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Showing papers by "North Carolina State University published in 1986"



Journal ArticleDOI
TL;DR: In this paper, a conceptual clarification of the sources and meaning of cross-sectional price variability is used to motivate a theoretical and econometric framework for the estimation of crosssectional demand functions.
Abstract: A conceptual clarification of the sources and meaning of cross-sectional price variability is used to motivate a theoretical and econometric framework for the estimation of cross-sectional demand functions. Quality effects are distinguished from supply-related price variability to identify cross-sectional demand for disaggregated food commodities. An empirical application using data from the 1977-78 Nationwide Food Consumption Survey indicates that parameter differences resulting from a failure to adjust cross-sectional prices for quality effects are likely to be small for relatively homogenous, disaggregated food commodities. In demand analysis with cross-sectional, household budget data, it is usually assumed that prices are constant (Allen and Bowley, Prais and Houthakker, George and King). Given this assumption, Engel functions are estimated where expenditure (or quantity) is regressed on income (or total expenditures), family size, and other demographic characteristics. The assumption that cross-sectional price effects are absent or are captured adequately by spatial and temporal dummy variables has not been evaluated empirically. Whether cross-sectional price effects can be treated in this manner has implications for the specification of cross-sectional demand functions as well as the estimation of Engel functions. There is a considerable literature on estimating price elasticities with cross-sectional data. Most of the applications utilize timeseries/cross-sectional data. Annual (or quarterly) household consumption surveys and

448 citations


Journal ArticleDOI
14 Feb 1986-Cell
TL;DR: A 3547 bp DNA fragment from male-sterile maize mitochondria, designated TURF 2H3, selected because of its unique and abundant transcripts appears to be uniquely altered in cms-T plants restored to fertility by the nuclear restorer genes Rf1 and Rf2.

446 citations


Journal ArticleDOI
TL;DR: In this paper, the effects of high density dc current pulses (10 3 A/mm 2 for 60 μs) on the flow stress of a number of polycrystalline metals (Al, Cu, Ni, Fe, Nb, W and Ti) tested in uniaxial tension at 300 K were investigated with the objective of determining the mechanisms responsible for concurrent load drops.

368 citations


Journal ArticleDOI
TL;DR: In this paper, the authors investigated sediment accumulation on the Brazilian continental shelf near the Amazon River using radiochemical (e.g. 210Pb, 14C) techniques to provide a better understanding of this major dispersal system of fine-grained sediment.

339 citations


Journal ArticleDOI
TL;DR: It is shown that the method is capable of generating membership functions in accordance with the possibility-probability consistency principle for fuzzy sets whose elements have a defining feature with a known probability density function in the universe of discourse.

333 citations


Journal ArticleDOI
TL;DR: In this article, the authors examined the effects of component commonality on optimal safety stock levels in a two-product, two-level inventory model, where the criterion is to minimize system safety stock subject to a service level constraint.
Abstract: We examine the effects of component commonality on optimal safety stock levels in a two-product, two-level inventory model. The criterion is to minimize system safety stock subject to a service level constraint. Although our model is specialized, its analysis provides insights not available in other multilevel inventory models.

316 citations


Journal ArticleDOI
15 Oct 1986-Virology
TL;DR: The complete nucleotide sequence of the tobacco etch virus (TEV) RNA genome has been determined excepting only the nucleotide(s) present at the extreme 5' terminus, and a function for the large nuclear inclusion protein is suggested by a comparison of the deduced amino acid sequence with a protein data bank.

