.

Where the first map is the Veronese, and the second is a projection.

-
The dimensions of the vector spaces H^0(X,L^d) do not form a bounded sequence. Take, for example, h^0(P^1, O(d)) = d+1. –  Alberto García-Raboso Nov 22 '09 at 16:03
but the dimensions of the images of X do. They are bounded by the dimension of X –  David Lehavi Nov 22 '09 at 19:27
Sure. I did not get that from you answer though. Maybe you should edit it to clarify. –  Alberto García-Raboso Nov 22 '09 at 20:10
Another reason to edit it is that I cannot undo the downvote unless you do... –  Alberto García-Raboso Nov 22 '09 at 20:11


text:
## Name

SlaterOrbital — Class for representing a Slater orbital.

## Synopsis

Namespace: NanoLanguage
SlaterOrbital(
principal_quantum_number,
angular_momentum,
slater_coefficients,
weights
)

## Description

Constructor for the Slater orbitals.

### SlaterOrbital Arguments

principal_quantum_number

The Principal quantum number (n) of the orbital.

Type: Positive integer.

angular_momentum

The Azimuthal quantum number (l) of the orbital.

Type: Positive integer.

slater_coefficients

The Slater coefficients as inverse length

Type: A single value or array of strictly positive PhysicalQuantity instances with a unit of inverse length, e.g. 0.3*Bohr**(-1) or [0.3, 0.4]*Bohr**(-1).

weights

The weight for each of the Slater coefficients.

Type: A single value or array of strictly positive dimensionless values, with each value corresponding to a given Slater coefficient, e.g. 0.1 or [0.3, 0.5].

### SlaterOrbital Methods

A SlaterOrbital object provides the following methods:

• angularMomentum(): Return the angular momentum for the orbital.

### Usage Examples

Define a 1s Slater orbital from a single exponential function

carbon_2s = SlaterOrbital(
principal_quantum_number=2,
angular_momentum=0,
slater_coefficients=[ 2.0249*1/Bohr ],
weights=[ 0.76422]
)

Define a 2p Slater orbital as superposition of two exponential functions

carbon_2p = SlaterOrbital(
principal_quantum_number=2,
angular_momentum=1,
slater_coefficients=[ 1.62412*1/Bohr , 2.17687*1/Bohr ],
weights=[ 0.27152, 0.73886]
)

### Notes

Within the extended-Hückel Model, the electronic structure is expanded in a basis of local atomic orbitals (LCAO's)

where is a spherical harmonic and is a Slater orbital

The Slater orbital is described by the adjustable parameters , and . These parameters must be defined for each angular shell of valence orbitals for each element.

Table 26: Slater orbital parameters

Symbol SlaterOrbital parameters
principal_quantum_number
angular_momentum
slater_coefficients
weights

In the current version we provide a Hoffmann parameter set which is appropriate for organic molecules. The parameter set is available with the keyword HoffmannHuckelParameters.ElementName, where ElementName is the name of the element. For crystal parameters, we refer to the website of J. Cerda. and his paper [11].


text:
# Understanding Dempster et al. on expectation maximization

I'm reading about expectation maximization from Dempster, Laird and Rubin's original paper which can be found from the following link:

http://web.mit.edu/6.435/www/Dempster77.pdf

My questions are from pages 1 and 2. I have added those particular parts into the image below and tried to be as clear as possible with my questions (4 questions in the image, highlighted with red numbers 1, 2, 3, 4). Hope someone could make things clearer for me :)

To summarize my questions in the picture are:

1) Have I understood the relationship between the variables correctly?

2) What does the text in the green box mean exactly?

