Root system of singular perturbations of the harmonic oscillator type operators

We analyze perturbations of the harmonic oscillator type operators in a Hilbert space H, i.e. of the self-adjoint operator with simple positive eigenvalues μ k satisfying μ k+1 − μ k ≥ Δ > 0. Perturbations are considered in the sense of quadratic forms. Under a local subordination assumption, the eigenvalues of the perturbed operator become eventually simple and the root system contains a Riesz basis.

A proposed framework to operationalize ESS for the mitigation of soil threats

Despite various research activities in the last decades across the world, many challenges remain to integrate the concept of ecosystem services (ESS) in decision-making, and a coherent approach to assess and value ESS is still lacking. There are a lot of different – often context-specific – ESS frameworks with their own definitions and understanding of terms. Based on a thorough review, the EU FP7 project RECARE (www.recare-project.eu) suggests an adapted framework for ecosystem services related to soils that can be used for practical application in preventing and remediating degradation of soils in Europe. This lays the foundation for the development and selection of appropriate methods to measure, evaluate, communicate and negotiate the services we obtain from soils with stakeholders in order to improve land management. Similar to many ESS frameworks, the RECARE framework distinguishes between an ecosystem and human well-being part. As the RECARE project is focused on soil threats, this is the starting point on the ecosystem part of the framework. Soil threats affect natural capital, such as soil, water, vegetation, air and animals, and are in turn influenced by those. Within the natural capital, the RECARE framework focuses especially on soil and its properties, classified in inherent and manageable properties. The natural capital then enables and underpins soil processes, while at the same time being affected by those. Soil processes, finally, are the ecosystem’s capacity to provide services, thus they support the provision of soil functions and ESS. ESS may be utilized to produce benefits for individuals and human society. Those benefits are explicitly or implicitly valued by individuals and human society. The values placed on those benefits influence policy and decision-making and thus lead to a societal response. Individual (e.g. farmers’) and societal decision making and policy determine land management and other (human) driving forces, which in turn affect soil threats and natural capital. In order to improve ESS with Sustainable Land Management (SLM) – i.e. measures aimed to prevent or remediate soil threats, the services identified in the framework need to be “manageable” (modifiable) for the stakeholders. To this end, effects of soil threats and prevention / remediation measures are captured by key soil properties as well as through bio-physical (e.g. reduced soil loss), socio-economic (e.g. reduced workload) and socio-cultural (e.g. aesthetics) impact indicators. In order to use such indicators in RECARE, it should be possible to associate the changes in soil processes to impacts of prevention / remediation measures (SLM). This requires the indicators to be sensitive enough to small changes, but still sufficiently robust to provide evidence of the change and attribute it to SLM.

Absolute polarity determination of teeth cementum by phase sensitive second harmonic generation microscopy

The absolute sign of local polarity in relation to the biological growth direction has been investigated for teeth cementum using phase sensitive second harmonic generation microscopy (PS-SHGM) and a crystal of 2-cyclooctylamino-5-nitropyridine (COANP) as a nonlinear optic (NLO) reference material. A second harmonic generation (SHG) response was found in two directions of cementum: radial (acellular extrinsic fibers that are oriented more or less perpendicular to the root surface) and circumferential (cellular intrinsic fibers that are oriented more or less parallel to the surface). A mono-polar state was demonstrated for acellular extrinsic cementum. However, along the different parts of cementum in circumferential direction, two corresponding domains were observed featuring an opposite sign of polarity indicative for a bi-polar microscopic state of cellular intrinsic cementum. The phase information showed that the orientation of radial collagen fibrils of cementum is regularly organized with the donor (D) groups pointing to the surface. Circumferential collagen molecules feature orientational disorder and are oriented up and down in random manner showing acceptor or donor groups at the surface of cementum. Considering that the cementum continues to grow in thickness throughout life, we can conclude that the cementum is growing circumferentially in two opposite directions and radially in one direction. A Markov chain type model for polarity formation in the direction of growth predicts D-groups preferably appearing at the fiber front.