311 citations


Journal ArticleDOI
TL;DR: Th thin films of silicon nitride grown by remote plasma-enhanced chemical-vapor deposition and studied the chemical bonding by infrared absorption, x-ray photoelectron spectroscopy, Rutherford backscattering, and Auger-electronSpectroscopy are found to have a stoichiometric composition.
Abstract: We have grown thin films of silicon nitride by remote plasma-enhanced chemical-vapor deposition and have studied the chemical bonding by infrared absorption, x-ray photoelectron spectroscopy, Rutherford backscattering, and Auger-electron spectroscopy. Films were grown using two different gases as the source of nitrogen, ${\mathrm{N}}_{2}$ and ${\mathrm{NH}}_{3}$. We have found that films grown from ${\mathrm{N}}_{2}$ and deposited at substrate temperatures in excess of 350 \ifmmode^\circ\else\textdegree\fi{}C have a composition corresponding to stoichiometric ${\mathrm{Si}}_{3}$${\mathrm{N}}_{4}$, whereas films deposited from ${\mathrm{NH}}_{3}$ require substrate temperatures in excess of about 500 \ifmmode^\circ\else\textdegree\fi{}C to eliminate bonded H and yield the same stoichiometric composition. In contrast films grown from ${\mathrm{NH}}_{3}$ at temperatures in the range of 50 to 100 \ifmmode^\circ\else\textdegree\fi{}C have a chemical composition corresponding to silicon diimide, Si(NH${)}_{2}$. Films grown from ${\mathrm{NH}}_{3}$ at intermediate substrate temperatures are solid solutions of ${\mathrm{Si}}_{3}$${\mathrm{N}}_{4}$ and Si(NH${)}_{2}$.

286 citations


Journal ArticleDOI
TL;DR: In this paper, a finite volume formulation for the Euler equations using Cartesian grids is presented and used to study complex two-dimensional configurations, and results using this approach for single element airfoils are shown to be competitive with and as accurate as other methods that employ mapped grids.
Abstract: A finite volume formulation for the Euler equations using Cartesian grids is presented and used to study complex two-dimensional configurations. The formulation extends methods developed for the potential equation to the Euler equations. Results using this approach for single element airfoils are shown to be competitive with and as accurate as other methods that employ mapped grids. Further, it is demonstrated that this method provides a simple and accurate procedure for solving flow problems involving multielement airfoils.

283 citations


Journal ArticleDOI
TL;DR: In this paper, the authors examined the seafloor stratigraphy at the mouth of the Amazon River using high-frequency (3.5-kHz) seismic records from about 6,000 km of ship track.
Abstract: Despite the annual discharge of more than a billion tons of sediment by the Amazon River, the sedimentary environment near the river mouth has little subaerial expression and thus does not meet the classic definition of a delta. The river mouth, however, is not an estuary, either. These observations raise a major question as to what type of sedimentary environment the Amazon river mouth represents. Seismic stratigraphy has been examined on the continental shelf at the mouth of the Amazon River using high-frequency (3.5-kHz) seismic records from about 6,000 km of ship track. These records demonstrate three regions. (1) The Amazon River has built a subaqueous feature which stretches for hundreds of kilometres offshore and alongshore from its mouth. The feature is prograding seaward and accreting upward, and it contains fine-scale stratification typical of classic deltas. The feature forming at the mouth of the Amazon is a subaqueous delta; it differs from classic deltas primarily in its lack of subaerial expression. Subaqueous deltas, such as the Amazon, represent the general case of a major river entering an energetic oceanic regime.

Journal ArticleDOI
TL;DR: A formula is derived for the apparent relative risk under misclassification (R), as a function of the sensitivity (U) and specificity (V) of the test for exposure and of the true relative risk (R) and true prevalence of exposure (P(E) in the population.
Abstract: In epidemiologic studies, individuals may be misclassified with respect to exposure to a risk factor for disease. Such misclassification causes the relative risk of disease associated with the exposure in the population to be biased toward the null value. Here, a formula is derived for the apparent relative risk under misclassification (R) as a function of the sensitivity (U) and specificity (V) of the test for exposure and of the true relative risk (R) and true prevalence of exposure (P(E] in the population. The relative influence of U and V on the bias in R depends both on R and on P(E), with U tending to be more influential at higher values of P(E). When there is misclassification of exposure, variation in P(E) may bias comparisons of relative risk between groups or exposures, either by producing spurious differences or by masking true differences, and may generate spurious trends associated with a third variable such as age. Because the possible effects of misclassification of exposure on relative risk are complex and not easily generalized, the potential degree of bias should be evaluated individually in each situation.

