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The potential of crustose coralline algae as high-resolution archives of past ocean variability in mid- to high-latitudes has only recently been recognized. Few comparisons of coralline algal proxies, such as temperature-dependent algal magnesium to calcium (Mg/Ca) ratios, with in situ -measured surface ocean data exist, even rarer are well replicated records from individual sites. We present Mg/Ca records from nine coralline algal specimens ( Clathromorphum compactum ) from a single site in the Gulf of Maine, North Atlantic. Sections from algal mounds were analyzed using Laser Ablation-Inductively Coupled Plasma Mass Spectrometry (LA-ICP-MS) yielding individual Mg/Ca records of up to 30 years in length. We first test intra- and intersample signal replication and show that algal Mg/Ca ratios are reproducible along several transects within individual sample specimens and between different samples from the same study site. In addition, LA-ICP-MS-derived Mg/Ca ratios are compared to electron microprobe (EMP) analyzed data on the longest-lived specimens and were found to be statistically commensurable. Second, we evaluate whether relationships between algal-based SST reconstructions and in situ temperature data can be improved by averaging Mg/Ca records from multiple algal specimens (intersample averages). We found that intersample averages yield stronger relationships to sea surface temperature (SST) data than Mg/Ca records derived from individual samples alone. Thus, Mg/Ca-based paleotemperature reconstructions from coralline algae can benefit from using multiple samples per site, and can expand temperature proxy precision from seasonal to monthly.

In this paper we present a new OCR-concept designed for the requirements of historic prints in the context of mass-digitizations. The core part is the glyph recognition, based on pattern matching with patterns that are derived from computer font glyphs and are generated on-the-fly. The classification of a sample is organized as a search process for the most similar glyph pattern. This results in consistently good hit rates for arbitrary fonts without any training. In particular, we investigate the performance of our prototype in comparison to popular commercially available OCR-software. HighlightsNew OCR-concept designed for the requirements of historic prints.Pattern matching with on-the-fly generated patterns.Integration of a RIP into an OCR software.Outperforms established OCR softwares especially for out-of-the-ordinary fonts.Consistently good hit rates for arbitrary fonts.

Data on micromechanical properties of ancient and medieval glass fragments and glasses of early modern and today's manufacturing were compiled to offer a tentative look on changes in the brittleness of glass over the past 2000 years. Chronology of glass making was based on glass chemistry using rare earth element (REE) pattern, fluxing agents and provenance analysis while cracking and brittleness were evaluated from Vickers indentation in the course of the mean crack initiation load CR and the crack length-to-half diagonal ratio c/a. A structural analysis revealed that CR increases and c/a decreases with increasing molar volume i.e. decreasing atomic packing fraction, which allows us to classify periods of high and low crack-resistant and brittle glasses along the time line of historic glass technology.

Despite the importance of palaeoecosystems with Ediacara-type fossils for the early evolution of metazoans, only little is known about the interplay of geological and biological processes in these environments. The reason is that sedimentary structures, biogenic structures and (bio-) geochemical signatures (e.g. hydrocarbon biomarkers) are commonly not well preserved due to the predominance of volcanic and siliciclastic lithologies. The Shibantan Member (Dengying Formation, South China) is one of only few carbonate settings with Ediacara-type organisms worldwide and its lithology promises an excellent preservation of sedimentary facies and (bio-) geochemical signatures. Here we provide the first comprehensive geobiological characterisation of the Shibantan Member in order to reconstruct the interplay between sedimentary and (bio-) geochemical processes and to assess the microbial activities in the palaeoecosystem with Ediacara-type fossils. Facies analyses revealed that carbonate and organic matter were autochthonously formed by (bio-) geochemical processes linked to microbial mats. However, the material was frequently reworked and re-deposited within the same setting (i.e. para-autochthonous) as evidenced by small-scale (hummocky-) cross stratification, erosional contacts, lenticular bedding and load casts. Negative Ce anomalies (Ce/Ce*) and low V/Cr ratios demonstrate that molecular O 2 was present in the water column, whereas characteristic Ni/Co-, V/(V + Ni), and V/Sc ratios suggest the contemporaneous presence of sub- to anoxic water. Taken together, these observations imply a temporarily stratified water body frequently mixed and ventilated by storms. 13 C-enrichments in the Shibantan carbonates (δ 13 C = +3.29 to +3.98‰, VPDB) together with 13 C-depletions of syngenetic n -alkanes cleaved from the extraction residue using catalytic hydropyrolysis (HyPy; δ 13 C = −31.7 to −36.3‰, VPDB) could indicate a significant withdrawal of 12 C by primary producers that thrived within the mats. At the same time, sulphurised biomarkers in the bitumen and HyPy-pyrolysate hint at organic matter decomposition and concomitant sulphide production by sulphate reducing bacteria. When oxygen was available at the sediment–water interface due to mixing by storms, sulphide oxidising bacteria were possibly temporarily favoured. The results demonstrated that palaeoenvironmental conditions dynamically changed through a complex interplay of biogenic and abiogenic processes.

