Search

Let p(n, ni) be the number of partitions of n with at most m summands1, \( \omega \left( n \right) = \frac{1}{2}\left( {3{n^2} - n} \right),n \in \mathbb{Z}\) be the pentagonal numbers2 and \( {\sigma _j}\left( n \right) = \sum\nolimits_{d\left| n \right.} {{d^j}},j \in \mathbb{N},\) be the divisor functions. Then σ(n) – the number of the divisors of n – satisfies $$ {\sigma _0}\left( n \right) = g\left( {n,0} \right) + g\left( {n,1} \right) +, \ldots, + g\left( {n,n - 1} \right) $$ (1) Where $$ g\left( {n,m} \right) = p\left( {n,m} \right) - \sum\limits_{i = 1}^\infty {{{\left( { - 1} \right)}^{i - 1}}} \left( {p\left( {n - \omega \left( i \right),m} \right) + p\left( {n - \omega \left( { - i} \right),m} \right)} \right). $$ Pentagonal numbers are given by a well-known identity due to Euler $$ {\left( q \right)_\infty }\mathop = \limits^{def} \prod\limits_{n = 1}^\infty {\left( {1 - {q^n}} \right)} = \sum\limits_{n = - \infty }^\infty {{{\left( { - 1} \right)}^n}} {q^{n\left( {3n - 1} \right)/2}}.$$ (2) They are correlated with the number of partition p(n) of \( n \in \mathbb{N},\) generated by $$\sum\limits_{{n = 0}}^{\infty } {p\left( n \right)} {{q}^{n}} = \frac{1}{{{{{\left( q \right)}}_{\infty }}}}, $$ (3) through the identity $$ 1 = \frac{{{{\left( q \right)}_\infty }}}{{{{\left( q \right)}_\infty }}} = \left( {1 - {q^1} - {q^2} + {q^5} + {q^7} - \cdot \cdot \cdot } \right) \cdot \left( {p\left( 0 \right){q^0} + p\left( 1 \right){q^1} + \cdot \cdot \cdot } \right) $$ or equivalently $$ 0 = p\left( n \right) - \sum\limits_{j = 1}^\infty {{{\left( { - 1} \right)}^{j - 1}}} \left( {p\left( {n - \omega \left( j \right)} \right) + p\left( {n - \omega \left( { - j} \right)} \right)} \right).$$ (4) On the other hand, the pentagonal numbers are connected with the divisor function σ 1 (n), for instance, by3 $$ {\sigma _1}\left( n \right) = {\sum\limits_{i = 1}^\infty {\left( { - 1} \right)} ^{i - 1}}\left( {\omega \left( i \right)p\left( {n - \omega \left( i \right)} \right) + \omega \left( { - i} \right)p\left( {n - \omega \left( { - i} \right)} \right)} \right). $$ Our statement (1) is a similar identity for ao(n). By way of illustration, for n = 5 we obtain \( \mathop {\lim }\limits_{x \to \infty } \left( {n - {a_n}} \right) = \sum\limits_{i = 1}^\infty {{\sigma _0}} \left( i \right){q^i}\) where the sequence an is defined by a0 = 0 and $$ {a_n} = 1 + \left( {1 - {q^{n - 1}}} \right){a_{n - 1}}.$$ (6) Iterating the recurrence leads to $$ {a_n} = \prod\limits_{i = 1}^{n - 1} {\left( {1 - {q^i}} \right)} \sum\limits_{j = 0}^{n - 1} {\frac{1}{{\left( {1 - q} \right) \ldots \left( {1 - {q^j}} \right).}}}$$ (7) Now, theroduct \( {\left( {\left( {1 - q} \right) \ldots \left( {1 - {q^m}} \right)} \right)^{ - 1}}\mathop = \limits^{def} \left( q \right)_m^{ - 1}\) is well-known as generating function of the numbers p(n, m), hence $$ \sum\limits_{n = 0}^\infty {p\left( {n,m} \right){q^n}} = \frac{1}{{\left( {1 - q} \right)\left( {1 - {q^2}} \right) \ldots \left( {1 - {q^m}} \right)}},m \geqslant 0. $$ (8) With (8) the equation (7) can be written as $${{a}_{n}} = \sum\limits_{{m = 0}}^{{n - 1}} {\underbrace{{{{{\left( q \right)}}_{{n - 1}}}\sum\limits_{{h = 0}}^{\infty } {p\left( {h,m} \right){{q}^{h}}.} }}_{{\mathop{ = }\limits^{{def}} {{H}_{{n,m}}}\left( q \right)}}} $$ (9) For \( \sum\limits_{n = 0}^\infty {g\left( {n,m} \right){q^n}} = \mathop {\lim }\limits_{x \to \infty } {H_{n,m}}\left( q \right)\mathop = \limits^{\left( 2 \right)} \sum\limits_{i = - \infty }^\infty {{{\left( { - 1} \right)}^i}{q^{i\left( {3i - 1} \right)/2}}} \sum\limits_{j = 0}^\infty {p\left( {j,m} \right){q^j}}\) with g(0, m) = 1 and $$ \begin{gathered} g\left( {n,m} \right) = p\left( {n,m} \right) - p\left( {n - 1,m} \right) - p\left( {n - 2,m} \right) + p\left( {n - 5,m} \right) + \cdots ,m \geqslant 1. \hfill \\ \hfill \\ \end{gathered} $$ Note that p(n, m) = p(n), for m ≥ n. This implies \( g\left( {n,m} \right)\mathop = \limits^{\left( 4 \right)} 0,form \geqslant n \geqslant 1.\) Therefore $$ \mathop {\lim }\limits_{n \to \infty } (n - a_n ) = \sum\limits_{j = 1}^\infty {\left( {g\left( {j,0} \right) + \cdots + g\left( {j,j - 1} \right)} \right)q^j } $$ which, together with (5), completes the proof of (1).

