GEVREY SOLVABILITY AND GEVREY REGULARITY IN DIFFERENTIAL COMPLEXES ASSOCIATED TO LOCALLY INTEGRABLE STRUCTURES

In this work we study some properties of the differential complex associated to a locally integrable (involutive) structure acting on forms with Gevrey coefficients. Among other results we prove that, for such complexes, Gevrey solvability follows from smooth solvability under the sole assumption of a regularity condition. As a consequence we obtain the proof of the Gevrey solvability for a first order linear PDE with real-analytic coefficients satisfying the Nirenberg-Treves condition (P).

Toeplitz operators on Bergman spaces with locally integrable symbols

We study the boundedness of Toeplitz operators $T_a$ with locally integrable symbols on Bergman spaces $A^p(\mathbb{D})$, $1 < p < \infty$. Our main result gives a sufficient condition for the boundedness of $T_a$ in terms of some ``averages'' (related to hyperbolic rectangles) of its symbol. If the averages satisfy an ${o}$-type condition on the boundary of $\mathbb{D}$, we show that the corresponding Toeplitz operator is compact on $A^p$. Both conditions coincide with the known necessary conditions in the case of nonnegative symbols and $p=2$. We also show that Toeplitz operators with symbols of vanishing mean oscillation are Fredholm on $A^p$ provided that the averages are bounded away from zero, and derive an index formula for these operators.

Water wave scattering by finite arrays of circular structures

The scattering of small amplitude water waves by a finite array of locally axisymmetric structures is considered. Regions of varying quiescent depth are included and their axisymmetric nature, together with a mild-slope approximation, permits an adaptation of well-known interaction theory which ultimately reduces the problem to a simple numerical calculation. Numerical results are given and effects due to regions of varying depth on wave loading and free-surface elevation are presented.

On Ito's formula for elliptic diffusion processes

Bardina and Jolis [Stochastic process. Appl. 69 (1997) 83-109] prove an extension of Ito's formula for F(Xt, t), where F(x, t) has a locally square-integrable derivative in x that satisfies a mild continuity condition in t and X is a one-dimensional diffusion process such that the law of Xt has a density satisfying certain properties. This formula was expressed using quadratic covariation. Following the ideas of Eisenbaum [Potential Anal. 13 (2000) 303-328] concerning Brownian motion, we show that one can re-express this formula using integration over space and time with respect to local times in place of quadratic covariation. We also show that when the function F has a locally integrable derivative in t, we can avoid the mild continuity condition in t for the derivative of F in x.

A mass-transportation approach to a one dimensional fluid mechanics model with nonlocal velocity

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Darboux-Egoroff metrics, rational Landau-Ginzburg potentials and the Painleve VI equation

We present a class of three-dimensional integrable structures associated with the Darboux-Egoroff metric and classical Euler equations of free rotations of a rigid body. They are obtained as canonical structures of rational Landau-Ginzburg potentials and provide solutions to the Painleve VI equation.

Polyelectrolytes and their counterions studied by EPR spectroscopy

In this thesis methods of EPR spectroscopy were used to investigate polyion-counterion interactions in polyelectrolyte solutions. The fact that EPR techniques are local methods is exploited and by employing spin-carrying (i.e., EPR-active) probe ions it is possible to examine polyelectrolytes from the counterions’ point of view. It was possible to gain insight into i) the dynamics and local geometry of counterion attachment, ii) conformations and dynamics of local segments of the polyion in an indirect manner, and iii) the spatial distribution of spin probe ions that surround polyions in solution. Analysis of CW EPR spectra of dianion nitroxide spin probe Fremy’s salt (FS, potassium nitrosodisulfonate) in solutions of cationic PDADMAC polyelectrolyte revealed that FS ions and PDADMAC form transient ion pairs with a lifetime of less than 1 ns. This effect was termed as dynamic electrostatic attachment (DEA). By spectral simulation taking into account the rotational dynamics as a uniaxial Brownian reorientation, also the geometry of the attached state could be characterized. By variation of solvent, the effect of solvent viscosity and permittivity were investigated and indirect information of the polyelectrolyte chain motion was obtained. Furthermore, analysis of CW EPR data also indicates that in mixtures of organic solvent/water PDADMAC chains are preferentially solvated by the organic solvent molecules, while in purely aqueous mixtures the PDADMAC chain segments were found in different conformations depending on the concentration ratio R of FS counterions to PDADMAC repeat units.Broadenings in CW EPR spectra of FS ions were assigned to spin-exchange interaction and hence contain information on the local concentrations and distributions of the counterions. From analysis of these broadenings in terms of a modified cylindrical cell approach of polyelectrolyte theory, radial distribution functions for the FS ions in the different solvents were obtained. This approach breaks down in water above a threshold value of R, which again indicates that PDADMAC chain conformations are altered as a function of R. Double electron-electron resonance (DEER) measurements of FS ions were carried out to probe the distribution of attached counterions along polyelectrolyte chains. For a significant fraction of FS spin probes in solution with a rigid-rod model polyelectrolyte containing charged Ru2+-centers, a bimodal distance distribution was found that nicely reproduced the spacings of direct and next-neighbor Ru2+-centers along the polyelectrolyte: 2.35 and 4.7 nm. For the system of FS/PDADMAC, DEER data could be simulated by assuming a two-state distribution of spin probes, one state corresponding to a homogeneous (3-dimensional) distribution of spin probes in the polyelectrolyte bulk and the other to a linear (1-dimensional) distribution of spin probes that are electrostatically condensed along locally extended PDADMAC chain segments. From this analysis it is suggested that the PDADMAC chains form locally elongated structures of a size of at least ~5 nm.