3) How to interpret these formulas

4) WHAT IS GOING ON HERE?!...this doesn't seem clear at all! x)

• The text clearly states what $g(y|\phi)$ is: a "$\text{family of sampling densities}$", though depending on how you view $\phi$, you could think of it as a conditional density or a family indexed by $\phi$. Why would it be a probability? In 4, $\pi$ is just a parameter there, on which the 4 population probabilities depend. – Glen_b Nov 28 '13 at 22:17

1. $\mathcal{Y}$: observed $\mathcal{X}$: unobserved In other words,X is the set of latent variables. So, your picture makes sense.


text:
# CVA using difference between 2 counterparty's spreads

The approximation to calculate CVA as a spread is $CVA = Spread * Expected$ $Exposure$. I assume this means the counterparty's spread over a proxy for the risk free rate such as LIBOR or OIS. Is this an incorrect understanding?

I came across an FRM exam practice question created by GARP (the entity that runs the exam) which gave a scenario where both the bank and its counterparty experienced spread widenings due to rating downgrades. Where the banks spread went from 20bps to 150bps and its counterparty's spread went from 130bps to 170bps. The CVA a was given by (170-150)*Expected Exposure and was a reduction from the previous CVA of (130-20)*Expected Exposure. (Note, there is an assumption to ignore DVA)

This doesn't make sense to me. The counterparty to the bank suffered a downgrade and a resulting spread widening yet the CVA charge decreases?

I can't share the exact question, but here is essentially what it was

This was the question:

Foo Company is a frequent user of swaps with Acme Bank. Acme bank was recently downgraded from a rating of AA- to A+ and at the same time, Foo Company was downgraded from A to A-. As a result of the downgrades, the credit spread for Acme bank increased from 20bps to 150bps, and the credit spread for Foo Company increased from 130bps to 170 bps. The question asks what realistic changes the counterparties can request to their CVA charge, given a set of multiple choice.

Because Foo Company has a lower credit rating than the bank, it would typically pay a CVA charge which would be a function of the relative credit spreads between the two entities. As the the credit spread between the two has narrowed after the downgrade to only 20bps, Foo Company can request a reduction in their CVA charge.

• It is hard to understand since we do not have the context. Is those practice questions openly available? – Gordon Nov 22 '15 at 15:40
• I'll try and find it, they are not publicly available – AfterWorkGuinness Nov 22 '15 at 15:41
• I've updated the question. – AfterWorkGuinness Nov 22 '15 at 16:00
• It appears to me that the DVA is considered. Then the charge is basically CVA - DVA. As the downgraded spreads are now closer than they were previously, the bilateral CVA is reduced. – Gordon Nov 22 '15 at 16:41

What GARP considered for the question is a first-to-default CVA, meaning that the bank looks at what it expects to lose if its counterparty defaults before it does. In this case the formula would be: $\mathrm{CVA}=\left(Spread_{Counterparty} - Spread_{Bank} \right) \times EE$


text:
#### Archived

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

# OpenGL Fonts using SDL/OpenGL

This topic is 5619 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic.

## Recommended Posts

Hi there, I''ve been looking through the net for a few hours now but couldn''t find anything realted to what I''m looking for. I want to write text to the screen i.e. using fonts. I''ve found lots of examples, but they all use the Windows API. However, in my application I''m using SDL to allow portability. Also on NeHe''s site there is a port to SDL, but it still contains some Linux specific stuff. So during my search I found a small library called BFont++. It uses SDL and works nice IF I don''t use any openGL. They provide a sample source, but as I said, it doesn''t use OpenGL. Pure SDL here. However, I want to be able to draw some text to my OpenGL Surface. Now I have no clue about how I could do this. I though maybe I could use 2 SDL_Surfaces and somehow render the game to one and the font to the other and then combine them. However, I have no clue about how this could be done. So if anyone knows a place where I could find information about using fonts with SDL/OpenGL in Win32 that''s be nice. Or of you have any suggestion or idea or whatever, please post it. Thanks in advance

##### Share on other sites
Porting a simple Windows OGL application to SDL is TRIVIAL.
Just look on the SDL samples, on OGL, and you will have no problems adapting the NEHE tutorials to SDL (as long as they don''t use windows functions to do the fonts stuff, so try the BMP font routines).
But what you should do is to write your very own fonts function.
Just load the fonts from a texture, and draw small rectangles, with the letters. It took me only like 2 hours to do a printstring() function, that does that.

