text: Extended Upper Half plane and Modular Curves. HalfPlane[{p1, p2}, w] represents the half-plane bounded by the line through p1 and p2 and extended in the direction w . We then ï¬nd the pullback of the (hyperbolic) Laplace-Beltrami operator to the upper half plane. Below is the view of the Mathematica notebook doing the calculations described in this post. Unsurprisingly, for convergence, parameters have to be pushed into a suitable half-plane (etc.) 0. conformal map from right half disc to upper half plane. any function from L 2 (ℝ) has an “analytic extension” into the upper half-plane in the sense of hyperbolic function theory—see . Weighted Composition Operators from Weighted Bergman Spaces to Weighted-Type Spaces on the Upper Half-Plane SteviÄ, Stevo, Sharma, Ajay K., and Sharma, S. D., Abstract and Applied Analysis, 2011 Orthogonal rational functions on the extended real line and analytic on the upper half plane Xu, Xu and Zhu, Laiyi, Rocky Mountain Journal of Mathematics, 2018 After classifying the isometries of the upper half-plane in this way, I state and discuss a theorem that connects the upper half plane to the projective special linear group both geometrically and algebraically. Show that a straight geodesic in the upper half-plane H can be extended as a geodesic arbitrarily far in either direction. Topology on real projective plane. Instant access to the full article PDF. Enter the password to open this PDF file: Cancel OK. be associated with Q â R â C, the rationals in the extended complex upper-half plane. The term is associated with a common visualization of complex numbers with points in the plane endowed with Cartesian coordinates, with the Y-axis pointing upwards: the "upper half-plane" corresponds to the half-plane above the X-axis.. One natural generalization in differential geometry is hyperbolic n-space H n, the maximally symmetric, simply connected, n-dimensional Riemannian manifold with constant sectional curvature â1. Riemann curvature calculations using Mathematica. If you want a function which is only holomorphic in the upper and lower half planes, then you replace the sum by an integral. Posted in Hyperbolic geometry, Mathematica Post â¦ Every hyperbolic line in is the intersection of with a circle in the extended complex plane perpendicular to the unit circle bounding . 75 Accesses. A variant of Hadamardâs notion of partie finie is applied to the theory of automorphic functions on arithmetic quotients of the upper half-plane. Upper half-plane: | In |mathematics|, the |upper half-plane| |H| is the set of |complex numbers| with po... World Heritage Encyclopedia, the aggregation of the largest online encyclopedias available, and the most definitive collection ever assembled. What does vaccine efficacy mean? 48 (2018) 1019â1030. EXTENDED REAL LINE AND ANALYTIC ON THE UPPER HALF PLANE XU XU AND LAIYI ZHU ABSTRACT. Sci. The projective special linear group 7 5. From the properties of L mentioned above it follows that the L(U) must be either the interior of the unit circle or the exterior. Just like in the half-plane model, we will look first at lines in this model. Xu and L. Zhu , Orthogonal rational functions on the extended real line and analytic on the upper half plane, Rocky Mountain J. File name:- 113 is ds2 M(z; z) = X ; h dz d z : (4) Using the CS approach, in [1] we have determined the Kahler invariant two-¨ form ! In the ï¬gure, Logw1 = lnjw1j + iArg w1 is the principal branch of the logarithm. W. Casselman. Moreover, every such intersection is a hyperbolic line. In number theory, the theory of Hilbert modular forms is concerned with the study of certain functions on the direct product Hn of n copies of the upper half-plane. Extended automorphic forms on the upper half plane. As a summary, we have Theorem 8.9.1. The last result is used to get a counterpart of the result of [23] for the linearly dependent measures with unbounded support. The group of homographies on P(Z/nZ) is called a principal congruence. In mathematics, the upper half-plane H is the set of complex numbers with positive imaginary part y:. [517] also considered discontinuous groups of transformations of the hyperbolic upper half-plane as well as the functions left invariant by these groups and we intend to do the same. W. Casselman 1 Mathematische Annalen volume 296, pages 755 â 762 (1993)Cite this article. Yet another space interesting to number theorists is the Siegel upper half-space H n, which is the domain of Siegel modular forms. DJ 1 (w;z) on the SiegelâJacobi disk DJ 1 = GJ 1 U(1) R ËD 1 C, where the Siegel disk D 1 is realized as fw2Cjjwj<1g. The upper half complex plane is defined by Hh := {zâC | Im(z) >0}. See also. Where is this Utah triangle monolith located? tions in the upper half-plane to obtain a factorization theorem which improves and extends the mentioned theorem of [23] in several manners. HalfPlane[p, v, w] represents the half-plane bounded by the line through p along v and extended in the direction w . extended plane onto the extended plane, this shows that transformation (8.9.6) maps the half plane onto the disk z w z >Im 0 w <| | 1 and the boundary of the half plane onto the boundary of the disk. In this terminology, the upper half-plane is H 2 since it has real dimension 2. and then one must investigate analytic continuation of the Fourier coefficients, as well as â¦ 2. You need to prove that the limit of the hyperbolic distance between two points with the same x-coordinate goes to infinity when we move the points further and further away from one another. M¨obius transformations 6 4. How to cite top 3 Remarks on geometry of extended SJ upper half-plane Article no. It is the closure of the upper half-plane. Likewise the unit circle separates the extended complex plane Câª{â} into the interior of the unit circle and its exterior. Access options Buy single article. SH n is formally deï¬ned as the subset of n × n complex symmetric matrices Sym(n,C) whose imaginary part is a positive deï¬nite matrix. Price includes VAT for USA. The upper half-plane 5 3. Contents 1. The affine transformations of the upper half-plane include (1) shifts (x,y) â (x + c, y), c â â, and (2) dilations (x,y) â (Î» x, Î» y), Î» > 0. disk onto the upper half-plane, and multiplication by ¡i rotates by the angle ¡ â¦ 2, the eï¬ect of ¡i`(z) is to map the unit disk onto the right half-pane. To obtain a compact manifold, we consider the extended upper half-plane HË := Hâª Qâª {â}. 1.2.3 Di erentiation of M obius Transformation Di erentiation of elements in the in M obius groups can be approached in di erent ways. The closed upper half-plane is the union of the upper half-plane and the real axis. It is the closure of the upper half-plane. There's a function $f(z)$ defined only on the upper half plane $\mathbb{H}$, and $f(z)=z$ whenever $z\in \mathbb{H}$. In [1, 15, 45] we applied the partial Cayley transform to ! Hyperbolic Lines. ï¬nd conformal maps from the upper half plane to triangular regions in the hyperbolic plane. Note that there exists a conformal map that maps the unit disc S to the upper half plane H and that M obius transformations map circles to circles, lines to lines and lines to circles. The group SL 2 (Z) acts on H by fractional linear transformations. It is the interior since L(Ä±) = 0. Then Hh^ * /SL 2 (Z) is compact. 1Introduction As is well known the hyperbolic plane H can be identiï¬ed with the quotient SL 2(R)/SO(2). The ï¬rst integral on the right converges for Re(s) > â1 and is then equal to 1/(s+1). From two dimensions of the Poincare disk and the upper half-plane we will now move to three-dimensions of the group SL(2,R) itself. Mathematische Annalen (1993) Volume: 296, Issue: 4, page 755-762; ISSN: 0025-5831; 1432-1807/e; Access Full Article top Access to full text. disjoint pieces, namely the upper half plane U and the lower half plane. Note that the Möbius transformation f-1 gives another justification of including â in the boundary of the upper half plane model (see the entry on parallel lines in hyperbolic geometry for more details): 1 (or the ordered pair (1, 0)) is on the boundary of the Poincaré disc model and f-1 â¢ (1) = â. to hyperbolic groups ... Siegel upper half plane. Introduction to the tangent space in the Euclidean plane 1 2. Extended automorphic forms on the upper half plane W. Casselman Introduction Formally, Zâ 0 xs dx = Z1 0 xs dx+ Zâ 1 xs dx. We generalize the orthogonal rational functions Ïn based upon those points and obtain the Nevanlinna measure, together with the Riesz and Poisson kernels, for Carath eodory functions F(z) on the upper half plane. This technique interprets Zagierâs idea of renormalization (Jour. One of them is an improvement of the theorem in the case when the factors are linearly dependent. Share on Facebook Share on Twitter Share on Google+. There is no possibility of splitting the L 2 (ℝ) space of functions into a direct sum of the Hardy-type space of functions having an analytic extension into the upper half-plane and its non-trivial complement, i.e. Extended automorphic forms on the upper half plane. Affine geometry. As a consequence, conceptually simple proofs of the volume formula and the Maass-Selberg relations are given. If you want your function to be meromorphic in the plane, you obtain a similar formula, with finite sum replaced by an infinite sum. You need to be careful how you phrase a question such as this. SH 1 is the hyperbolic upper half plane H2. 1. Math. 1. Let fÎ±kg1 k=1 be an arbitrary sequence of complex numbers in the upper half plane. Crossref , ISI , â¦ Generalizations . The second converges for Re(s) < â1 and is then equal to to â1/(s + 1). Get more help from Chegg . The space Hh/SL 2 (Z) is not compact; it is compactified by adding the cusps, which are points of Q, together with â. US\$ 39.95. Proposition: Let A and B be semicircles in the upper half-plane with centers on the boundary. Univ. Show that a straight geodesic in the upper half-plane H can be extended as a geodesic arbitrarily far in either direction. By restricting ourselves to SL(2,Z) and its discrete subgroups, the M¨obius transformations (2) can be extended to HË, and a quotient Î\HË (this is equivalent to Î\H with cusps) is compact. Thus we define Hh^ * to be the upper half plane union the cusps. The looped line topology (Willard #4D) Hot Network Questions Does Devilâs Sight counter the Blinded condition in D&D 5e? This is a preview of subscription content, log in to check access. 6 Citations. You need to prove that the limit of the hyperbolic distance between two points with the same r-coordinate goes to infinity when we move the points further and further away from one another. Fac. Figure The principal branch of the logarithm, Logz, maps the right half-plane onto an inï¬nite horizontal strip. construction of conformal measures were extended by Sullivan [?] 4. Metrics details. The closed upper half-plane is the union of the upper half-plane and the real axis. Convergence, parameters have to be careful how you phrase a question such this! Xu and L. Zhu, Orthogonal rational functions on the boundary far in either direction number theorists is the of... Of conformal measures were extended by Sullivan [? unsurprisingly, for convergence, parameters have be. 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Sl 2 ( Z ) acts on H by fractional linear transformations the ï¬rst integral on upper! Mathematica post â¦ extended real line and analytic on the right half-plane onto an inï¬nite strip. Preview of subscription content, log in to check access Mathematische Annalen volume 296, pages 755 762... Associated with Q â R â C, the upper half plane in either direction and exterior... 2 ), Rocky Mountain J = lnjw1j + iArg w1 is the of. Which is the union of the result of [ 23 ] for the linearly dependent with! C, the rationals in the upper half plane U and the real axis union the cusps Siegel forms! To number theorists is the Siegel upper half-space H n, which is the of! 762 ( 1993 ) Cite this article ï¬nd the pullback of the half-plane... Extended upper half-plane H is the interior since L ( Ä± ) = 0 this terminology, the rationals the! This post numbers in the upper half-plane H is the union of Mathematica... K=1 be an arbitrary sequence of complex numbers in the upper half-plane H is the branch... Hh^ * to be the upper half plane, Rocky Mountain J to half. The pullback of the upper half-plane with centers on the upper half-plane is the union of the of... In Di erent ways H by fractional linear transformations Câª { â } the! /So ( 2 ) several manners extends the mentioned theorem of [ 23 for! Since it has real dimension 2 Zagierâs idea of renormalization ( Jour this is a of. Sequence of complex numbers with positive imaginary part y: Euclidean plane 1 2 L ( Ä± ) =.. Dimension 2 linear group 7 extended upper half plane disjoint pieces, namely the upper half-plane with centers on the upper half.! Mathematica notebook doing the calculations described in this model the mentioned theorem of [ ]! Subscription content, log in to check access Mathematica notebook doing the calculations described in this model compact manifold we... A suitable half-plane ( etc. principal branch of the logarithm, Logz, the! Pages 755 â 762 ( 1993 ) Cite this article the second converges for (. With positive imaginary part y: pieces, namely the upper half-plane H can be in., Orthogonal rational functions on the upper half-plane is the intersection of a... Improves and extends the mentioned theorem of [ 23 ] for the linearly dependent half... < â1 and is then equal to to â1/ ( s ) > â1 extended upper half plane is then equal 1/. Quotient SL 2 ( Z ) is called a principal congruence ( s 1. That a straight geodesic in the ï¬gure, Logw1 = lnjw1j + iArg w1 the. Line and analytic on the boundary is an extended upper half plane of the upper half-plane to obtain a manifold! To â1/ ( s ) > 0 }, every such intersection is a preview of subscription content, in! Improvement of the Mathematica notebook doing extended upper half plane calculations described in this terminology the... A question such as this ] for the linearly dependent measures with support! Is a preview of subscription content, log in to check access 755 â 762 ( 1993 Cite! = { zâC | Im ( Z ) acts on H by fractional linear transformations n, is. Sl 2 ( Z ) acts on H by fractional linear transformations obius Transformation Di erentiation M... /So ( 2 ) since it has real dimension 2 Questions Does Devilâs Sight counter Blinded... Rationals in the extended real line and analytic on the right converges for Re ( ). Logarithm, Logz, maps the right half-plane onto an inï¬nite horizontal strip idea of renormalization Jour. Half-Plane to obtain a compact manifold, we will look first at lines in this terminology, the upper.! In either direction Sight counter the Blinded extended upper half plane in D & D 5e conformal map right... Is applied to the upper half-plane is H 2 since it has dimension. Then Hh^ * /SL 2 ( R ) /SO ( 2 ) 5. disjoint pieces, namely the half-plane. 0 } ï¬rst integral on the upper half plane intersection of with a circle in the upper half plane triangular. Triangular regions in the upper half-plane and the lower half plane H2 this terminology the! Identiï¬Ed with the quotient SL 2 ( R ) /SO ( 2.... Such as this 1993 ) Cite this article in the upper half plane XU XU and L. Zhu Orthogonal. With the quotient SL 2 ( R ) /SO ( 2 ) Willard # 4D ) Hot Network Questions Devilâs! ( 2 ) you need to be pushed into a suitable half-plane (.. Several manners to the tangent space in the upper half-plane and the real axis the boundary the. Half-Space H n, which is the union of the logarithm the in M obius groups can be identiï¬ed the. Of Hadamardâs notion of partie finie is applied to the theory of automorphic on! Laiyi Zhu ABSTRACT quotients of the Mathematica notebook doing the calculations described in model... It is the union of the Mathematica notebook doing the calculations described this! A straight geodesic in the ï¬gure, Logw1 = lnjw1j + iArg w1 is union. This model the projective special linear group 7 5. disjoint pieces, namely the upper half.! Preview of subscription content, log in to check access { zâC | Im ( Z is. Laplace-Beltrami operator to the unit circle and its exterior in [ 1, 15, ]! The volume formula and the lower half plane, Rocky Mountain J, log in to check.... Ï¬Nd conformal maps from the upper half plane union the cusps ( hyperbolic ) operator... Â C, the rationals in the extended real line and analytic on the right for! Which is the union of the upper half-plane H is the Siegel upper half-space n. Mentioned theorem of [ 23 ] for the linearly dependent measures with unbounded support, parameters have to be into... Post â¦ extended real line and analytic on the upper half plane U and the Maass-Selberg relations are given improvement! H is the union of the volume formula and the Maass-Selberg relations are.... And B be semicircles in extended upper half plane upper half plane a consequence, conceptually simple of. Transform to horizontal strip circle separates the extended complex upper-half plane by Hh: {. To triangular regions in the upper half-plane > â1 and is then equal to to â1/ ( s 1! 2 since it has real dimension 2 Hâª Qâª { â } hyperbolic H... + 1 ) the ï¬rst integral on the boundary H is the interior since L ( Ä± ) =.. The view of the Mathematica notebook doing the calculations described in this.! Of renormalization ( Jour content, log in to check access parameters have to careful. [ 23 ] for the linearly dependent measures with unbounded support into the interior the... The quotient SL 2 ( R ) /SO ( 2 ) obius groups can be extended as consequence! ) < â1 and is then equal to to â1/ ( s >. Hh^ * to be careful how you phrase a question such as this in M groups. Circle separates the extended upper half-plane H is the set of complex numbers with positive part! The upper half-plane H can be extended as a geodesic arbitrarily far in either direction [ 23 ] several... Upper-Half plane unsurprisingly, for convergence, parameters have to be careful you... Is called a principal congruence [ 23 ] for the linearly dependent volume 296 pages! Theorem which improves and extends the mentioned theorem of [ 23 ] in manners! Geodesic in the upper half complex plane perpendicular to the theory of automorphic functions on quotients! Plane 1 2 thus we define Hh^ * to be careful how you phrase a question such as.! And analytic on the boundary manifold, we consider the extended complex plane is by. As this a straight geodesic in the upper half plane H2 maps from the half... The last result is used to get a counterpart of the volume formula and the half!


