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Research in 1970 vaulted Becán to prominence on the landscape of great Maya centers. Mapping, excavation, and ceramic stratigraphy revealed that its enigmatic earthwork, first recorded archaeologically in 1934, was a fortification built at the end of the Preclassic period. Large-scale warfare thus unexpectedly turned out to have very deep roots in the Maya lowlands. The site's wider implications remained obscure, however, in the absence of dates and other inscriptions. The ever-increasing dependence on historical and iconographic information in our narratives, along with the invisibility of its Preclassic buildings and plazas, unfortunately marginalized Becán. Some colleagues even claimed that we have misinterpreted both the nature of the earthworks (not fortifications) and their dating (not Preclassic). We rehabilitate Becán by dispelling these claims and by showing that standard archaeological evidence, contextualized in what we know today, has much to say about Becán's role in lowland culture history. We identify intervals of crisis when the earthwork remained useful long after it was originally built, especially during the great hegemonic struggles of the Snake and Tikal dynasties, and introduce new ceramic and lithic data about Becán's settlement history and political entanglements. Our most important message is that inscriptions and iconography, for all their dramatic chronological detail and historical agency, must always be complemented by standard fieldwork.

This concise monograph explores how core ideas in Hardy space function theory and operator theory continue to be useful and informative in new settings, leading to new insights for noncommutative multivariable operator theory. Beginning with a review of the confluence of system theory ideas and reproducing kernel techniques, the book then covers representations of backward-shift-invariant subspaces in the Hardy space as ranges of observability operators, and representations for forward-shift-invariant subspaces via a Beurling–Lax representer equal to the transfer function of the linear system. This pair of backward-shift-invariant and forward-shift-invariant subspace form a generalized orthogonal decomposition of the ambient Hardy space. All this leads to the de Branges–Rovnyak model theory and characteristic operator function for a Hilbert space contraction operator. The chapters that follow generalize the system theory and reproducing kernel techniques to enable an extension of the ideas above to weighted Bergman space multivariable settings.

Nonmetric (morphological) and metric analyses of dental traits and dentition are an established and effective, but still much underutilized, means of determining biological relationships among the individuals comprising a population over several generations. Combining such dental analyses, a social organizational typology adapted from social psychology, and small sample statistics, this study hazards a trial examination of the evidence for biological affinity within and between three archaeologically perceived social groups represented in the Classic-period Belize Valley community of Buenavista del Cayo. The groups comprise traditional high elite and commoner categories, and a putative middle level of intermediate elites. Findings suggest a dichotomous kinship structure of elites and non-elites, but one within which there had emerged an emically and archaeologically distinct “middle” status group of intermediate elites or subelites that remained affined by blood to the subordinate non-elite commoners and peasantry. The study differs from previous examinations of ancient Maya social organization in employing a truly integrated bioarchaeological approach to the topic rather than what have generally been intrinsically insular archaeological or osteometric approaches.

We develop a Sz.-Nagy–Foias-type functional model for a commutative contractive operator tuple \( \underline {T} = (T_1, \dots , T_d)\) having T = T1⋯Td equal to a completely nonunitary contraction. We identify additional invariants \({\mathbb G}_\sharp , {\mathbb W}_\sharp \) in addition to the Sz.-Nagy–Foias characteristic function ΘT for the product operator T so that the combined triple \(({\mathbb G}_\sharp , {\mathbb W}_\sharp , \Theta _T)\) becomes a complete unitary invariant for the original operator tuple \( \underline {T}\). For the case d ≥ 3 in general there is no commutative isometric lift of \( \underline {T}\); however there is a (not necessarily commutative) isometric lift having some additional structure so that, when compressed to the minimal isometric-lift space for the product operator T, generates a special kind of lift of \( \underline {T}\), herein called a pseudo-commutative contractive lift of \( \underline {T}\), which in turn leads to the functional model for \( \underline {T}\). This work has many parallels with recently developed model theories for symmetrized-bidisk contractions (commutative operator pairs (S, P) having the symmetrized bidisk Γ as a spectral set) and for tetrablock contractions (commutative operator triples (A, B, P) having the tetrablock domain \({\mathbb E}\) as a spectral set).

