Ln X2 Research Articles

Analysis of Corn (Zea mays) Demand in Boyolali

The research aims to analyze the factors of corn price, corn demand, and the elasticity of corn demand in Boyolali Regency. The basic method used in this research is analytical-descriptive. The selection of the research location was purposive, with Boyolali Regency chosen as the location due to the consistent increase in corn demand. The results of the data analysis using multiple linear regression reveal the equation Ln Qd = -367.983 - 0.191 Ln X1 + 0.541 Ln X2 + 0.875 Ln X3 - 0.729 Ln X4 + 27.253 Ln X5 + e. This model has an R?² value of 21.9%, indicating that 21.9% of the corn demand in Boyolali Regency cannot be explained by the variables of corn price, rice price, soybean price, per capita income, and population, while the remaining 78.1% is explained by other variables not studied. Based on the F-test, the combined effect of corn price, rice price, soybean price, per capita income, and population on corn demand in Boyolali Regency is not significant. The t-test for individual variables also indicates that corn price, rice price, soybean price, per capita income, and population have no significant effect on corn demand in Boyolali Regency at both 99% and 95% confidence levels. The coefficient of price elasticity is -0.191, indicating inelasticity as it is less than one. Rice price has a positive cross-elasticity value of 0.541, signifying that rice is a substitute good for corn. Soybean price has a positive cross-elasticity value of 0.875, also acting as a substitute for corn. The coefficient of income elasticity is -0.729, indicating that corn is an inferior good due to its negative sign.

Approximating activation edge-cover and facility location problems

What approximation ratio can we achieve for the Facility Location problem if whenever a client u connects to a facility v, the opening cost of v is at most θ times the service cost of u? We show that this and many other problems are a particular case of the Activation Edge-Cover problem. Here we are given a multigraph G=(V,E), a set R⊆V of terminals, and thresholds {tue,tve} for each uv-edge e∈E. The goal is to find an assignment a={av:v∈V} to the nodes minimizing ∑v∈Vav, such that the edge set Ea={e=uv:au≥tue,av≥tve} activated by a covers R. We obtain ratio 1+maxx≥1⁡ln⁡x1+x/θ≈ln⁡θ−ln⁡ln⁡θ for the problem, where θ≤maxe∈E⁡max⁡{tue,tve}min⁡{tue,tve} is a problem parameter. This result is based on a simple generic algorithm for the problem of minimizing a sum of a decreasing and a sub-additive set functions, which is of independent interest. As an application, we get the same ratio for the above variant of Facility Location. If for each facility all service costs are identical then we show a better ratio 1+maxk∈N⁡Hk−11+k/θ, where Hk=∑i=1k1/i. For the Min-Power Edge-Cover problem we improve the ratio 1.406 of [4] (achieved by iterative randomized rounding) to 1.2785. For unit thresholds we improve the ratio 73/60≈1.217 of [4] to 15551347≈1.155.

PENDAPATAN MASYARAKAT PETANI PENYADAP KARET DI TEMBAWANG DI DESA BANUA TENGAH KECAMATAN PUTUSSIBAU UTARA KABUPATEN KAPUAS HULU

Rubber is a forestry plant producing sap. Rubber latex is needed for various industrial purposes. Rubber is a side business as well as additional income for the community besides farming in Banua Tengah Village. The method used is a survey method with interview techniques. Sampling was done intentionally (purposive sampling). The number of samples taken was 61 respondents who were ; rubber farmers, married, worked tapping rubber and owning rubber plantations. Data analysis consists of calculating total income and multiple linear regression analysis. The analysis results obtained total income / Tr received by farmers around Rp. 390,000 - Rp. 2,840,500 / month, when compared to the UMR established by the Government in 2018, UMR Kapuas Hulu Regency is Rp. 2,204,650.00 / month, there are 2 (two) farmers who have an income above the minimum wage while 59 other farmers are still under the UMR There are four factors that influence the income of rubber farmers in Desa Banua Tengah namely land area, work experience, rubber age and workdays, of the four most influential factors are land area and workday variables, while the work experience and rubber age variables are not very influential. Factors of land area, work experience, rubber age and working days together greatly affect farmers' incomes with the equation of total income of rubber farmers as follows: ln Y = 9,817 + 0,397 ln X1 + 0,098 ln X2 + 0,061 ln X3 + 1,194 ln X4 Correlation value R = 0.928 and the value of determination R2 = 0.861 From these equations obtained a constant value of 9,817 which shows that income from rubber farmers (Ŷ) in Desa Banua Tengah is Rp. 9,817 if X₁, X₂, X3 and X4 are considered zero. Ŷ is positively correlated with X₁, X₂, X3 and X4.Keywords: Influential factors, Latex, Rubber farmers, Total income

