Computing the depth of an arrangement of axis-aligned rectangles in parallel

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "Computing the depth of an arrangement of axis-aligned rectangles in parallel"

Transcription

1 Computing the depth of an arrangement of axis-aigned rectanges in parae Hemut At Ludmia Scharf Abstract We consider the probem of computing the depth of the arrangement of n axis-aigned rectanges in the pane, which is the maximum number of rectanges containing a common point. For this probem we give a sequentia O(n og n) time agorithm, and a parae agorithm with running time O(og 2 n) in the cassica PRAM mode. We aso describe how to adopt the paraeization to a shared memory machine mode with a fixed number of processing units. 1 Introduction In this paper we consider a basic geometric probem: how to compute the depth of the arrangement of n axis-aigned rectanges in R 2. The depth of a point p is defined as the number of rectanges containing p, and the depth of the arrangement is the maximum depth over a points in R 2, or, equivaenty, it is the maximum number of rectanges that contain a common point, see Figure 1 for an exampe. Figure 1: Arrangement of axis-parae rectanges with ces of maxima depth 4 (shaded). This research was partiay supported by the German Research Foundation (DFG) in the project Parae agorithms in computationa geometry with focus on shape matching, contract number AL 253/7-1. Institute of Computer Science, Freie Universität Berin, 1

2 We describe a parae agorithm for this probem for a shared memory parae machine mode. The agorithm has a running time O(og 2 n) and tota work O(n og 2 n) in the cassica EREW-PRAM mode. We aso describe how to adopt the paraeization to a more reaistic assumption of having a fixed number k of processing units in a shared memory machine, which fits better the modern muti-core processors. The current trend in the microprocessor industry is to increase the performance in computing not by increasing the CPU cock rates but by mutipe CPU cores working on shared memory and common cache. This trend in the hardware deveopment makes the design of parae agorithms once again an active topic in the agorithmic community. In this paper we first describe a sequentia O(n og n) time agorithm for computing the depth of the arrangement of axis-aigned rectanges in the pane. Namey, we construct a baanced search tree on the x-coordinates of the corners of rectanges and then perform a pane sweep aong the y-axis, whie updating the box coverage information in the tree. To our knowedge no O(n og n) agorithm for the depth probem has been given before expicity, athough the resut is somehow fokore knowedge in the computationa geometry community. In fact, the scheme of agorithms given for soving Kee s measure probem (KMP), i.e., computing the voume of the union of n axis-parae boxes, can be used for computing the depth of arrangements. For the two-dimensiona KMP Bentey described but did not pubish such an agorithm [2] the idea of which is given in [6], however. Our agorithm is simiar to some extent. We deveop and describe it in detai, mosty in order to derive from it in Section 3 the efficient parae agorithm for the probem. For the appications of the depth computation probem we mention two exampes: One is a geometric pattern matching probem. For two m-point sets A and B in R 2 finding a transformation minimizing the directed L -Hausdorff distance from A to B can be reduced to finding the depth in an arrangement of O(m 2 ) boxes. Another exampe is a custering probem: For a given set of n points in R 2 and a given radius r find a L -disk of radius r containing the argest number of points, that is, the densest custer of radius r. This custering probem is dua to determining the deepest point in the arrangement of n boxes with side ength 2r. For genera shape (agebraic) regions, not just axis-aigned rectanges, there is no better agorithm known for computing the depth of their arrangement than to construct the compete arrangement and then to traverse it. For arrangements of disks the probem is known to be 3-SUM hard [1], so sub-quadratic agorithms are not ikey to exist. For an arrangement of axis-aigned boxes in higher dimensions Chan [3] describes a sequentia agorithm with running time O((n d/2 / og d/2 1 n) og d/2 og n) for d 3. 2 Sequentia Agorithm In this section we describe the sequentia agorithm for computing the depth of the arrangement of axis-aigned rectanges. The genera idea is the foowing: For a given set of n axis-aigned rectanges we buid a baanced binary search tree T on the x-coordinates of the vertica sides of the rectanges, so that a x-coordinates are in the eaves of the tree. Let x 1, x 2,..., x 2n be the x-coordinates of the vertica sides of the rectanges in sorted order. With the eaf abeed with x i, i = 1,..., 2n 1, we associate the interva [x i, x i+1 ). The ast eaf, abeed with x 2n, is associated with the interva [x 2n, x 2n ]. With an interna node v we associate the union of the intervas 2

3 of its chidren. Space requirement for the tree is inear in the number of rectanges. Next we perform a top-down sweep aong the y-axis. Each sweepine event, i.e., a y- coordinate of the top or bottom of a rectange, has two x-coordinates a and b, with a, b {x 1,..., x 2n } and a < b, of the vertica sides of the corresponding rectange and an event vaue d associated with it. The event vaue is d = 1 if it is the top of the rectange (the rectange is opened ) and d = 1 if it is the bottom (the rectange is cosed ). To process a sweepine event we traverse the tree T from the root node to the eaves abeed a and b. In the nodes of the tree we want to count the number of rectanges covering the associated x-interva, and to update this information with each y-event. Of course, we cannot store this information directy and update it for a covered nodes for each rectange, since that coud make up to inear time per update. Instead, we maintain in every interna node v for the current state of the sweepine in counters and r the number of rectanges covering the interva of the eft and right chid of v that were opened minus the number of ones cosed since the ast traversa of that chid. In other words, the counters and r store the additive update of the information about how many open rectanges cover the interva of the eft and right chid, respectivey, at the current position of the sweepine. Additionay, counters m and r m store the maximum of this additive update for the eft and right chid, respectivey, since the ast traversa of the corresponding chid node. Every eaf node contains counters c and c m, which keep track of the current and maximum coverage of the associated interva during the sweep. The information in counters, r, m and r m is exacty as described above if the node v is traversed, and thus updated, by the current sweepine event. For subsequent events that do not traverse v the information may get outdated. Thus, the counters of the interna node v store the updates that happened between the ast traversa of the corresponding chid node and the ast traversa of v. The counters c and c m in the eaf nodes are ony updated for the open- and cose-events of the corresponding rectange. During each traversa of v by one of the searches the counter vaues are propagated from v to its chid on the search path in temporary counters t and t m, which are initiay set to 0. I.e., once we updated v as described beow and move to its eft (right) chid, t and t m are set to the vaues of v. and v. m (v.r and v.r m ), and then v., v. m (v.r, v.r m ) are reset to 0. Thus, when we enter the chid node w the counter t is the additive change since the ast update of w of the number of open rectanges that competey cover the interva of w; t m is either the maximum vaue of that change between the ast update of w and the current event, or 0 if the additive updates were a negative. An update of an interna node v is performed sighty differenty depending on whether both x-coordinates a and b associated with the event are contained in the subtree rooted at v (see Procedure 1: SearchBoth), or the search paths for a and b spit earier in the tree and the subtree of v contains ony a (see Procedure 2: SearchLeft) or ony b (procedure SearchRight). If both a and b are contained in the subtree rooted at v we need to update the counters of v ony with the vaues propagated from the parent node, without considering the event vaue. For and r we simpy add the vaue of t (ines 3 and 4 of procedure SearchBoth). The max-counters ( m and r m ) are set to the maximum of their od vaue, and the sum of the od counter ( or r, resp.) and t m (ines 1 and 2 of procedure SearchBoth). If both a and b are contained in the same, say eft, subtree of v then t and t m are set to and m, the search for both x-coordinates is continued in the eft subtree, and the counters and m are reset to 0. If the paths to a and b spit in the node v, we perform two separate 3

