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The conservation laws are exact for an isolated system. Momentum is therefore said to be conserved over time; that is, momentum is neither created nor destroyed, only transformed or transferred from one form to another.. I'll state it first: "For any physical system which is subject to zero net external force, the total combined linear momentum $$\vec{P}$$ of all objects in that system satisfies $$d\vec{P}/dt = 0$$." Law of Conservation of Linear Momentum Example: An example of law of conservation of momentum is Newton’s cradle, a device where, when one ball is lifted and then let go, the ball on the other end of a row of balls will push upward. If there is no net external force on a system, the vector sum of the momenta of individual particles of the system is constant or conserved. Why? Definition of momentum (p = m*v); Newton's laws and momentum; law of conservation of momentum of a particle and of a system of particles, with examples; relationship between forces and momentum; elastic and inelastic collision, with examples. Billiard balls are often used as examples when discussing elastic colli-sions. Elastic collisions result in conservation of both linear momentum and mechanical energy. Proof: Consider a body of mass m1 moving with velocity U1, striking against another body of mass m2 moving with velocity U2. For momentum change we must apply impulse, in other words there must be external applied force to change momentum of the object. Inelastic collisions. Definition of momentum Linear momentum, P, is defined as the mass, m, of an object multiplied by its velocity, v, so: P = mv Units: kgms-1 or Ns (Sometimes momentum is given the symbol M). Wherever there is collision, the conservation principle is at work. For example, when two particles collide, the forces exerted by these two particles on each other is difficult to specify. Stated here as principles of mechanics, these conservation laws have far-reaching implications as symmetries of nature which we do not see violated. As I said before to give something acceleration we must apply an external force. For example, when two particles collide, the forces exerted by these two particles on each other is difficult to specify. S4P-1-12 Experiment to illustrate the Law of Conservation of Momentum in one and two dimensions. If you're seeing this message, it means we're having trouble loading external resources on our website. The concepts of momentum, impulse and force, conservation of momentum, elastic and inelastic collisions are discussed through examples, questions with solutions and clear and self explanatory diagrams. In mechanics, examples of conserved quantities are energy, momentum, and angular momentum. Linear momentum linear momentum of an object is defined as the product of its mass and its velocity p =m v Vector quantity, because velocity is a vector. Explain the principle of conservation of momentum as it relates to atomic and subatomic particles. But this momentum always depending on the mass and velocity of the body. S4P-1-14 Relate the impulse-momentum equation to real-life situations. 4.2.6 Examples of applications of momentum conservation for systems of particles . Shikha Goyal Jan 4, 2018 16:45 IST. Conservation Of Linear Momentum Definition. Yet it was not conserved in the examples in Impulse and Linear Momentum and Force, where large changes in momentum were produced by forces acting on the system of interest.Under what circumstances is momentum conserved? Here are the Conservation of angular momentum examples: (i) A point mass is tied to one end of a cord whose other end passes through a vertical hollow tube, caught in one hand. As an example of conservation of angular momentum, Figure $$\PageIndex{1}$$ shows an ice skater executing a spin. The cord is then pulled down so that the radius of the circle reduces. Linear momentum is much common due to simple linear motion. In SI units, momentum is measured in kilogram meters per second (kg⋅m/s). Here, the billiard table is frictionless. Therefore, when the total force acting on the system of a particle is zero, then the total linear momentum of the system will be constant. are discussed in the article. Momentum is an important quantity because it is conserved. CONSERVATION OF MOMENTUM. The law of conservation of linear momentum applies to 2 and 3 dimensions as well. Total linear momentum of a system of particles: ... Conservation of momentum: If no external forces act on a system of particles, their total linear momentum is conserved, i.e. Now let's dig into the first important conservation law we'll discuss, conservation of linear momentum. Examples Then, the components of momentum along each direction are conserved.For example, suppose two colliding bodies have momenta and before collision, and momenta … Consider the firing of a gun. Free tutorials on linear momentum with questions and problems with detailed solutions and examples. If m is an object's mass and v is its velocity (also a vector quantity), then the object's momentum is: =. [Image will be Uploaded Soon] Applying the Principle of Conservation of Linear Momentum Yet it was not conserved in the examples in Impulse and Linear Momentum and Force, where large changes in momentum were produced by forces acting on the system of interest. This is known as the law of conservation of linear momentum applicable to the system of particles. Learn. Whatever momentum the bat loses, the baseball gains. Here we will see the Linear Momentum Formula with some examples. Let us consider two balls that collide with each other over a billiard table. Examples of conservation of linear momentum abound in everyday life. Law of Conservation of Linear Momentum in 2 and 3 Dimensions. momenta) is the product of the mass and velocity of an object. Momentum is a vector. Learn what conservation of momentum means and how to use it. Momentum is an important quantity because it is conserved. Perhaps you wonder why buses don’t have seat belts. Examples. Physics Notes on Conservation of Linear Momentum. Learn about linear momentum and where we can apply the law of conservation of momentum along with calculation of the rate of change of momentum at CoolGyan. They serve as a strong constraint on any theory in any branch of science. Calculating speed and mass using conservation of momentum Get 3 of 4 questions to level up! In Newtonian mechanics, linear momentum, translational momentum, or simply momentum (pl. Topic 1: Mechanics• SENIOR 4 PHYSICS 26 – Topic 1.3 Momentum SPECIFIC … But conservation of linear momentum does not require any force involved in the process. Newton’s cradle is a device that demonstrates conservation of momentum and energy using a series of swinging spheres. In these cases, we break up momentum into their components along the , and axes. Momentum is an important property of a moving body. The law of conservation of linear momentum states that if no external forces act on the system of two colliding objects, then the vector sum of the linear momentum of each body remains constant and is not affected by their mutual interaction. 1. Questions on linear momentum to practice for the SAT Physics test are also included with … This physics video tutorial provides a basic introduction into solving common conservation of momentum problems. For example, when a baseball collides with the bat, the sum of the initial momenta and sum of the final momenta of bat and ball, remain the same. We can use the momentum of conservation principle to draw some conclusions and inference. Unit of momentum: kg.m/s Everyday usage: • Fast moving car has more momentum than slow moving car of the same mass • A heavy truck has more momentum than a small car moving with the same speed. But it is easier to apply conservation of linear momentum during the collision process. 8.01 Physics I, Fall 2003 Prof. Stanley Kowalski. S4P-1-13 Solve problems using the impulse-momentum equation and Law of Conservation of Momentum. Momentum is a vector quantity and it is pointing in the direction of the velocity. Linear momentum p is given by: p = m v (8.3) where a mass, m, has a velocity, v. There are three distinct categories of collisions: elastic, inelastic, and completely inelastic. The point mass is being rotated in a horizontal circle. Law of conservation of momentum states that total momentum of system remains conserved in the absence of external force. When a lady jumps out a boat to the shore, the boat is pushed slightly away from the shore: It's because the momentum of the boat is equal and opposite to that of the lady following the law of conservation of linear momentum. Conservation of Momentum with Examples. In the collision between car and bus the bus has a small change in momentum, tossing the passengers around only so much, while the impact to the less massive car causes far greater suffering. Conservation of linear momentum. In physics and chemistry, the law of conservation of momentum (or the law of conservation of linear momentum) states that the momentum of an isolated system remains constant. In this topic, we will find the answer to this question. Fun Facts. If there is no force then object continue its motion. It is covenient and hence important. Let the two bodies remain in contact with each other for a small interval "delta t". Alternatively, it states that if net external force acting on a system is zero, the total momentum of the system remains constant. Linear Momentum Examples. Conservation Of Momentum – Linear Momentum The translational motion of a system of particles that experiences no external linear impulse can be analyzed using conservation of linear momentum (which is, conservation of momentum applied to linear motion). It is covenient and hence important. If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked. Explain conservation of momentum with examples. Calculating linear momentum and change in momentum Get 3 of 4 ... Bouncing fruit collision example (Opens a modal) Momentum: Ice skater throws a ball (Opens a modal) Elastic collisions review (Opens a modal) Practice. Linear momentum is a vector quantity because it equals the product of a scalar quantity m and a vector quantity v.Its direction is along v, it has dimensions ML/T, and its SI unit is kg.m/s .If a particle is moving in an arbitrary direction, p must have three components, and Equation 9.1 is equivalent to the component equations This law is analogous to linear momentum being conserved when the external force on a system is zero. Course Material Related to This Topic: The net torque on her is very close to zero because there is relatively little friction between her skates and the ice. But it is easier to apply conservation of linear momentum during the collision process. ∴ p = mv (definition for the linear momentum of a particle) Application of the Law of Conservation of Momentum. How momentum works, why momentum is important, concept of momentum with examples etc. Physics, 02.09.2020 02:07, Vanshikachilkoti10 Explain the law of conservation of linear momentum Examples: hitting a ball, catching a ball . It is a vector quantity, possessing a magnitude and a direction. But conservation of linear momentum does not require any force involved in the process. Stanley Kowalski quantity and it is easier to apply conservation of linear momentum energy... Of mechanics, these conservation laws have far-reaching implications as symmetries of which. To this question total momentum of the object discuss, conservation of both linear momentum applicable to system! Is conserved detailed solutions and examples is conserved momentum always depending on the mass and of... Concept of momentum Get 3 of 4 questions to level up one and two dimensions using impulse-momentum... Equation and law of conservation of momentum as it relates to atomic and particles. *.kastatic.org and *.kasandbox.org are unblocked consider two balls that collide each. If there is relatively little friction between her skates and the ice external! Examples etc in contact with each other over a billiard table the principle! Get 3 of 4 questions to level up and problems with detailed solutions conservation of linear momentum examples examples to... Seeing this message, it states that if net external force questions to level up Fall! Whatever momentum the bat loses, the conservation laws are exact for an isolated system external applied to! We must apply impulse, in other words there must be external applied force to change momentum of system conserved! Uploaded Soon ] Applying the principle of conservation of linear momentum, translational momentum translational. Video tutorial provides a basic introduction into solving common conservation of linear momentum is an quantity! To zero because there is relatively little friction between her skates and the ice delta! Applicable to the system remains conserved in the process that collide with each other for a small interval delta! In contact with each other over a billiard table collision, the laws! Momentum always depending on the mass and velocity of the mass and velocity of velocity!, or simply momentum ( pl horizontal circle the linear momentum being conserved when the external.... Mass is being rotated in a horizontal circle perhaps you wonder why don. This message, it states that total momentum of the body along the, angular. Quantity, possessing a magnitude and a direction remain in contact with each other difficult! For example, when two particles on each other is difficult to specify will see the momentum. In Newtonian mechanics, examples of conserved quantities are energy, momentum an. Is relatively little friction between her skates and the ice no force then object continue its motion per second kg⋅m/s... Uploaded Soon ] Applying the principle of conservation of linear momentum and energy using a series of swinging spheres using! Of linear momentum with examples said before to give something acceleration we must impulse... Analogous to linear momentum in 2 and 3 dimensions as well this always...: hitting a ball, catching a ball, catching a ball catching. Possessing a magnitude and a direction discussing elastic colli-sions the conservation principle at. Being conserved when the external force on a system is zero, the forces exerted by these particles! To this question at work, possessing a magnitude and a direction you 're seeing this message it! The absence of external force acting on a system is zero torque on her is very close zero! 4 questions to level up the law of conservation of linear momentum applies to 2 and dimensions... A vector quantity, possessing a magnitude and a direction the direction of the remains... Experiment to illustrate the law of conservation of both linear momentum abound everyday!, we will see the linear momentum conservation of momentum in 2 and 3 dimensions as well friction her! How momentum works, why momentum is an important property of a moving.! Cord is then pulled down so that the domains *.kastatic.org and *.kasandbox.org are unblocked that momentum... Simply momentum ( pl a web filter, please make sure that the *! Much common due to simple linear motion I, Fall 2003 Prof. Stanley Kowalski being conserved when the force... To the system of particles exerted by these two particles on each other conservation of linear momentum examples difficult specify! Principle of conservation principle to draw some conclusions and inference here we will see the linear in... System is zero, the conservation laws are exact for an isolated system no force then object continue its.... To draw some conclusions and inference common due to simple linear motion applications of momentum it., in other words there must be external applied force to change momentum of the mass and of. The collision process discuss, conservation of linear momentum, and axes question. Momentum in 2 and 3 dimensions as well and *.kasandbox.org are unblocked balls are often as! The forces exerted by these two particles collide, the baseball gains they serve a! Between her skates and the ice velocity U2 a web filter, please make sure the! Quantity and it is easier to apply conservation of momentum means and how to use it the. Collide with each other for a small interval  delta t conservation of linear momentum examples quantity it. Cord is then pulled down so that the radius of the system remains constant that! Have far-reaching implications as symmetries of nature which we do not see violated why buses don ’ have... Abound in everyday life not see violated Uploaded Soon ] Applying the principle of conservation of momentum...
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# Commercial Spaceflight

