Function Spaces of Posets with Projections

This paper investigates function spaces of structures consisting of a partially ordered set together with some directed family of projections.More precisely, given a fixed directed index set (I,), we consider triples (D,,(p _i ) _iI ) with (D,) a poset and (p _i ) _iI a monotone net of projections of D. We call them (I,)-pop's (posets with projections). Our main purpose is to study structure preserving maps between (I,)-pop's. Such homomorphisms respect both order and projections.Any (I,)-pop is known to induce a uniformity and thus a topology. The set of all homomorphisms between two (I,)-pop's turns out to form an (I,)-pop itself. We show that its uniformity is the uniformity of uniform convergence. This enables us to prove that properties such as completeness and compactness transfer to function pop's.Concerning categorical properties of (I,)-pop's, we will see that we are in a lucky situation from a computer scientist's point of view: we obtain Cartesian closed categories. Moreover, by a D -construction we get (I,)-pop's that are isomorphic to their own exponent. This yields new models for the untyped -calculus.     

A Modal Logic Based on Linearly Ordered f-Spaces

A modal logic associated with the -spaces introduced by Ershov is examined. We construct a modal calculus that is complete w.r.t. the class of all strictly linearly ordered -frames, and the class of all strictly linearly ordered -frames.     

Flow Compactifications of Nondiscrete Monoids, Idempotents and Hindman's Theorem

We describe the extension of the multiplication on a not-necessarily-discrete topological monoid to its flow compactification. We offer two applications. The first is a nondiscrete version of Hindman's Theorem, and the second is a characterization of the projective minimal and elementary flows in terms of idempotents of the flow compactification of the monoid.     

Large electron polarization of H-like20Ne-ions traversing gd foils at very high velocities

It is shown that transient magnetic fields in Gd-host for²⁰Ne ions at a mean velocity of 12.5v₀(v₀=c/137), considerably beyond the Bohr velocity of 1s electrons of Ne ions (v_1s=10v₀), are dominated by the Fermi contact field of these electrons. The first excited 2⁺-state of²Ne was used as probe. The derived value for the mean degree of polarization p_1s=0.32(13), is surprisingly large, though still consistent with values obtained at lower velocities. Present calculations of spin exchange cross sections severely underestimate the observed polarization at this high velocity.The authors are grateful to the operating staff of the UNILAC for providing excellent beam conditions. They also thank Dr. P. Maier-Komor for preparing the delicate targets. Support by the BMFT is acknowledged.     

Matroid Shellability, β-Systems,and Affine Hyperplane Arrangements

The broken-circuit complex is fundamental to the shellability and homology of matroids, geometric lattices, and linear hyperplane arrangements. This paper introduces and studies the -system of a matroid, nbc(M), whose cardinality is Crapo's -invariant. In studying the shellability and homology of base-pointed matroids, geometric semilattices, and afflne hyperplane arrangements, it is found that the -system acts as the afflne counterpart to the broken-circuit complex. In particular, it is shown that the -system indexes the homology facets for the lexicographic shelling of the reduced broken-circuit complex , and the basic cycles are explicitly constructed. Similarly, an EL-shelling for the geometric semilattice associated with M is produced,_and it is shown that the -system labels its decreasing chains.Basic cycles can be carried over from The intersection poset of any (real or complex) afflnehyperplane arrangement is a geometric semilattice. Thus the construction yields a set of basic cycles, indexed by nbc(M), for the union of such an arrangement.     

Alpha-decay of neutron-deficient 200Fr and heavier neighbours

A new measurement of the ²⁰⁰Fr -decay half-life, with improved accuracy compared to previous measurements, has been carried out at the Isolde-CERN on-line mass separator. A half-life of 49(4) ms has been obtained, which is substantially different from earlier literature values. For the ¹⁹⁶At daughter decay, a half-life of 389(54) ms and an branching ratio b = 94(5)% were measured. In addition, the half-lives of ^{201, 203, 205}Fr and ^197,199At are reported.     

Optical Properties of Films of Cu x Ag1−x InSe2 Solid Solutions Obtained by Laser Evaporation

The structure and optical properties of the films of ternary compounds AgInSe₂, CuInSe₂ and Cu _x Ag_1–x InSe₂ solid solutions obtained by pulsed laser evaporation are investigated. It has been established that the films like bulk crystals have the structure of chalcopyrite. By the transmission and reflection spectra near the edge of natural absorption the refractive index and coefficient of optical absorption are calculated and the energies of interband transitions and the crystalline and spinorbit splitting are determined.     

Optimisation of the ultrasound-assisted extraction of betalains and polyphenols from Amaranthus hypochondriacus var. Nutrisol

The present study optimised the ultrasound-assisted extraction (UAE) of bioactive compounds from Amaranthus hypochondriacus var. Nutrisol. Influence of temperature (25.86–54.14 °C) and ultrasonic power densities (UPD) (76.01–273.99 mW/mL) on total betalains (BT), betacyanins (BC), betaxanthins (BX), total polyphenols (TP), antioxidant activity (AA), colour parameters (L*, a*, and b*), amaranthine (A), and isoamaranthine (IA) were evaluated using response surface methodology. Moreover, betalain extraction kinetics and mass transfer coefficients (K_La) were determined for each experimental condition. BT, BC, BX, TP, AA, b*, K_La, and A were significantly affected (p < 0.05) by temperature extraction and UPD, whereas L*, a*, and IA were only affected (p < 0.05) by temperature. All response models were significantly validated with regression coefficients (R²) ranging from 87.46 to 99.29%. BT, A, IA, and K_La in UAE were 1.38, 1.65, 1.50, and 29.93 times higher than determined using conventional extraction, respectively. Optimal UAE conditions were obtained at 41.80 °C and 188.84 mW/mL using the desired function methodology. Under these conditions, the experimental values for BC, BX, BT, TP, AA, L*, a*, b*, K_La, A, and IA were closely related to the predicted values, indicating the suitability of the developed quadratic models. This study proposes a simple and efficient UAE method to obtain betalains and polyphenols with high antioxidant activity, which can be used in several applications within the food industry.     

Du Bois–Reymond Type Lemma and Its Application to Dirichlet Problem with the p(t)–Laplacian on a Bounded Time Scale

This paper is devoted to study the existence of solutions and their regularity in the p(t)–Laplacian Dirichlet problem on a bounded time scale. First, we prove a lemma of du Bois–Reymond type in time-scale settings. Then, using direct variational methods and the mountain pass methodology, we present several sufficient conditions for the existence of solutions to the Dirichlet problem.