Height Map Editor | Eternal Lands | Fast User Directory

##### Share on other sites
@Jeff K: Thanks for the link. Though FTGL seems a little bit of an overkill for what I''m trying to do. I just need some simple text to display the score of the player. Nothing fancy needed.

@Raduprv: I can port the Windows Code from NeHe to OpenGL. However the point is that he does use windows specific function to Build the Font. He uses CreateFont(...) and then a wgl function

  GLvoid BuildFont(GLvoid)					{	HFONT	font;								HFONT	oldfont;	base = glGenLists(96);							font = CreateFont(-24, 0, 0, 0, FW_BOLD, FALSE,	FALSE,FALSE,							ANSI_CHARSET,					OUT_TT_PRECIS,					CLIP_DEFAULT_PRECIS,			ANTIALIASED_QUALITY,			FF_DONTCARE|DEFAULT_PITCH,		"Courier New");						oldfont = (HFONT)SelectObject(hDC, font);             wglUseFontBitmaps(hDC, 32, 96, base);					SelectObject(hDC, oldfont);						DeleteObject(font);						}

So that''s what NeHe uses for Building the DisplayLists. I pretty much understand what is going on, but I don''t know how I would go about implementing my own version of that using SDL.

Everything else in his code is perfectly clear and I know how to port it. Just not this one.

##### Share on other sites
There are quite a few fonts tutorials on NeHe, some of them do not use windows specific functions.

Height Map Editor | Eternal Lands | Fast User Directory

##### Share on other sites
Why not use SDL_ttf ( http://www.libsdl.org/projects/SDL_ttf/ ) it works on Windows and Linux and allows you to use True Type fonts and is built to work with SDL. I have used it myself in the JEDI-SDL ( Delphi/Kylix headers @ http://www.sf.net/projects/jedi-sdl )

Alternatively, have a look at tutorial Nehe''s Tutorial 21 ( http://nehe.gamedev.net/data/lessons/lesson.asp?lesson=21 ) which uses Bitmap fonts texture in a simple Ortho game. The SDL port can be downloaded from http://nehe.gamedev.net/data/lessons/linuxsdl/lesson21.tar.gz.

Either way you should be up an running in no time.

1. 1
2. 2
3. 3
Rutin
19
4. 4
5. 5

• 14
• 30
• 13
• 11
• 11
• ### Forum Statistics

• Total Topics
631780
• Total Posts
3002314
×


text:
# Prove: $\binom{n}{0}F_0+\binom{n}{1}F_1+\binom{n}{2}F_2+\cdots+\binom{n}{n}F_n=F_{2n}$

Prove: $\binom{n}{0}F_0+\binom{n}{1}F_1+\binom{n}{2}F_2+\cdots+\binom{n}{n}F_n=F_{2n}$; I was stuck with this question for a while... Help me please!!! Thanks!!!

-
Induction is sufficient. –  mez Feb 10 '13 at 13:41

Hint: Binet's formula + Binomial formula. Also, $\varphi^2=\varphi+1$ and $\varphi^{-2}=2-\varphi$.

$$\hskip 1.5in \displaystyle \sum_{\ell=0}^n \binom{n}{\ell}\frac{\varphi^\ell-(1-\varphi)^\ell}{\sqrt5}=\frac{(1+\varphi)^{\ell}-(2-\varphi)^\ell}{\sqrt5}=F_{2n}$$

