Mixing Homogeneity Research Articles

Optimal 𝐿^{𝑝} and Hölder estimates for the Kohn solution of the \overline∂-equation on strongly pseudoconvex domains

Let Ω \Omega be an open, relatively compact subset in C n + 1 {{\mathbf {C}}^{n + 1}} , and assume the boundary of Ω \Omega , ∂ Ω \partial \Omega , is smooth and strongly pseudoconvex. Let Op ⁡ ( K ) \operatorname {Op}(K) be an integral operator with mixed type homogeneities defined on Ω ¯ \overline \Omega : i.e., K K has the form as follows: \[ ∑ k , l ≥ 0 E k H l , \sum \limits _{k,l \geq 0} {{E_k}{H_l},} \] where E k {E_k} is a homogeneous kernel of degree − k - k in the Euclidean sense and H l {H_l} is homogeneous of degree − l - l in the Heisenberg sense. In this paper, we study the optimal L p {L^p} and Hölder estimates for the kernel K K . We also use Lieb-Range’s method to construct the integral kernel for the Kohn solution ∂ ∗ ¯ N \overline {{\partial ^\ast }} {\mathbf {N}} of the Cauchy-Riemann equation on the Siegel upper-half space and then apply our results to ∂ ∗ ¯ N \overline {{\partial ^\ast }} {\mathbf {N}} . On the other hand, we prove Lieb-Range’s kernel gains 1 1 in "good" directions (hence gains 1 / 2 1/2 in all directions) via Phong-Stein’s theory. We also discuss the transferred kernel from the Siegel upper-half space to Ω \Omega .

Mixing problems of low flow hepatic artery infusion. Improvement with small caliber double lumen balloon catheters.

The problem of inhomogeneous mixing encountered during hepatic artery (HA) chemotherapy infusion was assessed and a practical solution examined. A glass model of the human HA distribution was used to determine mixing homogeneity of low flow (1.4 mL/minute) dye infusion into pulsatile flow (280-300 mL/minute) of a fluid isoviscous to blood. Dye concentration in each of 16 HA branches was determined by photospectrometry. Dye infusion was carried out through 2-2.5F double lumen end hole or proximal side hole balloon catheters without balloon inflation, with balloon inflation maintaining full HA flow, and with the balloon inflated so that HA flow was reduced by 50%. The measurements taken without balloon inflation showed gross inhomogeneity of dye concentration in various branches. The inhomogeneity was not improved during balloon inflation as long as full HA flow was maintained. After balloon inflation reduced HA flow by 50%, dye mixing was improved significantly, with infusion through side hole catheters (alpha = .002) but not significantly (alpha = .2) with infusion through end hold catheters. This investigation suggests that the proposed technique might be useful for clinical application and deserves further evaluation in an in vivo system.

Quantitative retrieval of bacterial spores from oils

Membrane filtration and emulsification by ultrasonic mixing or ultraturrax homogenization were evaluated for their efficacy to retrieve bacterial spores from edible oils. Membrane filtration of oils containing spores, with subsequent transfer of the membrane to culture media, allowed at most 18% recovery of the spores. Emulsification of the oils by ultrasonication or ultraturrax homogenization with surface active agents showed generally high spore retrieval.

Generation of corticosteroid binder IB from binder II by a sulfhydryl dependent renal cytosolic factor

It has long been debated whether binder IB represents a unique form of the glucocorticoid receptor or is derived from the larger molecular weight form, binder II, by limited proteolysis. Transformed glucocorticoid receptors in kidney, liver and mixed kidney/liver cytosols were examined using anion exchange and gel filtration chromatography. The transformed receptor in liver cytosols chromatographs as binder II on DEAE-Sephadex A-50 anion exchange columns and has a Stokes radius of approx 6.0 nm. The transformed receptor in kidney cytosols chromatographs as binder IB on DEAE-Sephadex A-50 anion exchange columns and has a Stokes radius of 3.0–4.0 nm (3.2 nm on agarose; 3.0–4.0 nm on Sephadex G-100). Using cytosols prepared from mixed homogenates (2 g kidney plus 8 g liver tissue), our experiments show that binder II is converted to a lower molecular weight form R s = 3.2 nm on agarose; R s = 3.9 nm on Sephadex G-100) that is identical to binder IB in its elution position from DEAE-Sephadex anion exchange resin. Identical results are obtained using kidney/liver/cytosols mixed in vitro in which only the hepatic receptor, binder II, is labelled with [ 3H]TA. These results support the hypothesis that the renal receptor, binder IB, is a proteolytic fragment of binder II and does not represent a polymorphic form of the glucocorticoid receptor. The renal converting activity is dependent on free-SH for full activity but is insensitive to the protease inhibitors leupeptin, antipain, and PMSF. The conversion of hepatic binder II to binder IB in in vitro mixing experiments can be prevented if kidney cytosol is gel filtered on Sephadex G-25 and the eluted macromolecular fraction is adjusted to 10 mM EGTA (or EDTA) prior to mixing with the [ 3H]TA labelled hepatic cytosol.

