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A subspace $X$ of a vector space over a field $K$ is hyperinvariant with respect to an endomorphism $f$ of $V$ if it is invariant for all endomorphisms of $V$ that commute with $f$. We assume that $f$ is locally nilpotent, that is, every $ x \in V $ is annihilated by some power of $f$, and that $V$ is an infinite direct sum of $f$-cyclic subspaces. In this note we describe the lattice of hyperinvariant subspaces of $V$. We extend results of Fillmore, Herrero and Longstaff (Linear Algebra Appl. 17 (1977), 125--132) to infinite dimensional spaces., Comment: 6 pages

Roth’s theorem on the consistency of the generalized Sylvester equationAX−YB=Cis a special case of a rank minimization theorem.

Neurofibromatosis type 1 (NF1) is a frequent neurocutaneous syndrome that predisposes for various benign and malignant tumors. Most characteristic are neurofibromas which occur in almost all NF1 patients at some point in lifetime. Although neurofibromas are benign tumors they can be disfiguring and plexiform neurofibromas may progress to malignant peripheral nerve sheath tumors. Overall survival rates of patients with these malignant tumors are poor. Other neoplasias frequently observed in NF1 patients are pilocytic astrocytomas, gastrointestinal stromal tumors, pheochromocytomas and juvenile myelomonocytic leukemia. Several other tumors have been reported in NF1 patients but it is unclear if there is a true association between the particular tumor type and NF1. Some of these tumors might be caused by a rare recessively inherited childhood cancer syndrome termed constitutive mismatch repair deficiency syndrome which shows certain phenotypic overlap with NF1 but includes a broad spectrum of tumors which usually do not occur in NF1. The development of NF1-associated tumors is largely explained by the underlying defect of the NF1 gene which results in activation of the RAS proto-oncogene- a key mechanism of tumorigenesis. Several downstream effectors of activated RAS as well as cooperating molecular pathways have been identified. These insights provide the basis to develop novel targeted treatment strategies which are urgently needed to improve the outcome for patients with NF1-associated malignancies.

The reduced transition probability B(E2;0(+)→2(+)) has been measured for the neutron-rich nucleus (74)Ni in an intermediate energy Coulomb excitation experiment performed at the National Superconducting Cyclotron Laboratory at Michigan State University. The obtained B(E2;0(+)→2(+))=642(-226)(+216) e(2) fm(4) value defines a trend which is unexpectedly small if referred to (70)Ni and to a previous indirect determination of the transition strength in (74)Ni. This indicates a reduced polarization of the Z=28 core by the valence neutrons. Calculations in the pfgd model space reproduce well the experimental result indicating that the B(E2) strength predominantly corresponds to neutron excitations. The ratio of the neutron and proton multipole matrix elements supports such an interpretation.

The Gamow-Teller strength in the β(+) direction to (46)Sc was extracted via the (46)Ti(t,(3)He + γ) reaction at 115 MeV/u. The γ-ray coincidences served to precisely measure the very weak Gamow-Teller transition to a final state at 991 keV. Although this transition is weak, it is crucial for accurately estimating electron-capture rates in astrophysical scenarios with relatively low stellar densities and temperatures, such as presupernova stellar evolution. Shell-model calculations with different effective interactions in the pf shell-model space do not reproduce the experimental Gamow-Teller strengths, which is likely due to sd-shell admixtures. Calculations in the quasiparticle random phase approximation that are often used in astrophysical simulations also fail to reproduce the experimental Gamow-Teller strength distribution, leading to strongly overestimated electron-capture rates. Because reliable theoretical predictions of Gamow-Teller strengths are important for providing astrophysical electron-capture reaction rates for a broad set of nuclei in the lower pf shell, we conclude that further theoretical improvements are required to match astrophysical needs.

For discrete-time linear systems over a principal ideal domain, three types of (C,A)-invariance can be distinguished. Connections between these notions are investigated. For pure submodules, necessary and sufficient conditions for dynamic (C,A)-injection invariance are given. Sufficient conditions are obtained in the general case.

