On error estimates of some higher order projection and penalty-projection methods for Navier-Stokes equations

Summary This paper is a continuation of our previous work [10] on projection methods. We study first existing higher order projection schemes in the semidiscretized form for the Navier-Stokes equations. One error analysis suggests that the precision of these schemes is most likely plagued by the inconsistent Neumann boundary condition satisfied by the pressure approximations. We then propose a penalty-projection scheme for which we obtain improved error estimates.This work is partially supported by NSF grant MS-8802596.     

On Jensen's functional equation

Summary Letf be a map from a groupG into an abelian groupH satisfyingf(xy) + f(xy ^–1) = 2f(x), f(e) = 0, wherex, y G ande is the identity inG. A set of necessary and sufficient conditions forS(G, H) = Hom(G, H) is given whenG is abelian, whereS(G, H) denotes all the solutions of the functional equation. The case whenG is non-abelian is also discussed.     

Functional inequality characterizing nonnegative concave functions in (0, ∞) k

Summary In the present note we prove that every functionf: (0, ) [0, ) satisfying the inequalityaf(s) + bf(t) f(as + bt), s, t > 0, for somea andb such that 0 <a < 1 <a + b must be of the formf(t) = f(1)t, (t > 0). This improves our recent result in [2], where the inequality is assumed to hold for alls, t 0, and gives a positive answer to the question raised there.An analogue for functions of several real variables of the above result characterizes concave functions. Conjugate functions and some relations to Hölder's and Minkowski's inequalities are mentioned.     

Problème inverse de la théorie du potentiel logarithmique pour les lemniscates

The paper is related to the question of uniqueness in the inverse logarithmic potential problem. This question is to find the conditions on which two domains D ₁ and D ₂ producing the same external potential must coincide. Assuming the general hypothesis of regularity and an additional condition of connectivity of (D₁D₂)_c, we prove a theorem of uniqueness in the case when one of the domains is a lemniscate. The main tool is one lemma for Cauchy's potential due to M. Sakai. We give a simple proof of its extension to Newtonian potential.

     

Countable Fréchetα 1-spaces may be first countable

It is shown to be consistent that countable, Fréchet, ₁-spaces are first countable. The result is obtained by using a countable support iteration of proper partial orders of length ₂.The research of both authors is partially supported by NSERC     

Wavelength-modulated,continuum-source excited atomic fluorescence spectrometric system for wear metals in jet engine lubricating oils using electrothermal atomization

A system for measuring atomic fluorescence of atoms produced via an electrically-heated graphite filament in a flame (acetylene/air or acetylene/nitrous oxide) and excited with a 300-W Eimac xenon are lamp is described. The experimental system also included wavelength modulation for background emission/fluorescence/scatter correction and an optically-triggered electronic integrator for efficient monitoring of the analyte fluorescence signal. Copper, aluminum and molybdenum were determined in jet engine lubricating oil samples (1 μl) with no pretreatment. The determinations are evaluated with respect to the accuracy and repeatability criteria of the U.S. Joint Oil Analysis Program.     

A note on debye potentials for spherically gyrotropic media

The Debye potentials are generalized to the case of electromagnetic fields in spherically gyrotropic media. A medium is called spherically gyrotropic if it is locally gyrotropic with the distinguished axis having a radial direction determined by a central point. Expressions for electromagnetic fields in terms of the generalized potentials are presented and the system of differential equations for the potentials is derived. The results are summarized in the form of a theorem. Basic facts about the Debye potentials in isotropic media are recalled.     

On bounds for the range of ordered variates II

Letx ₁, ,x _n be real numbers with ₁ ⁿ x _j =0, |x ₁ ||x ₂ ||x _n |, and ₁ ⁿ f(|x _i |)=A>0, wheref is a continuous, strictly increasing function on [0, ) withf(0)=0. Using a generalized Chebycheff inequality (or directly) it is easy to see that an upper bound for |x _m | isf ^–1 (A/(n–m+1)). If (n–m+1) is even, this bound is best possible, but not otherwise. Best upper bounds are obtained in case (n–m+1) is odd provided either (i)f is strictly convex on [0, ), or (ii)f is strictly concave on [0, ). Explicit best bounds are given as examples of (i) and (ii), namely the casesf(x)=x ^p forp>1 and 0<p<1 respectively.     