This study explores the potential of detrital rutile geochemistry and thermometry as a provenance tracer in rocks from the Central Dabie ultrahigh-pressure metamorphic (UHPM) zone in east-central China that formed during Triassic continental collision. Trace element data of 176 detrital rutile grains selected from local river sediments and 91 rutile grains from distinct bedrocks in the Shuanghe and Bixiling areas, obtained by both electron microprobe (EMP) and in situ LA-ICP-MS analyses, suggest that geochemical compositions and thermometry of detrital rutiles are comparable to those from their potential source rocks. After certification of the Cr–Nb discrimination method for the Central Dabie UHPM zone, we show that 29% of the detrital rutiles in the Shuanghe area were derived from metamafic sources whereas in the Bixiling area that it is up to 76%. Furthermore, the proportion of distinct types of detrital rutiles combined with modal abundances of rutile in metapelites and metamafic bedrocks can be used to estimate the proportion of different source lithologies. Based on this method the proportion of mafic source rocks was estimated to ∼10% at Shuanghe and >60% at Bixiling, respectively, which is consistent with the proportions of eclogite (the major rutile-bearing metamafic rock) distribution in the field. Therefore, the investigation of detrital rutiles is a potential way to evaluate the proportion of metamafic rocks and even to prospect for metamafic bodies in UHPM terranes. Zr-in-rutile temperatures were calculated at different pressures and compared with temperatures derived from rock-in rutiles and garnet-clinopyroxene Fe–Mg thermometers. Temperatures calculated for detrital rutiles range from 606 °C to 707 °C and 566 °C to 752 °C in Shuanghe and Bixiling, respectively, at P = 3 GPa with an average temperatures of ca. 630 °C for both areas. These temperature averages and ranges are similar to those calculated for rutiles from surrounding source rocks. Combined with comparable Zr distribution characteristics between detrital and source rock rutiles, demonstrating a close source–sediment link for rutiles from clastic and rock in UHPM terranes. Thus rutiles can be accurate tracers of source rock lithologies in sedimentary provenance studies even at a small regional scale. In Bixiling, Nb/Ta ratios of metamafic and metapelitic detrital rutiles fall between 11.0 to 27.3 and 7.7 to 20.5, respectively. In contrast, in Shuanghe, these ratios are highly variable, ranging from 10.9 to 71.0 and 7.6 to 87.1, respectively. When ignoring four outlier compositions with extremely high Nb/Ta in Shuanghe, a distinct clustering of Nb/Ta ratios in rutiles is shown: metapelitic detrital rutiles have Nb/Ta of 7–40 vs. metamafic detrital rutiles with Nb/Ta = 11–25. The Nb/Ta characteristics in detrital rutiles from both areas may reflect the degree of fluid–rock interaction during metamorphism and/or different source lithologies. Therefore, the trace element compositions in detrital rutiles can accurately trace the lithology, proportion and fluid–rock interaction of different source rocks.

Magmatism at Andean Central Volcanic Zone (CVZ), or Central Andes, is strongly influenced by differentiation and assimilation at high pressures that occurred at lower levels of the thick continental crust. This is typically shown by high light to heavy rare earth element ratios (LREE/HREE) of the erupted lavas at this volcanic zone. Increase of these ratios with time is interpreted as a change to magma evolution in the presence of garnet during evolution of Central Andes. Such geochemical signals could be introduced into the magmas be high-pressure fractionation with garnet on the liquidus and/or assimilation from crustal rocks with a garnet-bearing residue. However, lavas erupted at San Pedro–Linzor volcanic chain show no evidence of garnet fractionation in their trace element patterns. This volcanic chain is located in the active volcanic arc, between 22°00 ′ S and 22°30 ′ S, over a continental crust ∼70 km thick. Sampled lavas show Sr/Y and Sm/Yb ratios 87 Sr/ 86 Sr ratios from San Pedro–Linzor lava flows vary between 0.7063 and 0.7094. This is at the upper range, and even higher than those observed at other recent Central Andean volcanic rocks (