Because of the importance of the complement system in disease resistance through direct lysis of target cells and support of other mechanisms of the immune System, individual Variation in haemolytic complement activity and C3 concentration in pigs prior and after vaccination were evaluated. Possible effects on the variation of these parameters were investigated. Total complement activity was determined based on complement-mediated haemolysis of antibody-sensitised erythrocytes and C3c levels were measured by immunonephelometry in Gemian Landrace pigs and an experimental pig population. Both methods revealed remarkable individual differences. The arithmetic means of total haemolytic complement activity including all pigs were 42.3 ± 28.2 U/ml before vaccination and 59.1 ± 50.6 U/ml after three immunisations. Mean plasma concentrations of C3c were between .102 ± .035 g/1 before immunisation and .126 ± .038 g/1 on day 4 after Aujeszky vaccination. Existing phenotypic variation may be in part influenced by pig genetic factors. Both haemolytic complement activity as well as C3c semm levels are potentially useful measures of complement capacity on the way to improve defence power against many pathogens by breeding.

If two solutions Y⩽Z of the DARE are given then the set of solutions X with Y⩽X⩽Z can be parametrized by invariant subspaces of the closed loop matrix corresponding to Y. The paper extends the geometric theory of Willems from the continuous-time to the discrete-time ARE making the weakest possible assumptions.

The almond β-glucosidase, and the β-galactosidases from Escherichia coli, Kluyveromyces lactis, and Bacillus circulans were used to catalyze the stereoselective hydrolysis of diastereoisomeric mixtures of alkyl-β-D-glucopyranosides and alkyl-β-D-galactopyranosides which were derived from the cis- and trans-isomers of 2-(4-alkoxybenzyl)-1-cyclohexanols by the Koenigs-Knorr synthesis. Stereoselective preference of the enzymes towards the respective diastereoisomers of the glycosides were studied (both chiral alcohols and alkyl-O-glycosides were prepared). Higher stereoselectivity was achieved for the glycosides derived from trans-2-(4-alkoxybenzyl)-1-cyclohexanols. The practical significance of this research is in the biological screening of selected alkyl-O-glycosides (glycosidic juvenogens, i.e., biochemically activated hormonogen complexes), using the β-glycosidases studied, as modern systemic and environmentally safe pesticides. Chirality 11:451–458, 1999. © 1999 Wiley-Liss, Inc.

Let ℂ n = ℒ ⊕ %plane1D;4B2; be a given direct sum decomposition. We determine the largest number r i such that all subspaces ℳ for which the gap θ between ℒ and %plane1D;4B2; satisfies θ(ℒℳ) have the property dim (ℳ∩%plane1D;4B2;). The problem involves angles between subspaces, i.e. singular values of products of projections.

If f is an endomorphism of a finite dimensional vector space over a field K then an invariant subspace X ⊆ V is called hyperinvariant (respectively, characteristic) if X is invariant under all endomorphisms (respectively, automorphisms) that commute with f . According to Shoda (Math. Zeit. 31, 611–624, 1930) only if |K| = 2 then there exist endomorphisms f with invariant subspaces that are characteristic but not hyperinvariant. In this paper we obtain a description of the set of all characteristic non-hyperinvariant subspaces for nilpotent maps f with exactly two unrepeated elementary divisors. Mathematics subject classification (2010): 15A18, 47A15, 15A57.

Companion matrices of the second type are characterized by properties that involve bilinear maps.

The transition rates from the yrast 2+ and 4+ states in the self-conjugate 72Kr nucleus were studied via lifetime measurements employing the GRETINA array with a novel application of the recoil-distance method. The large collectivity observed for the 4+→2+ transition suggests a prolate character of the excited states. The reduced collectivity previously reported for the 2+→0+ transition was confirmed. The irregular behavior of collectivity points to the occurrence of a rapid oblate-prolate shape transition in 72Kr, providing stringent tests for advanced theories to describe the shape coexistence and its evolution.

