Moment inequality and complete convergence of moving average processes under asymptotically linear negative quadrant dependence assumptions

Let {Y, Y _i , −∞ < i < ∞} be a doubly infinite sequence of identically distributed and asymptotically linear negative quadrant dependence random variables, {a _i , −∞ < i < ∞} an absolutely summable sequence of real numbers. We are inspired by Wang et al. (Econometric Theory 18:119–139, 2002) and Salvadori (Stoch Environ Res Risk Assess 17:116–140, 2003). And Salvadori (Stoch Environ Res Risk Assess 17:116–140, 2003) have obtained Linear combinations of order statistics to estimate the quantiles of generalized pareto and extreme values distributions. In this paper, we prove the complete convergence of under some suitable conditions. The results obtained improve and generalize the results of Li et al. (1992) and Zhang (1996). The results obtained extend those for negative associated sequences and ρ^*-mixing sequences. CIC Number O211, AMS (2000) Subject Classification 60F15, 60G50 Research supported by National Natural Science Foundation of China     

Attenuation of P,S, and coda waves in Koyna region,India

The attenuation properties of the crust in the Koyna region of the Indian shield have been investigated using 164 seismograms from 37 local earthquakes that occurred in the region. The extended coda normalization method has been used to estimate the quality factors for P waves and S waves , and the single back-scattering model has been used to determine the quality factor for coda waves (Q _c). The earthquakes used in the present study have the focal depth in the range of 1–9 km, and the epicentral distance vary from 11 to 55 km. The values of and Q _c show a dependence on frequency in the Koyna region. The average frequency dependent relationships (Q = Q ₀ f ⁿ) estimated for the region are , and . The ratio is found to be greater than one for the frequency range considered here (1.5–18 Hz). This ratio, along with the frequency dependence of quality factors, indicates that scattering is an important factor contributing to the attenuation of body waves in the region. A comparison of Q _c and in the present study shows that for frequencies below 4 Hz and for the frequencies greater than 4 Hz. This may be due to the multiple scattering effect of the medium. The outcome of this study is expected to be useful for the estimation of source parameters and near-source simulation of earthquake ground motion, which in turn are required in the seismic hazard assessment of a region.     

An algorithm for the optimum distribution of a regional seismic network — II. An analysis of the accuracy of location of local earthquakes depending on the number of seismic stations

Summary Seven optimal networks consisting of 4 to 10 stations are compared for a given region, where velocity-depth profiles and the distribution of seismic intensity are known. Assuming that the standard error of arrival time is _t =0.05 s and the standard errors of the parameters of velocity-depth profiles are equal to 5% of their values, the average standard errors of the origin time and focus coordinates are estimated. The application of optimum methods to the planning of seismic networks in the Lublin Coal Basin is presented, and maps of standard errors of origin time , depth and epicenter ( _xy ) for the case of an optimum network of 6 seismic stations are given.     

Steady flows driven by sources of random strength in heterogeneous aquifers with application to partially penetrating wells

Average steady source flow in heterogeneous porous formations is modelled by regarding the hydraulic conductivity K(x) as a stationary random space function (RSF). As a consequence, the flow variables become RSFs as well, and we are interested into calculating their moments. This problem has been intensively studied in the case of a Neumann type boundary condition at the source. However, there are many applications (such as well-type flows) for which the required boundary condition is that of Dirichlet. In order to fulfill such a requirement the strength of the source must be proportional to K(x), and therefore the source itself results a RSF. To solve flows driven by sources whose strength is spatially variable, we have used a perturbation procedure similar to that developed by Indelman and Abramovich (Water Resour Res 30:3385–3393, 1994) to analyze flows generated by sources of deterministic strength. Due to the linearity of the mathematical problem, we have focused on the explicit derivation of the mean head distribution G _d (x) generated by a unit pulse. Such a distribution represents the fundamental solution to the average flow equations, and it is termed as mean Green function. The function G _d (x) is derived here at the second order of approximation in the variance σ² of the fluctuation (where K _A is the mean value of K(x)), for arbitrary correlation function ρ(x), and any dimensionality d of the flow domain. We represent G _d (x) as product between the homogeneous Green function G _d ⁽⁰⁾(x) valid in a domain with constant K _A , and a distortion term Ψ _d (x) = 1 + σ²ψ _d (x) which modifies G _d ⁽⁰⁾(x) to account for the medium heterogeneity. In the case of isotropic formations ψ _d (x) is expressed via one quadrature. This quadrature can be analytically calculated after adopting specific (e.g.. exponential and Gaussian) shape for ρ(x). These general results are subsequently used to investigate flow toward a partially-penetrating well in a semi-infinite domain. Indeed, we construct a σ²-order approximation to the mean as well as variance of the head by replacing the well with a singular segment. It is shown how the well-length combined with the medium heterogeneity affects the head distribution. We have introduced the concept of equivalent conductivity K ^eq(r,z). The main result is the relationship where the characteristic function ψ^(w)(r,z) adjusts the homogeneous conductivity K _A to account for the impact of the heterogeneity. In this way, a procedure can be developed to identify the aquifer hydraulic properties by means of field-scale head measurements. Finally, in the case of a fully penetrating well we have expressed the equivalent conductivity in analytical form, and we have shown that (being the effective conductivity for mean uniform flow), in agreement with the numerical simulations of Firmani et al. (Water Resour Res 42:W03422, 2006).     

