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In this monograph we consider the general setting of conformal graph directed Markov systems modeled by countable state symbolic subshifts of finite type. We deal with two classes of such systems: attracting and parabolic. The latter being treated by means of the former. We prove fairly complete asymptotic counting results for multipliers and diameters associated with preimages or periodic orbits ordered by a natural geometric weighting. We also prove the corresponding Central Limit Theorems describing the further features of the distribution of their weights. These results have direct applications to a wide variety of examples, including the case of Apollonian Circle Packings, Apollonian Triangle, expanding and parabolic rational functions, Farey maps, continued fractions, Mannenville-Pomeau maps, Schottky groups, Fuchsian groups, and many more. This gives a unified approach which both recovers known results and proves new results. Our new approach is founded on spectral properties of complexified Ruelle–Perron–Frobenius operators and Tauberian theorems as used in classical problems of prime number theory.

Atmospheric carbon monoxide (CO) concentrations have been decreasing since 2000, as observed by both satellite- and ground-based instruments, but global bottom-up emission inventories estimate increasing anthropogenic CO emissions concurrently. In this study, we use a multi-species atmospheric Bayesian inversion approach to attribute satellite-observed atmospheric CO variations to its sources and sinks in order to achieve a full closure of the global CO budget during 2000–2017. Our observation constraints include satellite retrievals of the total column mole fraction of CO, formaldehyde (HCHO), and methane (CH4) that are all major components of the atmospheric CO cycle. Three inversions (i.e., 2000–2017, 2005–2017, and 2010–2017) are performed to use the observation data to the maximum extent possible as they become available and assess the consistency of inversion results to the assimilation of more trace gas species. We identify a declining trend in the global CO budget since 2000 (three inversions are broadly consistent during overlapping periods), driven by reduced anthropogenic emissions in the US and Europe (both likely from the transport sector), and in China (likely from industry and residential sectors), as well as by reduced biomass burning emissions globally, especially in equatorial Africa (associated with reduced burned areas). We show that the trends and drivers of the inversion-based CO budget are not affected by the inter-annual variation assumed for prior CO fluxes. All three inversions contradict the global bottom-up inventories in the world's top two emitters: for the sign of anthropogenic emission trends in China (e.g., here -0.8±0.5 % yr−1 since 2000, while the prior gives 1.3±0.4 % yr−1) and for the rate of anthropogenic emission increase in South Asia (e.g., here 1.0±0.6 % yr−1 since 2000, smaller than 3.5±0.4 % yr−1 in the prior inventory). The posterior model CO concentrations and trends agree well with independent ground-based observations and correct the prior model bias. The comparison of the three inversions with different observation constraints further suggests that the most complete constrained inversion that assimilates CO, HCHO, and CH4 has a good representation of the global CO budget, and therefore matches best with independent observations, while the inversion only assimilating CO tends to underestimate both the decrease in anthropogenic CO emissions and the increase in the CO chemical production. The global CO budget data from all three inversions in this study can be accessed from https://doi.org/10.6084/m9.figshare.c.4454453.v1 (Zheng et al., 2019).

This paper is an interval dynamics counterpart of three theories founded earlier by the authors, S. Smirnov and others in the setting of the iteration of rational maps on the Riemann sphere: the equivalence of several notions of non-uniform hyperbolicity, Geometric Pressure, and Nice Inducing Schemes methods leading to results in thermodynamical formalism. We work in a setting of generalized multimodal maps, that is smooth maps

Gravity inversion quantitatively provides a 3D model of density contrasts, significantly enhancing the information extracted from acquired data. However, the inherent non-uniqueness of inversion poses challenges in precisely determining the boundaries of anomalous bodies. We have developed an iterative algorithm of gravity inversion that reconstructs the geometric features of the anomalous bodies by discretizing the 3D interpretation model with vertical and juxtaposed prism cells. These prisms incorporate sheet-like initial models which are typically derived from prior information or imaging results. This study proposed a new parameter, the Thickness Factor (TF), which is determined by the thickness of the prism cells under the assumption of homogeneous anomalous bodies. The TF establishes an approximate linear relationship between the source geometry and gravity anomalies, enabling the reconstruction of the source geometry to be formulated as a linear optimization problem. The approach demonstrates the potential for target inversion in the presence of multiple causative sources in synthetic cases and shows insensitivity to noise signals and reliability in reconstructing the geometry of complex sources. The proposed method is then applied to real data from the Galinge iron ore deposit in Northwest China and the drilling data is used as prior information. The inversion results are consistent with previous drilling interpretations and allow a rough estimation of the volume of the ore bodies.

We study conformal symmetry breaking differential operators which map differential forms on

An inversion sequence of length$n$is an integer sequence$e=e_{1}e_{2}\\dots e_{n}$such that$0\\leq e_{i}

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