The Late Jurassic Jingshan granite located at the south-eastern margin of the North China Craton contains abundant garnets which can be subdivided into three types based on texture and composition: (i) euhedral garnet in mafic biotite and garnet rich enclave (Grt I), (ii) coarse-grained garnet (Grt II) in the host granite, and (iii) small euhedral garnet in aplite (Grt III). In general, Grt I has higher FeO, CaO and lower MnO contents than Grt II. Grt III has higher Mn, but lower Ca contents than others. Grt I has lower MREE and HREE contents than Grt II. Grt III has prominent and distinctly negative Eu anomaly as well as higher MREE composition compared to the others. Systematic variations in oxygen isotope compositions are observed among the three garnet types, with δ 18 O values of 4.7‰ in Grt III. Some of the Grt II and Grt III display two distinct zonings with cores having similar major and trace element compositions to Grt I. Cathodoluminescence (CL) images revealed that the zircons from different garnet-bearing samples possess fine-scale oscillatory zoned magmatic rims with inherited cores. In situ zircon U–Pb dating and trace element analyses show that the dark-luminescent magmatic rims all have Jurassic concordia ages (∼160 Ma) and similar trace element patterns. Most of the inherited cores also display similar Triassic ages of 210–236 Ma, which is similar to the ages of ultrahigh pressure (UHP) metamorphic rocks of the Dabie–Sulu orogen (230 Ma). In addition, Jurassic concordia ages were also found in a zircon inclusion in Grt I, implying that the Grt I was formed shortly before the main magmatic event. The age data suggest that the three different garnet types may be genetically related and modified by cogenetic magmatic events. Based on the zircon U–Pb ages from different garnet-bearing samples, the major element, trace element, oxygen isotope, and zoning textures of the three kinds of garnet we suggest that Grt I may be peritectic garnet, whereas Grt II and III are probably the results of magmatic dissolution–precipitation processes and re-equilibration of garnets with changing magmatic conditions during melting, differentiation, crystallization, and cooling within the granite. We conclude from the oxygen isotopic character of the garnets and ages of the zircons that the source rocks for the Jingshan granites are from Dabie–Sulu orogen representing the South China Craton.

Sets of 20 soda ash glasses, 16 soda lime glasses and 23 wood ash glasses mainly from excavations in Europe (additional soda ash glasses from Egypt) were analysed on 61 chemical elements. Average SiO2 is about 62% in soda glasses and 50% in wood ash glasses. The three groups of glasses contain on average 13% Na2O, 18% Na2O and 13% K2O as fluxes to lower the melting temperature of quartz at their production. The starting materials beside quartz were halophytic plant ash for soda ash glass, trona (Na3H(CO3)2·2H2O) and lime (clamshells) for soda lime glass and beech ash for wood ash glass. Each of the three major glass types contains specific Rare Earth Element (REE) concentrations mainly contained in quartz and its intergrown minerals. 50 Paleozoic and Mesozoic sandstones from Central Europe represent the quartz composition. The REE pattern of these glasses apparently indicates major compositional stages of the Continental Earth's Crust. The boron to lithium and sodium to potassium ratios as in seawater suggest reactions of materials for soda glass with seawater. Negative Ce anomalies in the three glasses are caused by reactions of quartz with seawater.

Medieval wood ash glass classified as 6 early medieval wood ash glasses, 17 wood ash glasses, 5 early wood ash lime glasses, 7 wood ash lime glasses and 9 mixed alkali glasses has been analyzed by microprobe and ICP-mass spectrometry on 61 elements. Their calcium oxide to potassium oxide ratio (CaO/K2O) increases from early to late medieval glasses according to an increase of the proportion of twigs in the bulk amount of wood (logs plus twigs). Twigs because of their relatively large proportion of bark contain more calcium than wood logs. The ratio CaO/K2O of the glasses from not yet evaluated excavations can be used for dating. The observation that the 25 minor elements Be, Sc, V, Cr, Ge, Y, Nb, REE (La to Lu), Ta, W and Bi occur in almost equal concentrations in the five subtypes of wood ash glass makes it highly probable that these elements were introduced into the starting mixtures of the glasses by means of quartz from quartz-rich sand with heavy minerals. The majorities of the wood ash glasses contain so-called europium anomalies within the group of rare-earth elements (REE). Their Eu concentrations normalized to those of the Continental Earth's Crust are lower than the normalized samarium and gadolinium concentrations. These Eu anomalies are apparently inherited from the granitic source of quartz in the upper Continental Earth's Crust. Soda ash and soda lime glass as the other major types in the history of glass contain no Eu anomaly. Therefore a different source of quartz has caused this important element constellation for these glass types. The elements K, Cu, Rb and S are physiologically separated from Ca, P, Mn, Sr and B during the growth of the wood and bark, respectively, in the trees. Different sources of the metals Cu and Co were used for colouring the glasses of our report.

