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The natural boundary is intuitively understood to be the line dividing the bed of a water body from the adjacent land. It is used in many jurisdictions to define the boundary of ownership between a land parcel and a state-owned watercourse. It is typically defined on the ground through observations by a professional surveyor. Predicting changes to the natural boundary has obvious utility (e.g., with climate change); however, its' observational nature does not lend itself to such predictions. This paper uses a case study of a large lake to explore the relationship between shoreline morphology and hydrology, and the elevation of the natural boundary. Significant correlation was found between the natural boundary elevation and average wave power, but not with variables beach slope, sediment type, or presence of vegetation. Below 0.4 W/m of average wave power, the correlation with natural boundary elevation is very weak, suggesting a lower limit of influence. Two process-based methods for estimation of natural boundary change are proposed, one based on the observed statistical relationship between the average wave power and the natural boundary elevation, and another method based on detailed analytical modelling of bottom stress from breaking waves using the Xbeach software (v1.23). Both methods were used to estimate natural boundary change under a hypothetical change in water level regime due to proposed weir upgrades. While observational data are not available to support evaluation, both approaches predict similar changes to the natural boundary despite their significantly different basis. While the modelling approach requires significant analyst and computational effort, the parametric approach is comparatively efficient, making it practical to apply at high resolution over very large shorelines. [ABSTRACT FROM AUTHOR]

The distribution and quantification of water masses on the East China Sea (ECS) shelf is important for identifying and understanding historical climate-driven changes in ocean properties and circulation in the region. We applied an extended Optimum Multiparameter (eOMP) analysis to quantify the relative contribution of water masses using wintertime temperature, salinity, nitrate (NO3−), phosphate (PO43−), and silicate (SiO32−) measurements from a five-cruises dataset spanning from 2013 to 2018. Average ratios (NO3−:PO43−:SiO32− = 47:1:35) derived from field observations were used to correct the equations referring to the chemical parameters. Our analysis indicated that wintertime seawater on the ECS shelf consisted mainly of Changjiang Dilute Water (CDW), Yellow Sea Coastal Water (YSCW), Taiwan Warm Current Water (TWCW), and East China Sea Shelf Water (ECSSW). The results from the eOMP analysis demonstrated the natural boundaries of four water masses during winter. The interannual variability of water masses showed that the CDW distribution was relatively stable in winter, and there was strong anticorrelation between the YSCW and TWCW extents, suggesting that these two water masses mostly displace each other in the north-south direction. [ABSTRACT FROM AUTHOR]

We investigate convergence properties of random Taylor series whose coefficients are ψ-mixing random variables. In particular, we give sufficient conditions such that the circle of the convergence of the series forms almost surely a natural boundary. [ABSTRACT FROM AUTHOR]

In this work, we studied the tourist and recreational resources - relict, unique landscapes of the specially protected natural area of the Sharyn. The work is the result of many years of field research on landscapes and summer field practice in 2019 in the Sharyn River basin, the study and systematization of published scientific materials. 4 key sections were laid along 2 routes. On this basis, foci of landscape diversity were identified: relic tracts of Sarytugai with Sogdian ash (Fraxinus sogdiana Bunge), tracts Kurtogay, Moyyntugay and Temirlik with relict morphological sculptures. A digital thematic map was created on ArtGIS 10.1. The “passport” of the existing tourist routes and the “passport” of the recreational load of the protected areas Sharyn have been completed. To remove the anthropogenic load on the Sharyn Canyon, it was proposed to develop two more routes: "Small Canyon" and "Temirlik tract." The scientific base of the tourist and recreational potential has been created and the feasibility of further development of international tourism has been substantiated.

We survey some recent developments in the analytic theory of multiple Dirichlet series with arithmetical coefficients as numerators. [ABSTRACT FROM AUTHOR]

The main result of this paper describes the meromorphic continuation of a class of Bateman-like totient zeta function associated to a special class of arithmetical multiplicative functions, discovering a comb-like form of the region of meromorphic continuation, and verifying the expected natural boundary by clustering logarithmic type singularities. Then, a standard application of the Selberg-Delange classical method allows us to derive the distribution of values of a class of multivariate multiplicative functions. We also use Balazard-Diamond convolution method to improve in some cases the error term given by Selberg-Delange classical method. [ABSTRACT FROM AUTHOR]

