Showing papers by "Bielefeld University published in 1977"

On Time Versus Space

Abstract: It is shown that every deterministic multitape Turing machine of time complexity t(n) can be simulated by a deterministic Turing machine of tape complexity t(n)/logt(n). Consequently, for tape constructable t(n), the class of languages recognizable by multitape Turing machines of time complexity t(n) is strictly contained in the class of languages recognized by Turing machines of tape complexity t(n). In particular the context-sensitive languages cannot be recognized in linear time by deterministic multitape Turing machines.

On Expected Figures and a Strong Law of Large Numbers for Random Elements in Quasi-Metric Spaces

Abstract: One can find in nature various sorts of figures which challenge one to study them by probabilistic methods. In this paper we are concerned with the notion of expected figures based on ideas of Freenet [5] on expected elements (‘positions moyennes’) in metric spaces.

Extension of KMS states and chemical potential

Abstract: We present an algebraic description of the concept of chemical potential for a general compact gauge groupG, as a first step in the classification of thermodynamical equilibrium states of a given temperature. Adopting first the usual setting of a field algebra ℱ containing the observable algebra\(\mathfrak{A}\) as its gauge invariant part, we establish the following results (i) the existence and uniqueness, up to gauge, of τ-weakly clustering states ф of ℱ extending a given such state ω of\(\mathfrak{A}\) (τ an asymptotically abelian automorphism group of ℱ commuting withG) (ii) in the case of an ω faithful and β-KMS for a time evolution commuting with τ, and of a time-invariant ф, the fact that ф is β-KMS for a one-parameter group of time and gauge whose gauge part lies in the center of the stabilizerGφ of ф. (iii) a description of the general case where ф is neither time invariant nor faithful: ф is then in general vacuum-like in directions of the gauge space governed by an “asymmetry subgroup”. We further analyze the representations and von Neumann algebras determined by ω, ф and the gauge average\(\bar \omega \) of ф. The covariant representation generated by\(\bar \omega \) is shown to be obtained by inducing up fromGφ toG the representation generated by ф. Finally we present, for the case whereG is ann-dimensional torus, an intrinsic description of the chemical potential in terms of cocycle Radon-Nicodym derivatives of the state ω w.r.t. its (quasi equivalent) transforms by localized automorphisms of\(\mathfrak{A}\). Our main result (ii) is established using two independant techniques, the first making systematic use of clustering properties, the second relying on the analysis of representations. Both proofs are basically concerned with Tannaka duality—the second with a version thereof formulated in Robert's theory of Hilbert spaces in a von Neumann algebra.

Unendlich-dimensionale Wienerprozesse mit Wechselwirkung

Abstract: Suppose Ф is a superstable pair potential on ℝϒ with finite range and three times continuously differentiable and Ωi(t) (i=1,2,⋯; t≧0) are independent ϒ-dimensional standard-Wiener-processes related to a probability space (Ω,\(\mathfrak{F}\)), Ω: = (Ωi)i=1,2,⋯ The atoms aieℝϒ (i = 1,2,⋯) of an element aeℳ, the space of the Radon counting measures on ℝv, may move according to the following equations (G) $$x_i (t;a,\omega ) = a_i + \int\limits_o^t {ds( - \tfrac{1}{2}\sum\limits_{j \pm i} {grad} } \Phi (x_i (s;a,\omega ) - x_j (s;a,\omega ))) + \omega _i (t)$$ $$(\omega \in \Omega ; i = 1,2,...; t\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{ \geqslant } 0)$$ (ΩeΩ; i = 1,2,⋯; t≧0). Let ∇ the σ-algebra generated by the vague topology on ℳ, Μ a probability measure on (ℳ, ∇). Call a ℳ-valued stochastic process x(t) = xi(t): i = 1,2,⋯ (xi(t)eℝv, t≧0,ieIN) on (ℳ × Ω, ∇, Μ ⊗ Q) a Μ-solution of (G), if x(t) satisfies some measurability conditions and the xi(t; a, Ω) (i= 1, 2,⋯; t ≧0) satisfy the equations (G) for Μ ⊗ Q-almost every (a, Ω). Call a Μ-solution x(t) Μ ⊗ Q-invariant, if Μ ⊗ Qx(t)eB=Μ(B) for all t≧0 and Be∇Be93. Then for all tempered Gibbs-measures Μ associated to Ф holds: A Μ-solution of (G) exists. There is a Μ ⊗ Q-a.e. unique Μ ⊗ Q-invariant solution of (G). The Μ ⊗ Q-invariant solution x(t) is a reversible markov process.

