On numerical solution of arbitrary symmetric linear systems by approximate orthogonalization

A very important class of inverse problems are those modelled by integral equations of the first kind. These equations are usually ill-conditioned, such that any discretization technique will produce an ill-conditioned system, in classical or least-squares formulation. For such kind of symmetric problems, we propose in this paper a stable iterative solver based on an approximate orthogonalization algorithm introduced by Z. Kovarik. We prove convergence of our algorithm for general symmetric least-squares problems and present some numerical experiments ilustrating its good behaviour on problems concerned with the determination of charge distribution generating a given electric field and gravity surveying, both modelled by first kind integral equations.     

Magnetic order and evolution of the electronic state aroundx=0.12 in La2?xBaxCuO4 and La2?xSrxCuO4

Muon spin rotation (gif" alt="mgr" align="MIDDLE" BORDER="0"> ⁺SR) measurement provides clear evidence of the antiferromagnetic order of Cu moments below 35 K for La_2–x Ba _x CuO₄ and below 15 K for La_2–x Sr _x CuO₄ in the narrow range ofx where the high-T _c superconductivity (SC) is suppressed remarkably. The results suggest that the change of the electronic state coupled with the lattice instability is relevant to the local suppression of SC and freezing of spin fluctuations of the Cu moment.     

Computing presentations for subgroups of polycyclic groups and of context-free groups

Algorithms for solving uniform decision problems for algebraic structures crucially depend on the chosen finite presentations for the structures under consideration. Rewriting techniques have been used very successfully to solve uniform decision problems, when the presentations considered involve finite, noetherian, and (gif" alt="lambda" align="BASELINE" BORDER="0">)-confluent rewriting systems. Whenever the class of algebraic structures considered is closed under the operation of taking finitely generated substructures, then the algorithms for solving the uniform decision problems can be applied to the substructures as well. However, since these algorithms depend on the form of the presentations, this involves the task of constructing a presentation of a certain form for a substructure given a presentation of this form for the structure itself and a finite set of generating elements for the substructure.This problem, which has received a lot of attention in algebra, is here investigated from an algorithmic point of view. The structures considered are the following two classes of groups, which have been studied extensively before: the polycyclic groups and the context-free groups.Finitely generated context-free groups can be presented by finite, monadic, and gif" alt="lambda" align="BASELINE" BORDER="0">-confluent string-rewriting systems. Due to their nice algorithmic properties these systems provide a way to effectively solve many decision problems for context-free groups. Since finitely generated subgroups of context-free groups are again contextfree, they can be presented in the same way. Here we describe a process that, from a finite, monadic, and gif" alt="lambda" align="BASELINE" BORDER="0">-confluent string-rewriting system presenting a context-free groupG and a finite subsetU ofG, determines a presentation of this form for the subgroup gif" alt="lang" align="MIDDLE" BORDER="0">Ugif" alt="rang" align="MIDDLE" BORDER="0"> ofG that is generated byU. For finitely presented polycyclic groups we obtain an analogous result, when we use finite confluent PCP2-presentations to describe these groups.This work was performed while this author was visiting at the Fachbereich Informatik, Universität Kaiserslautern, during his sabbatical 1991/92     

Superconductivity in the tetragonal phase of La1.9Bi0.1CuO4+δ annealed under high oxygen pressure

We have investigated the relation between the crystal structure and superconductivity in La_1.9Bi_0.1CuO_{4+gif" alt="delta" align="BASELINE" BORDER="0">} , in which the phase separation observed in La₂CuO_{4+gif" alt="delta" align="BASELINE" BORDER="0">} is suppressed. A phase diagram in theT–gif" alt="delta" align="BASELINE" BORDER="0"> plane is given for La_1.9Bi_0.1CuO_{4+gif" alt="delta" align="BASELINE" BORDER="0">} with excess oxygen. For very smallgif" alt="delta" align="BASELINE" BORDER="0"> values, the crystal structure is orthorhombic, and an orthorhombic-tetragonal phase transition occurs markedly atgif" alt="delta" align="BASELINE" BORDER="0"> gif" alt="sim" align="MIDDLE" BORDER="0"> 0.03 in the measured temperature range between 13 and 293 K. Superconductivity is observed in the range of 0.04<gif" alt="delta" align="BASELINE" BORDER="0"><0.11. This is clear evidence thathigh-T _c superconductivity also appears in the tetragonal phase.     

A mathematical programming approach to a problem in variance penalised Markov decision processes

In this paper we present three algorithms for solving a problem in which it is required to get an optimal compromise between the average expected reward per unit time and the variance of the reward per unit time. The algorithms lead to angif" alt="epsiv" align="BASELINE" BORDER="0">-optimal solution, wheregif" alt="epsiv" align="BASELINE" BORDER="0">>0 is arbitrary.     

On several concepts for ɛ-efficiency

We introduce two new concepts for?-efficiency and investigate these and some known concepts under the following aspects: (1) What are the relationships between the efficient and the?-efficient point set? (2) If the sequence (v ^?) of?-efficient points converges forε → 0, is the limit efficient, or weakly efficient? (3) Can the distance between the?-efficient and the efficient point set be estimated in terms ofε?     