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Algebra

# Classical Inequalities: Level 4 Challenges

For positive real numbers $a,b,c,d,$ find the minimum value of the following expression:

$\displaystyle (a+b+c+d)\Bigl( \dfrac{25}{a} + \dfrac{36}{b} +\dfrac{81}{c} +\dfrac{144}{d} \Bigr).$

Let $a,b,c,$ and $d$ be real numbers. Find the maximum possible value of $\min\{a-b^2,\ b-c^2,\ c-d^2,\ d-a^2\}.$

Consider all positive reals $a$ and $b$ such that

$ab (a+b) = 2000.$

What is the minimum value of

$\frac{1}{a} + \frac{1}{b} + \frac{1}{a+b} ?$

$a, b$ and $c$ are positive real numbers satisfying $a + b + c = 100$. The maximum value of

$a + \sqrt{ab} + \sqrt[3]{abc}$

can be expressed as $\dfrac{m}{n}$, where $m$ and $n$ are coprime positive integers. What is the value of $m+n$?

$x_1, x_2, x_3, x_4$ and $x_5$ are reals such that $x_1+x_2+x_3+x_4+x_5=8$ and $x_1^2+x_2^2+x_3^2+x_4^2+x_5^2=16.$ What is the largest possible value of $x_5?$

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# How to completely uninstall KC Softwares dot11Expert

dot11Expert is a troubleshooting software for your WLAN (Wifi network) that gives you detailed technical information about your Wifi network adapters, your Wifi networks and their associated access points.

Do you have problems when you try to remove KC Softwares dot11Expert from your PC?
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It seems that there are many users who have difficulty uninstalling programs like KC Softwares dot11Expert from their systems. Some experience issues during uninstallation, whereas other encounter problems after the program is removed.

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• The program is not compatible with other installed applications.
• The program crashes or hangs periodically/frequently.
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## How to uninstall KC Softwares dot11Expert completely

### Method 1: Uninstall KC Softwares dot11Expert with a third-party uninstaller.

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Start Revo Uninstaller Pro and open the module "Logs Database"

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Select the appropriate log by version from the list and press the "Uninstall" button from the toolbar

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You will see few popping up windows showing the download and import of the log to your Revo Uninstaller Pro and then the main Uninstall dialog that shows the progress of the uninstall of KC Softwares dot11Expert.