Analysis of calf-thymus satellite DNA: evidence for specific methylation of cytosine in C-G sequences.

Abstract: Digestion of purified calf tymus satellite I (θ= 1.714 g/cm3) with a series of restriction enzymes shows that modification in this satellite occurs preferentially in the sequence C-G. This was also shown to be the case in the other satellites and in bulk chromosomal calf thymus DNA. Cloning of purified satellite I DNA in Escherichia coli makes sites, previously modified, available for cutting with certain restriction enzymes. All these ‘new’ sites contain the sequence C-G. High-resolution mass spectroscopy establishes that the satellites contain a low concentration of 5-methylcytosine. This iners that methylation which inhibits restriction enzyme cutting must occur preferentially in the sequence C-G. Hybridization of cRNA of cloned satellite I DNA with the satellites III (θ= 1.706 g/cm3) and IV (θ= 1.710 g/cm3) shows that there is no or little sequence homology between these satellites. Digestion of calf thymus satellite I DNA with endoR ·EcoRI and subsequent hybridization studies with the fragments shows two EcoRI fragments in addition to the usual 1400-base-pair EcoRI repeat unit.

On quantum theory in terms of white noise

Abstract: It has often been pointed out that a much more manageable structure is obtained from quantum theory if the time parameter t is chosen imaginary instead of real. Under a replacement of t by i·t the Schrodinger equation turns into a generalized heat equation, time ordered correlation functions transform into the moments of a probability measure, etc. More recently this observation has become extremely important for the construction of quantum dynamical models, where criteria were developed by E. Nelson, by K. Osterwalder and R. Schrader and others [8] which would permit the reverse transition to real time after one has constructed an imaginary time (“Euclidean”) model.

A Note on Hunziker's Theorem

Abstract: We prove Hunziker's theorem that the essential spectrum of the internal Hamiltonian of an N-particle system is bounded below by the lowest 2- particle threshold. Our assumptions are given in terms of the Hamiltonian alone without reference to potentials. They include the previously treated cases.

A Simple Game Model of Kidnapping

Abstract: Hostage taking situations such as kidnapping a rich person in order to extort ransom money undoubtedly have some game theoretical aspects. In the following a very simple game model will be developed which cannot claim to be more than a first attempt to gain some insight into the strategic problems faced by a kidnapper — he will be called player K — and by the hostage’s family, called player F who has to pay the ransom money.

Three-Photon Excitation of Xenon and Carbon Monoxide

Abstract: With intense light of a pulsed tunable dye laser, the $^{3}P_{1}$ resonance state of xenon and the $P$, $Q$, and $R$ branches of the (2-0) band of CO in the fourth positive system ($A^{1}\ensuremath{\Pi}\ensuremath{\leftarrow}X^{1}\ensuremath{\Sigma}^{+}$) are excited by simultaneous absorption of three visible laser photons. The excitation is monitored by detecting the fluorescent decay in the vacuum ultraviolet.

Field Emission of Monoenergetic Spin-Polarized Electrons

Abstract: Field emission from a tungsten tip, covered by a layer of crystallized ferromagnetic europium sulfide, leads to an electron beam with a current of 10 -8 A, an energy width of less than 100 meV, and a spin polarization of about 0.85 at a tip temperature of 9 K. Proper annealing of the EuS layer is crucial.

Infrared multiphoton dissociation of SF6 in a molecular beam: Observation of F atoms by chemi‐ionization detection

Abstract: a) Supported in part by NSF grant CHE-76-10332. Acknowledgment is made also to the Donors of the Petroleum Research Fund, administered by the American Chemical Society, for partial support of the research. l(a) D. F. Tuan and O. Sinanoglu, J. Chem. Phys. 41, 2677 (1964); (b) V. McKoy and O. Sinanoglu, J. Chem. Phys. 41, 2689 (1964). 2A. D. Walsh, Prog. in Stereochem. 1, 1 (1954). 30. Sinanoglu and D. R. Herrick, J. Chern. Phys. 62, 886 (1975); 65, 850E (1976). 4C. E. Wulfman, Chern. Phys. Lett. 23, 370 (1973). 5D. R. Herrick, J. Math. Phys. 16, 1047 (1975). sF. H. Read, J. Phys. B 10, 449 (1977).