A Boundary Layer Model for the MOCVD Process in a Vertical Cylinder Reactor

The transport process in metalorganic chemical vapor deposition (MOCVD) is investigated for a vertical reactor where two kinds of reactants are mixed just above the horizontally-attached substrate. A boundary layer model is developed and the epitaxial growth of the compound semiconductor is described. The model predicts that the growth rate is a function of reactant partial pressure, boundary layer thickness and the degree of mixing. It also predicts that uniformity in thickness is obtained by controling the homogeneity of mixing. Results of experimental studies on ZnSe epitaxial growth rate agree well with the calculated growth rate.

Performance of annular membrane and screen-tee reactors for postcolumn-reaction detection of metal ions separated by liquid chromatography

The experimental factors that contribute to base line noise in the postcolumn-reaction detection of metal ions eluted from high-performance dynamic ion exchangers have been evaluated and compared for a screen-tee reactor (approx. 1 ..mu..L internal volume) and three annular membrane reactions having internal volumes of 1.5, 5.3, and 9.6 ..mu..L. Measurements of mixing homogeneity, performed with pulseless gas-pressure pumping, showed that both reactor designs gave a mixing homogeneity that was 99.983% of that theoretically possible (perfect mixing) for two solutions differing in absorbance by 2.38 units. For normal operation with high-performance reciprocating pumps for eluent delivery, pump pulsations were responsible for 90-100% of the observed peak-to-peak noise. Column efficiency measurements with a series of lanthanide metal ions gave similar curves for both designs (HETP values of 0.01-0.04 mm). Both reactors gave reproducible peak areas, had good peak shapes, and operated reliably. With the membrane reactors some leakage of eluent into the reagent solution occurred at high eluent or reagent flow rates, but this was not a problem for normal operating conditions.

Pigment removal from canola oil using chlorophyllase

AbstractFrost‐damaged or prematurely harvested canola seed (rapeseed) may yield oil with a high chlorophyll content (50–60 µg/ml). Enzymatic hydrolysis of chlorophyll, added to buffer/surfactant, buffer/acetone or buffer/acetone/canola oil, to produce water‐soluble chlorophyllide (green pigment) was studied using a crude chlorophyllase preparation (acetone‐dried chloroplasts) from 15 to 20‐day‐old sugar beet seedlings. In buffer/surfactant, the optimum pH for enzyme activity was temperature dependent. At 30 C and 0.24% Triton X‐100 (or 30% acetone), chlorophyllase showed maximum activity toward a crude chlorophyll preparation over the range of pH 8–10. At 60 C, the activity was more than twofold higher, with a sharp maximum at ∼pH 8. Mg2+ enhanced the activity with an optimal concentration of 50 mM. At pH 7.5, 50 C and in the presence of only 6% acetone, the enzyme showed high affinity for chlorophyll (Km=15µM or 13.5 µg/ml), suggesting that the natural chlorophyll concentrations found in green canola oils might facilitate high enzymatic efficiencies. The crude enzyme was stable in buffer/acetone at pH 7.5 and 50 C for at least two hr.With acetone concentrations as low as 6%, maximum enzyme activities in buffer and buffer/canola oil required intensive mixing (homogenization) of the various substrate, enzyme and liquid phases. In general, the rate and extent of chlorophyll hydrolysis were greater in buffer than in buffer/oil. In both reaction systems, chlorophyll hydrolysis slowed down with time due to accumulation of phytol, which proved to be a competitive inhibitor (Ki=11 µM or 3.3 µg/ml). The other hydrolysis product, chlorophyllide, did not affect enzymatic activity.Crude canola oil used in the reconstitution of green oil did not support enzymatic chlorophyll hydrolysis without prior degumming and desoaping. The optimum buffer/oil ratio of the reaction mixtures was above 2/1 (v/v).