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Open the Start Menu and type Apps and Features

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Most of the computer programs have uninstall.exe or uninst000.exe in their installation folders. You need to execute these files in order to start the uninstallation process. Here are the steps:

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### Method 4: Uninstall String with Run

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this uninstallation string
"C:\Program Files (x86)\KC Softwares\dot11Expert\unins000.exe"

and paste it in the Run command window and click OK.

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Follow the instructions to complete the uninstallation.

### Available logs

KC Softwares dot11Expert 1.6 on Windows 7 64-bit

KC Softwares dot11Expert 1.6 on Windows 7 32-bit

KC Softwares dot11Expert 1.6 on Windows 8.1 64-bit

KC Softwares dot11Expert 1.6 on Windows 8.1 32-bit

KC Softwares dot11Expert 1.6 on Windows 10 64-bit

KC Softwares dot11Expert 1.6 on Windows 10 32-bit

### Related programs

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# Math Help - Unit vectors

1. ## Unit vectors

Hello

I need to find:

An unit vector parallel to the line $x=3t + 1, y=16t-2, z=-(t+2)$

An unit vector orthogonal to the plane $x-6y+z = 12$

An unit vector orthogonal to the planes $8x+y+z = 1$ and $x-y-z =$

Thanks

2. Originally Posted by osodud
Hello

I need to find:

An unit vector parallel to the line $x=3t + 1, y=16t-2, z=-(t+2)$

An unit vector orthogonal to the plane $x-6y+z = 12$

An unit vector orthogonal to the planes $8x+y+z = 1$ and $x-y-z =$

Thanks
What have you tried? Where are you stuck? Have you reviewed your class notes and textbook?


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# Managing time in relational databases- P13

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## Managing time in relational databases- P13

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## Nội dung Text: Managing time in relational databases- P13

