Distribution Of Rn Research Articles

Lithological Impact on Radon Levels: A Study of Indoor and Soil Gas Radon in the Centre Region of Cameroon

AbstractThe objectives of the current study are to carry out soil gas radon (Rn) measurements, to evaluate the total inhalation effective dose, to determine risk levels over the lithological formations of the study area. The behavior investigation of Rn activity concentration distributions in dwellings and soils, and soil Rn mapping were also conducted. Soil gas Rn measurements were made at 102 sampling points by Markus 10 instrument. This data was combined with previously reported results from 140 indoor Rn RADTRAK dosimeters to determine the total inhalation effective dose and to conduct a statistical analysis. Overall, the Rn activity concentrations in soil and dwellings range from 4 to 66 kBq m−3 and from 15 to 140 Bq m−3, with averages of 31 ± 15 kBq m−3 and 41 ± 24 Bq m−3 respectively. The corresponding total inhalation effective dose ranges from 0.35 to 3.53 mSv y−1, with a mean value of 1.37 ± 0.58 mSv y−1. For soil gas Rn, the chlorite schist lithology showed the highest average concentration level. Which could be justified by the possible presence, within chlorite minerals, highly emitting zones of alpha particles, leading to the formation of radioactive halos. Normal and high‐risk level of Rn were found for about 82% and 11% of the total area surveyed respectively. These findings highlight the need for preventive measure against Rn exposure in homes within the investigated areas. This study contributes valuable insights into Rn distribution patterns and risk assessment, offering a basis for targeted interventions in the region.

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We provide a characterization of those log-concave distributions in Rn\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{\\mathbb {R}}}^n$$\\end{document} that are contoured distributions, through the Kp\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$K_p$$\\end{document}-bodies of the distribution, defined by Ball. Our method uses the logarithmic integral for the solution of a Bernstein type approximation problem. In the second part of the paper we state a question for contoured distributions that would provide an alternative approach to the isotropic constant problem.

Representation formulae for nonhomogeneous differential operators and applications to PDEs

We obtain integral representation formulae for functions u∈Lloc1(RN) which satisfy P(−Δ)u=μ in the sense of distributions in RN, where μ is a positive Radon measure on RN and P(z)=zm(zσ+aσ−1zσ−1+⋯+a1z+a0) is a nonconstant real polynomial whose roots belong to the interval (−∞,0], m,σ≥0, N>2m. Further, we apply these results to a number of nonhomogeneous higher order differential inequalities.

Modeling of soil gas radon as an in situ partitioning tracer for quantifying LNAPL contamination

In the last decades radon (Rn) has been widely proposed as a naturally occurring tracer for non-aqueous phase liquids (NAPL) in the soil. This work examines the feasibility of using soil gas data collected at some distance from the source zone for the application of the Rn deficit technique for the identification and quantification of NAPL contamination. To this end, we used a steady-state 1-D analytical solution that is based on a 3-layer model that allows to simulate the transport and distribution of Rn in the source zone, capillary fringe and overlying unsaturated soil. The analytical solution was first validated against a more detailed numerical model available in the literature. Then, a series of simulations were carried out to evaluate the vertical concentration profiles of Rn in soil gas above the source zone and in background location not impacted by NAPL. Simulation results showed that the parameters that most influence the migration and distribution of Rn in the subsurface are the distance of the soil gas probe from the source zone and, to a lower extent, the type of contamination (e.g. diesel or gasoline) and the soil type. On the basis of these results, we developed some easy-to-use nomographs to estimate the residual NAPL phase based on the observed radon deficit in soil gas and on the probe to source distance and soil and NAPL characteristics. According to the obtained results, the radon deficit technique results a feasible method for a qualitative identification of residual NAPL when radon in soil gas is measured at distances lower than 2 m from the contaminated zone. However, for an accurate quantitative estimation of the NAPL phase content, soil gas probes should be preferably located at distances lower than 1 m from the source zone.

Health Risk Implication and Spatial Distribution of Radon in Groundwater Along the Lithological Contact in South India.

