C(k)-solvability near the characteristic set for a class of planar complex vector fields of infinite type

This paper deals with semi-global C(k)-solvability of complex vector fields of the form L = partial derivative/partial derivative t + x(r) (a(x) + ib(x))partial derivative/partial derivative x, r >= 1, defined on Omega(epsilon) = (-epsilon, epsilon) x S(1), epsilon > 0, where a and b are C(infinity) real-valued functions in (-epsilon, epsilon). It is shown that the interplay between the order of vanishing of the functions a and b at x = 0 influences the C(k)-solvability at Sigma = {0} x S(1). When r = 1, it is permitted that the functions a and b of L depend on the x and t variables, that is, L = partial derivative/partial derivative t + x(a(x, t) + ib(x, t))partial derivative/partial derivative x, where (x, t) is an element of Omega(epsilon).

Nonexistence of global solutions for a class of complex vector fields on two-torus

The goal of this paper is study the global solvability of a class of complex vector fields of the special form L = partial derivative/partial derivative t + (a + ib)(x)partial derivative/partial derivative x, a, b epsilon C(infinity) (S(1) ; R), defined on two-torus T(2) congruent to R(2)/2 pi Z(2). The kernel of transpose operator L is described and the solvability near the characteristic set is also studied. (c) 2008 Elsevier Inc. All rights reserved.

Gevrey solvability near the characteristic set for a class of planar complex vector fields of infinite type

We study the Gevrey solvability of a class of complex vector fields, defined on Omega(epsilon) = (-epsilon, epsilon) x S(1), given by L = partial derivative/partial derivative t + (a(x) + ib(x))partial derivative/partial derivative x, b not equivalent to 0, near the characteristic set Sigma = {0} x S(1). We show that the interplay between the order of vanishing of the functions a and b at x = 0 plays a role in the Gevrey solvability. (C) 2008 Elsevier Inc. All rights reserved.

Solvability in the large for a class of complex vector fields on the cylinder

This work deals with global solvability of a class of complex vector fields of the form L = partial derivative/partial derivative t + (a(x, t)+ ib(x, t))partial derivative/partial derivative x, where a and b are real-valued C-infinity functions, defined on the cylinder Omega = R x S-1. Relatively compact (Sussmann) orbits are allowed. The connection with Malgrange's notion of L-convexity for supports is investigated. (C) 2011 Elsevier Masson SAS. All rights reserved.

Solvability near the characteristic set for a special class of complex vector fields

This work deals with the solvability near the characteristic set Sigma = {0} x S-1 of operators of the form L = partial derivative/partial derivative t+(x(n) a(x)+ ix(m) b(x))partial derivative/partial derivative x, b not equivalent to 0 and a(0) not equal 0, defined on Omega(epsilon) = (-epsilon, epsilon) x S-1, epsilon > 0, where a and b are real-valued smooth functions in (-epsilon, epsilon) and m >= 2n. It is shown that given f belonging to a subspace of finite codimension of C-infinity (Omega(epsilon)) there is a solution u is an element of L-infinity of the equation Lu = f in a neighborhood of Sigma; moreover, the L-infinity regularity is sharp.

Globally solvable systems of complex vector fields

We consider a class of involutive systems of n smooth vector fields on the n + 1 dimensional torus. We obtain a complete characterization for the global solvability of this class in terms of Liouville forms and of the connectedness of all sublevel and superlevel sets of the primitive of a certain 1-form in the minimal covering space.

The Scored Patient-Generated Subjective Global Assessment (PG-SGA) and its Association with Quality of Life in Ambulatory Patients Receiving Radiotherapy

OBJECTIVE: To evaluate the scored Patient-generated Subjective Global Assessment (PG-SGA) tool as an outcome measure in clinical nutrition practice and determine its association with quality of life (QoL). DESIGN: A prospective 4 week study assessing the nutritional status and QoL of ambulatory patients receiving radiation therapy to the head, neck, rectal or abdominal area. SETTING: Australian radiation oncology facilities. SUBJECTS: Sixty cancer patients aged 24-85 y. INTERVENTION: Scored PG-SGA questionnaire, subjective global assessment (SGA), QoL (EORTC QLQ-C30 version 3). RESULTS: According to SGA, 65.0% (39) of subjects were well-nourished, 28.3% (17) moderately or suspected of being malnourished and 6.7% (4) severely malnourished. PG-SGA score and global QoL were correlated (r=-0.66, P<0.001) at baseline. There was a decrease in nutritional status according to PG-SGA score (P<0.001) and SGA (P<0.001); and a decrease in global QoL (P<0.001) after 4 weeks of radiotherapy. There was a linear trend for change in PG-SGA score (P<0.001) and change in global QoL (P=0.003) between those patients who improved (5%) maintained (56.7%) or deteriorated (33.3%) in nutritional status according to SGA. There was a correlation between change in PG-SGA score and change in QoL after 4 weeks of radiotherapy (r=-0.55, P<0.001). Regression analysis determined that 26% of the variation of change in QoL was explained by change in PG-SGA (P=0.001). CONCLUSION: The scored PG-SGA is a nutrition assessment tool that identifies malnutrition in ambulatory oncology patients receiving radiotherapy and can be used to predict the magnitude of change in QoL.

Reducing the global burden of depression : population level analysis of intervention cost-effectiveness in 14 world regions

International evidence on the cost and effects of interventions for reducing the global burden of depression remain scarce. Aims: To estimate the population-level cost-effectiveness of evidence-based depression interventions and their contribution towards reducing current burden. Method: Primary-care-based depression interventions were modelled at the level of whole populations in 14 epidemiological subregions of the world. Total population-level costs (in international dollars or I$) and effectiveness (disability adjusted life years (DALYs) averted) were combined to form average and incremental cost-effectiveness ratios. Results: Evaluated interventions have the potential to reduce the current burden of depression by 10–30%. Pharmacotherapy with older antidepressant drugs, with or without proactive collaborative care, are currently more cost-effective strategies than those using newer antidepressants, particularly in lower-income subregions. Conclusions: Even in resource-poor regions, each DALYaverted by efficient depression treatments in primary care costs less than 1 year of average per capita income, making such interventions a cost-effective use of health resources. However, current levels of burden can only be reduced significantlyif there is a substantialincrease substantial increase intreatment coverage.