“Pandora box” — Matrix in the calculus of observations

Summary If the condition R(A)=k(n), whereA is the design matrix of the type n × k and k the number of parameters to be determined, is not satisfied, or if the covariance matrixH is singular, it is possible to determine the adjusted value of the unbiased estimable function of the parameters f(), its dispersion D( (x)) and ² as the unbiased estimate of the value of ² by means of an arbitrary g-inversion of the matrix . The matrix , because of its remarkable properties, is called the Pandora Box matrix. The paper gives the proofs of these properties and the manner in which they can be employed in the calculus of observations.     

Nonlinear Magnetoconvection and the Geostrophic Flow - Subcritical Solutions

The magnetoconvection problem under the magnetostrophic approximation is investigated as the nonlinear regime is entered. The model consists of a fluid filled sphere, internally heated, and rapidly rotating in the presence of a prescribed, axisymmetric, toroidal magnetic field. For simplicity only a dipole parity and a single azimuthal wavenumber (m = 2) is considered here. The leading order nonlinearity at small amplitude is the geostrophic flow U _g which is introduced to the previously linear model (Walker and Barenghi, 1997a, b). Walker and Barenghi (1997c) considered parameter space above critical and found that U _g acts as an equilibration mechanism for moderately supercritical solutions. However, for solutions well above critical a Taylor state is approached and the system can no longer equilibrate. More importantly though, in the context of this paper, is that subcritical solutions were found. Here subcritical solutions are considered in more detail. It was found that, at is strongly dependent on . ( is the critical value of the modified Rayleigh number is a measure of the maximum amplitude of the generated geostrophic flow while , the Elsasser number, defines the strength of the prescribed toroidal field.) R_m at proves to be the key measure in determining how far into the subcritical regime the system can advance.     

Basaltic thermals and Subplinian plumes: Constraints from acoustic measurements at Shishaldin volcano, Alaska

The 1999 basaltic eruption of Shishaldin volcano (Alaska, USA) included both Strombolian and Subplinian activity, as well as a “pre-Subplinian” phase interpreted as the local coalescence within a long foam in the conduit. Although few visual observations were made of the eruption, a great deal of information regarding gas velocity, gas flux at the vent and plume height may be inferred by using acoustic recordings of the eruption. By relating acoustic power to gas velocity, a time series of gas velocity is calculated for the Subplinian and pre-Subplinian phases. These time series show trends in gas velocity that are interpreted as plumes or, for those signals lasting only a short time, thermals. The Subplinian phase is shown to be composed of a thermal followed by five plumes with a total expelled gas volume of .The initiation of the Subplinian activity is probably related to the arrival of a large overpressurised bubble close to the top of the magma column. A gradual increase in low-frequency (0.01–0.5 Hz) signal prior to this “trigger bubble” may be due to the rise of the bubble in the conduit. This delay corresponds to a reservoir located at ≈3.9 km below the surface, in good agreement with studies on other volcanoes.The presence of two thermal phases is also identified in the middle of the pre-Subplinian phase with a total gas release of and . Gas velocity at the vent is found to be and for the Subplinian plumes and the pre-Subplinian thermals respectively.The agreement is very good between estimates of the gas flux from modelling the plume height and those obtained from acoustic measurements, leading to a new method by which eruption physical parameters may be quantified. Furthermore, direct measurements of gas velocity can be used for better estimates of the flux released during the eruption.     