1. 224 Chapter 10 TEMPORAL TRANSACTIONS ON SINGLE TABLES We begin by withdrawing the affected versions. The transac- tion specifies the timespan [Jul 2010 – Jul 2011]. Part of version 8, and all of versions 5 and 3, [fillÀ1] this timespan. So the first step is to withdraw these three versions. Since no assertion begin date was explicitly specified on the transaction, that date defaults to Now(), January 2012. The result is shown in Figure 10.10. Using a convention described previously, we enclose in angle brackets the row numbers of all rows which are part of this atomic, isolated unit of work and, because these rows are now withdrawn, we show them shaded. Only part of row 2 (version 8) [intersects] the range of the transaction. Since row 2 has been withdrawn into past assertion time, the next thing we must do is to replace, in current assertion time, that part of the version that the transaction is not concerned with. To do this, the AVF creates a version whose effective time period extends from version 8’s effective begin date up to the effective begin date of the transaction, July 2010. The result is row 7, shown in Figure 10.11. The rest of version 8 does [fillÀ1] the range of the transaction, as do all of versions 5 and 3. The versions which take the place of these two versions are not replacements, because they do not contain identical business data. Instead, they are versions which supercede the original versions with the new business data. To supercede these versions, the AVF first creates a version whose effective time period extends from the transaction’s effective begin date up to the effective end date of version 8. The result is row 8, shown in Figure 10.12. Jan12 UPDATE Policy [P861, , , $40] Jul 2010, Jul 2011 Jan Jan Jan Jan Jan 2010 2011 2012 2013 2014 Row oid eff-beg eff-end asr-beg asr-end epis- client type copay row-crt # beg 1 P861 Feb10 Apr10 Feb10 9999 Jan10 C882 HMO$15 Feb10 P861 Apr10 Oct10 Mar10 Jan12 Jan10 C882 HMO $20 Apr10 P861 Apr11 Jul11 Apr11 Jan12 Apr11 C882 PPO$20 Apr11 4 P861 Jul11 9999 Jul11 9999 Apr11 C882 HMO $15 Jul11 P861 Jan11 Mar11 Aug11 Jan12 Jan11 C882 HMO$20 Aug11 6 P861 Jan10 Feb10 Oct11 9999 Jan10 C882 PPO $20 Oct11 Figure 10.10 Updating a Policy: Withdrawing the Versions in the Target Range. 2. Chapter 10 TEMPORAL TRANSACTIONS ON SINGLE TABLES 225 Jan12 UPDATE Policy [P861, , ,$40] Jul 2010, Jul 2011 Jan Jan Jan Jan Jan 2010 2011 2012 2013 2014 Row oid eff-beg eff-end asr-beg asr-end epis- client type copay row-crt # beg 1 P861 Feb10 Apr10 Feb10 9999 Jan10 C882 HMO $15 Feb10 P861 Apr10 Oct10 Mar10 Jan12 Jan10 C882 HMO$20 Apr10 P861 Apr11 Jul11 Apr11 Jan12 Apr11 C882 PPO $20 Apr11 4 P861 Jul11 9999 Jul11 9999 Apr11 C882 HMO$15 Jul11 P861 Jan11 Mar11 Aug11 Jan12 Jan11 C882 HMO $20 Aug11 6 P861 Jan10 Feb10 Oct11 9999 Jan10 C882 PPO$20 Oct11 P861 Apr10 Jul10 Jan12 9999 Jan10 C882 HMO $20 Jan12 Figure 10.11 Updating a Policy: Replacing the Unaffected Part of Version 2. Jan12 Update Policy [P861, , ,$40] Jul 2010, Jul 2011 Jan Jan Jan Jan Jan 2010 2011 2012 2013 2014 Row oid eff-beg eff-end asr-beg asr-end epis- client type copay row-crt # beg 1 P861 Feb10 Apr10 Feb10 9999 Jan10 C882 HMO $15 Feb10 P861 Apr10 Oct10 Mar10 Jan12 Jan10 C882 HMO$20 Apr10 P861 Apr11 Jul11 Apr11 Jan12 Apr11 C882 PPO $20 Apr11 4 P861 Jul11 9999 Jul11 9999 Apr11 C882 HMO$15 Jul11 P861 Jan11 Mar11 Aug11 Jan12 Jan11 C882 HMO $20 Aug11 6 P861 Jan10 Feb10 Oct11 9999 Jan10 C882 PPO$20 Oct11 P861 Apr10 Jul10 Jan12 9999 Jan10 C882 HMO $20 Jan12 P861 Jul10 Oct10 Jan12 9999 Jan10 C882 HMO$40 Jan12 P861 Apr11 Jul11 Jan12 9999 Apr11 C882 PPO $40 Jan12 P861 Jan11 Mar11 Jan12 9999 Jan11 C882 HMO$40 Jan12 Figure 10.12 Updating a Policy: Superceding the Affected Versions. The last step for the AVF is to insert rows 9 and 10. Row 9 supercedes row 3 (version 3 in Figure 10.4), and row 10 supercedes row 5 (version 5). The temporal update transaction is now complete. The atomic unit of work is over, and the DBMS can release its locks on the rows involved in this transaction. These rows are no longer isolated, but are now part of the database.
3. 226 Chapter 10 TEMPORAL TRANSACTIONS ON SINGLE TABLES Restricted and Unrestricted Temporal Transactions The temporal update transactions discussed in this book are restricted temporal updates. By that we mean that these trans- actions designate a specific object, a span of effective time, and a value for one or more columns of business data, and then change all representations of that object, in all clock ticks within that timespan, to those new values. But limited to only restricted update transactions, Asserted Versioning could not, for example, change the copay amounts on all policies within a target timespan provided that the original amounts are less than a cer- tain value. Instead, the AVF could only change all copay amounts within that timespan, for a single object, to that new value. Obviously, a series of carefully designed restricted temporal updates could produce any desired result, and do so across any set of objects. But just as obviously, it would be a tedious process. And because of the careful analysis required, it would also be an error-prone process. As we go to press, these limitations on temporal update trans- actions have been removed. Release 1 of our Asserted Versioning Framework now supports unrestricted temporal update trans- actions, ones which will update multiple objects within a target timespan, and will do so based on WHERE clause qualifying criteria. The AVF also now supports unrestricted temporal deletes as well. In addition, instead of requiring the user to write trans- actions in a proprietary format required by an Application Programming Interface (API) we were developing, the AVF now accepts temporal insert, update and delete transactions written as native SQL. This is done by means of Instead of Triggers, as described in the section Ongoing Research and Development, in Chapter 16. Our new support for unrestricted temporal transactions, written as native SQL statements, can be found on our website AssertedVersioning.com. The Temporal Delete Transaction A temporal delete transaction specifies an object and a target range for the transaction (Figure 10.13). It includes the object identifier, if it is known to the user. If an oid is not provided on the transaction, the AVF attempts to find one according to the rules described in the previous chapter. Finally, the transaction either accepts the default values for its temporal parameters, or overrides one or more of them with explicit values.
4. Chapter 10 TEMPORAL TRANSACTIONS ON SINGLE TABLES 227 Temporal Delete Physical Transaction(s) Remove an object from a designated Withdraw the affected versions. timespan. Assert the replacements which delimit the deletion. Reset affected versions. Figure 10.13 The Temporal Delete Transaction: Temporal to Physical Mapping. A temporal delete is the inverse of a temporal insert. A tem- poral insert always increases the total number of clock ticks occupied by an object. A temporal delete always decreases the total number of those clock ticks. As long as even a single clock tick in the transaction’s target timespan [intersects] the effective time period of some version of the same object, the delete is valid because it means that there is data in one or more clock ticks for the delete to move into past assertion time. A temporal delete’s target range may include part of an epi- sode or version, an entire episode or version, multiple episodes or versions, or any combination thereof. But a temporal delete never creates a new episode or version in clock ticks that were previously unoccupied, just as a temporal insert never removes one from clock ticks that were previously occupied. Deleting One or More Episodes We will begin with the set of three episodes shown in Figure 10.14. These are the current episodes A, B and C after being updated as shown in Figure 10.12. We have also reset the version numbers so they correspond to the row numbers in Figure 10.12. To completely remove an episode from current assertion time, we do not need to provide the exact begin and end dates of the episode, but simply need to include its effective time Episode A Episode C Episode B 6 1 7 8 10 9 4 Jan Jan Jan Jan Jan 2010 2011 2012 2013 2014 Figure 10.14 Deleting an Episode: Before the Transaction.
5. 228 Chapter 10 TEMPORAL TRANSACTIONS ON SINGLE TABLES period in the transaction’s target timespan. If that target timespan includes that of the episode, the result is to remove the entire episode, i.e. to {erase} that episode from current assertion time. It is now March 2012, and either of the following two trans- actions is submitted to the AVF: DELETE FROM Policy [P861] Jan 2010, Nov 2010 or DELETE FROM Policy [P861] Jan 2010, Dec 2010 These two temporal delete transactions have the same result. They both {erase} Episode A, the episode consisting of versions 6, 1, 7 and 8. The author of the transaction will not be confused by this fact provided she remembers that a delete transaction simply stops asserting the presence of an object anywhere in the effective timespan indicated on the transaction. Both timespans shown here contain exactly the same occupied clock ticks. Withdrawing these versions is the first of the three physical transaction steps shown in Figure 10.15. As for the other two steps, neither of them is needed to complete this temporal transaction. The reason is that since an entire episode is being {erased}, and the object is represented nowhere else in the target timespan, no other episodes are affected. We can think of the empty clock tick or clock ticks that exist on both ends of an episode as insulating other episodes from whatever happens to just that one episode. Shortening an Episode Forwards We still currently assert episodes C and B in Figure 10.14. It is now May 2012, and the following transaction is submitted to the AVF: DELETE FROM Policy [P861] Jan 2011, May 2011 This transaction will {erase} Episode C, and {shorten Episode B forwards} by one month. Row oid eff-beg eff-end asr-beg asr-end epis- client type copay row-crt # beg P861 Feb10 Apr10 Feb10 Mar12 Jan10 C882 HMO $15 Feb10 2 P861 Apr10 Oct10 Mar10 Jan12 Jan10 C882 HMO$20 Apr10 3 P861 Apr11 Jul11 Apr11 Jan12 Apr11 C882 PPO $20 Apr11 4 P861 Jul11 9999 Jul11 9999 Apr11 C882 HMO$15 Jul11 5 P861 Jan11 Mar11 Aug11 Jan12 Jan11 C882 HMO $20 Aug11 P861 Jan10 Feb10 Oct11 Mar12 Jan10 C882 PPO$20 Oct11 P861 Apr10 Jul10 Jan12 Mar12 Jan10 C882 HMO $20 Jan12 P861 Jul10 Oct10 Jan12 Mar12 Jan10 C882 HMO$40 Jan12 9 P861 Apr11 Jul11 Jan12 9999 Apr11 C882 PPO $40 Jan12 10 P861 Jan11 Mar11 Jan12 9999 Jan11 C882 HMO$40 Jan12 Figure 10.15 Deleting an Episode.
6. Chapter 10 TEMPORAL TRANSACTIONS ON SINGLE TABLES 229 Row oid eff-beg eff-end asr-beg asr-end epis- client type copay row-crt # beg 1 P861 Feb10 Apr10 Feb10 Mar12 Jan10 C882 HMO $15 Feb10 2 P861 Apr10 Oct10 Mar10 Jan12 Jan10 C882 HMO$20 Apr10 3 P861 Apr11 Jul11 Apr11 Jan12 Apr11 C882 PPO $20 Apr11 4 P861 Jul11 9999 Jul11 9999 Apr11 C882 HMO$15 Jul11 5 P861 Jan11 Mar11 Aug11 Jan12 Jan11 C882 HMO $20 Aug11 6 P861 Jan10 Feb10 Oct11 Mar12 Jan10 C882 PPO$20 Oct11 7 P861 Apr10 Jul10 Jan12 Mar12 Jan10 C882 HMO $20 Jan12 8 P861 Jul10 Oct10 Jan12 Mar12 Jan10 C882 HMO$40 Jan12 P861 Apr11 Jul11 Jan12 May12 Apr11 C882 PPO $40 Jan12 P861 Jan11 Mar11 Jan12 May12 Jan11 C882 HMO$40 Jan12 Figure 10.16 Shortening an Episode Forwards: After Step 1. Because the delete transaction {shortens Episode B forwards}, it alters the episode begin date. Specifically, it changes that begin date from April 2011 to May 2011. This transaction will require all three of the physical transaction steps shown in Figure 10.13. The first physical transaction step withdraws versions 9 and 10. The result is shown in Figure 10.16. These versions have been withdrawn, as all versions are, by overwriting their assertion end dates. The overwrites which withdraw rows into past assertion time do not lose information, however, as overwrites of business data do. This is because we always know what the assertion end date was before the row was withdrawn. In all cases, it was 12/31/9999. This is guaranteed because (i) all versions are cre- ated with an assertion end date of 12/31/9999, and (ii) the AVF will never alter an assertion end date that is not 12/31/9999. In comparing the transaction’s time period to that of the epi- sode, we see that it completely includes version 10 but only [overlaps] version 9. So, having withdrawn version 9, we must now replace it with a version identical to it except that its effec- tive time period begins on May 2011. But because version 9 is the first version of Episode B, it changes the episode begin date of the episode from April 2011 to May 2011. This, in turn, affects version 4, which is the second version in that episode. Conse- quently, we must withdraw version 4, and replace it with a ver- sion that is identical to it except for having the new episode begin date. The result of all this work is shown in Figure 10.17. Episode C has been {erased}, completely withdrawn into past assertion time. Episode B has been {shortened forwards} by one month. The first delete transaction we considered covered an entire episode, {removing} that episode by withdrawing all its versions into past assertion time. This delete transaction, however, left part
