m-a-p/arxiv_image_cap_mini · Datasets at Hugging Face

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Figure 3: The diphoton event distribution from the theoreti al simulation for √S = 1.96GeV, withthe sele tion riteria imposed in the CDF measurement, as a fun tion of the various kinemati variables des ribed in the text, shown for QT < Q and QT > Q separately.	{ "x1": 72, "x2": 539.8804321289062, "y1": 396.0799865722656, "y2": 436.6800842285156 }	Figure	[ "R", "ut", "p", "T", "uts", "Q(GeV", ")", "j", "yj", "os", "?", "Q", "T(GeV", ")", "0.5", "1", "2.5", "1008060402001008060", "40", "1", "-12", "QT", ">", "QQT", "<", "QKinemati", "al", "distributions", "in", "the", "Tevatron", "Run-2", "(CDF)", "01", "0", "1.5", "2", "3", "'", "(rad)", "200", "0" ]	3	14	{ "x1": 144, "x2": 471, "y1": 41.233943939208984, "y2": 383 }	[ "A s atter plot of event distributions from our theoreti al simulation for CDF kinemati uts and arbitrary luminosity is shown in Fig. 3.", " The region QT > QIt is evident from Fig. 3 that the ∆ϕ < π/2 region is populated mostly by events with QT > Q.", " Fig. 3).", " For values of Q below the kinemati uto at about 30 GeV, the uts shown in Fig. 3 suppress diphoton produ tion at small QT , and 〈QT /Q〉 grows toward1 as Q de reases ( orresponding to produ tion only at QT lose to Q)." ]
Fig. 1. Examples of sparsity-certifying decompositions: (a) a 3-arborescence; (b) a 2-map-graph; (c) a (2,1)-maps-and-trees. Edges with the same line style belong to the same subgraph. The 2-map-graph is shown with a certifying orientation.	{ "x1": 72, "x2": 525.3064575195312, "y1": 361.5296325683594, "y2": 395.7250061035156 }	Figure	[ "(c)", "(b)", "4", "3", "2", "1", "(a)", "d", "e", "c", "b", "a" ]	1	2	{ "x1": 120, "x2": 477, "y1": 94.8900146484375, "y2": 347.92901611328125 }	[ " Figure 1(a) shows an example of a 3-arborescence.", " Figure 1(b) shows an example of a 2-map-graphs; the edges are oriented in one possible configuration certifying that each color forms a map-graph." ]
Fig. 2. (a) A graph with a 3T2 decomposition; one of the three trees is a single vertex in the bottom right corner. (b) The highlighted subgraph inside the dashed countour has three black tree-pieces and one gray tree-piece. (c) The highlighted subgraph inside the dashed countour has three gray tree-pieces (one is a single vertex) and one black tree-piece.	{ "x1": 72, "x2": 525.3055419921875, "y1": 330.6646423339844, "y2": 378.4090270996094 }	Figure	[ "(c)", "5", "4", "3", "2", "1", "0", "(b)", "5", "4", "3", "2", "1", "0", "(a)", "5", "4", "3", "2", "1", "0" ]	2	3	{ "x1": 149, "x2": 449, "y1": 95.8900146484375, "y2": 317.06402587890625 }	[ " Figure 2(a) shows an example of a 3T2.", "Figure 2(a) shows a graph with a 3T2 decomposition; we note that one of the trees is an isolated vertex in the bottom-right corner.", " The subgraph in Figure 2(b) has three black treepieces and one gray tree-piece: an isolated vertex at the top-right corner, and two single edges.", " Figure 2(c) shows another subgraph; in this case there are three gray tree-pieces and one black one." ]
Fig. 3. Examples of pebble game with colors moves: (a) add-edge. (b) pebble-slide. Pebbles on vertices are shown as black or gray dots. Edges are colored with the color of the pebble on them.	{ "x1": 72, "x2": 525.3045043945312, "y1": 308.56268310546875, "y2": 329.20806884765625 }	Figure	[ "⇒", "⇒", "(b)", "(a)", "⇒", "⇒" ]	3	4	{ "x1": 81, "x2": 517, "y1": 227.8900146484375, "y2": 294.9620361328125 }	[ "Figure 3(a) shows examples of the add-edge move.", " Figure 3(b) shows examples." ]
Fig. 4. A (2,2)-tight graph with one possible pebble-game decomposition. The edges are oriented to show (1,0)-sparsity for each color. (a) The graph K4 with a pebble-game decomposition. There is an empty black tree at the center vertex and a gray spanning tree. (b) The highlighted subgraph has two black trees and a gray tree; the black edges are part of a larger cycle but contribute a tree to the subgraph. (c) The highlighted subgraph (with a light gray background) has three empty gray trees; the black edges contain a cycle and do not contribute a piece of tree to the subgraph.	{ "x1": 71.99999237060547, "x2": 525.305908203125, "y1": 227.05963134765625, "y2": 301.90203857421875 }	Figure	[ "(a)", "(b)", "(c)" ]	4	5	{ "x1": 101, "x2": 496, "y1": 95.8900146484375, "y2": 213.458984375 }	[ " Figure 4(a) shows an example of a (2,2)-tight graph with a pebble-game decomposition.", " The orientation of the edges in Figure 4(a) shows this.", "For example Figure 4(a) shows a (2,2)-tight graph with one possible pebble-game decomposition.", " The subgraph in Figure 4(b) has a black tree and a gray tree, with the edges of the black tree coming from a cycle in the larger graph.", " In Figure 4(c), however, the black cycle does not contribute a tree-piece." ]
Fig. 5. Creating monochromatic cycles in a (2,0)-pebble game. (a) A type (M1) move creates a cycle by adding a black edge. (b) A type (M2) move creates a cycle with a pebble-slide move. The vertices are labeled according to their role in the definition of the moves.	{ "x1": 71.99996948242188, "x2": 525.3038330078125, "y1": 331.76263427734375, "y2": 365.95703125 }	Figure	[ "(b)", "w", "v", "w", "⇒", "v", "(a)", "⇒", "vw", "vw" ]	5	10	{ "x1": 162, "x2": 435, "y1": 91.8900146484375, "y2": 318.1610107421875 }	[ "Figure 5(a) and Figure 5(b) show examples of (M1) and (M2) map-graph creation moves, respectively, in a (2,0)-pebble game construction." ]
Fig. 6. Outline of the shortcut construction: (a) An arbitrary simple path from v to w with curved lines indicating simple paths. (b) An (M2) step. The black edge, about to be flipped, would create a cycle, shown in dashed and solid gray, of the (unique) gray tree rooted at w. The solid gray edges were part of the original path from (a). (c) The shortened path to the gray pebble; the new path follows the gray tree all the way from the first time the original path touched the gray tree at w′. The path from v to w′ is simple, and the shortcut construction can be applied inductively to it.	{ "x1": 72, "x2": 525.3057250976562, "y1": 519.109619140625, "y2": 593.9520263671875 }	Figure	[ "(c)", "w'", "v", "w", "(b)", "w", "v", "v", "(a)", "w" ]	6	11	{ "x1": 134.87135314941406, "x2": 462.5532531738281, "y1": 231.9584197998047, "y2": 505.5090026855469 }	[ " The main idea, captured in Lemma 15 and illustrated in Figure 6, is to avoid creating cycles while collecting pebbles.", "Figure 6 shows the structure of the proof." ]
Fig. 7. Eliminating (M2) moves: (a) an (M2) move; (b) avoiding the (M2) by moving along another path. The path where the pebbles move is indicated by doubled lines.	{ "x1": 72, "x2": 525.297607421875, "y1": 329.109619140625, "y2": 349.7550048828125 }	Figure	[ "(b)", "⇒", "(a)", "⇒" ]	7	12	{ "x1": 162, "x2": 435, "y1": 91.8900146484375, "y2": 315.50799560546875 }	[]
Fig. 8. Eliminating (M2) moves: (a) the first step to move the black pebble along the doubled path is (M2); (b) avoiding the (M2) and simplifying the path.	{ "x1": 72, "x2": 525.3060302734375, "y1": 581.5916748046875, "y2": 602.238037109375 }	Figure	[ "⇒", "(b)", "⇒", "(a)" ]	8	12	{ "x1": 163, "x2": 435, "y1": 363.8900146484375, "y2": 567.9910278320312 }	[ "Figure 7 and Figure 8 illustrate the construction used in the proof of Lemma 15." ]
Table 1. Sparse graph and decomposition terminology used in this paper.	{ "x1": 72, "x2": 390.9814758300781, "y1": 237.56866455078125, "y2": 244.6650390625 }	Table	[ "Term", "Meaning", "Sparse", "graph", "G", "Every", "non-empty", "subgraph", "on", "n′", "vertices", "has", "≤", "kn′−", "`", "edges", "Tight", "graph", "G", "G", "=", "(V,E)", "is", "sparse", "and", "\|V", "\|=", "n,", "\|E\|=", "kn−", "`", "Block", "H", "in", "G", "G", "is", "sparse,", "and", "H", "is", "a", "tight", "subgraph", "Component", "H", "of", "G", "G", "is", "sparse", "and", "H", "is", "a", "maximal", "block", "Map-graph", "Graph", "that", "admits", "an", "out-degree-exactly-one", "orientation", "(k,", "`)-maps-and-trees", "Edge-disjoint", "union", "of", "`", "trees", "and", "(k−", "`)", "map-grpahs", "`Tk", "Union", "of", "`", "trees,", "each", "vertex", "is", "in", "exactly", "k", "of", "them", "Set", "of", "tree-pieces", "of", "an", "`Tk", "induced", "on", "V", "′", "⊂V", "Pieces", "of", "trees", "in", "the", "`Tk", "spanned", "by", "E(V", "′)", "Proper", "`Tk", "Every", "V", "′", "⊂V", "contains", "≥", "`", "pieces", "of", "trees", "from", "the", "`Tk" ]	1	1	{ "x1": 72, "x2": 570, "y1": 91.8900146484375, "y2": 233.8900146484375 }	[ "Table 1 summarizes the sparse graph terminology used in this paper.", "Table 1 contains the decomposition terminology used in this paper." ]
Table 2. Pebble game notation used in this paper.	{ "x1": 72, "x2": 287.30145263671875, "y1": 409.2216491699219, "y2": 416.3180236816406 }	Table	[ "Notation", "Meaning", "span(V", "′)", "Number", "of", "edges", "spanned", "in", "H", "by", "V", "′", "⊂V", ";", "i.e.", "\|EH(V", "′)\|", "peb(V", "′)", "Number", "of", "pebbles", "on", "V", "′", "⊂V", "out(V", "′)", "Number", "of", "edges", "vw", "in", "H", "with", "v", "∈V", "′", "and", "w", "∈V", "−V", "′", "pebi(v)", "Number", "of", "pebbles", "of", "color", "ci", "on", "v", "∈V", "outi(v)", "Number", "of", "edges", "vw", "colored", "ci", "for", "v", "∈V" ]	2	5	{ "x1": 72, "x2": 381, "y1": 318.8900146484375, "y2": 405.8900146484375 }	[ "Table 2 lists the pebble game notation used in this paper." ]
Figure 2, the solar days / year vs. the age of the Earth	{ "x1": 151.6199951171875, "x2": 488.5828552246094, "y1": 76.61536407470703, "y2": 85.91998291015625 }	Figure	[ "480", "460", "440", "420", "400", "380", "360", "ye", "ar", "ay", "s/", "ar", "d", "S", "ol", "3.5", "3.6", "3.7", "3.8", "3.9", "4.0", "4.1", "4.2", "4.3", "4.4", "4.5", "4.6", "The", "age", "of", "the", "Earth", "(109", "years)" ]	2	21	{ "x1": 100.54000091552734, "x2": 505.56866455078125, "y1": 121.86924743652344, "y2": 418.32000732421875 }	[]
FIG. 1: Principal isentrope and shock Hugoniot for air (perfect gas): numerical calculations for general material models, compared with analytic solutions.	{ "x1": 72, "x2": 538.2794189453125, "y1": 275.2254333496094, "y2": 302.39990234375 }	Figure	[ "Hugoniot", "isentrope", "mass", "density", "(g/cm3)", "%", ")", "ce", "(", "er", "en", "d", "iff", "su", "re", "pr", "es", "0.001", "0.01", "1", "0.1", "0.01", "0.001", "0.0001", "Hugoniot", "isentrope", "mass", "density", "(g/cm3)", "P", "a)", "(", "G", "su", "re", "pr", "es", "0.001", "0.01", "0.01", "0.001", "0.0001" ]	1	26	{ "x1": 80.85079956054688, "x2": 533.0890502929688, "y1": 79.8526840209961, "y2": 235.61602783203125 }	[ "1% respectively, for a compression increment of 1% along the isentrope and a solution tolerance of 10−6 GPa for each shock state (Fig. 1).", " Each of these scenarios may occur in turn following the impact of a projectile with a target: if the target is layered then a shock is transmitted across each interface with a release or a reshock reflected back, depending on the materials; release ultimately occurs at the rear of the projectile and the far end of the target, and the oppositely-moving release waves subject the projectile and target to tensile stresses when they interact (Fig. 10).", "3GPa in the LiF, using the same material properties (Fig. 11)." ]
FIG. 10: Schematic of uniaxial wave interactions induced by the impact of a flat projectile with a composite target.	{ "x1": 72, "x2": 538.2787475585938, "y1": 349.9854431152344, "y2": 377.0400085449219 }	Figure	[ "release", "interactions:", "free", "surface", "release", "impact", "shocks", "transmitted", "shock;", "reflected", "wave", "target", "w", "d", "o", "w", "in", "ct", "ile", "ro", "je", "e", "p", "ti", "m", "tension" ]	10	35	{ "x1": 212.6199951171875, "x2": 405.7367248535156, "y1": 73.25399017333984, "y2": 310.79998779296875 }	[]
FIG. 11: Hydrocode simulation of Al projectile at 3.6 km/s impacting a Mo target with a LiF release window, 1.1 µs after impact. Structures on the waves are elastic precursors.	{ "x1": 72, "x2": 538.2661743164062, "y1": 312.7854309082031, "y2": 339.8399963378906 }	Figure	[ "original", "shock", "state", "shock", "release", "transmitted", "reflected", "LiFAl", "Mo", "position", "(mm)", "P", "a)", "s", "(G", "tr", "es", "al", "s", "no", "rm", "0", "5", "10", "15", "20", "70", "60", "50", "40", "30", "20", "10", "0" ]	11	36	{ "x1": 172.49200439453125, "x2": 439.1109924316406, "y1": 81.55197143554688, "y2": 271.9320068359375 }	[]
FIG. 2: Shock Hugoniot for Al in pressure-temperature space, for different representations of the equation of state.	{ "x1": 72, "x2": 538.2723999023438, "y1": 312.7854309082031, "y2": 339.8399963378906 }	Figure	[ "solid:", "Grueneisen", "dashed:", "SESAME", "3716", "temperature", "(K)", "P", "a)", "s", "(G", "tr", "es", "al", "s", "no", "rm", "0", "1000", "2000", "3000", "4000", "5000", "120", "100", "80", "60", "40", "20", "0" ]	2	27	{ "x1": 172.49200439453125, "x2": 444.66998291015625, "y1": 81.55197143554688, "y2": 271.9320068359375 }	[ " Taking a SESAME type EOS, thermodynamic loci were calculated with {ρ, e} or {ρ, T} primitive states, for comparison (Fig. 2).", " Temperatures were in good agreement (Fig. 2)." ]
FIG. 3: Principal adiabat and shock Hugoniot for Be in normal stress-compression space, neglecting strength (dashed), for Steinberg-Guinan strength (solid), and for elastic-perfectly plastic with Y = 10 GPa (dotted).	{ "x1": 72, "x2": 538.282958984375, "y1": 312.7854309082031, "y2": 361.5599060058594 }	Figure	[ "each", "pair", "of", "lines:", "upper", "is", "Hugoniot,", "lower", "is", "adiabat", "volume", "compression", "P", "a)", "s", "(G", "tr", "es", "al", "s", "no", "rm", "0.7", "0.75", "0.8", "0.85", "0.9", "0.95", "1", "90", "80", "70", "60", "50", "40", "30", "20", "10", "0" ]	3	28	{ "x1": 172.49200439453125, "x2": 436.3299865722656, "y1": 81.55197143554688, "y2": 271.9320068359375 }	[ "greater heating obtained by integrating along the adiabat compared with jumping from the initial to the final state on the Hugoniot (Fig. 3)." ]
FIG. 4: Principal adiabat and shock Hugoniot for Be in shock speed-normal stress space, neglecting strength (dashed), for Steinberg-Guinan strength (solid), and for elastic-perfectly plastic with Y = 10 GPa (dotted).	{ "x1": 72, "x2": 538.282958984375, "y1": 312.7854309082031, "y2": 361.5599060058594 }	Figure	[ "plastic", "shock", "elastic", "wave", "normal", "stress", "(GPa)", "/s", ")", "(k", "m", "ee", "d", "k", "sp", "sh", "oc", "0", "20", "40", "60", "80", "100", "120", "140", "15", "14", "13", "12", "11", "10", "9", "8" ]	4	29	{ "x1": 172.49200439453125, "x2": 433, "y1": 81.55197143554688, "y2": 271.9320068359375 }	[ " In Be with the high flow stress of nanosecond response, the relation between shock and particle speeds is significantly different from the relation for low flow stress (Fig. 4)." ]
FIG. 5: Principal adiabat, shock Hugoniot, and release adiabat for Be in normal stress-temperature space, neglecting strength (dashed), for Steinberg-Guinan strength (solid), and for elastic-perfectly plastic with Y = 10 GPa (dotted).	{ "x1": 72, "x2": 538.2528686523438, "y1": 312.7854309082031, "y2": 361.5599060058594 }	Figure	[ "release", "adiabat", "principal", "Hugoniot", "principal", "adiabat", "temperature", "(K)", "P", "a)", "s", "(G", "tr", "es", "al", "s", "no", "rm", "0", "1000", "2000", "3000", "4000", "5000", "200", "150", "100", "50", "0" ]	5	30	{ "x1": 172.49200439453125, "x2": 444.66998291015625, "y1": 81.55197143554688, "y2": 271.9320068359375 }	[ " (Fig. 5." ]
FIG. 6: Demonstration of shock Hugoniot solution across a phase boundary: shock-melting of Al, for different initial porosities.	{ "x1": 72, "x2": 538.2545776367188, "y1": 312.7854309082031, "y2": 339.8399963378906 }	Figure	[ "30%", "20%", "solid", "Hugoniot", "10%", "melt", "locus", "temperature", "(K)", "P", "a)", "s", "(G", "tr", "es", "al", "s", "no", "rm", "0", "1000", "2000", "3000", "4000", "5000", "140", "120", "100", "80", "60", "40", "20", "0" ]	6	31	{ "x1": 172.49200439453125, "x2": 444.66998291015625, "y1": 81.55197143554688, "y2": 271.9320068359375 }	[ "397MJ/kg, the shock Hugoniot algorithm was found to operate stably across the phase transition (Fig. 6)." ]
FIG. 7: Wave interactions for the impact of a flat projectile moving from left to right with a stationary target. Dashed arrows are a guide to the sequence of states. For a projectile moving from right to left, the construction is the mirror image reflected in the normal stress axis.	{ "x1": 72, "x2": 538.2923583984375, "y1": 301.9854431152344, "y2": 350.7599182128906 }	Figure	[ "of", "target", "of", "projectile", "shock", "state:", "intersection", "principal", "Hugoniot", "principal", "Hugoniot", "of", "target", "initial", "state", "of", "projectile", "0", "es", "s", "s", "tr", "rm", "al", "n", "o", "particle", "speed", "initial", "state" ]	7	32	{ "x1": 194.02000427246094, "x2": 423.7277526855469, "y1": 73, "y2": 259.8599853515625 }	[ " Examples of these wave interactions are the impact of a projectile with a stationary target (Fig. 7), release of a shock state at a free surface or a material (e." ]
FIG. 8: Wave interactions for the release of a shocked state (shock moving from left to right) into a stationary ‘window’ material to its right. The release state depends whether the window has a higher or lower shock impedance than the shocked material. Dashed arrows are a guide to the sequence of states. For a shock moving from right to left, the construction is the mirror image reflected in the normal stress axis.	{ "x1": 72, "x2": 538.3157348632812, "y1": 328.9854431152344, "y2": 421.0802307128906 }	Figure	[ "window", "release", "target", "release", "at", "free", "surface", "target", "release", "isentrope", "low", "impedance", "window", "principal", "Hugoniot:", "high", "impedance", "window", "of", "target", "initial", "shock", "state", "in", "target", "secondary", "Hugoniot", "0", "es", "s", "s", "tr", "rm", "al", "n", "o", "particle", "speed", "states" ]	8	33	{ "x1": 161.97999572753906, "x2": 455.92578125, "y1": 73, "y2": 286.8600158691406 }	[ " a window) of lower shock impedance (hence reflecting a release wave into the shocked material – Fig. 8), reshocking at a surface with a material of higher shock impedance (Fig." ]
FIG. 9: Wave interactions for the release of a shocked state by tension induced as materials try to separate in opposite directions when joined by a bonded interface. Material damage, spall, and separation are neglected: the construction shows the maximum tensile stress possible. For general material properties, e.g. if plastic flow is included, the state of maximum tensile stress is not just the negative of the initial shock state. Dashed arrows are a guide to the sequence of states. The graph shows the initial state after an impact by a projectile moving from right to left; for a shock moving from right to left, the construction is the mirror image reflected in the normal stress axis.	{ "x1": 71.99996948242188, "x2": 538.3623657226562, "y1": 439.38543701171875, "y2": 574.8001098632812 }	Figure	[ "initial", "shock", "state", "projectile", "release", "target", "release", "target", "release", "0", "es", "s", "s", "tr", "rm", "al", "n", "o", "particle", "speed", "final", "tensile", "state", "in", "projectile", "and", "target", "in", "projectile", "and", "target", "projectile", "release" ]	9	34	{ "x1": 194.02000427246094, "x2": 425.2499694824219, "y1": 73, "y2": 397.25994873046875 }	[ " 8), or tension induced as materials try to separate in opposite directions when joined by a bonded interface (Fig. 9)." ]
TABLE I: Interface to material models required for explicit forward-time continuum dynamics simulations.	{ "x1": 72, "x2": 538.3253173828125, "y1": 84.06546783447266, "y2": 111.23992919921875 }	Table	[ "etc.", "that", "mass", "density", "is", "positive,", "volume", "or", "mass", "fractions", "of", "components", "of", "a", "mixture", "add", "up", "to", "one,", "calculations", "of", "the", "shock", "Hugoniot", "and", "ramp", "compression.", "Checks", "for", "self-consistency", "include", "that", "is", "most", "robust", "for", "explicit,", "forward-time", "numerical", "solutions", "and", "can", "also", "be", "used", "for", "the", "instantaneous,", "local", "state.”", "The", "evolution", "functions", "are", "shown", "in", "the", "operator-split", "structure", "Parentheses", "in", "the", "interface", "calls", "denote", "functions,", "e.g.", "“stress(state)”", "for", "“stress", "as", "a", "function", "of", "check", "for", "self-consistency", "multiply", "state", "by", "a", "scalar", "add", "states", "manipulation", "of", "states", "create", "and", "delete", "internal", "evolution", "of", "state", "d(state)/dt", "evolution", "of", "state", "(heating)", "d(state)/dt(state,ė)", "evolution", "of", "state", "(deformation)", "d(state)/dt(state,grad", "~u)", "time", "step", "control", "sound", "speed(state)", "continuum", "dynamics", "equations", "stress(state)", "program", "set-up", "read/write", "material", "data", "purpose", "interface", "calls" ]	I	23	{ "x1": 72, "x2": 538.2662353515625, "y1": 127, "y2": 498.3597412109375 }	[ " The continuum dynamics programs and the material properties relations can be developed and maintained independently of each other, provided that the interface remains the same (Table I).", " At the highest level, different types of behavior are characterized by different structures for the state s (Table II).", " For our application, polymorphism is used at several levels in the hierarchy of objects, from the overall type of a material (such as ‘one represented by a pressure-density-energy EOS’ or ‘one represented by a deviatoric stress model’) through the type of relation used to describe the properties of that material type (such as perfect gas, polytropic, or Grüneisen for a pressure-density-energy EOS, or Steinberg-Guinan [13] or Preston-Tonks-Wallace [14] for a deviatoric stress model), to the type of general mathematical function used to represent some of these relations (such as a polynomial or a tabular representation of γ(ρ) in a polytropic EOS) (Table III)." ]
