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Strukturuntersuchung von Eisen in TeO₂ - Me₂O(Me = Li, Na)- und TeO₂-P₂O₅-Gläsern mit der Elektronenspinresonanz (ESR)
No full textTeO₂-Me₂O (with Me = Li, Na) and TeO₂-P₂O₅ glasses with varying composition and Fe₂O₃-content were examined by ESR. Both systems allow conveniently to follow the structure of iron in glass. In practice, owing to the deformation of the TeO₂-network and the moderate field strength of tellurium (1,0), Fe(III) enters the alkali tellurite glass only as network former. This explains why only the (g ≈ 4,2) resonance was observed. Two network formers are present in the TeO₂-P₂O₅ System with phosphorous exhibiting higher field strength (2,0). A series of glasses was obtained which allowed the introduction of iron, varying structurally from Fe(III) as a network former (with g ≈ 4,2) to Fe(III) as a modifier (g ≈ 2). By following the structural behavior of Fe(III) it is possible to determine the character of the glass. For example, a 90 TeO₂-10 P₂O₅ (amount of substance in %) glass shows a tellurite character, a 80 TeO₂-20 P₂O₅ glass has a tellurite phosphate character, while a 70 TeO₂-30 P₂O₅ glass already shows a phosphate character.Des verres TeO₂-Me₂O (Me = Li, Na) et TeO₂-P₂O₅ de compositions variables et contenant des concentrations différentes du Fe₂O₃ sont étudies à l'aide de la résonance de spin électronique (ESR). Les deux systèmes sont appropriés pour étudier la systématique structurale du fer dans les verres d'oxydes. Dans les verres alcalitellureux le Fe(III) se trouve pratiquement en tant que formateur seulement à cause de la déformation facile du réseau TeO₂ et aussi à cause de l'intensité du champ moyenne de tellure (1,0). De ce fait on observe dans ces verres seule la résonance g ≈ 4,2. Le système TeO₂-P₂O₅ lui contient deux formateurs de réseau, dont le phosphore avec son intensité de champ très forte (2,0). Par variation de la composition du système on obtient des verres permettant de suivre facilement la variation du Fe(III) de la structure de formateur (g ≈ 4,2) à la structure de modificateur (g ≈ 2). A l'aide du comportement structural du Fe(III) on peut déterminer le caractère des verres. C'est ainsi que le verre (quantité en %) 90 TeO₂-10 P₂O₅ est un verre de caractère tellureux, celui de 80 TeO₂-20 P₂O₅ un tellureux phosphate et celui de 70 TeO₂-30 P₂O₅ un verre de phosphate.TeO₂-Me₂O(Me = Li, Na)- und TeO₂-P₂O₅-Gläser mit unterschiedlichen Zusammensetzungen und zusätzlich unterschiedlichen Fe₂O₃-Konzentrationen wurden mit der ESR untersucht. Beide Systeme sind gut geeignet, um die Systematik des Einbaus von Eisen in Oxidglas zu verfolgen. In Alkalitelluritglas tritt wegen des leicht deformierbaren TeO₂-Netzwerks und wegen der mittleren Feldstärke (1,0) des Tellurs das Fe(III) praktisch nur als Netzwerkbildner auf. Dafür wird auch nur die Resonanz g ≈ 4,2 beobachtet. Im System TeO₂-P₂O₅ liegen zwei Netzwerkbildner mit einer starken Feldstärke (2,0) des Phosphors vor. Durch Variation der Zusammensetzung dieses Systems wurden Gläser erhalten, mit denen eine Verschiebung der Fe(III)-Bildnerstruktur (g≈4,2) zur Fe(III)-Wandlerstruktur (g ≈ 2) leicht verfolgt werden kann. Durch das strukturelle Verhalten des Fe(III) kann auch der Charakter der Gläser erfaßt werden. So hat das Glas mit (Stoffmengengehalt in %) 90 TeO₂ und 10 P₂O₅ Telluritcharakter, das mit 80 TeO₂ und 20 P₂O₅ Telluritphosphatcharakter und das mit 70 TeO₂ und 30 P₂O₅ bereits Phosphatcharakter
