Boxicity of Circular Arc Graphs

A k-dimensional box is a Cartesian product R(1)x...xR(k) where each R(i) is a closed interval on the real line. The boxicity of a graph G, denoted as box(G), is the minimum integer k such that G can be represented as the intersection graph of a collection of k-dimensional boxes. That is, two vertices are adjacent if and only if their corresponding boxes intersect. A circular arc graph is a graph that can be represented as the intersection graph of arcs on a circle. We show that if G is a circular arc graph which admits a circular arc representation in which no arc has length at least pi(alpha-1/alpha) for some alpha is an element of N(>= 2), then box(G) <= alpha (Here the arcs are considered with respect to a unit circle). From this result we show that if G has maximum degree Delta < [n(alpha-1)/2 alpha] for some alpha is an element of N(>= 2), then box(G) <= alpha. We also demonstrate a graph having box(G) > alpha but with Delta = n (alpha-1)/2 alpha + n/2 alpha(alpha+1) + (alpha+2). For a proper circular arc graph G, we show that if Delta < [n(alpha-1)/alpha] for some alpha is an element of N(>= 2), then box(G) <= alpha. Let r be the cardinality of the minimum overlap set, i.e. the minimum number of arcs passing through any point on the circle, with respect to some circular arc representation of G. We show that for any circular arc graph G, box(G) <= r + 1 and this bound is tight. We show that if G admits a circular arc representation in which no family of k <= 3 arcs covers the circle, then box(G) <= 3 and if G admits a circular arc representation in which no family of k <= 4 arcs covers the circle, then box(G) <= 2. We also show that both these bounds are tight.

Reactions of Titanocene Bis(trimethylsilyl)acetylene Complexes with Carbodiimides: An Experimental and Theoretical Study of Complexation versus C-N Bond Activation

The reaction of the low valent metallocene(II) sources Cp'Ti-2(eta(2)-Me3SiC2SiMe3) (Cp' = eta(5)-cyclopentadienyl, 1a or eta(5)-pentamethylcyclopentadienyl, 1b) with different carbodiimide substrates RN=C=NR' 2-R-R' (R = t-Bu; R' = Et; R = R' = i-Pr; t-Bu; SiMe3; 2,4,6-Me-C6H2 and 2,6-i-Pr-C6H3) was investigated to explore the frontiers of ring strained, unusual four-membered heterometallacycles 5-R. The product complexes show dismantlement, isomerization, or C-C coupling of the applied carbodiimide substrates, respectively, to form unusual mono-, di-, and tetranuclear titanium(III) complexes. A detailed theoretical study revealed that the formation of the unusual complexes can be attributed to the biradicaloid nature of the unusual four-membered heterometallacycles 5-R, which presents an intriguing situation of M-C bonding. The combined experimental and theoretical study highlights the delicate interplay of electronic and steric effects in the stabilization of strained four-membered heterometallacycles, accounting for the isolation of the obtained complexes.

Cubicity and Bandwidth

A unit cube in (or a k-cube in short) is defined as the Cartesian product R (1) x R (2) x ... x R (k) where R (i) (for 1 a parts per thousand currency sign i a parts per thousand currency sign k) is a closed interval of the form a (i) , a (i) + 1] on the real line. A k-cube representation of a graph G is a mapping of the vertices of G to k-cubes such that two vertices in G are adjacent if and only if their corresponding k-cubes have a non-empty intersection. The cubicity of G is the minimum k such that G has a k-cube representation. From a geometric embedding point of view, a k-cube representation of G = (V, E) yields an embedding such that for any two vertices u and v, ||f(u) - f(v)||(a) a parts per thousand currency sign 1 if and only if . We first present a randomized algorithm that constructs the cube representation of any graph on n vertices with maximum degree Delta in O(Delta ln n) dimensions. This algorithm is then derandomized to obtain a polynomial time deterministic algorithm that also produces the cube representation of the input graph in the same number of dimensions. The bandwidth ordering of the graph is studied next and it is shown that our algorithm can be improved to produce a cube representation of the input graph G in O(Delta ln b) dimensions, where b is the bandwidth of G, given a bandwidth ordering of G. Note that b a parts per thousand currency sign n and b is much smaller than n for many well-known graph classes. Another upper bound of b + 1 on the cubicity of any graph with bandwidth b is also shown. Together, these results imply that for any graph G with maximum degree Delta and bandwidth b, the cubicity is O(min{b, Delta ln b}). The upper bound of b + 1 is used to derive upper bounds for the cubicity of circular-arc graphs, cocomparability graphs and AT-free graphs in terms of the maximum degree Delta.