TABLE II: Examples of types of material model, distinguished by different structures in the state vector.	{ "x1": 72, "x2": 538.1466674804688, "y1": 84.06546783447266, "y2": 111.23992919921875 }	Table	[ "triangular", "components,", "e.g.", "using", "Voigt", "notation.", "tensors", "such", "as", "the", "stress", "deviator", "are", "represented", "more", "compactly", "by", "their", "6", "unique", "upper", "transferring", "mass", "between", "components", "representing", "diﬀerent", "types", "of", "molecule.", "Symmetric", "components.", "Gas-phase", "reaction", "can", "be", "represented", "as", "a", "homogeneous", "mixture,", "reactions", "products;", "reaction,", "a", "process", "of", "internal", "evolution,", "transfers", "material", "from", "unreacted", "to", "reacted", "solid", "explosives", "can", "be", "represented", "as", "heterogeneous", "mixtures,", "one", "component", "being", "the", "reacted", "plastic", "part", "of", "velocity", "gradient,", "G:", "shear", "modulus,", "ǫ̇e,p:", "elastic", "and", "plastic", "parts", "of", "strain", "rate", "deviator,", "ǫ̃p:", "scalar", "equivalent", "plastic", "strain,", "fǫ:", "factor", "in", "eﬀective", "strain", "magnitude.", "Reacting", "fm:", "mass", "fraction,", "σ:", "stress", "deviator,", "fp:", "fraction", "of", "plastic", "work", "converted", "to", "heat,", "gradup:", "The", "symbols", "are", "ρ:", "mass", "density;", "e:", "speciﬁc", "internal", "energy,", "T", ":", "temperature,", "fv:", "volume", "fraction,", "fǫ\|\|ǫ̇2", "p\|\|", "ρ", ",", "Gǫ̇e,", "√", "thermal", "equation", "of", "state", "ρ,", "T", "−ρdiv~u,−pdiv~u/ρcv", "heterogeneous", "mixture", "{ρ,", "e,", "fv}i", "{−ρdiv~u,−pdiv~u/ρ,", "0}i", "homogeneous", "mixture", "ρ,", "T,", "{fm}i", "{−ρdiv~u,−pdiv~u/ρcv", ",", "0i", "traditional", "deviatoric", "strength", "ρ,", "e,", "σ,", "ǫ̃p", "−ρdiv~u,", "−pdiv~u+fp\|\|σǫ̇p\|\|", "mechanical", "equation", "of", "state", "ρ,", "e", "−ρdiv~u,−pdiv~u/ρ", "s", "ṡm(s,", "gradu)", "model", "state", "vector", "eﬀect", "of", "mechanical", "strain" ]	II	24	{ "x1": 72, "x2": 538.12841796875, "y1": 127, "y2": 519 }	[]
TABLE III: Outline hierarchy of material models, illustrating the use of polymorphism (in the object-oriented programming sense).	{ "x1": 72, "x2": 538.2804565429688, "y1": 84.66544342041016, "y2": 111.83990478515625 }	Table	[ "plus", "its", "volume", "fraction.", "set", "of", "‘pure’", "material", "properties", "of", "any", "type,", "and", "the", "state", "is", "the", "set", "of", "states", "for", "each", "component", "the", "state", "is", "the", "set", "of", "states", "and", "mass", "fractions", "for", "each.", "Heterogeneous", "mixtures", "are", "deﬁned", "as", "a", "represented", "by", "a", "solid", "state", "plus", "a", "void", "fraction", "fv,", "with", "operations", "deﬁned", "by", "extending", "those", "of", "the", "solid", "material.", "Homogeneous", "mixtures", "are", "deﬁned", "as", "a", "set", "of", "thermal", "equations", "of", "state,", "and", "are", "deﬁned", "by", "extending", "those", "of", "the", "mechanical", "equation", "of", "state.", "Spalling", "materials", "can", "be", "The", "reactive", "equation", "of", "state", "has", "an", "additional", "state", "parameter", "λ,", "and", "the", "software", "operations", "handled", "transparently", "by", "the", "object-oriented", "software", "structure.", "state),", "the", "speciﬁc", "model", "type", "(e.g.", "polytropic),", "and", "the", "state", "of", "material", "of", "that", "type", "are", "all", "with", "an", "abstract", "material", "state.", "The", "actual", "type", "of", "a", "material", "(e.g.", "mechanical", "equation", "of", "Continuum", "dynamics", "programs", "can", "refer", "to", "material", "properties", "as", "an", "abstract", "‘material", "type’", "heterogeneous", "mixture", "equilibration", "and", "reaction", "models", "homogeneous", "mixture", "mixing", "and", "reaction", "models", "Wallace,", "etc", "Steinberg-Lund,", "Preston-Tonks-", "deviatoric", "stress", "elastic-plastic,", "Steinberg-Guinan,", "spall", "Cochran-Banner", "Wilkins-Lee", "reactive", "equation", "of", "state", "modiﬁed", "polytropic,", "reactive", "Jones-", "etc", "Lee,", "quasiharmonic,", "(ρ,", "T", ")", "table,", "thermal", "equation", "of", "state", "temperature-based", "Jones-Wilkins-", "Jones-Wilkins-Lee,", "(ρ,", "T", ")", "table,", "etc", "mechanical", "equation", "of", "state", "polytropic,", "Grüneisen,", "energy-based", "material", "(or", "state)", "type", "model", "type" ]	III	25	{ "x1": 72.0013427734375, "x2": 538.2540283203125, "y1": 130, "y2": 673.199951171875 }	[]
Fig. 1.— Three color image of the area mapped in Serpens. The color mapping is: blue/4.5µm, green/8.0µm, and red/24µm. The locations of Cluster A (Core Cluster), Cluster B (Serpens G3-G6 Cluster), and VV Ser are indicated.	{ "x1": 72, "x2": 539.9144287109375, "y1": 659.7764282226562, "y2": 697.5599975585938 }	Figure	[]	1	4	{ "x1": 120, "x2": 521, "y1": 117, "y2": 636 }	[ " Figure 1 shows the entire area mapped with all four IRAC bands and MIPS at 24 and 70µm and also indicates the locations of several areas mentioned in the text.", " Figure 10 shows the two-point correlation function, W, for the YSO’s in our Serpens catalog and the sample of objects classified as extra-galactic background sources.", " These results are consistent with the appearance of the source distributions as shown, for example, in Figure 13 of Paper I.", " As shown in Figure 10, the slope and magnitude of the correlation for our sample of background extragalactic objects is consistent with that found by, for example, Maddox et al.", " Figure 11 shows no such correlation; in fact, if anything there appears to be a lack of relatively blue colors for the brightest objects.", "Fig. 13.", " Symbols as in Figure 12." ]
Fig. 10.— Left panel: the two-point correlation function, W, for Serpens. The dotted histogram is for sources identified as Class I and “Flat” SED objects, i.e. α ≥ −0.3. The solid histogram is for the Class II/III objects, i.e. α < −0.3. The dashed lines show several possible power law slopes for the portions of the YSO curves. Right panel: the dashed histogram is for the objects classified as likely background galaxies with S/N > 7 in all four IRAC bands. The dash-dot line shows the slope and amplitude found by Maddox et al. (1990) for the bright end of the extra-galactic population, which is a quite good fit to our estimate of the background contamination in our sample.	{ "x1": 71.99957275390625, "x2": 540.0379028320312, "y1": 647.7764282226562, "y2": 765.0001831054688 }	Figure	[]	10	24	{ "x1": 34, "x2": 551, "y1": 296, "y2": 610 }	[]
Fig. 11.— Color-color and color-magnitude plots of the 235 Serpens YSO’s compared with the distributions from models of Robitaille et al. (2007). The symbols are for the three different luminosity groups discussed in the text: open diamonds, L > 1 L⊙; light filled circles, 0.02 L⊙< L < 1 L⊙; plus signs, L < 0.02 L⊙. The model data were those for their model cluster, with a distance of 260 pc for Serpens and with the c2d completeness limits. Also shown are the rough areas from Robitaille et al. (2007) occupied by mainly stage I, II, and III models.	{ "x1": 71.99984741210938, "x2": 540.0189819335938, "y1": 647.7764282226562, "y2": 749.1599731445312 }	Figure	[ "–", "27", "–" ]	11	26	{ "x1": 61, "x2": 491, "y1": 62, "y2": 618 }	[]
Fig. 12.— Spectral Energy Distributions of the Class I sources in the sample. The open dots signal the observed fluxes from J-band to MIPS-70 when available. The label gives the index in Table 2.	{ "x1": 72, "x2": 540.0562744140625, "y1": 678.7363891601562, "y2": 716.52001953125 }	Figure	[]	12	30	{ "x1": 72, "x2": 498, "y1": 108, "y2": 659 }	[]
Fig. 14.— Spectral Energy Distributions of the Flat sources in the sample. Symbols as in Figure 12.	{ "x1": 72, "x2": 540.0361328125, "y1": 683.5364379882812, "y2": 705.3598022460938 }	Figure	[]	14	32	{ "x1": 72, "x2": 498, "y1": 113, "y2": 664 }	[]
Fig. 15.— Spectral Energy Distributions (SED) of the Class II sources in the sample. The open and solid dots are the observed and dereddened fluxes respectively. The grey line is the stellar model of a K7 star and the dashed line is the median SED of the TTauri stars in Taurus by Hartmann et al. (2005) normalized to the dereddened J-band flux for comparison. See text for more information.	{ "x1": 72, "x2": 540.036865234375, "y1": 678.7363891601562, "y2": 748.3200073242188 }	Figure	[]	15	33	{ "x1": 72, "x2": 498, "y1": 108, "y2": 659 }	[]
Fig. 16.— Spectral Energy Distributions of the Class II sources in the sample (continued).	{ "x1": 72, "x2": 536.4183959960938, "y1": 691.0964965820312, "y2": 697.080078125 }	Figure	[]	16	34	{ "x1": 72, "x2": 498, "y1": 120, "y2": 671 }	[]
Fig. 17.— Spectral Energy Distributions of the Class II sources in the sample (continued).	{ "x1": 72, "x2": 536.4183959960938, "y1": 691.0964965820312, "y2": 697.080078125 }	Figure	[]	17	35	{ "x1": 72, "x2": 498, "y1": 120, "y2": 671 }	[]
Fig. 18.— Spectral Energy Distributions of the Class II sources in the sample (continued).	{ "x1": 72, "x2": 536.4183959960938, "y1": 691.0964965820312, "y2": 697.080078125 }	Figure	[]	18	36	{ "x1": 72, "x2": 498, "y1": 120, "y2": 671 }	[]
Fig. 19.— Spectral Energy Distributions of the Class III sources in the sample.	{ "x1": 72, "x2": 478.5708312988281, "y1": 691.4562377929688, "y2": 697.4398193359375 }	Figure	[]	19	37	{ "x1": 72, "x2": 498, "y1": 121, "y2": 672 }	[]
Fig. 2.— The distribution of visual extinctions found toward the roughly 50,000 sources classified as stars in our Serpens observations.	{ "x1": 72, "x2": 539.860107421875, "y1": 668.056396484375, "y2": 689.8801879882812 }	Figure	[]	2	8	{ "x1": 65, "x2": 568, "y1": 265, "y2": 638 }	[ " This reddening was accomplished by randomly applying extinction to each SWIRE source according to the extinction profile of Serpens, shown in Figure 2.", "Fig. 24." ]
Fig. 20.— Spectral Energy Distributions of the Class III sources in the sample.	{ "x1": 72, "x2": 478.5708312988281, "y1": 567.9764404296875, "y2": 573.9600219726562 }	Figure	[]	20	38	{ "x1": 123, "x2": 490, "y1": 375, "y2": 495 }	[]
Fig. 21.— Distribution of disk to star luminosity ratios. The solid and dashed lines are the total sample and T Tauri-like sample of SEDs, respectively. Also marked are the typical ranges of Ldisk/Lstar ratios for debris disks, passive irradiated disks and accretion disks. The figure indicates that objects of all three evolutionary stages are found in Serpens, with a predominance of young accreting T Tauri-type stars.	{ "x1": 72, "x2": 540.0541381835938, "y1": 529.576416015625, "y2": 599.1599731445312 }	Figure	[]	21	40	{ "x1": 54, "x2": 441, "y1": 218, "y2": 510 }	[ " The corresponding distribution is shown in Figure 21." ]
Fig. 22.— Distribution of excess slopes αexcess with respect to the wavelength at which the infrared excess begins λturn−off for the sample of wTTs (solid dots), a sample of cTTs in Lupus from Cieza et al. (2006), the median SED of cTTs in Taurus from D’Alessio et al. (1999) in asterisks (marked as D99), and a sample of debris disks from Chen et al. (2005) in diamonds. The arrows represent the limits for the class II objects in Serpens and the triangles the Class III sources. The diagram shows a much larger spread in inner disk morphologies in the more evolved objects than in the least evolved ones. The Serpens objects follow the previously observed trend.	{ "x1": 72, "x2": 540.0654907226562, "y1": 548.4164428710938, "y2": 665.6397705078125 }	Figure	[]	22	41	{ "x1": 82, "x2": 554, "y1": 140, "y2": 452 }	[ " (2006) found that λexcess is well correlated with evolutionary phase and also, as seen in Figure 22, that α is observed over wider ranges for later evolutionary phases." ]
Fig. 23.— Three-color image of the Cluster A area of Serpens. The color coding is: blue/4.5µm, green/8.0µm, and red/24µm. Some of the more obvious objects that are likely to be jets are marked by arrows. The region of the disappearing source 81 of Eiroa & Casali (1992) is circled.	{ "x1": 71.99972534179688, "x2": 539.9332885742188, "y1": 651.8563842773438, "y2": 705.480224609375 }	Figure	[]	23	43	{ "x1": 539.9332885742188, "x2": 591, "y1": 149, "y2": 665 }	[ " Interestingly, though, this area marked in Figure 23 appears to contain several small knots of emission that may represent shocked gas.", "— Three-color image of the Cluster B area of Serpens as for Figure 23." ]
Fig. 3.— Color-magnitude and color-color diagrams for the Serpens Cloud (left), full SWIRE (center), and trimmed SWIRE regions. The black dashed lines show the “fuzzy” colormagnitude cuts that define the YSO candidate criterion in the various color-magnitude spaces. The red dashed lines show hard limits, fainter than which objects are excluded from the YSO category.	{ "x1": 72, "x2": 540.0781860351562, "y1": 647.7764282226562, "y2": 717.3599853515625 }	Figure	[ "–", "12", "–" ]	3	11	{ "x1": 100, "x2": 513, "y1": 76.81640625, "y2": 624 }	[ " In our new classification we have extended this concept to include the color and magnitude spaces in Figure 3 together with several additional criteria to compute a proxy for the probability that a source is a YSO or a background galaxy.", " Figure 3 shows a collection of three color-magnitude diagrams and one color-color diagram used to classify the sources found in our 3.", " Basically we form the product of individual probabilities from each of the three color-magnitude diagrams in Figure 3 and then use additional factors to modify that total “probability” based on source properties such as: its K - [4.", " The right panels in Figure 3, which use the resampled version of the SWIRE catalog, show that the effects of sensitivity and, especially, the extinction in Serpens make our cutoff limits particularly conservative in terms of likelihood of misclassification.", " (2007) have classified four AGB stars by their Spitzer-IRS spectra in the Serpens cloud; these are identified in the diagrams of Figure 3 by black open diamonds and obviously are not included in our final list of high-probability YSO’s.", " On the other hand, as we discuss in §6, some of the faint red objects in Figure 3 (below the dashed line) may also be young substellar objects.", "is based on the color-magnitude diagrams shown in Figure 3." ]
Fig. 4.— Plot of the number of sources versus probability (of being a background contaminant) for the Serpens cloud and for the trimmed SWIRE catalog described in the text. The vertical dashed line shows the separation chosen for YSO’s versus extra-galactic candidates. For both samples, only sources with detections in all four IRAC bands are plotted to keep the number counts of contaminants on scale!	{ "x1": 72, "x2": 539.9786376953125, "y1": 647.7764282226562, "y2": 717.3599853515625 }	Figure	[]	4	12	{ "x1": 85, "x2": 572, "y1": 125, "y2": 630 }	[]
Fig. 5.— Left panel: image of the entire mapped area of Serpens at 8.0µm with the positions of YSO’s plotted with circles and likely extra-galactic background contaminants with asterisks; center panel: same image with YSO’s of luminosity L < 2×10−2L⊙ plotted with boxes, and higher luminosity YSO’s plotted with circles; right panel: contours of visual extinction Av at levels of 5, 10, 20, 30 magnitudes as derived from fitting the energy distributions of sources that were well-fit as reddened stellar photospheres in our data set.	{ "x1": 71.99932861328125, "x2": 539.99365234375, "y1": 683.7764282226562, "y2": 769.2001953125 }	Figure	[]	5	13	{ "x1": 90, "x2": 491, "y1": 111, "y2": 630 }	[ " Figure 5 shows such a plot in addition to a plot of visual extinction discussed later.", " Figure 5 presented in §3.", " We also showed in Figure 5 that the spatial distribution of our high quality YSO candidates was highly clustered." ]
Fig. 6.— Luminosity function for Serpens YSO’s (solid) and estimate of correction for completeness effects (dashed).	{ "x1": 72, "x2": 540.0196533203125, "y1": 667.6964111328125, "y2": 689.6397705078125 }	Figure	[]	6	18	{ "x1": 85, "x2": 569, "y1": 145, "y2": 650 }	[ " With all these caveats in mind, we display in Figure 6 the histogram of total luminosities for the 235 YSO’s found in Serpens in our survey with the assumed distance of 260 pc.", " Of course an important question to ask is to what extent this luminosity distribution in Figure 6 is influenced by selection effects.", " The lower panel of Figure 7 then shows this ratio as our estimate of the completeness function at the range of luminosities of Serpens YSO’s observed in Figure 6.", " In Figure 6, then, we also indicate how the YSO luminosity function might be adjusted to account for this estimate of our survey completeness (with an assumed completeness of 100% at the bright end)." ]
Fig. 7.— Upper panel – number counts for the full SWIRE catalog as processed through the c2d pipeline for objects detected in all four IRAC bands versus those for the “trimmed” version of the catalog with completeness limits for each individual band comparable to those for c2d. Lower panel – the ratio of the two number counts, i.e. completeness factor.	{ "x1": 72, "x2": 540.043701171875, "y1": 652.2164306640625, "y2": 705.8397827148438 }	Figure	[]	7	19	{ "x1": 100, "x2": 504, "y1": 103, "y2": 645 }	[]
Fig. 8.— Histogram of distribution of spectral slopes, “alpha”, for three luminosity “classes” of YSO’s.	{ "x1": 72, "x2": 539.7640991210938, "y1": 669.2564086914062, "y2": 691.0802001953125 }	Figure	[]	8	20	{ "x1": 96, "x2": 572, "y1": 146, "y2": 651 }	[]
Fig. 9.— Histogram of distribution of average extinction for stars within 80” of each YSO for “high” and “low” luminosity YSO’s (above or below 2 × 10−2L⊙).	{ "x1": 72, "x2": 540.0201416015625, "y1": 667.6964111328125, "y2": 691.4398193359375 }	Figure	[]	9	21	{ "x1": 90, "x2": 507, "y1": 97, "y2": 649 }	[ " The off-cloud fields (when normalized to the same area as the Serpens data) provide the best handle on the degree of contamination from AGB stars; in Paper I we saw one object classified as a YSO candidate in the off-cloud panel of Figure 9 with [8.", " Finally, Figure 9 shows the distribution of extinction for stars nearby each YSO." ]
Table 1. YSO vs. X-Gal Discrimination Criteria	{ "x1": 178.79998779296875, "x2": 433.0876159667969, "y1": 286.6964111328125, "y2": 292.67999267578125 }	Table	[ "K", "-", "[4.5]", "Prob/(K", "−", "[4.5])", "[4.5]", "(for", "[4.5]-[8.0]", "<", "0.5)", "Smooth", "increase", "for", "[4.5]", ">", "14.5", "[4.5]", "(for", "0.5", "<", "[4.5]-[8.0]", "<", "1.4,", "Extended)", "Smooth", "increase", "for", "[4.5]", ">", "12.5", "[4.5]", "(for", "0.5", "<", "[4.5]-[8.0]", "<", "1.4,", "Pointlike)", "Smooth", "increase", "for", "[4.5]", ">", "14.5", "[4.5]", "(for", "1.4", "<", "[4.5]-[8.0])", "Smooth", "increase", "for", "[4.5]", ">", "13.0", "([8.0]", "−", "[24]", "−", "3.5)2/1.7", "+", "([24]", "−", "9.0)2/2", "Smooth", "increase", "for", "values", "<", "1", "[4.5]", "−", "[8.0]", "−", "0.55(10.", "−", "[24])", "Smooth", "increase", "for", "values", ">", "1", "[24]", "(for", "all", "colors)", "100%", "probability", "for", "[24]", ">", "10.0", "Extended", "at", "3.6", "or", "4.5µm", "Twice", "as", "likely", "to", "be", "X-gal", "F70", "X-gal", "prob", "×", "0.1", "for", "F70", ">", "400", "mJy", "Criterion", "Contaminant", "Probability" ]	1	49	{ "x1": 92, "x2": 520, "y1": 306, "y2": 523 }	[ " Table 1 summarizes the criteria used for this class separation.", " After inclusion of these three color-magnitude criteria, we added the additional criteria listed in Table 1.", " Table 10 summarizes the results of this effort.", " In addition, as shown in Table 10, we find small extended features at the positions of most of the known HH objects in Serpens that were within our covered area." ]
Table 10. Probable High Velocity Outflows in Serpens	{ "x1": 163.91998291015625, "x2": 448.057373046875, "y1": 293.4164123535156, "y2": 299.3999938964844 }	Table	[ "141", "18", "29", "49.6", "+01", "15", "21", "SMM", "1", "Jets", "to", "NW", "and", "SE", "146", "18", "29", "51.2", "+01", "16", "41", "SMM", "5", "Jets", "to", "NW", "and", "SE", "75", "18", "29", "09.0", "+00", "31", "30", "Jets", "to", "N", "and", "S", "18", "29", "18.8", "+01", "14", "15", "HH", "106A,B,E", "18", "29", "47.7", "+01", "25", "52", "HH", "107A", "18", "30", "22.7", "+01", "16", "18", "HH", "455A", "18", "30", "22.6", "+01", "16", "05", "HH", "455B,D", "18", "30", "02.6", "+01", "14", "45", "HH", "459A,B", "18", "29", "38.5", "+01", "18", "26", "HH", "460A,B,C,D", "18", "29", "56.6", "+01", "15", "37", "HH", "478A,B", "YSO", "ID", "RA", "(J2000)", "Dec", "(J2000)", "Matching", "Name", "Comments" ]	10	91	{ "x1": 102, "x2": 510, "y1": 315, "y2": 517 }	[]