4 searches in the eft and right subtrees (ines 12 and 13) v. m = max(v. m, v. + t m ) v.r m = max(v.r m, v.r + t m ) v. = v. + t v.r = v.r + t if a < b v.x then SearchBoth (v.eft, a, b, v., v. m ) v. = v. m = 0 if v.x < a < b then SearchBoth (v.right, a, b, v.r, v.r m ) v.r = v.r m = 0 if a v.x < b then SearchLeft(v.eft, a, v., v. m ) SearchRight(v.right, b, v.r, v.r m ) v. = v. m = v.r = v.r m = 0 Procedure 1 : SearchBoth(v, a, b, t, t m ) Notice that the update instructions for the counters make sure that the stored vaues are not the absoute numbers of simutaneousy opened rectanges but an additive update to the information stored in the corresponding subtree. To iustrate this remark we consider an exampe of a (sub-)sequence of update events for a node v starting from some event, that resets the counters and m to 0, that is, the event updates the eft chid of v with the information gathered so far, see Figure 2. Assume that the node v now gets the foowing events: two cosing, three opening, and one cosing, where the eft chid is not traversed by the events, but the corresponding rectanges cover the interva of the eft chid. Then the vaues of and m counters are updated as shown in Figure 2. At the end of this sub-sequence the interva of the eft chid is covered by exacty as many rectanges as at the beginning: two od rectanges were cosed, three new opened and one new cosed, thus = 0. However, during this sub-sequence, between the ast two events, the interva of the eft chid was covered by one more rectange than in the beginning. This additiona coverage is maxima over the whoe sub-sequence, therefore, m = 1. Once the search path for a and b spits in some vertex, we know that the current rectange spans a intervas of the right subtrees of the eft search path, i.e., path to a, and a intervas of the eft subtrees of the right search path, i.e., path to b. Therefore, for a node v on the eft (right) search path we aso add the event vaue d to the counter r (). When we reach the eaves containing a and b we can update the current and maximum depth of the associated intervas. The updates are described in the procedure SearchLeft for the search path of a. The search for b is performed in a procedure caed SearchRight, which is anaogous to procedure SearchLeft and, therefore, is not expicity given here. After a sweepine events have been processed, the depth of the arrangement is determined as the maximum of the c m counters of the eaf nodes. The correctness of the agorithm is based on the foowing observation: Once we reach the bottom of a rectange, the counter c m in the eaf node abeed with the x-coordinate of its eft vertica boundary contains the maximum coverage of the associated x-interva between the highest y-coordinate and the y-coordinate of the bottom of the rectange. Since, ceary, 4

5 ... events 1st event of the sub-sequence m 0 0 sweep direction cose cose open open open cose interva of v interva of the eft chid of v Figure 2: An exampe of a sub-sequence of sweepine events and the corresponding updates of the counters and m of an interna node v if a v.x and v is an interna node then v.r m = max(v.r m, v.r + t m, v.r + t + d) v.r = v.r + t + d SearchLeft(v.eft, a, v. + t, max(v. m, v. + t m )) v. = v. m = 0 if a > v.x then v. m = max(v. m, v. + t m ); v. = v. + t SearchLeft(v.right, a, v.r + t, max(v.r m, v.r + t m )) v.r = v.r m = 0 if a = v.x and v is a eaf then c m = max (c m, c + t m, c + t + d) c = c + t + d Procedure 2 : SearchLeft(v, a, t, t m ) 5

6 every maximay covered ce has a eft vertica boundary that is a part of a eft boundary of a rectange, and thus covers at east one eaf interva, we capture at east one ce with maximum depth this way, i.e., store its depth in a counter c m of one of the eaves. If we want not ony to compute the depth, but aso get a point with maximum depth, we can additionay store a y-coordinate for each max-counter. This y-coordinate has to be updated with the y-vaue of that event which resuts in the counter update. The time needed to construct the tree and to sort the y-events is O(n og n). Each of the 2n events is processed in O(og n) time. Theorem 1 summarizes the resut of this section: Theorem 1. The depth of an arrangement of n axis-aigned rectanges in R 2 can be computed in time O(n og n) with O(n) additiona memory. 3 Parae Agorithm To enabe a parae execution of the agorithm we maintain so-caed history ists in the nodes of the tree T. A history ist of a node v contains an entry for each event of the sweepine that traverses the node v, i.e., for each y-coordinate of a top or bottom side of a rectange spanning the interva [a, b] in x-direction, such that a or b is contained in the subtree rooted at v. A history entry α of an interna node contains its timestamp the y-coordinate (or the rank of the y-coordinate) of the sweepine event, the corresponding x-vaues, the event vaue d and the counters, r, m, r m, as described in Section 2, and reset-fags ρ, ρ r. The reset fags indicate whether the vaues of the eft or right counters, respectivey, survive unti the next event: The vaue of ρ /ρ r in the entry α is 0 if the event of α causes the traversa of the eft/right subtree, since in this case the counter vaues are propagated to the subtree and wi be reset in the node v. Otherwise, the vaue is 1. Additionay, every history event has a pointer to the corresponding event, i.e., the event with the same y-coordinate, in the parent node. A history entry of a eaf node contains ony its y-coordinate, the event vaue d, and two counters c and c m. Every y-event appears in at most two nodes of each eve of the tree and requires constant space. Thus, the space for the tree is O(n og n). A information of a history event, except for the counter vaues, m, r, r m, is known at the construction time of the tree and can be set during the tree construction. Now we can fi out the counter vaues in the history ists starting with the root node down to the eaves. The eft/right counters in a root node events are set to 0. For an interna node v et α (i) be the i-th history event of v and et α (j) be the corresponding history event in the parent node of v, i.e., y (i) = y (j). Then the counters of α (i) are computed according to the foowing rues: Let t (i) and t (i) m denote the vaues of r (j) and r (j) m parent node, and vaues of (j) and (j) m of the event α (j) if v is a right chid of its otherwise. If α (i) contains both x-coordinates a and b 6