Asymptotically-good, multigroup decodable space-time block codes

For a family of Space-Time Block Codes (STBCs) C-1, C-2,..., with increasing number of transmit antennas N-i, with rates R-i complex symbols per channel use, i = 1, 2,..., we introduce the notion of asymptotic normalized rate which we define as lim(i ->infinity) R-i/N-i, and we say that a family of STBCs is asymptotically-good if its asymptotic normalized rate is non-zero, i. e., when the rate scales as a non-zero fraction of the number of transmit antennas. An STBC C is said to be g-group decodable, g >= 2, if the information symbols encoded by it can be partitioned into g groups, such that each group of symbols can be ML decoded independently of the others. In this paper we construct full-diversity g-group decodable codes with rates greater than one complex symbol per channel use for all g >= 2. Specifically, we construct delay-optimal, g-group decodable codes for number of transmit antennas N-t that are a multiple of g2left perpendicular(g-1/2)right perpendicular with rate N-t/g2(g-1) + g(2)-g/2N(t). Using these new codes as building blocks, we then construct non-delay-optimal g-group decodable codes with rate roughly g times that of the delay-optimal codes, for number of antennas N-t that are a multiple of 2left perpendicular(g-1/2)right perpendicular, with delay gN(t) and rate Nt/2(g-1) + g-1/2N(t). For each g >= 2, the new delay-optimal and non-delay- optimal families of STBCs are both asymptotically-good, with the latter family having the largest asymptotic normalized rates among all known families of multigroup decodable codes with delay T <= gN(t). Also, for g >= 3, these are the first instances of g-group decodable codes with rates greater than 1 reported in the literature.

LOWER BOUNDS FOR BOXICITY

An axis-parallel b-dimensional box is a Cartesian product R-1 x R-2 x ... x R-b where R-i is a closed interval of the form a(i),b(i)] on the real line. For a graph G, its boxicity box(G) is the minimum dimension b, such that G is representable as the intersection graph of boxes in b-dimensional space. Although boxicity was introduced in 1969 and studied extensively, there are no significant results on lower bounds for boxicity. In this paper, we develop two general methods for deriving lower bounds. Applying these methods we give several results, some of which are listed below: 1. The boxicity of a graph on n vertices with no universal vertices and minimum degree delta is at least n/2(n-delta-1). 2. Consider the g(n,p) model of random graphs. Let p <= 1 - 40logn/n(2.) Then with high `` probability, box(G) = Omega(np(1 - p)). On setting p = 1/2 we immediately infer that almost all graphs have boxicity Omega(n). Another consequence of this result is as follows: For any positive constant c < 1, almost all graphs on n vertices and m <= c((n)(2)) edges have boxicity Omega(m/n). 3. Let G be a connected k-regular graph on n vertices. Let lambda be the second largest eigenvalue in absolute value of the adjacency matrix of G. Then, the boxicity of G is a least (kappa(2)/lambda(2)/log(1+kappa(2)/lambda(2))) (n-kappa-1/2n). 4. For any positive constant c 1, almost all balanced bipartite graphs on 2n vertices and m <= cn(2) edges have boxicity Omega(m/n).

Lower bounds on Ricci flow invariant curvatures and geometric applications

We consider Ricci flow invariant cones C in the space of curvature operators lying between the cones ``nonnegative Ricci curvature'' and ``nonnegative curvature operator''. Assuming some mild control on the scalar curvature of the Ricci flow, we show that if a solution to the Ricci flow has its curvature operator which satisfies R + epsilon I is an element of C at the initial time, then it satisfies R + epsilon I is an element of C on some time interval depending only on the scalar curvature control. This allows us to link Gromov-Hausdorff convergence and Ricci flow convergence when the limit is smooth and R + I is an element of C along the sequence of initial conditions. Another application is a stability result for manifolds whose curvature operator is almost in C. Finally, we study the case where C is contained in the cone of operators whose sectional curvature is nonnegative. This allows us to weaken the assumptions of the previously mentioned applications. In particular, we construct a Ricci flow for a class of (not too) singular Alexandrov spaces.