-

I accidentally stumbled across this old question while studying some facts about generating functions and could not resist posting this answer. Take an ordinary generating function of the LHS: $$G(x)=\sum_{n\ge0}\sum_{0\le k\le n}\left(\begin{array}{c} n\\ k \end{array}\right)F_kx^n$$ Change the order of summation to obtain

$$G(x)=\sum_{k\ge0}\sum_{n\ge k}\left(\begin{array}{c} n\\ k \end{array}\right)F_kx^n=\sum_{k\ge0}F_k\sum_{n\ge0}\left(\begin{array}{c} n+k\\ k \end{array}\right)x^{n+k}\\=\sum_{k\ge0}F_kx^k\sum_{n\ge0}\left(\begin{array}{c} n+k\\ n \end{array}\right)x^n=\sum_{k\ge0}F_kx^k\frac{1}{\left(1-x\right)^{1+k}}\\=\frac{1}{1-x}\sum_{k\ge0}F_k\left(\frac{x}{1-x}\right)^k$$ Now the expression under the sum is just the ordinary generating $F(z)$function for $F_n$ $$F(z)=\frac{z}{1-z-z^2}$$ where $z=\frac{x}{1-x}$. Substituting we obtain $$G(x)=\frac{x}{1-3x-x^2}$$ The last expression is the generating function for $F_{2n}$ as can be ascertained by calculating $\frac{1}{2}\left[F(x)+F(-x)\right]$

-

A counting argument:

The number of ways of climbing $n$ stairs, taking $1$ or $2$ steps at a time is $F_n$ (Try proving it).

Now suppose we had to climb $2n$ stairs. Note that we need to take at least $n$ moves.

We now consider the position after taking exactly $n$ moves. For each such position, we consider where we are and how many ways we can cover the rest.

This we do by considering the number of steps of $2$ we take.

If we take $k$ steps of $2$, then we take $n-k$ steps of $1$ for the first $n$ moves. We end up at step $n+k$, thus leaving $n-k$ steps to cover. These $n-k$ steps can be covered in $F_{n-k}$ ways and the number of ways of getting there is same as the number of ways of choosing $k$ moves of $2$ from $n$, which is $\binom{n}{k}$.

Thus as $k$ ranges from $0$ to $n$, we have that the number of ways of covering $2n$ stairs is

$$F_{2n} = \sum_{k=0}^{n} \binom{n}{k} F_{n-k}$$

Since $\binom{n}{k} = \binom{n}{n-k}$ we get

$$\binom{n}{0}F_0 + \binom{n}{1}F_1 + \dots + \binom{n}{n}F_n = F_{2n}$$

A simple generalization of this argument gives us, for $2n \le m$

$$\binom{n}{0} F_{m-2n} + \binom{n}{1} F_{m-2n+1} + \dots + \binom{n}{n} F_{m-n} = F_m$$

-


text:
# How do I keep a string of text together without it doing a line break?

I'm writing up a long paper, in which in prose I have various equations. However, I do not want a line break to occur within the equation - I want the equation to stick together. I want to do this without displaying the equation, though. Is there a way to do this?

-
Preventing an in-line math expression to break (boxing it with, for example, \mbox) will produce overfull boxes (the equation will overflow the margin), which isn't desirable; you could try rephrasing the lines containing the equation so that a line break won't occur inside the equation. –  Gonzalo Medina Mar 21 '12 at 2:39
Welcome to TeX.SE! Please consider providing a bit more information about your documrnt's setup (such as the line width) and the average length of the inline equations. –  Mico Mar 21 '12 at 4:19
You could force a line break before the equation with \linebreak[4] –  Vivi Mar 21 '12 at 7:02
if breaking an in-line expression is really bad, an experienced copyeditor would most likely display it without a number -- $...$ will accomplish that. this is usually better than forcing a line break and stretching out the preceding text, or leaving a short line. –  barbara beeton Mar 21 '12 at 13:23

Anything you enclose within an \hbox or the equivalent LaTeX \mbox will not break. However overflowing into the margins is not a good idea. In the minimal below you can see the effect by using the geometry package to show a border around the normal text area.

\documentclass{octavo}
\usepackage[showframe=true]{geometry}
\begin{document}
\mbox{This is an extremely long line. This is extremely long. $a^2+c^2=42$ }
\end{document}

For long equations rather use the breqn package to break them at an appropriate point.

