Truncated selection procedures for the most probable event and the least probable event

This paper proposes two sequential procedures for selecting respectively the multinomial cell with the largest cell probability and the multinomial cell with the smallest cell probability. The stopping rule for both procedures uses truncation of the procedure studied by Ramey and Alam (1979, Biometrika, 66, 171–173). A property of the least favorable configuration of the proposed procedures is proved, which partially solves a conjecture given in Ramey and Alam (1979). The proposed procedures are compared with other procedures which have been considered in the literature and are found to be better in certain respects.     

The spectrum of iodine excited in the presence of argon

The band systems of iodine in the regions 3455-3015 Å, 2785-2750 Å and 2730-2520 Å obtained by earlier workers using prism spectrographs are now photographed in the first and second orders of a 21-ft. grating spectrograph. A large number of new bands are obtained in all these three systems which are now extended to the regions 3461-3015 Å, 2785-2731 Å and 2729-2486 Å. The wavelengths and wavenumbers of all the bands are recorded along with their visually estimated intensities. The Deslandres schemes for the three systems representing all the bands are given and are found to be supported by the corresponding intensity distributions of the expected type. It was found that the two systems 3460-3015 Å and 2785-2731 Å do not involve for their lower levels the ground state as assumed by the earlier workers but the³Π_u (O _u ⁺) state at 15642 cm.^?1, which is also the lower state for the 4420-4000 Å system. The band system in the region 2730-2486 Å has for its lower level the ground state of the molecule as reported by the earlier workers. A reanalysis of this system made to include all the bands observed in the present experiments, gave vibrational constants slightly different from those obtained by earlier workers. The vibrational constants of the upper states of the four different systems that one gets by exciting iodine in the presence of argon are

System	Te	ωe	ωeXe	ωeYe
4400-4000Å	41411 cm.-1	102·2 cm.-1	0·34 cm.-1	..
3460-3015Å	45937 cm.-1	103·7 cm.-1	0·95 cm.-1	..
2785-2731Å	51847 cm.-1	112·4 cm.-1	0·711 cm.-1	0·004 cm.-1
2730-2486Å	47207 cm.-1	96·5 cm.-1	0·510 cm.-1	0·0033 cm.-1

     

The emission spectrum of iodine bromide excited in the presence of Argon

IBr vapour was excited in the presence of argon by an uncondensed transformer discharge. Four band systems were obtained in the regions 5425–5360 Å, 4520–4415 Å, 4120–4010 Å and 3915–3540 Å of which the first three are discussed in this paper. The wavelengths and wavenumbers of the band heads in three systems as measured from the plates obtained with a 3-prism Steinheil glass spectrograph are given along with their visually estimated relative intensities. The three band systems, which are new, are analysed and the following vibrational constants expressed in cm.^?1 are obtained:

Band system	v e	w e ″	w e ″x e ″	w e ″y e ″	w e ′	w e ′x e ′
5425-5360 Å	18613	65·5	0·24	?0·01	43·0	0·026
4520-4415 Å	22312	65·5	0·24	?0·01	77·0	0·5
4120-4010 Å	24540	160·6	1·125	..	128·4	0·1

     

Most probable explanations in Bayesian networks: Complexity and tractability

One of the key computational problems in Bayesian networks is computing the maximal posterior probability of a set of variables in the network, given an observation of the values of another set of variables. In its most simple form, this problem is known as the MPE-problem. In this paper, we give an overview of the computational complexity of many problem variants, including enumeration variants, parameterized problems, and approximation strategies to the MPE-problem with and without additional (neither observed nor explained) variables. Many of these complexity results appear elsewhere in the literature; other results have not been published yet. The paper aims to provide a fairly exhaustive overview of both the known and new results.     

Phantom without pathologies in the ultraviolet domain

We present a simple model in which the weak energy condition is violated for spatially homogeneous, slowly evolving fields. The excitations in Minkowski space in an external field with violation of the Lorentz invariance do not contain ghosts, tachyons, or superluminal modes at spatial momenta ranging from some low scale ε to the ultraviolet cutoff scale, while tachyons and possibly ghosts do exist for three-dimensional momenta less than ε. We show that in the absence of other matter, a slow-roll cosmological regime is possible. In this regime, the weak energy condition is violated, and yet homogeneity and isotropy are not completely spoiled (at the cost of fine tuning), because for a given conformal momentum, the tachyon mode increases during a sufficiently short time. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 149, No. 3, pp. 409–426, December, 2006.     

Solitons in fibre lasers and mode-locked systems

Soliton propagation in a laser fibre is investigated using multiple-scale perturbation analysis. The perturbative terms are linear loss and saturable nonlinear gain. Furthermore, we show the possibility of stable soliton-like propagation in an amplitude pulse mode-locked system consisting of a semiconductor laser coupled to a nonlinear fibre through a centre mirror. The soliton-like pulse is slightly asymmetric due to asymmetric gain amplification in the semiconductor laser.     

The ultraviolet and infrared spectra of some lichen depsides and depsidones

The ultraviolet and infrared spectral data for a number of lichen depsides, depsidones and their fission products have been recorded. The U.V. spectra of the orcinol depsides, orcinol depsidones andβ-orcinol depsidones are characteristic while those of theβ-orcinol depsides less useful for diagnostic purposes. The I.R. spectra are more useful and the carbonyl region is significant for this purpose.     

The geometry and number of the root invariant regions for linear systems

The stability domain is a feasible set for numerous optimization problems. D-decomposition technique is targeted to describe the stability domain in the parameter space for linear parameter-dependent systems. This technique is very simple and efficient for robust stability analysis and design of low-order controllers. However, the geometry of the arising parameter space decomposition into root invariant regions has not been studied in detail; it is an objective of the present paper. We estimate the number of root invariant regions and provide examples, where this number is attained.     

Centerlines of regions in the sphere

Given a region U in the 2-sphere S such that the boundary of U contains at least two points, let D(U) be the collection of open circular disks (called maximal disks) in U whose boundary meets the boundary of U in at least two points and let U₂ be the collection of all regions U⊂S such that for each D∈D(U), D meets the boundary of U in at most two points. In this paper we study geometric properties of regions U∈U₂. We show for such U that the centerline (i.e., the set of centers of maximal disks) is always a smooth, connected 1-manifold. We also show that the boundary of U has at most two components and, if it has exactly two components, then the boundary is locally connected.These results are related the set of points E(X,Y) which are equidistant to two disjoint closed sets X and Y. In particular we investigate when the equidistant set is a 1-manifold.     

The effect of ultraviolet radiation on the stress relaxation rate of polymers

The effect of UV radiation on the stress relaxation rate for four different polymers was investigated. A reversible increase in the stress relaxation rate was noted: the rate increased during irradiation and declined after its termination. It is assumed that this effect involves the rupture of stressed polymer macromolecules by the action of UV rays.Mekhanika Polimerov, Vol. 3, No. 4, pp. 615–618, 1967     

The normal density of prime ideals in small regions

For a Gaussian prime (i) define ()=min|–| where runs through Gaussian primes satisfying ||>||. We prove that, subject to the Riemann Hypothesis for appropriateL-functions

The global instability of uniform flows in non-one-dimensional regions

The conditions for the instability of flows or states, which are independent of time and coordinates, in extended non-one-dimensional regions are considered in a linear approximation. An extension of the idea of global instability, previously introduced for the one-dimensional case, is given. A method is proposed for weakly unstable flows, which enables one to investigate under what conditions perturbations, which grow without limit with time, and which do not depend on the specific form of boundary conditions (provided they are not degenerate), exist. The case of a two-dimensional rectangular region is considered in detail.