Pengaruh Industri Pariwisata terhadap PDRB Kota Padang

The contribution of tourism industry fluctuates to PDRB of Padang city in 2013 - 2017 as well as the number of tourists. The hotel rates are relatively high and the prices of food and beverages sold still do not have a standard price. The above will certainly have PDRB Padang city. The purpose of research to determine the influence of the number of tourists, number of hotels and the number of restaurants to PDRB. Padang city partially and simultaneously. type of research is quantitative, data collection using survey method.
 The study used time series data analyzed by multiple linear regression technique. Equation of data analysis obtained Ln Y = 3.418 + 0.058 Ln X1 + 0.103 Ln X2 + 0.258 Ln X3 + e. After hypothesis testing at 5% significance level, the number of tourists, number of hotel and number of restaurant have significant positive effect to PDRB of Padang city partially and simultaneously because (3.317> 2.021) and (2.134> 2.021) and 93.168> 2.021) and (5.889> 2.61). The number of hotels and number of restaurants with PDRB of Padang city strong (0.749) and value of Adjusted R Square = 0.602 means the PDRB of Padang is explained by the number of tourists, the number of hotels and the number of restaurants is 60.2% while the remaining 39.8% is explained by other variables not included in the research model. Keywords: Gross Domestic Product, tourist, hotel, restaurant

Determining the Diet of Whooping Cranes (Grus americana) Through Field Measurements

Though an important measure for ecological studies, obtaining foraging data through direct observation is rarely assessed independently. Using field measurements (foraging habitat, food acquisition behavior, and food manipulation time), the summer diet of Whooping Cranes (Grus americana) in Wisconsin, USA, was determined; foods consumed based on foraging behavior were identified; and ingestion for Sandhill Cranes (Antigone canadensis) was assessed. Based on 102 observations, Whooping Cranes occupying six territories consumed 17 food items (verified with images), of which 90 samples from nine foods were modeled. Food manipulation time predicted food size: ln(y) = 3.50 0.45ln(x) - 0.05 ln(x2) (r2 = 0.63, P< 0.001). Classification tree analysis identified consumed food using foraging behavior (error rate = 17%). A schematic model with the same three behavioral variables and an additional variable of direct observation identified 93% of 90 items. With Sandhill Cranes, observed swallows predicted actual swallows (y = 1.12x - 6.18 (r2 = 0.85, 95% CI of slope = 0.79 to 1.45, 95% CI of y-intercept = -50.55 to 38.19)). Field observation of diet and ingestion can be applied to any bird species that uses open habitats where food acquisition behavior and food size vary enough to inform models of foraging behavior.

ANALISIS PENGGUNAAN FAKTOR-FAKTOR PRODUKSI PADA USAHATANI JANGGELAN DI KECAMATAN KARANGTENGAH KABUPATEN WONOGIRI

&lt;div class="WordSection1"&gt;&lt;p&gt;&lt;em&gt;This research was aimed to analyze the amount of the costs, the revenue and the income of black grass jelly farming, and analyze the use of factors which influence the production of black grass jelly in Karangtengah Sub-District, Wonogiri District. The location of the research was determined by purposive sampling method. The Village that used on this research was selected bypurposive sampling method. The samples in this research were 40 respondents selected by using proportional random sampling method. The data used in this research was primary and secondary data. The data analysis that usedon this research were:(1) the analysis of the costs, the reception and the income of the farming, (2) the analysis of production function by Cobb-Douglas.The reseach result, based on the analysis of the black grass jelly farming with the land area of 0,37 Ha explained the cost of establishing the farming was Rp 4.425.482,50/PT , the reception of the farming was Rp19.930.000,00/PT and the income of the farming was Rp 15.504.517,50/PT. The equation function by Cobb-Douglas was : Ln&lt;/em&gt;&lt;em&gt; = 7,224 + 0,767 ln X1 – 0,162 ln X2 + 0,107 ln X3 + 0,001 ln X4+ 0,317 ln X5 + 0,007 ln X6. The result of regression showed that production factors such as; land area, the number of seeds, urea fertilizer, phonska fertilizer, manure, and the labors had the real impact toward the production of black grass jelly&lt;span style="text-decoration: underline;"&gt;.&lt;/span&gt;Individually, the production factors such as; urea fertilizer, phonska fertilizer, and the labors did not have the real impact on production of black grass jelly.&lt;/em&gt;&lt;/p&gt;&lt;/div&gt;