Earth system commitments due to delayed mitigation

As long as global CO₂ emissions continue to increase annually, long-term committed Earth system changes grow much faster than current observations. A novel metric linking this future growth to policy decisions today is the mitigation delay sensitivity (MDS), but MDS estimates for Earth system variables other than peak temperature (ΔT max) are missing. Using an Earth System Model of Intermediate Complexity, we show that the current emission increase rate causes a ΔT max increase roughly 3–7.5 times as fast as observed warming, and a millenial steric sea level rise (SSLR) 7–25 times as fast as observed SSLR, depending on the achievable rate of emission reductions after the peak of emissions. These ranges are only slightly affected by the uncertainty range in equilibrium climate sensitivity, which is included in the above values. The extent of ocean acidification at the end of the century is also strongly dependent on the starting time and rate of emission reductions. The preservable surface ocean area with sufficient aragonite supersaturation for coral reef growth is diminished globally at an MDS of roughly 25%–80% per decade. A near-complete loss of this area becomes unavoidable if mitigation is delayed for a few years to decades. Also with respect to aragonite, 12%–18% of the Southern Ocean surface become undersaturated per decade, if emission reductions are delayed beyond 2015–2040. We conclude that the consequences of delaying global emission reductions are much better captured if the MDS of relevant Earth system variables is communicated in addition to current trends and total projected future changes.

Decision strategies for policy decisions under uncertainties: The case of mitigation measures addressing methane emissions from ruminants

Decision strategies aim at enabling reasonable decisions in cases of uncertain policy decision problems which do not meet the conditions for applying standard decision theory. This paper focuses on decision strategies that account for uncertainties by deciding whether a proposed list of policy options should be accepted or revised (scope strategies) and whether to decide now or later (timing strategies). They can be used in participatory approaches to structure the decision process. As a basis, we propose to classify the broad range of uncertainties affecting policy decision problems along two dimensions, source of uncertainty (incomplete information, inherent indeterminacy and unreliable information) and location of uncertainty (information about policy options, outcomes and values). Decision strategies encompass multiple and vague criteria to be deliberated in application. As an example, we discuss which decision strategies may account for the uncertainties related to nutritive technologies that aim at reducing methane (CH4) emissions from ruminants as a means of mitigating climate change, limiting our discussion to published scientific information. These considerations not only speak in favour of revising rather than accepting the discussed list of options, but also in favour of active postponement or semi-closure of decision-making rather than closure or passive postponement.

Operationalizing ecosystem services for the mitigation of soil threats: A proposed framework

Despite numerous research efforts over the last decades, integrating the concept of ecosystem servicesinto land management decision-making continues to pose considerable challenges. Researchers havedeveloped many different frameworks to operationalize the concept, but these are often specific to acertain issue and each has their own definitions and understandings of particular terms. Based on acomprehensive review of the current scientific debate, the EU FP7 project RECARE proposes an adaptedframework for soil-related ecosystem services that is suited for practical application in the preventionand remediation of soil degradation across Europe. We have adapted existing frameworks by integratingcomponents from soil science while attempting to introduce a consistent terminology that is understand-able to a variety of stakeholders. RECARE aims to assess how soil threats and prevention and remediationmeasures affect ecosystem services. Changes in the natural capital’s properties influence soil processes,which support the provision of ecosystem services. The benefits produced by these ecosystem servicesare explicitly or implicitly valued by individuals and society. This can influence decision- and policymak-ing at different scales, potentially leading to a societal response, such as improved land management.The proposed ecosystem services framework will be applied by the RECARE project in a transdisciplinaryprocess. It will assist in singling out the most beneficial land management measures and in identifyingtrade-offs and win–win situations resulting from and impacted by European policies. The framework thusreflects the specific contributions soils make to ecosystem services and helps reveal changes in ecosystemservices caused by soil management and policies impacting on soil. At the same time, the framework issimple and robust enough for practical application in assessing soil threats and their management withstakeholders at various levels.

The Harmonic Oscillator, a Review of Classical and Elementary Quantum Mechanics

The classical harmonic oscillator and an elementary discussion of the quantum mechanical solutions for the harmonic oscillator are discussed.

Guessing Harmonic Oscillator Wavefunctions Using Maple

The guessing of eigenfunctions is not trivial at higher quantum numbers, no matter what the system being considered. Instead of guessing, one can employ a symbolic calculus progam (Maple in this case) to aid in the reasoning process.

The Harmonic Oscillator's Frobenius Solution

The Frobenius solution to the differential equations associated with the harmonic oscillator (QM) is carried out in detail.