7 associated with y (i) then set (i) = (i 1) ρ (i 1) + t (i) (1) { } m (i) = max m (i 1) ρ (i 1), (i 1) ρ (i 1) + t (i) m (2) r (i) = r (i 1) ρ (i 1) r + t (i) (3) { } r m (i) = max r m (i 1) ρ (i 1) r, r (i 1) ρ (i 1) r + t (i) m, (4) where the vaues with the high-index (i 1) denote the vaues of the history event preceding α (i) in the node v. Aso if a history event α (i) of a node v contains ony a, and a is in the right subtree of v, or if α (i) contains ony b, and b is in the eft subtree of v, the counters are set as above. That is, the vaues from the parent node v are propagated to the corresponding chid node but the interva associated with the chid is not competey covered by the rectange causing the event, and thus, we do not need to consider the event vaue d. In case α (i) contains ony a, and a is in the eft subtree of v, then the compete right subtree is covered by the current rectange. Therefore, the right counters are incremented by the event vaue d (i) : r (i) = r (i 1) ρ (i 1) r + t (i) + d (i) (5) { r m (i) = max r m (i 1) ρ (i 1) r, r (i 1) ρ (i 1) r + t (i) m, r (i)}. (6) The eft counters are updated as in equations (1), (2). In case α (i) contains ony b, and b is in the right subtree of v the eft counters must be adjusted anaogousy: (i) = (i 1) ρ (i 1) + t (i) + d (i) (7) { m (i) = max m (i 1) ρ (i 1), (i 1) ρ (i 1) + t (i) m, (i)}. (8) and the right counters are updated as in equations (3), (4). The counters of the i-th entry in a eaf node are updated as foows: c (i) = c (i 1) + t (i) + d (i) (9) { c (i) m = max c (i 1) m, c (i 1) + t m (i), c (i 1) + t (i) + d (i)}. (10) Then, after a events have been processed, each eaf node stores the maxima coverage of its associated interva up to the position where the (ast) rectange with the corresponding vertica side was cosed. The depth of the arrangement is then the maximum over the c m counters of the eaves. So we coud buid the tree T and then traverse it eve-by-eve starting from the root node to the eaves, and node-by-node within one eve, setting the counters in a history events. Thus, we woud have a sequentia agorithm with running time in O(n og n) as before but with O(n og n) memory usage. Parae impementation on a PRAM. For the parae agorithm we assume that there are O(n) processors on a EREW-PRAM machine avaiabe. Then sorting of the corner points 7

8 of the rectanges once by y-coordinates and once by x-coordinates can be performed in O(og n) time, i.e., O(n og n) tota work, using, for exampe, the sorting agorithm by Coe [4]. In the foowing we assume that a x-coordinates of the vertica sides of the rectanges are distinct, which simpifies the anaysis and the description. With carefu consideration of technica detais the anaysis can be extended to the genera setting within the same time and tota work bounds as beow. The tree T without the history ists can be buid straightforwardy in time O(og n) on pre-sorted x-coordinates of the vertica sides of the rectanges. The unsorted history ists for each eve of the tree can be constructed in constant time per eve with O(n) processing units: We assign one processor to every history event. Every processor writes an entry for its event to the history ists of the corresponding two eaf nodes. Then, each processor creates eve-by-eve parent entries for its event in the history ists of the nodes on the path from the two eaves to the root node. At the end of this process the history ists contain entries with correcty set timestamps (the y-coordinates), pointers to the parent events, the event vaue d, and, for the interna nodes, the reset switches ρ, ρ r. The counter vaues remain open. Severa processors can write their entries to the history ist of the same node in parae since, if we organize the history ists as arrays, every processor independenty can easiy compute the index of its entry in the ist. The tota time for the construction of the unsorted history ists is O(og n). Now we can sort a history ists by timestamps in parae. The tota size of the history ists in one eve is at this stage 2n and the tota size of a history ists in the tree is O(n og n). We can sort the history ists eve-by-eve, processing a ists of one eve in parae in time O(og n) per eve with O(n) processors. Then, for the compete tree, the construction time of the sorted history ists is O(og 2 n). The computation of the eft/right counters in the event entries is performed eve-by-eve starting with the root node down to the eaves. We first observe that the computation of the counters (i) and r (i) according to equations (1), (3), (5), (7) corresponds to a prefix sum computation: Consider an interna node v and its eft counter of the i-th history entry (i). Let j be the highest index i with ρ (j) = 0. Then the vaue of (i) is the sum i k=j+1 (t(k) +d (k) ), where d (k) is set to 0 if the computation of (k+1) foows equation (1). Thus, if we can subdivide the -counters of a history ist into subsequences corresponding to bocks of ones terminated by a zero of the ρ -switches, then we can in a first step set each (i) to t (i) or t (i) +d (i), respectivey, and then perform parae prefix sum computations on the subsequences. For the subdivision into subsequences we can again use the parae prefix sum computation. First, we invert the vaues in the ρ -sequence, shift it by one to the right, and add a preceding 0, i.e., ˆρ (i) = 1 ρ (i 1) for i > 1 and ˆρ (1) = 0. Now we can compute the prefix sum of the ˆρ -vaues. The bocks of equa vaues in this new sequence correspond exacty to the subsequences in the -sequence. Then in the prefix sum computation of the -vaues we ony need to consider those entries that have the same ˆρ -vaue. The r-counter vaues are computed anaogousy. Prefix sum computation can be performed in O(og n) time [5].The tota size of a prefix sum ists of one eve is O(n), and there are O(og n) eves. So we need O(og 2 n) time in tota. For the computation of the max-counters according to equations (2), (4) or (6), (8), e.g., for m (i), we need the vaues m (i 1), (i 1), t m, and possiby (i). A of these vaues, except for m (i 1), are computed by now. Observe, that these equations are of the form u (i) = 8

9 max ( u (i 1) ρ (i 1), v (i)) (, where, e.g., in (6) u (i) = r m (i) and v (i) = max r i 1 ρ (i 1) + t (i) m, r ). (i) So the u (i) are prefix maxima of the previousy computed v (i) and can be computed in O(og n) time anaogousy to the prefix sums. We summarize the preceding sketch of the parae agorithm and its anaysis: Theorem 2. The depth of an arrangement of n axis-aigned rectanges in R 2 can be computed on a EREW-PRAM with O(n) processing units in time O(og 2 n). Parae impementation for a fixed number k of processors with shared memory: Sorting of the x- and y-coordinates of the vertica and horizonta sides of the rectanges can obviousy be performed on a k-processor machine in time O( n k og n). Then we have to spit the work performed by the agorithm between k processors. For this purpose we spit the tree construction into k subtrees, each containing at most 2n/k x-coordinates. Each of the subtrees is constructed by one processor sequentiay. Afterwards, the k subtrees are combined into a singe tree by adding a tree of height og k on top of the subtrees. The tree construction incudes the history ists except for the vaues of the counters r,, r m, m in the interna nodes, and the counters c, c m in the eaves. For the computation of the counters in the history ists we appy the same idea: for the top tree we appy parae prefix sum computation by processing the history ists in bocks of at most k eements. There are O(n/k) such bocks in each eve, and each bock is processed in O(og k) time. Thus, the og k eves of the top tree can be processed in O( n k og2 k) time. For the k subtrees we appy the sequentia agorithm to find the maximum depth in each subtree. The size of the subtrees is O(n/k), thus, the time for the remaining eves is O( n k og n). The tota time is then O( n k (og2 k + og n)). Summarizing, we have: Coroary 1. The depth of an arrangement of n axis-parae rectanges can be computed in parae by k processors with shared memory in time O(n/k(og 2 k + og n)). 4 Future Work Athough the depth computation of a set of rectanges in R 2 is an interesting probem on its own, we pan to deveop parae agorithms for higher dimensiona depth computation. Further, we are interested in an impementation of the agorithm presented here, and possiby agorithms for higher dimensiona probems, and in their experimenta evauation. The impementations shoud be performed for currenty avaiabe parae hardware patforms, such as muticore CPUs and genera purpose GPUs. References [1] B. Aronov and S. Har-Peed. On approximating the depth and reated probems. SIAM J. Comput., 38(3): , [2] J. L. Bentey. Agorithms for Kee s rectange probems. Unpubished notes, [3] T. M. Chan. A (sighty) faster agorithm for Kee s measure probem. In SCG 08: Proceedings of the twenty-fourth annua symposium on Computationa geometry, pages , New York, NY, USA, ACM. 9

