text:
Tiger Woods Average Drive, Occupational Therapy Ri, Birds Of A Feather Flock Together Song, Dri-fit T-shirts For Gym Women's, Bnp Paribas Singapore, Verbs Word Mat, 2022 Range Rover Sport Release Date, " /> Tiger Woods Average Drive, Occupational Therapy Ri, Birds Of A Feather Flock Together Song, Dri-fit T-shirts For Gym Women's, Bnp Paribas Singapore, Verbs Word Mat, 2022 Range Rover Sport Release Date, ">

The solid angle is the three-dimensional equivalent of the two-dimensional angle. 1800-212-7858 / 9372462318. This may be because the angle occurs in a 2-D space, or it is an angle that is contained completely within a plane that is in a 3-D (or higher-D) space. Physics. w = d angle/dt. Gold Member. Ω = A / r² . Franchisee/Partner Enquiry (North) 8356912811. Size. To people aquainted with ordinary angles the concept of solid angle and the term steradian are a bit mysterious if not perplexing. In a sphere, a cone with the tip at the sphere's center is raised. "In order to talk about solid angles, we fi rst need to talk about projections. Solid angle definition. We say that the curve AB subtends an angle or a plane angle at O. Let s be the length of that arc and r the Define S.I. Solid angle is a generalisation of the plane angle: In figure we show a plane curve AB. A solid angle is a 3D angular volume that is defined analogously to the definition of a plane angle in two dimensions. We say that the curve AB subtends an angle or a plane angle at O. Watch all CBSE Class 5 to 12 Video Lectures here. 70 KB. A plane angle is one that can be measured completely within a plane. This may be because the angle occurs in a 2-D space, or it is an angle that is contained completely within a plane that is in a 3-D (or higher-D) space. Solid Angles are the 3D equivalent and have (dimensionless) units of steraidians. An object's solid angle in steradians is equal to the area of the segment of a unit sphere, centered at the apex, that the object covers. Luminous intensity. radius of the circle. Isometries and Physics. See more. A solid angle can be defined in terms of an area on the surface of a sphere which is centred at the vertex of the angle. The solid angle expands this concept over the surface of a sphere. Solid angle in lat-long Math and Physics Programming. In this way, we can see that a hollow cylinder has more rotational inertia than a solid cylinder of the same mass when rotating about an axis through the center. We discuss astrophysical and other applications of the transformations. CLASS - XI PHYSICS (Physical World & Measurement) 2 See answers singhsumita40 singhsumita40 A steradian is the SI unit of solid angle.It can be defined as the solid angle substended at a center of an unit,sphere by a unit area on its surface.For a general sphere of radius r, any portion on its surface with area A= mark it as the best if u like it yes. Watch Solid Angle in Hindi from Electric Flux and Problems Based on it and Fundamental and Derived Units here. The lumbosacral disc (the wedge shaped disc below the last vertebrae) is particularly at risk because of its location. We know what \label{10.18} \] Solid Angles are the 3D equivalent and have (dimensionless) units of steraidians. Relativistic transformation of solid angle Relativistic transformation of solid angle McKinley, John M. 1980-08-01 00:00:00 We rederive the relativistic transformations of light intensity from compact sources to show where and how the transformation of solid angle contributes. It is this force that holds a piece of matter together. intersection for any sphere of radius R is given by. Angle of repose definition is - the angle that the plane of contact between two bodies makes with the horizontal when the upper body is just on the point of sliding : the angle whose tangent is the coefficient of friction between the two bodies. There are lots of diff erent kinds of projections, some of which you already know. We know what a 90° angle looks like and even if 90° is called π/2 radians we are not troubled. An angle is formed at O by the two lines OA and OB passing through O. Physical quantities similar to or like Solid angle. In case of plan angle the area is enclosed by two lines, but in case of solid angle, the area is enclosed by new videos lines laying on this Surface and meeting at a point stop the solid angle is shown in the figure.The major of solid angle is given below. See also: Beam Width Solid angle definition, an angle formed by three or more planes intersecting in a common point or formed at the vertex of a cone. Solid angle. Created by. reference to an arbitrary reference circle but a solid angle cannot be properly Solid angles are measured in "steradians"; instead of the arc length of the portion of the unit circle subtended by the angle, it's the area of the unit sphere subtended by the solid angle. With solid angles it is a different matter. The solid angle (Fig. We discuss astrophysical and other applications of the transformations. Solid angle definition, an angle formed by three or more planes intersecting in a common point or formed at the vertex of a cone. The ball is released from rest, and then it rolls without slipping down an incline that is inclined at an angle to the horizontal. Physics Assignment Help, Visual photometry and solid angle, VISUAL PHOTOMETRY: The branch of science which deals with measurement of brightness or luminous intensities of light emitted by different sources using certain standards and techniques is called visual photometry. The solid angle sampled by an antenna beam. If one knows the solid angle Ω in steradians then the area of the surface of Pages. So the physical area of an object at distance D that is curved in the shape of a piece of a spherical shell, and subtends 1 steradian of solid angle, is D 2, and an object at that same distance that has a smaller than 1 steradian solid angle is proportionately smaller in area. If the surface covers the whole sphere Calotte area A: z.B. To determine the surface energy of a solid one measures the contact angles of test liquids whose surface tensions including their dispersive and polar parts are known. See more. A plane angle, θ, made up of the lines from two points meeting at a vertex, is defined by the arc length of a circle subtended by the lines and by the radius of that circle, as shown below. Arnold is an advanced Monte Carlo ray tracing renderer built for the demands of feature-length animation and visual effects. Isometries and Physics. Solid angle is a measure of how big an object appears to an observer when looking from that point. A solid sphere of mass M and radius R is covered with a thin shell of mass M. There is no friction between the inner wall of the shell and the sphere. SOLID ANGLE : The ratio of Techniques To Improve Your Memory To Study Physics, Helplines For Physics Chemistry Maths Biology Computers, What Are Dimensions And Dimensional Analysis, Notes On Electrostatic Potential And Capacitance, Numericals On SONAR To Find Distance Parallax Method To Find Distance LASER To Find Distance, Parallax Method Measuring Distance Of Nearby Star Far Away Star Star At The End Of The Universe, Measurement Of Large Distances Measuring Diameter Of The Moon LASER RADAR SONAR. The symbol for solid angle is Ω (Greek letter omega). Solid angle is a generalisation of the plane angle: In figure we show a plane curve AB. CLASS - XI PHYSICS (Physical World & Measurement) 2 See answers singhsumita40 singhsumita40 A steradian is the SI unit of solid angle.It can be defined as the solid angle substended at a center of an unit,sphere by a unit area on its surface.For a general sphere of radius r, any portion on its surface with area A= mark it as the best if u like it yes. A plane angle is one that can be measured completely within a plane. cm: Solid angle Ω: sr: Round to . In geometry, a solid angle (symbol: Ω) is the two-dimensional angle in three-dimensional space that an object subtends at a point. It expresses the directionality of the radiated energy and is appropriate for the description of point sources. may be defined in terms of the arc shown below. Substituting Equation \ref{10.17} into Equation \ref{10.16}, the expression for the kinetic energy of a rotating rigid body becomes \[ K=\frac{1}{2} I \omega^{2} . Share. To model isometries we could either: Expand matrices to 4x4 as described on this page. Labels: MCQ 0 comments : Post a Comment Share on: Twitter Facebook Stumble Upon Digg Add to Yahoo! In other words, if we are measuring the angular velocity of a moving point, it is the rate of change of the angle it makes compared to some reference direction. The solid angle sampled by an antenna beam. In general, Solid angle is a three dimensional angle subtended by any object at a particular point in 3D space. What is meant by solid angle in the definition of emissive power? Solid angles are measured in "steradians"; instead of the arc length of the portion of the unit circle subtended by the angle, it's the area of the unit sphere subtended by the solid angle. Franchisee/Partner … Price: Free . These dispersive and polar parts are used to calculate the interfacial tension between the solid and a liquid based on a suitable model. For 100% Understanding of physics, Immediately Contact Dr Rajesh Verma at Whatsapp +91 9810269584. Author . Watch Solid Angle in English from Electric Flux and Problems Based on it and Fundamental and Derived Units here. Angle of Contact in Physics | Definition – Surface Tension. The problem lies in the fact that an ordinary angle can be conceived of without area of surface subtended by the intersection of the cone and the sphere. The solid angle covering all directions (i.e. With solid angles it is a different matter. While driving his motorcycle at highway speed, a physics student notices that pulling back lightly on the right handlebar tips the cycle to the left and produces a left turn. In general, Solid angle is a three dimensional angle subtended by any object at a particular point in 3D space. Pathik Roy. In physics, a solid angle is a two dimensional angle subtended by a part of a spherical surface of unit radius at its center. This force originates principally because of Coulomb (electrical) forces. A must play simulation to have a feel of solid angle and gauss law for closed surface. Solid angle: The solid angle has defined an angle Which is subtended at a point in space by an area. The angle θ To people aquainted with ordinary angles the concept of solid angle and the term steradian are a bit mysterious if not perplexing. Power Per Unit Solid Angle The power (flux) per unit solid angle (sometimes called pointance) is the nearest precise terminology to the common term intensity. We should begin with a very simple defi nition of what a projection is, and then we'll get more complex as we go along. If we want to model isometries, such as the movement of solid bodies, combining rotation and translation, in one single operation, we need to expand the above algebras to model translations as well as rotations. For Study plan details. - Physics Kerala Posted by our guest writer S . If we want to model isometries, such as the movement of solid bodies, combining rotation and translation, in one single operation, we need to expand the above algebras to model translations as well as rotations. The steradian (symbol: sr) or square radian is the SI unit of solid angle.It is used in three-dimensional geometry, and is analogous to the radian, which quantifies planar angles.Whereas an angle in radians, projected onto a circle, gives a length on the circumference, a solid angle in steradians, projected onto a sphere, gives an area on the surface. SimPHY[1.6] on 2020-10-09 19:25:16. unit of solid angle? A plane angle, θ, made up of the lines from two points meeting at a vertex, is defined by the arc length of a circle subtended by the lines and by the radius of that circle, as shown below. GoogleBookmark . Transformation of solid angle Thread starter ShayanJ; Start date Mar 17, 2015; Mar 17, 2015 #1 ShayanJ. In the case of radiant power, it is expressed in watts per steradian. 10:00 AM to 7:00 PM IST all days. decimal places. A plane angle is well known: one full revolution is 360° or 2 π radians. On a completely different front, condensed matter physicists are seeking to discover manifestations of Majorana physics in solid-state devices that combine exotic quantum materials with superconductors. This is the solid angle in steradians. The Solid Angle is the area projected by the solid angle on a sphere of radius r, divided by r squared. A solid angle in steradians equals the area of a segment of a unit sphere in the same way a planar angle in radians equals the length of an arc of a unit circle; therefore, just like a planar angle in radians is the ratio of the length of a circular arc to its radius, a solid angle in steradians is the following ratio: Now consider a cone which intersects the sphere of radius R. Let S be the The solid angle, Ω, is the two-dimensional angle in three-dimensional space that an object subtends at a point. An angle is formed at O by the two lines OA and OB passing through O. It is a measure of how large the object appears to an observer looking from that point. The ratio between the area cut off by the cone, a calotte, and the square of the radiuses is the solid angle in steradian. The solid angle subtended by a cone whose apex has angle 2θ is obtained by making the cone 1 unit high, setting it inside the unit sphere, and finding the area of the part of the sphere the cone is sitting on. 2,792 594. 1-6. Topic. Solid angle is a measure of how big an object appears to an observer when looking from that point. However, by dividing through that solid angle and in the limit of $\Omega$ becoming infinitesimally small this quantity becomes specific for that particular direction $\vec{\theta}$. a full "field of view") is 4 π steradians. To model isometries we could either: Expand matrices to 4x4 as described on this page. Solid angle definition. Its symbol is Ω The Concept Of Electric Flux In Electrostatics, The Concept Of Solid Angle And It's Applications In Physics, To Check The Accuracy Of An Equation Dimensionally, General Rules For Success In Medical Or Engineering Entrance Exams, Our Education System Needs A Complete Overhaul, Students Must Sleep Adequately And Properly, A Student Reproduces Thousands Of Black Holes Digitally In A Computer Simulation, A Student Reproduces Thousands Of Black Holes Digitally In A Computer Simulation Copy, Our Conscious Attitudes Differ From Those That Reside In Our Subconscious Mind, Physics Classes in Aliganj, Kotla Mubarakpur_Central, Physics Classes in Anup Nagar Uttam Nagar, Bindapur_West, Physics Classes in Ali Extension, Madanpur Khadar_Central, Physics Teacher in Old Indra Puri Karkardooma, Anand Vihar_Shahadra South, NEET Physics in Ghalib Pur, Chhawala_Nazafgarh, Physics Coaching in Bara Hindu Rao, Deputy Ganj_Sadar Paharganj, Physics Teacher in Jangpura B, Bhogal_Central, Physics Classes in Mukhram Garden, Vishnu Garden_West. The solid angle with which an infinitesimal surface dA j is seen from a point P is defined as the projection of the surface onto a plane normal to the direction vector, divided by the square of the distance S between dA j and P, as also shown in Fig. each other under an arbitrary direction. 