text:
# Ho, Mun S.

2021
Jing Cao, Mun S. Ho, Rong Ma, and Fei Teng. 2021. “When carbon emission trading meets a regulated industry: Evidence from the electricity sector of China.” Journal for Public Economics, 200, August, Pp. 104470. Publisher's VersionAbstract
This paper provides retrospective firm-level evidence on the effectiveness of China’s carbon market pilots in reducing emissions in the electricity sector. We show that the carbon emission trading system (ETS) has no effect on changing coal efficiency of regulated coal- fired power plants. Although we find a significant reduction in coal consumption associated with ETS participation, this reduction was achieved by reducing electricity production. The output contraction in the treated plants is not due to their optimizing behavior but is likely driven by government decisions, because the impacts of emission permits on marginal costs are small relative to the controlled electricity prices and the reduction is associated with financial losses. In addition, we find no evidence of carbon leakage to other provinces, but a significant increase in the production of non-coal-fired power plants in the ETS regions.
Jing Cao, Hancheng Dai, Shantong Li, Chaoyi Guo, Mun Ho, Wenjia Cai, Jianwu He, Hai Huang, Jifeng Li, Yu Liu, Haoqi Qian, Can Wang, Libo Wu, and Xiliang Zhang. 2021. “The general equilibrium impacts of carbon tax policy in China: a multi-model assessment.” Energy Economics, 99, July, Pp. 105284. Publisher's VersionAbstract
We conduct a multi-model comparison of a carbon tax policy in China to examine how different models simulate the impacts in both near-term 2020, medium-term 2030, and distant future 2050. Though Top-down computable general equilibrium(CGE) models have been applied frequently on climate or other environmental/energy policies to assess emission reduction, energy use and economy-wide general equilibrium outcomes in China, the results often vary greatly across models, making it challenging to derive policies. We compare 8 China CGE models with different characteristics to examine how they estimate the effects of a plausible range of carbon tax scenarios – low, medium and high carbon taxes.. To make them comparable we impose the same population growth, the same GDP growth path and world energy price shocks. We find that the 2030 NDC target for China are easily met in all models, but the 2060 carbon neutrality goal cannot be achieved even with our highest carbon tax rates. Through this carbon tax comparison, we find all 8 CGE models differ substantially in terms of impacts on the macroeconomy, aggregate prices, energy use and carbon reductions, as well as industry level output and price effects. We discuss the reasons for the divergent simulation results including differences in model structure, substitution parameters, baseline renewable penetration and methods of revenue recycling.
Jaume Freire-González and Mun S. Ho. 2021. “Voluntary actions in households and climate change mitigation.” Journal of Cleaner Production, 321, 25 October, Pp. 128930. Publisher's VersionAbstract
Governments foster voluntary actions within households to mitigate climate change. However, the literature suggests that they may not be as effective as expected due to rebound effects. We use a dynamic economy–energy–environment computable general equilibrium (CGE) model of the Catalan economy to simulate the effect of 75 different actions on GDP and net CO2 emissions, over a 20-year period. We also examine how a carbon tax could counteract the carbon rebound effects. We find energy rebound effects ranging from 61.77% to 117.49% for voluntary energy conservation actions, depending on where the spending is redirected, with similar carbon rebound values. In our main scenarios, where energy savings are redirected to savings and all non-energy goods proportionally, the rebound is between 64.47% and 66.90%. We also find, for these scenarios, that a carbon tax of between 2.4 and 3.6 €/ton per percentage point of voluntary energy reduction would totally offset carbon rebound effects. These results suggest that voluntary actions in households need additional measures to provide the expected results in terms of energy use reduction and climate change mitigation.
2020
Jing Cao, Mun S. Ho, and Wenhao Hu. 2020. “Analyzing carbon price policies using a general equilibrium model with household energy demand functions.” In Measuring Economic Growth and Productivity: Foundations, KLEMS Production Models, and Extensions, edited by Barbara Fraumeni. Cambridge, MA: Academic Press. Publisher's VersionAbstract

Multi-sector general equilibrium models are used to simulate the effects of environmental policies on industry output and consumption at disaggregated levels. The specification of household demand in such models often use simpler forms such as CES or Linear Expenditure Systems since there are few estimates of more flexible systems. We estimate a 2-stage translog utility function that explicitly accounts for detailed energy expenditures to allow us to capture the price and income effects more accurately than these simpler forms. We incorporate this into a China growth model to simulate the effects of a carbon price to achieve the government targets for the Climate Change (Paris) agreements.

Final Manuscript in DASH.
An edited volume dedicated to Prof. Dale W. Jorgenson by his students and collaborators.

Jing Cao, Mun S Ho, and Rong Ma. 2020. “Analyzing carbon pricing policies using a general equilibrium model with production parameters estimated using firm data.” Energy Economics, 92, October, Pp. 104958. Publisher's VersionAbstract

Policy simulation results of Computable General Equilibrium (CGE) models largely hinge on the choices of substitution elasticities among key input factors. Currently, most CGE models rely on the common elasticities estimated from aggregated data, such as the GTAP model elasticity parameters. Using firm level data, we apply the control function method to estimate CES production functions with capital, labor and energy inputs and find significant heterogeneity in substitution elasticities across different industries. Our capital-labor substitution elasticities are much lower than the GTAP values while our energy elasticities are higher. We then incorporate these estimated elasticities into a CGE model to simulate China's carbon pricing policies and compare with the results using GTAP parameters. Our less elastic K-L substitution lead to lower base case GDP growth, but our more elastic energy substitution lead to lower coal use and carbon emissions. In the carbon tax policy exercises, we find that our elasticities lead to easier reductions in coal use and carbon emissions.