From valid inequalities to heuristics : a unified view of primal-dual approximation algortithms [sic] in covering problems
No full textIncludes bibliographical references (p. 26-27).Supported by a Presidential Young Investigator Award. DDM-9158118 Partially supported by Draper Laboratory and the National University of Singapore.Dimitris Bertsimas, Chung-Piaw Teo
Native defects and -type dopability in transparent -TeO: A first-principles study
No full textAlthough -TeO is a promising -type transparent conducting oxide (TCO) due to the large optical gap ( 3.7 eV) and a light effective hole mass, its hole dopability still remains unexplored. In this work, electronic structure of -TeO and its point defects are investigated using the HSEsol functional with the band-gap-tuned mixing parameter. Our calculations reveal that -TeO exhibits a significant difference between the fundamental and optical band gaps because lower energy optical transitions are dipole forbidden. Additionally, it has a low hole effective mass, especially in-plane. The point defect calculations show that -TeO is intrinsically an insulator. From systematic calculations of the trivalent dopants as well as hydrogen, Bi doping is suggested as the best candidate as an acceptor dopant. This work paves the way for the material design of the -type -TeO
The Cobalt(II) Oxidotellurate(IV) Hydroxides Co₂(TeO₃)(OH)₂ and Co₁₅(TeO₃)₁₄(OH)₂
No full textPreviously unknown Co₂(TeO₃)(OH)₂ and Co₁₅(TeO₃)₁₄(OH)₂ were obtained under mild hydrothermal reaction conditions (210 °C, autogenous pressure) from alkaline solutions. Their crystal structures were determined from single-crystal X-ray diffraction data. Co₂(TeO₃)(OH)₂ (Z = 2, P (Formula presented.), a = 5.8898(5), b = 5.9508(5), c = 6.8168(5) Å, α = 101.539(2), β = 100.036(2), γ = 104.347(2)°, 2120 independent reflections, 79 parameters, R[F² > 2σ(F²)] = 0.017) crystallizes in a unique structure comprised of undulating ²∝[Co₂(OH)₆/₃O₃/₃O₂/₂O₁/₁]⁴⁻ layers. Adjacent layers are linked by TeIV atoms along the [001] stacking direction. Co₂(TeO₃)(OH)₂ is stable up to 450 °C and decomposes under the release of water into Co₆Te₅O₁₆ and CoO. Magnetic measurements of Co₂(TeO₃)(OH)₂ showed antiferromagnetic ordering at ≈ 70 K. The crystal structure of Co₁₅(TeO₃)₁₄(OH)₂ (Z = 3, R (Formula presented.), a = 11.6453(2), c = 27.3540(5) Å, 3476 independent reflections, 112 parameters, R[F² > 2σ(F²)] = 0.026) is isotypic with Co₁₅(TeO₃)₁₄F₂. A quantitative structural comparison revealed that the main structural difference between the two phases is connected with the replacement of F by OH, whereas the remaining part of the three-periodic network defined by [CoO₆], [CoO₅(OH)], [CoO₅] and [TeO₃] polyhedra is nearly unaffected. Consequently, the magnetic properties of the two phases are similar, namely being antiferromagnetic at low temperatures
Strukturverhalten von Fe(III) in Gläsern des Systems TeO₂-P₂O₅.
