On Bounded Strictly Positive Operators of Closed Range and Some Applications to Asymptotic Hyperstability of Dynamic Systems

The problem discussed is the stability of two input-output feedforward and feedback relations, under an integral-type constraint defining an admissible class of feedback controllers. Sufficiency-type conditions are given for the positive, bounded and of closed range feed-forward operator to be strictly positive and then boundedly invertible, with its existing inverse being also a strictly positive operator. The general formalism is first established and the linked to properties of some typical contractive and pseudocontractive mappings while some real-world applications and links of the above formalism to asymptotic hyperstability of dynamic systems are discussed later on.

Black Holes, Cosmological Solutions, Future Singularities, and Their Thermodynamical Properties in Modified Gravity Theorie

54 p.

Clinical factors associated with a Candida albicans Germ Tube Antibody positive test in Intensive Care Unit patients

Background: Poor outcomes of invasive candidiasis (IC) are associated with the difficulty in establishing the microbiological diagnosis at an early stage. New scores and laboratory tests have been developed in order to make an early therapeutic intervention in an attempt to reduce the high mortality associated with invasive fungal infections. Candida albicans IFA IgG has been recently commercialized for germ tube antibody detection (CAGTA). This test provides a rapid and simple diagnosis of IC (84.4% sensitivity and 94.7% specificity). The aim of this study is to identify the patients who could be benefited by the use of CAGTA test in critical care setting. Methods: A prospective, cohort, observational multicentre study was carried out in six medical/surgical Intensive care units (ICU) of tertiary-care Spanish hospitals. Candida albicans Germ Tube Antibody test was performed twice a week if predetermined risk factors were present, and serologically demonstrated candidiasis was considered if the testing serum dilution was >= 1: 160 in at least one sample and no other microbiological evidence of invasive candidiasis was found. Results: Fifty-three critically ill non-neutropenic patients (37.7% post surgery) were included. Twenty-two patients (41.5%) had CAGTA-positive results, none of them with positive blood culture for Candida. Neither corrected colonization index nor antifungal treatment had influence on CAGTA results. This finding could corroborate that the CAGTA may be an important biomarker to distinguish between colonization and infection in these patients. The presence of acute renal failure at the beginning of the study was more frequent in CAGTA-negative patients. Previous surgery was statistically more frequent in CAGTA-positive patients. Conclusions: This study identified previous surgery as the principal clinical factor associated with CAGTA-positive results and emphasises the utility of this promising technique, which was not influenced by high Candida colonization or antifungal treatment. Our results suggest that detection of CAGTA may be important for the diagnosis of invasive candidiasis in surgical patients admitted in ICU.

The Slow Search for Solutions: Lessons from Historical Energy Transitions by Sector and Service

28 p.

Solutions for New Terrestrial Broadcasting Systems Offering Simultaneously Stationary and Mobile Services

221 p.

The role of H-bonds on the structure and dynamics of very concentrated polymer solutions

153 p.

Approximate Solutions by Truncated Taylor Series Expansions of Nonlinear Differential Equations and Related Shadowing Property with Applications

This paper investigates the errors of the solutions as well as the shadowing property of a class of nonlinear differential equations which possess unique solutions on a certain interval for any admissible initial condition. The class of differential equations is assumed to be approximated by well-posed truncated Taylor series expansions up to a certain order obtained about certain, in general nonperiodic, sampling points t(i) is an element of [t(0), t(J)] for i = 0, 1, . . . , J of the solution. Two examples are provided.

On Nonnegative Solutions of Fractional q-Linear Time-Varying Dynamic Systems with Delayed Dynamics

This paper is devoted to the investigation of nonnegative solutions and the stability and asymptotic properties of the solutions of fractional differential dynamic linear time-varying systems involving delayed dynamics with delays. The dynamic systems are described based on q-calculus and Caputo fractional derivatives on any order.

Distribution theory and fundamental solutions of differential operators

The objective of this dissertation is to study the theory of distributions and some of its applications. Certain concepts which we would include in the theory of distributions nowadays have been widely used in several fields of mathematics and physics. It was Dirac who first introduced the delta function as we know it, in an attempt to keep a convenient notation in his works in quantum mechanics. Their work contributed to open a new path in mathematics, as new objects, similar to functions but not of their same nature, were being used systematically. Distributions are believed to have been first formally introduced by the Soviet mathematician Sergei Sobolev and by Laurent Schwartz. The aim of this project is to show how distribution theory can be used to obtain what we call fundamental solutions of partial differential equations.