The K–T boundary strata north of Korsnæb, Stevns Klint, Denmark – evolution and geometry revealed in a long, horizontal profile

A 460 m long profile of the Cretaceous–Paleogene (K–T) boundary strata at Stevns Klint was measured by the late Professor A. Rosenkrantz probably in 1944. The measured profile was inherited by Finn Surlyk around 1974 together with other original boundary data. This material was dug up in a long-forgotten drawer in connection with detailed field work by the co-authors on the boundary succession in the late spring and summer of 2021. The profile illustrates the stratigraphy, geometry and palaeotopography of the boundary strata in unprecedented detail. The part of the cliff illustrated in the profile is today partly covered by beach ridges composed of flint rubble but is situated below the finest section of the lower Danian bryozoan mounds exposed at Stevns Klint. This coastal section is situated immediately adjacent to a large limestone quarry and was planned to be quarried away around 1937, but was saved by A. Rosenkrantz who demonstrated its great scientific and educational value to the authorities.

Marketing Scholarship and the Sustainable Development Goals: Thoughts on Moving Forward

This article is a commentary on how marketing scholarship can be more relevant as it tackles the human development challenges presented by the Sustainable Development Goals (SDGs). The commentary argues that as businesses are transforming themselves into purpose-driven organizations, marketing needs to be a part of that transformation. SDG 1 No Poverty and SDG 12 Sustainable Consumption and Production are discussed within the article. The commentary also tackles the institutional barriers that work against path-breaking SDG marketing scholarship: normative promotion and publication expectations along with the practitioner-academic research divide. Without realigning the incentives that reward original, boundary-spanning SDG marketing scholarship, the marketing discipline will be stuck in a cycle of rewarding one behavior while hoping for another.

Local Dynamics of Logistic Equation with Delay and Diffusion

The behavior of all the solutions of the logistic equation with delay and diffusion in a sufficiently small positive neighborhood of the equilibrium state is studied. It is assumed that the Andronov–Hopf bifurcation conditions are met for the coefficients of the problem. Small perturbations of all coefficients are considered, including the delay coefficient and the coefficients of the boundary conditions. The conditions are studied when these perturbations depend on the spatial variable and when they are time-periodic functions. Equations on the central manifold are constructed as the main results. Their nonlocal dynamics determines the behavior of all the solutions of the original boundary value problem in a sufficiently small neighborhood of the equilibrium state. The ability to control the dynamics of the original problem using the phase change in the perturbing force is set. The numerical and analytical results regarding the dynamics of the system with parametric perturbation are obtained. The asymptotic formulas for the solutions of the original boundary value problem are given.

Simulation of J-Solution Solving Process of Navier–Stokes Equation

To avoid grid degradation, the numerical analysis of the j-solution of the Navier–Stokes equation has been studied. The Navier–Stokes equations describe the motion of viscous fluid substances. On the basis of the advantages and disadvantages of the Navier–Stokes equations, the incompressible terms and the nonlinear terms are separated, and the original boundary conditions satisfying the j-solution of the Navier–Stokes equation are analyzed. Secondly, the development of a computational grid has been introduced; the turbulence model has also been described. The fluid form and the initial value of the j-solution of the Navier–Stokes equation are combined. The original boundary conditions are solved by a computer, and the nonlinear turbulence equations are derived, which control the fluid flow. The simulation of the fine grid is comprehended to analyze the research outcome. Simulation analysis is carried out to generate multiblock-structured grids with high quality. The j-solution on the grid points is the j-solution that can be used with a fewer number of meshes under the same conditions. The proposed work is easy to implement, and it consumes lesser memory. The results obtained are able to avoid mesh degradation skillfully, and the generated mesh exhibits the characteristics of smoothness, orthogonality, and controllability, which eventually improves the calculation accuracy.

Multipartite entanglement and topology in holography

Starting from the entanglement wedge of a multipartite mixed state we describe a purification procedure which involves the gluing of several copies. The resulting geometry has non-trivial topology and a single oriented boundary for each original boundary region. In the purified geometry the original multipartite entanglement wedge cross section is mapped to a minimal surface of a particular non-trivial homology class. In contrast, each original bipartite entanglement wedge cross section is mapped to the minimal wormhole throat around each boundary. Using the bit thread formalism we show how maximal flows for the bipartite and multipartite entanglement wedge cross section can be glued together to form maximal multiflows in the purified geometry. The defining feature differentiating the flows is given by the existence of threads which cross between different copies of the original entanglement wedge. Together these demonstrate a possible connection between multipartite entanglement and the topology of holographic spacetimes.