No full textIt is known that Fe(III) in glass can occur either as networkformer (4-fold coordination) or as networkmodifier (6-fold coordination). The ratio of the two coordinations depends on the Fe₂O₃ concentration and the glass composition [1]. Both structures of Fe(III) can be detected by means of ESR: the resonance line at g ≈ 4,2 represents Fe(III) in 4-fold coordination, g ≈ 2 Fe(III) in 6-fold coordination. In a previous work [2] glasses of the system TeO₂-P₂O₅ with various concentrations of Fe₂O₃ were investigated. The composition of the glasses in the present work is: (100 - x) TeO₂-x P₂O₅ with x = 10 , 20, 30 mol%. The behaviour of iron in these glasses was studied with the help of ESR. Some of the glasses were de vitrified via thermal treatment. The resulting products are analysed in this work. It is found that iron reacts sensitively with respect to the glass structure and thus serves as a probe. With increasing P₂O₅ iron and tellurium act essentially as networkmodifiers, e. g. in the case of 26 mol% P₂O₅. Possible structures of Fe(III) in glasses of the system TeO₂-P₂O₅ are presented.II est connu, que le Fe(III) agit dans les verres aussi bien en tant que formateur de réseau que modificateur. Le rapport des deux coordinances dépend si bien de la concentration en Fe₂O₃ que de la composition du verre [1]. Les deux structures peuvent être détectées à l'aide de la RSE. La ligne de résonance se trouvant à g ≈ 4,2 représente le Fe(III) à coordinance 4 et g ≈ 2 le Fe(III) à coordinance 6. Dans le travail précédant [2] on a étudié des verres du système TeO₂-P₂O₅ contenant diverses teneurs de Fe₂O₃. La composition des verres est: (100 - x) TeO₂-x P₂O₅, avec x = 10,20, 30 mol%. Le comportement du fer dans les verres fut étudié avec la RSE. Quelques verres furent cristallisés par traitement thermique. Les produits qui en résultent sont analysés dans le présent travail. II s'avère que le fer est très sensible à la structure du verre et peut ainsi servir de sonde. Avec l'augmentation du P₂O₅ le Fe et le Te se comportent essentiellement comme des modificateurs de réseau, par exemple pour 26 mol% P₂O₅. Des structures possibles du Fe(III) dans les verres du système TeO₂-P₂O₅ sont présentées.Es ist bekannt, daß Fe(III) in Gläsern sowohl als Netzwerkbildner (Vierer-Koordination) als auch als Netzwerkwandler (Sechser-Koordination) auftritt. Das Verhältnis der beiden Koordinationen hängt von der Fe₂O₃-Konzentration und der Zusammensetzung des Glases [1] ab. Die beiden Fe(III)-Strukturen können mit Hilfe der ESR nachgewiesen werden: Die Resonanzlinie bei g ≈ 4,2 steht Fe(III) in Vierer- und g ≈ 2 in Sechser-Koordination dar. In der vorangegangenen Arbeit [2] wurden Gläser des Systems TeO₂-P₂O₅ mit unterschiedlichen Fe₂O₃-Gehalten untersucht. Die Zusammensetzung dieser Gläser lautet: (100 - x ) TeO₂-x P₂O₅ mit x = 10, 20, 30 (Stoffmengengehalt in %). Das Verhalten des Eisens in den Gläsern wurde mit der ESR verfolgt. Einige dieser Gläser wurden durch eine Wärmebehandlung zur Kristallisation gebracht. Die erhaltenen Produkte werden in der vorliegenden Arbeit analysiert. Es zeigt sich, daß Eisen empfindlich auf die Glasstruktur reagiert und daher als Sonde dienen kann. Mit zunehmendem P₂O₅-Gehalt wirken Eisen und TeUur im wesentlichen als Netzwerkwandler, so z. B. bei einem Stoffmengengehalt (in %) von 26 P₂O₅. Mögliche Strukturen des Fe(III) in Gläsern des Systems TeO₂-P₂O₅ werden dargestellt
O teo-politico na dominação colonial (Theo-politics of colonial domination) - DOI: 10.5752/P.2175-5841.2009v7n15p32
No full textEste artigo pretende fundamentar o conceito teo-político na análise do regime colonial estabelecido na conquista da América. Estudando a construção do Padroado na península Ibérica, buscamos identificar como a crença, o poder, a doutrina eclesiástica e o direito civil estão articulados, tanto na Europa quanto no Novo Mundo. Com esse roteiro básico, chegamos ao estudo do Regalismo desenvolvido pelos pensadores ligados ao Estado. Demonstramos ainda que as idéias dos teólogos que pensaram a relação igreja e Estado no século XVIII não eram tão distintas das elaboradas pelo laicato. Essa relação entre o poder e o crer percorre a história humana, mas cremos que conceito de soberania característico da Idade Moderna sobrepõe de modo específico os reinos divino e terrestre. Perceber essas variações dentro da economia teo-política contribui para entender melhor a secularização do Estado no decorrer do século XIX latino-americano e a herança deixada na difícil construção da democracia através do continente.Palavras-chave: Cristandade, Estado, Igreja, Soberania, Crença AbstractThis article explain the concept of teo-political to analysis of the colonial established in conquest of America. Study the construction of Padroado in Iberian Peninsula, seek to identify manners of belief, power, ecclesiastical doctrine and civil law are articulated, in Europe and New World. In this way , we study the Regalismo developed by thinkers linked to the State. Demonstrate that the ideas of theologians who reflecting the relationship between Church and State in the 18th century were not as further than those established by laicato. This relationship between power and believe is presente in human history, but we believe that modern concept of sovereignty characteristic of Enlightment overlaps specific divine and secular kingdoms. Realize these historical variations within the teo-political economy contributes to better understand of Secularization of States in the 19th century Latin American and contribute to identify the inheritances in building democratical sistems in this continent.Keywords: Christianity, State, Church, Sovereignty, Beliefs
Nonlinear formulations and improved randomized approximation algorithms for multiway and multicut problems
No full textCover title.Includes bibliographical references (p. 21-22).D. Bertsimas, C. Teo and R. Vohra
The parsimonious property of cut covering problems and its applications
No full textIncludes bibliographical references (p. 26-27).Supported by a Presidential Young Investigator Award. DDM-91568118 Supported by Draper Laboratory.Dimitris Bertsimas and Chungpiaw Teo
Synidotea poorei Cai & Teo 2012, sp. nov.