Bearing Capacity Factors for Ring Foundations

Bearing capacity factors because of the components of cohesion, surcharge, and unit weight, respectively, have been computed for smooth and rough ring footings for different combinations of r(i)= r(o) and. by using lower and upper bound theorems of the limit analysis in conjunction with finite elements and linear optimization, where r(i) and r(o) refer to the inner and outer radii of the ring, respectively. It is observed that for a smooth footing with a given value of r(o), the magnitude of the collapse load decreases continuously with an increase in r(i). Conversely, for a rough base, for a given value of r(o), hardly any reduction occurs in the magnitude of the collapse load up to r(i)= r(o) approximate to 0.2, whereas for r(i)= r(o) > 0.2, the magnitude of the collapse load, similar to that of a smooth footing, decreases continuously with an increase in r(i)= r(o). The results from the analysis compare reasonably well with available theoretical and experimental data from the literature. (C) 2015 American Society of Civil Engineers.

Comportamiento agronomico, fitosanitario y calidad de grano de tres hibridos y cuatro variedades comerciales de cafe (Coffea arabica L.) agroforestal en Masatepe, Nicaragua

Se establecieron parce las en el Centro Jardín Botánico y Campos Azúles (Masatepe, Masaya) las variedades de café Pacas , Catrenic, Pacas injerta sobre Robusta, Catrenic injerta sobre Robusta y tres híbrido F1: Caturra 9*ET 15 L2, A.30 ( Híbrido 2), Caturra * ET 15 L3, A17 ( Híbrid o 3) y T 5296*ET6 L.13, A.12 ( Híbrido 4) , con el propósito de determinar el comportamiento fitosanitario, productivo y de calidad de grano . Se midieron de octubre 2006 a diciembre 2007 , variables morfológicas y fitosanitarias de la planta de café y d el 2004 al 2007 componentes producción de grano y a nális is físico organoléptico del grano de café verde. Los datos fueron evaluados mediante análisis de varianza para experimentos unifactoriables en bloques completos al azar con cuatro y ocho repeticiones par a e l factor variedades . E l área de muestreo fue con stituida por 12 plantas a 2 x 1. 25, café establecido bajo sombra de Inga laurina (Sw.) Willd , Simarouba glauca DC ; Samanea Saman (Jacq.) Merr , Tabebuia rosea (Bertol.) DC en combinación con fertilización orgánica moderado (OM) y convencional moderado (CM). Los resultados indican que las variedades comerciales Pacas y Catrenic obtuvieron mayo r altura de 160.14 a 190. 61 los híbridos e xpre saron un diámetro de tronco superior , evidenciaron también menor desarr ollo de ramas secundarias productivas, pero una mayo r cantidad de ramas primarias y superior área de copa . Pacas mostró mayo r i ncidencia de H. vastatrix Berk y Br , mientras que Catrenic presento resistencia. Leucoptera coffeella Guerin - Meneville , Colletotr ichum coffeanum Noack , Chasparria en frutos e H y pot h enemus hampie Ferrari no su peraron niveles de incidencia tolerable en ninguna variedad. Ante Cercospora coffeicola Berk y Cooke los Híbrido 2 e Híbrido 3 expresaron susceptibilidad. Catrenic obtuvo el may o r peso de fruto, requiriendo menor número de frutos para componer un kilogramo de café uva. El mayo r rendimiento de caf é en el tiempo fue presentado por el Híbrido 2 , aumentando 314 kg a 65 kg oro superior a l Híbrido 3 y 4. Todas las variedades producen l os mayo res porcentajes de granos con cribas entre 15 a 17, en las tres cosechas. Tanto Pacas y Híbrido 2 expresaron un a calidad buena de acidez en el 37. 5 % y 25 % respectivamente de l total de las muestras. El aroma y cuerpo obtenido por Híbrido 4, Híbrido 2 y Catrenic fue superior. El tipo de café producido se clasific ó en Tipo Lavado Nicaragua (GW) en la mayo r proporción de muestras y Tipo Estri ctamente de Altura (SHG) donde Híbrido 2 y Catrenic obtuvieron la mayo r distribución . Según los resultados antes descritos, las siete variedades desarrollaron un café de tipo BB mercado de exigencia

Heating, current drive and confinement regimes with the JET ICRH and lhcd systems