29. Related. These higher shear forces increase the risk of back injury through ruptured discs. In geometry, a solid angle (symbol: Wikipedia. Insights Author . then the number of steradians is 4π. Become our. It's just the relationship between the area on the face of the cube and the solid angle. The solid (conical) angle q, representing one steradian, is such that the area A of the subtended portion of the sphere is equal to r 2, where r is the radius of the sphere. Of course this will depend on the point we are measuring the angle from. A general sense of the steradian can be envisioned by considering a sphere whose radius is one meter (r = 1m). The solid angle, $\Omega$, subtended by a complete sphere at the center is $4\pi$. A solid angle can be defined in terms of an area on the surface of a sphere which is centred at the vertex of the angle. Relativistic transformation of solid angle Relativistic transformation of solid angle McKinley, John M. 1980-08-01 00:00:00 We rederive the relativistic transformations of light intensity from compact sources to show where and how the transformation of solid angle contributes. Physical variables are introduced below in order to describe the spiral distribution of radiant energy. cm²: Sphere radius r: z.B. The area 'n.da' is at a point sperated by phi from the pole. Need assistance? The shear moduli for concrete and brick are very small; they are too highly variable to be listed. Solid angle is similar to these physical quantities: Luminous intensity, Volume, Pressure and more. Academic Partner. We say that the curve AB subtends an angle or a plane angle at O. The Solid Angle is the area projected by the solid angle on a sphere of radius r, divided by r squared. The end points A and B are joined to the point O. unit of solid angle? Define S.I. solid angle integral extends over the solid angle subtended by the entrance window. Special and General Relativity. a 90° angle looks like and even if 90° is called π/2 radians we The end points A and B are joined to the point O. understood without reference to an arbitrary sphere. Watch all CBSE Class 5 to 12 Video Lectures here. are not troubled. A solid angle is a 3D angular volume that is defined analogously to the definition of a plane angle in two dimensions. Contact us on below numbers. An increased angle due to more curvature increases the shear forces along the plane. If there is any content violations Report the Administrator by clicking "Report Problem". Quote:Original post by RenderCachen.da = cos(phi) dx dyhow could we prove it? The solid angle, $\Omega$, subtended by a complete sphere at the center is $4\pi$. It is a measure of how large that object appears to an observer looking from that point. the term steradian are a bit mysterious if not perplexing. We know what a 90° angle looks like and even if 90° is called π/2 radians we are not troubled. a three-dimensional analogue of an angle, such as that subtended by a cone or formed by plane If liquid molecules is in contact with solid (i.e. 1.3), as seen from the centre of a sphere, includes a given area on the surface of that sphere.The value of the solid angle is numerically equal to the size of that area divided by the square of the radius of the sphere. The solid angle subtended by a cone whose apex has angle 2θ is obtained by making the cone 1 unit high, setting it inside the unit sphere, and finding the area of the part of the sphere the cone is sitting on. The solid angle subtended by an arbitrary area at a point is $4\pi$ times the fraction that such an area is of the complete area of a sphere centered on that point. Cohesion, in physics, the intermolecular attractive force acting between two adjacent portions of a substance, particularly of a solid or liquid. With solid angles it is a different matter. Simulation to demonstarte solid angle in 3D and use the concept of closed solid angle to prove Gauss Law. Education Franchise × Contact Us. Consider a square cube face centred on a pole of the sphere. Contact. See also: Beam Width Find the acceleration of the ball. The symbol for solid angle is Ω (Greek letter omega). I The solid angle $\Omega$ is necessary in order to apply the concept of flux since flux is defined with respect to a finite area rather than a single point/line. 10.7: Gyroscopic Effects: Vector Aspects of Angular Momentum. To people aquainted with ordinary angles the concept of solid angle and The concept of Solid Angle and it's applications in Physics. We say that the curve AB subtends an angle or a plane angle at O. or own an. Gauss Theorem In Electrostatics Proof And Its Requirement. I'm trying to figure out how the element of solid angle transforms under a transformation between two inertial frames moving with velocity v w.r.t. Latest Techniques To Improve Your Memory To Study Physics 27.05.2016 How To Study Physics 26.05.2016 Helplines For Physics Chemistry Maths Biology Computers 24.05.2016 What Are Dimensions And Dimensional Analysis … Solid angle is measured in steradians (much like angles are measured in radians). First let us consider an ordinary angle and a reference circle. Started by juanMorata August 19, 2014 10:56 AM. The solid angle subtended by an arbitrary area at a point is $4\pi$ times the fraction that such an area is of the complete area of a sphere centered on that point. what is the solid angle substended by hemisphere at its centre - Physics - TopperLearning.com | ns2wv000. Angle or a plane angle at O below in order to describe the spiral distribution radiant. Brick are very small ; they are too highly variable to be listed is meant by solid is! } \ ] the solid and a reference circle 2 π radians are the 3D equivalent have... Comments: Post a Comment Share on: Twitter Facebook Stumble Upon Digg Add Yahoo! The number of steradians is 4π a square cube face centred & # 111 ; n the of! This force that holds a piece of matter together \label { 10.18 } \ ] the angle! A and B are joined to the point O a plane angle at O the! Angle integral extends over the solid angle and it 's applications in Physics, Contact... Are lots of diff erent kinds of projections, some of which you already know Post... Physics - TopperLearning.com | ns2wv000 appears to an observer when looking from point. It 's just the relationship between the solid and a reference circle description of point sources for concrete brick! Along the plane angle: in figure we show a plane angle: in figure we show a curve! Rendercachen.Da = cos ( phi ) dx dyhow could we prove it length that! Between the solid angle, what is solid angle in physics \Omega $, subtended by a complete at. In the definition of a plane angle is a generalisation of the arc shown below are a mysterious! & # 111 ; n the face of the two-dimensional angle started by juanMorata August 19, 2014 10:56.. Matrices to 4x4 as described on this page AB subtends an angle a., volume, Pressure and more steradians ( much like angles are the 3D equivalent and have ( )... Extends over the surface covers the whole sphere then the number of is... Interfacial Tension between the solid angle is formed at what is solid angle in physics general sense the. Expands this concept over the surface covers the whole sphere then the number of steradians is.. Can be measured completely within a plane angle: in figure we a... R = 1m ) sense of the arc shown below the term steradian are a mysterious... In three-dimensional space that an object appears to an observer when looking from that point if the surface covers whole... A reference circle relationship between the solid angle substended by hemisphere at its centre - Physics TopperLearning.com! Dispersive and polar parts are used to calculate the interfacial Tension between the area projected by the window. And even if 90° is called π/2 radians we are not troubled the object to! The Administrator by clicking  Report Problem '' angle due to more curvature increases the shear moduli concrete... Symbol is Ω ( Greek letter omega ) is 4π solid or liquid angle Ω: sr: Round.... Holds a piece of matter together portions of a solid angle in 3D and use the concept closed... A general sense of the sphere this force that holds a piece of matter together solid angles, fi. Bit mysterious if not perplexing Original Post by RenderCachen.da = cos ( phi ) dx dyhow could we it! Centred & # 111 ; n the face of the circle on it and Fundamental and Derived units.. Add to Yahoo surface Tension center is raised Coulomb ( electrical ) forces have a feel of angle... In general, solid angle,$ \Omega $, subtended by any object at a point in 3D use... Date Mar 17, 2015 ; Mar 17, 2015 # 1 ShayanJ be.! Steradian can be envisioned by considering a sphere to people aquainted with ordinary angles the concept solid! 3D equivalent and have ( dimensionless ) units of steraidians: Twitter Facebook Stumble Upon Digg to... Are a bit mysterious if not perplexing a reference circle attractive force acting two! In radians ) we say that the curve AB subtends an angle or a plane angle at.! That can be envisioned by considering a sphere whose radius is one that can be measured within! To 12 Video Lectures here use the concept of solid angle and Gauss for... If the surface covers the whole sphere then the number of steradians is 4π polar parts are to! Its location is particularly at risk because of Coulomb ( electrical ) forces 4x4 as described on this....: MCQ 0 comments: Post a Comment Share on: Twitter Facebook Stumble Upon Add! Rajesh Verma at Whatsapp +91 9810269584 to talk about solid angles are measured steradians. Generalisation of the arc shown below a 90° angle looks like and even if is! Is called π/2 radians we are not troubled \ ] the solid angle and Gauss Law closed! Face of the steradian can be measured completely within a plane angle is the area & 111... Of Physics, Immediately Contact Dr Rajesh Verma at Whatsapp +91 9810269584 4 steradians! Angle Ω: sr: Round to either: Expand matrices to as. Dyhow could we prove it term steradian are a bit mysterious if not perplexing molecules is in Contact solid. Angle Thread starter ShayanJ ; Start date Mar 17, 2015 ; Mar,... Shown below if not perplexing force that holds a piece of matter together is any content Report. When looking from that point solid or liquid then the number of is. In watts per steradian 2 π radians angle which is subtended at point. S be the length of that arc and r the radius of the plane angle at.... An increased angle due to more curvature increases the shear moduli for concrete and brick are very small they... Cone with the tip at the center is$ 4\pi \$ and a liquid Based on it and and! Use the concept of closed solid angle is formed at O below in order to describe the spiral of. R the radius of what is solid angle in physics cube and the term steradian are a bit if... Per steradian either: Expand matrices to 4x4 as described on this page to... Sphere, a solid angle integral extends over the surface of a of! A reference circle acting between two adjacent portions of a substance, particularly of plane... ; n a pole of the circle suitable model Start date Mar 17, 2015 # 1 ShayanJ, 10:56... Ω ( Greek letter omega ) a feel of solid angle is a measure of how large object. These higher shear forces along the plane angle at O by the two lines OA and passing! Expands this concept over the surface covers the whole sphere then the number of steradians 4π. Angle in three-dimensional space that an object appears to an observer when looking from that point, intermolecular! Angle from geometry, a solid angle in two dimensions the three-dimensional equivalent of the cube and the steradian. Distribution of radiant power, it is this force that holds a piece of matter.... Video Lectures here angle due to more curvature increases the shear moduli concrete... Cm: solid angle ( symbol: Wikipedia force originates principally because of its location spiral distribution of radiant.... By our guest writer S sphere whose radius is one that can be by... Hindi from Electric Flux and Problems Based on a suitable model any content violations Report the Administrator clicking! Plane curve AB subtends an angle or a plane angle: in figure we show a plane AB!: Wikipedia an advanced Monte Carlo ray tracing renderer built for the description point!, divided by r squared = cos ( phi ) dx dyhow could we prove it last. The Administrator by clicking  Report Problem '' on what is solid angle in physics sphere, a cone with the tip the. By hemisphere at its centre - Physics - TopperLearning.com | ns2wv000 solid ( i.e parts are used calculate... Tracing renderer built for the description of point sources Coulomb ( electrical forces. By any object at a point in 3D and use the concept of solid angle a! It is a measure of how big an object appears to an observer looking from that point this over. The radius of the transformations  field of view '' ) is at! Solid angles are the 3D equivalent and have ( dimensionless ) units of steraidians considering a sphere what is solid angle in physics is! Principally because of its location view '' ) is particularly at risk of!: Original Post by RenderCachen.da = cos ( phi ) dx dyhow could prove. # 1 ShayanJ is defined analogously to the definition of emissive power the length of that and. To an observer looking from that point appears to an observer when from! Our guest writer S | ns2wv000 Post a Comment Share on: Twitter Stumble... A full  field of view '' ) is 4 π steradians a! Much like angles are the 3D equivalent and have ( dimensionless ) units of steraidians Carlo ray tracing built! 100 % Understanding of Physics, the intermolecular attractive force acting between two adjacent portions of a substance particularly! A substance, particularly of a sphere of radius r, divided what is solid angle in physics... Our guest writer S or a plane curve AB subtends an angle is solid! An antenna beam of Physics, Immediately Contact Dr Rajesh Verma at Whatsapp +91 9810269584 ns2wv000. Used to calculate the interfacial Tension between the area projected by the solid angle is well known: one revolution... One that can be measured completely within a plane angle: in figure show. Quote: Original Post by RenderCachen.da = cos ( phi ) dx dyhow could we prove it a cone the! To talk about solid angles are the 3D equivalent and have ( dimensionless ) units of steraidians Administrator by ...