This paper deals with the existence and uniqueness of unmixed solutions of the discrete-time algebraic Riccati equation (DARE). Sets of solutions of the DARE are parametrized by invariant subspaces of the state transition matrix.

The set of solutions of the discrete-time algebraic Riccati equation is described. It is shown that each solution is a combination of a pair of opposite unmixed solutions. There is a one-to-one correspondence between solutions and invariant subspaces of the closed loop matrix associated to an unmixed solution. The results of the paper are a counterpart of the parametrization theory of continuous-time algebraic Riccati equations due to Willems, Coppel and Shayman.

Roth's similarity theorem on the consistency of Sylvester's matrix equation AX − XA = C can be extended to a theorem on rank minimization if the common eigenvalues of A and B are nonderogatory or semisimple.

Catalytic properties of commercially available lipases from Candida cylindracea, Rhizopus arrhizus, Aspergillus niger, Penicillium roqueforti, Geotrichum candidum , and porcine pancreas, and those of a crude lipase isolated from G. candidum were studied. Esterification of the racemic cis - and trans -isomers of 2-(4-methoxymethoxybenzyl)-1-cyclohexanol in organic solvents and hydrolysis of the racemic cis - and trans -isomers of 2-(4-methoxymethoxybenzyl)-1-cyclohexyl acetates were investigated, and all existing enantiomers of 2-(4-methoxymethoxy-benzyl)-1-cyclohexanol were prepared, isolated, and characterized by their physicochemical properties. Alcohols 2a and 2b and acetates 4a and 4b were found to be the principle products of enzymemediated reactions. The optimum reaction conditions for the enzyme-mediated hydrolysis of 1a and 1b and for the enzyme-mediated esterification of 3a or 3b were found, when G. candidum was used. We also compare the advantages and disadvantages of employing the appropriate enzymes.

The set of all negative-semidefinite solutions of the CAREA*X+XA+XBB*X−C*C=0 is homeomorphic to a well defined set ofA-invariant subspaces provided that the purely imaginary eigenvalues ofA are controllable. Based on that homeomorphism isolated n.s.d. solutions of the CARE are characterized by properties of their kernels.

In order to meet the requirements of advanced process and device design, a new generation of TCAD frameworks is emerging These are based on a data level providing a common data interchange format. Such a format must be suitable for building simulation databases, and needs to be accompanied by supporting tools and by a procedural interface with multi-language bindings for data storage and retrieval by application programs. The complexity and scope of a rigorous TCAD framework requires special efforts to create a system which is both transparent to the user and comprehensible to the programmer. A consistent architecture and strict adherence to general software engineering guidelines can contribute significantly to the solution of this problem. We discuss general requirements and architectural issues of the data level, the user interface and the task level environment, and present their implementation in VISTA, the Viennese Integrated System for Technology CAD Applications.

Canonical angles between subspaces of a unitary space are characterized by a min-max property which involves inner products.

The (18)F(p,α)(15)O reaction rate is crucial for constraining model predictions of the γ-ray observable radioisotope (18)F produced in novae. The determination of this rate is challenging due to particular features of the level scheme of the compound nucleus, (19)Ne, which result in interference effects potentially playing a significant role. The dominant uncertainty in this rate arises from interference between J(π)=3/2(+) states near the proton threshold (S(p)=6.411 MeV) and a broad J(π)=3/2(+) state at 665 keV above threshold. This unknown interference term results in up to a factor of 40 uncertainty in the astrophysical S-factor at nova temperatures. Here we report a new measurement of states in this energy region using the (19)F((3)He,t)(19)Ne reaction. In stark contrast to previous assumptions we find at least 3 resonances between the proton threshold and E(cm)=50 keV, all with different angular distributions. None of these are consistent with J(π)=3/2(+) angular distributions. We find that the main uncertainty now arises from the unknown proton width of the 48 keV resonance, not from possible interference effects. Hydrodynamic nova model calculations performed indicate that this unknown width affects (18)F production by at least a factor of two in the model considered.

