NEW SPECIMENS OF ANGOLASAURUS BOCAGEI AND COMMENTS ON THE EARLY RADIATIONS OF PLIOPLATECARPINE MOSASAURS POLCYN, Michael, SMU, Dallas, TX, USA; JACOBS, Louis, SMU, Dallas, TX, USA; MATEUS, Octávio, Museu da Lourinhã, Lourinhã, Portugal; SCHULP, Anne, Natuurhistorisch Museum Maastricht, Maastricht, Netherlands New, well preserved material of the Turonian mosasaur Angolasaurus bocagei from the Tadi Beds of the Itombe Formation in northern Angola, allows detailed redescription of its morphology and reassessment of its phylogenetic relationships. Angolasaurus had been previously referred to the genus Platecarpus; however, phylogenetic analysis confirms the valid taxonomic status of A. bocagei, and reconstructs that taxon within a clade that also includes the genera Selmasaurus and Ectenosaurus. These forms are united by an elaborated infrastapedial process of the quadrate and a unique ridge-like descending process of the parietal forming the supraoccipital articulation, but also retain a relatively plesiomorphic configuration of the braincase. That clade is united with all other plioplatecarpines by a number of derived characters including the presence of a novel basicranial circulation pattern. In Africa, North and South America, early plioplatecarpines are known by the Middle Turonian and Angolasaurus and closely related forms appear by the Upper Turonian. Selmasaurus and Ectenosaurus are a rare faunal component of the Santonian and Campanian of North America. Platecarpus planifrons appears in the Coniacian of North America and represents the plesiomorphic condition of the clade containing the remaining species of Platecarpus and Plioplatecarpus, that appears in the Santonian and persist until the end of the Cretaceous, reaching global distribution. The temporal and geographic distribution of these radiations suggest influence of paleogeography and eustatic sea levels.

THE SAUROPOD DINOSAUR TURIASAURUS RIODEVENSIS IN THE LATE JURASSIC OF PORTUGAL MATEUS, Octávio, New University of Lisbon (CICEGe-FCT) & Museum of Lourinhã, Lisboa, Portugal A partial sauropod was found in 1996 in Vale Pombas, north of Lourinhã, Central West of Portugal, in the Lourinhã Formation, top of Amoreira Porto Novo member dated as c. 150 M.a. (Early Tithonian, Late Jurassic) and is currently housed at Museum of Lourinhã, in Portugal. The specimen (ML368) comprises a complete tooth with root, anterior chevron and almost complete right forelimb including partial scapula, complete coracoid, humerus, ulna, radius, metacarpals I, III and V, phalanx, and ungual phalanx I. It can be ascribed to Turiasaurus riodevensis, which was previously described from the Villar del Arzobispo Formation at Riodeva (Teruel, Spain). Characters shared with T. riodevensis holotype include: curvature and asymmetry of tooth crown, expansion of crown, outline of humerus, medial deflection of the proximal end of humerus, shape and prominence of deltopectoral crest, vertical ridge in the distal half of the ulna (considered as diagnostic of Turiasauria), configuration of metacarpals, and bone proportions. It differs from T. riodevensis holotype by the smaller size and the more rectangular ungual phalanx in lateral view. The sediments from which the Riodeva specimen was recovered were previsouly thought to be Tithonian to Berriasian in age. The presence of this species in Portugal, in beds confidently dated as Early Tithonian, may allow a more precise date for the Riodeva type locality of early Tithonian in age. The humerus of the Portuguese T. riodevensis is 152 cm long. Although shorter than the Spanish specimen (790 mm), it represents a large individual. All adult sauropods recovered in Portugal thus far are very large individuals: Dinheirosaurus (estimated body length is 20- 25 m), Lusotitan (humerus length estimated to be 205 cm), Lourinhasaurus (femur length: 174 cm), and Turiasaurus here reported. The lack of of small or medium adult body-size sauropods in the Late Jurassic of Portugal, suggests browsing niches thought to be occupied by smaller forms, could be have been available for other dinosaurs, like the long necked stegosaur Miragaia longicollum.

n/a

n/a

n/a

n/a

n/a

n/a

n/a

n/a

n/a

Let \(\alpha,\beta\in(0,1)\) and
\[
K^{\alpha,\beta}:=\left\{a\in L^\infty(\mathbb{T}):\
\sum_{k=1}^\infty |\widehat{a}(-k)|^2 k^{2\alpha}<\infty,\
\sum_{k=1}^\infty |\widehat{a}(k)|^2 k^{2\beta}<\infty
\right\}.
\]
Mark Krein proved in 1966 that \(K^{1/2,1/2}\) forms a Banach algebra. He also observed that this algebra is important in the asymptotic theory of finite Toeplitz matrices. Ten years later, Harold Widom extended
earlier results of Gabor Szegö for scalar symbols and established the asymptotic trace formula
\[
\operatorname{trace}f(T_n(a))=(n+1)G_f(a)+E_f(a)+o(1)
\quad\text{as}\ n\to\infty
\]
for finite Toeplitz matrices \(T_n(a)\) with matrix symbols \(a\in K^{1/2,1/2}_{N\times N}\). We show that if \(\alpha+\beta\ge 1\) and \(a\in K^{\alpha,\beta}_{N\times N}\), then the Szegö-Widom asymptotic trace formula holds with \(o(1)\) replaced by \(o(n^{1-\alpha-\beta})\).

n/a

n/a