Irreducibility of generalized Hermite–Laguerre polynomials III

For a positive integer n and a real number α, the generalized Laguerre polynomials are defined byLn(α)(x)=∑j=0n(n+α)(n−1+α)⋯(j+1+α)(−x)jj!(n−j)!. These orthogonal polynomials are solutions to Laguerre's Differential Equation which arises in the treatment of the harmonic oscillator in quantum mechanics. Schur studied these Laguerre polynomials for its interesting algebraic properties. He obtained irreducibility results of Ln(±12)(x) and Ln(±12)(x2) and derived that the Hermite polynomials H2n(x) and H2n+1(x)x are irreducible for each n. In this article, we extend Schur's result by showing that the family of Laguerre polynomials Ln(q)(x) and Ln(q)(xd) with q∈{±13,±23,±14,±34}, where d is the denominator of q, are irreducible for every n except when q=14, n=2 where we give the complete factorization. In fact, we derive it from a more general result.

Irreducibility of generalized Laguerre polynomials [formula omitted] with integer u

Generalized Laguerre polynomials Ln(α)(x) are classical orthogonal polynomial sequences that play an important role in various branches of analysis and mathematical physics. Schur (1929) was the first to study the algebraic properties of these polynomials by proving that Ln(α)(x) where α∈{0,1,−n−1} are irreducible. For α=u+12 with integer u satisfying 1≤u≤45, we prove that Ln(α)(x) and Ln(α)(x2) of degrees n and 2n, respectively, are irreducible except when (u,n)=(10,3) where we give a factorization. The cases u=−1,0 are due to Schur. Further we consider more general polynomials Gα(x) and Gα(x2) of degrees n and 2n, respectively, and prove that they are either irreducible or have a factor of degree in {1,n−1}, {1,2,2n−2,2n−1}, respectively, except for an explicitly given finite set of pairs (u,n). We also show that these exceptional pairs other than one for Gα(x) and six for Gα(x2) are necessary. Further for a general u>0 we give an upper bound for the degree of factor of Gα(x) and Gα(x2) in terms of u.

Seven coordinated cobalt(II) complexes with 2,6-diacetylpyridine bis(4-acylhydrazone) ligands: Synthesis, characterization, DNA-binding and nuclease activity

Abstract A new series of pentadentate 2,6-diacetylpyridine bis(4-acylhydrazone)s (H2L1 and H2L2) based seven-coordinated cobalt(II) complexes, [Co(Ln)X2] (n = 1 and X = DMF for (1); n = 2 and X = H2O for (2)); [Co(H2Ln)Y2] (n = 1 or 2; Y = N3− or NCS−), has been synthesized and characterized by using spectroscopic techniques. Single crystal X-ray study of [Co(L1)(DMF)2] (1) complex exhibits pentagonal–bipyramidal coordination geometry where the pentadentate N3O2 ligand in the equatorial plane of the bipyramid and two dimethylformamide molecules in the axial area. Interaction of the cobalt(II) complexes with CT DNA has been investigated by absorption titration method and viscosity measurements which reveal that the cobalt(II) complexes could bind with CT DNA through intercalation. Cleavage activity of the complexes (1) and (2) with pBR 322 plasmid DNA was evaluated by agarose gel electrophoresis demonstrating that the ability of the complexes to cleave the pBR 322 plasmid DNA via oxidative pathway, possibly due to the involvement of a diffusible hydroxyl radical mechanism in presence and absence of an oxidative agent. The nuclease activity of the Co(II) complexes has strong dependence on the concentration of complex and reaction time, both in presence and absence of hydrogen peroxide.

Solubilities of Calix[6]arene and 4-tert-Butylcalix[4]arene in Pressurized Hot Water

Aqueous solubilities of calix[6]arene and 4-tert-butylcalix[4]arene were measured at temperatures of (433 to 533) K and (433 to 513) K, respectively, along the 5 MPa isobar. The relative rates of increase in the aqueous solubility with temperature, (∂ ln x2/∂T)P,σ, for the two solutes differ markedly, with values of 0.042 K–1 for calix[6]arene and 0.080 K–1 for 4-tert-butylcalix[4]arene. The solubility (equilibrium mole fraction) of 4-tert-butylcalix[4]arene is always lower than that of calix[6]arene at the same temperature, possibly reflecting the presence of four bulky 4-tert-butyl groups in the former molecule and also the presence of only four hydroxyl groups in the former molecule compared with six in the latter. Best-fit coefficients of the modified Apelblat equation are also reported for the two calixarenes.