Table 2. YSO’s in Serpens	{ "x1": 310.67999267578125, "x2": 452.824462890625, "y1": 97.6964111328125, "y2": 103.67999267578125 }	Table	[ "1", "18275381−0002333", "25.5±", "1.2", "20.2±", "1.0", "15.6±", "0.7", "13.9±", "0.7", "22.7±", "2.1", "·", "·", "·", "2b", "18280503+0006593", "783±", "55", "426±", "29", "358±", "18", "218±", "14", "76.4±", "7.1", "·", "·", "·", "3", "18280845−0001064", "140±", "7", "108±", "8", "129±", "6", "122±", "8", "161±", "14", "314±", "36", "4b", "18281100−0001393", "104±", "5", "63.4±", "3.2", "54.6±", "2.6", "35.4±", "1.9", "9.51±0.90", "·", "·", "·", "5", "18281350−0002491", "CDF88-2", "105±", "5", "88.1±", "4.7", "77.5±", "3.7", "94.3±", "5.0", "254±", "23", "382±", "43", "6", "18281501−0002588", "33.3±", "1.6", "45.6±", "2.3", "61.5±", "3.1", "96.3±", "5.8", "225±", "20", "320±", "41", "7", "18281519−0001405", "7.18±0.35", "6.18±0.30", "5.15±0.25", "5.01±0.26", "8.00±0.77", "·", "·", "·", "8", "18281525−0002432", "CoKu", "Ser-G1", "174±", "9", "177±", "9", "180±", "11", "191±", "11", "1200±", "25", "1670±", "169", "9", "18281628−0003161", "53.1±", "2.7", "48.4±", "2.4", "45.4±", "2.1", "46.2±", "2.5", "74.7±", "6.9", "129±", "24", "10", "18281852−0003329", "3.38±0.17", "3.14±0.15", "3.13±0.16", "2.99±0.15", "2.96±0.36", "·", "·", "·", "11", "18281981−0001474", "5.52±0.27", "5.28±0.26", "4.90±0.24", "4.02±0.21", "5.58±0.54", "·", "·", "·", "12", "18282010+0029145", "237±", "21", "109±", "9", "116±", "8", "76.6±", "4.8", "17.5±", "1.6", "·", "·", "·", "13", "18282143+0010411", "13.7±", "0.7", "10.1±", "0.6", "9.99±0.49", "8.90±0.50", "10.5±", "1.0", "·", "·", "·", "14", "18282158+0000164", "60.3±", "3.0", "54.0±", "2.8", "45.5±", "2.2", "61.4±", "3.4", "170±", "15", "126±", "21", "15b", "18282432+0034545", "D-002", "62.4±", "4.2", "46.1±", "3.0", "41.1±", "2.5", "32.5±", "2.0", "13.9±", "1.3", "·", "·", "·", "16", "18282738−0011499", "1130±", "60", "660±", "35", "631±", "30", "399±", "22", "120±", "11", "·", "·", "·", "17", "18282740+0000239", "87.3±", "4.5", "54.6±", "2.7", "47.3±", "2.2", "32.3±", "1.6", "12.9±", "1.2", "·", "·", "·", "18", "18282849+0026500", "2.47±0.16", "2.28±0.15", "2.27±0.15", "2.52±0.16", "2.62±0.37", "·", "·", "·", "19", "18282905+0027561", "D-007", "9.80±0.57", "8.51±0.47", "7.03±0.38", "5.46±0.30", "43.4±", "4.0", "·", "·", "·", "20", "18284025+0016173", "3.71±0.20", "3.86±0.20", "3.60±0.19", "3.59±0.18", "2.89±0.35", "·", "·", "·", "21", "18284052+0022145", "68.2±", "3.7", "41.2±", "2.4", "39.2±", "2.0", "25.5±", "1.4", "11.7±", "1.1", "·", "·", "·", "22", "18284186−0003213", "13.7±", "0.7", "24.8±", "1.2", "39.6±", "1.9", "49.0±", "2.6", "155±", "14", "538±", "54", "23", "18284400+0053379", "18.1±", "0.9", "29.7±", "1.4", "40.3±", "2.0", "49.9±", "2.5", "260±", "24", "·", "·", "·", "24", "18284477+0051257", "0.65±0.04", "1.77±0.09", "3.08±0.16", "4.81±0.23", "37.6±", "3.5", "·", "·", "·", "SSTc2dJ...", "(mJy)", "(mJy)", "(mJy)", "(mJy)", "(mJy)", "(mJy)", "ID", "Name/Position", "Prev.", "Namea", "3.6", "µm", "4.5", "µm", "5.8", "µm", "8.0", "µm", "24.0", "µm", "70.0", "µm" ]	2	50	{ "x1": 101, "x2": 663, "y1": 119, "y2": 523.80029296875 }	[ " These are the objects in Table 2 numbered 127, 137, and 182.", " Table 2 lists the 235 YSO’s that resulted from this selection process.", " We have indicated these five objects in Table 2 with a footnote “b”.", " Each SED is labeled with the identification number in Table 2." ]
Table 3. YSO Candidates in Serpens Without 4-Band IRAC Observations	{ "x1": 188.27999877929688, "x2": 575.3508911132812, "y1": 97.6964111328125, "y2": 103.67999267578125 }	Table	[ "236", "18273421+0040260", "·", "·", "·", "·", "·", "·", "·", "·", "·", "·", "·", "·", "17.8±", "1.7", "·", "·", "·", "237", "18274024+0035221", "·", "·", "·", "·", "·", "·", "·", "·", "·", "·", "·", "·", "1.36±0.25", "·", "·", "·", "238", "18274264+0020389", "·", "·", "·", "·", "·", "·", "·", "·", "·", "·", "·", "·", "42.0±", "3.9", "·", "·", "·", "239", "18274399+0025135", "IRAC", "18251+0023", "·", "·", "·", "·", "·", "·", "·", "·", "·", "·", "·", "·", "5430±", "509", "655±", "68", "240", "18274484+0052436", "·", "·", "·", "·", "·", "·", "·", "·", "·", "·", "·", "·", "1.49±0.27", "·", "·", "·", "241", "18274506+0006110", "IRAS", "18251+0004", "1730±", "93", "·", "·", "·", "965±", "47", "·", "·", "·", "173±", "16", "·", "·", "·", "242", "18275926+0056012", "·", "·", "·", "·", "·", "·", "·", "·", "·", "·", "·", "·", "40.7±", "3.9", "·", "·", "·", "243", "18280449+0049498", "·", "·", "·", "·", "·", "·", "·", "·", "·", "·", "·", "·", "15.2±", "1.4", "·", "·", "·", "244", "18281904+0101333", "IRAS", "18257+0059", "·", "·", "·", "·", "·", "·", "·", "·", "·", "·", "·", "·", "112±", "10", "·", "·", "·", "245", "18282591−0032587", "IRAS", "18258-0034", "·", "·", "·", "·", "·", "·", "·", "·", "·", "·", "·", "·", "279±", "43", "·", "·", "·", "246", "18283708+0149440", "·", "·", "·", "·", "·", "·", "·", "·", "·", "·", "·", "·", "57.3±", "5.3", "·", "·", "·", "247", "18283939+0106157", "IRAS", "18261+0104", "·", "·", "·", "·", "·", "·", "·", "·", "·", "·", "·", "·", "356±", "33", "·", "·", "·", "248", "18284039+0106144", "IRAS", "18261+0104", "·", "·", "·", "·", "·", "·", "·", "·", "·", "·", "·", "·", "160±", "14", "·", "·", "·", "249", "18285056+0101121", "4.43±0.22", "·", "·", "·", "3.08±0.16", "·", "·", "·", "1.93±0.31", "·", "·", "·", "250", "18285486+0108548", "IRAS", "18264+0106", "·", "·", "·", "·", "·", "·", "·", "·", "·", "·", "·", "·", "329±", "30", "·", "·", "·", "251", "18295035+0008472", "·", "·", "·", "322±", "26", "·", "·", "·", "258±", "14", "89.4±", "8.3", "·", "·", "·", "252", "18295096−0033057", "·", "·", "·", "299±", "20", "·", "·", "·", "146±", "7", "50.8±", "4.7", "·", "·", "·", "253", "18295439+0002476", "·", "·", "·", "·", "·", "·", "·", "·", "·", "·", "·", "·", "77.5±", "7.2", "·", "·", "·", "254", "18300035+0011201", "·", "·", "·", "96.0±", "6.5", "·", "·", "·", "60.7±", "3.3", "19.5±", "1.8", "·", "·", "·", "255", "18300130+0159309", "·", "·", "·", "·", "·", "·", "·", "·", "·", "·", "·", "·", "1.14±0.22", "·", "·", "·", "256", "18300155+0037339", "·", "·", "·", "3.72±0.20", "·", "·", "·", "1.94±0.11", "1.22±0.20", "·", "·", "·", "257", "18300181−0037039", "IRAS", "18275-0039", "·", "·", "·", "·", "·", "·", "·", "·", "·", "·", "·", "·", "29.9±", "2.8", "·", "·", "·", "258", "18300237+0040549", "·", "·", "·", "4.56±0.22", "·", "·", "·", "4.52±0.22", "3.45±0.38", "·", "·", "·", "259", "18300403+0034240", "·", "·", "·", "·", "·", "·", "·", "·", "·", "·", "·", "·", "217±", "20", "798±", "77", "SSTc2dJ...", "(mJy)", "(mJy)", "(mJy)", "(mJy)", "(mJy)", "(mJy)", "ID", "Name/Position", "Prev.", "Name", "3.6", "µm", "4.5", "µm", "5.8", "µm", "8.0", "µm", "24.0", "µm", "70.0", "µm" ]	3	61	{ "x1": 90, "x2": 673, "y1": 119, "y2": 523.80029296875 }	[ "8 deg2; 51 of these are outside the IRAC/MIPS overlap area and are listed in Table 3." ]
Table 4. Matching Spitzer Sources/Fluxes For Previously Identified IR Sources In Serpens	{ "x1": 146.8800048828125, "x2": 616.614990234375, "y1": 98.41641235351562, "y2": 104.39999389648438 }	Table	[ "D002", "18282432+0034545", "62.4±", "4.2", "46.1±", "3.0", "41.1±", "2.5", "32.5±", "2.0", "13.9±", "1.3", "·", "·", "·", "D001", "18282442+0026509", "105±", "9", "95.6±", "7.8", "97.9±", "6.5", "65.0±", "4.2", "13.9±", "1.3", "·", "·", "·", "D003", "18282649+0031421", "38.1±", "2.7", "25.8±", "1.7", "20.1±", "1.2", "12.2±", "0.8", "1.26±0.28", "·", "·", "·", "D004", "18282783+0028390", "6.72±0.45", "4.47±0.29", "3.44±0.21", "2.27±0.14", "<", "1.53", "·", "·", "·", "D005", "18282792+0029288", "5.12±0.32", "3.56±0.25", "2.76±0.16", "1.79±0.12", "<", "1.45", "·", "·", "·", "D006", "18282864+0024120", "5.68±0.38", "3.71±0.25", "3.27±0.20", "1.92±0.12", "<", "1.44", "·", "·", "·", "D007", "18282905+0027561", "9.80±0.57", "8.51±0.47", "7.03±0.38", "5.46±0.30", "43.4±", "4.0", "·", "·", "·", "D008", "18282912+0034193", "193±", "13", "93.2±", "6.4", "86.6±", "4.5", "49.3±", "2.9", "5.99±0.58", "·", "·", "·", "D010", "18283208+0025036", "11.2±", "0.6", "6.47±0.38", "5.42±0.27", "3.15±0.20", "<", "1.25", "·", "·", "·", "D009", "18283221+0035361", "33.6±", "2.0", "20.6±", "1.1", "16.1±", "0.9", "9.61±0.49", "0.99±0.23", "·", "·", "·", "D011", "18283261+0037322", "15.0±", "0.9", "9.38±0.50", "7.02±0.39", "4.40±0.23", "<", "1.41", "·", "·", "·", "D012", "18283317+0025451", "24.9±", "1.5", "15.0±", "0.9", "12.1±", "0.6", "7.15±0.41", "0.70±0.25", "·", "·", "·", "D013", "18283351+0026595", "60.6±", "3.6", "34.5±", "2.2", "26.4±", "1.4", "15.9±", "0.9", "1.46±0.22", "·", "·", "·", "D014", "18283434+0031119", "10.2±", "0.6", "7.06±0.41", "5.39±0.31", "3.42±0.19", "<", "1.54", "·", "·", "·", "D015", "18283503+0026406", "53.0±", "3.2", "34.2±", "2.1", "31.8±", "1.7", "19.2±", "1.1", "2.71±0.35", "·", "·", "·", "D017", "18283572+0038458", "227±", "15", "130±", "7", "104±", "5", "61.0±", "3.5", "6.91±0.66", "·", "·", "·", "D016", "18283576+0038231", "6.23±0.38", "4.19±0.23", "2.82±0.16", "1.72±0.10", "<", "1.19", "·", "·", "·", "D018", "18283579+0026160", "191±", "12", "122±", "8", "114±", "6", "63.5±", "3.9", "7.10±0.69", "·", "·", "·", "D019", "18283639+0026388", "31.8±", "1.9", "21.1±", "1.3", "19.4±", "1.0", "11.3±", "0.7", "1.20±0.23", "·", "·", "·", "D020", "18283741+0027100", "9.45±0.54", "6.52±0.40", "5.68±0.36", "3.35±0.20", "<", "1.26", "·", "·", "·", "D021", "18283752+0032311", "7.64±0.49", "5.69±0.30", "4.05±0.24", "2.52±0.14", "<", "1.22", "·", "·", "·", "D022", "18283791+0025512", "46.4±", "2.8", "26.1±", "1.6", "26.5±", "1.4", "15.3±", "0.9", "2.38±0.31", "·", "·", "·", "SSTc2dJ...", "(mJy)", "(mJy)", "(mJy)", "(mJy)", "(mJy)", "(mJy)", "Sourcea", "Spitzer", "3.6µm", "4.5µm", "5.8µm", "8.0µm", "24µm", "70µm" ]	4	64	{ "x1": 125, "x2": 638, "y1": 121, "y2": 519.5999755859375 }	[ " Table 4 lists the sources from each of these previous studies and the best-matching Spitzer source from our complete catalog.", " Table 4 shows that we also see no obvious source at the position of EC92-81, other than a low S/N single-band detection of a source moderately distant from the nominal position." ]
Table 5. Average/Std Dev of Spectral Slope α Versus Luminosity of YSO’s	{ "x1": 109.91999816894531, "x2": 502.0306091308594, "y1": 183.73638916015625, "y2": 189.719970703125 }	Table	[ ">", "1.0", "L⊙", "-0.60", ".74", "<", "0.02", "L⊙", "-0.73", "1.47", "0.02", "−−1.0", "L⊙", "-0.70", "1.04", "Luminosity", "Range", "Average", "α", "σα" ]	5	82	{ "x1": 204, "x2": 408, "y1": 206, "y2": 296 }	[ " Likewise Figure 8 shows the distribution of spectral slopes, α, for the low luminosity sample relative to two higher luminosity samples, and Table 5 lists the average and standard deviation for the spectral slopes for three luminosity samples.", " Figure 8 that displays the distribution of spectral slopes and the accompanying Table 5 also show no measurable effect within the scatter for a dependence of spectral slope on luminosity." ]
Table 6. Numbers, Densities, Star Formation Rates	{ "x1": 168.83999633789062, "x2": 439.3006591796875, "y1": 467.2964172363281, "y2": 473.2799987792969 }	Table	[ "Cluster", "A", "0.20", "44", "4580", "222", "500", "11", "56", "Cluster", "B", "0.14", "17", "2450", "119", "315", "4.3", "30", "Rest", "of", "Cloud", "17.2", "174", "209", "10.1", "2.5", "44", "2.5", "All", "of", "Cloud", "17.5", "235", "276", "13.4", "3.2", "59", "3.4", "(pc2)", "(deg−2)", "(pc−2)", "(pc−3)", "(M⊙", "Myr−1)", "(M⊙", "Myr−1pc−2)", "Region", "Area", "N(YSOs)", "N/Ω", "N/Area", "N/Vol", "SFR", "SFR/Area" ]	6	82	{ "x1": 71, "x2": 570, "y1": 489, "y2": 627 }	[ " In particular, if we define the cluster edges by the Av = 20 contour for comparison with other c2d clusters, we obtain the values in Table 6 for the number of stars per solid angle and per square parsec.", "The overall picture of star formation in Serpens is summarized in Table 6.", " These values are also given in Table 6.", " The surface density of YSOs in the clusters exceeds that of the rest of the cloud by factors of 10 to 20 (Table 6)." ]
Table 7. Disk Modeling Results in Class II Sources	{ "x1": 171.95999145507812, "x2": 439.8692932128906, "y1": 129.856201171875, "y2": 135.83978271484375 }	Table	[ "1", "L", "2.9", "0.33", "0.088", "5.8", "-0.7", "3", "T", "4.6", "1.06", "0.330", "2.2", "-0.8", "5", "T", "4.9", "1.64", "0.165", "3.6", "-0.5", "7", "L", "3.8", "0.09", "0.110", "3.6", "-1.0", "9", "L", "6.6", "0.91", "0.141", "3.6", "-0.8", "10", "L", "9.9", "0.05", "0.190", "3.6", "-1.3", "11", "L", "8.4", "0.07", "0.186", "2.2", "-1.2", "13", "L", "2.8", "0.19", "0.084", "5.8", "-1.0", "14", "L", "6.6", "1.03", "0.182", "3.6", "-0.7", "18", "L", "10.8", "0.07", "0.098", "3.6", "-1.1", "19", "LU", "12.6", "0.33", "0.073", "3.6", "-0.4", "20", "L", "14.3", "0.09", "0.160", "2.2", "-1.4", "25", "T", "4.8", "0.09", "0.159", "3.6", "-0.9", "27", "L", "4.0", "0.54", "0.112", "3.6", "-1.4", "28", "L", "15.7", "67.31", "0.197", "2.2", "-1.8", "29", "L", "12.7", "0.14", "0.253", "2.2", "-1.3", "30", "L", "8.3", "33.93", "0.291", "2.2", "-1.5", "31", "T", "10.4", "0.02", "0.454", "2.2", "-1.1", "33", "L", "10.2", "5.58", "0.111", "2.2", "-2.0", "35", "L", "7.4", "0.03", "0.113", "3.6", "-1.2", "38", "T", "18.9", "0.05", "0.588", "2.2", "-1.1", "39", "T", "5.1", "0.21", "0.104", "5.8", "-0.4", "47", "LU", "14.5", "0.02", "0.247", "4.5", "-0.6", "49", "T", "5.4", "0.13", "0.141", "3.6", "-0.9", "50", "L", "18.4", "1.31", "0.201", "3.6", "-1.0", "51", "L", "7.4", "0.57", "0.155", "2.2", "-1.2", "52", "L", "10.0", "0.29", "0.148", "2.2", "-1.1", "53", "T", "10.5", "0.12", "0.305", "2.2", "-0.7", "54", "T", "9.3", "3.14", "0.409", "2.2", "-0.8", "55", "L", "23.3", "2.50", "0.198", "2.2", "-1.4", "56", "T", "10.4", "1.06", "0.306", "2.2", "-0.8", "57", "L", "12.0", "0.06", "0.146", "2.2", "-1.6", "58", "T", "6.1", "1.94", "0.147", "3.6", "-0.6", "Star", "SED", "Type", "AV", "Lstar", "Ldisk/Lstar", "λturn−oﬀ", "αexcess" ]	7	83	{ "x1": 146, "x2": 466, "y1": 152, "y2": 675.238525390625 }	[]
Table 8. Disk Modeling Results in Class III Sources	{ "x1": 169.67999267578125, "x2": 442.146728515625, "y1": 129.856201171875, "y2": 135.83978271484375 }	Table	[ "2", "L", "6.3", "19.19", "0.013", "24.0", "-99.0", "4", "L", "7.6", "2.50", "0.028", "24.0", "-99.0", "12", "L", "9.1", "8.76", "0.015", "24.0", "-99.0", "15", "L", "7.7", "2.02", "0.025", "8.0", "-1.9", "16", "L", "10.8", "31.18", "0.041", "8.0", "-2.3", "17", "L", "11.1", "2.69", "0.036", "8.0", "-2.1", "21", "L", "11.7", "2.16", "0.038", "8.0", "-2.0", "48", "L", "2.5", "1.13", "0.054", "8.0", "0.6", "65", "L", "0.0", "0.70", "0.016", "8.0", "-0.9", "73", "L", "7.5", "3.06", "0.022", "24.0", "-99.0", "74", "L", "0.0", "0.60", "0.010", "8.0", "-1.3", "81", "L", "8.7", "9.23", "0.021", "24.0", "-99.0", "83", "L", "8.0", "28.57", "0.034", "8.0", "-1.6", "85", "L", "7.2", "1.66", "0.048", "5.8", "-1.5", "90", "L", "7.7", "3.50", "0.034", "8.0", "-2.3", "91", "L", "8.5", "3.55", "0.020", "24.0", "-99.0", "93", "L", "16.7", "38.30", "0.051", "8.0", "-2.2", "95", "L", "8.5", "23.79", "0.015", "24.0", "-99.0", "101", "L", "8.6", "6.09", "0.074", "5.8", "-2.2", "105", "LU", "0.7", "11.61", "0.010", "24.0", "1.2", "107", "L", "8.3", "15.02", "0.055", "5.8", "-2.3", "109", "L", "10.7", "7.62", "0.037", "8.0", "-2.3", "112", "L", "7.4", "0.24", "0.018", "8.0", "-1.9", "115", "L", "9.7", "3.90", "0.044", "8.0", "-2.1", "122", "L", "9.6", "0.96", "0.028", "8.0", "-1.5", "126", "LU", "3.3", "0.36", "0.062", "8.0", "0.3", "140", "L", "8.8", "2.25", "0.032", "8.0", "-2.2", "143", "L", "4.2", "0.21", "0.052", "5.8", "-1.3", "148", "LU", "0.0", "0.67", "0.017", "24.0", "2.3", "161", "L", "11.2", "4.26", "0.032", "8.0", "-2.2", "165", "L", "0.7", "0.94", "0.014", "8.0", "-1.6", "170", "L", "3.7", "0.07", "0.079", "5.8", "-1.3", "192", "L", "8.1", "0.20", "0.034", "8.0", "-0.5", "Star", "SED", "Type", "AV", "Lstar", "Ldisk/Lstar", "λturn−oﬀ", "αexcess" ]	8	88	{ "x1": 146, "x2": 466, "y1": 152, "y2": 675.238525390625 }	[]
Table 9. The Coldest YSO’s (F70/F24 > 8)	{ "x1": 269.2799987792969, "x2": 494.5198974609375, "y1": 98.29641723632812, "y2": 106.08001708984375 }	Table	[ "40", "18285404+0029299", "5.81±0.50", "27.6±", "2.3", "44.8±", "2.6", "56.4±", "3.2", "918±", "85", "11100±", "1040", "42", "18285486+0029525", "1.94±0.12", "10.6±", "0.6", "20.4±", "1.1", "30.2±", "1.6", "765±", "70", "7250±", "675", "48", "18285808+0017244", "52.5±", "3.0", "36.7±", "2.5", "31.2±", "1.7", "28.5±", "1.7", "9.74±0.92", "1040±", "101", "60", "18290211+0031206", "1.19±0.07", "1.62±0.09", "1.58±0.10", "1.13±0.07", "22.1±", "2.0", "276±", "29", "68", "18290675+0030343", "3.27±0.21", "11.7±", "0.7", "14.9±", "0.8", "20.7±", "1.2", "1000±", "105", "11400±", "1180", "105", "18293254−0013233", "654±", "39", "370±", "19", "276±", "13", "156±", "8", "39.7±", "3.7", "429±", "47", "135", "18294810+0116449", "1.96±0.10", "6.98±0.42", "12.1±", "0.6", "16.7±", "0.8", "219±", "21", "14900±", "1420", "141", "18294963+0115219", "0.85±0.08", "2.64±0.27", "2.32±0.28", "3.54±0.31", "1180±", "117", "82800±", "7810", "146", "18295114+0116406", "31.1±", "2.6", "72.6±", "4.6", "141±", "7", "208±", "10", "992±", "92", "8480±", "805", "148", "18295130+0027479", "33.8±", "2.0", "22.3±", "1.3", "16.2±", "0.9", "10.1±", "0.6", "4.81±0.50", "163±", "18", "150", "18295219+0115478", "7.38±0.41", "33.0±", "2.1", "41.3±", "2.2", "40.0±", "2.6", "1640±", "154", "15200±", "1420", "154", "18295252+0036117", "2.49±0.14", "4.24±0.23", "5.18±0.28", "6.55±0.36", "100±", "9", "1910±", "179", "166", "18295430+0036013", "2.39±0.25", "6.57±0.42", "7.32±0.44", "5.80±0.31", "16.0±", "1.5", "1270±", "121", "195", "18295927+0114016", "2.72±0.28", "5.76±0.44", "7.78±1.16", "36.0±", "5.4", "109±", "19", "12200±", "1160", "203", "18300070+0113014", "0.38±0.04", "1.23±0.10", "2.08±0.16", "3.55±0.21", "95.8±11.4", "8640±", "829", "Tbl", "2", "SSTc2dJ...", "(mJy)", "(mJy)", "(mJy)", "(mJy)", "(mJy)", "(mJy)", "ID", "Name/Position", "3.6", "µm", "4.5", "µm", "5.8", "µm", "8.0", "µm", "24.0", "µm", "70.0", "µm" ]	9	90	{ "x1": 125, "x2": 639, "y1": 121, "y2": 400 }	[ "Table 9 lists the 15 YSO’s that display the coldest energy distributions." ]
Figure 2.1: A graph and its isometric embedding into Q3.	{ "x1": 179.63999938964844, "x2": 431.6497802734375, "y1": 326.0986633300781, "y2": 332.51983642578125 }	Figure	[]	2.1	2	{ "x1": 186, "x2": 426, "y1": 249, "y2": 309 }	[]
Figure 2.2: A nonisometric path in the cube Q3.	{ "x1": 199.8000030517578, "x2": 411.369384765625, "y1": 244.7386474609375, "y2": 251.1597900390625 }	Figure	[]	2.2	3	{ "x1": 249, "x2": 362, "y1": 124, "y2": 228 }	[]
Figure 4.1: Fundamental sets in a partial cube.	{ "x1": 202.55999755859375, "x2": 408.6446838378906, "y1": 419.9386901855469, "y2": 424.9200134277344 }	Figure	[]	4.1	10	{ "x1": 214, "x2": 395, "y1": 296, "y2": 405 }	[]
Figure 4.2: Graph G.	{ "x1": 259.0799865722656, "x2": 352.0893859863281, "y1": 396.65869140625, "y2": 401.6400146484375 }	Figure	[]	4.2	11	{ "x1": 229, "x2": 392, "y1": 277, "y2": 387 }	[]
Figure 4.3: An illustration to the proof of theorem 4.2.	{ "x1": 185.75999450683594, "x2": 425.4627380371094, "y1": 401.57867431640625, "y2": 406.55999755859375 }	Figure	[]	4.3	12	{ "x1": 225, "x2": 388, "y1": 301, "y2": 392 }	[]
Figure 7.1: Pasting of two trees.	{ "x1": 235.1999969482422, "x2": 376.10467529296875, "y1": 260.33868408203125, "y2": 265.32000732421875 }	Figure	[]	7.1	18	{ "x1": 145, "x2": 466, "y1": 192, "y2": 243 }	[]
Figure 7.2: Another pasting of the same trees.	{ "x1": 204.60000610351562, "x2": 406.8235778808594, "y1": 358.7386779785156, "y2": 363.7200012207031 }	Figure	[]	7.2	18	{ "x1": 145, "x2": 466, "y1": 291, "y2": 342 }	[]
Figure 7.3: Pasting partial cubes G1 and G2.	{ "x1": 207.1199951171875, "x2": 404.0495910644531, "y1": 518.4586791992188, "y2": 524.8802490234375 }	Figure	[]	7.3	18	{ "x1": 164, "x2": 447, "y1": 425, "y2": 512 }	[]
Figure 7.4: An example of vertex-pasting.	{ "x1": 214.32000732421875, "x2": 397.23193359375, "y1": 285.2986755371094, "y2": 290.2799987792969 }	Figure	[]	7.4	19	{ "x1": 141, "x2": 471, "y1": 208, "y2": 268 }	[]
Figure 7.5: An example of edge-pasting.	{ "x1": 218.0399932861328, "x2": 393.3875427246094, "y1": 553.2586669921875, "y2": 558.239990234375 }	Figure	[]	7.5	21	{ "x1": 168, "x2": 444, "y1": 473, "y2": 536 }	[]
Figure 7.6: Edge-pasting of graphs G1 and G2.	{ "x1": 203.16000366210938, "x2": 408.129638671875, "y1": 388.8586730957031, "y2": 395.28021240234375 }	Figure	[]	7.6	22	{ "x1": 233, "x2": 378, "y1": 299, "y2": 381 }	[]
Figure 7.7: Semicubes forming an edge in Sc(G1).	{ "x1": 196.8000030517578, "x2": 414.37091064453125, "y1": 335.81866455078125, "y2": 342.2398376464844 }	Figure	[]	7.7	24	{ "x1": 250, "x2": 359, "y1": 245, "y2": 319 }	[]
Figure 8.1: Expansion/contraction processes.	{ "x1": 207.36000061035156, "x2": 404.0686950683594, "y1": 506.69866943359375, "y2": 511.67999267578125 }	Figure	[]	8.1	26	{ "x1": 200, "x2": 418, "y1": 335, "y2": 490 }	[]
Figure 8.2: An expansion of the cycle C4.	{ "x1": 214.9199981689453, "x2": 396.36944580078125, "y1": 208.378662109375, "y2": 214.7998046875 }	Figure	[]	8.2	29	{ "x1": 155, "x2": 456, "y1": 125, "y2": 191 }	[]
Figure 8.3: Another isometric expansion of the cycle C4.	{ "x1": 182.16000366210938, "x2": 429.0095520019531, "y1": 297.2986755371094, "y2": 303.7198486328125 }	Figure	[]	8.3	29	{ "x1": 151, "x2": 459, "y1": 226, "y2": 280 }	[]
Figure 8.4: A shortest path which is not a projection of a shortest path.	{ "x1": 148.0800018310547, "x2": 463.21405029296875, "y1": 504.898681640625, "y2": 509.8800048828125 }	Figure	[]	8.4	29	{ "x1": 152, "x2": 459, "y1": 416, "y2": 488 }	[]
Figure 8.5: A shortest path from x to y.	{ "x1": 217.67999267578125, "x2": 393.609619140625, "y1": 523.9786376953125, "y2": 528.9599609375 }	Figure	[]	8.5	30	{ "x1": 215, "x2": 405, "y1": 441, "y2": 514 }	[]
Table 1. Dimension Formula for Mk(Γ0(4N))	{ "x1": 179.52008056640625, "x2": 420.5982360839844, "y1": 568.6466064453125, "y2": 575.8802490234375 }	Table	[ "So", "Φr,e(4N)", "is", "surjective", "since", "the", "map", "Φr,e(4N)", "is", "injective.", "This", "completes", "our", "claim.", "N", "=", "1", "n", "+", "1", "n", "+", "1", "n", "+", "1", "N", "=", "2", "2n+", "1", "2n+", "2", "2n+", "1", "N", "=", "3", "4n+", "1", "4n+", "3", "4n+", "1", "N", "=", "4", "4n+", "2", "4n+", "4", "4n+", "1", "k", "=", "2n", "k", "=", "2n+", "3", "2", "N", "k", "=", "2n", "+", "1", "2" ]	1	8	{ "x1": 85.19999694824219, "x2": 526.6981811523438, "y1": 589, "y2": 717 }	[ " The dimension formula of Mλ+ 1 2 (Γ0(4N)) (see Table 1) together with the results in (3.", " So from Table 1 we have (4.", "1 and Table 1, it is enough to show that ψr,e(4N) is injective." ]