An investigation of the use of UV fluorescence microscopy as a method for quantifying the homogeneity of powder mixes

An experimental study was made to assess a potential new method for quantifying the homogeneity of pharmaceutical ordered mixes. A UV fluorescence microscope fitted with a photomultiplier system was used to determine the distribution of fluorescing fine drug particles on the surface of non-fluorescing coarser excipient particles after mixing. The concentration of drug in a given field of view was related to the fluorescence level determined by measuring the current output from the photomultiplier. The change in current levels measured in different sample fields was used to quantify homogeneity. Mechanistic interpretation of data was also possible by comparison of quantitative and qualitative microscopical analyses. Homogeneity data obtained using UV fluorescence microscopic analysis was compared with data obtained from similar experiments using UV spectrophotometric analysis. It was found that the two methods produced quantitatively similar results. It was considered that the fluorescence microscope method offered several potential advantages over other conventionally used analytical methods for assessing powder homogeneity.

Maximal functions associated with curves and the Calderón-Zygmund method of rotations

Let δ t ( t > 0 ) {\delta _t}(t > 0) be a dilation in R n ( n ⩾ 2 ) {{\mathbf {R}}^n}(n \geqslant 2) defined by \[ δ t x = ( t α 1 x 1 , t α 2 x 2 , … , t α n x n ) ( x = ( x 1 , x 2 , … , x n ) ) , {\delta _t}x = ({t^{{\alpha _1}}}{x_1},{t^{{\alpha _2}}}{x_2}, \ldots ,{t^{{\alpha _n}}}{x_n})\qquad (x = ({x_1},{x_2}, \ldots ,{x_n})), \] where α i > 0 ( i = 1 , 2 , … , n ) {\alpha _i} > 0(i = 1,2, \ldots ,n) and α i ≠ α j {\alpha _i} \ne {\alpha _j} if i ≠ j i \ne j . For ν ∈ R n \nu \in {{\mathbf {R}}^n} with | ν | = 1 |\nu | = 1 , let Γ ν : ( 0 , ∞ ) → R n {\Gamma _\nu }:(0,\infty ) \to {{\mathbf {R}}^n} be a curve defined by Γ ν ( t ) = δ t ν ( 0 > t > ∞ ) {\Gamma _\nu }(t) = {\delta _t}\nu \,(0 > t > \infty ) . Using maximal functions associated with the curves Γ ν {\Gamma _\nu } , we define an operator M M which is a nonisotropic analogue of the one studied in R. Fefferman [2]. It is proved that M M is a bounded operator on L p ( R n ) {L^p}({{\mathbf {R}}^n}) for some p p with 1 > p > 2 1 > p > 2 . As its application we prove the L p {L^p} boundedness of operators of the form T ∗ ( f ) ( x ) = sup ε > 0 | T ε ( f ) ( x ) | {T^{\ast }}(f)(x) = {\sup _{\varepsilon > 0}}|{T_\varepsilon }(f)(x)| , where T ε {T_\varepsilon } is an integral operator associated with a variable kernel with mixed homogeneity.

Effects of Adhesion on Mixing Homogeneity II: Highest Attainable Degree of Mixing of a Polydisperse Ingredient and a Monodisperse Diluent

The highest attainable degree of mixing of a polydisperse ingredient adherent to a monodisperse diluent was derived from the Poisson distribution and found to equal the quality of the noninteractive random mixture. The derivation assumes the arrangement of the ingredient particles onto the surface of the diluent to be random in the equilibrium situation. To produce ordered mixtures of a higher degree of homogeneity should require an ordering mechanism which must enforce the arrangement of the adherent particles to become ordered.