No full text<i>Synidotea poorei</i> sp. nov. <p>Figures 1-4</p> <p> <i>Material examined</i>. Holotype: male, tl 11.4 mm, ZRC.2005.0118, North Pandan Buoy, 1°15'48.12" N, 103°45'10.81" E, Terumbu Pandan, Singapore, coll. Y. Cai, S. L. M. Teo, K. S. Tan and T. M. Sin, 11 Apr. 2002. Paratypes: 25 males, tl 4.6–12.2 mm, 15 females, tl 5.6-8.1 mm, ZRC.2005.0119, data same as holotype; 2 females, 7.4, 10.2 mm; 4 ovigerous females, tl 6.9-8.6 mm; 4 males, tl 10.2-12.9 mm, NVM J62812, data same as holotype.Other specimens: 4 males, tl 6.0- 9.1 mm, 2 females, tl 7.0- 7.4 mm, ZRC.2005.0120, North West Sudong Buoy, 1°13'07.22" N, 103°42'59.10" E, near Pulau Sudong, Singapore, 19 Jul. 2002; 1 female, tl 8.4 mm, ZRC.2005.0121, Perimbi Buoy, 1°25'45.11" N, 103°53'14.75" E, East Johor Strait, Singapore, coll. Y. Cai, 21 May 2002; 1 male, tl 12.0 mm, ZRC.2005.0122, Retan-D Buoy, 1°17'35.63" N, 103°45'25.48" E, off Sungei Pandan, West Coast, Singapore, coll. Y.Cai, K.S. Tan & S. C.Lim, 17 Oct.2003; 1 female,tl 5.9 mm, ZRC.2005.0123, Sirdhana Buoy, 1°14'43.00" N, 103°52'55.02" E, off Marina Bay, Singapore, coll. Y. Cai, K. S. Tan, T. M. Sin & S. L. M Teo, 5 Jun. 2002; 6 males, tl 6.2-10.8 mm, 1 female, tl 7.0 mm, ZRC.2005.0124, Mooring Buoys at Marina Bay, Singapore, 1°17'06.26" N, 103°51'20.09" E, coll. K. S. Tan & S. C. Lim, 14 Jul. 2003; 84 males, tl 6.8-13.2 mm, 54 females, tl 7.3-10.0 mm, ZRC.2005.0125, CAAS2 Buoy, 1°23'38.65" N, 103°59'37.13" E, off Changi Beach, Singapore, coll. Y. Cai, S. L. M. Teo & T. M. Sin, 23 Apr. 2002; 3 males, tl 4.8-10.3 mm, 1 female, tl 8.0 mm, ZRC.2005.0126, Jetty of St John’s Island, 1°13'20.95" N, 103°50'56.33" E, Singapore, coll. Y. Cai, 22 Mar. 2004.</p> <p> <i>Description of male</i>. Maximum size: 11.4 x 4.0 mm (holotype). Body 2.9–3.1 times as long as wide; depressed and smooth, without tubercles or carina, lateral margin smooth. Colour brownish with darker spots. Cephalon frontal margin almost straight, with indistinct median excavation, dorsal surface with anterior and posterior transverse grooves and longitudinal lateral grooves. Eyes bulge outward, forming part of contour of lateral margin of head. Ratio of post-orbital head width to width of pereonite 3 (widest pereonite) 0.56.</p> <p>Antenna 1 flagellum uniarticulate, with 10 pairs of jointed aesthetascs. Antenna 2 0.6 body length; article 4 2.4 times as long as wide; article 5 3.6 times as long as wide; flagellum with 16-22 articles, 1.2 length of peduncle.</p> <p>Dorsum of each pereonite smooth, margin slightly arched; dorsomarginal areas of pereonites 2–7 slightly enlarged, distinctly depressed, lateral margins slightly upturned, marginal areas becoming progressively less depressed, and sloping gently on posterior pereonites; lunettes on pereonites 2–4 with posterior margin subtriangular or rounded; distolateral angle of pereonites 1–4 rounded, those of pereonites 5–7 subrectangular.</p> <p>Pleotelson about 1.4 times as long as wide, dorsum smooth, evenly convex, lateral margin sub- parallel over anterior twothirds, then tapering beyond curved margin to rounded posterior margin, with a shallow medial excavation.</p> <p>Mandible incisor with 4 strong, unequal cusps. Lacinia mobilis stout, 4-cusped, with additional large serrate spine-like process. Molar process large, truncate, surrounded by short spines, bearing laterally 3 stiff setulose setae and many denticles along distal end.