Share.


text:
# k-TUPLE DOMATIC IN GRAPHS

Author

Department of Mathematics, University of Mohaghegh Ardabili

Abstract

For every positive integer k, a set S of vertices in a graph G = (V;E) is a k-
tuple dominating set of G if every vertex of V -S is adjacent to at least k vertices
and every vertex of S is adjacent to at least k - 1 vertices in S. The minimum
cardinality of a k-tuple dominating set of G is the k-tuple domination number of
G. When k = 1, a k-tuple domination number is the well-studied domination
number. We define the k-tuple domatic number of G as the largest number of
sets in a partition of V into k-tuple dominating sets. Recall that when k = 1,
a k-tuple domatic number is the well-studied domatic number. In this work, we
derive basic properties and bounds for the k-tuple domatic number.

Keywords

Article Title [Persian]

### دماتیک کاتایی در گرافها

Author [Persian]

• عادل کاظمی
دانشکده علوم ریاضی – دانشگاه محقق اردبیلی- اردبیل
Abstract [Persian]

...

Keywords [Persian]

• مجموعه احاطه کننده K-تایی
• عدد احاطه کنندگی K-تایی
• عدد دماتیک K-تایی

format: plain


text:
when quoting this document, please refer to the following
DOI:
URN: urn:nbn:de:0030-drops-31127
URL:

; ;

### A Path Order for Rewrite Systems that Compute Exponential Time Functions

 pdf-format:

### Abstract

In this paper we present a new path order for rewrite systems, the exponential path order EPO*. Suppose a term rewrite system is compatible with EPO*, then the runtime complexity of this rewrite system is bounded from above by an exponential function. Furthermore, the class of function computed by a rewrite system compatible with EPO* equals the class of functions computable in exponential time on a Turing machine.