The exponential increase in areal density of magnetic hard disk drives during the last years has led to incredibly tighter manufacturing tolerances. For the lithography process that is being used to make the principal component in a hard disk drive, the read-write head, this means that improved process control is required with respect to imaging and positioning performance. Beside the overlay performance from layer to layer, the relative placement of images in a single critical layer is being looked at as an important performance requirement on state-of-the-art DUV and I-line steppers. The terms stitching and collinearity [1] characterize the relative placement of images in a single layer. In this paper verification tests for stitching and collinear imaging are presented, as they are developed by ASML. Since these tests require an understanding of the terms stitching and collinearity, the definitions of these terms are outlined. The results for the two tests on an ASML PAS 5500/300 DUV stepper are presented and discussed. Also the effects of certain error sources and some ideas for future optimization are shown.

This paper analyzes and demonstrates the possibility of producing lithographic images at or below the 'diffraction limit' for synchrotron radiation-based x-ray proximity lithography. It is shown that at reasonable mask/wafer gaps of 15-30 micrometers , for feature sizes down to approximately 100 nm, a 30-40 nm uniform positive bias is observed. In proximity lithography, masks with clear features on a dark background demonstrate better linewidth control and more stable process optimization in terms of achieving smaller features: Sub-100 nm imaging requires positive bias for mask features: clear features have to be increased in sizes and the proper bias will depend on the mask/wafer gap. Features down to 43-46 nm have been formed in negative resists, and down to 60 nm in positive resist. The extendibility of synchrotron radiation-based x-ray proximity lithography into the sub-50 nm region at reasonable mask/wafer gaps of 20-30 micrometers was demonstrated.

Despite growing expectations of significant progress in projection lithography using shorter wavelengths (such as 193 nm, 157 nm, 126 nm ∼14 nm versus 1 nm for XRL), X-ray Lithography is still the most developed and production ready technology compared with the other NGL approaches. For the timely introduction of this technology into the manufacturing environment the development of fully integrated X-ray lithography systems becomes very important. Reflecting manufacturing and R&D demands, the X-ray technology integration has to been pursued for both synchrotron radiation and X-ray point source based approaches. While the synchrotron-based approach provides the high volume platform, the point source will provide the platform for low volume production and R&D efforts. SAL recognizes the needs for both, a synchrotron based stepper as well as a point source stepper and is focused on meeting those needs. This paper will present the status of integration efforts at SAL utilizing a point source system.

Availability of production-worthy x-ray masks is of great concern to the lithographic community in anticipation of insertion of x-ray lithography as the leading contender among the next generation lithographies.

