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### Recent Submissions

• #### LCA of PEM Fuel Cell Vehicles Powered by Grey and Blue Hydrogen: A Case Study in Saudi Arabia

(2022-09-26) [Poster]
Global warming, overpopulation, rampant pollution, and resource depletion are all significant environmental challenges that the world is facing. Like other countries all over the world, Saudi Arabia is also battling these issues. These issues are exacerbated by increasing human population, industrialization, urbanization, and transport development [1]. There is rising economic and environmental pressure to mitigate greenhouse gas (GHG) emissions, consisting of carbon dioxide (CO2) (74.4%), methane (CH4) (17.5%), nitrous oxide (N2O) (6.2%), and other emissions (HFCs, CFCs, SF6) (2.1%) [2], which are the principal contributors to global warming. The Kingdom of Saudi Arabia (KSA) heavily relies on fossil fuels such as crude oil and natural gas as its main energy provider [3]. The total CO2 emissions reached about 588.8 million tons in 2020 [1, 4], with the transport sector accounting for about 25% [1] of this emission. A number of strategies have been developed to mitigate GHG emissions and diversify energy sources, with the goal of reducing 4% in the total CO2 emissions by 2030 and achieving 3.45 gigawatts from renewable energy by 2020, 9.5 gigawatts by 2030, and 54 gigawatts by 2040 [5, 6]. KSA government has committed to a net-zero emissions target for 2060 aligned with the Paris Agreement [7]. Saudi Arabia seeks to alleviate the power sector's dependence on fossil fuels and will vigorously develop technologies that contribute to global decarbonization [8]. Reducing the transport sector's emissions is also a key requirement of the net-zero pledge. The increasing attention to combat climate change in Saudi Arabia has boosted the development of highly energy-efficient and alternative fuel vehicles (AFVs), such as hydrogen proton-exchange membrane (PEM) fuel cell vehicles (FCV) and battery electric vehicles (BEVs). BEVs, zero-emission vehicles in the operation phase, play a critical role in the direct coupling between the transport sector and electric utilities [9, 10]. However, the long charging time, limited driving range, high battery cost, and the lack of charging stations make BEVs less competitive [11]. Further, because of the obvious larger cell size and weight requirements, BEV technology is particularly difficult to be utilized for heavy-duty transport. Hydrogen PEM fuel cell vehicles, with their only products being water and heat, offer a promising alternative solution for decarbonizing the transport sector. Currently, three forms of hydrogen are used to power the PEM fuel cell vehicle - 'grey' hydrogen produced from natural gas, 'blue' hydrogen that is also from natural gas but with CO2 emissions captured using carbon capture and storage (CCS), and 'green' hydrogen made from water electrolysis powered by zero/ low carbon energy sources [12]. In the short to medium term, grey and blue hydrogen are more cost-competitive than green hydrogen due to the technology availability and cost advantage [13]. Further, only 2% of global hydrogen was green hydrogen in 2018, whereas 76% was grey hydrogen [13]. As the sixth largest natural gas reserve, with 333 trillion cubic feet (Tcf), Saudi Arabia has tremendous potential for natural gas development [14]. During the last two decades, natural gas production and consumption in KSA have been growing consistently and are expected to continue to grow due to the KSA government's initiative to utilize natural gas and renewable energy sources instead of fossil fuels to generate electricity [14]. Therefore, grey and blue hydrogen sources are considered to be more accessible and feasible for PEM fuel cell vehicle development in Saudi Arabia. Inspired by this, we propose to assess the life-cycle GHG emissions of 100 PEM fuel cell (FC) buses operating in Makkah using grey and blue H2 produced in KSA. For this, to compare, 100 BE buses using electricity from the KSA s grid and 100 internal combustion engine (ICE) buses using diesel as the fuel will also be examined across their entire life.
• #### A techno-economic analysis of a thermally regenerative ammonia-based battery

(2022-09-26) [Poster]
A substantial low-grade thermal energy (temperature <130°C) remains unexploited worldwide. Studies have found that approximately 50% of global energy input is lost in waste heat across five sectors (industrial, commercial, residential, transport, and electricity), being low-grade waste heat the most significant fraction. The thermally regenerative ammonia-based battery (TRAB) is an electrochemical and membrane-based system that effectively converts this low-grade thermal energy into electricity. The TRAB has a fourth level in the technology readiness level (TRL) framework, which involves finding process models, analyzing technical data, and making simulations and laboratory-scale applications. Hence, to scale up the TRAB technology and implement it in real-world conditions, this technology must follow a sustainable technology development. This study performs a first-of-a-kind techno-economic analysis (TEA) of an all-aqueous copper thermally regenerative ammonia-based battery (Cuaq-TRAB). The TEA methodology is an effective tool to identify a process technical feasibility and cost; subsequently, it will evaluate the scalability and potential applications of a TRAB. The levelized cost of storage (LCOS) is assessed as the ultimate key economic indicator of the TEA. For a 20-year lifetime project of a Cuaq-TRAB using Br-(aq) as the primary ligand, 407 $\$$/MWh and 1887 \$$/MWh for the power application (0.44 h) and energy application scenario (15h), respectively, were obtained. An alternative scenario using Cl-(aq) as a base ligand implies reducing the LCOS to 379$\/MWh. TEA shows that the developed Cuaq-TRAB offers competitive LCOS for short and long-duration energy storage.
• #### Direct numerical simulation of ammonia Lagrangian sprays at different ambient temperatures.

(2022-09-26) [Poster]
The recent transition to zero-carbon fuels imposes the scientific community to perform physics-based studies on the properties of new fuels. In particular, this study focuses on the spray dynamics of diluted ammonia spray jets. Direct numerical simulations are performed in the OpenFOAM framework at different pre-heating conditions and qualitatively compared. In particular, the differences in terms of penetration length and jet width are analyzed and related to the relatively low saturation temperature of ammonia at ambient pressure.


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# Conservation Law from Metric

• I
Consider the following metric for a 2D spacetime:
##g_{tt} = -x ##
##g_{tx} = g_{xt} = 3##
##g_{xx} = 0##

i.e.
$$g_{\mu \nu} = \left( \begin{array}{cc} -x & 3\\ 3 & 0 \end{array} \right)$$

Now, since the metric is independent of time (t), there is supposedly a conservation law containing ##\frac{dx(\tau)}{d\tau}## and ##\frac{dt(\tau)}{d\tau}##. What is this conservation law, and why does the time independence of the metric imply it?

haushofer
To find the isometries of such a spacetime, you have to solve for the Killing equations. The tt-component of this equation should answer your question.

A note: GR in two dimensions is a bit problematic; the Einstein-Hilbert action is a topological term, meaning that the Einstein equations are an identity.

vanhees71
pervect
Staff Emeritus
Consider the following metric for a 2D spacetime:
##g_{tt} = -x ##
##g_{tx} = g_{xt} = 3##
##g_{xx} = 0##

i.e.
$$g_{\mu \nu} = \left( \begin{array}{cc} -x & 3\\ 3 & 0 \end{array} \right)$$

Now, since the metric is independent of time (t), there is supposedly a conservation law containing ##\frac{dx(\tau)}{d\tau}## and ##\frac{dt(\tau)}{d\tau}##. What is this conservation law, and why does the time independence of the metric imply it?

Consider a curve ##u^0(\tau) = t(\tau), u^1(\tau) = x(\tau)##. The tangent to this curve is a vector, i.e.

$$\left( \frac{dt}{d\tau}, \frac{dx}{d\tau} \right)$$

is a vector.

Because none of the components of the metric is a function of time, the vector (in the above sense) ##\xi^a = (1,0) = dt/d\tau## is a Killing vector.

The dot product of a tangent vector of a geodesic curve and a Killing vector is a conserved quantity - it is the same everywhere along the geodesic curve. If we let ##u^a = (u^0(\tau), u^1(\tau) ) = (t(\tau), x(\tau))## be a geodesic curve then we can say that the dot product is given by ##g_{ab} \xi^a u^b = \xi_b u^b## is constant. Because ##\xi^a = (1,0)## and ##\xi_a = (-x,3)## we can say that ##-x (dt/d\tau) + 3 (dx/d\tau)## is constant along the curve, i.e. is independent of ##\tau##.

As a check, we can consider ## (d/d\tau) (-x (dt/d\tau) + 3 (dx/d\tau)) = 0##, we know ##d/d\tau## of a constant is zero. Expanding this out using the chain rule, we get:
$$-\frac{dx}{d\tau} \frac{dt}{d\tau} + -x \frac{dt^2}{d\tau^2} + 3 \frac{dx^2}{d\tau^2} = 0$$

We can derive this from the geodesic equation. We compute the christoffel symbols

$$\Gamma^t{}_{tt} = \frac{1}{6} \quad \Gamma^x{}_{tt} = \frac{x}{18} \quad \Gamma^x{}_{tx} = -\frac{1}{6}$$

and confirm that we can derive the above from the geodesic equations, which in tensor notation are:

$$\frac{d^2 u^i}{d\tau^2} + \Gamma^i{}_{jk} \frac{du^j}{d\tau}\frac{du^k}{d\tau} = 0$$

Tensor notaton is very compact - the non-repeated index i generates two equations, one where we substitute i=0, the other where we substitute i=1. For each of these equations, j and k are repeated indices, so we sum over the repeated indicies, i.e we sum , for all four combinations of j,k, (0,0), (0,1), (1,0), (1,1).

format: plain


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# Project 2: Review of Merchandising Cycle [The following information applies to the questions disp...

Project 2: Review of Merchandising Cycle

[The following information applies to the questions displayed below.]