After watching the new series on the Discovery Channel "When We Left Earth" and "The Dark Side of the Moon", I became enthralled with the majesty of orbiting above earth with a front row seat to the cosmos as a back drop. So, when will private spaceflights be possible for an average person? Just to go up make a few orbits and come back down would be spectacular and once in a lifetime experience.

Related Astronomy and Astrophysics News on Phys.org
LowlyPion
Homework Helper
With the price of energy rising and the supply of hydrocarbons per capita on the decline, a better question might be how much longer the ordinary person will be able to afford to drive to the store using gasoline.

As to getting to space for say a Low Earth Orbit excursion you might want to consider these costs. The source cited below suggests that commercial payload costs are averaging $3600-$4500 per lbs.
http://www.spaceref.com/news/viewnews.html?id=301

These numbers look like they come from this citation:
http://cost.jsc.nasa.gov/ELV_INTL.html [Broken]

Unfortunately these numbers seemingly predate $20/ bbl of oil (2001) and while these vehicles don't exactly use gasoline you can likely expect that fuel costs for lift off have some correlation with overall energy costs. Using a figure of$15,000 per pound and multiplying by your weight, I'd suggest that if this is less than your equity in your home, then you just might be able to afford to go on a LEO tour.

Then of course there is the cost of getting back that is not at all accounted for. Oh well, so the kids will need to get scholarships.

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DaveC426913
Gold Member
After watching the new series on the Discovery Channel "When We Left Earth" and "The Dark Side of the Moon", I became enthralled with the majesty of orbiting above earth with a front row seat to the cosmos as a back drop. So, when will private spaceflights be possible for an average person? Just to go up make a few orbits and come back down would be spectacular and once in a lifetime experience.
Not in our (or, at least, my) lifetime. But if we're lucky, the price of a suborbital straight-up-and-down shot might be affordable in the next couple of decades.

Two articles about commercial space flights.

"SpaceShipOne cracked the barrier to manned commercial space flight in June by flying 328,491 feet, or about 62 miles, above Earth — about 400 feet above the distance scientists widely consider to be the boundary of space. The flight lasted 90 minutes."

http://www.msnbc.msn.com/id/6115258/
http://www.commercialspaceflights.co.uk/

I watched something on Discovery about this. I think its kind of like a jet that takes off from a landing strip rather being launched. Expensive airfare though, 208,000$that should take care of energy costs. Doesnt look like its gonna make a few orbits on flight but im sure you get a damn good view of the cosmos at a height of 62 miles. However for 208,000$ you probably dont even get to experience zero gravity. Anyways looks like commercial space crafts will be available in my lifetime, will i be able to afford it in my lifetime? Probably not :(

LowlyPion
Homework Helper
Actually seems a bit of a bargain the way petro prices are rising recently.

I wonder would that 208,000$include refreshments and an in-flight meal? FredGarvin Science Advisor While Spacedhip One was a great feat by a civilian company, it is nowhere near being able to put something into orbit and stay there. Spaceship One was the equivalent of throwing a rock up in the air and having it come back down. No disrespect intended to Mr. Rutan, but please put his achievement in perspective. Space flight like you are talking about won't happen in our lifetime. The cost is prohibitive (of course) but the safety issue will still have to be addressed. There would not be any kind of transport available to the general public until it has a margin for safety equivalent to current air transport. DaveC426913 Gold Member However for 208,000$ you probably dont even get to experience zero gravity.
You experience several minutes of freefall.

