We establish well-posedness of initial-boundary value problems for continuity equations with BV (bounded total variation) coefficients. We do not prescribe any condition on the orientation of the coefficients at the boundary of the domain. We also discuss some examples showing that, regardless the orientation of the coefficients at the boundary, uniqueness may be violated as soon as the BV regu...

We consider linear first order scalar equations of the form ρt + div(ρv) + aρ = f with appropriate initial and boundary conditions. It is shown that approximate solutions computed using the discontinuous Galerkin method will converge in L[0, T ;L(Ω)] when the coefficients v and a and data f satisfy the minimal assumptions required to establish existence and uniqueness of solutions. In particula...

We give a simple proof of a well-known theorem of Gál and of the recent related results of Aistleitner, Berkes and Seip [1] regarding the size of GCD sums. In fact, our method obtains the asymptotically sharp constant in Gál’s theorem, which is new. Our approach also gives a transparent explanation of the relationship between the maximal size of the Riemann zeta function on vertical lines and b...

The comparison of groups in regression models for binary outcomes is complicated by an identification problem inherent in these models. Traditional tests of the equality of coefficients across groups confound the magnitude of the regression coefficients with residual variation. If the amount of residual variation differs between groups, the test can lead to incorrect conclusions (Allison 1999)....

Introduction. In 1923 M. Fekete [2]2 introduced the concept of factor sequences that left invariant the class of a Fourier series. That is, Fekete investigated the conditions to which a sequence of constants (X„) must be subjected in order that (X„a„, X„i„) be Fourier coefficients of a function of the same class, K, as that of the function determined by (an, bn). Whenever (X„) has this property...

In small-area variation analysis, the variation of health care utilization rates, e.g., admission rates, among small areas is calculated. Frequently, the variation of one diagnosis, diagnosis-related group (DRG), or procedure is compared with the variation of another. Unfortunately, the methods generally used to make these comparisons are not consistent. They differ on whether they 1) adjust fo...

A generalization of Émery’s inequality for stochastic integrals is shown for convolution integrals of the form ( ∫ t 0 g(t − s)Y (s−) dZ(s))t>0, where Z is a semimartingale, Y an adapted càdlàg process, and g a deterministic function. The function g is assumed to be absolutely continuous with a derivative that is continuous or of bounded variation or a sum of such functions. The function g may ...

Statistical study In general 3 experiments were taken into account in order to calculate dispersion parameters as standard deviation and variation coefficient (RSD). The last column in Table S1 shows the percentage variation of the interfacial impedance modulus when recognition reaction was taking place. Indeed the interfacial impedance variation on a surface coated with BSA is in a linear rela...

warp and weft spacing and its coefficient of variation affect the physical properties of fabrics such as fabric hand, frictional and mechanical properties. in this paper the weft and warp spacing and its coefficient of variation for plain weave is calculated using fourier transforms. different methods have been used in this work including autocorrelation function. first, two dimensional power s...

In this study, different derivative spectrophotometric methods are proposed for the simultaneous determination of chlorpheniramine maleate (CP), phenylephrine HCl (PE) and phenylpropanolamine HCl (PP) in their ternary mixtures and in pharmaceutical dosage forms. Spectra of single component and ternary mixtures of various concentrations and combinations from zero- to fourth-derivation were obtai...