Fig. 1	{ "x1": 270.4519958496094, "x2": 306.8551330566406, "y1": 245.9059600830078, "y2": 252.4949951171875 }	Figure	[ "・", "・", "・", "b1", "a1", "b1", "a1", "b1", "a1" ]	1	13	{ "x1": 157, "x2": 454, "y1": 131, "y2": 237 }	[ " Take 2g curves in M , ai, bi, as in Figure 1." ]
FIG. 1: non-spectator effects contribution to lifetime of Ξccd	{ "x1": 161.0399932861328, "x2": 448.8367004394531, "y1": 346.5052185058594, "y2": 353.759765625 }	Figure	[ "(d)", "l̄", "νl", "d", "c", "c", "d", "c", "c", "(c)", "d", "u", "c", "d", "c", "d", "c", "c", "(b)", "d̄", "u", "d", "c", "c", "d", "c", "c", "(a)", "s", "u", "c", "d", "c", "c", "d", "c" ]	1	14	{ "x1": 90.76210021972656, "x2": 514.9379272460938, "y1": 73.9257583618164, "y2": 316.26629638671875 }	[ "(i) The inclusive decays of Ξ+ cc: There are four diagrams which contribute to the the width of Ξ+ cc, as shown in Fig.1.", " Fig 1.", "(a),(c) are the W-exchange diagrams (WE), while Fig 1.", " Here Fig 1." ]
FIG. 2: non-spectator effects contribution to lifetime of Ξccu	{ "x1": 160.79998779296875, "x2": 449.0186767578125, "y1": 347.58544921875, "y2": 354.7200927734375 }	Figure	[ "(c)", "d̄", "d", "u", "c", "c", "c", "u", "c", "(b)", "s̄", "s", "u", "c", "c", "c", "u", "c", "(a)", "d̄", "s", "u", "c", "c", "c", "c", "u" ]	2	15	{ "x1": 93.46995544433594, "x2": 517.2801513671875, "y1": 75.9457015991211, "y2": 317.24200439453125 }	[ " (ii) The inclusive decays of Ξ++ cc : The non-spectator contribution to the width of Ξ++ cc come from the diagrams shown in Fig.2." ]
FIG. 3: non-spectator effects contribution to lifetime of Ωccs	{ "x1": 161.0404815673828, "x2": 448.87091064453125, "y1": 347.5848693847656, "y2": 354.7195129394531 }	Figure	[ "(d)", "s", "u", "c", "s", "c", "s", "c", "c", "(c)", "s̄", "u", "s", "c", "c", "c", "s", "c", "(b)", "l̄", "νl", "s", "c", "c", "c", "s", "c", "(a)", "d̄", "u", "s", "c", "c", "c", "c", "s" ]	3	16	{ "x1": 93.46995544433594, "x2": 516.1638793945312, "y1": 75.9457015991211, "y2": 317.24200439453125 }	[]
TABLE I: The numerical results about the contributions from the different components and the evaluated lifetime for the doubly charmed baryons. For a comparison, in the following table, we list the corresponding lifetimes predicted by the authors of ref.[7] where the diquark picture was employed. It is noted that in ref.[7], the authors used various input parameters and obtained slightly diverse results, we take average values of the numbers in the table. There is only one datum for the lifetimes on τΞ+ cc given by the SELEX collaboration which is also listed the table.	{ "x1": 72, "x2": 538.2841796875, "y1": 84.06546783447266, "y2": 202.7999267578125 }	Table	[ "2.01", "4.25", "1.10", "0.21", "0.22", "−", "Ω+", "cc", "Γspec(10", "−12GeV)", "ΓWE", "non", "(10−14GeV)", "ΓPI", "non(10−12GeV)", "τΩ+", "cc", "(ps)", "τΩ+", "cc", "(ps)", "in", "ref.[7]", "2.01", "-1.02", "0.67", "0.52", "−", "Ξ++", "cc", "Γspec(10", "−12GeV)", "ΓPI", "non(10−12GeV)", "τΞ++", "cc", "(ps)", "τΞ++", "cc", "(ps)", "in", "ref.[7]", "2.01", "6.43", "-3.36", "0.25", "0.19", "0.033", "Ξ+", "cc", "Γspec(10", "−12GeV)", "ΓWE", "non", "(10−13GeV)", "ΓPI", "non(10−15GeV)", "τΞ+", "cc", "(ps)", "τΞ+", "cc", "(ps)", "in", "ref.[7]", "exp(ps)" ]	I	10	{ "x1": 80, "x2": 530, "y1": 211, "y2": 345 }	[]
Figure 1. Radial-velocity Fourier amplitude spectra from the 1991 combined data are shown for α = 3000 km s−1 and 900 km s−1 for the Hβ line (top left panel and second left panel from the top) and for 3000 km s−1 and 1200 km s−1 for the Hγ line (top right panel and second right panel from the top). Ω denotes the orbital frequency of the system, 2Ω its first harmonic and ω + Ω the upper orbital side band where ω is the spin frequency. The data were prewhitened by the orbital frequency and are displayed in the third panels from the top. Window spectra are plotted below the amplitude spectra (bottom panels).	{ "x1": 305.15985107421875, "x2": 544.2506713867188, "y1": 386.6052551269531, "y2": 470.8802185058594 }	Figure	[]	1	1	{ "x1": 317, "x2": 536, "y1": 55, "y2": 378 }	[ " This is illustrated in Figure 10, where the position of the observer at pulse maximum is indicated, and the axis of the magnetic pole is shown.", " The overflow stream hits the magnetosphere, probably causing a second bright spot on the slowly rotating magnetosphere (Figure 10).", "5 M⊙) as proposed in Figure 10, it is clear that we see spin-varying emission from two opposite magnetic poles, producing a fairly symmetric structure in the spin-folded line profiles (Hellier et al." ]
Figure 10. A model of EX Hya in quiescence. The figures are drawn over the orbital cycle (left) and spin cycle (right) and show the magnetosphere extending to the outer edge of the ring, and the chunk of material corotating with the field lines. A verticaly extended material (VEM) is irradiated by the white dwarf in its inner regions (left).	{ "x1": 42.11907958984375, "x2": 544.2117919921875, "y1": 281.7252502441406, "y2": 306.2399597167969 }	Figure	[ "0.25", "maximum", "redshift", "phase", "of", "of", "Ηα", "BBC", "phase", "of", "minimum", "intensity", "upper", "pole", "magnetic", "axis", "through", "of", "phase", "of", "phase", "of", "maximum", "intensity", "Ηα", "BBC", "maximum", "blueshift", "part", "of", "disc", "corotating", "with", "field", "outer", "disc", "0.9", "0.4", "0.75", "0.7", "Observer", "1.0", "0.5", "phase", "of", "maximum", "blueshift", "of", "the", "HVC", "chunk", "of", "material", "with", "field", "corotating", "narrow", "s−wave", "of", "the", "s−wave", "overflowing", "stream", "chunk", "of", "material’s", "phases", "of", "maximum", "redshift", "phase", "of", "maximum", "blueshift", "phases", "of", "maximum", "blueshift", "of", "the", "magnetic", "axis", "through", "upper", "pole", "VEM", "0.25", "0.8", "ring", "of", "material", "0.7", "0.3", "0.4", "0.5", "0.75", "0.0", "Observer" ]	10	7	{ "x1": 44.160301208496094, "x2": 540.7478637695312, "y1": 51.7234001159668, "y2": 270.359619140625 }	[]
Figure 2. Radial velocity amplitude spectra shown for the Hα line from 2001, for α = 3500 km s−1 and 1200 km s−1. The vertical dashed line shows the expected position of the orbital and spin period peaks. The data were prewhitened by Ω and are shown in the third panel from the top. A window spectrum is shown at the bottom.	{ "x1": 42.11981201171875, "x2": 281.2600402832031, "y1": 344.9652404785156, "y2": 389.4002990722656 }	Figure	[]	2	2	{ "x1": 77, "x2": 247, "y1": 50, "y2": 333 }	[ " The Hβ and Hγ amplitude spectra from 1991 (24 and 25 April) are shown in Figure 1 and the Hα amplitude spectra from 2001 are shown in Figure 2." ]
Figure 3. The panels show the Hα, Hβ, Hγ and HeI λ4471 orbital Doppler maps from 2001, and Hβ tomograms of 1991, constructed using the Back-Projection Method with the application of a filter (top panels) and after subtracting the average of the line profile (bottom panels). The positions of the Roche lobe and stream trajectories are shown (velocity amplitudes of K1 = 74 km s−1 and K2 = 360 km s−1 for the primary and secondary stars, respectively, were used). The two curves with marked intervals represent the gas stream velocity (upper curve) and the Keplerian velocity along the stream (lower curve). The circles on all tomograms represent 0.1 of the distance from the L1 point to the primary. The three crosses are centres of mass of the secondary, system and primary, from top-to-bottom. The asterisk represents the velocity of closest approach. All the maps are plotted on the same velocity scale. The lookup table of this figure is such that the brightest emission features appear with decreasing intensity from yellow/green to light blue in the online edition, or white to grey in the printed edition.	{ "x1": 42.11761474609375, "x2": 544.2548217773438, "y1": 276.32525634765625, "y2": 350.6400451660156 }	Figure	[]	3	3	{ "x1": 45, "x2": 542, "y1": 50, "y2": 265 }	[ "The Hβ, Hγ and HeI λ4471 Doppler tomograms (Figure 3 and 4) show strong emission at the bright spot, some at the Roche lobe and the stream, and some from the disc.", "87 (Figure 3 and 4) was observed and suggests the presence of VEM at the outer edge of the ring of material obscuring the emission at these phases." ]
Figure 4. 2001 Hα, Hβ, Hγ and HeI λ4471 trailed spectra (top row of panels) and MEM orbital Doppler maps (second row of panels from the top) as well as the average-subtracted trailed spectra (third row of panels) are shown plotted on the same scale except for Hα panels. The HVC and the NSC are indicated. The fourth row shows the average-subtracted Doppler maps and the models plotted for q = 0.21, i = 78◦ and M1 = 0.50M⊙ . The bottom panels are the reconstruction of the average-subtracted data. The fourth and bottom panels are also plotted on the same scale except for Hα panels. The lookup table of this figure is such that the brightest emission features appear with decreasing intensity from black to light grey.	{ "x1": 42.11846923828125, "x2": 281.2676086425781, "y1": 521.1251831054688, "y2": 615.35986328125 }	Figure	[]	4	4	{ "x1": 42, "x2": 284, "y1": 51, "y2": 510 }	[ " The BPM Doppler maps are shown in Figure 3 and those constructed using MEM are shown in Figure 4.", " Average-subtracted trailed spectra (Figure 4) show the corresponding NSC.", " The first one is the asymmetry in the intensity of the s-wave (Figure 4).", "25 (Figure 4)." ]
Figure 5. The Hβ (top panel), Hγ (middle panel) and Hα (bottom panel) spin radial velocities of the narrow component from the 1991 combined data (Hβ and Hγ) and 2001 data (Hα). The radial velocities were prewhitened by the orbital frequency and phase-folded on the spin frequency using 30 bins and are shown plotted as a function of the spin phase.	{ "x1": 305.1597900390625, "x2": 544.2033081054688, "y1": 308.9652404785156, "y2": 353.4002990722656 }	Figure	[ "SPIN", "PHASE", ")", "km", "/s", "ity", "(", "el", "oc", "ia", "l", "V", "R", "ad", "α", "=1200", "αΗ", "α", "=", "900", "Ηγα", "=1200", "Ηβ" ]	5	4	{ "x1": 335.4169921875, "x2": 516, "y1": 53, "y2": 297 }	[ " Figure 5 shows the variation of the Hβ, Hγ and Hα narrow components with ω.", "8 (Figure 5)." ]
Figure 6. The spin radial velocity curves of the Hα narrow (crosses) and broad (dots) components from 2001 (30 bins) plotted as a function of the spin phase. The solid line represents a fit to the data.	{ "x1": 305.1600036621094, "x2": 544.1339721679688, "y1": 472.0452575683594, "y2": 496.5599670410156 }	Figure	[]	6	4	{ "x1": 325, "x2": 524, "y1": 380, "y2": 461 }	[ "Figure 6 shows the Hα narrow component (α = 1200 km s−1) and the broad-base component (α = 3500 km s−1) overplotted." ]
Figure 7. The Hα, Hβ, Hγ and HeI λ4471 trailed spectra from 2001 folded on the spin period are shown at the top panels and the average-subtracted spectra are shown at the second panels. Doppler maps constructed from the phase-invariant subtracted spectra are shown in the bottom panels. The Doppler maps were constructed using the BPM and are shown on the same velocity scale with the trailed spectra. The lookup table is as in Figure 3.	{ "x1": 42.11956787109375, "x2": 281.2146911621094, "y1": 315.68524169921875, "y2": 370.080078125 }	Figure	[]	7	5	{ "x1": 48, "x2": 275, "y1": 50, "y2": 305 }	[ "The Hβ and Hγ trailed spectra in Figure 7 seem to support these results." ]
Figure 8. Hα, Hβ and Hγ trailed spectra of 2001 folded on the spin period are shown in the top panels and the phase-invariant subtracted trailed spectra are shown in the second panels from the top. MEM spin Doppler tomograms constructed from the phase-invariant subtracted spectra are shown in the third panels with the reconstructed spectra in the bottom panels. The spin wave observed in the Hα phase-invariant subtracted trailed spectra, which was caused by the Hα narrow component, is shown expanded on a smaller velocity scale. The first column of panels are plotted between -1500 km s−1 and 1500 km s−1 and the last two column are plotted between -2000 km s−1 and +2000 km s−1. The lookup table is as in Figure 4.	{ "x1": 305.15966796875, "x2": 544.2210083007812, "y1": 441.68524169921875, "y2": 535.919921875 }	Figure	[]	8	5	{ "x1": 311, "x2": 538, "y1": 50, "y2": 431 }	[ " The results are shown in the second panels from the top of Figure 8.", "A spin-wave (to differentiate it from the s-wave which is normally caused by the bright spot) in the Hα trailed spectra (Figure 8) was detected from the data after the phase-invariant subtraction was performed.", "panded in the second column of panels in Figure 8 (the narrow peak component was selected by hand over a velocity range of ±500 km s−1).", "4, with an estimated velocity amplitude of ∼ 900 km s−1 and corresponds to the emission near the “3 o’clock” position in the tomogram (Figure 8).", "A spin wave was detected in the spin-folded trailed spectra of Hα (Figure 8) with a velocity semi-amplitude of ∼ 500-600 km s−1.", "4 (Figure 8), in agreement with the accretion curtain model.", " There is evidence for strong Hα emission of the narrow s-wave component in the spin tomograms, centred around ∼ 100 km s−1 (Figure 8), that is not accounted for by these models." ]
Figure 9. A depiction of the regions where Hα was formed. Both the narrow and broad base components fall along the same radial direction, OA, resulting in similar phase variation.	{ "x1": 42.11981201171875, "x2": 281.23211669921875, "y1": 463.0452575683594, "y2": 487.5599670410156 }	Figure	[ "Observer", "A", "O", "B" ]	9	7	{ "x1": 77, "x2": 246.54859924316406, "y1": 336.0127868652344, "y2": 451.68035888671875 }	[]
Table 1. Table of spectroscopic observations during quiescence in 1991 and 2001. The column Date denotes the date at the beginning of the observing night (before midnight), the column Time denotes the number of observing hours and Spectra the number of spectra obtained.	{ "x1": 42.11980438232422, "x2": 281.18377685546875, "y1": 173.48524475097656, "y2": 207.9600830078125 }	Table	[ "24-04-91", "2448371.3884097", "3.28", "90", "25-04-91", "2448372.3603850", "2.93", "72", "29-04-91", "2448376.2402973", "7.00", "100", "24-03-01", "2451993.5427099", "2.79", "42", "25-03-01", "2451994.3581177", "3.77", "56", "25-03-01", "2451994.5147196", "3.96", "66", "26-03-01", "2451995.4360089", "1.94", "48", "26-03-01", "2451995.5412087", "2.92", "50", "Date", "HJD", "(start)", "Time", "Spectra" ]	1	1	{ "x1": 72, "x2": 251, "y1": 53, "y2": 157 }	[ " The observing log is given in Table 1 together with the starting times of the observations.", " The observations covered the period 24 April - 26 April 2001 and, in total, 262 spectra were obtained (Table 1)." ]
FIG. 10: Comparison of the measured variation of f+(q2)/f+(0) obtained in the present analysis and in the FOCUS experiment [5]. The band corresponds to lattice QCD [19] with the estimated uncertainty.	{ "x1": 54, "x2": 299.09454345703125, "y1": 324.0768127441406, "y2": 360.00018310546875 }	Figure	[ "BABAR", "FOCUS", "Lattice-QCD", "(αpole", "=", "0.50(4))", ")", "+", "(0", "2", ")", "/", "f", "f", "+", "(q", "q2(GeV2)", "0", "0.5", "1", "1.5", "2", "2", "1.5", "1" ]	10	16	{ "x1": 59.20277404785156, "x2": 277.5876159667969, "y1": 87, "y2": 303.0580139160156 }	[ "In Fig. 10, the dependence of the form factor on q2 is presented." ]
FIG. 11: Measured values for P×Φ×f+ are plotted versus −z and requiring that P ×Φ× f+ = 1 for z = zmax. The straight lines represent the result for the modified pole ansatz, the fit in the center and the statistical and total uncertainty.	{ "x1": 317.0400085449219, "x2": 562.186767578125, "y1": 324.0768127441406, "y2": 360.00018310546875 }	Figure	[ ")", "Modif.", "pole", "fit", "BaBar", "m", "ax", "f", "+", "(z", "P", "Φ", "z)", "/", "f", "+", "(", "P", "Φ", "-z", "-0.05", "-0.025", "0", "0.025", "0.05", "1.4", "1.2", "1" ]	11	16	{ "x1": 329.4460144042969, "x2": 539, "y1": 87, "y2": 302.1570129394531 }	[ " Figure 11 shows the product P ×Φ× f+ as a function of z.", " The data are compatible with a linear dependence, which is fully consistent with the modified pole ansatz for f+(q2), as illustrated in Fig. 11." ]
FIG. 12: Events selected for the reference channel D∗+ → D0π+, D0 → K−π+. a) Kπ mass distribution for events selected in the range δ(m) ∈ [0.143, 0.148] GeV/c2. b) δ(m) distribution for events selected in the range m(Kπ) ∈ [1.83, 1.89] GeV/c2. c) same distribution as in b), displayed on a larger mass range with the non-peaking background indicated (shaded area). d) δ(m) distribution after non-peaking background subtraction, data (points with statistical errors) and simulated events (shaded histogram).	{ "x1": 53.9998779296875, "x2": 562.1865844726562, "y1": 484.3968200683594, "y2": 530.7595825195312 }	Figure	[ "d)", "/c", "2", "M", "eV", "/", "0", ".1", "nt", "s", "E", "ve", "m(D0π)-m(D0)", "(GeV/c2)", "Data", "MC", "0.14", "0.1425", "0.145", "0.1475", "0.15", "10", "4", "10", "3", "10", "2", "10", "1", "10", "-1", "10", "-2", "c)", "2", "eV", "/c", "/", "1", "M", "nt", "s", "E", "ve", "m(D0π)-m(D0)", "(GeV/c2)", "Data", "MC", "bkg", "0.14", "0.16", "0.18", "0.2", "10", "5", "10", "4", "10", "3", "10", "2", "10", "1", "b)", "/c", "2", "M", "eV", "/", "0", ".1", "nt", "s", "E", "ve", "m(D0π)-m(D0)", "(GeV/c2)", "D0→K-π+", "D0→K-π+γ", "π→µ", "Other", "bkg", "0.14", "0.1425", "0.145", "0.1475", "0.15", "10", "5", "10", "4", "10", "3", "10", "2", "10", "1", "a)", "/c", "2", "M", "eV", "/", "2", ".5", "nt", "s", "E", "ve", "m(Kπ)", "(GeV/c2)", "D0→K-π+", "D0→K-π+γ", "D0→K-K+", "D0→π-π+", "π→µ", "Other", "1.75", "1.8", "1.85", "1.9", "1.95", "10", "5", "10", "4", "10", "3", "10", "2", "10", "1" ]	12	17	{ "x1": 115.48231506347656, "x2": 478.67822265625, "y1": 92, "y2": 441.49700927734375 }	[ "The δ(m) distribution for candidate events is shown in Fig. 12-c.", "200 GeV/c2 (see Fig. 12-c).", " After background subtraction, the δ(m) distributions obtained in data and simulation can be compared in Fig. 12-d." ]
FIG. 13: δ(m) distribution for D0 → K−π+π0 events analyzed as if they were semileptonic decays. Distributions have been normalized to unity; note that the bin size is not uniform. The bottom plot shows the ratio of the two distributions above.	{ "x1": 317.0400085449219, "x2": 562.214111328125, "y1": 353.3568115234375, "y2": 399.719970703125 }	Figure	[ "/", "M", "C", "at", "a", "0.15", "0.2", "0.25", "0.3", "δ(m)", "(GeV/c2)", "D", "1.25", "1", "tio", "n", "Fr", "ac", "Data", "MC", "0.15", "0.2", "0.25", "0.3", "0.2", "0.1", "0" ]	13	18	{ "x1": 333.27301025390625, "x2": 560.9656372070312, "y1": 89, "y2": 321.18701171875 }	[ " The δ(m) distributions are compared in Fig. 13." ]
FIG. 3: MC simulations of some of the variables used in the Fisher discriminant analysis to reduce the cc̄-event background: a) the D0 momentum after the kinematic fit, b) the mass of the spectator system (peaks, at low mass values correspond to events with a single charged pion or photon reconstructed in the spectator system), c) the cosine of the angle between the spectator system momentum and the thrust direction, d) the cosine of the angle of the positron direction, relative to the kaon direction, in the eνe c.m. frame.	{ "x1": 317.0400085449219, "x2": 562.1553344726562, "y1": 348.3168029785156, "y2": 437.3992614746094 }	Figure	[ "•", "the", "charged", "lepton", "momentum,", "pe,", "in", "the", "c.m.", "frame.", "•", "the", "direction", "of", "the", "lepton", "relative", "to", "the", "kaon", "di-", "rection,", "in", "the", "dilepton", "rest", "frame,", "cos", "θe;", "•", "the", "direction", "of", "the", "leading", "spectator", "track", "relative", "to", "the", "thrust", "axis;" ]	3	9	{ "x1": 333.0008544921875, "x2": 562.2141723632812, "y1": 461.4874267578125, "y2": 541.079345703125 }	[ " Distributions for four of the most discriminating variables are given in Fig. 3." ]
FIG. 4: Distribution of the values of the Fisher variable in the signal region (δ(m) < 0.16 GeV/c2 in a), and for masses above the signal region (δ(m) > 0.16 GeV/c2 in b).	{ "x1": 53.99989318847656, "x2": 298.9486999511719, "y1": 353.3568115234375, "y2": 378.719970703125 }	Figure	[ "/", "0", ".1", "b)", "nt", "s", "E", "ve", "Fcc", "-1", "0", "1", "2", "3", "1", "10", "10", "2", "10", "3", "10", "4", "10", "5", "10", "6", "a)", "/", "0", ".1", "nt", "s", "E", "ve", "Data", "signal", "c", "bkg.", "B+", "bkg.", "B0", "bkg.", "uds", "bkg.", "-1", "0", "1", "2", "3", "1", "10", "10", "2", "10", "3", "10", "4", "10", "5", "10", "6" ]	4	10	{ "x1": 64.74690246582031, "x2": 294.1747131347656, "y1": 96.69039916992188, "y2": 326.5115966796875 }	[ " This selection retains 77% of signal events that were kept by the previous selection requirement and rejecting 66% of the background (Fig. 4).", " This is done by comparing the distributions of this variable measured in data and in simulation as given in Fig. 4 for two selected intervals in δ(m)." ]
FIG. 5: The measured q2 r distribution (data points) compared to the sum of the estimated background and of the fitted signal components.	{ "x1": 317.0400085449219, "x2": 562.1619873046875, "y1": 352.5168151855469, "y2": 377.87994384765625 }	Figure	[ "2", "G", "eV", "/", "0", ".2", "nt", "s", "E", "ve", "q2", "r", "(GeV2)", "Data", "Signal", "Background", "0", "0.5", "1", "1.5", "2", "15000", "10000", "5000", "0" ]	5	10	{ "x1": 322.5420227050781, "x2": 565.0991821289062, "y1": 90, "y2": 328.4779968261719 }	[ "bution, where q2 r = (pD − pK) 2 , is given in Fig. 5." ]
FIG. 6: The efficiency as a function of q2, measured with simulated signal events, after all selection criteria applied.	{ "x1": 53.99983215332031, "x2": 298.9818420410156, "y1": 324.0768127441406, "y2": 339.1202087402344 }	Figure	[ "nc", "y", "ic", "ie", "E", "ff", "0", "0.5", "1", "1.5", "2", "q2", "(GeV2)", "0.08", "0.06", "0.04" ]	6	11	{ "x1": 63.854698181152344, "x2": 277.3628234863281, "y1": 87, "y2": 298.8559875488281 }	[ "The variation of the selection efficiency as a function of q2 is given in Fig. 6." ]