The presence of radioactive elements in groundwater results in high health risks on surrounding populations. Hence, a study was conducted in central Tamil Nadu, South India, to measure the radon levels in groundwater and determine the associatedhealth risk. The study was conducted along the lithological contact of hard rock and sedimentary formation. The concentrations of uranium (U) varied from 0.28 to 84.65µg/L, and the radioactivity of radon (Rn) varied from 258 to 7072Bq/m3 in the collected groundwater samples.The spatial distribution of Rn in the study area showed that higher values were identified along the central and northern regions of the study area. The data also indicate that granitic and gneissic rocks are the major contributors to Rn in groundwater through U-enriched lithological zones. The radon levels in all samples were below the maximum concentration level, prescribed by Environmental Protection Agency. The effective dose levels for ingestion and inhalation were calculated according to parameters introduced by UNSCEAR and were found to be lesser (0.235-6.453 μSvy-1) than the recommended limit. Hence, the regional groundwater in the study area does not pose any health risks to consumers. The spatial distribution of Rn's effective dose level indicates the higher values were mainly in the central and northern portion of the study area consist of gneissic, quarzitic, and granitic rocks. The present study showed that Rn concentrations in groundwater depend on the lithology, structural attributes, the existence of uranium minerals in rocks, and the redox conditions. The results of this study provide information on the spatial distribution of Rn in the groundwater and its potential health risk in central Tamil Nadu, India. It is anticipated that these data will help policymakers to develop plans for management of drinking water resources in the region.

Spatial Distribution of Rn, CO2, Hg, and H2 Concentrations in Soil Gas Across a Thrust Fault in Xinjiang, China

Spatial distribution characteristics and origin of soil gases were discussed in this study. We also examine the correlation between the spatial variation of soil gases and fault activity, based on the measurements of Rn, Hg, H2, and CO2 concentrations in the eastern segment of the BLT fault zone in the southern Tianshan Mountains, Xinjiang, China. The results show that the Rn and CO2 concentrations on the hanging wall were higher than those near the fault zone and on the footwall of the fault. Moreover, the Hg and H2 concentrations on the footwall were also higher than those near the fault and on the hanging wall of the fault. The main factors affecting the variations in soil gas spatial distribution were gaseous origin structure of the crust, fault activity, fault fracture degree, stratigraphic lithology, and the cover layer. The results of active structural fault mapping show that the BLT fault has been active since the Late Quaternary and the thrust has broken the fault surface. Under the influence of tectonic compressive stress, the tension zone was formed on the hanging wall of the fault and fractures were developed. This result is consistent with the characteristics of soil gas concentrations measured in this study, indicating that the concentrations of Rn, Hg, H2, and CO2 are closely related to the fault activity. These findings can be applied to identify seismic precursors from gas monitoring data of the studied area.

Multivariate reciprocal inverse Gaussian distributions from the Sabot–Tarrès–Zeng integral

In Sabot and Tarrès (2015), the authors have explicitly computed the integral STZn=∫exp(−〈x,y〉)(detMx)−1∕2dxwhere Mx is a symmetric matrix of order n with fixed non-positive off-diagonal coefficients and with diagonal (2x1,…,2xn). The domain of integration is the part of Rn for which Mx is positive definite. We calculate more generally for b1≥0,…bn≥0 the integral ∫exp−〈x,y〉−12b⊤Mx−1b(detMx)−1∕2dx,we show that it leads to a natural family of distributions in Rn, called the MRIGn probability laws. This family is stable by marginalization and by conditioning, and it has number of properties which are multivariate versions of familiar properties of univariate reciprocal inverse Gaussian distribution. In general, if the power of detMx under the integral in STZn is distinct from −1∕2 it is not known how to compute the integral. However, introducing the graph G having V={1,…,n} for set of vertices and the set E of {i,j}′ s of non-zero entries of Mx as set of edges, we show also that in the particular case where G is a tree, the integral ∫exp(−〈x,y〉)(detMx)q−1dxwhere q>0, is computable in terms of the MacDonald function Kq.