-
+1: I like the idea of using the geometry package to visualize the size of boxes. –  Tatjana Heuser Mar 21 '12 at 9:26
@TatjanaHeuser -- Thanks there are also the layouts and layout packages, you should give them a try. –  Yiannis Lazarides Mar 21 '12 at 9:29

I use a solution to this problem that cannot be used always. Once I finish my work, I go thru the "almost-final" version of the whole paper and when an inappropriate break appears (inside equation, stupidly-broken name/date/... that does not look good in my opinion), I rephrase the text so that this piece appears in the middle of the line. Actually, you have to do the very same thing with overfull \hboxes anyways, but they are at least listed in the log.

Of course this needs you to be the author (of to have the author's permission to do small modifications) and it might be against the idea of TeX/LaTeX in someone's opinion (the idea is that you shouldn't have to do such things manually).

Edit / Added: You can decide to enclose your math into \mbox{...} to disallow like breaking, as Yiannis Lazarides says in his answer. In this case the inline math will often go out of the line. You can visualize these overfull boxes by adding [draft] parameter to your \documentclass (works for most standard classes).

-
+1 This is the best solution. That is what I do as well. I have an overfullrule1pt normally during drafts and helps me visualize as I go along. Between various edits they tend to disappear. –  Yiannis Lazarides Mar 21 '12 at 10:41
I could mention the draft option that visualizes overfull \hbox, I'm adding that. –  yo' Mar 21 '12 at 10:50
@tohecz -- if you've read the texbook, you'd know that this is exactly what don knuth recommends (or at least practices himself). so it's not "against the idea of tex". –  barbara beeton Mar 21 '12 at 13:25
@barbarabeeton Thanks for details, I changed "is completely" to "might be" ;) –  yo' Mar 21 '12 at 13:26


text:
# Wydawnictwa / Czasopisma IMPAN / Fundamenta Mathematicae / Wszystkie zeszyty

## Torsion in graph homology

### Tom 190 / 2006

Fundamenta Mathematicae 190 (2006), 139-177 MSC: Primary 57M27; Secondary 05C15, 55N35. DOI: 10.4064/fm190-0-5

#### Streszczenie

Khovanov homology for knots has generated a flurry of activity in the topology community. This paper studies the Khovanov type cohomology for graphs with a special attention to torsion. When the underlying algebra is $\mathbb{Z}[x]/(x^2)$, we determine precisely those graphs whose cohomology contains torsion. For a large class of algebras, we show that torsion often occurs. Our investigation of torsion led to other related general results. Our computation could potentially be used to predict the Khovanov–Rozansky $sl(m)$ homology of knots (in particular $(2,n)$ torus knot). We also predict that our work is connected with Hochschild and Connes cyclic homology of algebras.

#### Autorzy

• Laure Helme-GuizonDepartment of Mathematics
The George Washington University
1922 F street NW
Washington, DC 20052, U.S.A.
e-mail
• Józef H. PrzytyckiDepartment of Mathematics
The George Washington University
Old Main Bldg, 1922 F St. NW
Washington, DC 20052, U.S.A.
e-mail
• Yongwu RongDepartment of Mathematics
The George Washington University
1922 F street NW
Washington, DC 20052, U.S.A.
e-mail

## Przeszukaj wydawnictwa IMPAN

Zbyt krótkie zapytanie. Wpisz co najmniej 4 znaki.

Odśwież obrazek


text:
# More On Data Types Ans.

Home / U2: Math & Logic / More On Data Types Ans.

Print the type of all of the following variables. Try to guess what it is beforehand.

In [4]:
w = "1"

x = 2.0

y = 3

z = x + y

print(type(w))
print(type(x))
print(type(y))
print(type(z))

<class 'str'>
<class 'float'>
<class 'int'>
<class 'float'>

In [8]:
# one will need conversion!
answer = int(w) + x + y + z

11.0

Now, add all of them together. If an error is produced, find and fix it.

