On a Functional Equation in Actuarial Mathematics

AbstractIn 1839, De Morgan gave a mathematical justification of Gompertz's law of mortality through a composite functional equation, f(x+y)+f(x+z)=f(x+h(y,z)). A slightly more general version of this equation was studied in 1905 by M. Chini. Both solved their equations in the class of differentiable functions on the real line. Here we solve the equation f(x)+f(x+y)=cf(x+g(y)), which is a generalization of Chini's equation, on intervals in the class of locally bounded functions and in the class of continuous functions

Electric Current Perturbation Calculations for Half-Penny Cracks

The electric current perturbation (ECP) method1–4 consists of inducing or injecting an electric current flow in the material to be examined and then detecting localized perturbations of the magnetic flux associated with current flow around material defects such as cracks or inclusions. Empirically, ECP data has shown strong correlations among certain signal features and crack size characteristics, and thus promises to be a useful method for quantitative NDE. To aid in the further development of the method, the objectives of the work reported in this paper are (1) to develop a mathematical model of the ECP flux distribution for a half-penny crack, (2) to determine the degree of validity of the model through comparisons with experimental data, and (3) to develop a detailed theory of sizing relationships for half-penny cracks

On Factor Universality in Symbolic Spaces

The study of factoring relations between subshifts or cellular automata is central in symbolic dynamics. Besides, a notion of intrinsic universality for cellular automata based on an operation of rescaling is receiving more and more attention in the literature. In this paper, we propose to study the factoring relation up to rescalings, and ask for the existence of universal objects for that simulation relation. In classical simulations of a system S by a system T, the simulation takes place on a specific subset of configurations of T depending on S (this is the case for intrinsic universality). Our setting, however, asks for every configurations of T to have a meaningful interpretation in S. Despite this strong requirement, we show that there exists a cellular automaton able to simulate any other in a large class containing arbitrarily complex ones. We also consider the case of subshifts and, using arguments from recursion theory, we give negative results about the existence of universal objects in some classes

Increased CD16 expression on NK cells is indicative of antibody-dependent cell-mediated cytotoxicity in chronic-active antibody-mediated rejection

Chronic-active antibody mediated rejection (c-aABMR) contributes significantly to late renal allograft failure. The antibodies directed against donor-derived antigens, e.g. anti-HLA antibodies, cause inflammation at the level of the microvascular endothelium. This is characterized by signs of local activation of the complement system and accumulation of immune cells within the capillaries. Non-invasive biomarkers of c-aABMR are currently not available but could be valuable for early detection. We therefore analyzed the activation profiles of circulating T and B cells, NK cells and monocytes in the peripheral blood of 25 kidney transplant recipients with c-aABMR and compared them to 25 matched recipients to evaluate whether they could serve as a potential biomarker. No significant differences were found in the total percentage and distribution of NK cells, B cells and T cells between the c-aABMRpos and c-aABMRneg cases. There was however a higher percentage of monocytes present in c-aABMRpos cases (p < .05). Additionally, differences were found in activation status of circulating monocytes, NK cells and γδ T cells, mainly concerning the activation marker CD16. Although statistically significant, these differences were not sufficient for use as a biomarker of c-aABMR

A model for hysteretic magnetic properties under the application of noncoaxial stress and field

Although descriptions of the effect of stress on spontaneous magnetization within a single domain already exist, there remains no adequate mathematical model for the effects of noncoaxial magnetic field and stress on bulk magnetization in a multidomained specimen. This article addresses the problem and provides a phenomenological theory that applies to the case of bulk isotropic materials. The magnetomechanical hysteresis model of Sablik and Jiles is thus extended to treat magnetic properties in the case of noncoaxial stress and magnetic field in an isotropic, polycrystalline medium. In the modeling, noncollinearity between magnetization and magnetic field is taken into account. The effect of roll‐axis anisotropy is also considered. Both magnetic and magnetostrictive hysteresis are describable by the extended model. Emphasis in this article is on describing properties like coercivity, remanence,hysteresis loss, maximum flux density, and maximum differential permeability as a function of stress for various angular orientations between field and stress axis. The model predictions are compared with experimental results

Modeling the interrelating effects of plastic deformation and stress on magnetic properties of materials