Figure 3: The diphoton event distribution from the theoreti al simulation for √S = 1.96GeV, withthe sele tion riteria imposed in the CDF measurement, as a fun tion of the various kinemati variables des ribed in the text, shown for QT < Q and QT > Q separately.

{ "x1": 72, "x2": 539.8804321289062, "y1": 396.0799865722656, "y2": 436.6800842285156 }

Figure

[ "R", "ut", "p", "T", "uts", "Q(GeV", ")", "j", "yj", "os", "?", "Q", "T(GeV", ")", "0.5", "1", "2.5", "1008060402001008060", "40", "1", "-12", "QT", ">", "QQT", "<", "QKinemati", "al", "distributions", "in", "the", "Tevatron", "Run-2", "(CDF)", "01", "0", "1.5", "2", "3", "'", "(rad)", "200", "0" ]

3

14

{ "x1": 144, "x2": 471, "y1": 41.233943939208984, "y2": 383 }

[ "A s atter plot of event distributions from our theoreti al simulation for CDF kinemati uts and arbitrary luminosity is shown in Fig. 3.", " The region QT > QIt is evident from Fig. 3 that the ∆ϕ < π/2 region is populated mostly by events with QT > Q.", " Fig. 3).", " For values of Q below the kinemati uto at about 30 GeV, the uts shown in Fig. 3 suppress diphoton produ tion at small QT , and 〈QT /Q〉 grows toward1 as Q de reases ( orresponding to produ tion only at QT lose to Q)." ]

Fig. 1. Examples of sparsity-certifying decompositions: (a) a 3-arborescence; (b) a 2-map-graph; (c) a (2,1)-maps-and-trees. Edges with the same line style belong to the same subgraph. The 2-map-graph is shown with a certifying orientation.

{ "x1": 72, "x2": 525.3064575195312, "y1": 361.5296325683594, "y2": 395.7250061035156 }

Figure

[ "(c)", "(b)", "4", "3", "2", "1", "(a)", "d", "e", "c", "b", "a" ]

1

2

{ "x1": 120, "x2": 477, "y1": 94.8900146484375, "y2": 347.92901611328125 }

[ " Figure 1(a) shows an example of a 3-arborescence.", " Figure 1(b) shows an example of a 2-map-graphs; the edges are oriented in one possible configuration certifying that each color forms a map-graph." ]

Fig. 2. (a) A graph with a 3T2 decomposition; one of the three trees is a single vertex in the bottom right corner. (b) The highlighted subgraph inside the dashed countour has three black tree-pieces and one gray tree-piece. (c) The highlighted subgraph inside the dashed countour has three gray tree-pieces (one is a single vertex) and one black tree-piece.

{ "x1": 72, "x2": 525.3055419921875, "y1": 330.6646423339844, "y2": 378.4090270996094 }

Figure

[ "(c)", "5", "4", "3", "2", "1", "0", "(b)", "5", "4", "3", "2", "1", "0", "(a)", "5", "4", "3", "2", "1", "0" ]

2

3

{ "x1": 149, "x2": 449, "y1": 95.8900146484375, "y2": 317.06402587890625 }

[ " Figure 2(a) shows an example of a 3T2.", "Figure 2(a) shows a graph with a 3T2 decomposition; we note that one of the trees is an isolated vertex in the bottom-right corner.", " The subgraph in Figure 2(b) has three black treepieces and one gray tree-piece: an isolated vertex at the top-right corner, and two single edges.", " Figure 2(c) shows another subgraph; in this case there are three gray tree-pieces and one black one." ]

Fig. 3. Examples of pebble game with colors moves: (a) add-edge. (b) pebble-slide. Pebbles on vertices are shown as black or gray dots. Edges are colored with the color of the pebble on them.

{ "x1": 72, "x2": 525.3045043945312, "y1": 308.56268310546875, "y2": 329.20806884765625 }

Figure

[ "⇒", "⇒", "(b)", "(a)", "⇒", "⇒" ]

3

4

{ "x1": 81, "x2": 517, "y1": 227.8900146484375, "y2": 294.9620361328125 }

[ "Figure 3(a) shows examples of the add-edge move.", " Figure 3(b) shows examples." ]

Fig. 4. A (2,2)-tight graph with one possible pebble-game decomposition. The edges are oriented to show (1,0)-sparsity for each color. (a) The graph K4 with a pebble-game decomposition. There is an empty black tree at the center vertex and a gray spanning tree. (b) The highlighted subgraph has two black trees and a gray tree; the black edges are part of a larger cycle but contribute a tree to the subgraph. (c) The highlighted subgraph (with a light gray background) has three empty gray trees; the black edges contain a cycle and do not contribute a piece of tree to the subgraph.

{ "x1": 71.99999237060547, "x2": 525.305908203125, "y1": 227.05963134765625, "y2": 301.90203857421875 }

Figure

[ "(a)", "(b)", "(c)" ]

4

5

{ "x1": 101, "x2": 496, "y1": 95.8900146484375, "y2": 213.458984375 }

[ " Figure 4(a) shows an example of a (2,2)-tight graph with a pebble-game decomposition.", " The orientation of the edges in Figure 4(a) shows this.", "For example Figure 4(a) shows a (2,2)-tight graph with one possible pebble-game decomposition.", " The subgraph in Figure 4(b) has a black tree and a gray tree, with the edges of the black tree coming from a cycle in the larger graph.", " In Figure 4(c), however, the black cycle does not contribute a tree-piece." ]

Fig. 5. Creating monochromatic cycles in a (2,0)-pebble game. (a) A type (M1) move creates a cycle by adding a black edge. (b) A type (M2) move creates a cycle with a pebble-slide move. The vertices are labeled according to their role in the definition of the moves.

{ "x1": 71.99996948242188, "x2": 525.3038330078125, "y1": 331.76263427734375, "y2": 365.95703125 }

Figure

[ "(b)", "w", "v", "w", "⇒", "v", "(a)", "⇒", "vw", "vw" ]

5

10

{ "x1": 162, "x2": 435, "y1": 91.8900146484375, "y2": 318.1610107421875 }

[ "Figure 5(a) and Figure 5(b) show examples of (M1) and (M2) map-graph creation moves, respectively, in a (2,0)-pebble game construction." ]

Fig. 6. Outline of the shortcut construction: (a) An arbitrary simple path from v to w with curved lines indicating simple paths. (b) An (M2) step. The black edge, about to be flipped, would create a cycle, shown in dashed and solid gray, of the (unique) gray tree rooted at w. The solid gray edges were part of the original path from (a). (c) The shortened path to the gray pebble; the new path follows the gray tree all the way from the first time the original path touched the gray tree at w′. The path from v to w′ is simple, and the shortcut construction can be applied inductively to it.

{ "x1": 72, "x2": 525.3057250976562, "y1": 519.109619140625, "y2": 593.9520263671875 }

Figure

[ "(c)", "w'", "v", "w", "(b)", "w", "v", "v", "(a)", "w" ]

6

11

{ "x1": 134.87135314941406, "x2": 462.5532531738281, "y1": 231.9584197998047, "y2": 505.5090026855469 }

[ " The main idea, captured in Lemma 15 and illustrated in Figure 6, is to avoid creating cycles while collecting pebbles.", "Figure 6 shows the structure of the proof." ]

Fig. 7. Eliminating (M2) moves: (a) an (M2) move; (b) avoiding the (M2) by moving along another path. The path where the pebbles move is indicated by doubled lines.

{ "x1": 72, "x2": 525.297607421875, "y1": 329.109619140625, "y2": 349.7550048828125 }

Figure

[ "(b)", "⇒", "(a)", "⇒" ]

7

12

{ "x1": 162, "x2": 435, "y1": 91.8900146484375, "y2": 315.50799560546875 }

[]

Fig. 8. Eliminating (M2) moves: (a) the first step to move the black pebble along the doubled path is (M2); (b) avoiding the (M2) and simplifying the path.

{ "x1": 72, "x2": 525.3060302734375, "y1": 581.5916748046875, "y2": 602.238037109375 }

Figure

[ "⇒", "(b)", "⇒", "(a)" ]

8

12

{ "x1": 163, "x2": 435, "y1": 363.8900146484375, "y2": 567.9910278320312 }

[ "Figure 7 and Figure 8 illustrate the construction used in the proof of Lemma 15." ]

Table 1. Sparse graph and decomposition terminology used in this paper.

{ "x1": 72, "x2": 390.9814758300781, "y1": 237.56866455078125, "y2": 244.6650390625 }

Table

[ "Term", "Meaning", "Sparse", "graph", "G", "Every", "non-empty", "subgraph", "on", "n′", "vertices", "has", "≤", "kn′−", "`", "edges", "Tight", "graph", "G", "G", "=", "(V,E)", "is", "sparse", "and", "|V", "|=", "n,", "|E|=", "kn−", "`", "Block", "H", "in", "G", "G", "is", "sparse,", "and", "H", "is", "a", "tight", "subgraph", "Component", "H", "of", "G", "G", "is", "sparse", "and", "H", "is", "a", "maximal", "block", "Map-graph", "Graph", "that", "admits", "an", "out-degree-exactly-one", "orientation", "(k,", "`)-maps-and-trees", "Edge-disjoint", "union", "of", "`", "trees", "and", "(k−", "`)", "map-grpahs", "`Tk", "Union", "of", "`", "trees,", "each", "vertex", "is", "in", "exactly", "k", "of", "them", "Set", "of", "tree-pieces", "of", "an", "`Tk", "induced", "on", "V", "′", "⊂V", "Pieces", "of", "trees", "in", "the", "`Tk", "spanned", "by", "E(V", "′)", "Proper", "`Tk", "Every", "V", "′", "⊂V", "contains", "≥", "`", "pieces", "of", "trees", "from", "the", "`Tk" ]

1

{ "x1": 72, "x2": 570, "y1": 91.8900146484375, "y2": 233.8900146484375 }

[ "Table 1 summarizes the sparse graph terminology used in this paper.", "Table 1 contains the decomposition terminology used in this paper." ]

Table 2. Pebble game notation used in this paper.

{ "x1": 72, "x2": 287.30145263671875, "y1": 409.2216491699219, "y2": 416.3180236816406 }

Table

[ "Notation", "Meaning", "span(V", "′)", "Number", "of", "edges", "spanned", "in", "H", "by", "V", "′", "⊂V", ";", "i.e.", "|EH(V", "′)|", "peb(V", "′)", "Number", "of", "pebbles", "on", "V", "′", "⊂V", "out(V", "′)", "Number", "of", "edges", "vw", "in", "H", "with", "v", "∈V", "′", "and", "w", "∈V", "−V", "′", "pebi(v)", "Number", "of", "pebbles", "of", "color", "ci", "on", "v", "∈V", "outi(v)", "Number", "of", "edges", "vw", "colored", "ci", "for", "v", "∈V" ]

2

5

{ "x1": 72, "x2": 381, "y1": 318.8900146484375, "y2": 405.8900146484375 }

[ "Table 2 lists the pebble game notation used in this paper." ]

Figure 2, the solar days / year vs. the age of the Earth

{ "x1": 151.6199951171875, "x2": 488.5828552246094, "y1": 76.61536407470703, "y2": 85.91998291015625 }

Figure

[ "480", "460", "440", "420", "400", "380", "360", "ye", "ar", "ay", "s/", "ar", "d", "S", "ol", "3.5", "3.6", "3.7", "3.8", "3.9", "4.0", "4.1", "4.2", "4.3", "4.4", "4.5", "4.6", "The", "age", "of", "the", "Earth", "(109", "years)" ]

2

21

{ "x1": 100.54000091552734, "x2": 505.56866455078125, "y1": 121.86924743652344, "y2": 418.32000732421875 }

[]

FIG. 1: Principal isentrope and shock Hugoniot for air (perfect gas): numerical calculations for general material models, compared with analytic solutions.

{ "x1": 72, "x2": 538.2794189453125, "y1": 275.2254333496094, "y2": 302.39990234375 }

Figure

[ "Hugoniot", "isentrope", "mass", "density", "(g/cm3)", "%", ")", "ce", "(", "er", "en", "d", "iff", "su", "re", "pr", "es", "0.001", "0.01", "1", "0.1", "0.01", "0.001", "0.0001", "Hugoniot", "isentrope", "mass", "density", "(g/cm3)", "P", "a)", "(", "G", "su", "re", "pr", "es", "0.001", "0.01", "0.01", "0.001", "0.0001" ]

1

26

{ "x1": 80.85079956054688, "x2": 533.0890502929688, "y1": 79.8526840209961, "y2": 235.61602783203125 }

[ "1% respectively, for a compression increment of 1% along the isentrope and a solution tolerance of 10−6 GPa for each shock state (Fig. 1).", " Each of these scenarios may occur in turn following the impact of a projectile with a target: if the target is layered then a shock is transmitted across each interface with a release or a reshock reflected back, depending on the materials; release ultimately occurs at the rear of the projectile and the far end of the target, and the oppositely-moving release waves subject the projectile and target to tensile stresses when they interact (Fig. 10).", "3GPa in the LiF, using the same material properties (Fig. 11)." ]

FIG. 10: Schematic of uniaxial wave interactions induced by the impact of a flat projectile with a composite target.

{ "x1": 72, "x2": 538.2787475585938, "y1": 349.9854431152344, "y2": 377.0400085449219 }

Figure

[ "release", "interactions:", "free", "surface", "release", "impact", "shocks", "transmitted", "shock;", "reflected", "wave", "target", "w", "d", "o", "w", "in", "ct", "ile", "ro", "je", "e", "p", "ti", "m", "tension" ]

10

35

{ "x1": 212.6199951171875, "x2": 405.7367248535156, "y1": 73.25399017333984, "y2": 310.79998779296875 }

[]

FIG. 11: Hydrocode simulation of Al projectile at 3.6 km/s impacting a Mo target with a LiF release window, 1.1 µs after impact. Structures on the waves are elastic precursors.

{ "x1": 72, "x2": 538.2661743164062, "y1": 312.7854309082031, "y2": 339.8399963378906 }

Figure

[ "original", "shock", "state", "shock", "release", "transmitted", "reflected", "LiFAl", "Mo", "position", "(mm)", "P", "a)", "s", "(G", "tr", "es", "al", "s", "no", "rm", "0", "5", "10", "15", "20", "70", "60", "50", "40", "30", "20", "10", "0" ]

11

36

{ "x1": 172.49200439453125, "x2": 439.1109924316406, "y1": 81.55197143554688, "y2": 271.9320068359375 }

[]

FIG. 2: Shock Hugoniot for Al in pressure-temperature space, for different representations of the equation of state.

{ "x1": 72, "x2": 538.2723999023438, "y1": 312.7854309082031, "y2": 339.8399963378906 }

Figure

[ "solid:", "Grueneisen", "dashed:", "SESAME", "3716", "temperature", "(K)", "P", "a)", "s", "(G", "tr", "es", "al", "s", "no", "rm", "0", "1000", "2000", "3000", "4000", "5000", "120", "100", "80", "60", "40", "20", "0" ]

2

27

{ "x1": 172.49200439453125, "x2": 444.66998291015625, "y1": 81.55197143554688, "y2": 271.9320068359375 }

[ " Taking a SESAME type EOS, thermodynamic loci were calculated with {ρ, e} or {ρ, T} primitive states, for comparison (Fig. 2).", " Temperatures were in good agreement (Fig. 2)." ]

FIG. 3: Principal adiabat and shock Hugoniot for Be in normal stress-compression space, neglecting strength (dashed), for Steinberg-Guinan strength (solid), and for elastic-perfectly plastic with Y = 10 GPa (dotted).

{ "x1": 72, "x2": 538.282958984375, "y1": 312.7854309082031, "y2": 361.5599060058594 }

Figure

[ "each", "pair", "of", "lines:", "upper", "is", "Hugoniot,", "lower", "is", "adiabat", "volume", "compression", "P", "a)", "s", "(G", "tr", "es", "al", "s", "no", "rm", "0.7", "0.75", "0.8", "0.85", "0.9", "0.95", "1", "90", "80", "70", "60", "50", "40", "30", "20", "10", "0" ]

3

28

{ "x1": 172.49200439453125, "x2": 436.3299865722656, "y1": 81.55197143554688, "y2": 271.9320068359375 }

[ "greater heating obtained by integrating along the adiabat compared with jumping from the initial to the final state on the Hugoniot (Fig. 3)." ]

FIG. 4: Principal adiabat and shock Hugoniot for Be in shock speed-normal stress space, neglecting strength (dashed), for Steinberg-Guinan strength (solid), and for elastic-perfectly plastic with Y = 10 GPa (dotted).

{ "x1": 72, "x2": 538.282958984375, "y1": 312.7854309082031, "y2": 361.5599060058594 }

Figure

[ "plastic", "shock", "elastic", "wave", "normal", "stress", "(GPa)", "/s", ")", "(k", "m", "ee", "d", "k", "sp", "sh", "oc", "0", "20", "40", "60", "80", "100", "120", "140", "15", "14", "13", "12", "11", "10", "9", "8" ]

4

29

{ "x1": 172.49200439453125, "x2": 433, "y1": 81.55197143554688, "y2": 271.9320068359375 }

[ " In Be with the high flow stress of nanosecond response, the relation between shock and particle speeds is significantly different from the relation for low flow stress (Fig. 4)." ]

FIG. 5: Principal adiabat, shock Hugoniot, and release adiabat for Be in normal stress-temperature space, neglecting strength (dashed), for Steinberg-Guinan strength (solid), and for elastic-perfectly plastic with Y = 10 GPa (dotted).

{ "x1": 72, "x2": 538.2528686523438, "y1": 312.7854309082031, "y2": 361.5599060058594 }

Figure

[ "release", "adiabat", "principal", "Hugoniot", "principal", "adiabat", "temperature", "(K)", "P", "a)", "s", "(G", "tr", "es", "al", "s", "no", "rm", "0", "1000", "2000", "3000", "4000", "5000", "200", "150", "100", "50", "0" ]

5

30

{ "x1": 172.49200439453125, "x2": 444.66998291015625, "y1": 81.55197143554688, "y2": 271.9320068359375 }

[ " (Fig. 5." ]

FIG. 6: Demonstration of shock Hugoniot solution across a phase boundary: shock-melting of Al, for different initial porosities.

{ "x1": 72, "x2": 538.2545776367188, "y1": 312.7854309082031, "y2": 339.8399963378906 }

Figure

[ "30%", "20%", "solid", "Hugoniot", "10%", "melt", "locus", "temperature", "(K)", "P", "a)", "s", "(G", "tr", "es", "al", "s", "no", "rm", "0", "1000", "2000", "3000", "4000", "5000", "140", "120", "100", "80", "60", "40", "20", "0" ]

6

31

{ "x1": 172.49200439453125, "x2": 444.66998291015625, "y1": 81.55197143554688, "y2": 271.9320068359375 }

[ "397MJ/kg, the shock Hugoniot algorithm was found to operate stably across the phase transition (Fig. 6)." ]

FIG. 7: Wave interactions for the impact of a flat projectile moving from left to right with a stationary target. Dashed arrows are a guide to the sequence of states. For a projectile moving from right to left, the construction is the mirror image reflected in the normal stress axis.

{ "x1": 72, "x2": 538.2923583984375, "y1": 301.9854431152344, "y2": 350.7599182128906 }

Figure

[ "of", "target", "of", "projectile", "shock", "state:", "intersection", "principal", "Hugoniot", "principal", "Hugoniot", "of", "target", "initial", "state", "of", "projectile", "0", "es", "s", "s", "tr", "rm", "al", "n", "o", "particle", "speed", "initial", "state" ]

7

32

{ "x1": 194.02000427246094, "x2": 423.7277526855469, "y1": 73, "y2": 259.8599853515625 }

[ " Examples of these wave interactions are the impact of a projectile with a stationary target (Fig. 7), release of a shock state at a free surface or a material (e." ]

FIG. 8: Wave interactions for the release of a shocked state (shock moving from left to right) into a stationary ‘window’ material to its right. The release state depends whether the window has a higher or lower shock impedance than the shocked material. Dashed arrows are a guide to the sequence of states. For a shock moving from right to left, the construction is the mirror image reflected in the normal stress axis.

{ "x1": 72, "x2": 538.3157348632812, "y1": 328.9854431152344, "y2": 421.0802307128906 }

Figure

[ "window", "release", "target", "release", "at", "free", "surface", "target", "release", "isentrope", "low", "impedance", "window", "principal", "Hugoniot:", "high", "impedance", "window", "of", "target", "initial", "shock", "state", "in", "target", "secondary", "Hugoniot", "0", "es", "s", "s", "tr", "rm", "al", "n", "o", "particle", "speed", "states" ]

8

33

{ "x1": 161.97999572753906, "x2": 455.92578125, "y1": 73, "y2": 286.8600158691406 }

[ " a window) of lower shock impedance (hence reflecting a release wave into the shocked material – Fig. 8), reshocking at a surface with a material of higher shock impedance (Fig." ]

FIG. 9: Wave interactions for the release of a shocked state by tension induced as materials try to separate in opposite directions when joined by a bonded interface. Material damage, spall, and separation are neglected: the construction shows the maximum tensile stress possible. For general material properties, e.g. if plastic flow is included, the state of maximum tensile stress is not just the negative of the initial shock state. Dashed arrows are a guide to the sequence of states. The graph shows the initial state after an impact by a projectile moving from right to left; for a shock moving from right to left, the construction is the mirror image reflected in the normal stress axis.

{ "x1": 71.99996948242188, "x2": 538.3623657226562, "y1": 439.38543701171875, "y2": 574.8001098632812 }

Figure

[ "initial", "shock", "state", "projectile", "release", "target", "release", "target", "release", "0", "es", "s", "s", "tr", "rm", "al", "n", "o", "particle", "speed", "final", "tensile", "state", "in", "projectile", "and", "target", "in", "projectile", "and", "target", "projectile", "release" ]

9

34

{ "x1": 194.02000427246094, "x2": 425.2499694824219, "y1": 73, "y2": 397.25994873046875 }

[ " 8), or tension induced as materials try to separate in opposite directions when joined by a bonded interface (Fig. 9)." ]

TABLE I: Interface to material models required for explicit forward-time continuum dynamics simulations.

{ "x1": 72, "x2": 538.3253173828125, "y1": 84.06546783447266, "y2": 111.23992919921875 }

Table

[ "etc.", "that", "mass", "density", "is", "positive,", "volume", "or", "mass", "fractions", "of", "components", "of", "a", "mixture", "add", "up", "to", "one,", "calculations", "of", "the", "shock", "Hugoniot", "and", "ramp", "compression.", "Checks", "for", "self-consistency", "include", "that", "is", "most", "robust", "for", "explicit,", "forward-time", "numerical", "solutions", "and", "can", "also", "be", "used", "for", "the", "instantaneous,", "local", "state.”", "The", "evolution", "functions", "are", "shown", "in", "the", "operator-split", "structure", "Parentheses", "in", "the", "interface", "calls", "denote", "functions,", "e.g.", "“stress(state)”", "for", "“stress", "as", "a", "function", "of", "check", "for", "self-consistency", "multiply", "state", "by", "a", "scalar", "add", "states", "manipulation", "of", "states", "create", "and", "delete", "internal", "evolution", "of", "state", "d(state)/dt", "evolution", "of", "state", "(heating)", "d(state)/dt(state,ė)", "evolution", "of", "state", "(deformation)", "d(state)/dt(state,grad", "~u)", "time", "step", "control", "sound", "speed(state)", "continuum", "dynamics", "equations", "stress(state)", "program", "set-up", "read/write", "material", "data", "purpose", "interface", "calls" ]

I

23

{ "x1": 72, "x2": 538.2662353515625, "y1": 127, "y2": 498.3597412109375 }

[ " The continuum dynamics programs and the material properties relations can be developed and maintained independently of each other, provided that the interface remains the same (Table I).", " At the highest level, different types of behavior are characterized by different structures for the state s (Table II).", " For our application, polymorphism is used at several levels in the hierarchy of objects, from the overall type of a material (such as ‘one represented by a pressure-density-energy EOS’ or ‘one represented by a deviatoric stress model’) through the type of relation used to describe the properties of that material type (such as perfect gas, polytropic, or Grüneisen for a pressure-density-energy EOS, or Steinberg-Guinan [13] or Preston-Tonks-Wallace [14] for a deviatoric stress model), to the type of general mathematical function used to represent some of these relations (such as a polynomial or a tabular representation of γ(ρ) in a polytropic EOS) (Table III)." ]

TABLE II: Examples of types of material model, distinguished by different structures in the state vector.

{ "x1": 72, "x2": 538.1466674804688, "y1": 84.06546783447266, "y2": 111.23992919921875 }

Table

[ "triangular", "components,", "e.g.", "using", "Voigt", "notation.", "tensors", "such", "as", "the", "stress", "deviator", "are", "represented", "more", "compactly", "by", "their", "6", "unique", "upper", "transferring", "mass", "between", "components", "representing", "diﬀerent", "types", "of", "molecule.", "Symmetric", "components.", "Gas-phase", "reaction", "can", "be", "represented", "as", "a", "homogeneous", "mixture,", "reactions", "products;", "reaction,", "a", "process", "of", "internal", "evolution,", "transfers", "material", "from", "unreacted", "to", "reacted", "solid", "explosives", "can", "be", "represented", "as", "heterogeneous", "mixtures,", "one", "component", "being", "the", "reacted", "plastic", "part", "of", "velocity", "gradient,", "G:", "shear", "modulus,", "ǫ̇e,p:", "elastic", "and", "plastic", "parts", "of", "strain", "rate", "deviator,", "ǫ̃p:", "scalar", "equivalent", "plastic", "strain,", "fǫ:", "factor", "in", "eﬀective", "strain", "magnitude.", "Reacting", "fm:", "mass", "fraction,", "σ:", "stress", "deviator,", "fp:", "fraction", "of", "plastic", "work", "converted", "to", "heat,", "gradup:", "The", "symbols", "are", "ρ:", "mass", "density;", "e:", "speciﬁc", "internal", "energy,", "T", ":", "temperature,", "fv:", "volume", "fraction,", "fǫ||ǫ̇2", "p||", "ρ", ",", "Gǫ̇e,", "√", "thermal", "equation", "of", "state", "ρ,", "T", "−ρdiv~u,−pdiv~u/ρcv", "heterogeneous", "mixture", "{ρ,", "e,", "fv}i", "{−ρdiv~u,−pdiv~u/ρ,", "0}i", "homogeneous", "mixture", "ρ,", "T,", "{fm}i", "{−ρdiv~u,−pdiv~u/ρcv", ",", "0i", "traditional", "deviatoric", "strength", "ρ,", "e,", "σ,", "ǫ̃p", "−ρdiv~u,", "−pdiv~u+fp||σǫ̇p||", "mechanical", "equation", "of", "state", "ρ,", "e", "−ρdiv~u,−pdiv~u/ρ", "s", "ṡm(s,", "gradu)", "model", "state", "vector", "eﬀect", "of", "mechanical", "strain" ]

II

24

{ "x1": 72, "x2": 538.12841796875, "y1": 127, "y2": 519 }

[]

TABLE III: Outline hierarchy of material models, illustrating the use of polymorphism (in the object-oriented programming sense).