The crystallization history of zoned K-feldspar phenocrysts in microgranular magmatic enclaves in the Karkonosze granite (SW Poland) reveals that the crystals grew in stirred coeval magmas of contrasting compositions. The growth mechanism and crystal compositions are investigated using cathodoluminescence and profiling by Electron Microprobe and Laser Ablation ICP-MS. These methods provide insight into the crystallization process and the varying compositions of the host melt. The phenocrysts show two types of growth patterns — with or without resorption interfaces. The trace-element distribution, heterogeneous across different zones and within single phenocryst zones, reflects a dynamic process of crystal growth from compositionally heterogeneous magma. Hybridization is also reflected in the density of structural Al–O−–Al defects — features that relate to coupled Ba–Al incorporation into the crystal structure. Differences in structural-defect densities and crystal composition trace the degree of hybridization in the granitic magma during the growth of the K-feldspar phenocrysts.

The formation of the continental crust (CC) is one of the most important processes in the evolution of the silicate Earth. Exactly how the CC formed is the subject of ongoing debate that focuses on its subchondritic Nb/Ta ratio. Nb and Ta are “geochemical identical twins,” so they usually do not fractionate from each other. Here, we show that rutile grains from hydrous rutile-bearing eclogitic layers recovered from drillcores in the Dabie-Sulu ultrahigh pressure terrain have highly variable Nb/Ta values (ranging from 5.4 to 29.1, with an average of 9.8 ± 0.6), indicating major fractionation of Nb and Ta most likely occurred during blueschist to amphibole–eclogite transformation in the absence of rutile. It is suggested that the released fluids with subchondritic Nb/Ta were transported to, and retained by, hydrous rutile-bearing eclogite in colder regions, resulting in suprachondritic Nb/Ta ratios for drier eclogite in hotter regions. Further dehydration of hydrous rutile-bearing eclogites cannot transfer the fractionated Nb/Ta values to the CC due to the low solubility of Nb and Ta in fluids in the presence of rutile, while dehydration-melting results in a major component of the CC, the tonalite–trondhjemite–granodiorite (TTG) component, which is responsible for the low Nb/Ta of the CC. Consequently, residual eclogites have variable but overall suprachondritic Nb/Ta.

Hydrogen isotope investigations on hydrothermal quartz reveal two H-reservoirs: (i) trapped fluid inclusions, and (ii) structurally bound water in homogenously distributed small clusters or bubbles. Varying mixing ratios of the two reservoirs are sampled by means of mechanical and thermal decrepitation applied to different grain size fractions. A two-component mixing calculation results in an isotopic characterisation of the two H-reservoirs, which fractionate hydrogen isotopes close to the known MOH–H 2 O system, with water being enriched in deuterium. Temperature controls both the internal fractionation as well as the abundance ratio of inclusion water to bonded water. At high temperatures, fractionation is small but bound water becomes more abundant, comprising a significant amount of water from both thermal and mechanical extraction techniques. Hence, the isotope composition of the extracted water does not reflect the original hydrogen isotope composition of the hydrothermal fluid especially at temperatures higher than 200°C. Previously reported δ D data of fluid inclusion, which were used to elucidate the origin of the hydrothermal fluid, tend to be too low.

In this paper, we present a new method for mapping a static set of n keys, each an integer between 0 and N−1, into a hash table of size n without any collision. Our data structure requires only an additional array of n integers, each less than n, and achieves a worst-case lookup time of O(1). This method is based on a randomized compression scheme, and it finds a minimal perfect hash function in average time O(n). Our concept can be easily adapted for dynamic key sets. Then, the hash table has no longer minimal size but the storage location remains very small. Because of its simplicity our approach is particularly interesting for practical purposes.

