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It’s complicated. disposable income. Disposable personal income is often monitored as one of the many key economic indicators used to gauge the overall state of the economy., DPI=Personal Income−Personal Income Taxes\begin{aligned} &\text{DPI} = \text{Personal Income} - \text{Personal Income Taxes} \\ \end{aligned}DPI=Personal Income−Personal Income Taxes. For several months in 2005 and 2006, the average personal savings rate dipped into negative territory for the first time since 1933. This means that in those years, Americans were spending all of their disposable income each month and then tapping into savings or debt for further spending. With the price of living steadily rising and wages failing to keep up with the trend everyone is needing to tighten their belts a little bit more. Learn More. Household disposable income measures the income of households (wages and salaries, self-employed income, income from unincorporated enterprises, social benefits, etc. U.S. PCE are the value of the goods and services purchased by, or on the behalf of, U.S. residents and are tracked as an important measure of the economy's strength. U.S. per capita disposable personal income by state 2019 | Statista David Kindness is an accounting, tax and finance expert. Everyday essentials from food to travel have slowly increased in price and the uncertainty surrounding Brexit isn’t helping matters either. Aggregate demand is the total amount of goods and services demanded in the economy at a given overall price level at a given time. This is actually referred to as the … An accurate general definition of income is not easy to provide. After-tax income. "Disposable Personal Income." Fact Sheet #30: The Federal Wage Garnishment Law, Consumer Credit Protection Act's Title III (CCPA). https://www.sofi.com/learn/content/what-is-disposable-income Bureau of Economic Analysis. Personal outlays increased by $217.5 billion in September 2020 from the month before.. Business. Disposable Income is the amounts of money left with the person after paying all the direct taxes. He has helped individuals and companies worth tens of millions achieve greater financial success. Voluntary deductions such as 401 ( k ) contributions and health and life insurance are generally considered part of disposable income. Discretionary income is disposable income (after-tax income), minus all payments that are necessary to meet current bills. 이 문서는 2018년 2월 18일 (일) 15:30에 마지막으로 편집되었습니다. It suggests we have "disposable" money that we really don't care about. What Do Americans Really Spend Their Money On? PCTP are non-tax payments made to governments—licenses, permits, and fees. The U.S. Bureau of Economic Analysis (BEA) releases data on the monthly changes in personal income, DPI, and consumer spending, which is known more formally as personal consumption expenditures (PCE). While employment got within 3.7 per cent of its pre-pandemic levels during the quarter, it wasn’t enough to offset the wind-down of government supports, as employment insurance benefits dropped almost 50 per cent in the quarter, the report said. Learn more. Disposable Income vs. Disposable income minus all payments for necessities (mortgage, health insurance, food, transportation) equals discretionary income. The formula is … By using Investopedia, you accept our, Investopedia requires writers to use primary sources to support their work. It's calculated using the following simple formula: disposable income = personal income – personal current taxes. Accessed July 30, 2020. Disposable income determines what sort of lodging one can afford, how often one can go out to eat, how much one can save, etc. Court orders for child support or alimony may specify garnishments of up to 60 percent of disposable income. As of 2019, the amount garnished may not exceed 25% of a person's disposable income or the amount by which a person's weekly income exceeds 30 times the federal minimum wage, whichever is less.. The personal savings rate is the percentage of disposable income that goes into savings (such as for retirement) or use at a later date. Marginal propensity to consume represents the percentage of each additional dollar of disposable income that gets spent, while marginal propensity to save denotes the percentage that gets saved. Discretionary income can be spent on restaurant meals, investments, travel, entertainment, and any other non-essential items or services. Creditors may garnish up to 25 percent of disposable earnings, or the amount of disposable earnings in excess of 30 times the federal minimum wage, whichever is less. Personal Saving Rate: Is It Real and Is It a Puzzle?" Learn more about disposable income, its importance as an economic indicator, and how it differs from discretionary income. Therefore, the calculation of disposable income will be as follows, = 720,000 – 60… https://corporatefinanceinstitute.com/.../disposable-income Bureau of Economic Analysis. Disposable income, that portion of an individual’s income over which the recipient has complete discretion. Disposable income is the portion of income available to an income earner after all income taxes are deducted. It's an important economic indicator for the country. Disposable income, also known as disposable personal income (DPI) or net pay, is the amount of money you have left over from your total annual income after paying all direct federal, state, … Accessed Oct. 31, 2020. Disposable income is the portion of an worker’s paycheck that is subject to garnishments. Five ways to boost your income in 2020. Page 491. For most people, taxes far and away represent the greatest component of the deducted amount. Disposable income is an often-misunderstood term. In the Household Income and Basic Amenities Survey Report 2019 released today, the Department of Statistics Malaysia’s (DOSM) figures showed income inequality calculated based on two categories ― gross income (which is before tax and contributions to social security scheme are paid) and disposable income (which is after deducting tax, zakat and social security scheme contributions). You might look at it as your fun money to spend on things you don’t really need, after your essential expenses are covered. Disposable Personal Income in the United States averaged 5611.19 USD Billion from 1959 until 2020, reaching an all time high of 19035.90 USD Billion in April of 2020 and a record low of 351.54 USD Billion in January of 1959. Disposable income is the net income available to invest, save, or spend after deducting income taxes. Bureau of Economic Analysis. Think of it as the money you have discretion over—e.g. n. 1. The amount of disposable income for the residents of a country is closely followed by economists, as is the level of consumer spending, which depends in part on disposable income. Accessed July 30, 2020. Disposable income has two definitions, depending on whether an individual is going through a wage garnishment or bankruptcy. This household's disposable income would then be$75,000 ($100,000 –$25,000). As such, businesses that sell discretionary goods tend to suffer the most during recessions and are watched closely by economists for signs of both recession and recovery. The fiscal multiplier measures the effect that increases in fiscal spending will have on a nation's economic output, or gross domestic product (GDP). It is total personal income after subtracting taxes and minimal survival expenses (such as food, medicine, rent or mortgage , utilities, insurance, transportation, property maintenance, child support, etc.) Based on the above information you are required to calculate the Personal Disposable Income for the entire year. Compare with discretionary income ‘the rents of tenants in work reached 21 per cent of disposable income’ Disposable income is calculated by subtracting income taxes from income. A country's average disposable income is … disposable income. (Economics) the total amount of money that the individuals in a community, country, etc, have available to buy consumer goods. The savings rate is the percentage of money taken from personal income and saved. Personal Income. For example, consider a family with a household income of $100,000, and the family has an effective income tax rate of 25% (versus marginal tax rate). The federal government uses a slightly different method to calculate disposable income for wage garnishment purposes. Not only is it one of the major determinants of consumer spending, but it is also one of the five determinants of demand. What Is Disposable Income? Spend & Save. Disposable income is the money you have left from your income after you pay taxes. Sometimes, the government garnishes an income earner's wages for payment of back taxes or delinquent child support. Cambridge Dictionary +Plus You can learn more about the standards we follow in producing accurate, unbiased content in our. The BEA estimated U.S. PCE increased by$201.4 billion, or 1.4%, during the same time period. Household disposable income measures the income of households (wages and salaries, self-employed income, income from unincorporated enterprises, social benefits, etc. The Decline in the U.S. Disposable income can be calculated as personal income – personal current taxes. Investopedia uses cookies to provide you with a great user experience. Please note that OECD reference year from 2010 to 2015 changed on Tuesday 3rd of December, 2019. The rate was 14.3 percent in September 2020, down from 14.8% in August.. It can also be described as the percentage of their income they have left after taxes and spending. The amount that U.S. residents have left to spend or save after paying taxes is important not just to individuals but to the whole economy. We also reference original research from other reputable publishers where appropriate. For a person living in an economic family, disposable income is deemed to be a portion of the total family income after taxes. U.S. Department of Labor. How to use disposable income in a sentence. 