 Wally’s Widget Company (WWC) incorporated near the end of 2011. Operations began in January of 2012. WWC prepares adjusting entries and financial statements at the end of each month. Balances in the accounts at the end of January are as follows:
 Cash $21,170 Unearned Revenue (40 units)$ 5,200 Accounts Receivable $12,200 Accounts Payable (Jan Rent)$ 3,000 Allowance for Doubtful Accounts $(1,750) Notes Payable$ 14,500 Inventory (45 units) $3,825 Contributed Capital$ 6,700 Retained Earnings – Feb 1, 2012 $6,045  • WWC establishes a policy that it will sell inventory at$165 per unit. • In January, WWC received a $5,200 advance for 40 units, as reflected in Unearned Revenue. • WWC’s February 1 inventory balance consisted of 45 units at a total cost of$3,825. • WWC’s note payable accrues interest at a 12% annual rate. • WWC will use the FIFO inventory method and record COGS on a perpetual basis.
 February Transactions 02/01 Included in WWC’s February 1 Accounts Receivable balance is a $1,500 account due from Kit Kat, a WWC customer. Kit Kat is having cash flow problems and cannot pay its balance at this time. WWC arranges with Kit Kat to convert the$1,500 balance to a note, and Kit Kat signs a 6-month note, at 9% annual interest. The principal and all interest will be due and payable to WWC on August 1, 2012. 02/02 WWC paid a $900 insurance premium covering the month of February. The amount paid is recorded directly as an expense. 02/05 An additional 150 units of inventory are purchased on account by WWC for$11,250 – terms 2/15, n30. 02/05 WWC paid Federal Express $450 to have the 150 units of inventory delivered overnight. Delivery occurred on 02/06. 02/10 Sales of 120 units of inventory occurred during the period of 02/07 – 02/10. The sales terms are 2/10, net 30. 02/15 The 40 units that were paid for in advance and recorded in January are delivered to the customer. 02/15 10 units of the inventory that had been sold on 2/10 are returned to WWC. The units are not damaged and can be resold. Therefore, they are returned to inventory. Assume the units returned are from the 2/05 purchase. 02/16 WWC pays the first 2 weeks wages to the employees. The total paid is$2,500. 02/17 Paid in full the amount owed for the 2/05 purchase of inventory. WWC records purchase discounts in the current period rather than as a reduction of inventory costs. 02/18 Wrote off a customer’s account in the amount of $1,850. 02/19$6,000 of rent for January and February was paid. Because all of the rent will soon expire, the February portion of the payment is charged directly to expense. 02/19 Collected $9,700 of customers’ Accounts Receivable. Of the$9,700, the discount was taken by customers on $6,500 of account balances; therefore WWC received less than$9,700. 02/26 WWC recovered $570 cash from the customer whose account had previously been written off (see 02/18). 02/27 A$800 utility bill for February arrived. It is due on March 15 and will be paid then. 02/28 WWC declared and paid a $650 cash dividend.  Adjusting Entries:  02/29 Record the$2,500 employee salary that is owed but will be paid March 1. 02/29 WWC decides to use the aging method to estimate uncollectible accounts. WWC determines 6% of the ending balance is the appropriate end of February estimate of uncollectible accounts. 02/29 Record February interest expense accrued on the note payable. 02/29 Record one month’s interest earned Kit Kat’s note (see 02/01).

References

Section BreakProject 2: Review of Merchandising Cycle

1.

value:
20.00 points

Required information

Project 2: Part 1 & 2

 Required:
 1-a. Prepare all February journal entries and adjusting entries. (If no entry is required for a transaction/event, select "No Journal Entry Required" in the first account field.)

 1-b. Post all February entries (transactions and adjustments) to the T-accounts.

 1-c. Prepare the financial statements at the end of February. (Balance Sheet only, items to be deducted must be indicated with a negative amount.)

 2 Prepare all February 29 closing entries for WWC. Post to the T-Accounts in requirement 1-b. (If no entry is required for a transaction/event, select "No Journal Entry Required" in the first account field.)

References

General JournalProject 2: Part 1 & 2Difficulty: Hard

Check my work

2.

value:
5.00 points

Required information

Project 2: Part 3

 Required:
 1 What is the WWC’s gross profit for February?

 2 What is the gross profit percentage? (Round your answer to 1 decimal place.)

 3 What were WWC’s net sales for February?

 5 How many units are in ending inventory?

 6 What is the cost per unit of the ending inventory?

 7 If WWC had chosen LIFO, calculate its February cost of goods sold.


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Given a social network with nonuniform selection cost of the users, the problem of \textit{Budgeted Influence Maximization} (BIM in short) asks for selecting a subset of the nodes within an allocated budget for initial ...
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In this paper, we prove that most of the boolean functions, f : {−1, 1} n → {−1, 1}satisfy the Fourier Entropy Inﬂuence (FEI) Conjecture due to Friedgut and Kalai(Proc. AMS’96)[1]. The conjecture says that the Entropy of ...
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# NCERT Solutions for Class 9 Science Chapter 1 Matter in Our Surroundings

These NCERT Solutions for Class 9 Science Chapter 1 Matter in Our Surroundings Questions and Answers are prepared by our highly skilled subject experts to help students while preparing for their exams.

## Matter in Our Surroundings NCERT Solutions for Class 9 Science Chapter 1

### Class 9 Science Chapter 1 Matter in Our Surroundings InText Questions and Answers

Question 1.
Which of the following are matter?
Chair, air, love, smell, hate, almonds, thought, cold, cold drink, smell of perfume.
Anything that occupies space and has mass is called matter. Matter can exist in three physical states—solid, liquid, and gaseous.

Chair and almond are forms of matter in the solid state.
Cold drink is a liquid state of matter.
Air is a gaseous state of matter.

Note: The sense of smell is not matter. However, the smell or odour of a substance is classified as matter. The smell of any substance (say, perfume) can be classified as matter. This is because, perfume is in liquid state inside the bottle.

It comes out in the form of tiny droplets. These droplets of perfume are matter and spread out in the atmosphere to create a sense of smell. This smell can be detected by our olfactory system.

Question 2.
Give reasons for the following observation:
The smell of hot sizzling food reaches you several metres away, but to get the smell from cold food you have to go close.
Solids diffuse at a very slow rate. But, if the temperature of the solid is increased, then the rate of diffusion of the solid particles into air increases. This is due to an increase in the kinetic energy of solid particles. Hence, the smell of hot sizzling food reaches us even at a distance, but to get the smell from cold food we have to go close.

Question 3.
A diver is able to cut through water in a swimming pool. Which property of matter does this observation show?
The ability of a diver to cut through water in a swimming pool shows that the particles of matter have intermolecular spaces. The intermolecular spaces in liquids is fair enough to let the diver pass through it.

Question 4.
What are the characteristics of particles of matter?
The characteristics of particles of mat¬ter are:

• Particles of matter have spaces between them.
• Particles of matter are continuously moving.
• Particles of matter attract each other.

Question 5.
The mass per unit volume of a substance is called density (density = mass/volume). Arrange the following in order of increasing density – air, exhaust from chimney, honey, water, chalk, cotton, and iron.
The given substances in the increasing order of their densities can be represented as:
Air < Exhaust from chimney < Cotton < Water < Honey < Chalk < Iron

Question 6.
(a) Tabulate the differences in the characteristics of states of matter.
(b) Comment upon the following: rigidity, compressibility, fluidity, filling a gas container, shape, kinetic energy, and density.
Ans. (a) The differences in the characteristic states of matter are given in the following table.

(b) Rigidity can be expressed as the tendency of matter to resist a change in shape. Compressibility is the ability to be reduced to a lower volume when force is applied.

• Fluidity is the ability to flow.
• By filling a gas container we mean the attainment of shape of the container by gas.
• Shape defines a definite boundary.
• Kinetic energy is the energy possessed by a particle due to its motion.
• Density is mass per unit volume.

Question 7.
Give reasons:
(a) A gas fills completely the vessel in which it is kept.
(b) A gas exerts pressure on the walls of the container.
(c) A wooden table should be called a solid.
(d) We can easily move our hand in air, but to do the same through a solid block of wood, we need a karate expert.
(a) There is little attraction between particles of gas. Thus, gas particles move freely in all directions. Therefore, gas completely fills the vessel in which it is kept.

(b) Particles of gas move randomly in all directions at high speed. As a result, the particles hit each other and also hit the walls of the container with a force. Therefore, gas exerts pressure on the walls of the container.

(c) A wooden table has a definite shape and volume. It is very rigid and cannot be compressed i.e., it has the characteristics of a solid. Hence, a wooden table should be called a solid.

(d) Particles of air have large spaces between them. On the other hand, wood has little space between its particles. Also, it is rigid. For this reason, we can easily move our hands in air, but to do the same through a solid block of wood, we need a karate expert.

Question 8.
Liquids generally have lower density as compared to solids. But you must have observed that ice floats on water. Find out why.
The mass per unit volume of a substance is called density (density = mass/volume). As the volume of a substance increases, its density decreases.

Though ice is a solid, it has large number of empty spaces between its particles. These spaces are larger as compared to the spaces present between the particles of water. Thus, the volume of ice is greater than that of water. Hence, the density of ice is less than that of water. A substance with lower density than water can float on water. Therefore, ice floats on water.

Question 9.
Convert the following temperature to Celsius scale:
(a) 300 K (b) 573 K
(a) 300 K = (300 – 273)°C = 27°C
(b) 573 K = (573 – 273)°C = 300°C

Question 10.
What is the physical state of water at:
(a) 250°C
(b) 100°C
(a) Water at 250°C exists in gaseous state.
(b) At 100°C, water can exist in both liquid and gaseous form. At this temperature, after getting the heat equal to the latent heat of vaporization, water starts changing from liquid state to gaseous state.

Question 11.
For any substance, why does the temperature remain constant during the change of state?
During a change of state, the temperature remains constant. This is because all the heat supplied to increase the temperature is utilised in changing the state by overcoming the forces of attraction between the particles. Therefore, this heat does not contribute in increasing the temperature of the substance.

Question 12.
Suggest a method to liquefy atmospheric gases.
By applying pressure and reducing the temperature, atmospheric gases can be liquefied.

Question 13.
Why does a desert cooler cool better on a hot dry day?
When a liquid evaporates, the particles of the liquid absorb energy from the surroundings to compensate the loss of energy during evaporation. This makes the surroundings cool.

In a desert cooler, the water inside it is made to evaporate. This leads to absorption of energy from the surroundings, thereby cooling the sur¬roundings. Again, we know that evaporation depends on the amount of water vapour present in air (humidity). If the amount of water vapour present in air is less, then evaporation is more. On a hot dry day, the amount of water vapour present in air is less. Thus, water present inside the desert cooler evaporates more, thereby cooling the surroundings more. That is why a desert cooler cools better on a hot dry day.

Question 14.
How does water kept in an earthen pot (matka) become cool during summers?
There are some pores in an earthen pot through which the liquid inside the pot evaporates. This evaporation makes the water inside the pot cool. In this way, water kept in an earthen pot becomes cool during summers.