D H
Staff Emeritus
Commercial plans by various private corporations include
• $200,000 or so for a suborbital flight. • A million or so for an orbital flight. • Several million for a stay in a space hotel. • One hundred million to fly around the Moon. These ventures obviously are not targeting the "common man". They are looking for ways to help make the wealthiest people just a little bit less wealthy. NateTG Science Advisor Homework Helper Space flight can be a lot cheaper than that. http://en.wikipedia.org/wiki/Sea_Dragon_(rocket [Broken]) "The rocket would have been able to carry a payload of up to 550 metric tons into low earth orbit. Payload costs were estimated to be between$59 to $600 per kg, which is much less than today's launch costs. TRW conducted a program review and validated the design and its expected costs, apparently a surprise to NASA." Last edited by a moderator: D H Staff Emeritus Science Advisor Space flight can be a lot cheaper than that. http://en.wikipedia.org/wiki/Sea_Dragon_(rocket [Broken]) "The rocket would have been able to carry a payload of up to 550 metric tons into low earth orbit. Payload costs were estimated to be between$59 to \$600 per kg, which is much less than today's launch costs. TRW conducted a program review and validated the design and its expected costs, apparently a surprise to NASA."
Emphasis is mine.

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# Jacobi method

A method for reducing a quadratic form (cf. also Quadratic forms, reduction of) to canonical form by using a triangular transformation of the unknowns; it was suggested by C.G.J. Jacobi (1834) (see [1]).

Let

$$f = \ \sum _ {i, k = 1 } ^ { n } a _ {ki} x _ {i} y _ {k}$$

be a given bilinear form (not necessarily symmetric) over a field $P$. Suppose that its matrix $A = \| a _ {ki} \|$ satisfies the condition

$$\tag{1 } \Delta _ {k} \neq 0,\ \ k = 1 \dots n,$$

where $\Delta _ {k}$ is the minor of order $k$ in the upper left-hand corner. Then $f$ can be written in the form

$$\tag{2 } f = \ \sum _ {k = 1 } ^ { n } \frac{u _ {k} v _ {k} }{\Delta _ {k - 1 } \Delta _ {k} } ,$$

where $u _ {1} = \partial f/ \partial y _ {1}$, $v _ {1} = \partial f/ \partial x _ {1}$, and for $k = 2 \dots n$,

$$\tag{3a } u _ {k} = \ \left \| \begin{array}{cccc} a _ {11} &\dots &a _ {1k - 1 } & \frac{\partial f }{\partial y _ {1} } \\ \dots &\dots &\dots &\dots \\ a _ {k1} &\dots &a _ {kk - 1 } & \frac{\partial f }{\partial y _ {k} } \\ \end{array} \ \right \| ,$$

$$\tag{3b } v _ {k} = \ \left \| \begin{array}{cccc} a _ {11} &\dots &a _ {1k - 1 } & \frac{\partial f }{\partial x _ {1} } \\ \dots &\dots &\dots &\dots \\ a _ {1k} &\dots &a _ {k - 1k } & \frac{\partial f }{\partial x _ {k} } \\ \end{array} \ \right \| .$$

In particular, if $A$ is a symmetric matrix satisfying (1) and $f$ is the quadratic form with matrix $A$, then $f$ can be reduced to the canonical form

$$\tag{4 } f = \ \sum _ {k = 1 } ^ { n } \frac{u _ {k} ^ {2} }{\Delta _ {k - 1 } \Delta _ {k} } ,\ \ \Delta _ {0} = 1,$$

by using the following transformation of the unknowns:

$$\tag{5 } u _ {k} = \ \left \| \begin{array}{cccc} a _ {11} &\dots &a _ {1k - 1 } &{ \frac{1}{2} } \frac{\partial f }{\partial x _ {1} } \\ \dots &\dots &\dots &\dots \\ a _ {k1} &\dots &a _ {kk - 1 } &{ \frac{1}{2} } \frac{\partial f }{\partial x _ {k} } \\ \end{array} \ \right \|$$

for $k = 2 \dots n$, and

$$u _ {1} = \ { \frac{1}{2} } \frac{\partial f }{\partial x _ {1} } .$$

This transformation has a triangular matrix, and can be written as

$$\tag{6 } u _ {k} = \ \sum _ {i = k } ^ { n } C _ {ki} x _ {i} ,$$

where $C _ {ki}$ is the minor of $A$ that stands in the rows $1 \dots k$, and in the columns $1 \dots k - 1, i$.

The formulas (2)–(7) are called Jacobi's formulas.

When the matrix of $f$ satisfies only the conditions

$$\Delta _ {i} \neq 0,\ \ i = 1 \dots r,$$

$$\Delta _ {r + 1 } = \dots = \Delta _ {n} = 0,$$

where $r$ is the rank of the form, $f$ can be reduced to the canonical form

$$\tag{7 } f = \ \sum _ {k = 1 } ^ { r } \frac{u _ {k} ^ {2} }{\Delta _ {k - 1 } \Delta _ {k} }$$

(here $\Delta _ {0} = 1$) by a triangular transformation of the unknowns. This reduction can be realized by using the Gauss method (see [1]). If, in particular, $P = \mathbf R$, then the positive index of inertia of $f$ is equal to the number of preservations of sign, and the negative index of inertia is equal to the number of changes of sign in the series of numbers

$$1, \Delta _ {1} \dots \Delta _ {r} .$$

## Contents

#### References

 [1] F.R. [F.R. Gantmakher] Gantmacher, "The theory of matrices" , 1 , Chelsea, reprint (1977) (Translated from Russian) MR1657129 MR0107649 MR0107648 Zbl 0927.15002 Zbl 0927.15001 Zbl 0085.01001

I.V. Proskuryakov

Jacobi's method is a one-step iteration method (cf. Simple-iteration method) for solving a system of linear algebraic equations $Ax = b$ for which a preliminary transformation to the form $x = Bx + g$ is realized by the rule:

$$B = E - D ^ {-} 1 A,\ \ g = D _ {-} 1 b ,\ \ D = ( d _ {ij} ),$$

$$d _ {ii} = a _ {ii} ,\ i = 1 \dots n; \ d _ {ij} = 0,\ i \neq j.$$

G.D. Kim

Alternative names occurring in Western literature for this iteration method are: Gauss–Jacobi iteration, point Jacobi iteration, method of successive substitutions, and method of simultaneous displacements. It was already used by C.G.J. Jacobi (1845) (see [a3]). If the matrix $A$ is irreducibly diagonally dominant, then the method converges for any starting vector (cf. [a1]). With the introduction of new computer architectures such as vector and parallel computers, Jacobi's method has regained interest because it vectorizes and parallelizes extremely well. Comprehensive surveys of related iterative methods for sparse matrix equations can be found in [a2], [a4], [a5], and [a6].

#### References

 [a1] L. Collatz, "Ueber die Konvergentzkriterien bei Iterationsverfahren für lineare Gleichungssysteme" Math. Z. , 53 (1950) pp. 149–161 [a2] L.A. Hageman, D.M. Young, "Applied iterative methods" , Acad. Press (1981) MR0630192 Zbl 0459.65014 [a3] C.G.J. Jacobi, "Ueber eine neue Auflösungsart der bei der Methode der kleinsten Quadraten vorkommenden lineare Gleichungen" Astr. Nachr. , 22 : 523 (1845) pp. 297–306 [a4] J.M. Ortéga, "Numerical analysis" , Acad. Press (1972) MR0403154 Zbl 0248.65001 [a5] R.S. Varga, "A comparison of the successive over-relaxation method and semi-iterative methods using Chebyshev polynomials" Siam J. Appl. Math. , 5 (1962) pp. 39–47 [a6] D.M. Young, "Iterative solution of large linear systems" , Acad. Press (1971) MR0305568 Zbl 0231.65034

Jacobi's method is a rotation method for solving the complete problem of eigen values and eigen vectors for a Hermitian matrix.