During its 1990 operation, 2 large RF systems were available on JET. The Ion Cyclotron Resonance Heating (ICRH) system was equipped with new beryllium screens and with feedback matching systems. Specific impurities generated by ICRH were reduced to negligible levels even in the most stringent H-mode conditions. A maximum power of 22 MW was coupled to L-mode plasmas. High quality H-modes (tau-E greater-than-or-equal-to 2.5 tau-EG) were achieved using dipole phasing. A new high confinement mode was discovered. It combines the properties of the H-mode regime to the low central diffusivities obtained by pellet injection. A value of n(d) tau-E T(i) = 7.8 x 10(20) m-3 s keV was obtained in this mode with T(e) approximately T(i) approximately 11 keV. In the L-mode regime, a regime, a record (140 kW) D-He-3 fusion power was generated with 10 - 14 MW of ICRH at the He-3 cyclotron frequency. Experiments were performed with the prototype launcher of the Lower Hybrid Current Drive (LHCD) systems with coupled power up to 1.6 MW with current drive efficiencies up to < n(e) > R I(CD)/P = 0.4 x 10(20) m-2 A/W. Fast electrons are driven by LHCD to tail temperatures of 100 keV with a hollow radial profile. Paradoxically, LHCD induces central heating particularly in combination with ICRH. Finally we present the first observations of the synergistic acceleration of fast electrons by Transit Time Magnetic Pumping (TTMP) (from ICRH) and Electron Landau Damping (ELD) (from LHCD). The synergism generates TTMP current drive even without phasing the ICRH antennae.

PICES Science: the first ten years and a look to the future

Introduction [pdf, 0.17 MB] Warren S. Wooster [pdf, 0.12 MB] PICES - the first decade, and beyond Paul H. LeBlond [pdf, 0.03 MB] The Physical Oceanography and Climate Committee: The first decade D.E. Harrison and Neville Smith [pdf, 0.04 MB] Ocean observing systems and prediction - the next ten years Tsutomu Ikeda and Patricia A. Wheeler [pdf, 0.85 MB] Ocean impacts from the bottom of the food web to the top: Biological Oceanography Committee (BIO) retrospective Timothy R. Parsons [pdf, 0.2 MB] Future needs for biological oceanographic studies in the Pacific Ocean Douglas E. Hay, Richard J. Beamish, George W. Boehlert, Vladimir I. Radchenko, Qi-Sheng Tang, Tokio Wada, Daniel W. Ware and Chang-Ik Zhang [pdf, 0.2 MB] Ten years FIS in PICES: An introspective, retrospective, critical and constructive review of fishery science in PICES Richard F. Addison, John E. Stein and Alexander V. Tkalin [pdf, 0.12 MB] Marine Environmental Committee in review Robie W. Macdonald, Brian Morton, Richard F. Addison and Sophia C. Johannessen [pdf, 1.89 MB] Marine environmental contaminant issues in the North Pacific: What are the dangers and how do we identify them? R. Ian Perry, Anne B. Hollowed and Takashige Sugimoto [pdf, 0.36 MB] The PICES Climate Change and Carrying Capacity Program: Why, how, and what next? List of acronyms [pdf, 0.07 MB] (Document contains 108 pages)

Workshop on Conceptual/Theoretical Studies and Model Development including the MODEL Task Team Report; BASS Team Report; REX Task Team Reports

A workshop was convened by the MODEL Task Team and held June 23-28, 1996, in Nemuro, Japan, to develop the modeling requirements of the PICES Climate Change and Carrying Capacity (CCCC) Program. It was attended by over 40 scientists from all member nations of PICES. The principal objectives of the workshop were to • review the roles and limitations of modeling for the CCCC program; • propose the level of modeling required; and • provide a plan for how to promote these modeling activities. Secondary activities at the workshop included organisational meetings of the Regional comparisons (REX) and Basin-scale experiment (BASS) Task Teams, and a symposium by Japan-GLOBEC on “Development and application of new technologies for measurement and modeling in marine ecosystems.” This report serves as a record of the proceedings of this workshop. (PDF contains 89 pages)

Using Remote Sensing and Spatial Information Technologies to Detect and Map Two Aquatic Macrophytes

This paper describes the light reflectance characteristics ofwaterhyacinth [Eichhornia crassipes (Mort.) Solms] and hydrilla [Hydrilla verticillata (L.F.) Royle] and the application of airborned videography with global positioning system (GPS) and geographic information system (GIS) technologies for distinguishing and mapping the distribution of these two aquatic weeds in waterways of southern Texas. Field reflectance measurements made at several locations showed that waterhyacinth generally had higher near-infrared (NIR) reflectance than associated plant species and water. Hydrilla had lower NIR reflectance than associated plant species and higher NIR reflectance than water. Reflectance measurements made on hydrilla plants submerged below the water surface had similar spectral characteristics to water. Waterhyacinth and hydrilla could be distinguished in color-infrared (CIR) video imagery where they had bright orange-red and reddish-brown image responses, respectively. Computer analysis of the imagery showed that waterhyacinth and hydrilla infestaions could be quantified. An accuracy assessment performed on the classified image showed an overall accuracy of 87.7%. Integration of the GPS with the video imagery permitted latitude/longitude coordinates of waterhyacinth and hydrilla infestation to be recorded on each image. A portion of the Rio Grande River in extreme southern Texas was flown with the video system to detect waterhyacinth and hydrilla infestaions. The GPS coordinates on the CIR video scenes depicting waterhyacinth and hydrilla infestations were entered into a GIS to map the distribution of these two noxious weeds in the Rio Grande River.