Expressing relative differences (in percent) by the difference of natural logarithms

Most psychophysical investigations measure stimuli or performance in Système International units and use relative differences between them for comparison. In this theoretical note, we propose the ratio’s natural logarithm or the difference between the Napierian logarithms, as a desirable measure of relative differences between two psychophysical quantities. It challenges the more frequently used (x2−x1)/x1, (x2−x1)/x2, as well as (x2−x1)/xM, where x1,x2, and xM are the initial value in a change, the larger value, and a mean value between x1 and x2, respectively. As for the three aforementioned expressions, it can be conveniently expressed as a percentage. For two physical measures, x1 and x2(x1>0;x2>0), the difference between natural logarithms DNL=Ln(x2)−Ln(x1)=Ln(x2/x1) sits between (x2−x1)/x2 and (x2−x1)/x1; it is actually the mean value of (x2−x1)/x for all x values between x1 and x2. Unlike other estimates, it satisfies all three of the following properties: symmetry, i.e. Δ(x1;x2)=−Δ(x2;x1); agreement between inverted units, such as hertz and second, i.e. Δ(x1;x2)=−Δ(k/x1;k/x2) thus |Δ(x1;x2)|=|Δ(k/x1;k/x2)|; and additivity “à la Chasles”, i.e. Δ(x1;x2)+Δ(x2;x3)=Δ(x1;x3). Finally, it complies with the Weber–Fechner and Stevens laws.

Economic thresholds of Thrips palmi (Thysanoptera: Thripidae) for eggplants in a greenhouse

Thrips palmi Karny has recently been implicated in damage to eggplant fruits. This thrips causes cosmetic scars on and deforms fruits, thus lowering their market value. To investigate the relationship between the density of thrips and the resulting damage, experimental plots with initial release densities of 0, 20, 40, 70, and 100 adults thrips per plot were established under greenhouse conditions. Thrips density (for flower sampling = x1; for sticky trap = x2) was monitored using flower sampling and blue sticky trap counts, and was found to be directly related to the proportion of damaged-fruits (y) and the reduction in fruit yield: significant relationships were found for the flower samples (y = 1.2261x1 − 0.6232, r2 = 0.8582) and for the trap catches (y = 11.667 ln(x2) − 9.5, r2 = 0.8896). The proportion of damaged fruits that could be tolerated from an economic perspective, based on the cost of controlling the thrips population chemically and the market value of the fruit, was 6.67–11.76 %; this translated into economic thresholds of 1.05–1.5 adults and/or larvae of T. palmi per flower or 4.91–10.17 adults T. palmi per four-day sticky card count.

Solubility of Solid Ferrocene in Pressurized Hot Water

Aqueous solubilities of ferrocene (bis(cyclopentadienyl)iron(II), C10H10Fe) were measured at temperatures within (313 to 433) K along a 5 MPa isobar. The activity coefficients of ferrocene in aqueous solutions at saturation were obtained employing three different approximations of the solute heat capacity difference, ΔCP2. The relative rate of increase in aqueous solubility of ferrocene with temperature, (∂ ln x2/∂T)P,σ, is distinctly lower than the corresponding values in aromatic hydrocarbons naphthalene (C10H8) and anthracene (C14H10) possibly because of less endothermic solute−water interactions because of less contact surface of the ferrocene molecule.

Tracer Diffusion of Molybdenum in Crystallized Fe&lt;sub&gt;79-y&lt;/sub&gt;Mo&lt;sub&gt;8&lt;/sub&gt;Cu&lt;sub&gt;1&lt;/sub&gt;B&lt;sub&gt;12+y&lt;/sub&gt; Alloy

99Mo tracer diffusion in Fe79-yMo8Cu1B12+y (y = 0, 3, 5) alloys was studied using serial sectioning method in the temperature range 573 – 773 K. Sputtering by Ar+ ions was applied as a sectioning technique. The measurement was carried out with the ribbon-like samples prepared by planar flow casting technique and crystallized before the diffusion experiment by a thermal shock in vacuum. The structure was formed by areas of three distinct types differing in chemical composition r = at. % Mo / at. % Fe: (i) r = 0.02 (crystallites of Fe, mean size d ~ 150 nm), (ii) r = 0.09 (relaxed phase; d ~ 150 nm) and (iii) r = 0.83 (boride phase; d ~ 30 nm). The measured profiles were linear in co-ordinates ln cMo vs. x1.5 (cMo – concentration of Mo in depth x), indicating that the diffusion of 99Mo was controlled by „type A-B” kinetics.