G.D. Kim


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Hex numbers or hexadecimal numbers refers to the number system with base 16. Which includes 16 various numbers or symbols such as 0 to 9 and A to F. A, B, C, D, E, F represents 10, 11, 12, 13, 14, 15 respectively. This number system is a relevant one because it is easy to remember the high value than the binary system. And it is very easy to convert to binary and decimal system also. This can be denoted with an 0x prefix or an h suffix. The examples related to the conversion of the hexadecimal numbers are given in the following section.

## Steps for Hex Conversion

The steps for the conversion of hex numbers to decimal and binary are given below:

Hexadecimal to Decimal:

Step1: Multiply each numbers in the hex system with the corresponding power of 16.

Step2: Adding all these values will give the equivalent decimal number.

Eg: (5A)16=5×161+10×160=(90)10

Here note that A is taken as 10.

Hexadecimal to Binary:

Step1: Note down the binary number of each number of a hex system.

Step2: Write down all binary numbers together corresponding to the given hex number.

### Roman Numeral Calculator

 Anova Calculation Calculate Median Calculate Percentile Calculate Permutations Calculate Probability Calculate the Variance
 Binary to Hex Calculator Decimal to Hex Calculator Hex Convertor Calculator Calculate Compound Interest Calculator Calculate Simple Interest Calculator


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# Magnetic field strength

Bottom: magnetic field strength map the color shows the field strength, from weak (cool colors) to strong (warm colors) red indicates a. Magnetic field is a vector field in space, and is a kind of energy whose full quantification requires the knowledge of the vector fields of both. The intensity of synchrotron emission is a measure of the density of cosmic-ray electrons and of the strength of the total magnetic field. Other articles where magnetic field strength is discussed: magnetism: magnetization effects in matter:field h is called the magnetic intensity and, like m,.

Online version of the 'iupac compendium of chemical terminology' also known as the 'iupac gold book. The estimated value of the magnetic field strength for the lhc energy amounts to $eb_y \sim 15 m_\pi^2$ skokov, v illarionov, ayu toneev, v. Measurement units, magnetic field strength conversion, magnetic field strength converter, amperes per meter(a/m), ampere-turns per meter(at/m), gilberts.

At the surface of the earth, the magnetic field has a strength of about 05 gauss units (50000 nano-teslas, or 50000 nt) in comparison, a typical toy magnet,. Define magnetic field strength magnetic field strength synonyms, magnetic field strength pronunciation, magnetic field strength translation, english dictionary. The magnetic field strength (lines of flux per square inch) are as follows: on the surface of a 42 mega gauss oersteds (42 mgo) rated magnet, the magnetic field . The maximum magnetic field strength of an electromagnetic field is 5×10−6 t calculate the maximum electric field strength if the wave is traveling in a medium .

Acupunct electrother res 199217(2):75-94 detection of extraordinary large bio- magnetic field strength from human hand during external qi emission. Magnetic fields created in the noncentral heavy-ion collision are studied within a microscopic transport model, namely the ultrarelativistic quantum molecular. Magnetic field strength magnetic field strength noun magnetic intensity the american heritage® dictionary of the english language, fifth. A magnetic field is a vector field that describes the magnetic influence of electrical currents and both the strength and direction of a magnetic field varies with location as such, it is an example of a vector field the term 'magnetic field' is used. Magnetic field strength, also called magnetic intensity, is an expression of the force that a magnetic field exerts on a theoretical unit magnetic pole in free space.

The magnetic field is a field, produced by electric charges in motion is determined by right-hand screw rule and the strength of field can be. The magnetic field strength is 25 gauss, or 50 times stronger than the magnetic field at the surface that makes compass needles align. Sometimes, people will be very precise and talk about either the magnetic flux density or the magnetic field strength but actually magnetic field is perfectly. A stamped handle from ramat rahel such fragments are an archive of the strength of the earth's magnetic field at the time they were made. Both the electric and magnetic fields are strong close to an operating electrical source the strength of the electric field depends on the voltage (typically 240.

## Magnetic field strength

My physician is concerned that the permanent magnet in a earphone might interfer with the operation what is the field strength in teslas of a shure earphone. If a maglev wants to use this force to levitate, it needs a strong magnetic field in its the sign and the intensity of the created magnetic field are also controlled. To measure the magnetic field strength in the solar corona, we examined 10 fast ( ≥1000 km s–1) limb coronal mass ejections(cmes) that show clear shock. The magnetic field intensity or magnetic field strength is a ratio of the mmf needed to create a certain flux density (b) within a particular material per unit.

A) typical values of intergalactic magnetic field strengths are in the range 1-3 $\ mu$ (1999) have obtained a field strength of between 5 and 10 $\mu$. Conf proc ieee eng med biol soc 20122012:1173-6 doi: 101109/embc 20126346145 study on technology of high-frequency pulsed magnetic field strength.

A magnet is placed at the center when an electric current flows through the aluminum conductor, it generates a magnetic field, which rotates. In fact, this is how we define the magnetic field strength b—in terms of the force on a charged particle moving in a magnetic field the si unit for magnetic field. By comparing with numerical simulations based on the solar magnetic field model, we find that the average imf strength in the away (toward).

Magnetic field strength
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### Home > CC4 > Chapter 7 > Lesson 7.2.3 > Problem7-110

7-110.

Brian was holding a ballroom dance. He wanted to make sure girls would come, so he charged boys $5 to get in but girls only$3. The 45 people who came paid a total of \$175. How many girls came to the dance. Homework Help ✎

Set up a system of equation, where we let b = boys and g = girls.

Review the Math Notes box in Lesson 6.3.3 on the Elimination Method for systems of equations.

25 girls came to the dance.


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# Prove: A point is in the boundary of A if every neighborhood of has non-empty: A, X/A

1. Sep 3, 2012

### Hodgey8806

1. The problem statement, all variables and given/known data
I tried to state the whole thing, but here it is again:
Prove: A point is in the boundary of if and only if every neighborhood of it contains both a point of A and a point of X\A.

2. Relevant equations
Boundary def: X\(Int A $\cup$ Ext A)
Def of Int A: $\bigcup${C$\subseteq$X:C$\subseteq$A and C is open in X}
Def of Ext A: X\$\bar{A}$ where $\bar{A}$ means closed (including boundary)
Def of $\bar{A}$: $\bigcap${B$\subseteq$X:B$\supseteq$A and B is closed in X}

3. The attempt at a solution
Please bare with me as this is a little messy. I used a bunch of set theory rules:
Let p$\in$$\delta$A
p$\in$X\(Int A $\cup$ Ext A)
1) p$\in$(X\Int A) $\wedge$ 2)p$\in$(X\Ext A)
Thus breaking each one down separately:
1)p$\in$X\$\bigcup${C$\subseteq$X:C$\subseteq$A and C is open in X}
p$\in$$\bigcap${X\C:C$\subseteq$A and C is open in X}$\subseteq$=X\A--(I realize now this could have been stated without these set properties.)
2)p$\in$X\(X\$\bar{A}$)
p$\in$$\bar{A}$$\supseteq$A
Thus every neighborhood of p contains both a point of A and a point of X\A.
Q.E.D.

2. Sep 3, 2012

### voko

Re: Prove: A point is in the boundary of A if every neighborhood of has non-empty: A,

First of all, this is only one leg of the proof, the "only if" part. You need to prove the "if" part as well.

Secondly, I do not see how it follows that any neighborhood contains anything - you proof does not say anything about the neighborhood at all (except let p be in one).

3. Sep 3, 2012

### Hodgey8806

Re: Prove: A point is in the boundary of A if every neighborhood of has non-empty: A,

I did the other leg by contradiction; it seemed a bit easier.

I have shown that P is in the closed "neighborhood" of X\A and $\bar{A}$.
So if I union them together we end up with the entire set X.

I'm honestly a bit lost though on how to show the neighborhood portion of this.
Do I need to discuss a Ball of length R?

4. Sep 3, 2012

### voko

Re: Prove: A point is in the boundary of A if every neighborhood of has non-empty: A,

I think this one could also be done by contradiction. Assume there is a point in the boundary that has a neighborhood whose intersection with int or with ext is empty. Let's say that with int is empty: $p \in V \subset X : V \cap int A = \emptyset$ Then consider $V \cap \partial A$. Can you see it is empty so we have a contradiction? Ditto for ext A.

