Symmetries and exact solutions of KP equation with an arbitrary nonlinear term

The generalized KP (GKP) equations with an arbitrary nonlinear term model and characterize many nonlinear physical phenomena. The symmetries of GKP equation with an arbitrary nonlinear term are obtained. The condition that must satisfy for existence the symmetries group of GKP is derived and also the obtained symmetries are classified according to different forms of the nonlinear term. The resulting similarity reductions are studied by performing the bifurcation and the phase portrait of GKP and also the corresponding solitary wave solutions of GKP
equation are constructed.

Eigenfunctions and fundamental solutions of the fractional Laplace and Dirac operators: the Riemann-Liouville case

In this paper we study eigenfunctions and fundamental solutions for the three parameter fractional Laplace operator $\Delta_+^{(\alpha,\beta,\gamma)}:= D_{x_0^+}^{1+\alpha} +D_{y_0^+}^{1+\beta} +D_{z_0^+}^{1+\gamma},$ where $(\alpha, \beta, \gamma) \in \,]0,1]^3$, and the fractional derivatives $D_{x_0^+}^{1+\alpha}$, $D_{y_0^+}^{1+\beta}$, $D_{z_0^+}^{1+\gamma}$ are in the Riemann-Liouville sense. Applying operational techniques via two-dimensional Laplace transform we describe a complete family of eigenfunctions and fundamental solutions of the operator $\Delta_+^{(\alpha,\beta,\gamma)}$ in classes of functions admitting a summable fractional derivative. Making use of the Mittag-Leffler function, a symbolic operational form of the solutions is presented. From the obtained family of fundamental solutions we deduce a family of fundamental solutions of the fractional Dirac operator, which factorizes the fractional Laplace operator. We apply also the method of separation of variables to obtain eigenfunctions and fundamental solutions.

Detection of mesoscale thermal fronts from 4km data using smoothing techniques: Gradient-based fronts classification and basin scale application

In order to optimize frontal detection in sea surface temperature fields at 4 km resolution, a combined statistical and expert-based approach is applied to test different spatial smoothing of the data prior to the detection process. Fronts are usually detected at 1 km resolution using the histogram-based, single image edge detection (SIED) algorithm developed by Cayula and Cornillon in 1992, with a standard preliminary smoothing using a median filter and a 3 × 3 pixel kernel. Here, detections are performed in three study regions (off Morocco, the Mozambique Channel, and north-western Australia) and across the Indian Ocean basin using the combination of multiple windows (CMW) method developed by Nieto, Demarcq and McClatchie in 2012 which improves on the original Cayula and Cornillon algorithm. Detections at 4 km and 1 km of resolution are compared. Fronts are divided in two intensity classes (“weak” and “strong”) according to their thermal gradient. A preliminary smoothing is applied prior to the detection using different convolutions: three type of filters (median, average and Gaussian) combined with four kernel sizes (3 × 3, 5 × 5, 7 × 7, and 9 × 9 pixels) and three detection window sizes (16 × 16, 24 × 24 and 32 × 32 pixels) to test the effect of these smoothing combinations on reducing the background noise of the data and therefore on improving the frontal detection. The performance of the combinations on 4 km data are evaluated using two criteria: detection efficiency and front length. We find that the optimal combination of preliminary smoothing parameters in enhancing detection efficiency and preserving front length includes a median filter, a 16 × 16 pixel window size, and a 5 × 5 pixel kernel for strong fronts and a 7 × 7 pixel kernel for weak fronts. Results show an improvement in detection performance (from largest to smallest window size) of 71% for strong fronts and 120% for weak fronts. Despite the small window used (16 × 16 pixels), the length of the fronts has been preserved relative to that found with 1 km data. This optimal preliminary smoothing and the CMW detection algorithm on 4 km sea surface temperature data are then used to describe the spatial distribution of the monthly frequencies of occurrence for both strong and weak fronts across the Indian Ocean basin. In general strong fronts are observed in coastal areas whereas weak fronts, with some seasonal exceptions, are mainly located in the open ocean. This study shows that adequate noise reduction done by a preliminary smoothing of the data considerably improves the frontal detection efficiency as well as the global quality of the results. Consequently, the use of 4 km data enables frontal detections similar to 1 km data (using a standard median 3 × 3 convolution) in terms of detectability, length and location. This method, using 4 km data is easily applicable to large regions or at the global scale with far less constraints of data manipulation and processing time relative to 1 km data.