The most important (biggest) contributions to overlay inaccuracy are coming from well-known sources like mask pattern placement accuracy, alignment system accuracy and stage performance of the exposure tools. As the allowances for overlay budget decrease, and improvements in mask fabrication and stage performance are made, a number of previously less significant contributions, such as resolution, optical interference, and focusing accuracy of alignment system, as well as from wafer processing, have to be considered. These contributions are characterized in detail in this paper. The investigation was focused on a proven optical alignment system (ALX) and overlay contribution as they apply to x-ray and optical lithography. Special emphasis was made on contributions from wafer processing (resist coating and metallization).

Crucial to any viable lithographic mask technology is the requirement that a given mask pattern be usable for the hundreds of thousands of exposures in a production environment. In a conventional approach this would be accomplished by making robust masks. A better strategy to ensure the longevity of the pattern itself, is realized by producing many defect-free copies of master masks. This approach is especially important in the case of x-ray masks, although the optical masks also have a limited usable lifetime. X-ray mask generation is accomplished today via e- beam lithography, which as a replication method has several inherent disadvantages, including low speed and high cost. X- ray replication is the best solution. In this paper, we describe the development of a mask replication method realized on a Suss x-ray stepper. The approach is based on supporting parent mask and the daughter blank in fully kinematic fixtures during replication, ensuring a minimum of distortion, excellent gap control and optimized exposure conditions. Minor modifications of the mask mounting fixtures, the replication setup, and details of processing are presented. Preliminary results of mask replication are also shown.

The prototype of a high volume production stepper for x-ray lithography, designed and built by Suss Advanced Lithography, Inc. (SAL), has been installed for beta testing at the Center for X-ray Lithography (CXrL) at the University of Wisconsin. SAL has put substantial efforts into the design and construction of this third generation x-ray stepper in order to meet industry requirements, mainly throughput, CD-control and overlay. Several design changes -- compared to the second generation XRS200 -- have been implemented to assure those goals. This includes a scanning beamline end to achieve exposure times of 1 sec as well as a high speed xy-stage for combined step end expose times below 2 seconds. Together with an improved optical alignment system (ALX70) for overlay accuracy below 50 nm (3(sigma) ) and a state-of-the-art loading/unloading wafer handler the measured throughput is currently between 26 WLPH (32 fields/200 mm wafer). Proximity gap is controlled to an accuracy of plus or minus 0.4 micrometer while minimum proximity gap is currently at 20 micrometer. Mask and wafer chuck are mounted kinematically to avoid mechanical stress to either mask or wafer for improved distortion control. A 3-axis-state-of-the-art HP laser interferometric system with a resolution of 2.5 nm controls mask to wafer movement to better than 20 nm. While this prototype is designed for wafer sizes of 75 to 200 mm, design changes are on the way to enable 300 mm wafer handling with increased throughput. Results obtained during a GaAs based MMIC and QWIP device fabrication program with 0.2 micrometer CD, demonstrate consistency with the prototype specification. Areas have been defined to further enhance the capabilities of the production stepper XRS 2000.

The metabasites from the KTB pilot and main drill holes can be divided into two major associations. The first is the metagabbro-amphibolite suite which is composed principally of metagabbros, basalts, and basaltic andesites with tholeiitic P-MORB affinities. The second is the amphibolite-gneiss suite that is characterized by alternating layers of metabasites which intimately interfinger with metasedimentary rocks. Metabasites from the amphibolite-gneiss suite are alkaline, and they include metamorphosed basanites, basalts, basaltic andesites, and trachy-andesites. A distinctive subgroup of the amphibolite-gneiss suite are basanitic metabasites which are interlayered with marble. With regard to trace elements, the alkaline rocks are distinguished from the tholeiites by steeper slopes of their spidergrams and REE patterns, and distinctively higher Nb concentrations (20–50 vs 3–20 ppm). Oxygen isotope studies establish that the most primitive metabasites of both series have mantle like δ18O values between 5 and 7‰. More differentiated samples have δ18O values reaching 8‰, and some alkaline metabasites have values as high as 10.5‰ indicating extensive interaction with sedimentary material. In general, ɛNd values decrease with differentiation. Gabbroic samples from the tholeiitic suite have highest ɛNd(0) values at approximately +5, whereas andesitic samples have values as low as –5. At least three components are needed to explain the trace element and isotope trends found in the metabasites: (a) an enriched asthenospheric MORB-type mantle; (b) a within-plate plume source; and (c) continental detritus with the composition of paragneiss. Melts from the two mantle sources mixed extensively, and the andesitic rocks are those with the highest contribution from the sedimentary component. Most probably all ZEV rocks were deposited in an oceanic basin close to an active continental margin where magmas were alternately derived from a tholeiitic mantle source as well as highly enriched within-plate magma source.