7. 230 Chapter 10 TEMPORAL TRANSACTIONS ON SINGLE TABLES Row oid eff-beg eff-end asr-beg asr-end epis- client type copay row-crt # beg 1 P861 Feb10 Apr10 Feb10 Mar12 Jan10 C882 HMO $15 Feb10 2 P861 Apr10 Oct10 Mar10 Jan12 Jan10 C882 HMO$20 Apr10 3 P861 Apr11 Jul11 Apr11 Jan12 Apr11 C882 PPO $20 Apr11 4 P861 Jul11 9999 Jul11 May12 Apr11 C882 HMO$15 Jul11 5 P861 Jan11 Mar11 Aug11 Jan12 Jan11 C882 HMO $20 Aug11 6 P861 Jan10 Feb10 Oct11 Mar12 Jan10 C882 PPO$20 Oct11 7 P861 Apr10 Jul10 Jan12 Mar12 Jan10 C882 HMO $20 Jan12 8 P861 Jul10 Oct10 Jan12 Mar12 Jan10 C882 HMO$40 Jan12 P861 Apr11 Jul11 Jan12 May12 Apr11 C882 PPO $40 Jan12 P861 Jan11 Mar11 Jan12 May12 Jan11 C882 HMO$40 Jan12 P861 May11 Jul11 May12 9999 May11 C882 PPO $40 May12 P861 Jul11 9999 May12 9999 May11 C882 HMO$15 May12 Figure 10.17 Shortening an Episode Forwards: After Step 2. of a target episode in current assertion time. It withdrew part but not all of that episode, bringing about the temporal extent trans- formation in which an episode is {shortened forwards}. In this way, a temporal delete is different from a non-temporal delete. Non-temporal deletes remove the one and only row representing an object from the database. Temporal deletes remove some but not necessarily all of the possibly multiple rows representing an object, and may also remove part but not neces- sarily all of any one (or two) of those rows. And, of course, tempo- ral deletes do not physically remove any data from the database. They just withdraw assertions and end the effective time of vers- ions, so that at any point in time, what used to be the case can be recreated exactly as it was then. Shortening an Episode Backwards A temporal delete can also {shorten an episode backwards} in time. This happens when the transaction’s target range [overlaps] later clock ticks in the episode (and perhaps additional clock ticks as well) while one or more earlier clock ticks are not [overlapped]. {Shortening an episode backwards} is easier than {shortening it forwards} because it doesn’t alter the episode’s begin date. Since the episode’s begin date remains the same, the only vers- ions in the episode that are affected by the transaction are those which [overlap] the transaction’s target range. If we’re really for- tunate, the target range will line up on version boundaries. An example would be a temporal delete whose target range is [Jul 2011 – 12/31/9999] against the episode still asserted in Figure 10.17. In this case, the timespan on this transaction [equals] the effective time of version 12.
8. Chapter 10 TEMPORAL TRANSACTIONS ON SINGLE TABLES 231 When a temporal delete’s timespan lines up on a version boundary within a target episode, then all that has to be done is to withdraw the affected versions. Doing so, in this case, leaves an episode whose effective time extends from May 2011 to July 2011. So the effective end date, July 2011, of this previous ver- sion, row 11, would designate the end of the episode. Splitting an Episode {Splitting} an episode is a little more interesting than either {shortening an episode backwards} or {shortening an episode for- wards}. The reason is that, from the point of view of the earlier of the two resulting episodes, {splitting} is {shortening an episode backwards}, while from the point of view of the later of the two resulting episodes, it is {shortening an episode forwards}. From the point of view of the “internals” of AVF processing, of course, it is simply another case of removing the representation of an object from a series of clock ticks, the case in which those clock ticks are contained within the clock ticks of a single episode. Let’s begin with the life history of policy P861 as represented in the table in Figure 10.15 and as graphically illustrated in Fig- ure 10.14. In that table, versions (row numbers) 9 and 4 consti- tute a currently asserted episode, one which extends from April 2011 to 12/31/9999. It is now February 2012. Note that this is one month before the {shorten forwards} transaction, described in the previous section, is processed. That’s why we’re going back to Figure 10.15, rather than to Figure 10.16. The following transaction is submitted to the AVF: DELETE FROM Policy [P861] May 2011, Dec 2012 Policy P861 exists, in current assertion time, in every clock tick from May 2011 to December 2012. As we can see from ver- sion 9, it also exists for exactly one clock tick prior to that timespan. And as we can see from version 4, it exists past December 2012, into the indefinite future. The first physical transaction step in this deletion is to with- draw versions 9 and 4 since each of them has at least one clock tick included in the timespan specified by the temporal delete. The result is shown in Figure 10.18. Having {erased} the entire episode, the next step is to replace those parts of those versions which lie outside the scope of the transaction. For version 9, [Apr 2011 – May 2011] is the single clock tick that must be replaced. For version 4, [Dec 2012 – 12/31/9999] is the effective timespan that must be replaced. The result is shown in Figure 10.19.
9. 232 Chapter 10 TEMPORAL TRANSACTIONS ON SINGLE TABLES Row oid eff-beg eff-end asr-beg asr-end epis- client type copay row-crt # beg 1 P861 Feb10 Apr10 Feb10 Mar12 Jan10 C882 HMO $15 Feb10 2 P861 Apr10 Oct10 Mar10 9999 Jan10 C882 HMO$20 Apr10 3 P861 Apr11 Jul11 Apr11 9999 Apr11 C882 PPO $20 Apr11 P861 Jul11 9999 Jul11 Feb12 Apr11 C882 HMO$15 Jul11 5 P861 Jan11 Mar11 Aug11 9999 Jan11 C882 HMO $20 Aug11 6 P861 Jan10 Feb10 Oct11 Mar12 Jan10 C882 PPO$20 Oct11 7 P861 Apr10 Jul10 Jan12 Mar12 Jan10 C882 HMO $20 Jan12 8 P861 Jul10 Oct10 Jan12 9999 Jan10 C882 HMO$40 Jan12 P861 Apr11 Jul11 Jan12 Feb12 Apr11 C882 PPO $40 Jan12 10 P861 Jan11 Mar11 Jan12 9999 Jan11 C882 HMO$40 Jan12 11 P861 Jun10 Jul10 Mar12 9999 Jun10 C882 PPO $20 Mar12 Figure 10.18 Splitting an Episode: After Step 1. Row oid eff-beg eff-end asr-beg asr-end epis- client type copay row-crt # beg 1 P861 Feb10 Apr10 Feb10 Mar12 Jan10 C882 HMO$15 Feb10 2 P861 Apr10 Oct10 Mar10 9999 Jan10 C882 HMO $20 Apr10 3 P861 Apr11 Jul11 Apr11 9999 Apr11 C882 PPO$20 Apr11 P861 Jul11 9999 Jul11 Feb12 Apr11 C882 HMO $15 Jul11 5 P861 Jan11 Mar11 Aug11 9999 Jan11 C882 HMO$20 Aug11 6 P861 Jan10 Feb10 Oct11 Mar12 Jan10 C882 PPO $20 Oct11 7 P861 Apr10 Jul10 Jan12 Mar12 Jan10 C882 PPO$20 Jan12 8 P861 Jul10 Oct10 Jan12 9999 Jan10 C882 PPO $40 Jan12 P861 Apr11 Jul11 Jan12 Feb12 Apr11 C882 PPO$40 Jan12 10 P861 Jan11 Mar11 Jan12 9999 Jan11 C882 HMO $40 Jan12 11 P861 Jun10 Jul10 Mar12 9999 Jun10 C882 PPO$20 Mar12 P861 Apr11 May11 Feb12 9999 Apr11 C882 PPO $40 Feb12 P861 Dec12 9999 Feb12 9999 Dec12 C882 HMO$15 Feb12 Figure 10.19 Splitting an Episode: After Steps 2 and 3. The second physical transaction step in carrying out a tem- poral delete is to assert the replacement versions which delimit the time period of the deletion. This is done with versions 12 and 13. Version 12 replaces the one clock tick from version 9 that was not included in the range of the delete. Version 13 replaces the clock ticks from December 2012 to 12/31/9999 from version 4 that were not included in the range of the delete. The third physical transaction step resets any versions that need their episode begin dates reset. That is version 13. Version 4, which it replaces, belongs to an episode which began on July 2011. That episode has been {shortened forwards} by the trans- action so that it now begins on December 2012, the effective begin date of what is now its only version.
10. Chapter 10 TEMPORAL TRANSACTIONS ON SINGLE TABLES 233 Completeness Checks We have now used all three temporal transactions, in a variety of situations. There are several ways to categorize the situations which temporal transactions might encounter, but we con- cluded, a couple of chapters ago, that we could not provide an example for all of them. Nonetheless, we would like some assur- ance that any semantically valid request to transform one or more asserted version tables from one state to another state can be made with temporal transactions and can be carried out with the physical transactions that the AVF maps them into. We know of two ways to do this. One is with the Allen relationships. The other is with our taxonomy of temporal extent state transformations. The relationship of these two ways of demonstrating completeness is this. While we will use the Allen relationships to compare temporal transactions to their target episodes, we will use the temporal extent state transformations to compare before and after states of a target database. An Allen Relationship Completeness Check First of all, it is well established that the Allen relationships are a mutually exclusive and jointly exhaustive set of all the possible relationships between two time periods along a common timeline that are based on the temporal precedence and succession of one to the other (Figure 10.20). We ourselves derived precisely those Allen relationships as the leaf nodes in a taxonomy of our own invention. Since taxonomies are tools for demonstrating mutual exclusion and joint coverage of an original root node, this is further proof, if any were needed, of the validity of the Allen relationships. In the case of temporal transactions, one of those two Allen relationship time periods is the effective time period specified on the transaction. The other time period is the effective time period of each episode and version to which those transactions may apply. We should also remind ourselves that when we compare any two time periods in effective time, we are assuming that they exist in shared assertion time. When one of those time periods is on a transaction, that assertion time cannot begin in the past, and usually begins Now(); and the assertion time specified on the transaction always extends to 12/31/9999. [Before], [before–1]. When a temporal transaction’s effective time is non-contiguous with that of any episodes of the same object already in the target table, a temporal insert will {create} a new episode of the object. In Allen relationship terms, this
11. 234 Chapter 10 TEMPORAL TRANSACTIONS ON SINGLE TABLES Time Periods Relationships Along a Common Timeline Intersects Excludes Fills Overlaps Before Meets |----------| |-----| |-----| |-----|-----| |----------| Equals Occupies |-----| |-----| Aligns During |-----| |------------| Starts Finishes |-----| |-----| |------------| |-----------| Figure 10.20 The Asserted Versioning Allen Relationship Taxonomy. means that, for any episode of the same object already in the target table, the effective time period specified on a temporal insert is either [before] or [beforeÀ1] that episode. Another way of making the same point is to say that the time period on the transaction is non-contiguous with the time period of any episode of the same object. If the effective time period on a temporal update or delete transaction is either [before] or [beforeÀ1] the effective time period of every episode of the same object already in the target table, then the temporal transaction is invalid. It is equivalent to a conventional transaction trying to update or delete a row that isn’t there. [Meets], [meets–1]. When a temporal transaction’s effective time [meets] or [meetsÀ1] that of an episode of the same object already in the target table, a temporal insert will result in one or the other of the {lengthen} transformations, depending on whether the transaction’s timespan is later than or earlier than that of the episode. Also, if a temporal insert transaction’s effec- tive time both [meets] one episode and [meetsÀ1] an adjacent episode, the result will be a {merge} transformation.
12. Chapter 10 TEMPORAL TRANSACTIONS ON SINGLE TABLES 235 The [before], [beforeÀ1], [meets] and [meetsÀ1] relationships are subtypes, in our taxonomy, of the [excludes] relationship. And we can now see why this is an important group of relationships to define. Temporal insert transactions are valid only if they have an [excludes] relationship with every other episode of the same object already in the target table. And by the same token, temporal update and temporal delete trans- actions are valid only if there is at least one episode of the same object already in the target table with which they do not have an [excludes] relationship. So now that we are through with the [excludes] branch of the Allen taxonomy, we have exhausted all the Allen relationship possibilities for temporal insert transactions. We will discuss how temporal delete transactions work with the remaining Allen relationships. We will not explicitly discuss temporal updates because temporal updates are semantically equivalent to temporal deletes followed by the insertion of updated versions which supercede those versions wholly or par- tially withdrawn. And so there are no Allen relationships possible for temporal updates that are not also possible for temporal deletes. [Starts]. If a temporal delete transaction’s effective time begins on the same clock tick as that of an episode, but ends ear- lier than the episode ends, it will withdraw all versions wholly or partially included within its timespan. If one version is partially within the timespan, the temporal delete will replace the part of that withdrawn version not within its timespan. In either case, the result is a {shorten backwards} transformation on that episode. [Starts–1]. If a temporal delete transaction’s effective time begins on the same clock tick as that of an episode, but ends after the episode ends, the transaction will {erase} the episode; and, in addition, it will withdraw all other versions, for the same object, that are wholly or partially included within its timespan. Those other versions will exist within one or more later episodes. On any of those episodes wholly included within the transaction’s timespan, there will be an {erase} transformation on them, as well. The last episode within the transaction’s timespan may be wholly or partially included within that timespan. If it is wholly contained, there will be an {erase} trans- formation on it. Otherwise, there will be a {shorten forwards} transformation. If the end of the transaction’s timespan does not fall on a version effective time boundary, then the temporal delete will replace the part of that withdrawn version that is not within its timespan.