Question 15.
Why does our palm feel cold when we put some acetone or petrol or perfume on it?
When we put some acetone or petrol or perfume on our palm, it evaporates. During evaporation, particles of die liquid absorb energy from the surrounding or the surface of the palm to compensate for the loss of energy, making the surroundings cool. Hence, our palm feels cold when we put some acetone or petrol or perfume on it.

Question 16.
Why are we able to sip hot tea or milk faster from a saucer than a cup?
A liquid has a larger surface area in a saucer than in a cup. Thus, it evaporates faster and cools faster in a saucer than in a cup. For this reason, we are able to sip hot tea or milk faster from a saucer than a cup.

Question 17.
What type of clothes should we wear in summers?
We should wear cotton clothes in summers. During summers, we sweat more. On the other hand, cotton is a good absorber of water. Thus, it absorbs sweat from our body and exposes the liquid to the atmosphere, making evaporation faster. During this evaporation, particles on the surface of the liquid gain energy from our body surface, making the body cool.

### Class 9 Science Chapter 1 Matter in Our Surroundings Textbook Questions and Answers

Question 1.
Convert the following temperatures to Celsius scale.
(a) 293 K
(b) 470 K
Kelvin is an SI unit of temperature, where 0°C = 273.16 K (approximately 273 K)
(a) 293 K = (293 – 273) °C = 20 °C
(b) 470 K = (470 – 273) °C= 197 °C

Question 2.
Convert the following temperatures to Kelvin scale.
(a) 25°C
(b) 373°C
Kelvin is an SI unit of temperature, where 0°C = 273.16 K (approximately 273 K)
(a) 25 °C = (25 + 273) K = 298 K
(b) 373 °C = (373 + 273) K = 646 K

Question 3.
Give reason for the following observations.
(a) Naphthalene balls disappear with time without leaving any solid.
(b) We can get the smell of perfume sitting several metres away.
(a) Naphthalene undergoes sublimation easily i.e., the change of state of naphthalene from solid to gas takes place easily. Thus, naphthalene balls disappear with time without leaving any solid.

(b) Gaseous particles possess high speed and large spaces between them. Particles of perfume diffuse into these gaseous particles at a very fast rate and reach our nostrils. This enables us to smell the perfume from a distance.

Question 4.
Arrange the following substances in increasing order of forces of attraction between particles-water, sugar, oxygen.
Sugar is a solid; the forces of attraction between the particles of sugar are strong. Water is a liquid; the forces of attraction here are weaker than sugar. Oxygen is a gas; the forces of attraction are the weakest in gases.

Thus, the increasing order of forces of attraction between the particles of water, sugar and oxygen is
Oxygen < Water < Sugar

Question 5.
What is the physical state of water at
(a) 25°C
(b) 0°C
(c) 100°C
(a) Water at 25°C is present in the liquid state.

(b) At 0°C, water can exist as both solid and liquid. At this temperature, after getting the heat equal to the latent heat of fusion, the solid form of water i.e., ice starts changing into its liquid form i. e., water.

(c) At 100 °C, water can exist as both liquid and gas. At this temperature, after getting the heat equal to the latent heat of vaporization, water starts changing from its liquid state to its gaseous state, i.e., water vapours.

Question 6.
Give two reasons to justify that
(a) water at room temperature is a liquid.
(b) an iron almirah is a solid at room temperature.
(a) At room temperature (25 °C), water is a liquid because it has the following characteristic of liquid:

• At room temperature, water has no shape but has a fixed volume that is, it occupies the shape of the container in which it is kept.
• At room temperature, water flows.

(b) An iron almirah is a solid at room temperature (25 °C) because:

• it has a definite shape and volume like a solid at room temperature.
• it is rigid as solid at room temperature.

Question 7.
Why is ice at 273 K more effective in cooling than water at the same temperature?
Ice at 273 K has less energy than water (although both are at the same temperature). Water possesses the additional latent heat of fusion. Hence, at 273 K, ice is more effective in cooling than water.

Question 8.
What produces more severe bums, boiling water or steam?
Steam has more energy than boiling water. It possesses the additional latent heat of vaporization. Therefore, bums produced by steam are more severe than those produced by boiling water.

Question 9.
Name A, B, C, D, E and F in the following diagram showing change in its state.

### Class 9 Science Chapter 1 Matter in Our Surroundings Additional Important Questions and Answers

Multiple Choice Questions
Choose the correct option:

Question 1.
Which one of the following sets of phenomena would increase on raising the temperature?
(a) Diffusion, evaporation, compression of gases
(b) Evaporation, compression of gases, solubility
(c) Evaporation, diffusion, expansion of gases
(d) Evaporation, solubility, diffusion, compression of gases
(c) Evaporation, diffusion, expansion of gases

Question 2.
Seema visited a Natural Gas Compressing Unit and found that the gas can be liquefied under specific conditions of temperature and pressure. While sharing her experience with friends she got confused. Help her to identify the correct set of conditions
(a) Low temperature, low pressure
(b) High temperature, low pressure
(c) Low temperature, high pressure
(d) High temperature, high pressure
(c) Low temperature, high pressure

Question 3.
The property to flow is unique to fluids. Which one of the following statements is correct?
(a) Only gases behave like fluids
(b) Gases and solids behave like fluids
(c) Gases and liquids behave like fluids
(d) Only liquids are fluids
(c) Gases and liquids behave like fluids

Question 4.
During summer, water kept in an earthen pot becomes cool because of the phenomenon of
(a) diffusion
(b) transpiration
(c) osmosis
(d) evaporation
(d) evaporation

Question 5.
A few substances are arranged in the increasing order of forces of attraction between their particles. Which one of the following represents a correct arrangement?
(a) Water, air, wind
(b) Air, sugar, oil.
(c) Oxygen, water, sugar
(d) Salt, juice, air
(c) Oxygen, water, sugar

Question 6.
On converting 25°C, 38°C and 66°C to kelvin scale, the correct sequence of temperature will be
(a) 298 K, 311 K and 339 K
(b) 298 K, 300 K and 338 K
(c) 273 K, 278 K and 543 K
(d) 298 K, 310 K and 338 K
(a) 298 K, 311 K and 339 K

Question 7.
Choose the correct statement of the following
(a) conversion of solid into vapours without passing through the liquid state is called vapourisation.
(b) conversion of vapours into solid without passing through the liquid state is called sublimation.
(c) conversion of vapours into solid without passing through the liquid state is called freezing.
(d) conversion of solid into liquid is called sublimation.
(b) conversion of vapours into solid without passing through the liquid state is called sublimation.

Question 8.
The boiling points of diethyl ether, acetone and n-butyl alcohol are 35°C, 56°C and 118°C respectively. Which one of the following correctly represents their boiling points in kelvin scale?
(a) 306 K, 329 K, 391K
(b) 308 K, 329 K, 392 K
(c) 308 K, 329 K, 391 K
(d) 329 K, 392 K, 308 K
(c) 308 K, 329 K, 391 K

Question 9.
Which condition out of the following will increase the evaporation of water?
(a) Increase in temperature of water
(b) Decrease in temperature of water
(c) Less exposed surface area of water
(d) Adding common salt to water
(a) Increase in temperature of water

Question 10.
In which of the following conditions, the distance between the molecules of hydrogen gas would increase?
(i) Increasing pressure on hydrogen contained in a closed container
(ii) Some hydrogen gas leaking out of the container
(iii) Increasing the volume of the container of hydrogen gas
(iv) Adding more hydrogen gas to the container without increasing the volume of the container
(a) (i) and (iii)
(b) (i) and (iv)
(c) (ii) and (iii)
(d) (ii) and (iv)
(c) (ii) and (iii)

Question 1.
Name any two things that are not the state of matter.
The feelings of love and hate are not the state of matter.

Question 2.
Name any two substances which exist in all the three states of matter at low range of temperature.
Water and wax.

Question 3.
Define the specific heat of a substance.
It is the amount of heat required to raise the temperature of a gram of substance by 1°C.

Question 4.
How is the boiling point of a liquid affected with the increasing or decreasing pressure?
The boiling of a liquid is proportional to the pressure i.e. with the increasing pressure, boiling point will increase and with the decreasing pressure, it will decrease.

Question 5.
What is the advantage of boiling the acids under low pressure conditions?
It helps to concentrate them without them undergoing any decomposition.

Question 6.
What is the S.I. unit for expressing the specific heat of a substance?
Cal/g/°C

Question 7.
The calorie and joule are the units used to measure the heat energy. How are they interrelated?
1 Joule = 1 / 4.18 calorie or 1 calorie = 4.18 Joules

Question 8.
What happens when a body warms up?
When a body warms up showing the rise in temperature, it absorbs the heat from its surroundings.

Question 9.
What happens when a hot body is left at room temperature to cool?
When a hot body is left at room temperature to cool, it looses the heat to the surroundings.

Question 10.
What effect does the evaporation of a liquid has on the liquid?
Evaporation of a liquid has cooling effect i.e., the temperature of a liquid falls with increasing evaporation.

Question 11.
Why are the earthen pots more effective in Cooling water in rural areas?
In rural areas where there is no electricity, the earthen pots are effective means for cooling water because they allow the evaporation of water from the surface.

Question 12.
When will the clothes spread on a cloth line will dry faster, on a hot humid day or hot dry day?
On hot dry day as the relative atmospheric humidity is less, the rate of evaporation will be more and hence the domes will dry faster.

Question 13.
Alcohol and water are two liquids. Alcohol has lower boiling point than water. Which of the two would evaporate faster at a given temperature?
Alcohol, it has low boiling point as compared to the water.

Question 14.
State the two precautions you will observe when measuring the volume of a liquid using a measuring cylinder?
The two precautions include placing the measuring cylinder on the flat surface and reading the lower meniscus if water, with eyes in line of the meniscus.

Question 15.
What is dry ice?
It is the solidified form of carbon dioxide at low temperature and high pressure conditions.

Question 16.
What are the three properties of the state of matter?
Mass, volume and inertia are the three properties of states of matter.

Question 17.
What happens to the particles of a matter when it is heated?
The particles of matter gain the thermal energy and use it to increase their kinetic energy.

