The Small-Is-Very-Small Principle

The central result of this paper is the small-is-very-small principle for restricted sequential theories. The principle says roughly that whenever the given theory shows that a property has a small witness, i.e. a witness in every definable cut, then it shows that the property has a very small witness: i.e. a witness below a given standard number. We draw various consequences from the central result. For example (in rough formulations): (i) Every restricted, recursively enumerable sequential theory has a finitely axiomatized extension that is conservative w.r.t. formulas of complexity $\leq n$. (ii) Every sequential model has, for any $n$, an extension that is elementary for formulas of complexity $\leq n$, in which the intersection of all definable cuts is the natural numbers. (iii) We have reflection for $\Sigma^0_2$-sentences with sufficiently small witness in any consistent restricted theory $U$. (iv) Suppose $U$ is recursively enumerable and sequential. Suppose further that every recursively enumerable and sequential $V$ that locally inteprets $U$, globally interprets $U$. Then, $U$ is mutually globally interpretable with a finitely axiomatized sequential theory. The paper contains some careful groundwork developing partial satisfaction predicates in sequential theories for the complexity measure depth of quantifier alternations

High pressure transport study of non-Fermi liquid behaviour in U2Pt2In and U3Ni3Sn4

The strongly correlated metals U2Pt2In and U3Ni3Sn4 show pronounced non-Fermi liquid (NFL) phenomena at ambient pressure. Here we review single-crystal electrical resistivity measurements under pressure (p <= 1.8 GPa) conducted to investigate the stability of the NFL phase. For tetragonal U2Pt2In (I||a) we observe a rapid recovery of the Fermi-liquid T^2-term with pressure. The Fermi-liquid temperature varies as T_FL ~ p-p_c, where p_c= 0 is a critical pressure. The analysis within the magnetotransport theory of Rosch provides evidence for the location of U2Pt2In at a zero pressure antiferromagnetic quantum critical point (QCP). In the case of cubic U3Ni3Sn4 we find T_FL ~ (p-p_c)^1/2. The analysis provides evidence for an antiferromagnetic QCP in U3Ni3Sn4 at a negative pressure p_c= -0.04+-0.04 GPa.Comment: 6 pages (4 figures); to appear in Proc. of Int. Conf. PPHMF-IV (20-25 Oct. 2001, Santa Fe

Muon localization site in U(Pt,Pd)3

The angular and temperature (10-250 K) variation of the Knight shift of single-crystalline U(Pt0.95Pd0.05)3 has been measured in transverse field (B=0.6 T) mSR experiments. By analysing the temperature variation of the Knight shift with a modified Curie-Weiss expression the muon localization site in this hexagonal material is determined at (0,0,0).Comment: 12 pages (including 4 figures); postscript file; Proc. 8th Int. Conf. on Muon Spin Rotation, Relaxation and Resonance (Aug.30-Sept.3, Les Diablerets); 2nd version with minor correction

Pairs, sets and sequences in first-order theories

Asuransi sebagai aktivitas bisnis diharuskan memenuhi prinsip-prinsip hukum asuransi. Salah satu prinsip yang harus dipegang teguh adalah principle of  utmost good faith, di samping prinsip yang lain. Prinsip ini berbunyi bahwa seorang tertanggung wajib memberi informasi secara jujur terhadap apa yang dipertanggungkan kepada penanggung. Dalam bisnis Islam, kejujuran merupakan prinsip yang harus dijunjung tinggi. Secara hukum, prinsip ini diatur dalam KUH Dagang. Persoalannya adalah apakah prinsip ini dianggap cukup dari sudut pandang hukum perjanjian syariah. Secara sekilas bahwa prinsip iktikad baik sempurna ini telah memenuhi asas perjanjian syariah, namun demikian tidak memiliki kriteria maksimal kejujuran. Ketiadaan kejujuran dalam bisnis asuransi akan berdampak pada batalnya perjanjian asuransi karena ada unsur cacat kehendak (‘uyub ar-ridla). Insurance as a business activity must fulfill principles of insurance law. One of the principles that must be hold on is the principle of  utmost good faith. The principle says that an endured person must honestly give information of  what should be given responsibility to the guarantor. In Islamic business, honesty is a principle that should be respected. From point of  view of  law, the principle is settled in commerce law. The problem is that whether the principle is represenative enough if it is viewed from law of  syariah agreement. At glance, the principle has fulfilled the basic of syariah agreement, however, it does not have maximum criteria of  honesty. Unavailability of honesty in insurance business will give effect of  invalidate of  insurance agreement, for there is a deformity of desire (‘uyub ar-ridla).</p