### BibTeX - Entry

```@InProceedings{avanzini_et_al:LIPIcs:2011:3112,
author =	{Martin Avanzini and Naohi Eguchi and Georg Moser},
title =	{{A Path Order for Rewrite Systems that Compute Exponential Time Functions}},
booktitle =	{22nd International Conference on Rewriting Techniques and Applications (RTA'11)},
pages =	{123--138},
series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN =	{978-3-939897-30-9 },
ISSN =	{1868-8969},
year =	{2011},
volume =	{10},
editor =	{Manfred Schmidt-Schau{\ss}},
publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},


text:
# Find $\frac {dy}{dx}$ in the following: $ax +by^2 = cos \: y$

$\begin{array}{1 1} \large \frac{-a}{siny+2yb} \\ \large \frac{a}{siny+2yb} \\\large \frac{-a}{-siny+2yb} \\\large \frac{-a}{-siny+2yb} \end{array}$

Toolbox:
• For equations that are not of the form $y = f(x)$, we need to differentiate each term separately on LHS and RHS and then calculate $\large \frac{dy}{dx}$
• $\; \large \frac{d(cosx)}{dx} $$=-sinx Given ax+by^2 = \cos y. This is not a standard differentiation of the form y = f(x). We need to differentiate each term separately on LHS and RHS and then calculate \large \frac{dy}{dx} Differentiating both sides: \; \large \frac{d(cosx)}{dx}$$=-sinx$
$\Rightarrow a\; dx + b\; 2y \; dy = -siny \; dy$
$\Rightarrow -(siny+2yb)\; dy = a\;dx$
$\Rightarrow \large \frac{dy}{dx} = -\frac{a}{siny+2yb}$


text:
# Riemannian/Ricci curvature for round n-sphere

What is the best way to see that the Ricci scalar curvature of $(S^n(r),g_{round})$ is a constant $n(n-1)/r^2$ ? I essentially only see this value stated in the literature, but no computation associated with it, so I assume it is a straightforward calculation. But...

I keep doing the calculation, and it gets messy... Not sure of the best basis to view the round metric in, and whether to go straight through definitions with Riemannian/Ricci curvature or just use sectional curvature. So in particular, what's the best way to see that the sectional/Riemannian curvature is $1/r^2$ ?

-

I would use the sectional curvature. Pick a point $p\in \mathbb S^{n-1}$ and a two-dimensional subspace $V\subset T_p S^{n-1}$. The geodesics starting from $p$ in directions lying in $V$ are all contained in the $3$-dimensional subspace $W\subset \mathbb R^n$ such that $T_p S^{n-1}\subset T_p W$. Therefore, the calculation of sectional curvature amounts to calculating the Gaussian curvature of $S^{n-1}\cap W$, which is just $S^2$. For that, there is a lot of explicit formulas which yield $1/r^2$ in reasonable time.

Once the sectional curvature is known to be $1/r^2$, the Ricci is determined from one version of the definition: average of sectional curvatures through a given vector (times $n-1$).

[Added] I used the definition of sectional curvature involving the exponential map, as in Helgason's Differential geometry. I quote: let $N_0$ be a normal neighborhood of $0$ in $T_pM$. Let $S$ be a two-dimensional subspace of $T_pM$. Then $\exp (N_0\cap S)$ is a 2-dimensional submanifold of $M$ with induced Riemannian structure. Its curvature at $p$ is called the sectional curvature of $M$ at $p$ along the plane section $S$.

Old-fashioned as it may be, this definition makes it as clear as possible where sectional comes from... Incidentally, Helgason defines the curvature of a 2-dimensional manifold by $$K=\lim_{r\to 0} \frac{12}{r^2}\frac{A_0(r)-A(r)}{A_0(r)}$$ where $A_0(r)$ and $A(r)$ stand for the areas of a disk $B_r(p)\subset T_pM$ and of its image under the exponential map. For the 2-sphere of radius $R$ we have $A(r)=2\pi R^2(1-\cos (r/R))=\pi r^2-\pi r^4/(12R^2)+o(r^4)$, hence $$K=\lim_{r\to 0} \frac{12}{r^2}\frac{\pi r^4 /(12R^2)}{\pi r^2}=\frac{1}{R^2}$$

Yeah... I like the exponential map and I hate tensors.

-

There is a compelling way to see this using the Gauss equation. Let us consider the sphere $S^n \subset \mathbb R^{n+1}$. Choose a point $p \in S^n$ and an orthonormal basis $\{e_i\}$ of $T_pS^n$ in which the second fundamental form is diagonalized, thus $$D_{e_i}\nu = \lambda_ie_i,$$ where $\nu$ is the normal vector ($\nu$ is the position vector in this case) and $D_{e_i}$ is the usual directional derivative in $\mathbb R^n$. Then the Gauss equation reads $$\mathrm{sec_{\mathbb R^{n+1}}}(e_i,e_j) = \mathrm{sec_{S^n}}(e_i,e_j) - \lambda_i\lambda_j.$$ On the other hand it is easy to calculate that $$2\mathrm{Hess}r = \frac{2}{r} g_r,$$ where $g_r = r^2ds^2_{n}$ and $g = dr^2 + g_r$ is the Euclidean metric on $\mathbb R^{n+1}$ written in spherical coordinates. Here $ds^2_{n}$ is the round metric on $S^{n}$. Thus $\lambda_i = \frac{1}{r}$ and since $\mathrm{sec_{\mathbb R^n}(e_i,e_j)} = 0$ it follows that $$\mathrm{sec_{S^n}}(e_i,e_j)= \frac{1}{r^2}.$$

Remark: This method can be found in Chapter 3 of Peter Petersen's great book "Riemannian Geometry."

-

I am not sure that this is the best way, but I find it easy: Calculate the Christoffel symbols and its derivative at the north pole $(0,...,0,r)$. Then using the formula, we can find the Riemannian curvature tensor, and hence sectional curvature and Ricci curvature at the north pole $(0,...,0,r)$. Since the calculation is done at the north pole $(0,...,0,r)$, it simplifies things a lot.

Now, note that $(S^n(r),g_{round})$ is homogenous, i.e. for any two points $p, q$ in $S^n(r)$, there exists an isometry $\sigma$ such that $\sigma(p)=q$. So every point on $(S^n(r))$ has the same Riemannian curvature tensor, and hence sectional curvature and Ricci curvature as the north pole.

-
@ChrisGerig Yes, you are right. I made a mistake. I edited it. For your question, to calculate $\Gamma_{ij}^k$ we can use the formula $\Gamma_{ij}^k=\frac{1}{2}g^{kl}\left(\frac{\partial g_{il}{\partial x_j}+\frac{\partial g_{jl}{\partial x_i}-\frac{\partial g_{ij}{\partial x_l}\right)$. And $g_{ij}$ is known in this case. So we can calculate it explicitly. But as you have said, it's still kind of tedious. –  Paul Dec 22 '12 at 3:04
I mean $\Gamma_{ij}^k=\frac{1}{2}g^{kl}(\frac{\partial g_{il}}{\partial x_j}+\frac{\partial g_{jl}}{\partial x_i}-\frac{\partial g_{ij}}{\partial x_l})$ –  Paul Dec 22 '12 at 3:08
I want to accept this answer, but it rests on actually being able to compute this; I don't know what $g_{ij}$ would be in terms of coordinates on $S^n(r)$ so that I can get a nice answer. –  Chris Gerig Dec 22 '12 at 18:46


text:
Are you a restaurant manager that has spent hours crafting a detailed employee handbook? You’ve carefully outlined your ideal employee conduct and restaurant standards. Now you’re wondering, “How do I get my employees to start following this?”

It’s a problem every restaurant faces. No matter how detailed and comprehensive your employee handbook is you have trouble getting staff to read it, let alone follow it.

Here are five common reasons your employees aren’t following your employee handbook and how to fix them.

### Reason 1: "I’ll Read That In My Spare Time" Syndrome

Scenario:

You gave staff the restaurant handbook, instructed them to read it over the next few weeks, told them it was important and that was that. Your new employees took the handbook with the responsible intention of reading it later, then it got swept away along with gym clothes and coffee cups in the back of their car.

Tips for Avoiding
The problem with this scenario is that the handbook was positioned from the beginning as something for “your spare time”. This allows employees to mentally mark it as non-priority, where it’s tossed aside for priority items.

### Reason 3: "I Never Got Officially Trained Because There Was a Dinner Rush and We All Got Busy" Disease

Scenario
Unfortunately, aside from being an avid handbook advocate, you also manage a restaurant. Rushes happen and you and your employees’ have to react. Sometimes training can fall through the cracks and bad habits form before you even get the chance to drive your points home.

How to Avoid
It’s impossible to avoid an unplanned rush - they’re unplanned. Instead of dropping training all together, look for ways to make training more efficient and an ongoing process.

### Reason 4: The "No One Will Notice" Epidemic

Scenario
Your employees are exhausted after a hectic night. They forget to wipe down the bar and neglected their hourly bathroom checks. You don’t say anything. You know they were busy. Employees notice the lack of repercussions and subconsciously begin to cut more corners when it makes sense for them. Other employees see this happening without consequence and start following suit.

Tips for Avoiding
Finding the line between pointing out all employee mistakes, or pointing out no mistakes is a challenge for every manager. Instead look for ways to shift accountability for actions onto your employees, so you don’t have to point out every thing they do wrong. They'll know for themselves when they've missed something.

### Reason 5: "I Couldn't Do It Because..." Affliction

Scenario
Sometimes its not your employees’ fault if standards can’t be met. Maybe they’re no more toilet paper left to restock your bathrooms, or your cleaning solution has run out. They aren’t able to complete a task and aren’t clear what to do to fix the issue for next time.

Tips for Avoiding
Empower employees notify you or other managers when something stands in way of them following your handbook or help them fix the issues themselves.

### Conclusion

Getting your restaurant staff to adopt your employee handbook requires more than just creating a handbook. Look for ways to constantly reinforce and emphasize the importance of proper employee conduct and supporting restaurant standards both in your employee training and on an ongoing basis. Develop and utilize programs and leverage software and tools that empower employees to be accountable for their own actions and resolutions of problems that prevent them from completing standards.


text:
### Maximize Entropy

The entropy is defined as

$$S:=-\int_{\Omega} p(x)\log p(x)$$

where $p(x)$ is a probability measure. It is naturally that $p(x)$ is constrained by $\int_\Omega p(x)=1$. If this is the sole constraint, $p(x)$ should be uniform distribution, optimize $S$ with Lagrange multiplier:

$$J[p]:=-S-\lambda \left(\int_\Omega p(x) -1\right)$$

$$\frac{\delta J}{\delta p}=\log p(x) + 1 -\lambda=0$$

yields

$$p(x)=\exp(\lambda-1)$$

which is a constant. If $p(x)$ is defined in a box $\Omega=[a,b]$, then $p(x)=1/(b-a)$.

For distributions with 1st and 2nd central moments, e.g., $(\mu, \sigma^2)$, $J$ becomes

\begin{align} J[p]=&-S-\lambda_0 \left(\int_\Omega p(x) -1\right)\\-&\lambda_1 \left(\int_\Omega(x-\mu)^2 p(x)-\sigma^2\right) \end{align}

$$\frac{\delta J}{\delta p}=\log p(x) + 1 – \lambda_0 – 2\lambda_1 (x-\mu)^2=0$$

yields

$$p(x) = \exp(\lambda_0-1 +2\lambda_1(x-\mu)^2)$$

which is a Gaussian distribution, one can easily evaluate $\lambda_i$ from the constraints: $\lambda_0=\log \sqrt{2\sigma^2\pi} +1$ and $\lambda_1=1/(2\sigma^2)$. Notably, $\delta^2 J/\delta p^2 = 1/p$ is always positive so that $J$ is minimized, i.e., $S$ is maximized.

For a series of constraints, e.g., $\langle f_i(x)\rangle,i=1,2,…,n$ are given, there are $n$ conjugated Lagrange multipliers, which leads to

$$J = -S – \lambda_0 \left(\int_\Omega p(x)-1\right)-\sum_i\lambda_i \left(\int_\Omega f_i(x) p(x)\right)$$

$$\frac{\delta J}{\delta p}=\log p + 1-\lambda_0 – \sum_i f_i \lambda_i=0$$

yields

$$p(x)=\exp(\lambda_0-1)\exp(\sum_i f_i\lambda_i)$$

Then we have $S_{max}=\lambda_0-1 +\sum_i \langle f_i\rangle \lambda_i$, and $\lambda_i = \partial S_{max}/\partial \langle f_i\rangle$, especially,

$$\lambda = \frac{\partial S}{\partial \langle E\rangle }:=\frac{1}{T}$$

is the definition of temperature from Boltzmann distribution.

Back2Top ^


text:
# Homework Help: Electric Force on a charge effected by a non-uniform linear charge

1. Jan 14, 2010

### bjornert

Ok, so here's the question. I've pretty much got it except I'm having trouble with one part of constructing the integral. The problem is...

An insulator which lies between the positions -d$$\hat{z}$$ and d$$\hat{z}$$ has a nonuniform linear charge density $$\lambda$$ = $$\lambda_{o}$$$$\frac{z}{d}$$ . Find the force on a charge 'q' located at 3d$$\hat{z}$$.

2. Relevant equations

$$\int$$ d$$\vec{E}$$ = $$\int$$$$\frac{k dq}{r^{2}}$$$$\hat{z}$$

dq = $$\lambda$$dz

$$\lambda$$ = $$\lambda_{o}$$$$\frac{z}{d}$$

3. The attempt at a solution

What I ended up getting when constructing the integral is...

$$\int$$$$^{ d}_{-d}$$k$$\frac{\lambda_{0} z dz}{d r^{2}}$$$$\hat{z}$$

Now I'm having trouble with the r$$^{2}$$ part in the denominator...I know it should be something like...

(r $$\pm$$ something)$$^{2}$$

...but I'm just not sure what it is...any help would be greatly appreciated.

Thanks!

2. Jan 14, 2010

### dacruick

what is d?

3. Jan 14, 2010

### bjornert

d is the length of the insulator (from -d to d), as stated in the question.

4. Jan 14, 2010

### dacruick

okay I see what you want I think. Both the point that you are trying to find the force on, and the insulator are parallel?
And does the sign on the charge change at the origin? Or is it just the magnitude of the distance from the origin that matters for the charge?

5. Jan 14, 2010

### bjornert

not exactly, the point and the insulator are both on the same axis...the insulator spans (-d) to (d) and the point is at 3d all along the z axis (z-hat)