자세한 내용은 이용 약관을 참조하십시오. Learn more about disposable income, its importance as an economic indicator, and how it differs from discretionary income. ; 개인정보처리방침 She is a financial writer and editor with experience at several major financial publications. Accessed Oct. 31, 2020. Disposable income is sometimes referred to as disposable personal income, net pay or take-home pay. Income includes wages and salaries, interest and dividend payments from financial assets, and … Disposable Personal Income in Canada is expected to be 1382690.00 CAD Million by the end of this quarter, according to Trading Economics global macro models and analysts expectations. Discretionary income is disposable income minus the cost of all necessary expenses, including food and housing. It is the actual income which is spent by individuals and families on consumption after paying direct taxes. Definition of disposable income. U.S. personal income is the income received by, or on behalf of, all U.S. residents from all sources, both domestic and global. How much disposable income a person or a population of people has can help economists determine how much money they might spend on goods and services or save. Disposable income should not to be confused with discretionary income, which is what is left of your disposable income after you’ve paid for necessities like housing (in the form of rent or a mortgage payment), health care, food, electricity, and transportation. Please refer to the dataset Disposable income and net lending – net borrowing, 2019 archive to access longer time series based on the methodology prior to the 2019 benchmark revisions. Discretionary income is the amount of an individual's income that is left for spending, investing, or saving after taxes and necessities are paid. "Fact Sheet #30: The Federal Wage Garnishment Law, Consumer Credit Protection Act's Title III (CCPA)." Disposable income is the money you have left from your income after you pay federal, state, and local taxes and any other mandatory payments to a government. • Real personal disposable income rose 15 percent over the period. Disposable income, also known as disposable personal income (DPI), is the amount of money that households have available for spending and … • A Labour victory would have boosted their disposable income by £311, mainly because of the increase in child benefit. Bureau of Economic Analysis. disposable income 어의, 의미, disposable income의 의미: the amount of money you have left to spe...: 자세히 알아보기. Disposable Income Definition. Household adjusted disposable income includes income from economic activity (wages and salaries; profits of self-employed business owners), property income (dividends, interests and rents), social benefits in cash (retirement pensions, unemployment benefits, family allowances, basic income support, etc. after your financial obligations, you can choose to save or to spend what’s left on … "Personal Saving Rate." Real DPI and real PCE increased an estimated 0.7% and 1.2%, respectively, in September 2020 from August 2020. The amount that U.S. residents have left to spend or save after paying taxes is important not just to individuals but to the whole economy. It is used by analysts to measure consumer spending, payment ability, probable future savings, and the overall health of a nation’s economy. The money you have left over from your salary or wages after you’ve paid federal, state, and local taxes is your disposable income or disposable personal income (DPI). Economists use DPI as a starting point to gauge households' rates of savings and spending. For example, economists use disposable income as a starting point to calculate metrics such as discretionary income, personal savings rates, marginal propensity to consume (MPC), and marginal propensity to save (MPS). Discretionary income is the amount of disposable income you have left after you pay for necessities like housing, food, and healthcare. Taxes and legally-required deductions don’t count towards disposable earnings. Disposable Personal Income in the United States decreased to 17277.62 USD Billion in November from 17515.20 USD Billion in October of 2020. What You Need to Know About U.S. Tax Returns If You Have a Green Card, Options for Paying Off Tax Debts With the IRS, U.S. GDP Jumps 33.1% in Third Quarter After Record Contraction, What Durable Goods Orders Tell You About the Future, The Worst Economic Contractions in U.S. History, Personal Income and Outlays, September 2020. Discretionary income is the first to shrink amid a job loss, pay reduction, or economic downturn. The BEA also tracks U.S. personal outlays, which are the sum of all PCE, personal interest payments (PIP), and personal current transfer payments (PCTP). : income that is left after paying taxes and for things that are essential, such as food and housing I don't have enough disposable income to … The federal wage garnishment law states that for the purpose of wage garnishment, disposable earnings is the amount of money you have left after subtracting deductions required by federal, state and local laws from your paycheck. Contact Personnel. If you want to be a better budgeter, you'll need to brush up on some budgeting terms. In addition to income taxes, the government subtracts from gross income retirement plan contributions required by law when calculating disposable income for wage garnishment purposes. Returning to the above example, if the family described is required to contribute $5,000 to a retirement plan, the household's disposable income for wage garnishment purposes shrinks from$75,000 to $70,000. James Moore Will Britons’ £200bn pandemic savings fuel recovery? You can also choose to save a lot or a little of it. Disposable Income UK Definition. With a wage garnishment, disposable income is the amount of money left after an employer has made all the required deductions. The amount of money a creditor may legally garnish from your income is a percentage of your disposable earnings. ), after taking into account net interest and dividends received and the payment of taxes and social contributions. (money available for luxuries) 가처분 소득 : Disposable income is what you have left after you have paid for … The multiplier effect measures the impact that a change in investment will have on final economic output. disposable income n noun: Refers to person, place, thing, quality, etc. Lifestyle. disposable income definition: 1. the money that you can spend as you want and not the money that you spend on taxes, food, and…. From the Cambridge English Corpus However, an increase in government expenditure will not necessarily induce a lower expected present value … to maintain a certain standard of living . These include white papers, government data, original reporting, and interviews with industry experts. Disposable income can be calculated for a household or for a nation and has important economic significance. Those three levels of taxes consist of income and property taxes and paycheck deductions for Social Security, Medicare, and unemployment insurance. Rachel Morgan Cautero has been a financial planning expert for The Balance since 2017. (However, it does not include realized or unrealized capital gains or losses from investments.) The formula is simple: personal income minus personal current taxes. Accessed July 30, 2020. What is Disposable Personal Income? Definition: Disposable income, sometimes called disposable personal income (DPI), is the total earnings a household makes that are available to save or spend after taxes have been paid.In other words, it’s a household’s take home pay after taxes and other employee … Personal Saving Rate: Is It Real and Is It a Puzzle? Disposable income definition is - income that is left after paying taxes and for things that are essential, such as food and housing. But the truth is, most of … It includes every form of income, e.g., salaries and wages, retirement income, near cash government transfers like food stamps, and investment gains. The amount of money a creditor may legally garnish from your "Personal Income and Outlays, September 2020," Pages 2 and 6. Accessed July 30, 2020. It uses disposable income as a starting point to determine how much to seize from the earner's paycheck. Discretionary Income, Consumer Expectations for Spending Jumps to 4-Year High, Car and Truck Sales Help Drive Consumer Spending, Consumer Spending Increases 41.0% in Q3 2020, Why the Fed Uses a Special Measurement for Inflation. Marginal propensity to consume represents the proportion of a pay raise that is spent on the consumption of goods and services, as opposed to being saved. Alternate names: Disposable personal income, disposable earnings, after-tax income. This portion of disposable income can be spent on what the income earner chooses or, alternatively, it can be saved. PIP are non-mortgage interest payments made by households. [7] Disposable Personal Income in the United States averaged 5611.19 USD Billion from 1959 until 2020, reaching an all time high of 19035.90 USD Billion in April of 2020 and a record low of 351.54 USD Billion in January of 1959. The federal wage garnishment law states that for the purpose of wage garnishment, disposable earnings is the amount of money you have left after subtracting deductions required by federal, state and local laws from your paycheck. ), after taking into account net interest and dividends received and the payment of taxes and social contributions. The U.S. personal saving rate is the percentage of their DPI that U.S. residents don't spend. It also is the foundation of your budget -- the starting point for how you decide to spend your money. Disposable income is the money you have left from your income after you pay taxes. Income remaining after deduction of taxes and social security charges, available to be spent or saved as one wishes. "Personal Income and Outlays, September 2020," Page 1. Many useful statistical measures and economic indicators derive from disposable income. Unsurprisingly, in terms of disposable income Switzerland leads the world by a huge margin, with an average disposable income of$6300, which is 2 to 3 times that of its neighbours – Germany ($2850), France ($2,760) and Italy ($2,120). Accessed Oct. 31, 2020. Disposable income is closest to the concept of income as generally understood in economics. This page provides - United States Disposable Personal Income - actual values, historical data, forecast, chart, statistics, economic calendar and news. 2. • The percentage of disposable income spent at grocery stores and supermarkets has been declining since the 1970s. A negative disposable income indicates that an individual is borrowing in order to cover his/her expenses. The costs of licenses, permits, and other mandatory fees you pay to a government agency at any level are also subtracted from personal income to calculate disposable income, as are any withholdings for retirement savings that are mandated by a government, such as federal government employee contributions to the Basic Benefit Plan. 내용은 크리에이티브 커먼즈 저작자표시-동일조건변경허락 라이선스에 따라 사용할 수 있으며 추가적인 조건이 적용될 수 있습니다. Looking forward, we estimate Disposable Personal Income in Canada to stand at 1371225.00 in 12 months time. Solution Use below given data for the calculation of disposable income First, we need to calculate the yearly gross salary and yearly federal taxes. It's calculated using the following simple formula: disposable income = personal income – personal current taxes. Federal Reserve Bank of St. Louis Review. Disposable income is an important measure of household financial resources. Wilson and Wilson’s family earn around monthly$60,000 and they pay $5,000 as monthly federal tax. Those figures were adjusted to exclude inflation.. (Economics) the money a person has available to spend after paying taxes, pension contributions, etc. Bureau of Economic Analysis. Household income is a measure of the combined incomes of all people sharing a particular household or place of residence. Disposable income is closest to the concept of income as generally understood in economics. The BEA estimated that U.S. personal income increased by$170.3 billion, or 0.9%, and that U.S. DPI increased by $150.3 billion, or 0.9%, in September 2020 from the prior month. "Personal Income and Outlays, September 2020," Page 2. "The Decline in the U.S. Disposable income, also known as disposable personal income (DPI), is the amount of money that households have available for spending and saving after income taxes have been accounted for. Lower income households tended to have a higher debt to disposable income ratio, the agency has said. 