Quantitative microbial risk assessment: uncertainty and measures of central tendency for skewed distributions

In the past, arithmetic and geometric means have both been used to characterise pathogen densities in samples used for microbial risk assessment models. The calculation of total (annual) risk is based on cumulative independent (daily) exposures and the use of an exponential dose–response model, such as that used for exposure to Giardia or Cryptosporidium. Mathematical analysis suggests that the arithmetic mean is the appropriate measure of central tendency for microbial concentration with respect to repeated samples of daily exposure in risk assessment. This is despite frequent characterisation of microbial density by the geometric mean, since the microbial distributions may be Log normal or skewed in nature. Mathematical derivation supporting the use of the arithmetic mean has been based on deterministic analysis, prior assumptions and definitions, the use of point-estimates of probability, and has not included from the outset the influence of an actual distribution for microbial densities. We address these issues by experiments using two real-world pathogen datasets, together with Monte Carlo simulation, and it is revealed that the arithmetic mean also holds in the case of a daily dose with a finite distribution in microbial density, even when the distribution is very highly-skewed, as often occurs in environmental samples. Further, for simplicity, in many risk assessment models, the daily infection risk is assumed to be the same for each day of the year and is represented by a single value, which is then used in the calculation of p _Σ, which is a numerical estimate of annual risk, P _Σ, and we highlight the fact that is simply a function of the geometric mean of the daily complementary risk probabilities (although it is sometimes approximated by the arithmetic mean of daily risk in the low dose case). Finally, the risk estimate is an imprecise probability with no indication of error and we investigate and clarify the distinction between risk and uncertainty assessment with respect to the predictive model used for total risk assessment.     

Improved method to determine the molar volume and compositions of the NaCl-H<Subscript>2</Subscript>O-CO<Subscript>2</Subscript> system inclusion

On the basis of Parry’s method (1986), an improved method was established to determine the molar volume (Vm) and compositions (X) of the NaCl-H2O-CO2 (NHC) system inclusion. To use this method, the determination of Vm-X only requires three microthermometric data of a NHC inclusion: partial homog-enization temperature (Th ,CO2), salinity (S) and total homogenization temperature (Th). Theoretically, four associated equations are needed containing four unknown parameters: X CO2, XNaCl, Vm and F (volume fraction of CO2 phase in total inclusion when occurring partial homogenization). When they are released, the Vm-X are determined. The former three equations, only correlated with Th ,CO2, S and F, have simplified expressions:XCO2=f1(Th,CO2,S,F),XNaCl=f2(Th,CO2,S,F),Vm=f3(Th,CO2,S,F). The last one is the thermodynamic relationship of X CO2, XNaCl, Vm and Th:f4(XCO2,XNaCl,Vm,Th)=0.Since the above four associated equations are complicated, it is necessary to adopt iterative technique to release them. The technique can be described by:(i) Freely input a F value (0≤F≤1),with Th ,CO2 and S, into the former three equations. As a result,X CO 2,XNaCl and the molar volume value recorded as Vm1 are derived. (ii) Input the X CO2 and XNaCl gotten in the step above into the last equation, and another molar volume value recorded as Vm2 is determined. (iii) If Vm1 is unequal to Vm2, the calculation will be restarted from “(i)”. The iteration is completed until Vm1 is equal to Vm2, which means that the four associated equations are released. Compared to Parry’s (1986) solution method, the improved method is more convenient to use, as well as more accurate to determine X CO 2. It is available for a NHC inlusion whose partial homogenization temperature is higher than clatherate melting temperature and there are no solid salt crystals in the inclusion at parital homogenization.     

Propagation of surface waves on the surface of a non-homogeneous aeolotropic cylindrical shell

Summary The object of the present paper is to investigate the propagation of surface waves on a non-homogeneous aeolotropic cylindrical shell surrounded by vacuum. The elastic constantsc _ij (i, j=1,2...) and density of the material of the shell are assumed to be of the form and respectively, where _ij, ₀ are constants andk ₁,k ₂ are any integers.     