Effects of Interparticulate Interactions on Mixing Homogeneity

By theoretical approach, the highest degree of mixing of cohesive, interactive powders was derived to conform to the homogeneity of the random mixture of free-flowing, non-interactive constituents. Particulate interactions like adherence of a cohesive drug ingredient to the diluent component, cannot yield ordered mixtures of higher degree of homogeneity under real mixing conditions.These conclusions were confirmed by mixing experiments, using minor proportions of free-flowing and of cohesive drug constituents, and diluents in excess. With both types of drug powders, the quality of the random mixture was attained. Ordered mixtures of higher degree of homogeneity could not be produced.

On Hypersingular Integrals and Anisotropic Bessel Potential Spaces

In this paper we characterize anisotropic potential spaces in terms of hypersingular integrals of mixed homogeneity with respect to a general dilation matrix.

On hypersingular integrals and anisotropic Bessel potential spaces

In this paper we characterize anisotropic potential spaces in terms of hypersingular integrals of mixed homogeneity with respect to a general dilation matrix.

Possible origin of K-rich volcanic rocks from Virunga, East Africa, by metasomatism of continental crustal material: Pb, Nd and Sr isotopic evidence

The isotopic compositions of Sr, Nd and Pb together with the abundances of Rb, Sr, U and Pb have been determined for mafic and felsic potassic alkaline rocks from the young Virunga volcanic field in the western branch of the East African rift system. 87Sr/ 86Sr varies from 0.7055 to 0.7082 in the mafic rocks and from 0.7073 to 0.7103 in the felsic rocks. The latter all come from one volcano, Sabinyo. Sabinyo rocks have negative ε Ndvalues ofε Nd = −10. Nd and Sr isotopic variations in the basic potassic rocks are correlated and plot between Sabinyo and previously reported [1] compositions (ε Nd = +2.5; 87Sr/ 86Sr≈ 0.7047) for Nyiragongo nephelinites. The Pb isotopic compositions for Sabinyo rocks are nearly uniform and average 206Pb/ 204Pb≈ 19.4, 207Pb/ 204Pb= 15.79–15.84, 208Pb/ 204Pb≈ 41.2. The basic potassic rocks have similar 206Pb/ 204Pb values but range in 207Pb/ 204Pb and 208Pb/ 204Pb from the Sabinyo values to less radiogenic compositions. Excellent correlations of 87Sr/ 86Sr with Rb/Sr, 1/Sr and 207Pb/ 206Pb for Sabinyo rocks suggest these to be members of a hybrid magma series. However, the nearly uniform Pb compositions for this series points to radiogenic growth of 87Sr in the magma source region following an event which homogenized the isotopic compositions but not Rb/Sr. The Rb-Sr age derived from the erupted Sabinyo isochron-mixing line is consistent with the ∼500 Myr Pb-Pb age from Nyiragongo [1], which suggests that this event affected all Virunga magma sources. The event can again be traced in the Pb-Pb, Pb-Sr and Nd-Sr isotopic correlations for all Virunga rocks, including Nyiragongo, when allowances are made for radiogenic growth subsequent to this mixing or incomplete homogenization event. Inferred parent/daughter element fractionations point to a metasomatic event during which a mantle fluid invaded two lithospheric reservoirs: a +ε Nd reservoir sampled by the Nyiragongo nephelinites and suggested to be the subcontinental mantle and a −ε Nd reservoir sampled by the mafic and felsic potasssic volcanism. Whether this −ε Nd reservoir is the crust, continental crustal material in the mantle or anomalous mantle cannot be decided from the data. The simplest answer, that this reservoir is the continental crust, seems to be at variance with experimental evidence suggesting a subcrustal origin for basic potassic magmas. Partial melting of the ancient metasomatised lithospheric domains and ensuing volcanism seems to be entirely a response to decompression and rising geotherms during rifting and thinning of the lithosphere.