Journal ArticleDOI
TL;DR: This technique permits qualitative study of environmental parameters that regulate gaseous N losses via denitrification and nitrification in soils by exploiting the differential sensitivity of these processes to C(2)H(2).
Abstract: The source of N2O produced in soil is often uncertain because denitrification and nitrification can occur simultaneously in the same soil aggregate. A technique which exploits the differential sensitivity of these processes to C2H2 inhibition is proposed for distinguishing among gaseous N losses from soils. Denitrification N2O was estimated from 24-h laboratory incubations in which nitrification was inhibited by 10-Pa C2H2. Nitrification N2O was estimated from the difference between N2O production under no C2H2 and that determined for denitrification. Denitrification N2 was estimated from the difference between N2O production under 10-kPa C2H2 and that under 10 Pa. Laboratory estimates of N2O production were significantly correlated with in situ N2O diffusion measurements made during a 10-month period in two forested watersheds. Nitrous oxide production from nitrification was most important on well-drained sites of a disturbed watershed where ambient NO3− was high. In contrast, denitrification N2O was most important on poorly drained sites near the stream of the same watershed. Distinction between N2O production from nitrification and denitrification was corroborated by correlations between denitrification N2O and water-filled pore space and between nitrification N2O and ambient NO3−. This technique permits qualitative study of environmental parameters that regulate gaseous N losses via denitrification and nitrification.

Journal ArticleDOI
01 Dec 1986-Genetics
TL;DR: Phylogenetic analysis of restriction map haplotypes suggest that the major twofold component of ADH activity variation is due to sequence variation tightly linked to and possibly distinct from that underlying the allozyme difference.
Abstract: Variation in the DNA restriction map of a 13-kb region of chromosome II including the alcohol dehydrogenase structural gene (Adh) was examined in Drosophila melanogaster from natural populations. Detailed analysis of 48 D. melanogaster lines representing four eastern United States populations revealed extensive DNA sequence variation due to base substitutions, insertions and deletions. Cloning of this region from several lines allowed characterization of length variation as due to unique sequence insertions or deletions [nine sizes; 21–200 base pairs (bp)] or transposable element insertions (several sizes, 340 bp to 10.2 kb, representing four different elements). Despite this extensive variation in sequences flanking the Adh gene, only one length polymorphism is clearly associated with altered Adh expression (a copia element approximately 250 bp 5' to the distal transcript start site). Nonetheless, the frequency spectra of transposable elements within and between Drosophila species suggests they are slightly deleterious. Strong nonrandom associations are observed among Adh region sequence variants, ADH allozyme (Fast vs. Slow), ADH enzyme activity and the chromosome inversion ln(2L) t. Phylogenetic analysis of restriction map haplotypes suggest that the major twofold component of ADH activity variation (high vs. low, typical of Fast and Slow allozymes, respectively) is due to sequence variation tightly linked to and possibly distinct from that underlying the allozyme difference. The patterns of nucleotide and haplotype variation for Fast and Slow allozyme lines are consistent with the recent increase in frequency and spread of the Fast haplotype associated with high ADH activity. These data emphasize the important role of evolutionary history and strong nonrandom associations among tightly linked sequence variation as determinants of the patterns of variation observed in natural populations.