Question 18.
Why do we feel our palm cool after placing an ice cube on it?
Ice cube placed on palm extracts the heat from the palm surface to melt. This extraction of heat cools the palm.

Question 19.
What is a pure substance?
A substance which has its specific melting point, boiling point and density is called a pure substance. All the elements and compounds are examples of pure substance.

Question 20.
What are volatile liquids?
Liquids which vapourise even at the room temperature are called volatile liquids for example alcohol, acetone, etc.

Question 1.
What is matter? State its different forms.
Anything in our surroundings that occupies space and has its own mass is called matter. All forms of the matter are made of the small particles that are invisible to naked eyes.

Question 2.
What happens when 10g of table salt is dissolved in the 100 ml of water? Does it bring any change in the volume of the solution?
When salt is added to water, the particles of the salt occupies the spaces present in between the particles of the water hence, their occur no evident change in its volume.

Question 3.
A student mixed 100 ml alcohol and 100 ml of water together in a container. What would be the net volume of mixture in the container? Why?
The net volume of the mixture in the container would be slightly less than 200 ml because the particles of the water and alcohol would occupy the spaces present between each other.

Question 4.
How will you experimentally prove that matter is made up of small particles?
Take a known volume of water in a container and dissolve a small amount of table salt in water by continuous stirring. When the volume of the solution is measured, it shows no difference to show that the matter is made of small particles with spaces among them that can be occupied by the others.

Question 5.
(a) What is diffusion?
(b) State the different factors which affect the diffusion.
(a) Diffusion refers to the phenomenon of the intermixing of particles of the two or more substances on their own based on the concentration differences.
(b) Diffusion is affected by the concentration differences, mass of the diffusing particles, the medium in which the particles have to diffuse and the distance in between the source and sink.

Question 6.
Why do you smell a lighted incense stick put away in the house temple on ground floor when studying in your study room on the first floor?
The particles of perfume in incense stick mix with the air and freely move in all directions from the area of their higher concentration in the temple room to the other rooms. The incoming of these perfume particles because of their diffusion, makes you smell the sweet smell of incense.

Question 7.
What are the different states of matter? Give examples.
There are three states of matter, solid, liquid and gases.

• Solid: Stone, brick, salt, sugar, a metal block, etc.
• Liquid: liquid water, alcohol, milk, oil, petrol, etc.
• Gases: Oxygen, nitrogen, hydrogen, carbon dioxide, etc.

Question 8.
Classify the constituents of body into the different states of matter.
Solid: Bones, teeth and muscles.
Liquid: Water, blood and lymph Gases: Inhaled air and exhaled air.

Question 9.
A rubber band can be stretched unlike solids then why shall it be considered a solid?
A rubber band is a solid despite of the fact that it can be stretched because it does not change its shape at its own. An external force needs to be applied on it to force it change its shape and after the removal of the force, it mostly regains its shape.

Question 10.
A handful of salt or sugar take the shape of the container like liquids then why are they considered solids than liquids?
A handful of salt or sugar does take the shape of the container like liquids yet they are considered solids because the individual crystal they contain, has a fixed shape.

Question 11.
Why is a sponge considered a solid when it can be compressed like gases or liquids?
A sponge is considered solid even when it can be compressed like gases or liquids because its compression is because of the presence of minute air holes or cavities filled with air rather than the solid matter it has in its structure.

Question 12.
Define volume? Write its S.I. unit.
Volume is the space occupied by a substance. All the solids and liquids have definite volume. It’s S.I. unit cubic metre (m3) but commonly used in cm3 when, 1 cm3 = 1000 ml = 1 litre.

Question 13.
Define density. State its S.I. unit.
Density refers to the mass per unit
volume of a substance. It is measured in kg/m3 or g/cm3.
Density = $$\frac{\text { Mass }}{\text { Volume }}$$

Question 14.
Which have more density, solids or liquids? Why?
Solids have more density than liquids because with particles placed close together, they have more mass per unit volume as compared to liquids in which the particles are loosely packed.

Question 15.
Why gases can be compressed but not solids?
The gases can be compressed because their particles have very less force of attraction in between them so that they are in random motion with large distance among one another. Hence, when external pressure is applied, the particles come close to each other and the gas compresses but in solids the particles have large force of attraction hence, the distance is very less such that even upon applying the external pressure, they fail to be compressed.

Question 16.
Can particles of a solid diffuse into another solid? If yes, give example.
Yes, the particles of a solid can diffuse into another solid but the diffusion takes a long time. For example if two metal blocks are tied together and left undisturbed for a long time i.e. for years, the particles of one diffuse into another as it become difficult to separate mem from each other.

Question 17.
What do you understand by the compression of a gas? Give examples of the use of compressed gas in daily life.
The compression of a gas refers to reducing of the volume of a gas in a container on applying external pressure. The different compressed gases are used in daily life such as LPG (Liquefied petroleum gas) used for cooking, oxygen gas used in hospitals and CNG (Compressed natural gas) used as fuel in vehicles.

Question 18.
Why liquids have definite volume but not shape?
Liquids have definite volume but not shape because they have moderate force of attraction between particles such that the distance between the particles is also moderate giving them a definite volume but not shape.

Question 19.
What do you understand by the anomalous behaviour of water? What is its advantage to living organisms?
Water has anomalous behaviour because unlike other substances, on freezing its density decreases and therefore the ice floats on the water surface. The floating of ice is important for aquatic living organisms as they can survive in water below the surface of thick ice in oceans such as Arctic ocean and polar regions.

Question 20.
What happens when a crystal of potassium permanganate is gently placed at the bottom of the water rilled beaker?
The crystal of potassium permanganate gets dissolved in water. The dissolution involves the diffusion of its particles in water. This diffusion continues until the particles of potassium permanganate get evenly distributed in water.

Question 21.
State the relation in between the density and diffusion of a given substance into another substance.
Diffusion involves the free intermixing of a substance into another. It is inversely proportional to the under root of the density of the substance. Therefore, an ink with low density dissolves or diffuses faster in water than a drop of honey which is denser than ink.

Question 22.
How will you test the purity of honey bought from a shop?
A drop of the honey to be tested is poured in a glass of water. If it forms a streak going down the water than its pure, otherwise not.

Question 23.
How do the aquatic plants and animals manage to survive in water?
All aquatic plants and animals require carbon dioxide or oxygen or both for their successful survival. These gases are soluble in water. Carbon dioxide dissolves in water forming carbonic acid which is a very acid weak and oxygen is sparingly soluble in water, about 0.7% per litre of water.

Question 24.
Arrange the following
Liquid, solid, gas
in the increasing order of the rate of diffusion of their particles with reason.
In solids the force of attraction are very strong hence, the particles are” bound close to each other but in gases, the force of attraction between the particles is very less, hence, they are free to move randomly. Therefore, in gases the rate of the diffusion is maximum than in solids.

The liquids have moderate force of attraction, therefore they lie in between solids and liquids for the rate of diffusion.
Solids < Liquids < Gases

Question 25.
Why does a gas stored in the container exerts pressure on its walls?
A gas stored in a container exerts pressure on its walls because the gas particles are in free random motion. Whenever, they hit the wall of the container, they exert pressure which is proportional to the motion of the particles and their density.

Question 26.
Why does an inflated balloon when kept in sun expands in size and when kept in deep freezer, it shrinks?
A balloon kept in sun expands because at high temperature, the Heat energy gained by the particles is transformed into their increased kinetic energy and therefore, they hit the walls of the balloon with greater force exerting more pressure.

When the same balloon is kept in deep freezer because of the low. temperature conditions, the particles lose their kinetic energy and hit the balloon walls with low pressure, making it to contract in size.

Question 27.
Define pressure and atmospheric pressure.
Pressure is denned as the thrust acting per emit area. It’s S.I. unit is Pascal but it can also be measured in terms of atmospheric pressure.

The normal atmospheric pressure is the pressure exerted by the air at sea level. It is 760 mm of Hg.
1 Atmospheric pressure (atm) = 1 × 10s Pascal.

Question 28.
How is a vapour different from a gas? Give example.
Vapour refers to the gaseous state of a substance that at room temperature exists in its liquid form such as the water vapours formed after the evaporation of liquid water whereas the gas refers to an element or compound that exits in gaseous state even at the room temperature such as oxygen and nitrogen present in air.

Question 29.
What happens when a solid cube of ice is heated in a beaker?
When a solid cube of ice is heated, the heat supplied is used up in increasing the vibrations of the particles of the solid but soon the force of attraction reduces enough to allow the particles become free and flow, making the ice to melt.

When the water is continued to be heated, there comes a time when the force of attraction reduces enough to allow particles to leave the water surface and fly free in the atmospheric air in form of vapours.

Question 30.
Define the folio wings:
(i) Latent heat of fusion
(ii) Latent heat of vapourisation
(i) Latent heat of fusion: It refers to the heat required to change 1 kg of solid substance into its liquid state at normal atmospheric pressure without any change in temperature at its melting point.

(ii) Latent heat of vapourisation: It refers to the amount of heat required to change 1 kg of liquid substance into its vapours at atmospheric pressure without any change in temperature at normal on its boiling point.

Question 31.
Is the boiling point of water is same in Rajasthan, Shimla, Nanital and Srinagar? Give reason for your answer.
No, the boiling point varies with altitude. With the increasing altitude, the boiling point decreases because boiling point is the temperature at which the vapour pressure equals the atmospheric pressure. Hence, as we go at the higher altitudes, the boiling point will decrease with decreasing atmospheric pressure.

Question 32.
On which day, you expect the wet clothes spread on a line to dry faster and why?
(i) Cloudy day or dry day.
(ii) Calm dry day or windy dry day.
(i) The wet clothes will dry faster on a dry day as the percentage of water vapours are less in atmospheric air. The atmospheric pressure would be less to oppose the release of vapours from clothes than on a cloudy in which because of the presence of the water vapours, the atmospheric pressure would be more to prevent the release of water vapours.

(ii) On a windy dry day, the clothes will dry faster as the blowing wind would maintain a low pressure over the clothes forcing the wafer vapours to leave the clothes surface.

Question 33.
Why does evaporation cause the cooling of the surface?
Evaporation involves the leaving of the particles of a liquid in gaseous state in air. A particle to leave the surface of the liquid has to have some extra energy. The evaporating particles absorb this required extra energy from the surface producing the cooling effect.

