Fast solitons on star graphs

We define the Schr\"odinger equation with focusing, cubic nonlinearity on one-vertex graphs. We prove global well-posedness in the energy domain and conservation laws for some self-adjoint boundary conditions at the vertex, i.e. Kirchhoff boundary condition and the so called $\delta$ and $\delta'$ boundary conditions. Moreover, in the same setting we study the collision of a fast solitary wave with the vertex and we show that it splits in reflected and transmitted components. The outgoing waves preserve a soliton character over a time which depends on the logarithm of the velocity of the ingoing solitary wave. Over the same timescale the reflection and transmission coefficients of the outgoing waves coincide with the corresponding coefficients of the linear problem. In the analysis of the problem we follow ideas borrowed from the seminal paper \cite{[HMZ07]} about scattering of fast solitons by a delta interaction on the line, by Holmer, Marzuola and Zworski; the present paper represents an extension of their work to the case of graphs and, as a byproduct, it shows how to extend the analysis of soliton scattering by other point interactions on the line, interpreted as a degenerate graph.Comment: Sec. 2 revised; several misprints corrected; added references; 32 page

The public health safety of using human excreta from urine diverting toilets for agriculture: the Philippine experience

To determine the safety of using human excreta in agriculture, an observational study was conducted to determine the length of time necessary to eradicate parasitic ova and pathogenic bacteria in human excreta kept in the storage vaults of urine-diverting dehydration toilets in Cagayan de Oro City, Philippines for ten (10) months, from August 2007 to May 2008. The study was conducted using seven (7) urine-diverting toilets. Baseline data for parasite ova and pathogenic bacteria were taken and duly recorded. Results show that microorganisms do not pose a public health threat if human excreta from UDDT vaults are used in agriculture. However, helminth eggs, particularly those of Ascaris lumbricoides, may still be infective and six months may not be sufficient to dehydrate human feces and render them safe for agricultural use. Secondary treatment is strongly recommended to render human excreta safe for agricultural use

Wave operator bounds for 1-dimensional Schr\"odinger operators with singular potentials and applications

Boundedness of wave operators for Schr\"odinger operators in one space dimension for a class of singular potentials, admitting finitely many Dirac delta distributions, is proved. Applications are presented to, for example, dispersive estimates and commutator bounds.Comment: 16 pages, 0 figure

Initial-boundary value problems for a reaction-diffusion equation

This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in J. Math. Phys. 60, 081509 (2019); doi: 10.1063/1.5118767 and may be found at https://aip.scitation.org/doi/10.1063/1.5118767.A novel approach that utilizes Fokas’s unified transform is employed for studying a reaction-diffusion equation with power nonlinearity formulated either on the half-line or on a finite interval with data in Sobolev spaces. This approach was recently introduced for initial-boundary value problems involving dispersive nonlinear equations such as the nonlinear Schrödinger and the Korteweg-de Vries equations. Thus, the present work extends the new approach from dispersive equations to diffusive ones, demonstrating the universality of the unified transform in the analysis of nonlinear evolution equations on domains with a boundary

An early Cambrian agglutinated tubular lophophorate with brachiopod characters.

The morphological disparity of lophotrochozoan phyla makes it difficult to predict the morphology of the last common ancestor. Only fossils of stem groups can help discover the morphological transitions that occurred along the roots of these phyla. Here, we describe a tubular fossil Yuganotheca elegans gen. et sp. nov. from the Cambrian (Stage 3) Chengjiang Lagerstätte (Yunnan, China) that exhibits an unusual combination of phoronid, brachiopod and tommotiid (Cambrian problematica) characters, notably a pair of agglutinated valves, enclosing a horseshoe-shaped lophophore, supported by a lower bipartite tubular attachment structure with a long pedicle with coelomic space. The terminal bulb of the pedicle provided anchorage in soft sediment. The discovery has important implications for the early evolution of lophotrochozoans, suggesting rooting of brachiopods into the sessile lophotrochozoans and the origination of their bivalved bauplan preceding the biomineralization of shell valves in crown brachiopods