Empirische Untersuchung zur Frage der Beziehung zwischen durchschnittlicher und kennzeichnender Wellenperiode im Seegang

Zusammenfassung Als Zusammenhang zwischen der kennzeichnenden Wellenperiode und der durchschnittlichen Periode im Seegang wird die Formel angesetzt. Mit Hilfe empirischer Unterlagen wird nachgewiesen, daßc eine Funktion des von D. E. Cartwright und M. S. Longuet-Higgins [1956] eingeführten Spektralparameters ist. Es wird eine vorläufige quantitative Beziehung zwischenc und abgeleitet.

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Empirical investigations of the relation between the mean and the significant wave period in the sea

Summary It is supposed that the formula represents the relation between the significant wave period and the mean period in the sea. With the aid of empirical data it is demonstrated thatc is a function of the spectral parameter introduced by D. E. Cartwright and M. S. Longuet-Higgins [1956]. A preliminary quantitative relation betweenc and is derived.

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Etudes empiriques de la relation entre la période moyenne et la période significative des vagues dans la houle

Résumé On suppose que la formule représente la relation entre la période significative des vagues et la période moyenne dans la houle. A l'aide des données empiriques on montre quec est une fonction du paramètre spectral , introduit par D. E. Cartwright et M. S. Longuet-Higgins [1956]. Une relation quantitative préliminaire entrec et est dérivée.

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The viscosity of hydrous dacitic liquids: implications for the rheology of evolving silicic magmas

The viscosity of a series of six synthetic dacitic liquids, containing up to 5.04 wt% dissolved water, was measured above the glass transition range by parallel-plate viscometry. The temperature of the 10¹¹ Pa s isokom decreases from 1065 K for the anhydrous liquid, to 864 K and 680 K for water contents of 0.97 and 5.04 wt% H₂O. Including additional measurements at high temperatures by concentric-cylinder and falling-sphere viscometry, the viscosity (η) can be expressed as a function of temperature and water content w according to: where η is in Pa s, T is temperature in K, and w is in weight percent. Within the conditions of measurement, this parameterization reproduces the 76 viscosity data with a root-mean square deviation (RMSD) of 0.16 log units in viscosity, or 7.8 K in temperature. The measurements show that water decreases the viscosity of the dacitic liquids more than for andesitic liquids, but less than for rhyolites. At low temperatures and high water contents, andesitic liquids are more viscous than the dacitic liquids, which are in turn more viscous than rhyolitic liquids, reversing the trend seen for high temperatures and low water contents. This suggests that the relative viscosity of different melts depends on temperature and water content as much as on bulk melt composition and structure. At magmatic temperatures, rhyolites are orders of magnitude more viscous than dacites, which are slightly more viscous than andesites. During degassing, all three liquids undergo a rapid viscosity increase at low water contents, and both dacitic and andesitic liquids will degas more efficiently than rhyolitic liquids. During cooling and differentiation, changing melt chemistry, decreasing temperature and increasing crystal content all lead to increases in the viscosity of magma (melt plus crystals). Under closed system conditions, where melt water content can increase during crystallization, viscosity increases may be small. Conversely, viscosity increases are very abrupt during ascent and degassing-induced crystallization.     

Intrinsic and Scattering Seismic Attenuation in Southwestern Anatolia

The intrinsic dissipation and scattering attenuation in southwestern (SW) Anatolia, which is a tectonically active region, is studied using the coda waves. First the coda quality factor (Q_c) assuming single scattering is estimated from the slope of the coda-wave amplitude decay. Then the Multiple Lapse Time Window (MLTW) analysis is performed with a uniform earth model. Three non-overlapping temporal data windows are used to calculate the scattered seismic energy densities against the source-receiver distances, which, in turn, are used to calculate separate estimates of the intrinsic and scattering factors. In order to explore the frequency dependency, the observed seismograms are band pass-filtered at the center frequencies of 0.75, 1.5, 3.0, 6.0 and 12.0. The scattering attenuation (Q_s⁻¹) is found lower than the intrinsic attenuation (Q_i⁻¹) at all frequencies except at 0.75 Hz where the opposite is observed. Overall the intrinsic attenuation dominates over the scattering attenuation in the SW Anatolia region. The integrated energy curves obtained for the first energy window (i.e., 0–15 s) are somewhat irregular with distance while the second (i.e., 15–30 s) and third (i.e., 30–45 s) data windows exhibit more regular change with distance at most frequencies. The seismic albedo B₀ is determined as 0.61 at 0.75 Hz and 0.34 at 12.0 Hz while the total attenuation factor denoted by L_e⁻¹ changes in the range 0.034–0.017. For the source-station range 20–180 km considered the scattering attenuation is found strongly frequency dependent given by the power law Q_s⁻¹ = 0.010*f^−1.508. The same relations for Q_i⁻¹, Q_t⁻¹ (total), Q_c⁻¹ and (expected) hold as Q_i⁻¹ = 0.0090*f^−1.17, Q_t⁻¹ = 0.019*f^−1.31, Q_c⁻¹ = 0.008*f^−0.84 and respectively. Compared to the other attenuation factors Q_c⁻¹ and are less dependent on the frequency.     