Jing Cao, Mun S. Ho, Wenhao Hu, and Dale Jorgenson. 2020. “Effective labor supply and growth outlook in China.” China Economic Review, 61, June, Pp. 101398. Publisher's VersionAbstract
The falling projections of working-age population in China has led to predictions of much slower economic growth. We consider three mechanisms that could contribute to higher effective labor supply growth – further improvement in educational attainment due to cohort replacement and rising college enrollment, improvement in aggregate labor quality due to urbanization, and higher labor force participation due to later retirement. We find that these factors result in a projected growth rate of effective labor input of 0.40% for 2015-2030 compared to -0.60% for working age population. As a result, the projected growth rate of GDP will be 5.80% for 2015-2030 compared to 5.23% if these factors are ignored.
Richard Goettle, Mun S. Ho, and Peter Wilcoxen. 2020. “Emissions accounting and carbon tax incidence in CGE models: bottom-up versus top-down.” In Measuring Economic Growth and Productivity: Foundations, KLEMS Production Models, and Extensions, edited by Fraumeni, B, 1st ed. Cambridge, MA: Academic Press. Publisher's VersionAbstract
Multi-sector general equilibrium models are the work-horses used to analyze the impact of carbon prices in climate policy discussions. Such models often have distinct industries to represent coal, liquid fuels, and gas production where the output over time is represented by quantity and price indexes. The industries that buy these fuels, however, do not use a common homogenous quantity (e.g., steam coal vs. metallurgical coal) and have distinct purchasing price indexes. In accounting for energy use or CO2 emissions, modelers choose to attach coefficients either bottom-up to a sector specific input index or top-down to an average output index and this choice has a direct bearing on the incidence of carbon taxation. We discuss how different accounting methods for the differences in prices can have a large effect on the simulated impact of carbon prices. We emphasize the importance for modelers to be explicit about their methods.
An edited volume dedicated to Prof. Dale W. Jorgenson by his students and collaborators.  Final Manuscript in DASH
Jing Cao, Mun S. Ho, Wenhao Hu, and Dale W. Jorgensen. 2020. “Estimating flexible consumption functions for urban and rural households in China.” China Economic Review, 61, June, Pp. 101453. Publisher's VersionAbstract

There are few comprehensive studies of household consumption in China due to data restrictions. This prevents the calculation of inequality indices based on consumption. Secondly, this makes a comprehensive analysis of policies that affect consumption difficult; economy-wide models used for analysis often have to employ simple consumption forms with unit income elasticities. We estimate a translog demand system distinguished by demographic characteristics, giving price and income elasticities that should be useful for policy analysis. We estimate separate functions for urban and rural households using household expenditure data and detailed commodity prices (1995-2006). This allows future analysis of social welfare and inequality based on consumption to supplement existing studies based on income. To illustrate an application of the model, we project consumption composition based on projected prices, incomes and demographic changes – aging, education improvement and urbanization.