Eigenfunctions and fundamental solutions of the Caputo fractional Laplace and Dirac operators

In this paper, by using the method of separation of variables, we obtain eigenfunctions and fundamental solutions for the three parameter fractional Laplace operator defined via fractional Caputo derivatives. The solutions are expressed using the Mittag-Leffler function and we show some graphical representations for some parameters. A family of fundamental solutions of the corresponding fractional Dirac operator is also obtained. Particular cases are considered in both cases.

Manganese toxicity in Portuguese Cambisols derived from granite: causes, limitations of soil analyses and possible solutions

Cambisols are the major soil type in Portugal. The yield of annual crops in these soils is generally poor, and the situation is aggravated in wet winters. In the south of Portugal, manganese toxicity has been identified as the major cause of poor growth and leaching as the main reason for the negative effect of rainfall observed in Cambisols derived from granite Manganese toxicity also appears to be present in the Cambisols in other regions of Portugal. Manganese toxicity is cross-related to the magnesium concentration, either in the soil solution or in plant shoots. Therefore soil amendment using dolomitic limestone is needed to overcome the problem. Current soil test methods are unable to predict the level of Mn toxicity. However, new approach using the extraction of soil solution is proposed, although further work is needed to fully implement the method.

Investigation into various fungicides and alternative solutions for controlling postharvest diseases in papaya fruit

In Australia, Sportak® (a.i., prochloraz) has been registered since the early 1980's for the postharvest control of both anthracnose and stem-end rots in papaya fruit, despite the persistence of fruit breakdown due to disease during transit and at market destinations. Consequently, the Australian papaya industry has been concerned over the efficacy of prochloraz and whether substitute or alternative solutions were available for better disease control, particularly during times of peak disease pressure. This study therefore investigated the effects of various postharvest treatments for disease control in papaya. Fruit were harvested at colour break from coastal farms in Far North Queensland and treated with commercial rates of various fungicides, including prochloraz, imazalil, thiabendazole and fludioxonil. Additional solutions known to inhibit disease were examined, including chitosan and carnauba wax both with and without ammonium carbonate (AC). Following treatment, fruit were ripened and assessed for quality over their shelf life. Fludioxonil when applied as a hot dip was found to be a more efficacious treatment for control of disease in papaya than prochloraz. The other fungicides were moderately effective, as both thiabendazol and prochloraz exhibited an intermediate response and imazalil was the least effective. Disease severity was lowest in fruit treated with AC followed by chitosan, whilst chitosan delayed degreening. Overall, the study found that hot fludioxonil provided an effective replacement of the currently registered chemical prochloraz, and that alternate solutions such chitosan and AC may also be beneficial, particularly for low chemical input farming systems.

A single theoretical framework for circular features processing in humans: orientation and direction of motion compared

Common computational principles underlie processing of various visual features in the cortex. They are considered to create similar patterns of contextual modulations in behavioral studies for different features as orientation and direction of motion. Here, I studied the possibility that a single theoretical framework, implemented in different visual areas, of circular feature coding and processing could explain these similarities in observations. Stimuli were created that allowed direct comparison of the contextual effects on orientation and motion direction with two different psychophysical probes: changes in weak and strong signal perception. One unique simplified theoretical model of circular feature coding including only inhibitory interactions, and decoding through standard vector average, successfully predicted the similarities in the two domains, while different feature population characteristics explained well the differences in modulation on both experimental probes. These results demonstrate how a single computational principle underlies processing of various features across the cortices.

