Worst-case Calculations Research Articles

Cost-Aware DU Placement and Flow Routing in 5G Packet xHaul Networks

Packet-switched xHaul networks based on Ethernet technology are considered a promising solution for assuring convergent, cost-effective transport of diverse radio data traffic flows in dense 5G radio access networks (RANs). A challenging optimization problem in such networks is the placement of distributed processing units (DUs), which realize a subset of virtualized baseband processing functions on general-purpose processors at selected processing pool (PP) facilities. The DU placement involves the problem of routing of related fronthaul and midhaul data flows between network nodes. In this work, we focus on developing optimization methods for joint placement of DUs and routing of flows with the goal to minimize the overall cost of PPs activation and processing in the network, which we refer to as the PPC-DUP-FR problem. We account for limited processing and transmission resources as well as for stringent latency requirements of data flows in 5G RAN. The latency constraint makes the problem particularly difficult in a packet-switched xHaul network since it involves the non-linear and dynamic estimation of the latencies caused by buffering of packets in the switches. The latency model that we apply in this work is based on worst-case calculations with improved latency estimations that skip from processing the co-routed, but non-affecting flows. We use a mixed-integer programming (MIP) approach to formulate and solve the PPC-DUP-FR optimization problem. Moreover, we develop a heuristic method that provides optimized solutions to larger PPC-DUP-FR problem instances, which are too complex for the MIP method. Numerical experiments performed in different network scenarios indicate on the effectiveness of the heuristic in solving the PPC-DUP-FR problem. In particular, the heuristic achieves up to 63% better results than MIP (at the MIP optimality gap equal to 76%) in a medium-size mesh network, in which the MIP problem is unsolvable for higher traffic demands within reasonable runtime limits. In larger networks, MIP is able to provide some results only for the PPC-DUP-FR problem instances with very low traffic demands, whereas the solutions generated by the heuristic are at least 83% better than the ones achieved with MIP. Also, the analysis performed shows a significant impact of the PP cost factors considered and of the level of cost differentiation of PP nodes on the overall PP cost in the network. Finally, simulation results of a case-study packet xHaul network confirm the correctness of the latency model used.

A Conjoint Analysis of Propellant Budget and Maneuver Life for a Communication Satellite

Maneuvers require velocity augmentation to control a satellite at the defined orbit. The velocity augmentation provides achieving geostationary orbit, compensating orbital perturbation, orbit dispersion correction, and any other maneuver's operations for a communication satellite. All maneuvers and propellant consumption must be taken into account in the propellant budget for successful mission management. In this study, a straightforward method was proposed to calculate satellite maneuver life or associated propellant budget for general purposes. The method provides enough accuracy for general mission planning. However, communication satellite accurate end of life estimation, especially in the last three months is vitally important and depends on many factors. According to the performance requirement of procurement's standard, the propellant budget and associated satellite maneuver's life are calculated based on the worst-case or adverse three-sigma. The worst-case calculations include allocations for inefficiencies, velocity uncertainties, dispersions resulting from thruster firings, propellant residuals, the selected thrusting, and maneuver strategies' performance. High accuracy remaining propellant estimation is necessary for a successful end of life operation and decommissioning. The cost of early deorbit because of propellant misestimation is millions of dollars. Accurate remaining propellant and associated maneuver life analysis can be performed in different methods.The most common three methods are pressure, volume, temperature (PVT), bookkeeping (BK), and thermal propellant gauging (TPG). The propellant accuracy analysis shows that the propagation of uncertainties is related to system design, tank fill ratio, propellant load accuracy, orbital maneuver's inefficiency, pressure and temperature sensors, transducers, telemetry resolution, and error in equipment test data. Comparing the methods, PVT provides accuracy between ±27.81 kg to ±38.93 kg, depending on equipment size and accuracy. BK currently provides the best estimation and the highest gauging accuracy between ±9.83 kg to ±13.76 kg. TPG provides accuracy between ±10.52 to ±14.73 kg for some cases. However, the satellite operators request ±1 kg estimation of the remaining propellant to extend the lifetime and reduce costs. The satellite manufacturers should optimize propulsiıon and attitude control subsystem design and manufacturing, including propellant management device performance, applied sensors reliability and accuracy, and tank expansion performance over a mission life.

Influence of Gadolinium-Based Contrast Agents on Tissue Sodium Quantification in Sodium Magnetic Resonance Imaging.