Estimation of coda wave attenuation in East Central Iran

The attenuation of coda waves, Q _c , has been estimated in Zarand, Jiroft, and Bam regions of east central Iran using a single back-scattering model of S-coda envelopes. For this purpose, the recordings of 97 earthquakes by three seismic networks and a local strong ground motion network have been used. In this research, the frequency-dependent Q _c values are estimated at central frequencies of 1.5, 3, 6, 8, 12, 16, and 24 Hz using different lapse time windows from 20 to 60 s. The frequency-dependent relationships obtained are for Zarand, for Jiroft, and for Bam region. From the strong ground motion data, we obtain the relation . The Q _c frequency-dependent relationship for the entire region of east central Iran from all data (both seismograms and accelerograms) is . The average Q _c values estimated and their frequency dependent relationships correlate well with a highly heterogeneous and highly tectonically active region. Results also show that the attenuation is higher in Bam region compared to Zarand and Jiroft regions.     

Dependence of the concentration of a passive substance on the duration of the measurement

Zusammenfassung Der Artikel hatte zur Aufgabe den Einfluss von Ver?nderung Beobachtungs-Intervalls auf die Konzentration der passiven, von erh?hter und steitiger Punktquelle ausgelassenen Substanz auszudrücken. Zu diesem Zwecke wurde ein Modell der sog, nichtstation?ren Rauchspur—einer durchschnittlichen Rauchspur im Messintervall T—konstruiert. Man setzt voraus, dass die Verteilung von Teilchen in der nichtstation?ren Rauchspur eine Gauss'sche ist mit der Dispersion in den Richtungen y, z. Für die Dispersion wurde die Beziehung (15) abgeleitet. Analoge Beziehung gilt auch in der Richtung z. Wenn uns die Auslenkung der Achse der nichtstation?ren Rauchspur von der Achse der station?ren Rauchspur, der Geraden (t,O, H), bekannt ist, so k?nnen wir die Konzentration q_T(t,y,z) explizit ausdrücken.

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Address: Dúbravská cesta 4, Bratislava-Patr?nka.     

The dynamics of magma mixing in a rising magma batch

The conditions under which two magmas can become mixed within a rising magma batch are investigated by scaling analyses and fluid-dynamical experiments. The results of scaling analyses show that the fluid behaviours in a squeezed conduit are determined mainly by the dimensionless number where ₁ is the viscosity of the fluid, U is the velocity, g is the acceleration due to gravity, is the density difference between the two fluids, and R is the radius of the tube. The parameter I represents a balance between the viscous effects in the uppermost magma which prevent it from being moved off the conduit walls, and the buoyancy forces which tend to keep the interface horizontal. The experiments are carried out using fluid pairs of various density and viscosity contrasts in a squeezed vinyl tube. They show that overturning of the initial density stratification and mixing occur when I>order 10^-1; the two fluids remain stratified when I 10^-3. Transitional states are observed when 10^-3<I<10^-1. These results are nearly independent of Reynolds number and viscosity ratio in the range of and Re ₁<300. Applying these results to magmas shows that silicic to intermediate magmas overlying mafic magma will be prone to mixing in a rising magma batch. This mechanism can explain some occurrences of small-volume mixed lava flows.     