Solubility of Solid Polycyclic Aromatic Hydrocarbons in Pressurized Hot Water at Temperatures from 313 K to the Melting Point

Aqueous solubilities of two- to four-ring solid polycyclic aromatic hydrocarbons (PAHs) (naphthalene, anthracene, 1,2-benzanthracene, triphenylene, and p-terphenyl) were measured at temperatures within 313 K to the PAH melting point and pressures within the range (4 to 8) MPa by dynamic method combined with gas chromatography/mass spectrometry. A novel feature of the apparatus was the use of a capillary restrictor to minimize the system volume downstream of the sampling point. The results for naphthalene and anthracene compare favorably with the literature data whereas the solubilities of 1,2-benzanthracene, triphenylene, and p-terphenyl in pressurized hot water are reported for the first time. The solubilities (equilibrium mole fractions, x2) of PAHs are discussed in terms of temperature and hydrocarbon structure. Mean values of the relative change in the PAH solubility with temperature, (∂ ln x2/∂T)σ, range from 5.4 × 10-2 K-1 in naphthalene to 7.2 × 10-2 K-1 in p-terphenyl. The ln x2 versus T plot for ...

A thermodynamic model of Fe–Cr spinels

A new thermodynamic model for multi-component spinel solid solutions has been developed which takes into account thermodynamic consequences of cation mixing in spinel sublattices. It has been applied to the evaluation of thermodynamic functions of cation mixing and thermodynamic properties of Fe3O4–FeCr2O4 spinels using intracrystalline cation distribution in magnetite, lattice parameters and activity-composition relations of magnetite–chromite solid solutions. According to the model, cation distribution in binary spinels, (Fe1-x2+ Fex3+)[Fex2+Fe2-2y-x3+Cr2y]O4, and their thermodynamic properties depend strongly on Fe2+–Cr3+ cation mixing. Mixing of Fe2+–Fe3+ and Fe3+–Cr3+ can be accepted as ideal. If Fe2+, Fe3+ and Cr are denoted as 1, 3 and 4 respectively, the equation of cation distribution is −RT ln(x2/((1−x)(2−2y−x)))= ΔG13* + (1−2x)W13+y(W14−W13−W34) where ΔG13* is the difference between the Gibbs energy of inverse and normal magnetite, Wij is a Margules parameter of cation mixing and ΔG13*, J/mol =−23,000+13.4 T, W14=36 kJ/mol, W13=W34=0. The positive nonconfigurational Gibbs energy of mixing is the main reason for changing activity–composition relations with temperature. According to the model, the solvus in Fe3O4–FeCr2O4 spinel has a critical temperature close to 500°C, which is consistent with mineralogical data.

Characteristics of activity coefficient models for liquid solutions

AbstractLiquid–phase activity coefficient models (or excess Gibbs energy models) with three or fewer adjustable parameters are often sufficient to model the liquid solutions present for the vapor–liquid equilibria (VLE) or the vapor–liquid–liquid equilibria (VLLE) calculations of phase equilibria. Our purpose here is to show the flexibility of three such equations in the correlation and prediction of (1) extrema and inflection points on the popular ln γi vs. x1 diagram for binary solutions, (2) liquid–liquid phase splitting, and (3) homogeneous azeotropes. The empirical equations investigated here are (a) the two‐constant Margules model, (b) the van Laar model, and (c) the three‐constant NRTL model. New mathematical procedures lead to new graphs and equations, which allow the reader to identify the presence of any of the above three phenomena by inspection without performing detailed calculations such as a Gibbs energy minimization for liquid phase splitting. © 2004 American Institute of Chemical Engineers AIChE J, 50: 854–861, 2004

Low-temperature behaviour of haematite: susceptibility and magnetization increase on cycling through the Morin transition