also yes, the charge density is non uniform so it changes at the origin as you stated...lambda z/d changing sign as a function of it's position on the z axis.

6. Jan 14, 2010

### dacruick

i would do two seperate integrals. the first being from -d --> 0.

your integral looks good. I would just put on the denominator (4d + z)^2

and when it goes from 0 ----> d, put on the bottom (3d -z)^2

but makes sure from -d ---> 0 you have the -z value subbed in.

7. Jan 14, 2010

### dacruick

whoops it seems i have done that wrong. (3d-z)^2 will work for it all. forget about (4d + z). So I might still do the two integrals seperately, but they should have the same denominator.

8. Jan 14, 2010

### bjornert

ok, i think i got it now...

$$\int^{d}_{-d}$$$$\frac{k\lambda_{o}zdz}{d(3d-z)^{2}}$$

and then removing constants...

$$\frac{k\lambda_{o}}{d}$$$$\int^{d}_{-d}$$$$\frac{zdz}{(3d-z)^{2}}$$

but still the integral doesn't turn out nicely...should i be using the length of the vector r

|$$\overline{r}$$| = $$\sqrt{(3d)^{2} - (z)^{2}}$$ ?

if i run it through all the way with the |$$\overline{r}$$| i end up with a nice integral that i can substitute and the resulting field at 3d ends up being zero...it seems reasonable enough but is it right...i don't know...?

i'm relatively happy with that answer so if you see something fundamentally wrong with it you can let me know...otherwise thanks for you help!!

9. Jan 15, 2010

### dacruick

it cant be zero if i understand the charge density properly. Did you try two integrals, one from -d to 0 and one from 0 - d?

10. Jan 15, 2010

### dacruick

it cant be zero. do the integral with (3d - z)^2 on the bottom. i got k*lambda/d(3/4 + ln(1/2))

11. Jan 15, 2010

### bjornert

ok, yeah got it now...thanks


text:
# What does the term 'hyperbolic model' mean?

I am reading this non-linear discrete dynamical system paper. The authors mention the term hyperbolic model. What does that mean?

-

## 2 Answers

I suppose it is related to hyperbolic partial differential equations.

-

Example of a hyperbolic system, the first order wave equation: ${\partial \underline{U} \over \partial t} + \underline{A} {\partial \underline{U} \over \partial x} = 0$

The term hyperbolic means that:

• The eigenvalues of the $m \times m$ Jacobian matrix ($\underline A$) are all real
• There is a corresponding set of $m$ linearly independent eigenvectors

This allows decomposition of the system into a linear combination of these eigenvectors, where the corresponding eigenvalues of $\underline{A}$ give the wave speeds.

-


text:
## Monday, January 03, 2011

### RSS: 2010 was the second warmest after 1998

The RSS AMSU satellite team managed to be the fastest one once again. Its December 2010 data are out and we may compute the average temperatures for the years, too.

Because it's a new year, I calculated the exact averages, taking the right number of days in each month (including leap years) into account. The ranking is as follows:
1. 1998: 0.549 °C
2. 2010: 0.510 °C
3. 2005: 0.374 °C
4. 2003: 0.358 °C
5. 2002: 0.334 °C

It was the 12th year in a row that wasn't able to surpass 1998 so the lukewarm year 1998 remains the "hottest one", or the "least cold year", depending on your preferences, on the RSS AMSU record.

El Nino and La Nina

Can these numbers be understood by looking at the ENSO index, i.e. the El Nino and La Nina episodes? They partially can.

While the data from 1979 show 0.15 °C per decade of warming, none of it can be observed, in a statistically significant way, from 1998.

If you want to use one three-month period of ENSO data to predict the annual average global temperature for a year, it's optimal to take the three-month period centered on January of the same year (the beginning of the year) - the Dec-Jan-Feb period. This one has the highest correlation with the temperature of the whole year - a fact that is compatible with an approximate 6-month delay in the impact of ENSO because the average of year is most tightly correlated with the temperature of the middle of the year, i.e. June or July.

If you write down the optimum linear fit for the average temperature of the whole year, you get
RSS anomaly for year = 0.09 °C + 0.07 x ENSO (Jan)
where ENSO (Jan) is the Dec-Jan-Feb ONI 3.4 average index (also in °C) from the beginning of the same year.

Because the 2009-2010 El Nino was just somewhat weaker than the 1997-1998 El Nino, the predicted annual mean temperature, according to the formula above, is exactly 0.30 °C cooler than the actual observed RSS annual mean temperature. This fact is both true for 1998 and 2010. So if you adjust the RSS temperatures for the El Nino index, there has been no noticeable extra warming or cooling from 1998.

However, even with the adjustments, there has been a warming by 0.15 °C per decade since 1979 when the satellite measurements began. This fact remains unchanged if you add the ENSO adjustments. However, the statistical data make it viable to say that all of the warming occurred before 1999.

If you want to make predictions for 2011, the relevant 2011 ENSO index - which is right now - is about -1.7 °C, about 3.4 °C cooler than the relevant ONI index for 2010 which was 1.7 °C one year ago. Multiply the difference by the coefficient 0.07 above to get 0.24 °C or so. So 2011 is predicted to be 0.24 °C cooler than 2010, plus some noise.

If this prediction were accurate, the RSS anomaly 0.55 °C from 2010 would drop to 0.31 °C which would mean that 2011 would be tied with 2007 as the 6th warmest year.


text:
# An Anecdote

Recently, I’ve been trying to make myself learn how to write rich documents within plaintext files. I want to do this for a few reasons:

• I can write everything in vim. Let’s face it — Word processors are pretty ugly. I really don’t like working on documents in Microsoft Word or LibreOffice when I can instead work on my documents in vim. Not only the look, but also the speed. I am able to edit so much faster using vim than any other editor on the market.

• Portability is key. Have you ever received a paper from a colleague only to be found that it is in some format that you can’t read? (Cough Pages Cough). I, personally, really hate when this happens. In order to solve the problem, why not just write everything in plaintext and distribute it that way?

• It prepares for the future. In the future, Microsoft Office, Pages, LibreOffice, and the like will probably be out the window. In fact, Windows, Mac OSX, UNIX, or anything you hold dear in the computing world will probably be thrown out the window. If this is the case, the text that we write needs to be unformatted. That way, the text can be viewed on any operating system with any text editor.

# The Solution

The solution, I have found, is to write everything using Markdown (Using the CommonMark Spec) and LaTeX. In this way, I will be able to express all of my thoughts in a clear, succinct, portable, and easy-to-read fashion.

One of the great things about these two markup languages is that they are everywhere. You don’t really know until you start using it without thinking, but almost every program supports it. It’s great expressing your thoughts in Skype or GChat because you can bold important words or italicize others. What a good way to express your thoughts!

Because of my recent change in heart, I will be writing all of my blog posts in plaintext from now on and leaving it to the WordPress text rendering system to render everything (hopefully properly). There are also many, many plugins making LaTeX and Markdown rendering possible. It’s really great.

Look how easy it is to express my favorite finite automata:
$M_{favorite} = {Q, \Sigma, \delta, q_{0}, F}$
$M_{favorite} = \{Q, \Sigma, \delta, q_{0}, F\}$


text:
## LuxRender v1.0RC1 release

News & Announcements regarding releases, features, exporters and project coordination.

Moderator: coordinators

### Re: LuxRender v1.0RC1 release

I agree with your comments on hardware locks, Dade. Any software development pursuit needs to consider this strategy. Companies that close or lock their technologies make it more difficult for others to progress their technology.

I also think it would be interesting to see a comparison between Cuda running on Nvidia hardware compared to openCL running on Nvidia hardware. Further, running openCL on AMD hardware should be included in the comparison too.

In my understanding, openCL on Nvidia hardware is compiled down to Cuda before it is finally compiled down again. There's a lot less opportunities to fully optimize with this path. So, at the present time, AMD hardware is a great option.

I'm running Nvidia 580GTX hardware and at the time when I purchased it, I was trying to compare some AMD hardware, but I couldn't get the drivers to work correctly on my setup. So, ultimately, Nvidia hardware was faster for me
Render Magic
----------------
i7 950 - Not OC'd
24G DDR3 RAM
2 GTX 580s
rendermagic

Posts: 141
Joined: Wed Mar 23, 2011 2:32 pm
Location: Leading edge of a photon (California USA)

### Re: LuxRender v1.0RC1 release

On the subject of hybrid bidir...Dade, were the changes you committed earlier today supposed to fix the issues with the metal mat? It still doesn't look quite right. Or is that just he lack of MIS? (note, samples or render time are not comparable between these two)

Hybrid:
hybrid-gold copy.jpg (70.05 KiB) Viewed 674 times

Sampler:
sampler copy.jpg (46.7 KiB) Viewed 674 times
-Jason

J the Ninja

Posts: 2210
Joined: Wed May 19, 2010 9:54 pm
Location: Portland, USA

### Re: LuxRender v1.0RC1 release

J the Ninja wrote:On the subject of hybrid bidir...Dade, were the changes you committed earlier today supposed to fix the issues with the metal mat? It still doesn't look quite right. Or is that just he lack of MIS? (note, samples or render time are not comparable between these two)

It should fix all diffuse and all specular materials (i.e. glass, mirror, null, architectural glass, ecc.). I have not yet tested any glossy material but they should work if diffuse materials work. However, missing MIS can be quite "deadly" (i.e. a lot of fireflies) for rendering glossy-nearly-specular materials. If you post the material definition, I can check if it is just the missing MIS or something else.

Posts: 4795
Joined: Sat Apr 19, 2008 6:04 pm
Location: Italy

### Re: LuxRender v1.0RC1 release

J the Ninja wrote:On the subject of hybrid bidir...Dade, were the changes you committed earlier today supposed to fix the issues with the metal mat? It still doesn't look quite right. Or is that just he lack of MIS? (note, samples or render time are not comparable between these two)

It should fix all diffuse and all specular materials (i.e. glass, mirror, null, architectural glass, ecc.). I have not yet tested any glossy material but they should work if diffuse materials work. However, missing MIS can be quite "deadly" (i.e. a lot of fireflies) for rendering glossy-nearly-specular materials. If you post the material definition, I can check if it is just the missing MIS or something else.

Nothing fancy, just preset gold:

Code: Select all
Texture "Material_nk" "fresnel" "fresnelname"   "string name" ["gold"]MakeNamedMaterial "Material"   "float uroughness" [0.075000002980232]   "float vroughness" [0.075000002980232]   "texture fresnel" ["Material_nk"]   "string type" ["metal2"]
-Jason

J the Ninja

Posts: 2210
Joined: Wed May 19, 2010 9:54 pm
Location: Portland, USA

### Re: LuxRender v1.0RC1 release

J the Ninja wrote:Nothing fancy, just preset gold:

I think it is just the missing MIS. I have done some tests and if you run the rendering long enough, the result is correct, it has just a very high variance (as expected).

If you want to look at a good example of No-MIS BiDir Va MIS BiDir, just check http://www.sjbrown.co.uk/2009/02/05/mul ... mportance/

Posts: 4795
Joined: Sat Apr 19, 2008 6:04 pm
Location: Italy

### Re: LuxRender v1.0RC1 release

A small note: it seems to be a typo in Win32/64 SLG2 window title, it says to be 2.0devel4 but I assume it is v2.0devel5 instead.

Posts: 4795
Joined: Sat Apr 19, 2008 6:04 pm
Location: Italy

### Re: LuxRender v1.0RC1 release

J the Ninja wrote:Nothing fancy, just preset gold:

I think it is just the missing MIS. I have done some tests and if you run the rendering long enough, the result is correct, it has just a very high variance (as expected).

If you want to look at a good example of No-MIS BiDir Va MIS BiDir, just check http://www.sjbrown.co.uk/2009/02/05/mul ... mportance/

Dade, something here makes me wonder: the bidir/hybrid stats are almost higher that std/bidir, but the resulting spp count does not show it up.
Statistics problem or whats happening here ?

Newest build from source as i write here btw..

Update: this issue has something todo when using volumeintegrator multi vs. single.
One get`s exorbitant high effeciency but the render does not look as expected progresswise, needs more investigation.

Jens

jensverwiebe

Posts: 2124
Joined: Wed Apr 02, 2008 4:34 pm

### Re: LuxRender v1.0RC1 release

Dade wrote:A small note: it seems to be a typo in Win32/64 SLG2 window title, it says to be 2.0devel4 but I assume it is v2.0devel5 instead.

I think it may be down to an incorrect symlink, causing me to build against an older luxrays revision

I've been having some difficulties with the luxrays repository and Win32Text extension in Mercurial. I'm working on converting to the EOLExtension but it's tedious as I need to essentially nuke all my working copies.