Journal ArticleDOI
01 Jul 1986-The Auk
TL;DR: Early-winter body mass was associated positively with overwinter as well as annual survival for young Canvasbacks in some years, and it is suspected that the lack of established wintering patterns among these birds may underlie the less consistent result.
Abstract: -Mass and recapture histories of 6,000 Canvasbacks (Aythya valisineria) banded in upper Chesapeake Bay were used to test two hypotheses: (1) early-winter body mass is associated with the probability of surviving the winter, and (2) early-winter body mass is associated with annual survival probability. Data were analyzed by a binary regression method that treated mass as a continuous variable and estimated parameters to describe a general relationship between body mass and survival probability. Results for adult males, which provided our largest data sets, presented strong evidence that birds with high relative earlywinter masses had both greater overwinter and annual survival probabilities. Results of overwinter analyses necessarily are qualified by the alternative explanation of mass-dependent emigration, i.e. the possibility that lighter birds move south in response to cold weather and leave only heavy birds for recapture. Such a phenomenon remains to be documented. Results concerning annual survival probabilities are not vulnerable to this alternative explanation because of the strong fidelity of Canvasbacks at the banding site. Because of small sample size, data were inadequate to permit mass/survival inferences for adult females. Sample sizes were adequate for young Canvasbacks, but the results were less consistent than for adult males. Although early-winter body mass was associated positively with overwinter as well as annual survival for young Canvasbacks in some years, we suspect that the lack of established wintering patterns among these birds may underlie the less consistent result. Received 11 February 1985, accepted 9 January 1986. FOR several species of waterfowl, evidence now exists for a relationship between the physiological state or "condition" of an individual and its subsequent reproductive performance (e.g. Ankney and MacInnes 1978; Raveling 1979; Krapu 1979, 1981). It is also reasonable to expect that the "physiological condition" of an individual at some time t is related to its probability of surviving some subsequent period (t, t + A), especially if the period is one in which food resources are limited or environmental conditions are energetically stressful, or both. This expectation has been accepted in the literature not only for waterfowl, but for birds and mammals in general, and it is now a tacit assumption of most published studies dealing with physiological condition during nonbreeding periods. We are aware of few efforts that use birds, however, to test the hypothesis that particular physiological characteristics are related to survival probability. There is considerable speculation and some evidence for several bird species that food supplies may be limited during winter and that both food availability and winter weather are related to survival probability (Lack 1966; Fretwell 1968, 1972; Goss-Custard 1979; North and Morgan 1979; Pulliam and Parker 1979; van Balen 1980; Ekman et al. 1981; Jansson et al. 1981). Winter is thus a logical time to look for a relationship between physiological condition and survival within many Temperate Zone birds. Two general approaches have been used to draw inferences about the relationship between condition and survival in wintering birds. The first involves comparisons of variables believed to reflect condition (e.g. body mass, percentage of fat or lipid in the body, percentage of protein in the body) between two groups: (1) birds found dead during periods of severe winter weather, and (2) birds collected during "normal" or mild winter weather and believed to be representative of live wintering birds. There are large differences between these two groups for Eurasian Coots (Fulica atra; Visser 1978), Common Redshanks (Tringa totanus; Davidson and Evans 1982), and Eurasian Oystercatchers (Haematopus ostralegus; Davidson and Evans 1982, Swennen and Duiven 1983). Thus, these results provided evidence that lipid and 506 The Auk 103: 506-514. July 1986 This content downloaded from 157.55.39.100 on Thu, 25 Aug 2016 04:57:15 UTC All use subject to http://about.jstor.org/terms July 1986] Canvasback Mass and Survival 507 protein reserves are mobilized during periods of severe weather and may be important to winter survival. Nevertheless, these studies did not demonstrate that variation in survival probability is associated with variation in body mass or nutrient reserves. The second general approach permits stronger inferences about this relationship. Birds are captured and weighed (or assigned to a condition category by some other means) at the beginning of a winter period. Recaptures or resightings of the birds at the end of the period are then used to draw inferences about variation in survival probabilities for birds of different masses or condition categories. We are aware of two such studies on wintering birds. In a 2-yr study, Fretwell (1968) captured and banded 85 Field Sparrows (Spizella pusilla) in early winter and assigned them to two fat categories (above and below average). The proportion of birds seen later in winter was significantly greater for the above-average category in 1 of 2 years. In another study, Kikkawa (1980) weighed and color-banded 388 first-year Gray-backed White-eyes (Zosterops lateralis) at the beginning of winter over a 3-yr period. Resightings at the end of each winter showed no significant difference between the proportion of birds above vs. below average in initial mass. We use an approach similar to the second described above with Canvasbacks (Aythya valisineria) wintering on Chesapeake Bay. Winter weather conditions on Chesapeake Bay are frequently subfreezing, and prolonged ice cover may limit food availability for Canvasbacks. In addition, resource-related differences in winter mortality associated with behavioral dominance or fasting endurance may be important selective forces in the evolution of winter distribution patterns in this species (Nichols and Haramis 1980, Alexander 1983, Haramis et al. 1985). In ducks, there is generally a good correlation between body mass and both fat (Owen and Cook 1977, Bailey 1979) and total nutrient (lipid + protein) reserves (Wishart 1979). Therefore, we expect high body masses to reflect good reserves and possibly confer a greater probability of surviving the winter. In our study, masses and recapture histories of Canvasbacks were used to test two hypotheses: (1) Canvasback body mass in early winter is associated with the probability of surviving that winter, and (2) Canvasback body mass in early winter is associated with subsequent annual survival probability.

Journal ArticleDOI
TL;DR: All species of poultry are capable of AA synthesis and dietary supplementation with AA is not necessary when the animal is managed properly, however, when the birds are subjected to stressful condi...
Abstract: All species of poultry are capable of AA synthesis and dietary supplementation with AA is not necessary when the animal is managed properly. However, when the birds are subjected to stressful condi...