10 [4] R. Coe. Parae merge sort. SIAM J. Comput., 17(4): , [5] D. W. Hiis and G. L. Steee. Data parae agorithms. Communications of the ACM, December [6] J. van Leeuwen and D. Wood. The measure probem for rectanguar ranges in d-space. J. Agorithms, 2(3): ,

Probabilistic Systems Analysis Autumn 2016 Tse Lecture Note 12

Probabilistic Systems Analysis Autumn 2016 Tse Lecture Note 12 EE 178 Probabiistic Systems Anaysis Autumn 2016 Tse Lecture Note 12 Continuous random variabes Up to now we have focused excusivey on discrete random variabes, which take on ony a finite (or countaby infinite)

More information

Math: Fundamentals 100

Math: Fundamentals 100 Math: Fundamentas 100 Wecome to the Tooing University. This course is designed to be used in conjunction with the onine version of this cass. The onine version can be found at http://www.tooingu.com. We

More information

EE 178/278A Probabilistic Systems Analysis. Spring 2014 Tse/Hussami Lecture 11. A Brief Introduction to Continuous Probability

EE 178/278A Probabilistic Systems Analysis. Spring 2014 Tse/Hussami Lecture 11. A Brief Introduction to Continuous Probability EE 178/278A Probabiistic Systems Anaysis Spring 2014 Tse/Hussami Lecture 11 A Brief Introduction to Continuous Probabiity Up to now we have focused excusivey on discrete probabiity spaces Ω, where the

More information

1.3 The Real Numbers.

1.3 The Real Numbers. 24 CHAPTER. NUMBERS.3 The Rea Numbers. The rea numbers: R = {numbers on the number-ine} require some rea anaysis for a proper definition. We sidestep the anaysis, reying instead on our ess precise notions

More information

Test Adequacy Assessment using Control Flow and Data Flow

Test Adequacy Assessment using Control Flow and Data Flow CSE592 Advanced Topics in Computer Science Software Engineering Test Adequacy Assessment using Contro Fow and Data Fow Lecture 14 Conditions Any expression that evauates to true or fase constitutes a condition.

More information

Sorting, Merge Sort and the Divide-and-Conquer Technique

Sorting, Merge Sort and the Divide-and-Conquer Technique Inf2B gorithms and Data Structures Note 7 Sorting, Merge Sort and the Divide-and-Conquer Technique This and a subsequent next ecture wi mainy be concerned with sorting agorithms. Sorting is an extremey

More information

HYBRID FUZZY LOGIC PID CONTROLLER. Abstract

HYBRID FUZZY LOGIC PID CONTROLLER. Abstract HYBRID FUZZY LOGIC PID CONTROLLER Thomas Brehm and Kudip S. Rattan Department of Eectrica Engineering Wright State University Dayton, OH 45435 Abstract This paper investigates two fuzzy ogic PID controers

More information

3.5 Pendulum period. 2009-02-10 19:40:05 UTC / rev 4d4a39156f1e. g = 4π2 l T 2. g = 4π2 x1 m 4 s 2 = π 2 m s 2. 3.5 Pendulum period 68

3.5 Pendulum period. 2009-02-10 19:40:05 UTC / rev 4d4a39156f1e. g = 4π2 l T 2. g = 4π2 x1 m 4 s 2 = π 2 m s 2. 3.5 Pendulum period 68 68 68 3.5 Penduum period 68 3.5 Penduum period Is it coincidence that g, in units of meters per second squared, is 9.8, very cose to 2 9.87? Their proximity suggests a connection. Indeed, they are connected

More information

A Guide to Lesson Planning

A Guide to Lesson Planning Lesson Pan HOW TO PREPARE A LESSON PLAN A Guide to Lesson Panning MUST be a minimum of 2 fu pages (singe-spaced) and no more than 5 pages incuding a attachments/materias. This is meant to be a concise

More information

Experiment #11 BJT filtering

Experiment #11 BJT filtering Jonathan Roderick Hakan Durmus Experiment #11 BJT fitering Introduction: Now that the BJT has bn expored in static and dynamic operation, the BJT, combined with what has bn aready presented, may be used

More information

SAT Math Facts & Formulas

SAT Math Facts & Formulas Numbers, Sequences, Factors SAT Mat Facts & Formuas Integers:..., -3, -2, -1, 0, 1, 2, 3,... Reas: integers pus fractions, decimas, and irrationas ( 2, 3, π, etc.) Order Of Operations: Aritmetic Sequences:

More information

The Radix-4 and the Class of Radix-2 s FFTs

The Radix-4 and the Class of Radix-2 s FFTs Chapter 11 The Radix- and the Cass of Radix- s FFTs The divide-and-conuer paradigm introduced in Chapter 3 is not restricted to dividing a probem into two subprobems. In fact, as expained in Section. and

More information

3.14 Lifting Surfaces

3.14 Lifting Surfaces .0 - Marine Hydrodynamics, Spring 005 Lecture.0 - Marine Hydrodynamics Lecture 3.4 Lifting Surfaces 3.4. D Symmetric Streamined Body No separation, even for arge Reynods numbers. stream ine Viscous effects

More information

Fast Robust Hashing. ) [7] will be re-mapped (and therefore discarded), due to the load-balancing property of hashing.

Fast Robust Hashing. ) [7] will be re-mapped (and therefore discarded), due to the load-balancing property of hashing. Fast Robust Hashing Manue Urueña, David Larrabeiti and Pabo Serrano Universidad Caros III de Madrid E-89 Leganés (Madrid), Spain Emai: {muruenya,darra,pabo}@it.uc3m.es Abstract As statefu fow-aware services

More information

Perfect competition. By the end of this chapter, you should be able to: 7 Perfect competition. 1 Microeconomics. 1 Microeconomics

Perfect competition. By the end of this chapter, you should be able to: 7 Perfect competition. 1 Microeconomics. 1 Microeconomics erfect 7 12 By the end of this chapter, you shoud be abe to: HL expain the assumptions of perfect HL distinguish between the demand curve for the industry and for the firm in perfect HL expain how the

More information

25.4. Solution Using Fourier Series. Introduction. Prerequisites. Learning Outcomes

25.4. Solution Using Fourier Series. Introduction. Prerequisites. Learning Outcomes Soution Using Fourier Series 25.4 Introduction In this Section we continue to use the separation of variabes method for soving PDEs but you wi find that, to be abe to fit certain boundary conditions, Fourier

More information

Pay-on-delivery investing

Pay-on-delivery investing Pay-on-deivery investing EVOLVE INVESTment range 1 EVOLVE INVESTMENT RANGE EVOLVE INVESTMENT RANGE 2 Picture a word where you ony pay a company once they have deivered Imagine striking oi first, before