The two German Continental Deep Drilling Program (KTB) boreholes provided samples for studies of fluid inclusions (paleofluids), “free fluids” of the crystalline basement, and their fingerprints on the chemical and isotopic composition of minerals and rocks to 9101 m depth, which allowed reconstruction of the evolution of fluids, their migration pathways, and their sources. Aqueous fluids were largely lost during the Devonian amphibolite facies metamorphism. Thereafter, radiogenic, nucleogenic, and fissiogenic gases, together with NH4-fixed nitrogen, were released from host rocks and partly enclosed in secondary inclusions. During the Hercynian uplift, Na-Cl fluids (formation water) infiltrated and dissolved noble gases and N2 largely originating from the host rocks. In the course of the Cretaceous denudation, high-salinity Ca-Na-Cl brines, possibly derived from Permo-Carboniferous sediments but altered by fluid/rock interaction, migrated into their present position. This fluid introduced low-maturity hydrocarbons released together with nitrogen from early metamorphic organic-rich sediments. The 4000-m fluid from the KTB pilot hole pumping test, which was analyzed chemically and isotopically, seems to be a mixture of an ascending basement brine and a descending paleometeoric water, from which the late alteration minerals calcite and laumontite precipitated in fractures. The calcite is neither chemically nor isotopically in equilibrium with the recovered “free fluid.” Hydraulic tests indicate a communicating system of fractures between the boreholes with a distinct matrix and fracture porosity.

We present an integrated virtual learning based approach to support undergraduate students in developing their mathematical knowledge and skills. The approach consists of three elements. First, a pre-study web-based mathematics training course for pre-assessment and self-study. Secondly, the traditional classroom lecture that is supplemented with specific examples from application fields involving dedicated literature and case examples from other courses (e.g., physical chemistry). Finally, lectures have been recorded using an easy-to-use system to provide the students with after-class self-learning material. The latter proves especially useful for extra-occupational students. The approach has been developed and implemented for chemistry undergraduate courses but can be easily adapted for any kind of engineering study course.

We report on an IC lithographic resolution study in which APEX-E resist on polysilicon coated wafers was exposed to synchrotron x radiation through a high-resolution mask that contained Au-electroplated features ranging in size from 0.5 down to 0.15-micrometers . Exposures were made at mask-to-substrate gaps ranging from 20 to 35 micrometers and at doses from 100 to 134 mJ/cm2. We probed the wafers with an SEM, both before and after etch, and electrically. From the electrical linewidth probing, we found that for isolated lines and 1:2 L:S patterns the feature widths were linear down to 0.18-micrometers . For the 1:1 and 2:1 L:S arrays, the widths were linear down to 0.25-micrometers . Dense and isolated lines down to 0.25-micrometers exhibited +/- 15% dose latitude over a 10-micrometers gap range. Contact holes were examined only by SEM. The smallest size that printed was nominally 0.225 micrometers , but was measured to be 0.20-micrometers after etch. Critical dimension uniformity, calculated with each feature type allowed its own mean value, was approximately equals 40 nm (3(sigma) ), including intrafield and across wafer variation. The mask CD uniformity was approximately equals 30 nm (mean + 3(sigma) ). The wafer-to-wafer CD variation was found to be 6 nm (3(sigma) ) and the electrical test-to-test CD variation was 3 nm (3(sigma) ). We use regression analysis to separate the component of CD variation that is assignable to intrafield form that assignable to interfield. The regression analysis to separate the component of CD variation that is assignable to intrafield from that assignable to interfield. The regression analysis indicates that these components of CD variation are systematic rather than random. The main contributor to the interfield component may be polysilicon etch. The intrafield error is believed to be caused predominantly by beamline nonuniformity and not by errors on the 1x mask.

For a graph G=(V, E) its line graph L(G) has the node set E and two nodes of L(G) are adjacent if the corresponding edges of G have a common endpoint. The problem of finding G for a given L was already optimally solved by Lehot[7] and Roussopoulos[11]. Here we present a new dynamic solution to this problem, where we can add or delete a node v in L(G) in time proportional to the size of its adjacency list.