On Eigenfunctions of the Fourier Transform

A nontrivial example of an eigenfunction in the sense of the theory of distributions for the planar Fourier transform was described by the authors in their previous work. In this paper, a method for obtaining other eigenfunctions is proposed. Positive homogeneous distributions in ℝn of order −n/2 are considered, and it is shown that F(ω)|x|−n/2, |ω| = 1, is an eigenfunction in the sense of the theory of distributions of the Fourier transform if and only if F(ω) is an eigenfunction of a certain singular integral operator on the unit sphere of ℝn. Since $$ {Y}_{m,n}^{(k)}\left(\omega \right){\left|\mathbf{x}\right|}^{-n/2} $$ , where $$ {Y}_{m,n}^{(k)} $$ denote the spherical functions of order m in ℝn, are eigenfunctions of the Fourier transform, it follows that $$ {Y}_{m,n}^{(k)} $$ are eigenfunctions of the above-mentioned singular integral operator. In the planar case, all eigenfunctions of the Fourier transform of the form F(ω)|x|−1 are described by means of the Fourier coefficients of F(ω).

Geometry of rank 2 distributions with nonzero Wilczynski invariants

In the famous 1910 “cinq variables” paper Cartan showed in particular that for maximally nonholonomic rank 2 distributions in ℝ5 with non-zero covariant binary biquadratic form the dimension of the pseudo-group of local symmetries does not exceed 7 and among such distributions he described the one-parametric family of distributions for which this pseudo-group is exactly 7-dimensional. Using the novel interpretation of the Cartan covariant binary biquadratic form via the classical Wilczynski invariant of curves in projective spaces associated with abnormal extremals of the distributions [4, 27, 28] one can generalize this Cartan result to rank 2 distributions in ℝn satisfying certain genericity assumption, called maximality of class, for arbitrary n ≥ 5.In the present paper for any rank 2 distribution of maximal class with at least one nonvanishing generalized Wilczynski invariants we construct the canonical frame on a (2n — 3)-dimensional bundle and describe explicitly the moduli spaces of the most symmetric models. The relation of our results to the divergence equivalence of Lagrangians of higher order is given as well.

The resistance of randomly grown trees

An electrical network with the structure of a random tree is considered: starting from a root vertex, in one iteration each leaf (a vertex with zero or one adjacent edges) of the tree is extended by either a single edge with probability p or two edges with probability 1 − p. With each edge having a resistance equal to 1Ω, the total resistance Rn between the root vertex and a busbar connecting all the vertices at the nth level is considered. A dynamical system is presented which approximates Rn, it is shown that the mean value 〈Rn〉 for this system approaches (1 + p)/(1 − p) as n → ∞, the distribution of Rn at large n is also examined. Additionally, a random sequence construction akin to a random Fibonacci sequence is used to approximate Rn; this sequence is shown to be related to the Legendre polynomials and its mean is shown to converge with |〈Rn〉 − (1 + p)/(1 − p)| ∼ n−1/2.

Rn, He and CO2 soil gas geochemistry for the study of active and inactive faults

Abstract Two Italian areas, characterized by different seismological histories, were investigated to enhance the basic knowledge of gas migration mechanisms during earthquakes. Sharp variations occur in the movement and concentration of some gaseous species due to the evolution of the local stress regime. The first area (Colpasquale) is located in the central Italian region of Marche and provided a good location to study gas migration in a seismically active region. The area was devastated by a sequence of shallow earthquakes over a 3 month-long period (September–December, 1997). The occurrence of this catastrophic event, as well as the long duration of the “seismic sequence”, presented a unique opportunity to study gas migration in a zone undergoing active displacement. Soil gas surveys were performed 1 day, 1 week, 1 year and 2 years after the main shock (Ms 5.6) in the Colpasquale area. In particular, results highlight a change in the Rn distribution during the three monitoring years indicating a variation of gas migration that may be linked to the evolution of the stress regime. The second study area is located in the Campidano Graben (southern part of Sardinia Island). This area is characterized by seismic quiescence, displaying an almost complete lack of historical earthquakes and instrumentally recorded seismicity. The consistently low values observed for all analyzed gases suggest that the studied area is likely characterized by sealed, non-active faults that prevent significant gas migration. The comparison of data from both studied areas indicate that soil gas geochemistry is useful to locate tectonic discontinuities even when they intersect non-cohesive clastic rocks near the surface and thus are not visible (i.e., “blind faults”).

