Reverse Partition Research Articles

A bijective proof of the generating function for the number of reverse plane partitions via lattice paths

Recently, Hillman and Grassl gave a bijective proof for the generating function for the number of reverse plane partitions of a fixed shape λ. We give another bijective proof for this generating function via completelv different methods. Our bijection depends on a lattice path coding of reverse plane partitions and a new method for constructing bisections out of certain pairs of involutions due to Garsia and Milne.

Partitioning of Zr and Nb between coexisting opaque phases in lunar rocks—determined by quantitative proton microprobe analysis

Proton microprobe analyses were carried out on Zr and Nb in coexisting opaque phases in lunar rocks. Zr contents in armalcolite and coexisting ilmenite in Apollo 17 rocks were determined in mineral pairs of two different origins: (a) in olivine porphyritic basalts where ilmenite was formed by reaction of armalcolite with the basaltic liquid or with Fe 0; (b) in plagioclase poikilitic basalts where ilmenite crystallized directly from the melt either simultaneously with armalcolite or after it. In armalcolite- and ilmenite-bearing assemblages Zr partitions in favor of armalcolite in (a); in favor of ilmenite in (b). These results can be understood by extensive equilibration between armalcolite and ilmenite in (a) due to the reactions involving armalcolite. The reverse partitioning in (b) may represent initial ratios because equilibration was not accomplished. In Apollo 15 rocks coexisting Cr-ulvöspinel and ilmenite occur in two distinct assemblages, (a) ulvöspinel with ilmenite lamellae formed by subsolidus reactions, (b) ulvöspinel and ilmenite involved in the isobarically invariant reaction ulvöspinel + silica → ilmenite + fayalite. In the first case Zr partitions between ilmenite and ulvöspinel, in the second case between ulvöspinel and ilmenite, and between ilmenite and silica. Experimental partitioning data for Zr [6] of the ulvöspinel and ilmenite pair are not applicable to assemblages containing primary ulvöspinel with ilmenite formed later in the above reaction. In both assemblages, Zr shows a zonal distribution in Cr-ulvöspinel as a function of Fe 2TiO 4 content and FFM ratio. Therefore Zr contents in the natural assemblages should always be measured at the contacts of the coexisting phases. The Zr/Nb ratio in ilmenites in the groundmass of Apollo 14 breccia 14305,55 is much lower (0.18–0.25) than that in a gabbro clast from the same breccia (1.25). Limited equilibration between groundmass and clasts in the breccia during thermal metamorphism is indicated.

Tableaux and matrix correspondences

The Robinson-Schensted correspondence, a bijection between nonnegative matrices and pair of tableaux, is investigated. The representation, in the tableau, of the dihedral symmetries of the matrix are derived in a simple manner using a shape-preserving anti-isomorphism of the platic monoid. The Robinson-Schensted correspondence is shown to be equivalent to the Hillman-Grassl bijection between reverse plane partitions and tabloids. A generalized insertion method for the Robinson-Schensted correspondence is obtained.

Two types of kinetic regulation of the activated ATPase in the chloroplast photophosphorylation system.

The inhibition by light of chloroplast coupling factor ATPase is not due simply to competing photophosphorylation. This inhibition is only partially relieved by either an arsenate-pool trap for released phosphate, or a pyruvate kinase/phosphoenolpyruvate trap for ADP. Moreover, the amount of product return that does occur in the absence of trapping systems, ascertained by incorporation of 32Pi or [2-3H]ADP back into ATP during the hydrolysis reaction, is insufficient to account for the observed activity decrease. In intermediate pi:H2O oxygen exchange studies, the number of water oxygens incorporated into each molecule of Pi produced does not vary with light intensity during the ATPase assay. This indicates that the light-induced change in ATPase activity is not due to an alteration of rat constants involved in the forward and reverse partitioning of the E.ADP.Pi complex. In contrast, ammonium chloride, an uncoupler of photophosphorylation which stimulates membrane-bound coupling factor ATPase when added after light activation, causes a shift in the pattern of intermediate Pi:H2O oxygen exchange toward a lower number of water oxygens incorporated per Pi formed. The effect of NH4+ consistent with ATPase activity stimulation caused by enhanced partitioning forward of the E.products complex. These observations suggest the operation of two mechanisms of regulation of ATP ase activity during chloroplast de-energization. However, a direct effect of NH4+ on the coupling factor itself, independent of the membrane energization effect, cannot be ruled out by the present studies. Additional oxygen exchange experiments lead to the conclusion that the binding of ATP at a site catalyzing extensive ATP:H2O back exchange in the native chloroplast system ( Wimmer, M. J., and Rose, I. A. (1977) J. Biol. Chem. 252, 6769-6775) is different from the binding of ATP for net hydrolysis in the system activated for ATPase.