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It’s complicated. disposable income. Disposable personal income is often monitored as one of the many key economic indicators used to gauge the overall state of the economy., DPI=Personal Income−Personal Income Taxes\begin{aligned} &\text{DPI} = \text{Personal Income} - \text{Personal Income Taxes} \\ \end{aligned}DPI=Personal Income−Personal Income Taxes. For several months in 2005 and 2006, the average personal savings rate dipped into negative territory for the first time since 1933. This means that in those years, Americans were spending all of their disposable income each month and then tapping into savings or debt for further spending. With the price of living steadily rising and wages failing to keep up with the trend everyone is needing to tighten their belts a little bit more. Learn More. Household disposable income measures the income of households (wages and salaries, self-employed income, income from unincorporated enterprises, social benefits, etc. U.S. PCE are the value of the goods and services purchased by, or on the behalf of, U.S. residents and are tracked as an important measure of the economy's strength. U.S. per capita disposable personal income by state 2019 | Statista David Kindness is an accounting, tax and finance expert. Everyday essentials from food to travel have slowly increased in price and the uncertainty surrounding Brexit isn’t helping matters either. Aggregate demand is the total amount of goods and services demanded in the economy at a given overall price level at a given time. This is actually referred to as the … An accurate general definition of income is not easy to provide. After-tax income. "Disposable Personal Income." Fact Sheet #30: The Federal Wage Garnishment Law, Consumer Credit Protection Act's Title III (CCPA). https://www.sofi.com/learn/content/what-is-disposable-income Bureau of Economic Analysis. Personal outlays increased by $217.5 billion in September 2020 from the month before.. Business. Disposable Income is the amounts of money left with the person after paying all the direct taxes. He has helped individuals and companies worth tens of millions achieve greater financial success. Voluntary deductions such as 401 ( k ) contributions and health and life insurance are generally considered part of disposable income. Discretionary income is disposable income (after-tax income), minus all payments that are necessary to meet current bills. 이 문서는 2018년 2월 18일 (일) 15:30에 마지막으로 편집되었습니다. It suggests we have "disposable" money that we really don't care about. What Do Americans Really Spend Their Money On? PCTP are non-tax payments made to governments—licenses, permits, and fees. The U.S. Bureau of Economic Analysis (BEA) releases data on the monthly changes in personal income, DPI, and consumer spending, which is known more formally as personal consumption expenditures (PCE). While employment got within 3.7 per cent of its pre-pandemic levels during the quarter, it wasn’t enough to offset the wind-down of government supports, as employment insurance benefits dropped almost 50 per cent in the quarter, the report said. Learn more. Disposable Income vs. Disposable income minus all payments for necessities (mortgage, health insurance, food, transportation) equals discretionary income. The formula is … By using Investopedia, you accept our, Investopedia requires writers to use primary sources to support their work. It's calculated using the following simple formula: disposable income = personal income – personal current taxes. Accessed July 30, 2020. Disposable income determines what sort of lodging one can afford, how often one can go out to eat, how much one can save, etc. Court orders for child support or alimony may specify garnishments of up to 60 percent of disposable income. As of 2019, the amount garnished may not exceed 25% of a person's disposable income or the amount by which a person's weekly income exceeds 30 times the federal minimum wage, whichever is less.. The personal savings rate is the percentage of disposable income that goes into savings (such as for retirement) or use at a later date. Marginal propensity to consume represents the percentage of each additional dollar of disposable income that gets spent, while marginal propensity to save denotes the percentage that gets saved. Discretionary income can be spent on restaurant meals, investments, travel, entertainment, and any other non-essential items or services. Creditors may garnish up to 25 percent of disposable earnings, or the amount of disposable earnings in excess of 30 times the federal minimum wage, whichever is less. Personal Saving Rate: Is It Real and Is It a Puzzle?" Learn more about disposable income, its importance as an economic indicator, and how it differs from discretionary income. Therefore, the calculation of disposable income will be as follows, = 720,000 – 60… https://corporatefinanceinstitute.com/.../disposable-income Bureau of Economic Analysis. Disposable income, that portion of an individual’s income over which the recipient has complete discretion. Disposable income is the portion of income available to an income earner after all income taxes are deducted. It's an important economic indicator for the country. Disposable income, also known as disposable personal income (DPI) or net pay, is the amount of money you have left over from your total annual income after paying all direct federal, state, … Accessed Oct. 31, 2020. Disposable income is the portion of an worker’s paycheck that is subject to garnishments. Five ways to boost your income in 2020. Page 491. For most people, taxes far and away represent the greatest component of the deducted amount. Disposable income is an often-misunderstood term. In the Household Income and Basic Amenities Survey Report 2019 released today, the Department of Statistics Malaysia’s (DOSM) figures showed income inequality calculated based on two categories ― gross income (which is before tax and contributions to social security scheme are paid) and disposable income (which is after deducting tax, zakat and social security scheme contributions). You might look at it as your fun money to spend on things you don’t really need, after your essential expenses are covered. Disposable Personal Income in the United States averaged 5611.19 USD Billion from 1959 until 2020, reaching an all time high of 19035.90 USD Billion in April of 2020 and a record low of 351.54 USD Billion in January of 1959. Disposable income is the net income available to invest, save, or spend after deducting income taxes. Bureau of Economic Analysis. Think of it as the money you have discretion over—e.g. n. 1. The amount of disposable income for the residents of a country is closely followed by economists, as is the level of consumer spending, which depends in part on disposable income. Accessed July 30, 2020. Disposable income has two definitions, depending on whether an individual is going through a wage garnishment or bankruptcy. This household's disposable income would then be$75,000 ($100,000 –$25,000). As such, businesses that sell discretionary goods tend to suffer the most during recessions and are watched closely by economists for signs of both recession and recovery. The fiscal multiplier measures the effect that increases in fiscal spending will have on a nation's economic output, or gross domestic product (GDP). It is total personal income after subtracting taxes and minimal survival expenses (such as food, medicine, rent or mortgage , utilities, insurance, transportation, property maintenance, child support, etc.) Based on the above information you are required to calculate the Personal Disposable Income for the entire year. Compare with discretionary income ‘the rents of tenants in work reached 21 per cent of disposable income’ Disposable income is calculated by subtracting income taxes from income. A country's average disposable income is … disposable income. (Economics) the total amount of money that the individuals in a community, country, etc, have available to buy consumer goods. The savings rate is the percentage of money taken from personal income and saved. Personal Income. For example, consider a family with a household income of $100,000, and the family has an effective income tax rate of 25% (versus marginal tax rate). The federal government uses a slightly different method to calculate disposable income for wage garnishment purposes. Not only is it one of the major determinants of consumer spending, but it is also one of the five determinants of demand. What Is Disposable Income? Spend & Save. Disposable income is the money you have left from your income after you pay taxes. Sometimes, the government garnishes an income earner's wages for payment of back taxes or delinquent child support. Cambridge Dictionary +Plus You can learn more about the standards we follow in producing accurate, unbiased content in our. The BEA estimated U.S. PCE increased by$201.4 billion, or 1.4%, during the same time period. Household disposable income measures the income of households (wages and salaries, self-employed income, income from unincorporated enterprises, social benefits, etc. The Decline in the U.S. Disposable income can be calculated as personal income – personal current taxes. Investopedia uses cookies to provide you with a great user experience. Please note that OECD reference year from 2010 to 2015 changed on Tuesday 3rd of December, 2019. The rate was 14.3 percent in September 2020, down from 14.8% in August.. It can also be described as the percentage of their income they have left after taxes and spending. The amount that U.S. residents have left to spend or save after paying taxes is important not just to individuals but to the whole economy. We also reference original research from other reputable publishers where appropriate. For a person living in an economic family, disposable income is deemed to be a portion of the total family income after taxes. U.S. Department of Labor. How to use disposable income in a sentence. 