{ "x1": 72, "x2": 538.2804565429688, "y1": 84.66544342041016, "y2": 111.83990478515625 }

Table

[ "plus", "its", "volume", "fraction.", "set", "of", "‘pure’", "material", "properties", "of", "any", "type,", "and", "the", "state", "is", "the", "set", "of", "states", "for", "each", "component", "the", "state", "is", "the", "set", "of", "states", "and", "mass", "fractions", "for", "each.", "Heterogeneous", "mixtures", "are", "deﬁned", "as", "a", "represented", "by", "a", "solid", "state", "plus", "a", "void", "fraction", "fv,", "with", "operations", "deﬁned", "by", "extending", "those", "of", "the", "solid", "material.", "Homogeneous", "mixtures", "are", "deﬁned", "as", "a", "set", "of", "thermal", "equations", "of", "state,", "and", "are", "deﬁned", "by", "extending", "those", "of", "the", "mechanical", "equation", "of", "state.", "Spalling", "materials", "can", "be", "The", "reactive", "equation", "of", "state", "has", "an", "additional", "state", "parameter", "λ,", "and", "the", "software", "operations", "handled", "transparently", "by", "the", "object-oriented", "software", "structure.", "state),", "the", "speciﬁc", "model", "type", "(e.g.", "polytropic),", "and", "the", "state", "of", "material", "of", "that", "type", "are", "all", "with", "an", "abstract", "material", "state.", "The", "actual", "type", "of", "a", "material", "(e.g.", "mechanical", "equation", "of", "Continuum", "dynamics", "programs", "can", "refer", "to", "material", "properties", "as", "an", "abstract", "‘material", "type’", "heterogeneous", "mixture", "equilibration", "and", "reaction", "models", "homogeneous", "mixture", "mixing", "and", "reaction", "models", "Wallace,", "etc", "Steinberg-Lund,", "Preston-Tonks-", "deviatoric", "stress", "elastic-plastic,", "Steinberg-Guinan,", "spall", "Cochran-Banner", "Wilkins-Lee", "reactive", "equation", "of", "state", "modiﬁed", "polytropic,", "reactive", "Jones-", "etc", "Lee,", "quasiharmonic,", "(ρ,", "T", ")", "table,", "thermal", "equation", "of", "state", "temperature-based", "Jones-Wilkins-", "Jones-Wilkins-Lee,", "(ρ,", "T", ")", "table,", "etc", "mechanical", "equation", "of", "state", "polytropic,", "Grüneisen,", "energy-based", "material", "(or", "state)", "type", "model", "type" ]

III

25

{ "x1": 72.0013427734375, "x2": 538.2540283203125, "y1": 130, "y2": 673.199951171875 }

[]

Fig. 1.— Three color image of the area mapped in Serpens. The color mapping is: blue/4.5µm, green/8.0µm, and red/24µm. The locations of Cluster A (Core Cluster), Cluster B (Serpens G3-G6 Cluster), and VV Ser are indicated.

{ "x1": 72, "x2": 539.9144287109375, "y1": 659.7764282226562, "y2": 697.5599975585938 }

Figure

[]

1

4

{ "x1": 120, "x2": 521, "y1": 117, "y2": 636 }

[ " Figure 1 shows the entire area mapped with all four IRAC bands and MIPS at 24 and 70µm and also indicates the locations of several areas mentioned in the text.", " Figure 10 shows the two-point correlation function, W, for the YSO’s in our Serpens catalog and the sample of objects classified as extra-galactic background sources.", " These results are consistent with the appearance of the source distributions as shown, for example, in Figure 13 of Paper I.", " As shown in Figure 10, the slope and magnitude of the correlation for our sample of background extragalactic objects is consistent with that found by, for example, Maddox et al.", " Figure 11 shows no such correlation; in fact, if anything there appears to be a lack of relatively blue colors for the brightest objects.", "Fig. 13.", " Symbols as in Figure 12." ]

Fig. 10.— Left panel: the two-point correlation function, W, for Serpens. The dotted histogram is for sources identified as Class I and “Flat” SED objects, i.e. α ≥ −0.3. The solid histogram is for the Class II/III objects, i.e. α < −0.3. The dashed lines show several possible power law slopes for the portions of the YSO curves. Right panel: the dashed histogram is for the objects classified as likely background galaxies with S/N > 7 in all four IRAC bands. The dash-dot line shows the slope and amplitude found by Maddox et al. (1990) for the bright end of the extra-galactic population, which is a quite good fit to our estimate of the background contamination in our sample.

{ "x1": 71.99957275390625, "x2": 540.0379028320312, "y1": 647.7764282226562, "y2": 765.0001831054688 }

Figure

[]

10

24

{ "x1": 34, "x2": 551, "y1": 296, "y2": 610 }

[]

Fig. 11.— Color-color and color-magnitude plots of the 235 Serpens YSO’s compared with the distributions from models of Robitaille et al. (2007). The symbols are for the three different luminosity groups discussed in the text: open diamonds, L > 1 L⊙; light filled circles, 0.02 L⊙< L < 1 L⊙; plus signs, L < 0.02 L⊙. The model data were those for their model cluster, with a distance of 260 pc for Serpens and with the c2d completeness limits. Also shown are the rough areas from Robitaille et al. (2007) occupied by mainly stage I, II, and III models.

{ "x1": 71.99984741210938, "x2": 540.0189819335938, "y1": 647.7764282226562, "y2": 749.1599731445312 }

Figure

[ "–", "27", "–" ]

11

26

{ "x1": 61, "x2": 491, "y1": 62, "y2": 618 }

[]

Fig. 12.— Spectral Energy Distributions of the Class I sources in the sample. The open dots signal the observed fluxes from J-band to MIPS-70 when available. The label gives the index in Table 2.

{ "x1": 72, "x2": 540.0562744140625, "y1": 678.7363891601562, "y2": 716.52001953125 }

Figure

[]

12

30

{ "x1": 72, "x2": 498, "y1": 108, "y2": 659 }

[]

Fig. 14.— Spectral Energy Distributions of the Flat sources in the sample. Symbols as in Figure 12.

{ "x1": 72, "x2": 540.0361328125, "y1": 683.5364379882812, "y2": 705.3598022460938 }

Figure

[]

14

32

{ "x1": 72, "x2": 498, "y1": 113, "y2": 664 }

[]

Fig. 15.— Spectral Energy Distributions (SED) of the Class II sources in the sample. The open and solid dots are the observed and dereddened fluxes respectively. The grey line is the stellar model of a K7 star and the dashed line is the median SED of the TTauri stars in Taurus by Hartmann et al. (2005) normalized to the dereddened J-band flux for comparison. See text for more information.

{ "x1": 72, "x2": 540.036865234375, "y1": 678.7363891601562, "y2": 748.3200073242188 }

Figure

[]

15

33

{ "x1": 72, "x2": 498, "y1": 108, "y2": 659 }

[]

Fig. 16.— Spectral Energy Distributions of the Class II sources in the sample (continued).

{ "x1": 72, "x2": 536.4183959960938, "y1": 691.0964965820312, "y2": 697.080078125 }

Figure

[]

16

34

{ "x1": 72, "x2": 498, "y1": 120, "y2": 671 }

[]

Fig. 17.— Spectral Energy Distributions of the Class II sources in the sample (continued).

{ "x1": 72, "x2": 536.4183959960938, "y1": 691.0964965820312, "y2": 697.080078125 }

Figure

[]

17

35

{ "x1": 72, "x2": 498, "y1": 120, "y2": 671 }

[]

Fig. 18.— Spectral Energy Distributions of the Class II sources in the sample (continued).

{ "x1": 72, "x2": 536.4183959960938, "y1": 691.0964965820312, "y2": 697.080078125 }

Figure

[]

18

36

{ "x1": 72, "x2": 498, "y1": 120, "y2": 671 }

[]

Fig. 19.— Spectral Energy Distributions of the Class III sources in the sample.

{ "x1": 72, "x2": 478.5708312988281, "y1": 691.4562377929688, "y2": 697.4398193359375 }

Figure

[]

19

37

{ "x1": 72, "x2": 498, "y1": 121, "y2": 672 }

[]

Fig. 2.— The distribution of visual extinctions found toward the roughly 50,000 sources classified as stars in our Serpens observations.

{ "x1": 72, "x2": 539.860107421875, "y1": 668.056396484375, "y2": 689.8801879882812 }

Figure

[]

2

8

{ "x1": 65, "x2": 568, "y1": 265, "y2": 638 }

[ " This reddening was accomplished by randomly applying extinction to each SWIRE source according to the extinction profile of Serpens, shown in Figure 2.", "Fig. 24." ]

Fig. 20.— Spectral Energy Distributions of the Class III sources in the sample.

{ "x1": 72, "x2": 478.5708312988281, "y1": 567.9764404296875, "y2": 573.9600219726562 }

Figure

[]

20

38

{ "x1": 123, "x2": 490, "y1": 375, "y2": 495 }

[]

Fig. 21.— Distribution of disk to star luminosity ratios. The solid and dashed lines are the total sample and T Tauri-like sample of SEDs, respectively. Also marked are the typical ranges of Ldisk/Lstar ratios for debris disks, passive irradiated disks and accretion disks. The figure indicates that objects of all three evolutionary stages are found in Serpens, with a predominance of young accreting T Tauri-type stars.

{ "x1": 72, "x2": 540.0541381835938, "y1": 529.576416015625, "y2": 599.1599731445312 }

Figure

[]

21

40

{ "x1": 54, "x2": 441, "y1": 218, "y2": 510 }

[ " The corresponding distribution is shown in Figure 21." ]

Fig. 22.— Distribution of excess slopes αexcess with respect to the wavelength at which the infrared excess begins λturn−off for the sample of wTTs (solid dots), a sample of cTTs in Lupus from Cieza et al. (2006), the median SED of cTTs in Taurus from D’Alessio et al. (1999) in asterisks (marked as D99), and a sample of debris disks from Chen et al. (2005) in diamonds. The arrows represent the limits for the class II objects in Serpens and the triangles the Class III sources. The diagram shows a much larger spread in inner disk morphologies in the more evolved objects than in the least evolved ones. The Serpens objects follow the previously observed trend.

{ "x1": 72, "x2": 540.0654907226562, "y1": 548.4164428710938, "y2": 665.6397705078125 }

Figure

[]

22

41

{ "x1": 82, "x2": 554, "y1": 140, "y2": 452 }

[ " (2006) found that λexcess is well correlated with evolutionary phase and also, as seen in Figure 22, that α is observed over wider ranges for later evolutionary phases." ]

Fig. 23.— Three-color image of the Cluster A area of Serpens. The color coding is: blue/4.5µm, green/8.0µm, and red/24µm. Some of the more obvious objects that are likely to be jets are marked by arrows. The region of the disappearing source 81 of Eiroa & Casali (1992) is circled.

{ "x1": 71.99972534179688, "x2": 539.9332885742188, "y1": 651.8563842773438, "y2": 705.480224609375 }

Figure

[]

23

43

{ "x1": 539.9332885742188, "x2": 591, "y1": 149, "y2": 665 }

[ " Interestingly, though, this area marked in Figure 23 appears to contain several small knots of emission that may represent shocked gas.", "— Three-color image of the Cluster B area of Serpens as for Figure 23." ]

Fig. 3.— Color-magnitude and color-color diagrams for the Serpens Cloud (left), full SWIRE (center), and trimmed SWIRE regions. The black dashed lines show the “fuzzy” colormagnitude cuts that define the YSO candidate criterion in the various color-magnitude spaces. The red dashed lines show hard limits, fainter than which objects are excluded from the YSO category.

{ "x1": 72, "x2": 540.0781860351562, "y1": 647.7764282226562, "y2": 717.3599853515625 }

Figure

[ "–", "12", "–" ]

3

11

{ "x1": 100, "x2": 513, "y1": 76.81640625, "y2": 624 }

[ " In our new classification we have extended this concept to include the color and magnitude spaces in Figure 3 together with several additional criteria to compute a proxy for the probability that a source is a YSO or a background galaxy.", " Figure 3 shows a collection of three color-magnitude diagrams and one color-color diagram used to classify the sources found in our 3.", " Basically we form the product of individual probabilities from each of the three color-magnitude diagrams in Figure 3 and then use additional factors to modify that total “probability” based on source properties such as: its K - [4.", " The right panels in Figure 3, which use the resampled version of the SWIRE catalog, show that the effects of sensitivity and, especially, the extinction in Serpens make our cutoff limits particularly conservative in terms of likelihood of misclassification.", " (2007) have classified four AGB stars by their Spitzer-IRS spectra in the Serpens cloud; these are identified in the diagrams of Figure 3 by black open diamonds and obviously are not included in our final list of high-probability YSO’s.", " On the other hand, as we discuss in §6, some of the faint red objects in Figure 3 (below the dashed line) may also be young substellar objects.", "is based on the color-magnitude diagrams shown in Figure 3." ]

Fig. 4.— Plot of the number of sources versus probability (of being a background contaminant) for the Serpens cloud and for the trimmed SWIRE catalog described in the text. The vertical dashed line shows the separation chosen for YSO’s versus extra-galactic candidates. For both samples, only sources with detections in all four IRAC bands are plotted to keep the number counts of contaminants on scale!

{ "x1": 72, "x2": 539.9786376953125, "y1": 647.7764282226562, "y2": 717.3599853515625 }

Figure

[]

4

12

{ "x1": 85, "x2": 572, "y1": 125, "y2": 630 }

[]

Fig. 5.— Left panel: image of the entire mapped area of Serpens at 8.0µm with the positions of YSO’s plotted with circles and likely extra-galactic background contaminants with asterisks; center panel: same image with YSO’s of luminosity L < 2×10−2L⊙ plotted with boxes, and higher luminosity YSO’s plotted with circles; right panel: contours of visual extinction Av at levels of 5, 10, 20, 30 magnitudes as derived from fitting the energy distributions of sources that were well-fit as reddened stellar photospheres in our data set.

{ "x1": 71.99932861328125, "x2": 539.99365234375, "y1": 683.7764282226562, "y2": 769.2001953125 }

Figure

[]

5

13

{ "x1": 90, "x2": 491, "y1": 111, "y2": 630 }

[ " Figure 5 shows such a plot in addition to a plot of visual extinction discussed later.", " Figure 5 presented in §3.", " We also showed in Figure 5 that the spatial distribution of our high quality YSO candidates was highly clustered." ]

Fig. 6.— Luminosity function for Serpens YSO’s (solid) and estimate of correction for completeness effects (dashed).

{ "x1": 72, "x2": 540.0196533203125, "y1": 667.6964111328125, "y2": 689.6397705078125 }

Figure

[]

6

18

{ "x1": 85, "x2": 569, "y1": 145, "y2": 650 }

[ " With all these caveats in mind, we display in Figure 6 the histogram of total luminosities for the 235 YSO’s found in Serpens in our survey with the assumed distance of 260 pc.", " Of course an important question to ask is to what extent this luminosity distribution in Figure 6 is influenced by selection effects.", " The lower panel of Figure 7 then shows this ratio as our estimate of the completeness function at the range of luminosities of Serpens YSO’s observed in Figure 6.", " In Figure 6, then, we also indicate how the YSO luminosity function might be adjusted to account for this estimate of our survey completeness (with an assumed completeness of 100% at the bright end)." ]

Fig. 7.— Upper panel – number counts for the full SWIRE catalog as processed through the c2d pipeline for objects detected in all four IRAC bands versus those for the “trimmed” version of the catalog with completeness limits for each individual band comparable to those for c2d. Lower panel – the ratio of the two number counts, i.e. completeness factor.

{ "x1": 72, "x2": 540.043701171875, "y1": 652.2164306640625, "y2": 705.8397827148438 }

Figure

[]

7

19

{ "x1": 100, "x2": 504, "y1": 103, "y2": 645 }

[]

Fig. 8.— Histogram of distribution of spectral slopes, “alpha”, for three luminosity “classes” of YSO’s.

{ "x1": 72, "x2": 539.7640991210938, "y1": 669.2564086914062, "y2": 691.0802001953125 }

Figure

[]

8

20

{ "x1": 96, "x2": 572, "y1": 146, "y2": 651 }

[]

Fig. 9.— Histogram of distribution of average extinction for stars within 80” of each YSO for “high” and “low” luminosity YSO’s (above or below 2 × 10−2L⊙).

{ "x1": 72, "x2": 540.0201416015625, "y1": 667.6964111328125, "y2": 691.4398193359375 }

Figure

[]

9

21

{ "x1": 90, "x2": 507, "y1": 97, "y2": 649 }

[ " The off-cloud fields (when normalized to the same area as the Serpens data) provide the best handle on the degree of contamination from AGB stars; in Paper I we saw one object classified as a YSO candidate in the off-cloud panel of Figure 9 with [8.", " Finally, Figure 9 shows the distribution of extinction for stars nearby each YSO." ]

Table 1. YSO vs. X-Gal Discrimination Criteria

{ "x1": 178.79998779296875, "x2": 433.0876159667969, "y1": 286.6964111328125, "y2": 292.67999267578125 }

Table

[ "K", "-", "[4.5]", "Prob/(K", "−", "[4.5])", "[4.5]", "(for", "[4.5]-[8.0]", "<", "0.5)", "Smooth", "increase", "for", "[4.5]", ">", "14.5", "[4.5]", "(for", "0.5", "<", "[4.5]-[8.0]", "<", "1.4,", "Extended)", "Smooth", "increase", "for", "[4.5]", ">", "12.5", "[4.5]", "(for", "0.5", "<", "[4.5]-[8.0]", "<", "1.4,", "Pointlike)", "Smooth", "increase", "for", "[4.5]", ">", "14.5", "[4.5]", "(for", "1.4", "<", "[4.5]-[8.0])", "Smooth", "increase", "for", "[4.5]", ">", "13.0", "([8.0]", "−", "[24]", "−", "3.5)2/1.7", "+", "([24]", "−", "9.0)2/2", "Smooth", "increase", "for", "values", "<", "1", "[4.5]", "−", "[8.0]", "−", "0.55(10.", "−", "[24])", "Smooth", "increase", "for", "values", ">", "1", "[24]", "(for", "all", "colors)", "100%", "probability", "for", "[24]", ">", "10.0", "Extended", "at", "3.6", "or", "4.5µm", "Twice", "as", "likely", "to", "be", "X-gal", "F70", "X-gal", "prob", "×", "0.1", "for", "F70", ">", "400", "mJy", "Criterion", "Contaminant", "Probability" ]

1

49

{ "x1": 92, "x2": 520, "y1": 306, "y2": 523 }

[ " Table 1 summarizes the criteria used for this class separation.", " After inclusion of these three color-magnitude criteria, we added the additional criteria listed in Table 1.", " Table 10 summarizes the results of this effort.", " In addition, as shown in Table 10, we find small extended features at the positions of most of the known HH objects in Serpens that were within our covered area." ]

Table 10. Probable High Velocity Outflows in Serpens

{ "x1": 163.91998291015625, "x2": 448.057373046875, "y1": 293.4164123535156, "y2": 299.3999938964844 }

Table

[ "141", "18", "29", "49.6", "+01", "15", "21", "SMM", "1", "Jets", "to", "NW", "and", "SE", "146", "18", "29", "51.2", "+01", "16", "41", "SMM", "5", "Jets", "to", "NW", "and", "SE", "75", "18", "29", "09.0", "+00", "31", "30", "Jets", "to", "N", "and", "S", "18", "29", "18.8", "+01", "14", "15", "HH", "106A,B,E", "18", "29", "47.7", "+01", "25", "52", "HH", "107A", "18", "30", "22.7", "+01", "16", "18", "HH", "455A", "18", "30", "22.6", "+01", "16", "05", "HH", "455B,D", "18", "30", "02.6", "+01", "14", "45", "HH", "459A,B", "18", "29", "38.5", "+01", "18", "26", "HH", "460A,B,C,D", "18", "29", "56.6", "+01", "15", "37", "HH", "478A,B", "YSO", "ID", "RA", "(J2000)", "Dec", "(J2000)", "Matching", "Name", "Comments" ]

10

91

{ "x1": 102, "x2": 510, "y1": 315, "y2": 517 }

[]

Table 2. YSO’s in Serpens

{ "x1": 310.67999267578125, "x2": 452.824462890625, "y1": 97.6964111328125, "y2": 103.67999267578125 }

Table

[ "1", "18275381−0002333", "25.5±", "1.2", "20.2±", "1.0", "15.6±", "0.7", "13.9±", "0.7", "22.7±", "2.1", "·", "·", "·", "2b", "18280503+0006593", "783±", "55", "426±", "29", "358±", "18", "218±", "14", "76.4±", "7.1", "·", "·", "·", "3", "18280845−0001064", "140±", "7", "108±", "8", "129±", "6", "122±", "8", "161±", "14", "314±", "36", "4b", "18281100−0001393", "104±", "5", "63.4±", "3.2", "54.6±", "2.6", "35.4±", "1.9", "9.51±0.90", "·", "·", "·", "5", "18281350−0002491", "CDF88-2", "105±", "5", "88.1±", "4.7", "77.5±", "3.7", "94.3±", "5.0", "254±", "23", "382±", "43", "6", "18281501−0002588", "33.3±", "1.6", "45.6±", "2.3", "61.5±", "3.1", "96.3±", "5.8", "225±", "20", "320±", "41", "7", "18281519−0001405", "7.18±0.35", "6.18±0.30", "5.15±0.25", "5.01±0.26", "8.00±0.77", "·", "·", "·", "8", "18281525−0002432", "CoKu", "Ser-G1", "174±", "9", "177±", "9", "180±", "11", "191±", "11", "1200±", "25", "1670±", "169", "9", "18281628−0003161", "53.1±", "2.7", "48.4±", "2.4", "45.4±", "2.1", "46.2±", "2.5", "74.7±", "6.9", "129±", "24", "10", "18281852−0003329", "3.38±0.17", "3.14±0.15", "3.13±0.16", "2.99±0.15", "2.96±0.36", "·", "·", "·", "11", "18281981−0001474", "5.52±0.27", "5.28±0.26", "4.90±0.24", "4.02±0.21", "5.58±0.54", "·", "·", "·", "12", "18282010+0029145", "237±", "21", "109±", "9", "116±", "8", "76.6±", "4.8", "17.5±", "1.6", "·", "·", "·", "13", "18282143+0010411", "13.7±", "0.7", "10.1±", "0.6", "9.99±0.49", "8.90±0.50", "10.5±", "1.0", "·", "·", "·", "14", "18282158+0000164", "60.3±", "3.0", "54.0±", "2.8", "45.5±", "2.2", "61.4±", "3.4", "170±", "15", "126±", "21", "15b", "18282432+0034545", "D-002", "62.4±", "4.2", "46.1±", "3.0", "41.1±", "2.5", "32.5±", "2.0", "13.9±", "1.3", "·", "·", "·", "16", "18282738−0011499", "1130±", "60", "660±", "35", "631±", "30", "399±", "22", "120±", "11", "·", "·", "·", "17", "18282740+0000239", "87.3±", "4.5", "54.6±", "2.7", "47.3±", "2.2", "32.3±", "1.6", "12.9±", "1.2", "·", "·", "·", "18", "18282849+0026500", "2.47±0.16", "2.28±0.15", "2.27±0.15", "2.52±0.16", "2.62±0.37", "·", "·", "·", "19", "18282905+0027561", "D-007", "9.80±0.57", "8.51±0.47", "7.03±0.38", "5.46±0.30", "43.4±", "4.0", "·", "·", "·", "20", "18284025+0016173", "3.71±0.20", "3.86±0.20", "3.60±0.19", "3.59±0.18", "2.89±0.35", "·", "·", "·", "21", "18284052+0022145", "68.2±", "3.7", "41.2±", "2.4", "39.2±", "2.0", "25.5±", "1.4", "11.7±", "1.1", "·", "·", "·", "22", "18284186−0003213", "13.7±", "0.7", "24.8±", "1.2", "39.6±", "1.9", "49.0±", "2.6", "155±", "14", "538±", "54", "23", "18284400+0053379", "18.1±", "0.9", "29.7±", "1.4", "40.3±", "2.0", "49.9±", "2.5", "260±", "24", "·", "·", "·", "24", "18284477+0051257", "0.65±0.04", "1.77±0.09", "3.08±0.16", "4.81±0.23", "37.6±", "3.5", "·", "·", "·", "SSTc2dJ...", "(mJy)", "(mJy)", "(mJy)", "(mJy)", "(mJy)", "(mJy)", "ID", "Name/Position", "Prev.", "Namea", "3.6", "µm", "4.5", "µm", "5.8", "µm", "8.0", "µm", "24.0", "µm", "70.0", "µm" ]

2

50

{ "x1": 101, "x2": 663, "y1": 119, "y2": 523.80029296875 }

[ " These are the objects in Table 2 numbered 127, 137, and 182.", " Table 2 lists the 235 YSO’s that resulted from this selection process.", " We have indicated these five objects in Table 2 with a footnote “b”.", " Each SED is labeled with the identification number in Table 2." ]