The sets of negative semidefinite solutions T i of two algebraic Riccati equations R i (X)=A ∗ i X+XA i +XB i B ∗ i −C ∗ i C i =(I, X)H i (I, X) ∗ , i=1, 2, are compared under the hypothesis that H1⩽H2. If X+1 and X+2 are the greatest solutions in T 1 and T 2 respectively, then X+1⩽X+2. A more general result will be proved which allows the comparison of other solutions of T 1 and T 2 besides the extremal ones and which in the case of stabilizability leads to a Galois connection between T 1 and T 2. The comparison results are based on one hand on a decomposition of the equations R i (X)=0 into Lyapunov matrix equations and genuine Riccati equations which induce a corresponding decomposition of the solutions in T i, and the other hand on a parametrization of the Riccati components by Ai-invariant subspaces.

Negative-semidefinite solutions of the ARE ${\cal R}(X)=A^{*}X+XA +XBB^{*}X-C^{*}C=0$ are studied. With respect to an appropriate basis the ARE breaks up into a Lyapunov equation $A_{0}^{*}X_{0}+X_{0}A_{0}=0$, where $A_0$ has only purely imaginary eigenvalues, and an indecomposable Riccati equation ${\cal R}_{r}(X_{r})=A_{r}^{*}X_{r} +X_{r}A_{r}+X_{r}B_{r}B_{r}^{*}X_{r}-C_{r}${*}C_{r}=0$ such that each solution $C \leq 0$ is of the form $X = \diag(X_{0}, X_{r})$. The focus is on the solutions ${\cal S}=\{X\|X=\diag(0,X_{r}), {\cal R}_{r}(X_{r})=0,X_{r} \leq 0\}$. The set $\cal S$ has as an order-isomorphic image a well- defined set $\cal N$ of $A$-invariant subspaces. The characterization of $\cal N$ involves the stabilizable and the uncontrollable subspace of $(A,B,C)$.

This note deals with the consistency of complex matrix equations AX − YB = C and AX − XB = C under the constraints Y = X ∗ and X = X ∗ .

The discrete-time algebraic Riccati equation is studied. Necessary and sufficient conditions for the existence of positive-definite and positive-semidefinite solutions are given.

We performed at ISOLDE the spectroscopy of the decay of the ${8}^{\ensuremath{-}}$ isomer in ${}^{136}$Cs by $\ensuremath{\gamma}$ and conversion-electron detection. For the first time the excitation energy of the isomer and the multipolarity of its decay have been measured. The half-life of the isomeric state was remeasured to ${T}_{1/2}=17.5(2)$ s. This isomer decays via a very slow 518-keV $E3$ transition to the ground state. In addition to this, a much weaker decay branch via a 413-keV $M4$ and a subsequent 105-keV $E2$ transition has been found. Thus we have found a new level at 105 keV with spin ${4}^{+}$ between the isomeric and the ground state. The results are discussed in comparison to shell-model calculations.

Review on NF1 (neurofibromin 1), with data on DNA, on the protein encoded, and where the gene is implicated.

Other names: Von Recklinghausen neurofibromatosis; Peripheral neurofibromatosis Inheritance: autosomal dominant with almost complete penetrance; frequency is 30/10 newborns (and 1 of 200 mentally handicapped persons): one of the most frequent genetically inheritable disease; neomutation in 50%, mostly from the paternal allele; highly variable expressivity, from very mild to very severe; expressivity is also age-related.