Mixing properties in lattice systems

Abstract: We study mixing or spatial cluster properties and some of their consequences in classical lattice systems, in particular complete regularity and the weaker notion of strong mixing. Introducing the notion of reflection positivity as a generalization ofT-positivity of [1], we construct a generalized transfer matrixP and relate complete regularity to a spectral gap inP. It is shown that all reflection invariant Ising systems with n.n. and ferromagnetic n.n.n. interaction satisfy reflection positivity. For Ising ferromagnets with reflection positivity, exponential decay of the truncated 2-point function implies complete regularity. In particular, the 2-dimensional spin-1/2 Ising model is completely regular, except at the critical point. This complements a result of [2] that strong mixing fails at the critical point of this model and in this case verifies the suggestion of Jona-Lasinio [3] that critical behaviour should be linked with failure of strong mixing. We then show that strong mixing imposes severe restrictions on the possible form of limits of block spins. Strong mixing in each direction allows onlyindependent Gaussians as non-zero limit if the 2-point function exists; strong mixing in a single direction only will allow infinitely divisible distributions.

Time-space trade-offs in a pebble game

Abstract: A certain pebble game on graphs has been studied in various contexts as a model for the time and space requirements of computations. In this note it is shown that there exists a family of directed acyclic graphs $G_n$ and constants $c_1$, $c_2$, $c_3$ such that (1) $G_n$ has n nodes and each node in $G_n$ has indegree at most 2. (2) Each graph $G_n$ can be pebbled with $c_1\sqrt{n}$ pebbles in n moves. (3) Each graph $G_n$ can also be pebbled with $C_2\sqrt{n}$ pebbles, $c_2$ > $c_1$, but every strategy which achieves this has at least $2^{c_3\sqrt{n}}$ moves.

Die Kristall- und Molekülstruktur von [Bis(trimethylsilyl)amino]-bis(trimethylsilylimino)phosphoran

Abstract: Die Struktur der Titelverbindung 1 wurde aus bei + 18 und − 130°C ermittelten Diffraktometer-Einkristalldaten bestimmt und zu einem R-Wert von 4.3% (−130°C) verfeinert. Die Verbindung kristallisiert monoklin in der Raumgruppe C2/c. Z = 4. Ein Vergleich der Bindungslangen in 1 bei den verschiedenen Temperaturen zeigt fur die endstandigen Trimethylsilylgruppen die Notwendigkeit einer Korrektur der durch thermische Schwingungen scheinbar verkurzten Abstande. Das zentrale Phosphoratom weist eine planare dreifache Koordination von Stickstoffatomen auf. Bindungslangen und die Symmetrie des Molekuls deuten auf die Existenz von pπ-pπ-Bindungen zwischen Phosphor und Stickstoff hin. Der P−NImin-Abstand betragt 1.515, der P−NAmin-Abstand 1.638 A. Die NImin–Si- und NAmin–Si-Bindungslangen wurden zu 1.703 bzw. 1.787 A beobachtet. Der P = N-Si-Winkel betragt 146.8° (alle Werte fur −130°C). The Crystal and Molecular Structure of [Bis(trimethylsilyl)amino]-bis(trimethylsilylimino)phosphorane The crystal structure of the title compound 1 was determined from single crystal X-ray data (measured at +18 and −130°C) and was refined to R = 0.043 (−130°C). The compound crystallizes in the monoclinic space group C2/c. Comparison of bond lengths in 1 at the two temperatures demonstrates the necessity of a correction for shortening due to thermal motion for the SiR3-groups (R = methyl). The planar threefold nitrogen coordination of the phosphorus seems to favor the assumption of pπ-pπ-bonds. The P−Nimine and P−Namine bond lengths were found to be 1.515 and 1.638 A, respectively; Nimine–Si 1.703, Namine−Si 1.787 A, angle P = N−Si 146.8° (all values for −130°C).

Mapping of the two mitochondrial antimycin A resistance loci in Saccharomyces cerevisiae.

Abstract: Retention or loss of the two new mitochondrial antimycin A resistance loci AI and AII has been analyzed in a large number of stable cytoplasmic petite mutants. Using these deletion mutants it was possible to localize the two antimycin A resistance loci in the OI--OII region of mitochondrial DNA. The genetic loci are mapped in the following order: OII--AI--AII--cobl--OI. The mapping relationship of mutants resistant to antimycin A or funiculosin to various cob mutants is described.

Digital lock-in technique for measurement of polarization of radiation.

Abstract: A highly versatile polarimeter has been constructed for determining all the Stokes parameters for a beam of radiation. Polarization measurements are performed using digital lock-in techniques by replacing the linear retardation plate with an electro-optic crystal, which can be externally modulated. The device lends itself readily to laboratory applications and provides the possibility of measuring small polarization quite accurately.