More information

Apprenticeships. Everything you need to know about Apprenticeships with West Sussex County Council. Apprenticeships

Apprenticeships. Everything you need to know about Apprenticeships with West Sussex County Council. Apprenticeships Apprenticeships Everything you need to know about Apprenticeships with West Sussex County Counci Apprenticeships Apprenticeships September 2013 What is an Apprenticeship? An apprenticeship is a nationay

More information

The Use of Cooling-Factor Curves for Coordinating Fuses and Reclosers

The Use of Cooling-Factor Curves for Coordinating Fuses and Reclosers he Use of ooing-factor urves for oordinating Fuses and Recosers arey J. ook Senior Member, IEEE S& Eectric ompany hicago, Iinois bstract his paper describes how to precisey coordinate distribution feeder

More information

Lecture 5: Solution Method for Beam Deflections

Lecture 5: Solution Method for Beam Deflections Structura Mechanics.080 Lecture 5 Semester Yr Lecture 5: Soution Method for Beam Defections 5.1 Governing Equations So far we have estabished three groups of equations fuy characterizing the response of

More information

Advanced ColdFusion 4.0 Application Development - 3 - Server Clustering Using Bright Tiger

Advanced ColdFusion 4.0 Application Development - 3 - Server Clustering Using Bright Tiger Advanced CodFusion 4.0 Appication Deveopment - CH 3 - Server Custering Using Bri.. Page 1 of 7 [Figures are not incuded in this sampe chapter] Advanced CodFusion 4.0 Appication Deveopment - 3 - Server

More information

PERFORMANCE ANALYSIS OF GANG SCHEDULING IN A PARTITIONABLE PARALLEL SYSTEM

PERFORMANCE ANALYSIS OF GANG SCHEDULING IN A PARTITIONABLE PARALLEL SYSTEM PERFORMANCE ANALYSIS OF GANG SCHEDULING IN A PARTITIONABLE PARALLEL SYSTEM Heen D. Karatza Department of Informatics Aristote University of Thessaoniki 54124 Thessaoniki, Greece E-mai: karatza@csd.auth.gr

More information

Chapter 1 Structural Mechanics

Chapter 1 Structural Mechanics Chapter Structura echanics Introduction There are many different types of structures a around us. Each structure has a specific purpose or function. Some structures are simpe, whie others are compex; however

More information

Teamwork. Abstract. 2.1 Overview

Teamwork. Abstract. 2.1 Overview 2 Teamwork Abstract This chapter presents one of the basic eements of software projects teamwork. It addresses how to buid teams in a way that promotes team members accountabiity and responsibiity, and

More information

ENERGY AND BOLTZMANN DISTRIBUTIONS

ENERGY AND BOLTZMANN DISTRIBUTIONS MISN--159 NRGY AND BOLTZMANN DISTRIBUTIONS NRGY AND BOLTZMANN DISTRIBUTIONS by J. S. Kovacs and O. McHarris Michigan State University 1. Introduction.............................................. 1 2.

More information

Secure Network Coding with a Cost Criterion

Secure Network Coding with a Cost Criterion Secure Network Coding with a Cost Criterion Jianong Tan, Murie Médard Laboratory for Information and Decision Systems Massachusetts Institute of Technoogy Cambridge, MA 0239, USA E-mai: {jianong, medard}@mit.edu

More information

nπt a n cos y(x) satisfies d 2 y dx 2 + P EI y = 0 If the column is constrained at both ends then we can apply the boundary conditions

nπt a n cos y(x) satisfies d 2 y dx 2 + P EI y = 0 If the column is constrained at both ends then we can apply the boundary conditions Chapter 6: Page 6- Fourier Series 6. INTRODUCTION Fourier Anaysis breaks down functions into their frequency components. In particuar, a function can be written as a series invoving trigonometric functions.

More information

Determining the User Intent of Chinese-English Mixed Language Queries Based On Search Logs

Determining the User Intent of Chinese-English Mixed Language Queries Based On Search Logs Determining the User Intent of Chinese-Engish Mixed Language Queries Based On Search Logs Hengyi Fu, Forida State University, City University of New York Abstract With the increasing number of mutiingua

More information

A New Statistical Approach to Network Anomaly Detection

A New Statistical Approach to Network Anomaly Detection A New Statistica Approach to Network Anomay Detection Christian Caegari, Sandrine Vaton 2, and Michee Pagano Dept of Information Engineering, University of Pisa, ITALY E-mai: {christiancaegari,mpagano}@ietunipiit

More information

Angles formed by 2 Lines being cut by a Transversal

Angles formed by 2 Lines being cut by a Transversal Chapter 4 Anges fored by 2 Lines being cut by a Transversa Now we are going to nae anges that are fored by two ines being intersected by another ine caed a transversa. 1 2 3 4 t 5 6 7 8 If I asked you

More information

INDUSTRIAL AND COMMERCIAL

INDUSTRIAL AND COMMERCIAL Finance TM NEW YORK CITY DEPARTMENT OF FINANCE TAX & PARKING PROGRAM OPERATIONS DIVISION INDUSTRIAL AND COMMERCIAL ABATEMENT PROGRAM PRELIMINARY APPLICATION AND INSTRUCTIONS Mai to: NYC Department of Finance,

More information

The Computation of the Inverse of a Square Polynomial Matrix

The Computation of the Inverse of a Square Polynomial Matrix The Computation of the Inverse of a Square Poynomia Matrix Ky M. Vu, PhD. AuLac Technoogies Inc. c 2008 Emai: kymvu@auactechnoogies.com Abstract An approach to cacuate the inverse of a square poynomia

More information

Finance 360 Problem Set #6 Solutions

Finance 360 Problem Set #6 Solutions Finance 360 Probem Set #6 Soutions 1) Suppose that you are the manager of an opera house. You have a constant margina cost of production equa to $50 (i.e. each additiona person in the theatre raises your

More information

Chapter 3: e-business Integration Patterns

Chapter 3: e-business Integration Patterns Chapter 3: e-business Integration Patterns Page 1 of 9 Chapter 3: e-business Integration Patterns "Consistency is the ast refuge of the unimaginative." Oscar Wide In This Chapter What Are Integration Patterns?

More information

Irish Life Tables No. 14

Irish Life Tables No. 14 3 June 004 Life epectancy at birth Irish Life Tabes No. 14 001-003 Life epectancy 85 80 75 70 65 60 55 Maes Femaes Life epectancy at birth Area Maes Femaes Ireand 75.1 80.3 EU 15 75.8 81.6 EU 5 74.8 81.1

More information

Artificial neural networks and deep learning

Artificial neural networks and deep learning February 20, 2015 1 Introduction Artificia Neura Networks (ANNs) are a set of statistica modeing toos originay inspired by studies of bioogica neura networks in animas, for exampe the brain and the centra

More information

Early access to FAS payments for members in poor health

Early access to FAS payments for members in poor health Financia Assistance Scheme Eary access to FAS payments for members in poor heath Pension Protection Fund Protecting Peope s Futures The Financia Assistance Scheme is administered by the Pension Protection

More information

Introduction to XSL. Max Froumentin - W3C

Introduction to XSL. Max Froumentin - W3C Introduction to XSL Max Froumentin - W3C Introduction to XSL XML Documents Stying XML Documents XSL Exampe I: Hamet Exampe II: Mixed Writing Modes Exampe III: database Other Exampes How do they do that?