Reduced uncertainty in the thermonuclear rate of the {sup 33}S(p,{gamma}){sup 34}Cl reaction would help to improve our understanding of nucleosynthesis in classical nova explosions. At present, models are generally in concordance with observations that nuclei up to roughly the calcium region may be produced in these explosive phenomena; better knowledge of this rate would help with the quantitative interpretation of nova observations over the S-Ca mass region, and contribute towards the firm establishment of a nucleosynthetic endpoint. As well, models find that the ejecta of nova explosions on massive oxygen-neon white dwarfs may contain as much as 150 times the solar abundance of {sup 33}S. This characteristic isotopic signature of a nova explosion could possibly be observed through the analysis of microscopic grains formed in the environment surrounding a nova and later embedded within primitive meteorites. An improved {sup 33}S(p,{gamma}){sup 34}Cl rate (the principal destruction mechanism for {sup 33}S in novae) would help to ensure a robust model prediction for the amount of {sup 33}S that may be produced. Finally, constraining this rate could confirm or rule out the decay of an isomeric state of {sup 34}Cl(E{sub x} = 146 keV, t{sub 1/2} = 32 m) as a source formore » observable gamma-rays from novae. We have performed several complementary experiments dedicated to improving our knowledge of the {sup 33}S(p,{gamma}){sup 34}Cl rate, using both indirect methods (measurement of the {sup 34}S({sup 3}He,t){sup 34}Cl and {sup 33}S({sup 3}He,d){sup 34}Cl reactions with the Munich Q3D spectrograph) and direct methods (in normal kinematics at CENPA, University of Washington, and in inverse kinematics with the DRAGON recoil mass separator at TRIUMF). Our results will be used with nova models to facilitate comparisons of model predictions with present and future nova observables.« less

A polynomial approach is described to deal with problems of the following type. Given two companion matrices A and Z , when does there exist a nonsingular matrix S such that S -1 AS is upper triangular and S -1 ZS is lower triangular, and the eigenvalues of A and Z appear in the main diagonals of S -1 AS and S -1 ZS in a prescribed ordering? Such problems are related to complete minimal factorizations in systems theory.

The "island of inversion" nucleus 32 Mg has been studied by a (t, p) two neutron transfer reaction in inverse kinematics at REX-ISOLDE. The shape coexistent excited 0+ state in 32 Mg has been identified by the characteristic angular distribution of the protons of the Δ L=0 transfer. The excitation energy of 1058 keV is much lower than predicted by any theoretical model. The low γ-ray intensity observed for the decay of this 0+ state indicates a lifetime of more than 10 ns. Deduced spectroscopic amplitudes are compared with occupation numbers from shell-model calculations.

With the Q3D magnetic spectrograph of the Maier-Leibnitz-Laboratorium at M\"unchen at a resolution of about 3 keV, angular distributions and excitation functions of the reaction $^{208}\mathrm{Pb}$($p,{p}^{\ensuremath{'}}$) were measured at some scattering angles ${20}^{\ifmmode^\circ\else\textdegree\fi{}}$--${138}^{\ifmmode^\circ\else\textdegree\fi{}}$ for several proton energies $14.8$--$18.1$ MeV. All seven known isobaric analog resonances in $^{209}\mathrm{Bi}$ are covered. By the excitation near the $j{}_{15/2}$ intruder resonance in $^{209}\mathrm{Bi}$, several new positive parity states in $^{208}\mathrm{Pb}$ with excitation energies $4.6$--$6.2$ MeV are identified by comparison of the mean cross section to the known single particle widths. The dominant configuration for 27 positive parity states is determined and compared to the schematic shell model.

We study reachability matrices R(A, b) = (b,Ab,...,A n 1 b), where A is an n × n matrix over a field K and b is in K n . We characterize those matrices that are reachability matrices for some pair (A,b). In the case of a cyclic matrix A and an n-vector of indeterminates x, we derive a factorization of the polynomial det R(A, x) � .