Sodium magnetic resonance (MR) imaging provides noninvasive insights to cellular processes by measuring tissue sodium concentration (TSC). Many clinical studies combine sodium MR imaging with clinical standard MR procedures, in which contrast media is frequently administered. This work investigates the influence of gadolinium-based contrast agents on quantification of TSC. Thus, either scan pauses between early and late contrast-enhanced acquisitions can be used efficiently or sodium imaging can be performed as the final scan after dynamic contrast-enhanced acquisition. For this study, 2 gadolinium-based contrast agents, Dotarem and Gadovist, were diluted with saline solution covering contrast agent concentrations in a clinical range. In addition, agarose-based sample series were created to simulate tissue relaxation time behavior. In vivo, the influence of Dotarem on sodium acquisition and TSC quantification was investigated in 1 ischemic stroke patient. Proton relaxation times decreased for increasing contrast agent concentrations as hyperbolic functions. Sodium relaxation times displayed a negative slope in regression analysis in most cases. The largest influence (-1.52 milliseconds per mmol/L contrast agent) was measured for sodium T1. Worst case calculations in ultrashort echo time sequence signal analysis showed a signal drop of (1.21% ± 0.56%) on tissue sodium quantification. In vivo sodium brain acquisitions of a stroke patient before and after Dotarem injection resulted in statistically nonsignificant differences in TSC quantification of relevant tissues and stroke areas (P > 0.05). Our study showed a quantitative influence of Dotarem and Gadovist on sodium relaxation times. However, quantification of TSC was not impaired, which was proven by worst case calculations and nonsignificant differences in vivo in an ischemic stroke patient. We suggest performing sodium imaging in useful clinical positions in protocols regardless of included Dotarem or Gadovist administrations. Being flexible in the study protocol design will strengthen ongoing sodium imaging investigations for various pathologies.

Factors influencing separation distances against odour annoyance calculated by Gaussian and Lagrangian dispersion models

Direction-dependent separation distances to avoid odour annoyance, calculated with the Gaussian Austrian Odour Dispersion Model AODM and the Lagrangian particle diffusion model LASAT at two sites, are analysed and compared. The relevant short-term peak odour concentrations are calculated with a stability-dependent peak-to-mean algorithm. The same emission and meteorological data, but model-specific atmospheric stability classes are used. The estimate of atmospheric stability is obtained from three-axis ultrasonic anemometers using the standard deviations of the three wind components and the Obukhov stability parameter. The results are demonstrated for the Austrian villages Reidling and Weissbach with very different topographical surroundings and meteorological conditions. Both the differences in the wind and stability regimes as well as the decrease of the peak-to-mean factors with distance lead to deviations in the separation distances between the two sites. The Lagrangian model, due to its model physics, generally calculates larger separation distances. For worst-case calculations necessary with environmental impact assessment studies, the use of a Lagrangian model is therefore to be preferred over that of a Gaussian model. The study and findings relate to the Austrian odour impact criteria.

Characterizing transient thermal interactions between lunar regolith and surface spacecraft

We present a new method, its development, implementation, and verification, for calculating the transient thermal interaction between lunar regolith and moving spacecraft travelling across the surface of the Moon. Regolith temperatures can be determined for lunar landscapes as defined by laser altimeter remote sensing data refined with local crater and boulder models. The purpose of this approach is to enable more detailed, dynamic thermal analyses of mobile systems on the lunar surface rather than relying on worst case, boundary condition design approaches typically used for spacecraft thermal engineering.This new simulation method is based on integrating models that represent small and large scale landscapes; reproduce regolith and boulder temperatures on the Moon; define the position of the Sun; and perform ray tracing to determine infrared and solar heat fluxes between passing objects and the surface. The thermal model of the lunar regolith enhances established models with a slope- and depth-dependent density. The simulation results were verified against remote sensing data obtained from the Diviner Lunar Radiometer Experiment of the Lunar Reconnaissance Orbiter (LRO) and from other sources cited in the literature.The verification results for isolated regolith surface patches showed a deviation from established models of about ±3–6K (±1–6%) during lunar day, and lunar night. For real landscapes such as Crater Calippus and Crater Marius A, the deviation is less than ±15K (±10%) compared to remote sensing data for the majority of measured data points. Only in regions with presumed different regolith material properties, such as steep slopes or depressions, or in regions with a low resolution on the topographic map, were the deviations up to 100K (60%). From the results, empirical equations were derived, which can be used for worst case calculations or to calculate initial temperatures for more elaborate time marching numerical models.The proposed new method could be further enhanced to address scientific questions by incorporating more detailed regolith and boulder models, or be used as-is to evaluate the dynamic thermal envelope of moving spacecraft.