Reversible and Resistant Components of PCB Adsorption-Desorption: Adsorbent Concentration Effects

Laboratory experiments and analysis of field data from Saginaw Bay show that the concentration of suspended adsorbent affects the partition coefficient of PCB. The coefficient consistently decreases as adsorbent concentration increases. In addition it has been found that adsorption and desorption are not completely reversible. An analysis of this effect is presented within the framework of the resistant-reversible component model of adsorption-desorption. The partition coefficients for these two components are found to behave quite regularly: the resistant component exhibits essentially constant partitioning whereas the reversible component partition coefficient is exactly inverse to adsorbent concentration. The interplay of these components determines the variation of the adsorption and desorption partition coefficients as functions of adsorbent concentration and the degree of reversibility to be expected. Saginaw Bay field data conform to the relationship derived from the resistant-reversible model.

The Hillman-Grassl correspondence and the enumeration of reverse plane partitions

Hillman and Grassl have devised a correspondence between reverse plane partitions and nonnegative integer arrays of the same shape that allowed them to easily enumerate reverse plane partitions and provided a combinatorial connection between hook lengths and plane partitions. In this work, a collection of properties of this correspondence are presented, including two characterizations that relate this map to the familiar Schensted-Knuth correspondence. These properties are used to derive simple expressions for the generating functions of reverse plane partitions and symmetric reverse plane partitions with respect to sums along the diagonals. Equally general results are obtained for shifted reverse plane partitions using a new type of hook, thereby proving a conjecture of Stanley.

Toxicological analysis of phenylethylamines by high performance reversed-phase ion-pair partition thin-layer and liquid chromatographies.

A rapid and specific method was developed to identify phenylethylamines in urine. After an organic extraction at appropriate pH, reverse phase ion-pair partition chromatographies were used: a high performance thin-layer test followed by high performance liquid chromatography. The use and benefits of the procedure are described in detail and compared with other methods. In a very short time (10 min) the presence of phenylethylamine is detected on a thin-layer plate. In the case of positive result the product is then specifically identified by high performance liquid chromatography by means of a complete UV spectrum traced directly on the eluated compound. The sensitivity of the method is highly increased because the detection is operated at 215 nm.

Bonded Reverse Phase Ion Exchange Columns for the Liquid Chromatographic Separations of Neutral and Ionic Organic Compounds

Octadecylsilane was chemically bonded in situ on cation and anion exchange packings. The columns were tested for the liquid chromatographic separations of neutral and charged organic solutes which included nucleotides, polynuclear aromatic hydrocarbons, amines, carboxylic acids, and organometallic compounds. While some separations were effected predominantly by either the ion exchange sites or the reverse phase moieties, most separations appeared to be the combined effects of both stationary phases. The reverse phase partitioning, apparently induced by the solvophobic interaction, can make the elution volume and order of a charged solute significantly different from that found in a conventional ion exchange column. The mixed mode of ion exchange and reverse phase solvophobic interactions are illustrated.

Functions on tableau frames

In a previous paper the authors used an algorithm for a bijection from the set F of all functions with nonnegative integral values defined on a Young tableau frame Φ onto the set E of all reverse plane partitions (rpp) on Φ in their new proof of R.P. Stanley's generating function for rpp. The algorithm gave new and clear combinatorial significance to the hook numbers of Φ as lengths of zigzag paths but left open the question of invariance of the bijection under interchange of the roles of rows and columns. Here this invariance is proved and the bijection is generalized to allow the entries to be in any linearly ordered additive group. The new algorithms involve n-tuples of paths and use the discreteness of the frame to introduce quantum falls or rises in the entries. New light is shed by considering a tableau frame to be a union of certain rectangles and the hook number of a node to be the number of these rectangles containing the node.