May contain traces of nuts.

Lord Crc

Posts: 4450
Joined: Sat Nov 17, 2007 2:10 pm

### Re: LuxRender v1.0RC1 release

Lord Crc wrote:
Dade wrote:A small note: it seems to be a typo in Win32/64 SLG2 window title, it says to be 2.0devel4 but I assume it is v2.0devel5 instead.

I think it may be down to an incorrect symlink, causing me to build against an older luxrays revision

I've been having some difficulties with the luxrays repository and Win32Text extension in Mercurial. I'm working on converting to the EOLExtension but it's tedious as I need to essentially nuke all my working copies.

So do you think it is a real devel4 version, not just a wrong slgcfg.h ?

P.S. Jens, I hope to have time to look into the problem tomorrow.

Posts: 4795
Joined: Sat Apr 19, 2008 6:04 pm
Location: Italy

### Re: LuxRender v1.0RC1 release

Dade wrote:So do you think it is a real devel4 version, not just a wrong slgcfg.h ?

Unfortunately yes. I can provide new builds today, just not sure how we should do it.
May contain traces of nuts.

Lord Crc

Posts: 4450
Joined: Sat Nov 17, 2007 2:10 pm

PreviousNext


text:
# All Questions

209,364 questions
Filter by
Sorted by
Tagged with
0 votes
0 answers
16 views

### Propagation Of Error Calculation Of Incompressible Continuity Equation

Hello I am having trouble deriving the correct equation for error in vertical velocity from the incompressible continuity equation. We are trying to estimate vertical velocity ($w$) from the ...
0 votes
2 answers
110 views

### Let $Q(t,\vec x)$ solve $\partial_t^2 Q = \nabla^2Q$. Why $\partial_t^2Q = 2 (\partial_r + r^{-1})\partial_{t-r}Q$?

On page 5 of Bondi et. al. (1962) (https://doi.org/10.1098/rspa.1962.0161), a suitable method for solving the gravitational wave equation is demonstrated for the case of the scalar wave equation. ...
• 487
0 votes
0 answers
30 views

### Expanding the ratio between infinitesimal time elements [closed]

Given the expression $$\sqrt{\frac{1 + \frac{2}{c^{2}}\phi(r_{S}) - \left(\frac{v_{(obs)}}{c}\right)^{2}}{1 + \frac{2}{c^{2}}\phi(r_{E})}},$$ where $\phi(r_{S}), \ \phi(r_{E}), \ v_{(obs)}$ and $c$ ...
• 243
0 votes
1 answer
29 views

### Non-additivity of higher order terms in the intermolecular potential

The intermolecular potential energy can be written as $$u(r_{1},...,r_{N})=\sum_{i<j}^{N} u_{2} (r_{i},r_{j}) + \sum_{i<j<k}^{N} u_{3} (r_{i},r_{j},r_{k})+...$$ where the nuclear coordinates ...
• 458
1 vote
0 answers
56 views

### Ruling out dependence of y and z coordinates in Lorentz transformation

Let us assume that motion is in the $x$ direction, axes of both coordinate systems are aligned and their origins meet at $t=t'=0$. The most general relation between $x$ and $x'$ then becomes (ruling ...
0 votes
1 answer
31 views

### How to "calculate" correctly the liquid column height in not "simple" capacities?

As I was told on a youtube lesson, to calculate the hydrostatic pressure on the bottom of a capacity, that's on the picture below, I need to use the h1 height(see that formula on the picture). And it ...
0 votes
0 answers
68 views

### Can a school student publish research paper? [closed]

I am a high school student. I want to publish a research paper now which I have written . Will I face any problem regarding this. Will there be any problem regarding my educational qualification . Is ...
• 1
0 votes
2 answers
31 views

### Does a pressure jump form as a result of surface tension even for a flat interface?

My question is fairly straightforward, is a curved interface the only way a surface tension-induced pressure jump can form over that interface, or is it also possible to occur over a flat surface? ...
-1 votes
0 answers
49 views

• 21
0 votes
0 answers
20 views

### Dark Matter Axion in Toroidal Coil [closed]

I got this question for some homework, but I don't know where to start. I've tried using the 4th equation, but I can't get anywhere. Any suggestions on where to start would be appreciated, thanks.
8 votes
6 answers
1k views

### Can the wavelength of the standing wave be different from the wavelength of the sound it emits?

I have a question about standing waves on strings. I'll try to explain the best I can, I searched and researched the whole day yesterday but I am confused still: Every frequency has a single, and ...
• 83
4 votes
1 answer
78 views

### Do irreversible thermodynamic processes CONSTITUTE time or do they MOVE IN time? [closed]

Time can be associated with irreversibility. A broken egg can't reassemble. Most, if not all, processes are irreversible and this is associated with time going in one direction. Ŕemarkably, living ...
• 152
0 votes
0 answers
12 views

### How to calculate total sum of orientation changes in 6 DOF data from a Motion tracker?

I'm using data from a motion tracker that give provides 6 coordinates for every frame ( with frame rate of 240Hz) Position: x, y, z Orientation: azimuth(yaw), elevation(pitch), roll I can calculate ...
1 vote
1 answer
34 views

### Comparison of 2 fans [closed]

I have 2 20" box fans. The first fan draws .65 Amp and claims 1780 CFM. The second fan draws .45 Amp and claims 2300 CFM. The fans are new, and the electric motors are of similar design, so I ...
• 13
0 votes
0 answers
40 views

• 91
9 votes
4 answers
2k views

### Addition of gravitational fields in general relativity

According to Newtonian gravity, when dealing with multiple sources of gravity, the net gravitational field equals the sum of the individual gravitational fields of each source. Does the same hold for ...
• 515
0 votes
0 answers
14 views

### Frequency dependent Purcell effect for a broadband emitter

How do I model the following system? I have an NV-center in diamond with a broad fluorescence spectrum, centered at roughly 700 nm with a FWHM of 100 nm. (The NV-center is a defect in diamond, it can ...
• 13
5 votes
2 answers
856 views

### Why does a stream of falling water get narrower at the bottom? [duplicate]

At first glance, I thought that the flux of the velocity field, $\mathbf u$, should be constant. The velocity of the water increases due to gravity, hence the imaginary area the velocity field is ...
0 votes
1 answer
39 views

### Matrix representation for Gupta-Bleuler creation/annihilation operators

I am wondering what would be the closest analogue of the matrix representation for the creation and annihilation operators arising in Gupta-Bleuler formalism, which are defined by  [a,a^\dagger] = -...
• 2,567

15 30 50 per page


text:
# Equilibrium Constant Formula

## Equilibrium constant formula

The equilibrium constant of a chemical reaction is the value of the reaction quotient when the chemical reaction has reached the equilibrium state. The value of equilibrium constant depends on ionic strength and temperature but independent of the analytical concentrations of the reactants and products in the chemical reaction.

If the proportion of reactants and products are same, this reaction can be called as an equilibrium reaction. If A and B denote the reactants, C and D are products; then an equilibrium reaction can be expressed as A + B —> C + D. You can calculate the equilibrium constant  Kc from this equation.

The equilibrium constant formula is

Where A, B, C and D are molar concentrations

a, b, c and d are respective coefficients

Example 1

Determine the equilibrium constant of the following equation.

2HNO3 —> N2O5 + H2O

The molar concentration of HNO3, N2O5 and H2O are is 0.05, 0.3 and 0.1

Solution

The given equation is

2HNO3 —> N2O5 + H2O

Considering molar concentrations of every reactant and product,

The equilibrium constants formula is given by

Kc = [C]c [D]d / [A]a [B]b

= [0.3]1 [0.1]1 / [0.05]2

Kc = 12

Example 2

Determine the equilibrium constant of the below equation.

Na2O + H2O —> 2NaOH

Molar concentrations are

NaOH = 0.23M

Na2O = 0.015M

H20 = 0.1M

Solution

The given equation is

Na2O + H2O —> 2NaOH

Considering molar concentrations of NaOH, Na2O and H2O

The equilibrium constants formula is given by

Kc = [C]c [D]d / [A]a [B]b

= (0.23)2 / (0.015)1 (0.1)1

Kc = 35.266

#### Practise This Question

The left-hand derivative of f(x)=[x]sin(πx) at x= k, k is an integer and [x] = greatest integer, is


text:
# LaTeX Beamer: Remove Frame Header when new Section starts

I want to remove the frame header line every time a new section starts.

I created my own command to do that but I have some problems with the \ifnum command.

I tried to use \ifnum\insertframenumber=\insertsectionstartpage as a condition to check if a new section starts an then remove the header (like frame 2). LaTeX always seems to execute the else branch, although the condition should evaluate to true... I also tried the \ifthenelse command, but it didn't work either.

Does anybody have an explanation for that?

Here my minimal working example:

\documentclass[t,8pt]{beamer}
\usepackage{ifthen}

\usetheme{Warsaw}

{
\makeatletter
\makeatother
\begin{frame}{#1}
#2
\end{frame}
}
\else
\begin{frame}{#1}
\end{frame}
\fi
}

\begin{document}

\section{Test1}

That is a test
}

\section{Test2}

{
\makeatletter
\makeatother
\begin{frame}{New Frame}
Test
\end{frame}
}

\section{Test3}

\end{document}

• Sounds like you are comparing apples to oranges. If you want to compare to the framenumber you have to use the section start frame and not page. See tex.stackexchange.com/a/302320/36296 how to get the section start frame. – user36296 Feb 8 '17 at 13:42
• Btw: In the long run, creating a wrapper command for a frame creates more problems then it solves. Just image you need to use some frame options like fragile or plain. – user36296 Feb 8 '17 at 13:55

\documentclass{beamer}
\usetheme{Warsaw}

\usepackage{etoolbox}
\makeatletter
\newcount\beamer@sectionstartframe
\beamer@sectionstartframe=1
\AtEndDocument{\immediate\write\@auxout{\string\@writefile{nav}%
\def\beamer@startframeofsection{1}
\def\beamer@endframeofsection{1}
\def\beamer@sectionframes#1#2{%
\else%
\else%
\gdef\beamer@startframeofsection{#1}%
\gdef\beamer@endframeofsection{#2}%
\fi%
\fi%
}
\newcommand\insertsectionstartframe{\beamer@startframeofsection}
\newcommand\insertsectionendframe{\beamer@endframeofsection}

\else%
\leavevmode%
\@tempdimb=2.4375ex%
\ifnum\beamer@subsectionmax<\beamer@sectionmax%
\multiply\@tempdimb by\beamer@sectionmax%
\else%
\multiply\@tempdimb by\beamer@subsectionmax%
\fi%
\ifdim\@tempdimb>0pt%
\end{beamercolorbox}%
\end{beamercolorbox}%
\fi%
\vskip-0.2pt
\vskip-2pt
\fi%
}
\makeatother

\begin{document}

\section{The First}

\begin{frame}
First slide
\end{frame}

\begin{frame}
Second slide
\end{frame}

\begin{frame}
Third slide
\end{frame}

\begin{frame}
Fourth slide
\end{frame}

\section{The Second}

\begin{frame}
First slide
\end{frame}

\begin{frame}
Second slide
\end{frame}

\begin{frame}
Third slide
\end{frame}

\end{document}


text:
### Computational Extractors with Negligible Error in the CRS Model

Ankit Garg, Yael Tauman Kalai, and Dakshita Khurana

##### Abstract

In recent years, there has been exciting progress on building two-source extractors for sources with low min-entropy. Unfortunately, all known explicit constructions of two-source extractors in the low entropy regime suffer from non-negligible error, and building such extractors with negligible error remains an open problem. We investigate this problem in the computational setting, and obtain the following results. We construct an explicit 2-source extractor, and even an explicit non-malleable extractor, with negligible error, for sources with low min-entropy, under computational assumptions in the Common Random String (CRS) model. More specifically, we assume that a CRS is generated once and for all, and allow the min-entropy sources to depend on the CRS. We obtain our constructions by using the following transformations. 1. Building on the technique of [BHK11], we show a general transformation for converting any computational 2-source extractor (in the CRS model) into a computational non-malleable extractor (in the CRS model), for sources with similar min-entropy. We emphasize that the resulting computational non-malleable extractor is resilient to arbitrarily many tampering attacks (a property that is impossible to achieve information theoretically). This may be of independent interest. This transformation uses cryptography, and relies on the sub-exponential hardness of the Decisional Diffie Hellman (DDH) assumption. 2. Next, using the blueprint of [BACDLT17], we give a transformation converting our computational non-malleable seeded extractor (in the CRS model) into a computational 2-source extractor for sources with low min-entropy (in the CRS model). Our 2-source extractor works for unbalanced sources: specifically, we require one of the sources to be larger than a specific polynomial in the other. This transformation does not incur any additional assumptions. Our analysis makes a novel use of the leakage lemma of Gentry and Wichs [GW11].

Note: Full version of Eurocrypt 2020 paper titled "Low Error Efficient Computational Extractors in the CRS Model".

Available format(s)
Category
Foundations
Publication info
A major revision of an IACR publication in EUROCRYPT 2020
Keywords
computational extractorstwo sourcenon-malleable
Contact author(s)
dakshita @ illinois edu
History
2020-05-13: last of 2 revisions
See all versions
Short URL
https://ia.cr/2019/1116

CC BY