Management of Environmental Risks in the Life Cycle of Human Pharmaceuticals in Lithuania

The paper analyzes and outlines the peculiarities and importance of different stages of the life cycle of human pharmaceuticals in Lithuania with regard to their environmental impact, and points out to the need of risk reduction measures. Use stage and disposal of unused, unwanted or expired medicines are those stages when the biggest emissions occur and risk management is not adequate yet. Pharmaceuticals consumption distribution profile is presented in the article. Environmental risk assessment was carried out indicating that for Lithuania pharmaceutical substances consumed in amounts over 25 kg/year might be causing a risk to the environment. Three substances have PEC/PNEC ratios above 1 under the worst case calculations. In reality in spite of high environmental load, one of them - amoxicillin - is not likely to pose a risk due to its low environmantal stability and high removal rates in WWTPs. The other two substances show a potential of environmental risk even after calculation of the refined PEC/PNEC ratio. The importance of proper wastewater treatment needs to be underlined due to inevitable excretion of pharmaceutical substances from the use phase. The most popular way to dispose of unused, unwanted or expired medicines in Lithuania is via the household waste. The system for collection of residual medicines is not properly functioning yet. Good management of environmental risk requires establishment of an effective system to collect and destroy pharmaceuticals in an environmentally sound manner.

Induction of DNA strand breaks by dental composite components compared to X-ray exposure in human gingival fibroblasts

The toxicity of dental composites has been attributed to the release of residual monomers from polymerized resin-based composites due to degradation processes or incomplete polymerization. Some of these eluted substances have a genotoxic potential. We tested the hypothesis that realistic concentrations (and/or worst case concentrations/situations) of bisphenol-A-glycidyldimethacrylate (BisGMA), triethyleneglycol dimethacrylate (TEGDMA), 2-hydroxyethyl methacrylate (HEMA) and methyl methacrylate (MMA) found in elution experiments can cause DNA strand breaks in human gingival fibroblasts (HGF). Such DNA damage was compared with that resulting from ionizing radiation coming from natural sources, dental radiography or tumor therapy. TEGDMA, HEMA and MMA did not induce DNA strand breaks at concentrations of up to 10mM. About 24h after incubation with 0.25mM BisGMA, significantly more DNA strand breaks were found in HGF compared to controls. DNA strand breaks caused by 0.25mM BisGMA, correspond to DNA strand breakage caused by irradiation with 4Gy, only used in the high single-dose irradiation tumor therapy. But 0.25mM BisGMA is more than 100-fold higher than that concentration found in worst case calculations. Therefore, our data did not support our hypothesis.

Investigation into the migration potential of coating materials from cookware products

Twenty-six non-stick-coated cookware samples were purchased, covering a variety of products, coating/metal types and food contact applications. The polymer coatings were identified to be polyethersulphone, polytetrafluoroethylene (PTFE), bisphenol A/epichlorohydrin and one coating for which no good match was obtained with infra-red library spectra. All of the products intended for stove-top use had a polymer coating containing PTFE. The coatings were analysed as purchased and after heating at 250°C for 30 min to simulate actual conditions of use. Total solvent extractables were measured and the overall migration was determined into simulants. None of the products exceeded an overall migration limit of 10 mg dm−2. Coating materials were analysed by headspace gas chromatography–mass spectrometry (GC–MS), by liquid extraction followed by GC–MS and by liquid extraction followed by liquid chromatography–mass spectroscopy with a particle-beam interface. Benzene was detected in two samples, at 1.4 and 2.4 µg dm−2. These levels in the coatings are too low to give any detectable migration into foods. There was no detectable release of perfluorochemicals. Several other substances were identified and the worst-case migration was calculated. The origin of many of the substances detected was considered to be by pick-up from the printed packaging materials in which the cookware was sold. Potential consumer exposure was calculated. None of the substances identified had the potential to exceed their tolerable daily intake (TDI) value. To confirm these worst-case calculations, the migration of certain phthalates and of bisphenol A was measured into food simulants. Migration levels were very low.

Estimated intake of the artificial sweeteners acesulfame-K, aspartame, cyclamate and saccharin in a group of Swedish diabetics.