We survey various Nevanlinna-Pick type interpolation problems for contractive multipliers between two vector Fock spaces of noncommutative formal power series. An adaptation of Potapov’s method leads to a chain-matrix linear-fractional parametrization for the set of all solutions for the case where the Pick operator is invertible. The most general problem considered here is a noncommutative multivariable analogue of the Abstract Interpolation Problem formulated by Katsnelson, Kheifets and Yuditskii for the single-variable case; we obtain a Redheffer-type linear-fractional parametrization for the set of all solutions (including in degenerate cases) via an adaptation of ideas of Arov and Grossman.

Between 1984 and 1989, a number of depositional contexts were excavated at the Classic Maya center/site of Buenavista del Cayo in the upper Belize Valley that appeared to be products of sudden cessations of activity or architectural “terminations” dating to sometime in the late 7th to mid-8th century. Ceramic furnishings also linked at least two elite status burials on the Central Plaza of the site to these deposits. Conjunctive analysis of the deposits, burials, and their contents together with applicable epigraphic history recorded at a nearby major city, Naranjo, suggests that they are the result of and directly reflect successful military action by Naranjo against Buenavista in a.d. 696. An examination of the contexts and epigraphic history concerned; the archaeological grounds for linking the two; and the rich, composite understanding of the deposits and their behavioral, cultural, and historical significance illustrate the rewards and advantages of 21st century Maya archaeology’s new paradig...

The Bounded Real Lemma, i.e., the state-space linear matrix inequality characterization (referred to as Kalman-Yakubovich-Popov or KYP inequality) of when an input/state/output linear system satisfies a dissipation inequality, has recently been studied for infinite-dimensional discrete-time systems in a number of different settings: with or without stability assumptions, with or without controllability/observability assumptions, with or without strict inequalities. In these various settings, sometimes unbounded solutions of the KYP inequality are required while in other instances bounded solutions suffice. In a series of reports we show how these diverse results can be reconciled and unified. This first instalment focusses on the state-space-similarity approach to the bounded real lemma. We shall show how these results can be seen as corollaries of a new State-Space-Similarity theorem for infinite-dimensional linear systems., Comment: 25 pages, to appear in Journal of Operator Theory

We use ceramic and obsidian data from the ancient Maya port site of Vista Alegre to discuss long-distance exchange during the Terminal Classic (c. AD 850–1100) period. This is a time often associated with increased international trade relations and the growth of Chichen Itza as a dominant regional power in the northern Maya lowlands. Critical to the increased volume of international trade were the merchants who transported goods along the coast of Yucatan in large trading canoes. By combining a macroscopic assessment of the ceramics with visual, XRF, and INAA analyses of the obsidian artifacts, we gain insight into the various socioeconomic forces at work moving goods around the Peninsula. Given the paucity of Terminal Classic settlement in the interior Yalahau region, Vista Alegre appears to be an isolated site during this period, approximately 40 km from the nearest coastal neighbor. This allows us to focus on coastal exchange as the sole means by which goods arrived at the site. Our preliminary data contribute to the growing literature on the role market economies played in the Maya area, and the increased opportunities this afforded coastal peoples as circum-peninsular trade became more common through time.

We present a solution of the operator-valued Schur-function realization problem on the right-half plane by developing the corresponding de Branges–Rovnyak canonical conservative simple functional model. This model corresponds to the closely connected unitary model in the disk setting, but we work the theory out directly in the right-half plane, which allows us to exhibit structure which is absent in the disk case. A main feature of the study is that the connecting operator is unbounded, and so we need to make use of the theory of well-posed continuous-time systems. In order to strengthen the classical uniqueness result (which states uniqueness up to unitary similarity), we introduce non-invertible intertwinements of system nodes.