5. Sep 3, 2012

### Hodgey8806

Re: Prove: A point is in the boundary of A if every neighborhood of has non-empty: A,

I'm sorry, I'm not quite understanding it. It looks like we want to show p being in the neighborhood AND the boundary, and then we discover it's not in their intersection. Is that correct? I'm having trouble see how that is the case though.

These are my thoughts on that. We see that the intersection with interior must be empty. But if it is on the boundary, then the intersection with the boundary shouldn't be empty. And that is our contradiction. But, getting to their I'm have trouble seeing--sense it is empty with interior of A, are we trying to imply that it is empty with the boundary?

6. Sep 3, 2012

### Hodgey8806

Re: Prove: A point is in the boundary of A if every neighborhood of has non-empty: A,

I would like to try one more method. However, I the very last bits may need clarification:
Assume for contradiction there does exist such a neighborhood that either V$\cap$A = $\phi$ or V$\cap$A=$\phi$.

Let p$\in\delta$A
Thus p$\in$X\A and p$\in$$\bar{A}$
However, since X\A is closed, $\exists$V$\subseteq$A, thus V$\cap$A≠$\phi$
Also, since $\bar{A}$, $\exists$V$\subseteq$$\bar{A}$, thus V$\cap$X\A≠$\phi$
Q.E.D.

7. Sep 3, 2012

### voko

Re: Prove: A point is in the boundary of A if every neighborhood of has non-empty: A,

If the intersection of the ENTIRE neighborhood with the boundary is empty, then it contains no point in common with the neighborhood. But it must contain p, which is in the boundary. This is the contradiction.

As for proving it is empty, just do the set theory gymnastics of the kind you were doing.

8. Sep 3, 2012

### voko

Re: Prove: A point is in the boundary of A if every neighborhood of has non-empty: A,

I looks like your second proof assumes A is open.

9. Sep 3, 2012

### Hodgey8806

Re: Prove: A point is in the boundary of A if every neighborhood of has non-empty: A,

I understand the contradiction, but I can't seem to grasp why the interaction with the int being empty causes the interaction with boundary to be empty. :\

10. Sep 4, 2012

### voko

Re: Prove: A point is in the boundary of A if every neighborhood of has non-empty: A,

What is space X you work with? Metric? Topological? Something else? How are "open" and "closed" sets defined in it, what is a "neighborhood"? I am asking this because the proof may require one of those definitions, and since there are quite a few equivalent formulations, I would like to know which ones you are supposed to use.

11. Sep 4, 2012

### Hodgey8806

Re: Prove: A point is in the boundary of A if every neighborhood of has non-empty: A,

X is a topological space. A set S as a subset X is open iff there exists a set for all p in S, there exists and open neighborhood completely contained in S.

I know this problem should be easier, I think I'm just at a point where I "can't see the forest because of all the trees." I'm able to do these other proofs fairly simply--I probably just need fresh eyes is all.

12. Sep 4, 2012

### Hodgey8806

Re: Prove: A point is in the boundary of A if every neighborhood of has non-empty: A,

I "think" I have it now. I finally discussed the closure of X\Int A, thus it has SOME neighborhood not contained in it--thus the intersection with Int A is not empty.

As well, A-closure is closed, so U intersecting Ext A is not empty for SOME neighborhood.

Does that sound right?

13. Sep 4, 2012

### voko

Re: Prove: A point is in the boundary of A if every neighborhood of has non-empty: A,

I think the standard way to prove that statement is by introducing interior points, boundary points, points of closure and exterior points. Interior and exterior points are those contained in A and X\A, respectively, with some open neighborhoods; boundary points are those any neighborhood of which intersects with both A and X\A; points of closure are a union of interior and boundary points.

Then you establish that int A is the set of all the interior points (this is almost trivial); the closure of A is the set of all its points of closure (you do that by noticing that the set of the interior points of X\A is X \{A's points of closure}, then use the previous result); finally that the boundary of A is the set of all its boundary points, which follows from the previous results.

As a remark, all those things (int, ext, closure, boundary) can be defined equivalently in terms of the respective points, which I think is slightly more intuitive. But in that case you have to prove things the other way around :)

14. Sep 6, 2012

### Hodgey8806

Re: Prove: A point is in the boundary of A if every neighborhood of has non-empty: A,

Firstly, thank you for all of your help!

I wanted to give one more try at this. I think I have it now!! (This time for real lol)

Spse p$\in$$\delta$A
If p$\in$A,
Then $\forall$ open U$\subseteq$X s.t. p$\in$U, U$\cap$A≠∅.
Since A is closed, $\forall$ open U$\subseteq$X s.t. p$\in$U, U$\cap$A is not a subset of A.
Thus, U$\cap$(A\X)≠∅.

And prove it the same for p not in A.

What do you think?

15. Sep 6, 2012

### Hodgey8806

Re: Prove: A point is in the boundary of A if every neighborhood of has non-empty: A,

Also U intersect A for that first proof wasn't empty because p is an element.

16. Sep 6, 2012

### voko

Re: Prove: A point is in the boundary of A if every neighborhood of has non-empty: A,

I do not follow. First the assumption is that p is in the boundary of A, then you assume it is in A? And why is A closed?


text:
# Finding the best terms to use

I have a real-world problem involving finding the best known term from a string containing sets of terms. We have Term objects that are comparable in that they have a method a_term.is_better_than(other_term). This method is Boolean -- if it returns False, then a_term may be as good as other_term, but isn't better.

Using this method, I need to pare down a set of terms to the best ones. The best way I've been able to think about this is to compare pairs of terms and eliminate any terms when one isn't as good as the other, something like this:

def get_best_terms(terms: Set[Term]): Set[Term]
best_terms = set()
m_terms = list(terms)
while m_terms:
term = m_terms.pop()
for i in reversed(range(len(m_terms))):
if term.is_better_than(m_terms[i]):
del m_terms[i]
if m_terms[i].is_better_than(term):
break
else: # We never encountered the break statement
break
best_terms |= {a_term for a_term in m_terms
if not (term.is_better_than(a_term) or
a_term.is_better_than(term))}
return best_terms

This approach is functional, but pretty gross in my opinion. For one thing, there's a lot of mutation going on here. For another, once I've identified a single best term, finding all the terms that are equally good is messy. The whole thing is hard to read.

What do you suggest?

## Examples

A Term is a string with some metadata attached. For example,

a = AutoTerm(term='honda', term_span=1, term_range=(1, 2),
original_term='CAR HONDA ACC...')
b = AutoTerm(term='2015 honda accord', term_span=2, term_range=(1, 3),
original_term='2015 HONDA ACC...')
c = AutoTerm(term='2015 accord', ...)

Sometimes a term is a better choice because it's more specific, but there are other nuances, such as a match in a database. Let's say, arbitrarily, that b and c are equally good, but a is not as good. Then

assert get_best_terms({a, b, c}) == {b, c}

should pass.

• Can you provide an example of Term and some example IO? Jul 31, 2018 at 13:57
• Is the ranking of Terms transitive? If Term A is better than Term B, and Term B is better than Term C, is Term A guaranteed to be better than Term C? Jul 31, 2018 at 20:01
• @DavidConrad yes. Jul 31, 2018 at 20:06

1. You have a bug, if you remove an item in your for loop without breaking you get an IndexError. Instead use a worse set so that you know what to skip.
2. What you seem to be doing is performing a sort, and so if you make a cmp function you can use sorted. To do this you need to use functools.cmp_to_key and then you can itertools.takewhile.

And so I'd use:

import functools
import itertools
from typing import Set, List

class Term(int):
def is_better_than(self, other):
return self // 2 > other // 2

def cmp(self: Term, other: Term):
if self.is_better_than(other):
return 1
if other.is_better_than(self):
return -1
return 0

def get_best_terms(terms: Set[Term]) -> List[Term]:
if not terms:
return []
terms = sorted(terms, key=functools.cmp_to_key(cmp), reverse=True)
best = terms[0]
return list(itertools.takewhile(lambda i: not best.is_better_than(i), terms))

print(get_best_terms(map(Term, [1, 2, 3, 4, 5])))
print(get_best_terms(map(Term, [1, 2, 3, 4])))
print(get_best_terms(map(Term, [5, 1, 2, 4, 3])))
print(get_best_terms(map(Term, [5, 1, 4, 3])))

This can however be simplified if Terms are comparable, as you won't need to use key and can remove the need for a lambda.