Few sweetener intake studies have been performed on the general population and only one study has been specifically designed to investigate diabetics and children. This report describes a Swedish study on the estimated intake of the artificial sweeteners acesulfame-K, aspartame, cyclamate and saccharin by children (0-15 years) and adult male and female diabetics (types I and II) of various ages (16-90 years). Altogether, 1120 participants were asked to complete a questionnaire about their sweetener intake. The response rate (71%, range 59-78%) was comparable across age and gender groups. The most consumed 'light' foodstuffs were diet soda, cider, fruit syrup, table powder, table tablets, table drops, ice cream, chewing gum, throat lozenges, sweets, yoghurt and vitamin C. The major sources of sweetener intake were beverages and table powder. About 70% of the participants, equally distributed across all age groups, read the manufacturer's specifications of the food products' content. The estimated intakes showed that neither men nor women exceeded the ADI for acesulfame-K; however, using worst-case calculations, high intakes were found in young children (169% of ADI). In general, the aspartame intake was low. Children had the highest estimated (worst case) intake of cyclamate (317% of ADI). Children's estimated intake of saccharin only slightly exceeded the ADI at the 5% level for fruit syrup. Children had an unexpected high intake of tabletop sweeteners, which, in Sweden, is normally based on cyclamate. The study was performed during two winter months when it can be assumed that the intake of sweeteners was lower as compared with during warm, summer months. Thus, the present study probably underestimates the average intake on a yearly basis. However, our worst-case calculations based on maximum permitted levels were performed on each individual sweetener, although exposure is probably relatively evenly distributed among all sweeteners, except for cyclamate containing table sweeteners.

Estimated intake of the artificial sweeteners acesulfame-K, aspartame, cyclamate and saccharin in a group of Swedish diabetics

Few sweetener intake studies have been performed on the general population and only one study has been specifically designed to investigate diabetics and children. This report describes a Swedish study on the estimated intake of the artificial sweeteners acesulfame-K, aspartame, cyclamate and saccharin by children (0-15 years) and adult male and female diabetics (types I and II) of various ages (16-90 years). Altogether, 1120 participants were asked to complete a questionnaire about their sweetener intake. The response rate (71%, range 59-78%) was comparable across age and gender groups. The most consumed 'light' foodstuffs were diet soda, cider, fruit syrup, table powder, table tablets, table drops, ice cream, chewing gum, throat lozenges, sweets, yoghurt and vitamin C. The major sources of sweetener intake were beverages and table powder. About 70% of the participants, equally distributed across all age groups, read the manufacturer's specifications of the food products' content. The estimated intakes showed that neither men nor women exceeded the ADI for acesulfame-K; however, using worst-case calculations, high intakes were found in young children (169% of ADI). In general, the aspartame intake was low. Children had the highest estimated (worst case) intake of cyclamate (317% of ADI). Children's estimated intake of saccharin only slightly exceeded the ADI at the 5% level for fruit syrup. Children had an unexpected high intake of tabletop sweeteners, which, in Sweden, is normally based on cyclamate. The study was performed during two winter months when it can be assumed that the intake of sweeteners was lower as compared with during warm, summer months. Thus, the present study probably underestimates the average intake on a yearly basis. However, our worst-case calculations based on maximum permitted levels were performed on each individual sweetener, although exposure is probably relatively evenly distributed among all sweeteners, except for cyclamate containing table sweeteners.

Particulate Organic Matter in Permeable Marine Sands—Dynamics in Time and Depth

In a North Sea intertidal sandflat sediment, depth profiles of dissolved and particulate compounds were measured and evaluated with respect to transport and degradation of particulate organic matter (POM). Bimonthly from July 1997 to July 1998, the amount was measured of fine-grained (<70μm) material in the permeable sand matrix, its N, Corgand chlorophyll content as well as porewater DIC, NO−x and NH+4 concentrations. Depth profiles of fine particle concentrations indicated hydrodynamic influence down to 4–8cm below the sediment surface. Worst-case calculations on the macrofaunal contribution to particle transport resulted in a biodiffusion coefficient of DB≤1·85×10−6cm2s−1, corresponding to less than 50% of total transport. Chl and POC contents and DIN concentrations exhibited summer/autumn and winter/spring characteristics in their profiles, revealing the seasonal importance of early diagenesis and advective transport, respectively. Areal inventories of POC, PN and Chl indicated the dominance of degradation and hydrodynamic removal of organic material during autumn/winter and fresh POM input throughout spring and summer. In the upper 5cm, seasonal variation in the particle, POC, PN and Chl concentrations of the sediment was 1·4–5·3 times as large as below. Calculations based on POC loss or short-term DIC accumulation yielded estimates of annual carbon turnover rates ranging between 55 and 123gCm−2yr−1. Possible implications of POM dynamics on the role of permeable sands in the marine carbon cycle are discussed.