Comparing time-varying autoregressive structures of locally stationary processes

In this paper, a novel statistical test is introduced to compare two locally stationary time series. The proposed approach is a Wald test considering time-varying autoregressive modeling and function projections in adequate spaces. The covariance structure of the innovations may be also time- varying. In order to obtain function estimators for the time- varying autoregressive parameters, we consider function expansions in splines and wavelet bases. Simulation studies provide evidence that the proposed test has a good performance. We also assess its usefulness when applied to a financial time series.

The structures underlying soliton solutions in integrable hierarchies

We point out that a common feature of integrable hierarchies presenting soliton solutions is the existence of some special ''vacuum solutions'' such that the Lax operators evaluated on them, lie in some abelian subalgebra of the associated Kac-Moody algebra. The soliton solutions are constructed out of those ''vacuum solitons'' by the dressing transformation procedure.

Layout and material gradation in topology optimization of functionally graded structures: a global-local approach

By means of continuous topology optimization, this paper discusses the influence of material gradation and layout in the overall stiffness behavior of functionally graded structures. The formulation is associated to symmetry and pattern repetition constraints, including material gradation effects at both global and local levels. For instance, constraints associated with pattern repetition are applied by considering material gradation either on the global structure or locally over the specific pattern. By means of pattern repetition, we recover previous results in the literature which were obtained using homogenization and optimization of cellular materials.

Prognostic factors in locally advanced colon cancer treated by extended resection

The impact of clinical, pathologic, and surgical variables on the postoperative morbidity, mortality, and survival of patients undergoing extended resections of colon carcinoma were evaluated. METHODS: The medical records of 95 patients who underwent extended resections for colon carcinoma between 1953 and 1996 were reviewed. In all cases, in addition to colectomy, 1 or more organs and/or structures were resected en bloc due to a macroscopically based suspicion of tumor invasion. The clinical, pathologic, and surgical parameters were analyzed. Overall survival rates were analyzed according to the method of Kaplan and Meier. Multivariate analysis was performed using the Cox proportional hazards model. RESULTS: Eighty-six patients were treated by curative surgeries and the remaining by palliative resections. Invasion of the organs and/or adjacent structures and regional lymph nodes was found microscopically in 48 and 31 patients, respectively. The median follow-up without postoperative mortality was 47.7 months. The 5-year overall survival rates was 52.6%. The 5-year overall survival rates for patients undergoing curative and palliative surgeries was 58.3% and 0%, respectively. The mean survival time in the palliative surgery group was 3.1 months. Multivariate analysis showed that Karnofsky performance status was strongly related to the risk of postoperative complications (P = .01), and postoperative deaths were associated with the type of surgery and Karnofsky performance status at the time of admission (P = .001). CONCLUSIONS: Some patients with locally advanced colon adenocarcinomas undergoing extended resections have a 5-year overall survival rates of 58.3%. Patients could benefit from palliative-intent procedures, but these measures should cautiously be indicated and avoided in patients with low Karnofsky performance status due to high rates of postoperative mortality and poor survival.

Climate oscillations and species interactions: large-scale congruence but regional differences in the phylogeographic structures of an alpine plant and its monophagous insect