자세한 내용은 이용 약관을 참조하십시오. Learn more about disposable income, its importance as an economic indicator, and how it differs from discretionary income. ; 개인정보처리방침 She is a financial writer and editor with experience at several major financial publications. Accessed Oct. 31, 2020. Disposable income is sometimes referred to as disposable personal income, net pay or take-home pay. Income includes wages and salaries, interest and dividend payments from financial assets, and … Disposable Personal Income in Canada is expected to be 1382690.00 CAD Million by the end of this quarter, according to Trading Economics global macro models and analysts expectations. Discretionary income is disposable income minus the cost of all necessary expenses, including food and housing. It is the actual income which is spent by individuals and families on consumption after paying direct taxes. Definition of disposable income. U.S. personal income is the income received by, or on behalf of, all U.S. residents from all sources, both domestic and global. How much disposable income a person or a population of people has can help economists determine how much money they might spend on goods and services or save. Disposable income should not to be confused with discretionary income, which is what is left of your disposable income after you’ve paid for necessities like housing (in the form of rent or a mortgage payment), health care, food, electricity, and transportation. Please refer to the dataset Disposable income and net lending – net borrowing, 2019 archive to access longer time series based on the methodology prior to the 2019 benchmark revisions. Discretionary income is the amount of an individual's income that is left for spending, investing, or saving after taxes and necessities are paid. "Fact Sheet #30: The Federal Wage Garnishment Law, Consumer Credit Protection Act's Title III (CCPA)." Disposable income is the money you have left from your income after you pay federal, state, and local taxes and any other mandatory payments to a government. • Real personal disposable income rose 15 percent over the period. Disposable income, also known as disposable personal income (DPI), is the amount of money that households have available for spending and … • A Labour victory would have boosted their disposable income by £311, mainly because of the increase in child benefit. Bureau of Economic Analysis. disposable income 어의, 의미, disposable income의 의미: the amount of money you have left to spe...: 자세히 알아보기. Disposable Income Definition. Household adjusted disposable income includes income from economic activity (wages and salaries; profits of self-employed business owners), property income (dividends, interests and rents), social benefits in cash (retirement pensions, unemployment benefits, family allowances, basic income support, etc. after your financial obligations, you can choose to save or to spend what’s left on … "Personal Saving Rate." Real DPI and real PCE increased an estimated 0.7% and 1.2%, respectively, in September 2020 from August 2020. The amount that U.S. residents have left to spend or save after paying taxes is important not just to individuals but to the whole economy. It is used by analysts to measure consumer spending, payment ability, probable future savings, and the overall health of a nation’s economy. The money you have left over from your salary or wages after you’ve paid federal, state, and local taxes is your disposable income or disposable personal income (DPI). Economists use DPI as a starting point to gauge households' rates of savings and spending. For example, economists use disposable income as a starting point to calculate metrics such as discretionary income, personal savings rates, marginal propensity to consume (MPC), and marginal propensity to save (MPS). Discretionary income is the amount of disposable income you have left after you pay for necessities like housing, food, and healthcare. Taxes and legally-required deductions don’t count towards disposable earnings. Disposable Personal Income in the United States decreased to 17277.62 USD Billion in November from 17515.20 USD Billion in October of 2020. What You Need to Know About U.S. Tax Returns If You Have a Green Card, Options for Paying Off Tax Debts With the IRS, U.S. GDP Jumps 33.1% in Third Quarter After Record Contraction, What Durable Goods Orders Tell You About the Future, The Worst Economic Contractions in U.S. History, Personal Income and Outlays, September 2020. Discretionary income is the first to shrink amid a job loss, pay reduction, or economic downturn. The BEA also tracks U.S. personal outlays, which are the sum of all PCE, personal interest payments (PIP), and personal current transfer payments (PCTP). : income that is left after paying taxes and for things that are essential, such as food and housing I don't have enough disposable income to … The federal wage garnishment law states that for the purpose of wage garnishment, disposable earnings is the amount of money you have left after subtracting deductions required by federal, state and local laws from your paycheck. Contact Personnel. If you want to be a better budgeter, you'll need to brush up on some budgeting terms. In addition to income taxes, the government subtracts from gross income retirement plan contributions required by law when calculating disposable income for wage garnishment purposes. Returning to the above example, if the family described is required to contribute $5,000 to a retirement plan, the household's disposable income for wage garnishment purposes shrinks from$75,000 to $70,000. James Moore Will Britons’ £200bn pandemic savings fuel recovery? You can also choose to save a lot or a little of it. Disposable Income UK Definition. With a wage garnishment, disposable income is the amount of money left after an employer has made all the required deductions. The amount of money a creditor may legally garnish from your income is a percentage of your disposable earnings. ), after taking into account net interest and dividends received and the payment of taxes and social contributions. (money available for luxuries) 가처분 소득 : Disposable income is what you have left after you have paid for … The multiplier effect measures the impact that a change in investment will have on final economic output. disposable income n noun: Refers to person, place, thing, quality, etc. Lifestyle. disposable income definition: 1. the money that you can spend as you want and not the money that you spend on taxes, food, and…. From the Cambridge English Corpus However, an increase in government expenditure will not necessarily induce a lower expected present value … to maintain a certain standard of living . These include white papers, government data, original reporting, and interviews with industry experts. Disposable income can be calculated for a household or for a nation and has important economic significance. Those three levels of taxes consist of income and property taxes and paycheck deductions for Social Security, Medicare, and unemployment insurance. Rachel Morgan Cautero has been a financial planning expert for The Balance since 2017. (However, it does not include realized or unrealized capital gains or losses from investments.) The formula is simple: personal income minus personal current taxes. Accessed July 30, 2020. What is Disposable Personal Income? Definition: Disposable income, sometimes called disposable personal income (DPI), is the total earnings a household makes that are available to save or spend after taxes have been paid.In other words, it’s a household’s take home pay after taxes and other employee … Personal Saving Rate: Is It Real and Is It a Puzzle? Disposable income definition is - income that is left after paying taxes and for things that are essential, such as food and housing. But the truth is, most of … It includes every form of income, e.g., salaries and wages, retirement income, near cash government transfers like food stamps, and investment gains. The amount of money a creditor may legally garnish from your "Personal Income and Outlays, September 2020," Pages 2 and 6. Accessed July 30, 2020. It uses disposable income as a starting point to determine how much to seize from the earner's paycheck. Discretionary Income, Consumer Expectations for Spending Jumps to 4-Year High, Car and Truck Sales Help Drive Consumer Spending, Consumer Spending Increases 41.0% in Q3 2020, Why the Fed Uses a Special Measurement for Inflation. Marginal propensity to consume represents the proportion of a pay raise that is spent on the consumption of goods and services, as opposed to being saved. Alternate names: Disposable personal income, disposable earnings, after-tax income. This portion of disposable income can be spent on what the income earner chooses or, alternatively, it can be saved. PIP are non-mortgage interest payments made by households. [7] Disposable Personal Income in the United States averaged 5611.19 USD Billion from 1959 until 2020, reaching an all time high of 19035.90 USD Billion in April of 2020 and a record low of 351.54 USD Billion in January of 1959. The federal wage garnishment law states that for the purpose of wage garnishment, disposable earnings is the amount of money you have left after subtracting deductions required by federal, state and local laws from your paycheck. ), after taking into account net interest and dividends received and the payment of taxes and social contributions. The U.S. personal saving rate is the percentage of their DPI that U.S. residents don't spend. It also is the foundation of your budget -- the starting point for how you decide to spend your money. Disposable income is the money you have left from your income after you pay taxes. Income remaining after deduction of taxes and social security charges, available to be spent or saved as one wishes. "Personal Income and Outlays, September 2020," Page 1. Many useful statistical measures and economic indicators derive from disposable income. Unsurprisingly, in terms of disposable income Switzerland leads the world by a huge margin, with an average disposable income of$6300, which is 2 to 3 times that of its neighbours – Germany ($2850), France ($2,760) and Italy ($2,120). Accessed Oct. 31, 2020. Disposable income is closest to the concept of income as generally understood in economics. This page provides - United States Disposable Personal Income - actual values, historical data, forecast, chart, statistics, economic calendar and news. 2. • The percentage of disposable income spent at grocery stores and supermarkets has been declining since the 1970s. A negative disposable income indicates that an individual is borrowing in order to cover his/her expenses. The costs of licenses, permits, and other mandatory fees you pay to a government agency at any level are also subtracted from personal income to calculate disposable income, as are any withholdings for retirement savings that are mandated by a government, such as federal government employee contributions to the Basic Benefit Plan. 내용은 크리에이티브 커먼즈 저작자표시-동일조건변경허락 라이선스에 따라 사용할 수 있으며 추가적인 조건이 적용될 수 있습니다. Looking forward, we estimate Disposable Personal Income in Canada to stand at 1371225.00 in 12 months time. Solution Use below given data for the calculation of disposable income First, we need to calculate the yearly gross salary and yearly federal taxes. It's calculated using the following simple formula: disposable income = personal income – personal current taxes. Federal Reserve Bank of St. Louis Review. Disposable income is an important measure of household financial resources. Wilson and Wilson’s family earn around monthly$60,000 and they pay $5,000 as monthly federal tax. Those figures were adjusted to exclude inflation.. (Economics) the money a person has available to spend after paying taxes, pension contributions, etc. Bureau of Economic Analysis. Household income is a measure of the combined incomes of all people sharing a particular household or place of residence. Disposable income is closest to the concept of income as generally understood in economics. The BEA estimated that U.S. personal income increased by$170.3 billion, or 0.9%, and that U.S. DPI increased by $150.3 billion, or 0.9%, in September 2020 from the prior month. "Personal Income and Outlays, September 2020," Page 2. "The Decline in the U.S. Disposable income, also known as disposable personal income (DPI), is the amount of money that households have available for spending and saving after income taxes have been accounted for. Lower income households tended to have a higher debt to disposable income ratio, the agency has said. 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Mathematics-Online lexicon:

# Subspace

 A B C D E F G H I J K L M N O P Q R S T U V W X Y Z overview

A subset of a -vector space is called a vector subspace (or simply a subspace) of , if itself, endowed with the addition and the scalar multiplication defined in , forms a vector space.

if and , then it immediatetly follows that and .

(Authors: App/Burkhardt/Kimmerle)

format: plain


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# 17 COMPLETE THE CHART Then the teacher will resume the video to allow you to check your answersSUNSTANCEPure substance or mixtureHeinent/compound

###### Question:

17 COMPLETE THE CHART Then the teacher will resume the video to allow you to check your answers SUNSTANCE
Pure substance or mixture
Heinent/compound and
Homogeneou/eterejnen
Orarige place without puid
Tap water
AN
Fruit Loops Cereal
24K gold
Distilled water
14K gold

### What is the vertex in the following function? y = 3(x + 5)^2 − 4 a. (5, -4) b. (-5, -4) c. (-15, -4) d. (-5, 4)

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### 19823988388939049942090834+98298748 712787803280438919823

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### Question 1 with 1 blankel hijo de mi hermano question 2 with 1 blankla esposa de mi padre, pero no soy

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## itsladyrw 2 years ago Simplify completely( x^2 + x - 12 / x^2 - x - 20) * (12x^2 -48x -60 / 3x^2 - 24x + 45) Please best answer I will give a metal<3

1. Tabatabachoii

factor out each expression first. then simplify. it goes like this.

2. Tabatabachoii

you simplify 12x2-48x-60. divide it by 12 since all of them are divisible by 12. you also simplify 3x2-24x+45 by dividing it by 3. you'll get x2-4x-5 and x2-8x+15.

Thanks you!! :D

4. Tabatabachoii

no problem. :)

5. Azteck

@Tabatabachoii You're incorrect. $\frac{ (x+4)(x-3) }{ (x-5)(x+4) }\times \frac{ 12(x-5)(x+1) }{ 3(x-3)(x-5) }$ $=\frac{ 12(x+1) }{ 3(x-5) }$ $=\frac{ 4(x+1) }{ x-5 }$

6. Azteck

@itsladyrw You must not eliminate the 12 and 3 when you factor out that part of the expression.

7. Tabatabachoii

ohw, I forgot to. I admit my mistake. Sorry.


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## Homological calculations with the analytic structure group

Siegel, Paul.  The Pennsylvania State University. ProQuest Dissertations Publishing, 2012. 3569313.


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find_markers {dtangle} R Documentation

## Find marker genes for each cell type.

### Description

Find marker genes for each cell type.

### Usage

find_markers(Y, references = NULL, pure_samples = NULL,
data_type = NULL, gamma = NULL, marker_method = "ratio")

### Arguments

 Y Expression matrix. (Required) Two-dimensional numeric. Must implement as.matrix. Each row contains expression measurements for a particular sample. Each columm contains the measurements of the same gene over all individuals. Can either contain just the mixture samples to be deconvolved or both the mixture samples and the reference samples. See pure_samples and references for more details. references Cell-type reference expression matrix. (Optional) Two-dimensional numeric. Must implement as.matrix. Must have same number of columns as Y. Columns must correspond to columns of Y. Each row contains expression measurements for a reference profile of a particular cell type. Columns contain measurements of reference profiles of a gene. Optionally may merge this matrix with Y and use pure_samples to indicate which rows of Y are pure samples. If pure_samples is not specified references must be specified. In this case each row of references is assumed to be a distinct cell-type. If both pure_samples and references are specified then multiple rows of references may refer be the same cell type, and pure_samples specifies to which cell-type each row of references corresponds. pure_samples The pure sample indicies. (Optional) List of one-dimensional integer. Must implement as.list. The i-th element of the top-level list is a vector of indicies (rows of Y or references) that are pure samples of type i. If references is not specified then this argument identifies which rows of Y correspond to pure reference samples of which cell-types. If references is specified then this makes same idenficiation but for the references matrix instead. data_type Type of expression measurements. (Optional) One-dimensional string. An optional string indicating the type of the expression measurements. This is used to set gamma to a pre-determined value based upon the data type. Valid values are for probe-level microarray as “microarray-probe”, gene-level microarray as “microarray-gene” or rna-seq as “rna-seq”. Alternatively can set gamma directly. gamma Expression adjustment term. (Optional) One-dimensional positive numeric. If provided as a single positive number then that value will be used for gamma and over-ride the value of gamma chosen by the data_type argument. If neither gamma nor data_type are specified then gamma will be set to one. marker_method Method used to rank marker genes. (Optional) One-dimensional string. The method used to rank genes as markers. If not supplied defaults to “ratio”. Only used if markers are not provided to argument “markers”. Options are 'ratio' selects and ranks markers by the ratio of the mean expression of each gene in each cell type to the mean of that gene in all other cell types. 'regression ' selects and ranks markers by estimated regression coefficients in a series of regressions with single covariate that is indicator of each type. 'diff' selects and ranks markers based upon the difference, for each cell type, between the median expression of a gene by each cell type and the median expression of that gene by the second most highly expressed cell type. 'p.value' selects and ranks markers based upon the p-value of a t-test between the median expression of a gene by each cell type and the median expression of that gene by the second most highly expressed cell type.

### Value

List with four elements. “L” is respective ranked markers for each cell type and “V” is the corresponding values of the ranking method (higher are better) used to determine markers and sort them, “M” is the matrix used to create the other two arguments after sorting and subsetting, and “sM” is a sorted version of M.

### Examples

truth = shen_orr_ex$annotation$mixture
pure_samples <- lapply(1:3, function(i) {
which(truth[, i] == 1)
})
Y <- shen_orr_ex$data$log
find_markers(Y=Y,pure_samples=pure_samples,
data_type='microarray-gene',marker_method='ratio')

[Package dtangle version 2.0.9 Index]


text:
?

Free Version
Easy

# Equivalent Resistance: Four Identical Resistors

APPHEM-TYHR0J

Four identical resistors are wired as shown in the diagram below.

If the resistance of each is $R$, what is the equivalent resistance of this combination?