To further improve the performance of alignment systems for high resolution lithographic exposure systems, the various contributions to the overall alignment accuracy must be identified and separately reduced. We have measured the contributions to the performance of the ALX100 alignment system of the SUSS XRS200 x-ray stepper emerging from recognition repeatability, focus setting, and gap setting. We have found asymmetric alignment profiles during the alignment of a metal-layer process wafer combined with stepfield dependent offsets. After modification of the signal evaluation the stepfield dependent offset was largely reduced and the performance increased.

Overlay accuracy is known as one of the most important subjects for ULSI device production. Significant contributions such as alignment accuracy and mask distortions are well known. By breaking the 100 nm range on overlay accuracy a number of influences have to take into account, which were usually neglected for relaxed design rules. One of these influences to the overlay is directly related to wafer distortions induced by flatness deviations of wafer chucks. This impact was characterized by investigating the elastic behavior of 4' wafers (525 micrometers thick), fixed on a wafer chuck. Induced elastical deformation due to flatness error of the chuck causes strains and elongations in the wafer surface and therefore wafer distortions. The results obtained by exposure experiments and calculations show that even a point size defect has a 30 mm spreading. Therefore the induced distortions arrives about 100 nm in case of a 3 micrometers flatness irregularity. The final result of the investigations induces that the flatness differences between different wafer chucks or steppers should be smaller than 1 micrometers for design rules below quarter micron.

Demands on advanced exposure tools for ULSI applications have increased rapidly during the last few years. Overlay accuracy, one of the key subjects, has been under continuous development. In X-ray lithography the overlay is mainly determined by pattern displacement on X-ray masks, by process-induced wafer distortions and by stepper-related contributions, generated by a limited alignment accuracy and displacements during the pattern replication. It is the aim of this paper to characterize the stepper-related contributions to the overlay budget. For this purpose we investigated the overlay performance of vertical XRS-200 type X-ray steppers equipped with an advanced optical alignment system. Using a multiple exposure technique, a series of alignment experiments were performed on typical CMOS layers. The results show that the wafer chuck flatness has, beside the alignment accuracy, a major influence on the overlay accuracy.

Stepper related contributions to the overlay budget, such as alignment accuracy and displacements during pattern replication were investigated. By improving the alignment system, a value of 70 nm (mean + 3σ) was realized. Displacement errors induced by the stepper mechanism during pattern replication found to be in the range of 35 nm (3σ). This value was improved using a wafer chuck with high flatness. Summerizing the results, the total overlay contribution of the stepper (including alignment) is 75 nm (mean + 3σ).

The Voronoi diagram of a set of sites in the plane partitions the plane into regions, called Voronoi regions, one to a site. The Voronoi region of a site s is the set of points in the plane for which 8 is the closest site among all the sites. The Voronoi diagram has many applications in diverse fields, cf. Leven and Sharir [LS86] or Aurenhammer [Aur90] for a list of applications and a history of Voronoi diagrams. Different types of diagrams result from considering different notions of distance, e.g. Euclidean or Lp-norm or convex distance functions, and different sorts of sites, e.g. points, line segments, or circles. For many types of diagrams efficient construction algorithms have been found; these are either based on the divide-and-conquer technique due to Shamos and Hoey [SH75], the sweepline technique due to Fortune [For87], or geometric transforms due to Brown [Bro79] and Edelsbrunner and Seidel [ES86]. A unifying approach to Voronoi diagrams was proposed by Klein [Kle88a, Kle88b, Kle89a, KleS9b], cf. [ES86] for a related approach. Klein does not use the concept of distance as the basic notion but rather the concept of bisecting curve, i.e. he assumes for each pair {p, q} of sites the existence of a bisector J(p, q) which is homeomorphic to a line and divides the plane into a p-region and a q-region. The intersection of all p-regions for different q's is then the Voronoi-region of site p. He also postulates that Voronoi-regions are simply-connected and partition the plane. He shows that these so-called abstract Voronoi diagrams have already many of the properties of concrete Voronoi diagrams. In [MMO91] and the refinement [KMM91] we present a randomized incremental algorithm that can handle abstract Voronoi diagrams in (almost) their full generality. When n denotes the number of sites, the algorithm runs in O(nlog n) expected time, the average being taken over all permutations of the input. The algorithm is simple enough to be of great practical importance. It is uniform in the sense that only a single operation, namely the construction of a Voronoi diagram for 5 sites, depends on the specific type of Voronoi diagram and has to be newly programmed in order to adapt the algorithm to the type of the diagram. Moreover, this operation is the only geometric operation in our algorithm, and using this operation, abstract Voronoi diagrams can be constructed in a

Based on the transport theory, we present a modeling approach to light scattering in turbid material. It uses an efficient and general statistical description of the material's scattering and absorption behavior. The model estimates the spatial distribution of intensity and the flow direction of radiation, both of which are required, e.g., for adaptable predictions of the appearance of colors in halftone prints. This is achieved by employing a computational particle method, which solves a model equation for the probability density function of photon positions and propagation directions. In this framework, each computational particle represents a finite probability of finding a photon in a corresponding state, including properties like wavelength. Model evaluations and verifications conclude the discussion.

