Transversality Properties: Primal Sufficient Conditions

The paper studies 'good arrangements' (transversality properties) of collections of sets in a normed vector space near a given point in their intersection. We target primal (metric and slope) characterizations of transversality properties in the nonlinear setting. The Holder case is given a special attention. Our main objective is not formally extending our earlier results from the Holder to a more general nonlinear setting, but rather to develop a general framework for quantitative analysis of transversality properties. The nonlinearity is just a simple setting, which allows us to unify the existing results on the topic. Unlike the well-studied subtransversality property, not many characterizations of the other two important properties: semitransversality and transversality have been known even in the linear case. Quantitative relations between nonlinear transversality properties and the corresponding regularity properties of set-valued mappings as well as nonlinear extensions of the new transversality properties of a set-valued mapping to a set in the range space due to Ioffe are also discussed.Comment: 33 page

On a nonlinear heat equation associated with Dirichlet -- Robin conditions

This paper is devoted to the study of a nonlinear heat equation associated with Dirichlet-Robin conditions. At first, we use the Faedo -- Galerkin and the compactness method to prove existence and uniqueness results. Next, we consider the properties of solutions. We obtain that if the initial condition is bounded then so is the solution and we also get asymptotic behavior of solutions as. Finally, we give numerical resultsComment: 20 page

An induction theorem and nonlinear regularity models

A general nonlinear regularity model for a set-valued mapping $F:X\times R_+\rightrightarrows Y$, where $X$ and $Y$ are metric spaces, is considered using special iteration procedures, going back to Banach, Schauder, Lusternik and Graves. Namely, we revise the induction theorem from Khanh, J. Math. Anal. Appl., 118 (1986) and employ it to obtain basic estimates for studying regularity/openness properties. We also show that it can serve as a substitution of the Ekeland variational principle when establishing other regularity criteria. Then, we apply the induction theorem and the mentioned estimates to establish criteria for both global and local versions of regularity/openness properties for our model and demonstrate how the definitions and criteria translate into the conventional setting of a set-valued mapping $F:X\rightrightarrows Y$.Comment: 28 page

Willingness to Pay for the Preservation of Lo Go - Xa Mat National Park in Vietnam

Lo Go - Xa Mat National Park has great value in terms of biodiversity but preserving the park is a great challenge for the Vietnamese government. This study estimated the willingness to pay of households to preserve Lo Go - Xa Mat National Park, using the contingent valuation method. We employed the single-bounded dichotomous choice question format to estimate how much households in Ho Chi Minh City were willing to contribute towards a preservation plan for the park. This plan comprised twelve preservation activities and compensating the local communities for their foregone income. The study found that households in Ho Chi Minh City were willing to pay at least VND 6,209 per month for three years for the preservation of Lo Go - Xa Mat National Park. With protest votes included, factors strongly affecting households' willingness to pay were bid amount and the amount of their monthly electricity bill. The education level of the respondents and the number of working people in the household had significant but lesser impact on their willingness to pay. Without protest votes, the bid amount, monthly electricity bill amount and education level of respondents significantly affected willingness to pay. We found that the annualized benefit value of the project was larger than its annualized cost. This indicated that the preservation plan was economically viable. This study does not provide the total value of Lo Go - Xa Mat National Park, but it shows the great value of the park in terms of local households' willingness to pay for its preservation and this is important information for policy-makers in deciding how to protect the park efficiently.willingness to pay, Vietnam

Relationship between the molecular composition, visible light absorption, and health-related properties of smoldering woodsmoke aerosols

Organic aerosols generated from the smoldering combustion of wood critically impact air quality and health for billions of people worldwide; yet, the links between the chemical components and the optical or biological effects of woodsmoke aerosol (WSA) are still poorly understood. In this work, an untargeted analysis of the molecular composition of smoldering WSA, generated in a controlled environment from nine types of heartwood fuels (African mahogany, birch, cherry, maple, pine, poplar, red oak, redwood, and walnut), identified several hundred compounds using gas chromatography mass spectrometry (GCMS) and nano-electrospray high-resolution mass spectrometry (HRMS) with tandem multistage mass spectrometry (MSn). The effects of WSA on cell toxicity as well as gene expression dependent on the aryl hydrocarbon receptor (AhR) and estrogen receptor (ER) were characterized with cellular assays, and the visible mass absorption coefficients (MACvis) of WSA were measured with ultraviolet-visible spectroscopy. The WSAs studied in this work have significant levels of biological and toxicological activity, with exposure levels in both an outdoor and indoor environment similar to or greater than those of other toxicants. A correlation between the HRMS molecular composition and aerosol properties found that phenolic compounds from the oxidative decomposition of lignin are the main drivers of aerosol effects, while the cellulose decomposition products play a secondary role; e.g., levoglucosan is anticorrelated with multiple effects. Polycyclic aromatic hydrocarbons (PAHs) are not expected to form at the combustion temperature in this work, nor were they observed above the detection limit; thus, biological and optical properties of the smoldering WSA are not attributed to PAHs. Syringyl compounds tend to correlate with cell toxicity, while the more conjugated molecules (including several compounds assigned to dimers) have higher AhR activity and MACvis. The negative correlation between cell toxicity and AhR activity suggests that the toxicity of smoldering WSA to cells is not mediated by the AhR. Both mass-normalized biological outcomes have a statistically significant dependence on the degree of combustion of the wood. In addition, our observations support the fact that the visible light absorption of WSA is at least partially due to charge transfer effects in aerosols, as previously suggested. Finally, MACvis has no correlation with toxicity or receptor signaling, suggesting that key chromophores in this work are not biologically active on the endpoints tested

The 'Sphere': A Dedicated Bifurcation Aneurysm Flow-Diverter Device.

We present flow-based results from the early stage design cycle, based on computational modeling, of a prototype flow-diverter device, known as the 'Sphere', intended to treat bifurcation aneurysms of the cerebral vasculature. The device is available in a range of diameters and geometries and is constructed from a single loop of NITINOL(®) wire. The 'Sphere' reduces aneurysm inflow by means of a high-density, patterned, elliptical surface that partially occludes the aneurysm neck. The device is secured in the healthy parent vessel by two armatures in the shape of open loops, resulting in negligible disruption of parent or daughter vessel flow. The device is virtually deployed in six anatomically accurate bifurcation aneurysms: three located at the Basilar tip and three located at the terminus bifurcation of the Internal Carotid artery (at the meeting of the middle cerebral and anterior cerebral arteries). Both steady state and transient flow simulations reveal that the device presents with a range of aneurysm inflow reductions, with mean flow reductions falling in the range of 30.6-71.8% across the different geometries. A significant difference is noted between steady state and transient simulations in one geometry, where a zone of flow recirculation is not captured in the steady state simulation. Across all six aneurysms, the device reduces the WSS magnitude within the aneurysm sac, resulting in a hemodynamic environment closer to that of a healthy vessel. We conclude from extensive CFD analysis that the 'Sphere' device offers very significant levels of flow reduction in a number of anatomically accurate aneurysm sizes and locations, with many advantages compared to current clinical cylindrical flow-diverter designs. Analysis of the device's mechanical properties and deployability will follow in future publications