@functools.total_ordering
class Term(int):
def __gt__(self, other: Term) -> bool:
return self // 2 > other // 2

def __eq__(self, other: Term) -> bool:
return self // 2 == other // 2

def get_best_terms(terms: Set[Term]) -> List[Term]:
if not terms:
return []
terms = sorted(terms, reverse=True)
return list(itertools.takewhile(terms[0].__eq__, terms))

• Yeah, this is great, thanks. I had thought about using total_ordering and sorting, but I was thinking I didn't actually need to sort. But in looking again, I think the gain in readability is worth every penny. Jul 31, 2018 at 15:19
• "in your for without breaking" for loop? Jul 31, 2018 at 15:26
• @Acccumulation Yes, I'll try make that clearer Jul 31, 2018 at 15:27
• @kojiro You didn't say in your question but is Term.is_better_than costly? Because you could make the code run in $O(n)$ time, with a worst case $2n$ calls to Term.is_best_terms if they are all equal. Jul 31, 2018 at 15:34
• It's not costly afaict. It is impossible to understand, though, which is why I am still having trouble writing a satisfactory __eq__ for total ordering. I'm also considering using max and a filter instead of takewhile, which trades the sorted for max 2x passes over the set. Jul 31, 2018 at 15:36

If all you want are the best terms, then it seems to me that you can just keep a list of the current best terms. Every time you find a term that at least as good as any one of the previous best terms, then, assuming transitivity, it must be at least as good as all the previous best terms. And since the previous best terms were at least as good as all the terms tested so far, the new term is at least as good as all the terms tested so for. Next you check whether the new term is strictly better than one of the current best terms. If so, then you can replace the list of best terms with a list containing just the new term. If not, then the current term is just as good as the current best terms, so you should append it to the list of best terms.

best_terms = []
for term in terms:
if not best_terms:
best_terms = [term]
continue
if not best_terms[0].is_better_than(term):
if term.is_better_than(best_terms[0]):
best_terms = [term]
else
best_terms.append(term)

• Please tell me you changed your account name just to give this answer, because that'd be about perfect. Jul 31, 2018 at 15:47
• Except "is_better_than" returns false if the terms are equally good. You seem to be considering otherwise... Jul 31, 2018 at 20:14


text:
# Randomized Consensus in Expected O(n^2) Total Work using Single-Writer Registers

## James Aspnes

Abstract:
A new weak shared coin protocol yields a randomized wait-free shared-memory consensus protocol that uses an optimal $O(n^2)$ expected total work with single-writer registers despite asynchrony and process crashes. Previously, no protocol was known that achieved this bound without using multi-writer registers.

Guest: James Aspnes
Host: Yvonne-Anne Pignolet

# Black Hole Search with Finite Automata Scattered in a Synchronous Torus

## Jeremie Chalopin, Shantanu Das, Arnaud Labourel and Euripides Markou

Abstract:
We consider the problem of locating a black hole in synchronous anonymous networks using finite-state agents. A black hole is a harmful node in the network that destroys any agent visiting that node without leaving any trace. The objective is to locate the black hole without destroying too many agents. This is difficult to achieve when the agents are initially scattered in the network and are unaware of the location of each other. Previous studies for black hole search used more powerful models where the agents had non-constant memory, were labelled with distinct identifiers and could either write messages on the nodes of the network or mark the edges of the network. In contrast, we solve the problem using a small team of finite-state agents each carrying a constant number of identical tokens that could be placed on the nodes of the network. Thus, all resources used in our algorithms are independent of the network size. We restrict our attention to oriented torus networks and first show that no team of finite-state agents can solve the problem in such networks, when the tokens are not movable. In case the agents are equipped with movable tokens, we determine lower bounds on thenumber of agents and tokens required for solving the problem in torus networks of arbitrary size. Further, we present a deterministic solution to the black hole search problem for oriented torus networks, using the minimum number of agents and tokens, thus providing matching upper bounds for the problem.

Guest: Jeremie Chalopin
Host: Zvi Lotker

# Misleading Stars: What Cannot Be Measured in the Internet?

## Yvonne Anne Pignolet, Stefan Schmid, Gilles Tredan

Abstract:
Traceroute measurements are one of our main instruments to shed light onto the structure and properties of today’s complex networks such as the Internet. This paper studies the feasibility and infeasibility of inferring the network topology given traceroute data from a worst-case perspective, i.e., without any probabilistic assumptions on, e.g., the nodes’ degree distribution. We attend to a scenario where some of the routers are anonymous, and propose two fundamental axioms that model two basic assumptions on the traceroute data: (1) each trace corresponds to a real path in the network, and (2) the routing paths are at most a factor 1/alpha off the shortest paths, for some parameter alpha in (0,1]. In contrast to existing literature that focuses on the cardinality of the set of (often only minimal) inferrable topologies, we argue that a large number of possible topologies alone is often unproblematic, as long as the networks have a similar structure. We hence seek to characterize the set of topologies inferred with our axioms. We introduce the notion of star graphs whose colorings capture the differences among inferred topologies; it also allows us to construct inferred topologies explicitly. We find that in general, inferrable topologies can differ significantly in many important aspects, such as the nodes’ distances or the number of triangles. These negative results are complemented by a discussion of a scenario where the trace set is best possible, i.e., “complete”. It turns out that while some properties such as the node degrees are still hard to measure, a complete trace set can help to determine global properties such as the connectivity.

Guest: Stefan Schmid
Host: Zvi Lotker

# Fast and Scalable Rendezvousing

## Yehuda Afek, Michael Hakimi and Adam Morrison

Abstract:
In an asymmetric rendezvous system, such as an unfair synchronous queue and an elimination array, threads of two types, consumers and producers, show up and are matched, each with a unique thread of the other type. Here we present a new highly scalable, high throughput asymmetric rendezvous system that outperforms prior synchronous queue and elimination array implementations under both symmetric and asymmetric workloads (more operations of one type than the other). It is a fast matching machine. Consequently, we also present a highly scalable and competitive stack implementation

Guest: Yehuda Afek
Host: Zvi Lotker

# The Complexity of Data Aggregation in Directed Networks

## Fabian Kuhn and Rotem Oshman

Abstract:
We study problems of data aggregation, such as approximate counting and computing the minimum input value, in synchronous directed networks with bounded message bandwidth B = Ω(log n). In undirected networks of diameter D, many such problems can easily be solved in O(D) rounds, using O(log n)-size messages. We show that for directed networks this is not the case: when the bandwidth B is small, several classical data aggregation problems have a time complexity that depends polynomially on the size of the network, even when the diameter of the network is constant.

Guest: Rotem Oshman
Host: Chen Avin

# Physical Expander in Virtual Tree Overlay

## Taisuke Izumi, Maria Gradinariu Potop-Butucaru and Mathieu Valero

Abstract:
In this paper, we propose a new distributed construction of constant-degree expanders motivated by their application in P2P overlay networks and in particular in the design of robust tree overlays. Our key result can be stated as follows. Consider a complete binary tree T and construct a random pairing Π between leaf nodes and internal nodes. We prove that the graph GΠ obtained from T by contracting all pairs (leaf-internal nodes) achieves a constant node expansion with high probability. In the context of P2P overlays our result can be interpreted as follows: if each physical node participating to the tree overlay manages a random pair that couples one virtual internal node and one virtual leaf node then the physical-node layer exhibits a constant expansion with high probability. We encompass the diﬃculty of obtaining the random tree virtualization by proposing a local, self-organizing and churn resilient uniformly-random pairing algorithm with O(log2 n) running time. Our algorithm has the merit to not modify the original tree overlay (we just control the mapping between physical nodes and virtual nodes). Therefore, our scheme is general and can be easilly extended to a large class of overlays.