Mun Ho, Wolfgang Britz, Ruth Delzeit, Florian Leblanc, Roson Roberto, Franziska Schuenemann, and Matthias Weitzel. 2020. “Modelling consumption and constructing long-term baselines in final demand.” Journal of Global Economic Analysis, 5, 1, Pp. 63-108. Publisher's VersionAbstract
Modelling and projecting consumption, investment and government demand by detailed commodities in CGE models poses many data and methodological challenges. We review the state of knowledge of modelling consumption of commodities (price and income elasticities and demographics), as well as the historical trends that we should be able to explain. We then discuss the current approaches taken in CGE models to project the trends in demand at various levels of commodity disaggregation. We examine the pros and cons of the various approaches to adjust parameters over time or using functions of time and suggest a research agenda to improve modelling and projection. We compare projections out to 2050 using LES, CES and AIDADS functions in the same CGE model to illustrate the size of the differences. In addition, we briefly discuss the allocation of total investment and government demand to individual commodities.
Jing Cao, Mun S Ho, Wenhao Hu, and Dale W Jorgenson. 2020. “Urban household consumption in China: price, income and demographic effects.” Review of Development Economics, 152, 25 October, Pp. 810-833. Publisher's Version
2019
Jaume Freire-González and Mun S. Ho. 2019. “Carbon taxes and the double dividend hypothesis in a recursive-dynamic CGE model for Spain.” Economic Systems Research, 31, 2, Pp. 267-284.Abstract
A carbon tax is potentially a policy that can reduce CO2 emissions and mitigate climate risks, at lowest economy-wide costs. We develop a dynamic CGE model for Spain to assess the economic and environmental effects of a carbon tax, and test the double dividend (DD) hypothesis. We simulate the impact of three carbon taxes: €10, €20 and €30 per ton of CO2. For each tax, four ‘revenue recycling’ scenarios are examined: a reduction of taxes on capital, on labor, on value-added tax, and a scenario in which revenues are not recycled. We find a DD for taxes of €10/ton and lower, within five to seven years of implementation. We estimate an annual CO2 emissions reduction of around 10% with this tax. Under some circumstances, the DD can be achieved for a tax of €20/ton. In any case, recycling revenues to cut pre-existing taxes reduces costs of imposing carbon taxes.
Jing Cao, Mun S. Ho, Dale W. Jorgenson, and Chris P. Nielsen. 2019. “China’s emissions trading system and an ETS-carbon tax hybrid.” Energy Economics, 81, June, Pp. 741-753. Publisher's VersionAbstract
China is introducing a national carbon emission trading system (ETS), with details yet to be finalized. The ETS is expected to cover only the major emitters but it is often argued that a more comprehensive system will achieve the emission goals at lower cost. We first examine an ETS that covers both electricity and cement sectors and consider an ambitious cap starting in 2017 that will meet the official objective to reduce the carbon-GDP intensity by 60-65% by 2030 compared to 2005 levels. The two ETS-covered industries are compensated with an output-based subsidy to represent the intention to give free permits to the covered enterprises. We then consider a hybrid system where the non-ETS sectors pay a carbon tax and share in the CO2 reduction burden. Our simulations indicate that hybrid systems will achieve the same CO2 goals with lower permit prices and GDP losses. We also show how auctioning of the permits improves the efficiency of the ETS and the hybrid systems. Finally, we find that these CO2 control policies are progressive in that higher incomes households bear a bigger burden.
Jing Cao, Mun S. Ho, Yating Li, Richard G. Newell, and William A. Pizer. 2019. “Chinese residential electricity consumption estimation and forecast using micro-data.” Resource and Energy Economics, 56, May, Pp. 6-27. Publisher's VersionAbstract
Based on econometric estimation using data from the Chinese Urban Household Survey, we develop a preferred forecast range of 85–143 percent growth in residential per capita electricity demand over 2009–2025. Our analysis suggests that per capita income growth drives a 43% increase, with the remainder due to an unexplained time trend. Roughly one-third of the income-driven demand comes from increases in the stock of specific major appliances, particularly AC units. The other two-thirds comes from non-specific sources of income-driven growth and is based on an estimated income elasticity that falls from 0.28 to 0.11 as income rises. While the stock of refrigerators is not projected to increase, we find that they contribute nearly 20 percent of household electricity demand. Alternative plausible time trend assumptions are responsible for the wide range of 85–143 percent. Meanwhile we estimate a price elasticity of demand of −0.7. These estimates point to carbon pricing and appliance efficiency policies that could substantially reduce demand.
Jing Cao, Mun S Ho, and Wenhao Hu. 2019. “Energy consumption of urban households in China.” China Economic Review, 58, 101343. Publisher's VersionAbstract
We estimate China urban household energy demand as part of a complete system of consumption demand so that it can be used in economy-wide models. This allows us to derive cross-price elasticities unlike studies which focus on one type of energy. We implement a two-stage approach and explicitly account for electricity, domestic fuels and transportation demand in the first stage and gasoline, coal, LPG and gas demand in the second stage. We find income inelastic demand for electricity and home energy, but the elasticity is higher than estimates in the rich countries. Demand for total transportation is income elastic. The price elasticity for electricity is estimated to be −0.5 and in the range of other estimates for China, and similar to long-run elasticities estimated for the U.S.
2018
Govinda R. Timilsina, Jing Cao, and Mun S. Ho. 2018. “Carbon tax for achieving China's NDC: Simulations of some design features using a CGE model.” Climate Change Economics, 9, 3. Publisher's VersionAbstract
China has set a goal of reducing its CO2 intensity of GDP by 60–65% from the 2005 level in 2030 as its nationally determined contribution (NDC) under the Paris Climate Change Agreement. While the government is considering series of market and nonmarket measures to achieve its target, this study assesses the economic consequences if the target were to meet through a market mechanism, carbon tax. We used a dynamic computable general equilibrium model of China for the analysis. The study shows that the level of carbon tax to achieve the NDC target would be different depending on its design features. An increasing carbon tax that starts at a small rate in 2015 and rises to a level to meet the NDC target in 2030 would cause smaller GDP loss than the carbon tax with a constant rate would do. The GDP loss due to the carbon tax would be smaller when the tax revenue is utilized to cut existing distortionary taxes than when it is transferred to households as a lump-sum rebate.
Jaume Freire-González and Mun S. Ho. 2018. “Environmental fiscal reform and the double dividend: evidence from a dynamic general equilibrium model.” Sustainability, 10, 2. Publisher's VersionAbstract
An environmental fiscal reform (EFR) represents a transition of a taxation system toward one based in environmental taxation, rather than on taxation of capital, labor, or consumption. It differs from an environmental tax reform (ETR) in that an EFR also includes a reform of subsidies which counteract environmental policy. This research details different ways in which an EFR is not only possible but also a good option that provides economic and environmental benefits. We have developed a detailed dynamic CGE model examining 101 industries and commodities in Spain, with an energy and an environmental extension comprising 31 pollutant emissions, in order to simulate the economic and environmental effects of an EFR. The reform focuses on 39 industries related to the energy, water, transport and waste sectors. We simulate an increase in taxes and a reduction on subsidies for these industries and at the same time we use new revenues to reduce labor, capital and consumption taxes. All revenue recycling options provide both economic and environmental benefits, suggesting that the “double dividend” hypothesis can be achieved. After three to four years after implementing an EFR, GDP is higher than the base case, hydrocarbons consumption declines and all analyzed pollutants show a reduction.
Xiaolin Guo, Mun Sing Ho, Liangzhi You, Jing Cao, Yu Fang, Taotao Tu, and Yang Hong. 2018. “Industrial water pollution discharge taxes in China: A multi-sector dynamic analysis.” Water, 10, 12, Pp. 1742. Publisher's VersionAbstract
We explore how water pollution policy reforms in China could reduce industrial wastewater pollution with minimum adverse impact on GDP growth. We use a multi-sector dynamic Computable General Equilibrium (CGE) model, jointly developed by Harvard University and Tsinghua University, to examine the long-term impact of pollution taxes. A firm-level dataset of wastewater and COD discharge is compiled and aggregated to provide COD-intensities for 22 industrial sectors. We simulated the impact of 4 different sets of Pigovian taxes on the output of these industrial sectors, where the tax rate depends on the COD-output intensity. In the baseline low rate of COD tax, COD discharge is projected to rise from 36 million tons in 2018 to 48 million in 2030, while GDP grows at 6.9% per year. We find that raising the COD tax by 8 times will lower COD discharge by 1.6% by 2030, while a high 20-times tax will cut it by 4.0%. The most COD-intensive sectors—textile goods, apparel, and food products—have the biggest reduction in output and emissions. The additional tax revenue is recycled by cutting existing taxes, including taxes on profits, leading to higher investment. This shift from consumption to investment leads to a slightly higher GDP over time.
2016
Jing Cao, Mun S. Ho, and Huifang Liang. 2016. “Household energy demand in urban China: Accounting for regional prices and rapid economic change.” The Energy Journal, 37. Publisher's VersionAbstract

Understanding the rapidly rising demand for energy in China is essential to efforts to reduce the country's energy use and environmental damage. In response to rising incomes and changing prices and demographics, household use of various fuels, electricity and gasoline has changed dramatically in China. In this paper, we estimate both income and price elasticities for various energy types using Chinese urban household micro-data collected by National bureau of Statistics, by applying a two-stage budgeting AIDS model. We find that total energy is price and income inelastic for all income groups after accounting for demographic and regional effects. Our estimated electricity price elasticity ranges from - 0.49 to -0.57, gas price elasticity ranges from -0.46 to -0.94, and gasoline price elasticity ranges from -0.85 to -0.94. Income elasticity for various energy types range from 0.57 to 0.94. Demand for coal is most price and income elastic among the poor, whereas gasoline demand is elastic for the rich.

2013
Chris P Nielsen and Mun S Ho. 2013. “Atmospheric Environment in China: Introduction and Research Review.” In Clearer Skies Over China: Reconciling Air Quality, Climate, and Economic Goals, Pp. 3-58. Cambridge, MA: MIT Press. Publisher's VersionAbstract

A groundbreaking U.S.–Chinese inquiry into the effects of recent air pollution controls and prospective carbon taxes on China's economy and environment.