Marine life in the North Pacific: the known, unknown, and unknowable

Special Publication 2 On-line version On-line version includes links to the following files (these files are not included into publication): Bacterioplankton [pdf] Phytoplankton [pdf] Zooplankton [pdf] Non-exploited fish and invertebrates [pdf] Commercially-important fish and invertebrates [pdf] Marine birds [pdf] Mammals [pdf] Supplemental table of Unknowns [html]

Phase behavior of complex superprotonic solid acids

Superprotonic phase transitions and thermal behaviors of three complex solid acid systems are presented, namely Rb3H(SO4)2-RbHSO4 system, Rb3H(SeO4)2-Cs3H(SeO4)2 solid solution system, and Cs6(H2SO4)3(H1.5PO4)4. These material systems present a rich set of phase transition characteristics that set them apart from other, simpler solid acids. A.C. impedance spectroscopy, high-temperature X-ray powder diffraction, and thermal analysis, as well as other characterization techniques, were employed to investigate the phase behavior of these systems.

Rb3H(SO4)2 is an atypical member of the M3H(XO4)2 class of compounds (M = alkali metal or NH4+ and X = S or Se) in that a transition to a high-conductivity state involves disproportionation into two phases rather than a simple polymorphic transition [1]. In the present work, investigations of the Rb3H(SO4)2-RbHSO4 system have revealed the disproportionation products to be Rb2SO4 and the previously unknown compound Rb5H3(SO4)4. The new compound becomes stable at a temperature between 25 and 140 °C and is isostructural to a recently reported trigonal phase with space group P3̅m of Cs5H3(SO4)4 [2]. At 185 °C the compound undergoes an apparently polymorphic transformation with a heat of transition of 23.8 kJ/mol and a slight additional increase in conductivity.

The compounds Rb3H(SeO4)2 and Cs3H(SeO4)2, though not isomorphous at ambient temperatures, are quintessential examples of superprotonic materials. Both adopt monoclinic structures at ambient temperatures and ultimately transform to a trigonal (R3̅m) superprotonic structure at slightly elevated temperatures, 178 and 183 °C, respectively. The compounds are completely miscible above the superprotonic transition and show extensive solubility below it. Beyond a careful determination of the phase boundaries, we find a remarkable 40-fold increase in the superprotonic conductivity in intermediate compositions rich in Rb as compared to either end-member.

The compound Cs6(H2SO4)3(H1.5PO4)4 is unusual amongst solid acid compounds in that it has a complex cubic structure at ambient temperature and apparently transforms to a simpler cubic structure of the CsCl-type (isostructural with CsH2PO4) at its transition temperature of 100-120 °C [3]. Here it is found that, depending on the level of humidification, the superprotonic transition of this material is superimposed with a decomposition reaction, which involves both exsolution of (liquid) acid and loss of H2O. This reaction can be suppressed by application of sufficiently high humidity, in which case Cs6(H2SO4)3(H1.5PO4)4 undergoes a true superprotonic transition. It is proposed that, under conditions of low humidity, the decomposition/dehydration reaction transforms the compound to Cs6(H2-0.5xSO4)3(H1.5PO4)4-x, also of the CsCl structure type at the temperatures of interest, but with a smaller unit cell. With increasing temperature, the decomposition/dehydration proceeds to greater and greater extent and unit cell of the solid phase decreases. This is identified to be the source of the apparent negative thermal expansion behavior.

References

[1] L.A. Cowan, R.M. Morcos, N. Hatada, A. Navrotsky, S.M. Haile, Solid State Ionics 179 (2008) (9-10) 305.

[2] M. Sakashita, H. Fujihisa, K.I. Suzuki, S. Hayashi, K. Honda, Solid State Ionics 178 (2007) (21-22) 1262.

[3] C.R.I. Chisholm, Superprotonic Phase Transitions in Solid Acids: Parameters affecting the presence and stability of superprotonic transitions in the MHnXO4 family of compounds (X=S, Se, P, As; M=Li, Na, K, NH4, Rb, Cs), Materials Science, California Institute of Technology, Pasadena, California (2003).