Suspension polymerisation and its application to the preparation of polymer supports

Abstract The details of design and construction of a cylindrical suspension polymerisation reactor vessel and two symmetrically matching stirrers are given. An important feature of the apparatus, i.e. a variable capacity of about 75–500 ml for preparation of ca. 5–50 g beaded polymer product, is demonstrated by appropriate choice and positioning of either of the two stirrers. Two general suspension systems are described for bead polymerisation, respectively, of water-insoluble (e.g. styrene-based) and water-soluble (acrylic-based) monomer mixtures. The preparation of a wide range of polymer supports having well-defined characteristics such as particle size, degree of crosslinking and functionality is thus reported. Practical aspects of laboratory scale suspension polymerisation such as the choice of stabiliser, polymerisation conditions, particle size, etc., are discussed with special relevance to the synthesis of polymer supports for chemical applications. The particle size distribution of a typical preparation is given and its relative homogeneity is discussed in terms of the overall symmetry of the stirrer/vessel configuration and the homogeneity of mixing.

Compositions of singular integral operators

The composition of two Calderón-Zygmund singular integral operators is given explicitly in terms of the kernels of the operators. For φ ϵ L 1( R n ) and ε = 0 or 1 and ∝ φ = 0 if ε = 0, let Ker(φ) be the unique function on R n + 1 homogeneous of degree − n − 1 of parity ε that equals φ on the hypersurface x 0 = 1. Let Sing(φ, ε) denote the singular integral operator Sing(φ, ε)f(x 0, x) = lim δ → 0 ∝∝ ¦y 0¦ ⩾ δ f(x 0 − y 0, x − y), Ker(φ)(y 0, y) dy 0 dy , which exists under suitable growth conditions on ƒ and φ. Then Sing( φ, ε 1) Sing( ψ, ε 2) f = −2 π 2(∝ φ)(∝ ψ) f + Sing( A, ε 1, + ε 2) f, where A(x)= lim δ→0 ∫∫ δ⩽|λ|⩽δ−1 |λ+1| ϵ 1+ϵ 2 n |λ| ϵ 2 θ(x+λ(x−y))ψ(y)dλdy (with notation ¦t¦ 0 a = ¦t¦ a and ¦t¦ 1 a = ¦t¦ a sgn t ). This result is used to show that the mapping ψ → A is a classical pseudo-differential operator of order zero if φ is smooth, with top-order symbol ω 0(x,ϵ)=−πiθ(ϵ)∫θ(x−y) sgn y·ϵdy if ϵ 1=1 , =−2θ(ϵ)∫θ(x−y) log|y·ϵ|dy if ϵ 1=0 where θ(ξ) is a cut-off function. These results are generalized to singular integrals with mixed homogeneity.

Survival of Fecal Coliforms in Frozen Vegetable Homogenates

The resistance to freezing of fecal coliforms isolated from frozen vegetables was compared to that of Escherichia coli isolated from fecal sources. The objective was to see if lower resistance to freezing might explain frozen vegetable samples that contain fecal coliforms but not E. coli. Survivals after 200 d at −10°C in vegetable homogenates ranged from 0.014 to 75% for resuscitated vegetable isolates compared to 0.49 to 18% for resuscitated E. coli isolated from fecal sources. Resuscitation 1 h on Trypticase Soy Agar followed by an overlay with Violet Red Bile Agar (VRBA) increased recoveries about 11-fold over that obtained when the cultures were plated directly on VRBA. Mixed vegetable homogenates permitted higher survivals than homogenates prepared from snap beans, broccoli or mustard greens.

Definition and conversion of the mean particle diameter referring to mixing homogeneity

Definition and conversion of the mean particle diameter referring to mixing homogeneity

Hypersingular integrals and parabolic potentials

In this paper we characterize the potential spaces associated with the heat equation in terms of singular integrals of mixed homogeneity.

Effects of adhesion on mixing homogeneity part I: ordered adhesion—random adhesion

According to Hersey, adhesion of a finely powdered, monosized ingredient to a course, monosized diluent may yield ordered powder mixtures of a higher degree of homogeneity than conforming to random mixtures. However, this concept implies the adherence of an identical (or almost identical) number of the fine particles to each of the carriers (‘ordered adhesion’). If, on the contrary, a random variation of the number of adhering fines per diluent particle is assumed (‘random adhesion’), pseudorandom mixtures can be formed at best. This type of mixture shows the degree of homogeneity as well as the statistical properties of fully randomized systems. To produce ordered powder mixtures, it is thus the basic requirement that ordered but not random adhesion must be achieved during mixing. So far, no mechanism has been established that may yield ordered adhesion.