Journal ArticleDOI
TL;DR: It is speculated that the riparian zone is a major site of depletion of NO(3) from the soil solution via denitrification, based on in situ N(2)O diffusion measurements and laboratory incubations.
Abstract: Gaseous N losses from disturbed and reference forested watersheds at the Coweeta Hydrologic Laboratory in western North Carolina were studied by in situ N(2)O diffusion measurements and laboratory incubations throughout a 10-month period. Soil temperature, percent base saturation, and water-filled pore space accounted for 43% of the variation in in situ N(2)O diffusion measurements. Laboratory incubations distinguished the gaseous N products of nitrification and denitrification. Nitrifying activity, ambient NO(3), and nitrification N(2)O were positively correlated with percent base saturation. However, differences between watersheds in soil N substrate caused by presence of leguminous black locust in the disturbed watershed were confounded with differences in soil acidity. Denitrification was most strongly affected by soil moisture, which in turn was determined by precipitation events and slope position. Gaseous N losses from well-drained midslope and toeslope landscape positions appeared to be minor relative to other N transformations. Favorable conditions for denitrification occurred at a poorly drained site near the stream of the disturbed watershed. Laboratory incubations revealed high rates of NO(3) reduction in these soils. We speculate that the riparian zone is a major site of depletion of NO(3) from the soil solution via denitrification.


Journal ArticleDOI
TL;DR: It is indicated that the surface on which cows were observed had a profound effect on sexual behavior; however, postpartum interval, season of year, and milk yield were of minor importance.

Journal ArticleDOI
TL;DR: Carbon exchange capacity of cucumber germinated and grown in controlled environment chambers at 1000 microliters per liter CO(2) decreased from the vegetative growth stage to the fruiting stage, during which time capacity of plants grown at 350 microliter per liter increased.
Abstract: Carbon exchange capacity of cucumber (Cucumis sativus L.) germinated and grown in controlled environment chambers at 1000 microliters per liter CO2 decreased from the vegetative growth stage to the fruiting stage, during which time capacity of plants grown at 350 microliters per liter increased. Carbon exchange rates (CERs) measured under growth conditions during the fruiting period were, in fact, lower in plants grown at 1000 microliters per liter CO2 than those grown at 350. Progressive decreases in CERs in 1000 microliters per liter plants were associated with decreasing stomatal conductances and activities of ribulose bisphosphate carboxylase and carbonic anhydrase. Leaf starch concentrations were higher in 1000 microliters per liter CO2 grown-plants than in 350 microliters per liter grown plants but calcium and nitrogen concentrations were lower, the greatest difference occurring at flowering. Sucrose synthase and sucrose-P-synthase activities were similar in 1000 microliters per liter compared to 350 microliters per liter plants during vegetative growth and flowering but higher in 350 microliters per liter plants at fruiting. The decreased carbon exchange rates observed in this cultivar at 1000 microliters per liter CO2 could explain the lack of any yield increase (MM Peet 1986 Plant Physiol 80: 59-62) when compared with plants grown at 350 microliters per liter.

Journal ArticleDOI
TL;DR: A single-pedicle, axial-pattern, island-tubed skin flap was created in crossbred Yorkshire weanling pigs in one surgical procedure, then transferred 2 or 6 days later to a computer-controlled temperature-regulated perfusion chamber for 10-to 12-hr studies.


Journal ArticleDOI
TL;DR: In this article, the Hellinger distance between a nonparametric density estimator and a model family is minimized to produce estimates of location and covariance in multivariate data.
Abstract: The Hellinger distance between a nonparametric density estimator and a model family is minimized to produce estimates of location and covariance in multivariate data. With suitable restrictions on the density estimators and the model family, these minimum Hellinger distance estimators (MHDE's) are shown to be affine invariant, consistent, and asymptotically normal. The robustness of the MHDE as measured by the breakdown point compares favorably against the previously studied M-estimators. Monte Carlo results suggest that the MHDE's are an attractive robust alternative to the usual sample means and covariance matrix.