製剤からの薬物溶出のシミュレーション(第5報)膜の分配率

To date, the apparent membrane partition coefficient (Pa) has been obtained by an apparent decrease of concentration in a membrane-solution system. However, a part of the solute molecules absorbed by the membrane seems to be in the immobile state because the molecules are tightly restricted by the membrane component. The partition coefficient which is related to the diffusion must be defined by the mobile solute only. We may call the partition coefficient defined by the mobile solute"reversible partition coefficient (Pr)", and the partition coefficient defined by the immobile solute"irreversible partition coefficient (P1r)". The Pr can be obtained by 2 step experiments (absorption of solute by, and release of solute from the membrane). Theories on the Pr of the membrane and the porous membrane are proposed here. Silicone rubber membrane was prepared from the silicone rubber compound (SRC : Shinetsu Kagaku KE-102RTV) and concentration dependence of the Pa and Pr were measured on the SRC-membrane-salicylic acid (SA) solution system. The Pa and Pr values decreased with an increase in SA-concentration and the Pa value approached the Pr value. On the other hand, the Pa and Pr values were measured on the benzene-SA-solution and silicone oil-SA-solution systems and it is clear that the Pa value is nearly equal to the Pr value in the liquid-liquid system. The Pr value of the SRC-membrane is 6 times greater than the Pr value of the silicone oil. The permeation of SA through the SRC-membrane was measured on the SA-solution-memberane-water system, the results were compared with the simulation results carried out on the basis of the theory and technique reported before (Ref. 5 and 6), and good agreements were obtained between them. The experimental results disagreed with the simulation results which were obtained by using the Pa value.

Drug Partitioning: Relationships between Forward and Reverse Rate Constants and Partition Coefficient

The rate constant, k1, of drug transport from an aqueous phase to an organic phase and the rate constant, k2, of the reverse process can be described as functions of the partition coefficient, P: log k1 = log P − log (βP + 1) + c′ and log k2 = −log (βP + 1) + c′. In a homologous series, where log P is a simple function of the number of CH2 groups, log k1 and log k2 also can be described as functions of the number of CH2 groups. The relationships between these equations and current physicochemical models of drug absorption are discussed.

Isolation and Identification of Drugs of Forensic Interest by High Performance Reverse Phase Ion Pair Partition Chromatography

Abstract A method is presented for the isolation and identification of milligram or microgram quantities of drugs of forensic interest. High performance reverse phase ion pair partition chromatography is performed on a 9.4 millimeter internal diameter microparticulate octadecylsilane column employing a water, methanol, acetic acid, alkylsulfonate mobile phase. Subsequent to collection from the liquid chromatograph, a simple extraction is performed followed by Infrared (IR) analysis and/or solid probe Mass Spectrometry (MS). A study is presented using phenylpropanolamine hydrochloride and ephedrine hydrochloride as a test model for the determination of the optimum concentration of counter ion required for a semi-preparative separation. The method is applied to an LSD seizure from a clandestine laboratory, methamphetamine in a street exhibit, and an amobarbital - secobarbital mixture in a multi-barbiturate capsule.

Reverse phase ion-pair partition chromatography of 4-(2-pyridylazo)resorcinolato complexes and its application to the spectrophotometric determination of iron, cobalt and nickel

A novel method for the separation of metal ions by reverse phase ion-pair partition chromatography is developed based on the ion-pair formation of anionic metal-4-(2-pyridylazo)resorcinolato (PAR, H2L) complexes with quaternary ammonium cation. The quantitative separation of cobalt (III)-, iron(III)-, and nickel(II)-PAR complexes was accomplished within 20 min on a 3.9 mm ×300 mm μ-Bondapak C18 column (Waters Associates), where 56.2% (v/v) methanol-water mixture containing 0.014 mol dm-3 of tetrabutylammonium bromide was used as a mobile phase in a flow rate of 0.91 cm3 min-1. These metal ions of (10-610-5)mol dm-3 level can be determined with the peak height calibration curves obtained at 254 nm using 0.04 absorbance unit full-scale. The order of the peak positions of the singly charged anions such as [CoL2]- [FeL2]- and HL- were well correlated to that of their ion-pair extraction constants.