More information

ELEVATING YOUR GAME FROM TRADE SPEND TO TRADE INVESTMENT

ELEVATING YOUR GAME FROM TRADE SPEND TO TRADE INVESTMENT Initiatives Strategic Mapping Success in The Food System: Discover. Anayze. Strategize. Impement. Measure. ELEVATING YOUR GAME FROM TRADE SPEND TO TRADE INVESTMENT Foodservice manufacturers aocate, in

More information

SAT Math Must-Know Facts & Formulas

SAT Math Must-Know Facts & Formulas SAT Mat Must-Know Facts & Formuas Numbers, Sequences, Factors Integers:..., -3, -2, -1, 0, 1, 2, 3,... Rationas: fractions, tat is, anyting expressabe as a ratio of integers Reas: integers pus rationas

More information

Fourier Series. The Main Fourier Series Expansions.

Fourier Series. The Main Fourier Series Expansions. Fourier Series Roughy speaking, a Fourier series expansion for a function is a representation of the function as sum of s and coes. Expresg a musica tone as a sum of a fundamenta tone and various harmonics

More information

Recognition of Prior Learning

Recognition of Prior Learning Recognition of Prior Learning Information Guideines for Students EXTENDED CAMPUS This subject materia is issued by Cork Institute of Technoogy on the understanding that: Cork Institute of Technoogy expressy

More information

Budgeting Loans from the Social Fund

Budgeting Loans from the Social Fund Budgeting Loans from the Socia Fund tes sheet Pease read these notes carefuy. They expain the circumstances when a budgeting oan can be paid. Budgeting Loans You may be abe to get a Budgeting Loan if:

More information

Estimation of Tail Development Factors in the Paid-Incurred Chain Reserving Method

Estimation of Tail Development Factors in the Paid-Incurred Chain Reserving Method Estimation of Tai Deveopment Factors in the aid-incurred Chain Reserving Method by Michae Merz and Mario V Wüthrich AbSTRACT In many appied caims reserving probems in &C insurance the caims settement process

More information

Course MA2C02, Hilary Term 2012 Section 8: Periodic Functions and Fourier Series

Course MA2C02, Hilary Term 2012 Section 8: Periodic Functions and Fourier Series Course MAC, Hiary Term Section 8: Periodic Functions and Fourier Series David R. Wikins Copyright c David R. Wikins Contents 8 Periodic Functions and Fourier Series 37 8. Fourier Series of Even and Odd

More information

GWPD 4 Measuring water levels by use of an electric tape

GWPD 4 Measuring water levels by use of an electric tape GWPD 4 Measuring water eves by use of an eectric tape VERSION: 2010.1 PURPOSE: To measure the depth to the water surface beow and-surface datum using the eectric tape method. Materias and Instruments 1.

More information

AUSTRALIA S GAMBLING INDUSTRIES - INQUIRY

AUSTRALIA S GAMBLING INDUSTRIES - INQUIRY Mr Gary Banks Chairman Productivity Commission PO Box 80 BELCONNEN ACT 2616 Dear Mr Banks AUSTRALIA S GAMBLING INDUSTRIES - INQUIRY I refer to the Issues Paper issued September 1998 seeking submissions

More information

PREFACE. Comptroller General of the United States. Page i

PREFACE. Comptroller General of the United States. Page i - I PREFACE T he (+nera Accounting Office (GAO) has ong beieved that the federa government urgenty needs to improve the financia information on which it bases many important decisions. To run our compex

More information

DISPLAYING NASDAQ LEVEL II DATA

DISPLAYING NASDAQ LEVEL II DATA 14 NASDAQ LEVEL II windows et you view Leve II data for NAS- DAQ stocks. Figure 14-1 is an exampe of a NASDAQ Leve II window. Figure 14-1. NASDAQ Leve II Window Exampe Information in Leve II windows is

More information

1B11 Operating Systems. Input/Output and Devices

1B11 Operating Systems. Input/Output and Devices University Coege London 1B11 Operating Systems Input/Output and s Prof. Steve R Wibur s.wibur@cs.uc.ac.uk Lecture Objectives How do the bits of the I/O story fit together? What is a device driver? 1B11-5

More information

Simulation-Based Booking Limits for Airline Revenue Management

Simulation-Based Booking Limits for Airline Revenue Management OPERATIONS RESEARCH Vo. 53, No. 1, January February 2005, pp. 90 106 issn 0030-364X eissn 1526-5463 05 5301 0090 informs doi 10.1287/opre.1040.0164 2005 INFORMS Simuation-Based Booking Limits for Airine

More information

Physics 100A Homework 11- Chapter 11 (part 1) The force passes through the point A, so there is no arm and the torque is zero.

Physics 100A Homework 11- Chapter 11 (part 1) The force passes through the point A, so there is no arm and the torque is zero. Physics A Homework - Chapter (part ) Finding Torque A orce F o magnitude F making an ange with the x axis is appied to a partice ocated aong axis o rotation A, at Cartesian coordinates (,) in the igure.

More information

Guidance for safe bitumen tank management

Guidance for safe bitumen tank management Guidance for safe bitumen tank management Minera Products Association mpa asphat Minera Products Association 2 - guidance for safe bitumen tank management MPA Asphat is part of the Minera Products Association

More information

Subject: Corns of En gineers and Bureau of Reclamation: Information on Potential Budgetarv Reductions for Fiscal Year 1998

Subject: Corns of En gineers and Bureau of Reclamation: Information on Potential Budgetarv Reductions for Fiscal Year 1998 GAO United States Genera Accounting Office Washington, D.C. 20548 Resources, Community, and Economic Deveopment Division B-276660 Apri 25, 1997 The Honorabe Pete V. Domenici Chairman The Honorabe Harry

More information

Fast Idea Generator. Copyright 2016 The Open University

Fast Idea Generator. Copyright 2016 The Open University Fast Idea Generator Copyright 2016 The Open University 2 of 15 Wednesday 16 November 2016 Contents Fast Idea Generator 4 1 When to use the fast idea generator 4 1.1 Using the Fast Idea Generator Too 5

More information

A Description of the California Partnership for Long-Term Care Prepared by the California Department of Health Care Services

A Description of the California Partnership for Long-Term Care Prepared by the California Department of Health Care Services 2012 Before You Buy A Description of the Caifornia Partnership for Long-Term Care Prepared by the Caifornia Department of Heath Care Services Page 1 of 13 Ony ong-term care insurance poicies bearing any

More information

WEBSITE ACCOUNT USER GUIDE SECURITY, PASSWORD & CONTACTS

WEBSITE ACCOUNT USER GUIDE SECURITY, PASSWORD & CONTACTS WEBSITE ACCOUNT USER GUIDE SECURITY, PASSWORD & CONTACTS Password Reset Process Navigate to the og in screen Seect the Forgot Password ink You wi be asked to enter the emai address you registered with

More information

TERM INSURANCE CALCULATION ILLUSTRATED. This is the U.S. Social Security Life Table, based on year 2007.

