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Utilizing the gauge framework, software under development at Baylor University, we explicitly construct all layer 1 weakly coupled free fermionic heterotic string (WCFFHS) gauge models up to order 32 in four to ten large spacetime dimensions. These gauge models are well suited to large scale systematic surveys and, while they offer little phenomenologically, are useful for understanding the structure of the WCFFHS region of the string landscape. Herein, we present the gauge groups statistics for this swath of the landscape for both supersymmetric and non-supersymmetric models.

In this paper, we use corrected $f(R)$ gravitational model which is a polynomial function with a logarithmic term. We employ the slow-roll conditions and obtain the number of cosmological parameters. This helps us to verify the swampland conjectures which guarantees validation of low energy quantum field theory. The obtained results show that the corresponding model is consistent with the swampland conjectures. Also, the upper and lower limits of the parameter $n$ are, respectively, 0.15 and 0.0033. Finally, by using scalar spectrum index $n_s$ and tensor-to-scalar ratio $r$ relations and comparing with the Planck 2018 data, we obtain the coefficients $\alpha$, $\beta$ and $\gamma$. Also, the corresponding results are constructed by several figures, literature and also Planck 2018 data.

Analytical (rational) mechanics is the mathematical structure of Newtonian deterministic dynamics developed by D'Alembert, Lagrange, Hamilton, Jacobi, and many other luminaries of applied mathematics. Diffusion as a stochastic process of an overdamped individual particle immersed in a fluid, initiated by Einstein, Smoluchowski, Langevin and Wiener, has no momentum since its path is nowhere differentiable. In this exposition, we illustrate how analytical mechanics arises in stochastic dynamics from a randomly perturbed ordinary differential equation dX_t = b(X_t)dt+ϵdW_t, where W_t is a Brownian motion. In the limit of vanishingly small ϵ, the solution to the stochastic differential equation other than are all rare events. However, conditioned on an occurrence of such an event, the most probable trajectory of the stochastic motion is the solution to Lagrangian mechanics with and Hamiltonian equations with H(p, q) = ‖p‖²+b(q)⋅p. Hamiltonian conservation law implies that the most probable trajectory for a "rare" event has a uniform "excess kinetic energy" along its path. Rare events can also be characterized by the principle of large deviations which expresses the probability density function for X_t as f(x, t) = e^{-u(x, t)/ϵ}, where u(x, t) is called a large-deviation rate function which satisfies the corresponding Hamilton–Jacobi equation. An irreversible diffusion process with ∇×b≠0 corresponds to a Newtonian system with a Lorentz force . The connection between stochastic motion and analytical mechanics can be explored in terms of various techniques of applied mathematics, for example, singular perturbations, viscosity solutions and integrable systems.

The existence of a new ultraviolet scale Λ = gM_P for effective theories with gravity and U(1) gauge fields has recently been conjectured as a possible criterion for distinguishing parts of the swampland from the string landscape. Here we discuss a possible phenomenological signature of this scale, for electromagnetic fields, in astrophysical observations.

To further explore the specific application of nonlinear system in the construction of landscape architecture and promote the parametric development of landscape design, in this exploration, based on the digital elevation model (DEM) and nonlinear algorithm theory, the road selection scheme using cost distance algorithm and path distance algorithm is explored. The results suggest that there are obvious differences between cost distance algorithm and path distance algorithm in the consideration of parameters in use. The path distance algorithm needs to further consider the influence of surface grid and vertical system parameters. Environmental factors and different classification methods have great influence on road selection. When the limit value is greater than $\pm 30^{\circ }$, there is no obvious change in road selection. However, when SLOPE values are $15^{\circ }$, $30^{\circ }$ and $45^{\circ }$, respectively, the difference in road selection is small, and the application effect is good. This exploration can provide the sufficient reference for the follow-up study of landscape road selection.

Aggregate quarrying plays an important role in the local economy of the UK's national parks, providing local jobs and expenditure on local services. There are also adverse local impacts from traffic, dust, noise and blasting. However, it is the status of the parks as crucial features of the nation's landscape capital that increases the significance of localised landscape impacts to a level which outweighs any benefits that quarrying provides. This article is based upon commissioned research into the impact of quarrying on the national parks and assesses those impacts against the functions of the parks as nationally important designated landscapes.

The settlements of the Supe society, with Caral as its most prominent and known example, display a number of interesting characteristics. The buildings of these settlements appear to be oriented in such a way that they include references to not only the local landscape, notably the Supe Valley floor, but also the sky, notably the Moon. In this chapter, we address this phenomenology and try to answer the question of whether the inhabitants of this valley had a choice among the different possible orientations of the river flow. The answer provides an interesting result that might also be applied to other riverine cultures, such as ancient Egypt and its river, the Nile.

The interaction of human cultures and the built environment allows a wide range of interpretations and has been studied inside the domain of many disciplines. This paper discusses three interpretations descending from a systemic approach to the question:

- architecture as an "emergence" of the settlement system;

- place (and space) as an "accumulator" of time and a "flux" of systems;

- landscape as one representation/description of the human settlement.

Architecture emerges as a new physical conformation or layout, or as a change in a specific site, arising from actions and representations of political, religious, economical or social powers, being shaped at all times by the material culture belonging to a specific time and place in the course of human evolution.

Any inhabited space becomes over time a place as well as a landscape, i.e. a representation of the settlement and a relationship between setting and people. Therefore, any place owns a landscape which, in turn, is a system of physical systems; it could be defined as a system of sites that builds up its own structure stemming from the orographical features and the geometry of land surfaces that set out the basic characters of its space.