Effect of diet on phosphine toxicity, rate of development and reproduction of the rice weevil Sitophilus oryzae (Linnaeus)

One of the loci responsible for strong phosphine resistance encodes dihydrolipoamide dehydrogenase (DLD). The strong co-incidence of enzyme complexes that contain DLD, and enzymes that require thiamine as a cofactor, motivated us to test whether the thiamine deficiency of polished white rice could influence the efficacy of phosphine fumigation against insect pests of stored grain. Three strains of Sitophilus oryzae (susceptible, weak and strong resistance) were cultured on white rice (thiamine deficient), brown rice or whole wheat. As thiamine is an essential nutrient, we firstly evaluated the effect of white rice on developmental rate and fecundity and found that both were detrimentally affected by this diet. The mean time to reach adult stage for the three strains ranged from 40 to 43 days on brown rice and 50–52 days on white rice. The mean number of offspring for the three strains ranged from 7.7 to 10.3 per female over a three day period on brown rice and 2.1 to 2.6 on white rice. Growth and reproduction on wheat was similar to that on brown rice except that the strongly resistant strain showed a tendency toward reduced fecundity on wheat. The susceptible strain exhibited a modest increase in tolerance to phosphine on white rice as expected if thiamine deficiency could mimic the effect of the dld resistance mutation at the rph2 locus. The strongly resistant strain did not respond to thiamine deficiency, but this was expected as these insects are already strongly resistant. We failed, however, to observe the expected synergistic increase in resistance due to combining thiamine deficiency with the weakly resistant strain. The lack of interaction between thiamine content of the diet and the resistance genotype in determining the phosphine resistance phenotype suggests that the mode of inhibition of the complexes is a critical determinant of resistance.

Linear non-local diffusion problems in metric measure spaces

The aim of this paper is to provide a comprehensive study of some linear non-local diffusion problems in metric measure spaces. These include, for example, open subsets in ℝN, graphs, manifolds, multi-structures and some fractal sets. For this, we study regularity, compactness, positivity and the spectrum of the stationary non-local operator. We then study the solutions of linear evolution non-local diffusion problems, with emphasis on similarities and differences with the standard heat equation in smooth domains. In particular, we prove weak and strong maximum principles and describe the asymptotic behaviour using spectral methods.

Coastal modelling studies for forecasting and remediation solutions

The coastal area along the Emilia-Romagna (ER), in the Italian side of the northern Adriatic Sea, is considered to implement an unstructured numerical ocean model with the aim to develop innovative tools for the coastal management and a forecasting system for the storm surge risk reduction. The Adriatic Sea has been the focus of several studies because of its peculiar dynamics driven by many forcings acting at basin and local scales. The ER coast is particularly exposed to storm surge events. In particular conditions, winds, tides and seicehs may combine and contribute to the flooding of the coastal area. The global sea level rise expected in the next decades will increase even more the hazard along the ER and Adriatic coast. Reliable Adriatic and Mediterranean scale numerical ocean models are now available to allow the dynamical downscaling of very high-resolution models in limited coastal areas. In this work the numerical ocean model SHYFEM is implemented in the Goro lagoon (named GOLFEM) and along the ER coast (ShyfER) to test innovative solutions against sea related coastal hazards. GOLFEM was succesfully applied to analyze the Goro lagoon dynamics and to assess the dynamical effects of human interventions through the analysis of what-if scenarios. The assessment of storm surge hazard in the Goro lagoon was carried out through the development of an ensemble storm surge forecasting system with GOLFEM using forcing from different operational meteorological and ocean models showing the fundamental importance of the boundary conditions. The ShyfER domain is used to investigate innovative solutions against storm surge related hazard along the ER coast. The seagrass is assessed as a nature-based solution (NBS) for coastal protection under present and future climate conditions. The results show negligible effects on sea level but sensible effects in reducing bottom current velocity.

Access to climate justice: the main procedural hurdles, and possible solutions, within the italian legal framework and the IBA Model Statute

The thesis deals with standing and justiciability in climate litigation against governments and the private sector. The first part addresses the impacts of climate change on human rights, the major developments in international climate law, and the historical reasons for climate litigation. The second part analyses several cases, divided into categories. It then draws to a comparative conclusion with regard to each category. The third part deals with the Italian legal tradition on standing and justiciability – starting from the historical roots of such rules. The fourth part introduces the ‘Model Statute’ drafted by the International Bar Association, arguing that the 'ratio legis' of this proposal could be implemented in Italy or the EU. The thesis develops arguments, based on the existing legal framework, to help plaintiffs establish standing and justiciability in proceedings pending before Italian courts. It further proposes the idea that 'citizen suits' are consistent with the Italian and EU legal tradition and that the EU could rely on citizen suits to privately enforce its climate law and policies under the ‘European Green Deal.’