TERM INSURANCE CALCULATION ILLUSTRATED. This is the U.S. Social Security Life Table, based on year 2007. This is the U.S. Socia Security Life Tabe, based on year 2007. This is avaiabe at http://www.ssa.gov/oact/stats/tabe4c6.htm. The ife eperiences of maes and femaes are different, and we usuay do separate

More information

Overview of Health and Safety in China

Overview of Health and Safety in China Overview of Heath and Safety in China Hongyuan Wei 1, Leping Dang 1, and Mark Hoye 2 1 Schoo of Chemica Engineering, Tianjin University, Tianjin 300072, P R China, E-mai: david.wei@tju.edu.cn 2 AstraZeneca

More information

5. Introduction to Robot Geometry and Kinematics

5. Introduction to Robot Geometry and Kinematics V. Kumar 5. Introduction to Robot Geometry and Kinematics The goa of this chapter is to introduce the basic terminoogy and notation used in robot geometry and kinematics, and to discuss the methods used

More information

Divide and Conquer Approach

Divide and Conquer Approach Divide and Conquer Approac Deiverabes Divide and Conquer Paradigm nteger Mutipication Strassen Matrix Mutipication Cosest Pair of points nfinite Wa Probem 6/7/01 8:58 PM Copyrigt @ gdeepak.com Divide and

More information

A Supplier Evaluation System for Automotive Industry According To Iso/Ts 16949 Requirements

A Supplier Evaluation System for Automotive Industry According To Iso/Ts 16949 Requirements A Suppier Evauation System for Automotive Industry According To Iso/Ts 16949 Requirements DILEK PINAR ÖZTOP 1, ASLI AKSOY 2,*, NURSEL ÖZTÜRK 2 1 HONDA TR Purchasing Department, 41480, Çayırova - Gebze,

More information

AA Fixed Rate ISA Savings

AA Fixed Rate ISA Savings AA Fixed Rate ISA Savings For the road ahead The Financia Services Authority is the independent financia services reguator. It requires us to give you this important information to hep you to decide whether

More information

NCH Software FlexiServer

NCH Software FlexiServer NCH Software FexiServer This user guide has been created for use with FexiServer Version 1.xx NCH Software Technica Support If you have difficuties using FexiServer pease read the appicabe topic before

More information

Avaya Remote Feature Activation (RFA) User Guide

Avaya Remote Feature Activation (RFA) User Guide Avaya Remote Feature Activation (RFA) User Guide 03-300149 Issue 5.0 September 2007 2007 Avaya Inc. A Rights Reserved. Notice Whie reasonabe efforts were made to ensure that the information in this document

More information

Ministry of. Education SAMPLE LESSON PLANS. STRANDS: Number, Measurement, Geometry, Statistics and Probability and Algebra. Ministry of Education 2011

Ministry of. Education SAMPLE LESSON PLANS. STRANDS: Number, Measurement, Geometry, Statistics and Probability and Algebra. Ministry of Education 2011 Ministry of Education SAMPLE LESSON PLANS STRANDS: Number, Measurement, Geometry, Statistics and Probabiity and Agebra Ministry of Education 2011 Sampe Lessons copyedits-juy.indd 1 8/27/12 7:37 PM Acknowedgements

More information

WINMAG Graphics Management System

WINMAG Graphics Management System SECTION 10: page 1 Section 10: by Honeywe WINMAG Graphics Management System Contents What is WINMAG? WINMAG Text and Graphics WINMAG Text Ony Scenarios Fire/Emergency Management of Fauts & Disabement Historic

More information

Key Features of Life Insurance

Key Features of Life Insurance Key Features of Life Insurance Life Insurance Key Features The Financia Conduct Authority is a financia services reguator. It requires us, Aviva, to give you this important information to hep you to decide

More information

Vacancy Rebate Supporting Documentation Checklist

Vacancy Rebate Supporting Documentation Checklist Vacancy Rebate Supporting Documentation Checkist The foowing documents are required and must accompany the vacancy rebate appication at the time of submission. If the vacancy is a continuation from the

More information

An Idiot s guide to Support vector machines (SVMs)

An Idiot s guide to Support vector machines (SVMs) An Idiot s guide to Support vector machines (SVMs) R. Berwick, Viage Idiot SVMs: A New Generation of Learning Agorithms Pre 1980: Amost a earning methods earned inear decision surfaces. Linear earning

More information

Absorption Materials and Room Acoustics

Absorption Materials and Room Acoustics Absorption Materias and Room Acoustics How room characteris tics can impact the effectiveness of absorption materias. By Howard K. Peton Insuation and sound contractors work in a wide variety of environments,

More information

NCH Software BroadCam Video Streaming Server

NCH Software BroadCam Video Streaming Server NCH Software BroadCam Video Streaming Server This user guide has been created for use with BroadCam Video Streaming Server Version 2.xx NCH Software Technica Support If you have difficuties using BroadCam

More information

READING A CREDIT REPORT

READING A CREDIT REPORT Name Date CHAPTER 6 STUDENT ACTIVITY SHEET READING A CREDIT REPORT Review the sampe credit report. Then search for a sampe credit report onine, print it off, and answer the questions beow. This activity

More information

Quantum Numbers (and their meaning)

Quantum Numbers (and their meaning) Quantum Numbers (and their meaning) Soution of the Schrödinger equation for the Hydrogen atom The three quantum numbers: n Principa quantum number Orbita anguar momentum quantum number m Magnetic quantum

More information

Insertion and deletion correcting DNA barcodes based on watermarks

Insertion and deletion correcting DNA barcodes based on watermarks Kracht and Schober BMC Bioinformatics (2015) 16:50 DOI 10.1186/s12859-015-0482-7 METHODOLOGY ARTICLE Open Access Insertion and deetion correcting DNA barcodes based on watermarks David Kracht * and Steffen

More information

A Branch-and-Price Algorithm for Parallel Machine Scheduling with Time Windows and Job Priorities

A Branch-and-Price Algorithm for Parallel Machine Scheduling with Time Windows and Job Priorities A Branch-and-Price Agorithm for Parae Machine Scheduing with Time Windows and Job Priorities Jonathan F. Bard, 1 Siwate Rojanasoonthon 2 1 Graduate Program in Operations Research and Industria Engineering,

More information

The guaranteed selection. For certainty in uncertain times

The guaranteed selection. For certainty in uncertain times The guaranteed seection For certainty in uncertain times Making the right investment choice If you can t afford to take a ot of risk with your money it can be hard to find the right investment, especiay

More information

Calibration of the Horizontal Pushrod Dilatometer

Calibration of the Horizontal Pushrod Dilatometer Caibration of the Horizonta Pushrod Diatometer Štefan Vaovič, Igor Štubňa Physics Dpt., Constantine the Phiosopher Univ., A. Hinku 1, 949 74 Nitra, Sovakia E-mai: svaovic@ukf.sk, istubna@ukf.sk Abstract

More information

CLOUD service providers manage an enterprise-class

CLOUD service providers manage an enterprise-class IEEE TRANSACTIONS ON XXXXXX, VOL X, NO X, XXXX 201X 1 Oruta: Privacy-Preserving Pubic Auditing for Shared Data in the Coud Boyang Wang, Baochun Li, Member, IEEE, and Hui Li, Member, IEEE Abstract With