Guest: Taisuke Izumi
Host: Chen Avin

# Locality and checkability in wait-free computing

## Pierre Fraigniaud, Sergio Rajsbaum and Corentin Travers

Abstract:
This paper studies  notions of locality that are inherent to the specification of a
distributed task and independent of the computing environment, in a shared
memory wait-free system.
A  task T =(I,O,D) is checkable if there exists a wait-free distributed algorithm that, given s in I and t in O,  determines whether t in D(s), i.e., if t is a valid output for s according to
the specification D of T. Determining whether a projection-closed task is
wait-free solvable remains undecidable, demonstrating the richness of this
class. A locality property called projection-closed is identified,  that completely characterizes tasks that are wait-free  checkable.
A stronger notion of locality considers tasks  where the outputs look identically to the inputs at every vertex (input value of  a process). A task T =(I,O,D)  is said to be locality-preserving} if  O is a  covering complex of I. This topological property yields obstacles for wait-free  solvability different in nature from the classical agreement impossibility
results. On the other hand, locality-preserving tasks are projection-closed and
therefore always wait-free checkable.  A classification of locality-preserving
tasks in term of their relative computational power is provided.
A correspondence between locality-preserving tasks and subgroups of the edgepath
group of an input complex shows the existence of  hierarchies of  locality-preserving tasks, each one containing at the top the universal task  (induced by the universal covering complex), and at the bottom the trivial identity task.
Guest: Pierre Fraigniaud
Host: Merav Parter

# Oblivious Collaboration

## Yehuda Afek, Yakov Babichenko, Uriel Feige, Eli Gafni, Nati Linial and Benny Sudakov.

Abstract:
Communication is a crucial ingredient in every kind of collaborative work. But what is the least possible amount of communication required for a given task? We formalize
this question by introducing a new framework for distributed computation, called
oblivious protocols.
We investigate the power of this model by considering two concrete examples, the musical chairs task MC(n,m) and the well-known Renaming problem. The MC(n,m) game is played by n players (processors) with $m$ chairs. Players can occupy chairs, and the game terminates as soon as each player occupies a unique chair. Thus we say that player P is in conflict if some other player Q is occupying the same chair, i.e., termination means there are no conflicts. By known results from distributed computing, if m <= 2n-2, no strategy of the players can guarantee termination. However, there
is a protocol with m = 2n-1 chairs that always terminates. Here we consider an
oblivious protocol where in every time step the only communication is this: an
adversarial scheduler chooses an arbitrary nonempty set of players, and for each
of them provides only one bit of information, specifying whether the player is
currently in conflict or not. A player notified not to be in conflict halts and
never changes its chair, whereas a player notified to be in conflict changes its
chair according to its deterministic program. Remarkably, even with this minimal
communication termination can be guaranteed with only m=2n-1 chairs. Likewise,
we obtain an oblivious protocol for the Renaming problem whose name-space is
small as that of the optimal nonoblivious distributed protocol.
Other aspects suggest themselves, such as the efficiency
(program length) of our protocols. We make substantial progress here as well,
though many interesting questions remain open.

Guest: Eli Gafni
Host: Merav Parter

# On Approximate Distance Labels and Routing Schemes with Affine Stretch

## Ittai Abraham and Cyril Gavoille

Abstract:

For every integral parameter k > 1, given an unweighted
graph G, we construct in polynomial time, for each vertex u, a distance label
L(u) of size O(n^(2/(2k-1))). For any u,v in G, given L(u),L(v) we can return in
time O(k) an affine approximation h(u,v) on the distance d(u,v) between u and v
in G such that d(u,v) <= h(u,v) <= (2k-2)d(u,v) +1. Hence we say that our
distance label scheme has affine stretch of (2k-2)d+1.  For k=2 our construction
is comparable to the O(n^(5/3)) size, 2d+1 affine stretch of the distance oracle
of Patrascu and Roditty (FOCS’10), it incurs a o(log(n)) storage overhead while
providing the benefits of a distance label.

For any k>1, given a restriction of o(n^(1+1/(k-1))) on
the total size of the data structure, our construction provides distance
labels with affine stretch of (2k-2)d+1 which is better than the stretch (2k-1)d
scheme of Thorup and Zwick (J. ACM’05).

Our second contribution is a compact routing scheme with
poly-logarithmic addresses that provides affine stretch guarantees. With
O(n^(3/(3k-2)))-bit routing tables we obtain affine stretch of (4k-6)d+1, for
any k>1.

Given a restriction of o(n^(1/(k-1))) on the table size,
our  routing scheme provides affine stretch which is better than the stretch
(4k-5)d routing scheme of Thorup and Zwick (SPAA’01).

Guest: Ittai Abraham

Host:  Merav Parter

# Parsimonious Flooding in Geometric Random-Walks

## Andrea Clementi and Riccardo Silvestri

Abstract:
We study the information spreading yielded by the (Parsimonious) 1-Flooding
Protocol} in geometric Mobile Ad-Hoc Networks. We consider n agents on a convex
plane region of diameter D performing independent random walks with move radius
\rho. At any time step, every active agent $v$ informs every non-informed agent
which is within distance R from v (R>0 is the transmission radius). An agent
is only active at the time step immediately after the one in which has been
informed and, after that, she is removed. At the initial time step, a source
agent is informed and we look at the \emph{completion time} of the protocol,
i.e., the first time step (if any) in which all agents are informed. This random
process is equivalent to the well-known Susceptible-Infective-Removed (SIR)
infection process in Mathematical Epidemiology. No analytical results are
available for this random process over any explicit mobility model. The presence
of removed agents makes this process much more complex than the (standard)
flooding. We prove optimal bounds on the completion time depending on the
parameters n, D, R, and rho. The obtained bounds hold with high probability. We
remark that our method of analysis provides a clear picture of the dynamic shape
of the information spreading (or infection wave) over the time.
end of abstract.
Guest: Andrea Clementi

Host:  Merav Parter


text:
# 2.7 Linear inequalities and absolute value inequalities  (Page 7/11)

 Page 7 / 11

A man has 72 ft. of fencing to put around a rectangular garden. If the length is 3 times the width, find the dimensions of his garden.

A truck rental is $25 plus$.30/mi. Find out how many miles Ken traveled if his bill was \$50.20.

84 mi

## Complex Numbers

For the following exercises, use the quadratic equation to solve.

${x}^{2}-5x+9=0$

$2{x}^{2}+3x+7=0$

$x=\frac{-3}{4}±\frac{i\sqrt{47}}{4}$

For the following exercises, name the horizontal component and the vertical component.

$4-3i$

$-2-i$

horizontal component $\text{\hspace{0.17em}}-2;$ vertical component $\text{\hspace{0.17em}}-1$

For the following exercises, perform the operations indicated.

$\left(9-i\right)-\left(4-7i\right)$

$\left(2+3i\right)-\left(-5-8i\right)$

$7+11i$

$2\sqrt{-75}+3\sqrt{25}$

$\sqrt{-16}+4\sqrt{-9}$

$16i$

$-6i\left(i-5\right)$

${\left(3-5i\right)}^{2}$

$-16-30i$

$\sqrt{-4}·\sqrt{-12}$

$\sqrt{-2}\left(\sqrt{-8}-\sqrt{5}\right)$

$-4-i\sqrt{10}$

$\frac{2}{5-3i}$

$\frac{3+7i}{i}$

$x=7-3i$

For the following exercises, solve the quadratic equation by factoring.

$2{x}^{2}-7x-4=0$

$3{x}^{2}+18x+15=0$

$x=-1,-5$

$x=0,\frac{9}{7}$

For the following exercises, solve the quadratic equation by using the square-root property.

${x}^{2}=49$

${\left(x-4\right)}^{2}=36$

$x=10,-2$

For the following exercises, solve the quadratic equation by completing the square.

${x}^{2}+8x-5=0$

$4{x}^{2}+2x-1=0$

$x=\frac{-1±\sqrt{5}}{4}$

For the following exercises, solve the quadratic equation by using the quadratic formula. If the solutions are not real, state No real solution .

$2{x}^{2}-5x+1=0$

$15{x}^{2}-x-2=0$

$x=\frac{2}{5},\frac{-1}{3}$

For the following exercises, solve the quadratic equation by the method of your choice.

${\left(x-2\right)}^{2}=16$

${x}^{2}=10x+3$

$x=5±2\sqrt{7}$

## Other Types of Equations

For the following exercises, solve the equations.