China's carbon dioxide emissions now outstrip those of other countries and its domestic air quality is severely degraded, especially in urban areas. Its sheer size and its growing, fossil-fuel-powered economy mean that China's economic and environmental policy choices will have an outsized effect on the global environmental future. Over the last decade, China has pursued policies that target both fossil fuel use and atmospheric emissions, but these efforts have been substantially overwhelmed by the country's increasing energy demands. With a billion citizens still living on less than $4,000 per year, China's energy and environmental policies must be reconciled with the goals of maintaining economic growth and raising living standards. This book, a U.S.–Chinese collaboration of experts from Harvard and Tsinghua University, offers a groundbreaking integrated analysis of China's economy, emissions, air quality, public health, and agriculture. It first offers essential scientific context and accessible summaries of the book's policy findings; it then provides the underlying scientific and economic research. These studies suggest that China's recent sulfur controls achieved enormous environmental health benefits at unexpectedly low costs. They also indicate that judicious implementation of carbon taxes could reduce not only China's carbon emissions but also its air pollution more comprehensively than current single-pollutant policies, all at little cost to economic growth. 2013. Clearer Skies Over China: Reconciling Air Pollution, Climate, and Economic Goals. Cambridge, MA: MIT Press. Publisher's VersionAbstract A groundbreaking U.S.–Chinese inquiry into the effects of recent air pollution controls and prospective carbon taxes on China's economy and environment. China's carbon dioxide emissions now outstrip those of other countries and its domestic air quality is severely degraded, especially in urban areas. Its sheer size and its growing, fossil-fuel-powered economy mean that China's economic and environmental policy choices will have an outsized effect on the global environmental future. Over the last decade, China has pursued policies that target both fossil fuel use and atmospheric emissions, but these efforts have been substantially overwhelmed by the country's increasing energy demands. With a billion citizens still living on less than$4,000 per year, China's energy and environmental policies must be reconciled with the goals of maintaining economic growth and raising living standards.

This book, a U.S.–Chinese collaboration of experts from Harvard and Tsinghua University, offers a groundbreaking integrated analysis of China's economy, emissions, air quality, public health, and agriculture. It first offers essential scientific context and accessible summaries of the book's policy findings; it then provides the underlying scientific and economic research. These studies suggest that China's recent sulfur controls achieved enormous environmental health benefits at unexpectedly low costs. They also indicate that judicious implementation of carbon taxes could reduce not only China's carbon emissions but also its air pollution more comprehensively than current single-pollutant policies, all at little cost to economic growth.


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# The following is an 8051 instruction: CJNE A, # 'Q' ,AHEAD a) what is the opcode for this instruction? b) how many bytes long is this instruction? c) explain the purpose of each byte of this instruction. d) how many machine cycles are required to execute this instruction? e) If an 8051 is operating from a 10 MHz crystal, how longdoes this instruction take to execute?

Question
Other
The following is an 8051 instruction: CJNE A, # 'Q' ,AHEAD
a) what is the opcode for this instruction?
b) how many bytes long is this instruction?
c) explain the purpose of each byte of this instruction.
d) how many machine cycles are required to execute this instruction?
e) If an 8051 is operating from a 10 MHz crystal, how longdoes this instruction take to execute?

2021-04-26
a)OPCODE OxB4
b)no.ofbytes 3
c)the first byte contains the first operand
direct data specified
the second and third byte are relative address AHEAD

### Relevant Questions

We will now add support for register-memory ALU operations to the classic five-stage RISC pipeline. To offset this increase in complexity, all memory addressing will be restricted to register indirect (i.e., all addresses are simply a value held in a register; no offset or displacement may be added to the register value). For example, the register-memory instruction add x4, x5, (x1) means add the contents of register x5 to the contents of the memory location with address equal to the value in register x1 and put the sum in register x4. Register-register ALU operations are unchanged. The following items apply to the integer RISC pipeline:
a. List a rearranged order of the five traditional stages of the RISC pipeline that will support register-memory operations implemented exclusively by register indirect addressing.
b. Describe what new forwarding paths are needed for the rearranged pipeline by stating the source, destination, and information transferred on each needed new path.
c. For the reordered stages of the RISC pipeline, what new data hazards are created by this addressing mode? Give an instruction sequence illustrating each new hazard.
d. List all of the ways that the RISC pipeline with register-memory ALU operations can have a different instruction count for a given program than the original RISC pipeline. Give a pair of specific instruction sequences, one for the original pipeline and one for the rearranged pipeline, to illustrate each way.
Hint for (d): Give a pair of instruction sequences where the RISC pipeline has “more” instructions than the reg-mem architecture. Also give a pair of instruction sequences where the RISC pipeline has “fewer” instructions than the reg-mem architecture.
A 2.4-kg object is attached to a horizontal spring of forceconstant k=4.5 kN/m. The spring is stretched 10 cm fromequilibrium and released. Find (a) the frequency of themotion, (b) the period, (c) the amplitude, (d) the maximum speed,and (e) the maximum acceleration. (f) When does the objectfirst reach its equilibrium position? What is itsacceleration at this time?
Two identical blocks placed one on top of the other rest on africtionless horizontal air track. The lower block isattached to a spring of spring constant k= 600 N/m. Whendisplaced slightly from its equilibrium position, the systemoscillates with a frequency of 1.8 Hz. When the amplitude ofoscillation exceeds 5 cm, the upper block starts to slide relativeto the lower one. (a) What are the masses of the twoblocks? (b) What is the coefficient of static frictionbetween the two blocks?
The bulk density of soil is defined as the mass of dry solidsper unit bulk volume. A high bulk density implies a compact soilwith few pores. Bulk density is an important factor in influencing root development, seedling emergence, and aeration. Let X denotethe bulk density of Pima clay loam. Studies show that X is normally distributed with $$\displaystyle\mu={1.5}$$ and $$\displaystyle\sigma={0.2}\frac{{g}}{{c}}{m}^{{3}}$$.
(a) What is thedensity for X? Sketch a graph of the density function. Indicate onthis graph the probability that X lies between 1.1 and 1.9. Findthis probability.
(b) Find the probability that arandomly selected sample of Pima clay loam will have bulk densityless than $$\displaystyle{0.9}\frac{{g}}{{c}}{m}^{{3}}$$.
(c) Would you be surprised if a randomly selected sample of this type of soil has a bulkdensity in excess of $$\displaystyle{2.0}\frac{{g}}{{c}}{m}^{{3}}$$? Explain, based on theprobability of this occurring.
(d) What point has the property that only 10% of the soil samples have bulk density this high orhigher?
(e) What is the moment generating function for X?