Application of Reverse Phase Ion-Pair Partition Chromatography to Drugs of Forensic Interest

A method is described for determining a wide range of abused drugs by using 1 column, a single isocratic system, and a fixed wavelength (254 nm) ultraviolet detector. Paired-ion chromatography is performed on a reverse phase muBondapak C18 column. Acidic, basic, and neutral drugs, including their corresponding salts, can be determined without prior cleanup. A counter ion, 1-heptane sulfonate, is dissolved in the aqueous organic mobile phase to give a final pH of approximately 3.5. This technique is applicable to ergot alkaloids, phenylethylamines, opium alkaloids, local anesthetics, barbiturates, and other drugs of forensic interest. Five major opium alkaloids in gum opium, namely, morphine, codeine, thebaine, narcotine, and papaverine, can be separated in approximately 20 min.

A radioimmunoassay for 13,14-dihydro-15-keto prostaglandin F 2α with chromatography and internal recovery standard

Antibodies to the 13,14-dihydro-15-keto metabolite of prostaglandin F 2α(PGF 2αM) were raised in sheep using a bovine thyroglobulin conjugate of PGF 2αM. Labeled 13,14-dihydro-15-keto prostaglandin A 2 (PGA 2M), 13,14-dihydro-15-keto prostaglandin E 2 (PGE 2M) and PGF 2αM were prepared from their corresponding high specific activity parent prostaglandins with swine kidney homogenate and purified using reverse phase liquid-liquid partition chromatography. A rapid method of column chromatography for use prior to radioimmunnoassay was developed. Mathematical corrections for the effect of recovery tracer on the logit/log transformation are presented with a new approach to expression of radioimmunoassay cross reactions allowing continuous expression of the variation of these cross reactions with displacement. These mathematical approaches are widely applicable to other radioimmunoassay systems and transformations. The assay was used for measurement in groups of human volunteers: males, females, women at delivery and paired venous umbilical cord bloods. A correlation between venous cord and maternal peripheral PGF 2αM levels is demonstrated with a gradient from the cord plasma to maternal plasma.

Reverse plane partitions and tableau hook numbers

The generating function of R. P. Stanley for reverse plane partitions on a tableau shape is obtained by a direct method that clearly shows the combinatorial significance of the hook numbers for the shape. The process generalizes the hooks into zigzag paths.

Estimation of free car☐yl groups in protein by reverse dye partition technique

Estimation of free car☐yl groups in protein by reverse dye partition technique

Determination of degree of substitution in sodium carboxymethylcellulose by a reverse dye partition technique

Determination of degree of substitution in sodium carboxymethylcellulose by a reverse dye partition technique

Estrogen production by trophoblastic tumors in tissue culture.

The pure trophoblastic cell lines BeWo and Jar derived from human ch oriocarcinomas produced estrone and estradiol from tritiated androstenedione and dehydroepiandrosterone. Typically, 8 million cells were incubated at 37 degrees C for 10 hours in 10 ml meduim containing the appropriate labeled substrate. Products were isolated by reverse phase and partition chromatography, and purified by recrystallation to constant specific activity and formation of acetate derivatives. In 1 experiment the Jar line produced 2120 ng estrone and 14,200 ng estradiol per g cells per day from androstenedione, although the cells began retracting after 2 hours of incubation. In 3 experiments, BeWo cells synthesized 24-113 ng estrone and 42-1000 ng estradiol per g cells per day from androstenedione, and in 1 experiment BeWo cells produced 107 ng estrone and 148 mg estradiol per g cells per day from dehydroepiandrosterone. These cells contained lipid droplets like those seen in normal term placenta. These 2 biosynthetic pathways and the absence of 16-hydroxylase for estriol synthesis resemble the metabolism of normal placenta.

Estimation of endgroups in poly(vinyl acetate) and the corresponding poly(vinyl alcohol) to study the hydrolysis reaction

AbstractThe mode of branching in poly(vinyl acetate) has been studied using reverse dye partition (RDP) technique developed in this laboratory. It has been observed that during hydrolysis of poly(vinyl acetate) the degree of polymerization of the polymer decreases in all cases. This degradation is found to be erratic. It may be caused by the separation of branches which were connected to the main chain through ester linkage. This idea has been confirmed by the detection of average one carboxyl endgroup in the resulting shorter polymer chains.The change in the number of endgroups in the parent and the corresponding hydrolysed polymer has been used as a tool for the estimation of number of branches in poly(vinyl acetate) molecules.