A method for estimating the statistical error of the solution in the inverse spectroscopy problem

A method for obtaining the interval of statistical error of the solution of the inverse spectroscopy problem, for the estimation of the statistical error of experimental data of which the normal distribution law can be applied, has been proposed. With the help of mathematical modeling of the statistical error of partial spectral components obtained from the numerically stable solution of the inverse problem, it has become possible to specify the error of the corresponding solution. The problem of getting the inverse solution error interval is actual because the existing methods of solution error evaluation are based on the analysis of smooth functional dependences under rigid restrictions on the region of acceptable solutions (compactness, monotonicity, etc.). Their use in computer processing of real experimental data is extremely difficult and therefore, as a rule, is not applied. Based on the extraction of partial spectral components and the estimation of their error, a method for obtaining an interval of statistical error for the solution of inverse spectroscopy problems has been proposed in this work. The necessity and importance of finding the solution error interval to provide reliable results is demonstrated using examples of processing Mössbauer spectra.

APPROXIMATING EXPECTED VALUE OF AN OPTION WITH NON-LIPSCHITZ PAYOFF IN FRACTIONAL HESTON-TYPE MODEL

In this paper, we consider option pricing in a framework of the fractional Heston-type model with [Formula: see text]. As it is impossible to obtain an explicit formula for the expectation [Formula: see text] in this case, where [Formula: see text] is the asset price at maturity time and [Formula: see text] is a payoff function, we provide a discretization schemes [Formula: see text] and [Formula: see text] for volatility and price processes correspondingly and study convergence [Formula: see text] as the mesh of the partition tends to zero. The rate of convergence is calculated. As we allow [Formula: see text] to be non-Lipschitz and/or to have discontinuities of the first kind which can cause errors if [Formula: see text] is replaced by [Formula: see text] under the expectation straightforwardly, we use Malliavin calculus techniques to provide an alternative formula for [Formula: see text] with smooth functional under the expectation.

CLOSURE OF FINITE FUNCTIONS IN ONE WEIGHT SOBOLEV TYPE SPACE

The description of the closure of finite or smooth finite functions in functional spaces are classical tasks of functional space theory. This task is important in smooth functional spaces such as those of Sobolev, Nikolski, Besov and in their various generalizations. Usually, in a weightless space of smooth functions, the set of compactly finite functions, generally speaking, is not dense. But in the weighted space of smooth functions, for example, in the Sobolev weighted space, with strong degeneracy of the weight, many compactly finite functions can be dense. Therefore, an important issue is the problem of characterizing the closure of compactly finite functions in the weight space under consideration. Here we consider a weighted space of Sobolev type of the second order with three weights and it describes the closure of the set of functions with compact supports.

Conscience Relevance and Sensitivity in Psychiatric Evaluations in the Youth-span

Background: While practice parameters recommend assessment of conscience and values, few resources are available to guide clinicians. Objective: To improve making moral inquiry in youth aged 15 to 24. Method: After documenting available resources for behavioral health clinicians who are inquiring about their patient’s moral life, we consider our studies of conscience development and functioning in youth. We align descriptions of domains of conscience with neurobiology. We compare youth reared in relative advantage, who have fairly smooth functional progressions across domains, with youth reared in adverse circumstances. We offer the heuristic conscience developmental quotient to help mind the gap between conscience in adversity and conscience in advantage. Next, we consider severity of psychopathological interference as distinct from delay. A case illustration is provided to support the distinction be Results: Our findings support the hypotheses that youth who experience adverse childhood experiences show evidence of fragmentation, unevenness and delay in their conscience stage-attainment. We demonstrate proof of concept for conscience sensitive psychiatric assessment in the youth-span. Conscience sensitive inquiries improve upon merely conscience relevant interpretations by affording better appreciation of moral wounding, in turn setting the stage for moral-imaginative efforts that elicit and make the latent values of the youth more explicit. Conclusions: A conscience sensitive approach should be part of both psychiatric and general medical education, supported explicitly by clinical guidelines recommending conscience sensitive interview techniques that aim to acquire information aligned with current neurobiological terminology..

Closed-form exact solutions for thick bi-directional functionally graded circular beams

PurposeThere exists a clear paucity of models for curved bi-directional functionally graded (BDFG) beams wherein the material properties vary along the axis and thickness of the beam simultaneously; such structures may help fulfil practical design requirements of the future and improve structural efficiency. In this context, the purpose of this paper is to extend the analytical model developed earlier to thick BDFG circular beams by using first-order shear deformation theory which allows for a non-zero shear strain distribution through the thickness of the beam.Design/methodology/approachSmooth functional variations of the material properties have been assumed along the axis and thickness of the beam simultaneously. The governing equations developed have been solved analytically for some representative determinate circular beams. In order to ascertain the effects of shear deformation in these structures, the total strain energy has been decomposed into its bending and shear components and the effects of the beam thickness and the arch angle on the shear energy component have been studied.FindingsClosed-form exact solutions involving through-the-thickness integrals carried out numerically are presented for the bending of circular beams under the action of a variety of concentrated/distributed loads.Originality/valueThe results clearly indicate the importance of capturing shear deformation in thick BDFG beams and demonstrate the capability of tuning the response of these beams to fit a wide variety of structural requirements.