A model has been developed that describes the interrelating effects of plastic deformation and applied stress on hysteresis loops based on the theory of ferromagnetichysteresis. In the current model the strength of pinning sites for domain walls is characterized by the pinning coefficient keff given by keff=k0+k′σ. The term k0 depicts pinning of domain walls by dislocations and is proportional to ρn, where ρ is the number density of dislocation which is related to the amount of plastic strain, and the exponent n depends on the strength of pinning sites. The second term k′σ∝−3/2λs/2mσ, where m is magnetization and λs is magnetostriction constant, describes the changes in pinning strength on a domain wall induced by an applied stress σ. The model was capable of reproducing the stress dependence of hysteresis loop properties such as coercivity and remanence of a series of nickel samples which were pre-strained to various plastic strain levels. An empirical relation was found between the parameter k0 and the plastic strain, which can be interpreted in terms of the effects on the strength of domain wall pinning of changes in dislocation density and substructure under plastic deformation

Application of magnetomechanical hysteresis modeling to magnetic techniques for monitoring neutron embrittlement and biaxial stress. Progress report, June 1991--December 1991

The objective is to investigate experimentally and theoretically the effects of neutron embrittlement and biaxial stress on magnetic properties in steels, using various magnetic measurement techniques. Interaction between experiment and modeling should suggest efficient magnetic measurement procedures for determining neutron embrittlement biaxial stress. This should ultimately assist in safety monitoring of nuclear power plants and of gas and oil pipelines. In the first six months of this first year study, magnetic measurements were made on steel surveillance specimens from the Indian Point 2 and D.C. Cook 2 reactors. The specimens previously had been characterized by Charpy tests after specified neutron fluences. Measurements now included: (1) hysteresis loop measurement of coercive force, permeability and remanence, (2) Barkhausen noise amplitude; and (3) higher order nonlinear harmonic analysis of a 1 Hz magnetic excitation. Very good correlation of magnetic parameters with fluence and embrittlement was found for specimens from the Indian Point 2 reactor. The D.C. Cook 2 specimens, however showed poor correlation. Possible contributing factors to this are: (1) metallurgical differences between D.C. Cook 2 and Indian Point 2 specimens; (2) statistical variations in embrittlement parameters for individual samples away from the stated men values; and (3) conversion of the D.C. Cook 2 reactor to a low leakage core configuration in the middle of the period of surveillance. Modeling using a magnetomechanical hysteresis model has begun. The modeling will first focus on why Barkhausen noise and nonlinear harmonic amplitudes appear to be better indicators of embrittlement than the hysteresis loop parameters

Monitoring neutron embrittlement in nuclear pressure vessel steels using micromagnetic Barkhausen emissions

In nuclear power plants, neutron embrittlement of pressure vessel steels has been one of the main concerns. The use of micromagnetic Barkhausen emissions is a promising method to monitor the variations in microstructural and subsurface stress states due to their influence on these emissions. Measurements of these emissions can reveal neutron irradiationdegradation in nuclear power plant components. Samples which were irradiated at differentneutron fluences and annealed at different temperatures were obtained from three reactor surveillance programs. The results of different neutron fluences and annealing procedures showed noticeable fractional changes in the magnetic Barkhausen effect signal parameter, ΔMBE/MBE, and in the mechanical properties of these specimens. For example, increased intensity of neutron fluence decreased the ΔMBE/MBE as well as impact energy and upper‐shelf energy, but increased Rockwell hardness and yield strength. Typical changes in this parameter were in the range from −20% to −45% for fluences of up to 25×1018 n cm−2

High-throughput mapping of protein occupancy identifies functional elements without the restriction of a candidate factor approach

There are a variety of in vivo and in vitro methods to determine the genome-wide specificity of a particular trans-acting factor. However there is an inherent limitation to these candidate approaches. Most biological studies focus on the regulation of particular genes, which are bound by numerous unknown trans-acting factors. Therefore, most biological inquiries would be better addressed by a method that maps all trans-acting factors that bind particular regions rather than identifying all regions bound by a particular trans-acting factor. Here, we present a high-throughput binding assay that returns thousands of unbiased measurements of complex formation on nucleic acid. We applied this method to identify transcriptional complexes that form on DNA regions upstream of genes involved in pluripotency in embryonic stem cells (ES cells) before and after differentiation. The raw binding scores, motif analysis and expression data are used to computationally reconstruct remodeling events returning the identity of the transcription factor(s) most likely to comprise the complex. The most significant remodeling event during ES cell differentiation occurred upstream of the REST gene, a transcriptional repressor that blocks neurogenesis. We also demonstrate how this method can be used to discover RNA elements and discuss applications of screening polymorphisms for allelic differences in binding