Study of the potential employment of Malvaceae Species in composites materials

The employ of vegetal fibers for textiles and composites represents a great potential in economic and social sustainable development. Some Malvaceae species are considered tropical cosmopolitans, such as from Sida genus. Several species of this genus provide excellent textile bast fibers, which are very similar in qualities to the jute textile fiber. The objective of the present study is present the physicochemical characterization of six Brazilian vegetal fibers: Sida rhombifolia L.; Sida carpinifolia L. f.; Sidastrum paniculatum (L.) Fryxell; Sida cordifolia L.; Malvastrum coromandelianum (L.) Gurck; Wissadula subpeltata (Kuntze) R.E.Fries. Respectively the two first species are from Brazilian Atlantic Forest biome and the four remaining from Brazilian Cerrado biome, despite of present in other regions of the planet. The stems of these species were retted in water at 37oC for 20 days. The fibers were tested in order to determine tensile rupture strength, tenacity, elongation, Young’s modulus, cross microscopic structure, Scanning Electronic Microscopy (SEM), regain, combustion, acid, alkali, organic solvent and cellulase effects, pH of the aqueous extract, Differential Scanning Calorimetry (DSC) and Thermogravimetric Analysis (TGA). The obtained values were compared with those from fibers of recognized applicability in the textile industry including hemp. The results are promising in terms of their employment in thermoset and thermoplastic medium resistance composites.FAPESP (“Fundação de Amparo à Pesquisa do Estado de São Paulo”), CAPES (Coordenação de Aperfeiçoamento de Pessoal de Nível Superior) and CNPq (“Conselho Nacional de Desenvolvimento Científico e Tecnológico”) are gratefully acknowledged. The authors would also like to thank Mr. Ervin Sriubas Jr. and Kellinton José Mendonça Francisco for their technical support

Present and projected future mean radiant temperature for three European cities

Present-day and projected future changes in mean radiant temperature, T mrt in one northern, one mid-, and one southern European city (represented by Gothenburg, Frankfurt, and Porto), are presented, and the concept of hot spots is adopted. Air temperature, T a , increased in all cities by 2100, but changes in solar radiation due to changes in cloudiness counterbalanced or exacerbated the effects on T mrt. The number of days with high T mrt in Gothenburg was relatively unchanged at the end of the century (+1 day), whereas it more than doubled in Frankfurt and tripled in Porto. The use of street trees to reduce daytime radiant heat load was analyzed using hot spots to identify where trees could be most beneficial. Hot spots, although varying in intensity and frequency, were generally confined to near sunlit southeast-southwest facing walls, in northeast corner of courtyards, and in open spaces in all three cities. By adding trees in these spaces, the radiant heat load can be reduced, especially in spaces with no or few trees. A set of design principles for reducing the radiant heat load is outlined based on these findings and existing literature

Evaluation of Effects of Continuous Glucose Monitoring on Physical Activity Habits and Blood Lipid Levels in Persons With Type 1 Diabetes Managed With MDI: An Analysis Based on the GOLD Randomized Trial (GOLD 8)

Background: People with type 1 diabetes generally view it easier to exercise when having continuous information of the glucose levels. We evaluated whether patients with type 1 diabetes managed with multiple daily insulin injections (MDI) exercised more after initiating continuous glucose monitoring (CGM) and whether the improved glycemic control and well-being associated with CGM translates into improved blood lipids and markers of inflammation. Method: The GOLD trial was a randomized cross-over trial over 16 months where patients used either CGM or capillary self-monitoring of blood glucose (SMBG) over six months, with a four-month wash-out period between the two treatment periods. We compared grade of physical activity, blood lipids, apolipoproteins, and high-sensitivity C-reactive protein (hsCRP) levels during CGM and SMBG. Results: There were 116 patients with information of physical activity estimated by the International Physical Activity Questionnaire (IPAQ) during both CGM and SMBG. No changes were found during CGM or SMBG, IPAQ scores 3305 versus 3878 (P =.16). In 136 participants with information of blood lipid levels with no change in lipid-lowering medication during the two treatment periods, HbA1c differed by 4.2 mmol/mol (NGSP 0.39%) between SMBG and CGM treatment (P <.001). No significant changes existed in low-density lipoprotein, high-density lipoprotein, triglycerides, total cholesterol, apolipoprotein A1, apolipoprotein B1, or hsCRP, during CGM and SMBG. Conclusion: Although many patients experience it easier to perform physical activity when monitoring glucose levels with CGM, it does not influence the amount of physical activity in persons with type 1 diabetes. Blood lipids, apolipoprotein, and hsCRP levels were similar during CGM and SMBG