Cornelian Cherry (Cornus mas L.) Extracts Exert Cytotoxicity in Two Selected Melanoma Cell Lines—A Factorial Analysis of Time-Dependent Alterations in Values Obtained with SRB and MTT Assays

Despite the fact that phytochemicals of Cornaceae species have long been discussed as possible auxiliary agents in contemporary treatment, the insights on their properties remain relatively scarce. This study focuses on Cornus mas L. (Cornelian cherry), the extracts of which are reported to exert a pleiotropic effect shown in both in vivo and in vitro studies. This study aimed to explore the cytotoxic effect of extracts from fruits of red (Cornus mas L. ‘Podolski’) and yellow (Cornus mas L. ‘Yantarnyi’ and ‘Flava’) Cornelian cherries on two melanoma cell lines (A375 and MeWo). The extracts were characterized in the context of the concentration of bioactive compounds of antioxidative properties. Cytotoxicity was investigated with the use of the following two assays: SRB and MTT. An additional, alternative protocol for the SRB assay was used in this study so as to account for possible bias. Cytotoxicity was assessed as a difference in the whole time series of cell viability, instead of analyzing differences in raw values (often found in the literature). Both extracts from Cornus mas L. induced cytotoxicity in both A375 and MeWo cell lines, although the response of these cells was different. Moreover, based on this study, there is no evidence for claiming a different magnitude of cytotoxicity between these two extracts.     

Human Serum Amyloid a Impaired Structural Stability of High-Density Lipoproteins (HDL) and Apolipoprotein (Apo) A-I and Exacerbated Glycation Susceptibility of ApoA-I and HDL

Human serum amyloid A (SAA) is an exchangeable apolipoprotein (apo) in high-density lipoprotein (HDL) that influences HDL quality and functionality, particularly in the acute phase of inflammation. On the other hand, the structural and functional correlations of HDL containing SAA and apoA-I have not been reported. The current study was designed to compare the change in HDL quality with increasing SAA content in the lipid-free and lipid-bound states in reconstituted HDL (rHDL). The expressed recombinant human SAA1 (13 kDa) was purified to at least 98% and characterized in the lipid-free and lipid-bound states with apoA-I. The dimyristoyl phosphatidylcholine (DMPC) binding ability of apoA-I was impaired severely by the addition of SAA, while SAA alone could not bind with DMPC. The recombinant human SAA1 was incorporated into the rHDL (molar ratio 95:5:1, 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC): cholesterol: apoA-I) with various apoA-I:SAA molar ratios from 1:0 to 1:0.5, 1:1 and 1:2. With increasing SAA1 content, the rHDL particle size was reduced from 98 Å to 93 Å, and the α-helicity of apoA-I:SAA was decreased from 73% to 40% for (1:0) and (1:2), respectively. The wavelength maximum fluorescence (WMF) of tryptophan in rHDL was red-shifted from 339 nm to 345 nm for (1:0) and (1:2) of apoA-I:SAA, respectively, indicating that the addition of SAA to rHDL destabilized the secondary structure of apoA-I. Upon denaturation by urea treatment from 0 M to 8 M, SAA showed only a 3 nm red-shift in WMF, while apoA-I showed a 16 nm red-shift in WMF, indicating that SAA is resistant to denaturation and apoA-I had higher conformational flexibility than SAA. The glycation reaction of apoA-I in the presence of fructose was accelerated up to 1.8-fold by adding SAA in a dose-dependent manner than that of apoA-I alone. In conclusion, the incorporation of SAA in rHDL impaired the structural stability of apoA-I and exacerbated glycation of HDL and apoA-I.