Table 3. YSO Candidates in Serpens Without 4-Band IRAC Observations

{ "x1": 188.27999877929688, "x2": 575.3508911132812, "y1": 97.6964111328125, "y2": 103.67999267578125 }

Table

[ "236", "18273421+0040260", "·", "·", "·", "·", "·", "·", "·", "·", "·", "·", "·", "·", "17.8±", "1.7", "·", "·", "·", "237", "18274024+0035221", "·", "·", "·", "·", "·", "·", "·", "·", "·", "·", "·", "·", "1.36±0.25", "·", "·", "·", "238", "18274264+0020389", "·", "·", "·", "·", "·", "·", "·", "·", "·", "·", "·", "·", "42.0±", "3.9", "·", "·", "·", "239", "18274399+0025135", "IRAC", "18251+0023", "·", "·", "·", "·", "·", "·", "·", "·", "·", "·", "·", "·", "5430±", "509", "655±", "68", "240", "18274484+0052436", "·", "·", "·", "·", "·", "·", "·", "·", "·", "·", "·", "·", "1.49±0.27", "·", "·", "·", "241", "18274506+0006110", "IRAS", "18251+0004", "1730±", "93", "·", "·", "·", "965±", "47", "·", "·", "·", "173±", "16", "·", "·", "·", "242", "18275926+0056012", "·", "·", "·", "·", "·", "·", "·", "·", "·", "·", "·", "·", "40.7±", "3.9", "·", "·", "·", "243", "18280449+0049498", "·", "·", "·", "·", "·", "·", "·", "·", "·", "·", "·", "·", "15.2±", "1.4", "·", "·", "·", "244", "18281904+0101333", "IRAS", "18257+0059", "·", "·", "·", "·", "·", "·", "·", "·", "·", "·", "·", "·", "112±", "10", "·", "·", "·", "245", "18282591−0032587", "IRAS", "18258-0034", "·", "·", "·", "·", "·", "·", "·", "·", "·", "·", "·", "·", "279±", "43", "·", "·", "·", "246", "18283708+0149440", "·", "·", "·", "·", "·", "·", "·", "·", "·", "·", "·", "·", "57.3±", "5.3", "·", "·", "·", "247", "18283939+0106157", "IRAS", "18261+0104", "·", "·", "·", "·", "·", "·", "·", "·", "·", "·", "·", "·", "356±", "33", "·", "·", "·", "248", "18284039+0106144", "IRAS", "18261+0104", "·", "·", "·", "·", "·", "·", "·", "·", "·", "·", "·", "·", "160±", "14", "·", "·", "·", "249", "18285056+0101121", "4.43±0.22", "·", "·", "·", "3.08±0.16", "·", "·", "·", "1.93±0.31", "·", "·", "·", "250", "18285486+0108548", "IRAS", "18264+0106", "·", "·", "·", "·", "·", "·", "·", "·", "·", "·", "·", "·", "329±", "30", "·", "·", "·", "251", "18295035+0008472", "·", "·", "·", "322±", "26", "·", "·", "·", "258±", "14", "89.4±", "8.3", "·", "·", "·", "252", "18295096−0033057", "·", "·", "·", "299±", "20", "·", "·", "·", "146±", "7", "50.8±", "4.7", "·", "·", "·", "253", "18295439+0002476", "·", "·", "·", "·", "·", "·", "·", "·", "·", "·", "·", "·", "77.5±", "7.2", "·", "·", "·", "254", "18300035+0011201", "·", "·", "·", "96.0±", "6.5", "·", "·", "·", "60.7±", "3.3", "19.5±", "1.8", "·", "·", "·", "255", "18300130+0159309", "·", "·", "·", "·", "·", "·", "·", "·", "·", "·", "·", "·", "1.14±0.22", "·", "·", "·", "256", "18300155+0037339", "·", "·", "·", "3.72±0.20", "·", "·", "·", "1.94±0.11", "1.22±0.20", "·", "·", "·", "257", "18300181−0037039", "IRAS", "18275-0039", "·", "·", "·", "·", "·", "·", "·", "·", "·", "·", "·", "·", "29.9±", "2.8", "·", "·", "·", "258", "18300237+0040549", "·", "·", "·", "4.56±0.22", "·", "·", "·", "4.52±0.22", "3.45±0.38", "·", "·", "·", "259", "18300403+0034240", "·", "·", "·", "·", "·", "·", "·", "·", "·", "·", "·", "·", "217±", "20", "798±", "77", "SSTc2dJ...", "(mJy)", "(mJy)", "(mJy)", "(mJy)", "(mJy)", "(mJy)", "ID", "Name/Position", "Prev.", "Name", "3.6", "µm", "4.5", "µm", "5.8", "µm", "8.0", "µm", "24.0", "µm", "70.0", "µm" ]

3

61

{ "x1": 90, "x2": 673, "y1": 119, "y2": 523.80029296875 }

[ "8 deg2; 51 of these are outside the IRAC/MIPS overlap area and are listed in Table 3." ]

Table 4. Matching Spitzer Sources/Fluxes For Previously Identified IR Sources In Serpens

{ "x1": 146.8800048828125, "x2": 616.614990234375, "y1": 98.41641235351562, "y2": 104.39999389648438 }

Table

[ "D002", "18282432+0034545", "62.4±", "4.2", "46.1±", "3.0", "41.1±", "2.5", "32.5±", "2.0", "13.9±", "1.3", "·", "·", "·", "D001", "18282442+0026509", "105±", "9", "95.6±", "7.8", "97.9±", "6.5", "65.0±", "4.2", "13.9±", "1.3", "·", "·", "·", "D003", "18282649+0031421", "38.1±", "2.7", "25.8±", "1.7", "20.1±", "1.2", "12.2±", "0.8", "1.26±0.28", "·", "·", "·", "D004", "18282783+0028390", "6.72±0.45", "4.47±0.29", "3.44±0.21", "2.27±0.14", "<", "1.53", "·", "·", "·", "D005", "18282792+0029288", "5.12±0.32", "3.56±0.25", "2.76±0.16", "1.79±0.12", "<", "1.45", "·", "·", "·", "D006", "18282864+0024120", "5.68±0.38", "3.71±0.25", "3.27±0.20", "1.92±0.12", "<", "1.44", "·", "·", "·", "D007", "18282905+0027561", "9.80±0.57", "8.51±0.47", "7.03±0.38", "5.46±0.30", "43.4±", "4.0", "·", "·", "·", "D008", "18282912+0034193", "193±", "13", "93.2±", "6.4", "86.6±", "4.5", "49.3±", "2.9", "5.99±0.58", "·", "·", "·", "D010", "18283208+0025036", "11.2±", "0.6", "6.47±0.38", "5.42±0.27", "3.15±0.20", "<", "1.25", "·", "·", "·", "D009", "18283221+0035361", "33.6±", "2.0", "20.6±", "1.1", "16.1±", "0.9", "9.61±0.49", "0.99±0.23", "·", "·", "·", "D011", "18283261+0037322", "15.0±", "0.9", "9.38±0.50", "7.02±0.39", "4.40±0.23", "<", "1.41", "·", "·", "·", "D012", "18283317+0025451", "24.9±", "1.5", "15.0±", "0.9", "12.1±", "0.6", "7.15±0.41", "0.70±0.25", "·", "·", "·", "D013", "18283351+0026595", "60.6±", "3.6", "34.5±", "2.2", "26.4±", "1.4", "15.9±", "0.9", "1.46±0.22", "·", "·", "·", "D014", "18283434+0031119", "10.2±", "0.6", "7.06±0.41", "5.39±0.31", "3.42±0.19", "<", "1.54", "·", "·", "·", "D015", "18283503+0026406", "53.0±", "3.2", "34.2±", "2.1", "31.8±", "1.7", "19.2±", "1.1", "2.71±0.35", "·", "·", "·", "D017", "18283572+0038458", "227±", "15", "130±", "7", "104±", "5", "61.0±", "3.5", "6.91±0.66", "·", "·", "·", "D016", "18283576+0038231", "6.23±0.38", "4.19±0.23", "2.82±0.16", "1.72±0.10", "<", "1.19", "·", "·", "·", "D018", "18283579+0026160", "191±", "12", "122±", "8", "114±", "6", "63.5±", "3.9", "7.10±0.69", "·", "·", "·", "D019", "18283639+0026388", "31.8±", "1.9", "21.1±", "1.3", "19.4±", "1.0", "11.3±", "0.7", "1.20±0.23", "·", "·", "·", "D020", "18283741+0027100", "9.45±0.54", "6.52±0.40", "5.68±0.36", "3.35±0.20", "<", "1.26", "·", "·", "·", "D021", "18283752+0032311", "7.64±0.49", "5.69±0.30", "4.05±0.24", "2.52±0.14", "<", "1.22", "·", "·", "·", "D022", "18283791+0025512", "46.4±", "2.8", "26.1±", "1.6", "26.5±", "1.4", "15.3±", "0.9", "2.38±0.31", "·", "·", "·", "SSTc2dJ...", "(mJy)", "(mJy)", "(mJy)", "(mJy)", "(mJy)", "(mJy)", "Sourcea", "Spitzer", "3.6µm", "4.5µm", "5.8µm", "8.0µm", "24µm", "70µm" ]

4

64

{ "x1": 125, "x2": 638, "y1": 121, "y2": 519.5999755859375 }

[ " Table 4 lists the sources from each of these previous studies and the best-matching Spitzer source from our complete catalog.", " Table 4 shows that we also see no obvious source at the position of EC92-81, other than a low S/N single-band detection of a source moderately distant from the nominal position." ]

Table 5. Average/Std Dev of Spectral Slope α Versus Luminosity of YSO’s

{ "x1": 109.91999816894531, "x2": 502.0306091308594, "y1": 183.73638916015625, "y2": 189.719970703125 }

Table

[ ">", "1.0", "L⊙", "-0.60", ".74", "<", "0.02", "L⊙", "-0.73", "1.47", "0.02", "−−1.0", "L⊙", "-0.70", "1.04", "Luminosity", "Range", "Average", "α", "σα" ]

5

82

{ "x1": 204, "x2": 408, "y1": 206, "y2": 296 }

[ " Likewise Figure 8 shows the distribution of spectral slopes, α, for the low luminosity sample relative to two higher luminosity samples, and Table 5 lists the average and standard deviation for the spectral slopes for three luminosity samples.", " Figure 8 that displays the distribution of spectral slopes and the accompanying Table 5 also show no measurable effect within the scatter for a dependence of spectral slope on luminosity." ]

Table 6. Numbers, Densities, Star Formation Rates

{ "x1": 168.83999633789062, "x2": 439.3006591796875, "y1": 467.2964172363281, "y2": 473.2799987792969 }

Table

[ "Cluster", "A", "0.20", "44", "4580", "222", "500", "11", "56", "Cluster", "B", "0.14", "17", "2450", "119", "315", "4.3", "30", "Rest", "of", "Cloud", "17.2", "174", "209", "10.1", "2.5", "44", "2.5", "All", "of", "Cloud", "17.5", "235", "276", "13.4", "3.2", "59", "3.4", "(pc2)", "(deg−2)", "(pc−2)", "(pc−3)", "(M⊙", "Myr−1)", "(M⊙", "Myr−1pc−2)", "Region", "Area", "N(YSOs)", "N/Ω", "N/Area", "N/Vol", "SFR", "SFR/Area" ]

6

82

{ "x1": 71, "x2": 570, "y1": 489, "y2": 627 }

[ " In particular, if we define the cluster edges by the Av = 20 contour for comparison with other c2d clusters, we obtain the values in Table 6 for the number of stars per solid angle and per square parsec.", "The overall picture of star formation in Serpens is summarized in Table 6.", " These values are also given in Table 6.", " The surface density of YSOs in the clusters exceeds that of the rest of the cloud by factors of 10 to 20 (Table 6)." ]

Table 7. Disk Modeling Results in Class II Sources

{ "x1": 171.95999145507812, "x2": 439.8692932128906, "y1": 129.856201171875, "y2": 135.83978271484375 }

Table

[ "1", "L", "2.9", "0.33", "0.088", "5.8", "-0.7", "3", "T", "4.6", "1.06", "0.330", "2.2", "-0.8", "5", "T", "4.9", "1.64", "0.165", "3.6", "-0.5", "7", "L", "3.8", "0.09", "0.110", "3.6", "-1.0", "9", "L", "6.6", "0.91", "0.141", "3.6", "-0.8", "10", "L", "9.9", "0.05", "0.190", "3.6", "-1.3", "11", "L", "8.4", "0.07", "0.186", "2.2", "-1.2", "13", "L", "2.8", "0.19", "0.084", "5.8", "-1.0", "14", "L", "6.6", "1.03", "0.182", "3.6", "-0.7", "18", "L", "10.8", "0.07", "0.098", "3.6", "-1.1", "19", "LU", "12.6", "0.33", "0.073", "3.6", "-0.4", "20", "L", "14.3", "0.09", "0.160", "2.2", "-1.4", "25", "T", "4.8", "0.09", "0.159", "3.6", "-0.9", "27", "L", "4.0", "0.54", "0.112", "3.6", "-1.4", "28", "L", "15.7", "67.31", "0.197", "2.2", "-1.8", "29", "L", "12.7", "0.14", "0.253", "2.2", "-1.3", "30", "L", "8.3", "33.93", "0.291", "2.2", "-1.5", "31", "T", "10.4", "0.02", "0.454", "2.2", "-1.1", "33", "L", "10.2", "5.58", "0.111", "2.2", "-2.0", "35", "L", "7.4", "0.03", "0.113", "3.6", "-1.2", "38", "T", "18.9", "0.05", "0.588", "2.2", "-1.1", "39", "T", "5.1", "0.21", "0.104", "5.8", "-0.4", "47", "LU", "14.5", "0.02", "0.247", "4.5", "-0.6", "49", "T", "5.4", "0.13", "0.141", "3.6", "-0.9", "50", "L", "18.4", "1.31", "0.201", "3.6", "-1.0", "51", "L", "7.4", "0.57", "0.155", "2.2", "-1.2", "52", "L", "10.0", "0.29", "0.148", "2.2", "-1.1", "53", "T", "10.5", "0.12", "0.305", "2.2", "-0.7", "54", "T", "9.3", "3.14", "0.409", "2.2", "-0.8", "55", "L", "23.3", "2.50", "0.198", "2.2", "-1.4", "56", "T", "10.4", "1.06", "0.306", "2.2", "-0.8", "57", "L", "12.0", "0.06", "0.146", "2.2", "-1.6", "58", "T", "6.1", "1.94", "0.147", "3.6", "-0.6", "Star", "SED", "Type", "AV", "Lstar", "Ldisk/Lstar", "λturn−oﬀ", "αexcess" ]

7

83

{ "x1": 146, "x2": 466, "y1": 152, "y2": 675.238525390625 }

[]

Table 8. Disk Modeling Results in Class III Sources

{ "x1": 169.67999267578125, "x2": 442.146728515625, "y1": 129.856201171875, "y2": 135.83978271484375 }

Table

[ "2", "L", "6.3", "19.19", "0.013", "24.0", "-99.0", "4", "L", "7.6", "2.50", "0.028", "24.0", "-99.0", "12", "L", "9.1", "8.76", "0.015", "24.0", "-99.0", "15", "L", "7.7", "2.02", "0.025", "8.0", "-1.9", "16", "L", "10.8", "31.18", "0.041", "8.0", "-2.3", "17", "L", "11.1", "2.69", "0.036", "8.0", "-2.1", "21", "L", "11.7", "2.16", "0.038", "8.0", "-2.0", "48", "L", "2.5", "1.13", "0.054", "8.0", "0.6", "65", "L", "0.0", "0.70", "0.016", "8.0", "-0.9", "73", "L", "7.5", "3.06", "0.022", "24.0", "-99.0", "74", "L", "0.0", "0.60", "0.010", "8.0", "-1.3", "81", "L", "8.7", "9.23", "0.021", "24.0", "-99.0", "83", "L", "8.0", "28.57", "0.034", "8.0", "-1.6", "85", "L", "7.2", "1.66", "0.048", "5.8", "-1.5", "90", "L", "7.7", "3.50", "0.034", "8.0", "-2.3", "91", "L", "8.5", "3.55", "0.020", "24.0", "-99.0", "93", "L", "16.7", "38.30", "0.051", "8.0", "-2.2", "95", "L", "8.5", "23.79", "0.015", "24.0", "-99.0", "101", "L", "8.6", "6.09", "0.074", "5.8", "-2.2", "105", "LU", "0.7", "11.61", "0.010", "24.0", "1.2", "107", "L", "8.3", "15.02", "0.055", "5.8", "-2.3", "109", "L", "10.7", "7.62", "0.037", "8.0", "-2.3", "112", "L", "7.4", "0.24", "0.018", "8.0", "-1.9", "115", "L", "9.7", "3.90", "0.044", "8.0", "-2.1", "122", "L", "9.6", "0.96", "0.028", "8.0", "-1.5", "126", "LU", "3.3", "0.36", "0.062", "8.0", "0.3", "140", "L", "8.8", "2.25", "0.032", "8.0", "-2.2", "143", "L", "4.2", "0.21", "0.052", "5.8", "-1.3", "148", "LU", "0.0", "0.67", "0.017", "24.0", "2.3", "161", "L", "11.2", "4.26", "0.032", "8.0", "-2.2", "165", "L", "0.7", "0.94", "0.014", "8.0", "-1.6", "170", "L", "3.7", "0.07", "0.079", "5.8", "-1.3", "192", "L", "8.1", "0.20", "0.034", "8.0", "-0.5", "Star", "SED", "Type", "AV", "Lstar", "Ldisk/Lstar", "λturn−oﬀ", "αexcess" ]

8

88

{ "x1": 146, "x2": 466, "y1": 152, "y2": 675.238525390625 }

[]

Table 9. The Coldest YSO’s (F70/F24 > 8)

{ "x1": 269.2799987792969, "x2": 494.5198974609375, "y1": 98.29641723632812, "y2": 106.08001708984375 }

Table

[ "40", "18285404+0029299", "5.81±0.50", "27.6±", "2.3", "44.8±", "2.6", "56.4±", "3.2", "918±", "85", "11100±", "1040", "42", "18285486+0029525", "1.94±0.12", "10.6±", "0.6", "20.4±", "1.1", "30.2±", "1.6", "765±", "70", "7250±", "675", "48", "18285808+0017244", "52.5±", "3.0", "36.7±", "2.5", "31.2±", "1.7", "28.5±", "1.7", "9.74±0.92", "1040±", "101", "60", "18290211+0031206", "1.19±0.07", "1.62±0.09", "1.58±0.10", "1.13±0.07", "22.1±", "2.0", "276±", "29", "68", "18290675+0030343", "3.27±0.21", "11.7±", "0.7", "14.9±", "0.8", "20.7±", "1.2", "1000±", "105", "11400±", "1180", "105", "18293254−0013233", "654±", "39", "370±", "19", "276±", "13", "156±", "8", "39.7±", "3.7", "429±", "47", "135", "18294810+0116449", "1.96±0.10", "6.98±0.42", "12.1±", "0.6", "16.7±", "0.8", "219±", "21", "14900±", "1420", "141", "18294963+0115219", "0.85±0.08", "2.64±0.27", "2.32±0.28", "3.54±0.31", "1180±", "117", "82800±", "7810", "146", "18295114+0116406", "31.1±", "2.6", "72.6±", "4.6", "141±", "7", "208±", "10", "992±", "92", "8480±", "805", "148", "18295130+0027479", "33.8±", "2.0", "22.3±", "1.3", "16.2±", "0.9", "10.1±", "0.6", "4.81±0.50", "163±", "18", "150", "18295219+0115478", "7.38±0.41", "33.0±", "2.1", "41.3±", "2.2", "40.0±", "2.6", "1640±", "154", "15200±", "1420", "154", "18295252+0036117", "2.49±0.14", "4.24±0.23", "5.18±0.28", "6.55±0.36", "100±", "9", "1910±", "179", "166", "18295430+0036013", "2.39±0.25", "6.57±0.42", "7.32±0.44", "5.80±0.31", "16.0±", "1.5", "1270±", "121", "195", "18295927+0114016", "2.72±0.28", "5.76±0.44", "7.78±1.16", "36.0±", "5.4", "109±", "19", "12200±", "1160", "203", "18300070+0113014", "0.38±0.04", "1.23±0.10", "2.08±0.16", "3.55±0.21", "95.8±11.4", "8640±", "829", "Tbl", "2", "SSTc2dJ...", "(mJy)", "(mJy)", "(mJy)", "(mJy)", "(mJy)", "(mJy)", "ID", "Name/Position", "3.6", "µm", "4.5", "µm", "5.8", "µm", "8.0", "µm", "24.0", "µm", "70.0", "µm" ]

9

90

{ "x1": 125, "x2": 639, "y1": 121, "y2": 400 }

[ "Table 9 lists the 15 YSO’s that display the coldest energy distributions." ]

Figure 2.1: A graph and its isometric embedding into Q3.

{ "x1": 179.63999938964844, "x2": 431.6497802734375, "y1": 326.0986633300781, "y2": 332.51983642578125 }

Figure

[]

2.1

2

{ "x1": 186, "x2": 426, "y1": 249, "y2": 309 }

[]

Figure 2.2: A nonisometric path in the cube Q3.

{ "x1": 199.8000030517578, "x2": 411.369384765625, "y1": 244.7386474609375, "y2": 251.1597900390625 }

Figure

[]

2.2

3

{ "x1": 249, "x2": 362, "y1": 124, "y2": 228 }

[]

Figure 4.1: Fundamental sets in a partial cube.

{ "x1": 202.55999755859375, "x2": 408.6446838378906, "y1": 419.9386901855469, "y2": 424.9200134277344 }

Figure

[]

4.1

10

{ "x1": 214, "x2": 395, "y1": 296, "y2": 405 }

[]

Figure 4.2: Graph G.

{ "x1": 259.0799865722656, "x2": 352.0893859863281, "y1": 396.65869140625, "y2": 401.6400146484375 }

Figure

[]

4.2

11

{ "x1": 229, "x2": 392, "y1": 277, "y2": 387 }

[]

Figure 4.3: An illustration to the proof of theorem 4.2.

{ "x1": 185.75999450683594, "x2": 425.4627380371094, "y1": 401.57867431640625, "y2": 406.55999755859375 }

Figure

[]

4.3

12

{ "x1": 225, "x2": 388, "y1": 301, "y2": 392 }

[]

Figure 7.1: Pasting of two trees.

{ "x1": 235.1999969482422, "x2": 376.10467529296875, "y1": 260.33868408203125, "y2": 265.32000732421875 }

Figure

[]

7.1

18

{ "x1": 145, "x2": 466, "y1": 192, "y2": 243 }

[]

Figure 7.2: Another pasting of the same trees.

{ "x1": 204.60000610351562, "x2": 406.8235778808594, "y1": 358.7386779785156, "y2": 363.7200012207031 }

Figure

[]

7.2

18

{ "x1": 145, "x2": 466, "y1": 291, "y2": 342 }

[]

Figure 7.3: Pasting partial cubes G1 and G2.

{ "x1": 207.1199951171875, "x2": 404.0495910644531, "y1": 518.4586791992188, "y2": 524.8802490234375 }

Figure

[]

7.3

18

{ "x1": 164, "x2": 447, "y1": 425, "y2": 512 }

[]

Figure 7.4: An example of vertex-pasting.

{ "x1": 214.32000732421875, "x2": 397.23193359375, "y1": 285.2986755371094, "y2": 290.2799987792969 }

Figure

[]

7.4

19

{ "x1": 141, "x2": 471, "y1": 208, "y2": 268 }

[]

Figure 7.5: An example of edge-pasting.

{ "x1": 218.0399932861328, "x2": 393.3875427246094, "y1": 553.2586669921875, "y2": 558.239990234375 }

Figure

[]

7.5

21

{ "x1": 168, "x2": 444, "y1": 473, "y2": 536 }

[]

Figure 7.6: Edge-pasting of graphs G1 and G2.

{ "x1": 203.16000366210938, "x2": 408.129638671875, "y1": 388.8586730957031, "y2": 395.28021240234375 }

Figure

[]

7.6

22

{ "x1": 233, "x2": 378, "y1": 299, "y2": 381 }

[]

Figure 7.7: Semicubes forming an edge in Sc(G1).

{ "x1": 196.8000030517578, "x2": 414.37091064453125, "y1": 335.81866455078125, "y2": 342.2398376464844 }

Figure

[]

7.7

24

{ "x1": 250, "x2": 359, "y1": 245, "y2": 319 }

[]

Figure 8.1: Expansion/contraction processes.

{ "x1": 207.36000061035156, "x2": 404.0686950683594, "y1": 506.69866943359375, "y2": 511.67999267578125 }

Figure

[]

8.1

26

{ "x1": 200, "x2": 418, "y1": 335, "y2": 490 }

[]

Figure 8.2: An expansion of the cycle C4.

{ "x1": 214.9199981689453, "x2": 396.36944580078125, "y1": 208.378662109375, "y2": 214.7998046875 }

Figure

[]

8.2

29

{ "x1": 155, "x2": 456, "y1": 125, "y2": 191 }

[]

Figure 8.3: Another isometric expansion of the cycle C4.

{ "x1": 182.16000366210938, "x2": 429.0095520019531, "y1": 297.2986755371094, "y2": 303.7198486328125 }

Figure

[]

8.3

29

{ "x1": 151, "x2": 459, "y1": 226, "y2": 280 }

[]

Figure 8.4: A shortest path which is not a projection of a shortest path.

{ "x1": 148.0800018310547, "x2": 463.21405029296875, "y1": 504.898681640625, "y2": 509.8800048828125 }

Figure

[]

8.4

29

{ "x1": 152, "x2": 459, "y1": 416, "y2": 488 }

[]

Figure 8.5: A shortest path from x to y.