In this work, we studied the tourist and recreational resources - relict, unique landscapes of the specially protected natural area of the Sharyn. The work is the result of many years of field research on landscapes and summer field practice in 2019 in the Sharyn River basin, the study and systematization of published scientific materials. 4 key sections were laid along 2 routes. On this basis, foci of landscape diversity were identified: relic tracts of Sarytugai with Sogdian ash (Fraxinus sogdiana Bunge), tracts Kurtogay, Moyyntugay and Temirlik with relict morphological sculptures. A digital thematic map was created on ArtGIS 10.1. The "passport" of the existing tourist routes and the "passport" of the recreational load of the protected areas Sharyn have been completed. To remove the anthropogenic load on the Sharyn Canyon, it was proposed to develop two more routes: "Small Canyon" and "Temirlik tract." The scientific base of the tourist and recreational potential has been created and the feasibility of further development of international tourism has been substantiated. [ABSTRACT FROM AUTHOR]

This work builds upon previous studies of centered polygonal lacunary functions by presenting proofs of theorems showing how rotational and dihedral mirror symmetry manifest in these lacunary functions at the modulus level. These theorems then provide a general framework for constructing other lacunary functions that exhibit the same symmetries. These investigations enable one to better explore the effects of the gap behavior on the qualitative features of the associated lacunary functions. Further, two renormalized products of centered polygonal lacunary functions are defined and a connection to Ramanunjan’s triangular lacunary series is made via several theorems.

This work investigates centered polygonal lacunary functions restricted from the unit disk onto symmetry angle space which is defined by the symmetry angles of a given centered polygonal lacunary function. This restriction allows for one to consider only the p-sequences of the centered polygonal lacunary functions which are bounded, but not convergent, at the natural boundary. The periodicity of the p-sequences naturally gives rise to a convergent subsequence, which can be used as a grounds for decomposition of the restricted centered polygonal lacunary functions. A mapping of the unit disk to the sphere allows for the study of the line integrals of restricted centered polygonal that includes analytic progress towards closed form representations. Obvious closures of the domain obtained from the spherical map lead to four distinct topological spaces of the “broom topology” type.

Abstract Integer sequences express and capture many important concepts in number theory. They also arise naturally in some parts of dynamical systems, and we will explain some of the questions and relationships that arise in looking at integer sequences from these two perspectives. One of these connections occurs between prime numbers and closed orbits. In algebraic and geometric settings, there are hints of a quite widespread Pólya–Carlson dichotomy. [ABSTRACT FROM AUTHOR]

We study the analytic behavior of adelic versions of Igusa integrals given by integer polynomials defining elliptic curves. By applying results on the meromorphic continuation of symmetric power L-functions and the Sato–Tate conjectures, we prove that these global Igusa zeta functions have some meromorphic continuation until a natural boundary beyond which no continuation is possible. [ABSTRACT FROM AUTHOR]

This paper demonstrates some connections between the coefficients of a Taylor series and singularities of the function. There are many known results of this type, for example, counting the number of poles on the circle of convergence, and doing convergence or overconvergence for f on any arc of holomorphy. A new approach proposed here is that these kinds of results are extended by relaxing the classical conditions for singularities and convergence theorems. This is done by allowing the coefficients to be sufficiently small instead of being zero. [ABSTRACT FROM AUTHOR]

Greenspace is undoubtedly a main component of urban ecosystems. An urban greenspace system should not only include parks and attached greenspace within the city but should also encompass larger areas of greenspace around the city. However, in mega-cities that are undergoing rapid urbanization, intense changes in land use and land cover are occurring as large areas of farmland and forest are built up. In urban agglomerations, urban boundaries can extend beyond administrative boundaries; this process can exert a substantial influence on the index of urban greenspace. In contrast, mountains and rivers may effectively act as natural boundaries for the control of urban sprawl. What are the correlations among metropolitan boundaries, natural boundaries, and urban boundaries (called the “three types of boundary”) and their influence on the level of greenspace? By analyzing Tokyo, New York, London, Paris, Hong Kong, and Shanghai as cases, this study examines the patterns and interrelations among these three types of boundary. Model analysis results indicated that different models of the three types of boundary gave rise to different levels of greenspace. There are benefits to improving the level of greenspace (1) when metropolitan boundaries exceed urban boundaries; (2) when metropolitan boundaries are consistent with natural boundaries; or (3) when farmland around the city can be incorporated into greenspace and made part of the urban GI, which occurred in London and was presumed to contribute to its high figure for per capita greenspace. Furthermore, it was determined that the current administrative boundaries of Shanghai could be optimized by breaking with the administrative boundaries established in 1958 and redrawing its western boundary to conform to natural boundaries. Optimized metropolitan boundaries can facilitate the establishment of larger areas of greenspace, which can increase per capita greenspace, provide new spaces for development, and enhance international competitiveness. [ABSTRACT FROM AUTHOR]