Question 34.
A student kept equal volume of water in same shape and size of the two containers, A of clay and B of plastic at same place for 2 hours. After two hours, water in which container will have lower temperature? Why?
In container A, the temperature of water would be less because the clay surface is more porous than plastic hence, from its surface there will be more evaporation of water. The cooling effect of evaporation will reduce more temperature in container A than in container B.

Question 1.
How will you prove that the particles are very-very small beyond our imagination.
The matter is made up of very-very tiny particles that are invisible to naked eyes and are even invisible under a microscope but their existence can be proved by the activities like:

• Take 100 ml of water in a beaker and dissolve 2-3 crystals of potassium permanganate.
• Take 10 ml of the above solution and add it to 100 ml of clear water in other beaker.
• Keep diluting the solution like above for 6-8 times.

We only observe that the colour only fades with each dilution but does not disappear i.e. the 2-3 crystals of potassium permanganate added to the water initially had millions of the particles that kept distributing themselves with each dilution.

Question 2.
How will you show that gases are more compressible than liquids?
To show that the gases undergo compression more easily than liquids, take two 100 ml syringes.

Close their nozzle by inserting them in a rubber cork. Remove the piston, fill the air in one syringe and some water in the other syringe. Place the piston back in its position and apply the pressure.

In syringe filled with air, pressure is applied more easily than in syringe filled with water because, the air, a mixture of gases is more compressible than water.

Question 3.
A student takes a metallic kettle pot partially filled with water and places it over a burner as shown in the figure. What observations will he make when

(a) places the kettle pot on the flame.
(b) after some time of heating over the flame.
(c) he brings a plate filled with ice cubes near the mouth of the kettle’s nozzle. Why?
(a) When the kettle is placed over the burner, first kettle body gains heat that is further gained by the water and hence, its temperature starts increasing with increasing time.
(b) After some time, he would see the water vapours in form of steam coming out of the mouth of nozzle.
(c) When he brings a plate filled with ice cubes over the mouth of the nozzle the water vapours present in steam would condense back in liquid water droplets.

Question 4.
What is evaporation? State some its advantages.
Evaporation is the loss of water in form of water vapours from the surface of water in a container or a surface at room temperature. The advantage of evaporation include:

• The cooling effect it creates on the surface which is used in rural areas to cool the water and by plants to keep their leaf surface cool.
• The addition of water vapours to atmosphere to regulate the water cycle.
• In loss of solvent in process of crystallization such as extraction of salt from the saline water.

Question 5.
Describe the different factors which affect the rate of evaporation.
A number of factors affect the rate of evaporation. These factors include

• Surface area available for evaporation. The rate of evaporation increases with increasing surface area.
• Temperature affects the rate of evaporation as with increasing temperature, the rate of evaporation also increases simultaneously.
• Wind speed, with increasing wind speed, the rate of evaporation also increases. Therefore, the wet clothes dry faster on a hot, dry and windy day.
• Relative humidity, with increasing relative humidity, the rate of evaporation decreases. Therefore, wet clothes dry slower on a humid day than on a dry day.
• Mass of the solvent particles, with the increasing mass, their evaporation decreases.

Question 6.
Graphically describe the heating curve which a student will plot on heating an ice cube until it gets transformed in state of water vapours.


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# Why cant it be symmetric?

Algebra Level 5

$$a,b,c>0$$ are real numbers. Find the greatest constant k such that $$\frac { kabc }{ a+b+c } \le { (a+b) }^{ 2 }+(a+b+4c)^{ 2 }$$.

×


text:
# vector of three RVs that are pairwise Gaussian is Gaussian [duplicate]

If $$(X,Y)$$, $$(X,Z)$$, and $$(Y,Z)$$ are all Gaussian, does it follow that $$(X,Y,Z)$$ is also Gaussian? I'm having trouble coming up with a counterexample...

• Possible duplicate of Is it possible to have a pair of Gaussian random variables for which the joint distribution is not Gaussian? A straightforward counterexample is to extend the example in the upper right figure in @whuber's answer to three dimensions. – Jarle Tufto Nov 19 '19 at 20:13
• Why do three normal random variable necessarily have to have a Gaussian joint distribution? They're not necessarily independent. @Konstantin – Bindiya12 Nov 19 '19 at 20:18
• @Konstantin - Just being able to construct a covariance matrix does not mean the three variables are jointly Gaussian. – jbowman Nov 19 '19 at 21:14
• @jbowman Thank you, you are so right, I've learned from the post Jarle Tufto ponted at. – Konstantin Nov 19 '19 at 21:20
• The example in the duplicate was posted by @Cardinal, not by me. However, at stats.stackexchange.com/a/434151/919 I recently posted an example of a triviariate distribution that has uniform 2D marginals but is not uniform. By treating this as a copula one obtains an (intriguing) example involving pairwise Gaussian variables that are not jointly Gaussian, but in a subtle way. This approach extends to any univariate distribution whatsoever. – whuber Nov 19 '19 at 21:33


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# Is String Theory A Waste Of Time?

by Juan R.
Tags: string, theory, time, waste
HW Helper
P: 1,204
 Quote by RandallB But the classical was unable to depict how gravity worked. So we have the first really significant application of Riemannian geometry (from mid 1800’s I think) in order to build General Relativity. As 4D thinking to create “Warped space-time” was needed.
This is outside my area, but there are a few physicists who are convinced that gravity can be done on a Euclidean basis. I think the best explanation is that of David Hestenes:

 Lasenby, Doran and Gull have recently created a powerful coordinate-free reformulation, re¯nement, and extension of general relativity [1,2]. It is a gauge theory on °at spacetime, but it retains the attractive geometric structure of Einstein's theory. ... Indeed, the method amounts to a new approach to differential geometry which could fairly be called gauge geometry. ... Part II develops gauge covariant Riemannian geometry on flat spacetime. The main objective is to clarify the fundamental ideas and provide a systematic account of the definitions, theorems, proofs, and computational techniques needed to apply the spacetime calculus efficiently to any physical problem. Specific physical applications are not addressedhere; excellent examples, which amply demonstrate the computational power of the calculus, have been worked out in [1,2] and [9-13]. ...
http://modelingnts.la.asu.edu/pdf/NEW_GRAVITY.pdf

Unfortunately, understanding the above paper requires a certain amount of understanding of "geometric algebra", which is a type of Clifford algebra where the basis vectors are associated with the tangent vectors at a given point of the manifold of space-time.

Carl
P: 416
 Quote by CarlB This is outside my area, but there are a few physicists who are convinced that gravity can be done on a Euclidean basis. Carl
Well, the popular understanding of GR is that gravity is spacetime curvature, but this is rather difficult to believe by several motives.

1) Nobody has measured spacetime curvature directly.

2) Spacetime curvature does not imply curved space. Usual popular image of curved space around Sun is pictorial only.

3) The curved spacetime view is not exclusive. E.g. torsion formulations, Cartan-Ehelers reformulation, etc.

4) The curved spacetime view is problematic on the Newtonian limit. Far from common understanding, nobody has derived the Newtonian limit from GR. This is easy to understand. In the limit c -> infinite the curvature of spacetime may be zero like correspond to the Newtonian approach but then, if gravity is curvature, gravity may be zero. Textbook’s derivation of Newton second law is a derivation valid only when c is finite and the approximation is non linear. c finite contradicts Newtonian theory. Ehlers reformulation of GR does not obtain the Newtonian limit (even if Ehlers claims the contrary). His formulation on flat spacetime has problems: I) the splitting of curved derivatives is not unique and additional equations does not contained in GR are needed, ii) the compatibility with Newtonian limit is done invoking “asymptotic flatness”, which is experimentally unsustainable.

5) The geometric approach breaks the unification with rest of forces.

6) Far from standard claims the geometric approach of GR does not explain the misterium of gravity. This is easy to understand. In Newtonian theory, one has an equation for computing the force, but none explaining of underlying mechanism of it. In Einstein (really Hilbert-Einstein-Grossmann) theory, one has equations for computing spacetime curvature, but none explaining of underlying mechanism of it. GR substitutes the question "How does Earth know that force that Sun does" by "How does Earth know the curvature that Sun does". Far from common statements in GR literature, GR does not explain gravity.

The solution is not a geometric approach to quantum gravity. The solution is a force-like approach to GR that can be quantized more a demonstration of that GR is, strictly speaking, wrong.

Regarding your link, not only the choosing of Minkoskian spacetime metric is not correct (related to imposibility for obtaining correct Newtonian limit, that was the source for the search of alternatives like NCG and similar), moreover, i see fundamental difficulties with the "gauge" line element (7.7) that appears to be the basis of all the "gauge" approach.
 P: 1,308 At best String Theory can only be an effective theory, not a TOE. This is because there seems to be nothing in String/M-theory itself that explains where the strings or membranes came from to begin with. What process creates these membranes/strings from the background? I suppose that there was a background without strings when the universe was very, very small, and then at some later time some process gave rise to strings and/or other membranes. How did that happen? I suspect that if we knew the process by which strings/membranes come into existence, then this might give us constraints on which strings/branes can exist and allow a choice from the landscape.
P: 1,545
 Quote by CarlB there are a few physicists who are convinced that gravity can be done on a Euclidean basis. I think the best explanation is that of David Hestenes: http://modelingnts.la.asu.edu/pdf/NEW_GRAVITY.pdf
If you know of one, I’d love to see where someone makes a serious attempt at a Euclidean explanation, I’ve never seen one.

I have to disagree on David Hestenes. He cannot be talking about a Euclidean basis while using GR and Riemannian geometry. That is 4D and Euclidean is 3D where time is just a variable. GR/Riemannian is also “Background Independent” as I understand it, and Euclidean would be Background Dependent.
While the successful current theories GR and QM are not.
At least I think QM is background independent.

The ideas that wish to replace or correct GR and/or QM, all seem to get more complex in both their concept and mathematics. Maybe that’s because reality is complex.

I still feel that String theory has been successful in showing that 11 dimensions “appear” to be required. Therefore, in my opinion any proposed new theory needs to explain why that appeared to be true. That includes variations on Strings, canonical science, and even Euclidean explanations.