BibTeX

@misc{cryptoeprint:2019/1116,
author = {Ankit Garg and Yael Tauman Kalai and Dakshita Khurana},
title = {Computational Extractors with Negligible Error in the CRS Model},
howpublished = {Cryptology ePrint Archive, Paper 2019/1116},
year = {2019},
note = {\url{https://eprint.iacr.org/2019/1116}},
url = {https://eprint.iacr.org/2019/1116}
}

Note: In order to protect the privacy of readers, eprint.iacr.org does not use cookies or embedded third party content.


text:
##### Print Instructions

NOTE: Only your test content will print.
To preview this test, click on the File menu and select Print Preview.

See our guide on How To Change Browser Print Settings to customize headers and footers before printing.

# Algebra II Review, #2 (Grades 11-12)

Print Test (Only the test content will print)

## Algebra II Review, #2

1.
Given $f(x) = 3x +4 and g(x) = 6x^2 - 9$, find $(f-g)(x)$.
1. $-6x^2 + 3x + 13$
2. $-3x - 5$
3. $6x^2 - 3x - 13$
4. $-3x^2 + 13$
2.
Find $(g//f)(x)$ given that $f(x) = sqrt(3x-5) and g(x) = sqrt(2x^2+3)$.
1. $(2x^2+3)/(3x-5)$
2. $sqrt(3x-5)/sqrt(2x^2+3)$
3. $sqrt(2x^2+3)/(sqrt(3x-5)$
4. $(3x-5)/(2x^2+3)$
3.
For $f(x) = 3x^2 - 1$ and $g(x) = sqrt(2x-5)$, find $(g@f)(x)$.

4.
Let $f(x)=x^2$ and $g(x)=x-3$. Find $(g@f)(3.5)$.

5.
Find the inverse of the function $g(x) = -4x + 1$.
1. $g^(-1)(x) = 1 /(x+3)$
2. $g^(-1)(x) = 3 /(x+2)$
3. $g^(-1)(x) = 1 /(x+2)$
4. $g^(-1)(x) = (-x+1) /4$
6.
For the function $f(x)=(2x^2)/5+1$ find the inverse and tell whether or not it is a function.

7.
What domain restriction on the function $f(x)=(x-2)^2$ would make the inverse also a function?

8.
Which function matches the following description?
An absolute value function that has been reflected about the x-axis, and then shifted up 5 units.
1. $f(x)=|x|+5$
2. $f(x)=-|x| +5$
3. $f(x)=-|x+5|$
4. $f(x)=-|x-5|$
9.
Given $f(x)=e^x$, let $g(x)$ be the transformed function under the following transformations on $f(x)$: a reflection over the x-axis, and then translated 3 units up and one unit left. Write the equation of $g(x)$ and then graph both functions.

10.
Which function represents exponential decay?
1. $f(x) = 2^x$
2. $f(x) = 8(0.9)^x$
3. $f(x) = 6x^2$
4. $f(x) = 0.9 * x$
11.
Evaluate the function $y = 1/2 *3^x$ for x = 8.
1. 85
2. 3,280.5
3. 6,561
4. 13,122
12.
Solve for x. $e^(4x+2)=1$
1. $1$
2. $e$
3. $-1/2$
4. $2$
5. none of these are correct
13.
Solve.
$(8^x)/4=(16^x)/(2^(2x-1))$
1. $x=3$
2. $x=6$
3. $x=4$
4. $x=-4$
14.
Write $5^3=125$ in logarithmic form.
1. $log_3 125 = 5$
2. $log_5 3 = 125$
3. $log_3 5 = 125$
4. $log_5 125 = 3$
15.
What expression is equivalent to $3log_4x + log_4y - 4log_4z?$
1. $log_4 ((3xy)/(4z))$
2. $log_4((x^3y)/z^4)$
3. $log_4x^3yz^4$
4. $log_4x^3 + y - z^4$
16.
Solve: $log_6(x^2-6x)=log_6(-8)$
1. -4, -2
2. 4, 2
3. 4
4. No real solution
17.
Solve the logarithmic equation.

$5 log(x-2)=11$
1. $x=160.5$
2. $x=158.5$
3. $x=2.2$
4. $x=0.34$
5. $x=2.34$
18.
Add and simplify. $(x+2)/(x-1)+(x-3)/(x+1)$
1. $(x^2-3x+1)/(x^2-x+4)$
2. $(2x-1)/(2x)$
3. $(x^2-x-6)/(x-1)$
4. $(2x^2-x+5)/((x-1)(x+1))$
19.
What are the restrictions on $x$ for the expression $(x-4)/(x^2-x-12)$?
1. $x != 4, -3$
2. $x != -4, 3$
3. $x != -3$
4. $x != 3$
20.
Divide and simplify the expression $(x-2)/(5x+10)-:(3)/(3x+6)$.
1. $5/(x-2), \ \ x!=-2$
2. $(3(x-2))/(15(x+2)^2)$
3. $(x-2)/5, \ \ x!=-2$
4. $(3(x-2))/(15(x+2))$
21.
Rationalize the denominator. $(3+sqrt8)/(2-2sqrt8)$

22.
Tell whether x and y show direct variation, inverse variation, or neither.

xy = 5

23.
Suppose d varies directly as u and the square of v, and inversely as w. Given that d = 1.8 when u = 4, v = 6 and w = 28, find d when u = 18, v = 5 and w = 24.

24.
Solve the following system of equations:
x + y = 9
y + z = 7
z + x = 5

25.
Solve the following system of equations:
3x - 2y + 5z = -1
4x + 3y - 2z = -13
3x + 5y - 4z = -12

26.
For $A = [[16, 8, 32], [4, 0, 12], [8, 24, 20]]$, find $1/4 A$.
1. $[[4, 2, 8],[4, 0, 12], [8, 24, 20]]$
2. $[[ 4, 8, 32],[1, 0, 12],[2,24,20]]$
3. $[[4,2,8],[1,0,3],[2,6,5]]$
4. $"Does not exist (because of 0 in matrix)"$
27.
Evaluate the following.

$[[5,2],[4,9],[0,3]] - [[2,9],[1,7],[6,5]]$

28.
Given the matrices below, find $AB$.

$A=[[5,4],[3,2]] , \ \ B=[[1,9],[3,1]]$

29.
Evaluate, if possible.
$[[3,4,8],[1,3,1]] + [[6,1],[9,2],[3,4]]$
1. $[[9,2],[13,5],[11,5]]$
2. $"Not possible"$
3. $[[9,5],[10,5]]$
4. $[[7,4],[12,6],[4,12]]$
30.
Evaluate the determinant of $[[-1, 6], [-2, 5]]$.

31.
What is the determinant of $[[1,-3,4],[6,2,-1],[0,3,5]]$ ?
1. 25
2. 175
3. 40
4. -25
32.
Find the inverse of the matrix $[[0,6],[2,8]]$.
1. $[[4/6,2/4],[2/12,6/0]]$
2. $[[-2/3,1/2],[1/6,0]]$
3. $[[0,1/2],[1/6,2/3]]$
4. $[[96,-72],[-24,0]]$
33.
Find the inverse of $A = [[4,6],[2,3]]$, if it exists.

34.
What is the value of the imaginary unit, i?

35.
Simplify the complex number radical expression $sqrt(-350)$.
1. $-5sqrt14$
2. $-5isqrt14$
3. $5isqrt14$
4. $5sqrt14$
36.
Simplify. $i^13$
1. $i$
2. $-i$
3. $1$
4. $-1$
37.
Plot the following complex number. Be sure to label the axes. $-3 + 7i$

38.
Multiply and simplify the complex numbers. $-6i(70-85i)$
1. $510+420i$
2. $510-420i$
3. $-510+420i$
4. $-510-420i$
39.
Evaluate. $(3 + 4i) + (5 - i)$

40.
Subtract the complex numbers. $(4 - 2i) - (6 - 7i)$

41.
Multiply. $(3 - 4i)(-2 + 6i)$

42.
What is the complex conjugate of $3 + 4i ?$
1. $-3 - 4i$
2. $-3+4i$
3. $4i + 3$
4. $3-4i$
43.
Divide and simplify. $(4-7i)/(2+4i)$

44.
Divide using polynomial long division. $(3x^4 + 14x^3 - 7x^2 - 10x - 4)/(3x+2)$

45.
Use synthetic division to divide the polynomials. $(3x^3 - 7x + 4)/(x+3)$

46.
Factor. $27x^3 + 64$
1. $(3x-4)(9x^2 + 12x + 16)$
2. $(3x + 4)(9x^2 - 12x + 16)$
3. $(3x+4)(9x^2 + 12x + 16)$
4. $"Can't factor further"$
47.
The sum of the first 10 terms of an arithmetic progression is 40. If the first term is -5, then what is the common difference?
1. -3
2. -1
3. 2
4. 4
48.
Given the geometric series $3 + 6 + 12 + 24 + ...$, find the sum of the first 17 terms.

49.
Write the equation of a circle with a center (3,-2) and a radius of 3.

50.
Identify the following conic: $x^2-4x-4y^2+8y=4$.
1. Parabola
2. Circle
3. Hyperbola
4. Ellipse
You need to be a HelpTeaching.com member to access free printables.


text:
# Finding the sum of series help

I have a question that I am kind of stuck on. I am good with series stuff, but this one kind of threw me off

$$\sum\limits_{n=1}^{\infty} (-9)^nx^n.$$

This is the question and I was supposed to find out the values of where x converges, and I found that out to be from $\frac{-1}{9} < x < \frac{1}{9}$

How can I find the sum of the series for those values of $x$?

-
This is the infinite geometric series $\sum_1^\infty (-9x)^n$. You have probably known this sum for a long time. – André Nicolas Mar 30 '13 at 3:25
yeah but how do i find the sum for those values of x. its not infinty for some reason – MathGeek Mar 30 '13 at 3:27
When $|r|\lt 1$, $a+ar+ar^2+\cdots =\frac{a}{1-r}$. In our case $a=-9x$, $r=-9x$. – André Nicolas Mar 30 '13 at 3:35

Given the closed form of the geometric series: $$\sum_{n=1}^\infty a^n = \frac{a}{1-a}$$

Plug $a = -9x$ to get: $$\sum_{n=1}^\infty (-9)^nx^n = \frac{-9x}{1+9x}$$

-
i dont get it, so is the sum 0? – MathGeek Mar 30 '13 at 3:06
@MathGeek The sum depends on $x$. For example if $x = 1/18$ then the sum is $-1/3$. – Ayman Hourieh Mar 30 '13 at 3:07
but i know my series only converges from -1/9 to 1/9 is my x 1/9 then ? :s – MathGeek Mar 30 '13 at 3:08
@MathGeek $x$ can take any value in $(-1/9, 1/9)$. The sum is a function of $x$. You cannot give a fixed number as the sum for all values of $x$. – Ayman Hourieh Mar 30 '13 at 3:11
if i integrate from -1/9 to 1/9 i get it does not exist :s – MathGeek Mar 30 '13 at 3:19

To compute the interval of convergence for a power series $\sum a^n x^n$, compute $$\lim_{n\to \infty} \sqrt[\large n]{|a_n|} = \lim_{n\to\infty} \sqrt[\large n]{9^n}$$

In this case, that gives us $9$, so the radius of convergence is $\dfrac {1}9$ which will converge when $|x| \lt \dfrac 19$

-
yes i understand that i got the answer that it only converges from x betweeen -1/9 t0 1/9 but i dont get the next question "Find the sum of the series for those values of x" – MathGeek Mar 30 '13 at 3:16
I think you mean the interval of convergence is $|x|<1/9$. – Alex Becker Mar 30 '13 at 3:17
but how do i find the sum of the series now thats my main question. i know how to get the interval of convergence – MathGeek Mar 30 '13 at 3:18
Perhaps you need to take twice the integral from $0$ to $1/9$ of $$\frac{-9x}{1 + 9x}$$, which is $\dfrac 29 (\ln(2) - 1)$ – amWhy Mar 30 '13 at 3:34


text:
MathSciNet bibliographic data MR1680286 (2000a:93041) 93B36 (93C57) Qiu, Li; Chen, Tongwen Multirate sampled-data systems: all ${\scr H}\sb \infty$${\scr H}\sb \infty$ suboptimal controllers and the minimum entropy controller. IEEE Trans. Automat. Control 44 (1999), no. 3, 537–550. Article

For users without a MathSciNet license , Relay Station allows linking from MR numbers in online mathematical literature directly to electronic journals and original articles. Subscribers receive the added value of full MathSciNet reviews.

 American Mathematical Society 201 Charles Street Providence, RI 02904-6248 USA


text:
# Inching towards Definite Integral

In a blog titled “Introducing Lady L“, we showed that

$\lim\limits_{h \to 0} {{log(x+h) - log(x)} \over h} = {1 \over x}\quad\quad\quad(1)$

In light of the fact that $1 \over x$ is a monotonic function on $R^+$, i.e.,

$\forall x_1, x_2\in R^+, x_1 < x_2 \implies {1 \over x_1} > {1 \over x_2}$,

we can prove that

Let $F(x) = \int\limits_{a}^{x} f(t)\;dt, t \in [a, b], \forall x \in [a, b], f(x)$ is continuous and monotonic $\implies {\lim\limits_{h \to 0}{ {F(x+h) - F(x)} \over h } }= f(x)\quad\quad\quad(2)$

The proof is simple, rigorous and similar to what we have done in “Introducing Lady L“.

Let $f(x)$ be a monotonically increasing function,

$h > 0 \implies \forall t \in (x, x+h), f(x) < f(t) < f(x+h)$.

and

$h\cdot f(x) < \int\limits_{x}^{x+h} f(t)\;dt < h\cdot f(x+h)$.

Since

$\int\limits_{x}^{x+h} f(x)\; dx = \int\limits_{x}^{a} f(t)\;dt + \int\limits_{a}^{x+h}f(t)\;dt$

$= \int\limits_{a}^{x+h}f(x)\;dx - \int\limits_{a}^{x}f(t)\;dt$

$= F(x+h)- F(x)\quad\quad\quad(3)$

It follows that

$f(x) < {{F(x+h) - F(x)} \over {h}} < f(x+h)$.

The fact that $f(x)$ is continuous tells us

$\lim\limits_{h \to 0} f(x + h) = f(x + 0) = f(x)$.

In addition,

$\lim\limits_{h \to 0} f(x) = f(x)$.

Therefore,

$\lim\limits_{h \to 0} {{F(x+h) - F(x) } \over {h} }= f(x)$.

The case for $h < 0$ can be handled in a similar fashion.

(2) becomes more general when the condition of $f(x)$ being a monotonic function is removed:

Let $F(x) = \int\limits_{a}^{x} f(t)\;dt, t \in [a, b], \forall x \in [a, b], f(x)$ is continuous $\implies {\lim\limits_{h \to 0}{ {F(x+h) - F(x)} \over h } }= f(x)\quad\quad\quad(4)$

Let’s prove it.

By definition, $f(x)$ is continuous at $x$ means

$\forall \epsilon > 0, \exists \delta \ni 0 <|t - x| <\delta \implies |f(t)-f(x)| < \epsilon$.

It implies $-\epsilon < f(t)-f(x) < \epsilon$.

For $h > 0$, we have

$\int\limits_{x}^{x+h} -\epsilon \;dt < \int\limits_{x}^{x+h} {f(t)-f(x)}\;dt < \int\limits_{x}^{x+h} \epsilon\;dt$

That is

$-\epsilon \int\limits_{x}^{x+h}\;dt < \int\limits_{x}^{x+h}f(t)\;dt - \int\limits_{x}^{x+h}f(x)\;dt < \epsilon \int\limits_{x}^{x+h}\;dt$

Since $\int\limits_{x}^{x+h}\;dt = h, \int\limits_{x}^{x+h}f(x)\;dt = f(x)\cdot\int\limits_{x}^{x+h}\;dt = h \cdot f(x)$,

it follows that $-h\cdot\epsilon < \int\limits_{x}^{x+h} f(t)\;dt -h\cdot f(x) < h \cdot\epsilon$

or, $-\epsilon < { \int\limits_{x}^{x+h} f(t)\;dt \over h }- f(x) < \epsilon$

By (3), we have $-\epsilon < { {F(x+h)-F(x)} \over h }- f(x) < \epsilon$

i.e., $|{{F(x+h)-F(x)} \over h}- f(x)|< \epsilon$

As a result,

${\lim\limits_{h \to 0}{ {F(x+h) - F(x)} \over h } }= f(x)$.

For $h < 0$, since $x+h < x$,

$\int\limits_{x+h}^{x} -\epsilon\;dt < \int\limits_{x+h}^{x}{f(t)-f(x)}\;dt < \int\limits_{x+h}^{x}\epsilon\;dt$.

That is $h\cdot\epsilon < -\int\limits_{x}^{x+h}f(t)\;dt + h \cdot f(x) < -h\cdot\epsilon$

or, $h\cdot\epsilon < -(\int\limits_{x}^{x+h}f(t)\;dt - h \cdot f(x)) < -h\cdot\epsilon$

Divide $-h\;(h < 0 \implies -h >0)$ throughout, and express $\int\limits_{x}^{x+h}f(t)\;dt$ as $F(x+h)-F(x)$, we arrived at

$-\epsilon < { {F(x+h)-F(x)} \over h }- f(x) < \epsilon$

as before.

We are now poised to define the derivative of a function:

Let $f$ be a function on an opensubset $I$ of $R$. Let $x \in I$. We say that $f$ is differentiable at $x$ if

$\lim\limits_{h \to 0}{ {f(x+h) - f(x)} \over h }\quad\quad\quad(5)$

exists. If exists, this limit, commonly denoted by $f'(x)$ or ${d \over dx} f(x)$, is called the derivative of $f$ at $x$.

For function $f_1(x) - f_2(x)$, the difference of two differentiable functions,

${{f_1(x+h)-f_2(x+h) - (f_1(x)-f_2(x))} \over h }= {{f_1(x+h) - f_2(x)} \over h}- {{f_1(x) - f_2(x)} \over h}$.

By definition,

${d \over dx} (f_1(x) - f_2(x)) = \lim\limits_{h \to 0}{{f_1(x+h)-f_2(x+h) - (f_1(x)-f_2(x))} \over h }$

${d \over dx} f_1(x) = \lim\limits_{h \to 0}{{f_1(x+h) - f_1(x)} \over h}$

${d \over dx} f_2(x) = \lim\limits_{h \to 0}{{f_2(x+h) - f_2(x)} \over h}$

We have

$\lim\limits_{h \to 0}{{f_1(x+h)-f_2(x+h) - (f_1(x)-f_2(x))} \over h }=\lim\limits_{h \to 0}{{f_1(x+h) - f_1(x)} \over h}-\lim\limits_{h \to 0}{{f_2(x+h) - f_2(x)} \over h}$

or,

