Recurrence relations for polynomial sequences via Riordan matrices

We give recurrence relations for any family of generalized Appell polynomials unifying so some known recurrences of many classical sequences of polynomials. Our main tool to get our goal is the Riordan group. We use the product of Riordan matrices to interpret some relationships between different families of polynomials. Moreover using the Hadamard product of series we get a general recurrence relation for the polynomial sequences associated to the so called generalized umbral calculus.Comment: 41 page

E-Connectedness, Finite Approximations, Shape Theory and Coarse Graining in Hyperspaces

We use upper semifinite hyperspaces of compacta to describe "-connectedness and to compute homology from finite approximations. We find another connection between "- connectedness and the so called Shape Theory. We construct a geodesically complete R-tree, by means of "-components at different resolutions, whose behavior at infinite captures the topological structure of the space of components of a given compact metric space. We also construct inverse sequences of finite spaces using internal finite approximations of compact metric spaces. These sequences can be converted into inverse sequences of polyhedra and simplicial maps by means of what we call the Alexandroff-McCord correspondence. This correspondence allows us to relate upper semifinite hyperspaces of finite approximation with the Vietoris-Rips complexes of such approximations at different resolutions. Two motivating examples are included in the introduction. We propose this procedure as a different mathematical foundation for problems on data analysis. This process is intrinsically related to the methodology of shape theory. Finally this paper reinforces Robins’s idea of using methods from shape theory to compute homology from finite approximations

Coupling far and near tectonic signals in syn-orogenic sediments: The Olvena growth strata (Sierras Marginales, southern Pyrenees)

The Olvena area (Sierras Marginales, southern Pyrenees) provides an outstanding example for studying the relationships between tectonics and sedimentation related to fold-and-thrust systems having shallow décollements. Stratigraphic and sedimentological features allow infer i) the relationship between Oligocene-Miocene locallysourced alluvial fans and a far-sourced wider fluvial system, and ii) the control exerted by tectonics on the stratigraphic architecture. Initially, uplift resulting from folding and thrusting in the Sierras Marginales precluded the entrance through this area into the Ebro basin of a wide fluvial system sourced in internal zones of the Pyrenean chain (including the Axial Zone). A subsiding area was created in the southern front of the Sierras where west-flowing alluvial fans generated, having their source areas in the rejuvenated reliefs. The subsequent cessation of movement of the tectonic structures permitted these reliefs to be subdued and the overpassing of the north-coming fluvial system that progressively covered a wider area. Sequential evolution and stratigraphic architecture evidence thrust emplacement geometry and chronology, including out-of-sequence reactivation of structures and the influence of evaporite flow along the décollement. Although these syn-tectonic deposits belong to the Ebro basin succession, its megasequential evolution differs from the general sequence established for the basin fill, highlighting the importance of differentiating the influence of near-coming sedimentary systems when interpreting basin-scale sequence stratigraphy

Coupling far and near tectonic signals in syn-orogenic sediments: the Olvena growth strata (Sierras Marginales, southern Pyrenees)

The Olvena area (Sierras Marginales, southern Pyrenees) provides an outstanding example for studying the relationships between tectonics and sedimentation related to fold-and-thrust systems having shallow décollements. Stratigraphic and sedimentological features allow infer i) the relationship between Oligocene-Miocene locallysourced alluvial fans and a far-sourced wider fluvial system, and ii) the control exerted by tectonics on the stratigraphic architecture. Initially, uplift resulting from folding and thrusting in the Sierras Marginales precluded the entrance through this area into the Ebro basin of a wide fluvial system sourced in internal zones of the Pyrenean chain (including the Axial Zone). A subsiding area was created in the southern front of the Sierras where west-flowing alluvial fans generated, having their source areas in the rejuvenated reliefs. The subsequent cessation of movement of the tectonic structures permitted these reliefs to be subdued and the overpassing of the north-coming fluvial system that progressively covered a wider area. Sequential evolution and stratigraphic architecture evidence thrust emplacement geometry and chronology, including out-of-sequence reactivation of structures and the influence of evaporite flow along the décollement. Although these syn-tectonic deposits belong to the Ebro basin succession, its megasequential evolution differs from the general sequence established for the basin fill, highlighting the importance of differentiating the influence of near-coming sedimentary systems when interpreting basin-scale sequence stratigraphy

Complementary Riordan arrays

Abstract Recently, the concept of the complementary array of a Riordan array (or recursive matrix) has been introduced. Here we generalize the concept and distinguish between dual and complementary arrays. We show a number of properties of these arrays, how they are computed and their relation with inversion. Finally, we use them to find explicit formulas for the elements of many recursive matrices

Fe-rich microspheres pseudomorphs after pyrite framboids in Holocene fluvial deposits from NE Spain: Relationship with environmental conditions and bacterial activity