More information

Improving the error rates of the Begg and Mazumdar test for publication bias in fixed effects meta-analysis

Improving the error rates of the Begg and Mazumdar test for publication bias in fixed effects meta-analysis Gjerdevik and Heuch BMC Medica Research Methodoogy 2014, 14:109 http://www.biomedcentra.com/1471-2288/14/109 RESEARCH ARTICLE Improving the error rates of the Begg and Mazumdar test for pubication bias

More information

Breakeven analysis and short-term decision making

Breakeven analysis and short-term decision making Chapter 20 Breakeven anaysis and short-term decision making REAL WORLD CASE This case study shows a typica situation in which management accounting can be hepfu. Read the case study now but ony attempt

More information

Available online Journal of Scientific and Engineering Research, 2016, 3(2): Research Article

Available online  Journal of Scientific and Engineering Research, 2016, 3(2): Research Article Avaiabe onine www.jsaer.com Journa of Scientific and Engineering Research, 016, ():1- Research Artice ISSN: 9-60 CODEN(USA): JSERBR A simpe design of a aboratory testing rig for the experimenta demonstration

More information

LESSON LEVERAGE ANALYSIS 21.0 AIMS AND OBJECTIVES 21.1 INTRODUCTION 21.2 OPERATING LEVERAGE CONTENTS

LESSON LEVERAGE ANALYSIS 21.0 AIMS AND OBJECTIVES 21.1 INTRODUCTION 21.2 OPERATING LEVERAGE CONTENTS LESSON 21 LEVERAGE ANALYSIS CONTENTS 21.0 Aims and Objectives 21.1 Introduction 21.2 Operating Leverage 21.3 Financia Leverage 21.4 EBIT-EPS Anaysis 21.5 Combined Leverage 21.6 Let us Sum up 21.7 Lesson-end

More information

Dynamic Pricing Trade Market for Shared Resources in IIU Federated Cloud

Dynamic Pricing Trade Market for Shared Resources in IIU Federated Cloud Dynamic Pricing Trade Market or Shared Resources in IIU Federated Coud Tongrang Fan 1, Jian Liu 1, Feng Gao 1 1Schoo o Inormation Science and Technoogy, Shiiazhuang Tiedao University, Shiiazhuang, 543,

More information

Constrained Optimization: Step by Step. Maximizing Subject to a set of constraints:

Constrained Optimization: Step by Step. Maximizing Subject to a set of constraints: Constrained Optimization: Step by Step Most (if not a) economic decisions are the resut of an optimization probem subject to one or a series of constraints: Consumers make decisions on what to buy constrained

More information

NCH Software MoneyLine

NCH Software MoneyLine NCH Software MoneyLine This user guide has been created for use with MoneyLine Version 2.xx NCH Software Technica Support If you have difficuties using MoneyLine pease read the appicabe topic before requesting

More information

Manifold Technology. ----------------------------------------------------- made in Germany

Manifold Technology. ----------------------------------------------------- made in Germany Manifod Technoogy. ----------------------------------------------------- made in Germany I EVERYTHING UNDER CONTROL. Manifod Technoogy BEULCO heating and cooing manifods made of high-quaity brass ensure

More information

Learning from evaluations Processes and instruments used by GIZ as a learning organisation and their contribution to interorganisational learning

Learning from evaluations Processes and instruments used by GIZ as a learning organisation and their contribution to interorganisational learning Monitoring and Evauation Unit Learning from evauations Processes and instruments used by GIZ as a earning organisation and their contribution to interorganisationa earning Contents 1.3Learning from evauations

More information

Life Contingencies Study Note for CAS Exam S. Tom Struppeck

Life Contingencies Study Note for CAS Exam S. Tom Struppeck Life Contingencies Study Note for CAS Eam S Tom Struppeck (Revised 9/19/2015) Introduction Life contingencies is a term used to describe surviva modes for human ives and resuting cash fows that start or

More information

1 Basic concepts in geometry

1 Basic concepts in geometry 1 asic concepts in geometry 1.1 Introduction We start geometry with the simpest idea a point. It is shown using a dot, which is abeed with a capita etter. The exampe above is the point. straight ine is

More information

6 Electromagnetic induction

6 Electromagnetic induction 6 ectromagnetic induction PHY67 Spring 006 Michae Faraday s experiment: Changing current in the primary coi resuts in surges of current in the secondary coi. The effect is stronger if both cois are winded

More information

LADDER SAFETY Table of Contents

LADDER SAFETY Table of Contents Tabe of Contents SECTION 1. TRAINING PROGRAM INTRODUCTION..................3 Training Objectives...........................................3 Rationae for Training.........................................3

More information

Comparison of Traditional and Open-Access Appointment Scheduling for Exponentially Distributed Service Time

Comparison of Traditional and Open-Access Appointment Scheduling for Exponentially Distributed Service Time Journa of Heathcare Engineering Vo. 6 No. 3 Page 34 376 34 Comparison of Traditiona and Open-Access Appointment Scheduing for Exponentiay Distributed Service Chongjun Yan, PhD; Jiafu Tang *, PhD; Bowen

More information

Internal Control. Guidance for Directors on the Combined Code

Internal Control. Guidance for Directors on the Combined Code Interna Contro Guidance for Directors on the Combined Code ISBN 1 84152 010 1 Pubished by The Institute of Chartered Accountants in Engand & Waes Chartered Accountants Ha PO Box 433 Moorgate Pace London

More information

Simultaneous Routing and Power Allocation in CDMA Wireless Data Networks

Simultaneous Routing and Power Allocation in CDMA Wireless Data Networks Simutaneous Routing and Power Aocation in CDMA Wireess Data Networks Mikae Johansson *,LinXiao and Stephen Boyd * Department of Signas, Sensors and Systems Roya Institute of Technoogy, SE 00 Stockhom,

More information

Service life of asphalt materials for asset management purposes

Service life of asphalt materials for asset management purposes Service ife of asphat materias for asset management purposes Minera Products Association mpa asphat Minera Products Association 2 - SERVICE LIFE OF ASPHALT MATERIALS FOR ASSET MANAGEMENT PURPOSES Asphat

More information

c? Society for Industrial and Applied Mathematics

c? Society for Industrial and Applied Mathematics SIAM J. SCI. COMPUT. Vo.?, No.?, pp.?? c? Society for Industria and Appied Mathematics ABSOLUTE VALUE PRECONDITIONING FOR SYMMETRIC INDEFINITE LINEAR SYSTEMS EUGENE VECHARYNSKI AND ANDREW KNYAZEV Abstract.

More information

Packet Classification with Network Traffic Statistics

Packet Classification with Network Traffic Statistics Packet Cassification with Network Traffic Statistics Yaxuan Qi and Jun Li Research Institute of Information Technoogy (RIIT), Tsinghua Uniersity Beijing, China, 100084 Abstract-- Packet cassification on

More information

Multi-Robot Task Scheduling

Multi-Robot Task Scheduling Proc of IEEE Internationa Conference on Robotics and Automation, Karsruhe, Germany, 013 Muti-Robot Tas Scheduing Yu Zhang and Lynne E Parer Abstract The scheduing probem has been studied extensivey in

More information