We present a discrete model for light reflection and transmission of turbid media based on lattice paths. We compare the results with the popular Kubelka–Munk model. We introduce a substitution that allows for a lateral scattering interpretation of the scattering and absorption coefficients. The underlying mathematical structure is governed by Chebyshev polynomials of the second kind.

The design of a gamut mapping algorithm (GMA) is always a compromise between preserving different competing aspects such as color, contrast, and lightness. A natural requirement of a GMA is that the algorithmic treatment of this competition has to avoid any additional artifacts such as discontinuities or loss of contrast. In this work, several common gamut mapping algorithms are studied from this aspect, resulting in the observation that problems with geometric discontinuities are widespread. For the assessment of the phenomena induced by local mapping properties, an algorithmic test is developed and applied. This new test supports both the quality check of existing as well as the development of new GMAs.

A Suss Advanced Lithography X‐ray Stepper designed as a production tool for high throughput in the sub‐quarter‐micron device range has been installed and is being commissioned at the University of Wisconsin’s Center for X‐ray Lithography (CXrL). Illumination for the stepper is provided by a scanning beamline designed and constructed at CXrL. The beamline optical components are a gold‐coated plane mirror, a 1‐micron‐thick silicon carbide window, and a 25‐micron‐thick beryllium exit window. Beamline features include synchronized scanning of the mirror and exit window, variable scan velocity to compensate for reflectivity changes as a function of incident angle, and a horizontal oscillation of the beryllium window during vertical scanning to average the effects of nonuniform beryllium window transmission. A helium purged snout transports the x‐rays from the beamline exit window, to the exposure plane in the stepper. This snout is retractable to allow for the loading and unloading of masks into the stepper. T...

An XRS 200 model 2M X-ray stepper has been installed at the Center for X-ray Lithography. This paper describes the capability of the machine and its installation. Of greater interest is the performance the stepper gives with respect to the dose control and the mask/wafer alignment. How robust a process is depends on the latitude of each process parameter and the control tolerance accorded the machines and materials that affect each one. The dose repeatabillty and uniformity is determined by the optical elements in the beamline, the helium delivery system, and the accuracy of the scanning stage. Test results are reported for dose control using three separate methods. The scan speed is measured using Suss supplied equipment and is verified separately by CXrL's own technique. The dose delivered is analysed by the response of radiachromic film. Also important is the behavior and performance of the ALX-100 alignment system. The optical set-up is described as a model that includes the ALX hardware and illumination as well as the mask and wafer. The signal and contrast from the mask and wafer are compared to data for several substrates. A figure of merit is discussed for determining which membranes will give the best overlay.

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. A number of settlements and other traces of occupation have been identified in the mountainous areas near to tin and copper deposits in the Erzgebirge, and some of them excavated. The newly collected evidence seems to suggest that many small sources of metals, both tin and copper, were exploited, the former metal by washing from the river and creek beds. Though these sources were more modest than the British and Spanish tin supply, they seem to have served the Bohemian and Saxon Bronze Age cultures well.

1. Der Ascitestumor der Maus erwies sich als hervorragend geeignet zur Testung cytostatischer Substanzen. 2. Für eine Reihe bisher nicht untersuchter Stoffe konnte cytostatische Wirkung gesichert werden. Die Hydrazinderivate 7, 13 und 26 sowie CoCl2 und Isonicotinsäure-hydrazid scheinen zur Behandlung von Tumoren geeignet. 3. Eine Beziehung zwischen Struktur und Wirkung konnte trotz systematischer Abwandlung der Verbindungen nicht gefunden werden. Hingegen erscheint ein „kolligativer“ Effekt33 als möglich. 4. Eine Parallelität zwischen bakteriostatischer und cytostatischer Wirkung wurde nicht festgestellt.

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.