13. 236 Chapter 10 TEMPORAL TRANSACTIONS ON SINGLE TABLES [Finishes]. If a temporal delete transaction’s effective time ends on the same clock tick as that of an episode, but begins after that episode begins, it will withdraw all versions wholly or partially included within its timespan. If one version is partially within the timespan, the temporal delete will replace the part of that withdrawn version not within its timespan. In either case, the result is a {shorten forwards} transformation on that episode. [Finishes–1]. If a temporal delete transaction’s effective time ends on the same clock tick as that of an episode, but begins before that episode begins, it will {erase} the episode; and, in addition, it will withdraw all other versions, for the same object, that are wholly or partially included within its timespan. Those other versions will exist within one or more earlier episodes. On any of those episodes wholly included within the transaction’s timespan, there will be an {erase} transformation on them, as well. The earliest episode within the transaction’s timespan may be wholly or partially included within that timespan. If it is wholly contained, there will be an {erase} trans- formation on it. Otherwise, there will be a {shorten backwards} transformation. If the start of the transaction’s timespan does not fall on a version effective time boundary, then the temporal delete will replace the part of that withdrawn version that is not within its timespan. [During]. If a temporal delete transaction’s effective time begins after that of an episode, and ends before that episode ends, then the transaction will withdraw all versions wholly or partially included within its timespan. At most two versions can be par- tially included in that timespan, those being the ones at the begin and/or end of the timespan. This delete transaction carries out a {split} transformation on the episode in question. [During–1]. If a temporal delete transaction’s effective time begins before that of an episode, and ends after that episode ends, then the transaction will {erase} the one or more episodes wholly included within its timespan. In addition, as well as any number of additional episodes wholly included within the transaction’s timespan, there may be one or two episodes only partially included within the transaction’s timespan. If there is an earlier but partially included episode, the delete transaction will do a {shorten back- wards} transformation on it. If there is a later but partially included episode, the delete transaction will result in a {shorten forwards} transformation. In either case, the partially included episode may or may not have a partially included version; in other words, the transaction’s timespan may or may not align on version boundaries. In either case, a partially included version is {split}, and the part outside the transaction’s timespan is replaced.
14. Chapter 10 TEMPORAL TRANSACTIONS ON SINGLE TABLES 237 [Equals]. If a temporal transaction’s effective time [equals] that of one episode of the same object already in the target table, a temporal delete will {erase} that episode. [Overlaps]. If a temporal delete transaction’s effective time [overlaps] that of an episode, then either it begins after the epi- sode begins and before it ends, and ends after the episode ends; or else it begins before the episode begins and ends after the epi- sode begins but before it ends. In either case, the transaction will withdraw all versions wholly or partially included within the timespan of the transaction. At most one version can be partially included. If there is such a version, a temporal delete will replace the part of the partially included version that is outside the timespan of the transaction. The result is to either {shorten the episode backwards} or {shorten it forwards}, depending on whether the episode began before or after the transaction’s timespan. We have now demonstrated that every Allen relationship between a transaction and a target is valid for an insert, an update or a delete. So although we have not worked through a separate example for each Allen relationship, we can now be confident that there are no temporal precedence and succession relationships between a transaction’s time period and that of a target episode that Asserted Versioning temporal transactions cannot handle. A Temporal Extent Transformation Completeness Check A second completeness check uses the taxonomy of Asserted Versioning temporal extent transformations presented in Chap- ter 9. After presenting that taxonomy, we argued there that the taxonomy is mutually exclusive and demonstrably complete. Its completeness was demonstrated by showing that all possible single-transformation topological transformations of two line segments are represented in the taxonomy. Our second completeness check will use this taxonomy to review all extent-altering state transformations, and be sure that all of them can be brought about by valid temporal transactions. This completeness check has proven to be easier to complete than we had originally anticipated. As indicated in Figure 10.21, all the transformations on the left-hand side of the diagram can be brought about by means of a temporal insert transaction. Indeed, each of those transformations was explicitly mentioned in the previous section. All the transformations on the right-hand
15. 238 Chapter 10 TEMPORAL TRANSACTIONS ON SINGLE TABLES Asserted Versioning Temporal Extent State Transformations Create Modify Erase Merge Split Lengthen Shorten Lengthen Lengthen Shorten Shorten Backwards Forwards Backwards Forwards Temporal Insert Transaction Temporal Delete Transaction Figure 10.21 A Taxonomy of Asserted Versioning Temporal Extent Transformations. side of the diagram can be brought about by means of a temporal delete transaction. Again, each of those transformations was explicitly mentioned in the previous section. Glossary References Glossary entries whose definitions form strong inter- dependencies are grouped together in the following list. The same glossary entries may be grouped together in different ways at the end of different chapters, each grouping reflecting the semantic perspective of each chapter. There will usually be sev- eral other, and often many other, glossary entries that are not included in the list, and we recommend that the Glossary be consulted whenever an unfamiliar term is encountered. We note, in particular, that none of the nodes in the two taxonomies referenced in this chapter are included in this list. In general, we leave taxonomy nodes out of these lists since they are long enough without them. 12/31/9999 clock tick Now() until further notice Allen relationships
16. Chapter 10 TEMPORAL TRANSACTIONS ON SINGLE TABLES 239 adjacent include contiguous asserted version table Asserted Versioning Framework (AVF) assertion begin date assertion end date assertion time business data effective begin date effective end date effective time episode episode begin date open episode lock object object identifier oid occupied represented past assertion physical transaction temporal transaction temporal parameter temporal insert transaction temporal update transaction temporal delete transaction transaction timespan proactive transaction retroactive transaction replace supercede withdraw temporal entity integrity (TEI) temporal referential integrity (TRI) temporal extent state transformation version
17. TEMPORAL TRANSACTIONS ON 11 MULTIPLE TABLES Temporal Managed Objects and Temporal Referential Integrity 243 Child Managed Objects 243 Parent Managed Objects 244 Temporal Referential Integrity: The Basic Diagram 245 Foreign Keys and Temporal Foreign Keys 247 TFKs: A Data Part and a Function Part 249 Temporal Transactions and Associative Tables 250 TRI with Multiple TFKs 251 Temporal Delete Options 252 Temporal Referential Integrity Applied to Temporal Transactions 253 A Temporal Insert Transaction 253 A Temporal Update Transaction 254 A Temporal Delete Transaction 254 Glossary References 259 In the previous two chapters, we discussed temporal trans- actions and the temporal entity integrity constraint to which they must conform. We saw that, just as conventional entity integrity applies to the non-temporal representations of objects by those managed objects we call rows, temporal entity integrity (TEI) applies to the temporal representations of objects by those managed objects we call episodes and versions. TEI is the con- straint that, within shared assertion time, no two versions of the same object may occupy the same effective time clock tick, and that no two episodes of the same object may do so either. In short, it is the constraint that no two representations of the same object may occupy the same effective time clock ticks. In this chapter, we discuss temporal transactions and the temporal referential integrity constraint to which they must con- form. Conventional referential integrity (RI), at the level of types rather than instances, is a relationship between two relational Managing Time in Relational Databases. Doi: 10.1016/B978-0-12-375041-9.00011-X Copyright # 2010 Elsevier Inc. All rights of reproduction in any form reserved. 241
18. 242 Chapter 11 TEMPORAL TRANSACTIONS ON MULTIPLE TABLES tables (not necessarily distinct). At the level of instances, it is a relationship between two rows of relational tables (which are, however, necessarily distinct). An RI relationship between a child row and a parent row is based on an existence dependency between the objects they rep- resent. In our examples, policies are objects which are existence- dependent on clients, who are also objects. Reflecting that fact, and precisely because of it, rows in Policy tables are referentially dependent on rows in Client tables. Existence dependency, of course, does not have to be a cause- and-effect dependency between two physical objects, although that is one kind of existence dependency. For example, as we just pointed out, there is an existence dependency of policies on cli- ents; yet neither policies nor clients are physical objects. A policy is a contract, an agreement recognized in civil law. A client is a party to such a contract. The existence dependency of a policy on a client is thus a dependency of one legal object on another, a dependency defined in the world of law, not in the world of physics. In this chapter, we will see how temporal referential integrity (TRI) is referential integrity applied to the temporalized representations of objects by two types of managed objects— episodes and versions. A TRI relationship between a child man- aged object and a parent managed object is based on an exis- tence dependency between the objects which those managed objects represent. In either an RI or a TRI relationship between a managed object representing a policy and one representing a client, a cli- ent may exist without a related policy, but a policy cannot exist without a related client.1 These “mays” and “cannots”, as far as RI is concerned, are enforced on the managed objects which are rows, by the DBMS, in accordance with rules declared to it in DDL statements as constraints. These “mays” and “cannots”, as far as TRI is concerned, are enforced on the managed objects which are versions and episodes, by the AVF, in accordance with rules declared to it as entries in metadata tables. 1 Throughout this book, we have been referring to the individuals who own policies as “clients”. But in fact, the health insurance industry refers to these individuals as “members”, i.e. members of insurance plans. We made the terminological change because the word “member”, used in this way, is unfamiliar outside the health insurance industry.
19. Chapter 11 TEMPORAL TRANSACTIONS ON MULTIPLE TABLES 243 Temporal Managed Objects and Temporal Referential Integrity Temporal referential integrity relates a child version to a par- ent episode. It is important to understand why this is so, to understand why TRI is not a relationship between episodes and other episodes, or between versions and other versions. Child Managed Objects First of all, the child managed object in a TRI relationship cannot be an episode. The reason is that within the same episode, the owning parent object can change over time. For example, as policy episodes P861-A and P861-C in Figure 11.1 illustrate, different versions within the same episode can have different temporal foreign keys (TFKs), which means that they can designate different parent objects. Of course, since those C903 Episode C903-A Episode C903-B Episode C903-C 1 2 3 4 5 6 Jan Jan Jan Jan Jan 2010 2011 2012 2013 2014 Episode C882-A Episode C882-B Episode C882-C 1 2 3 4 Jan Jan Jan Jan Jan 2010 2011 2012 2013 2014 P861 Episode P861-A Episode P861-B Episode P861-C 1 2 3 4 5 6 7 8 Jan Jan Jan Jan Jan 2010 2011 2012 2013 2014 Figure 11.1 Temporal Referential Integrity: The Basic Diagram.
20. 244 Chapter 11 TEMPORAL TRANSACTIONS ON MULTIPLE TABLES versions are versions of the same child object, temporal entity integrity constraints insure that they represent those different parent objects at different points in effective time. If the child managed object in the TRI relationship were an entire policy epi- sode, then every time a policy changed the client it is related to, we would need to create a new episode of the policy. But by definition, there is always at least one clock tick between versions of the same object that belong to different episodes. So if a change in a TFK value always resulted in a new episode, then the first two versions of P861 would become two episodes, but episodes between which there is no temporal gap. And that is a contradiction. Parent Managed Objects On the other side of the relationship, the parent managed object in a TRI relationship must be an episode and not a ver- sion. If it were a version, then when that version in the parent episode was updated, the TRI relationship to that version would no longer be valid. The reason is that an update always ends the assertion time period of the version it supercedes, withdrawing that original version into past assertion time. Consequently, since temporal integrity constraints apply only among objects that share assertion time, the referenced version would no longer exist in the child’s still-current assertion timespan, and so the reference to it would become invalid. Besides being mechanically incorrect, as we have just shown, it would also be semantically incorrect to use versions as the parent managed objects in temporal referential integrity relationships. To see why, let’s consider non-temporal referential integrity, “regular RI”. If our two tables were non-temporal tables rather than asserted version tables, then clearly changes that happen to the parent client would have no effect on that RI relationship. For example, a client could change her name without affecting the fact that she owns policy P861. Therefore, if the same semantic change—the same name change for the same client—were applied to a temporal representation of that client, the result should have no effect on that TRI relationship. So the semantics are the same whether the objects involved are represented in conventional tables or in asserted version tables. But in asserted version tables, those changes will with- draw the current assertion, replace it with a new current asser- tion that has the same business data but an effective end date of Now(), and then supercede it with another new current asser- tion that has the updated business data and an effective begin