Twenty-three clastic metasediments from the Kongling high-grade terrain of the Yangtze craton, South China were analyzed for major, trace and rare earth elements and Sm-Nd isotopic ratios. Associated dioritic-tonalitic-trondhjemitic (DTT) and granitic gneisses as well as amphibolites were also analyzed in order to constrain provenance. The results show that the clastic metasediments can be classified into 3 distinct groups in terms of mineralogical, geochemical and Sm-Nd isotopic compositions. Group A is characterized by having no to slight negative Eu anomalies (Eu/Eu∗ = 0.82–1.07), being high in Cr (191–396 ppm) and Ni (68–137 ppm), and low in Th (3.3–7.8 ppm) and REE (ΣREE = 99–156 ppm). These characteristics are similar to those of metasediments from Archean greenstone belts. In addition, the Group A metasediments have the value of the Chemical Index of Alteration (CIW) close to felsic gneisses. Their Sm-Nd isotopic, REE and trace element compositions can be interpreted by mixtures of the DTT gneisses and amphibolites. Dating of detrital zircons from 2 Group A samples by SHRIMP reveals a major concordant age group of 2.87–3.0 Ga, which is identical to the age of the trondhjemitic gneiss. These results strongly suggest that Group A was principally the first-cycle erosion product of the local Kongling DTT gneiss and amphibolite. Moreover, the higher than amphibolite Cr content and slight Eu depletion exhibited by some samples from this group infer that ultramafic rocks like komatiite and granite of probably 3.0–3.3 Ga in age also played a role. Group B is characterized by the presence of graphite and shows a more evolved composition similar to post-Archean shales with a prominent negative Eu anomaly (Eu/Eu∗ = 0.48–0.77) and high CIW. On paired Cr/Th vs La/Co and Co/Th plots, Group B samples conform to a two-end member mixing line of the Kongling granitic gneiss and amphibolite. However, data on Nd model age and CIW suggest that the granite component should be younger than the sampled granitic gneiss and derived from a distal source. Both Groups A and B exhibit a clear positive correlation between CIW and TDM and a negative one between CIW and Eu/Eu∗. These correlations point to the crustal evolution of the Yangtze craton towards coupled increasing CIW and Eu depletion with decreasing age. This in turn reflects the change of granitoid magmatism from local Na-rich dioritic-tonalitic-trondhjemitic rocks to widespread K-feldspar granite. The change led to the intracrustal differentiation, stabilization and growth of the craton. Group C is restite and contains abundant sillimanite and garnet and unusually high ilmenite (7–11vol%), which can be seen to be dehydration melting products of biotite under the microscope. This group shows extremely varied REE distributions from LREE enriched to depleted and from negative to strong positive (Eu/Eu∗ = 1.63) Eu anomalies. Compared to Groups A and B, Group C is severely depleted in Na2O, K2O, LREE, Rb and Ba, whereas TiO2, Co, V, Sc and HREE and Y are considerably enriched. This is accompanied by anomalous high Sm/Nd (0.21–0.28), 147Sm/144Nd (0.1361–0.1738) and 143Nd/144Nd (0.511589–0.511958) ratios. TDM correlates clearly with Sm/Nd ratio and 2 out of 3 samples give significantly older to unrealistic TDM (3.9–4.9 Ga). The results document redistribution of REE and an open behavior of the Sm-Nd isotope system during the biotite dehydration melting of metasediments.

Microthermometry and stable isotope data enable us to distinguish between two contrasting sets of fluids involved in the Hercynian and Alpine metamorphic events in the Western Carpathians. High-temperature smoky quartz (450–500°C) was probably formed during the syn-kinematic phase of the Hercynian metamorphism, when chemical and isotopic equilibrium had been established between aqueous solutions and the surrounding rocks. This is indicated by fixed Na/Ca ratios and narrow ranges of δ D and δ18O values in the inclusion fluids (−59 ± 5‰ and + 7 to + 7.5‰ SMOW, respectively). In contrast, Alpine quartz precipitating at temperatures between 300° and 400°C in extension-related structures displayed a non-equilibrium signature characterized by a much larger compositional and isotopic variability. Presence of CO2 in quartz from granitoid-hosted shear zones indicates externally derived fluids with δ13C values between −11.9 to −7.7‰ PDB. These values can be interpreted to reflect an admixture of a lighter CO2 generated by decomposition of organic matter in underlying low- to medium-grade sediments. The essentially identical isotopic composition of the inclusion CO2 from the presumably Hercynian as well as Alpine metamorphic quartzes supports the concept of Hercynian overthrusting of granitoids onto metamorphites in the crystalline basement of the Western Carpathians.

