On uniform continuous dependence of solution of Cauchy problem on a parameter

Suppose that an $n$-dimensional Cauchy problem \frac{dx}{dt}=f(t,x,\mu) (t \in I, \mu \in M), x(t_0)=x^0 satisfies the conditions that guarantee existence, uniqueness and continuous dependence of solution x(t,t_0,\mu) on parameter \mu in an open set M. We show that if one additionally requires that family \{f(t,x,\cdot)\}_{(t,x)} is equicontinuous, then the dependence of solution x(t,t_0,\mu) on parameter \mu \in M is uniformly continuous. An analogous result for a linear n \times n-dimensional Cauchy problem \frac{dX}{dt}=A(t,\mu)X+\Phi(t,\mu) (t \in I, \mu \in M), X(t_0,\mu)=X^0(\mu) is valid under the assumption that the integrals \int_I\|A(t,\mu_1)-A(t,\mu_2)\|dt and \int_I \|\Phi(t,\mu_1)-\Phi(t,\mu_2)\|dt can be made smaller than any given constant (uniformly with respect to \mu_1, \mu_2 \in M) provided that \|\mu_1-\mu_2\| is sufficiently small

Disconjugacy of a second order linear differential equation and periodic solutions

The present paper is devoted to a new criterion for disconjugacy of a second order linear differential equation. Unlike most of the classical sufficient conditions for disconjugacy, our criterion does not involve assumptions on the smallness of the coefficients of the equation. We compare our criterion with several known criteria for disconjugacy, for which we provide detailed proofs, and discuss the applications of the property of disconjugacy to the problem of factorization of linear ordinary differential operators, and to the proof of the generalized Rolle's theorem. The paper is self-contained, and may serve as a brief introduction to theory of disconjugacy of a second order linear differential equation

Distributions with dynamic test functions and multiplication by discontinuous functions

As follows from the Schwartz Impossibility Theorem, multiplication of two distributions is in general impossible. Nevertheless, often one needs to multiply a distribution by a discontinuous function, not by an arbitrary distribution. In the present paper we construct a space of distributions where the general operation of multiplication by a discontinuous function is defined, continuous, commutative, associative and for which the Leibniz product rule holds. In the new space of distributions, the classical delta-function $\delta_\tau$ extends to a family of delta-functions $\delta_\tau^\alpha$, dependent on the \textit{shape} $\alpha$. We show that the various known definitions of the product of the Heaviside function and the delta-function in the classical space of distributions $\mathcal D'$ become particular cases of the multiplication in the new space of distributions, and provide the applications of the new space of distributions to the ordinary differential equations which arise in optimal control theory. Also, we compare our approach of the Schwartz distribution theory with the approach of the Colombeau generalized functions algebra, where the general operation of multiplication of two distributions is defined

Propagation of millimeter and submillimeter waves

Coherent radiation methods of measuring absorption spectra in planetary atmosphere, and millimeter and submillimeter wave propagatio

Who Speaks for Me?: Addressing Variability in Informed Consent Practices for Minimal Risk Research Involving Foster Youth

Background: Youth in protective custody (i.e., foster care) are at higher risk for poorer physical and mental health outcomes compared with those who are not. These differences may be due in part to the lack of research on the population to create evidence-based recommendations for health care delivery. A potential contributor to this lack of research is difficulties in obtaining informed consent for empirical studies in this population. The objective of this study was to describe the approaches to obtaining informed consent in minimal risk studies of foster youth and provide recommendations for future requirements. Methods: We conducted a systematic review of the literature to characterize the informed consent approaches in published minimal risk research involving youth in foster care. We searched PubMed, CINAHL, PsychINFO, Embase, ERIC, Scopus, and EBMR. Inclusion criteria were: studies conducted in the United States, included current foster youth, minimal risk, peer reviewed, and published in English. Full text was reviewed, and individuals required to consent and assent were extracted. Results: Forty-nine publications from 33 studies were identified. Studies required 0 to 3 individuals to consent. Individuals required to give consent included case workers (16, 48%), foster caregivers (12, 36%), biological parents (7, 21%), judges (5, 15%), and guardian ad litems (2, 6%). Twenty-nine (88%) studies required the youth’s assent. The studies used 14 different combinations of individuals. One (3%) study utilized a waiver of consent. Conclusions: There is no consistent approach for obtaining informed consent for foster youth to participate in minimal risk research. Consent should ideally involve individuals with legal authority and knowledge of the individual youth’s interests and should not be burdensome. Consensus regarding consent requirements may facilitate research involving foster youth

On the Inversion of Light Scattering Data into Information on Aerosol Properties

The Backus-Gilbert inversion technique was applied to scattering data and calculated examples were given to ascertain its ability to recover the aerosol properties with no a-priori assumptions. In order to cheque this inversion procedure as well as other techniques (such as Daves' and Herman's et al.), a controlled experiment was performed. The experiment dealt with spherical particles the Mie scattering curves of which was measured by use of a dye-laser. These curves were used to accurately determine the refractive index of the particles. Mixtures of three different known sizes were then prepared and the scattering intensity vs. wavelength was measured at 90 deg scattering angle. The mixtures contained also various known relative concentrations of the three sizes. The analysis of the measured results will be shown and discussed

Trained laser-patterned carbon as high-performance mechanical sensors

We describe the mechanical properties of turbostratically graphitized carbon films obtained by carbon laser-patterning (CLaP) and their application as bending or mechanical pressure sensors. Stable conductive carbonized films were imprinted on a flexible polyethylene terephthalate (PET) substrate by laser-induced carbonization. After initial gentle bending, i.e. training, these sponge-like porous films show a quantitative and reversible change in resistance upon bending or application of pressure in normal loading direction. Maximum response values of ΔR/R0 = 388% upon positive bending (tensile stress) and −22.9% upon negative bending (compression) are implicit for their high sensitivity towards mechanical deformation. Normal mechanical loading in a range between 0 and 500 kPa causes a response between ΔR/R0 = 0 and −15%. The reversible increase or decrease in resistance is attributed to compression or tension of the turbostratically graphitized domains, respectively. This mechanism is supported by a detailed microstructural and chemical high-resolution transmission electron microscopic analysis of the cross-section of the laser-patterned carbon

Laser Doppler Measurement of Atmopsheric Wind Velocity

Our presentation consists of two parts: (1) a summary review of laser Doppler principles and applications, and (2) operational design and preliminary laboratory tests of a CO2 laser system for NOAA applications