Distribution of sympathetic fiber areas of radial nerve in the forearm: an immunohistochemical study in cadavers

Secondary to peripheral nerve injuries, involvement of sympathetic fibers complications such as complex regional pain syndrome (CRPS) have been reported. There are limited studies on the sympathetic fibers and their distribution in the upper limb nerves. There are no reports available in the distribution of the sympathetic fibers/areas of radial nerve in the forearm. The aim of the present study was an attempt to find the distribution of sympathetic fibers in the radial nerve just above cubital fossa (RN), superficial branch of radial nerve at cubital fossa (SBRN-1) and above wrist (SBRN-2). We have studied on 19 fresh human cadaveric RN, SBRN-1, and SBRN-2 samples. Frozen sections of these nerves were processed by immunohistochemical (tyrosine hydroxylase) method for sympathetic fibers. The sympathetic fibers area (Asym) was found to be more in RN when compared to SBRN-1 and SBRN-2. The comparison of the sympathetic index (SI = sympathetic fibers area/total fascicular area of the nerve) between RN and SBRN-1 (p < 0.001), RN and SBRN-2 (p < 0.001), and SBRN-1 and SBRN-2 (p = 0.016) were statistically significant. The sympathetic index (SI) for SBRN-1 was more when compared to RN and SBRN-2. Sympathetic fibers area (Asym) was found to be more in RN when compared to SBRN-1 and SBRN-2. The sympathetic ratio (SI) and percentage of sympathetic fibers area (Asym %) was more in SBRN-1 when compared to RN and SBRN-2. These results of the study might help to explain sympathetic system-related diseases in the area of distribution of RN and SBRN.

Soil–gas monitoring: A tool for fault delineation studies along Hsinhua Fault (Tainan), Southern Taiwan

Many studies have shown the soil gas method to be one of the most reliable investigation tools in the research of earthquake precursory signals and fault delineation. The present research is aimed finding the relationship between soil gas distribution and tectonic systems in the vicinity of the Hsinhua Fault zone in the Tainan area of Southern Taiwan. More than 110 samples were collected along 13 traverses to find the spatial distribution of Rn, He, CO2 and N2. The spatial congruence of all the gases shows that N2 is the most probable carrier gas of He, whereas CO2 seems to be a good carrier gas of Rn in this area. From the spatial distribution of Rn, He, CO2 and N2 the trace of Hsinhua Fault and neotectonic features can be identified. The spatial distribution of studied gases shows a clear anomalous trend ENE–SWS along the Hsinhua Fault.

On local geometry of non-holonomic rank 2 distributions

In 1910 E. Cartan constructed a canonical frame and found the most symmetric case for maximally non-holonomic rank 2 distributions in ℝ5. We solve the analogous problem for germs of generic rank 2 distributions in ℝn for n > 5. We use a completely different approach based on the symplectification of the problem. The main idea is to consider a special odd-dimensional submanifold WD of the cotangent bundle associated with any rank 2 distribution D. It is naturally foliated by characteristic curves, which are also called the abnormal extremals of the distribution D. The dynamics of vertical fibers along characteristic curves defines certain curves of flags of isotropic and coisotropic subspaces in a linear symplectic space. Using the classical theory of curves in projective spaces, we construct the canonical frame of the distribution D on a certain (2n − 1)-dimensional fiber bundle over WD with the structure group of all Möbius transformations, preserving 0. The paper is the detailed exposition of the constructions and the results, announced in the short note (B. Doubrov and I. Zelenko, C. R. Math. Acad. Sci. Paris, Ser. I (8) 342 (2006) 589–594).