</p> <p>Mesial lobe of maxilla 1 with 2 stout distally serrated robust apical setae with mesial setules; outer lobe with 9 robust tooth-like serrated setae.</p> <p>Maxilla 2 3-lobed, with plumose, simple and comb setae on endopod as figured; mesial lobe of exopod lined with comb setae, Outer lobe enlarged, recurved laterally, fringed with extremely long plumose setae.</p> <p>Endite of maxilliped with 1 recurved coupling hook, lined with 7-10 apical moderately slender plumose setae. Palp 3-articulate, last article expanded and fringed with 6-10 long setae. Epipod laminar, distal margin rounded, outer and distal margin fringed with fine setae.</p> <p>Pereopod 1 carpus triangular, flexor margin densely lined with simple setae and denticles; propodus 1.9 times as long as greatest depth, tapering and curving distally, flexor margin with long simple setae; dactylus elongated, with simple setae.</p> <p>Pereopods 2-7 similar in form and size, slightly longer than pereopod 1; carpus subrectangular; flexor margins of ischium to propodus densely fringed with simple setae and pubescence; extensor margins of carpus and merus armed with 1 or 2 simple setae; dactylus more elongate and straighter than that of pereopod 1. Pereopod 2 propodus as long as merus and carpus together, 2.8 times as long as wide. Pereopod 4 propodus 2.4 times as long as wide. Pereopod 7 propodus 3.5 times as long as wide.</p> <p>Penes fused along entire length, 1.6 times as long as wide, swollen distally, with notched lateral and distal margins.</p> <p>Pleopods 1 and 2 with plumose marginal setae on endopods and exopods, both rami without sutures. Pleopods 1-3 with about 11, 5 and 3 coupling hooks on inner margin of peduncles respectively. Pleopod 2 with appendix masculina elongated, reaching beyond distal margin of endopod by one-sixth of its length, mostly straight, distal quarter slightly curving medisally, with numerous spinules distally. Pleopods 3-5 with few and short simple marginal setae, incomplete transverse suture present from near middle of the outer margin of exopod.</p> <p>Uropod 2.9 times as long as distal peduncle width, with short, simple setae, no oblique ridges on peduncle, distolateral angle with 3 plumose setae; endopod 0.3 length of peduncle, mesial length 0.7 proximal suture length, suture at 75° to long axis, distal margin truncate, at 75° to long axis, lateral margin gently convex between lateral and distal margins</p> <p> <i>Female</i>. Maximum size, 7.6 x 3.1 mm (one of paratypes). Body stouter than male, 2.3-2.6 times as long as wide; pleotelson 1.2 times as long as wide; pereonal margins more evenly curved than in male. Antenna 2 with 13-15 articled flagellum. Maxilla 2 3-lobed, with plumose, simple and comb setae on endopod as figured; both inner and outer lobes of exopod lined with comb setae; no dense pubescence on pereopods 2-7. Oostegites lamellar on pereonites 1-4.</p> <p> <i>Etymology</i>. The new species is named after Gary C. B. Poore, who has contributed significantly to our understanding of marine isopods in the Indo-Pacific region.</p> <p> <i>Habitats</i>. The new species was most commonly found in association with macroalgae and hydroids in the fouling community of Singapore waters.</p> <p> <i>Remarks.