Aim. To predict the fate of alpine interactions involving specialized species, using a monophagous beetle and its host-plant as a case study. Location. The Alps. Methods. We investigated genetic structuring of the herbivorous beetle Oreina gloriosa and its specific host-plant Peucedanum ostruthium. We used genome fingerprinting (in the insect and the plant) and sequence data (in the insect) to compare the distribution of the main gene pools in the two associated species and to estimate divergence time in the insect, a proxy for the temporal origin of the interaction. We quantified the similarity in spatial genetic structures by performing a Procrustes analysis, a tool from the shape theory. Finally, we simulated recolonization of an empty space analogous to the deglaciated Alps just after ice retreat by two lineages from two species showing unbalanced dependence, to examine how timing of the recolonization process, as well as dispersal capacities of associated species, could explain the observed pattern. Results. Contrasting with expectations based on their asymmetrical dependence, patterns in the beetle and plant were congruent at a large scale. Exceptions occurred at a regional scale in areas of admixture, matching known suture zones in Alpine plants. Simulations using a lattice-based model suggested these empirical patterns arose during or soon after recolonization, long after the estimated origin of the interaction c. 0.5 million years ago. Main conclusions. Species-specific interactions are scarce in alpine habitats because glacial cycles have limited opportunities for coevolution. Their fate, however, remains uncertain under climate change. Here we show that whereas most dispersal routes are paralleled at large scale, regional incongruence implies that the destinies of the species might differ under changing climate. This may be a consequence of the host-dependence of the beetle that locally limits the establishment of dispersing insects.

Radiochemotherapy in locally advanced squamous cell carcinomas of the head and neck.

Squamous cell carcinoma of the head and neck (SCCHN) is a common disease that develops in the upper aerodigestive epithelium. The most important risk factors are tobacco and alcohol consumption. There is also increasing evidence that human papillomavirus plays an important role in the cause of SCCHN. The complex anatomy, the vital functions of the upper aerodigestive tract and the close proximity to vital structures, explain that the goal of treatment is not only to improve survival outcomes, but also to preserve organ function. Radiotherapy and surgery are the standard modalities of treatment, reflecting the locoregional predominance of SCCHN. Chemotherapy plays an important role in the treatment of patients with locoregionally advanced disease, in conjunction with radiotherapy and surgery. Indeed, standard therapy for resectable locoregionally advanced (stage III or IV) SCCHN cancers consists either of surgery and adjuvant chemoradiotherapy or definitive concomitant chemoradiotherapy, depending upon disease site, stage and resectability of the tumour, or institutional experience. Concomitant chemoradiotherapy has been shown in several randomised trials to improve disease-free and overall survival in the postoperative setting for resected disease with poor prognostic factors. Furthermore, multiple randomised studies and meta-analyses have shown that definitive chemoradiotherapy, as well anti-epidermal growth factor receptor treatment in one randomised study, improved disease-free and overall survival when compared with radiotherapy alone. This overview reviews the most relevant published studies on the multidisciplinary management of SCCHN and discusses future strategies to reduce locoregional failures.

Application of the center manifold theory to the study of slewing flexible Non-ideal structures with nonlinear curvature: a case study

In this paper is Analyzed the local dynamical behavior of a slewing flexible structure considering nonlinear curvature. The dynamics of the original (nonlinear) governing equations of motion are reduced to the center manifold in the neighborhood of an equilibrium solution with the purpose of locally study the stability of the system. In this critical point, a Hopf bifurcation occurs. In this region, one can find values for the control parameter (structural damping coefficient) where the system is unstable and values where the system stability is assured (periodic motion). This local analysis of the system reduced to the center manifold assures the stable / unstable behavior of the original system around a known solution.

Performance Assessment of Sandwich Structures with Debonds and Dents

A sandwich construction is a special form of the laminated composite consisting of light weight core, sandwiched between two stiff thin face sheets. Due to high stiffness to weight ratio, sandwich construction is widely adopted in aerospace industries. As a process dependent bonded structure, the most severe defects associated with sandwich construction are debond (skin core bond failure) and dent (locally deformed skin associated with core crushing). Reasons for debond may be attributed to initial manufacturing flaws or in service loads and dent can be caused by tool drops or impacts by foreign objects. This paper presents an evaluation on the performance of honeycomb sandwich cantilever beam with the presence of debond or dent, using layered finite element models. Dent is idealized by accounting core crushing in the core thickness along with the eccentricity of the skin. Debond is idealized using multilaminate modeling at debond location with contact element between the laminates. Vibration and buckling behavior of metallic honeycomb sandwich beam with and without damage are carried out. Buckling load factor, natural frequency, mode shape and modal strain energy are evaluated using finite element package ANSYS 13.0. Study shows that debond affect the performance of the structure more severely than dent. Reduction in the fundamental frequencies due to the presence of dent or debond is not significant for the case considered. But the debond reduces the buckling load factor significantly. Dent of size 8-20% of core thickness shows 13% reduction in buckling load capacity of the sandwich column. But debond of the same size reduced the buckling load capacity by about 90%. This underscores the importance of detecting these damages in the initiation level itself to avoid catastrophic failures. Influence of the damages on fundamental frequencies, mode shape and modal strain energy are examined. Effectiveness of these parameters as a damage detection tool for sandwich structure is also assessed