RB
P: 416
 Quote by Mike2 At best String Theory can only be an effective theory, not a TOE. This is because there seems to be nothing in String/M-theory itself that explains where the strings or membranes came from to begin with. What process creates these membranes/strings from the background? I suppose that there was a background without strings when the universe was very, very small, and then at some later time some process gave rise to strings and/or other membranes. How did that happen? I suspect that if we knew the process by which strings/membranes come into existence, then this might give us constraints on which strings/branes can exist and allow a choice from the landscape.
An effective theory for that? From ST one can compute absolutely nothing and nothing can be explained on a sound basis. ST is mathematical gulash with no link with nothing of this world.

The strings of string M theory -really one would talk of the p-branes- are really inmortal on the formulation proposed. In fact some brane inspired cosmology models claim that the big bang was (of course is just a especulation) the outcome of a collision of two 5D branes.
P: 416
 Quote by RandallB If you know of one, I’d love to see where someone makes a serious attempt at a Euclidean explanation, I’ve never seen one. I have to disagree on David Hestenes. He cannot be talking about a Euclidean basis while using GR and Riemannian geometry. That is 4D and Euclidean is 3D where time is just a variable. GR/Riemannian is also “Background Independent” as I understand it, and Euclidean would be Background Dependent. While the successful current theories GR and QM are not. At least I think QM is background independent. RB
I will say nothing on your claim that QM is BI.

Regarding above link you would read it first before disagree . Already in the abstract you can see that are talking of a flat spacetime not a flat space. See also my post #131.

 Quote by RandallB The ideas that wish to replace or correct GR and/or QM, all seem to get more complex in both their concept and mathematics. Maybe that’s because reality is complex. RB
One may simply explain world. Often this is done by the use of more complex formulations and novel mathematical tools. All attempt to quantize gravity rely on new math and concepts do not included on GR + QM.

But whereas many of others approaches focus on physical insight, ST is just a mathematical goulash around an initially "beatiful" idea that was discarded in accelerator experiments many decades ago.

 Quote by RandallB I still feel that String theory has been successful in showing that 11 dimensions “appear” to be required. Therefore, in my opinion any proposed new theory needs to explain why that appeared to be true. That includes variations on Strings, canonical science, and even Euclidean explanations. RB
Required for what? for fulfilling ArXiv with dozens of ineffective preprints? After of more than 30 years, string theory is even poor that when began.

Things are much more simple: any proposed new theory needs to explain the world like it appears to us. Today we know that the world is 4D and non supersymmetric, therefore the first quantum theory of gravity may be a formulation for 4D and without supersimmetry. Precisely this is the point of LQG and other approaches.

If at 2007, supersimmetry is experimentally observed. No problem!! your theory will continue to be correct (as Newtonian mechanics is in Formula 1), simply you will need generalize to supersimmetry.

The problem of ST and M theory is that 11D and supersymmetry, and the rest of mathematical gulash, are just a mathematical gulash added to the theory because was internally inconsistent or violated experimental data. For example supersymmetry was added ad hoc in the 80s because string theory without it predicted tachions which were newer observed

The aim of physics is to explain universe as it is, is not to develop a theory of "like world would be for me".

All on string theory is about things that are not about our universe. Nothing of standard model or of GR is obtained from ST. At the best, one obtains certain models (after of tricks and ad hoc asumptions) that look like but are not equivalent.

Almost any young student knows the myth that ST predicts gravity or that GR is recovered in the low energy limit but both of those claims are not true.

In fact, causality in ST is defined in a flat metric whereas causality in GR is not. Then what? In the past they say like ST is not 100% compatible with GR and ST is mathematically "beatiful" then the problem may be with GR.

In fact, you appears to ignore that only some years ago string theorists claimed that one would do not take GR "too seriously" . Even today some guys claim that one would ignore experimental data of GR in favor of string theory!!!

All of this is a nonsense, ST is outside of physics.

Those "details" are do that ST was a waste of time or in the words of P.W. Anderson

 a futile exercise like physics
Astronomy
PF Gold
P: 22,675
 Quote by RandallB ... I still feel that String theory has been successful in showing that 11 dimensions “appear” to be required. Therefore, in my opinion any proposed new theory needs to explain why that appeared to be true. That includes variations on Strings, canonical science, and even Euclidean explanations.
strange thought, Randall

to the ancient alchemists, it appeared that all matter could be explained by combining 4 elements

shall we require of all future theories of matter that they explain why that appeared true to the alchemists?
P: 416
 Quote by marcus strange thought, Randall to the ancient alchemists, it appeared that all matter could be explained by combiniing 4 elements shall we require of all future theories of matter that they explain why that appeared true to the alchemists?

You explained better and shorter (= two time better) than my
Astronomy
PF Gold
P: 22,675
 Quote by Juan R. Nice reply!!! You explained better and shorter (= two time better) than my
I owe this entirely to your inspiring example, Juan
thank you kindly

however on another matter, I feel a deep attachment to the geometric explanation of gravity and, although I am disinclined to argue with you, I wish you would not so often castigate it with your disapproval

but if you must, by your very nature as Juan, then I guess you must
HW Helper
P: 1,204
 Quote by RandallB If you know of one, I’d love to see where someone makes a serious attempt at a Euclidean explanation, I’ve never seen one. I have to disagree on David Hestenes. He cannot be talking about a Euclidean basis while using GR and Riemannian geometry. That is 4D and Euclidean is 3D where time is just a variable.
Look at chapter IV of this link, which is from Foundations of Physics, 35: 1-67 (2005):
http://modelingnts.la.asu.edu/pdf/GTG.w.GC.FP.pdf
http://modelingnts.la.asu.edu/html/GCgravity.html

I think the above link is a better article in its explanation of the theory than the one I originally posted.

 Quote by RandallB GR/Riemannian is also “Background Independent” as I understand it, and Euclidean would be Background Dependent. While the successful current theories GR and QM are not. At least I think QM is background independent.
I believe that the standard model of QM is background dependent. Or more precisely, that it can be cast in a background dependent interpretation. Here's an arxiv article on the subject that explains it pretty much the way I see it, except that I think that background dependence is a good thing, not something to be gotten rid of:
http://arxiv.org/PS_cache/hep-th/pdf/0409/0409048.pdf

A typical QFT textbook will deal with the background dependence of the theory by showing that while the calculations do assume a background (in the form of a particular metric), the results of the calculations are compatible with Lorentz / Poincare symmetry. That is, if you assume a different reference frame, your calculation will be different but the final result will be the same. The fact that they have to show this is an indication that the theory is not in itself inherently background independent. From my point of view, this is evidence that the universe does have a "background". It's just that since we're a part of the universe, we have great difficulty figuring out exactly what that background is.

 Quote by RandallB The ideas that wish to replace or correct GR and/or QM, all seem to get more complex in both their concept and mathematics. Maybe that’s because reality is complex.
Even simple equations can have very complex solutions. If one were to look at the table of the elements, one might conclude that Schroedinger's wave equation, which pretty much explains the thing, must also be complex. My guess is that simplicity should be at the core.

 Quote by RandallB I still feel that String theory has been successful in showing that 11 dimensions “appear” to be required. Therefore, in my opinion any proposed new theory needs to explain why that appeared to be true. That includes variations on Strings, canonical science, and even Euclidean explanations.
I only bought one string theory text book. Different chapters in the book purport to prove why N dimensions are necessary for a consistent theory. The only problem is that N is not a constant but changes from chapter to chapter.

My guess is that quarks and leptons are the results of a two stage condensation. The second stage is the combination of left and right handed massless chiral particles to form fermions. This is almost a part of the standard model, the difference being that the standard model requires a Higgs particle to be absorbed (or emitted) at the vertices where left and right handed chiral fermions convert to each other. The first stage of the condensation is one that produces the massless chiral fermions and is beyond the scope of this discussion. But this sort of concept does get back to string theory, or at least to the concept of hidden dimensions, by the fact that if one ignores a condensation of subparticles, (that is, if one only looks at the interactions of the combined system), one will end up with unexplained degrees of freedom. These extra degrees of freedom can be naturally explained through the notion of hidden dimensions.

As an example, if two subparticles combine to form a tightly bound composite particle, we will use center of mass coordinates for the composite particle. But there will still be a set of relative coordinates for the two subparticles. Since it is a bound state, the relative coordinates will be compact and therefore will look (mathematically) like a space of compactified dimensions. This gives some hope of determining the topology of string theory from the mechanics of the subparticles.

Carl
P: 1,545
 Quote by marcus strange thought, Randall to the ancient alchemists, it appeared that all matter could be explained by combiniing 4 elements shall we require of all future theories of matter that they explain why that appeared true to the alchemists?
Excellent point and
YES WE SHOULD
BUT - “ancient alchemists” ideas have been explained as wrong, based on current science. And we do understand how their old view of reality; lead them to think they way they did.
So that job has been done.
I also understand need for a New Theory to show the old wrong theories to be wrong to make way for a new one.
However, loudly proclaiming that GR and QM are wrong is far short of showing them to be wrong.

True enough not every idea that falls off the truck should qualifies to set yet another standard that must be disproved of proved by any future new theory. That will always be an individual judgment call. But where rigorous scientific interpretation of observations and rigorous math has been applied to build a view of a theory - some explanation as to why the theory was constructed incorrectly should be proved by a replacing better theory. Just as has been done with Alchemists Theories. If it cannot do so what makes the new theory better?
In the worst case view of both GR and QM they have certainly met that standard.
But, for all those that have better answers than GR or QM, I've never seen a reasoned explanation as to why GR and QM work so well and are yet wrong.

Now I’m no String or M theory expert, in fact I don’t see how they could be correct. But based the quality of the people and the work they have done, I trust and I believe the ideas were rigorously formed. And for me the idea of 10 or 11 dimensions was reasonable reached in this case. So for me I feel they have met the standard. Even though I do not believe in extra dimensions myself I feel it’s only responsible to accept the higher standard. Therefore if I want to show strings to be wrong, and there is something better, I must understand how they made the mistake of assuming the extra dimensions. If I can’t take the responsibility to do that, then why should anyone take a new idea seriously?

I just find this a more reasoned and logic approach to the issue rather than just cobbling a bunch of ideas together with no proofs, and no explanations of how the others made the wrong conclusions.

Is that easy to do – of course not it's harder, nobody promised easy.