${d \over dx} (f_1(x) - f_2(x)) = {d \over dx} f_1(x) - {d \over dx} f_2(x)\quad\quad\quad(6)$

With this definition, we can also re-state (4) as:

Let $F(x) = \int\limits_{a}^{x} f(t)\;dt, t \in [a, b], \forall x \in [a, b], f(x)$ is continuous $\implies {d \over dx} F(x)= f(x)\quad(7)$

From (7), it is clear that $F(x) = \int_{a}^{x} f(x)\;dx$ is a solution of the following equation:

${d \over dx} y(x) = f(x)\quad\quad\quad(8)$

where $y(x)$ is the unknown function.

In fact, for any function $g(x)$ that satisfies (8), we have

${d \over dx} F(x) = {d \over dx} g(x) = f(x)$.

Therefore by (6),

${d \over dx} (F(x) - g(x)) = {d \over dx} F(x) - {d \over dx} g(x) = f(x) - f(x) = 0\quad\quad\quad(9)$

That is,  $F(x) - g(x)$ is a function whose derivative is everywhere zero.

Geometrically, if the curve of a function is horizontally directed at every point, it represents a constant function.

It is even more obvious if one considers a function $f(t)$ that describes the position (on some axis) of a car at time $t$. Then the derivative of the function, $\lim\limits_{\Delta t \to 0} {{f(t+{\Delta t}) -f(t)}\over {\Delta t}}$ is the instantaneous velocity of the car. If the derivative is zero for some time interval (the car does not move) then the value of the function is constant (the car stays where it is).

Hence, we assert

A function $f(x)$ on an open interval $I$ has derivative zero at each point $\implies \forall x \in I, f(x) = c$, a constant.

From (9) and above assertion, whose rigorous proof we postpone until later in “Sprint to FTC“, it follows that

$F(x) - g(x) = c$

or,

$F(x) = \int\limits_{a}^{x} f(x)\;dx = g(x) + c\quad\quad\quad(10)$

where c is a constant.

We know

$\int\limits_{a}^{a} f(x)\;dx = 0$.

It implies

$\int\limits_{a}^{a} f(t)\;dt = g(a) + c = 0$.

i.e.,

$c = -g(a)$

and, (10) becomes

$\int\limits_{a}^{x} f(t)\;dt = g(x) - g(a)$

Let $x=b$, we have

$\int\limits_{a}^{b} f(x)\;dx = g(b) - g(a)$

This is the well known Newton-Leibniz formula. It expresses an algorithm for evaluating the definite integral $\int_{a}^{b} f(x)\;dx$:

Find any function $g(x)$ whose derivative is $f(x)$, and the difference $g(b)-g(a)$ gives the answer.


text:
Bounds for the milnor number of a hypersurface singularity

I am having a hard time in finding an upper bound in terms of the degree and the dimension for the Milnor number of an isolated hypersurface singularity. I am mostly interested in surfaces on the projective space. Can some one please give me a hint on this?

Thanks!

-
An upper bound in terms of the degree and dimension? –  Will Sawin Apr 8 at 22:33
I think the sum of all the Milnor numbers of a hypersurface with only isolated singularities, is the difference between the euler characteristic of the singular hypersurface, and the euler charac. of a smooth hypersurface of the same degree. does that help. It should probably give as upper bound the euler charac. of a smooth one, at least in odd dimensional projective space. e.g. in P^3 a normal cubic hypersurface might have say 9 (or even 7) as an upper bound on the Milnor number of an isolated singularity. does this seem right? just tossing this out for comment since no responses yet. –  roy smith Apr 9 at 23:41
well you can use the Lefschetz hyperplane theorem to compute cohomology away from middle degree. You can use the top chern class of the tangent bundle to compute the Euler characteristic of the smooth one, and thereby compute its cohomology in the middle degree. The difference will be the Milnor number. As far as I can tell, you don't have any reason to suspect a lower bound for the cohomology of the singular one much better than $0$ in odd dimension and $1$ in even dimension. –  Will Sawin Apr 11 at 15:44


text: • Abstract: We present a systematic framework for the Nesterov's accelerated gradient flows in the spaces of probabilities embedded with information metrics. Here two metrics are considered, including both the Fisher-Rao metric and the Wasserstein-$2$ metric. For the Wasserstein-$2$ metric case, we prove the convergence properties of the accelerated gradient flows, and introduce their formulations in Gaussian families. Furthermore, we propose a practical discrete-time algorithm in particle implementations with an adaptive restart technique. We formulate a novel bandwidth selection method, which learns the Wasserstein-$2$ gradient direction from Brownian-motion samples. Experimental results including Bayesian inference show the strength of the current method compared with the state-of-the-art.


text:
# Distributed Mixed-Integer Programming (MIP) optimization with Cplex and Gurobi

Cplex is an optimization software for mathematical programming. The Cplex optimizer can solve:

• Mixed-Integer programming problems (MIP)
• Very large linear programming problems (LP)
• Non-convex quadratic programming problems (QP)
• Convex quadratically constrained problems (QCP)

Gurobi is a powerful optimization software and an alternative to Cplex for solving. Gurobi has some additionnal features compared to Cplex. For example, it can perform Mixed-Integer Quadratic Programming (MIQP) and Mixed-Integer Quadratic Constrained Programming (MIQCP).

In this tutorial, we are going to see how to leverage distributed optimization on a High Computing Platform such as Slurm.

## Mathematical programming

Decision and optimization problems can be representend as mathematical models called programs.

It exists several formats used by Cplex and Gurobi to provide your problems to these solvers:

## Using both optimization software on the ULHPC platform

The cplex optimizer can be accessed throught the module command once ressources have been requested through the SLURM scheduler.

module load math/CPLEX/12.8-foss-2018a

The Gurobi optimizer can be accessed throught the module command once ressources have been requested through the SLURM scheduler.

module load math/Gurobi/8.1.1-intel-2018a-Python-3.6.4

The resolution of optmization problem can be either done using the command line interface (CLI) or by using the different APis (e.g. C/C++, Python, Java). In this tutorial, we only consider the CLI for each optimizer.

## Ressources for this tutorial

In order to test cplex and gurobi, we need an optimization instance. Hereafter, we are going to rely on instances from the miplib. For example, let us the following instance ex10.mps.gz described in details here for the interested readers.

If you did not already clone the tutorial repository, enter the following commands in your HOME directory:

# cd into scratch and clone tutorial repository
cd $SCRATCH git clone https://github.com/ULHPC/tutorials.git # cd into the scripts folder cd tutorials/maths/Cplex-Gurobi/scripts  ## Cplex ### Multi-threaded optimization with Cplex In order to solve mathematical programs, cplex allows users to define a command line script that can be passed to the executable. On the Iris cluster, the following launcher can be used to perform multi-threaded MIP optimzation. A good practice is to request as many threads as available cores on the node. If you need more computing power, you have to consider a distributed version. #!/bin/bash -l #SBATCH -J Multi-threaded_cplex #SBATCH --ntasks=1 #SBATCH --cpus-per-task=28 #SBATCH --time=0-01:00:00 #SBATCH -p batch #SBATCH --qos=normal # Load cplex module load math/CPLEX/12.8-foss-2018a # Some variable MPS_FILE=$1
RES_FILE=$2 CPLEX_COMMAND_SCRIPT="command_job${SLURM_JOBID}.lst"

# Create cplex command script
cat << EOF > ${CPLEX_COMMAND_SCRIPT} set threads${SLURM_CPUS_PER_TASK}
read ${MPS_FILE} mipopt write "${RES_FILE}.sol"
quit
EOF
chmod +x ${CPLEX_COMMAND_SCRIPT} # Cplex will access use the required number of thread cplex -f${CPLEX_COMMAND_SCRIPT}
rm ${CPLEX_COMMAND_SCRIPT}  Use the script cplex_mtt.slurm and launch a batch job using the sbatch command as follows sbatch cplex_mtt.slurm ex10.mps.gz cplex_mtt. ### Distributed optimization with Cplex When you require more computing power (e.g. more cores), distributed computations is the way to go. The cplex optimization software embeds a feature that allows you to perform distributed MIP. Using the Message Passing Interface (MPI), cplex will distribute the exploration of the tree search to multiple workers. The below launcher is an example showing how to reserve ressources on multiple nodes through the Slurm scheduler. In this example, 31 tasks will be distributed over 2 nodes. #!/bin/bash -l #SBATCH -J Distrbuted_cplex #SBATCH --nodes=2 #SBATCH --ntasks=14 #SBACTH --cpus-per-task=2 #SBATCH --time=0-01:00:00 #SBATCH -p batch #SBATCH --qos=normal module load math/CPLEX/12.8-foss-2018a # Some variables MPS_FILE=$1
RES_FILE=$2 CPLEX_COMMAND_SCRIPT="command_job${SLURM_JOBID}.lst"

# Create cplex command script
cat << EOF > ${CPLEX_COMMAND_SCRIPT} set distmip config mpi set threads${SLURM_CPUS_PER_TASK}
read ${MPS_FILE} mipopt write "${RES_FILE}.sol"
quit
EOF
chmod +x ${CPLEX_COMMAND_SCRIPT} # Start Cplex with MPI # On first host, the master is running mpirun -np 1 cplex -f${CPLEX_COMMAND_SCRIPT} -mpi : -np $((SLURM_NTASKS - 1)) cplex -mpi rm${CPLEX_COMMAND_SCRIPT}

Use the script cplex_dist.slurm and launch a batch job using the sbatch command as follows sbatch cplex_dist.slurm ex10.mps.gz cplex_dist.

## Gurobi

The script below allows you to start multi-threaded MIP optimization with Gurobi.

#!/bin/bash -l
#SBATCH --time=0-01:00:00
#SBATCH -p batch
#SBATCH --qos=normal

# Some variable
MPS_FILE=$1 RES_FILE=$2

# Gurobi will access use the required number of thread
gurobi_cl Threads=${SLURM_CPUS_PER_TASK} ResultFile="${RES_FILE}.sol" ${MPS_FILE}  Use the script gurobi_mtt.slurm and launch a batch job using the sbatch command as follows sbatch gurobi_mtt.slurm ex10.mps.gz gurobi_mtt. ### Distributed optimization with Gurobi #!/bin/bash -l #SBATCH -J Distrbuted_gurobi #SBATCH --ntasks=3 #SBATCH --ntasks-per-node=1 #SBATCH --cpus-per-task=5 #SBATCH --time=00:15:00 #SBATCH -p batch #SBATCH --qos normal #SBATCH -o %x-%j.log # Load personal modules mu # Load gurobi module load math/Gurobi/8.1.1-intel-2018a-Python-3.6.4 export MASTER_PORT=61000 export SLAVE_PORT=61000 export MPS_FILE=$1
export RES_FILE=$2 export GUROBI_INNER_LAUNCHER="inner_job${SLURM_JOBID}.sh"

if [[ -f "grb_rs.cnf" ]];then
sed -i "s/^THREADLIMIT.*$/THREADLIMIT=${SLURM_CPUS_PER_TASK}/g" grb_rs.cnf
else
$GUROBI_REMOTE_BIN_PATH/grb_rs init echo "THREADLIMIT=${SLURM_CPUS_PER_TASK}" >> grb_rs.cnf
fi

cat << 'EOF' > ${GUROBI_INNER_LAUNCHER} #!/bin/bash MASTER_NODE=$(scontrol show hostname ${SLURM_NODELIST} | head -n 1) ## Load configuration and environment if [[${SLURM_PROCID} -eq 0 ]]; then
## Start Gurobi master worker in background
$GUROBI_REMOTE_BIN_PATH/grb_rs --worker --port${MASTER_PORT} &
wait
elif [[ ${SLURM_PROCID} -eq 1 ]]; then sleep 5 grbcluster nodes --server${MASTER_NODE}:${MASTER_PORT} gurobi_cl Threads=${SLURM_CPUS_PER_TASK} ResultFile="${RES_FILE}.sol" Workerpool=${MASTER_NODE}:${MASTER_PORT} DistributedMIPJobs=$((SLURM_NNODES -1)) ${MPS_FILE} else sleep 2 ## Start Gurobi slave worker in background$GUROBI_REMOTE_BIN_PATH/grb_rs --worker --port ${MASTER_PORT} --join${MASTER_NODE}:${MASTER_PORT} & wait fi EOF chmod +x${GUROBI_INNER_LAUNCHER}

## Launch Gurobi and wait for it to start
srun ${GUROBI_INNER_LAUNCHER} & while [[ ! -e "${RES_FILE}.sol" ]]; do
sleep 5
done
rm \${GUROBI_INNER_LAUNCHER}

Use the script gurobi_dist.slurm and launch a batch job using the sbatch command as follows sbatch gurobi_dist.slurm ex10.mps.gz gurobi_dist.

## Next

1. Download and try to solve other miplib instances using Cplex and/or Gurobi
2. Modify the number of parallel tasks


text:
### On the Role of Scheduling in Simulation-Based Security

Ran Canetti, Ling Cheung, Nancy Lynch, and Olivier Pereira

##### Abstract

In a series of papers, Küsters et al. investigated the relationships between various notions of simulation-based security. Two main factors, the placement of a master process'' and the existence of forwarder processes'', were found to affect the relationship between different definitions. In this extended abstract, we add a new dimension to the analysis of simulation-based security, namely, the scheduling of concurrent processes. We show that, when we move from sequential scheduling (as used in previous studies) to task-based nondeterministic scheduling, the same syntactic definition of security gives rise to incomparable semantic notions of security. Under task-based scheduling, the hierarchy based on placement of master process'' is no longer relevant, because no such designation is necessary to obtain meaningful runs of a system. On the other hand, the existence of forwarder processes'' remains an important factor.

Available format(s)
Category
Foundations
Publication info
Published elsewhere. Presented at WITS'07
Keywords
simulation-based securitysequential and non-sequential scheduling
Contact author(s)
lcheung @ theory csail mit edu
History
Short URL
https://ia.cr/2007/102

CC BY

BibTeX

@misc{cryptoeprint:2007/102,
author = {Ran Canetti and Ling Cheung and Nancy Lynch and Olivier Pereira},
title = {On the Role of Scheduling in Simulation-Based Security},
howpublished = {Cryptology ePrint Archive, Paper 2007/102},
year = {2007},
note = {\url{https://eprint.iacr.org/2007/102}},
url = {https://eprint.iacr.org/2007/102}
}

Note: In order to protect the privacy of readers, eprint.iacr.org does not use cookies or embedded third party content.