Journal ArticleDOI
TL;DR: The distribution and orientation of the S13-like and “URF 1”-like sequences are discussed and the possibility that they are active genes is discussed.
Abstract: A transcribed segment of mitochondrial DNA (mtDNA) from Nicotiana tabacum contains the F0-ATPase subunit 9 gene, an open reading frame with homology to the E. coli small subunit ribosomal protein S13 and an open reading frame with homology to a portion of the mammalian “URF 1” protein, recently shown to be a component of the NADH:ubiquinone reductase complex (NADH:Q 1). The transcriptional patterns of the tobacco ATPase 9 gene and S13-like open reading frame share eight RNA species indicating the two sequences are part of the same transcriptional unit. A maize mtDNA fragment contains the S13 homologous sequence and the NADH:Q 1 homologous sequence in an orientation similar to tobacco. The S13-like sequence is present as a single copy in maize and tobacco, as two copies in wheat, and is absent in pea and bean. We discuss the distribution and orientation of the S13-like and “URF 1”-like sequences and the possibility that they are active genes.

Journal ArticleDOI
TL;DR: A simulation model was developed to predict how long it would take a pest to adapt to two antibiotic, host-plant resistance factors if they were deployed sequentially, as a cultivar mixture, or combined in a single pyramided resistant cultivar, indicating that no single deployment strategy was most durable in all pest/cropping system combinations.
Abstract: A simulation model was developed to predict how long it would take a pest to adapt to two antibiotic, host-plant resistance factors if they were deployed sequentially, as a cultivar mixture, or combined in a single pyramided resistant cultivar. Results indicated that no single deployment strategy was most durable in all pest/cropping system combinations. When relative fitness of the insect pest on plants with both resistance factors was linearly related to the number of adaptive alleles that the insect possessed, sequential release of two cultivars with different single resistance factors or mixed planting of these two cultivars was expected to provide weaker but more durable resistance than pure plantings of a cultivar into which both resistance factors had been pyramided. If totally susceptible plants are grown adjacent to the pyramided cultivar in a ratio that causes the mean fitness of insects with no adaptive alleles to be equivalent to their mean fitness in the sequential-release plan, the durability of all three strategies is similar. If alleles for adaptation are recessive and epistasis is strong enough to make the two resistance factors largely redundant in plants possessing both factors, pyramided deployment of resistance factors is often expected to be much more durable than a sequential or mixed release. Durability of the pyramided cultivar is enhanced by adding some totally susceptible plants to the system. Structural linkage of the two insect loci would reduce durability of such a pyramided cultivar, but it would usually be more durable than sequential or mixed releases.

Journal ArticleDOI
TL;DR: An approximation procedure is developed for the analysis of tandem configurations consisting of single server finite queues linked in series and gives results in the form of the marginal probability distribution of the number of units in each queue of the tandem configuration.
Abstract: An approximation procedure is developed for the analysis of tandem configurations consisting of single server finite queues linked in series. External arrivals occur at the first queue which may be either finite or infinite. Departures from the queuing network may only occur from the last queue. All service times and interarrival times are assumed to be exponentially distributed. The approximation algorithm gives results in the form of the marginal probability distribution of the number of units in each queue of the tandem configuration. Other performance measures, such as mean queue-length and throughput, can be readily obtained. The approximation procedure was validated using exact and simulation data. The approximate results seem to have an acceptable error level.

Journal ArticleDOI
TL;DR: In this article, the effects of ozone on the quality of poultry chiller water and broiler carcasses were evaluated in a pilot plant size water recirculating chicken chiller and the microbial counts of ozone treated carcasses stored at 4.4°C were consistently lower than carcasses chilled under nonozonated conditions.
Abstract: The effects of ozone on the quality of poultry chiller water and broiler carcasses were evaluated in a pilot plant size water recirculating poultry chiller. The microbial counts of ozone treated carcasses stored at 4.4°C were consistently lower than carcasses chilled under nonozonated conditions. Greater than 99% of all microorganisms washed from the carcasses were destroyed by the residual ozone in addition to significant reductions of one third in the chemical oxygen demand (COD) and a significant increase in light transmission (500 nm) of the treated process water. No significant carcass skin color losses, lipid oxidation, or off flavors resulted from ozone contact.

Journal ArticleDOI
TL;DR: In this article, the phase relations in the Cu,In,Se system are reviewed with particular attention to compositions in the vicinity of CuInSe 2, and the pseudobinary Cu 2 Se-In 2 Se 3 is re-evaluated and the liquidus-solidus relationship of the δ phase is discussed.