</i> Currently, 14 species of the genus <i>Synidotea</i> belong to the ‘ <i>S. hirtipes</i> group’, which was defined as a group of similar species characterized by a smooth body, entire or slightly excavate front of the head, and excavated pleotelson apex (Monod, 1931; Menzies and Miller, 1972; Poore, 1996). The group contains: <i>S. hirtipes</i> (Milne Edwards, 1840), <i>S. laevidorsalis</i> (Miers, 1881), <i>S. laticauda</i> Benedict, 1879, <i>S. harfordi</i> Benedict, 1879, <i>S. variegata</i>, Collinge, 1917, <i>S. marplatensis</i> Giambiagi, 1922, <i>S. fluviatilis</i> Pillai, 1954, <i>S. worlinensis</i> Joshi and Bal, 1959, <i>S. brunnea</i> Pires and Moreira, 1975, <i>S. hunumantharoei</i> Kumari and Shyamasundari, 1984, <i>S. keablei</i> Poore and Lew Ton, 1993, <i>S. grisea</i> Poore and Lew Ton, 1993, <i>S. oahu</i> Moore, 2004, and <i>S. fosteri</i> Schotte and Heard, 2004. Two more species, <i>S. innatans</i> and <i>S. karumba</i> from Australia, were just described and added into the group (Poore, 2012).</p> <p> <i>Synidotea poorei</i> sp. nov. can be separated from <i>S. hirtipes</i> easily by its smooth uropodal peduncle (vs. two ridges in <i>S. hirtipes</i>). The new species is superficially similar to <i>S. lavidorsalis</i>, <i>S. laticauda</i>, <i>S. grisea</i> and <i>S. keablei,</i> but it can be separated from these species by the sub-parallel lateral margin of the pleotelson. It also differs from <i>S. laevidorsalis</i> by the shape of uropodal endopod (fig. 3G vs. fig. 1f in Poore, 1996) and the fused penial plates (fig. 3H vs. fig. 1k in Poore, 1996); from S. <i>laticauda</i> by the less excavated posterior end of the pleotelson; and from <i>S. keablei</i> by sexual dimorphism of the maxilla 2, and the elongated pleotelson. <i>Synidotea poorei</i> sp. nov. can be distinguished from <i>S. harfordi</i> by the shape of the lunette on the pereonites 2-4 (rounded vs. triangular) and the overall body form, which is more slender in the latter. <i>Synidotea poorei</i> is also similar to <i>S. brunnea</i> from which it can be separated by the more elongated antennae 1 and 2, and the shape of uropodal endopod (fig 3G vs. fig. 38 in Pires & Moreira, 1975). <i>Synidotea poorei</i>, also resembles <i>S. variegata</i> (cf. Collinge, 1917; Pillai, 1963) from which it differs by the more stout peduncle of antenna 2 (fig 3 in Collinge, 1917 vs. fig. 2C), stouter pleotelson (1.3 times as long as wide in female and 1.5 times in male of <i>S. poorei</i> vs. 1.7 times in <i>S. variegata</i>); and the shallower pleonal suture. With respect to the body form, the cephalon and the pleotelson, <i>S. poorei</i> is very similar to the Argentinean species <i>S. marplatensis</i>. It can be separated by the much longer appendix masculina (Fig. 3C, D vs. Fig. 4 in Giambiagi, 1922); and the smooth uropodal peduncle (vs. with an oblique ridge). <i>Synidotea poorei</i> can also be easily separated from the two recently described species, <i>S. fosteri</i> and <i>S. oahu</i> by its much longer antenna 2, and the smooth uropodal endopod.</p>Published as part of <i>Cai, Yixiong & Teo, Serena L. M., 2012, Synidotea poorei, a new isopod from the fouling community in Singapore waters (Valvifera, Idoteidae), pp. 237-243 in Memoirs of Museum Victoria 69</i> on pages 237-238, DOI: 10.24199/j.mmv.2012.69.02, <a href="http://zenodo.org/record/8065086">http://zenodo.org/record/8065086</a>
Author-wise bibliometric analysis based on entropy.
No full textAuthor-wise bibliometric analysis based on entropy.</p
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