An expansion of the type (@(&ij &(&n~&() = (fr(' (& pl&(&2l&0(@(&p~' @(&n~&p (x, ) Xi is derived, where yi -fl, ci] are labels for infinite-dimensional symmetric tensor representations of the Euclidean conformal group 0 (2@+1, 1), X, =[ l, , -ci], the constants C (y i) are real, and Q)( and u)x have the properties of vacuum expectation values of field products. The starting point is an infinite set of coupled nonlinear integral equations for Euclidean Green's functions in 2h space-time dimensions of the type written some 15 years ago by Fradkin and Symanzik. The Green's functions of the corresponding Gell-Mann-Low limit theory are expanded in conformal partial waves. The dynamical equations imply the existence of poles and factorization of residues in the partial waves as functions of the representation parameters. In proving the validity of the expansion we use some differential relations between partially equivalent exceptional representations of 0& (2 h + 1, 1), established in an earlier paper. This work completes the group-theoretical derivation of the vacuum operator-product expansion undertaken by Mack in 1973.

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ABSTRACT:Lakova, I. and Petrowa, S. 2013. Towards a standard Tithonian to Valanginian calpionellid zonation of the Tethyan Realm. Acta Geologica Polonica, 63 (2), 201-221. Warszawa.A calpionellid zonal scheme is proposed for the Tithonian through Valanginian pelagic carbonates of the Western Balkan Unit, based on the vertical ranges of 57 chitinoidellid and calpionellid species recognized. This zonal scheme consists of calpionellid zones that are widely accepted in the Mediterranean Realm, such as the zones of Chitinoidella, Praetintinnopsella, Crassicollaria, Calpionella, Calpionellopsis, Calpionellites and Tintinnopsella. Subzonal divisions are comparable to those in the Carpathians. Direct correlations between ammonite and calpionellid ranges suggest that the base of the Upper Tithonian corresponds to the FO of Chitinoidella boneti; that of the Upper Berriasian to the FO of the genus Calpionellopsis; and the base and top of the Lower Valanginian to the FO and LO of the genus Calpionellites respectively. Correlations of the calpionellid zonation in the study area with zonations in other areas are discussed.

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The present study is a contribution to the lithostratigraphy of Middle Jurassic strata in the area of the Zimevitsa Plateau (West Balkan Mts, West Bulgaria). Based on its lithological and regional properties, the Dobravitsa Member is distinguished from the surrounding rocks of the Etropole Formation. The new member consists of alternating shales, siltstones and fine-grained sandstones. It also contains abundant siderite and calcite concretions, which are distributed in discrete stratigraphic horizons in both the mudrocks and coarser lithologies. Fossils are extremely rare. Poorly preserved ammonites and belemnites are found only. Based on several ammonite finds, the Dobravitsa Member of the Etropole Formation is assigned to a narrow stratigraphic interval of the lower Bajocian (unlimited, probably lower part of the Witchellia laeviuscula Zone). Although it has restricted lateral distribution, which is exclusively confined to its type-area, the Dobravitsa Member has a proper place in the formal Bulgarian Jurassic lithostratigraphic scheme, as it represents a discernible atypical development of the Etropole Formation in the West Balkan Mts region. Another emphasis of this study is laid on concretions from the Etropole Formation. Besides siderite and calcite concretions, a few examples of iron oxyhydroxide concretions, from localities outside the Zimevitsa Plateau area, are also described. The latter are also an atypical component of the Etropole Formation, which deserves a further special study and systematization, as it implies unknown history of this lithofacies, in both depositional and diagenetic terms.

Magnetostratigraphy, calpionellid and calcareous nannofossil biostratigraphy of the upper Tithonian and lower Berriasian of section Barlya in the West Balkan Mts are herein presented. The studied interval comprises the magnetozones from M21r to M17r, with a large interval of partial remagnetization. It has been directly correlated with a continuous succession of the calpionellid Chitinoidella, Praetintinnopsella, Crassicollaria and Calpionella zones, and with the nannofossil zones from NJT 15b to NK-1. The accumulated evidence in the last twenty years on the magnetostratigraphy, calpionellid and calcareous nannofossil biostratigraphy and events across the J/K boundary in the European Tethys has provoked the authors to plot the main micropalaeontological events against magnetostratigraphic column in order to assess the extent of diachronism of these events. Data from Slovakia, Poland, Italy, Austria, Hungary, France, Spain and Bulgaria has shown specific behaviour of different calpionellid and nannofossil events with respect to the column of the magnetic polarity chrons, which have been considered as ‘isochronous’ or at least less diachronous than the microfossil events. Thus, some rather consistent events have appeared, such as the first occurrences (FOs) of calpionellids Calpionella grandalpina, Crassicollaria brevis, Calpionella minuta and Remaniella ferasini, and the FOs of calcareous nannofossils Nannoconus globulus minor, Hexalithus geometricus, Nannoconus wintereri, Nannoconus steinmannii minor and Nannoconus kamptneri minor. The J/K boundary, as widely accepted, has been traced in section Barlya at the base of the Calpionella alpina Subzone.Financial support from the Synthesys Program at the National History Museum, Stockholm, is gratefully acknowledged.

Fossil chela of an erymid lobster from a single locality of the upper Bajocian in the Western Fore-Balkan Mts (NW Bulgaria) was studied. Two segments of the thoracic appendages, probably belonging to one individual, were described: 1) P1 propodus with partially preserved pollex and dactylus; and 2) P1 carpus and P1 merus attached. These elements of the first pair of pereiopods of a lobster were identified as Eryma compressum (Eudes-Deslongchamps, 1842). Eryma compressum a is well-known taxon from numerous Jurassic localities in Europe but has not been recorded in Bulgaria to date. Therefore, albeit being an isolated finding with only a few elements, the Bulgarian example contributes to the overall record of European erymid faunas from the Middle Jurassic, and especially in Eastern Europe, from where only a few erymids have been reported.