Peptic hydrolysis of Trypsin inhibited by DFP yielded a fragment distinguished by its Rf from a corresponding fragment of native enzyme and containing both tryptophane and phosphorus. DFP protects one Try of Trypsin and Chymotrypsin against Oxidation by N-Bromosuccinimid. Differencespectroscopy revealed corresponding changes in absorption spectra of Trypsin and Chymotrypsin the significance of which is discussed in detail. Electrophoretic mobility of the isolated fragment excludes dissociable phosphate groups, proving the presence of DIP-residue. Hydrolysis of the fragment yielded equimolar Try., Leu., Val., and Ser.

1. Es werden Untersuchungen über den Einfluß von k.-Strophanthin (10—3-, 10—5-, 10—7-m.) auf die Ca- und Mg-aktivierte ATPase des Herzmuskelhomogenates, die Dissoziation, ATPase-Aktivität und Rekombination von nativem und gewaschenem Aktomyosin (mit und ohne Zugabe von 0,001-m. Ca¨) beschrieben. k.-Strophanthin hemmt die Ca-aktivierte um etwa 12% und um etwa 20% die Mg-aktivierte Dephosphorylierung des ATP durch Herzmuskelhomogenat als Enzymquelle. Das Ausmaß der Hemmung ist im Bereich von 10—-3- bis 10—7-m. k-Strophanthin unabhängig von der Konzentration des zugegebenen Strophanthins und ebenso im Bereich von 3 · 10—3- bis 3 · 10—4-m. Ca¨ von der des Aktivators. Dies spricht gegen eine direkte Einwirkung von Strophanthin auf die Herzmuskel-ATPase. 2. Die charakteristischen Viskositätsänderungen von Aktomyosin nach Zugabe von ATP werden durch k.-Strophanthin (10—5- bis 10—6-m.) nicht signifikant beeinflußt. 3. Auch eine kritische Betrachtung der widersprechenden Angaben der Lit. berechtigt unseres Erachtens zu der Annahme, daß ein eindeutiger Einfluß von Digitalisstoffen auf Zustandsänderungen und enzymatische Funktionen extrahierter kontraktiler Muskelproteine bisher nicht experimentell erhärtet werden konnte.

Two edges are called P4-adjacent if they belong to the same P4 (chordless path on four vertices). P4-components, in our terminology, are the equivalence classes of the transitive closure of the P4-adjacency relation. In this paper, new results on the structure of P4-components are obtained. On the one hand, these results allow us to improve the complexity of orienting P4-comparability graphs and of recognizing P4-indifference graphs from O(n5) and O(n6) to O(m2). On the other hand, by combining the modular decomposition with the substitution of P4-components, a new unique tree representation for arbitrary graphs is derived which generalizes the homogeneous decomposition introduced by Jamison and Olariu (SIAM J. Discrete Math. 8 (1995) 448–463).

The incorporation of hydrogen in enstatite in a hydrous system containing various amounts of NaCl was investigated at 25 kbar. The hydrogen content in enstatite shows a clear negative correlation to the NaCl-concentration in the system. The most favourable explanation is the reduction of water fugacity due to dilution. Other reasons for the limited hydrogen incorporation at high NaCl levels, such as a significant influence of Na+ on the defect chemistry or an exchange between OH- and Cl−in enstatite, appear much less important. A partition coefficient D Na En/Fluid = 0.0013 could be determined, demonstrating that Na is less incompatible in enstatite than H. The new results support the idea that dissolved components have to be considered when the total hydrogen storage capacity in nominally anhydrous minerals is estimated, especially in geological settings with high levels of halogens, such as subduction zones.

We consider a sequence of integer-valued random variables Xn, n ⩾ 1, representing a special Markov process with transition probability λn, l, satisfying Pn, l = (1 − λn, l) Pn−1, l + λn, l−1 Pn−1, l−1. Whenever the transition probability is given by λn, l = qαn + βl + γ and λn, l = 1 − qαn+βl+γ, we can find closed forms for the distribution and the moments of the corresponding random variables, showing that they involve functions such as the q-binomial coefficients and the q-Stirling numbers. In general, it turns out that the q-notation, up to now mainly used in the theory of q-hypergeometrical series, represents a powerful tool to deal with these kinds of problems. In this context we speak therefore about q-distributions. Finally, we present some possible, mainly graph theoretical interpretations of these random variables for special choices of α, β and γ.