Lease Defaults and the Efficient Mitigation of Damages

The traditional law of leases imposed no duty on landlords to mitigate damages in the event of tenant breach, whereas the modern law of leases does. An economic model of leases, in which absentee tenants may or may not intend to breach, shows that the traditional rule promotes tenant investment in the property by discouraging landlord entry. In contrast, the modern rule prevents the property from being left idle by encouraging landlords to enter and re-let abandoned property. The model reflects the historic use of the traditional rule for agricultural leases, where absentee use was valuable, and the emergence of the modern rule for residential leases, where the primary use entails continuous occupation.

Advance P. Chem. Problems (I) Populations, Partition Functions, Particle in Box, Harmonic Oscillators, Angular Momentum and Rigid Rotor

This is a set of P. Chem. problems posed at slightly higher than the normal text book level, for students who are continuing in the study of this subject.

Contractual Difficulties in Environmental Management and the Protection of Biodiversity: The Case of Conservation and Mitigation Banking

This paper offers a principal-agent model of feasible private contracting in mitigation and conservation banking aimed at the protection of natural habitat and bio-diversity of US wetlands and uplands. It is shown that while it is straightforward to design an incentive contract, such a contract may not achieve the federally mandated objective of no net loss of habitat. This is because the minimum payment required as an economic incentive to private agents may be greater than what they should receive for the habitat values that they actually created in the field. This possible problem is shown to derive from nonconvexity in the production possibility set between the biological value of land as natural habitat and in non-habitat uses such as in urban development. The paper concludes with a consideration of several institutional devises that may promote the convergence of private contracting and the attainment of no net loss. These include the payment of subsidies, greater accuracy in the identification of actual quality by the principal, and the use of several incentive alignment devises.

The Driven Harmonic Oscillator in Chemistry

The molecular dynamical simulation of the normal vibrational mode of water which involves H-O-H angle deformation, when driven by an external force, can be used to see how a driven harmonic oscillator, classically, is associated with the infra-red spectrum of water (and the absorption for this particular normal mode).

Molecular Dynamics and the Diatomic Molecule as Harmonic Oscillator and Rigid Rotor

The HCl molecule is simulated (using Maple) in its dynamics, for both vibrational (and implied) rotational motions. A discussion of the center of mass transformations involved is part of the total presentation.

Gravity potential spherical harmonic series

Time variable gravity fields, reflecting variations of mass distribution in the system Earth is one of the key parameters to understand the changing Earth. Mass variations are caused either by redistribution of mass in, on or above the Earth's surface or by geophysical processes in the Earth's interior. The first set of observations of monthly variations of the Earth gravity field was provided by the US/German GRACE satellite mission beginning in 2002. This mission is still providing valuable information to the science community. However, as GRACE has outlived its expected lifetime, the geoscience community is currently seeking successor missions in order to maintain the long time series of climate change that was begun by GRACE. Several studies on science requirements and technical feasibility have been conducted in the recent years. These studies required a realistic model of the time variable gravity field in order to perform simulation studies on sensitivity of satellites and their instrumentation. This was the primary reason for the European Space Agency (ESA) to initiate a study on ''Monitoring and Modelling individual Sources of Mass Distribution and Transport in the Earth System by Means of Satellites''. The goal of this interdisciplinary study was to create as realistic as possible simulated time variable gravity fields based on coupled geophysical models, which could be used in the simulation processes in a controlled environment. For this purpose global atmosphere, ocean, continental hydrology and ice models were used. The coupling was performed by using consistent forcing throughout the models and by including water flow between the different domains of the Earth system. In addition gravity field changes due to solid Earth processes like continuous glacial isostatic adjustment (GIA) and a sudden earthquake with co-seismic and post-seismic signals were modelled. All individual model results were combined and converted to gravity field spherical harmonic series, which is the quantity commonly used to describe the Earth's global gravity field. The result of this study is a twelve-year time-series of 6-hourly time variable gravity field spherical harmonics up to degree and order 180 corresponding to a global spatial resolution of 1 degree in latitude and longitude. In this paper, we outline the input data sets and the process of combining these data sets into a coherent model of temporal gravity field changes. The resulting time series was used in some follow-on studies and is available to anybody interested.