Difference equations of the form X(t) = F ∗ (t)X(t − 1)F(t) − F ∗ (t)X(t − 1)G(t)[I + G ∗ (t)X(t − 1)G(t) −1 G ∗ (t)X(t − 1)F(t) + Q(t) and their associated Hermitian matrices H(t) = ( F Q F ∗ −GG ∗ )(t) are studied. Solution of different Riccati equations can be compared if the difference of their corresponding Hermitian matrices is semidefinite for all t. An application to the discrete-time LQ optimal control problem is given.

The algebraic Riccati equation of the optimal control problem associated with the discrete-time system $x(k + 1) = Fx(k) + Gu(k)$ is studied. It is shown that in the case of a controllable system, there exist solutions with prescribed unmixed characteristic polynomial of the corresponding closed-loop matrix. Existence of solutions will also be proved under the weaker condition of modulus-controllability. Maximal solutions are discussed.

The authors discuss the classification of a large variety of multimedia communication applications (with the emphasis on broadband and hypermedia applications), the requirements at network levels, multimedia communications concepts with suitable platforms, and the modular standardization of multimedia teleservices and the corresponding technical systems. Appropriate technologies for meeting multimedia requirements comprise public and private networks, servers for information storage and processing, intelligent user and system agents, and multimedia terminals, e.g., workstations. The authors deal with the question of service-specific or service-integrated networks, the architecture, components, and functions of asynchronous transfer model (ATM) switching systems for broadband ISDN and ATM-based signaling, and management for controlling connectivity and interactivity. Network evolution, pilot applications, and coordinated standardization are briefly considered. >

Excited states in the well-deformed rare earth isotopes $^{154}$Sm and $^{166}$Er were populated via ``safe'' Coulomb excitation at the Munich MLL Tandem accelerator. Conversion electrons were registered in a cooled Si(Li) detector in conjunction with a magnetic transport and filter system, the Mini-Orange spectrometer. For the first excited $0^+$ state in $^{154}$Sm at 1099 keV a large value of the monopole strength for the transition to the ground state of $\rho^2(\text{E0}; 0^+_2 \to 0^+_\text{g}) = 96(42)\cdot 10^{-3}$ could be extracted. This confirms the interpretation of the lowest excited $0^+$ state in $^{154}$Sm as the collective $\beta$-vibrational excitation of the ground state. In $^{166}$Er the measured large electric monopole strength of $\rho^2(\text{E0}; 0^+_4 \to 0^+_1) = 127(60)\cdot 10^{-3}$ clearly identifies the $0_4^+$ state at 1934 keV to be the $\beta$-vibrational excitation of the ground state., Comment: submitted to Physics Letters B

An implementation of a technology CAD environment is presented, using a level concept for the system: a data level provides simulation data retrieval facilities, a tool level is used for tool integration and a task level aids complex developments and user interaction.

The 1789 keV state in 30Mg was identified as the first excited 0+ state via its electric monopole (E0) transition to the ground state. The measured small value of rho2(E0,0(2)+--0(1)+)=(26.2+/-7.5)x10(-3) implies within a two-level model a small mixing of competing configurations with largely different intrinsic quadrupole deformation near the neutron shell closure at N=20. Axially symmetric configuration mixing calculations identify the ground state of 30Mg to be based on neutron configurations below the N=20 shell closure, while the excited 0+ state mainly consists of two neutrons excited into the nu 1f7/2 orbital. The experimental result represents the first case where an E0 back decay from a strongly deformed second to the normal deformed first nuclear potential minimum well has been unambiguously identified, thus directly proving shape coexistence at the borderline of the much-debated "island of inversion."