Zinc Supplementation Prevents Alcoholic Liver Injury in Mice through Attenuation of Oxidative Stress

Alcoholic liver disease is associated with zinc decrease in the liver. Therefore, we examined whether dietary zinc supplementation could provide protection from alcoholic liver injury. Metallothionein-knockout and wild-type 129/Sv mice were pair-fed an ethanol-containing liquid diet for 12 weeks, and the effects of zinc supplementation on ethanol-induced liver injury were analyzed. Zinc supplementation attenuated ethanol-induced hepatic zinc depletion and liver injury as measured by histopathological and ultrastructural changes, serum alanine transferase activity, and hepatic tumor necrosis factor-alpha in both metallothionein-knockout and wild-type mice, indicating a metallothionein-independent zinc protection. Zinc supplementation inhibited accumulation of reactive oxygen species, as indicated by dihydroethidium fluorescence, and the consequent oxidative damage, as assessed by immunohistochemical detection of 4-hydroxynonenal and nitrotyrosine and quantitative analysis of malondialdehyde and protein carbonyl in the liver. Zinc supplementation suppressed ethanol-elevated cytochrome P450 2E1 activity but increased the activity of alcohol dehydrogenase in the liver, without affecting the rate of blood ethanol elimination. Zinc supplementation also prevented ethanol-induced decreases in glutathione concentration and glutathione peroxidase activity and increased glutathione reductase activity in the liver. In conclusion, zinc supplementation prevents alcoholic liver injury in an metallothionein-independent manner by inhibiting the generation of reactive oxygen species (P450 2E1) and enhancing the activity of antioxidant pathways.

Asymptotics for L2 functionals of the empirical quantile process, with applications to tests of fit based on weighted Wasserstein distances

Weighted L2 functionals of the empirical quantile process appear as a component of many test statistics, in particular in tests of fit to location-scale families of distributions based on weighted Wasserstein distances. An essentially complete set of distributional limit theorems for the squared empirical quantile process integrated with respect to general weights is presented. The results rely on limit theorems for quadratic forms in exponential random variables, and the proofs use only simple asymptotic theory for probability distributions in Rn. The limit theorems are then applied to determine the asymptotic distribution of the test statistics on which weighted Wasserstein tests are based. In particular, this paper contains an elementary derivation of the limit distribution of the Shapiro-Wilk test statistic under normality.

CORRELATED RANDOM WALKS WITH A FINITE MEMORY RANGE

We study a family of correlated one-dimensional random walks with a finite memory range M. These walks are extensions of the Taylor's walk as investigated by Goldstein, which has a memory range equal to one. At each step, with a probability p, the random walker moves either to the right or to the left with equal probabilities, or with a probability q = 1 -p performs a move, which is a stochastic Boolean function of the M previous steps. We first derive the most general form of this stochastic Boolean function, and study some typical cases which ensure that the average value &lt;Rn&gt; of the walker's location after n steps is zero for all values of n. In each case, using a matrix technique, we provide a general method for constructing the generating function of the probability distribution of Rn; we also establish directly an exact analytic expression for the step–step correlations and the variance [Formula: see text] of the walk. From the expression of [Formula: see text], which is not straightforward to derive from the probability distribution, we show that, for n approaching infinity, the variance of any of these walks behaves as n, provided p &gt; 0. Moreover, in many cases, for a very small fixed value of p, the variance exhibits a crossover phenomenon as n increases from a not too large value. The crossover takes place for values of n around 1/p. This feature may mimic the existence of a nontrivial Hurst exponent, and induce a misleading analysis of numerical data issued from mathematical or natural sciences experiments.

Poisson components of probability distributions in Rn

The author's results from [3] are extended and generalized to the multidimensional case.

On the first zero of an empirical characteristic function

We deal with the distribution of the first zero Rn of the real part of the empirical characteristic process related to a random variable X. Depending on the behaviour of the theoretical real part of the underlying characteristic function, cases with a slow exponential decrease to zero are considered. We derive the limit distribution of Rn in this case, which clarifies some recent results on Rn in relation to the behaviour of the characteristic function.

Monte Carlo counting efficiencies for measuring Rn in a charcoal canister

The level of 222Rn adsorbed in an activated charcoal canister may be determined by direct measurement of the canister, using a NaI detector. The counting efficiency of this arrangement depends on the Rn distribution in the charcoal, and this varies as a function of sampling period. Provided the Rn profile can be predicted, a Monte Carlo program can be used to simulate the counting arrangement. The Rn distribution in a canister used for surface emanation measurements can be described accurately by use of an empirical expression. Three time dependent coefficients were used in the expression to determine the shape of the distribution as a function of sampling period. Counting efficiencies were estimated by use of a simple Monte Carlo program and these were all found to be in close agreement with measured values for various sampling periods.