Uniform Approximation to the Solution of a Singularly Perturbed Boundary Value Problem with an Initial Jump

In this study, a third-order linear integro-differential equation with a small parameter at two higher derivatives was considered. An asymptotic expansion of the solution to the boundary value problem for the considered equation is constructed by considering the phenomenon of an initial jump of the second degree zeroth order on the left end of a given segment. The asymptotics of the solution has been sought in the form of a sum of the regular part and the part of the boundary layer. The terms of the regular part are defined as solutions of integro-differential boundary value problems, in which the equations and boundary conditions contain additional terms, called the initial jumps of the integral terms and solutions. Boundary layer terms are defined as solutions of third-order differential equations with initial conditions. A theorem on the existence, uniqueness, and asymptotic representation of a solution is presented along with an asymptotic estimate of the remainder term of the asymptotics. The purpose of this study is to construct a uniform asymptotic approximation to the solution to the original boundary value problem over the entire considered segment.

About one method for replacing variables for a wavean equation describing vibrations of systems with moving boundaries

An analytical method for solving the wave equation describing the oscillations of systems with moving boundaries is considered. By replacing variables that set boundaries and leave the equation invariant, the original boundary value problem is reduced to a system of functional – difference equations that can be solved using forward and reverse methods. The inverse method is described, which allows us to apply sufficiently diverse laws of boundary motion to the laws obtained from the solution of the inverse problem. New partial solutions for a fairly wide range of boundary motion laws are obtained. A direct asymptotic method for approximating the solution of a functional equation is considered. The errors of the approximate method are estimated depending on the speed of the border movement.

Wavelet Methods and Adaptive Grids in One-Dimensional Movable Boundary Problems

Adaptive wavelet collocation methods use wavelet transform and filtering to generate adaptive grids. However, if the boundary moves, the grid becomes aberrant. It baffles wavelet transform and makes the adaptive wavelet methods lose advantages on computational efficiency. This paper develops a series of methods or skills to effectively perform wavelet transform and to generate adaptive grids for one-dimensional movable boundary problems. The methods remain the original inner grid points and keep the grid in the original-nested structure, in order to remain scanty during the whole computing process. For boundary extending, the adaptive wavelet program begins to run on the very new grid beyond the original boundary once it reaches a nested structure, which is called the Intermittent Adaptive Method as a consequence. If the boundary extends tremendously, the new nested grids can be combined to a greater nested grid for further efficiency, which is named the Grid Combine Method. While for boundary contracting, a fictitious boundary is addressed to replace the original boundary that will recede, so wavelet transform can be successfully performed on the original nested grid. Finally, two numerical tests, local features moving and gas gun, were resolved and discussed to show the evolution process of the adaptive grids with the boundaries moving. For boundary contracting, the valid points decrease because the computation domain recedes; while for boundary extending, the valid point numbers vary between a range that almost remains unchanged.

The Analysis of Leading Edge Deformations on Turbomachine Blades

With recent advancements in the development of material and manufacturing technology, the leading edge geometry of turbomachine blades has attracted widespread attention. “Sharp” leading edges always have a better aerodynamic performance, though it is prone to deformations easily. Thus, flat plates and real compressor cascades with different leading edge deformations were investigated to study the influence, which is applicable for thin blades at low speeds. Different boundary layer characteristics, including the velocity profile, transition process, and loss, are compared. The results show that there are several kinds of contradictory influence mechanisms and that the final phenomenon is closely related to the condition of the original boundary layer. In low turbulence, with large and laminar separation, the deformations can suppress separation and decrease loss. In high turbulence, with short and transitional separation, deformations can promote the transition process and increase the loss. The sensitivities of different the original leading edge shapes are also compared. This indicates that a good design always has a better robustness at low turbulence values, while it is worse at high turbulence values. The cascade experiment and simulation show that the deformation influence is similar to flat plates and that it is enlarged near the hub, which affects the corner separation.

Re-establishment of Property Boundary using Geomatics Techniques

This study examined a parcel of land situated at Isheri-Olofin Community in Shomolu local government area of Lagos State whose boundary locations and lines have been obliterated with a view of re-establishing them to the required accuracy and standard using Geomatics techniques. The reconnaissance survey of the study area was carried out, and three (3) out of twenty (20) property boundary beacons were identified. The in situ check performed on the three beacons showed that they were in their original boundary locations. The three property beacons were used to relocate the positions of the remaining seventeen obliterated beacons using Geomatics instruments and conventional methods. The seventeen property beacons were re-established. In order to determine the accuracy of the re-established boundary beacons, a perimeter survey was carried out with a closed traverse method, and it commenced from three government control beacons which were within the study area. The in situ check of the three government control beacons was carried out prior to the commencement of the theodolite traversing. The acquired data were processed, the accuracy of the boundary survey was computed, the processed data was modelled using AutoCAD software and the property boundary plan was produced. The results of the study revealed that three of the property boundaries were in their original locations and seventeen (17) of them were obliterated. The obliterated property beacons in the study area were successfully re-established to the required standard and accuracy. The accuracy of the entire property boundary, which was within the allowable accuracy limits for 3rd order traverse survey, was 1:56,470. This indicates that the obliterated beacons were re-established accurately, their boundary locations and lines were well defined. The property boundary plan, which shows the twenty boundary beacons and contains mathematical and documentary evidence for the property description of the study area was produced.