RB
Emeritus
PF Gold
P: 8,147
 Quote by RandallB I have to disagree on David Hestenes. He cannot be talking about a Euclidean basis while using GR and Riemannian geometry. That is 4D and Euclidean is 3D where time is just a variable. GR/Riemannian is also “Background Independent” as I understand it, and Euclidean would be Background Dependent.
"Euclidean" in this context refers to any geometry where the line element $$ds^2 = g_{ab}dx^adx^b$$ is positive definite. So you can have Riemannian geometry that is Euclidean. The line element of GR is not positive definite, because the "time" term is a different sign from the "space" terms.

And "background independent" is a property of the physics together with the geometry, not the kind of geometry alone. If the physics acts on the geometry, and the geometry determines the physics, so there is self-interaction, then you have background indpendence.
Astronomy
PF Gold
P: 22,675
 Quote by selfAdjoint ...And "background independent" is a property of the physics together with the geometry, not the kind of geometry alone. If the physics acts on the geometry, and the geometry determines the physics, so there is self-interaction, then you have background independence.
nice way to put it. points up a positive quality instead of the negative quality of not being dependent on something like a prior fixed choice of background metric. different ways of saying the same thing but more intuitive/evocative to say it in this positive way
P: 416
 Quote by marcus however on another matter, I feel a deep attachment to the geometric explanation of gravity and, although I am disinclined to argue with you, I wish you would not so often castigate it with your disapproval
At the best, i think that you would only find difficulty with point 4) of post #131, since rest is standard or almost standard. And, of course, with my own solution to the problem.

I think that once the paper was published you could study it carefully and write a public comment if you consider that GR is still a good approach after of reading my work.

If i am wrong you will help to me to understand correctly gravitation .

If i am not wrong then I will help to you to understand correctly gravitation.
P: 416
 Quote by CarlB I only bought one string theory text book. Different chapters in the book purport to prove why N dimensions are necessary for a consistent theory. The only problem is that N is not a constant but changes from chapter to chapter. Carl
Very good point!!

In fact the history of dimensions is

4D, 5D, 26D, 10D, 11D, ...

According to B. Greene some string theorists are now working in the posibility of more than one time dimension whereas others claim that the fail of compactification may indicate that there are still unknown 4D-versions of "string" theory.

Also the size of strings changes from "chapter to chapter" from "infinitely" small (Planck) to mm range to again "infinitely" small to infinitely large. There is a version that says that compactified dimension are the usual 4D ones, etc.

The rest of "theory" is also chapter-dependant and even book-dependant or author-dependant!!
P: 416
 Quote by RandallB Now I’m no String or M theory expert, in fact I don’t see how they could be correct. But based the quality of the people and the work they have done, I trust and I believe the ideas were rigorously formed. And for me the idea of 10 or 11 dimensions was reasonable reached in this case. So for me I feel they have met the standard. Even though I do not believe in extra dimensions myself I feel it’s only responsible to accept the higher standard. Therefore if I want to show strings to be wrong, and there is something better, I must understand how they made the mistake of assuming the extra dimensions. If I can’t take the responsibility to do that, then why should anyone take a new idea seriously? I just find this a more reasoned and logic approach to the issue rather than just cobbling a bunch of ideas together with no proofs, and no explanations of how the others made the wrong conclusions. Is that easy to do – of course not it's harder, nobody promised easy. RB
This sounds like the main argument for studying string theory that some string theorists use: "Because Witten believes on it".

That is not a scientific argument.

The "quality" of people is a subjective concept and, moreover, is not guarantee of a good work. Look for example the history of QFT, almost all great guys Schrödinger, Dirac, etc. did the wrong work and a new generation of young people did QFT. In fact, this argument against string theory has been recently used by Dyson.

Regarding the "quality" of the work they have done, i could say that the quality is very low, with lot of wrong details that are corrected after of decades. Material known in other fields is introduced decades after in string theory. In concrete points, I can assure that the quality of Seiberg's work on NC geomstry is low, the quality of Schwartz's work on unitarity is low, the quality of Witten's work on QM foundations is low, the quality of Nanopoulos' work on the arrow of time problem is low, etc.

 Quote by RandallB So for me I feel they have met the standard.
Curiosly the standard in quantum gravity research is not that.

 Quote by RandallB Therefore if I want to show strings to be wrong, and there is something better, I must understand how they made the mistake of assuming the extra dimensions.
Curiously science does not work on that way. Are string theorists who may show that universe is 11D!! Curiously string theorists have shown nothing and none of their initial promises has been done after of more than 30 years!

It is time for exploring other alternatives.
P: 1,545
 Quote by Juan R. It is time for exploring other alternatives.
Well at least that's one point we completly agree on.
I just hope and even expect that a good alternative will prove strings wrong by show how/why it appeared to them there should be multi D's. I'd even expect proving so can be helpful.
RB
P: 1,545
 Quote by selfAdjoint "Euclidean" in this context refers to any geometry where the line element $$ds^2 = g_{ab}dx^adx^b$$ is positive definite. So you can have Riemannian geometry that is Euclidean. The line element of GR is not positive definite, because the "time" term is a different sign from the "space" terms. And "background independent" is a property of the physics together with the geometry, not the kind of geometry alone. If the physics acts on the geometry, and the geometry determines the physics, so there is self-interaction, then you have background indpendence.
So is GR consided background indpendent ??
Does "The line element of GR is not positive definite" address this issue?

The Lee Smolin link (Thanks for finding Marcus)
http://arxiv.org/abs/hep-th/0507235
Provides a firm argument the GR is “relational” or background independent.
At least where “warping” is concerned.
Is this generally accepted as the case or is this a “debated point” ?

 Related Discussions Beyond the Standard Model 5 Beyond the Standard Model 4 Beyond the Standard Model 47


text:
# Are the eigenvalues of Hecke operators distinct?

Given a Hecke operator which acts on the space of modular forms for $\mathrm{SL}_2(\mathbb{Z})$, are the eigenvalues necessarily distinct?

-
I would also like to know if there is a modular form for $\mathrm{SL}_2(\mathbb{Z})$ with a vanishing Hecke eigenvalue. –  GH from MO Aug 28 '12 at 14:13
Just to clarify, are you asking if a particular Hecke operator $T_\ell$ acting on the space $M_k(\mathrm{SL}_2(\mathbb{Z}))$ of forms of fixed weight $k$ for the full modular group has distinct eigenvalues (i.e. square-free characteristic polynomial)? –  Ramsey Aug 28 '12 at 14:28
@Will: That bound is right in weight $2$, but in general the bound for weight $k$ is $2p^{(k-1)/2}$. –  Ramsey Aug 28 '12 at 14:45
It's conjectured (Maeda's conjecture) that for any prime $p$ and any even weight $k \ge 12$, the characteristic polynomial of $T_p$ acting on $S_k(\operatorname{SL}_2(\mathbb{Z}))$ is irreducible over $\mathbb{Q}$; in particular, it has no multiple roots. Various authors (eg Buzzard, Kleinerman) have verified this for lots of values of $p$ and $k$. If I remember correctly, in all cases that have been tested the stronger statement holds that the char polys all have Galois group equal to the full symmetric group of the appropriate degree. –  David Loeffler Aug 28 '12 at 15:22
The way I understand the question: is it true that for any Hecke eigenform $f\in S_k(\operatorname{SL}_2(\mathbb{Z}))$ the Hecke eigenvalues $\lambda_f(p)$, normalized so that they lie between $\pm 2p^{(k-1)/2}$, are all distinct? –  GH from MO Aug 28 '12 at 15:30


text:
# PracticeDifferentiate 4

Differentiate.

#### Jason

##### Well-known member
I suppose the first step would be to take everything, bottom and top - both sides, to the cubed power - to get rid of the cubed root.

@MarkFL

However, there is also the square root there, though.

#### MarkFL

##### La Villa Strangiato
Math Helper
I would use the product/power/chain rules.


text:
Browse Questions

# Consider the reaction $2H_2O_2(aq)\rightarrow 2H_2O(l)+O_2(g)$ wen 1g of KI is added to $H_2O_2$,bubbles of $O_2$ are produced at an increased rate.When reaction is complete,mass of KI is 1g.The KI is a

$\begin{array}{1 1}(a)\;product\\(b)\;reactant\\(c)\;catalyst\\(d)\;reaction\;intermediate\end{array}$

Catalyst is substance which just increases rate of reaction by decreasing activation energy without being consumed in reaction.
Mass of KI before and after reaction is same (i.e) 1 gram.
So it is catalyst.
Hence (c) is the correct answer.


text:
gtsam  4.0.0 gtsam
gtsam::Values Class Reference

## Detailed Description

A non-templated config holding any types of Manifold-group elements.

A values structure is a map from keys to values. It is used to specify the value of a bunch of variables in a factor graph. A Values is a values structure which can hold variables that are elements on manifolds, not just vectors. It then, as a whole, implements a aggregate type which is also a manifold element, and hence supports operations dim, retract, and localCoordinates.

## Public Member Functions

Values ()
Default constructor creates an empty Values class.

Values (const Values &other)
Copy constructor duplicates all keys and values.

Values (Values &&other)
Move constructor.

Values (const Values &other, const VectorValues &delta)
Construct from a Values and an update vector: identical to other.retract(delta)

template<class ValueType >
Values (const Filtered< ValueType > &view)
Constructor from a Filtered view copies out all values.

template<class ValueType >
Values (const ConstFiltered< ValueType > &view)
Constructor from a Filtered or ConstFiltered view.

template<typename ValueType >
ValueType at (Key j) const
Retrieve a variable by key j. More...

double atDouble (size_t key) const
version for double

const Valueat (Key j) const
Retrieve a variable by key j. More...

bool exists (Key j) const
Check if a value exists with key j. More...

template<typename ValueType >
boost::optional< const ValueType & > exists (Key j) const
Check if a value with key j exists, returns the value with type Value if the key does exist, or boost::none if it does not exist. More...

iterator find (Key j)
Find an element by key, returning an iterator, or end() if the key was not found. More...

const_iterator find (Key j) const
Find an element by key, returning an iterator, or end() if the key was not found. More...

iterator lower_bound (Key j)
Find the element greater than or equal to the specified key. More...

const_iterator lower_bound (Key j) const
Find the element greater than or equal to the specified key. More...

iterator upper_bound (Key j)
Find the lowest-ordered element greater than the specified key. More...

const_iterator upper_bound (Key j) const
Find the lowest-ordered element greater than the specified key. More...

size_t size () const
The number of variables in this config.

bool empty () const
whether the config is empty

const_iterator begin () const

const_iterator end () const

iterator begin ()

iterator end ()

const_reverse_iterator rbegin () const

const_reverse_iterator rend () const

reverse_iterator rbegin ()

reverse_iterator rend ()

void insert (Key j, const Value &val)

void insert (const Values &values)

template<typename ValueType >
void insert (Key j, const ValueType &val)
Templated version to add a variable with the given j, throws KeyAlreadyExists<J> if j is already present.

void insertDouble (Key j, double c)
version for double

std::pair< iterator, bool > tryInsert (Key j, const Value &value)
insert that mimics the STL map insert - if the value already exists, the map is not modified and an iterator to the existing value is returned, along with 'false'. More...

void update (Key j, const Value &val)
single element change of existing element

template<typename T >
void update (Key j, const T &val)
Templated version to update a variable with the given j, throws KeyAlreadyExists<J> if j is already present if no chart is specified, the DefaultChart<ValueType> is used.

void update (const Values &values)
update the current available values without adding new ones

void erase (Key j)
Remove a variable from the config, throws KeyDoesNotExist<J> if j is not present.