A

$\frac{1}{4R}$

B

$\frac{1}{2R}$

C

$\frac{1}{R}$

D

$R$

E

$2R$


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# Landscape, the Scale of SUSY Breaking, and Inflation

ArticleinJournal of High Energy Physics 0412(12) · November 2004with6 Reads
DOI: 10.1088/1126-6708/2004/12/004 · Source: arXiv
Abstract
We argue that in the simplest version of the KKLT model, the maximal value of the Hubble constant during inflation cannot exceed the present value of the gravitino mass, H< m_{3/2}. This may have important implications for string cosmology and for the scale of the SUSY breaking in this model. If one wants to have inflation on high energy scale, one must develop phenomenological models with an extremely large gravitino mass. On the other hand, if one insists that the gravitino mass should be O(1 TeV), one will need to develop models with a very low scale of inflation. We show, however, that one can avoid these restrictions in a more general class of KKLT models based on the racetrack superpotential with more than one exponent. In this case one can combine a small gravitino mass and low scale of SUSY breaking with the high energy scale of inflation. Comment: 7 pages, 4 figs, revtex, typos corrected
• ##### Moduli Backreaction on Inflationary Attractors
• "On the one hand, the inflationary energy can destabilize the moduli. This was anticipated in [4], where it was shown that stabilizing the Kähler modulus in the simplest model of inflation leads to a bound H < m3 /2 on the inflationary Hubble scale H, related to the gravitino mass m3 /2 in the vacuum after inflation 1 . Conversely, the dynamics of the volume modulus may induce a backreaction which renders the inflaton scalar potential too steep to support inflation. "
[Show abstract] [Hide abstract] ABSTRACT: We investigate the interplay between moduli dynamics and inflation, focusing on the KKLT-scenario and cosmological $\alpha$-attractors. General couplings between these sectors can induce a significant backreaction and potentially destroy the inflationary regime; however, we demonstrate that this generically does not happen for $\alpha$-attractors. Depending on the details of the superpotential, the volume modulus can either be stable during the entire inflationary trajectory, or become tachyonic at some point and act as a waterfall field, resulting in a sudden end of inflation. In the latter case there is a universal supersymmetric minimum where the scalars end up, preventing the decompactification scenario. The observational predictions conform to the universal value of attractors, fully compatible with the Planck data, with possibly a capped number of e-folds due to the interplay with moduli.
Full-text · Article · Jul 2016 · Journal of High Energy Physics
• ##### Challenges for D-brane large-field inflation with stabilizer fields
• "For our purposes it suffices to leave the precise mechanism of moduli stabilization unspecified, and instead assume the existence of a superpotential piece W mod (ρ i ) ⊂ W which satisfies D ρ i W mod = 0 for all relevant moduli fields ρ i . Examples are known in the literature, they include the racetrack setup of [39] and a less fine-tuned mechanism using an additional stabilizer field [40]. 2 In many string-effective inflation models the inflaton and the moduli interact even if the moduli are much heavier than the dynamical scale of inflation. Through supergravity couplings this even happens in models where the superpotential separates, "
[Show abstract] [Hide abstract] ABSTRACT: We study possible string theory compactifications which, in the low-energy limit, describe chaotic inflation with a stabilizer field. We first analyze type IIA setups where the inflationary potential arises from a D6-brane wrapping an internal three-cycle, and where the stabilizer field is either an open-string or bulk K\"ahler modulus. We find that after integrating out the relevant closed-string moduli consistently, tachyonic directions arise during inflation which cannot be lifted. This is ultimately due to the shift symmetries of the type IIA K\"ahler potential at large compactification volume. This motivates us to search for stabilizer candidates in the complex structure sector of type IIB orientifolds, since these fields couple to D7-brane Wilson lines and their shift symmetries are generically broken away from the large complex structure limit. However, we find that in these setups the challenge is to obtain the necessary hierarchy between the inflationary and Kaluza-Klein scales.
Article · Jul 2016
• ##### A Pati-Salam Version of Subcritical Hybrid Inflation
• "Any discussion of dark matter must also include the discussion of the SUSY breaking sector of the theory. In particular, SUSY breaking must necessarily be decoupled from the inflationary sector such that the gravitino mass is less than the Hubble parameter during inflation, i.e. m 3/2 < H inf (see Refs. [22, 23, 24, 25]). In addition, the cosmological moduli [26, 27, 28, 29] and gravitino problems [30, 31, 32] must be ameliorated. "
[Show abstract] [Hide abstract] ABSTRACT: In this paper we present a model of subcritical hybrid inflation with a Pati-Salam [PS] symmetry group. Both the inflaton and waterfall fields contribute to the necessary e-foldings of inflation, while only the waterfall field spontaneously breaks PS hence monopoles produced during inflation are diluted during the inflationary epoch. The model is able to produce a tensor-to-scalar ratio, $r < 0.09$ consistent with the latest BICEP2/Keck and Planck data, as well as scalar density perturbations and spectral index, $n_s$, consistent with Planck data. For particular values of the parameters, we find $r = 0.084$ and $n_s = 0.0963$. The energy density during inflation is directly related to the PS breaking scale, $v_{PS}$. The model also incorporates a $\mathbb{Z}_4^R$ symmetry which can resolve the $\mu$ problem and suppress dimension 5 operators for proton decay, leaving over an exact $R$-parity. Finally the model allows for a complete three family extension with a $D_4$ family symmetry which reproduces low energy precision electroweak and LHC data.
Article · Jan 2016


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# 这是一篇关于凸优化的Final Exam作业代写

1. Basic Knowledge
2. Is the set {a R k | p(0) = 1, |p(t)| ≤ 1 for α t β}, where p(t) = a1 + a2t + · · · + akt k1 convex?

(10 points)

1. Prove that x = (1,1/2, 1) is optimal for the optimization problem

minimize 1/2T P x + q T x + r

subject to 1 xi 1, i = 1, 2, 3,

where

P = {13 12 2

12 17 6

2 6 12}

, q = { 22

− 14.5

13}, r = 1.

(10 points)

1. Equivalently reformulate the following problem into a standard convex optimization form, i.e., Linear Programming (LP), Second-Order Cone Programming (SOCP) and Semidefifinite Programming(SDP).

Minimize ||Ax b||

(10 points)

1. KKT Conditions

Let n 2. Consider the following minimization problem over x = [x1, . . . , xn] T ,

minx nXj=1cj xj

s.t.nXj=1xj = 1,

xj , j = 1, . . . , n,

where cj > 0, j,  > 0 are parameters.

(1) Determine whether this problem is convex or not, and provide your argument. (5 points)

(2) Write down the dual problem of (1). (5 points)

(3) Derive the KKT conditions of (1). (5 points)

(4) Derive the expression of the optimal solution of (1). (10 points)

III. Gradient Methods

1. Let f : R d R be a convex and difffferentiable function, it is said to be M-smooth if

f(y) f(x) + h∇f(x), y xi +M 2k y xk 2 2 , x, y R d (2)

Prove that the above M-smooth condition holds if and only if  k∇f(x) − ∇f(y)k 2 Mk x yk 2x, y R d (3)

(20 points)

1. The subgradient method updates are given by x ` +1 = x ` α ` g ` , where g ` ∂f(x ` ). Suppose f is convex with fifinite unconstrained minimum f ? , and is L-Lipschitz. Letting X ? denote the space of minimizers (taken to be non-empty and closed), defifine the distance function distX ? (u) =infz∈X ? k z uk 2, and suppose there exists some µ > 0 such that distX ? (y) 1µ (f(y) f ? ) for all y dom(f). Prove that dist2 X ? (x ` +1)  1 µ 2 L 2  ` +1 dist2 X ? (x 0 ).

(15 points)

IV.Proximal Algorithm

For 0 α, β 1, defifine hα,β : R n R as

hα,β(x) = α T x+ + β T x,

where x+ = max{x, 0} and x= max{−x, 0}, the maximum is taken elementwise.

Give a simple expression for the proximal operator of hα,β. (10 points)

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# How do you differentiate -3=xye^(x-y)?

Dec 2, 2015

$\frac{\mathrm{dy}}{\mathrm{dx}} = - \frac{y \left(x + 1\right)}{x \left(1 - y\right)}$

#### Explanation:

To find the implicit derivative, we'll use the chain rule and product rule. It's important to remember that when differentiating a $y$ term, a $\frac{\mathrm{dy}}{\mathrm{dx}}$ term will be spit out thanks to the chain rule.

$\frac{d}{\mathrm{dx}} \left[- 3 = x y {e}^{x - y}\right]$

$0 = y {e}^{x - y} \frac{d}{\mathrm{dx}} \left[x\right] + x {e}^{x - y} \frac{d}{\mathrm{dx}} \left[y\right] + x y \frac{d}{\mathrm{dx}} \left[{e}^{x - y}\right]$

Find each derivative.