Extraordinary behaviour of the Y1?xPrxBa2Cu3O7?δ system

Investigations of Y_1–x M _x Ba₂Cu₃O_{7–gif" alt="delta" align="BASELINE" BORDER="0">} (M=Ce, Th)c-axis oriented thin film specimens show that the rate of depression ofT _c withx is larger for M=Th, than for M=Ce and Pr, and suggest that Ce, like Th, is tetravalent in this compound. Hall effect measurements on Y_1–x Pr _x Ba₂Cu₃O_{7–gif" alt="delta" align="BASELINE" BORDER="0">} single crystals reveal aT ² dependence of the cotangent of the Hall angle in the normal state and a gif" alt="ldquo" align="MIDDLE" BORDER="0">negative Hall anomalygif" alt="rdquo" align="MIDDLE" BORDER="0"> belowT _c in the superconducting state, in agreement with recent reports. Our research shows that the depth, gif" alt="Delta" align="BASELINE" BORDER="0">, of the negative Hall signal scales withT/T _c and that the maximum value of gif" alt="Delta" align="BASELINE" BORDER="0"> decreases linearly withx and vanishes atxgif" alt="ap" align="MIDDLE" BORDER="0">0.24. Magnetoresistance measurements on Y_1–x Pr _x Ba₂Cu₃O_{7–gif" alt="delta" align="BASELINE" BORDER="0">} single crystals indicate that the irreversibility lineH(T ^*) obeys a universal scaling relation characterized by anm=3/2 power law nearT _c, with a crossover to a more rapid temperature dependence of belowT/T _c gif" alt="ap" align="MIDDLE" BORDER="0">0.6, similar to that observed for polycrystalline specimens.     

Role of electron-phonon interaction in lattice dynamics and superconductivity of oxide spinel LiTi2O4

The lattice dynamics of an oxide spinel LiTi₂O₄ is studied by taking account of the electron-phonon (EP) interaction derived on the basis of the realistic tight-binding bands fitted to the first-principles bands. Due to the characteristic dependences of the EP interaction on wavevectors and vibrational modes, a remarkable frequency renormalization of the O vibrational modes, which hybridize with the Ti vibrational modes, is obtained over a wide region of the Brillouin zone. The overall features of the calculated phonon density of states are in agreement with those observed by the inelastic neutron scattering measurements. By using the EP interaction and the renormalized phonon frequencies we have calculated the EP spectral functiongif" alt="agr" align="BASELINE" BORDER="0"> ² F(gif" alt="ohgr" align="BASELINE" BORDER="0">). The superconducting transition temperature, gap function, and tunneling spectra are calculated by solving the Éliashberg equation. The results agree well with the observations.     

Computer simulations of signal transduction mechanism in {alpha}1B-adrenergic and m3-muscarinic receptors

Molecular dynamices simulations of the hamster gif" ALT="{alpha}" BORDER="0">_1Badrenergicand the rat m3-muscarinic seven-helix bundle receptor modelshave been carried out. The free, agonist-bound and antagonist-boundforms have been considered. Moreover, three mutant forms ofthe m3-muscarinic recep-tor (N507gif" ALT="<-" BORDER="0">A, N507gif" ALT="<-" BORDER="0">D and N507gif" ALT="<-" BORDER="0">S) have alsobeen simulated; among these, the N507gif" ALT="<-" BORDER="0">S mutant shows a constitutiveactivity. A comparative structural/dynamics analysis has beenperformed to elucidate (i) the perturbations induced by thefunctionally different ligands upon binding to their targetreceptor, (ii) the features of the three single-point mutantswith respect to the receptor wild type and (iii) the propertiesshared by the agonist-boundforms of the gif" ALT="{alpha}" BORDER="0">_1B-adrenergic receptorand the m3-muscarinic receptor and by the constitutively activemutant N507gif" ALT="<-" BORDER="0">S. The consistency obtained between the structuralrearrangement of the transmembrane seven-helix bundle modelsconsidered, and the experimental pharmacological efficaciesof the ligands and of the mutants, constitute an important validationof the 3-D models obtained and allow the inference of the mechanismof ligand- or mutation-induced receptor activation at the molecularlevel.     

Functionally essential, invariant glutamate near the C-terminus of strand {beta}5 in various ({alpha}/{beta})8-barrel enzymes as a possible indicator of their evolutionary relatedness

Twelve different (gif" ALT="{alpha}" BORDER="0">/ß)₈-barrel enzymes belonging tothree structurally distinct families were found to contain,near the C-terminus of their strand ß5, a conservedinvariant glutamic acid residue that plays an important functionalrole in each of these enzymes. The search was based on the ideathat a conserved sequence region of an (gif" ALT="{alpha}" BORDER="0">/ß)₈-barrelenzyme should be more or less conserved also in the equivalentpart of the structure of the other enzymes with this foldingmotif owing to their mutual evolutionary relatedness. For thispurpose, the sequence region around the well conserved fifthß-strand of a-amylase containing catalytic glutamate(Glu230, Aspergillus oryzae gif" ALT="{alpha}" BORDER="0">-amylase numbering), was used asthe sequence-structural template. The isolated sequence stretchesof the 12 (gif" ALT="{alpha}" BORDER="0">/ß)₈-barrels are discussed from both thesequence-structural and the evolutionary point of view, theinvariant glutamate residue being proposed to be a joining featureof the studied group of enzymes remaining from their ancestral(gif" ALT="{alpha}" BORDER="0">/ß)₈-barrel