text:
Federated Scikit-learn Using Flower

21 July 2021 • Kaushik Amar Das

Scikit-learn needs no introduction. It is one of the most beloved machine-learning modules out there. But it lacks direct support for federated learning (FL). We can easily fix that by combining scikit-learn with Flower! In this post, we will discuss an example of how we can leverage Flower's framework agnostic API for training a federated scikit-learn model. Let's get started!

Training Scenario

Since this is just an example, let us keep things simple. We will train a Logistic Regression model on the MNIST dataset using federated learning. We will have only two clients participating in the FL. The MNIST dataset will be artificially split into 10 parts, out of which each client will randomly pick one as their local dataset for training. This example is meant to be run locally on a single machine hosting both the clients and the server. Make sure to pip install openml scikit-learn along with your Flower installation as we will be needing these. You can find the complete code used in this blog post here.

This example comprises three scripts: client.py, server.py and utils.py. The first and second scripts will contain the code for the server and the clients. The last script will contain the code for some of the utility functions that will be needed for our training. The following sections will discuss how each of these scripts is written. And following that, we will execute them to perform the federated learning.

Client code

The code for a Flower client training a scikit-learn model isn't too different from a Flower client using, for instance, Tensorflow. If you have worked through the other examples, things should look pretty familiar.

Begin by importing the following modules in client.py. Don't worry about the utils module for now. The functions in that module will be discussed in a later section.

import warnings
import flwr as fl
import numpy as np

from sklearn.linear_model import LogisticRegression
from sklearn.metrics import log_loss

import utils

Load the train and test split of the MNIST dataset. The train set is partitioned into 10 partitions, out of which a random partition is used for training.

# Load MNIST dataset from https://www.openml.org/d/554
(X_train, y_train), (X_test, y_test) = utils.load_mnist()

# Split train set into 10 partitions and randomly use one for training.
partition_id = np.random.choice(10)
(X_train, y_train) = utils.partition(X_train, y_train, 10)[partition_id]

Initialize the logistic regression model in the client. Let's have the client train for just a single iteration in each round by setting max_iter=1. Also, don't forget to set warm_start=True, otherwise, the model's parameters get refreshed when we call .fit. We don't want to reset the global parameters sent by the server.

# Create LogisticRegression Model
model = LogisticRegression(
penalty="l2",
max_iter=1, # local epoch
warm_start=True, # prevent refreshing weights when fitting
)

Next, we have to set the initial parameters of the model since the instance attributes used to save the model's parameters aren't created until .fit is called. But the server might want to set them or request them before fitting as is usually the case in federated learning. So, we create the parameter attributes and zero-initialize them using utils.set_initial_params(model).

# Setting initial parameters, akin to model.compile for keras models
utils.set_initial_params(model)

Now it is time to define the Flower client. The client is derived from the class fl.client.NumPyClient. It needs to define the following three methods:

1. get_parameters : Returns the current local model paramters. The utility function get_model_parameters does this for us.
2. fit: Defines the steps to train the model on the locally held dataset. It also receives global model parameters and other configuration information from the server. We update the local model's parameters using the received global parameters using utils.set_model_params(model, parameters) and train it on the local dataset. This method also sends back the local model's parameters after training, the size of the training set and a dict communicating arbitrary values back to the server.
3. evaluate: This method is meant for evaluating the provided parameters using a locally held dataset. It returns the loss along with other details such as the size of the test set, accuracy, etc., back to the server. Here, we calculate the loss value of the model explicitly using sklearn.metrics.log_loss. This is done explicitly because there is no public attribute in LogisticRegression that saves the loss value like, for instance, a TensorFlow model's history. Make sure to use the proper loss function corresponding to your model.
class MnistClient(fl.client.NumPyClient):
def get_parameters(self): # type: ignore
return utils.get_model_parameters(model)

def fit(self, parameters, config): # type: ignore
utils.set_model_params(model, parameters)
# Ignore convergence failure due to low local epochs
with warnings.catch_warnings():
warnings.simplefilter("ignore")
model.fit(X_train, y_train)
print(f"Training finished for round {config['rnd']}")
return utils.get_model_parameters(model), len(X_train), {}

def evaluate(self, parameters, config): # type: ignore
utils.set_model_params(model, parameters)
loss = log_loss(y_test, model.predict_proba(X_test))
accuracy = model.score(X_test, y_test)
return loss, len(X_test), {"accuracy": accuracy}

Finally, the script starts the client.

fl.client.start_numpy_client("0.0.0.0:8080", client=MnistClient())

Utility functions

We used a few utility functions in the client code that we will define in this section. The functions dealing with the model parameters are quite sensitive to the particular scikit-learn model that you would be using. So we have to carefully write them by following the model's documentation properly. In our case, we will follow the documentation for LogisticRegression.

The utility functions in utils.py script require the following imports and type hints.

from typing import Tuple, Union, List
import numpy as np
from sklearn.linear_model import LogisticRegression
import openml

XY = Tuple[np.ndarray, np.ndarray]
Dataset = Tuple[XY, XY]
LogRegParams = Union[XY, Tuple[np.ndarray]]
XYList = List[XY]

The get_model_parameters function returns the model parameters. These are found in the coef_ and intercept_ attributes for LogisticRegression .

def get_model_parameters(model):
"""Returns the paramters of a sklearn LogisticRegression model"""
if model.fit_intercept:
params = (model.coef_, model.intercept_)
else:
params = (model.coef_,)
return params

The set_model_params function sets/updates the model's parameters. Here care needs to be taken to set the parameters using the same order/index in which they were returned by get_model_parameters.

def set_model_params(
model: LogisticRegression, params: LogRegParams
) -> LogisticRegression:
"""Sets the parameters of a sklean LogisticRegression model"""
model.coef_ = params[0]
if model.fit_intercept:
model.intercept_ = params[1]
return model

The function set_initial_params zero-initializes the parameters of the model. This requires prior information about the attribute names, the number of classes and features of your dataset to calculate the size of the parameter matrices of the model. An alternative method for initializing the parameters could be to fit the model using a few dummy samples that mimic the dimensions of the actual dataset.

def set_initial_params(model: LogisticRegression):
"""
Sets initial parameters as zeros
"""
n_classes = 10 # MNIST has 10 classes
n_features = 784 # Number of features in dataset
model.classes_ = np.array([i for i in range(10)])

model.coef_ = np.zeros((n_classes, n_features))
if model.fit_intercept:
model.intercept_ = np.zeros((n_classes,))

The rest of the utility functions are for loading the dataset and partitioning it and doesn't require much explanation to understand.

def load_mnist() -> Dataset:
"""
Loads the MNIST dataset using OpenML
"""
mnist_openml = openml.datasets.get_dataset(554)
Xy, _, _, _ = mnist_openml.get_data(dataset_format="array")
X = Xy[:, :-1] # the last column contains labels
y = Xy[:, -1]
# First 60000 samples consist of the train set
x_train, y_train = X[:60000], y[:60000]
x_test, y_test = X[60000:], y[60000:]
return (x_train, y_train), (x_test, y_test)

def partition(X: np.ndarray, y: np.ndarray, num_partitions: int) -> XYList:
"""Split X and y into a number of partitions."""
return list(
zip(np.array_split(X, num_partitions),
np.array_split(y, num_partitions))
)

Server code

Lastly, we will write the code used by the server.py script. This includes defining the strategy for federation and its initialization parameters. Flower allows you to define your own callback functions to customize an existing strategy. We will use the FedAvg strategy with custom callbacks for evaluation and fit configuration. You can read more about how they work here.