{ "x1": 217.67999267578125, "x2": 393.609619140625, "y1": 523.9786376953125, "y2": 528.9599609375 }

Figure

[]

8.5

30

{ "x1": 215, "x2": 405, "y1": 441, "y2": 514 }

[]

Table 1. Dimension Formula for Mk(Γ0(4N))

{ "x1": 179.52008056640625, "x2": 420.5982360839844, "y1": 568.6466064453125, "y2": 575.8802490234375 }

Table

[ "So", "Φr,e(4N)", "is", "surjective", "since", "the", "map", "Φr,e(4N)", "is", "injective.", "This", "completes", "our", "claim.", "N", "=", "1", "n", "+", "1", "n", "+", "1", "n", "+", "1", "N", "=", "2", "2n+", "1", "2n+", "2", "2n+", "1", "N", "=", "3", "4n+", "1", "4n+", "3", "4n+", "1", "N", "=", "4", "4n+", "2", "4n+", "4", "4n+", "1", "k", "=", "2n", "k", "=", "2n+", "3", "2", "N", "k", "=", "2n", "+", "1", "2" ]

1

8

{ "x1": 85.19999694824219, "x2": 526.6981811523438, "y1": 589, "y2": 717 }

[ " The dimension formula of Mλ+ 1 2 (Γ0(4N)) (see Table 1) together with the results in (3.", " So from Table 1 we have (4.", "1 and Table 1, it is enough to show that ψr,e(4N) is injective." ]

Fig. 1

{ "x1": 270.4519958496094, "x2": 306.8551330566406, "y1": 245.9059600830078, "y2": 252.4949951171875 }

Figure

[ "・", "・", "・", "b1", "a1", "b1", "a1", "b1", "a1" ]

1

13

{ "x1": 157, "x2": 454, "y1": 131, "y2": 237 }

[ " Take 2g curves in M , ai, bi, as in Figure 1." ]

FIG. 1: non-spectator effects contribution to lifetime of Ξccd

{ "x1": 161.0399932861328, "x2": 448.8367004394531, "y1": 346.5052185058594, "y2": 353.759765625 }

Figure

[ "(d)", "l̄", "νl", "d", "c", "c", "d", "c", "c", "(c)", "d", "u", "c", "d", "c", "d", "c", "c", "(b)", "d̄", "u", "d", "c", "c", "d", "c", "c", "(a)", "s", "u", "c", "d", "c", "c", "d", "c" ]

1

14

{ "x1": 90.76210021972656, "x2": 514.9379272460938, "y1": 73.9257583618164, "y2": 316.26629638671875 }

[ "(i) The inclusive decays of Ξ+ cc: There are four diagrams which contribute to the the width of Ξ+ cc, as shown in Fig.1.", " Fig 1.", "(a),(c) are the W-exchange diagrams (WE), while Fig 1.", " Here Fig 1." ]

FIG. 2: non-spectator effects contribution to lifetime of Ξccu

{ "x1": 160.79998779296875, "x2": 449.0186767578125, "y1": 347.58544921875, "y2": 354.7200927734375 }

Figure

[ "(c)", "d̄", "d", "u", "c", "c", "c", "u", "c", "(b)", "s̄", "s", "u", "c", "c", "c", "u", "c", "(a)", "d̄", "s", "u", "c", "c", "c", "c", "u" ]

2

15

{ "x1": 93.46995544433594, "x2": 517.2801513671875, "y1": 75.9457015991211, "y2": 317.24200439453125 }

[ " (ii) The inclusive decays of Ξ++ cc : The non-spectator contribution to the width of Ξ++ cc come from the diagrams shown in Fig.2." ]

FIG. 3: non-spectator effects contribution to lifetime of Ωccs

{ "x1": 161.0404815673828, "x2": 448.87091064453125, "y1": 347.5848693847656, "y2": 354.7195129394531 }

Figure

[ "(d)", "s", "u", "c", "s", "c", "s", "c", "c", "(c)", "s̄", "u", "s", "c", "c", "c", "s", "c", "(b)", "l̄", "νl", "s", "c", "c", "c", "s", "c", "(a)", "d̄", "u", "s", "c", "c", "c", "c", "s" ]

3

16

{ "x1": 93.46995544433594, "x2": 516.1638793945312, "y1": 75.9457015991211, "y2": 317.24200439453125 }

[]

TABLE I: The numerical results about the contributions from the different components and the evaluated lifetime for the doubly charmed baryons. For a comparison, in the following table, we list the corresponding lifetimes predicted by the authors of ref.[7] where the diquark picture was employed. It is noted that in ref.[7], the authors used various input parameters and obtained slightly diverse results, we take average values of the numbers in the table. There is only one datum for the lifetimes on τΞ+ cc given by the SELEX collaboration which is also listed the table.

{ "x1": 72, "x2": 538.2841796875, "y1": 84.06546783447266, "y2": 202.7999267578125 }

Table

[ "2.01", "4.25", "1.10", "0.21", "0.22", "−", "Ω+", "cc", "Γspec(10", "−12GeV)", "ΓWE", "non", "(10−14GeV)", "ΓPI", "non(10−12GeV)", "τΩ+", "cc", "(ps)", "τΩ+", "cc", "(ps)", "in", "ref.[7]", "2.01", "-1.02", "0.67", "0.52", "−", "Ξ++", "cc", "Γspec(10", "−12GeV)", "ΓPI", "non(10−12GeV)", "τΞ++", "cc", "(ps)", "τΞ++", "cc", "(ps)", "in", "ref.[7]", "2.01", "6.43", "-3.36", "0.25", "0.19", "0.033", "Ξ+", "cc", "Γspec(10", "−12GeV)", "ΓWE", "non", "(10−13GeV)", "ΓPI", "non(10−15GeV)", "τΞ+", "cc", "(ps)", "τΞ+", "cc", "(ps)", "in", "ref.[7]", "exp(ps)" ]

I

10

{ "x1": 80, "x2": 530, "y1": 211, "y2": 345 }

[]

Figure 1. Radial-velocity Fourier amplitude spectra from the 1991 combined data are shown for α = 3000 km s−1 and 900 km s−1 for the Hβ line (top left panel and second left panel from the top) and for 3000 km s−1 and 1200 km s−1 for the Hγ line (top right panel and second right panel from the top). Ω denotes the orbital frequency of the system, 2Ω its first harmonic and ω + Ω the upper orbital side band where ω is the spin frequency. The data were prewhitened by the orbital frequency and are displayed in the third panels from the top. Window spectra are plotted below the amplitude spectra (bottom panels).

{ "x1": 305.15985107421875, "x2": 544.2506713867188, "y1": 386.6052551269531, "y2": 470.8802185058594 }

Figure

[]

1

{ "x1": 317, "x2": 536, "y1": 55, "y2": 378 }

[ " This is illustrated in Figure 10, where the position of the observer at pulse maximum is indicated, and the axis of the magnetic pole is shown.", " The overflow stream hits the magnetosphere, probably causing a second bright spot on the slowly rotating magnetosphere (Figure 10).", "5 M⊙) as proposed in Figure 10, it is clear that we see spin-varying emission from two opposite magnetic poles, producing a fairly symmetric structure in the spin-folded line profiles (Hellier et al." ]

Figure 10. A model of EX Hya in quiescence. The figures are drawn over the orbital cycle (left) and spin cycle (right) and show the magnetosphere extending to the outer edge of the ring, and the chunk of material corotating with the field lines. A verticaly extended material (VEM) is irradiated by the white dwarf in its inner regions (left).

{ "x1": 42.11907958984375, "x2": 544.2117919921875, "y1": 281.7252502441406, "y2": 306.2399597167969 }

Figure

[ "0.25", "maximum", "redshift", "phase", "of", "of", "Ηα", "BBC", "phase", "of", "minimum", "intensity", "upper", "pole", "magnetic", "axis", "through", "of", "phase", "of", "phase", "of", "maximum", "intensity", "Ηα", "BBC", "maximum", "blueshift", "part", "of", "disc", "corotating", "with", "field", "outer", "disc", "0.9", "0.4", "0.75", "0.7", "Observer", "1.0", "0.5", "phase", "of", "maximum", "blueshift", "of", "the", "HVC", "chunk", "of", "material", "with", "field", "corotating", "narrow", "s−wave", "of", "the", "s−wave", "overflowing", "stream", "chunk", "of", "material’s", "phases", "of", "maximum", "redshift", "phase", "of", "maximum", "blueshift", "phases", "of", "maximum", "blueshift", "of", "the", "magnetic", "axis", "through", "upper", "pole", "VEM", "0.25", "0.8", "ring", "of", "material", "0.7", "0.3", "0.4", "0.5", "0.75", "0.0", "Observer" ]

10

7

{ "x1": 44.160301208496094, "x2": 540.7478637695312, "y1": 51.7234001159668, "y2": 270.359619140625 }

[]

Figure 2. Radial velocity amplitude spectra shown for the Hα line from 2001, for α = 3500 km s−1 and 1200 km s−1. The vertical dashed line shows the expected position of the orbital and spin period peaks. The data were prewhitened by Ω and are shown in the third panel from the top. A window spectrum is shown at the bottom.

{ "x1": 42.11981201171875, "x2": 281.2600402832031, "y1": 344.9652404785156, "y2": 389.4002990722656 }

Figure

[]

2

{ "x1": 77, "x2": 247, "y1": 50, "y2": 333 }

[ " The Hβ and Hγ amplitude spectra from 1991 (24 and 25 April) are shown in Figure 1 and the Hα amplitude spectra from 2001 are shown in Figure 2." ]

Figure 3. The panels show the Hα, Hβ, Hγ and HeI λ4471 orbital Doppler maps from 2001, and Hβ tomograms of 1991, constructed using the Back-Projection Method with the application of a filter (top panels) and after subtracting the average of the line profile (bottom panels). The positions of the Roche lobe and stream trajectories are shown (velocity amplitudes of K1 = 74 km s−1 and K2 = 360 km s−1 for the primary and secondary stars, respectively, were used). The two curves with marked intervals represent the gas stream velocity (upper curve) and the Keplerian velocity along the stream (lower curve). The circles on all tomograms represent 0.1 of the distance from the L1 point to the primary. The three crosses are centres of mass of the secondary, system and primary, from top-to-bottom. The asterisk represents the velocity of closest approach. All the maps are plotted on the same velocity scale. The lookup table of this figure is such that the brightest emission features appear with decreasing intensity from yellow/green to light blue in the online edition, or white to grey in the printed edition.

{ "x1": 42.11761474609375, "x2": 544.2548217773438, "y1": 276.32525634765625, "y2": 350.6400451660156 }

Figure

[]

3

{ "x1": 45, "x2": 542, "y1": 50, "y2": 265 }

[ "The Hβ, Hγ and HeI λ4471 Doppler tomograms (Figure 3 and 4) show strong emission at the bright spot, some at the Roche lobe and the stream, and some from the disc.", "87 (Figure 3 and 4) was observed and suggests the presence of VEM at the outer edge of the ring of material obscuring the emission at these phases." ]

Figure 4. 2001 Hα, Hβ, Hγ and HeI λ4471 trailed spectra (top row of panels) and MEM orbital Doppler maps (second row of panels from the top) as well as the average-subtracted trailed spectra (third row of panels) are shown plotted on the same scale except for Hα panels. The HVC and the NSC are indicated. The fourth row shows the average-subtracted Doppler maps and the models plotted for q = 0.21, i = 78◦ and M1 = 0.50M⊙ . The bottom panels are the reconstruction of the average-subtracted data. The fourth and bottom panels are also plotted on the same scale except for Hα panels. The lookup table of this figure is such that the brightest emission features appear with decreasing intensity from black to light grey.

{ "x1": 42.11846923828125, "x2": 281.2676086425781, "y1": 521.1251831054688, "y2": 615.35986328125 }

Figure

[]

4

{ "x1": 42, "x2": 284, "y1": 51, "y2": 510 }

[ " The BPM Doppler maps are shown in Figure 3 and those constructed using MEM are shown in Figure 4.", " Average-subtracted trailed spectra (Figure 4) show the corresponding NSC.", " The first one is the asymmetry in the intensity of the s-wave (Figure 4).", "25 (Figure 4)." ]

Figure 5. The Hβ (top panel), Hγ (middle panel) and Hα (bottom panel) spin radial velocities of the narrow component from the 1991 combined data (Hβ and Hγ) and 2001 data (Hα). The radial velocities were prewhitened by the orbital frequency and phase-folded on the spin frequency using 30 bins and are shown plotted as a function of the spin phase.

{ "x1": 305.1597900390625, "x2": 544.2033081054688, "y1": 308.9652404785156, "y2": 353.4002990722656 }

Figure

[ "SPIN", "PHASE", ")", "km", "/s", "ity", "(", "el", "oc", "ia", "l", "V", "R", "ad", "α", "=1200", "αΗ", "α", "=", "900", "Ηγα", "=1200", "Ηβ" ]

5

4

{ "x1": 335.4169921875, "x2": 516, "y1": 53, "y2": 297 }

[ " Figure 5 shows the variation of the Hβ, Hγ and Hα narrow components with ω.", "8 (Figure 5)." ]

Figure 6. The spin radial velocity curves of the Hα narrow (crosses) and broad (dots) components from 2001 (30 bins) plotted as a function of the spin phase. The solid line represents a fit to the data.

{ "x1": 305.1600036621094, "x2": 544.1339721679688, "y1": 472.0452575683594, "y2": 496.5599670410156 }

Figure

[]

6

4

{ "x1": 325, "x2": 524, "y1": 380, "y2": 461 }

[ "Figure 6 shows the Hα narrow component (α = 1200 km s−1) and the broad-base component (α = 3500 km s−1) overplotted." ]

Figure 7. The Hα, Hβ, Hγ and HeI λ4471 trailed spectra from 2001 folded on the spin period are shown at the top panels and the average-subtracted spectra are shown at the second panels. Doppler maps constructed from the phase-invariant subtracted spectra are shown in the bottom panels. The Doppler maps were constructed using the BPM and are shown on the same velocity scale with the trailed spectra. The lookup table is as in Figure 3.

{ "x1": 42.11956787109375, "x2": 281.2146911621094, "y1": 315.68524169921875, "y2": 370.080078125 }

Figure

[]

7

5

{ "x1": 48, "x2": 275, "y1": 50, "y2": 305 }

[ "The Hβ and Hγ trailed spectra in Figure 7 seem to support these results." ]

Figure 8. Hα, Hβ and Hγ trailed spectra of 2001 folded on the spin period are shown in the top panels and the phase-invariant subtracted trailed spectra are shown in the second panels from the top. MEM spin Doppler tomograms constructed from the phase-invariant subtracted spectra are shown in the third panels with the reconstructed spectra in the bottom panels. The spin wave observed in the Hα phase-invariant subtracted trailed spectra, which was caused by the Hα narrow component, is shown expanded on a smaller velocity scale. The first column of panels are plotted between -1500 km s−1 and 1500 km s−1 and the last two column are plotted between -2000 km s−1 and +2000 km s−1. The lookup table is as in Figure 4.

{ "x1": 305.15966796875, "x2": 544.2210083007812, "y1": 441.68524169921875, "y2": 535.919921875 }

Figure

[]

8

5

{ "x1": 311, "x2": 538, "y1": 50, "y2": 431 }

[ " The results are shown in the second panels from the top of Figure 8.", "A spin-wave (to differentiate it from the s-wave which is normally caused by the bright spot) in the Hα trailed spectra (Figure 8) was detected from the data after the phase-invariant subtraction was performed.", "panded in the second column of panels in Figure 8 (the narrow peak component was selected by hand over a velocity range of ±500 km s−1).", "4, with an estimated velocity amplitude of ∼ 900 km s−1 and corresponds to the emission near the “3 o’clock” position in the tomogram (Figure 8).", "A spin wave was detected in the spin-folded trailed spectra of Hα (Figure 8) with a velocity semi-amplitude of ∼ 500-600 km s−1.", "4 (Figure 8), in agreement with the accretion curtain model.", " There is evidence for strong Hα emission of the narrow s-wave component in the spin tomograms, centred around ∼ 100 km s−1 (Figure 8), that is not accounted for by these models." ]

Figure 9. A depiction of the regions where Hα was formed. Both the narrow and broad base components fall along the same radial direction, OA, resulting in similar phase variation.

{ "x1": 42.11981201171875, "x2": 281.23211669921875, "y1": 463.0452575683594, "y2": 487.5599670410156 }

Figure

[ "Observer", "A", "O", "B" ]

9

7

{ "x1": 77, "x2": 246.54859924316406, "y1": 336.0127868652344, "y2": 451.68035888671875 }

[]

Table 1. Table of spectroscopic observations during quiescence in 1991 and 2001. The column Date denotes the date at the beginning of the observing night (before midnight), the column Time denotes the number of observing hours and Spectra the number of spectra obtained.

{ "x1": 42.11980438232422, "x2": 281.18377685546875, "y1": 173.48524475097656, "y2": 207.9600830078125 }

Table

[ "24-04-91", "2448371.3884097", "3.28", "90", "25-04-91", "2448372.3603850", "2.93", "72", "29-04-91", "2448376.2402973", "7.00", "100", "24-03-01", "2451993.5427099", "2.79", "42", "25-03-01", "2451994.3581177", "3.77", "56", "25-03-01", "2451994.5147196", "3.96", "66", "26-03-01", "2451995.4360089", "1.94", "48", "26-03-01", "2451995.5412087", "2.92", "50", "Date", "HJD", "(start)", "Time", "Spectra" ]

1

{ "x1": 72, "x2": 251, "y1": 53, "y2": 157 }

[ " The observing log is given in Table 1 together with the starting times of the observations.", " The observations covered the period 24 April - 26 April 2001 and, in total, 262 spectra were obtained (Table 1)." ]

FIG. 10: Comparison of the measured variation of f+(q2)/f+(0) obtained in the present analysis and in the FOCUS experiment [5]. The band corresponds to lattice QCD [19] with the estimated uncertainty.

{ "x1": 54, "x2": 299.09454345703125, "y1": 324.0768127441406, "y2": 360.00018310546875 }

Figure

[ "BABAR", "FOCUS", "Lattice-QCD", "(αpole", "=", "0.50(4))", ")", "+", "(0", "2", ")", "/", "f", "f", "+", "(q", "q2(GeV2)", "0", "0.5", "1", "1.5", "2", "2", "1.5", "1" ]

10

16

{ "x1": 59.20277404785156, "x2": 277.5876159667969, "y1": 87, "y2": 303.0580139160156 }

[ "In Fig. 10, the dependence of the form factor on q2 is presented." ]

FIG. 11: Measured values for P×Φ×f+ are plotted versus −z and requiring that P ×Φ× f+ = 1 for z = zmax. The straight lines represent the result for the modified pole ansatz, the fit in the center and the statistical and total uncertainty.

{ "x1": 317.0400085449219, "x2": 562.186767578125, "y1": 324.0768127441406, "y2": 360.00018310546875 }

Figure

[ ")", "Modif.", "pole", "fit", "BaBar", "m", "ax", "f", "+", "(z", "P", "Φ", "z)", "/", "f", "+", "(", "P", "Φ", "-z", "-0.05", "-0.025", "0", "0.025", "0.05", "1.4", "1.2", "1" ]

11

16

{ "x1": 329.4460144042969, "x2": 539, "y1": 87, "y2": 302.1570129394531 }

[ " Figure 11 shows the product P ×Φ× f+ as a function of z.", " The data are compatible with a linear dependence, which is fully consistent with the modified pole ansatz for f+(q2), as illustrated in Fig. 11." ]

FIG. 12: Events selected for the reference channel D∗+ → D0π+, D0 → K−π+. a) Kπ mass distribution for events selected in the range δ(m) ∈ [0.143, 0.148] GeV/c2. b) δ(m) distribution for events selected in the range m(Kπ) ∈ [1.83, 1.89] GeV/c2. c) same distribution as in b), displayed on a larger mass range with the non-peaking background indicated (shaded area). d) δ(m) distribution after non-peaking background subtraction, data (points with statistical errors) and simulated events (shaded histogram).

{ "x1": 53.9998779296875, "x2": 562.1865844726562, "y1": 484.3968200683594, "y2": 530.7595825195312 }

Figure

[ "d)", "/c", "2", "M", "eV", "/", "0", ".1", "nt", "s", "E", "ve", "m(D0π)-m(D0)", "(GeV/c2)", "Data", "MC", "0.14", "0.1425", "0.145", "0.1475", "0.15", "10", "4", "10", "3", "10", "2", "10", "1", "10", "-1", "10", "-2", "c)", "2", "eV", "/c", "/", "1", "M", "nt", "s", "E", "ve", "m(D0π)-m(D0)", "(GeV/c2)", "Data", "MC", "bkg", "0.14", "0.16", "0.18", "0.2", "10", "5", "10", "4", "10", "3", "10", "2", "10", "1", "b)", "/c", "2", "M", "eV", "/", "0", ".1", "nt", "s", "E", "ve", "m(D0π)-m(D0)", "(GeV/c2)", "D0→K-π+", "D0→K-π+γ", "π→µ", "Other", "bkg", "0.14", "0.1425", "0.145", "0.1475", "0.15", "10", "5", "10", "4", "10", "3", "10", "2", "10", "1", "a)", "/c", "2", "M", "eV", "/", "2", ".5", "nt", "s", "E", "ve", "m(Kπ)", "(GeV/c2)", "D0→K-π+", "D0→K-π+γ", "D0→K-K+", "D0→π-π+", "π→µ", "Other", "1.75", "1.8", "1.85", "1.9", "1.95", "10", "5", "10", "4", "10", "3", "10", "2", "10", "1" ]

12

17

{ "x1": 115.48231506347656, "x2": 478.67822265625, "y1": 92, "y2": 441.49700927734375 }

[ "The δ(m) distribution for candidate events is shown in Fig. 12-c.", "200 GeV/c2 (see Fig. 12-c).", " After background subtraction, the δ(m) distributions obtained in data and simulation can be compared in Fig. 12-d." ]

FIG. 13: δ(m) distribution for D0 → K−π+π0 events analyzed as if they were semileptonic decays. Distributions have been normalized to unity; note that the bin size is not uniform. The bottom plot shows the ratio of the two distributions above.

{ "x1": 317.0400085449219, "x2": 562.214111328125, "y1": 353.3568115234375, "y2": 399.719970703125 }

Figure

[ "/", "M", "C", "at", "a", "0.15", "0.2", "0.25", "0.3", "δ(m)", "(GeV/c2)", "D", "1.25", "1", "tio", "n", "Fr", "ac", "Data", "MC", "0.15", "0.2", "0.25", "0.3", "0.2", "0.1", "0" ]

13

18

{ "x1": 333.27301025390625, "x2": 560.9656372070312, "y1": 89, "y2": 321.18701171875 }

[ " The δ(m) distributions are compared in Fig. 13." ]

FIG. 3: MC simulations of some of the variables used in the Fisher discriminant analysis to reduce the cc̄-event background: a) the D0 momentum after the kinematic fit, b) the mass of the spectator system (peaks, at low mass values correspond to events with a single charged pion or photon reconstructed in the spectator system), c) the cosine of the angle between the spectator system momentum and the thrust direction, d) the cosine of the angle of the positron direction, relative to the kaon direction, in the eνe c.m. frame.

{ "x1": 317.0400085449219, "x2": 562.1553344726562, "y1": 348.3168029785156, "y2": 437.3992614746094 }

Figure

[ "•", "the", "charged", "lepton", "momentum,", "pe,", "in", "the", "c.m.", "frame.", "•", "the", "direction", "of", "the", "lepton", "relative", "to", "the", "kaon", "di-", "rection,", "in", "the", "dilepton", "rest", "frame,", "cos", "θe;", "•", "the", "direction", "of", "the", "leading", "spectator", "track", "relative", "to", "the", "thrust", "axis;" ]

3

9

{ "x1": 333.0008544921875, "x2": 562.2141723632812, "y1": 461.4874267578125, "y2": 541.079345703125 }

[ " Distributions for four of the most discriminating variables are given in Fig. 3." ]

FIG. 4: Distribution of the values of the Fisher variable in the signal region (δ(m) < 0.16 GeV/c2 in a), and for masses above the signal region (δ(m) > 0.16 GeV/c2 in b).

{ "x1": 53.99989318847656, "x2": 298.9486999511719, "y1": 353.3568115234375, "y2": 378.719970703125 }

Figure

[ "/", "0", ".1", "b)", "nt", "s", "E", "ve", "Fcc", "-1", "0", "1", "2", "3", "1", "10", "10", "2", "10", "3", "10", "4", "10", "5", "10", "6", "a)", "/", "0", ".1", "nt", "s", "E", "ve", "Data", "signal", "c", "bkg.", "B+", "bkg.", "B0", "bkg.", "uds", "bkg.", "-1", "0", "1", "2", "3", "1", "10", "10", "2", "10", "3", "10", "4", "10", "5", "10", "6" ]

4

10

{ "x1": 64.74690246582031, "x2": 294.1747131347656, "y1": 96.69039916992188, "y2": 326.5115966796875 }

[ " This selection retains 77% of signal events that were kept by the previous selection requirement and rejecting 66% of the background (Fig. 4).", " This is done by comparing the distributions of this variable measured in data and in simulation as given in Fig. 4 for two selected intervals in δ(m)." ]

FIG. 5: The measured q2 r distribution (data points) compared to the sum of the estimated background and of the fitted signal components.

{ "x1": 317.0400085449219, "x2": 562.1619873046875, "y1": 352.5168151855469, "y2": 377.87994384765625 }

Figure

[ "2", "G", "eV", "/", "0", ".2", "nt", "s", "E", "ve", "q2", "r", "(GeV2)", "Data", "Signal", "Background", "0", "0.5", "1", "1.5", "2", "15000", "10000", "5000", "0" ]

5

10

{ "x1": 322.5420227050781, "x2": 565.0991821289062, "y1": 90, "y2": 328.4779968261719 }

[ "bution, where q2 r = (pD − pK) 2 , is given in Fig. 5." ]

FIG. 6: The efficiency as a function of q2, measured with simulated signal events, after all selection criteria applied.

{ "x1": 53.99983215332031, "x2": 298.9818420410156, "y1": 324.0768127441406, "y2": 339.1202087402344 }

Figure

[ "nc", "y", "ic", "ie", "E", "ff", "0", "0.5", "1", "1.5", "2", "q2", "(GeV2)", "0.08", "0.06", "0.04" ]

6

11

{ "x1": 63.854698181152344, "x2": 277.3628234863281, "y1": 87, "y2": 298.8559875488281 }

[ "The variation of the selection efficiency as a function of q2 is given in Fig. 6." ]