SUMMARY It has been realized previously (e.g. Borradaile 1994) that cycling through the Morin transition (Tm, occurring in ideal a-Fe2O3 at x10 uC) may have implications for the NRM of some haematite-bearing rocks. We investigate the behaviour of the low-field susceptibility (xlf), several magnetizations (in fields of 5, 25, 100 and 1600 mT) and SIRM on cycling through Tm of several well-characterized haematite types of varying crystallinity and particle shape. Before low-temperature treatment, xlf of the haematites varied between y40 and y235r10 x8 m 3 kg x1 . Below Tm, where only haematite’s defect moment resides, xlf was much more uniform at y19 to y28r10 x8 m 3 kg x1 . After return to room temperature, increases in xlf of up to y50 per cent were observed (when cycling in the Earth’s magnetic field as well as in a field-free space), inferred to be a function of the domain state of the haematite. This was shown for one of the haematites (LH2 which occurs as small platelets and is particularly well crystalline) where a relation y=(8.60t1.01) ln(x)x2.98 was obtained, where x is the grain size (mm) and y is the percentage susceptibility increase. We suggest that transdomain changes induce the change in xlf. The nucleation of (additional) domain walls in ‘metastable’ single-domain (SD) to pseudo-single-domain (PSD) grains is made possible by the low anisotropy at the Morin transition. In view of this mechanism, small stable SD haematite particles would not be affected and the grain size corresponding to y= 0( y1.5 m mf or LH2) would represent the ‘real’ SD threshold size. Thermal cycling to over the Curie temperature (680 uC) is needed to return to the original domain state before the LT treatment, as expressed by a return to the original xlf values. Measuring xlf between alternating field (AF) demagnetization steps shows that AF demagnetization gradually removes the xlf increase, which appears to be soft; 30 mT is sufficient to erase 90 per cent. Thermal cycling in a 5 mT field between temperatures above Tm showed that irreversible changes in domain structure are noticeable before the isotropic point is passed. After cycling, magnetization is added to PSD and multidomain (MD) grains that intriguingly appears to be remanence, probably induced by the broadening and subsequent irreversible displacement of loosely pinned domain walls. Complete cycling through the isotropic point considerably enhances the new remanence component in ‘metastable’ SD to MD particles by an increase in the number of domains. If this behaviour can be extrapolated to the intensity of the Earth’s magnetic field, this would imply that large ‘metastable’ SD to MD specularite crystals with a well-developed Morin transition are susceptible to acquiring geologically irrelevant remanence components when subjected to low ambient temperatures. Fine-grained haematite pigment, on the other hand, would not be affected. Thermal demagnetization alone would not be able to separate these two remanences as the new domain structure persists up to close to the Curie temperature. Our findings indicate that a cleaning procedure consisting of an initial AF step followed by stepwise thermal demagnetization is preferable in order to isolate the original remanence component properly in haematite-bearing rocks.

Synthesis and Characterization of Lanthanide(III) Complexes Withsalicylidene-2-Aminopyridine

A series of lanthanide(III) complexes of the type [Ln(SAP)X2.2H2O], where Ln = La, Ce, Pr, Nd, Sm, Eu, Gd, Dy and Y; X = NO3 or CI, SAPH = salicylidene-2-aminopyridine, have been synthesised and characterized by elemental analyses, molar conductance, magnetic measurements, spectral (electronic, infrared, 1H NMR) and thermal studies. The elemental analyses indicate 1:1 (metal:ligand) stoichiometry for the complexes. The spectral studies show that the ligand acts as a monobasic tridentate ligand with the phenolic -CO, azomethine nitrogen and ring nitrogen as coordinating sites. The nitrate group is coordinated in a monodentate fashion. The ligand, metal salts and the complexes were screened for antibacterial and antifungal activities. It was found that the activity against Candida albicans of the ligand as well as the metal salts has significantly enhanced on complexation.

Consistency Tests for Binary VLE Data

Many VLE data papers are published each year for binary systems at either constant temperature or constant pressure. This manuscript examines consistency checks via Gibbs-Duhem equations and finds most powerful a two-step method that (1) uses a combination of the liquid and vapor Gibbs-Duhem equations to first check the internal consistency of (P, y, x) at constant temperature or (T, y, x) at constant pressure and (2) then uses the liquid-side Gibbs-Duhem equation to check the liquid-phase activity coefficients in a test more familiar to most workers. A new graphical method is developed in conjunction with step 1. The role of the assumed gas-phase model is examined. The common problem of published data of the activity coefficient of the solvent falling slightly under unity upon approaching the pure solvent end on the familiar ln Ai versus x1 diagram is explained as an artifact of usual data reduction procedures but corrected by the present procedures.