When a gas is taken from a to c along the curved path in the figure (Figure 1) , the work done by the gas is W = -40 J and the heat added to the gas is Q = -140 J . Along path abc, the work done by the gas is W = -50 J . (That is, 50 J of work is done on the gas.)
I keep on missing Part D. The answer for part D is not -150,150,-155,108,105( was close but it said not quite check calculations)
Part A
What is Q for path abc?
Express your answer to two significant figures and include the appropriate units.
Part B
f Pc=1/2Pb, what is W for path cda?
Express your answer to two significant figures and include the appropriate units.
Part C
What is Q for path cda?
Express your answer to two significant figures and include the appropriate units.
Part D
What is Ua?Uc?
Express your answer to two significant figures and include the appropriate units.
Part E
If Ud?Uc=42J, what is Q for path da?
Express your answer to two significant figures and include the appropriate units.
A stunt man whose mass is 70 kg swings from the end ofa 4.0 m long rope along thearc of a vertical circle. Assuming that he starts from rest whenthe rope is horizontal, find the tensions in the rope that are required to make him follow his circular path at each of the following points.
(a) at the beginning of his motion N
(b) at a height of 1.5 m above the bottom of the circular arc N
(c) at the bottom of the arc N
How long does it take for an investment to double in value if it is invested at $$14\%$$ compounded quarterly and compounded continuously?
a) At $$14\%$$ compounded quarterly, the investment doubles in how many years?
b) At $$14\%$$ compounded continuously, the investment doubles in how many years?
Hypothetical potential energy curve for aparticle of mass m
If the particle is released from rest at position r0, its speed atposition 2r0, is most nearly
a) $$\displaystyle{\left({\frac{{{8}{U}{o}}}{{{m}}}}\right)}^{{1}}{\left\lbrace/{2}\right\rbrace}$$
b) $$\displaystyle{\left({\frac{{{6}{U}{o}}}{{{m}}}}\right)}^{{\frac{{1}}{{2}}}}$$
c) $$\displaystyle{\left({\frac{{{4}{U}{o}}}{{{m}}}}\right)}^{{\frac{{1}}{{2}}}}$$
d) $$\displaystyle{\left({\frac{{{2}{U}{o}}}{{{m}}}}\right)}^{{\frac{{1}}{{2}}}}$$
e) $$\displaystyle{\left({\frac{{{U}{o}}}{{{m}}}}\right)}^{{\frac{{1}}{{2}}}}$$
if the potential energy function is given by
$$\displaystyle{U}{\left({r}\right)}={b}{r}^{{P}}-\frac{{3}}{{2}}\rbrace+{c}$$
where b and c are constants
which of the following is an edxpression of the force on theparticle?
1) $$\displaystyle{\frac{{{3}{b}}}{{{2}}}}{\left({r}^{{-\frac{{5}}{{2}}}}\right)}$$
2) $$\displaystyle{\frac{{{3}{b}}}{{{2}}}}{\left\lbrace{3}{b}\right\rbrace}{\left\lbrace{2}\right\rbrace}{\left({r}^{{-\frac{{1}}{{2}}}}\right)}$$
3) $$\displaystyle{\frac{{{3}{b}}}{{{2}}}}{\left\lbrace{3}\right\rbrace}{\left\lbrace{2}\right\rbrace}{\left({r}^{{-\frac{{1}}{{2}}}}\right)}$$
4) $$\displaystyle{2}{b}{\left({r}^{{-\frac{{1}}{{2}}}}\right)}+{c}{r}$$
5) $$\displaystyle{\frac{{{3}{b}}}{{{2}}}}{\left\lbrace{2}{b}\right\rbrace}{\left\lbrace{5}\right\rbrace}{\left({r}^{{-\frac{{5}}{{2}}}}\right)}+{c}{r}$$
The dominant form of drag experienced by vehicles (bikes, cars,planes, etc.) at operating speeds is called form drag. Itincreases quadratically with velocity (essentially because theamount of air you run into increase with v and so does the amount of force you must exert on each small volume of air). Thus
$$\displaystyle{F}_{{{d}{r}{u}{g}}}={C}_{{d}}{A}{v}^{{2}}$$
where A is the cross-sectional area of the vehicle and $$\displaystyle{C}_{{d}}$$ is called the coefficient of drag.
Part A:
Consider a vehicle moving with constant velocity $$\displaystyle\vec{{{v}}}$$. Find the power dissipated by form drag.
Express your answer in terms of $$\displaystyle{C}_{{d}},{A},$$ and speed v.
Part B:
A certain car has an engine that provides a maximum power $$\displaystyle{P}_{{0}}$$. Suppose that the maximum speed of thee car, $$\displaystyle{v}_{{0}}$$, is limited by a drag force proportional to the square of the speed (as in the previous part). The car engine is now modified, so that the new power $$\displaystyle{P}_{{1}}$$ is 10 percent greater than the original power ($$\displaystyle{P}_{{1}}={110}\%{P}_{{0}}$$).
Assume the following:
The top speed is limited by air drag.
The magnitude of the force of air drag at these speeds is proportional to the square of the speed.
By what percentage, $$\displaystyle{\frac{{{v}_{{1}}-{v}_{{0}}}}{{{v}_{{0}}}}}$$, is the top speed of the car increased?
Express the percent increase in top speed numerically to two significant figures.