Aquatic fate assessment of the polycyclic musk fragrance HHCB: Scenario and variability analysis in accordance with the EU risk assessment guidelines

By means of the environmental fate and distribution models laid down in the Technical Guidance Documents (TGD) and implemented in the European Union System for the Evaluation of Substances (EUSES) environmental concentrations of the polycyclic musk fragrance HHCB (1,3,4,6,7,8-hexahydro-4,6,6,7,8,8-hexamethyl-cyclopenta-[g]-2-benzopyrane; trade name: e.g. Galaxolide ®) were calculated for the aquatic environment under consideration of various scenarios. The results were then compared to monitoring data from the region of North Rhine-Westphalia (River Ruhr). An uncertainty analysis was carried out to determine sensitive parameters, to integrate environmental variability and to confirm the model's calculations. The standard scenario of EUSES overestimates the measured concentrations, which confirms the conservative nature of the calculations. The regional-specific scenarios lead to lower deviations from the measured values than the standard scenario. Deviations range from one to two orders of magnitude in the effluent of sewage treatment plants; they amount to one order of magnitude for surface water concentrations on a local scale and conform to monitoring data on a regional scale. The use of measured bioconcentration factors for fish instead of estimated ones reduces deviations remarkably. The investigation reveals that unrealistic worst-case calculations of HHCB can at best be ameliorated by the application of more realistic emission rates and measured bioconcentration factors. The use of regional-specific parameters also diminishes the deviations of the calculations from the measured concentrations.

Electrical current along balloon rigging line inside thunderstorms

We have designed a new instrument to measure the current flowing along balloon rigging line during flights through thunderstorms. This instrument was tested in a high voltage facility and used to collect line current data during one balloon flight into a thunderstorm. Using these data, worst-case calculations are made; as such, we claim that they are the upper limits of any alteration (to the measured electric field or particle charge) that may occur, and the real number is likely much less. It is postulated the rigging-line current could have two separate effects on the measured electric field: (1) reduction of the field due to emission of corona ions, and (2) enhancement of the field due to the insertion of a long thin `conductor.' Even with current as high as 1 μA (the largest measured was around 50–100 nA), these two effects were found to be about −1% and +1%, respectively. Also, the calculated worst-case alteration to charged precipitation measurements is about 0.1 pC. Thus, with proper efforts to make the rigging line as poor a conductor as possible, it seems that we are justified in stating that these effects are negligible.

Does intense fishing on males impair mating success of female Dungeness crabs

Commercial capture of female Dungeness crabs, Cancer magister, is prohibited and minimum size limits for commercial harvest of male crabs are designed to allow most males to mate at least once before capture. Annual exploitation rates often exceed 90%, however, and the resulting scarcity of large males might reduce mating success among large females. We present new data regarding (i) sizes of male and female crabs collected in premating embraces, (ii) carapace width frequencies of female Dungeness crabs, (iii) presence of sperm plugs and sperm, and (iv) fecundity. Minimum carapace width of hard-shelled mating males typically exceeds postmolt carapace width of soft-shelled females (i), but female Dungeness crabs exceeding the minimum legal size of males usually account for less than 5% of mature adult female crabs (ii), and sublegal-sized males actively participate in mating (i). Remnants of sperm plugs, definitive indicators of mating, were found in 97.5% of recently molted large females (iii), suggesting that virtually all molting females mate regardless of size. On the basis of (ii) and (iv), hypothetical worst-case calculations, assuming that no large females could find mates, suggest that total egg production would be reduced by no more than 2-25% among molting female crabs.