Ground-motion Attenuation Relation from Strong-motion Records of the 2001 Mw 7.7 Bhuj Earthquake Sequence (2001–2006), Gujarat, India

Predictive relations are developed for peak ground acceleration (PGA) from the engineering seismoscope (SRR) records of the 2001 M_w 7.7 Bhuj earthquake and 239 strong-motion records of 32 significant aftershocks of 3.1 ≤ M_w ≤ 5.6 at epicentral distances of 1 ≤ R ≤ 288 km. We have taken advantage of the recent increase in strong-motion data at close distances to derive new attenuation relation for peak horizontal acceleration in the Kachchh seismic zone, Gujarat. This new analysis uses the Joyner-Boore’s method for a magnitude-independent shape, based on geometrical spreading and anelastic attenuation, for the attenuation curve. The resulting attenuation equation is,

Recherches complémentaires sur le bases du calculateur météorologique «Temp»

Résumé La formule de base, traduisant une propriété analytique d'une classe très générale de fonctions, est un corollaire du théorème fondamental démontré dans un mémoire précédent, d'après lequel, étant donnés une fonction continue,p(, ,t) des points (, ) d'une surface régulière fermée et du temps et le champ d'un vecteur vitesse de transfert ou d'advection tangent à et ayant des lignes de flux fermées et régulières, il existe un opérateur spatial, linéaire, non singulierA tel que la fonctionA(p+Const.) soit purement advective par rapport a (sans creusement ni comblement). Ce théorème peut être exprimé par l'équation , où est un opérateur spatial, linéaire et non singulier, fonction deA.La détermination de peut être faite, soit en comparant deux formes différentes de la solution générale de l'équation en , soit en utilisant un raisonnement a priori très simple. On arrive ainsi au résultat pour un certain scalaireu(, ).Dans le cas oùp(, ,t) est la perturbation de la pression sur la surface du géoïde l'équation résulte aussi, comme nous l'avons montré dans le mémoire précédent, de notre théorie hydrodynamique des perturbations. On montre ici que la même équation peut encore être déduite de l'équation de continuité associée à la condition d'équilibre quasi statique selon la verticale.Comme applications de la formule de base (solution générale de l'équation enM), on étudie les problèmes suivants: 1^o creusement et comblement en général; 2^o creusement et comblement des centres et des cols; 3^o mouvement des centres et des cols; 4^o instabilité d'un champ moyen; 5^o propriétés spatiales des champsp(, ,t) et des vecteurs d'advection analytiques.Après une discussion des erreurs de la prévision d'un champp(, ,t) par la formule de base, du fait des erreurs des observations et du fonctionnement du calculateur, on examine quelques particularités du transfert ou advection d'un champf ₀(, ) par le vecteur . Enfin, le dernier chapitre du mémoire donne des éclaircissements complémentaires sur la structure du calculateur électronique «Temp» (qui effectue automatiquement les opérations mathématiques de la formule de base) et expose l'état actuel de sa construction.

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Summary The basic formula, expressing an analytical property of a very general class of functions, is a corollary of the fundamental theorem, proved in a previous paper, according to which, given a functionp(, ,t) of the points (, ) of a closed regular surface and of the time, and a transfer or advection velocity vector tangent to and having regular closed streamlines, there is a spatial, linear, non singular operatorA such thatA(p+const.) is a purely advective function in respect to (no deepening). This theorem can be expressed by the equation where is a spatial, linear, non singular operator depending onA.The determination of can be attained, either by the comparison of two different forms of the general solution of the -equation, or by a simple a priori reasonning. The conclusion is thus reached that for a certain scalaru(, ).Whenp(, ,t) is the pressure perturbation at sea level, it was shown, in the preceding paper, that the equation can also be derived from our hydrodynamical perturbation theory. We now show that for this particular case, the same equation is also a consequence of the equation of continuity together with the condition of quasi statical vertical equilibrium.The following problems are then analysed by means of the basic formula: 1^o deepening and filling in general; 2^o deepening and filling of the centres and cols; 3^o motion of the centres and cols; 4^o instability of a mean field; 5^o spatial properties of the analytical fields and advection vectors .The errors in the forecast of a field,p(, ,t) by means of the basic formula, due to the observational and computational errors, are discussed, and some peculiarities of the transfer or advection of a fieldf ₀(, ) by are examined. Finally, complementary points are disclosed on the structure of the electronic computer «Temp» which performs automatically the mathematical operations of the basic formula, and a brief report is given of the present state of its construction.