A random sample of $$n_1 = 14$$ winter days in Denver gave a sample mean pollution index $$x_1 = 43$$.
Previous studies show that $$\sigma_1 = 19$$.
For Englewood (a suburb of Denver), a random sample of $$n_2 = 12$$ winter days gave a sample mean pollution index of $$x_2 = 37$$.
Previous studies show that $$\sigma_2 = 13$$.
Assume the pollution index is normally distributed in both Englewood and Denver.
(a) State the null and alternate hypotheses.
$$H_0:\mu_1=\mu_2.\mu_1>\mu_2$$
$$H_0:\mu_1<\mu_2.\mu_1=\mu_2$$
$$H_0:\mu_1=\mu_2.\mu_1<\mu_2$$
$$H_0:\mu_1=\mu_2.\mu_1\neq\mu_2$$
(b) What sampling distribution will you use? What assumptions are you making? NKS The Student's t. We assume that both population distributions are approximately normal with known standard deviations.
The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations.
The standard normal. We assume that both population distributions are approximately normal with known standard deviations.
The Student's t. We assume that both population distributions are approximately normal with unknown standard deviations.
(c) What is the value of the sample test statistic? Compute the corresponding z or t value as appropriate.
(Test the difference $$\mu_1 - \mu_2$$. Round your answer to two decimal places.) NKS (d) Find (or estimate) the P-value. (Round your answer to four decimal places.)
(e) Based on your answers in parts (i)−(iii), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level \alpha?
At the $$\alpha = 0.01$$ level, we fail to reject the null hypothesis and conclude the data are not statistically significant.
At the $$\alpha = 0.01$$ level, we reject the null hypothesis and conclude the data are statistically significant.
At the $$\alpha = 0.01$$ level, we fail to reject the null hypothesis and conclude the data are statistically significant.
At the $$\alpha = 0.01$$ level, we reject the null hypothesis and conclude the data are not statistically significant.
(f) Interpret your conclusion in the context of the application.
Reject the null hypothesis, there is insufficient evidence that there is a difference in mean pollution index for Englewood and Denver.
Reject the null hypothesis, there is sufficient evidence that there is a difference in mean pollution index for Englewood and Denver.
Fail to reject the null hypothesis, there is insufficient evidence that there is a difference in mean pollution index for Englewood and Denver.
Fail to reject the null hypothesis, there is sufficient evidence that there is a difference in mean pollution index for Englewood and Denver. (g) Find a 99% confidence interval for
$$\mu_1 - \mu_2$$.
(Round your answers to two decimal places.)
lower limit
upper limit
(h) Explain the meaning of the confidence interval in the context of the problem.
Because the interval contains only positive numbers, this indicates that at the 99% confidence level, the mean population pollution index for Englewood is greater than that of Denver.
Because the interval contains both positive and negative numbers, this indicates that at the 99% confidence level, we can not say that the mean population pollution index for Englewood is different than that of Denver.
Because the interval contains both positive and negative numbers, this indicates that at the 99% confidence level, the mean population pollution index for Englewood is greater than that of Denver.
Because the interval contains only negative numbers, this indicates that at the 99% confidence level, the mean population pollution index for Englewood is less than that of Denver.

format: plain


text:
### MX_DTRNSP – General matrix transposition: B := alpha*A^T

Block SymbolLicensing group: STANDARD

Function Description
The function block MX_DTRNSP stores the scalar multiple of the general (i.e. rectangular) matrix referenced by uA into the matrix referenced by uB.

The output references yA and yB are always set to the corresponding input references uA and uB. If HLD = on then nothing else is done otherwise the BLAS-like function X_DTRNSP is called internally:

X_DTRNSP(M, N, ALPHA, uA, LDA, uB, LDB);

where parameters of X_DTRNSP are set in the following way:

• M is number of rows of the matrix referenced by uA.
• N is number of columns of the matrix referenced by uA.
• If the input alpha is equal to 0 then ALPHA is set to $1$ else ALPHA is set to alpha.
• LDA and LDB are leading dimensions of matrices referenced by uA and uB.

The error flag E is set to on if:

• the reference uA or uB is not defined (i.e. input uA or uB is not connected),
• the call of the function X_DTRNSP returns error using the function XERBLA, see the system log.

Inputs

 uA Input reference to matrix A Reference uB Input reference to matrix B Reference alpha Scalar coefficient alpha  $\odot$0.0 Double (F64) HLD Hold Bool

Outputs

 yA Output reference to matrix A Reference yB Output reference to matrix B Reference E Error indicator Bool

2020 © REX Controls s.r.o., www.rexygen.com


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# Boolean equation

2010 Mathematics Subject Classification: Primary: 06E [MSN][ZBL]

An equation of the form

$$f(x_1,\ldots,x_n)=0,\tag{*}$$

where $f$ is a Boolean function in $n$ variables. The set of all solutions of an equation of the form (*) can be described by a system of Boolean functions depending on $n$ arbitrary parameters.

#### References

 [1] G. Birkhoff, "Lattice theory" , Colloq. Publ. , 25 , Amer. Math. Soc. (1973)
How to Cite This Entry:
Boolean equation. Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Boolean_equation&oldid=34921
This article was adapted from an original article by T.S. Fofanova (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article


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# Isomorphism of G with product group $H \times N$.

This is a question I attempted from a text book. And I would like to know how far I am correct in my arguments and thought process.

Let $H$ be a subgroup of a group $G$, and let $\phi: G \to H$ be a homomorphism whose restriction to $H$ is the identity map: $\phi(h) = h$ , if $h \in H$. Let $N = ker(\phi)$

(a) Prove that if $G$ is abelian then it is isomorphic to the product group $H \times N$. (b) Find a bijective map $G\to H \times N$ without the assumption that $G$ is abelian, but show by an example that $G$ need not be isomorphic to the product group.

My attempt: (a) Aim is show a bijection and homomorphism between $G$ and $H \times N$. Denote the isomorphism as $\psi : H \times N \to G$

First looking at the homomorhism $\phi$, I see that it's surgective homomorphism since each element in the codomain $H$ is mapped at least to $H$ subgroup in $G$.

We have $\phi: G \to H$, i.e., the the whole group has $H$ as it's image which is also the image of $H$ subgroup in $G$. $\phi(H)=H$ and $\phi^{-1}(\phi(H))=G=NH$(also $=HN$ since $N$ is a normal subgroup). Thus $G = HN$ which assures the surgectivity of $\psi$

Next observation is that $H \cap N$ is $\{1\}$ since $\phi(h) = h$ , if $h \in H$. Consider elements $(h_1,n_1), (h_2,n_2)$ in $H \times N$ which have same image $h_1n_1=h_2n_2$ in $HN$. i.e., $h_1h_2^{-1}=n_1^{-1}n_2$. So, $h_1h_2^{-1}=n_1^{-1}n_2 = 1$. Hence $h_1=h_2$ and $n_1=n_2$. Injectivy of $\psi$ is shown.