One-loop energy-momentum tensor in QED with electriclike background

We have obtained nonperturbative one-loop expressions for the mean-energy-momentum tensor and current density of Dirac's field on a constant electriclike back-round. One of the goals of this calculation is to give a consistent description of backreaction in such a theory. Two cases of initial states are considered: the vacuum state and the thermal equilibrium state. First, we perform calculations for the vacuum initial state. In the obtained expressions, we separate the contributions due to particle creation and vacuum polarization. The latter contribution,, are related to the Heisenberg-Euler Lagrangian. Then, we Study the case of the thermal initial state. Here, we separate the contributions due to particle creation, vacuum polarization, and the contributions due to the work of the external field on the particles at the initial state. All these contributions are studied in detail, in different regimes of weak and strong fields and low and high temperatures. The obtained results allow us to establish restrictions on the electric field and its duration under which QED with a strong constant electric field is consistent. Under such restrictions, one can neglect the backreaction of particles created by the electric field. Some of the obtained results generalize the calculations of Heisenberg-Euler for energy density to the case of arbitrary strong electric fields.

Modeling diffraction in free-space optical interconnects by the mode expansion method

Free-space optical interconnects (FSOIs), made up of dense arrays of vertical-cavity surface-emitting lasers, photodetectors and microlenses can be used for implementing high-speed and high-density communication links, and hence replace the inferior electrical interconnects. A major concern in the design of FSOIs is minimization of the optical channel cross talk arising from laser beam diffraction. In this article we introduce modifications to the mode expansion method of Tanaka et al. [IEEE Trans. Microwave Theory Tech. MTT-20, 749 (1972)] to make it an efficient tool for modelling and design of FSOIs in the presence of diffraction. We demonstrate that our modified mode expansion method has accuracy similar to the exact solution of the Huygens-Kirchhoff diffraction integral in cases of both weak and strong beam clipping, and that it is much more accurate than the existing approximations. The strength of the method is twofold: first, it is applicable in the region of pronounced diffraction (strong beam clipping) where all other approximations fail and, second, unlike the exact-solution method, it can be efficiently used for modelling diffraction on multiple apertures. These features make the mode expansion method useful for design and optimization of free-space architectures containing multiple optical elements inclusive of optical interconnects and optical clock distribution systems. (C) 2003 Optical Society of America.

Rifampicin fails to eradicate mature biofilm formed by methicillin-resistant Staphylococcus aureus

INTRODUCTION: Antimicrobial activity on biofilms depends on their molecular size, positive charges, permeability coefficient, and bactericidal activity. Vancomycin is the primary choice for methicillin-resistant Staphylococcus aureus (MRSA) infection treatment; rifampicin has interesting antibiofilm properties, but its effectivity remains poorly defined. METHODS: Rifampicin activity alone and in combination with vancomycin against biofilm-forming MRSA was investigated, using a twofold serial broth microtiter method, biofilm challenge, and bacterial count recovery. RESULTS: Minimal inhibitory concentration (MIC) and minimal bactericidal concentration for vancomycin and rifampicin ranged from 0.5 to 1mg/l and 0.008 to 4mg/l, and from 1 to 4mg/l and 0.06 to 32mg/l, respectively. Mature biofilms were submitted to rifampicin and vancomycin exposure, and minimum biofilm eradication concentration ranged from 64 to 32,000 folds and from 32 to 512 folds higher than those for planktonic cells, respectively. Vancomycin (15mg/l) in combination with rifampicin at 6 dilutions higher each isolate MIC did not reach in vitro biofilm eradication but showed biofilm inhibitory capacity (1.43 and 0.56log10 CFU/ml reduction for weak and strong biofilm producers, respectively; p<0.05). CONCLUSIONS: In our setting, rifampicin alone failed to effectively kill biofilm-forming MRSA, demonstrating stronger inability to eradicate mature biofilm compared with vancomycin.