Get this program to run:

w = 10

x = "1"

y = "20"

z = 30.0

answer = x + y + z

I did the following. It is normal to see some variation, as long as the answer is right.

In [12]:
w = 10

x = "1"

y = "20"

z = 30.0

answer = w + int(x) + int(y) + z

61.0

print(type(answer))

<class 'float'>


text:
# Thread: Finding range of fuctions.

1. ## Finding range of fuctions.

hello.. Could someone please show me how to find the range of these equations. Thanks ~~

Find domain for the following relation:
a) (x + 2)^2 + (y-3)^2 = 49

Find the range of the following functions:
a) m(x) = (x^2 + 2x +5)
b) (x – 2)^2 + (y+1)^2 = 64
c) h(x) = √(x+4) + √(5-x)

Just some homework qus i m stuck with and cant work out... Thanks for your help

2. Originally Posted by tom_asian
hello.. Could someone please show me how to find the range of these equations. Thanks ~~

Find domain for the following relation:
a) (x + 2)^2 + (y-3)^2 = 49

Find the range of the following functions:
a) m(x) = (x^2 + 2x +5)
b) (x – 2)^2 + (y+1)^2 = 64
c) h(x) = √(x+4) + √(5-x)

Just some homework qus i m stuck with and cant work out... Thanks for your help
The simplest way to find the range is to graph the relation/function.
a) $(x + 2)^2 + (y - 3)^2 = 49$
This is a circle of radius 7, with center (-2, 3), so the y value is between 3 - 7 = -4 and 3 + 7 = 10. Thus the range is $[-4, 10 ]$.

a) $m(x) = \sqrt{x^2 + 2x +5}$
This can be modified to
$m(x) = \sqrt{(x + 1)^2 + 4}$
Thus the minimum value of the quadratic function is 4, so the minimum m value is 2. There is no upper limit on the radicand, so the upper "value" of m is $\infty$. Thus the range is $[2, \infty )$.

b) $(x - 2)^2 + (y + 1)^2 = 64$
This is a circle of radius 8, with center (2, -1). You do this one.

c) $h(x) = \sqrt{x + 4} + \sqrt{5 - x}$
This is a bit trickier to see what to do, so I graphed it. (See below.)
The minimum value of the range is apparently 3. The peak of the function is at x = 1/2 (we can prove this with Calculus, but you can also see it on the graph), so the maximum y value is $h \left ( \frac{1}{2} \right ) = \sqrt{\frac{1}{2} + 4} + \sqrt{5 - \frac{1}{2}} = 3 \sqrt{2}$
So the range is $[ 3, 3\sqrt{2} ]$

-Dan

3. Originally Posted by tom_asian
c) h(x) = √(x+4) + √(5-x)
Here is a purely algebraic way of doing this one.

The domain of this function is $-4\leq x\leq 5$.

Consider the equation for $y$:
$y=\sqrt{x+4}+\sqrt{5-x}$
The question is for what $y$ does this have at least one real solution for $x\mbox{ on }[-4,5]$.

Thus,
$y^2 = x+4 + 5 - x + 2\sqrt{(x+4)(5-x)}$
$y^2 - 9 = 2\sqrt{20+x-x^2}$
$(y^2-9)^2 = 80+4x-4x^2$
$-4x^2+4x+[80-(y^2-9)^2]=0$
In order to have a real solution we need,
$16 + 16[80-(y^2-9)^2]\geq 0$
$81 - (y^2-9)^2 \geq 0$
Thus,
$(y^2-9)^2 \leq 81$
With the solution,
$x=\frac{-4\pm \sqrt{16+16[80-(y^2-9)^2]}}{-8}$
$x=\frac{1\pm \sqrt{81-(y^2-9)^2}}{2}$
But we want,
$-4\leq 1-\sqrt{81-(y^2-9)^2} \mbox{ and }1+\sqrt{81-(y^2-9)^2} \leq 5$
If you solve these inequalities system (which is not that hard) you get what topsquark got.