Now consider the composition of two elements in $H \times N$ $(h_1,n_1)$ and $(h_2,n_2)$, $(h_1h_2,n_1n_2)$. It's image in $G=HN$ would be $h_1h_2n_1n_2$ while the composition of individual products in $G$ would be $h_1n_1h_2n_2$. Since $G$ is abelian we say these are equal. Hence we have a homomorphism along with bijection making it isomorhism for $\psi: H \times N \to G$ .

(b) If $G$ is not abelian, we don't have homomorphism, but we still have bijection $\psi: H \times N \to G$ defined by $\psi(h,n)=hn$

Please let me know if there are any incorrect/loose arguments. Thanks

I don't see where you have defined $\psi$. I presume your intended map is:

$\psi(h,n) = hn$. I don't see how you establish this is surjective.

What I would do is this, define:

$\psi: G \to H \times N$ by $\psi(g) = (\phi(g), \phi(g)^{-1}g)$

It may not be clear the second coordinate is in $N$, so let's demonstrate:

$\phi(\phi(g)^{-1}g) = \phi(\phi(g^{-1}))\phi(g) = \phi(g^{-1})\phi(g) = \phi(e) = e$

(because $\phi(g^{-1}) \in \text{im }\phi = H$, and $\phi$ is the identity on $H$), so $\phi(g)^{-1}g \in \text{ker }\phi = N$.

Now we can establish bijectivity of $\psi$. Suppose $\psi(g) = \psi(g')$.

Then $\phi(g) = \phi(g')$, and $\phi(g)^{-1}g = \phi(g')^{-1}g'$.

So the second equation becomes: $\phi(g)^{-1}g = \phi(g)^{-1}g' \implies g = g'$.

On the other hand, it is clear that $\psi(hn) = (\phi(hn),\phi(hn)^{-1}(hn))$

$= (\phi(h)\phi(n),\phi(n^{-1})\phi(h^{-1})hn) = (h,\phi(n)^{-1}h^{-1}hn) = (h,n)$, so $\psi$ is surjective.

Now the question becomes: is $\psi$ a homomorphism?

$\psi(gg') = (\phi(gg'), \phi(gg')^{-1}gg') = (\phi(g)\phi(g'),\phi(g')^{-1}\phi(g)^{-1}gg')$.

IF $G$ is Abelian, then $\phi(g')^{-1}\phi(g)^{-1}gg' = \phi(g)^{-1}g\phi(g')^{-1}g$, and we continue:

$= (\phi(g)\phi(g'), \phi(g)^{-1}g\phi(g')^{-1}g) = (\phi(g),\phi(g)^{-1}g)(\phi(g'),\phi(g')^{-1}g'))$

$=\psi(g)\psi(g')$.

To show (b) you need a COUNTER-EXAMPLE.

Let $G = D_3 = \{e,a,a^2,b,ba,ba^2\}$, the dihedral group of order 6.

Let $H = \{e,b\}$ and $N = \{e,a,a^2\}$. Define $\phi: G \to H$ by:

$\phi(a^kb^j) = b^j$ for $k = 0,1,2, j = 0,1$. I leave it to you to prove this is, in fact, a homomorphism.

Clearly, we have $\phi|_H = \text{id}_H$, and $\text{ker }\phi = N$.

However, $H \times N$ is abelian (since both $H,N$ are), while $G$ is not, so $G \neq H \times N$.

• Thanks, for your answer. I am still going through it. Meanwhile, I have shown that $G=HN$, i.e., every element in G can be written as $hn$ where $h \in H$ and $h \in N$. So for every $g=hn \in G$ I have an element $(h,n)$ in $H \times N$. Isn't sufficient to prove $\psi: H \times N \to G$ surgective? – levitt Mar 29 '15 at 17:37
• Your posted answer doesn't SHOW $G = HN$ it assumes it. I'm not saying that isn't a viable approach (in fact, it's true), however one CANNOT conclude that $G = HN$ and $H \cap N = \{e\}$ together imply $G \cong H \times N$, although one can conclude they are set-isomorphic. – David Wheeler Mar 29 '15 at 18:21
• True, I didn't prove it here. I wanted to know if the approach is right to show the surgectivity. Thanks. I have used $G = HN$ to show surgectivity and then $H \cap N = \{e\}$ to show injectivity. After that homorphisim is also shown if $G$ is abelian. Aren't these sufficient for isomorphism? – levitt Mar 29 '15 at 18:29
• Importantly, I want to know for sure, first of all, if I was right in concluding that $H \cap N = \{e\}$? – levitt Mar 29 '15 at 18:37
• It is true: if $g \in \text{im }\phi \cap \text{ker }\phi = H \cap N$, then $\phi(g) = e$ and $\phi(g) = g$, so that $g = e$. – David Wheeler Mar 29 '15 at 18:43


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2 added 197 characters in body

Sorry, I am in a similar situationmisread the question: I thought you wanted examples with no mixed Hodge structure and no Hodge structure of weight $\geq 2$. I tried to delete this post, but it did not work.

I am definitely not an algebraic geometer, but I was recently forced to deal with some of the structures you mentioned in some very simple settings.

I have learned a lot from the paper "Braid Groups and Hodge Structures" by Curt McMullen: http://www.math.harvard.edu/~ctm/papers/home/text/papers/bn/bn.pdf. In my opinion, McMullen's papers (on any subject) are absolutely fantastic, and are a great pleasure to read.

In the same direction, some nice examples come from Teichmuller curves. You can check out e.g. the two preprints by Alex Wright: http://arxiv.org/abs/1203.2683 ("Schwarz triangle mappings and Teichmüller curves I: abelian square-tiled surfaces") and http://arxiv.org/abs/1203.2685 ("Schwarz triangle mappings and Teichmüller curves II: the Veech-Ward-Bouw-Möller curves").

Also, some shameless self-advertising: there is http://arxiv.org/abs/1112.5872
by M. Kontsevich, A. Zorich and me (about square-tiled surfaces) which is mostly expository.