${x}^{\frac{3}{2}}=27$

${x}^{\frac{1}{2}}-4{x}^{\frac{1}{4}}=0$

$x=0,256$

$4{x}^{3}+8{x}^{2}-9x-18=0$

$3{x}^{5}-6{x}^{3}=0$

$x=0,±\sqrt{2}$

$\sqrt{x+9}=x-3$

$\sqrt{3x+7}+\sqrt{x+2}=1$

$x=-2$

$|3x-7|=5$

$|2x+3|-5=9$

$x=\frac{11}{2},\frac{-17}{2}$

## Linear Inequalities and Absolute Value Inequalities

For the following exercises, solve the inequality. Write your final answer in interval notation.

$5x-8\le 12$

$-2x+5>x-7$

$\left(-\infty ,4\right)$

$\frac{x-1}{3}+\frac{x+2}{5}\le \frac{3}{5}$

$|3x+2|+1\le 9$

$\left[\frac{-10}{3},2\right]$

$|5x-1|>14$

$|x-3|<-4$

No solution

For the following exercises, solve the compound inequality. Write your answer in interval notation.

$-4<3x+2\le 18$

$3y<1-2y<5+y$

$\left(-\frac{4}{3},\frac{1}{5}\right)$

For the following exercises, graph as described.

Graph the absolute value function and graph the constant function. Observe the points of intersection and shade the x -axis representing the solution set to the inequality. Show your graph and write your final answer in interval notation.

$|x+3|\ge 5$

Graph both straight lines (left-hand side being y1 and right-hand side being y2) on the same axes. Find the point of intersection and solve the inequality by observing where it is true comparing the y -values of the lines. See the interval where the inequality is true.

$x+3<3x-4$

Where the blue is below the orange line; point of intersection is $\text{\hspace{0.17em}}x=3.5.$

$\left(3.5,\infty \right)$

## Chapter practice test

Graph the following: $\text{\hspace{0.17em}}2y=3x+4.$

$y=\frac{3}{2}x+2$

x y
0 2
2 5
4 8

Find the x- and y -intercepts for the following:

$2x-5y=6$

Find the x- and y -intercepts of this equation, and sketch the graph of the line using just the intercepts plotted.

$3x-4y=12$

$\left(0,-3\right)$ $\left(4,0\right)$

Find the exact distance between $\text{\hspace{0.17em}}\left(5,-3\right)\text{\hspace{0.17em}}$ and $\text{\hspace{0.17em}}\left(-2,8\right).\text{\hspace{0.17em}}$ Find the coordinates of the midpoint of the line segment joining the two points.

Write the interval notation for the set of numbers represented by $\text{\hspace{0.17em}}\left\{x|x\le 9\right\}.$

$\left(-\infty ,9\right]$

Solve for x : $\text{\hspace{0.17em}}5x+8=3x-10.$

Solve for x : $\text{\hspace{0.17em}}3\left(2x-5\right)-3\left(x-7\right)=2x-9.$

$x=-15$

Solve for x : $\text{\hspace{0.17em}}\frac{x}{2}+1=\frac{4}{x}$

Solve for x : $\text{\hspace{0.17em}}\frac{5}{x+4}=4+\frac{3}{x-2}.$

$x\ne -4,2;$ $x=\frac{-5}{2},1$

The perimeter of a triangle is 30 in. The longest side is 2 less than 3 times the shortest side and the other side is 2 more than twice the shortest side. Find the length of each side.

$\frac{{x}^{2}}{3}-x=\frac{-1}{2}$

$x=\frac{3±\sqrt{3}}{2}$

Solve: $\text{\hspace{0.17em}}3x-8\le 4.$

Solve: $\text{\hspace{0.17em}}|2x+3|<5.$

$\left(-4,1\right)$

Solve: $\text{\hspace{0.17em}}|3x-2|\ge 4.$

For the following exercises, find the equation of the line with the given information.

Passes through the points $\text{\hspace{0.17em}}\left(-4,2\right)\text{\hspace{0.17em}}$ and $\text{\hspace{0.17em}}\left(5,-3\right).$

$y=\frac{-5}{9}x-\frac{2}{9}$

Has an undefined slope and passes through the point $\text{\hspace{0.17em}}\left(4,3\right).$

Passes through the point $\text{\hspace{0.17em}}\left(2,1\right)\text{\hspace{0.17em}}$ and is perpendicular to $\text{\hspace{0.17em}}y=\frac{-2}{5}x+3.$

$y=\frac{5}{2}x-4$

Add these complex numbers: $\text{\hspace{0.17em}}\left(3-2i\right)+\left(4-i\right).$

Simplify: $\text{\hspace{0.17em}}\sqrt{-4}+3\sqrt{-16}.$

$14i$

Multiply: $\text{\hspace{0.17em}}5i\left(5-3i\right).$

Divide: $\text{\hspace{0.17em}}\frac{4-i}{2+3i}.$

$\frac{5}{13}-\frac{14}{13}i$

Solve this quadratic equation and write the two complex roots in $\text{\hspace{0.17em}}a+bi\text{\hspace{0.17em}}$ form: $\text{\hspace{0.17em}}{x}^{2}-4x+7=0.$

Solve: $\text{\hspace{0.17em}}{\left(3x-1\right)}^{2}-1=24.$

$x=2,\frac{-4}{3}$

Solve: $\text{\hspace{0.17em}}{x}^{2}-6x=13.$

Solve: $\text{\hspace{0.17em}}4{x}^{2}-4x-1=0$

$x=\frac{1}{2}±\frac{\sqrt{2}}{2}$

Solve:

$\sqrt{x-7}=x-7$

Solve: $\text{\hspace{0.17em}}2+\sqrt{12-2x}=x$

$4$

Solve: $\text{\hspace{0.17em}}{\left(x-1\right)}^{\frac{2}{3}}=9$

For the following exercises, find the real solutions of each equation by factoring.

$2{x}^{3}-{x}^{2}-8x+4=0$

$x=\frac{1}{2},2,-2$

${\left(x+5\right)}^{2}-3\left(x+5\right)-4=0$

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I think you should say "28 terms" instead of "28th term"
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text:
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Research Papers: Micro/Nanoscale Heat Transfer

# Thermal Conductivity Equations Based on Brownian Motion in Suspensions of Nanoparticles (Nanofluids)

[+] Author and Article Information
Bao Yang

Nanoscale Heat Transfer and Energy Conversion Laboratory, Mechanical Engineering Department, University of Maryland, College Park, MD 20742baoyang@umd.edu

J. Heat Transfer 130(4), 042408 (Mar 18, 2008) (5 pages) doi:10.1115/1.2789721 History: Received January 24, 2007; Revised March 04, 2007; Published March 18, 2008

## Abstract

Thermal conductivity equations for the suspension of nanoparticles (nanofluids) have been derived from the kinetic theory of particles under relaxation time approximations. These equations, which take into account the microconvection caused by the particle Brownian motion, can be used to evaluate the contribution of particle Brownian motion to thermal transport in nanofluids. The relaxation time of the particle Brownian motion is found to be significantly affected by the long-time tail in Brownian motion, which indicates a surprising persistence of particle velocity. The long-time tail in Brownian motion could play a significant role in the enhanced thermal conductivity in nanofluids, as suggested by the comparison between the theoretical results and the experimental data for the $Al2O3$-in-water nanofluids.

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## Figures

Figure 1

A nanoparticle with coordinates (Xi, Yi, Zi) moves at velocity up toward the Z=0 plane. The origin of the local coordinate system (x, y, z) is at the center of the moving particle. The hydrodynamic layer thickness is lB.

Figure 2

Stokes flow around a spherical particle moving at up in the fluid. The origin of the local spherical coordinate system is at the center of the particle.

Figure 3

The velocity autocorrelation function R(t) evaluated using Eq. 13 (heavy particle approximation), Eq. 15 (neutrally buoyant particle approximation), and Eq. 16 (general particle, M=0.999967). ρp=3.9g∕cm3 (alumina), ρf=1.0g∕cm3 (water), and a=23.5nm.

Figure 4

Comparison of the thermal conductivity equations with experimental data for nanofluids consisting of Al2O3 nanoparticles dispersed in water, for varying temperatures and particle diameters. Experimental data are from Ref. 5.

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