$\frac{d}{\mathrm{dx}} \left[x\right] = 1$

$\frac{d}{\mathrm{dx}} \left[y\right] = \frac{\mathrm{dy}}{\mathrm{dx}}$

$\frac{d}{\mathrm{dx}} \left[{e}^{x - y}\right] = {e}^{x - y} \frac{d}{\mathrm{dx}} \left[x - y\right] = {e}^{x - y} \left(1 - \frac{\mathrm{dy}}{\mathrm{dx}}\right) = {e}^{x - y} - {e}^{x - y} \frac{\mathrm{dy}}{\mathrm{dx}}$

Plug them back in and solve for $\frac{\mathrm{dy}}{\mathrm{dx}}$.

$0 = y {e}^{x - y} + x {e}^{x - y} \frac{\mathrm{dy}}{\mathrm{dx}} + x y {e}^{x - y} - x y {e}^{x - y} \frac{\mathrm{dy}}{\mathrm{dx}}$

$- x y {e}^{x - y} - y {e}^{x - y} = \frac{\mathrm{dy}}{\mathrm{dx}} \left(x {e}^{x - y} - x y {e}^{x - y}\right)$

$\frac{- x y {e}^{x - y} - y {e}^{x - y}}{x {e}^{x - y} - x y {e}^{x - y}} = \frac{\mathrm{dy}}{\mathrm{dx}}$

$\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{{e}^{x - y} \left(- x y - y\right)}{{e}^{x - y} \left(x - x y\right)}$

$\frac{\mathrm{dy}}{\mathrm{dx}} = - \frac{y \left(x + 1\right)}{x \left(1 - y\right)}$


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#### Nonrepetitive Colouring via Entropy Compression

##### Vida Dujmović, Gwenaël Joret, Jakub Kozik, David R. Wood

A vertex colouring of a graph is \emph{nonrepetitive} if there is no path whose first half receives the same sequence of colours as the second half. A graph is nonrepetitively $k$-choosable if given lists of at least $k$ colours at each vertex, there is a nonrepetitive colouring such that each vertex is coloured from its own list. It is known that every graph with maximum degree $\Delta$ is $c\Delta^2$-choosable, for some constant $c$. We prove this result with $c=1$ (ignoring lower order terms). We then prove that every subdivision of a graph with sufficiently many division vertices per edge is nonrepetitively 5-choosable. The proofs of both these results are based on the Moser-Tardos entropy-compression method, and a recent extension by Grytczuk, Kozik and Micek for the nonrepetitive choosability of paths. Finally, we prove that every graph with pathwidth $k$ is nonrepetitively $O(k^{2})$-colourable.

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Next: Exercises Up: Quantum Dynamics Previous: Ehrenfest Theorem

# Schrödinger Wave Equation

Consider the motion of a particle in three dimensions in the Schrödinger picture. The fixed dynamical variables of the system are the position operators, , and the momentum operators, . The state of the system is represented as some time evolving ket .

Let represent a simultaneous eigenket of the position operators belonging to the eigenvalues . Note that, because the position operators are fixed in the Schrödinger picture, we do not expect the to evolve in time. The wavefunction of the system at time is defined

 (267)

The Hamiltonian of the system is taken to be

 (268)

The Schrödinger equation of motion, (229), yields

 (269)

where use has been made of the time independence of the . We adopt the Schrödinger representation in which the momentum conjugate to the position operator is written [see Equation (165)]

 (270)

Thus,

 (271)

where use has been made of Equation (169). Here, denotes the gradient operator written in terms of the position eigenvalues. We can also write

 (272)

where is a scalar function of the position eigenvalues. Combining Equations (268), (269), (271), and (272), we obtain

 (273)

which can also be written

 (274)

This is Schrödinger's famous wave equation, and is the basis of wave mechanics. Note, however, that the wave equation is just one of many possible representations of quantum mechanics. It just happens to give a type of equation that we know how to solve. In deriving the wave equation, we have chosen to represent the system in terms of the eigenkets of the position operators, instead of those of the momentum operators. We have also fixed the relative phases of the according to the Schrödinger representation, so that Equation (270) is valid. Finally, we have chosen to work in the Schrödinger picture, in which state kets evolve and dynamical variables are fixed, instead of the Heisenberg picture, in which the opposite is true.

Suppose that the ket is an eigenket of the Hamiltonian belonging to the eigenvalue : i.e.,

 (275)

The Schrödinger equation of motion, (229), yields

 (276)

This can be integrated to give

 (277)

Note that only differs from by a phase-factor. The direction of the vector remains fixed in ket space. This suggests that if the system is initially in an eigenstate of the Hamiltonian then it remains in this state for ever, as long as the system is undisturbed. Such a state is called a stationary state. The wavefunction of a stationary state satisfies

 (278)

Substituting the above relation into the Schrödinger wave equation, (274), we obtain

 (279)

where , and is the energy of the system. This is Schrödinger's time-independent wave equation. A bound state solution of the above equation, in which the particle is confined within a finite region of space, satisfies the boundary condition

 (280)

Such a solution is only possible if

 (281)

Since it is conventional to set the potential at infinity equal to zero, the above relation implies that bound states are equivalent to negative energy states. The boundary condition (280) is sufficient to uniquely specify the solution of Equation (279).

The quantity , defined by

 (282)

is termed the probability density. Recall, from Equation (121), that the probability of observing the particle in some volume element around position is proportional to . The probability is equal to if the wavefunction is properly normalized, so that

 (283)

The Schrödinger time-dependent wave equation, (274), can easily be transformed into a conservation equation for the probability density:

 (284)

The probability current, , takes the form

 (285)

We can integrate Equation (284) over all space, using the divergence theorem, and the boundary condition as , to obtain

 (286)

Thus, the Schrödinger wave equation conserves probability. In particular, if the wavefunction starts off properly normalized, according to Equation (283), then it remains properly normalized at all subsequent times. It is easily demonstrated that

 (287)

where denotes the expectation value of the momentum evaluated at time . Clearly, the probability current is indirectly related to the particle momentum.

In deriving Equations (284), we have, naturally, assumed that the potential is real. Suppose, however, that the potential has an imaginary component. In this case, Equation (284) generalizes to

 (288)

giving

 (289)

Thus, if then the total probability of observing the particle anywhere in space decreases monotonically with time. Thus, an imaginary potential can be used to account for the disappearance of a particle. Such a potential is often employed to model nuclear reactions in which incident particles are absorbed by nuclei.

Next: Exercises Up: Quantum Dynamics Previous: Ehrenfest Theorem
Richard Fitzpatrick 2013-04-08


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# How to find the number of different existing routes in a problem where there is a maze of interconnecting lines?

I had to solve this riddle from my book but so far I'm stuck at by doing several attempts and I felt it is like counting grains of sugar or some kind of sisyphean task. Can somebody help me with this?

The problem is as follows:

Using the figure from below, find the number of different routes which exist to go from point B to point A by traveling only in the directions indicated, being upwards, to the left, and in upward diagonals.

The existing alternatives given were:

$$\begin{array}{ll} 1.&63\\ 2.&39\\ 3.&48\\ 4.&56\\ 5.&52\\ \end{array}$$

Well for this one I'm totally lost. The only thing that I could come up with was to draw what it was the obvious choice, or in other words to draw the figure as depicted in orange line. But that was only one path that I could find. I tried to go in with another route which is colored as pear color, but that's how far I went.

Does it exist a way to solve this riddle more systematically and not just guessing or playing around with different combinations?.

An answer which would help me the most is one which could include perhaps an improved graphics or some sort of redrawing in Asymptote or any program showing a path or a way to solve this perhaps graphically if required.

I'd like somebody could help me with this question as I tried much effort and has not yet yielded results. Hence require assistance. Can somebody guide me on this?.