1

I am in a similar situation: I am definitely not an algebraic geometer, but I was forced to deal with some of the structures you mentioned.

I have learned a lot from the paper "Braid Groups and Hodge Structures" by Curt McMullen: http://www.math.harvard.edu/~ctm/papers/home/text/papers/bn/bn.pdf. In my opinion, McMullen's papers (on any subject) are absolutely fantastic, and are a great pleasure to read.

In the same direction, some nice examples come from Teichmuller curves. You can check out e.g. the two preprints by Alex Wright: http://arxiv.org/abs/1203.2683 ("Schwarz triangle mappings and Teichmüller curves I: abelian square-tiled surfaces") and http://arxiv.org/abs/1203.2685 ("Schwarz triangle mappings and Teichmüller curves II: the Veech-Ward-Bouw-Möller curves").

Also, some shameless self-advertising: there is http://arxiv.org/abs/1112.5872
by M. Kontsevich, A. Zorich and me (about square-tiled surfaces) which is mostly expository.


text:
Inscribed angles

CCSS Math: HSG.C.A.2

Video transcript

- [Voiceover] A circle is centered on point B. We see that right over there. That's the center of this big, blue circle. Points A, C, and D lie on its circumference. We see that. Points A, C, and D lie on the circumference. If angle ABC... So ABC; So that's this central angle right over here; measures 132 degrees. Alright, so this is 132 degrees. What does angle ADC measure? A, D, C. So let's think about how these are related. ABC is a central angle. ADC is an inscribed angle. And they intercept the same arc. The arc AC. They both intercept this arc right over here. And we know from the inscribed angle theorem that an inscribed angle that intercepts the same arc as a central angle is going to have half the angle measure. And it even looks that way right over here. So if ABC- if the central angle is 132 degrees, then the inscribed angle that intercepts the same arc is going to be half of that. So half of 132 degrees is what? It is 66 degrees. We can check our answer, and we got it right.


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# NCERT Class 11-Math՚s: Exemplar Chapter – 10 Straight Lines Part 2 (For CBSE, ICSE, IAS, NET, NRA 2022)

Glide to success with Doorsteptutor material for ICSE/Class-10 : get questions, notes, tests, video lectures and more- for all subjects of ICSE/Class-10.

10.1. 8 Intersection of two given lines

Two lines and are

(i) Intersecting

(ii) Parallel and distinct if

(ii)

Remarks

(i) The points and are on the same side of the line or on the opposite side of the line , if and are of the same sign or of opposite signs respectively.

(ii) The condition that the lines and are perpendicular is .

(iii) The equation of any line through the point of intersection of two lines and is . The value of is determined from extra condition given in the problem.

## 10.2 Solved Examples

Question 1:

Find the equation of a line which passes through the point and makes an angle of with the positive direction of axis.

Here the slope of the line is d the given point is . Therefore, using point slope formula of the equation of a line, we have

Question 2:

Find the equation of the line where length of the perpendicular segment from the origin to the line is and the inclination of the perpendicular segment with the positive direction of x-axis is .

The normal form of the equation of the line is ere and . Therefore, the equation of the line is

Question 3:

Prove that every straight line has an equation of the form , where and are constants.

Proof Given a straight line, either it cuts the y-axis, or is parallel to or coincident with it. We know that the equation of a line which cuts the y-axis (i.e.. , it has y-intercept) can be put in the form ; further, if the line is parallel to or coincident with the , its equation is of the form , where in the case of coincidence. Both of these equations are of the form given in the problem and hence the proof.

Question 4:

Find the equation of the straight line passing through and perpendicular to the line .

Let be the slope of the line whose equation is to be found out which is perpendicular to the line . The slope of the given line is . Therefore, using the condition of perpendicularity of lines, we have or (Why?)

Hence, the required equation of the line is or .

Question 5:

Find the distance between the lines and .

The equations of lines and may be rewritten as and

Since, the slope of these lines are same and hence they are parallel to each other. Therefore, the distance between them is given by

Question 6:

Show that the locus of the mid-point of the distance between the of the variable line is where p is a constant.

Changing the given equation of the line into intercept form, we have

which gives the coordinates , where the line intersects x-axis and y-axis, respectively.

Let denote the mid-point of the line segment joining the points

Then

This gives


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# How do you solve for v in Ve= 1/2 mv^2?

Apr 21, 2016

 color(green)(v =sqrt((2Ve) / ( m )

#### Explanation:

$V e = \frac{1}{2} m {v}^{2}$

Ve = color(blue)(1/2) * m * color(green)(v^2

(Ve ) * color(blue)(2/1) * 1 / m = color(green)(v^2

(2Ve) / ( m )= color(green)(v^2

 color(green)(v =sqrt((2Ve) / ( m )


text:
# Strings and Sorting

### Finding a Substring with index

Finding a substring depends on where you have lost it. If you happen to have lost it within a bigger string, you』re in luck because the index function can help you out. Here』s how it … Read the rest

# Directory Operations

### Moving Around the Directory Tree

Your program runs with a 「working directory,」 which is the starting point for relative pathnames. That is, if you refer to the file fred, that means fred in the current working directory.

The chdir … Read the rest

# File Tests

### File Test Operators

Before we start a program that creates a new file, let』s make sure that the file doesn』t already exist so that we don』t accidentally overwrite a vital spreadsheet datafile or that important birthday calendar. For this, we … Read the rest

# Perl Modules

There is a lot more to Perl than what we』re able to show you in this book, and there are a lot of people doing a lot of interesting things with Perl. If there is a problem to solve, then … Read the rest

# More Control Structures

### The unless Control Structure

In an if control structure, the block of code is executed only when the conditional expression is true. If you want to execute a block of code only when the conditional is false, change … Read the rest

# Processing Text with Regular Expressions

### Substitutions with s///

If you think of the m// pattern match as being like your word processor』s 「search」 feature, the 「search and replace」 feature would be Perl』s s/// substitution operator. This simply replaces whatever part of a variable matches a … Read the rest

# Matching with Regular Expression

### Matches with m//

We』ve been writing patterns in pairs of forward slashes, like /fred/. But this is actually a shortcut for the m// (pattern match) operator. As you saw with the qw// operator, you may choose any pair of … Read the rest