Energy conditions in f(R) gravity and Brans-Dicke theories

The equivalence between f(R) gravity and scalar-tensor theories is invoked to study the null, strong, weak and dominant energy conditions in Brans-Dicke theory. We consider the validity of the energy conditions in Brans-Dicke theory by invoking the energy conditions derived from a generic f(R) theory. The parameters involved are shown to be consistent with an accelerated expanding universe.Comment: 9 pages, 1 figure, to appear in IJMP

Molecule sublimation as a tracer of protostellar accretion: Evidence for accretion bursts from high angular resolution C18O images

The accretion histories of embedded protostars are an integral part of descriptions of their physical and chemical evolution. In particular, are the accretion rates smoothly declining from the earlier toward later stages or in fact characterized by variations such as intermittent bursts? We aim to characterize the impact of possible accretion variations in a sample of embedded protostars by measuring the size of the inner regions of their envelopes where CO is sublimated and relate those to their temperature profiles dictated by their current luminosities. Using observations from the Submillimeter Array we measure the extents of the emission from the C18O isotopologue toward 16 deeply embedded protostars. We compare these measurements to the predicted extent of the emission given the current luminosities of the sources through dust and line radiative transfer calculations. Eight out of sixteen sources show more extended C18O emission than predicted by the models. The modeling shows that the likely culprit for these signatures is sublimation due to increases in luminosities of the sources by about a factor five or more during the recent 10,000 years - the time it takes for CO to freeze-out again on dust grains. For four of those sources the increase would have had to have been a factor 10 or more. The compact emission seen toward the other half of the sample suggests that C18O only sublimates when the temperature exceeds 30 K - as one would expect if CO is mixed with H2O in the grain ice-mantles. The small-number statistics from this survey suggest that protostars undergo significant bursts about once every 20,000 years. This also illustrates the importance of taking the physical evolutionary histories into account for descriptions of the chemical structures of embedded protostars.Comment: Accepted by A&A; 11 pages, 5 figure

Angular spectrum of quantized light beams

We introduce a generalized angular spectrum representation for quantized light beams. By using our formalism, we are able to derive simple expressions for the electromagnetic vector potential operator in the case of: {a)} time-independent paraxial fields, {b)} time-dependent paraxial fields, and {c)} non-paraxial fields. For the first case, the well known paraxial results are fully recovered.Comment: 3 pages, no figure

Dirty black holes: Quasinormal modes for "squeezed" horizons

We consider the quasinormal modes for a class of black hole spacetimes that, informally speaking, contain a closely ``squeezed'' pair of horizons. (This scenario, where the relevant observer is presumed to be ``trapped'' between the horizons, is operationally distinct from near-extremal black holes with an external observer.) It is shown, by analytical means, that the spacing of the quasinormal frequencies equals the surface gravity at the squeezed horizons. Moreover, we can calculate the real part of these frequencies provided that the horizons are sufficiently close together (but not necessarily degenerate or even ``nearly degenerate''). The novelty of our analysis (which extends a model-specific treatment by Cardoso and Lemos) is that we consider ``dirty'' black holes; that is, the observable portion of the (static and spherically symmetric) spacetime is allowed to contain an arbitrary distribution of matter.Comment: 15 pages, uses iopart.cls and setstack.sty V2: Two references added. Also, the appendix now relates our computation of the Regge-Wheeler potential for gravity in a generic "dirty" black hole to the results of Karlovini [gr-qc/0111066

Microwave-induced excess quasiparticles in superconducting resonators measured through correlated conductivity fluctuations

We have measured the number of quasiparticles and their lifetime in aluminium superconducting microwave resonators. The number of excess quasiparticles below 160 mK decreases from 72 to 17 $\mu$m$^{-3}$ with a 6 dB decrease of the microwave power. The quasiparticle lifetime increases accordingly from 1.4 to 3.5 ms. These properties of the superconductor were measured through the spectrum of correlated fluctuations in the quasiparticle system and condensate of the superconductor, which show up in the resonator amplitude and phase respectively. Because uncorrelated noise sources vanish, fluctuations in the superconductor can be studied with a sensitivity close to the vacuum noise