• How do you get started if you can't use downward diagonals? – Jens Feb 14 at 17:46
• You can view this as a directed graph, and use linear algebra to count walks in a directed graph – Peter Kagey Feb 14 at 17:46
• If the question was "how many ways to get from B to A", the answer would be $52$. – Jens Feb 14 at 18:09
• @Jens I'm sorry. I tried to copy my attempt from my handwritten notes, the first thing I could come up with was to draw lines between $A$ to $B$. But because I was in a rush I didn't realized that it was the other way around in other words from $B$ to $A$. Please check the edited question. Yes I noticed that downward diagonals were not allowed. – Chris Steinbeck Bell Feb 15 at 16:28
• @Jens You're indeed correct, the question was find the way from $B$ to $A$ not as it was written earlier I edited the question to reflect what it was in the original source. I'm sorry because I did it in a rush. Now for the second part I don't know how you got to $52$. – Chris Steinbeck Bell Feb 15 at 16:30

You can do this using dynamic programming. You will label each node with the number of legal paths from $$B$$ to that node. Initially, $$B$$ itself is labeled with $$1$$. Starting with the nodes which are closer to $$B$$, write label each node with the sum of the labels of its neighbors in the $$\to,\searrow,\downarrow$$ and $$\swarrow$$ directions. If there are no nodes in those direction, skip them in the sum. If you try to add up the label of an unlabeled node, first find the label of that earlier node. This works because every path to a node is preceded by a path to one of its $$\to,\searrow,\downarrow,\swarrow$$ neighbors. Adding the numbers of these paths gives the number of paths to the original node.
If I compute correctly, the answer is $$52.$$
• In your graph each node has a number which indicates the number of paths allowed from $B$ to that node, am I right?. For example the one which is on the right of label $4$ says $1$, this is $1$ because the only allowed route to get there is an upward diagonal and a straight line up, so that accounts for one path, right?. Then $4$ is $1+1+2$ the other three left corners in that square. – Chris Steinbeck Bell Feb 15 at 16:47
• But precaution must be taken as $5$ which is in the upper square is $4+1$ and not $4+1+1$ because there is no link between the $1$ which is in the bottom right of that square with the label numbered $5$. Is this part right?. Gee I hope to be understanding you well because at looking at this maze initially I felt dumbfounded. – Chris Steinbeck Bell Feb 15 at 16:47
• I believe that your answer could be improved if you add zeros to the top corners on the right side of $A$ as you did below to the left side of $B$ as they indicate they're not nodes. The more I look on it, seems that this riddle wasn't that hard as it seemed to be. I'm left curious does this approach will work with this kinds of problems or should I be aware or some caveat or advise on using this what you called dynamic programming?. Since I don't know much about it, I'd like to be careful to not incur into any misunderstanding or any error. – Chris Steinbeck Bell Feb 15 at 16:51


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# Arcsine distribution

Short description: Type of probability distribution
Parameters Probability density function Cumulative distribution function none $\displaystyle{ x \in [0,1] }$ $\displaystyle{ f(x) = \frac{1}{\pi\sqrt{x(1-x)}} }$ $\displaystyle{ F(x) = \frac{2}{\pi}\arcsin\left(\sqrt x \right) }$ $\displaystyle{ \frac{1}{2} }$ $\displaystyle{ \frac{1}{2} }$ $\displaystyle{ x \in \{0,1\} }$ $\displaystyle{ \tfrac{1}{8} }$ $\displaystyle{ 0 }$ $\displaystyle{ -\tfrac{3}{2} }$ $\displaystyle{ \ln \tfrac{\pi}{4} }$ $\displaystyle{ 1 +\sum_{k=1}^{\infty} \left( \prod_{r=0}^{k-1} \frac{2r+1}{2r+2} \right) \frac{t^k}{k!} }$ $\displaystyle{ {}_1F_1(\tfrac{1}{2}; 1; i\,t)\ }$

In probability theory, the arcsine distribution is the probability distribution whose cumulative distribution function involves the arcsine and the square root:

$\displaystyle{ F(x) = \frac{2}{\pi}\arcsin\left(\sqrt x\right)=\frac{\arcsin(2x-1)}{\pi}+\frac{1}{2} }$

for 0 ≤ x ≤ 1, and whose probability density function is

$\displaystyle{ f(x) = \frac{1}{\pi\sqrt{x(1-x)}} }$

on (0, 1). The standard arcsine distribution is a special case of the beta distribution with α = β = 1/2. That is, if $\displaystyle{ X }$ is an arcsine-distributed random variable, then $\displaystyle{ X \sim {\rm Beta}\bigl(\tfrac{1}{2},\tfrac{1}{2}\bigr) }$. By extension, the arcsine distribution is a special case of the Pearson type I distribution.

The arcsine distribution appears in the Lévy arcsine law, in the Erdős arcsine law, and as the Jeffreys prior for the probability of success of a Bernoulli trial.[1] [2]

## Generalization

Parameters $\displaystyle{ -\infty \lt a \lt b \lt \infty \, }$ $\displaystyle{ x \in [a,b] }$ $\displaystyle{ f(x) = \frac{1}{\pi\sqrt{(x-a)(b-x)}} }$ $\displaystyle{ F(x) = \frac{2}{\pi}\arcsin\left(\sqrt \frac{x-a}{b-a} \right) }$ $\displaystyle{ \frac{a+b}{2} }$ $\displaystyle{ \frac{a+b}{2} }$ $\displaystyle{ x \in {a,b} }$ $\displaystyle{ \tfrac{1}{8}(b-a)^2 }$ $\displaystyle{ 0 }$ $\displaystyle{ -\tfrac{3}{2} }$

### Arbitrary bounded support

The distribution can be expanded to include any bounded support from a ≤ x ≤ b by a simple transformation

$\displaystyle{ F(x) = \frac{2}{\pi}\arcsin\left(\sqrt \frac{x-a}{b-a} \right) }$

for a ≤ x ≤ b, and whose probability density function is

$\displaystyle{ f(x) = \frac{1}{\pi\sqrt{(x-a)(b-x)}} }$

on (ab).

### Shape factor

The generalized standard arcsine distribution on (0,1) with probability density function

$\displaystyle{ f(x;\alpha) = \frac{\sin \pi\alpha}{\pi}x^{-\alpha}(1-x)^{\alpha-1} }$

is also a special case of the beta distribution with parameters $\displaystyle{ {\rm Beta}(1-\alpha,\alpha) }$.

Note that when $\displaystyle{ \alpha = \tfrac{1}{2} }$ the general arcsine distribution reduces to the standard distribution listed above.

## Properties

• Arcsine distribution is closed under translation and scaling by a positive factor
• If $\displaystyle{ X \sim {\rm Arcsine}(a,b) \ \text{then } kX+c \sim {\rm Arcsine}(ak+c,bk+c) }$
• The square of an arcsine distribution over (-1, 1) has arcsine distribution over (0, 1)
• If $\displaystyle{ X \sim {\rm Arcsine}(-1,1) \ \text{then } X^2 \sim {\rm Arcsine}(0,1) }$

## Characteristic function

The characteristic function of the arcsine distribution is a confluent hypergeometric function and given as $\displaystyle{ {}_1F_1(\tfrac{1}{2}; 1; i\,t)\ }$.

## Related distributions

• If U and V are i.i.d uniform (−π,π) random variables, then $\displaystyle{ \sin(U) }$, $\displaystyle{ \sin(2U) }$, $\displaystyle{ -\cos(2U) }$, $\displaystyle{ \sin(U+V) }$ and $\displaystyle{ \sin(U-V) }$ all have an $\displaystyle{ {\rm Arcsine}(-1,1) }$ distribution.
• If $\displaystyle{ X }$ is the generalized arcsine distribution with shape parameter $\displaystyle{ \alpha }$ supported on the finite interval [a,b] then $\displaystyle{ \frac{X-a}{b-a} \sim {\rm Beta}(1-\alpha,\alpha) \ }$
• If X ~ Cauchy(0, 1) then $\displaystyle{ \tfrac{1}{1+X^2} }$ has a standard arcsine distribution

## Application

The arcsine distribution has an application to beamforming and pattern synthesis.[3] It is also the classical probability density for the simple harmonic oscillator.

## References

1. Overturf, Drew; Buchanan, Kristopher; Jensen, Jeffrey; Wheeland, Sara; Huff, Gregory (2017). "Investigation of beamforming patterns from volumetrically distributed phased arrays". MILCOM 2017 - 2017 IEEE Military Communications Conference (MILCOM). pp. 817–822. doi:10.1109/MILCOM.2017.8170756. ISBN:978-1-5386-0595-0. https://ieeexplore.ieee.org/abstract/document/8170756/
2. K. Buchanan, J. Jensen, C. Flores-Molina, S. Wheeland and G. H. Huff, "Null Beamsteering Using Distributed Arrays and Shared Aperture Distributions," in IEEE Transactions on Antennas and Propagation, vol. 68, no. 7, pp. 5353-5364, July 2020, doi: 10.1109/TAP.2020.2978887.
3. Overturf, Drew; Buchanan, Kris; Jensen, Jeff; Flores-Molina, Carlos; Wheeland, Sara; Huff, Gregory H. (2017). "Investigation of beamforming patterns from volumetrically distributed phased arrays". MILCOM 2017 - 2017 IEEE Military Communications Conference (MILCOM). pp. 817–822. doi:10.1109/MILCOM.2017.8170756. ISBN 978-1-5386-0595-0.