This article introduces and investigates the basic features of a dynamical zeta function for group actions, motivated by the classical dynamical zeta function of a single transformation. A product formula for the dynamical zeta function is established that highlights a crucial link between this function and the zeta function of the acting group. A variety of examples are explored, with a particular focus on full shifts and closely related variants. Amongst the examples, it is shown that there are infinitely many non-isomorphic virtually cyclic groups for which the full shift has a rational zeta function. In contrast, it is shown that when the acting group has Hirsch length at least two, a dynamical zeta function with a natural boundary is more typical. The relevance of the dynamical zeta function in questions of orbit growth is also considered. [ABSTRACT FROM AUTHOR]

In this paper, we study quasi-stationary distributions (QSDs) for one-dimensional diffusions killed at 0, when 0 is a regular boundary and +∞ is a natural boundary. More precisely, we not only give a necessary and sufficient condition for the existence of a QSD, but we also construct all QSDs for the one-dimensional diffusions. Moreover, we give a sufficient condition for R -positivity of the process killed at the origin. This condition is only based on the drift, which is easy to check. [ABSTRACT FROM AUTHOR]

We study analytic properties of certain infinite products of cyclotomic polynomials that generalise some products introduced by Mahler. We characterise those that have the unit circle as a natural boundary and use associated Dirichlet series to obtain their asymptotic behaviour near roots of unity. [ABSTRACT FROM AUTHOR]

This work is an answer to a problem posed by N. Kurokawa and H. Ochiai concerning the natural boundary of meromorphy of a multivariate Euler product of Igusa type. More generally, we introduce and determine the maximal domain of meromorphy of a class of multivariate non-uniform Euler products. [ABSTRACT FROM AUTHOR]

Abstract: We present results and background rationale in support of a Pólya–Carlson dichotomy between rationality and a natural boundary for the analytic behaviour of dynamical zeta functions of compact group automorphisms. [Copyright &y& Elsevier]

Abstract: We present and exploit an analogy between lack of absolutely continuous spectrum for Schrödinger operators and natural boundaries for power series. Among our new results are generalizations of Hecke''s example and natural boundary examples for random power series where independence is not assumed. [Copyright &y& Elsevier]

In the present paper, we study analytic properties of the zeta functions defined by the Euler products over elements in subsets of the set of prime elements. [ABSTRACT FROM AUTHOR]

In this work, a GP method, short for the generalized particle dynamics method, is used to carry on multiscale analysis. The basic assumption of the GP method is that if the basic material structure can be kept the same as the real material at all scales, the multiscale analysis will be more accurate and more effective. Based on this assumption GP divides the simulation region into areas containing particles of different scales, n, where n = 1 is the atomistic scale and higher values of n correspond to the continuum scale. Natural nonlocal boundary conditions via material neighbor link cells are used for a seamless transition between domains of different scales. An inverse mapping method from the deformed particle domain β n into the corresponding atomic domain αn is proposed. All calculations of different scales can be conducted at the corresponding atomic αn domain by the same potential, same parameters, same cutoff radius, and same numerical algorithm. The inverse mapping method is proved mathematically. Governing equations controlling the deformation transition between the particle and atomic domains of a one-dimensional model are derived. Numerical results show that the transition of deformation between the atomistic and particle domains is seamless under various nonuniform loading conditions. The initiation strain and detail evolution patterns of defects (dislocations) at different strain levels for a tensile copper nanowire predicted by the GP method agree well with those obtained by molecular dynamics (MD). The successful comparison indicates that GP, the extended MD method, has a great potential to be used in a large material domain. [ABSTRACT FROM AUTHOR]

We study Ruelle's type zeta and L-functions for a torsion free abelian group Γ of rank ν ≥ 2 defined via an Euler product. It is shown that the imaginary axis is a natural boundary of this zeta function when ν = 2, 4 and 8, and in particular, such a zeta function has no determinant expression. Thus, conversely, expressions like Euler's product for the determinant of the Laplacians of the torus ℝν/Γ defined via zeta regularizations are investigated. Also, the limit behavior of an arithmetic function arising from the Ruelle type zeta function is observed. [ABSTRACT FROM AUTHOR]