In June 2013 and July 2014, soil samples were collected from unremediated locations within Fukushima prefecture, with special focus on the Fukushima exclusion zone. The soil samples were analyzed for radiocesium by gamma spectroscopy, and then 90Sr by liquid scintillation counting (LSC) after ion specific extraction chromatography. Activity concentrations are compared between sampling years, sampling sites, and soil layers, revealing a general downward trend in activities but also some inconsistencies. Maximum activity concentrations of 137Cs in soil were found in close vicinity of the gate of Fukushima Daichi Nuclear Power Plant and reached up to 106 Bq·kg−1 in 2013. Thirteen months later, these maximum levels were lower by a factor of at least 5. Activity ratios of 90Sr/137Cs were usually around 2 · 10−4, but locally increased to the 10−3 range, and in one spot even to the 10−1 range. Finally, attempts were made to analyze rare radionuclides in environmental samples from this area, in particular tritium (3H) and 60Fe, however no traces were found in the vegetation and soil samples, respectively.

Pairs of reproducing kernel Hilbert spaces associated with multiplicative Stieltjes functions are characterized in terms of shift invariance and structural identities.

A classical result of Sz.-Nagy asserts that a Hilbert-space contraction operator $T$ can be lifted to an isometry $V$. A more general multivariable setting of recent interest for these ideas is the case where (i) the unit disk is replaced by a certain domain contained in ${\mathbb C}^3$ (called the {\em tetrablock}), (ii) the contraction operator $T$ is replaced by a commutative triple $(T_1, T_2, T)$ of Hilbert-space operators having ${\mathbb E}$ as a spectral set (a tetrablock contraction) . The rational dilation question for this setting is whether a tetrablock contraction $(T_1, T_2, T)$ can be lifted to a tetrablock isometry $(V_1, V_2, V)$ (a commutative operator tuple which extends to a tetrablock-unitary tuple $(U_1, U_2, U)$---a commutative tuple of normal operators with joint spectrum contained in the distinguished boundary of the tetrablock). We discuss necessary conditions for a tetrablock contraction to have a tetrablock-isometric lift. We present an example of a tetrablock contraction which does have a tetrablock-isometric lift but violates a condition previously thought to be necessary for the existence of such a lift. Thus the question of whether a tetrablock contraction always has a tetrablock-isometric lift appears to be unresolved at this time., Comment: This is a follow-up paper of the work done in arXiv:1405.4985 [math.FA]. It is accepted for publication in Journal of Functional Analysis

Three major Maya centers recently discovered in the northern part of the uninhabited Calakmul Biosphere Reserve in eastern Campeche, Mexico, provided the first archaeological information obtained in an extensive, formerly unexplored area in the central lowlands of the Yucatan peninsula. Based on ALS (lidar) data, which were acquired for a broader area of 230 km2 and revealed a thoroughly modified and undisturbed archaeological landscape, and on additional information provided by subsequent field surveys and test excavations, we focus on the techniques of water management and agricultural intensification reflected in specific types of landscape modifications. By analyzing their characteristics, distribution and chronology, we discuss their practical functions, which in the region characterized by the lack of permanent water sources were of foremost importance, and further infer the sociopolitical structures involved in their construction and maintenance. We also interpret the significance of these features in Maya worldview and ritual and their role in landscape construction and conceptualization, and show their potential for addressing other fundamental questions of archaeological relevance, including population estimates, settlement dynamics, and the processes that led to the final demise of Classic Maya culture in the central lowlands.

The theory of positive kernels and associated reproducing kernel Hilbert spaces, especially in the setting of holomorphic functions, has been an important tool for the last several decades in a number of areas of complex analysis and operator theory. An interesting generalization of holomorphic functions, namely free noncommutative functions (e.g., functions of square-matrix arguments of arbitrary size satisfying additional natural compatibility conditions), is now an active area of research, with motivation and applications from a variety of areas (e.g., noncommutative functional calculus, free probability, and optimization theory in linear systems engineering). The purpose of this article is to develop a theory of positive kernels and associated reproducing kernel Hilbert spaces for the setting of free noncommutative function theory., Comment: 71 pages

A general interpolation problem with operator argument is studied for functions f from the de Branges-Rovnyak space H(s) associated with an analytic function s mapping the open unit disk D into the closed unit disk. The interpolation condition is taken in the Rosenblum-Rovnyak form f(A)c = b (with a suitable interpretation of f(A)c) for given Hilbert space operator A and two vectors b; c from the same space., Comment: 10 pages