The study of the evolution of nuclear shells far from stability provides fundamental information about the shape and symmetry of the nuclear mean field. Nuclei with large neutron/proton ratio allow to probe the density dependence of the effective interaction. Indeed, it was recently shown that tensor and three-body forces play an important role in breaking and creating magic numbers. Of particular interest is the region of 78 Ni where the large neutron excess coincides with a double shell closure.We have recently measured the B(E 2; 0+ → 2+ ) of the 74 Ni nucleus in an intermediate-energy Coulomb excitation experiment performed at the National Superconducting Cyclotron Laboratory of the Michigan State University. The 74 Ni secondary beam has been produced by fragmentation of 86 Kr at 140 AMeV on a thick Be target. Selected radioactive fragments impinged on a secondary 197 Au target where the measurement of the emitted γ -rays allows to extract the Coulomb excitation cross section and related structure information. Preliminary B(E2) values do not point towards an enhancement of the transition matrix element and the comparison to what was already measured by Aoi and co-workers in [1] opens new scenarios in the interpretation of the shell evolution of the Z=28 isotopes.

Neurofibromatosis type 1 (NF1), the most common tumor-predisposing disorder in humans, is caused by defects in the NF1 tumor-suppressor gene. Comprehensive mutation analysis applying RNA-based techniques complemented with FISH analysis achieves mutation detection rates of approximately 95% in NF1 patients. The majority of mutations are minor lesions, and approximately 5% are total gene deletions. We found 13 single- and/or multiexon deletions/duplications out of 1,050 detected mutations using our RNA-based approach in a cohort of 1,100 NF1 patients and confirmed these changes using multiplex ligation-dependent probe amplification (MLPA). With MLPA, we found another 12 novel multiexon deletion/duplications in 55 NF1 patients for whom analysis with multiple assays had not revealed a NF1 mutation, including 50 previously analyzed comprehensively. The extent of the 22 deletions and 3 duplications varied greatly, and there was no clustering of breakpoints. We also evaluated the sensitivity of MLPA in identifying deletions in a mosaic state. Furthermore, we tested whether the MLPA P122 NF1 area assay could distinguish between type I deletions, with breakpoints in low-copy repeats (NF1-LCRs), and type II deletions, caused by aberrant recombination between the JJAZ gene and its pseudogene. Our study showed that intragenic deletions and/or duplications represent only approximately 2% of all NF1 mutations. Although MLPA did not substantially increase the mutation detection rate in NF1 patients, it was a useful first step in a comprehensive mutation analysis scheme to quickly pinpoint patients with single- or multiexon deletions/duplications as well as patients with a total gene deletion who will not need full sequencing of the complete coding region.

An automatic grid design and adaption algorithm for Monte Carlo simulation of Ion Implantation (MCI') has been developed. This method has been successfully implemented in the two-dimensional process simulator PROMIS. Based on range parameters a dense initial grid is designed. Dose conservation and gradient resolution criteria are used to determine gridlines which can be deleted. Special attention has been focused on a homogenous variation of the grid spacing. The implemented algorithm produces a suitable grid for the resolution of implanted profiles, and can be successfully applied to the three-dimensional case.

In most cases, analgesia is required for extracorporeal shockwave lithotripsy (SWL) treatment. Commonly, a combination of a sedative and a synthetic opioid is used, with a wide range of undesirable side effects. To provide an alternative analgesic especially for outpatients, we performed a prospective trial investigating the usefulness of acupuncture.A series of 90 patients were included in the study, 49% of whom presented with renal calculi and 10% with proximal-, 10% with middle-, and 31% with distal-ureteral stones. Pain control was performed by acupuncture in the traditional Asian method. The intensity of pain and patient satisfaction were assessed a visual analog scale (VAS). Patients with previous SWL under conventional analgesia also were asked about differences in pain and satisfaction.No significant side effects occurred. The median pain score on the VAS was 2/10 (interquartile range 1). Six patients (6.6%) specified a pain intensity of4, and in 4 patients (4.4%), a conventional analgesic had to be given to finish SWL. The median satisfaction level was 2/5 (interquartile range 1). Nearly all (93.4%) of the patients would opt again for acupuncture in case of repeated SWL.In many patients, acupuncture achieves satisfactory pain control for SWL. Further randomized multi-institutional studies are needed to confirm this conclusion.