Overlay accuracy is one of the most important lithographic topics for ULSI device production [1]. Significant contributions to the overlay like alignment accuracy and mask distortion are well known and subject of continuous investigations [2]. Below an accuracy range of 100 nm additional influences must be taken into account [3,4], which were usually neglected for relaxed design rules. One of these influences is directly related to wafer distortions induced by flatness inaccuracies of wafer chucks used for instance in X-ray or optical stepper. This impact was characterised by investigating the elastic behaviour of 4” wafers, fixed on a wafer chuck. The resulting strains and elongations in the wafer surface were measured by exposure experiments and compared with additional FEM calculations. From these results we estimate that for design rules below quarter micron the flatness accuracy between different wafer chucks has to be smaller than 0.25 μm.

Applied to a chordal graph, lexicographic breadth first search computes a perfect elimination scheme. We present a short elegant proof for this fact using only a new property of separators in chordal graphs.

In [6] Geralcikova, Koubek describe an algorithm for finding the transitive closure of an acyclic digraph G with worst case runtime O(n·ered), where n is the number of nodes and ered is the number of edges in the transitive reduction of G. We present an improvement on their algorithm which runs in worst case time O(k·ered) and space O(n·k), where k is the width of a chain decomposition. For the expected values in the Gn,p model of a random acyclic digraph with 0 < p < 1 we have: $$\begin{gathered}E(k) = O(\frac{{\ln (p \cdot n)}}{p}) \hfill \\E(e_{red} ) = O(\min (n \cdot |lnp|,p \cdot n^2 )) = O(n \cdot \ln n) \hfill \\E(k \cdot e_{red} ) = \left\{ {\begin{array}{*{20}c}{O(n^2 )for\frac{{ln^2 n}}{n} \leqslant p < 1} \\{O(n^2 \cdot \ln \ln n)otherwise} \\\end{array} } \right. \hfill \\\end{gathered}$$

Hercynian granites from the Sudschwarzwald (plutons of Klemmbach, St. Blasien, Schluchsee, Barhalde) show a wide range of whole-rock δ 18 O-values from +2.5‰ to + 10.9‰ (SMOW). Detailed 18 O analysis of separated minerals indicates strong isotopic disequilibrium, a feature which can be explained by large-scale post-magmatic hydrothermal interaction of the granites with isotopically light meteoric water at temperatures below 500°C. Microthermometric investigation of homogenization and melting temperatures from two-phase (vapour, liquid) secondary fluid inclusions in quartz indicates a temperature range between 200° and 400°C for the alteration. The aqueous fluid inclusions typically have low salinities, but reach values up to 9 eq. wt.% NaCl in samples with evidence for secondary mineral development (i.e. chloritization, sericitization, etc.). Trace-element variations in K-feldspar (Rb, Sr, Ba, Tl, Pb, Bi) provide a guide to elemental mobilization with increasing water/rock ratios. A gain of Rb, Tl and Bi and a loss of Sr, Ba and Pb is observed during alteration. Combining all data, a three-stage reaction scheme for the hydrothermal alteration of the granites is proposed: (1) T∼400°C: granite (prim.) +fluid 1→granite (alter.) +fluid 2 (2) T∼200–300°C: fluid 2 +granite (alter.) → secondary mineralization+fluid 3 (3) T⩽200°C: fluid 3→gangue mineralization.

Summary With the majority of extruders currently in use, dualmode temperature control is employed. Electrical power is supplied to the resistance or induction heaters by means of electromagnetic contactors chiefly for the reason of simplicity and low cost. However, switching the power circuits by mechanical contacts can cause high frequency interference problems during both closing and opening of the contacts. Contact bounce, random contact opening, and sharp interruption of inductive circuits can lead to high induced voltage transients, contact arcing, dielectric breakdown and associated phenomena presenting severe disadvantages. The advent of advanced process control systems as well as process computers makes more versatile equipment, which allows continuous variation of the average power to the heaters, a necessity. The solution could be solid-state AC power actuators based upon variable-pulse-length switching control of thyristors (silicon controlled rectifiers and triacs) in conjunction with sophisticated integrated circuits. The paper describes a device which passes a variable number of full cycles of the AC supply in an specified period. This period may be made quite short, about two seconds or less, so that if a heater having a fairly large thermal capacity is used, power will appear to be varied continuously. Zero-crossing techniques are employed forcing the solid-state switch to close at the instant when the voltage across it is zero, and to open at the instant when the current through it is zero. The variation of average power to the heaters is linearly dependent on the actuator input signal which is 4 to 20 mA DC supplied by the output of continuousaction process controllers. A simplified version of the device, intended for use in conjunction with process computers or other digital equipment, operates in the on-off mode controlled by logic input signals. In both cases the input of the actuator is isolated from AC power.