KeyVector keys () const
Returns a set of keys in the config Note: by construction, the list is ordered.

Valuesoperator= (const Values &rhs)
Replace all keys and variables.

void swap (Values &other)
Swap the contents of two Values without copying data.

void clear ()
Remove all variables from the config.

size_t dim () const
Compute the total dimensionality of all values ( $$O(n)$$)

VectorValues zeroVectors () const
Return a VectorValues of zero vectors for each variable in this Values.

Filtered< Valuefilter (const boost::function< bool(Key)> &filterFcn)
Return a filtered view of this Values class, without copying any data. More...

template<class ValueType >
Filtered< ValueType > filter (const boost::function< bool(Key)> &filterFcn=&_truePredicate< Key >)
Return a filtered view of this Values class, without copying any data. More...

ConstFiltered< Valuefilter (const boost::function< bool(Key)> &filterFcn) const
Return a filtered view of this Values class, without copying any data. More...

template<class ValueType >
ConstFiltered< ValueType > filter (const boost::function< bool(Key)> &filterFcn=&_truePredicate< Key >) const
Return a filtered view of this Values class, without copying any data. More...

template<class ValueType >
size_t count () const

template<typename ValueType >
void update (Key j, const ValueType &val)

Testable
void print (const std::string &str="", const KeyFormatter &keyFormatter=DefaultKeyFormatter) const
print method for testing and debugging

bool equals (const Values &other, double tol=1e-9) const
Test whether the sets of keys and values are identical.

Manifold Operations
Values retract (const VectorValues &delta) const
Add a delta config to current config and returns a new config.

VectorValues localCoordinates (const Values &cp) const
Get a delta config about a linearization point c0 (*this)

## Public Types

typedef boost::shared_ptr< Valuesshared_ptr
A shared_ptr to this class.

typedef boost::shared_ptr< const Valuesconst_shared_ptr
A const shared_ptr to this class.

typedef boost::transform_iterator< boost::function1< KeyValuePair, const KeyValuePtrPair & >, KeyValueMap::iterator > iterator
Mutable forward iterator, with value type KeyValuePair.

typedef boost::transform_iterator< boost::function1< ConstKeyValuePair, const ConstKeyValuePtrPair & >, KeyValueMap::const_iterator > const_iterator
Const forward iterator, with value type ConstKeyValuePair.

typedef boost::transform_iterator< boost::function1< KeyValuePair, const KeyValuePtrPair & >, KeyValueMap::reverse_iterator > reverse_iterator
Mutable reverse iterator, with value type KeyValuePair.

typedef boost::transform_iterator< boost::function1< ConstKeyValuePair, const ConstKeyValuePtrPair & >, KeyValueMap::const_reverse_iterator > const_reverse_iterator
Const reverse iterator, with value type ConstKeyValuePair.

typedef KeyValuePair value_type

## Classes

class  ConstFiltered
A filtered view of a const Values, returned from Values::filter. More...

struct  ConstKeyValuePair
A key-value pair, which you get by dereferencing iterators. More...

class  Filtered
A filtered view of a Values, returned from Values::filter. More...

struct  KeyValuePair
A key-value pair, which you get by dereferencing iterators. More...

## Friends

class boost::serialization::access
Serialization function.

## ◆ at() [1/2]

template<typename ValueType >
 ValueType gtsam::Values::at ( Key j ) const

Retrieve a variable by key j.

The type of the value associated with this key is supplied as a template argument to this function.

Parameters
 j Retrieve the value associated with this key
Template Parameters
 ValueType The type of the value stored with this key, this method Throws DynamicValuesIncorrectType if this requested type is not correct. Dynamic matrices/vectors can be retrieved as fixed-size, but not vice-versa.
Returns
The stored value

## ◆ at() [2/2]

 const Value & gtsam::Values::at ( Key j ) const

Retrieve a variable by key j.

This version returns a reference to the base Value class, and needs to be casted before use.

Parameters
 j Retrieve the value associated with this key
Returns
A const reference to the stored value

## ◆ exists() [1/2]

 bool gtsam::Values::exists ( Key j ) const

Check if a value exists with key j.

See exists<>(Key j) and exists(const TypedKey& j) for versions that return the value if it exists.

## ◆ exists() [2/2]

template<typename ValueType >
 boost::optional< const ValueType & > gtsam::Values::exists ( Key j ) const

Check if a value with key j exists, returns the value with type Value if the key does exist, or boost::none if it does not exist.

Throws DynamicValuesIncorrectType if the value type associated with the requested key does not match the stored value type.

## ◆ filter() [1/4]

 Values::Filtered< Value > gtsam::Values::filter ( const boost::function< bool(Key)> & filterFcn )
inline

Return a filtered view of this Values class, without copying any data.

When iterating over the filtered view, only the key-value pairs with a key causing filterFcn to return true are visited. Because the object Filtered<Value> returned from filter() is only a view the original Values object must not be deallocated or go out of scope as long as the view is needed.

Parameters
 filterFcn The function that determines which key-value pairs are included in the filtered view, for which this function returns true on their keys.
Returns
A filtered view of the original Values class, which references the original Values class.

## ◆ filter() [2/4]

template<class ValueType >
 Values::Filtered< ValueType > gtsam::Values::filter ( const boost::function< bool(Key)> & filterFcn = &_truePredicate )

Return a filtered view of this Values class, without copying any data.

In this templated version, only key-value pairs whose value matches the template argument ValueType and whose key causes the function argument filterFcn to return true are visited when iterating over the filtered view. Because the object Filtered<Value> returned from filter() is only a view the original Values object must not be deallocated or go out of scope as long as the view is needed.

Template Parameters
 ValueType The type that the value in a key-value pair must match to be included in the filtered view. Currently, base classes are not resolved so the type must match exactly, except if ValueType = Value, in which case no type filtering is done.
Parameters
 filterFcn The function that determines which key-value pairs are included in the filtered view, for which this function returns true on their keys (default: always return true so that filter() only filters by type, matching ValueType).
Returns
A filtered view of the original Values class, which references the original Values class.

## ◆ filter() [3/4]

 Values::ConstFiltered< Value > gtsam::Values::filter ( const boost::function< bool(Key)> & filterFcn ) const
inline

Return a filtered view of this Values class, without copying any data.

When iterating over the filtered view, only the key-value pairs with a key causing filterFcn to return true are visited. Because the object Filtered<Value> returned from filter() is only a view the original Values object must not be deallocated or go out of scope as long as the view is needed.

Parameters
 filterFcn The function that determines which key-value pairs are included in the filtered view, for which this function returns true on their keys.
Returns
A filtered view of the original Values class, which references the original Values class.

## ◆ filter() [4/4]

template<class ValueType >
 Values::ConstFiltered< ValueType > gtsam::Values::filter ( const boost::function< bool(Key)> & filterFcn = &_truePredicate ) const

Return a filtered view of this Values class, without copying any data.

In this templated version, only key-value pairs whose value matches the template argument ValueType and whose key causes the function argument filterFcn to return true are visited when iterating over the filtered view. Because the object Filtered<Value> returned from filter() is only a view the original Values object must not be deallocated or go out of scope as long as the view is needed.

Template Parameters
 ValueType The type that the value in a key-value pair must match to be included in the filtered view. Currently, base classes are not resolved so the type must match exactly, except if ValueType = Value, in which case no type filtering is done.
Parameters
 filterFcn The function that determines which key-value pairs are included in the filtered view, for which this function returns true on their keys.
Returns
A filtered view of the original Values class, which references the original Values class.

## ◆ find() [1/2]

 iterator gtsam::Values::find ( Key j )
inline

Find an element by key, returning an iterator, or end() if the key was not found.

## ◆ find() [2/2]

 const_iterator gtsam::Values::find ( Key j ) const
inline

Find an element by key, returning an iterator, or end() if the key was not found.

## ◆ lower_bound() [1/2]

 iterator gtsam::Values::lower_bound ( Key j )
inline

Find the element greater than or equal to the specified key.

## ◆ lower_bound() [2/2]

 const_iterator gtsam::Values::lower_bound ( Key j ) const
inline

Find the element greater than or equal to the specified key.

## ◆ tryInsert()

 std::pair< Values::iterator, bool > gtsam::Values::tryInsert ( Key j, const Value & value )

insert that mimics the STL map insert - if the value already exists, the map is not modified and an iterator to the existing value is returned, along with 'false'.

If the value did not exist, it is inserted and an iterator pointing to the new element, along with 'true', is returned.

## ◆ upper_bound() [1/2]

 iterator gtsam::Values::upper_bound ( Key j )
inline

Find the lowest-ordered element greater than the specified key.

## ◆ upper_bound() [2/2]

 const_iterator gtsam::Values::upper_bound ( Key j ) const
inline

Find the lowest-ordered element greater than the specified key.

The documentation for this class was generated from the following files:
• /Users/dellaert/git/gtsam/gtsam/nonlinear/Values.h
• /Users/dellaert/git/gtsam/gtsam/nonlinear/Values-inl.h
• /Users/dellaert/git/gtsam/gtsam/nonlinear/Values.cpp