Evaluation of the Toxicological Risk Associated with the Use of Polyacrylamides in the Recovery of Nutrients from Food Processing Waste (I)

Trivalent metal ions such as iron and aluminum are currently employed to flocculate liquid-borne solids from food-processing waste streams. These captured nutrient-rich waste solids are disposed of mainly through land applications (e.g., subsoil injection) because of the potential toxicity associated with the metal salts. Low-toxicity, water-soluble polyacrylamide polymers are currently approved for and employed as flocculants in potable water applications. The use of these polymers in food-processing waste streams could enable the captured solids to be recycled as components of animal feed, thus decreasing the burden on landfills and making good use of the proteinaceous matrix. However, polyacrylamides contain very low concentrations of acryl-amide monomer, which is highly toxic and can cause neurotoxicity, cytogenic lesions, and an increase in tumor rates in experimental animals. With use of two industrial food processing wastes, experiments were conducted to determine how acrylamide monomer would partition during a solids/liquid separation and subsequent rendering. Based on the analytical data, 96% of the acrylamide monomer was measured in the water portion after separation. Because of background interferences, acrylamide could not be directly measured in the solids portion. With use of these results and worst-case calculations, &lt;2 ppb of acrylamide could be present in animal feed, thereby making the associated risk de minimis.

A simple call acceptance procedure in an ATM network

A simple link by link call set-up procedure is described using only straighforward bandwidth parameters. Analytical worst-case calculations for the overall load for a given cell loss probability are carried out for mixtures of different traffic classes, each characterized by the peak of their traffic streams and the total mean per class (corresponding to a selected set of typical teleservices). This is done for traffic having one and two priorities.

Radiation dose to various age groups from radionuclide impurities in 99mTc-pertechnetate (fission product 99Mo generator) radiopharmaceutical preparations.

Radionuclide impurities of radiopharmaceuticals do not provide any diagnostic information, but contribute to the radiation dose to the patient. For 99mTc, even small amounts of long lived radionuclide impurities may contribute significantly to the dose from 99mTc itself. In this preliminary study, estimates have been made for the radiation dose to specific organs and for the effective dose equivalent from impurities in 99mTc-sodium pertechnetate prepared from fission product 99Mo. In addition to 99Mo, 131I, 103Ru, 89Sr and 90Sr at maximum permissible levels as stipulated in the European Pharmacopoeia, 110mAg and 239Pu were taken as representative nuclides for beta-gamma emitters and alpha emitters. Using all of these radionuclides at such maximum permissible levels of impurity as stated in the European Pharmacopoeia, the total contribution from the impurities to the effective dose equivalent is approximately 30% of the effective dose equivalent from 99mTc-pertechnetate. In terms of specific organs, the liver and kidneys can receive doses of 3-4 times and 1-3 times the dose from 99mTc-pertechnetate itself. Although these are worst case calculations, a consistent approach should be reconsidered to limit the additional effective dose equivalent from impurities to e.g. 10% of the effective dose equivalent from 99mTc itself.

237Np aND 239Pu Solution Behavior During Hydrothermal Testing of Simulated Nuclear Waste Glass with Basalt and Steel

AbstractA series of hydrothermal experiments were carried out on 237Np- and 239Pu-doped PNL 76–68 glass, synthetic basalt groundwater, basalt, and cast steel. These hydrothermal experiments are part of the Basalt Waste Isolation Project investigation of the interactions of waste package components in a basalt repository. Experiments of three months duration were conducted in Dickson-type rocking autoclaves at 200°C and 30 MPa, with an initial fluid to solid weight ratio of 10:1. All solid materials were ground and sieved to a narrow size fraction. The experiments carried out were: glass and groundwater; glass, basalt, and groundwater; glass, steel, and groundwater; and glass, steel, basalt, and groundwater. Unfiltered, 4000 Â filtered, and 18 Å filtered solutions were analyzed to determine the concentrations of radionuclides in solution and those associated with colloids.The quantities of 237Np and 239Pu in solution were very small. Worstcase calculations indicate that 0.01% or less of the total radionuclide inventories were present in solution. The highest solution concentrations of the actinide dopants were observed in the experiments with basalt, even though smaller amounts of glass were dissolved than in the experiments without basalt. The observed differences in the solution concentrations of 237Np and 239Pu were probably controlled by differences in the reaction products, which were clinoptilolite in the experiments with basalt, and an Fe-Zn smectite clay in the experiments without basalt.

Worst-Case Considerations in Designing Logical Circuits

A method of design is presented for logical circuits, starting from worst-case considerations. The method represents an approach to dc optimization. Special attention is paid to temperature and tolerance problems in monolithic integrated circuits. In the worst-case design procedure outlined, the requirements for obtaining a properly functioning circuit are taken as the point of departure. This results in a whole field of possible circuits from which-depending on further specifications-it is comparatively easy to find special solutions. Three examples of worst-case calculations are developed-one for a transistor-transistor logic circuit, one for a diode-transistor logic circuit, and finally, one for a new type of circuit, termed emitter-follower transistor logic.