Three iron oxides-rich microsphere types (Type I to III) were detected in an Holocene 17 m-thick stratigraphic succession located in the Iberian Range (NE Spain). Lithofacies features indicate that the studied materials were generated in an alluvial-dominated setting, with a channeled area fringed by floodplain zones. During high water levels and high-energy floods, gravels and sands deposited in the active area and in lateral overbank areas. In these lateral areas, mud settling took place when flood decreased and then anoxic conditions could be reached due to microbial oxidation of organic matter and the low permeability of the marly sediment. X-ray diffraction (XRD) analysis of 32 samples and microtextural observation of 10 samples by Field Emission Scanning Electron Microscopy (FESEM) revealed the occurrence of Fe oxi-hydroxides microspheres showing different surficial structure. These microspheres are pseudomorphs after pyrite framboids although the formation of some primary Fe oxy-hydroxides aggregates cannot be rejected. Pyrite framboids genesis in sediments underlying oxic-dysoxic water column would have been favored by anoxic conditions reached in lateral overbank areas after main flooding, involving the activity of Fe reducing bacteria and sulfate-reducing bacteria (SRB), given the high SO 4 = availability provided by the highly mineralized groundwater from the upstream Baños de Ariño spring. Subsequent change to oxic conditions during the exposition of the floodplain enhanced the transformation of pyrite into Fe oxy-hydroxides, as well as in microenvironments around cracks and roots. Pyrite oxidation likely took place with the implication of neutrophilic iron oxidizing Bacteria and Archaea living in microaerophilic conditions, as well as cyanobacteria, given the close association of Fe oxides framboids with microbial features. In addition, pyrite and/or Fe oxi-hydroxides framboids from marl levels could have been incorporated to sand sediments during further overbank flooding episodes. Under these new oxic conditions pyrite oxidation would have been favored and even the formation of primary Fe oxy-hydroxides

Stress evolution and structural inheritance controlling an intracontinental extensional basin: The central-northern sector of the Neogene Teruel Basin

The Teruel Basin is a NNE-SSW trending intracontinental extensional basin located in central-eastern Iberia. It is asymmetrically bounded to the east by a major fault zone, but intrabasinal faults with diverse orientation (NNE-SSW to NE-SW, E-W, or NW-SE) also appear. Offsets of the successive sedimentary units and of two planation surfaces reveal that tectonic activity initiated at the border faults, while intrabasinal ones mainly developed in a later stage. Fractures on a map scale show a prevailing N-S strike in Neogene synrift rocks, while a dense network made of four main fracture sets (NE-SW, E-W to ESE-WNW, N-S and NNW-SSE), likely inherited from Mesozoic rifting stages, is observed in pre-rift units. The results of palaeostress analyses indicate an overall predominance of s3 directions around E-W, although two stress episodes have been distinguished during the Late Miocene-Pleistocene: (i) triaxial extension with s3 E-W; (ii) almost ‘radial’ extension (s1 vertical, s2 ˜ s3) with a somehow prevailing s3 ENE-WSW. A scenario in which the evolving extensional stress field was able to gradually activate major basement structures with different orientation, inherited from previous tectonic events, is proposed as responsible for the evolution and overall pattern of both the eastern active margin and central parts of the central-northern sector of the Teruel Basin

Some evolutionary patterns of palaeokarst developed in Pleistocene deposits (Ebro Basin, NE Spain): Improving geohazard awareness in present-day karst

Pleistocene detrital deposits in the central Ebro Basin frequently show deformation features due mainly to karstification in the underlying Neogene evaporites. In 123 cases, estimation of parameters of shape and minimum volume of materials involved was accomplished. Six of them were analysed in more detail to establish the main processes involved in their genesis and the succession of events. All the deformation features in the selected sites are synsedimentary. To achieve the objectives, intense fieldwork was made applying methods of sedimentology and structural geology. Usually, a complex evolutionary pattern was observed, with evidences of dissolution, sagging, collapse, gravity flow, suffosion, and plastic flow. In a schematic way, three main situations, independent of the age of the analysed deposits, can be distinguished: (a) slow subsidence, (b) collapse, and (c) temporal overlapping of both processes. In the first 2 scenarios, basins with smooth or abrupt borders, respectively, were generated on the land surface. In the third one, slow subsidence was followed by a collapse, located in the area of maximum flexure. These patterns are also observed in present-day dolines. Comparison of direct and indirect parameters between paleodolines and present-day dolines indicates a bigger size of the latter, probably caused by the different conditions of observation. This study helps to know the possibilities in the evolution of mantled karst features, to estimate the volume of material affected by karstification and to improve the knowledge of present-day dolines behaviour. Consequently, study of paleodolines must be considered to achieve a better urban planning in active karstic areas