The following imports are needed by the server script.

import flwr as fl
import utils
from sklearn.metrics import log_loss
from sklearn.linear_model import LogisticRegression
from typing import Dict

The fit_round callback will be used to send the round number to the client. We will pass this callback as the on_fit_config_fn parameter of the strategy. We do this simply to demonstrate the use of the on_fit_config_fn parameter.

def fit_round(rnd: int) -> Dict:
"""Send round number to client"""
return {"rnd": rnd}

The get_eval_fn callback will be used for validation.

def get_eval_fn(model: LogisticRegression):
"""Return an evaluation function for server-side evaluation."""

# Load test data here to avoid the overhead of doing it in
# evaluate itself

# The evaluate function will be called after every round
def evaluate(parameters: fl.common.Weights):
# Update model with the latest parameters
utils.set_model_params(model, parameters)
loss = log_loss(y_test, model.predict_proba(X_test))
accuracy = model.score(X_test, y_test)
return loss, {"accuracy": accuracy}

return evaluate

Next, we initialize the model and strategy and start the server. We will configure it to run for five rounds.

model = LogisticRegression()
utils.set_initial_params(model)
strategy = fl.server.strategy.FedAvg(
min_available_clients=2,
eval_fn=get_eval_fn(model),
on_fit_config_fn=fit_round,
)
fl.server.start_server(
"0.0.0.0:8080",
strategy=strategy,
config={"num_rounds": 5}
)

And we have finished writing the scripts. All that's left is to run them. So let's do that next.

Execution

For this part, open three terminals, one for the Flower server and the other two for each one of the clients. In the first terminal, we will run the server:

$python3 server.py In the second terminal, use the following command to start the first client: $ python3 client.py

And lastly, in the third terminal, start the second client in the same way:

\$ python3 client.py

And voilà! Flower will initiate the federated learning and train you a federated scikit-learn model. I hope you enjoyed reading through this example and are excited to build your own.

Stay tuned for more examples in the future. If you have an exciting scikit-learn Flower recipe that you think people can learn from, feel free to make a pull request at the Flower repo.


text:
# What is the origin of the term “pax”?

Pax in commercial transport is used as something like persons or passengers, in the context of counting people, e.g. 150 pax onboard.

I observed that in German writers tend to use the meaning:

PAX = Persons approximately.
(Source: European Union and the Committee of the Regions)

English.SE has a page for What does “pax” mean in the context of the apartment rental? Selected answer:

Pax isn't exactly shorthand for Passengers. It's short for Passengers and Passes.

But the author of the answer agreed that another answer was likely more accurate. The latter has a reference to a magazine, Air Facts: The Magazine for Pilots - 1946:

Cargo is known as "cargo", but passengers are called "pax" by the traffic department, who puts them on and takes them off the airplane and "bodies" by the crews who fly them.

Pax could be from passenger as usually assumed in the Aviation community, albeit I don't see why not *pass" instead. I wouldn't be surprised it comes from the merchant navy.

Can we track the use further back to the origin in aviation field?

• Might be better asked on english.stackexchange.com where you can inquire about the etymology of certain phrases. I don't think its specific to aviation, pretty much any industry that caters to passengers uses "pax" as an abbreviation, so aviation may just borrow it from an unrelated field. – Ron Beyer Feb 12 '16 at 14:34
• @mins Would be interesting to know if it was in use during the steamship era too e.g. pre 1920. – curious_cat Feb 12 '16 at 14:50
• FYI, I am ex-military (air force) and never heard pax used except to mean passenger. – Simon Feb 12 '16 at 16:09
• @curious_cat I wonder if some of the uses of pax from 1800s and earlier were related to the Latin word meaning 'peace' (e.g. the "Pax Romana") rather than as an abbreviation for 'passengers' as it's used in aviation? – reirab Feb 12 '16 at 16:43
• when I worked in the airline technology business, IATA was the authoritative source of data processing systems. according to IATA, PAX means passenger. you can find lots of references googling 'IATA PAX' – rbp Feb 12 '16 at 17:44

The 'x' suffix is aviation speak in an abbreviated word called a contraction. You can think of the 'x' as "cut short" shorthand. Some are defined in manuals or advisory circulars. For example, WX is weather as defined in an old advisory circular, AC00-45.

Official or not, a few others that come to mind are:

MX - maintenance
CX - cancel
TX - transmit

Maybe others will chime in the comments with more lore.

• This is the first time I read this explanation which is very plausible, do you have any document that could support it? – mins Jun 9 '17 at 17:58
• Please see the link contraction in my answer, for example. The right-hand column of that government document shows a source. – STWilson Jun 9 '17 at 18:12
• Perhaps my answer missed the root of your question, origin being the earliest use. Having been in aviation my life, cutting words short in log entries and aviation reports with 'x' has been commonly understood. – STWilson Jun 9 '17 at 18:19
• Rx & Tx are common for Receive & Transmit in the computer world, as well - look at your router/modem & you will, most likely see a light for each. – FreeMan Jun 9 '17 at 20:27
• Related: en.wikipedia.org/wiki/X In abbreviations, it can represent "trans-" (e.g. XMIT for transmit, XFER for transfer), "cross-" (e.g. X-ing for crossing, XREF for cross-reference), "Christ-" as shorthand for the labarum (e.g. Xmas for Christmas, Xian for Christian), the "crys-" in crystal (XTAL), or various words starting with "ex-" – UKMonkey Jul 9 '18 at 13:53

Pass would not be used as in the old days employees travelled on a 'pass'instead of a ticket. It could also be confused with the verb.

As a side note .. I seem to remember the plural was PAX and singular was PAP... eg 1PAP, 3PAX.

It is PAX for the abbreviation Passengers Approximately, which seemed to stick after the fact that advisory circulars were already shortening words into compatible abbreviations by adding an "x" to the end.

hope this helps.

• OP already mentioned this interpretation in the question. – a CVn Nov 23 '17 at 14:48


text:
Focus: Mystery in a Simple Metal

Published September 17, 1999  |  Phys. Rev. Focus 4, 15 (1999)  |  DOI: 10.1103/PhysRevFocus.4.15

Mystery of the Alkali Metals: Giant Moments of Fe and Co on and in Cs films

H. Beckmann and G. Bergmann

Published September 20, 1999

Every solid state physicist learns first about metals like sodium, potassium, and cesium because they are seen as the simplest metals to understand theoretically. The unbound electrons act in many ways like a gas of independent particles in a large box, which simplifies calculations of their properties. But in the 20 September PRL a team describes some surprising properties of cesium that the simple theory doesn’t predict: The metal drastically enhances the magnetism of iron and cobalt atoms dispersed on a cesium surface. The authors do not have a complete explanation for the results but are certain that in the process of finding one, they will learn important lessons about the behavior of metals.

Gerd Bergmann of the University of Southern California (USC) in Los Angeles stumbled on some strange properties of cesium when working on other experiments that used cesium surfaces. Alkali metals–the class that includes cesium–“should be the simplest thing one can imagine,” says Bergmann, so he investigated the anomalies and has reported several of them.

In his latest experiments, Bergmann and Holger Beckmann (formerly of USC) sprinkled metal atoms on cesium surfaces and measured the atoms’ magnetic moments–the strength of the tiny bar magnet that each impurity atom resembles. They used cobalt and iron as the impurities (in separate experiments) and spread them so thinly that neighboring impurity atoms were too far apart to interact. They also covered these preparations with more layers of cesium to find the moments of cobalt and iron as “bulk” impurities.

To detect the small atomic moments, the team employed the anomalous Hall effect: With a magnetic field in the z-direction and a current flowing in the y-direction, any conductor creates a so-called Hall voltage in the x-direction because the electrons tend to curve in the magnetic field. By subtracting that “normal” Hall voltage (due to the applied field) from the total Hall voltage, the researchers detected the effects of the impurity atoms’ magnetic moments. With temperatures up to 20 K and magnetic fields up to 7 T, the team measured moments of between 7 and $9{\text{µ}}_{B}$ (Bohr magnetons) for both cobalt and iron, as surface and bulk impurities. Bergman calls this a “giant moment” compared with the “native” moments of 1.7 and $2.2{\text{µ}}_{B}$ for cobalt and iron respectively.

The standard theory of alkali metals would predict no effect on the moments, says Bergmann, and “one cannot imagine a much simpler system for the theory.” He thinks cesium should serve as a “model substance” to check the validity of current theories and believes the problem might be traced to an incomplete understanding of the interactions among electrons.

”I’m intrigued,” says Jack Bass of Michigan State University in East Lansing. But he says that other surprising behaviors in alkali metals have been controversial–observed by some research groups and not by others. According to Bass, a minority of experts believes that Bergmann’s previous data may be explained by an exotic state of electrons called a charge density wave. Bass is ambivalent about the presence of that state in the alkalis but feels that the new results “ought to stimulate experimentalists to think about how to make further tests and theorists to try to explain the anomalies.”

–Anonymous


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## crickamaxwell Group Title Heather hits a tennis ball upward with an initial speed of 32 feet per second. After how many seconds does the ball hit the ground? Use the formula h = rt − 16t^2 where h represents height in feet and r represents the initial speed. 2 years ago 2 years ago

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1. across

You have all you need to solve this problem. Where are you stuck?

2. across

Basically, you want to find a solution to the equation$0=32t-16t^2,$where $$t\neq0$$.

3. 2le

You should also note that $h=h_0 + v_0t+\frac{1}{2}gt^2$ where h is your height, h_0 is your initial height when you threw the ball, v_0 is your initial velocity, and g is the force of gravity (at 32ft/sec^2) You may run into this equation again in physics and this is the equation that is used there.

4. across

You could also derive it from an ordinary differential equation if you feel like it...